LMFDB - Embedded newform 490.6.a.g.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,6,Mod(1,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-4,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$78.5880717084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	490.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -64.0000 q^{8} -162.000 q^{9} +100.000 q^{10} -187.000 q^{11} +144.000 q^{12} -627.000 q^{13} -225.000 q^{15} +256.000 q^{16} -1813.00 q^{17} +648.000 q^{18} -258.000 q^{19} -400.000 q^{20} +748.000 q^{22} +2970.00 q^{23} -576.000 q^{24} +625.000 q^{25} +2508.00 q^{26} -3645.00 q^{27} +1299.00 q^{29} +900.000 q^{30} -1916.00 q^{31} -1024.00 q^{32} -1683.00 q^{33} +7252.00 q^{34} -2592.00 q^{36} +6578.00 q^{37} +1032.00 q^{38} -5643.00 q^{39} +1600.00 q^{40} -6676.00 q^{41} +3178.00 q^{43} -2992.00 q^{44} +4050.00 q^{45} -11880.0 q^{46} +22001.0 q^{47} +2304.00 q^{48} -2500.00 q^{50} -16317.0 q^{51} -10032.0 q^{52} +26168.0 q^{53} +14580.0 q^{54} +4675.00 q^{55} -2322.00 q^{57} -5196.00 q^{58} -3932.00 q^{59} -3600.00 q^{60} +48740.0 q^{61} +7664.00 q^{62} +4096.00 q^{64} +15675.0 q^{65} +6732.00 q^{66} -44832.0 q^{67} -29008.0 q^{68} +26730.0 q^{69} +63736.0 q^{71} +10368.0 q^{72} -60470.0 q^{73} -26312.0 q^{74} +5625.00 q^{75} -4128.00 q^{76} +22572.0 q^{78} -43721.0 q^{79} -6400.00 q^{80} +6561.00 q^{81} +26704.0 q^{82} -97276.0 q^{83} +45325.0 q^{85} -12712.0 q^{86} +11691.0 q^{87} +11968.0 q^{88} -45560.0 q^{89} -16200.0 q^{90} +47520.0 q^{92} -17244.0 q^{93} -88004.0 q^{94} +6450.00 q^{95} -9216.00 q^{96} +57295.0 q^{97} +30294.0 q^{99} +O(q^{100})\)

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	9.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−36.0000	−0.408248
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	−162.000	−0.666667
$10$	100.000	0.316228
$11$	−187.000	−0.465972	−0.232986	−	0.972480i	$-0.574850\pi$
$11$	−187.000	−0.465972	−0.232986	+	0.972480i	$0.574850\pi$
$12$	144.000	0.288675
$13$	−627.000	−1.02899	−0.514493	−	0.857495i	$-0.672020\pi$
$13$	−627.000	−1.02899	−0.514493	+	0.857495i	$0.672020\pi$
$14$	0	0
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	−1813.00	−1.52151	−0.760756	−	0.649038i	$-0.775172\pi$
$17$	−1813.00	−1.52151	−0.760756	+	0.649038i	$0.775172\pi$
$18$	648.000	0.471405
$19$	−258.000	−0.163959	−0.0819796	−	0.996634i	$-0.526124\pi$
$19$	−258.000	−0.163959	−0.0819796	+	0.996634i	$0.526124\pi$
$20$	−400.000	−0.223607
$21$	0	0
$22$	748.000	0.329492
$23$	2970.00	1.17068	0.585338	−	0.810789i	$-0.300962\pi$
$23$	2970.00	1.17068	0.585338	+	0.810789i	$0.300962\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	2508.00	0.727602
$27$	−3645.00	−0.962250
$28$	0	0
$29$	1299.00	0.286823	0.143412	−	0.989663i	$-0.454193\pi$
$29$	1299.00	0.286823	0.143412	+	0.989663i	$0.454193\pi$
$30$	900.000	0.182574
$31$	−1916.00	−0.358089	−0.179045	−	0.983841i	$-0.557301\pi$
$31$	−1916.00	−0.358089	−0.179045	+	0.983841i	$0.557301\pi$
$32$	−1024.00	−0.176777
$33$	−1683.00	−0.269029
$34$	7252.00	1.07587
$35$	0	0
$36$	−2592.00	−0.333333
$37$	6578.00	0.789932	0.394966	−	0.918696i	$-0.370756\pi$
$37$	6578.00	0.789932	0.394966	+	0.918696i	$0.370756\pi$
$38$	1032.00	0.115937
$39$	−5643.00	−0.594085
$40$	1600.00	0.158114
$41$	−6676.00	−0.620236	−0.310118	−	0.950698i	$-0.600368\pi$
$41$	−6676.00	−0.620236	−0.310118	+	0.950698i	$0.600368\pi$
$42$	0	0
$43$	3178.00	0.262109	0.131055	−	0.991375i	$-0.458164\pi$
$43$	3178.00	0.262109	0.131055	+	0.991375i	$0.458164\pi$
$44$	−2992.00	−0.232986
$45$	4050.00	0.298142
$46$	−11880.0	−0.827793
$47$	22001.0	1.45277	0.726387	−	0.687286i	$-0.241198\pi$
$47$	22001.0	1.45277	0.726387	+	0.687286i	$0.241198\pi$
$48$	2304.00	0.144338
$49$	0	0
$50$	−2500.00	−0.141421
$51$	−16317.0	−0.878446
$52$	−10032.0	−0.514493
$53$	26168.0	1.27962	0.639810	−	0.768533i	$-0.279013\pi$
$53$	26168.0	1.27962	0.639810	+	0.768533i	$0.279013\pi$
$54$	14580.0	0.680414
$55$	4675.00	0.208389
$56$	0	0
$57$	−2322.00	−0.0946619
$58$	−5196.00	−0.202815
$59$	−3932.00	−0.147056	−0.0735281	−	0.997293i	$-0.523426\pi$
$59$	−3932.00	−0.147056	−0.0735281	+	0.997293i	$0.523426\pi$
$60$	−3600.00	−0.129099
$61$	48740.0	1.67711	0.838554	−	0.544819i	$-0.183402\pi$
$61$	48740.0	1.67711	0.838554	+	0.544819i	$0.183402\pi$
$62$	7664.00	0.253207
$63$	0	0
$64$	4096.00	0.125000
$65$	15675.0	0.460176
$66$	6732.00	0.190232
$67$	−44832.0	−1.22012	−0.610058	−	0.792357i	$-0.708854\pi$
$67$	−44832.0	−1.22012	−0.610058	+	0.792357i	$0.708854\pi$
$68$	−29008.0	−0.760756
$69$	26730.0	0.675890
$70$	0	0
$71$	63736.0	1.50051	0.750255	−	0.661148i	$-0.229931\pi$
$71$	63736.0	1.50051	0.750255	+	0.661148i	$0.229931\pi$
$72$	10368.0	0.235702
$73$	−60470.0	−1.32811	−0.664053	−	0.747685i	$-0.731165\pi$
$73$	−60470.0	−1.32811	−0.664053	+	0.747685i	$0.731165\pi$
$74$	−26312.0	−0.558566
$75$	5625.00	0.115470
$76$	−4128.00	−0.0819796
$77$	0	0
$78$	22572.0	0.420081
$79$	−43721.0	−0.788174	−0.394087	−	0.919073i	$-0.628939\pi$
$79$	−43721.0	−0.788174	−0.394087	+	0.919073i	$0.628939\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	26704.0	0.438573
$83$	−97276.0	−1.54992	−0.774962	−	0.632008i	$-0.782231\pi$
