LMFDB - Embedded newform 3610.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$1$
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	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +2.00000 q^{18} +1.00000 q^{20} +1.00000 q^{21} +3.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} -1.00000 q^{28} +3.00000 q^{29} +1.00000 q^{30} -2.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -1.00000 q^{35} -2.00000 q^{36} +10.0000 q^{37} -1.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} -1.00000 q^{42} +2.00000 q^{43} -2.00000 q^{45} -3.00000 q^{46} -1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} +3.00000 q^{51} +1.00000 q^{52} -3.00000 q^{53} -5.00000 q^{54} +1.00000 q^{56} -3.00000 q^{58} -3.00000 q^{59} -1.00000 q^{60} +8.00000 q^{61} +2.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} +7.00000 q^{67} -3.00000 q^{68} -3.00000 q^{69} +1.00000 q^{70} -12.0000 q^{71} +2.00000 q^{72} -13.0000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +1.00000 q^{78} -14.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +6.00000 q^{83} +1.00000 q^{84} -3.00000 q^{85} -2.00000 q^{86} -3.00000 q^{87} -6.00000 q^{89} +2.00000 q^{90} -1.00000 q^{91} +3.00000 q^{92} +2.00000 q^{93} +1.00000 q^{96} +10.0000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	2.00000	0.471405
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	0	0
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	1.00000	0.182574
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	3.00000	0.514496
$35$	−1.00000	−0.169031
$36$	−2.00000	−0.333333
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	−1.00000	−0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.00000	−0.154303
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	−3.00000	−0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	3.00000	0.420084
$52$	1.00000	0.138675
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.00000	−0.393919
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	−1.00000	−0.129099
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	2.00000	0.254000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	−3.00000	−0.363803
$69$	−3.00000	−0.361158
$70$	1.00000	0.119523
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	2.00000	0.235702
$73$	−13.0000	−1.52153	−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000	−1.52153	−0.760767	+	0.649025i	$0.775177\pi$
$74$	−10.0000	−1.16248
$75$	−1.00000	−0.115470
$76$	0	0
$77$	0	0
$78$	1.00000	0.113228
$79$	−14.0000	−1.57512	−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000	−1.57512	−0.787562	+	0.616236i	$0.788657\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	0.109109
$85$	−3.00000	−0.325396
$86$	−2.00000	−0.215666
$87$	−3.00000	−0.321634
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	2.00000	0.210819
$91$	−1.00000	−0.104828
$92$	3.00000	0.312772
$93$	2.00000	0.207390
$94$	0	0
$95$	0	0
$96$	1.00000	0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	1.00000	0.100000
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	−3.00000	−0.297044
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−1.00000	−0.0980581
$105$	1.00000	0.0975900
$106$	3.00000	0.291386
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	5.00000	0.481125
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	−1.00000	−0.0944911
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	0	0
$115$	3.00000	0.279751
$116$	3.00000	0.278543
$117$	−2.00000	−0.184900
$118$	3.00000	0.276172
$119$	3.00000	0.275010
$120$	1.00000	0.0912871
$121$	−11.0000	−1.00000
$122$	−8.00000	−0.724286
$123$	6.00000	0.541002
$124$	−2.00000	−0.179605
$125$	1.00000	0.0894427
$126$	−2.00000	−0.178174
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−1.00000	−0.0883883
