LMFDB - Embedded newform 7350.2.a.cq.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:	$0$
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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{12} -4.00000 q^{13} +1.00000 q^{16} +3.00000 q^{17} +1.00000 q^{18} -2.00000 q^{19} -3.00000 q^{23} +1.00000 q^{24} -4.00000 q^{26} +1.00000 q^{27} +1.00000 q^{31} +1.00000 q^{32} +3.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -2.00000 q^{38} -4.00000 q^{39} +9.00000 q^{41} +10.0000 q^{43} -3.00000 q^{46} -3.00000 q^{47} +1.00000 q^{48} +3.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} -2.00000 q^{57} +6.00000 q^{59} -8.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} +4.00000 q^{67} +3.00000 q^{68} -3.00000 q^{69} +3.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +10.0000 q^{74} -2.00000 q^{76} -4.00000 q^{78} +11.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} +10.0000 q^{86} +15.0000 q^{89} -3.00000 q^{92} +1.00000 q^{93} -3.00000 q^{94} +1.00000 q^{96} -7.00000 q^{97} +O(q^{100})$

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
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	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
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	0	0
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	0	0
$45$	0	0
$46$	−3.00000	−0.442326
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	0	0
$51$	3.00000	0.420084
$52$	−4.00000	−0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0	0
$57$	−2.00000	−0.264906
$58$	0	0
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	1.00000	0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	3.00000	0.363803
$69$	−3.00000	−0.361158
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	1.00000	0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	−2.00000	−0.229416
$77$	0	0
$78$	−4.00000	−0.452911
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.00000	0.993884
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	10.0000	1.07833
$87$	0	0
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	1.00000	0.103695
$94$	−3.00000	−0.309426
$95$	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
$99$	0	0
$100$	0	0
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	3.00000	0.297044
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	6.00000	0.582772
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	0	0
$113$	−21.0000	−1.97551	−0.987757	−	0.156001i	$-0.950140\pi$
$113$	−21.0000	−1.97551	−0.987757	+	0.156001i	$0.950140\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	0	0
$117$	−4.00000	−0.369800
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	−8.00000	−0.724286
$123$	9.00000	0.811503
$124$	1.00000	0.0898027
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	10.0000	0.880451
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	3.00000	0.257248
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	−3.00000	−0.255377
$139$	−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
$141$	−3.00000	−0.252646
$142$	3.00000	0.251754
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	14.0000	1.15865
$147$	0	0
$148$	10.0000	0.821995
$149$	−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
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.00000	−0.162221
$153$	3.00000	0.242536
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	11.0000	0.875113
$159$	6.00000	0.475831
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	9.00000	0.702782
$165$	0	0
$166$	0	0
$167$	−24.0000	−1.85718	−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000	−1.85718	−0.928588	+	0.371113i	$0.878976\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	−2.00000	−0.152944
$172$	10.0000	0.762493
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	6.00000	0.450988
$178$	15.0000	1.12430
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−8.00000	−0.594635	−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000	−0.594635	−0.297318	+	0.954779i	$0.596092\pi$
$182$	0	0
$183$	−8.00000	−0.591377
$184$	−3.00000	−0.221163
$185$	0	0
$186$	1.00000	0.0733236
$187$	0	0
$188$	−3.00000	−0.218797
$189$	0	0
$190$	0	0