$83$	−97276.0	−1.54992	−0.774962	+	0.632008i	$0.782231\pi$
$84$	0	0
$85$	45325.0	0.680441
$86$	−12712.0	−0.185339
$87$	11691.0	0.165597
$88$	11968.0	0.164746
$89$	−45560.0	−0.609689	−0.304845	−	0.952402i	$-0.598605\pi$
$89$	−45560.0	−0.609689	−0.304845	+	0.952402i	$0.598605\pi$
$90$	−16200.0	−0.210819
$91$	0	0
$92$	47520.0	0.585338
$93$	−17244.0	−0.206743
$94$	−88004.0	−1.02727
$95$	6450.00	0.0733248
$96$	−9216.00	−0.102062
$97$	57295.0	0.618283	0.309142	−	0.951016i	$-0.399958\pi$
$97$	57295.0	0.618283	0.309142	+	0.951016i	$0.399958\pi$
$98$	0	0
$99$	30294.0	0.310648
$100$	10000.0	0.100000
$101$	44970.0	0.438651	0.219326	−	0.975652i	$-0.429614\pi$
$101$	44970.0	0.438651	0.219326	+	0.975652i	$0.429614\pi$
$102$	65268.0	0.621155
$103$	101405.	0.941817	0.470908	−	0.882182i	$-0.343926\pi$
$103$	101405.	0.941817	0.470908	+	0.882182i	$0.343926\pi$
$104$	40128.0	0.363801
$105$	0	0
$106$	−104672.	−0.904828
$107$	−166002.	−1.40170	−0.700848	−	0.713311i	$-0.747195\pi$
$107$	−166002.	−1.40170	−0.700848	+	0.713311i	$0.747195\pi$
$108$	−58320.0	−0.481125
$109$	8289.00	0.0668245	0.0334123	−	0.999442i	$-0.489363\pi$
$109$	8289.00	0.0668245	0.0334123	+	0.999442i	$0.489363\pi$
$110$	−18700.0	−0.147353
$111$	59202.0	0.456067
$112$	0	0
$113$	263206.	1.93910	0.969549	−	0.244898i	$-0.0787545\pi$
$113$	263206.	1.93910	0.969549	+	0.244898i	$0.0787545\pi$
$114$	9288.00	0.0669360
$115$	−74250.0	−0.523542
$116$	20784.0	0.143412
$117$	101574.	0.685990
$118$	15728.0	0.103984
$119$	0	0
$120$	14400.0	0.0912871
$121$	−126082.	−0.782870
$122$	−194960.	−1.18589
$123$	−60084.0	−0.358093
$124$	−30656.0	−0.179045
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	30052.0	0.165335	0.0826674	−	0.996577i	$-0.473656\pi$
$127$	30052.0	0.165335	0.0826674	+	0.996577i	$0.473656\pi$
$128$	−16384.0	−0.0883883
$129$	28602.0	0.151329
$130$	−62700.0	−0.325394
$131$	120050.	0.611201	0.305600	−	0.952160i	$-0.401143\pi$
$131$	120050.	0.611201	0.305600	+	0.952160i	$0.401143\pi$
$132$	−26928.0	−0.134515
$133$	0	0
$134$	179328.	0.862752
$135$	91125.0	0.430331
$136$	116032.	0.537936
$137$	31776.0	0.144643	0.0723216	−	0.997381i	$-0.476959\pi$
$137$	31776.0	0.144643	0.0723216	+	0.997381i	$0.476959\pi$
$138$	−106920.	−0.477927
$139$	200162.	0.878708	0.439354	−	0.898314i	$-0.355207\pi$
$139$	200162.	0.878708	0.439354	+	0.898314i	$0.355207\pi$
$140$	0	0
$141$	198009.	0.838759
$142$	−254944.	−1.06102
$143$	117249.	0.479478
$144$	−41472.0	−0.166667
$145$	−32475.0	−0.128271
$146$	241880.	0.939113
$147$	0	0
$148$	105248.	0.394966
$149$	309642.	1.14260	0.571300	−	0.820741i	$-0.306439\pi$
$149$	309642.	1.14260	0.571300	+	0.820741i	$0.306439\pi$
$150$	−22500.0	−0.0816497
$151$	−208657.	−0.744716	−0.372358	−	0.928089i	$-0.621451\pi$
$151$	−208657.	−0.744716	−0.372358	+	0.928089i	$0.621451\pi$
$152$	16512.0	0.0579683
$153$	293706.	1.01434
$154$	0	0
$155$	47900.0	0.160142
$156$	−90288.0	−0.297042
$157$	−36010.0	−0.116593	−0.0582967	−	0.998299i	$-0.518567\pi$
$157$	−36010.0	−0.116593	−0.0582967	+	0.998299i	$0.518567\pi$
$158$	174884.	0.557324
$159$	235512.	0.738789
$160$	25600.0	0.0790569
$161$	0	0
$162$	−26244.0	−0.0785674
$163$	175670.	0.517879	0.258940	−	0.965893i	$-0.416627\pi$
$163$	175670.	0.517879	0.258940	+	0.965893i	$0.416627\pi$
$164$	−106816.	−0.310118
$165$	42075.0	0.120313
$166$	389104.	1.09596
$167$	157413.	0.436767	0.218383	−	0.975863i	$-0.429922\pi$
$167$	157413.	0.436767	0.218383	+	0.975863i	$0.429922\pi$
$168$	0	0
$169$	21836.0	0.0588107
$170$	−181300.	−0.481144
$171$	41796.0	0.109306
$172$	50848.0	0.131055
$173$	23471.0	0.0596233	0.0298117	−	0.999556i	$-0.490509\pi$
$173$	23471.0	0.0596233	0.0298117	+	0.999556i	$0.490509\pi$
$174$	−46764.0	−0.117095
$175$	0	0
$176$	−47872.0	−0.116493
$177$	−35388.0	−0.0849030
$178$	182240.	0.431116
$179$	612228.	1.42817	0.714086	−	0.700058i	$-0.246842\pi$
$179$	612228.	1.42817	0.714086	+	0.700058i	$0.246842\pi$
$180$	64800.0	0.149071
$181$	−528832.	−1.19983	−0.599917	−	0.800062i	$-0.704800\pi$
$181$	−528832.	−1.19983	−0.599917	+	0.800062i	$0.704800\pi$
$182$	0	0
$183$	438660.	0.968279
$184$	−190080.	−0.413897
$185$	−164450.	−0.353268
$186$	68976.0	0.146189
$187$	339031.	0.708982
$188$	352016.	0.726387
$189$	0	0
$190$	−25800.0	−0.0518484
$191$	540369.	1.07178	0.535892	−	0.844287i	$-0.319976\pi$
$191$	540369.	1.07178	0.535892	+	0.844287i	$0.319976\pi$
$192$	36864.0	0.0721688
$193$	960320.	1.85576	0.927882	−	0.372874i	$-0.121628\pi$
$193$	960320.	1.85576	0.927882	+	0.372874i	$0.121628\pi$
$194$	−229180.	−0.437192
$195$	141075.	0.265683
$196$	0	0
$197$	761944.	1.39881	0.699403	−	0.714728i	$-0.253449\pi$
$197$	761944.	1.39881	0.699403	+	0.714728i	$0.253449\pi$
$198$	−121176.	−0.219661
$199$	−125084.	−0.223908	−0.111954	−	0.993713i	$-0.535711\pi$
$199$	−125084.	−0.223908	−0.111954	+	0.993713i	$0.535711\pi$
$200$	−40000.0	−0.0707107
$201$	−403488.	−0.704434
$202$	−179880.	−0.310173
$203$	0	0
$204$	−261072.	−0.439223
$205$	166900.	0.277378
$206$	−405620.	−0.665965
$207$	−481140.	−0.780451
$208$	−160512.	−0.257246
$209$	48246.0	0.0764004
$210$	0	0
$211$	627547.	0.970376	0.485188	−	0.874410i	$-0.338751\pi$
$211$	627547.	0.970376	0.485188	+	0.874410i	$0.338751\pi$
