LMFDB - Embedded newform 640.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,4,Mod(1,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("640.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	640.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:	$37.7612224037$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	640.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-8.00000 q^{3} +5.00000 q^{5} -2.00000 q^{7} +37.0000 q^{9} -22.0000 q^{11} +10.0000 q^{13} -40.0000 q^{15} +10.0000 q^{17} -110.000 q^{19} +16.0000 q^{21} +154.000 q^{23} +25.0000 q^{25} -80.0000 q^{27} +222.000 q^{29} +92.0000 q^{31} +176.000 q^{33} -10.0000 q^{35} -34.0000 q^{37} -80.0000 q^{39} +398.000 q^{41} -268.000 q^{43} +185.000 q^{45} +10.0000 q^{47} -339.000 q^{49} -80.0000 q^{51} -582.000 q^{53} -110.000 q^{55} +880.000 q^{57} -746.000 q^{59} -226.000 q^{61} -74.0000 q^{63} +50.0000 q^{65} +172.000 q^{67} -1232.00 q^{69} -928.000 q^{71} +570.000 q^{73} -200.000 q^{75} +44.0000 q^{77} -64.0000 q^{79} -359.000 q^{81} +864.000 q^{83} +50.0000 q^{85} -1776.00 q^{87} -874.000 q^{89} -20.0000 q^{91} -736.000 q^{93} -550.000 q^{95} +306.000 q^{97} -814.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−8.00000	−1.53960	−0.769800	−	0.638285i	$-0.779644\pi$
$3$	−8.00000	−1.53960	−0.769800	+	0.638285i	$0.779644\pi$
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	0	0
$9$	37.0000	1.37037
$10$	0	0
$11$	−22.0000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−22.0000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	10.0000	0.213346	0.106673	−	0.994294i	$-0.465980\pi$
$13$	10.0000	0.213346	0.106673	+	0.994294i	$0.465980\pi$
$14$	0	0
$15$	−40.0000	−0.688530
$16$	0	0
$17$	10.0000	0.142668	0.0713340	−	0.997452i	$-0.477274\pi$
$17$	10.0000	0.142668	0.0713340	+	0.997452i	$0.477274\pi$
$18$	0	0
$19$	−110.000	−1.32820	−0.664098	−	0.747645i	$-0.731184\pi$
$19$	−110.000	−1.32820	−0.664098	+	0.747645i	$0.731184\pi$
$20$	0	0
$21$	16.0000	0.166261
$22$	0	0
$23$	154.000	1.39614	0.698070	−	0.716030i	$-0.254042\pi$
$23$	154.000	1.39614	0.698070	+	0.716030i	$0.254042\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−80.0000	−0.570222
$28$	0	0
$29$	222.000	1.42153	0.710765	−	0.703430i	$-0.248349\pi$
$29$	222.000	1.42153	0.710765	+	0.703430i	$0.248349\pi$
$30$	0	0
$31$	92.0000	0.533022	0.266511	−	0.963832i	$-0.414129\pi$
$31$	92.0000	0.533022	0.266511	+	0.963832i	$0.414129\pi$
$32$	0	0
$33$	176.000	0.928414
$34$	0	0
$35$	−10.0000	−0.0482945
$36$	0	0
$37$	−34.0000	−0.151069	−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000	−0.151069	−0.0755347	+	0.997143i	$0.524066\pi$
$38$	0	0
$39$	−80.0000	−0.328468
$40$	0	0
$41$	398.000	1.51603	0.758014	−	0.652238i	$-0.226170\pi$
$41$	398.000	1.51603	0.758014	+	0.652238i	$0.226170\pi$
$42$	0	0
$43$	−268.000	−0.950456	−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000	−0.950456	−0.475228	+	0.879863i	$0.657634\pi$
$44$	0	0
$45$	185.000	0.612848
$46$	0	0
$47$	10.0000	0.0310351	0.0155176	−	0.999880i	$-0.495060\pi$
$47$	10.0000	0.0310351	0.0155176	+	0.999880i	$0.495060\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	0	0
$51$	−80.0000	−0.219652
$52$	0	0
$53$	−582.000	−1.50837	−0.754187	−	0.656659i	$-0.771969\pi$
$53$	−582.000	−1.50837	−0.754187	+	0.656659i	$0.771969\pi$
$54$	0	0
$55$	−110.000	−0.269680
$56$	0	0
$57$	880.000	2.04489
$58$	0	0
$59$	−746.000	−1.64612	−0.823059	−	0.567956i	$-0.807734\pi$
$59$	−746.000	−1.64612	−0.823059	+	0.567956i	$0.807734\pi$
$60$	0	0
$61$	−226.000	−0.474366	−0.237183	−	0.971465i	$-0.576224\pi$
$61$	−226.000	−0.474366	−0.237183	+	0.971465i	$0.576224\pi$
$62$	0	0
$63$	−74.0000	−0.147986
$64$	0	0
$65$	50.0000	0.0954113
$66$	0	0
$67$	172.000	0.313629	0.156815	−	0.987628i	$-0.449878\pi$
$67$	172.000	0.313629	0.156815	+	0.987628i	$0.449878\pi$
$68$	0	0
$69$	−1232.00	−2.14950
$70$	0	0
$71$	−928.000	−1.55117	−0.775587	−	0.631241i	$-0.782546\pi$
$71$	−928.000	−1.55117	−0.775587	+	0.631241i	$0.782546\pi$
$72$	0	0
$73$	570.000	0.913883	0.456941	−	0.889497i	$-0.348945\pi$
$73$	570.000	0.913883	0.456941	+	0.889497i	$0.348945\pi$
$74$	0	0
$75$	−200.000	−0.307920
$76$	0	0
$77$	44.0000	0.0651203
$78$	0	0
$79$	−64.0000	−0.0911464	−0.0455732	−	0.998961i	$-0.514511\pi$
$79$	−64.0000	−0.0911464	−0.0455732	+	0.998961i	$0.514511\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	0	0
