LMFDB - Embedded newform 1530.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(1,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, 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("1530.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1530.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} +2.00000 q^{11} -6.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{20} -2.00000 q^{22} +1.00000 q^{25} +6.00000 q^{26} -4.00000 q^{28} +6.00000 q^{29} -1.00000 q^{32} -1.00000 q^{34} +4.00000 q^{35} -8.00000 q^{37} +1.00000 q^{40} +6.00000 q^{41} +6.00000 q^{43} +2.00000 q^{44} +8.00000 q^{47} +9.00000 q^{49} -1.00000 q^{50} -6.00000 q^{52} +6.00000 q^{53} -2.00000 q^{55} +4.00000 q^{56} -6.00000 q^{58} -12.0000 q^{59} +10.0000 q^{61} +1.00000 q^{64} +6.00000 q^{65} +10.0000 q^{67} +1.00000 q^{68} -4.00000 q^{70} -6.00000 q^{71} +8.00000 q^{74} -8.00000 q^{77} -1.00000 q^{80} -6.00000 q^{82} +12.0000 q^{83} -1.00000 q^{85} -6.00000 q^{86} -2.00000 q^{88} +24.0000 q^{91} -8.00000 q^{94} -8.00000 q^{97} -9.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	6.00000	1.17670
$27$	0	0
$28$	−4.00000	−0.755929
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.00000	−0.171499
$35$	4.00000	0.676123
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	0	0
$40$	1.00000	0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	0	0
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−6.00000	−0.832050
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	4.00000	0.534522
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	−4.00000	−0.478091
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	0	0
$77$	−8.00000	−0.911685
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	−6.00000	−0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	−1.00000	−0.108465
$86$	−6.00000	−0.646997
$87$	0	0
$88$	−2.00000	−0.213201
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	0	0
$93$	0	0
$94$	−8.00000	−0.825137
$95$	0	0
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−9.00000	−0.909137
$99$	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	$0.296350\pi$
$102$	0	0
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	−6.00000	−0.582772
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	−4.00000	−0.377964
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	12.0000	1.10469
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−10.0000	−0.905357
$123$	0	0
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−6.00000	−0.526235
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	0	0
$133$	0	0
$134$	−10.0000	−0.863868
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	4.00000	0.338062
$141$	0	0
$142$	6.00000	0.503509
$143$	−12.0000	−1.00349
$144$	0	0
$145$	−6.00000	−0.498273
$146$	0	0
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−8.00000	−0.655386	−0.327693	−	0.944784i	$-0.606271\pi$
$149$	−8.00000	−0.655386	−0.327693	+	0.944784i	$0.606271\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	0	0
$153$	0	0
$154$	8.00000	0.644658
$155$	0	0
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	0	0
$160$	1.00000	0.0790569
$161$	0	0
$162$	0	0
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−12.0000	−0.931381
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	1.00000	0.0766965
$171$	0	0
$172$	6.00000	0.457496
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	2.00000	0.150756
$177$	0	0
$178$	0	0
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	−24.0000	−1.77900
$183$	0	0
$184$	0	0
$185$	8.00000	0.588172
$186$	0	0
$187$	2.00000	0.146254
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	0	0
$193$	12.0000	0.863779	0.431889	−	0.901927i	$-0.357847\pi$
$193$	12.0000	0.863779	0.431889	+	0.901927i	$0.357847\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	9.00000	0.642857
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−12.0000	−0.844317
$203$	−24.0000	−1.68447
$204$	0	0
$205$	−6.00000	−0.419058
$206$	−10.0000	−0.696733
$207$	0	0
$208$	−6.00000	−0.416025
$209$	0	0
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	0	0
$215$	−6.00000	−0.409197
$216$	0	0
$217$	0	0
$218$	14.0000	0.948200
$219$	0	0
$220$	−2.00000	−0.134840
$221$	−6.00000	−0.403604
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	−2.00000	−0.133038
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	0	0
$232$	−6.00000	−0.393919
