LMFDB - Embedded newform 490.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,6,Mod(1,490)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$78.5880717084$
Analytic rank:	$1$
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)

$f(q)$

$=$

$q-4.00000 q^{2} -11.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +44.0000 q^{6} -64.0000 q^{8} -122.000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} -11.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +44.0000 q^{6} -64.0000 q^{8} -122.000 q^{9} -100.000 q^{10} +83.0000 q^{11} -176.000 q^{12} +83.0000 q^{13} -275.000 q^{15} +256.000 q^{16} +177.000 q^{17} +488.000 q^{18} +2082.00 q^{19} +400.000 q^{20} -332.000 q^{22} -3170.00 q^{23} +704.000 q^{24} +625.000 q^{25} -332.000 q^{26} +4015.00 q^{27} -8681.00 q^{29} +1100.00 q^{30} -1636.00 q^{31} -1024.00 q^{32} -913.000 q^{33} -708.000 q^{34} -1952.00 q^{36} +4298.00 q^{37} -8328.00 q^{38} -913.000 q^{39} -1600.00 q^{40} -2356.00 q^{41} +8738.00 q^{43} +1328.00 q^{44} -3050.00 q^{45} +12680.0 q^{46} +3641.00 q^{47} -2816.00 q^{48} -2500.00 q^{50} -1947.00 q^{51} +1328.00 q^{52} +33268.0 q^{53} -16060.0 q^{54} +2075.00 q^{55} -22902.0 q^{57} +34724.0 q^{58} +30968.0 q^{59} -4400.00 q^{60} -4560.00 q^{61} +6544.00 q^{62} +4096.00 q^{64} +2075.00 q^{65} +3652.00 q^{66} +37788.0 q^{67} +2832.00 q^{68} +34870.0 q^{69} -59304.0 q^{71} +7808.00 q^{72} +8910.00 q^{73} -17192.0 q^{74} -6875.00 q^{75} +33312.0 q^{76} +3652.00 q^{78} +27589.0 q^{79} +6400.00 q^{80} -14519.0 q^{81} +9424.00 q^{82} -67676.0 q^{83} +4425.00 q^{85} -34952.0 q^{86} +95491.0 q^{87} -5312.00 q^{88} -10700.0 q^{89} +12200.0 q^{90} -50720.0 q^{92} +17996.0 q^{93} -14564.0 q^{94} +52050.0 q^{95} +11264.0 q^{96} -65075.0 q^{97} -10126.0 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
$3$	−11.0000	−0.705650	−0.352825	−	0.935689i	$-0.614779\pi$
$3$	−11.0000	−0.705650	−0.352825	+	0.935689i	$0.614779\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	44.0000	0.498970
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	−122.000	−0.502058
$10$	−100.000	−0.316228
$11$	83.0000	0.206822	0.103411	−	0.994639i	$-0.467024\pi$
$11$	83.0000	0.206822	0.103411	+	0.994639i	$0.467024\pi$
$12$	−176.000	−0.352825
$13$	83.0000	0.136213	0.0681067	−	0.997678i	$-0.478304\pi$
$13$	83.0000	0.136213	0.0681067	+	0.997678i	$0.478304\pi$
$14$	0	0
$15$	−275.000	−0.315576
$16$	256.000	0.250000
$17$	177.000	0.148543	0.0742713	−	0.997238i	$-0.476337\pi$
$17$	177.000	0.148543	0.0742713	+	0.997238i	$0.476337\pi$
$18$	488.000	0.355008
$19$	2082.00	1.32311	0.661556	−	0.749896i	$-0.269896\pi$
$19$	2082.00	1.32311	0.661556	+	0.749896i	$0.269896\pi$
$20$	400.000	0.223607
$21$	0	0
$22$	−332.000	−0.146245
$23$	−3170.00	−1.24951	−0.624755	−	0.780821i	$-0.714801\pi$
$23$	−3170.00	−1.24951	−0.624755	+	0.780821i	$0.714801\pi$
$24$	704.000	0.249485
$25$	625.000	0.200000
$26$	−332.000	−0.0963174
$27$	4015.00	1.05993
$28$	0	0
$29$	−8681.00	−1.91679	−0.958395	−	0.285444i	$-0.907859\pi$
$29$	−8681.00	−1.91679	−0.958395	+	0.285444i	$0.907859\pi$
$30$	1100.00	0.223146
$31$	−1636.00	−0.305759	−0.152879	−	0.988245i	$-0.548855\pi$
$31$	−1636.00	−0.305759	−0.152879	+	0.988245i	$0.548855\pi$
$32$	−1024.00	−0.176777
$33$	−913.000	−0.145944
$34$	−708.000	−0.105035
$35$	0	0
$36$	−1952.00	−0.251029
$37$	4298.00	0.516134	0.258067	−	0.966127i	$-0.416915\pi$
$37$	4298.00	0.516134	0.258067	+	0.966127i	$0.416915\pi$
$38$	−8328.00	−0.935582
$39$	−913.000	−0.0961190
$40$	−1600.00	−0.158114
$41$	−2356.00	−0.218885	−0.109442	−	0.993993i	$-0.534907\pi$
$41$	−2356.00	−0.218885	−0.109442	+	0.993993i	$0.534907\pi$
$42$	0	0
$43$	8738.00	0.720677	0.360339	−	0.932822i	$-0.382661\pi$
$43$	8738.00	0.720677	0.360339	+	0.932822i	$0.382661\pi$
$44$	1328.00	0.103411
$45$	−3050.00	−0.224527
$46$	12680.0	0.883537
$47$	3641.00	0.240423	0.120212	−	0.992748i	$-0.461643\pi$
$47$	3641.00	0.240423	0.120212	+	0.992748i	$0.461643\pi$
$48$	−2816.00	−0.176413
$49$	0	0
$50$	−2500.00	−0.141421
$51$	−1947.00	−0.104819
$52$	1328.00	0.0681067
$53$	33268.0	1.62681	0.813405	−	0.581697i	$-0.197611\pi$
$53$	33268.0	1.62681	0.813405	+	0.581697i	$0.197611\pi$
$54$	−16060.0	−0.749482
$55$	2075.00	0.0924935
$56$	0	0
$57$	−22902.0	−0.933655
$58$	34724.0	1.35538
$59$	30968.0	1.15820	0.579099	−	0.815257i	$-0.303404\pi$
$59$	30968.0	1.15820	0.579099	+	0.815257i	$0.303404\pi$
$60$	−4400.00	−0.157788
$61$	−4560.00	−0.156906	−0.0784531	−	0.996918i	$-0.524998\pi$
$61$	−4560.00	−0.156906	−0.0784531	+	0.996918i	$0.524998\pi$
$62$	6544.00	0.216204
$63$	0	0
$64$	4096.00	0.125000
$65$	2075.00	0.0609165
$66$	3652.00	0.103198
$67$	37788.0	1.02841	0.514206	−	0.857667i	$-0.328087\pi$
$67$	37788.0	1.02841	0.514206	+	0.857667i	$0.328087\pi$
$68$	2832.00	0.0742713
$69$	34870.0	0.881717
$70$	0	0
$71$	−59304.0	−1.39617	−0.698085	−	0.716015i	$-0.745964\pi$
$71$	−59304.0	−1.39617	−0.698085	+	0.716015i	$0.745964\pi$
$72$	7808.00	0.177504
$73$	8910.00	0.195691	0.0978454	−	0.995202i	$-0.468805\pi$
$73$	8910.00	0.195691	0.0978454	+	0.995202i	$0.468805\pi$
$74$	−17192.0	−0.364962
$75$	−6875.00	−0.141130
$76$	33312.0	0.661556
$77$	0	0
$78$	3652.00	0.0679664
$79$	27589.0	0.497357	0.248678	−	0.968586i	$-0.420004\pi$