$83$	864.000	1.14261	0.571303	−	0.820739i	$-0.306438\pi$
$83$	864.000	1.14261	0.571303	+	0.820739i	$0.306438\pi$
$84$	0	0
$85$	50.0000	0.0638031
$86$	0	0
$87$	−1776.00	−2.18859
$88$	0	0
$89$	−874.000	−1.04094	−0.520471	−	0.853879i	$-0.674244\pi$
$89$	−874.000	−1.04094	−0.520471	+	0.853879i	$0.674244\pi$
$90$	0	0
$91$	−20.0000	−0.0230392
$92$	0	0
$93$	−736.000	−0.820641
$94$	0	0
$95$	−550.000	−0.593987
$96$	0	0
$97$	306.000	0.320305	0.160153	−	0.987092i	$-0.448801\pi$
$97$	306.000	0.320305	0.160153	+	0.987092i	$0.448801\pi$
$98$	0	0
$99$	−814.000	−0.826364
$100$	0	0
$101$	−930.000	−0.916222	−0.458111	−	0.888895i	$-0.651474\pi$
$101$	−930.000	−0.916222	−0.458111	+	0.888895i	$0.651474\pi$
$102$	0	0
$103$	−462.000	−0.441963	−0.220982	−	0.975278i	$-0.570926\pi$
$103$	−462.000	−0.441963	−0.220982	+	0.975278i	$0.570926\pi$
$104$	0	0
$105$	80.0000	0.0743543
$106$	0	0
$107$	1560.00	1.40945	0.704724	−	0.709482i	$-0.251071\pi$
$107$	1560.00	1.40945	0.704724	+	0.709482i	$0.251071\pi$
$108$	0	0
$109$	−1186.00	−1.04219	−0.521093	−	0.853500i	$-0.674475\pi$
$109$	−1186.00	−1.04219	−0.521093	+	0.853500i	$0.674475\pi$
$110$	0	0
$111$	272.000	0.232586
$112$	0	0
$113$	−1382.00	−1.15051	−0.575255	−	0.817974i	$-0.695097\pi$
$113$	−1382.00	−1.15051	−0.575255	+	0.817974i	$0.695097\pi$
$114$	0	0
$115$	770.000	0.624373
$116$	0	0
$117$	370.000	0.292363
$118$	0	0
$119$	−20.0000	−0.0154067
$120$	0	0
$121$	−847.000	−0.636364
$122$	0	0
$123$	−3184.00	−2.33408
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−1198.00	−0.837050	−0.418525	−	0.908205i	$-0.637453\pi$
$127$	−1198.00	−0.837050	−0.418525	+	0.908205i	$0.637453\pi$
$128$	0	0
$129$	2144.00	1.46332
$130$	0	0
$131$	−2314.00	−1.54332	−0.771661	−	0.636034i	$-0.780574\pi$
$131$	−2314.00	−1.54332	−0.771661	+	0.636034i	$0.780574\pi$
$132$	0	0
$133$	220.000	0.143432
$134$	0	0
$135$	−400.000	−0.255011
$136$	0	0
$137$	2394.00	1.49294	0.746472	−	0.665417i	$-0.231746\pi$
$137$	2394.00	1.49294	0.746472	+	0.665417i	$0.231746\pi$
$138$	0	0
$139$	−826.000	−0.504032	−0.252016	−	0.967723i	$-0.581094\pi$
$139$	−826.000	−0.504032	−0.252016	+	0.967723i	$0.581094\pi$
$140$	0	0
$141$	−80.0000	−0.0477817
$142$	0	0
$143$	−220.000	−0.128653
$144$	0	0
$145$	1110.00	0.635727
$146$	0	0
$147$	2712.00	1.52165
$148$	0	0
$149$	−2298.00	−1.26349	−0.631743	−	0.775178i	$-0.717660\pi$
$149$	−2298.00	−1.26349	−0.631743	+	0.775178i	$0.717660\pi$
$150$	0	0
$151$	−2120.00	−1.14254	−0.571269	−	0.820763i	$-0.693549\pi$
$151$	−2120.00	−1.14254	−0.571269	+	0.820763i	$0.693549\pi$
$152$	0	0
$153$	370.000	0.195508
$154$	0	0
$155$	460.000	0.238375
$156$	0	0
$157$	838.000	0.425985	0.212993	−	0.977054i	$-0.431679\pi$
$157$	838.000	0.425985	0.212993	+	0.977054i	$0.431679\pi$
$158$	0	0
$159$	4656.00	2.32229
$160$	0	0
$161$	−308.000	−0.150769
$162$	0	0
$163$	−1440.00	−0.691960	−0.345980	−	0.938242i	$-0.612454\pi$
$163$	−1440.00	−0.691960	−0.345980	+	0.938242i	$0.612454\pi$
$164$	0	0
$165$	880.000	0.415199
$166$	0	0
$167$	−2122.00	−0.983265	−0.491633	−	0.870803i	$-0.663600\pi$
$167$	−2122.00	−0.983265	−0.491633	+	0.870803i	$0.663600\pi$
$168$	0	0
$169$	−2097.00	−0.954483
$170$	0	0
$171$	−4070.00	−1.82012
$172$	0	0
$173$	−3306.00	−1.45289	−0.726447	−	0.687223i	$-0.758830\pi$
$173$	−3306.00	−1.45289	−0.726447	+	0.687223i	$0.758830\pi$
$174$	0	0
$175$	−50.0000	−0.0215980
$176$	0	0
$177$	5968.00	2.53436
$178$	0	0
$179$	2746.00	1.14662	0.573312	−	0.819337i	$-0.305658\pi$
$179$	2746.00	1.14662	0.573312	+	0.819337i	$0.305658\pi$
$180$	0	0
$181$	4062.00	1.66810	0.834050	−	0.551689i	$-0.186016\pi$
$181$	4062.00	1.66810	0.834050	+	0.551689i	$0.186016\pi$
$182$	0	0
$183$	1808.00	0.730334
$184$	0	0
$185$	−170.000	−0.0675603
$186$	0	0
$187$	−220.000	−0.0860320
$188$	0	0
$189$	160.000	0.0615782
$190$	0	0
$191$	1908.00	0.722817	0.361408	−	0.932408i	$-0.382296\pi$
$191$	1908.00	0.722817	0.361408	+	0.932408i	$0.382296\pi$
$192$	0	0
$193$	−2758.00	−1.02863	−0.514314	−	0.857602i	$-0.671953\pi$
$193$	−2758.00	−1.02863	−0.514314	+	0.857602i	$0.671953\pi$
$194$	0	0
$195$	−400.000	−0.146895
$196$	0	0
$197$	4322.00	1.56310	0.781548	−	0.623846i	$-0.214431\pi$
$197$	4322.00	1.56310	0.781548	+	0.623846i	$0.214431\pi$
$198$	0	0
$199$	2852.00	1.01594	0.507972	−	0.861373i	$-0.330395\pi$
$199$	2852.00	1.01594	0.507972	+	0.861373i	$0.330395\pi$
$200$	0	0
$201$	−1376.00	−0.482863
$202$	0	0
$203$	−444.000	−0.153511