$212$	418688.	0.639810
$213$	573624.	0.866320
$214$	664008.	0.991149
$215$	−79450.0	−0.117219
$216$	233280.	0.340207
$217$	0	0
$218$	−33156.0	−0.0472521
$219$	−544230.	−0.766782
$220$	74800.0	0.104195
$221$	1.13675e6	1.56561
$222$	−236808.	−0.322488
$223$	1.22110e6	1.64433	0.822166	−	0.569248i	$-0.192766\pi$
$223$	1.22110e6	1.64433	0.822166	+	0.569248i	$0.192766\pi$
$224$	0	0
$225$	−101250.	−0.133333
$226$	−1.05282e6	−1.37115
$227$	−390547.	−0.503047	−0.251524	−	0.967851i	$-0.580932\pi$
$227$	−390547.	−0.503047	−0.251524	+	0.967851i	$0.580932\pi$
$228$	−37152.0	−0.0473309
$229$	712124.	0.897360	0.448680	−	0.893692i	$-0.351894\pi$
$229$	712124.	0.897360	0.448680	+	0.893692i	$0.351894\pi$
$230$	297000.	0.370200
$231$	0	0
$232$	−83136.0	−0.101407
$233$	561576.	0.677671	0.338835	−	0.940846i	$-0.389967\pi$
$233$	561576.	0.677671	0.338835	+	0.940846i	$0.389967\pi$
$234$	−406296.	−0.485068
$235$	−550025.	−0.649700
$236$	−62912.0	−0.0735281
$237$	−393489.	−0.455053
$238$	0	0
$239$	−1.36084e6	−1.54103	−0.770515	−	0.637421i	$-0.780001\pi$
$239$	−1.36084e6	−1.54103	−0.770515	+	0.637421i	$0.780001\pi$
$240$	−57600.0	−0.0645497
$241$	−530050.	−0.587860	−0.293930	−	0.955827i	$-0.594963\pi$
$241$	−530050.	−0.587860	−0.293930	+	0.955827i	$0.594963\pi$
$242$	504328.	0.553573
$243$	944784.	1.02640
$244$	779840.	0.838554
$245$	0	0
$246$	240336.	0.253210
$247$	161766.	0.168712
$248$	122624.	0.126604
$249$	−875484.	−0.894849
$250$	62500.0	0.0632456
$251$	−990330.	−0.992192	−0.496096	−	0.868268i	$-0.665234\pi$
$251$	−990330.	−0.992192	−0.496096	+	0.868268i	$0.665234\pi$
$252$	0	0
$253$	−555390.	−0.545503
$254$	−120208.	−0.116909
$255$	407925.	0.392853
$256$	65536.0	0.0625000
$257$	1.81643e6	1.71548	0.857740	−	0.514083i	$-0.171868\pi$
$257$	1.81643e6	1.71548	0.857740	+	0.514083i	$0.171868\pi$
$258$	−114408.	−0.107006
$259$	0	0
$260$	250800.	0.230088
$261$	−210438.	−0.191215
$262$	−480200.	−0.432184
$263$	−1.95847e6	−1.74594	−0.872968	−	0.487777i	$-0.837808\pi$
$263$	−1.95847e6	−1.74594	−0.872968	+	0.487777i	$0.837808\pi$
$264$	107712.	0.0951162
$265$	−654200.	−0.572263
$266$	0	0
$267$	−410040.	−0.352004
$268$	−717312.	−0.610058
$269$	−218034.	−0.183715	−0.0918573	−	0.995772i	$-0.529280\pi$
$269$	−218034.	−0.183715	−0.0918573	+	0.995772i	$0.529280\pi$
$270$	−364500.	−0.304290
$271$	−1.26265e6	−1.04438	−0.522192	−	0.852828i	$-0.674886\pi$
$271$	−1.26265e6	−1.04438	−0.522192	+	0.852828i	$0.674886\pi$
$272$	−464128.	−0.380378
$273$	0	0
$274$	−127104.	−0.102278
$275$	−116875.	−0.0931944
$276$	427680.	0.337945
$277$	−1.10264e6	−0.863443	−0.431721	−	0.902007i	$-0.642094\pi$
$277$	−1.10264e6	−0.863443	−0.431721	+	0.902007i	$0.642094\pi$
$278$	−800648.	−0.621340
$279$	310392.	0.238726
$280$	0	0
$281$	−998213.	−0.754149	−0.377075	−	0.926183i	$-0.623070\pi$
$281$	−998213.	−0.754149	−0.377075	+	0.926183i	$0.623070\pi$
$282$	−792036.	−0.593092
$283$	386371.	0.286773	0.143387	−	0.989667i	$-0.454201\pi$
$283$	386371.	0.286773	0.143387	+	0.989667i	$0.454201\pi$
$284$	1.01978e6	0.750255
$285$	58050.0	0.0423341
$286$	−468996.	−0.339042
$287$	0	0
$288$	165888.	0.117851
$289$	1.86711e6	1.31500
$290$	129900.	0.0907014
$291$	515655.	0.356966
$292$	−967520.	−0.664053
$293$	783571.	0.533224	0.266612	−	0.963804i	$-0.414096\pi$
$293$	783571.	0.533224	0.266612	+	0.963804i	$0.414096\pi$
$294$	0	0
$295$	98300.0	0.0657656
$296$	−420992.	−0.279283
$297$	681615.	0.448382
$298$	−1.23857e6	−0.807940
$299$	−1.86219e6	−1.20461
$300$	90000.0	0.0577350
$301$	0	0
$302$	834628.	0.526594
$303$	404730.	0.253255
$304$	−66048.0	−0.0409898
$305$	−1.21850e6	−0.750025
$306$	−1.17482e6	−0.717248
$307$	−2.81773e6	−1.70629	−0.853147	−	0.521670i	$-0.825309\pi$
$307$	−2.81773e6	−1.70629	−0.853147	+	0.521670i	$0.825309\pi$
$308$	0	0
$309$	912645.	0.543758
$310$	−191600.	−0.113238
$311$	847398.	0.496806	0.248403	−	0.968657i	$-0.420094\pi$
$311$	847398.	0.496806	0.248403	+	0.968657i	$0.420094\pi$
$312$	361152.	0.210041
$313$	−364955.	−0.210561	−0.105281	−	0.994443i	$-0.533574\pi$
$313$	−364955.	−0.210561	−0.105281	+	0.994443i	$0.533574\pi$
$314$	144040.	0.0824440
$315$	0	0
$316$	−699536.	−0.394087
$317$	1.93744e6	1.08288	0.541439	−	0.840740i	$-0.317880\pi$
$317$	1.93744e6	1.08288	0.541439	+	0.840740i	$0.317880\pi$
$318$	−942048.	−0.522402
$319$	−242913.	−0.133652
$320$	−102400.	−0.0559017
$321$	−1.49402e6	−0.809270
$322$	0	0
$323$	467754.	0.249466
$324$	104976.	0.0555556
$325$	−391875.	−0.205797
$326$	−702680.	−0.366196
$327$	74601.0	0.0385812
$328$	427264.	0.219286
$329$	0	0
$330$	−168300.	−0.0850745
$331$	−61460.0	−0.0308335	−0.0154167	−	0.999881i	$-0.504907\pi$
$331$	−61460.0	−0.0308335	−0.0154167	+	0.999881i	$0.504907\pi$
$332$	−1.55642e6	−0.774962
$333$	−1.06564e6	−0.526621
$334$	−629652.	−0.308841
$335$	1.12080e6	0.545652
$336$	0	0
$337$	−3.74116e6	−1.79445	−0.897225	−	0.441574i	$-0.854420\pi$
$337$	−3.74116e6	−1.79445	−0.897225	+	0.441574i	$0.854420\pi$
$338$	−87344.0	−0.0415854
$339$	2.36885e6	1.11954
$340$	725200.	0.340221
$341$	358292.	0.166860
$342$	−167184.	−0.0772911
$343$	0	0
$344$	−203392.	−0.0926697
$345$	−668250.	−0.302267
$346$	−93884.0	−0.0421601
$347$	211334.	0.0942206	0.0471103	−	0.998890i	$-0.484999\pi$