$191$	−21.0000	−1.51951	−0.759753	−	0.650211i	$-0.774680\pi$
$191$	−21.0000	−1.51951	−0.759753	+	0.650211i	$0.774680\pi$
$192$	1.00000	0.0721688
$193$	−17.0000	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$194$	−7.00000	−0.502571
$195$	0	0
$196$	0	0
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	−18.0000	−1.26648
$203$	0	0
$204$	3.00000	0.210042
$205$	0	0
$206$	5.00000	0.348367
$207$	−3.00000	−0.208514
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	6.00000	0.412082
$213$	3.00000	0.205557
$214$	18.0000	1.23045
$215$	0	0
$216$	1.00000	0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	14.0000	0.946032
$220$	0	0
$221$	−12.0000	−0.807207
$222$	10.0000	0.671156
$223$	−19.0000	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$224$	0	0
$225$	0	0
$226$	−21.0000	−1.39690
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	−2.00000	−0.132453
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	30.0000	1.96537	0.982683	−	0.185296i	$-0.0593245\pi$
$233$	30.0000	1.96537	0.982683	+	0.185296i	$0.0593245\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	6.00000	0.390567
$237$	11.0000	0.714527
$238$	0	0
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−11.0000	−0.707107
$243$	1.00000	0.0641500
$244$	−8.00000	−0.512148
$245$	0	0
$246$	9.00000	0.573819
$247$	8.00000	0.509028
$248$	1.00000	0.0635001
$249$	0	0
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	0	0
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	10.0000	0.622573
$259$	0	0
$260$	0	0
$261$	0	0
$262$	12.0000	0.741362
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	15.0000	0.917985
$268$	4.00000	0.244339
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	9.00000	0.543710
$275$	0	0
$276$	−3.00000	−0.180579
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−2.00000	−0.119952
$279$	1.00000	0.0598684
$280$	0	0
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	−3.00000	−0.178647
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	0	0
$287$	0	0
$288$	1.00000	0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−7.00000	−0.410347
$292$	14.0000	0.819288
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	0	0
$296$	10.0000	0.581238
$297$	0	0
$298$	−6.00000	−0.347571
$299$	12.0000	0.693978
$300$	0	0
$301$	0	0
$302$	8.00000	0.460348
$303$	−18.0000	−1.03407
$304$	−2.00000	−0.114708
$305$	0	0
$306$	3.00000	0.171499
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	5.00000	0.284440
$310$	0	0
$311$	−9.00000	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$312$	−4.00000	−0.226455
$313$	5.00000	0.282617	0.141308	−	0.989966i	$-0.454869\pi$
$313$	5.00000	0.282617	0.141308	+	0.989966i	$0.454869\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	11.0000	0.618798
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	0	0
$321$	18.0000	1.00466
$322$	0	0
$323$	−6.00000	−0.333849
$324$	1.00000	0.0555556
$325$	0	0
$326$	−8.00000	−0.443079
$327$	2.00000	0.110600
$328$	9.00000	0.496942
$329$	0	0
$330$	0	0
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	0	0
$333$	10.0000	0.547997
$334$	−24.0000	−1.31322
$335$	0	0
$336$	0	0
$337$	−11.0000	−0.599208	−0.299604	−	0.954064i	$-0.596855\pi$
$337$	−11.0000	−0.599208	−0.299604	+	0.954064i	$0.596855\pi$
$338$	3.00000	0.163178
$339$	−21.0000	−1.14056
$340$	0	0
$341$	0	0
$342$	−2.00000	−0.108148
$343$	0	0
$344$	10.0000	0.539164
$345$	0	0
$346$	−18.0000	−0.967686
$347$	36.0000	1.93258	0.966291	−	0.257454i	$-0.0828835\pi$
$347$	36.0000	1.93258	0.966291	+	0.257454i	$0.0828835\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	0	0
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	15.0000	0.794998
$357$	0	0
$358$	−6.00000	−0.317110
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−8.00000	−0.420471
$363$	−11.0000	−0.577350
$364$	0	0
$365$	0	0
$366$	−8.00000	−0.418167
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−3.00000	−0.156386
$369$	9.00000	0.468521
$370$	0	0
$371$	0	0
$372$	1.00000	0.0518476
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	0	0
$376$	−3.00000	−0.154713
$377$	0	0
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	−21.0000	−1.07445