$204$	0	0
$205$	1990.00	0.677988
$206$	0	0
$207$	5698.00	1.91323
$208$	0	0
$209$	2420.00	0.800933
$210$	0	0
$211$	4310.00	1.40622	0.703111	−	0.711081i	$-0.251794\pi$
$211$	4310.00	1.40622	0.703111	+	0.711081i	$0.251794\pi$
$212$	0	0
$213$	7424.00	2.38819
$214$	0	0
$215$	−1340.00	−0.425057
$216$	0	0
$217$	−184.000	−0.0575610
$218$	0	0
$219$	−4560.00	−1.40701
$220$	0	0
$221$	100.000	0.0304377
$222$	0	0
$223$	2742.00	0.823399	0.411699	−	0.911320i	$-0.364935\pi$
$223$	2742.00	0.823399	0.411699	+	0.911320i	$0.364935\pi$
$224$	0	0
$225$	925.000	0.274074
$226$	0	0
$227$	1932.00	0.564896	0.282448	−	0.959283i	$-0.408854\pi$
$227$	1932.00	0.564896	0.282448	+	0.959283i	$0.408854\pi$
$228$	0	0
$229$	−6114.00	−1.76430	−0.882150	−	0.470969i	$-0.843904\pi$
$229$	−6114.00	−1.76430	−0.882150	+	0.470969i	$0.843904\pi$
$230$	0	0
$231$	−352.000	−0.100259
$232$	0	0
$233$	690.000	0.194006	0.0970030	−	0.995284i	$-0.469074\pi$
$233$	690.000	0.194006	0.0970030	+	0.995284i	$0.469074\pi$
$234$	0	0
$235$	50.0000	0.0138793
$236$	0	0
$237$	512.000	0.140329
$238$	0	0
$239$	1264.00	0.342098	0.171049	−	0.985263i	$-0.445284\pi$
$239$	1264.00	0.342098	0.171049	+	0.985263i	$0.445284\pi$
$240$	0	0
$241$	−3246.00	−0.867607	−0.433803	−	0.901008i	$-0.642829\pi$
$241$	−3246.00	−0.867607	−0.433803	+	0.901008i	$0.642829\pi$
$242$	0	0
$243$	5032.00	1.32841
$244$	0	0
$245$	−1695.00	−0.441998
$246$	0	0
$247$	−1100.00	−0.283366
$248$	0	0
$249$	−6912.00	−1.75916
$250$	0	0
$251$	−2422.00	−0.609065	−0.304532	−	0.952502i	$-0.598500\pi$
$251$	−2422.00	−0.609065	−0.304532	+	0.952502i	$0.598500\pi$
$252$	0	0
$253$	−3388.00	−0.841904
$254$	0	0
$255$	−400.000	−0.0982313
$256$	0	0
$257$	−1158.00	−0.281066	−0.140533	−	0.990076i	$-0.544882\pi$
$257$	−1158.00	−0.281066	−0.140533	+	0.990076i	$0.544882\pi$
$258$	0	0
$259$	68.0000	0.0163140
$260$	0	0
$261$	8214.00	1.94802
$262$	0	0
$263$	−3038.00	−0.712286	−0.356143	−	0.934432i	$-0.615908\pi$
$263$	−3038.00	−0.712286	−0.356143	+	0.934432i	$0.615908\pi$
$264$	0	0
$265$	−2910.00	−0.674566
$266$	0	0
$267$	6992.00	1.60263
$268$	0	0
$269$	3846.00	0.871728	0.435864	−	0.900013i	$-0.356443\pi$
$269$	3846.00	0.871728	0.435864	+	0.900013i	$0.356443\pi$
$270$	0	0
$271$	−6612.00	−1.48210	−0.741052	−	0.671447i	$-0.765673\pi$
$271$	−6612.00	−1.48210	−0.741052	+	0.671447i	$0.765673\pi$
$272$	0	0
$273$	160.000	0.0354712
$274$	0	0
$275$	−550.000	−0.120605
$276$	0	0
$277$	−7314.00	−1.58648	−0.793241	−	0.608907i	$-0.791608\pi$
$277$	−7314.00	−1.58648	−0.793241	+	0.608907i	$0.791608\pi$
$278$	0	0
$279$	3404.00	0.730438
$280$	0	0
$281$	−2102.00	−0.446245	−0.223122	−	0.974790i	$-0.571625\pi$
$281$	−2102.00	−0.446245	−0.223122	+	0.974790i	$0.571625\pi$
$282$	0	0
$283$	4620.00	0.970426	0.485213	−	0.874396i	$-0.338742\pi$
$283$	4620.00	0.970426	0.485213	+	0.874396i	$0.338742\pi$
$284$	0	0
$285$	4400.00	0.914504
$286$	0	0
$287$	−796.000	−0.163716
$288$	0	0
$289$	−4813.00	−0.979646
$290$	0	0
$291$	−2448.00	−0.493142
$292$	0	0
$293$	−4018.00	−0.801140	−0.400570	−	0.916266i	$-0.631188\pi$
$293$	−4018.00	−0.801140	−0.400570	+	0.916266i	$0.631188\pi$
$294$	0	0
$295$	−3730.00	−0.736166
$296$	0	0
$297$	1760.00	0.343857
$298$	0	0
$299$	1540.00	0.297861
$300$	0	0
$301$	536.000	0.102640
$302$	0	0
$303$	7440.00	1.41062
$304$	0	0
$305$	−1130.00	−0.212143
$306$	0	0
$307$	8596.00	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	8596.00	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	3696.00	0.680447
$310$	0	0
$311$	−1312.00	−0.239218	−0.119609	−	0.992821i	$-0.538164\pi$
$311$	−1312.00	−0.239218	−0.119609	+	0.992821i	$0.538164\pi$
$312$	0	0
$313$	1154.00	0.208396	0.104198	−	0.994557i	$-0.466772\pi$
$313$	1154.00	0.208396	0.104198	+	0.994557i	$0.466772\pi$
$314$	0	0
$315$	−370.000	−0.0661814
$316$	0	0
$317$	−7262.00	−1.28667	−0.643335	−	0.765585i	$-0.722450\pi$
$317$	−7262.00	−1.28667	−0.643335	+	0.765585i	$0.722450\pi$
$318$	0	0
$319$	−4884.00	−0.857215
$320$	0	0
$321$	−12480.0	−2.16999
$322$	0	0
$323$	−1100.00	−0.189491
$324$	0	0
$325$	250.000	0.0426692
$326$	0	0
$327$	9488.00	1.60455
$328$	0	0
$329$	−20.0000	−0.00335148
$330$	0	0
$331$	3098.00	0.514446	0.257223	−	0.966352i	$-0.417193\pi$
$331$	3098.00	0.514446	0.257223	+	0.966352i	$0.417193\pi$
$332$	0	0
$333$	−1258.00	−0.207021
$334$	0	0
$335$	860.000	0.140259
$336$	0	0
$337$	−7062.00	−1.14152	−0.570759	−	0.821118i	$-0.693351\pi$