$129$	−2.00000	−0.176090
$130$	−1.00000	−0.0877058
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	−7.00000	−0.604708
$135$	5.00000	0.430331
$136$	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
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	12.0000	1.00702
$143$	0	0
$144$	−2.00000	−0.166667
$145$	3.00000	0.249136
$146$	13.0000	1.07589
$147$	6.00000	0.494872
$148$	10.0000	0.821995
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	1.00000	0.0816497
$151$	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
$153$	6.00000	0.485071
$154$	0	0
$155$	−2.00000	−0.160644
$156$	−1.00000	−0.0800641
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	14.0000	1.11378
$159$	3.00000	0.237915
$160$	−1.00000	−0.0790569
$161$	−3.00000	−0.236433
$162$	−1.00000	−0.0785674
$163$	−22.0000	−1.72317	−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000	−1.72317	−0.861586	+	0.507611i	$0.830529\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−6.00000	−0.465690
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	−1.00000	−0.0771517
$169$	−12.0000	−0.923077
$170$	3.00000	0.230089
$171$	0	0
$172$	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	$0.426753\pi$
$174$	3.00000	0.227429
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	3.00000	0.225494
$178$	6.00000	0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−2.00000	−0.149071
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	1.00000	0.0741249
$183$	−8.00000	−0.591377
$184$	−3.00000	−0.221163
$185$	10.0000	0.735215
$186$	−2.00000	−0.146647
$187$	0	0
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	−1.00000	−0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−10.0000	−0.717958
$195$	−1.00000	−0.0716115
$196$	−6.00000	−0.428571
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−19.0000	−1.34687	−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000	−1.34687	−0.673437	+	0.739244i	$0.735183\pi$
$200$	−1.00000	−0.0707107
$201$	−7.00000	−0.493742
$202$	−12.0000	−0.844317
$203$	−3.00000	−0.210559
$204$	3.00000	0.210042
$205$	−6.00000	−0.419058
$206$	8.00000	0.557386
$207$	−6.00000	−0.417029
$208$	1.00000	0.0693375
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	25.0000	1.72107	0.860535	−	0.509390i	$-0.170129\pi$
$211$	25.0000	1.72107	0.860535	+	0.509390i	$0.170129\pi$
$212$	−3.00000	−0.206041
$213$	12.0000	0.822226
$214$	15.0000	1.02538
$215$	2.00000	0.136399
$216$	−5.00000	−0.340207
$217$	2.00000	0.135769
$218$	11.0000	0.745014
$219$	13.0000	0.878459
$220$	0	0
$221$	−3.00000	−0.201802
$222$	10.0000	0.671156
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	1.00000	0.0668153
$225$	−2.00000	−0.133333
$226$	−12.0000	−0.798228
$227$	15.0000	0.995585	0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000	0.995585	0.497792	+	0.867296i	$0.334144\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	−3.00000	−0.197814
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−3.00000	−0.195283
$237$	14.0000	0.909398
$238$	−3.00000	−0.194461
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	−1.00000	−0.0645497
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	11.0000	0.707107
$243$	−16.0000	−1.02640
$244$	8.00000	0.512148
$245$	−6.00000	−0.383326
$246$	−6.00000	−0.382546
$247$	0	0
$248$	2.00000	0.127000
$249$	−6.00000	−0.380235
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	2.00000	0.125491
$255$	3.00000	0.187867
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	2.00000	0.124515
$259$	−10.0000	−0.621370
$260$	1.00000	0.0620174
$261$	−6.00000	−0.371391
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	−3.00000	−0.184289
$266$	0	0
$267$	6.00000	0.367194
$268$	7.00000	0.427593
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−5.00000	−0.304290