$383$	21.0000	1.07305	0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000	1.07305	0.536525	+	0.843884i	$0.319737\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−17.0000	−0.865277
$387$	10.0000	0.508329
$388$	−7.00000	−0.355371
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	0	0
$393$	12.0000	0.605320
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−11.0000	−0.551380
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	4.00000	0.199502
$403$	−4.00000	−0.199254
$404$	−18.0000	−0.895533
$405$	0	0
$406$	0	0
$407$	0	0
$408$	3.00000	0.148522
$409$	−5.00000	−0.247234	−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000	−0.247234	−0.123617	+	0.992330i	$0.539449\pi$
$410$	0	0
$411$	9.00000	0.443937
$412$	5.00000	0.246332
$413$	0	0
$414$	−3.00000	−0.147442
$415$	0	0
$416$	−4.00000	−0.196116
$417$	−2.00000	−0.0979404
$418$	0	0
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	−40.0000	−1.94948	−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000	−1.94948	−0.974740	+	0.223341i	$0.928304\pi$
$422$	14.0000	0.681509
$423$	−3.00000	−0.145865
$424$	6.00000	0.291386
$425$	0	0
$426$	3.00000	0.145350
$427$	0	0
$428$	18.0000	0.870063
$429$	0	0
$430$	0	0
$431$	−27.0000	−1.30054	−0.650272	−	0.759701i	$-0.725345\pi$
$431$	−27.0000	−1.30054	−0.650272	+	0.759701i	$0.725345\pi$
$432$	1.00000	0.0481125
$433$	29.0000	1.39365	0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000	1.39365	0.696826	+	0.717241i	$0.254595\pi$
$434$	0	0
$435$	0	0
$436$	2.00000	0.0957826
$437$	6.00000	0.287019
$438$	14.0000	0.668946
$439$	−5.00000	−0.238637	−0.119318	−	0.992856i	$-0.538071\pi$
$439$	−5.00000	−0.238637	−0.119318	+	0.992856i	$0.538071\pi$
$440$	0	0
$441$	0	0
$442$	−12.0000	−0.570782
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	10.0000	0.474579
$445$	0	0
$446$	−19.0000	−0.899676
$447$	−6.00000	−0.283790
$448$	0	0
$449$	−21.0000	−0.991051	−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000	−0.991051	−0.495526	+	0.868593i	$0.665025\pi$
$450$	0	0
$451$	0	0
$452$	−21.0000	−0.987757
$453$	8.00000	0.375873
$454$	−6.00000	−0.281594
$455$	0	0
$456$	−2.00000	−0.0936586
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	4.00000	0.186908
$459$	3.00000	0.140028
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	0	0
$463$	−5.00000	−0.232370	−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000	−0.232370	−0.116185	+	0.993228i	$0.537067\pi$
$464$	0	0
$465$	0	0
$466$	30.0000	1.38972
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	−4.00000	−0.184900
$469$	0	0
$470$	0	0
$471$	8.00000	0.368621
$472$	6.00000	0.276172
$473$	0	0
$474$	11.0000	0.505247
$475$	0	0
$476$	0	0
$477$	6.00000	0.274721
$478$	15.0000	0.686084
$479$	27.0000	1.23366	0.616831	−	0.787096i	$-0.288416\pi$
$479$	27.0000	1.23366	0.616831	+	0.787096i	$0.288416\pi$
$480$	0	0
$481$	−40.0000	−1.82384
$482$	−14.0000	−0.637683
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	1.00000	0.0453609
$487$	31.0000	1.40474	0.702372	−	0.711810i	$-0.252124\pi$
$487$	31.0000	1.40474	0.702372	+	0.711810i	$0.252124\pi$
$488$	−8.00000	−0.362143
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	9.00000	0.405751
$493$	0	0
$494$	8.00000	0.359937
$495$	0	0
$496$	1.00000	0.0449013
$497$	0	0
$498$	0	0
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	−12.0000	−0.535586
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	3.00000	0.133235
$508$	16.0000	0.709885
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	−2.00000	−0.0883022
$514$	30.0000	1.32324
$515$	0	0
$516$	10.0000	0.440225
$517$	0	0
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	−15.0000	−0.657162	−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000	−0.657162	−0.328581	+	0.944476i	$0.606570\pi$
$522$	0	0
$523$	32.0000	1.39926	0.699631	−	0.714504i	$-0.253348\pi$
$523$	32.0000	1.39926	0.699631	+	0.714504i	$0.253348\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−9.00000	−0.392419
$527$	3.00000	0.130682
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	6.00000	0.260378
$532$	0	0
$533$	−36.0000	−1.55933
$534$	15.0000	0.649113
$535$	0	0
$536$	4.00000	0.172774
$537$	−6.00000	−0.258919
$538$	6.00000	0.258678
$539$	0	0
$540$	0	0