$337$	−7062.00	−1.14152	−0.570759	+	0.821118i	$0.693351\pi$
$338$	0	0
$339$	11056.0	1.77133
$340$	0	0
$341$	−2024.00	−0.321424
$342$	0	0
$343$	1364.00	0.214720
$344$	0	0
$345$	−6160.00	−0.961285
$346$	0	0
$347$	2240.00	0.346540	0.173270	−	0.984874i	$-0.444567\pi$
$347$	2240.00	0.346540	0.173270	+	0.984874i	$0.444567\pi$
$348$	0	0
$349$	12166.0	1.86599	0.932996	−	0.359887i	$-0.117185\pi$
$349$	12166.0	1.86599	0.932996	+	0.359887i	$0.117185\pi$
$350$	0	0
$351$	−800.000	−0.121655
$352$	0	0
$353$	−9318.00	−1.40495	−0.702475	−	0.711709i	$-0.747922\pi$
$353$	−9318.00	−1.40495	−0.702475	+	0.711709i	$0.747922\pi$
$354$	0	0
$355$	−4640.00	−0.693706
$356$	0	0
$357$	160.000	0.0237202
$358$	0	0
$359$	−5196.00	−0.763884	−0.381942	−	0.924186i	$-0.624745\pi$
$359$	−5196.00	−0.763884	−0.381942	+	0.924186i	$0.624745\pi$
$360$	0	0
$361$	5241.00	0.764106
$362$	0	0
$363$	6776.00	0.979746
$364$	0	0
$365$	2850.00	0.408701
$366$	0	0
$367$	12970.0	1.84476	0.922382	−	0.386279i	$-0.126240\pi$
$367$	12970.0	1.84476	0.922382	+	0.386279i	$0.126240\pi$
$368$	0	0
$369$	14726.0	2.07752
$370$	0	0
$371$	1164.00	0.162889
$372$	0	0
$373$	702.000	0.0974482	0.0487241	−	0.998812i	$-0.484484\pi$
$373$	702.000	0.0974482	0.0487241	+	0.998812i	$0.484484\pi$
$374$	0	0
$375$	−1000.00	−0.137706
$376$	0	0
$377$	2220.00	0.303278
$378$	0	0
$379$	6630.00	0.898576	0.449288	−	0.893387i	$-0.351678\pi$
$379$	6630.00	0.898576	0.449288	+	0.893387i	$0.351678\pi$
$380$	0	0
$381$	9584.00	1.28872
$382$	0	0
$383$	46.0000	0.00613705	0.00306853	−	0.999995i	$-0.499023\pi$
$383$	46.0000	0.00613705	0.00306853	+	0.999995i	$0.499023\pi$
$384$	0	0
$385$	220.000	0.0291227
$386$	0	0
$387$	−9916.00	−1.30248
$388$	0	0
$389$	−11914.0	−1.55286	−0.776432	−	0.630202i	$-0.782972\pi$
$389$	−11914.0	−1.55286	−0.776432	+	0.630202i	$0.782972\pi$
$390$	0	0
$391$	1540.00	0.199185
$392$	0	0
$393$	18512.0	2.37610
$394$	0	0
$395$	−320.000	−0.0407619
$396$	0	0
$397$	2994.00	0.378500	0.189250	−	0.981929i	$-0.439394\pi$
$397$	2994.00	0.378500	0.189250	+	0.981929i	$0.439394\pi$
$398$	0	0
$399$	−1760.00	−0.220828
$400$	0	0
$401$	−6402.00	−0.797258	−0.398629	−	0.917112i	$-0.630514\pi$
$401$	−6402.00	−0.797258	−0.398629	+	0.917112i	$0.630514\pi$
$402$	0	0
$403$	920.000	0.113718
$404$	0	0
$405$	−1795.00	−0.220233
$406$	0	0
$407$	748.000	0.0910982
$408$	0	0
$409$	6.00000	0.000725381 0	0.000362691	−	1.00000i	$-0.499885\pi$
$409$	6.00000	0.000725381 0	0.000362691		1.00000i	$0.499885\pi$
$410$	0	0
$411$	−19152.0	−2.29854
$412$	0	0
$413$	1492.00	0.177764
$414$	0	0
$415$	4320.00	0.510989
$416$	0	0
$417$	6608.00	0.776008
$418$	0	0
$419$	1770.00	0.206373	0.103186	−	0.994662i	$-0.467096\pi$
$419$	1770.00	0.206373	0.103186	+	0.994662i	$0.467096\pi$
$420$	0	0
$421$	3638.00	0.421153	0.210576	−	0.977577i	$-0.432466\pi$
$421$	3638.00	0.421153	0.210576	+	0.977577i	$0.432466\pi$
$422$	0	0
$423$	370.000	0.0425296
$424$	0	0
$425$	250.000	0.0285336
$426$	0	0
$427$	452.000	0.0512267
$428$	0	0
$429$	1760.00	0.198074
$430$	0	0
$431$	−13492.0	−1.50786	−0.753929	−	0.656956i	$-0.771844\pi$
$431$	−13492.0	−1.50786	−0.753929	+	0.656956i	$0.771844\pi$
$432$	0	0
$433$	−4478.00	−0.496995	−0.248498	−	0.968633i	$-0.579937\pi$
$433$	−4478.00	−0.496995	−0.248498	+	0.968633i	$0.579937\pi$
$434$	0	0
$435$	−8880.00	−0.978766
$436$	0	0
$437$	−16940.0	−1.85435
$438$	0	0
$439$	6796.00	0.738851	0.369425	−	0.929260i	$-0.379555\pi$
$439$	6796.00	0.738851	0.369425	+	0.929260i	$0.379555\pi$
$440$	0	0
$441$	−12543.0	−1.35439
$442$	0	0
$443$	−7692.00	−0.824962	−0.412481	−	0.910966i	$-0.635338\pi$
$443$	−7692.00	−0.824962	−0.412481	+	0.910966i	$0.635338\pi$
$444$	0	0
$445$	−4370.00	−0.465523
$446$	0	0
$447$	18384.0	1.94526
$448$	0	0
$449$	18818.0	1.97790	0.988949	−	0.148255i	$-0.0473657\pi$
$449$	18818.0	1.97790	0.988949	+	0.148255i	$0.0473657\pi$
$450$	0	0
$451$	−8756.00	−0.914199
$452$	0	0
$453$	16960.0	1.75905
$454$	0	0
$455$	−100.000	−0.0103035
$456$	0	0
$457$	11722.0	1.19985	0.599926	−	0.800056i	$-0.295197\pi$
$457$	11722.0	1.19985	0.599926	+	0.800056i	$0.295197\pi$
$458$	0	0
$459$	−800.000	−0.0813525
$460$	0	0
$461$	6846.00	0.691649	0.345824	−	0.938299i	$-0.387599\pi$
$461$	6846.00	0.691649	0.345824	+	0.938299i	$0.387599\pi$
$462$	0	0
$463$	−13802.0	−1.38539	−0.692693	−	0.721233i	$-0.743576\pi$
$463$	−13802.0	−1.38539	−0.692693	+	0.721233i	$0.743576\pi$
$464$	0	0