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	0	0
$235$	−8.00000	−0.521862
$236$	−12.0000	−0.781133
$237$	0	0
$238$	4.00000	0.259281
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	10.0000	0.640184
$245$	−9.00000	−0.574989
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	1.00000	0.0632456
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	0	0
$254$	14.0000	0.878438
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	32.0000	1.98838
$260$	6.00000	0.372104
$261$	0	0
$262$	−10.0000	−0.617802
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	0	0
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	2.00000	0.120824
$275$	2.00000	0.120605
$276$	0	0
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	−4.00000	−0.239046
$281$	−8.00000	−0.477240	−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000	−0.477240	−0.238620	+	0.971113i	$0.576695\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	12.0000	0.709575
$287$	−24.0000	−1.41668
$288$	0	0
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	0	0
$292$	0	0
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	8.00000	0.464991
$297$	0	0
$298$	8.00000	0.463428
$299$	0	0
$300$	0	0
$301$	−24.0000	−1.38334
$302$	−12.0000	−0.690522
$303$	0	0
$304$	0	0
$305$	−10.0000	−0.572598
$306$	0	0
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	−8.00000	−0.455842
$309$	0	0
$310$	0	0
$311$	6.00000	0.340229	0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000	0.340229	0.170114	+	0.985424i	$0.445586\pi$
$312$	0	0
$313$	20.0000	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	0	0
$317$	−34.0000	−1.90963	−0.954815	−	0.297200i	$-0.903947\pi$
$317$	−34.0000	−1.90963	−0.954815	+	0.297200i	$0.903947\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−6.00000	−0.332820
$326$	−16.0000	−0.886158
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−32.0000	−1.76422
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	12.0000	0.658586
$333$	0	0
$334$	−20.0000	−1.09435
$335$	−10.0000	−0.546358
$336$	0	0
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	−23.0000	−1.25104
$339$	0	0
$340$	−1.00000	−0.0542326
$341$	0	0
$342$	0	0
$343$	−8.00000	−0.431959
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−18.0000	−0.967686
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	6.00000	0.318447
$356$	0	0
$357$	0	0
$358$	16.0000	0.845626
$359$	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
$361$	−19.0000	−1.00000
$362$	14.0000	0.735824
$363$	0	0
$364$	24.0000	1.25794
$365$	0	0
$366$	0	0
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	0	0
$369$	0	0
$370$	−8.00000	−0.415900
$371$	−24.0000	−1.24602
$372$	0	0
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	−8.00000	−0.412568
$377$	−36.0000	−1.85409
$378$	0	0
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	0	0
$382$	−16.0000	−0.818631
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	0	0
$385$	8.00000	0.407718
$386$	−12.0000	−0.610784
$387$	0	0
$388$	−8.00000	−0.406138
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	0	0
$391$	0	0
$392$	−9.00000	−0.454569
$393$	0	0
$394$	18.0000	0.906827
$395$	0	0
$396$	0	0
$397$	−32.0000	−1.60603	−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000	−1.60603	−0.803017	+	0.595956i	$0.796773\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	1.00000	0.0500000
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	0	0
$403$	0	0
$404$	12.0000	0.597022
$405$	0	0
$406$	24.0000	1.19110
$407$	−16.0000	−0.793091
$408$	0	0
$409$	38.0000	1.87898	0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000	1.87898	0.939490	+	0.342578i	$0.111300\pi$
$410$	6.00000	0.296319
$411$	0	0
$412$	10.0000	0.492665
$413$	48.0000	2.36193
$414$	0	0
$415$	−12.0000	−0.589057
$416$	6.00000	0.294174
$417$	0	0
$418$	0	0
$419$	−14.0000	−0.683945	−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000	−0.683945	−0.341972	+	0.939710i	$0.611095\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−6.00000	−0.291386
$425$	1.00000	0.0485071
$426$	0	0
$427$	−40.0000	−1.93574
$428$	0	0
$429$	0	0
$430$	6.00000	0.289346
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	0	0
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	0	0
$435$	0	0
$436$	−14.0000	−0.670478
$437$	0	0
$438$	0	0
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	2.00000	0.0953463
$441$	0	0
$442$	6.00000	0.285391
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	0	0
