LMFDB - Embedded newform 7350.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7350,2,Mod(1,7350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7350, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7350.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7350.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:	$58.6900454856$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1050)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} -4.00000 q^{22} -7.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} +4.00000 q^{29} +5.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -6.00000 q^{38} -4.00000 q^{39} -7.00000 q^{41} -2.00000 q^{43} -4.00000 q^{44} -7.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -3.00000 q^{51} +4.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +6.00000 q^{57} +4.00000 q^{58} +14.0000 q^{59} -12.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} -12.0000 q^{67} +3.00000 q^{68} +7.00000 q^{69} -9.00000 q^{71} +1.00000 q^{72} +6.00000 q^{73} -2.00000 q^{74} -6.00000 q^{76} -4.00000 q^{78} -17.0000 q^{79} +1.00000 q^{81} -7.00000 q^{82} -4.00000 q^{83} -2.00000 q^{86} -4.00000 q^{87} -4.00000 q^{88} +7.00000 q^{89} -7.00000 q^{92} -5.00000 q^{93} +1.00000 q^{94} -1.00000 q^{96} -7.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−7.00000	−1.45960	−0.729800	−	0.683660i	$-0.760387\pi$
$23$	−7.00000	−1.45960	−0.729800	+	0.683660i	$0.760387\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−6.00000	−0.973329
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	−7.00000	−1.03209
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	0	0
$51$	−3.00000	−0.420084
$52$	4.00000	0.554700
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	6.00000	0.794719
$58$	4.00000	0.525226
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	5.00000	0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	3.00000	0.363803
$69$	7.00000	0.842701
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	1.00000	0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−6.00000	−0.688247
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−17.0000	−1.91265	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−17.0000	−1.91265	−0.956325	+	0.292306i	$0.905577\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−7.00000	−0.773021
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	−2.00000	−0.215666
$87$	−4.00000	−0.428845
$88$	−4.00000	−0.426401
$89$	7.00000	0.741999	0.370999	−	0.928633i	$-0.379015\pi$
$89$	7.00000	0.741999	0.370999	+	0.928633i	$0.379015\pi$
$90$	0	0
$91$	0	0
$92$	−7.00000	−0.729800
$93$	−5.00000	−0.518476
$94$	1.00000	0.103142
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−3.00000	−0.297044
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	2.00000	0.194257
$107$	−14.0000	−1.35343	−0.676716	−	0.736245i	$-0.736597\pi$
$107$	−14.0000	−1.35343	−0.676716	+	0.736245i	$0.736597\pi$
$108$	−1.00000	−0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	0	0
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	6.00000	0.561951
$115$	0	0
$116$	4.00000	0.371391
$117$	4.00000	0.369800
$118$	14.0000	1.28880
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	−12.0000	−1.08643
$123$	7.00000	0.631169
$124$	5.00000	0.449013
$125$	0	0
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	−12.0000	−1.03664
$135$	0	0
$136$	3.00000	0.257248
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	7.00000	0.595880
$139$	−2.00000	−0.169638	−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000	−0.169638	−0.0848189	+	0.996396i	$0.527031\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−9.00000	−0.755263