$465$	−3680.00	−0.367002
$466$	0	0
$467$	−15396.0	−1.52557	−0.762786	−	0.646651i	$-0.776169\pi$
$467$	−15396.0	−1.52557	−0.762786	+	0.646651i	$0.776169\pi$
$468$	0	0
$469$	−344.000	−0.0338688
$470$	0	0
$471$	−6704.00	−0.655847
$472$	0	0
$473$	5896.00	0.573147
$474$	0	0
$475$	−2750.00	−0.265639
$476$	0	0
$477$	−21534.0	−2.06703
$478$	0	0
$479$	−14584.0	−1.39115	−0.695574	−	0.718454i	$-0.744850\pi$
$479$	−14584.0	−1.39115	−0.695574	+	0.718454i	$0.744850\pi$
$480$	0	0
$481$	−340.000	−0.0322301
$482$	0	0
$483$	2464.00	0.232124
$484$	0	0
$485$	1530.00	0.143245
$486$	0	0
$487$	6910.00	0.642961	0.321480	−	0.946916i	$-0.395820\pi$
$487$	6910.00	0.642961	0.321480	+	0.946916i	$0.395820\pi$
$488$	0	0
$489$	11520.0	1.06534
$490$	0	0
$491$	−2710.00	−0.249085	−0.124542	−	0.992214i	$-0.539746\pi$
$491$	−2710.00	−0.249085	−0.124542	+	0.992214i	$0.539746\pi$
$492$	0	0
$493$	2220.00	0.202807
$494$	0	0
$495$	−4070.00	−0.369561
$496$	0	0
$497$	1856.00	0.167511
$498$	0	0
$499$	5522.00	0.495388	0.247694	−	0.968838i	$-0.420327\pi$
$499$	5522.00	0.495388	0.247694	+	0.968838i	$0.420327\pi$
$500$	0	0
$501$	16976.0	1.51384
$502$	0	0
$503$	3450.00	0.305821	0.152910	−	0.988240i	$-0.451135\pi$
$503$	3450.00	0.305821	0.152910	+	0.988240i	$0.451135\pi$
$504$	0	0
$505$	−4650.00	−0.409747
$506$	0	0
$507$	16776.0	1.46952
$508$	0	0
$509$	4590.00	0.399702	0.199851	−	0.979826i	$-0.435954\pi$
$509$	4590.00	0.399702	0.199851	+	0.979826i	$0.435954\pi$
$510$	0	0
$511$	−1140.00	−0.0986901
$512$	0	0
$513$	8800.00	0.757367
$514$	0	0
$515$	−2310.00	−0.197652
$516$	0	0
$517$	−220.000	−0.0187149
$518$	0	0
$519$	26448.0	2.23688
$520$	0	0
$521$	7242.00	0.608978	0.304489	−	0.952516i	$-0.401514\pi$
$521$	7242.00	0.608978	0.304489	+	0.952516i	$0.401514\pi$
$522$	0	0
$523$	−2732.00	−0.228417	−0.114208	−	0.993457i	$-0.536433\pi$
$523$	−2732.00	−0.228417	−0.114208	+	0.993457i	$0.536433\pi$
$524$	0	0
$525$	400.000	0.0332522
$526$	0	0
$527$	920.000	0.0760452
$528$	0	0
$529$	11549.0	0.949207
$530$	0	0
$531$	−27602.0	−2.25579
$532$	0	0
$533$	3980.00	0.323439
$534$	0	0
$535$	7800.00	0.630324
$536$	0	0
$537$	−21968.0	−1.76534
$538$	0	0
$539$	7458.00	0.595990
$540$	0	0
$541$	2486.00	0.197563	0.0987814	−	0.995109i	$-0.468506\pi$
$541$	2486.00	0.197563	0.0987814	+	0.995109i	$0.468506\pi$
$542$	0	0
$543$	−32496.0	−2.56821
$544$	0	0
$545$	−5930.00	−0.466079
$546$	0	0
$547$	−11860.0	−0.927051	−0.463526	−	0.886084i	$-0.653416\pi$
$547$	−11860.0	−0.927051	−0.463526	+	0.886084i	$0.653416\pi$
$548$	0	0
$549$	−8362.00	−0.650057
$550$	0	0
$551$	−24420.0	−1.88807
$552$	0	0
$553$	128.000	0.00984288
$554$	0	0
$555$	1360.00	0.104016
$556$	0	0
$557$	−23546.0	−1.79116	−0.895580	−	0.444901i	$-0.853239\pi$
$557$	−23546.0	−1.79116	−0.895580	+	0.444901i	$0.853239\pi$
$558$	0	0
$559$	−2680.00	−0.202776
$560$	0	0
$561$	1760.00	0.132455
$562$	0	0
$563$	−11792.0	−0.882724	−0.441362	−	0.897329i	$-0.645505\pi$
$563$	−11792.0	−0.882724	−0.441362	+	0.897329i	$0.645505\pi$
$564$	0	0
$565$	−6910.00	−0.514524
$566$	0	0
$567$	718.000	0.0531802
$568$	0	0
$569$	3702.00	0.272752	0.136376	−	0.990657i	$-0.456454\pi$
$569$	3702.00	0.272752	0.136376	+	0.990657i	$0.456454\pi$
$570$	0	0
$571$	12170.0	0.891942	0.445971	−	0.895048i	$-0.352859\pi$
$571$	12170.0	0.891942	0.445971	+	0.895048i	$0.352859\pi$
$572$	0	0
$573$	−15264.0	−1.11285
$574$	0	0
$575$	3850.00	0.279228
$576$	0	0
$577$	−6526.00	−0.470851	−0.235425	−	0.971892i	$-0.575648\pi$
$577$	−6526.00	−0.470851	−0.235425	+	0.971892i	$0.575648\pi$
$578$	0	0
$579$	22064.0	1.58368
$580$	0	0
$581$	−1728.00	−0.123390
$582$	0	0
$583$	12804.0	0.909584
$584$	0	0
$585$	1850.00	0.130749
$586$	0	0
$587$	−2624.00	−0.184504	−0.0922522	−	0.995736i	$-0.529407\pi$
$587$	−2624.00	−0.184504	−0.0922522	+	0.995736i	$0.529407\pi$
$588$	0	0
$589$	−10120.0	−0.707958
$590$	0	0
$591$	−34576.0	−2.40654
$592$	0	0
$593$	17218.0	1.19234	0.596171	−	0.802858i	$-0.296688\pi$
$593$	17218.0	1.19234	0.596171	+	0.802858i	$0.296688\pi$
$594$	0	0
$595$	−100.000	−0.00689008
$596$	0	0
$597$	−22816.0	−1.56415
$598$	0	0
$599$	−14236.0	−0.971064	−0.485532	−	0.874219i	$-0.661374\pi$
$599$	−14236.0	−0.971064	−0.485532	+	0.874219i	$0.661374\pi$
$600$	0	0
$601$	−19030.0	−1.29160	−0.645799	−	0.763508i	$-0.723475\pi$
$601$	−19030.0	−1.29160	−0.645799	+	0.763508i	$0.723475\pi$
$602$	0	0
$603$	6364.00	0.429788
$604$	0	0
$605$	−4235.00	−0.284590
$606$	0	0