$79$	27589.0	0.497357	0.248678	+	0.968586i	$0.420004\pi$
$80$	6400.00	0.111803
$81$	−14519.0	−0.245881
$82$	9424.00	0.154775
$83$	−67676.0	−1.07830	−0.539150	−	0.842210i	$-0.681254\pi$
$83$	−67676.0	−1.07830	−0.539150	+	0.842210i	$0.681254\pi$
$84$	0	0
$85$	4425.00	0.0664303
$86$	−34952.0	−0.509596
$87$	95491.0	1.35258
$88$	−5312.00	−0.0731226
$89$	−10700.0	−0.143189	−0.0715944	−	0.997434i	$-0.522809\pi$
$89$	−10700.0	−0.143189	−0.0715944	+	0.997434i	$0.522809\pi$
$90$	12200.0	0.158765
$91$	0	0
$92$	−50720.0	−0.624755
$93$	17996.0	0.215759
$94$	−14564.0	−0.170005
$95$	52050.0	0.591714
$96$	11264.0	0.124743
$97$	−65075.0	−0.702239	−0.351119	−	0.936331i	$-0.614199\pi$
$97$	−65075.0	−0.702239	−0.351119	+	0.936331i	$0.614199\pi$
$98$	0	0
$99$	−10126.0	−0.103836
$100$	10000.0	0.100000
$101$	149250.	1.45583	0.727915	−	0.685667i	$-0.240489\pi$
$101$	149250.	1.45583	0.727915	+	0.685667i	$0.240489\pi$
$102$	7788.00	0.0741183
$103$	−194315.	−1.80473	−0.902367	−	0.430968i	$-0.858172\pi$
$103$	−194315.	−1.80473	−0.902367	+	0.430968i	$0.858172\pi$
$104$	−5312.00	−0.0481587
$105$	0	0
$106$	−133072.	−1.15033
$107$	40538.0	0.342297	0.171148	−	0.985245i	$-0.445252\pi$
$107$	40538.0	0.342297	0.171148	+	0.985245i	$0.445252\pi$
$108$	64240.0	0.529964
$109$	−87651.0	−0.706628	−0.353314	−	0.935505i	$-0.614945\pi$
$109$	−87651.0	−0.706628	−0.353314	+	0.935505i	$0.614945\pi$
$110$	−8300.00	−0.0654028
$111$	−47278.0	−0.364210
$112$	0	0
$113$	−76314.0	−0.562222	−0.281111	−	0.959675i	$-0.590703\pi$
$113$	−76314.0	−0.562222	−0.281111	+	0.959675i	$0.590703\pi$
$114$	91608.0	0.660194
$115$	−79250.0	−0.558798
$116$	−138896.	−0.958395
$117$	−10126.0	−0.0683870
$118$	−123872.	−0.818970
$119$	0	0
$120$	17600.0	0.111573
$121$	−154162.	−0.957225
$122$	18240.0	0.110949
$123$	25916.0	0.154456
$124$	−26176.0	−0.152879
$125$	15625.0	0.0894427
$126$	0	0
$127$	−183128.	−1.00750	−0.503750	−	0.863849i	$-0.668047\pi$
$127$	−183128.	−1.00750	−0.503750	+	0.863849i	$0.668047\pi$
$128$	−16384.0	−0.0883883
$129$	−96118.0	−0.508546
$130$	−8300.00	−0.0430744
$131$	−216190.	−1.10067	−0.550335	−	0.834944i	$-0.685500\pi$
$131$	−216190.	−1.10067	−0.550335	+	0.834944i	$0.685500\pi$
$132$	−14608.0	−0.0729719
$133$	0	0
$134$	−151152.	−0.727197
$135$	100375.	0.474014
$136$	−11328.0	−0.0525177
$137$	−119844.	−0.545525	−0.272763	−	0.962081i	$-0.587937\pi$
$137$	−119844.	−0.545525	−0.272763	+	0.962081i	$0.587937\pi$
$138$	−139480.	−0.623468
$139$	−259298.	−1.13831	−0.569157	−	0.822229i	$-0.692730\pi$
$139$	−259298.	−1.13831	−0.569157	+	0.822229i	$0.692730\pi$
$140$	0	0
$141$	−40051.0	−0.169655
$142$	237216.	0.987241
$143$	6889.00	0.0281719
$144$	−31232.0	−0.125514
$145$	−217025.	−0.857215
$146$	−35640.0	−0.138374
$147$	0	0
$148$	68768.0	0.258067
$149$	−88518.0	−0.326637	−0.163319	−	0.986573i	$-0.552220\pi$
$149$	−88518.0	−0.326637	−0.163319	+	0.986573i	$0.552220\pi$
$150$	27500.0	0.0997940
$151$	115053.	0.410635	0.205317	−	0.978695i	$-0.434177\pi$
$151$	115053.	0.410635	0.205317	+	0.978695i	$0.434177\pi$
$152$	−133248.	−0.467791
$153$	−21594.0	−0.0745769
$154$	0	0
$155$	−40900.0	−0.136740
$156$	−14608.0	−0.0480595
$157$	324370.	1.05025	0.525124	−	0.851026i	$-0.324019\pi$
$157$	324370.	1.05025	0.525124	+	0.851026i	$0.324019\pi$
$158$	−110356.	−0.351685
$159$	−365948.	−1.14796
$160$	−25600.0	−0.0790569
$161$	0	0
$162$	58076.0	0.173864
$163$	236470.	0.697119	0.348560	−	0.937287i	$-0.386671\pi$
$163$	236470.	0.697119	0.348560	+	0.937287i	$0.386671\pi$
$164$	−37696.0	−0.109442
$165$	−22825.0	−0.0652681
$166$	270704.	0.762473
$167$	332853.	0.923552	0.461776	−	0.886997i	$-0.347212\pi$
$167$	332853.	0.923552	0.461776	+	0.886997i	$0.347212\pi$
$168$	0	0
$169$	−364404.	−0.981446
$170$	−17700.0	−0.0469733
$171$	−254004.	−0.664279
$172$	139808.	0.360339
$173$	435681.	1.10676	0.553380	−	0.832929i	$-0.313338\pi$
$173$	435681.	1.10676	0.553380	+	0.832929i	$0.313338\pi$
$174$	−381964.	−0.956421
$175$	0	0
$176$	21248.0	0.0517055
$177$	−340648.	−0.817283
$178$	42800.0	0.101250
$179$	−727852.	−1.69789	−0.848947	−	0.528478i	$-0.822763\pi$
$179$	−727852.	−1.69789	−0.848947	+	0.528478i	$0.822763\pi$
$180$	−48800.0	−0.112263
$181$	−287292.	−0.651819	−0.325910	−	0.945401i	$-0.605670\pi$
$181$	−287292.	−0.651819	−0.325910	+	0.945401i	$0.605670\pi$
$182$	0	0
$183$	50160.0	0.110721
$184$	202880.	0.441768
$185$	107450.	0.230822
$186$	−71984.0	−0.152565
$187$	14691.0	0.0307218
$188$	58256.0	0.120212
$189$	0	0
$190$	−208200.	−0.418405
$191$	−454581.	−0.901629	−0.450814	−	0.892618i	$-0.648866\pi$
$191$	−454581.	−0.901629	−0.450814	+	0.892618i	$0.648866\pi$
$192$	−45056.0	−0.0882063
$193$	−398780.	−0.770620	−0.385310	−	0.922787i	$-0.625905\pi$
$193$	−398780.	−0.770620	−0.385310	+	0.922787i	$0.625905\pi$
$194$	260300.	0.496558
$195$	−22825.0	−0.0429857
$196$	0	0
$197$	−959776.	−1.76199	−0.880997	−	0.473122i	$-0.843127\pi$
$197$	−959776.	−1.76199	−0.880997	+	0.473122i	$0.843127\pi$
$198$	40504.0	0.0734235
$199$	−342024.	−0.612243	−0.306122	−	0.951992i	$-0.599031\pi$
$199$	−342024.	−0.612243	−0.306122	+	0.951992i	$0.599031\pi$
$200$	−40000.0	−0.0707107
$201$	−415668.	−0.725699
$202$	−597000.	−1.02943
$203$	0	0