$143$	−16.0000	−1.33799
$144$	1.00000	0.0833333
$145$	0	0
$146$	6.00000	0.496564
$147$	0	0
$148$	−2.00000	−0.164399
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	24.0000	1.95309	0.976546	−	0.215308i	$-0.0690756\pi$
$151$	24.0000	1.95309	0.976546	+	0.215308i	$0.0690756\pi$
$152$	−6.00000	−0.486664
$153$	3.00000	0.242536
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−17.0000	−1.35245
$159$	−2.00000	−0.158610
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	−7.00000	−0.546608
$165$	0	0
$166$	−4.00000	−0.310460
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	−6.00000	−0.458831
$172$	−2.00000	−0.152499
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−14.0000	−1.05230
$178$	7.00000	0.524672
$179$	2.00000	0.149487	0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000	0.149487	0.0747435	+	0.997203i	$0.476186\pi$
$180$	0	0
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	0	0
$183$	12.0000	0.887066
$184$	−7.00000	−0.516047
$185$	0	0
$186$	−5.00000	−0.366618
$187$	−12.0000	−0.877527
$188$	1.00000	0.0729325
$189$	0	0
$190$	0	0
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	−1.00000	−0.0721688
$193$	−25.0000	−1.79954	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000	−1.79954	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−7.00000	−0.502571
$195$	0	0
$196$	0	0
$197$	−20.0000	−1.42494	−0.712470	−	0.701702i	$-0.752424\pi$
$197$	−20.0000	−1.42494	−0.712470	+	0.701702i	$0.752424\pi$
$198$	−4.00000	−0.284268
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	0	0
$201$	12.0000	0.846415
$202$	18.0000	1.26648
$203$	0	0
$204$	−3.00000	−0.210042
$205$	0	0
$206$	−7.00000	−0.487713
$207$	−7.00000	−0.486534
$208$	4.00000	0.277350
$209$	24.0000	1.66011
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	2.00000	0.137361
$213$	9.00000	0.616670
$214$	−14.0000	−0.957020
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	6.00000	0.406371
$219$	−6.00000	−0.405442
$220$	0	0
$221$	12.0000	0.807207
$222$	2.00000	0.134231
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	0	0
$225$	0	0
$226$	3.00000	0.199557
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	6.00000	0.397360
$229$	−8.00000	−0.528655	−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000	−0.528655	−0.264327	+	0.964433i	$0.585150\pi$
$230$	0	0
$231$	0	0
$232$	4.00000	0.262613
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	14.0000	0.911322
$237$	17.0000	1.10427
$238$	0	0
$239$	3.00000	0.194054	0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000	0.194054	0.0970269	+	0.995282i	$0.469067\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	−12.0000	−0.768221
$245$	0	0
$246$	7.00000	0.446304
$247$	−24.0000	−1.52708
$248$	5.00000	0.317500
$249$	4.00000	0.253490
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	28.0000	1.76034
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	2.00000	0.124515
$259$	0	0
$260$	0	0
$261$	4.00000	0.247594
$262$	8.00000	0.494242
$263$	27.0000	1.66489	0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000	1.66489	0.832446	+	0.554107i	$0.186940\pi$
$264$	4.00000	0.246183
$265$	0	0
$266$	0	0
$267$	−7.00000	−0.428393
$268$	−12.0000	−0.733017
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	0	0
$271$	−5.00000	−0.303728	−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000	−0.303728	−0.151864	+	0.988401i	$0.548528\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	−15.0000	−0.906183
$275$	0	0
$276$	7.00000	0.421350
$277$	16.0000	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$278$	−2.00000	−0.119952
$279$	5.00000	0.299342