$607$	−1966.00	−0.131462	−0.0657310	−	0.997837i	$-0.520938\pi$
$607$	−1966.00	−0.131462	−0.0657310	+	0.997837i	$0.520938\pi$
$608$	0	0
$609$	3552.00	0.236345
$610$	0	0
$611$	100.000	0.00662122
$612$	0	0
$613$	−16518.0	−1.08835	−0.544173	−	0.838973i	$-0.683156\pi$
$613$	−16518.0	−1.08835	−0.544173	+	0.838973i	$0.683156\pi$
$614$	0	0
$615$	−15920.0	−1.04383
$616$	0	0
$617$	17954.0	1.17148	0.585738	−	0.810500i	$-0.300805\pi$
$617$	17954.0	1.17148	0.585738	+	0.810500i	$0.300805\pi$
$618$	0	0
$619$	2494.00	0.161942	0.0809712	−	0.996716i	$-0.474198\pi$
$619$	2494.00	0.161942	0.0809712	+	0.996716i	$0.474198\pi$
$620$	0	0
$621$	−12320.0	−0.796110
$622$	0	0
$623$	1748.00	0.112411
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−19360.0	−1.23312
$628$	0	0
$629$	−340.000	−0.0215528
$630$	0	0
$631$	10600.0	0.668747	0.334373	−	0.942441i	$-0.391475\pi$
$631$	10600.0	0.668747	0.334373	+	0.942441i	$0.391475\pi$
$632$	0	0
$633$	−34480.0	−2.16502
$634$	0	0
$635$	−5990.00	−0.374340
$636$	0	0
$637$	−3390.00	−0.210858
$638$	0	0
$639$	−34336.0	−2.12568
$640$	0	0
$641$	4386.00	0.270260	0.135130	−	0.990828i	$-0.456855\pi$
$641$	4386.00	0.270260	0.135130	+	0.990828i	$0.456855\pi$
$642$	0	0
$643$	22128.0	1.35714	0.678572	−	0.734534i	$-0.262599\pi$
$643$	22128.0	1.35714	0.678572	+	0.734534i	$0.262599\pi$
$644$	0	0
$645$	10720.0	0.654418
$646$	0	0
$647$	−5650.00	−0.343314	−0.171657	−	0.985157i	$-0.554912\pi$
$647$	−5650.00	−0.343314	−0.171657	+	0.985157i	$0.554912\pi$
$648$	0	0
$649$	16412.0	0.992646
$650$	0	0
$651$	1472.00	0.0886209
$652$	0	0
$653$	−15238.0	−0.913184	−0.456592	−	0.889676i	$-0.650930\pi$
$653$	−15238.0	−0.913184	−0.456592	+	0.889676i	$0.650930\pi$
$654$	0	0
$655$	−11570.0	−0.690194
$656$	0	0
$657$	21090.0	1.25236
$658$	0	0
$659$	−13318.0	−0.787247	−0.393623	−	0.919272i	$-0.628779\pi$
$659$	−13318.0	−0.787247	−0.393623	+	0.919272i	$0.628779\pi$
$660$	0	0
$661$	5838.00	0.343528	0.171764	−	0.985138i	$-0.445053\pi$
$661$	5838.00	0.343528	0.171764	+	0.985138i	$0.445053\pi$
$662$	0	0
$663$	−800.000	−0.0468619
$664$	0	0
$665$	1100.00	0.0641446
$666$	0	0
$667$	34188.0	1.98465
$668$	0	0
$669$	−21936.0	−1.26771
$670$	0	0
$671$	4972.00	0.286054
$672$	0	0
$673$	74.0000	0.00423847	0.00211924	−	0.999998i	$-0.499325\pi$
$673$	74.0000	0.00423847	0.00211924	+	0.999998i	$0.499325\pi$
$674$	0	0
$675$	−2000.00	−0.114044
$676$	0	0
$677$	6194.00	0.351632	0.175816	−	0.984423i	$-0.443744\pi$
$677$	6194.00	0.351632	0.175816	+	0.984423i	$0.443744\pi$
$678$	0	0
$679$	−612.000	−0.0345897
$680$	0	0
$681$	−15456.0	−0.869714
$682$	0	0
$683$	−23532.0	−1.31834	−0.659171	−	0.751993i	$-0.729092\pi$
$683$	−23532.0	−1.31834	−0.659171	+	0.751993i	$0.729092\pi$
$684$	0	0
$685$	11970.0	0.667665
$686$	0	0
$687$	48912.0	2.71632
$688$	0	0
$689$	−5820.00	−0.321806
$690$	0	0
$691$	−18530.0	−1.02014	−0.510068	−	0.860134i	$-0.670380\pi$
$691$	−18530.0	−1.02014	−0.510068	+	0.860134i	$0.670380\pi$
$692$	0	0
$693$	1628.00	0.0892390
$694$	0	0
$695$	−4130.00	−0.225410
$696$	0	0
$697$	3980.00	0.216289
$698$	0	0
$699$	−5520.00	−0.298692
$700$	0	0
$701$	5142.00	0.277048	0.138524	−	0.990359i	$-0.455764\pi$
$701$	5142.00	0.277048	0.138524	+	0.990359i	$0.455764\pi$
$702$	0	0
$703$	3740.00	0.200650
$704$	0	0
$705$	−400.000	−0.0213686
$706$	0	0
$707$	1860.00	0.0989427
$708$	0	0
$709$	21438.0	1.13557	0.567786	−	0.823176i	$-0.307800\pi$
$709$	21438.0	1.13557	0.567786	+	0.823176i	$0.307800\pi$
$710$	0	0
$711$	−2368.00	−0.124904
$712$	0	0
$713$	14168.0	0.744174
$714$	0	0
$715$	−1100.00	−0.0575352
$716$	0	0
$717$	−10112.0	−0.526694
$718$	0	0
$719$	2624.00	0.136104	0.0680519	−	0.997682i	$-0.478322\pi$
$719$	2624.00	0.136104	0.0680519	+	0.997682i	$0.478322\pi$
$720$	0	0
$721$	924.000	0.0477275
$722$	0	0
$723$	25968.0	1.33577
$724$	0	0
$725$	5550.00	0.284306
$726$	0	0
$727$	−9410.00	−0.480052	−0.240026	−	0.970766i	$-0.577156\pi$
$727$	−9410.00	−0.480052	−0.240026	+	0.970766i	$0.577156\pi$
$728$	0	0
$729$	−30563.0	−1.55276
$730$	0	0
$731$	−2680.00	−0.135600
$732$	0	0
$733$	19142.0	0.964565	0.482282	−	0.876016i	$-0.339808\pi$
$733$	19142.0	0.964565	0.482282	+	0.876016i	$0.339808\pi$
$734$	0	0
$735$	13560.0	0.680501
$736$	0	0
$737$	−3784.00	−0.189125
$738$	0	0
$739$	2930.00	0.145848	0.0729241	−	0.997337i	$-0.476767\pi$
$739$	2930.00	0.145848	0.0729241	+	0.997337i	$0.476767\pi$
$740$	0	0
$741$	8800.00	0.436270
$742$	0	0