$347$	211334.	0.0942206	0.0471103	+	0.998890i	$0.484999\pi$
$348$	187056.	0.0827987
$349$	−3.39558e6	−1.49228	−0.746140	−	0.665789i	$-0.768095\pi$
$349$	−3.39558e6	−1.49228	−0.746140	+	0.665789i	$0.768095\pi$
$350$	0	0
$351$	2.28542e6	0.990142
$352$	191488.	0.0823730
$353$	3.88094e6	1.65768	0.828838	−	0.559489i	$-0.189003\pi$
$353$	3.88094e6	1.65768	0.828838	+	0.559489i	$0.189003\pi$
$354$	141552.	0.0600355
$355$	−1.59340e6	−0.671049
$356$	−728960.	−0.304845
$357$	0	0
$358$	−2.44891e6	−1.00987
$359$	3.24210e6	1.32767	0.663836	−	0.747878i	$-0.268927\pi$
$359$	3.24210e6	1.32767	0.663836	+	0.747878i	$0.268927\pi$
$360$	−259200.	−0.105409
$361$	−2.40954e6	−0.973117
$362$	2.11533e6	0.848411
$363$	−1.13474e6	−0.451990
$364$	0	0
$365$	1.51175e6	0.593947
$366$	−1.75464e6	−0.684676
$367$	−1.44430e6	−0.559749	−0.279874	−	0.960037i	$-0.590293\pi$
$367$	−1.44430e6	−0.559749	−0.279874	+	0.960037i	$0.590293\pi$
$368$	760320.	0.292669
$369$	1.08151e6	0.413490
$370$	657800.	0.249798
$371$	0	0
$372$	−275904.	−0.103371
$373$	3.43542e6	1.27852	0.639260	−	0.768991i	$-0.279241\pi$
$373$	3.43542e6	1.27852	0.639260	+	0.768991i	$0.279241\pi$
$374$	−1.35612e6	−0.501326
$375$	−140625.	−0.0516398
$376$	−1.40806e6	−0.513633
$377$	−814473.	−0.295137
$378$	0	0
$379$	−1.68635e6	−0.603044	−0.301522	−	0.953459i	$-0.597495\pi$
$379$	−1.68635e6	−0.603044	−0.301522	+	0.953459i	$0.597495\pi$
$380$	103200.	0.0366624
$381$	270468.	0.0954560
$382$	−2.16148e6	−0.757865
$383$	−2.64354e6	−0.920850	−0.460425	−	0.887699i	$-0.652303\pi$
$383$	−2.64354e6	−0.920850	−0.460425	+	0.887699i	$0.652303\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	−3.84128e6	−1.31222
$387$	−514836.	−0.174740
$388$	916720.	0.309142
$389$	−452099.	−0.151481	−0.0757407	−	0.997128i	$-0.524132\pi$
$389$	−452099.	−0.151481	−0.0757407	+	0.997128i	$0.524132\pi$
$390$	−564300.	−0.187866
$391$	−5.38461e6	−1.78120
$392$	0	0
$393$	1.08045e6	0.352877
$394$	−3.04778e6	−0.989105
$395$	1.09302e6	0.352482
$396$	484704.	0.155324
$397$	1.95530e6	0.622641	0.311321	−	0.950305i	$-0.399229\pi$
$397$	1.95530e6	0.622641	0.311321	+	0.950305i	$0.399229\pi$
$398$	500336.	0.158327
$399$	0	0
$400$	160000.	0.0500000
$401$	−4.76737e6	−1.48053	−0.740266	−	0.672314i	$-0.765300\pi$
$401$	−4.76737e6	−1.48053	−0.740266	+	0.672314i	$0.765300\pi$
$402$	1.61395e6	0.498110
$403$	1.20133e6	0.368469
$404$	719520.	0.219326
$405$	−164025.	−0.0496904
$406$	0	0
$407$	−1.23009e6	−0.368086
$408$	1.04429e6	0.310577
$409$	4.13199e6	1.22138	0.610690	−	0.791870i	$-0.290892\pi$
$409$	4.13199e6	1.22138	0.610690	+	0.791870i	$0.290892\pi$
$410$	−667600.	−0.196136
$411$	285984.	0.0835097
$412$	1.62248e6	0.470908
$413$	0	0
$414$	1.92456e6	0.551862
$415$	2.43190e6	0.693147
$416$	642048.	0.181901
$417$	1.80146e6	0.507322
$418$	−192984.	−0.0540232
$419$	−190512.	−0.0530136	−0.0265068	−	0.999649i	$-0.508438\pi$
$419$	−190512.	−0.0530136	−0.0265068	+	0.999649i	$0.508438\pi$
$420$	0	0
$421$	−5.19186e6	−1.42764	−0.713818	−	0.700332i	$-0.753035\pi$
$421$	−5.19186e6	−1.42764	−0.713818	+	0.700332i	$0.753035\pi$
$422$	−2.51019e6	−0.686160
$423$	−3.56416e6	−0.968515
$424$	−1.67475e6	−0.452414
$425$	−1.13312e6	−0.304302
$426$	−2.29450e6	−0.612581
$427$	0	0
$428$	−2.65603e6	−0.700848
$429$	1.05524e6	0.276827
$430$	317800.	0.0828863
$431$	−4.21781e6	−1.09369	−0.546845	−	0.837234i	$-0.684171\pi$
$431$	−4.21781e6	−1.09369	−0.546845	+	0.837234i	$0.684171\pi$
$432$	−933120.	−0.240563
$433$	4.86027e6	1.24578	0.622890	−	0.782310i	$-0.285959\pi$
$433$	4.86027e6	1.24578	0.622890	+	0.782310i	$0.285959\pi$
$434$	0	0
$435$	−292275.	−0.0740574
$436$	132624.	0.0334123
$437$	−766260.	−0.191943
$438$	2.17692e6	0.542197
$439$	2.03113e6	0.503011	0.251505	−	0.967856i	$-0.419074\pi$
$439$	2.03113e6	0.503011	0.251505	+	0.967856i	$0.419074\pi$
$440$	−299200.	−0.0736767
$441$	0	0
$442$	−4.54700e6	−1.10706
$443$	2.84199e6	0.688038	0.344019	−	0.938963i	$-0.388211\pi$
$443$	2.84199e6	0.688038	0.344019	+	0.938963i	$0.388211\pi$
$444$	947232.	0.228034
$445$	1.13900e6	0.272661
$446$	−4.88440e6	−1.16272
$447$	2.78678e6	0.659680
$448$	0	0
$449$	−4.59682e6	−1.07607	−0.538037	−	0.842921i	$-0.680834\pi$
$449$	−4.59682e6	−1.07607	−0.538037	+	0.842921i	$0.680834\pi$
$450$	405000.	0.0942809
$451$	1.24841e6	0.289012
$452$	4.21130e6	0.969549
$453$	−1.87791e6	−0.429962
$454$	1.56219e6	0.355708
$455$	0	0
$456$	148608.	0.0334680
$457$	4.93367e6	1.10504	0.552522	−	0.833498i	$-0.313665\pi$
$457$	4.93367e6	1.10504	0.552522	+	0.833498i	$0.313665\pi$
$458$	−2.84850e6	−0.634530
$459$	6.60838e6	1.46408
$460$	−1.18800e6	−0.261771
$461$	4.75667e6	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$461$	4.75667e6	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$462$	0	0
$463$	4.08619e6	0.885862	0.442931	−	0.896556i	$-0.353939\pi$
$463$	4.08619e6	0.885862	0.442931	+	0.896556i	$0.353939\pi$
$464$	332544.	0.0717058
$465$	431100.	0.0924582
$466$	−2.24630e6	−0.479186
$467$	4.15932e6	0.882531	0.441266	−	0.897377i	$-0.354530\pi$
$467$	4.15932e6	0.882531	0.441266	+	0.897377i	$0.354530\pi$
$468$	1.62518e6	0.342995
$469$	0	0
$470$	2.20010e6	0.459407
$471$	−324090.	−0.0673152
$472$	251648.	0.0519922
