LMFDB - Embedded newform 7600.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7600,2,Mod(1,7600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7600, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7600.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7600 = 2^{4} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7600.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:	$60.6863055362$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7600.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} -5.00000 q^{7} +6.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} -5.00000 q^{7} +6.00000 q^{9} +4.00000 q^{11} +1.00000 q^{13} +3.00000 q^{17} -1.00000 q^{19} +15.0000 q^{21} +7.00000 q^{23} -9.00000 q^{27} -3.00000 q^{29} +2.00000 q^{31} -12.0000 q^{33} +2.00000 q^{37} -3.00000 q^{39} -6.00000 q^{41} +6.00000 q^{43} +18.0000 q^{49} -9.00000 q^{51} +13.0000 q^{53} +3.00000 q^{57} +9.00000 q^{59} -12.0000 q^{61} -30.0000 q^{63} -3.00000 q^{67} -21.0000 q^{69} -11.0000 q^{73} -20.0000 q^{77} +2.00000 q^{79} +9.00000 q^{81} -10.0000 q^{83} +9.00000 q^{87} +2.00000 q^{89} -5.00000 q^{91} -6.00000 q^{93} +2.00000 q^{97} +24.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	0	0
$9$	6.00000	2.00000
$10$	0	0
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	15.0000	3.27327
$22$	0	0
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−9.00000	−1.73205
$28$	0	0
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	0	0
$33$	−12.0000	−2.08893
$34$	0	0
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	0	0
$51$	−9.00000	−1.26025
$52$	0	0
$53$	13.0000	1.78569	0.892844	−	0.450367i	$-0.148707\pi$
$53$	13.0000	1.78569	0.892844	+	0.450367i	$0.148707\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	3.00000	0.397360
$58$	0	0
$59$	9.00000	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$60$	0	0
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	0	0
$63$	−30.0000	−3.77964
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	0	0
$69$	−21.0000	−2.52810
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−20.0000	−2.27921
$78$	0	0
$79$	2.00000	0.225018	0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000	0.225018	0.112509	+	0.993651i	$0.464111\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	9.00000	0.964901
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	0	0
$93$	−6.00000	−0.622171
$94$	0	0
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	24.0000	2.41209
$100$	0	0
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−13.0000	−1.25676	−0.628379	−	0.777908i	$-0.716281\pi$
$107$	−13.0000	−1.25676	−0.628379	+	0.777908i	$0.716281\pi$
$108$	0	0
$109$	19.0000	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	6.00000	0.554700
$118$	0	0
$119$	−15.0000	−1.37505
$120$	0	0
$121$	5.00000	0.454545
$122$	0	0
$123$	18.0000	1.62301
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	0	0
$129$	−18.0000	−1.58481
$130$	0	0
$131$	−16.0000	−1.39793	−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000	−1.39793	−0.698963	+	0.715158i	$0.746355\pi$
$132$	0	0
$133$	5.00000	0.433555
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	4.00000	0.334497
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−54.0000	−4.45384
$148$	0	0
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	18.0000	1.45521
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	0	0
$159$	−39.0000	−3.09290
$160$	0	0
$161$	−35.0000	−2.75839
$162$	0	0
$163$	22.0000	1.72317	0.861586	−	0.507611i	$-0.169471\pi$
$163$	22.0000	1.72317	0.861586	+	0.507611i	$0.169471\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−6.00000	−0.458831
$172$	0	0
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−27.0000	−2.02944
$178$	0	0
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0	0
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	0	0
$183$	36.0000	2.66120
$184$	0	0
$185$	0	0
$186$	0	0
$187$	12.0000	0.877527
$188$	0	0
$189$	45.0000	3.27327
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	0	0
$199$	15.0000	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$199$	15.0000	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$200$	0	0
$201$	9.00000	0.634811
$202$	0	0
$203$	15.0000	1.05279
$204$	0	0
$205$	0	0
$206$	0	0
$207$	42.0000	2.91920
$208$	0	0
$209$	−4.00000	−0.276686
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	0	0
$219$	33.0000	2.22993
$220$	0	0
$221$	3.00000	0.201802