$743$	20250.0	0.999866	0.499933	−	0.866064i	$-0.333358\pi$
$743$	20250.0	0.999866	0.499933	+	0.866064i	$0.333358\pi$
$744$	0	0
$745$	−11490.0	−0.565048
$746$	0	0
$747$	31968.0	1.56579
$748$	0	0
$749$	−3120.00	−0.152206
$750$	0	0
$751$	−1916.00	−0.0930970	−0.0465485	−	0.998916i	$-0.514822\pi$
$751$	−1916.00	−0.0930970	−0.0465485	+	0.998916i	$0.514822\pi$
$752$	0	0
$753$	19376.0	0.937717
$754$	0	0
$755$	−10600.0	−0.510958
$756$	0	0
$757$	20494.0	0.983972	0.491986	−	0.870603i	$-0.336271\pi$
$757$	20494.0	0.983972	0.491986	+	0.870603i	$0.336271\pi$
$758$	0	0
$759$	27104.0	1.29620
$760$	0	0
$761$	14826.0	0.706231	0.353116	−	0.935580i	$-0.385122\pi$
$761$	14826.0	0.706231	0.353116	+	0.935580i	$0.385122\pi$
$762$	0	0
$763$	2372.00	0.112545
$764$	0	0
$765$	1850.00	0.0874338
$766$	0	0
$767$	−7460.00	−0.351193
$768$	0	0
$769$	−39194.0	−1.83793	−0.918967	−	0.394334i	$-0.870975\pi$
$769$	−39194.0	−1.83793	−0.918967	+	0.394334i	$0.870975\pi$
$770$	0	0
$771$	9264.00	0.432730
$772$	0	0
$773$	−35862.0	−1.66865	−0.834325	−	0.551273i	$-0.814142\pi$
$773$	−35862.0	−1.66865	−0.834325	+	0.551273i	$0.814142\pi$
$774$	0	0
$775$	2300.00	0.106604
$776$	0	0
$777$	−544.000	−0.0251170
$778$	0	0
$779$	−43780.0	−2.01358
$780$	0	0
$781$	20416.0	0.935393
$782$	0	0
$783$	−17760.0	−0.810588
$784$	0	0
$785$	4190.00	0.190506
$786$	0	0
$787$	−23060.0	−1.04447	−0.522236	−	0.852801i	$-0.674902\pi$
$787$	−23060.0	−1.04447	−0.522236	+	0.852801i	$0.674902\pi$
$788$	0	0
$789$	24304.0	1.09664
$790$	0	0
$791$	2764.00	0.124243
$792$	0	0
$793$	−2260.00	−0.101204
$794$	0	0
$795$	23280.0	1.03856
$796$	0	0
$797$	40466.0	1.79847	0.899234	−	0.437468i	$-0.144125\pi$
$797$	40466.0	1.79847	0.899234	+	0.437468i	$0.144125\pi$
$798$	0	0
$799$	100.000	0.00442772
$800$	0	0
$801$	−32338.0	−1.42648
$802$	0	0
$803$	−12540.0	−0.551092
$804$	0	0
$805$	−1540.00	−0.0674259
$806$	0	0
$807$	−30768.0	−1.34211
$808$	0	0
$809$	36090.0	1.56843	0.784213	−	0.620492i	$-0.213067\pi$
$809$	36090.0	1.56843	0.784213	+	0.620492i	$0.213067\pi$
$810$	0	0
$811$	−12022.0	−0.520530	−0.260265	−	0.965537i	$-0.583810\pi$
$811$	−12022.0	−0.520530	−0.260265	+	0.965537i	$0.583810\pi$
$812$	0	0
$813$	52896.0	2.28185
$814$	0	0
$815$	−7200.00	−0.309454
$816$	0	0
$817$	29480.0	1.26239
$818$	0	0
$819$	−740.000	−0.0315723
$820$	0	0
$821$	−15250.0	−0.648269	−0.324134	−	0.946011i	$-0.605073\pi$
$821$	−15250.0	−0.648269	−0.324134	+	0.946011i	$0.605073\pi$
$822$	0	0
$823$	45970.0	1.94704	0.973520	−	0.228603i	$-0.0734158\pi$
$823$	45970.0	1.94704	0.973520	+	0.228603i	$0.0734158\pi$
$824$	0	0
$825$	4400.00	0.185683
$826$	0	0
$827$	8160.00	0.343109	0.171554	−	0.985175i	$-0.445121\pi$
$827$	8160.00	0.343109	0.171554	+	0.985175i	$0.445121\pi$
$828$	0	0
$829$	−82.0000	−0.00343544	−0.00171772	−	0.999999i	$-0.500547\pi$
$829$	−82.0000	−0.00343544	−0.00171772	+	0.999999i	$0.500547\pi$
$830$	0	0
$831$	58512.0	2.44255
$832$	0	0
$833$	−3390.00	−0.141004
$834$	0	0
$835$	−10610.0	−0.439730
$836$	0	0
$837$	−7360.00	−0.303941
$838$	0	0
$839$	46796.0	1.92560	0.962799	−	0.270217i	$-0.0870955\pi$
$839$	46796.0	1.92560	0.962799	+	0.270217i	$0.0870955\pi$
$840$	0	0
$841$	24895.0	1.02075
$842$	0	0
$843$	16816.0	0.687039
$844$	0	0
$845$	−10485.0	−0.426858
$846$	0	0
$847$	1694.00	0.0687208
$848$	0	0
$849$	−36960.0	−1.49407
$850$	0	0
$851$	−5236.00	−0.210914
$852$	0	0
$853$	−18566.0	−0.745238	−0.372619	−	0.927984i	$-0.621540\pi$
$853$	−18566.0	−0.745238	−0.372619	+	0.927984i	$0.621540\pi$
$854$	0	0
$855$	−20350.0	−0.813983
$856$	0	0
$857$	21266.0	0.847646	0.423823	−	0.905745i	$-0.360688\pi$
$857$	21266.0	0.847646	0.423823	+	0.905745i	$0.360688\pi$
$858$	0	0
$859$	−22106.0	−0.878052	−0.439026	−	0.898474i	$-0.644676\pi$
$859$	−22106.0	−0.878052	−0.439026	+	0.898474i	$0.644676\pi$
$860$	0	0
$861$	6368.00	0.252057
$862$	0	0
$863$	6150.00	0.242582	0.121291	−	0.992617i	$-0.461297\pi$
$863$	6150.00	0.242582	0.121291	+	0.992617i	$0.461297\pi$
$864$	0	0
$865$	−16530.0	−0.649754
$866$	0	0
$867$	38504.0	1.50826
$868$	0	0
$869$	1408.00	0.0549633
$870$	0	0
$871$	1720.00	0.0669116
$872$	0	0
$873$	11322.0	0.438937
$874$	0	0
$875$	−250.000	−0.00965891
$876$	0	0
$877$	48038.0	1.84963	0.924816	−	0.380414i	$-0.124218\pi$
$877$	48038.0	1.84963	0.924816	+	0.380414i	$0.124218\pi$
$878$	0	0
$879$	32144.0	1.23344
$880$	0	0
$881$	34750.0	1.32890	0.664448	−	0.747335i	$-0.268667\pi$