$204$	−31152.0	−0.0524096
$205$	−58900.0	−0.0978883
$206$	777260.	1.27614
$207$	386740.	0.627326
$208$	21248.0	0.0340533
$209$	172806.	0.273649
$210$	0	0
$211$	−255043.	−0.394373	−0.197187	−	0.980366i	$-0.563180\pi$
$211$	−255043.	−0.394373	−0.197187	+	0.980366i	$0.563180\pi$
$212$	532288.	0.813405
$213$	652344.	0.985207
$214$	−162152.	−0.242040
$215$	218450.	0.322297
$216$	−256960.	−0.374741
$217$	0	0
$218$	350604.	0.499661
$219$	−98010.0	−0.138089
$220$	33200.0	0.0462468
$221$	14691.0	0.0202335
$222$	189112.	0.257535
$223$	198381.	0.267139	0.133570	−	0.991039i	$-0.457356\pi$
$223$	198381.	0.267139	0.133570	+	0.991039i	$0.457356\pi$
$224$	0	0
$225$	−76250.0	−0.100412
$226$	305256.	0.397551
$227$	−544967.	−0.701949	−0.350975	−	0.936385i	$-0.614150\pi$
$227$	−544967.	−0.701949	−0.350975	+	0.936385i	$0.614150\pi$
$228$	−366432.	−0.466827
$229$	1.45584e6	1.83454	0.917268	−	0.398271i	$-0.130390\pi$
$229$	1.45584e6	1.83454	0.917268	+	0.398271i	$0.130390\pi$
$230$	317000.	0.395130
$231$	0	0
$232$	555584.	0.677688
$233$	−65544.0	−0.0790939	−0.0395470	−	0.999218i	$-0.512591\pi$
$233$	−65544.0	−0.0790939	−0.0395470	+	0.999218i	$0.512591\pi$
$234$	40504.0	0.0483569
$235$	91025.0	0.107520
$236$	495488.	0.579099
$237$	−303479.	−0.350960
$238$	0	0
$239$	−621207.	−0.703464	−0.351732	−	0.936101i	$-0.614407\pi$
$239$	−621207.	−0.703464	−0.351732	+	0.936101i	$0.614407\pi$
$240$	−70400.0	−0.0788941
$241$	−1.02763e6	−1.13971	−0.569855	−	0.821745i	$-0.693001\pi$
$241$	−1.02763e6	−1.13971	−0.569855	+	0.821745i	$0.693001\pi$
$242$	616648.	0.676860
$243$	−815936.	−0.886422
$244$	−72960.0	−0.0784531
$245$	0	0
$246$	−103664.	−0.109217
$247$	172806.	0.180226
$248$	104704.	0.108102
$249$	744436.	0.760902
$250$	−62500.0	−0.0632456
$251$	−1.79275e6	−1.79612	−0.898060	−	0.439873i	$-0.855024\pi$
$251$	−1.79275e6	−1.79612	−0.898060	+	0.439873i	$0.855024\pi$
$252$	0	0
$253$	−263110.	−0.258426
$254$	732512.	0.712411
$255$	−48675.0	−0.0468765
$256$	65536.0	0.0625000
$257$	−1.15843e6	−1.09405	−0.547025	−	0.837116i	$-0.684240\pi$
$257$	−1.15843e6	−1.09405	−0.547025	+	0.837116i	$0.684240\pi$
$258$	384472.	0.359596
$259$	0	0
$260$	33200.0	0.0304582
$261$	1.05908e6	0.962340
$262$	864760.	0.778292
$263$	−639534.	−0.570130	−0.285065	−	0.958508i	$-0.592015\pi$
$263$	−639534.	−0.570130	−0.285065	+	0.958508i	$0.592015\pi$
$264$	58432.0	0.0515990
$265$	831700.	0.727532
$266$	0	0
$267$	117700.	0.101041
$268$	604608.	0.514206
$269$	−2.19619e6	−1.85050	−0.925252	−	0.379353i	$-0.876147\pi$
$269$	−2.19619e6	−1.85050	−0.925252	+	0.379353i	$0.876147\pi$
$270$	−401500.	−0.335178
$271$	−1.38063e6	−1.14197	−0.570985	−	0.820960i	$-0.693439\pi$
$271$	−1.38063e6	−1.14197	−0.570985	+	0.820960i	$0.693439\pi$
$272$	45312.0	0.0371356
$273$	0	0
$274$	479376.	0.385745
$275$	51875.0	0.0413644
$276$	557920.	0.440859
$277$	2.12298e6	1.66244	0.831222	−	0.555941i	$-0.187642\pi$
$277$	2.12298e6	1.66244	0.831222	+	0.555941i	$0.187642\pi$
$278$	1.03719e6	0.804910
$279$	199592.	0.153509
$280$	0	0
$281$	1.19699e6	0.904323	0.452162	−	0.891936i	$-0.350653\pi$
$281$	1.19699e6	0.904323	0.452162	+	0.891936i	$0.350653\pi$
$282$	160204.	0.119964
$283$	−281449.	−0.208898	−0.104449	−	0.994530i	$-0.533308\pi$
$283$	−281449.	−0.208898	−0.104449	+	0.994530i	$0.533308\pi$
$284$	−948864.	−0.698085
$285$	−572550.	−0.417543
$286$	−27556.0	−0.0199205
$287$	0	0
$288$	124928.	0.0887521
$289$	−1.38853e6	−0.977935
$290$	868100.	0.606143
$291$	715825.	0.495535
$292$	142560.	0.0978454
$293$	2.71466e6	1.84734	0.923669	−	0.383190i	$-0.125175\pi$
$293$	2.71466e6	1.84734	0.923669	+	0.383190i	$0.125175\pi$
$294$	0	0
$295$	774200.	0.517962
$296$	−275072.	−0.182481
$297$	333245.	0.219216
$298$	354072.	0.230968
$299$	−263110.	−0.170200
$300$	−110000.	−0.0705650
$301$	0	0
$302$	−460212.	−0.290363
$303$	−1.64175e6	−1.02731
$304$	532992.	0.330778
$305$	−114000.	−0.0701706
$306$	86376.0	0.0527339
$307$	2.68381e6	1.62519	0.812597	−	0.582826i	$-0.198053\pi$
$307$	2.68381e6	1.62519	0.812597	+	0.582826i	$0.198053\pi$
$308$	0	0
$309$	2.13746e6	1.27351
$310$	163600.	0.0966894
$311$	−25542.0	−0.0149746	−0.00748728	−	0.999972i	$-0.502383\pi$
$311$	−25542.0	−0.0149746	−0.00748728	+	0.999972i	$0.502383\pi$
$312$	58432.0	0.0339832
$313$	975975.	0.563090	0.281545	−	0.959548i	$-0.409153\pi$
$313$	975975.	0.563090	0.281545	+	0.959548i	$0.409153\pi$
$314$	−1.29748e6	−0.742637
$315$	0	0
$316$	441424.	0.248678
$317$	−1.45540e6	−0.813457	−0.406729	−	0.913549i	$-0.633331\pi$
$317$	−1.45540e6	−0.813457	−0.406729	+	0.913549i	$0.633331\pi$
$318$	1.46379e6	0.811730
$319$	−720523.	−0.396434
$320$	102400.	0.0559017
$321$	−445918.	−0.241542
$322$	0	0
$323$	368514.	0.196539
$324$	−232304.	−0.122940
$325$	51875.0	0.0272427
$326$	−945880.	−0.492938
$327$	964161.	0.498632
$328$	150784.	0.0773875
$329$	0	0
$330$	91300.0	0.0461515
$331$	−2.98186e6	−1.49595	−0.747975	−	0.663727i	$-0.768974\pi$
$331$	−2.98186e6	−1.49595	−0.747975	+	0.663727i	$0.768974\pi$
$332$	−1.08282e6	−0.539150
$333$	−524356.	−0.259129
$334$	−1.33141e6	−0.653050
$335$	944700.	0.459920
$336$	0	0
$337$	−928698.	−0.445451	−0.222725	−	0.974881i	$-0.571495\pi$
$337$	−928698.	−0.445451	−0.222725	+	0.974881i	$0.571495\pi$