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	7.00000	0.300676
$543$	−8.00000	−0.343313
$544$	3.00000	0.128624
$545$	0	0
$546$	0	0
$547$	−26.0000	−1.11168	−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000	−1.11168	−0.555840	+	0.831289i	$0.687603\pi$
$548$	9.00000	0.384461
$549$	−8.00000	−0.341432
$550$	0	0
$551$	0	0
$552$	−3.00000	−0.127688
$553$	0	0
$554$	28.0000	1.18961
$555$	0	0
$556$	−2.00000	−0.0848189
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	1.00000	0.0423334
$559$	−40.0000	−1.69182
$560$	0	0
$561$	0	0
$562$	9.00000	0.379642
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	−3.00000	−0.126323
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	3.00000	0.125877
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	0	0
$573$	−21.0000	−0.877288
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−8.00000	−0.332756
$579$	−17.0000	−0.706496
$580$	0	0
$581$	0	0
$582$	−7.00000	−0.290159
$583$	0	0
$584$	14.0000	0.579324
$585$	0	0
$586$	−24.0000	−0.991431
$587$	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
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	12.0000	0.493614
$592$	10.0000	0.410997
$593$	21.0000	0.862367	0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000	0.862367	0.431183	+	0.902264i	$0.358096\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	−11.0000	−0.450200
$598$	12.0000	0.490716
$599$	−3.00000	−0.122577	−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000	−0.122577	−0.0612883	+	0.998120i	$0.519521\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	8.00000	0.325515
$605$	0	0
$606$	−18.0000	−0.731200
$607$	−7.00000	−0.284121	−0.142061	−	0.989858i	$-0.545373\pi$
$607$	−7.00000	−0.284121	−0.142061	+	0.989858i	$0.545373\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	0	0
$611$	12.0000	0.485468
$612$	3.00000	0.121268
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	15.0000	0.603877	0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000	0.603877	0.301939	+	0.953327i	$0.402366\pi$
$618$	5.00000	0.201129
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	−3.00000	−0.120386
$622$	−9.00000	−0.360867
$623$	0	0
$624$	−4.00000	−0.160128
$625$	0	0
$626$	5.00000	0.199840
$627$	0	0
$628$	8.00000	0.319235
$629$	30.0000	1.19618
$630$	0	0
$631$	−37.0000	−1.47295	−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000	−1.47295	−0.736473	+	0.676467i	$0.763510\pi$
$632$	11.0000	0.437557
$633$	14.0000	0.556450
$634$	18.0000	0.714871
$635$	0	0
$636$	6.00000	0.237915
$637$	0	0
$638$	0	0
$639$	3.00000	0.118678
$640$	0	0
$641$	−33.0000	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$642$	18.0000	0.710403
$643$	38.0000	1.49857	0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000	1.49857	0.749287	+	0.662246i	$0.230396\pi$
$644$	0	0
$645$	0	0
$646$	−6.00000	−0.236067
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−8.00000	−0.313304
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	2.00000	0.0782062
$655$	0	0
$656$	9.00000	0.351391
$657$	14.0000	0.546192
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	−10.0000	−0.388661
$663$	−12.0000	−0.466041
$664$	0	0
$665$	0	0
$666$	10.0000	0.387492
$667$	0	0
$668$	−24.0000	−0.928588
$669$	−19.0000	−0.734582
$670$	0	0
$671$	0	0
$672$	0	0
$673$	19.0000	0.732396	0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000	0.732396	0.366198	+	0.930537i	$0.380659\pi$
$674$	−11.0000	−0.423704
$675$	0	0
$676$	3.00000	0.115385
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	−21.0000	−0.806500
$679$	0	0
$680$	0	0
$681$	−6.00000	−0.229920
$682$	0	0
$683$	−6.00000	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$684$	−2.00000	−0.0764719
$685$	0	0
$686$	0	0
$687$	4.00000	0.152610
$688$	10.0000	0.381246
$689$	−24.0000	−0.914327
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	36.0000	1.36654
$695$	0	0
$696$	0	0
$697$	27.0000	1.02270
$698$	−26.0000	−0.984115
$699$	30.0000	1.13470
$700$	0	0
$701$	−12.0000	−0.453234	−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000	−0.453234	−0.226617	+	0.973984i	$0.572767\pi$
$702$	−4.00000	−0.150970
$703$	−20.0000	−0.754314
$704$	0	0
$705$	0	0
$706$	−15.0000	−0.564532