$473$	−594286.	−0.122136
$474$	1.57396e6	0.321771
$475$	−161250.	−0.0327918
$476$	0	0
$477$	−4.23922e6	−0.853080
$478$	5.44335e6	1.08967
$479$	3.36040e6	0.669195	0.334597	−	0.942361i	$-0.391400\pi$
$479$	3.36040e6	0.669195	0.334597	+	0.942361i	$0.391400\pi$
$480$	230400.	0.0456435
$481$	−4.12441e6	−0.812828
$482$	2.12020e6	0.415680
$483$	0	0
$484$	−2.01731e6	−0.391435
$485$	−1.43238e6	−0.276505
$486$	−3.77914e6	−0.725775
$487$	7.05243e6	1.34746	0.673730	−	0.738977i	$-0.264691\pi$
$487$	7.05243e6	1.34746	0.673730	+	0.738977i	$0.264691\pi$
$488$	−3.11936e6	−0.592947
$489$	1.58103e6	0.298998
$490$	0	0
$491$	−83937.0	−0.0157127	−0.00785633	−	0.999969i	$-0.502501\pi$
$491$	−83937.0	−0.0157127	−0.00785633	+	0.999969i	$0.502501\pi$
$492$	−961344.	−0.179047
$493$	−2.35509e6	−0.436405
$494$	−647064.	−0.119297
$495$	−757350.	−0.138926
$496$	−490496.	−0.0895223
$497$	0	0
$498$	3.50194e6	0.632754
$499$	−7.10526e6	−1.27741	−0.638703	−	0.769454i	$-0.720529\pi$
$499$	−7.10526e6	−1.27741	−0.638703	+	0.769454i	$0.720529\pi$
$500$	−250000.	−0.0447214
$501$	1.41672e6	0.252167
$502$	3.96132e6	0.701586
$503$	−2.89147e6	−0.509564	−0.254782	−	0.966999i	$-0.582004\pi$
$503$	−2.89147e6	−0.509564	−0.254782	+	0.966999i	$0.582004\pi$
$504$	0	0
$505$	−1.12425e6	−0.196171
$506$	2.22156e6	0.385729
$507$	196524.	0.0339544
$508$	480832.	0.0826674
$509$	−1.03548e6	−0.177153	−0.0885764	−	0.996069i	$-0.528232\pi$
$509$	−1.03548e6	−0.177153	−0.0885764	+	0.996069i	$0.528232\pi$
$510$	−1.63170e6	−0.277789
$511$	0	0
$512$	−262144.	−0.0441942
$513$	940410.	0.157770
$514$	−7.26572e6	−1.21303
$515$	−2.53513e6	−0.421193
$516$	457632.	0.0756645
$517$	−4.11419e6	−0.676952
$518$	0	0
$519$	211239.	0.0344236
$520$	−1.00320e6	−0.162697
$521$	7.49715e6	1.21005	0.605023	−	0.796208i	$-0.293164\pi$
$521$	7.49715e6	1.21005	0.605023	+	0.796208i	$0.293164\pi$
$522$	841752.	0.135210
$523$	−3.53223e6	−0.564670	−0.282335	−	0.959316i	$-0.591109\pi$
$523$	−3.53223e6	−0.564670	−0.282335	+	0.959316i	$0.591109\pi$
$524$	1.92080e6	0.305600
$525$	0	0
$526$	7.83390e6	1.23456
$527$	3.47371e6	0.544837
$528$	−430848.	−0.0672573
$529$	2.38456e6	0.370483
$530$	2.61680e6	0.404651
$531$	636984.	0.0980375
$532$	0	0
$533$	4.18585e6	0.638213
$534$	1.64016e6	0.248905
$535$	4.15005e6	0.626858
$536$	2.86925e6	0.431376
$537$	5.51005e6	0.824556
$538$	872136.	0.129906
$539$	0	0
$540$	1.45800e6	0.215166
$541$	−4.99188e6	−0.733281	−0.366641	−	0.930363i	$-0.619492\pi$
$541$	−4.99188e6	−0.733281	−0.366641	+	0.930363i	$0.619492\pi$
$542$	5.05061e6	0.738491
$543$	−4.75949e6	−0.692725
$544$	1.85651e6	0.268968
$545$	−207225.	−0.0298848
$546$	0	0
$547$	5.12634e6	0.732553	0.366277	−	0.930506i	$-0.380632\pi$
$547$	5.12634e6	0.732553	0.366277	+	0.930506i	$0.380632\pi$
$548$	508416.	0.0723216
$549$	−7.89588e6	−1.11807
$550$	467500.	0.0658984
$551$	−335142.	−0.0470273
$552$	−1.71072e6	−0.238963
$553$	0	0
$554$	4.41055e6	0.610546
$555$	−1.48005e6	−0.203959
$556$	3.20259e6	0.439354
$557$	8.86866e6	1.21121	0.605606	−	0.795765i	$-0.292931\pi$
$557$	8.86866e6	1.21121	0.605606	+	0.795765i	$0.292931\pi$
$558$	−1.24157e6	−0.168805
$559$	−1.99261e6	−0.269707
$560$	0	0
$561$	3.05128e6	0.409331
$562$	3.99285e6	0.533264
$563$	−9.07277e6	−1.20634	−0.603169	−	0.797613i	$-0.706096\pi$
$563$	−9.07277e6	−1.20634	−0.603169	+	0.797613i	$0.706096\pi$
$564$	3.16814e6	0.419379
$565$	−6.58015e6	−0.867191
$566$	−1.54548e6	−0.202779
$567$	0	0
$568$	−4.07910e6	−0.530510
$569$	2.08310e6	0.269730	0.134865	−	0.990864i	$-0.456940\pi$
$569$	2.08310e6	0.269730	0.134865	+	0.990864i	$0.456940\pi$
$570$	−232200.	−0.0299347
$571$	−5.46368e6	−0.701286	−0.350643	−	0.936509i	$-0.614037\pi$
$571$	−5.46368e6	−0.701286	−0.350643	+	0.936509i	$0.614037\pi$
$572$	1.87598e6	0.239739
$573$	4.86332e6	0.618794
$574$	0	0
$575$	1.85625e6	0.234135
$576$	−663552.	−0.0833333
$577$	−7.66246e6	−0.958140	−0.479070	−	0.877777i	$-0.659026\pi$
$577$	−7.66246e6	−0.958140	−0.479070	+	0.877777i	$0.659026\pi$
$578$	−7.46845e6	−0.929845
$579$	8.64288e6	1.07143
$580$	−519600.	−0.0641356
$581$	0	0
$582$	−2.06262e6	−0.252413
$583$	−4.89342e6	−0.596267
$584$	3.87008e6	0.469556
$585$	−2.53935e6	−0.306784
$586$	−3.13428e6	−0.377046
$587$	1.57465e7	1.88620	0.943100	−	0.332510i	$-0.107896\pi$
$587$	1.57465e7	1.88620	0.943100	+	0.332510i	$0.107896\pi$
$588$	0	0
$589$	494328.	0.0587120
$590$	−393200.	−0.0465033
$591$	6.85750e6	0.807601
$592$	1.68397e6	0.197483
$593$	1.62409e7	1.89658	0.948292	−	0.317398i	$-0.102809\pi$
$593$	1.62409e7	1.89658	0.948292	+	0.317398i	$0.102809\pi$
$594$	−2.72646e6	−0.317054
$595$	0	0
$596$	4.95427e6	0.571300
$597$	−1.12576e6	−0.129273
$598$	7.44876e6	0.851787
$599$	−1.90793e6	−0.217268	−0.108634	−	0.994082i	$-0.534648\pi$
$599$	−1.90793e6	−0.217268	−0.108634	+	0.994082i	$0.534648\pi$
$600$	−360000.	−0.0408248
$601$	−3.52970e6	−0.398613	−0.199306	−	0.979937i	$-0.563869\pi$
$601$	−3.52970e6	−0.398613	−0.199306	+	0.979937i	$0.563869\pi$
$602$	0	0
$603$	7.26278e6	0.813411
$604$	−3.33851e6	−0.372358
$605$	3.15205e6	0.350110
$606$	−1.61892e6	−0.179079
$607$	−3.37799e6	−0.372123	−0.186061	−	0.982538i	$-0.559572\pi$
$607$	−3.37799e6	−0.372123	−0.186061	+	0.982538i	$0.559572\pi$