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	5.00000	0.331862	0.165931	−	0.986137i	$-0.446937\pi$
$227$	5.00000	0.331862	0.165931	+	0.986137i	$0.446937\pi$
$228$	0	0
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	60.0000	3.94771
$232$	0	0
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−6.00000	−0.389742
$238$	0	0
$239$	11.0000	0.711531	0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000	0.711531	0.355765	+	0.934575i	$0.384220\pi$
$240$	0	0
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	0	0
$249$	30.0000	1.90117
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	28.0000	1.76034
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	0	0
$261$	−18.0000	−1.11417
$262$	0	0
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6.00000	−0.367194
$268$	0	0
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	0	0
$271$	27.0000	1.64013	0.820067	−	0.572268i	$-0.193936\pi$
$271$	27.0000	1.64013	0.820067	+	0.572268i	$0.193936\pi$
$272$	0	0
$273$	15.0000	0.907841
$274$	0	0
$275$	0	0
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	0	0
$279$	12.0000	0.718421
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	30.0000	1.77084
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−6.00000	−0.351726
$292$	0	0
$293$	27.0000	1.57736	0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000	1.57736	0.788678	+	0.614806i	$0.210766\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−36.0000	−2.08893
$298$	0	0
$299$	7.00000	0.404820
$300$	0	0
$301$	−30.0000	−1.72917
$302$	0	0
$303$	24.0000	1.37876
$304$	0	0
$305$	0	0
$306$	0	0
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	0	0
$311$	−25.0000	−1.41762	−0.708810	−	0.705399i	$-0.750768\pi$
$311$	−25.0000	−1.41762	−0.708810	+	0.705399i	$0.750768\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−9.00000	−0.505490	−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000	−0.505490	−0.252745	+	0.967533i	$0.581333\pi$
$318$	0	0
$319$	−12.0000	−0.671871
$320$	0	0
$321$	39.0000	2.17677
$322$	0	0
$323$	−3.00000	−0.166924
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−57.0000	−3.15211
$328$	0	0
$329$	0	0
$330$	0	0
$331$	7.00000	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$332$	0	0
$333$	12.0000	0.657596
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	−55.0000	−2.96972
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−9.00000	−0.480384
$352$	0	0
$353$	−7.00000	−0.372572	−0.186286	−	0.982496i	$-0.559645\pi$
$353$	−7.00000	−0.372572	−0.186286	+	0.982496i	$0.559645\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	45.0000	2.38165
$358$	0	0
$359$	5.00000	0.263890	0.131945	−	0.991257i	$-0.457878\pi$
$359$	5.00000	0.263890	0.131945	+	0.991257i	$0.457878\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	0	0
$363$	−15.0000	−0.787296
$364$	0	0
$365$	0	0
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	−36.0000	−1.87409
$370$	0	0
$371$	−65.0000	−3.37463
$372$	0	0
$373$	23.0000	1.19089	0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000	1.19089	0.595447	+	0.803394i	$0.296975\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.00000	−0.154508
$378$	0	0
$379$	33.0000	1.69510	0.847548	−	0.530719i	$-0.178078\pi$
$379$	33.0000	1.69510	0.847548	+	0.530719i	$0.178078\pi$
$380$	0	0
$381$	18.0000	0.922168
$382$	0	0
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	36.0000	1.82998
$388$	0	0
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	0	0
$391$	21.0000	1.06202
$392$	0	0
$393$	48.0000	2.42128
$394$	0	0
$395$	0	0
$396$	0	0
$397$	16.0000	0.803017	0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000	0.803017	0.401508	+	0.915855i	$0.368486\pi$
$398$	0	0
$399$	−15.0000	−0.750939
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	2.00000	0.0996271
$404$	0	0
$405$	0	0
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	0	0
$411$	27.0000	1.33181
$412$	0	0
$413$	−45.0000	−2.21431
$414$	0	0
$415$	0	0
$416$	0	0
$417$	48.0000	2.35057
$418$	0	0
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	60.0000	2.90360
$428$	0	0
$429$	−12.0000	−0.579365
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	0	0
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−7.00000	−0.334855
$438$	0	0
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	0	0
$441$	108.000	5.14286
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	12.0000	0.567581
$448$	0	0
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	0	0
$451$	−24.0000	−1.13012