$446$	−2.00000	−0.0947027
$447$	0	0
$448$	−4.00000	−0.188982
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	12.0000	0.565058
$452$	2.00000	0.0940721
$453$	0	0
$454$	−20.0000	−0.938647
$455$	−24.0000	−1.12514
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	−2.00000	−0.0934539
$459$	0	0
$460$	0	0
$461$	28.0000	1.30409	0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000	1.30409	0.652045	+	0.758180i	$0.273911\pi$
$462$	0	0
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−22.0000	−1.01913
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	0	0
$469$	−40.0000	−1.84703
$470$	8.00000	0.369012
$471$	0	0
$472$	12.0000	0.552345
$473$	12.0000	0.551761
$474$	0	0
$475$	0	0
$476$	−4.00000	−0.183340
$477$	0	0
$478$	4.00000	0.182956
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	48.0000	2.18861
$482$	14.0000	0.637683
$483$	0	0
$484$	−7.00000	−0.318182
$485$	8.00000	0.363261
$486$	0	0
$487$	−24.0000	−1.08754	−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000	−1.08754	−0.543772	+	0.839233i	$0.683004\pi$
$488$	−10.0000	−0.452679
$489$	0	0
$490$	9.00000	0.406579
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	0	0
$493$	6.00000	0.270226
$494$	0	0
$495$	0	0
$496$	0	0
$497$	24.0000	1.07655
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−24.0000	−1.07117
$503$	44.0000	1.96186	0.980932	−	0.194354i	$-0.0622609\pi$
$503$	44.0000	1.96186	0.980932	+	0.194354i	$0.0622609\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	0	0
$507$	0	0
$508$	−14.0000	−0.621150
$509$	28.0000	1.24108	0.620539	−	0.784176i	$-0.286914\pi$
$509$	28.0000	1.24108	0.620539	+	0.784176i	$0.286914\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	−10.0000	−0.440653
$516$	0	0
$517$	16.0000	0.703679
$518$	−32.0000	−1.40600
$519$	0	0
$520$	−6.00000	−0.263117
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	0	0
$523$	38.0000	1.66162	0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000	1.66162	0.830812	+	0.556553i	$0.187876\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	0	0
$532$	0	0
$533$	−36.0000	−1.55933
$534$	0	0
$535$	0	0
$536$	−10.0000	−0.431934
$537$	0	0
$538$	26.0000	1.12094
$539$	18.0000	0.775315
$540$	0	0
$541$	−22.0000	−0.945854	−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000	−0.945854	−0.472927	+	0.881102i	$0.656803\pi$
$542$	−4.00000	−0.171815
$543$	0	0
$544$	−1.00000	−0.0428746
$545$	14.0000	0.599694
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−2.00000	−0.0854358
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	0	0
$552$	0	0
$553$	0	0
$554$	28.0000	1.18961
$555$	0	0
$556$	20.0000	0.848189
$557$	−34.0000	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$557$	−34.0000	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$558$	0	0
$559$	−36.0000	−1.52264
$560$	4.00000	0.169031
$561$	0	0
$562$	8.00000	0.337460
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	−2.00000	−0.0841406
$566$	20.0000	0.840663
$567$	0	0
$568$	6.00000	0.251754
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−12.0000	−0.501745
$573$	0	0
$574$	24.0000	1.00174
$575$	0	0
$576$	0	0
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	−6.00000	−0.249136
$581$	−48.0000	−1.99138
$582$	0	0
$583$	12.0000	0.496989
$584$	0	0
$585$	0	0
$586$	14.0000	0.578335
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	0	0
$589$	0	0
$590$	−12.0000	−0.494032
$591$	0	0
$592$	−8.00000	−0.328798
$593$	46.0000	1.88899	0.944497	−	0.328521i	$-0.106550\pi$
$593$	46.0000	1.88899	0.944497	+	0.328521i	$0.106550\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	−8.00000	−0.327693
$597$	0	0
$598$	0	0
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	24.0000	0.978167
$603$	0	0
$604$	12.0000	0.488273
$605$	7.00000	0.284590
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	0	0
$609$	0	0
$610$	10.0000	0.404888
$611$	−48.0000	−1.94187
$612$	0	0
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−22.0000	−0.887848
$615$	0	0
$616$	8.00000	0.322329
$617$	−26.0000	−1.04672	−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000	−1.04672	−0.523360	+	0.852111i	$0.675322\pi$
$618$	0	0
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	0	0
$622$	−6.00000	−0.240578
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	−20.0000	−0.799361
$627$	0	0
$628$	10.0000	0.399043
$629$	−8.00000	−0.318981
$630$	0	0