$608$	264192.	0.0289842
$609$	0	0
$610$	4.87400e6	0.530348
$611$	−1.37946e7	−1.49488
$612$	4.69930e6	0.507171
$613$	1.20412e6	0.129425	0.0647127	−	0.997904i	$-0.479387\pi$
$613$	1.20412e6	0.129425	0.0647127	+	0.997904i	$0.479387\pi$
$614$	1.12709e7	1.20653
$615$	1.50210e6	0.160144
$616$	0	0
$617$	−5.47330e6	−0.578810	−0.289405	−	0.957207i	$-0.593457\pi$
$617$	−5.47330e6	−0.578810	−0.289405	+	0.957207i	$0.593457\pi$
$618$	−3.65058e6	−0.384495
$619$	−3.22662e6	−0.338471	−0.169236	−	0.985576i	$-0.554130\pi$
$619$	−3.22662e6	−0.338471	−0.169236	+	0.985576i	$0.554130\pi$
$620$	766400.	0.0800712
$621$	−1.08256e7	−1.12648
$622$	−3.38959e6	−0.351295
$623$	0	0
$624$	−1.44461e6	−0.148521
$625$	390625.	0.0400000
$626$	1.45982e6	0.148889
$627$	434214.	0.0441098
$628$	−576160.	−0.0582967
$629$	−1.19259e7	−1.20189
$630$	0	0
$631$	1.36282e7	1.36259	0.681297	−	0.732007i	$-0.261416\pi$
$631$	1.36282e7	1.36259	0.681297	+	0.732007i	$0.261416\pi$
$632$	2.79814e6	0.278662
$633$	5.64792e6	0.560247
$634$	−7.74975e6	−0.765711
$635$	−751300.	−0.0739399
$636$	3.76819e6	0.369394
$637$	0	0
$638$	971652.	0.0945059
$639$	−1.03252e7	−1.00034
$640$	409600.	0.0395285
$641$	−1.92472e7	−1.85021	−0.925106	−	0.379710i	$-0.876024\pi$
$641$	−1.92472e7	−1.85021	−0.925106	+	0.379710i	$0.876024\pi$
$642$	5.97607e6	0.572240
$643$	1.28399e7	1.22472	0.612358	−	0.790580i	$-0.290221\pi$
$643$	1.28399e7	1.22472	0.612358	+	0.790580i	$0.290221\pi$
$644$	0	0
$645$	−715050.	−0.0676764
$646$	−1.87102e6	−0.176399
$647$	−2.00233e7	−1.88050	−0.940251	−	0.340481i	$-0.889410\pi$
$647$	−2.00233e7	−1.88050	−0.940251	+	0.340481i	$0.889410\pi$
$648$	−419904.	−0.0392837
$649$	735284.	0.0685241
$650$	1.56750e6	0.145520
$651$	0	0
$652$	2.81072e6	0.258940
$653$	−7.23655e6	−0.664124	−0.332062	−	0.943258i	$-0.607744\pi$
$653$	−7.23655e6	−0.664124	−0.332062	+	0.943258i	$0.607744\pi$
$654$	−298404.	−0.0272810
$655$	−3.00125e6	−0.273337
$656$	−1.70906e6	−0.155059
$657$	9.79614e6	0.885404
$658$	0	0
$659$	1.42474e7	1.27798	0.638989	−	0.769216i	$-0.279353\pi$
$659$	1.42474e7	1.27798	0.638989	+	0.769216i	$0.279353\pi$
$660$	673200.	0.0601567
$661$	−1.49265e7	−1.32878	−0.664391	−	0.747385i	$-0.731309\pi$
$661$	−1.49265e7	−1.32878	−0.664391	+	0.747385i	$0.731309\pi$
$662$	245840.	0.0218026
$663$	1.02308e7	0.903908
$664$	6.22566e6	0.547981
$665$	0	0
$666$	4.26254e6	0.372377
$667$	3.85803e6	0.335777
$668$	2.51861e6	0.218383
$669$	1.09899e7	0.949355
$670$	−4.48320e6	−0.385835
$671$	−9.11438e6	−0.781485
$672$	0	0
$673$	−1.55062e7	−1.31967	−0.659837	−	0.751409i	$-0.729375\pi$
$673$	−1.55062e7	−1.31967	−0.659837	+	0.751409i	$0.729375\pi$
$674$	1.49646e7	1.26887
$675$	−2.27812e6	−0.192450
$676$	349376.	0.0294053
$677$	7.80065e6	0.654122	0.327061	−	0.945003i	$-0.393942\pi$
$677$	7.80065e6	0.654122	0.327061	+	0.945003i	$0.393942\pi$
$678$	−9.47542e6	−0.791633
$679$	0	0
$680$	−2.90080e6	−0.240572
$681$	−3.51492e6	−0.290434
$682$	−1.43317e6	−0.117988
$683$	1.58547e7	1.30049	0.650243	−	0.759727i	$-0.274667\pi$
$683$	1.58547e7	1.30049	0.650243	+	0.759727i	$0.274667\pi$
$684$	668736.	0.0546531
$685$	−794400.	−0.0646864
$686$	0	0
$687$	6.40912e6	0.518091
$688$	813568.	0.0655274
$689$	−1.64073e7	−1.31671
$690$	2.67300e6	0.213735
$691$	−2.03656e7	−1.62257	−0.811284	−	0.584652i	$-0.801231\pi$
$691$	−2.03656e7	−1.62257	−0.811284	+	0.584652i	$0.801231\pi$
$692$	375536.	0.0298117
$693$	0	0
$694$	−845336.	−0.0666240
$695$	−5.00405e6	−0.392970
$696$	−748224.	−0.0585475
$697$	1.21036e7	0.943696
$698$	1.35823e7	1.05520
$699$	5.05418e6	0.391253
$700$	0	0
$701$	2.48036e7	1.90643	0.953213	−	0.302300i	$-0.0977543\pi$
$701$	2.48036e7	1.90643	0.953213	+	0.302300i	$0.0977543\pi$
$702$	−9.14166e6	−0.700136
$703$	−1.69712e6	−0.129517
$704$	−765952.	−0.0582465
$705$	−4.95022e6	−0.375104
$706$	−1.55237e7	−1.17215
$707$	0	0
$708$	−566208.	−0.0424515
$709$	1.81917e7	1.35912	0.679560	−	0.733620i	$-0.262171\pi$
$709$	1.81917e7	1.35912	0.679560	+	0.733620i	$0.262171\pi$
$710$	6.37360e6	0.474503
$711$	7.08280e6	0.525450
$712$	2.91584e6	0.215558
$713$	−5.69052e6	−0.419207
$714$	0	0
$715$	−2.93122e6	−0.214429
$716$	9.79565e6	0.714086
$717$	−1.22475e7	−0.889715
$718$	−1.29684e7	−0.938806
$719$	1.66202e7	1.19899	0.599493	−	0.800380i	$-0.295369\pi$
$719$	1.66202e7	1.19899	0.599493	+	0.800380i	$0.295369\pi$
$720$	1.03680e6	0.0745356
$721$	0	0
$722$	9.63814e6	0.688098
$723$	−4.77045e6	−0.339401
$724$	−8.46131e6	−0.599917
$725$	811875.	0.0573646
$726$	4.53895e6	0.319605
$727$	1.57591e7	1.10585	0.552925	−	0.833231i	$-0.313511\pi$
$727$	1.57591e7	1.10585	0.552925	+	0.833231i	$0.313511\pi$
$728$	0	0
$729$	6.90873e6	0.481481
$730$	−6.04700e6	−0.419984
$731$	−5.76171e6	−0.398803
$732$	7.01856e6	0.484139
$733$	2.15238e6	0.147965	0.0739827	−	0.997260i	$-0.476429\pi$
$733$	2.15238e6	0.147965	0.0739827	+	0.997260i	$0.476429\pi$
$734$	5.77721e6	0.395802
$735$	0	0
$736$	−3.04128e6	−0.206948
$737$	8.38358e6	0.568540
$738$	−4.32605e6	−0.292382
$739$	−2.27267e7	−1.53083	−0.765413	−	0.643540i	$-0.777465\pi$
$739$	−2.27267e7	−1.53083	−0.765413	+	0.643540i	$0.777465\pi$
$740$	−2.63120e6	−0.176634
$741$	1.45589e6	0.0974057
$742$	0	0
$743$	1.21153e7	0.805123	0.402561	−	0.915393i	$-0.368120\pi$