$338$	1.45762e6	0.693987
$339$	839454.	0.396732
$340$	70800.0	0.0332151
$341$	−135788.	−0.0632376
$342$	1.01602e6	0.469716
$343$	0	0
$344$	−559232.	−0.254798
$345$	871750.	0.394316
$346$	−1.74272e6	−0.782597
$347$	1.75435e6	0.782156	0.391078	−	0.920357i	$-0.372102\pi$
$347$	1.75435e6	0.782156	0.391078	+	0.920357i	$0.372102\pi$
$348$	1.52786e6	0.676292
$349$	1.78606e6	0.784934	0.392467	−	0.919766i	$-0.371622\pi$
$349$	1.78606e6	0.784934	0.392467	+	0.919766i	$0.371622\pi$
$350$	0	0
$351$	333245.	0.144376
$352$	−84992.0	−0.0365613
$353$	−1.23308e6	−0.526687	−0.263344	−	0.964702i	$-0.584825\pi$
$353$	−1.23308e6	−0.526687	−0.263344	+	0.964702i	$0.584825\pi$
$354$	1.36259e6	0.577907
$355$	−1.48260e6	−0.624386
$356$	−171200.	−0.0715944
$357$	0	0
$358$	2.91141e6	1.20059
$359$	−1.69914e6	−0.695812	−0.347906	−	0.937529i	$-0.613107\pi$
$359$	−1.69914e6	−0.695812	−0.347906	+	0.937529i	$0.613107\pi$
$360$	195200.	0.0793823
$361$	1.85862e6	0.750626
$362$	1.14917e6	0.460906
$363$	1.69578e6	0.675466
$364$	0	0
$365$	222750.	0.0875156
$366$	−200640.	−0.0782915
$367$	−1.82938e6	−0.708989	−0.354494	−	0.935058i	$-0.615347\pi$
$367$	−1.82938e6	−0.708989	−0.354494	+	0.935058i	$0.615347\pi$
$368$	−811520.	−0.312377
$369$	287432.	0.109893
$370$	−429800.	−0.163216
$371$	0	0
$372$	287936.	0.107879
$373$	−1.03316e6	−0.384501	−0.192250	−	0.981346i	$-0.561579\pi$
$373$	−1.03316e6	−0.384501	−0.192250	+	0.981346i	$0.561579\pi$
$374$	−58764.0	−0.0217236
$375$	−171875.	−0.0631153
$376$	−233024.	−0.0850024
$377$	−720523.	−0.261093
$378$	0	0
$379$	1.25601e6	0.449155	0.224577	−	0.974456i	$-0.427900\pi$
$379$	1.25601e6	0.449155	0.224577	+	0.974456i	$0.427900\pi$
$380$	832800.	0.295857
$381$	2.01441e6	0.710943
$382$	1.81832e6	0.637548
$383$	−3.64322e6	−1.26908	−0.634539	−	0.772891i	$-0.718810\pi$
$383$	−3.64322e6	−1.26908	−0.634539	+	0.772891i	$0.718810\pi$
$384$	180224.	0.0623713
$385$	0	0
$386$	1.59512e6	0.544910
$387$	−1.06604e6	−0.361822
$388$	−1.04120e6	−0.351119
$389$	3.67368e6	1.23091	0.615457	−	0.788171i	$-0.288972\pi$
$389$	3.67368e6	1.23091	0.615457	+	0.788171i	$0.288972\pi$
$390$	91300.0	0.0303955
$391$	−561090.	−0.185605
$392$	0	0
$393$	2.37809e6	0.776689
$394$	3.83910e6	1.24592
$395$	689725.	0.222425
$396$	−162016.	−0.0519182
$397$	5.64367e6	1.79716	0.898578	−	0.438815i	$-0.144602\pi$
$397$	5.64367e6	1.79716	0.898578	+	0.438815i	$0.144602\pi$
$398$	1.36810e6	0.432921
$399$	0	0
$400$	160000.	0.0500000
$401$	−4.22249e6	−1.31132	−0.655658	−	0.755058i	$-0.727609\pi$
$401$	−4.22249e6	−1.31132	−0.655658	+	0.755058i	$0.727609\pi$
$402$	1.66267e6	0.513147
$403$	−135788.	−0.0416484
$404$	2.38800e6	0.727915
$405$	−362975.	−0.109961
$406$	0	0
$407$	356734.	0.106748
$408$	124608.	0.0370592
$409$	−606470.	−0.179267	−0.0896336	−	0.995975i	$-0.528570\pi$
$409$	−606470.	−0.179267	−0.0896336	+	0.995975i	$0.528570\pi$
$410$	235600.	0.0692175
$411$	1.31828e6	0.384950
$412$	−3.10904e6	−0.902367
$413$	0	0
$414$	−1.54696e6	−0.443586
$415$	−1.69190e6	−0.482230
$416$	−84992.0	−0.0240793
$417$	2.85228e6	0.803252
$418$	−691224.	−0.193499
$419$	726668.	0.202209	0.101105	−	0.994876i	$-0.467762\pi$
$419$	726668.	0.202209	0.101105	+	0.994876i	$0.467762\pi$
$420$	0	0
$421$	−149315.	−0.0410580	−0.0205290	−	0.999789i	$-0.506535\pi$
$421$	−149315.	−0.0410580	−0.0205290	+	0.999789i	$0.506535\pi$
$422$	1.02017e6	0.278864
$423$	−444202.	−0.120706
$424$	−2.12915e6	−0.575164
$425$	110625.	0.0297085
$426$	−2.60938e6	−0.696647
$427$	0	0
$428$	648608.	0.171148
$429$	−75779.0	−0.0198795
$430$	−873800.	−0.227898
$431$	−5.70872e6	−1.48029	−0.740143	−	0.672449i	$-0.765242\pi$
$431$	−5.70872e6	−1.48029	−0.740143	+	0.672449i	$0.765242\pi$
$432$	1.02784e6	0.264982
$433$	1.66009e6	0.425513	0.212757	−	0.977105i	$-0.431756\pi$
$433$	1.66009e6	0.425513	0.212757	+	0.977105i	$0.431756\pi$
$434$	0	0
$435$	2.38728e6	0.604894
$436$	−1.40242e6	−0.353314
$437$	−6.59994e6	−1.65324
$438$	392040.	0.0976439
$439$	6.06987e6	1.50321	0.751603	−	0.659616i	$-0.229281\pi$
$439$	6.06987e6	1.50321	0.751603	+	0.659616i	$0.229281\pi$
$440$	−132800.	−0.0327014
$441$	0	0
$442$	−58764.0	−0.0143072
$443$	6.52331e6	1.57928	0.789639	−	0.613572i	$-0.210268\pi$
$443$	6.52331e6	1.57928	0.789639	+	0.613572i	$0.210268\pi$
$444$	−756448.	−0.182105
$445$	−267500.	−0.0640359
$446$	−793524.	−0.188896
$447$	973698.	0.230492
$448$	0	0
$449$	7.47982e6	1.75096	0.875478	−	0.483259i	$-0.160547\pi$
$449$	7.47982e6	1.75096	0.875478	+	0.483259i	$0.160547\pi$
$450$	305000.	0.0710017
$451$	−195548.	−0.0452702
$452$	−1.22102e6	−0.281111
$453$	−1.26558e6	−0.289764
$454$	2.17987e6	0.496353
$455$	0	0
$456$	1.46573e6	0.330097
$457$	6.18223e6	1.38470	0.692349	−	0.721563i	$-0.256576\pi$
$457$	6.18223e6	1.38470	0.692349	+	0.721563i	$0.256576\pi$
$458$	−5.82338e6	−1.29721
$459$	710655.	0.157444
$460$	−1.26800e6	−0.279399
$461$	1.01935e6	0.223394	0.111697	−	0.993742i	$-0.464371\pi$
$461$	1.01935e6	0.223394	0.111697	+	0.993742i	$0.464371\pi$
$462$	0	0
$463$	1.30513e6	0.282944	0.141472	−	0.989942i	$-0.454816\pi$
$463$	1.30513e6	0.282944	0.141472	+	0.989942i	$0.454816\pi$
$464$	−2.22234e6	−0.479198
$465$	449900.	0.0964903
$466$	262176.	0.0559279
$467$	2.73130e6	0.579531	0.289766	−	0.957098i	$-0.406423\pi$