$631$	36.0000	1.43314	0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000	1.43314	0.716569	+	0.697517i	$0.245712\pi$
$632$	0	0
$633$	0	0
$634$	34.0000	1.35031
$635$	14.0000	0.555573
$636$	0	0
$637$	−54.0000	−2.13956
$638$	−12.0000	−0.475085
$639$	0	0
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	40.0000	1.57256	0.786281	−	0.617869i	$-0.212004\pi$
$647$	40.0000	1.57256	0.786281	+	0.617869i	$0.212004\pi$
$648$	0	0
$649$	−24.0000	−0.942082
$650$	6.00000	0.235339
$651$	0	0
$652$	16.0000	0.626608
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	−10.0000	−0.390732
$656$	6.00000	0.234261
$657$	0	0
$658$	32.0000	1.24749
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	−12.0000	−0.465690
$665$	0	0
$666$	0	0
$667$	0	0
$668$	20.0000	0.773823
$669$	0	0
$670$	10.0000	0.386334
$671$	20.0000	0.772091
$672$	0	0
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	23.0000	0.884615
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	0	0
$679$	32.0000	1.22805
$680$	1.00000	0.0383482
$681$	0	0
$682$	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
$685$	2.00000	0.0764161
$686$	8.00000	0.305441
$687$	0	0
$688$	6.00000	0.228748
$689$	−36.0000	−1.37149
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	12.0000	0.455514
$695$	−20.0000	−0.758643
$696$	0	0
$697$	6.00000	0.227266
$698$	−18.0000	−0.681310
$699$	0	0
$700$	−4.00000	−0.151186
$701$	40.0000	1.51078	0.755390	−	0.655276i	$-0.227448\pi$
$701$	40.0000	1.51078	0.755390	+	0.655276i	$0.227448\pi$
$702$	0	0
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	6.00000	0.225813
$707$	−48.0000	−1.80523
$708$	0	0
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	−6.00000	−0.225176
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	12.0000	0.448775
$716$	−16.0000	−0.597948
$717$	0	0
$718$	−12.0000	−0.447836
$719$	−34.0000	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$720$	0	0
$721$	−40.0000	−1.48968
$722$	19.0000	0.707107
$723$	0	0
$724$	−14.0000	−0.520306
$725$	6.00000	0.222834
$726$	0	0
$727$	−2.00000	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$728$	−24.0000	−0.889499
$729$	0	0
$730$	0	0
$731$	6.00000	0.221918
$732$	0	0
$733$	−38.0000	−1.40356	−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000	−1.40356	−0.701781	+	0.712393i	$0.747612\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	0	0
$737$	20.0000	0.736709
$738$	0	0
$739$	52.0000	1.91285	0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000	1.91285	0.956425	+	0.291977i	$0.0943129\pi$
$740$	8.00000	0.294086
$741$	0	0
$742$	24.0000	0.881068
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	0	0
$745$	8.00000	0.293097
$746$	2.00000	0.0732252
$747$	0	0
$748$	2.00000	0.0731272
$749$	0	0
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	36.0000	1.31104
$755$	−12.0000	−0.436725
$756$	0	0
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	0	0
$761$	20.0000	0.724999	0.362500	−	0.931984i	$-0.381923\pi$
$761$	20.0000	0.724999	0.362500	+	0.931984i	$0.381923\pi$
$762$	0	0
$763$	56.0000	2.02734
$764$	16.0000	0.578860
$765$	0	0
$766$	32.0000	1.15621
$767$	72.0000	2.59977
$768$	0	0
$769$	−38.0000	−1.37032	−0.685158	−	0.728395i	$-0.740267\pi$
$769$	−38.0000	−1.37032	−0.685158	+	0.728395i	$0.740267\pi$
$770$	−8.00000	−0.288300
$771$	0	0
$772$	12.0000	0.431889
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	0	0
$775$	0	0
$776$	8.00000	0.287183
$777$	0	0
$778$	−24.0000	−0.860442
$779$	0	0
$780$	0	0
$781$	−12.0000	−0.429394
$782$	0	0
$783$	0	0
$784$	9.00000	0.321429
$785$	−10.0000	−0.356915
$786$	0	0
$787$	48.0000	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	0	0
$791$	−8.00000	−0.284447
$792$	0	0
$793$	−60.0000	−2.13066
$794$	32.0000	1.13564
$795$	0	0
$796$	8.00000	0.283552
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	10.0000	0.353112
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−12.0000	−0.422159
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	−24.0000	−0.842235
$813$	0	0
$814$	16.0000	0.560800
$815$	−16.0000	−0.560456
$816$	0	0
$817$	0	0
$818$	−38.0000	−1.32864
$819$	0	0
$820$	−6.00000	−0.209529
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	−12.0000	−0.418294	−0.209147	−	0.977884i	$-0.567069\pi$
$823$	−12.0000	−0.418294	−0.209147	+	0.977884i	$0.567069\pi$
$824$	−10.0000	−0.348367
$825$	0	0
$826$	−48.0000	−1.67013
$827$	32.0000	1.11275	0.556375	−	0.830932i	$-0.312192\pi$