$881$	34750.0	1.32890	0.664448	+	0.747335i	$0.268667\pi$
$882$	0	0
$883$	−46608.0	−1.77631	−0.888156	−	0.459541i	$-0.848014\pi$
$883$	−46608.0	−1.77631	−0.888156	+	0.459541i	$0.848014\pi$
$884$	0	0
$885$	29840.0	1.13340
$886$	0	0
$887$	−33906.0	−1.28349	−0.641743	−	0.766920i	$-0.721788\pi$
$887$	−33906.0	−1.28349	−0.641743	+	0.766920i	$0.721788\pi$
$888$	0	0
$889$	2396.00	0.0903929
$890$	0	0
$891$	7898.00	0.296962
$892$	0	0
$893$	−1100.00	−0.0412207
$894$	0	0
$895$	13730.0	0.512786
$896$	0	0
$897$	−12320.0	−0.458587
$898$	0	0
$899$	20424.0	0.757707
$900$	0	0
$901$	−5820.00	−0.215197
$902$	0	0
$903$	−4288.00	−0.158024
$904$	0	0
$905$	20310.0	0.745997
$906$	0	0
$907$	46256.0	1.69339	0.846695	−	0.532078i	$-0.178589\pi$
$907$	46256.0	1.69339	0.846695	+	0.532078i	$0.178589\pi$
$908$	0	0
$909$	−34410.0	−1.25556
$910$	0	0
$911$	−52092.0	−1.89450	−0.947248	−	0.320503i	$-0.896148\pi$
$911$	−52092.0	−1.89450	−0.947248	+	0.320503i	$0.896148\pi$
$912$	0	0
$913$	−19008.0	−0.689018
$914$	0	0
$915$	9040.00	0.326615
$916$	0	0
$917$	4628.00	0.166663
$918$	0	0
$919$	19988.0	0.717457	0.358729	−	0.933442i	$-0.383210\pi$
$919$	19988.0	0.717457	0.358729	+	0.933442i	$0.383210\pi$
$920$	0	0
$921$	−68768.0	−2.46035
$922$	0	0
$923$	−9280.00	−0.330937
$924$	0	0
$925$	−850.000	−0.0302139
$926$	0	0
$927$	−17094.0	−0.605653
$928$	0	0
$929$	−31950.0	−1.12836	−0.564179	−	0.825652i	$-0.690807\pi$
$929$	−31950.0	−1.12836	−0.564179	+	0.825652i	$0.690807\pi$
$930$	0	0
$931$	37290.0	1.31271
$932$	0	0
$933$	10496.0	0.368300
$934$	0	0
$935$	−1100.00	−0.0384747
$936$	0	0
$937$	18874.0	0.658043	0.329022	−	0.944322i	$-0.393281\pi$
$937$	18874.0	0.658043	0.329022	+	0.944322i	$0.393281\pi$
$938$	0	0
$939$	−9232.00	−0.320847
$940$	0	0
$941$	24038.0	0.832749	0.416374	−	0.909193i	$-0.363301\pi$
$941$	24038.0	0.832749	0.416374	+	0.909193i	$0.363301\pi$
$942$	0	0
$943$	61292.0	2.11659
$944$	0	0
$945$	800.000	0.0275386
$946$	0	0
$947$	11316.0	0.388301	0.194150	−	0.980972i	$-0.437805\pi$
$947$	11316.0	0.388301	0.194150	+	0.980972i	$0.437805\pi$
$948$	0	0
$949$	5700.00	0.194973
$950$	0	0
$951$	58096.0	1.98096
$952$	0	0
$953$	−48390.0	−1.64481	−0.822406	−	0.568901i	$-0.807369\pi$
$953$	−48390.0	−1.64481	−0.822406	+	0.568901i	$0.807369\pi$
$954$	0	0
$955$	9540.00	0.323254
$956$	0	0
$957$	39072.0	1.31977
$958$	0	0
$959$	−4788.00	−0.161223
$960$	0	0
$961$	−21327.0	−0.715887
$962$	0	0
$963$	57720.0	1.93147
$964$	0	0
$965$	−13790.0	−0.460016
$966$	0	0
$967$	21126.0	0.702551	0.351275	−	0.936272i	$-0.385748\pi$
$967$	21126.0	0.702551	0.351275	+	0.936272i	$0.385748\pi$
$968$	0	0
$969$	8800.00	0.291741
$970$	0	0
$971$	−42894.0	−1.41765	−0.708823	−	0.705387i	$-0.750773\pi$
$971$	−42894.0	−1.41765	−0.708823	+	0.705387i	$0.750773\pi$
$972$	0	0
$973$	1652.00	0.0544303
$974$	0	0
$975$	−2000.00	−0.0656936
$976$	0	0
$977$	9594.00	0.314165	0.157083	−	0.987585i	$-0.449791\pi$
$977$	9594.00	0.314165	0.157083	+	0.987585i	$0.449791\pi$
$978$	0	0
$979$	19228.0	0.627711
$980$	0	0
$981$	−43882.0	−1.42818
$982$	0	0
$983$	−55742.0	−1.80864	−0.904320	−	0.426855i	$-0.859622\pi$
$983$	−55742.0	−1.80864	−0.904320	+	0.426855i	$0.859622\pi$
$984$	0	0
$985$	21610.0	0.699037
$986$	0	0
$987$	160.000	0.00515994
$988$	0	0
$989$	−41272.0	−1.32697
$990$	0	0
$991$	11788.0	0.377859	0.188929	−	0.981991i	$-0.439498\pi$
$991$	11788.0	0.377859	0.188929	+	0.981991i	$0.439498\pi$
$992$	0	0
$993$	−24784.0	−0.792041
$994$	0	0
$995$	14260.0	0.454344
$996$	0	0
$997$	5074.00	0.161179	0.0805894	−	0.996747i	$-0.474320\pi$
$997$	5074.00	0.161179	0.0805894	+	0.996747i	$0.474320\pi$
$998$	0	0
$999$	2720.00	0.0861431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.4.a.b.1.1	yes	1
4.3	odd	2		640.4.a.d.1.1	yes	1
8.3	odd	2		640.4.a.a.1.1	✓	1
8.5	even	2		640.4.a.c.1.1	yes	1
16.3	odd	4		1280.4.d.h.641.2		2
16.5	even	4		1280.4.d.i.641.2		2
16.11	odd	4		1280.4.d.h.641.1		2
16.13	even	4		1280.4.d.i.641.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.4.a.a.1.1	✓	1	8.3	odd	2
640.4.a.b.1.1	yes	1	1.1	even	1	trivial
640.4.a.c.1.1	yes	1	8.5	even	2
640.4.a.d.1.1	yes	1	4.3	odd	2
1280.4.d.h.641.1		2	16.11	odd	4
1280.4.d.h.641.2		2	16.3	odd	4
1280.4.d.i.641.1		2	16.13	even	4
1280.4.d.i.641.2		2	16.5	even	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	640.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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