$280$	0	0
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	−1.00000	−0.0595491
$283$	−8.00000	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$284$	−9.00000	−0.534052
$285$	0	0
$286$	−16.0000	−0.946100
$287$	0	0
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	7.00000	0.410347
$292$	6.00000	0.351123
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	4.00000	0.232104
$298$	−6.00000	−0.347571
$299$	−28.0000	−1.61928
$300$	0	0
$301$	0	0
$302$	24.0000	1.38104
$303$	−18.0000	−1.03407
$304$	−6.00000	−0.344124
$305$	0	0
$306$	3.00000	0.171499
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	0	0
$309$	7.00000	0.398216
$310$	0	0
$311$	−21.0000	−1.19080	−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000	−1.19080	−0.595400	+	0.803429i	$0.703007\pi$
$312$	−4.00000	−0.226455
$313$	−27.0000	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$313$	−27.0000	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−17.0000	−0.956325
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−2.00000	−0.112154
$319$	−16.0000	−0.895828
$320$	0	0
$321$	14.0000	0.781404
$322$	0	0
$323$	−18.0000	−1.00155
$324$	1.00000	0.0555556
$325$	0	0
$326$	8.00000	0.443079
$327$	−6.00000	−0.331801
$328$	−7.00000	−0.386510
$329$	0	0
$330$	0	0
$331$	−34.0000	−1.86881	−0.934405	−	0.356214i	$-0.884068\pi$
$331$	−34.0000	−1.86881	−0.934405	+	0.356214i	$0.884068\pi$
$332$	−4.00000	−0.219529
$333$	−2.00000	−0.109599
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−3.00000	−0.163420	−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000	−0.163420	−0.0817102	+	0.996656i	$0.526038\pi$
$338$	3.00000	0.163178
$339$	−3.00000	−0.162938
$340$	0	0
$341$	−20.0000	−1.08306
$342$	−6.00000	−0.324443
$343$	0	0
$344$	−2.00000	−0.107833
$345$	0	0
$346$	6.00000	0.322562
$347$	−32.0000	−1.71785	−0.858925	−	0.512101i	$-0.828867\pi$
$347$	−32.0000	−1.71785	−0.858925	+	0.512101i	$0.828867\pi$
$348$	−4.00000	−0.214423
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	−4.00000	−0.213201
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	−14.0000	−0.744092
$355$	0	0
$356$	7.00000	0.370999
$357$	0	0
$358$	2.00000	0.105703
$359$	4.00000	0.211112	0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000	0.211112	0.105556	+	0.994413i	$0.466338\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−12.0000	−0.630706
$363$	−5.00000	−0.262432
$364$	0	0
$365$	0	0
$366$	12.0000	0.627250
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	−7.00000	−0.364900
$369$	−7.00000	−0.364405
$370$	0	0
$371$	0	0
$372$	−5.00000	−0.259238
$373$	−12.0000	−0.621336	−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000	−0.621336	−0.310668	+	0.950518i	$0.600553\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	1.00000	0.0515711
$377$	16.0000	0.824042
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	15.0000	0.767467
$383$	−31.0000	−1.58403	−0.792013	−	0.610504i	$-0.790967\pi$
$383$	−31.0000	−1.58403	−0.792013	+	0.610504i	$0.790967\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−25.0000	−1.27247
$387$	−2.00000	−0.101666
$388$	−7.00000	−0.355371
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	−21.0000	−1.06202
$392$	0	0
$393$	−8.00000	−0.403547
$394$	−20.0000	−1.00759
$395$	0	0
$396$	−4.00000	−0.201008
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−15.0000	−0.751882
$399$	0	0
$400$	0	0
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	12.0000	0.598506
$403$	20.0000	0.996271
$404$	18.0000	0.895533
$405$	0	0
$406$	0	0
$407$	8.00000	0.396545
$408$	−3.00000	−0.148522
$409$	−29.0000	−1.43396	−0.716979	−	0.697095i	$-0.754476\pi$