$743$	1.21153e7	0.805123	0.402561	+	0.915393i	$0.368120\pi$
$744$	1.10362e6	0.0730947
$745$	−7.74105e6	−0.510986
$746$	−1.37417e7	−0.904050
$747$	1.57587e7	1.03328
$748$	5.42450e6	0.354491
$749$	0	0
$750$	562500.	0.0365148
$751$	−2.07590e7	−1.34310	−0.671549	−	0.740961i	$-0.734371\pi$
$751$	−2.07590e7	−1.34310	−0.671549	+	0.740961i	$0.734371\pi$
$752$	5.63226e6	0.363193
$753$	−8.91297e6	−0.572842
$754$	3.25789e6	0.208693
$755$	5.21642e6	0.333047
$756$	0	0
$757$	−1.86222e7	−1.18111	−0.590556	−	0.806997i	$-0.701091\pi$
$757$	−1.86222e7	−1.18111	−0.590556	+	0.806997i	$0.701091\pi$
$758$	6.74539e6	0.426417
$759$	−4.99851e6	−0.314946
$760$	−412800.	−0.0259242
$761$	−2.65336e7	−1.66087	−0.830434	−	0.557117i	$-0.811907\pi$
$761$	−2.65336e7	−1.66087	−0.830434	+	0.557117i	$0.811907\pi$
$762$	−1.08187e6	−0.0674976
$763$	0	0
$764$	8.64590e6	0.535892
$765$	−7.34265e6	−0.453627
$766$	1.05742e7	0.651139
$767$	2.46536e6	0.151319
$768$	589824.	0.0360844
$769$	2.01595e7	1.22931	0.614657	−	0.788794i	$-0.289294\pi$
$769$	2.01595e7	1.22931	0.614657	+	0.788794i	$0.289294\pi$
$770$	0	0
$771$	1.63479e7	0.990433
$772$	1.53651e7	0.927882
$773$	5.86488e6	0.353029	0.176514	−	0.984298i	$-0.443518\pi$
$773$	5.86488e6	0.353029	0.176514	+	0.984298i	$0.443518\pi$
$774$	2.05934e6	0.123560
$775$	−1.19750e6	−0.0716178
$776$	−3.66688e6	−0.218596
$777$	0	0
$778$	1.80840e6	0.107114
$779$	1.72241e6	0.101693
$780$	2.25720e6	0.132841
$781$	−1.19186e7	−0.699196
$782$	2.15384e7	1.25950
$783$	−4.73486e6	−0.275996
$784$	0	0
$785$	900250.	0.0521422
$786$	−4.32180e6	−0.249522
$787$	1.63347e6	0.0940100	0.0470050	−	0.998895i	$-0.485032\pi$
$787$	1.63347e6	0.0940100	0.0470050	+	0.998895i	$0.485032\pi$
$788$	1.21911e7	0.699403
$789$	−1.76263e7	−1.00802
$790$	−4.37210e6	−0.249243
$791$	0	0
$792$	−1.93882e6	−0.109831
$793$	−3.05600e7	−1.72572
$794$	−7.82121e6	−0.440274
$795$	−5.88780e6	−0.330396
$796$	−2.00134e6	−0.111954
$797$	−2.07673e7	−1.15807	−0.579034	−	0.815303i	$-0.696570\pi$
$797$	−2.07673e7	−1.15807	−0.579034	+	0.815303i	$0.696570\pi$
$798$	0	0
$799$	−3.98878e7	−2.21041
$800$	−640000.	−0.0353553
$801$	7.38072e6	0.406460
$802$	1.90695e7	1.04689
$803$	1.13079e7	0.618860
$804$	−6.45581e6	−0.352217
$805$	0	0
$806$	−4.80533e6	−0.260547
$807$	−1.96231e6	−0.106068
$808$	−2.87808e6	−0.155087
$809$	3.53936e6	0.190131	0.0950656	−	0.995471i	$-0.469694\pi$
$809$	3.53936e6	0.190131	0.0950656	+	0.995471i	$0.469694\pi$
$810$	656100.	0.0351364
$811$	2.11480e7	1.12906	0.564530	−	0.825412i	$-0.309057\pi$
$811$	2.11480e7	1.12906	0.564530	+	0.825412i	$0.309057\pi$
$812$	0	0
$813$	−1.13639e7	−0.602976
$814$	4.92034e6	0.260276
$815$	−4.39175e6	−0.231603
$816$	−4.17715e6	−0.219611
$817$	−819924.	−0.0429753
$818$	−1.65280e7	−0.863646
$819$	0	0
$820$	2.67040e6	0.138689
$821$	265389.	0.0137412	0.00687061	−	0.999976i	$-0.497813\pi$
$821$	265389.	0.0137412	0.00687061	+	0.999976i	$0.497813\pi$
$822$	−1.14394e6	−0.0590503
$823$	3.09261e7	1.59157	0.795785	−	0.605579i	$-0.207058\pi$
$823$	3.09261e7	1.59157	0.795785	+	0.605579i	$0.207058\pi$
$824$	−6.48992e6	−0.332982
$825$	−1.05188e6	−0.0538058
$826$	0	0
$827$	−2.84152e7	−1.44473	−0.722367	−	0.691510i	$-0.756946\pi$
$827$	−2.84152e7	−1.44473	−0.722367	+	0.691510i	$0.756946\pi$
$828$	−7.69824e6	−0.390225
$829$	3.33547e7	1.68566	0.842832	−	0.538177i	$-0.180887\pi$
$829$	3.33547e7	1.68566	0.842832	+	0.538177i	$0.180887\pi$
$830$	−9.72760e6	−0.490129
$831$	−9.92374e6	−0.498509
$832$	−2.56819e6	−0.128623
$833$	0	0
$834$	−7.20583e6	−0.358731
$835$	−3.93532e6	−0.195328
$836$	771936.	0.0382002
$837$	6.98382e6	0.344572
$838$	762048.	0.0374863
$839$	5.66205e6	0.277695	0.138848	−	0.990314i	$-0.455660\pi$
$839$	5.66205e6	0.277695	0.138848	+	0.990314i	$0.455660\pi$
$840$	0	0
$841$	−1.88237e7	−0.917732
$842$	2.07674e7	1.00949
$843$	−8.98392e6	−0.435408
$844$	1.00408e7	0.485188
$845$	−545900.	−0.0263009
$846$	1.42566e7	0.684844
$847$	0	0
$848$	6.69901e6	0.319905
$849$	3.47734e6	0.165569
$850$	4.53250e6	0.215174
$851$	1.95367e7	0.924754
$852$	9.17798e6	0.433160
$853$	−2.19983e7	−1.03518	−0.517592	−	0.855628i	$-0.673171\pi$
$853$	−2.19983e7	−1.03518	−0.517592	+	0.855628i	$0.673171\pi$
$854$	0	0
$855$	−1.04490e6	−0.0488832
$856$	1.06241e7	0.495574
$857$	2.17568e7	1.01191	0.505956	−	0.862559i	$-0.331140\pi$
$857$	2.17568e7	1.01191	0.505956	+	0.862559i	$0.331140\pi$
$858$	−4.22096e6	−0.195746
$859$	4.09384e7	1.89299	0.946494	−	0.322721i	$-0.104598\pi$
$859$	4.09384e7	1.89299	0.946494	+	0.322721i	$0.104598\pi$
$860$	−1.27120e6	−0.0586095
$861$	0	0
$862$	1.68712e7	0.773355
$863$	5.65597e6	0.258512	0.129256	−	0.991611i	$-0.458741\pi$
$863$	5.65597e6	0.258512	0.129256	+	0.991611i	$0.458741\pi$
$864$	3.73248e6	0.170103
$865$	−586775.	−0.0266644
$866$	−1.94411e7	−0.880899
$867$	1.68040e7	0.759216
$868$	0	0
$869$	8.17583e6	0.367267
$870$	1.16910e6	0.0523665
$871$	2.81097e7	1.25548
$872$	−530496.	−0.0236260
$873$	−9.28179e6	−0.412189
$874$	3.06504e6	0.135724
$875$	0	0
$876$	−8.70768e6	−0.383391
$877$	2.61067e7	1.14618	0.573089	−	0.819493i	$-0.305745\pi$
$877$	2.61067e7	1.14618	0.573089	+	0.819493i	$0.305745\pi$
$878$	−8.12454e6	−0.355682
$879$	7.05214e6	0.307857