$271$	−7.00000	−0.425220	−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000	−0.425220	−0.212610	+	0.977137i	$0.568196\pi$
$272$	−3.00000	−0.181902
$273$	1.00000	0.0605228
$274$	−9.00000	−0.543710
$275$	0	0
$276$	−3.00000	−0.180579
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−8.00000	−0.479808
$279$	4.00000	0.239474
$280$	1.00000	0.0597614
$281$	−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
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	0	0
$287$	6.00000	0.354169
$288$	2.00000	0.117851
$289$	−8.00000	−0.470588
$290$	−3.00000	−0.176166
$291$	−10.0000	−0.586210
$292$	−13.0000	−0.760767
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	−6.00000	−0.349927
$295$	−3.00000	−0.174667
$296$	−10.0000	−0.581238
$297$	0	0
$298$	12.0000	0.695141
$299$	3.00000	0.173494
$300$	−1.00000	−0.0577350
$301$	−2.00000	−0.115278
$302$	−10.0000	−0.575435
$303$	−12.0000	−0.689382
$304$	0	0
$305$	8.00000	0.458079
$306$	−6.00000	−0.342997
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	2.00000	0.113592
$311$	−3.00000	−0.170114	−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000	−0.170114	−0.0850572	+	0.996376i	$0.527107\pi$
$312$	1.00000	0.0566139
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	10.0000	0.564333
$315$	2.00000	0.112687
$316$	−14.0000	−0.787562
$317$	−9.00000	−0.505490	−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000	−0.505490	−0.252745	+	0.967533i	$0.581333\pi$
$318$	−3.00000	−0.168232
$319$	0	0
$320$	1.00000	0.0559017
$321$	15.0000	0.837218
$322$	3.00000	0.167183
$323$	0	0
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	22.0000	1.21847
$327$	11.0000	0.608301
$328$	6.00000	0.331295
$329$	0	0
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	6.00000	0.329293
$333$	−20.0000	−1.09599
$334$	18.0000	0.984916
$335$	7.00000	0.382451
$336$	1.00000	0.0545545
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	12.0000	0.652714
$339$	−12.0000	−0.651751
$340$	−3.00000	−0.162698
$341$	0	0
$342$	0	0
$343$	13.0000	0.701934
$344$	−2.00000	−0.107833
$345$	−3.00000	−0.161515
$346$	−6.00000	−0.322562
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	−3.00000	−0.160817
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	1.00000	0.0534522
$351$	5.00000	0.266880
$352$	0	0
$353$	−33.0000	−1.75641	−0.878206	−	0.478282i	$-0.841260\pi$
$353$	−33.0000	−1.75641	−0.878206	+	0.478282i	$0.841260\pi$
$354$	−3.00000	−0.159448
$355$	−12.0000	−0.636894
$356$	−6.00000	−0.317999
$357$	−3.00000	−0.158777
$358$	0	0
$359$	−33.0000	−1.74167	−0.870837	−	0.491572i	$-0.836422\pi$
$359$	−33.0000	−1.74167	−0.870837	+	0.491572i	$0.836422\pi$
$360$	2.00000	0.105409
$361$	0	0
$362$	2.00000	0.105118
$363$	11.0000	0.577350
$364$	−1.00000	−0.0524142
$365$	−13.0000	−0.680451
$366$	8.00000	0.418167
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	3.00000	0.156386
$369$	12.0000	0.624695
$370$	−10.0000	−0.519875
$371$	3.00000	0.155752
$372$	2.00000	0.103695
$373$	31.0000	1.60512	0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000	1.60512	0.802560	+	0.596572i	$0.203471\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	3.00000	0.154508
$378$	5.00000	0.257172
$379$	−35.0000	−1.79783	−0.898915	−	0.438124i	$-0.855643\pi$
$379$	−35.0000	−1.79783	−0.898915	+	0.438124i	$0.855643\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	27.0000	1.38144
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.0000	−1.11977
$387$	−4.00000	−0.203331
$388$	10.0000	0.507673
$389$	−24.0000	−1.21685	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000	−1.21685	−0.608424	+	0.793612i	$0.708198\pi$
$390$	1.00000	0.0506370
$391$	−9.00000	−0.455150
$392$	6.00000	0.303046
$393$	0	0
$394$	−6.00000	−0.302276
$395$	−14.0000	−0.704416