$409$	−29.0000	−1.43396	−0.716979	+	0.697095i	$0.754476\pi$
$410$	0	0
$411$	15.0000	0.739895
$412$	−7.00000	−0.344865
$413$	0	0
$414$	−7.00000	−0.344031
$415$	0	0
$416$	4.00000	0.196116
$417$	2.00000	0.0979404
$418$	24.0000	1.17388
$419$	26.0000	1.27018	0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000	1.27018	0.635092	+	0.772437i	$0.280962\pi$
$420$	0	0
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	−22.0000	−1.07094
$423$	1.00000	0.0486217
$424$	2.00000	0.0971286
$425$	0	0
$426$	9.00000	0.436051
$427$	0	0
$428$	−14.0000	−0.676716
$429$	16.0000	0.772487
$430$	0	0
$431$	−39.0000	−1.87856	−0.939282	−	0.343146i	$-0.888507\pi$
$431$	−39.0000	−1.87856	−0.939282	+	0.343146i	$0.888507\pi$
$432$	−1.00000	−0.0481125
$433$	37.0000	1.77811	0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000	1.77811	0.889053	+	0.457804i	$0.151364\pi$
$434$	0	0
$435$	0	0
$436$	6.00000	0.287348
$437$	42.0000	2.00913
$438$	−6.00000	−0.286691
$439$	−17.0000	−0.811366	−0.405683	−	0.914014i	$-0.632966\pi$
$439$	−17.0000	−0.811366	−0.405683	+	0.914014i	$0.632966\pi$
$440$	0	0
$441$	0	0
$442$	12.0000	0.570782
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	9.00000	0.426162
$447$	6.00000	0.283790
$448$	0	0
$449$	−13.0000	−0.613508	−0.306754	−	0.951789i	$-0.599243\pi$
$449$	−13.0000	−0.613508	−0.306754	+	0.951789i	$0.599243\pi$
$450$	0	0
$451$	28.0000	1.31847
$452$	3.00000	0.141108
$453$	−24.0000	−1.12762
$454$	−22.0000	−1.03251
$455$	0	0
$456$	6.00000	0.280976
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−8.00000	−0.373815
$459$	−3.00000	−0.140028
$460$	0	0
$461$	−36.0000	−1.67669	−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000	−1.67669	−0.838344	+	0.545142i	$0.816476\pi$
$462$	0	0
$463$	7.00000	0.325318	0.162659	−	0.986682i	$-0.447993\pi$
$463$	7.00000	0.325318	0.162659	+	0.986682i	$0.447993\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	6.00000	0.277945
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	4.00000	0.184900
$469$	0	0
$470$	0	0
$471$	4.00000	0.184310
$472$	14.0000	0.644402
$473$	8.00000	0.367840
$474$	17.0000	0.780836
$475$	0	0
$476$	0	0
$477$	2.00000	0.0915737
$478$	3.00000	0.137217
$479$	−1.00000	−0.0456912	−0.0228456	−	0.999739i	$-0.507273\pi$
$479$	−1.00000	−0.0456912	−0.0228456	+	0.999739i	$0.507273\pi$
$480$	0	0
$481$	−8.00000	−0.364769
$482$	2.00000	0.0910975
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−5.00000	−0.226572	−0.113286	−	0.993562i	$-0.536138\pi$
$487$	−5.00000	−0.226572	−0.113286	+	0.993562i	$0.536138\pi$
$488$	−12.0000	−0.543214
$489$	−8.00000	−0.361773
$490$	0	0
$491$	38.0000	1.71492	0.857458	−	0.514554i	$-0.172042\pi$
$491$	38.0000	1.71492	0.857458	+	0.514554i	$0.172042\pi$
$492$	7.00000	0.315584
$493$	12.0000	0.540453
$494$	−24.0000	−1.07981
$495$	0	0
$496$	5.00000	0.224507
$497$	0	0
$498$	4.00000	0.179244
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	0	0
$502$	−4.00000	−0.178529
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	0	0
$506$	28.0000	1.24475
$507$	−3.00000	−0.133235
$508$	−16.0000	−0.709885
$509$	16.0000	0.709188	0.354594	−	0.935020i	$-0.384619\pi$
$509$	16.0000	0.709188	0.354594	+	0.935020i	$0.384619\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.00000	0.264906
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	2.00000	0.0880451
$517$	−4.00000	−0.175920
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	9.00000	0.394297	0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000	0.394297	0.197149	+	0.980374i	$0.436832\pi$
$522$	4.00000	0.175075
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	27.0000	1.17726
