Derivatives of Normal Density Function

Normal Density Derivatives

This table list the normal density function and its lower derivatives (to sixth derivative). For higher derivative, see Higher Derivatives of Normal Density Function

How To Use:

You need to find the value of first derivative of the Normal Density Function at Z = 0.02
Find the row with Z = 0.02
Find the column φ⁽¹⁾(x), the number inside the cell is 3z79772500.
See How To Read Numbers in Tables.
The result is -0.0079772500

Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
0.00	.398942280	0	.398942280	0	1.19682684	0	5.98413421
0.02	.398862500	3z79772500	.398702955	.023928559	1.19563029	.119626842	5.97575893
0.04	.398623254	.015944930	.397985457	.047809279	1.19204400	.238918874	5.95066324
0.06	.398224830	.023893490	.396791221	.071594453	1.18607800	.357542491	5.90893743
0.08	.397667706	.031813416	.395122632	.095236643	1.17774897	.475166491	5.85073151
0.10	.396952547	.039695255	.392983022	.118688812	1.16708018	.591463265	5.77625460
0.12	.396080212	.047529625	.390376657	.141904450	1.15410144	.706109971	5.68577398
0.14	.395051741	.055307244	.387308727	.164837709	1.13884890	.818789683	5.57961395
0.16	.393868362	.063018938	.383785332	.187443529	1.12136503	.929192520	5.45815435
0.18	.392531483	.070655667	.379813463	.209677757	1.10169839	1.03701674	5.32182895
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
0.20	.391042694	.078208539	.375400986	.231497275	1.07990350	1.14196980	5.17112356
0.22	.389403759	.085668827	.370556617	.252860110	1.05604063	1.24376938	5.00657387
0.24	.387616615	.093027988	.365289898	.273725551	1.03017556	1.34214434	4.82876317
0.26	.385683369	.100277676	.359611173	.294054257	1.00237941	1.43683568	4.63831979
0.28	.383606292	.107409762	.353531559	.313808360	.972728336	1.52759737	4.43591441
0.30	.381387815	.114416345	.347062912	.332951563	.941303267	1.61419723	4.22225717
0.32	.379030526	.121289768	.340217800	.351449233	.908189646	1.69641762	3.99809459
0.34	.376537162	.128022635	.333009466	.369268488	.873477112	1.77405617	3.76420646
0.36	.373910605	.134607818	.325451791	.386378281	.837259192	1.84692643	3.52140244
0.38	.371153879	.141038474	.317559259	.402749467	.799632980	1.91485840	3.27051871
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
0.40	.368270140	.147308056	.309346918	.418354879	.760698802	1.97769904	3.01241439
0.42	.365262673	.153410323	.300830337	.433169387	.720559869	2.03531269	2.74796802
0.44	.362134882	.159339348	.292025569	.447169947	.679321931	2.08758144	2.47807382
0.46	.358890291	.165089534	.282949105	.460335656	.637092914	2.13440537	2.20363810
0.48	.355532529	.170655614	.273617834	.472647788	.593982564	2.17570278	1.92557548
0.50	.352065327	.176032663	.264048995	.484089824	.550102073	2.21141033	1.64480520
0.52	.348492513	.181216107	.254260137	.494647485	.505563720	2.24148307	1.36224740
0.54	.344818001	.186201721	.244269072	.504308741	.460480497	2.26589443	1.07881949
0.56	.341045789	.190985642	.234093829	.513063828	.414965744	2.28463613	.795432491
0.58	.337179944	.195564367	.223752611	.520905249	.369132788	2.29771801	.512987491
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
0.60	.333224603	.199934762	.213263746	.527827771	.323094575	2.30516783	.232372177
0.62	.329183961	.204094056	.202645646	.533828412	.276963323	2.30703091	.045542547
0.64	.325062264	.208039849	.191916761	.538906425	.230850170	2.30336981	.319905826
0.66	.320863804	.211770110	.181095531	.543063271	.184864833	2.29426388	.589889990
0.68	.316592908	.215283177	.170200347	.546302591	.139115280	2.27980875	.854693552
0.70	.312253933	.218577753	.159249506	.548630161	.093707405	2.26011583	1.11354405
0.72	.307851260	.221652908	.148261167	.550053855	.048744725	2.23531162	1.36570074