$396$	0	0
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	19.0000	0.952384
$399$	0	0
$400$	1.00000	0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	7.00000	0.349128
$403$	−2.00000	−0.0996271
$404$	12.0000	0.597022
$405$	1.00000	0.0496904
$406$	3.00000	0.148888
$407$	0	0
$408$	−3.00000	−0.148522
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	6.00000	0.296319
$411$	−9.00000	−0.443937
$412$	−8.00000	−0.394132
$413$	3.00000	0.147620
$414$	6.00000	0.294884
$415$	6.00000	0.294528
$416$	−1.00000	−0.0490290
$417$	−8.00000	−0.391762
$418$	0	0
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	1.00000	0.0487950
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	−25.0000	−1.21698
$423$	0	0
$424$	3.00000	0.145693
$425$	−3.00000	−0.145521
$426$	−12.0000	−0.581402
$427$	−8.00000	−0.387147
$428$	−15.0000	−0.725052
$429$	0	0
$430$	−2.00000	−0.0964486
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	5.00000	0.240563
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	−2.00000	−0.0960031
$435$	−3.00000	−0.143839
$436$	−11.0000	−0.526804
$437$	0	0
$438$	−13.0000	−0.621164
$439$	−38.0000	−1.81364	−0.906821	−	0.421517i	$-0.861498\pi$
$439$	−38.0000	−1.81364	−0.906821	+	0.421517i	$0.861498\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	3.00000	0.142695
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−10.0000	−0.474579
$445$	−6.00000	−0.284427
$446$	14.0000	0.662919
$447$	12.0000	0.567581
$448$	−1.00000	−0.0472456
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	2.00000	0.0942809
$451$	0	0
$452$	12.0000	0.564433
$453$	−10.0000	−0.469841
$454$	−15.0000	−0.703985
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	35.0000	1.63723	0.818615	−	0.574342i	$-0.194742\pi$
$457$	35.0000	1.63723	0.818615	+	0.574342i	$0.194742\pi$
$458$	−26.0000	−1.21490
$459$	−15.0000	−0.700140
$460$	3.00000	0.139876
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	3.00000	0.139272
$465$	2.00000	0.0927478
$466$	6.00000	0.277945
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	−2.00000	−0.0924500
$469$	−7.00000	−0.323230
$470$	0	0
$471$	10.0000	0.460776
$472$	3.00000	0.138086
$473$	0	0
$474$	−14.0000	−0.643041
$475$	0	0
$476$	3.00000	0.137505
$477$	6.00000	0.274721
$478$	15.0000	0.686084
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	10.0000	0.455961
$482$	−4.00000	−0.182195
$483$	3.00000	0.136505
$484$	−11.0000	−0.500000
$485$	10.0000	0.454077
$486$	16.0000	0.725775
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−8.00000	−0.362143
$489$	22.0000	0.994874
$490$	6.00000	0.271052
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	6.00000	0.270501
$493$	−9.00000	−0.405340
$494$	0	0
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	12.0000	0.538274
$498$	6.00000	0.268866
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	1.00000	0.0447214
$501$	18.0000	0.804181
$502$	0	0
$503$	39.0000	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$504$	−2.00000	−0.0890871
$505$	12.0000	0.533993
$506$	0	0
$507$	12.0000	0.532939
$508$	−2.00000	−0.0887357
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−3.00000	−0.132842
$511$	13.0000	0.575086
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	18.0000	0.793946
$515$	−8.00000	−0.352522
$516$	−2.00000	−0.0880451
$517$	0	0
$518$	10.0000	0.439375
$519$	−6.00000	−0.263371
$520$	−1.00000	−0.0438529
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	6.00000	0.262613
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	0	0
$525$	1.00000	0.0436436
$526$	0	0
$527$	6.00000	0.261364
$528$	0	0
$529$	−14.0000	−0.608696
$530$	3.00000	0.130312
$531$	6.00000	0.260378
$532$	0	0
$533$	−6.00000	−0.259889
$534$	−6.00000	−0.259645
$535$	−15.0000	−0.648507
$536$	−7.00000	−0.302354
$537$	0	0