$527$	15.0000	0.653410
$528$	4.00000	0.174078
$529$	26.0000	1.13043
$530$	0	0
$531$	14.0000	0.607548
$532$	0	0
$533$	−28.0000	−1.21281
$534$	−7.00000	−0.302920
$535$	0	0
$536$	−12.0000	−0.518321
$537$	−2.00000	−0.0863064
$538$	10.0000	0.431131
$539$	0	0
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	−5.00000	−0.214768
$543$	12.0000	0.514969
$544$	3.00000	0.128624
$545$	0	0
$546$	0	0
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	−15.0000	−0.640768
$549$	−12.0000	−0.512148
$550$	0	0
$551$	−24.0000	−1.02243
$552$	7.00000	0.297940
$553$	0	0
$554$	16.0000	0.679775
$555$	0	0
$556$	−2.00000	−0.0848189
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	5.00000	0.211667
$559$	−8.00000	−0.338364
$560$	0	0
$561$	12.0000	0.506640
$562$	17.0000	0.717102
$563$	−2.00000	−0.0842900	−0.0421450	−	0.999112i	$-0.513419\pi$
$563$	−2.00000	−0.0842900	−0.0421450	+	0.999112i	$0.513419\pi$
$564$	−1.00000	−0.0421076
$565$	0	0
$566$	−8.00000	−0.336265
$567$	0	0
$568$	−9.00000	−0.377632
$569$	−45.0000	−1.88650	−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000	−1.88650	−0.943249	+	0.332086i	$0.892248\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	−16.0000	−0.668994
$573$	−15.0000	−0.626634
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−8.00000	−0.332756
$579$	25.0000	1.03896
$580$	0	0
$581$	0	0
$582$	7.00000	0.290159
$583$	−8.00000	−0.331326
$584$	6.00000	0.248282
$585$	0	0
$586$	−12.0000	−0.495715
$587$	42.0000	1.73353	0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000	1.73353	0.866763	+	0.498721i	$0.166197\pi$
$588$	0	0
$589$	−30.0000	−1.23613
$590$	0	0
$591$	20.0000	0.822690
$592$	−2.00000	−0.0821995
$593$	13.0000	0.533846	0.266923	−	0.963718i	$-0.413993\pi$
$593$	13.0000	0.533846	0.266923	+	0.963718i	$0.413993\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−6.00000	−0.245770
$597$	15.0000	0.613909
$598$	−28.0000	−1.14501
$599$	−31.0000	−1.26663	−0.633313	−	0.773896i	$-0.718305\pi$
$599$	−31.0000	−1.26663	−0.633313	+	0.773896i	$0.718305\pi$
$600$	0	0
$601$	−46.0000	−1.87638	−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000	−1.87638	−0.938190	+	0.346122i	$0.887498\pi$
$602$	0	0
$603$	−12.0000	−0.488678
$604$	24.0000	0.976546
$605$	0	0
$606$	−18.0000	−0.731200
$607$	29.0000	1.17707	0.588537	−	0.808470i	$-0.299704\pi$
$607$	29.0000	1.17707	0.588537	+	0.808470i	$0.299704\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	0	0
$611$	4.00000	0.161823
$612$	3.00000	0.121268
$613$	−4.00000	−0.161558	−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000	−0.161558	−0.0807792	+	0.996732i	$0.525741\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	0	0
$617$	−1.00000	−0.0402585	−0.0201292	−	0.999797i	$-0.506408\pi$
$617$	−1.00000	−0.0402585	−0.0201292	+	0.999797i	$0.506408\pi$
$618$	7.00000	0.281581
$619$	16.0000	0.643094	0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000	0.643094	0.321547	+	0.946894i	$0.395797\pi$
$620$	0	0
$621$	7.00000	0.280900
$622$	−21.0000	−0.842023
$623$	0	0
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−27.0000	−1.07914
$627$	−24.0000	−0.958468
$628$	−4.00000	−0.159617
$629$	−6.00000	−0.239236
$630$	0	0
$631$	7.00000	0.278666	0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000	0.278666	0.139333	+	0.990246i	$0.455504\pi$
$632$	−17.0000	−0.676224
$633$	22.0000	0.874421
$634$	−18.0000	−0.714871
$635$	0	0
$636$	−2.00000	−0.0793052
$637$	0	0
$638$	−16.0000	−0.633446
$639$	−9.00000	−0.356034
$640$	0	0
$641$	−9.00000	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$642$	14.0000	0.552536
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	0	0