0.74	.303389284	.224508070	.137253312	.550583591	3z43280787	2.20553714	1.61045709
0.76	.298872406	.227143028	.126243704	.550231272	.039444654	2.17094715	1.84714311
0.78	.294305030	.229557923	.115249850	.549010729	.082478820	2.13170944	2.07512746
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
0.80	.289691553	.231753242	.104288959	.546937652	.124683244	2.08800401	2.29381943
0.82	.285036358	.233729814	.093377911	.544029515	.165970469	2.04002228	2.50267061
0.84	.280343811	.235488801	.082533218	.540305505	.206256971	1.98796617	2.70117643
0.86	.275618247	.237031693	.071770992	.535786438	.245463362	1.93204726	2.88887745
0.88	.270863972	.238360295	.061106912	.530494673	.283514576	1.87248586	3.06536044
0.90	.266085250	.239476725	.050556197	.524454028	.320340032	1.80951008	3.23025923
0.92	.261286301	.240383397	.040133576	.517689684	.355873782	1.74335486	3.38325538
0.94	.256471294	.241083017	.029853259	.510228097	.390054635	1.67426103	3.52407854
0.96	.251644341	.241578567	.019728916	.502096895	.422826270	1.60247436	3.65250673
0.98	.246809491	.241873301	3z97736558	.493324784	.454137321	1.52824456	3.76836628
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
1.00	.241970725	.241970725	0	.483941449	.483941449	1.45182435	3.87153159
1.02	.237131952	.241874591	3z95801309	.473977449	.512197390	1.37346846	3.96192478
1.04	.232297005	.241588885	.018955436	.463464117	.538868988	1.29343272	4.03951497
1.06	.227469632	.241117810	.028115247	.452433459	.563925207	1.21197312	4.10431754
1.08	.222653499	.240465779	.037049542	.440918052	.587340122	1.12934487	4.15639308
1.10	.217852177	.239637395	.045748957	.428950937	.609092902	1.04580155	4.19584622
1.12	.213069147	.238637444	.054204791	.416565523	.629167758	.961594202	4.22282430
1.14	.208307790	.237470881	.062409014	.403795485	.647553895	.876970501	4.23751585
1.16	.203571388	.236142810	.070354272	.390674666	.664245427	.792173966	4.24014894
1.18	.198863119	.234658481	.078033888	.377236974	.679241293	.707443169	4.23098941
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
1.20	.194186055	.233023266	.085441864	.363516295	.692545146	.623011004	4.21033894
1.22	.189543158	.231242653	.092572878	.349546394	.704165236	.539103988	4.17853305
1.24	.184937281	.229322228	.099422282	.335360827	.714114272	.455941610	4.13593896
1.26	.180371163	.227267666	.105986096	.320992851	.722409279	.373735713	4.08295339
1.28	.175847430	.225084711	.112261000	.306475342	.729071437	.292689930	4.02000029
1.30	.171368592	.222779170	.118244329	.291840712	.734125911	.212999164	3.94752847
1.32	.166937042	.220356895	.123934060	.277120831	.737601677	.134849112	3.86600921
1.34	.162555055	.217823774	.129328802	.262346953	.739531323	.058415840	3.77593384
1.36	.158224790	.215185715	.134427782	.247549646	.739950865	.016134590	3.67781128
1.38	.153948287	.212448636	.139230831	.232758725	.738899533	.088646454	3.57216556
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
1.40	.149727466	.209618452	.143738367	.218003190	.736419567	.158974634	3.45953335
1.42	.145564130	.206701065	.147951382	.203311167	.732556003	.226984855	3.34046152
1.44	.141459965	.203702350	.151871419	.188709857	.727356450	.292553860	3.21550469
1.46	.137416539	.200628147	.155500556	.174225483	.720870873	.355569542	3.08522283
1.48	.133435304	.197484250	.158841386	.159883249	.713151366	.415931026	2.95017891
1.50	.129517596	.194276393	.161896995	.145707295	.704251926	.473548709	2.81093657
1.52	.125664637	.191010248	.164670940	.131720667	.694228234	.528344248	2.66805791
1.54	.121877537	.187691407	.167167230	.117945280	.683137421	.580250507	2.52210132
1.56	.118157295	.184325380	.169390298	.104401895	.671037851	.629211467	2.37361937
1.58	.114504800	.180917584	.171344983	.091110096	.657988900	.675182080	2.22315681
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