$452$	0	0
$453$	−30.0000	−1.40952
$454$	0	0
$455$	0	0
$456$	0	0
$457$	29.0000	1.35656	0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000	1.35656	0.678281	+	0.734802i	$0.262725\pi$
$458$	0	0
$459$	−27.0000	−1.26025
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	15.0000	0.692636
$470$	0	0
$471$	18.0000	0.829396
$472$	0	0
$473$	24.0000	1.10352
$474$	0	0
$475$	0	0
$476$	0	0
$477$	78.0000	3.57137
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	0	0
$483$	105.000	4.77767
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	0	0
$489$	−66.0000	−2.98462
$490$	0	0
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	0	0
$493$	−9.00000	−0.405340
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−42.0000	−1.88018	−0.940089	−	0.340929i	$-0.889258\pi$
$499$	−42.0000	−1.88018	−0.940089	+	0.340929i	$0.889258\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	0	0
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	36.0000	1.59882
$508$	0	0
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	55.0000	2.43306
$512$	0	0
$513$	9.00000	0.397360
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−42.0000	−1.84360
$520$	0	0
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	0	0
$523$	−9.00000	−0.393543	−0.196771	−	0.980449i	$-0.563046\pi$
$523$	−9.00000	−0.393543	−0.196771	+	0.980449i	$0.563046\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	6.00000	0.261364
$528$	0	0
$529$	26.0000	1.13043
$530$	0	0
$531$	54.0000	2.34340
$532$	0	0
$533$	−6.00000	−0.259889
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−24.0000	−1.03568
$538$	0	0
$539$	72.0000	3.10126
$540$	0	0
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	0	0
$543$	−78.0000	−3.34730
$544$	0	0
$545$	0	0
$546$	0	0
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	0	0
$549$	−72.0000	−3.07289
$550$	0	0
$551$	3.00000	0.127804
$552$	0	0
$553$	−10.0000	−0.425243
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	6.00000	0.253773
$560$	0	0
$561$	−36.0000	−1.51992
$562$	0	0
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−45.0000	−1.88982
$568$	0	0
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	−6.00000	−0.251092	−0.125546	−	0.992088i	$-0.540068\pi$
$571$	−6.00000	−0.251092	−0.125546	+	0.992088i	$0.540068\pi$
$572$	0	0
$573$	27.0000	1.12794
$574$	0	0
$575$	0	0
$576$	0	0
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	0	0
$579$	30.0000	1.24676
$580$	0	0
$581$	50.0000	2.07435
$582$	0	0
$583$	52.0000	2.15362
$584$	0	0
$585$	0	0
$586$	0	0
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	−66.0000	−2.71488
$592$	0	0
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−45.0000	−1.84173
$598$	0	0
$599$	26.0000	1.06233	0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000	1.06233	0.531166	+	0.847268i	$0.321754\pi$
$600$	0	0
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	0	0
$603$	−18.0000	−0.733017
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	0	0
$609$	−45.0000	−1.82349
$610$	0	0
$611$	0	0
$612$	0	0
$613$	20.0000	0.807792	0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000	0.807792	0.403896	+	0.914805i	$0.367656\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	0	0
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	0	0
$621$	−63.0000	−2.52810
$622$	0	0
$623$	−10.0000	−0.400642
$624$	0	0
$625$	0	0
$626$	0	0
$627$	12.0000	0.479234
$628$	0	0
$629$	6.00000	0.239236
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	−15.0000	−0.596196
$634$	0	0
$635$	0	0
$636$	0	0
$637$	18.0000	0.713186
$638$	0	0
$639$	0	0
$640$	0	0
$641$	8.00000	0.315981	0.157991	−	0.987441i	$-0.449498\pi$
$641$	8.00000	0.315981	0.157991	+	0.987441i	$0.449498\pi$
$642$	0	0
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	0	0
$649$	36.0000	1.41312
$650$	0	0
$651$	30.0000	1.17579
$652$	0	0
$653$	16.0000	0.626128	0.313064	−	0.949732i	$-0.398644\pi$
$653$	16.0000	0.626128	0.313064	+	0.949732i	$0.398644\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−66.0000	−2.57491
$658$	0	0
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	0	0
$661$	15.0000	0.583432	0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000	0.583432	0.291716	+	0.956505i	$0.405774\pi$
$662$	0	0
$663$	−9.00000	−0.349531
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−21.0000	−0.813123
$668$	0	0
$669$	6.00000	0.231973
$670$	0	0
$671$	−48.0000	−1.85302
$672$	0	0