$645$	0	0
$646$	−18.0000	−0.708201
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	1.00000	0.0392837
$649$	−56.0000	−2.19819
$650$	0	0
$651$	0	0
$652$	8.00000	0.313304
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	−7.00000	−0.273304
$657$	6.00000	0.234082
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	−34.0000	−1.32145
$663$	−12.0000	−0.466041
$664$	−4.00000	−0.155230
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	−28.0000	−1.08416
$668$	0	0
$669$	−9.00000	−0.347960
$670$	0	0
$671$	48.0000	1.85302
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	−3.00000	−0.115556
$675$	0	0
$676$	3.00000	0.115385
$677$	32.0000	1.22986	0.614930	−	0.788582i	$-0.289184\pi$
$677$	32.0000	1.22986	0.614930	+	0.788582i	$0.289184\pi$
$678$	−3.00000	−0.115214
$679$	0	0
$680$	0	0
$681$	22.0000	0.843042
$682$	−20.0000	−0.765840
$683$	−22.0000	−0.841807	−0.420903	−	0.907106i	$-0.638287\pi$
$683$	−22.0000	−0.841807	−0.420903	+	0.907106i	$0.638287\pi$
$684$	−6.00000	−0.229416
$685$	0	0
$686$	0	0
$687$	8.00000	0.305219
$688$	−2.00000	−0.0762493
$689$	8.00000	0.304776
$690$	0	0
$691$	24.0000	0.913003	0.456502	−	0.889723i	$-0.349102\pi$
$691$	24.0000	0.913003	0.456502	+	0.889723i	$0.349102\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−32.0000	−1.21470
$695$	0	0
$696$	−4.00000	−0.151620
$697$	−21.0000	−0.795432
$698$	18.0000	0.681310
$699$	−6.00000	−0.226941
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	−4.00000	−0.150970
$703$	12.0000	0.452589
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−15.0000	−0.564532
$707$	0	0
$708$	−14.0000	−0.526152
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	−17.0000	−0.637550
$712$	7.00000	0.262336
$713$	−35.0000	−1.31076
$714$	0	0
$715$	0	0
$716$	2.00000	0.0747435
$717$	−3.00000	−0.112037
$718$	4.00000	0.149279
$719$	7.00000	0.261056	0.130528	−	0.991445i	$-0.458333\pi$
$719$	7.00000	0.261056	0.130528	+	0.991445i	$0.458333\pi$
$720$	0	0
$721$	0	0
$722$	17.0000	0.632674
$723$	−2.00000	−0.0743808
$724$	−12.0000	−0.445976
$725$	0	0
$726$	−5.00000	−0.185567
$727$	−49.0000	−1.81731	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−49.0000	−1.81731	−0.908655	+	0.417548i	$0.862889\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−6.00000	−0.221918
$732$	12.0000	0.443533
$733$	−10.0000	−0.369358	−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000	−0.369358	−0.184679	+	0.982799i	$0.559125\pi$
$734$	−32.0000	−1.18114
$735$	0	0
$736$	−7.00000	−0.258023
$737$	48.0000	1.76810
$738$	−7.00000	−0.257674
$739$	14.0000	0.514998	0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000	0.514998	0.257499	+	0.966279i	$0.417102\pi$
$740$	0	0
$741$	24.0000	0.881662
$742$	0	0
$743$	−1.00000	−0.0366864	−0.0183432	−	0.999832i	$-0.505839\pi$
$743$	−1.00000	−0.0366864	−0.0183432	+	0.999832i	$0.505839\pi$
$744$	−5.00000	−0.183309
$745$	0	0
$746$	−12.0000	−0.439351
$747$	−4.00000	−0.146352
$748$	−12.0000	−0.438763
$749$	0	0
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	1.00000	0.0364662
$753$	4.00000	0.145768
$754$	16.0000	0.582686
$755$	0	0
$756$	0	0
$757$	16.0000	0.581530	0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000	0.581530	0.290765	+	0.956795i	$0.406090\pi$
$758$	20.0000	0.726433
$759$	−28.0000	−1.01634
$760$	0	0
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	16.0000	0.579619
$763$	0	0
$764$	15.0000	0.542681
$765$	0	0
$766$	−31.0000	−1.12008
$767$	56.0000	2.02204
$768$	−1.00000	−0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−25.0000	−0.899770
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	−2.00000	−0.0718885
$775$	0	0