$467$	2.73130e6	0.579531	0.289766	+	0.957098i	$0.406423\pi$
$468$	−162016.	−0.0341935
$469$	0	0
$470$	−364100.	−0.0760284
$471$	−3.56807e6	−0.741107
$472$	−1.98195e6	−0.409485
$473$	725254.	0.149052
$474$	1.21392e6	0.248166
$475$	1.30125e6	0.264622
$476$	0	0
$477$	−4.05870e6	−0.816753
$478$	2.48483e6	0.497424
$479$	322322.	0.0641876	0.0320938	−	0.999485i	$-0.489782\pi$
$479$	322322.	0.0641876	0.0320938	+	0.999485i	$0.489782\pi$
$480$	281600.	0.0557866
$481$	356734.	0.0703043
$482$	4.11052e6	0.805896
$483$	0	0
$484$	−2.46659e6	−0.478612
$485$	−1.62688e6	−0.314051
$486$	3.26374e6	0.626795
$487$	−2.87469e6	−0.549249	−0.274624	−	0.961552i	$-0.588554\pi$
$487$	−2.87469e6	−0.549249	−0.274624	+	0.961552i	$0.588554\pi$
$488$	291840.	0.0554747
$489$	−2.60117e6	−0.491922
$490$	0	0
$491$	−5.97817e6	−1.11909	−0.559544	−	0.828801i	$-0.689024\pi$
$491$	−5.97817e6	−1.11909	−0.559544	+	0.828801i	$0.689024\pi$
$492$	414656.	0.0772281
$493$	−1.53654e6	−0.284725
$494$	−691224.	−0.127439
$495$	−253150.	−0.0464371
$496$	−418816.	−0.0764397
$497$	0	0
$498$	−2.97774e6	−0.538039
$499$	−4.91507e6	−0.883647	−0.441823	−	0.897102i	$-0.645668\pi$
$499$	−4.91507e6	−0.883647	−0.441823	+	0.897102i	$0.645668\pi$
$500$	250000.	0.0447214
$501$	−3.66138e6	−0.651705
$502$	7.17100e6	1.27005
$503$	−6.65935e6	−1.17358	−0.586789	−	0.809740i	$-0.699608\pi$
$503$	−6.65935e6	−1.17358	−0.586789	+	0.809740i	$0.699608\pi$
$504$	0	0
$505$	3.73125e6	0.651067
$506$	1.05244e6	0.182735
$507$	4.00844e6	0.692558
$508$	−2.93005e6	−0.503750
$509$	1.11240e6	0.190312	0.0951559	−	0.995462i	$-0.469665\pi$
$509$	1.11240e6	0.190312	0.0951559	+	0.995462i	$0.469665\pi$
$510$	194700.	0.0331467
$511$	0	0
$512$	−262144.	−0.0441942
$513$	8.35923e6	1.40240
$514$	4.63372e6	0.773610
$515$	−4.85788e6	−0.807102
$516$	−1.53789e6	−0.254273
$517$	302203.	0.0497247
$518$	0	0
$519$	−4.79249e6	−0.780985
$520$	−132800.	−0.0215372
$521$	−2.31725e6	−0.374007	−0.187003	−	0.982359i	$-0.559878\pi$
$521$	−2.31725e6	−0.374007	−0.187003	+	0.982359i	$0.559878\pi$
$522$	−4.23633e6	−0.680477
$523$	−269108.	−0.0430202	−0.0215101	−	0.999769i	$-0.506847\pi$
$523$	−269108.	−0.0430202	−0.0215101	+	0.999769i	$0.506847\pi$
$524$	−3.45904e6	−0.550335
$525$	0	0
$526$	2.55814e6	0.403143
$527$	−289572.	−0.0454182
$528$	−233728.	−0.0364860
$529$	3.61256e6	0.561275
$530$	−3.32680e6	−0.514443
$531$	−3.77810e6	−0.581483
$532$	0	0
$533$	−195548.	−0.0298150
$534$	−470800.	−0.0714469
$535$	1.01345e6	0.153080
$536$	−2.41843e6	−0.363598
$537$	8.00637e6	1.19812
$538$	8.78478e6	1.30850
$539$	0	0
$540$	1.60600e6	0.237007
$541$	−1.13145e7	−1.66205	−0.831024	−	0.556236i	$-0.812245\pi$
$541$	−1.13145e7	−1.66205	−0.831024	+	0.556236i	$0.812245\pi$
$542$	5.52253e6	0.807495
$543$	3.16021e6	0.459956
$544$	−181248.	−0.0262589
$545$	−2.19128e6	−0.316013
$546$	0	0
$547$	−920240.	−0.131502	−0.0657511	−	0.997836i	$-0.520944\pi$
$547$	−920240.	−0.131502	−0.0657511	+	0.997836i	$0.520944\pi$
$548$	−1.91750e6	−0.272763
$549$	556320.	0.0787760
$550$	−207500.	−0.0292490
$551$	−1.80738e7	−2.53613
$552$	−2.23168e6	−0.311734
$553$	0	0
$554$	−8.49193e6	−1.17553
$555$	−1.18195e6	−0.162880
$556$	−4.14877e6	−0.569157
$557$	217416.	0.0296930	0.0148465	−	0.999890i	$-0.495274\pi$
$557$	217416.	0.0296930	0.0148465	+	0.999890i	$0.495274\pi$
$558$	−798368.	−0.108547
$559$	725254.	0.0981659
$560$	0	0
$561$	−161601.	−0.0216789
$562$	−4.78795e6	−0.639453
$563$	7.58971e6	1.00915	0.504573	−	0.863369i	$-0.331650\pi$
$563$	7.58971e6	1.00915	0.504573	+	0.863369i	$0.331650\pi$
$564$	−640816.	−0.0848273
$565$	−1.90785e6	−0.251433
$566$	1.12580e6	0.147713
$567$	0	0
$568$	3.79546e6	0.493620
$569$	1.06524e7	1.37933	0.689664	−	0.724130i	$-0.257758\pi$
$569$	1.06524e7	1.37933	0.689664	+	0.724130i	$0.257758\pi$
$570$	2.29020e6	0.295248
$571$	−4.60492e6	−0.591061	−0.295530	−	0.955333i	$-0.595496\pi$
$571$	−4.60492e6	−0.591061	−0.295530	+	0.955333i	$0.595496\pi$
$572$	110224.	0.0140859
$573$	5.00039e6	0.636235
$574$	0	0
$575$	−1.98125e6	−0.249902
$576$	−499712.	−0.0627572
$577$	−1.08802e7	−1.36049	−0.680246	−	0.732983i	$-0.738127\pi$
$577$	−1.08802e7	−1.36049	−0.680246	+	0.732983i	$0.738127\pi$
$578$	5.55411e6	0.691505
$579$	4.38658e6	0.543788
$580$	−3.47240e6	−0.428607
$581$	0	0
$582$	−2.86330e6	−0.350396
$583$	2.76124e6	0.336460
$584$	−570240.	−0.0691872
$585$	−253150.	−0.0305836
$586$	−1.08586e7	−1.30627
$587$	−1.61205e7	−1.93100	−0.965500	−	0.260403i	$-0.916145\pi$
$587$	−1.61205e7	−1.93100	−0.965500	+	0.260403i	$0.916145\pi$
$588$	0	0
$589$	−3.40615e6	−0.404553
$590$	−3.09680e6	−0.366255
$591$	1.05575e7	1.24335
$592$	1.10029e6	0.129033
$593$	−5.91061e6	−0.690233	−0.345117	−	0.938560i	$-0.612161\pi$
$593$	−5.91061e6	−0.690233	−0.345117	+	0.938560i	$0.612161\pi$
$594$	−1.33298e6	−0.155009
$595$	0	0
$596$	−1.41629e6	−0.163319
$597$	3.76226e6	0.432030
$598$	1.05244e6	0.120350
$599$	1.66052e7	1.89094	0.945471	−	0.325707i	$-0.105602\pi$
$599$	1.66052e7	1.89094	0.945471	+	0.325707i	$0.105602\pi$
$600$	440000.	0.0498970
$601$	−6.63144e6	−0.748896	−0.374448	−	0.927248i	$-0.622168\pi$
$601$	−6.63144e6	−0.748896	−0.374448	+	0.927248i	$0.622168\pi$
$602$	0	0
$603$	−4.61014e6	−0.516322