$538$	18.0000	0.776035
$539$	0	0
$540$	5.00000	0.215166
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	7.00000	0.300676
$543$	2.00000	0.0858282
$544$	3.00000	0.128624
$545$	−11.0000	−0.471188
$546$	−1.00000	−0.0427960
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	9.00000	0.384461
$549$	−16.0000	−0.682863
$550$	0	0
$551$	0	0
$552$	3.00000	0.127688
$553$	14.0000	0.595341
$554$	−8.00000	−0.339887
$555$	−10.0000	−0.424476
$556$	8.00000	0.339276
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	−4.00000	−0.169334
$559$	2.00000	0.0845910
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	18.0000	0.759284
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	12.0000	0.504844
$566$	−14.0000	−0.588464
$567$	−1.00000	−0.0419961
$568$	12.0000	0.503509
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	0	0
$573$	27.0000	1.12794
$574$	−6.00000	−0.250435
$575$	3.00000	0.125109
$576$	−2.00000	−0.0833333
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	8.00000	0.332756
$579$	−22.0000	−0.914289
$580$	3.00000	0.124568
$581$	−6.00000	−0.248922
$582$	10.0000	0.414513
$583$	0	0
$584$	13.0000	0.537944
$585$	−2.00000	−0.0826898
$586$	21.0000	0.867502
$587$	30.0000	1.23823	0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000	1.23823	0.619116	+	0.785299i	$0.287491\pi$
$588$	6.00000	0.247436
$589$	0	0
$590$	3.00000	0.123508
$591$	−6.00000	−0.246807
$592$	10.0000	0.410997
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	3.00000	0.122988
$596$	−12.0000	−0.491539
$597$	19.0000	0.777618
$598$	−3.00000	−0.122679
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	1.00000	0.0408248
$601$	34.0000	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$602$	2.00000	0.0815139
$603$	−14.0000	−0.570124
$604$	10.0000	0.406894
$605$	−11.0000	−0.447214
$606$	12.0000	0.487467
$607$	10.0000	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$608$	0	0
$609$	3.00000	0.121566
$610$	−8.00000	−0.323911
$611$	0	0
$612$	6.00000	0.242536
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	20.0000	0.807134
$615$	6.00000	0.241943
$616$	0	0
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	−8.00000	−0.321807
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	−2.00000	−0.0803219
$621$	15.0000	0.601929
$622$	3.00000	0.120289
$623$	6.00000	0.240385
$624$	−1.00000	−0.0400320
$625$	1.00000	0.0400000
$626$	1.00000	0.0399680
$627$	0	0
$628$	−10.0000	−0.399043
$629$	−30.0000	−1.19618
$630$	−2.00000	−0.0796819
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	14.0000	0.556890
$633$	−25.0000	−0.993661
$634$	9.00000	0.357436
$635$	−2.00000	−0.0793676
$636$	3.00000	0.118958
$637$	−6.00000	−0.237729
$638$	0	0
$639$	24.0000	0.949425
$640$	−1.00000	−0.0395285
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	−15.0000	−0.592003
$643$	50.0000	1.97181	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	50.0000	1.97181	0.985904	+	0.167313i	$0.0535092\pi$
$644$	−3.00000	−0.118217
$645$	−2.00000	−0.0787499
$646$	0	0
$647$	−33.0000	−1.29736	−0.648682	−	0.761060i	$-0.724679\pi$
$647$	−33.0000	−1.29736	−0.648682	+	0.761060i	$0.724679\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	−2.00000	−0.0783862
$652$	−22.0000	−0.861586
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	−11.0000	−0.430134
$655$	0	0
$656$	−6.00000	−0.234261
$657$	26.0000	1.01436
$658$	0	0
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	49.0000	1.90588	0.952940	−	0.303160i	$-0.0980418\pi$
$661$	49.0000	1.90588	0.952940	+	0.303160i	$0.0980418\pi$
$662$	5.00000	0.194331
$663$	3.00000	0.116510
$664$	−6.00000	−0.232845
$665$	0	0
$666$	20.0000	0.774984
$667$	9.00000	0.348481
$668$	−18.0000	−0.696441
$669$	14.0000	0.541271
$670$	−7.00000	−0.270434