$827$	32.0000	1.11275	0.556375	+	0.830932i	$0.312192\pi$
$828$	0	0
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	−6.00000	−0.208013
$833$	9.00000	0.311832
$834$	0	0
$835$	−20.0000	−0.692129
$836$	0	0
$837$	0	0
$838$	14.0000	0.483622
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	0	0
$844$	−4.00000	−0.137686
$845$	−23.0000	−0.791224
$846$	0	0
$847$	28.0000	0.962091
$848$	6.00000	0.206041
$849$	0	0
$850$	−1.00000	−0.0342997
$851$	0	0
$852$	0	0
$853$	12.0000	0.410872	0.205436	−	0.978671i	$-0.434139\pi$
$853$	12.0000	0.410872	0.205436	+	0.978671i	$0.434139\pi$
$854$	40.0000	1.36877
$855$	0	0
$856$	0	0
$857$	46.0000	1.57133	0.785665	−	0.618652i	$-0.212321\pi$
$857$	46.0000	1.57133	0.785665	+	0.618652i	$0.212321\pi$
$858$	0	0
$859$	−8.00000	−0.272956	−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000	−0.272956	−0.136478	+	0.990643i	$0.543578\pi$
$860$	−6.00000	−0.204598
$861$	0	0
$862$	−18.0000	−0.613082
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	14.0000	0.475739
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−60.0000	−2.03302
$872$	14.0000	0.474100
$873$	0	0
$874$	0	0
$875$	4.00000	0.135225
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	16.0000	0.539974
$879$	0	0
$880$	−2.00000	−0.0674200
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	−34.0000	−1.14419	−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000	−1.14419	−0.572096	+	0.820187i	$0.693869\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	−36.0000	−1.20944
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	56.0000	1.87818
$890$	0	0
$891$	0	0
$892$	2.00000	0.0669650
$893$	0	0
$894$	0	0
$895$	16.0000	0.534821
$896$	4.00000	0.133631
$897$	0	0
$898$	−6.00000	−0.200223
$899$	0	0
$900$	0	0
$901$	6.00000	0.199889
$902$	−12.0000	−0.399556
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	14.0000	0.465376
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	20.0000	0.663723
$909$	0	0
$910$	24.0000	0.795592
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	0	0
$913$	24.0000	0.794284
$914$	−6.00000	−0.198462
$915$	0	0
$916$	2.00000	0.0660819
$917$	−40.0000	−1.32092
$918$	0	0
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	0	0
$921$	0	0
$922$	−28.0000	−0.922131
$923$	36.0000	1.18495
$924$	0	0
$925$	−8.00000	−0.263038
$926$	−14.0000	−0.460069
$927$	0	0
$928$	−6.00000	−0.196960
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	0	0
$931$	0	0
$932$	22.0000	0.720634
$933$	0	0
$934$	−36.0000	−1.17796
$935$	−2.00000	−0.0654070
$936$	0	0
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	40.0000	1.30605
$939$	0	0
$940$	−8.00000	−0.260931
$941$	−34.0000	−1.10837	−0.554184	−	0.832394i	$-0.686970\pi$
$941$	−34.0000	−1.10837	−0.554184	+	0.832394i	$0.686970\pi$
$942$	0	0
$943$	0	0
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−12.0000	−0.390154
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	0	0
$955$	−16.0000	−0.517748
$956$	−4.00000	−0.129369
$957$	0	0
$958$	6.00000	0.193851
$959$	8.00000	0.258333
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−48.0000	−1.54758
$963$	0	0
$964$	−14.0000	−0.450910
$965$	−12.0000	−0.386294
$966$	0	0
$967$	54.0000	1.73652	0.868261	−	0.496107i	$-0.165238\pi$
$967$	54.0000	1.73652	0.868261	+	0.496107i	$0.165238\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−8.00000	−0.256865
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	−80.0000	−2.56468
$974$	24.0000	0.769010
$975$	0	0
$976$	10.0000	0.320092
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	0	0
$979$	0	0
$980$	−9.00000	−0.287494
$981$	0	0
$982$	20.0000	0.638226
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	0	0
$985$	18.0000	0.573528
$986$	−6.00000	−0.191079
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	0	0
$993$	0	0
$994$	−24.0000	−0.761234
$995$	−8.00000	−0.253617
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	4.00000	0.126618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.a.a.1.1	✓	1
3.2	odd	2		1530.2.a.m.1.1	yes	1
5.4	even	2		7650.2.a.cl.1.1		1
15.14	odd	2		7650.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.a.a.1.1	✓	1	1.1	even	1	trivial
1530.2.a.m.1.1	yes	1	3.2	odd	2
7650.2.a.bf.1.1		1	15.14	odd	2
7650.2.a.cl.1.1		1	5.4	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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.a (trivial)

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