$604$	1.84085e6	0.205317
$605$	−3.85405e6	−0.428084
$606$	6.56700e6	0.726416
$607$	−7.31847e6	−0.806211	−0.403105	−	0.915154i	$-0.632069\pi$
$607$	−7.31847e6	−0.806211	−0.403105	+	0.915154i	$0.632069\pi$
$608$	−2.13197e6	−0.233895
$609$	0	0
$610$	456000.	0.0496181
$611$	302203.	0.0327488
$612$	−345504.	−0.0372885
$613$	−1.26540e7	−1.36012	−0.680061	−	0.733155i	$-0.738047\pi$
$613$	−1.26540e7	−1.36012	−0.680061	+	0.733155i	$0.738047\pi$
$614$	−1.07352e7	−1.14919
$615$	647900.	0.0690749
$616$	0	0
$617$	−6.39256e6	−0.676023	−0.338012	−	0.941142i	$-0.609754\pi$
$617$	−6.39256e6	−0.676023	−0.338012	+	0.941142i	$0.609754\pi$
$618$	−8.54986e6	−0.900508
$619$	7.70898e6	0.808668	0.404334	−	0.914611i	$-0.367503\pi$
$619$	7.70898e6	0.808668	0.404334	+	0.914611i	$0.367503\pi$
$620$	−654400.	−0.0683698
$621$	−1.27276e7	−1.32439
$622$	102168.	0.0105886
$623$	0	0
$624$	−233728.	−0.0240298
$625$	390625.	0.0400000
$626$	−3.90390e6	−0.398165
$627$	−1.90087e6	−0.193100
$628$	5.18992e6	0.525124
$629$	760746.	0.0766678
$630$	0	0
$631$	1.16280e7	1.16260	0.581302	−	0.813688i	$-0.302543\pi$
$631$	1.16280e7	1.16260	0.581302	+	0.813688i	$0.302543\pi$
$632$	−1.76570e6	−0.175842
$633$	2.80547e6	0.278289
$634$	5.82161e6	0.575201
$635$	−4.57820e6	−0.450568
$636$	−5.85517e6	−0.573980
$637$	0	0
$638$	2.88209e6	0.280321
$639$	7.23509e6	0.700957
$640$	−409600.	−0.0395285
$641$	−1.15719e7	−1.11239	−0.556197	−	0.831051i	$-0.687740\pi$
$641$	−1.15719e7	−1.11239	−0.556197	+	0.831051i	$0.687740\pi$
$642$	1.78367e6	0.170796
$643$	4.51688e6	0.430836	0.215418	−	0.976522i	$-0.430889\pi$
$643$	4.51688e6	0.430836	0.215418	+	0.976522i	$0.430889\pi$
$644$	0	0
$645$	−2.40295e6	−0.227429
$646$	−1.47406e6	−0.138974
$647$	−6.71774e6	−0.630902	−0.315451	−	0.948942i	$-0.602156\pi$
$647$	−6.71774e6	−0.630902	−0.315451	+	0.948942i	$0.602156\pi$
$648$	929216.	0.0869319
$649$	2.57034e6	0.239541
$650$	−207500.	−0.0192635
$651$	0	0
$652$	3.78352e6	0.348560
$653$	−1.26522e7	−1.16114	−0.580569	−	0.814211i	$-0.697170\pi$
$653$	−1.26522e7	−1.16114	−0.580569	+	0.814211i	$0.697170\pi$
$654$	−3.85664e6	−0.352586
$655$	−5.40475e6	−0.492235
$656$	−603136.	−0.0547212
$657$	−1.08702e6	−0.0982481
$658$	0	0
$659$	−1.20321e7	−1.07927	−0.539633	−	0.841900i	$-0.681437\pi$
$659$	−1.20321e7	−1.07927	−0.539633	+	0.841900i	$0.681437\pi$
$660$	−365200.	−0.0326340
$661$	2.14150e7	1.90640	0.953199	−	0.302343i	$-0.0977689\pi$
$661$	2.14150e7	1.90640	0.953199	+	0.302343i	$0.0977689\pi$
$662$	1.19274e7	1.05780
$663$	−161601.	−0.0142778
$664$	4.33126e6	0.381236
$665$	0	0
$666$	2.09742e6	0.183232
$667$	2.75188e7	2.39505
$668$	5.32565e6	0.461776
$669$	−2.18219e6	−0.188507
$670$	−3.77880e6	−0.325212
$671$	−378480.	−0.0324516
$672$	0	0
$673$	−2.18091e7	−1.85610	−0.928048	−	0.372462i	$-0.878514\pi$
$673$	−2.18091e7	−1.85610	−0.928048	+	0.372462i	$0.878514\pi$
$674$	3.71479e6	0.314981
$675$	2.50938e6	0.211985
$676$	−5.83046e6	−0.490723
$677$	1.71852e7	1.44106	0.720531	−	0.693423i	$-0.243898\pi$
$677$	1.71852e7	1.44106	0.720531	+	0.693423i	$0.243898\pi$
$678$	−3.35782e6	−0.280532
$679$	0	0
$680$	−283200.	−0.0234866
$681$	5.99464e6	0.495331
$682$	543152.	0.0447157
$683$	2.63085e6	0.215796	0.107898	−	0.994162i	$-0.465588\pi$
$683$	2.63085e6	0.215796	0.107898	+	0.994162i	$0.465588\pi$
$684$	−4.06406e6	−0.332139
$685$	−2.99610e6	−0.243966
$686$	0	0
$687$	−1.60143e7	−1.29454
$688$	2.23693e6	0.180169
$689$	2.76124e6	0.221593
$690$	−3.48700e6	−0.278823
$691$	−1.29911e7	−1.03503	−0.517513	−	0.855675i	$-0.673142\pi$
$691$	−1.29911e7	−1.03503	−0.517513	+	0.855675i	$0.673142\pi$
$692$	6.97090e6	0.553380
$693$	0	0
$694$	−7.01742e6	−0.553068
$695$	−6.48245e6	−0.509070
$696$	−6.11142e6	−0.478211
$697$	−417012.	−0.0325137
$698$	−7.14425e6	−0.555032
$699$	720984.	0.0558127
$700$	0	0
$701$	−9.03664e6	−0.694564	−0.347282	−	0.937761i	$-0.612895\pi$
$701$	−9.03664e6	−0.694564	−0.347282	+	0.937761i	$0.612895\pi$
$702$	−1.33298e6	−0.102089
$703$	8.94844e6	0.682903
$704$	339968.	0.0258527
$705$	−1.00127e6	−0.0758718
$706$	4.93230e6	0.372424
$707$	0	0
$708$	−5.45037e6	−0.408642
$709$	1.41423e7	1.05658	0.528292	−	0.849063i	$-0.322833\pi$
$709$	1.41423e7	1.05658	0.528292	+	0.849063i	$0.322833\pi$
$710$	5.93040e6	0.441508
$711$	−3.36586e6	−0.249702
$712$	684800.	0.0506249
$713$	5.18612e6	0.382049
$714$	0	0
$715$	172225.	0.0125989
$716$	−1.16456e7	−0.848947
$717$	6.83328e6	0.496399
$718$	6.79654e6	0.492014
$719$	−6.27347e6	−0.452570	−0.226285	−	0.974061i	$-0.572658\pi$
$719$	−6.27347e6	−0.452570	−0.226285	+	0.974061i	$0.572658\pi$
$720$	−780800.	−0.0561317
$721$	0	0
$722$	−7.43450e6	−0.530773
$723$	1.13039e7	0.804236
$724$	−4.59667e6	−0.325910
$725$	−5.42562e6	−0.383358
$726$	−6.78313e6	−0.477627
$727$	5.20530e6	0.365267	0.182633	−	0.983181i	$-0.441538\pi$
$727$	5.20530e6	0.365267	0.182633	+	0.983181i	$0.441538\pi$
$728$	0	0
$729$	1.25034e7	0.871384
$730$	−891000.	−0.0618829
$731$	1.54663e6	0.107051
$732$	802560.	0.0553605
$733$	2.80490e7	1.92822	0.964111	−	0.265499i	$-0.0855368\pi$
$733$	2.80490e7	1.92822	0.964111	+	0.265499i	$0.0855368\pi$
$734$	7.31753e6	0.501331
$735$	0	0
$736$	3.24608e6	0.220884
$737$	3.13640e6	0.212698
$738$	−1.14973e6	−0.0777059