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	−20.0000	−0.770943	−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000	−0.770943	−0.385472	+	0.922720i	$0.625961\pi$
$674$	2.00000	0.0770371
$675$	5.00000	0.192450
$676$	−12.0000	−0.461538
$677$	15.0000	0.576497	0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000	0.576497	0.288248	+	0.957556i	$0.406927\pi$
$678$	12.0000	0.460857
$679$	−10.0000	−0.383765
$680$	3.00000	0.115045
$681$	−15.0000	−0.574801
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	9.00000	0.343872
$686$	−13.0000	−0.496342
$687$	−26.0000	−0.991962
$688$	2.00000	0.0762493
$689$	−3.00000	−0.114291
$690$	3.00000	0.114208
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	30.0000	1.13878
$695$	8.00000	0.303457
$696$	3.00000	0.113715
$697$	18.0000	0.681799
$698$	−14.0000	−0.529908
$699$	6.00000	0.226941
$700$	−1.00000	−0.0377964
$701$	48.0000	1.81293	0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000	1.81293	0.906467	+	0.422276i	$0.138769\pi$
$702$	−5.00000	−0.188713
$703$	0	0
$704$	0	0
$705$	0	0
$706$	33.0000	1.24197
$707$	−12.0000	−0.451306
$708$	3.00000	0.112747
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	12.0000	0.450352
$711$	28.0000	1.05008
$712$	6.00000	0.224860
$713$	−6.00000	−0.224702
$714$	3.00000	0.112272
$715$	0	0
$716$	0	0
$717$	15.0000	0.560185
$718$	33.0000	1.23155
$719$	33.0000	1.23069	0.615346	−	0.788257i	$-0.289016\pi$
$719$	33.0000	1.23069	0.615346	+	0.788257i	$0.289016\pi$
$720$	−2.00000	−0.0745356
$721$	8.00000	0.297936
$722$	0	0
$723$	−4.00000	−0.148762
$724$	−2.00000	−0.0743294
$725$	3.00000	0.111417
$726$	−11.0000	−0.408248
$727$	−13.0000	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$728$	1.00000	0.0370625
$729$	13.0000	0.481481
$730$	13.0000	0.481152
$731$	−6.00000	−0.221918
$732$	−8.00000	−0.295689
$733$	−4.00000	−0.147743	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000	−0.147743	−0.0738717	+	0.997268i	$0.523536\pi$
$734$	16.0000	0.590571
$735$	6.00000	0.221313
$736$	−3.00000	−0.110581
$737$	0	0
$738$	−12.0000	−0.441726
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	10.0000	0.367607
$741$	0	0
$742$	−3.00000	−0.110133
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	−2.00000	−0.0733236
$745$	−12.0000	−0.439646
$746$	−31.0000	−1.13499
$747$	−12.0000	−0.439057
$748$	0	0
$749$	15.0000	0.548088
$750$	1.00000	0.0365148
$751$	−2.00000	−0.0729810	−0.0364905	−	0.999334i	$-0.511618\pi$
$751$	−2.00000	−0.0729810	−0.0364905	+	0.999334i	$0.511618\pi$
$752$	0	0
$753$	0	0
$754$	−3.00000	−0.109254
$755$	10.0000	0.363937
$756$	−5.00000	−0.181848
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	35.0000	1.27126
$759$	0	0
$760$	0	0
$761$	−21.0000	−0.761249	−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000	−0.761249	−0.380625	+	0.924730i	$0.624291\pi$
$762$	−2.00000	−0.0724524
$763$	11.0000	0.398227
$764$	−27.0000	−0.976826
$765$	6.00000	0.216930
$766$	−24.0000	−0.867155
$767$	−3.00000	−0.108324
$768$	−1.00000	−0.0360844
$769$	−55.0000	−1.98335	−0.991675	−	0.128763i	$-0.958899\pi$
$769$	−55.0000	−1.98335	−0.991675	+	0.128763i	$0.958899\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	22.0000	0.791797
$773$	−21.0000	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$774$	4.00000	0.143777
$775$	−2.00000	−0.0718421
$776$	−10.0000	−0.358979
$777$	10.0000	0.358748
$778$	24.0000	0.860442
$779$	0	0
$780$	−1.00000	−0.0358057
$781$	0	0
$782$	9.00000	0.321839
$783$	15.0000	0.536056
$784$	−6.00000	−0.214286
$785$	−10.0000	−0.356915
$786$	0	0
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	14.0000	0.498098
$791$	−12.0000	−0.426671
$792$	0	0
$793$	8.00000	0.284088
$794$	−8.00000	−0.283909
$795$	3.00000	0.106399
$796$	−19.0000	−0.673437
