LMFDB - Embedded newform 1620.2.x.a.917.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1620,2,Mod(53,1620)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1620.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1620, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			917.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1620.917
Dual form			1620.2.x.a.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19067 + 0.448288i) q^{5} +(-2.73205 + 0.732051i) q^{7} +(2.44949 + 1.41421i) q^{11} +(-4.09808 - 1.09808i) q^{13} +(-1.41421 + 1.41421i) q^{17} +4.00000i q^{19} +(2.07055 - 7.72741i) q^{23} +(4.59808 - 1.96410i) q^{25} +(4.94975 - 8.57321i) q^{29} +(4.00000 + 6.92820i) q^{31} +(5.65685 - 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(1.22474 - 0.707107i) q^{41} +(-3.10583 - 11.5911i) q^{47} +(0.866025 - 0.500000i) q^{49} +(7.07107 + 7.07107i) q^{53} +(-6.00000 - 2.00000i) q^{55} +(-1.41421 - 2.44949i) q^{59} +(9.46979 + 0.568406i) q^{65} +(2.92820 - 10.9282i) q^{67} -5.65685i q^{71} +(7.00000 - 7.00000i) q^{73} +(-7.72741 - 2.07055i) q^{77} +(11.5911 - 3.10583i) q^{83} +(2.46410 - 3.73205i) q^{85} +1.41421 q^{89} +12.0000 q^{91} +(-1.79315 - 8.76268i) q^{95} +(-4.09808 + 1.09808i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7} - 12 q^{13} + 16 q^{25} + 32 q^{31} - 24 q^{37} - 48 q^{55} - 32 q^{67} + 56 q^{73} - 8 q^{85} + 96 q^{91} - 12 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 - 12 * q^13 + 16 * q^25 + 32 * q^31 - 24 * q^37 - 48 * q^55 - 32 * q^67 + 56 * q^73 - 8 * q^85 + 96 * q^91 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.19067	+	0.448288i	−0.979698	+	0.200480i
$5$	−2.19067	+	0.448288i	−0.979698	+	0.200480i
$6$		0			0
$7$	−2.73205	+	0.732051i	−1.03262	+	0.276689i	−0.735051	−	0.678012i	$-0.762842\pi$
$7$	−2.73205	+	0.732051i	−1.03262	+	0.276689i	−0.297567	+	0.954701i	$0.596175\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.44949	+	1.41421i	0.738549	+	0.426401i	0.821541	−	0.570149i	$-0.193114\pi$
$11$	2.44949	+	1.41421i	0.738549	+	0.426401i	−0.0829925	+	0.996550i	$0.526448\pi$
$12$		0			0
$13$	−4.09808	−	1.09808i	−1.13660	−	0.304552i	−0.359018	−	0.933331i	$-0.616888\pi$
$13$	−4.09808	−	1.09808i	−1.13660	−	0.304552i	−0.777584	+	0.628779i	$0.783555\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.07055	−	7.72741i	0.431740	−	1.61128i	−0.317009	−	0.948422i	$-0.602679\pi$
$23$	2.07055	−	7.72741i	0.431740	−	1.61128i	0.748749	−	0.662853i	$-0.230655\pi$
$24$		0			0
$25$	4.59808	−	1.96410i	0.919615	−	0.392820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.94975	−	8.57321i	0.919145	−	1.59201i	0.118428	−	0.992963i	$-0.462214\pi$
$29$	4.94975	−	8.57321i	0.919145	−	1.59201i	0.800717	−	0.599043i	$-0.204452\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.65685	−	2.82843i	0.956183	−	0.478091i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.22474	−	0.707107i	0.191273	−	0.110432i	−0.401305	−	0.915944i	$-0.631443\pi$
$41$	1.22474	−	0.707107i	0.191273	−	0.110432i	0.592578	+	0.805513i	$0.298110\pi$
$42$		0			0
$43$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$43$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.10583	−	11.5911i	−0.453032	−	1.69074i	−0.693811	−	0.720157i	$-0.744070\pi$
$47$	−3.10583	−	11.5911i	−0.453032	−	1.69074i	0.240779	−	0.970580i	$-0.422597\pi$
$48$		0			0
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	0.999599	−	0.0283132i	$-0.00901359\pi$
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	−0.0283132	+	0.999599i	$0.509014\pi$
$54$		0			0
$55$	−6.00000	−	2.00000i	−0.809040	−	0.269680i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.41421	−	2.44949i	−0.184115	−	0.318896i	0.759163	−	0.650901i	$-0.225609\pi$
$59$	−1.41421	−	2.44949i	−0.184115	−	0.318896i	−0.943278	+	0.332004i	$0.892275\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.46979	+	0.568406i	1.17458	+	0.0705021i