$739$	−4.42340e6	−0.297952	−0.148976	−	0.988841i	$-0.547598\pi$
$739$	−4.42340e6	−0.297952	−0.148976	+	0.988841i	$0.547598\pi$
$740$	1.71920e6	0.115411
$741$	−1.90087e6	−0.127176
$742$	0	0
$743$	−2.08246e7	−1.38390	−0.691950	−	0.721945i	$-0.743248\pi$
$743$	−2.08246e7	−1.38390	−0.691950	+	0.721945i	$0.743248\pi$
$744$	−1.15174e6	−0.0762823
$745$	−2.21295e6	−0.146077
$746$	4.13266e6	0.271883
$747$	8.25647e6	0.541369
$748$	235056.	0.0153609
$749$	0	0
$750$	687500.	0.0446292
$751$	2.13899e7	1.38391	0.691957	−	0.721939i	$-0.256749\pi$
$751$	2.13899e7	1.38391	0.691957	+	0.721939i	$0.256749\pi$
$752$	932096.	0.0601058
$753$	1.97202e7	1.26743
$754$	2.88209e6	0.184620
$755$	2.87632e6	0.183641
$756$	0	0
$757$	1.99739e7	1.26685	0.633423	−	0.773806i	$-0.281649\pi$
$757$	1.99739e7	1.26685	0.633423	+	0.773806i	$0.281649\pi$
$758$	−5.02405e6	−0.317600
$759$	2.89421e6	0.182358
$760$	−3.33120e6	−0.209202
$761$	−1.52078e7	−0.951932	−0.475966	−	0.879464i	$-0.657902\pi$
$761$	−1.52078e7	−0.951932	−0.475966	+	0.879464i	$0.657902\pi$
$762$	−8.05763e6	−0.502713
$763$	0	0
$764$	−7.27330e6	−0.450814
$765$	−539850.	−0.0333518
$766$	1.45729e7	0.897374
$767$	2.57034e6	0.157762
$768$	−720896.	−0.0441031
$769$	1.75417e7	1.06969	0.534843	−	0.844951i	$-0.320371\pi$
$769$	1.75417e7	1.06969	0.534843	+	0.844951i	$0.320371\pi$
$770$	0	0
$771$	1.27427e7	0.772016
$772$	−6.38048e6	−0.385310
$773$	2.01261e7	1.21146	0.605732	−	0.795669i	$-0.292881\pi$
$773$	2.01261e7	1.21146	0.605732	+	0.795669i	$0.292881\pi$
$774$	4.26414e6	0.255846
$775$	−1.02250e6	−0.0611518
$776$	4.16480e6	0.248279
$777$	0	0
$778$	−1.46947e7	−0.870387
$779$	−4.90519e6	−0.289609
$780$	−365200.	−0.0214929
$781$	−4.92223e6	−0.288758
$782$	2.24436e6	0.131243
$783$	−3.48542e7	−2.03166
$784$	0	0
$785$	8.10925e6	0.469685
$786$	−9.51236e6	−0.549202
$787$	−2.41718e7	−1.39114	−0.695571	−	0.718458i	$-0.744848\pi$
$787$	−2.41718e7	−1.39114	−0.695571	+	0.718458i	$0.744848\pi$
$788$	−1.53564e7	−0.880997
$789$	7.03487e6	0.402313
$790$	−2.75890e6	−0.157278
$791$	0	0
$792$	648064.	0.0367117
$793$	−378480.	−0.0213727
$794$	−2.25747e7	−1.27078
$795$	−9.14870e6	−0.513383
$796$	−5.47238e6	−0.306122
$797$	2.67019e7	1.48901	0.744503	−	0.667619i	$-0.232687\pi$
$797$	2.67019e7	1.48901	0.744503	+	0.667619i	$0.232687\pi$
$798$	0	0
$799$	644457.	0.0357131
$800$	−640000.	−0.0353553
$801$	1.30540e6	0.0718890
$802$	1.68899e7	0.927240
$803$	739530.	0.0404731
$804$	−6.65069e6	−0.362849
$805$	0	0
$806$	543152.	0.0294499
$807$	2.41581e7	1.30581
$808$	−9.55200e6	−0.514714
$809$	2.15124e7	1.15562	0.577812	−	0.816170i	$-0.303907\pi$
$809$	2.15124e7	1.15562	0.577812	+	0.816170i	$0.303907\pi$
$810$	1.45190e6	0.0777543
$811$	−3.50935e7	−1.87359	−0.936794	−	0.349882i	$-0.886222\pi$
$811$	−3.50935e7	−1.87359	−0.936794	+	0.349882i	$0.886222\pi$
$812$	0	0
$813$	1.51870e7	0.805832
$814$	−1.42694e6	−0.0754820
$815$	5.91175e6	0.311761
$816$	−498432.	−0.0262048
$817$	1.81925e7	0.953537
$818$	2.42588e6	0.126761
$819$	0	0
$820$	−942400.	−0.0489441
$821$	−1.26329e7	−0.654100	−0.327050	−	0.945007i	$-0.606055\pi$
$821$	−1.26329e7	−0.654100	−0.327050	+	0.945007i	$0.606055\pi$
$822$	−5.27314e6	−0.272201
$823$	1.55348e7	0.799475	0.399737	−	0.916630i	$-0.369101\pi$
$823$	1.55348e7	0.799475	0.399737	+	0.916630i	$0.369101\pi$
$824$	1.24362e7	0.638070
$825$	−570625.	−0.0291888
$826$	0	0
$827$	−3.89597e7	−1.98085	−0.990426	−	0.138043i	$-0.955919\pi$
$827$	−3.89597e7	−1.98085	−0.990426	+	0.138043i	$0.955919\pi$
$828$	6.18784e6	0.313663
$829$	−1.35099e7	−0.682757	−0.341379	−	0.939926i	$-0.610894\pi$
$829$	−1.35099e7	−0.682757	−0.341379	+	0.939926i	$0.610894\pi$
$830$	6.76760e6	0.340988
$831$	−2.33528e7	−1.17310
$832$	339968.	0.0170267
$833$	0	0
$834$	−1.14091e7	−0.567985
$835$	8.32132e6	0.413025
$836$	2.76490e6	0.136824
$837$	−6.56854e6	−0.324082
$838$	−2.90667e6	−0.142984
$839$	250486.	0.0122851	0.00614255	−	0.999981i	$-0.498045\pi$
$839$	250486.	0.0122851	0.00614255	+	0.999981i	$0.498045\pi$
$840$	0	0
$841$	5.48486e7	2.67409
$842$	597260.	0.0290324
$843$	−1.31669e7	−0.638136
$844$	−4.08069e6	−0.197187
$845$	−9.11010e6	−0.438916
$846$	1.77681e6	0.0853522
$847$	0	0
$848$	8.51661e6	0.406703
$849$	3.09594e6	0.147409
$850$	−442500.	−0.0210071
$851$	−1.36247e7	−0.644914
$852$	1.04375e7	0.492604
$853$	−2.87228e7	−1.35162	−0.675809	−	0.737077i	$-0.736206\pi$
$853$	−2.87228e7	−1.35162	−0.675809	+	0.737077i	$0.736206\pi$
$854$	0	0
$855$	−6.35010e6	−0.297074
$856$	−2.59443e6	−0.121020
$857$	−1.61269e7	−0.750066	−0.375033	−	0.927011i	$-0.622369\pi$
$857$	−1.61269e7	−0.750066	−0.375033	+	0.927011i	$0.622369\pi$
$858$	303116.	0.0140569
$859$	4.03773e7	1.86704	0.933521	−	0.358523i	$-0.116719\pi$
$859$	4.03773e7	1.86704	0.933521	+	0.358523i	$0.116719\pi$
$860$	3.49520e6	0.161148
$861$	0	0
$862$	2.28349e7	1.04672
$863$	−2.57025e7	−1.17476	−0.587378	−	0.809312i	$-0.699840\pi$
$863$	−2.57025e7	−1.17476	−0.587378	+	0.809312i	$0.699840\pi$
$864$	−4.11136e6	−0.187370
$865$	1.08920e7	0.494958
$866$	−6.64038e6	−0.300883
$867$	1.52738e7	0.690080
$868$	0	0
$869$	2.28989e6	0.102864
$870$	−9.54910e6	−0.427725
$871$	3.13640e6	0.140083
$872$	5.60966e6	0.249831
$873$	7.93915e6	0.352564
$874$	2.63998e7	1.16902