$797$	33.0000	1.16892	0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000	1.16892	0.584460	+	0.811423i	$0.301306\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	12.0000	0.423999
$802$	6.00000	0.211867
$803$	0	0
$804$	−7.00000	−0.246871
$805$	−3.00000	−0.105736
$806$	2.00000	0.0704470
$807$	18.0000	0.633630
$808$	−12.0000	−0.422159
$809$	33.0000	1.16022	0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000	1.16022	0.580109	+	0.814539i	$0.303010\pi$
$810$	−1.00000	−0.0351364
$811$	7.00000	0.245803	0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000	0.245803	0.122902	+	0.992419i	$0.460780\pi$
$812$	−3.00000	−0.105279
$813$	7.00000	0.245501
$814$	0	0
$815$	−22.0000	−0.770626
$816$	3.00000	0.105021
$817$	0	0
$818$	−22.0000	−0.769212
$819$	2.00000	0.0698857
$820$	−6.00000	−0.209529
$821$	−12.0000	−0.418803	−0.209401	−	0.977830i	$-0.567152\pi$
$821$	−12.0000	−0.418803	−0.209401	+	0.977830i	$0.567152\pi$
$822$	9.00000	0.313911
$823$	−31.0000	−1.08059	−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000	−1.08059	−0.540296	+	0.841475i	$0.681688\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−3.00000	−0.104383
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	−6.00000	−0.208514
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	−6.00000	−0.208263
$831$	−8.00000	−0.277517
$832$	1.00000	0.0346688
$833$	18.0000	0.623663
$834$	8.00000	0.277017
$835$	−18.0000	−0.622916
$836$	0	0
$837$	−10.0000	−0.345651
$838$	30.0000	1.03633
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	−1.00000	−0.0345033
$841$	−20.0000	−0.689655
$842$	17.0000	0.585859
$843$	18.0000	0.619953
$844$	25.0000	0.860535
$845$	−12.0000	−0.412813
$846$	0	0
$847$	11.0000	0.377964
$848$	−3.00000	−0.103020
$849$	−14.0000	−0.480479
$850$	3.00000	0.102899
$851$	30.0000	1.02839
$852$	12.0000	0.411113
$853$	50.0000	1.71197	0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000	1.71197	0.855984	+	0.517003i	$0.172952\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	15.0000	0.512689
$857$	−48.0000	−1.63965	−0.819824	−	0.572615i	$-0.805929\pi$
$857$	−48.0000	−1.63965	−0.819824	+	0.572615i	$0.805929\pi$
$858$	0	0
$859$	−16.0000	−0.545913	−0.272956	−	0.962026i	$-0.588002\pi$
$859$	−16.0000	−0.545913	−0.272956	+	0.962026i	$0.588002\pi$
$860$	2.00000	0.0681994
$861$	−6.00000	−0.204479
$862$	24.0000	0.817443
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−5.00000	−0.170103
$865$	6.00000	0.204006
$866$	−4.00000	−0.135926
$867$	8.00000	0.271694
$868$	2.00000	0.0678844
$869$	0	0
$870$	3.00000	0.101710
$871$	7.00000	0.237186
$872$	11.0000	0.372507
$873$	−20.0000	−0.676897
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	13.0000	0.439229
$877$	31.0000	1.04680	0.523398	−	0.852088i	$-0.324664\pi$
$877$	31.0000	1.04680	0.523398	+	0.852088i	$0.324664\pi$
$878$	38.0000	1.28244
$879$	21.0000	0.708312
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	−12.0000	−0.404061
$883$	38.0000	1.27880	0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000	1.27880	0.639401	+	0.768874i	$0.279182\pi$
$884$	−3.00000	−0.100901
$885$	3.00000	0.100844
$886$	24.0000	0.806296
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	10.0000	0.335578
$889$	2.00000	0.0670778
$890$	6.00000	0.201120
$891$	0	0
$892$	−14.0000	−0.468755
$893$	0	0
$894$	−12.0000	−0.401340
$895$	0	0
$896$	1.00000	0.0334077
$897$	−3.00000	−0.100167
$898$	−30.0000	−1.00111
$899$	−6.00000	−0.200111
$900$	−2.00000	−0.0666667
$901$	9.00000	0.299833
$902$	0	0
$903$	2.00000	0.0665558
$904$	−12.0000	−0.399114
$905$	−2.00000	−0.0664822
$906$	10.0000	0.332228
$907$	−35.0000	−1.16216	−0.581078	−	0.813848i	$-0.697369\pi$
$907$	−35.0000	−1.16216	−0.581078	+	0.813848i	$0.697369\pi$
$908$	15.0000	0.497792
$909$	−24.0000	−0.796030
$910$	1.00000	0.0331497