1.60	.110920835	.177473335	.173036502	.078088268	.644050734	.718128105	2.07124870
1.62	.107406075	.173997842	.174470428	.065353589	.629284100	.758025885	1.91841857
1.64	.103961095	.170496196	.175652667	.052922019	.613750112	.794862106	1.76517671
1.66	.100586368	.166973372	.176589428	.040808292	.597510050	.828633515	1.61201862
1.68	.097282269	.163434212	.177287208	.029025916	.580625162	.859346608	1.45942351
1.70	.094049077	.159883432	.177752756	.017587177	.563156470	.887017290	1.30785296
1.72	.090886979	.156325604	.177993060	3z65031451	.545164589	.911670512	1.15774966
1.74	.087796071	.152765163	.178015313	3z42163185	.526709544	.933339881	1.00953633
1.76	.084776361	.149206396	.177826895	.014562544	.507850609	.952067248	.863614686
1.78	.081827776	.145653441	.177435349	.024528040	.488646138	.967902284	.720364625
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
1.80	.078950158	.142110285	.176848355	.034106468	.469153421	.980902031	.580143448
1.82	.076143274	.138580758	.176073706	.043292629	.449428534	.991130447	.443285256
1.84	.073406813	.135068535	.175119292	.052082427	.429526210	.998657936	.310100450
1.86	.070740393	.131577132	.173993072	.060472850	.409499715	1.00356087	.180875358
1.88	.068143566	.128109904	.172703054	.068461933	.389400728	1.00592110	.055871972
1.90	.065615815	.124670048	.171257277	.076048729	.369279244	1.00582548	.064672194
1.92	.063156561	.121260598	.169663787	.083233274	.349183473	1.00336537	.180544138
1.94	.060765169	.117884428	.167930621	.090016549	.329159758	.998636126	.291555296
1.96	.058440944	.114544251	.166065787	.096400442	.309252497	.991736660	.397541369
1.98	.056183142	.111242621	.164077248	.102387708	.289504080	.982768912	.498362045
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
2.00	.053990967	.107981933	.161972900	.107981933	.269954833	.971837397	.593900632
2.02	.051863577	.104764425	.159760562	.113187485	.250642966	.959048730	.684063605
2.04	.049800088	.101592179	.157447957	.118009475	.231604543	.944511168	.768780068
2.06	.047799575	.098467124	.155042701	.122453716	.212873449	.928334168	.848001141
2.08	.045861076	.095391039	.152552284	.126526674	.194481371	.910627947	.921699273
2.10	.043983596	.092365552	.149984062	.130235428	.176457789	.891503067	.989867497
2.12	.042166107	.089392147	.147345244	.133587624	.158829969	.871070032	1.05251862
2.14	.040407554	.086472165	.144642880	.136591432	.141622975	.849438895	1.10968436
2.16	.038706856	.083606809	.141883852	.139255502	.124859672	.826718898	1.16141446
2.18	.037062910	.080797144	.139074864	.141588916	.108560757	.803018113	1.20777570
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
2.20	.035474593	.078044104	.136222437	.143601152	.092744776	.778443114	1.24885097
2.22	.033940763	.075348494	.133332894	.145302036	.077428162	.753098664	1.28473823
2.24	.032460266	.072710995	.130412363	.146701704	.062625274	.727087427	1.31554947
2.26	.031031932	.070132167	.127466765	.147810555	.048348441	.700509695	1.34140971
2.28	.029654585	.067612453	.124501809	.148639218	.034608011	.673463135	1.36245589
2.30	.028327038	.065152187	.121522992	.149198508	.021412408	.646042569	1.37883587
2.32	.027048100	.062751591	.118535591	.149499390	3z87681889	.618339759	1.39070730
2.34	.025816575	.060410787	.115544665	.149552943	3z33198918	.590443226	1.39823661
2.36	.024631269	.058129796	.112555048	.149370323	.014848817	.562438083	1.40159796
2.38	.023490985	.055908545	.109571352	.148962728	.025817236	.534405890	1.40097220
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
2.40	.022394530	.053746873	.106597964	.148341369	.036225392	.506424533	1.39654584
2.42	.021340715	.051644530	.103639048	.147517436	.046075051	.478568120	1.38851010
2.44	.020328356	.049601188	.100698543	.146502069	.055369419	.450906893	1.37705991