$673$	44.0000	1.69608	0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000	1.69608	0.848038	+	0.529936i	$0.177784\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	39.0000	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$678$	0	0
$679$	−10.0000	−0.383765
$680$	0	0
$681$	−15.0000	−0.574801
$682$	0	0
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	18.0000	0.686743
$688$	0	0
$689$	13.0000	0.495261
$690$	0	0
$691$	42.0000	1.59776	0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000	1.59776	0.798878	+	0.601494i	$0.205427\pi$
$692$	0	0
$693$	−120.000	−4.55842
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−18.0000	−0.681799
$698$	0	0
$699$	30.0000	1.13470
$700$	0	0
$701$	24.0000	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	0	0
$707$	40.0000	1.50435
$708$	0	0
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	0	0
$713$	14.0000	0.524304
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−33.0000	−1.23241
$718$	0	0
$719$	27.0000	1.00693	0.503465	−	0.864016i	$-0.332058\pi$
$719$	27.0000	1.00693	0.503465	+	0.864016i	$0.332058\pi$
$720$	0	0
$721$	−20.0000	−0.744839
$722$	0	0
$723$	36.0000	1.33885
$724$	0	0
$725$	0	0
$726$	0	0
$727$	23.0000	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	18.0000	0.665754
$732$	0	0
$733$	−36.0000	−1.32969	−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000	−1.32969	−0.664845	+	0.746981i	$0.731502\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−12.0000	−0.442026
$738$	0	0
$739$	10.0000	0.367856	0.183928	−	0.982940i	$-0.441119\pi$
$739$	10.0000	0.367856	0.183928	+	0.982940i	$0.441119\pi$
$740$	0	0
$741$	3.00000	0.110208
$742$	0	0
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−60.0000	−2.19529
$748$	0	0
$749$	65.0000	2.37505
$750$	0	0
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	0	0
$753$	−36.0000	−1.31191
$754$	0	0
$755$	0	0
$756$	0	0
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	0	0
$759$	−84.0000	−3.04901
$760$	0	0
$761$	11.0000	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$761$	11.0000	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$762$	0	0
$763$	−95.0000	−3.43923
$764$	0	0
$765$	0	0
$766$	0	0
$767$	9.00000	0.324971
$768$	0	0
$769$	−47.0000	−1.69486	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	−47.0000	−1.69486	−0.847432	+	0.530904i	$0.821852\pi$
$770$	0	0
$771$	66.0000	2.37693
$772$	0	0
$773$	51.0000	1.83434	0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000	1.83434	0.917171	+	0.398493i	$0.130467\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	30.0000	1.07624
$778$	0	0
$779$	6.00000	0.214972
$780$	0	0
$781$	0	0
$782$	0	0
$783$	27.0000	0.964901
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−39.0000	−1.39020	−0.695100	−	0.718913i	$-0.744640\pi$
$787$	−39.0000	−1.39020	−0.695100	+	0.718913i	$0.744640\pi$
$788$	0	0
$789$	−24.0000	−0.854423
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−12.0000	−0.426132
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−31.0000	−1.09808	−0.549038	−	0.835797i	$-0.685006\pi$
$797$	−31.0000	−1.09808	−0.549038	+	0.835797i	$0.685006\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	12.0000	0.423999
$802$	0	0
$803$	−44.0000	−1.55273
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−6.00000	−0.211210
$808$	0	0
$809$	25.0000	0.878953	0.439477	−	0.898254i	$-0.355164\pi$
$809$	25.0000	0.878953	0.439477	+	0.898254i	$0.355164\pi$
$810$	0	0
$811$	−37.0000	−1.29925	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000	−1.29925	−0.649623	+	0.760257i	$0.725073\pi$
$812$	0	0
$813$	−81.0000	−2.84079
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−6.00000	−0.209913
$818$	0	0
$819$	−30.0000	−1.04828
$820$	0	0
$821$	−52.0000	−1.81481	−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000	−1.81481	−0.907406	+	0.420255i	$0.861941\pi$
$822$	0	0
$823$	−43.0000	−1.49889	−0.749443	−	0.662069i	$-0.769679\pi$
$823$	−43.0000	−1.49889	−0.749443	+	0.662069i	$0.769679\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	0	0
$829$	35.0000	1.21560	0.607800	−	0.794090i	$-0.292052\pi$
$829$	35.0000	1.21560	0.607800	+	0.794090i	$0.292052\pi$
$830$	0	0
$831$	−24.0000	−0.832551
$832$	0	0
$833$	54.0000	1.87099
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−18.0000	−0.622171
$838$	0	0
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	54.0000	1.85986
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−25.0000	−0.859010
$848$	0	0
$849$	6.00000	0.205919
$850$	0	0
$851$	14.0000	0.479914