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	0	0
$913$	0	0
$914$	−35.0000	−1.15770
$915$	−8.00000	−0.264472
$916$	26.0000	0.859064
$917$	0	0
$918$	15.0000	0.495074
$919$	−1.00000	−0.0329870	−0.0164935	−	0.999864i	$-0.505250\pi$
$919$	−1.00000	−0.0329870	−0.0164935	+	0.999864i	$0.505250\pi$
$920$	−3.00000	−0.0989071
$921$	20.0000	0.659022
$922$	−6.00000	−0.197599
$923$	−12.0000	−0.394985
$924$	0	0
$925$	10.0000	0.328798
$926$	16.0000	0.525793
$927$	16.0000	0.525509
$928$	−3.00000	−0.0984798
$929$	21.0000	0.688988	0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000	0.688988	0.344494	+	0.938789i	$0.388051\pi$
$930$	−2.00000	−0.0655826
$931$	0	0
$932$	−6.00000	−0.196537
$933$	3.00000	0.0982156
$934$	−12.0000	−0.392652
$935$	0	0
$936$	2.00000	0.0653720
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	7.00000	0.228558
$939$	1.00000	0.0326338
$940$	0	0
$941$	−45.0000	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$942$	−10.0000	−0.325818
$943$	−18.0000	−0.586161
$944$	−3.00000	−0.0976417
$945$	−5.00000	−0.162650
$946$	0	0
$947$	24.0000	0.779895	0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000	0.779895	0.389948	+	0.920837i	$0.372493\pi$
$948$	14.0000	0.454699
$949$	−13.0000	−0.421998
$950$	0	0
$951$	9.00000	0.291845
$952$	−3.00000	−0.0972306
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	−6.00000	−0.194257
$955$	−27.0000	−0.873699
$956$	−15.0000	−0.485135
$957$	0	0
$958$	24.0000	0.775405
$959$	−9.00000	−0.290625
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	−10.0000	−0.322413
$963$	30.0000	0.966736
$964$	4.00000	0.128831
$965$	22.0000	0.708205
$966$	−3.00000	−0.0965234
$967$	44.0000	1.41494	0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000	1.41494	0.707472	+	0.706741i	$0.249835\pi$
$968$	11.0000	0.353553
$969$	0	0
$970$	−10.0000	−0.321081
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	−16.0000	−0.513200
$973$	−8.00000	−0.256468
$974$	2.00000	0.0640841
$975$	−1.00000	−0.0320256
$976$	8.00000	0.256074
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	−22.0000	−0.703482
$979$	0	0
$980$	−6.00000	−0.191663
$981$	22.0000	0.702406
$982$	−30.0000	−0.957338
$983$	−54.0000	−1.72233	−0.861166	−	0.508323i	$-0.830265\pi$
$983$	−54.0000	−1.72233	−0.861166	+	0.508323i	$0.830265\pi$
$984$	−6.00000	−0.191273
$985$	6.00000	0.191176
$986$	9.00000	0.286618
$987$	0	0
$988$	0	0
$989$	6.00000	0.190789
$990$	0	0
$991$	−2.00000	−0.0635321	−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000	−0.0635321	−0.0317660	+	0.999495i	$0.510113\pi$
$992$	2.00000	0.0635001
$993$	5.00000	0.158670
$994$	−12.0000	−0.380617
$995$	−19.0000	−0.602340
$996$	−6.00000	−0.190117
$997$	−46.0000	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	10.0000	0.316544
$999$	50.0000	1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.b.1.1		1
19.18	odd	2		190.2.a.c.1.1	✓	1
57.56	even	2		1710.2.a.d.1.1		1
76.75	even	2		1520.2.a.d.1.1		1
95.18	even	4		950.2.b.e.799.1		2
95.37	even	4		950.2.b.e.799.2		2
95.94	odd	2		950.2.a.a.1.1		1
133.132	even	2		9310.2.a.o.1.1		1
152.37	odd	2		6080.2.a.h.1.1		1
152.75	even	2		6080.2.a.p.1.1		1
285.284	even	2		8550.2.a.bd.1.1		1
380.379	even	2		7600.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.c.1.1	✓	1	19.18	odd	2
950.2.a.a.1.1		1	95.94	odd	2
950.2.b.e.799.1		2	95.18	even	4
950.2.b.e.799.2		2	95.37	even	4
1520.2.a.d.1.1		1	76.75	even	2
1710.2.a.d.1.1		1	57.56	even	2
3610.2.a.b.1.1		1	1.1	even	1	trivial
6080.2.a.h.1.1		1	152.37	odd	2
6080.2.a.p.1.1		1	152.75	even	2
7600.2.a.m.1.1		1	380.379	even	2
8550.2.a.bd.1.1		1	285.284	even	2
9310.2.a.o.1.1		1	133.132	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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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