2.46	.019356277	.047616441	.097780168	.145306331	.064113071	.423507169	1.36239299
2.48	.018423311	.045689810	.094887419	.143941179	.072311866	.396431288	1.34470892
2.50	.017528300	.043820751	.092023578	.142417442	.079972871	.369737589	1.32420833
2.52	.016670101	.042008654	.089191708	.140745795	.087104280	.343480393	1.30109199
2.54	.015847579	.040252851	.086394662	.138936740	.093715333	.317710012	1.27556010
2.56	.015059616	.038552618	.083635085	.137000583	.099816236	.292472767	1.24781146
2.58	.014305109	.036907181	.080915419	.134947417	.105418081	.267811020	1.21804284
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
2.60	.013582969	.035315720	.078237903	.132787107	.110532770	.243763226	1.18644824
2.62	.012892126	.033777370	.075604584	.130529270	.115172935	.220363991	1.15321833
2.64	.012231526	.032291230	.073017320	.128183265	.119351860	.197644149	1.11853985
2.66	.011600135	.030856359	.070477781	.125758178	.123083412	.175630838	1.08259509
2.68	.010996937	.029471790	.067987461	.123262815	.126381962	.154347604	1.04556139
2.70	.010420935	.028136524	.065547680	.120705688	.129262318	.133814494	1.00761072
2.72	3z98711538	.026849538	.063159590	.118095009	.131739654	.114048178	.968909315
2.74	3z93466384	.025609789	.060824184	.115438685	.133829447	.095062058	.929617272
2.76	3z88464544	.024416214	.058542297	.112744310	.135547407	.076866399	.889888295
2.78	3z83696892	.023267736	.056314617	.110019162	.136909421	.059468457	.849869418
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
2.80	3z79154516	.022163264	.054141689	.107270200	.137931493	.042872619	.809700798
2.82	3z74828725	.021101701	.052023923	.104504062	.138629685	.027080535	.769515533
2.84	3z70711049	.020081938	.049961599	.101727065	.139020067	.012091267	.729439535
2.86	3z66793237	.019102866	.047954873	.098945204	.139118666	3z20985675	.689591426
2.88	3z63067264	.018163372	.046003785	.096164157	.138941417	.015494652	.650082484
2.90	3z59525324	.017262344	.044108265	.093389281	.138504120	.028104822	.611016613
2.92	3z56159836	.016398672	.042268139	.090625621	.137822398	.039938916	.572490355
2.94	3z52963439	.015571251	.040483134	.087877912	.136911659	.051008630	.534592923
2.96	3z49928992	.014778982	.038752887	.085150581	.135787060	.061327373	.497406273
2.98	3z47049575	.014020773	.037076947	.082447756	.134463471	.070910120	.461005199
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
3.00	3z44318484	.013295545	.035454787	.079773271	.132955452	.079773271	.425457448
3.02	3z41729230	.012602227	.033885804	.077130673	.131277220	.087934514	.390823868
3.04	3z39275536	.011939763	.032369326	.074523225	.129442626	.095412683	.357158573
3.06	3z36951337	.011307109	.030904620	.071953920	.127465134	.102227630	.324509123
3.08	3z34750774	.010703238	.029490897	.069425485	.125357804	.108400096	.292916724
3.10	3z32668191	.010127139	.028127312	.066940389	.123133271	.113951582	.262416450
3.12	3z30698133	3z95778175	.026812977	.064500854	.120803733	.118904231	.233037466
3.14	3z28835343	3z90542979	.025546961	.062108862	.118380943	.123280713	.204803273
3.16	3z27074758	3z85556234	.024328294	.059766163	.115876192	.127104115	.177731955
3.18	3z25411500	3z80808571	.023155976	.057474288	.113300309	.130397831	.151836442
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
3.20	3z23840882	3z76290822	.022028975	.055234555	.110663653	.133185466	.127124771
3.22	3z22358394	3z71994030	.020946238	.053048081	.107976106	.135490738	.103600355
3.24	3z20959706	3z67909448	.019906690	.050915788	.105247080	.137337390	.081262258
3.26	3z19640659	3z64028547	.018909241	.048838415	.102485510	.138749105	.060105470
3.28	3z18397262	3z60343019	.017952784	.046816528	.099699859	.139749426	.040121176
3.30	3z17225689	3z56844775	.017036207	.044850527	.096898120	.140361687	.021297034