$852$	0	0
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	40.0000	1.36637	0.683187	−	0.730243i	$-0.260593\pi$
$857$	40.0000	1.36637	0.683187	+	0.730243i	$0.260593\pi$
$858$	0	0
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	0	0
$861$	−90.0000	−3.06719
$862$	0	0
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	24.0000	0.815083
$868$	0	0
$869$	8.00000	0.271381
$870$	0	0
$871$	−3.00000	−0.101651
$872$	0	0
$873$	12.0000	0.406138
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−33.0000	−1.11433	−0.557165	−	0.830402i	$-0.688111\pi$
$877$	−33.0000	−1.11433	−0.557165	+	0.830402i	$0.688111\pi$
$878$	0	0
$879$	−81.0000	−2.73206
$880$	0	0
$881$	10.0000	0.336909	0.168454	−	0.985709i	$-0.446122\pi$
$881$	10.0000	0.336909	0.168454	+	0.985709i	$0.446122\pi$
$882$	0	0
$883$	30.0000	1.00958	0.504790	−	0.863242i	$-0.331570\pi$
$883$	30.0000	1.00958	0.504790	+	0.863242i	$0.331570\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	0	0
$889$	30.0000	1.00617
$890$	0	0
$891$	36.0000	1.20605
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−21.0000	−0.701170
$898$	0	0
$899$	−6.00000	−0.200111
$900$	0	0
$901$	39.0000	1.29928
$902$	0	0
$903$	90.0000	2.99501
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	0	0
$909$	−48.0000	−1.59206
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	−40.0000	−1.32381
$914$	0	0
$915$	0	0
$916$	0	0
$917$	80.0000	2.64183
$918$	0	0
$919$	5.00000	0.164935	0.0824674	−	0.996594i	$-0.473720\pi$
$919$	5.00000	0.164935	0.0824674	+	0.996594i	$0.473720\pi$
$920$	0	0
$921$	−12.0000	−0.395413
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	24.0000	0.788263
$928$	0	0
$929$	−3.00000	−0.0984268	−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000	−0.0984268	−0.0492134	+	0.998788i	$0.515671\pi$
$930$	0	0
$931$	−18.0000	−0.589926
$932$	0	0
$933$	75.0000	2.45539
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−47.0000	−1.53542	−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000	−1.53542	−0.767712	+	0.640796i	$0.778605\pi$
$938$	0	0
$939$	−3.00000	−0.0979013
$940$	0	0
$941$	−51.0000	−1.66255	−0.831276	−	0.555860i	$-0.812389\pi$
$941$	−51.0000	−1.66255	−0.831276	+	0.555860i	$0.812389\pi$
$942$	0	0
$943$	−42.0000	−1.36771
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	−11.0000	−0.357075
$950$	0	0
$951$	27.0000	0.875535
$952$	0	0
$953$	24.0000	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	36.0000	1.16371
$958$	0	0
$959$	45.0000	1.45313
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	−78.0000	−2.51351
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	0	0
$969$	9.00000	0.289122
$970$	0	0
$971$	−28.0000	−0.898563	−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000	−0.898563	−0.449281	+	0.893390i	$0.648320\pi$
$972$	0	0
$973$	80.0000	2.56468
$974$	0	0
$975$	0	0
$976$	0	0
$977$	62.0000	1.98356	0.991778	−	0.127971i	$-0.0408466\pi$
$977$	62.0000	1.98356	0.991778	+	0.127971i	$0.0408466\pi$
$978$	0	0
$979$	8.00000	0.255681
$980$	0	0
$981$	114.000	3.63974
$982$	0	0
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	42.0000	1.33552
$990$	0	0
$991$	−30.0000	−0.952981	−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000	−0.952981	−0.476491	+	0.879180i	$0.658091\pi$
$992$	0	0
$993$	−21.0000	−0.666415
$994$	0	0
$995$	0	0
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	0	0
$999$	−18.0000	−0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7600.2.a.a.1.1		1
4.3	odd	2		950.2.a.c.1.1		1
5.4	even	2		1520.2.a.j.1.1		1
12.11	even	2		8550.2.a.bm.1.1		1
20.3	even	4		950.2.b.a.799.2		2
20.7	even	4		950.2.b.a.799.1		2
20.19	odd	2		190.2.a.b.1.1	✓	1
40.19	odd	2		6080.2.a.x.1.1		1
40.29	even	2		6080.2.a.b.1.1		1
60.59	even	2		1710.2.a.g.1.1		1
140.139	even	2		9310.2.a.u.1.1		1
380.379	even	2		3610.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.b.1.1	✓	1	20.19	odd	2
950.2.a.c.1.1		1	4.3	odd	2
950.2.b.a.799.1		2	20.7	even	4
950.2.b.a.799.2		2	20.3	even	4
1520.2.a.j.1.1		1	5.4	even	2
1710.2.a.g.1.1		1	60.59	even	2
3610.2.a.e.1.1		1	380.379	even	2
6080.2.a.b.1.1		1	40.29	even	2
6080.2.a.x.1.1		1	40.19	odd	2
7600.2.a.a.1.1		1	1.1	even	1	trivial
8550.2.a.bm.1.1		1	12.11	even	2
9310.2.a.u.1.1		1	140.139	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:	\( N \)	\(=\)	\( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7600.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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