$707$	0	0
$708$	6.00000	0.225494
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	11.0000	0.412532
$712$	15.0000	0.562149
$713$	−3.00000	−0.112351
$714$	0	0
$715$	0	0
$716$	−6.00000	−0.224231
$717$	15.0000	0.560185
$718$	12.0000	0.447836
$719$	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
$721$	0	0
$722$	−15.0000	−0.558242
$723$	−14.0000	−0.520666
$724$	−8.00000	−0.297318
$725$	0	0
$726$	−11.0000	−0.408248
$727$	−37.0000	−1.37225	−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000	−1.37225	−0.686127	+	0.727482i	$0.740691\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	30.0000	1.10959
$732$	−8.00000	−0.295689
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−3.00000	−0.110581
$737$	0	0
$738$	9.00000	0.331295
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	0	0
$741$	8.00000	0.293887
$742$	0	0
$743$	51.0000	1.87101	0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000	1.87101	0.935504	+	0.353315i	$0.114946\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	4.00000	0.146450
$747$	0	0
$748$	0	0
$749$	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	$0.594295\pi$
$752$	−3.00000	−0.109399
$753$	−12.0000	−0.437304
$754$	0	0
$755$	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	$0.406090\pi$
$758$	−16.0000	−0.581146
$759$	0	0
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	16.0000	0.579619
$763$	0	0
$764$	−21.0000	−0.759753
$765$	0	0
$766$	21.0000	0.758761
$767$	−24.0000	−0.866590
$768$	1.00000	0.0360844
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	30.0000	1.08042
$772$	−17.0000	−0.611843
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	10.0000	0.359443
$775$	0	0
$776$	−7.00000	−0.251285
$777$	0	0
$778$	6.00000	0.215110
$779$	−18.0000	−0.644917
$780$	0	0
$781$	0	0
$782$	−9.00000	−0.321839
$783$	0	0
$784$	0	0
$785$	0	0
$786$	12.0000	0.428026
$787$	−22.0000	−0.784215	−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000	−0.784215	−0.392108	+	0.919919i	$0.628254\pi$
$788$	12.0000	0.427482
$789$	−9.00000	−0.320408
$790$	0	0
$791$	0	0
$792$	0	0
$793$	32.0000	1.13635
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−11.0000	−0.389885
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	−9.00000	−0.318397
$800$	0	0
$801$	15.0000	0.529999
$802$	18.0000	0.635602
$803$	0	0
$804$	4.00000	0.141069
$805$	0	0
$806$	−4.00000	−0.140894
$807$	6.00000	0.211210
$808$	−18.0000	−0.633238
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	−56.0000	−1.96643	−0.983213	−	0.182462i	$-0.941593\pi$
$811$	−56.0000	−1.96643	−0.983213	+	0.182462i	$0.941593\pi$
$812$	0	0
$813$	7.00000	0.245501
$814$	0	0
$815$	0	0
$816$	3.00000	0.105021
$817$	−20.0000	−0.699711
$818$	−5.00000	−0.174821
$819$	0	0
$820$	0	0
$821$	−54.0000	−1.88461	−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000	−1.88461	−0.942306	+	0.334751i	$0.891348\pi$
$822$	9.00000	0.313911
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	5.00000	0.174183
$825$	0	0
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	−3.00000	−0.104257
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	28.0000	0.971309
$832$	−4.00000	−0.138675
$833$	0	0
$834$	−2.00000	−0.0692543
$835$	0	0
$836$	0	0
$837$	1.00000	0.0345651
$838$	−18.0000	−0.621800
$839$	−27.0000	−0.932144	−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−40.0000	−1.37849
$843$	9.00000	0.309976
$844$	14.0000	0.481900
$845$	0	0
$846$	−3.00000	−0.103142
$847$	0	0
$848$	6.00000	0.206041
$849$	−4.00000	−0.137280
$850$	0	0
$851$	−30.0000	−1.02839
$852$	3.00000	0.102778
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	0	0
$855$	0	0
$856$	18.0000	0.615227
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	0	0
$862$	−27.0000	−0.919624
$863$	15.0000	0.510606	0.255303	−	0.966861i	$-0.417825\pi$
$863$	15.0000	0.510606	0.255303	+	0.966861i	$0.417825\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	29.0000	0.985460
$867$	−8.00000	−0.271694
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−16.0000	−0.542139
$872$	2.00000	0.0677285
$873$	−7.00000	−0.236914
$874$	6.00000	0.202953
$875$	0	0
$876$	14.0000	0.473016
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−5.00000	−0.168742