$875$	0	0
$876$	−1.56816e6	−0.0690447
$877$	−1.75541e7	−0.770689	−0.385344	−	0.922773i	$-0.625917\pi$
$877$	−1.75541e7	−0.770689	−0.385344	+	0.922773i	$0.625917\pi$
$878$	−2.42795e7	−1.06293
$879$	−2.98613e7	−1.30358
$880$	531200.	0.0231234
$881$	2.13350e7	0.926088	0.463044	−	0.886335i	$-0.346757\pi$
$881$	2.13350e7	0.926088	0.463044	+	0.886335i	$0.346757\pi$
$882$	0	0
$883$	3.95442e7	1.70679	0.853397	−	0.521261i	$-0.174538\pi$
$883$	3.95442e7	1.70679	0.853397	+	0.521261i	$0.174538\pi$
$884$	235056.	0.0101167
$885$	−8.51620e6	−0.365500
$886$	−2.60932e7	−1.11672
$887$	3.42741e7	1.46271	0.731353	−	0.681999i	$-0.238889\pi$
$887$	3.42741e7	1.46271	0.731353	+	0.681999i	$0.238889\pi$
$888$	3.02579e6	0.128768
$889$	0	0
$890$	1.07000e6	0.0452802
$891$	−1.20508e6	−0.0508535
$892$	3.17410e6	0.133570
$893$	7.58056e6	0.318107
$894$	−3.89479e6	−0.162982
$895$	−1.81963e7	−0.759321
$896$	0	0
$897$	2.89421e6	0.120102
$898$	−2.99193e7	−1.23811
$899$	1.42021e7	0.586076
$900$	−1.22000e6	−0.0502058
$901$	5.88844e6	0.241651
$902$	782192.	0.0320108
$903$	0	0
$904$	4.88410e6	0.198776
$905$	−7.18230e6	−0.291502
$906$	5.06233e6	0.204894
$907$	3.72968e7	1.50541	0.752703	−	0.658361i	$-0.228750\pi$
$907$	3.72968e7	1.50541	0.752703	+	0.658361i	$0.228750\pi$
$908$	−8.71947e6	−0.350975
$909$	−1.82085e7	−0.730911
$910$	0	0
$911$	2.83311e7	1.13101	0.565505	−	0.824745i	$-0.308681\pi$
$911$	2.83311e7	1.13101	0.565505	+	0.824745i	$0.308681\pi$
$912$	−5.86291e6	−0.233414
$913$	−5.61711e6	−0.223016
$914$	−2.47289e7	−0.979129
$915$	1.25400e6	0.0495159
$916$	2.32935e7	0.917268
$917$	0	0
$918$	−2.84262e6	−0.111330
$919$	−9.27364e6	−0.362211	−0.181105	−	0.983464i	$-0.557968\pi$
$919$	−9.27364e6	−0.362211	−0.181105	+	0.983464i	$0.557968\pi$
$920$	5.07200e6	0.197565
$921$	−2.95219e7	−1.14682
$922$	−4.07741e6	−0.157964
$923$	−4.92223e6	−0.190177
$924$	0	0
$925$	2.68625e6	0.103227
$926$	−5.22051e6	−0.200072
$927$	2.37064e7	0.906081
$928$	8.88934e6	0.338844
$929$	−1.39068e7	−0.528674	−0.264337	−	0.964430i	$-0.585153\pi$
$929$	−1.39068e7	−0.528674	−0.264337	+	0.964430i	$0.585153\pi$
$930$	−1.79960e6	−0.0682289
$931$	0	0
$932$	−1.04870e6	−0.0395470
$933$	280962.	0.0105668
$934$	−1.09252e7	−0.409791
$935$	367275.	0.0137392
$936$	648064.	0.0241784
$937$	1.93922e6	0.0721570	0.0360785	−	0.999349i	$-0.488513\pi$
$937$	1.93922e6	0.0721570	0.0360785	+	0.999349i	$0.488513\pi$
$938$	0	0
$939$	−1.07357e7	−0.397345
$940$	1.45640e6	0.0537602
$941$	2.44080e7	0.898582	0.449291	−	0.893385i	$-0.351677\pi$
$941$	2.44080e7	0.898582	0.449291	+	0.893385i	$0.351677\pi$
$942$	1.42723e7	0.524042
$943$	7.46852e6	0.273499
$944$	7.92781e6	0.289550
$945$	0	0
$946$	−2.90102e6	−0.105396
$947$	36592.0	0.00132590	0.000662951	−	1.00000i	$-0.499789\pi$
$947$	36592.0	0.00132590	0.000662951		1.00000i	$0.499789\pi$
$948$	−4.85566e6	−0.175480
$949$	739530.	0.0266557
$950$	−5.20500e6	−0.187116
$951$	1.60094e7	0.574016
$952$	0	0
$953$	2.75598e7	0.982978	0.491489	−	0.870884i	$-0.336453\pi$
$953$	2.75598e7	0.982978	0.491489	+	0.870884i	$0.336453\pi$
$954$	1.62348e7	0.577531
$955$	−1.13645e7	−0.403221
$956$	−9.93931e6	−0.351732
$957$	7.92575e6	0.279744
$958$	−1.28929e6	−0.0453875
$959$	0	0
$960$	−1.12640e6	−0.0394471
$961$	−2.59527e7	−0.906512
$962$	−1.42694e6	−0.0497126
$963$	−4.94564e6	−0.171853
$964$	−1.64421e7	−0.569855
$965$	−9.96950e6	−0.344632
$966$	0	0
$967$	−1.42984e7	−0.491725	−0.245863	−	0.969305i	$-0.579071\pi$
$967$	−1.42984e7	−0.491725	−0.245863	+	0.969305i	$0.579071\pi$
$968$	9.86637e6	0.338430
$969$	−4.05365e6	−0.138687
$970$	6.50750e6	0.222067
$971$	−2.29801e7	−0.782176	−0.391088	−	0.920353i	$-0.627901\pi$
$971$	−2.29801e7	−0.782176	−0.391088	+	0.920353i	$0.627901\pi$
$972$	−1.30550e7	−0.443211
$973$	0	0
$974$	1.14988e7	0.388378
$975$	−570625.	−0.0192238
$976$	−1.16736e6	−0.0392266
$977$	−2.07391e7	−0.695111	−0.347556	−	0.937659i	$-0.612988\pi$
$977$	−2.07391e7	−0.695111	−0.347556	+	0.937659i	$0.612988\pi$
$978$	1.04047e7	0.347842
$979$	−888100.	−0.0296146
$980$	0	0
$981$	1.06934e7	0.354768
$982$	2.39127e7	0.791315
$983$	−2.95326e7	−0.974807	−0.487403	−	0.873177i	$-0.662056\pi$
$983$	−2.95326e7	−0.974807	−0.487403	+	0.873177i	$0.662056\pi$
$984$	−1.65862e6	−0.0546085
$985$	−2.39944e7	−0.787987
$986$	6.14615e6	0.201331
$987$	0	0
$988$	2.76490e6	0.0901128
$989$	−2.76995e7	−0.900493
$990$	1.01260e6	0.0328360
$991$	−3.56883e7	−1.15436	−0.577181	−	0.816616i	$-0.695847\pi$
$991$	−3.56883e7	−1.15436	−0.577181	+	0.816616i	$0.695847\pi$
$992$	1.67526e6	0.0540510
$993$	3.28005e7	1.05562
$994$	0	0
$995$	−8.55060e6	−0.273803
$996$	1.19110e7	0.380451
$997$	−3.48937e7	−1.11176	−0.555878	−	0.831264i	$-0.687618\pi$
$997$	−3.48937e7	−1.11176	−0.555878	+	0.831264i	$0.687618\pi$
$998$	1.96603e7	0.624832
$999$	1.72565e7	0.547064

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.d.1.1	✓	1	7.6	odd	2
350.6.a.h.1.1		1	35.34	odd	2
350.6.c.c.99.1		2	35.27	even	4
350.6.c.c.99.2		2	35.13	even	4
490.6.a.c.1.1		1	1.1	even	1	trivial
560.6.a.a.1.1		1	28.27	even	2
630.6.a.l.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 $\F_{q}$

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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