3.32	3z16122275	3z53525952	.016158389	.042940660	.094087825	.140608939	3z36174468
3.34	3z15083506	3z50378911	.015318206	.041087024	.091276045	.140513892	.012936176
3.36	3z14106023	3z47396236	.014514533	.039289584	.088469402	.140098857	.028385147
3.38	3z13186609	3z44570738	.013746249	.037548173	.085674078	.139385692	.042753251
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
3.40	3z12322192	3z41895452	.013012234	.035862507	.082895819	.138395759	.056066485
3.42	3z11509834	3z39363634	.012311379	.034232190	.080139954	.137149879	.068352819
3.44	3z10746733	3z36968763	.011642581	.032656726	.077411396	.135668295	.079641957
3.46	3z10030213	3z34704537	.011004749	.031135522	.074714662	.133970641	.089965108
3.48	4z93577216	3z32564871	.010396803	.029667900	.072053884	.132075914	.099354764
3.50	4z87268270	3z30543894	3z98176803	.028253102	.069432817	.130002450	.107844491
3.52	4z81352123	3z28635947	3z92663322	.026890300	.066854859	.127767905	.115468728
3.54	4z75806719	3z26835579	3z87417276	.025578600	.064323061	.125389237	.122262592
3.56	4z70611070	3z25137541	3z82428539	.024317052	.061840142	.122882699	.128261699
3.58	4z65745218	3z23536788	3z77687179	.023104652	.059408502	.120263828	.133501993
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
3.60	4z61190193	3z22028469	3z73183471	.021940356	.057030239	.117547438	.138019581
3.62	4z56927978	3z20607928	3z68907902	.020823075	.054707161	.114747622	.141850588
3.64	4z52941468	3z19270694	3z64851181	.019751691	.052440801	.111877751	.145031010
3.66	4z49214433	3z18012482	3z61004242	.018725056	.050232433	.108950480	.147596592
3.68	4z45731481	3z16829185	3z57358253	.017742000	.048083085	.105977751	.149582700
3.70	4z42478027	3z15716870	3z53904616	.016801334	.045993551	.102970803	.151024215
3.72	4z39440252	3z14671774	3z50634974	.015901855	.043964410	.099940184	.151955434
3.74	4z36605076	3z13690299	3z47541209	.015042352	.041996036	.096895763	.152409976
3.76	4z33960121	3z12769006	3z44615449	.014221608	.040088610	.093846744	.152420705
3.78	4z31493681	3z11904612	3z41850063	.013438402	.038242139	.090801680	.152019653
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
3.80	4z29194693	3z11093983	3z39237667	.012691517	.036456464	.087768495	.151237962
3.82	4z27052703	3z10334133	3z36771116	.011979740	.034731271	.084754497	.150105823
3.84	4z25057844	4z96222123	3z34443511	.011301866	.033066111	.081766403	.148652434
3.86	4z23200804	4z89555103	3z32248189	.010656699	.031460402	.078810354	.146905958
3.88	4z21472798	4z83314457	3z30178729	.010043058	.029913446	.075891938	.144893491
3.90	4z19865547	4z77475634	3z28228942	3z94597749	.028424439	.073016214	.142641037
3.92	4z18371250	4z72015299	3z26392872	3z89057000	.026992482	.070187730	.140173492
3.94	4z16982560	4z66911286	3z24664791	3z83797018	.025616588	.067410549	.137514625
3.96	4z15692563	4z62142551	3z23039194	3z78806698	.024295694	.064688270	.134687077
3.98	4z14494756	4z57689129	3z21510798	3z74075149	.023028670	.062024047	.131712358
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
4.00	4z13383023	4z53532090	3z20074534	3z69591717	.021814327	.059420620	.128610847
4.02	4z12351616	4z49653498	3z18725544	3z65345989	.020651424	.056880330	.125401805
4.04	4z11395140	4z46036365	3z17459177	3z61327804	.019538679	.054405144	.122103383
4.06	4z10508526	4z42664616	3z16270981	3z57527261	.018474774	.051996677	.118732639
4.08	5z96870208	4z39523045	3z15156700	3z53934728	.017458359	.049656213	.115305556
4.10	5z89261657	4z36597279	3z14112268	3z50540843	.016488065	.047384730	.111837068
4.12	5z82217817	4z33873740	3z13133803	3z47336520	.015562505	.045182914	.108341079
4.14	5z75699536	4z31339608	3z12217602	3z44312952	.014680281	.043051184	.104830495
4.16	5z69670154	4z28982784	3z11360137	3z41461612	.013839989	.040989712	.101317253