$880$	1.19680e6	0.0520973
$881$	−1.44294e6	−0.0626339	−0.0313170	−	0.999510i	$-0.509970\pi$
$881$	−1.44294e6	−0.0626339	−0.0313170	+	0.999510i	$0.509970\pi$
$882$	0	0
$883$	−1.52432e7	−0.657921	−0.328960	−	0.944344i	$-0.606698\pi$
$883$	−1.52432e7	−0.657921	−0.328960	+	0.944344i	$0.606698\pi$
$884$	1.81880e7	0.782807
$885$	884700.	0.0379698
$886$	−1.13679e7	−0.486517
$887$	3.31500e7	1.41473	0.707366	−	0.706847i	$-0.249883\pi$
$887$	3.31500e7	1.41473	0.707366	+	0.706847i	$0.249883\pi$
$888$	−3.78893e6	−0.161244
$889$	0	0
$890$	−4.55600e6	−0.192801
$891$	−1.22691e6	−0.0517747
$892$	1.95376e7	0.822166
$893$	−5.67626e6	−0.238195
$894$	−1.11471e7	−0.466464
$895$	−1.53057e7	−0.638698
$896$	0	0
$897$	−1.67597e7	−0.695481
$898$	1.83873e7	0.760899
$899$	−2.48888e6	−0.102708
$900$	−1.62000e6	−0.0666667
$901$	−4.74426e7	−1.94696
$902$	−4.99365e6	−0.204363
$903$	0	0
$904$	−1.68452e7	−0.685575
$905$	1.32208e7	0.536582
$906$	7.51165e6	0.304029
$907$	1.16963e7	0.472096	0.236048	−	0.971741i	$-0.424148\pi$
$907$	1.16963e7	0.472096	0.236048	+	0.971741i	$0.424148\pi$
$908$	−6.24875e6	−0.251524
$909$	−7.28514e6	−0.292434
$910$	0	0
$911$	2.89321e7	1.15501	0.577503	−	0.816389i	$-0.304027\pi$
$911$	2.89321e7	1.15501	0.577503	+	0.816389i	$0.304027\pi$
$912$	−594432.	−0.0236655
$913$	1.81906e7	0.722221
$914$	−1.97347e7	−0.781384
$915$	−1.09665e7	−0.433027
$916$	1.13940e7	0.448680
$917$	0	0
$918$	−2.64335e7	−1.03526
$919$	−4.57838e7	−1.78823	−0.894115	−	0.447838i	$-0.852194\pi$
$919$	−4.57838e7	−1.78823	−0.894115	+	0.447838i	$0.852194\pi$
$920$	4.75200e6	0.185100
$921$	−2.53596e7	−0.985129
$922$	−1.90267e7	−0.737116
$923$	−3.99625e7	−1.54400
$924$	0	0
$925$	4.11125e6	0.157986
$926$	−1.63448e7	−0.626399
$927$	−1.64276e7	−0.627878
$928$	−1.33018e6	−0.0507036
$929$	−2.46947e7	−0.938782	−0.469391	−	0.882990i	$-0.655526\pi$
$929$	−2.46947e7	−0.938782	−0.469391	+	0.882990i	$0.655526\pi$
$930$	−1.72440e6	−0.0653779
$931$	0	0
$932$	8.98522e6	0.338835
$933$	7.62658e6	0.286831
$934$	−1.66373e7	−0.624044
$935$	−8.47578e6	−0.317067
$936$	−6.50074e6	−0.242534
$937$	1.98926e7	0.740187	0.370094	−	0.928994i	$-0.379326\pi$
$937$	1.98926e7	0.740187	0.370094	+	0.928994i	$0.379326\pi$
$938$	0	0
$939$	−3.28460e6	−0.121568
$940$	−8.80040e6	−0.324850
$941$	3.73454e7	1.37488	0.687438	−	0.726243i	$-0.258735\pi$
$941$	3.73454e7	1.37488	0.687438	+	0.726243i	$0.258735\pi$
$942$	1.29636e6	0.0475991
$943$	−1.98277e7	−0.726095
$944$	−1.00659e6	−0.0367641
$945$	0	0
$946$	2.37714e6	0.0863630
$947$	5.10396e7	1.84941	0.924703	−	0.380689i	$-0.124313\pi$
$947$	5.10396e7	1.84941	0.924703	+	0.380689i	$0.124313\pi$
$948$	−6.29582e6	−0.227526
$949$	3.79147e7	1.36660
$950$	645000.	0.0231873
$951$	1.74369e7	0.625200
$952$	0	0
$953$	254832.	0.00908912	0.00454456	−	0.999990i	$-0.498553\pi$
$953$	254832.	0.00908912	0.00454456	+	0.999990i	$0.498553\pi$
$954$	1.69569e7	0.603218
$955$	−1.35092e7	−0.479316
$956$	−2.17734e7	−0.770515
$957$	−2.18622e6	−0.0771638
$958$	−1.34416e7	−0.473192
$959$	0	0
$960$	−921600.	−0.0322749
$961$	−2.49581e7	−0.871772
$962$	1.64976e7	0.574756
$963$	2.68923e7	0.934464
$964$	−8.48080e6	−0.293930
$965$	−2.40080e7	−0.829923
$966$	0	0
$967$	1.17012e7	0.402405	0.201203	−	0.979550i	$-0.435515\pi$
$967$	1.17012e7	0.402405	0.201203	+	0.979550i	$0.435515\pi$
$968$	8.06925e6	0.276786
$969$	4.20979e6	0.144029
$970$	5.72950e6	0.195518
$971$	−3.59080e7	−1.22220	−0.611101	−	0.791553i	$-0.709273\pi$
$971$	−3.59080e7	−1.22220	−0.611101	+	0.791553i	$0.709273\pi$
$972$	1.51165e7	0.513200
$973$	0	0
$974$	−2.82097e7	−0.952799
$975$	−3.52688e6	−0.118817
$976$	1.24774e7	0.419277
$977$	−5.50592e7	−1.84541	−0.922706	−	0.385504i	$-0.874028\pi$
$977$	−5.50592e7	−1.84541	−0.922706	+	0.385504i	$0.874028\pi$
$978$	−6.32412e6	−0.211423
$979$	8.51972e6	0.284098
$980$	0	0
$981$	−1.34282e6	−0.0445497
$982$	335748.	0.0111105
$983$	1.81317e7	0.598488	0.299244	−	0.954177i	$-0.403266\pi$
$983$	1.81317e7	0.598488	0.299244	+	0.954177i	$0.403266\pi$
$984$	3.84538e6	0.126605
$985$	−1.90486e7	−0.625565
$986$	9.42035e6	0.308585
$987$	0	0
$988$	2.58826e6	0.0843558
$989$	9.43866e6	0.306845
$990$	3.02940e6	0.0982355
$991$	−2.02908e7	−0.656318	−0.328159	−	0.944623i	$-0.606428\pi$
$991$	−2.02908e7	−0.656318	−0.328159	+	0.944623i	$0.606428\pi$
$992$	1.96198e6	0.0633018
$993$	−553140.	−0.0178017
$994$	0	0
$995$	3.12710e6	0.100135
$996$	−1.40077e7	−0.447425
$997$	−4.75390e7	−1.51465	−0.757325	−	0.653038i	$-0.773494\pi$
$997$	−4.75390e7	−1.51465	−0.757325	+	0.653038i	$0.773494\pi$
$998$	2.84211e7	0.903262
$999$	−2.39768e7	−0.760112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.6.a.g.1.1		1
7.6	odd	2		70.6.a.b.1.1	✓	1
21.20	even	2		630.6.a.i.1.1		1
28.27	even	2		560.6.a.e.1.1		1
35.13	even	4		350.6.c.g.99.2		2
35.27	even	4		350.6.c.g.99.1		2
35.34	odd	2		350.6.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.b.1.1	✓	1	7.6	odd	2
350.6.a.l.1.1		1	35.34	odd	2
350.6.c.g.99.1		2	35.27	even	4
350.6.c.g.99.2		2	35.13	even	4
490.6.a.g.1.1		1	1.1	even	1	trivial
560.6.a.e.1.1		1	28.27	even	2
630.6.a.i.1.1		1	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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