$776$	−7.00000	−0.251285
$777$	0	0
$778$	10.0000	0.358517
$779$	42.0000	1.50481
$780$	0	0
$781$	36.0000	1.28818
$782$	−21.0000	−0.750958
$783$	−4.00000	−0.142948
$784$	0	0
$785$	0	0
$786$	−8.00000	−0.285351
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	−20.0000	−0.712470
$789$	−27.0000	−0.961225
$790$	0	0
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−48.0000	−1.70453
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−15.0000	−0.531661
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	3.00000	0.106132
$800$	0	0
$801$	7.00000	0.247333
$802$	34.0000	1.20058
$803$	−24.0000	−0.846942
$804$	12.0000	0.423207
$805$	0	0
$806$	20.0000	0.704470
$807$	−10.0000	−0.352017
$808$	18.0000	0.633238
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	5.00000	0.175358
$814$	8.00000	0.280400
$815$	0	0
$816$	−3.00000	−0.105021
$817$	12.0000	0.419827
$818$	−29.0000	−1.01396
$819$	0	0
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	15.0000	0.523185
$823$	24.0000	0.836587	0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000	0.836587	0.418294	+	0.908312i	$0.362628\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	0	0
$827$	−20.0000	−0.695468	−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000	−0.695468	−0.347734	+	0.937593i	$0.613049\pi$
$828$	−7.00000	−0.243267
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	−16.0000	−0.555034
$832$	4.00000	0.138675
$833$	0	0
$834$	2.00000	0.0692543
$835$	0	0
$836$	24.0000	0.830057
$837$	−5.00000	−0.172825
$838$	26.0000	0.898155
$839$	25.0000	0.863096	0.431548	−	0.902090i	$-0.357968\pi$
$839$	25.0000	0.863096	0.431548	+	0.902090i	$0.357968\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	16.0000	0.551396
$843$	−17.0000	−0.585511
$844$	−22.0000	−0.757271
$845$	0	0
$846$	1.00000	0.0343807
$847$	0	0
$848$	2.00000	0.0686803
$849$	8.00000	0.274559
$850$	0	0
$851$	14.0000	0.479914
$852$	9.00000	0.308335
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	0	0
$855$	0	0
$856$	−14.0000	−0.478510
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	16.0000	0.546231
$859$	−24.0000	−0.818869	−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000	−0.818869	−0.409435	+	0.912339i	$0.634274\pi$
$860$	0	0
$861$	0	0
$862$	−39.0000	−1.32835
$863$	11.0000	0.374444	0.187222	−	0.982318i	$-0.440052\pi$
$863$	11.0000	0.374444	0.187222	+	0.982318i	$0.440052\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	37.0000	1.25731
$867$	8.00000	0.271694
$868$	0	0
$869$	68.0000	2.30674
$870$	0	0
$871$	−48.0000	−1.62642
$872$	6.00000	0.203186
$873$	−7.00000	−0.236914
$874$	42.0000	1.42067
$875$	0	0
$876$	−6.00000	−0.202721
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−17.0000	−0.573722
$879$	12.0000	0.404750
$880$	0	0
$881$	35.0000	1.17918	0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000	1.17918	0.589590	+	0.807703i	$0.299289\pi$
$882$	0	0
$883$	−6.00000	−0.201916	−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000	−0.201916	−0.100958	+	0.994891i	$0.532191\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	26.0000	0.873487
$887$	56.0000	1.88030	0.940148	−	0.340766i	$-0.110687\pi$
$887$	56.0000	1.88030	0.940148	+	0.340766i	$0.110687\pi$
$888$	2.00000	0.0671156
$889$	0	0
$890$	0	0
$891$	−4.00000	−0.134005
$892$	9.00000	0.301342
$893$	−6.00000	−0.200782
$894$	6.00000	0.200670
$895$	0	0
$896$	0	0
$897$	28.0000	0.934893
$898$	−13.0000	−0.433816
$899$	20.0000	0.667037
$900$	0	0
$901$	6.00000	0.199889
$902$	28.0000	0.932298
$903$	0	0
$904$	3.00000	0.0997785
$905$	0	0
$906$	−24.0000	−0.797347
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−22.0000	−0.730096