$879$	−24.0000	−0.809500
$880$	0	0
$881$	3.00000	0.101073	0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000	0.101073	0.0505363	+	0.998722i	$0.483907\pi$
$882$	0	0
$883$	−38.0000	−1.27880	−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000	−1.27880	−0.639401	+	0.768874i	$0.720818\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	6.00000	0.201574
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	0	0
$891$	0	0
$892$	−19.0000	−0.636167
$893$	6.00000	0.200782
$894$	−6.00000	−0.200670
$895$	0	0
$896$	0	0
$897$	12.0000	0.400668
$898$	−21.0000	−0.700779
$899$	0	0
$900$	0	0
$901$	18.0000	0.599667
$902$	0	0
$903$	0	0
$904$	−21.0000	−0.698450
$905$	0	0
$906$	8.00000	0.265782
$907$	16.0000	0.531271	0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000	0.531271	0.265636	+	0.964073i	$0.414418\pi$
$908$	−6.00000	−0.199117
$909$	−18.0000	−0.597022
$910$	0	0
$911$	39.0000	1.29213	0.646064	−	0.763283i	$-0.276414\pi$
$911$	39.0000	1.29213	0.646064	+	0.763283i	$0.276414\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	4.00000	0.132164
$917$	0	0
$918$	3.00000	0.0990148
$919$	−19.0000	−0.626752	−0.313376	−	0.949629i	$-0.601460\pi$
$919$	−19.0000	−0.626752	−0.313376	+	0.949629i	$0.601460\pi$
$920$	0	0
$921$	−28.0000	−0.922631
$922$	12.0000	0.395199
$923$	−12.0000	−0.394985
$924$	0	0
$925$	0	0
$926$	−5.00000	−0.164310
$927$	5.00000	0.164222
$928$	0	0
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	0	0
$931$	0	0
$932$	30.0000	0.982683
$933$	−9.00000	−0.294647
$934$	12.0000	0.392652
$935$	0	0
$936$	−4.00000	−0.130744
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	0	0
$939$	5.00000	0.163169
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	8.00000	0.260654
$943$	−27.0000	−0.879241
$944$	6.00000	0.195283
$945$	0	0
$946$	0	0
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	11.0000	0.357263
$949$	−56.0000	−1.81784
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	15.0000	0.485135
$957$	0	0
$958$	27.0000	0.872330
$959$	0	0
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−40.0000	−1.28965
$963$	18.0000	0.580042
$964$	−14.0000	−0.450910
$965$	0	0
$966$	0	0
$967$	49.0000	1.57573	0.787867	−	0.615846i	$-0.211185\pi$
$967$	49.0000	1.57573	0.787867	+	0.615846i	$0.211185\pi$
$968$	−11.0000	−0.353553
$969$	−6.00000	−0.192748
$970$	0	0
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	31.0000	0.993304
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−27.0000	−0.863807	−0.431903	−	0.901920i	$-0.642158\pi$
$977$	−27.0000	−0.863807	−0.431903	+	0.901920i	$0.642158\pi$
$978$	−8.00000	−0.255812
$979$	0	0
$980$	0	0
$981$	2.00000	0.0638551
$982$	−6.00000	−0.191468
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	9.00000	0.286910
$985$	0	0
$986$	0	0
$987$	0	0
$988$	8.00000	0.254514
$989$	−30.0000	−0.953945
$990$	0	0
$991$	59.0000	1.87420	0.937098	−	0.349065i	$-0.113501\pi$
$991$	59.0000	1.87420	0.937098	+	0.349065i	$0.113501\pi$
$992$	1.00000	0.0317500
$993$	−10.0000	−0.317340
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−40.0000	−1.26681	−0.633406	−	0.773819i	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	32.0000	1.01294
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.cq.1.1		1
5.4	even	2		7350.2.a.n.1.1		1
7.3	odd	6		1050.2.i.h.751.1	yes	2
7.5	odd	6		1050.2.i.h.151.1	✓	2
7.6	odd	2		7350.2.a.by.1.1		1
35.3	even	12		1050.2.o.e.499.2		4
35.12	even	12		1050.2.o.e.949.2		4
35.17	even	12		1050.2.o.e.499.1		4
35.19	odd	6		1050.2.i.m.151.1	yes	2
35.24	odd	6		1050.2.i.m.751.1	yes	2
35.33	even	12		1050.2.o.e.949.1		4
35.34	odd	2		7350.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.h.151.1	✓	2	7.5	odd	6
1050.2.i.h.751.1	yes	2	7.3	odd	6
1050.2.i.m.151.1	yes	2	35.19	odd	6
1050.2.i.m.751.1	yes	2	35.24	odd	6
1050.2.o.e.499.1		4	35.17	even	12
1050.2.o.e.499.2		4	35.3	even	12
1050.2.o.e.949.1		4	35.33	even	12
1050.2.o.e.949.2		4	35.12	even	12
7350.2.a.n.1.1		1	5.4	even	2
7350.2.a.bb.1.1		1	35.34	odd	2
7350.2.a.by.1.1		1	7.6	odd	2
7350.2.a.cq.1.1		1	1.1	even	1	trivial

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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