4.18	5z64095363	4z26791862	3z10558045	3z38774254	.013040225	.038998438	.097812347
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
4.20	5z58943068	4z24756088	4z98081265	3z36242914	.012279586	.037077095	.094325869
4.22	5z54183261	4z22865336	4z91073393	3z33859904	.011556678	.035225219	.090867034
4.24	5z49787902	4z21110070	4z84527909	3z31617819	.010870118	.033442173	.087444223
4.26	5z45730800	4z19481321	4z78417346	3z29509525	.010218537	.031727159	.084065011
4.28	5z41987503	4z17970651	4z72715637	3z27528162	3z96005844	.030079236	.080736209
4.30	5z38535197	4z16570135	4z67398059	3z25667138	3z90149278	.028497334	.077463898
4.32	5z35352603	4z15272324	4z62441182	3z23920126	3z84602588	.026980268	.074253463
4.34	5z32419887	4z14070231	4z57822813	3z22281055	3z79352934	.025526751	.071109634
4.36	5z29718568	4z12957296	4z53521952	3z20744112	3z74387742	.024135411	.068036520
4.38	5z27231436	4z11927369	4z49518732	3z19303731	3z69694721	.022804796	.065037644
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
4.40	5z24942471	4z10974687	4z45794377	3z17954589	3z65261876	.021533390	.062115979
4.42	5z22836772	4z10093853	4z42331153	3z16691599	3z61077522	.020319625	.059273982
4.44	5z20900478	5z92798122	4z39112318	3z15509907	3z57130291	.019161887	.056513631
4.46	5z19120710	5z85278365	4z36122080	3z14404880	3z53409142	.018058525	.053836452
4.48	5z17485501	5z78335045	4z33345550	3z13372105	3z49903367	.017007866	.051243558
4.50	5z15983741	5z71926835	4z30768702	3z12407379	3z46602595	.016008216	.048735675
4.52	5z14605118	5z66015134	4z28378329	3z11506702	3z43496794	.015057870	.046313176
4.54	5z13340066	5z60563902	4z26162005	3z10666272	3z40576274	.014155120	.043976106
4.56	5z12179717	5z55539509	4z24108045	4z98824781	3z37831687	.013298258	.041724213
4.58	5z11115850	5z50910593	4z22205467	4z91518919	3z35254025	.012485587	.039556974
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
4.60	5z10140852	5z46647920	4z20443958	4z84712622	3z32834619	.011715420	.037473621
4.62	6z92476737	5z42724252	4z18813837	4z78375077	3z30565135	.010986089	.035473164
4.64	6z84297914	5z39114232	4z17306025	4z72477107	3z28437570	.010295948	.033554415
4.66	6z76811711	5z35794257	4z15912007	4z66991100	3z26444251	3z96433768	.031716011
4.68	6z69962341	5z32742376	4z14623808	4z61890948	3z24577821	3z90267824	.029956431
4.70	6z63698252	5z29938178	4z13433961	4z57151982	3z22831243	3z84446051	.028274022
4.72	6z57971825	5z27362701	4z12335477	4z52750910	3z21197787	3z78953189	.026667012
4.74	6z52739100	5z24998333	4z11321819	4z48665756	3z19671022	3z73774344	.025133528
4.76	6z47959510	5z22828727	4z10386879	4z44875798	3z18244816	3z68895006	.023671615
4.78	6z43595639	5z20838715	5z95249495	4z41361516	3z16913320	3z64301062	.022279248
Z	φ(x)	φ⁽¹⁾(x)	φ⁽²⁾(x)	φ⁽³⁾(x)	φ⁽⁴⁾(x)	φ⁽⁵⁾(x)	φ⁽⁶⁾(x)
4.80	6z39612991	5z19014236	5z87307032	4z38104528	3z15670963	3z59978809	.020954347
4.82	6z35979780	5z17342254	5z79991686	4z35087542	3z14512445	3z55914966	.019694792
4.84	6z32666730	5z15810697	5z73257101	4z32294298	3z13432727	3z52096680	.018498429
4.86	6z29646887	5z14408387	5z67060072	4z29709518	3z12427023	3z48511527	.017363090
4.88	6z26895450	5z13124979	5z61360355	4z27318857	3z11490792	3z45147521	.016286594
4.90	6z24389607	5z11950908	5z56120487	4z25108857	3z10619725	3z41993111	.015266762
4.92	6z22108389	5z10877327	5z51305611	4z23066895	4z98097441	3z39037183	.014301422
4.94	6z20032523	6z98960665	5z46883316	4z21181145	4z90569861	3z36269053	.013388419
4.96	6z18144312	6z89995787	5z42823479	4z19440530	4z83577985	3z33678468	.012525621
4.98	6z16427506	6z81808979	5z39098121	4z17834685	4z77087294	3z31255598	.011710923
5.00	6z14867195	6z74335976	5z35681268	4z16353915	4z71065193	3z28991031	.010942256

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