$909$	18.0000	0.597022
$910$	0	0
$911$	19.0000	0.629498	0.314749	−	0.949175i	$-0.398080\pi$
$911$	19.0000	0.629498	0.314749	+	0.949175i	$0.398080\pi$
$912$	6.00000	0.198680
$913$	16.0000	0.529523
$914$	−18.0000	−0.595387
$915$	0	0
$916$	−8.00000	−0.264327
$917$	0	0
$918$	−3.00000	−0.0990148
$919$	−39.0000	−1.28649	−0.643246	−	0.765660i	$-0.722413\pi$
$919$	−39.0000	−1.28649	−0.643246	+	0.765660i	$0.722413\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	−36.0000	−1.18560
$923$	−36.0000	−1.18495
$924$	0	0
$925$	0	0
$926$	7.00000	0.230034
$927$	−7.00000	−0.229910
$928$	4.00000	0.131306
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	21.0000	0.687509
$934$	0	0
$935$	0	0
$936$	4.00000	0.130744
$937$	−6.00000	−0.196011	−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000	−0.196011	−0.0980057	+	0.995186i	$0.531246\pi$
$938$	0	0
$939$	27.0000	0.881112
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	4.00000	0.130327
$943$	49.0000	1.59566
$944$	14.0000	0.455661
$945$	0	0
$946$	8.00000	0.260102
$947$	32.0000	1.03986	0.519930	−	0.854209i	$-0.325958\pi$
$947$	32.0000	1.03986	0.519930	+	0.854209i	$0.325958\pi$
$948$	17.0000	0.552134
$949$	24.0000	0.779073
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	26.0000	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	3.00000	0.0970269
$957$	16.0000	0.517207
$958$	−1.00000	−0.0323085
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	−8.00000	−0.257930
$963$	−14.0000	−0.451144
$964$	2.00000	0.0644157
$965$	0	0
$966$	0	0
$967$	29.0000	0.932577	0.466289	−	0.884633i	$-0.345591\pi$
$967$	29.0000	0.932577	0.466289	+	0.884633i	$0.345591\pi$
$968$	5.00000	0.160706
$969$	18.0000	0.578243
$970$	0	0
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−5.00000	−0.160210
$975$	0	0
$976$	−12.0000	−0.384111
$977$	−3.00000	−0.0959785	−0.0479893	−	0.998848i	$-0.515281\pi$
$977$	−3.00000	−0.0959785	−0.0479893	+	0.998848i	$0.515281\pi$
$978$	−8.00000	−0.255812
$979$	−28.0000	−0.894884
$980$	0	0
$981$	6.00000	0.191565
$982$	38.0000	1.21263
$983$	28.0000	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$984$	7.00000	0.223152
$985$	0	0
$986$	12.0000	0.382158
$987$	0	0
$988$	−24.0000	−0.763542
$989$	14.0000	0.445174
$990$	0	0
$991$	7.00000	0.222362	0.111181	−	0.993800i	$-0.464537\pi$
$991$	7.00000	0.222362	0.111181	+	0.993800i	$0.464537\pi$
$992$	5.00000	0.158750
$993$	34.0000	1.07896
$994$	0	0
$995$	0	0
$996$	4.00000	0.126745
$997$	−16.0000	−0.506725	−0.253363	−	0.967371i	$-0.581537\pi$
$997$	−16.0000	−0.506725	−0.253363	+	0.967371i	$0.581537\pi$
$998$	28.0000	0.886325
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.bs.1.1		1
5.4	even	2		7350.2.a.v.1.1		1
7.3	odd	6		1050.2.i.d.751.1	yes	2
7.5	odd	6		1050.2.i.d.151.1	✓	2
7.6	odd	2		7350.2.a.ci.1.1		1
35.3	even	12		1050.2.o.l.499.2		4
35.12	even	12		1050.2.o.l.949.2		4
35.17	even	12		1050.2.o.l.499.1		4
35.19	odd	6		1050.2.i.r.151.1	yes	2
35.24	odd	6		1050.2.i.r.751.1	yes	2
35.33	even	12		1050.2.o.l.949.1		4
35.34	odd	2		7350.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.d.151.1	✓	2	7.5	odd	6
1050.2.i.d.751.1	yes	2	7.3	odd	6
1050.2.i.r.151.1	yes	2	35.19	odd	6
1050.2.i.r.751.1	yes	2	35.24	odd	6
1050.2.o.l.499.1		4	35.17	even	12
1050.2.o.l.499.2		4	35.3	even	12
1050.2.o.l.949.1		4	35.33	even	12
1050.2.o.l.949.2		4	35.12	even	12
7350.2.a.e.1.1		1	35.34	odd	2
7350.2.a.v.1.1		1	5.4	even	2
7350.2.a.bs.1.1		1	1.1	even	1	trivial
7350.2.a.ci.1.1		1	7.6	odd	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:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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