$66$		0			0
$67$	2.92820	−	10.9282i	0.357737	−	1.33509i	−0.519268	−	0.854611i	$-0.673795\pi$
$67$	2.92820	−	10.9282i	0.357737	−	1.33509i	0.877005	−	0.480481i	$-0.159538\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$		0			0
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	−0.166717	−	0.986005i	$-0.553317\pi$
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	0.986005	+	0.166717i	$0.0533166\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.72741	−	2.07055i	−0.880620	−	0.235961i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11.5911	−	3.10583i	1.27229	−	0.340909i	0.441382	−	0.897319i	$-0.354488\pi$
$83$	11.5911	−	3.10583i	1.27229	−	0.340909i	0.830908	+	0.556410i	$0.187822\pi$
$84$		0			0
$85$	2.46410	−	3.73205i	0.267269	−	0.404798i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.41421			0.149906			0.0749532	−	0.997187i	$-0.476119\pi$
$89$	1.41421			0.149906			0.0749532	+	0.997187i	$0.476119\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.79315	−	8.76268i	−0.183973	−	0.899032i
$96$		0			0
$97$	−4.09808	+	1.09808i	−0.416097	+	0.111493i	−0.460793	−	0.887508i	$-0.652435\pi$
$97$	−4.09808	+	1.09808i	−0.416097	+	0.111493i	0.0446959	+	0.999001i	$0.485768\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.22474	+	0.707107i	0.121867	+	0.0703598i	0.559694	−	0.828699i	$-0.310919\pi$
$101$	1.22474	+	0.707107i	0.121867	+	0.0703598i	−0.437828	+	0.899059i	$0.644252\pi$
$102$		0			0
$103$	2.73205	+	0.732051i	0.269197	+	0.0721311i	0.390892	−	0.920436i	$-0.372166\pi$
$103$	2.73205	+	0.732051i	0.269197	+	0.0721311i	−0.121695	+	0.992567i	$0.538833\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	−0.557047	−	0.830481i	$-0.688066\pi$
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	0.830481	+	0.557047i	$0.188066\pi$
$108$		0			0
$109$			8.00000i			0.766261i	0.923694	+	0.383131i	$0.125154\pi$
$109$			8.00000i			0.766261i	−0.923694	+	0.383131i	$0.874846\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.03528	−	3.86370i	0.0973906	−	0.363467i	−0.899980	−	0.435930i	$-0.856419\pi$
$113$	1.03528	−	3.86370i	0.0973906	−	0.363467i	0.997371	+	0.0724636i	$0.0230861\pi$
$114$		0			0
$115$	−1.07180	+	17.8564i	−0.0999456	+	1.66512i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.82843	−	4.89898i	0.259281	−	0.449089i
$120$		0			0
$121$	−1.50000	−	2.59808i	−0.136364	−	0.236189i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	0.106912	−	0.994268i	$-0.465904\pi$
$127$	−10.0000	−	10.0000i	−0.887357	−	0.887357i	−0.994268	+	0.106912i	$0.965904\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.44949	+	1.41421i	−0.214013	+	0.123560i	−0.603175	−	0.797609i	$-0.706098\pi$
$131$	−2.44949	+	1.41421i	−0.214013	+	0.123560i	0.389162	+	0.921169i	$0.372765\pi$
$132$		0			0
$133$	−2.92820	−	10.9282i	−0.253907	−	0.947595i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.10583	+	11.5911i	0.265349	+	0.990295i	0.962037	+	0.272921i	$0.0879897\pi$
$137$	3.10583	+	11.5911i	0.265349	+	0.990295i	−0.696688	+	0.717375i	$0.745344\pi$
$138$		0			0
$139$	−13.8564	+	8.00000i	−1.17529	+	0.678551i	−0.954919	−	0.296866i	$-0.904058\pi$
$139$	−13.8564	+	8.00000i	−1.17529	+	0.678551i	−0.220366	+	0.975417i	$0.570725\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.48528	−	8.48528i	−0.709575	−	0.709575i
$144$		0			0
$145$	−7.00000	+	21.0000i	−0.581318	+	1.74396i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.36396	−	11.0227i	−0.521356	−	0.903015i	−0.999691	−	0.0248379i	$-0.992093\pi$
$149$	−6.36396	−	11.0227i	−0.521356	−	0.903015i	0.478335	−	0.878177i	$-0.341240\pi$
$150$		0			0
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.8685	−	13.3843i	−0.953302	−	1.07505i
$156$		0			0
$157$	−3.29423	+	12.2942i	−0.262908	+	0.981186i	0.700610	+	0.713544i	$0.252911\pi$
$157$	−3.29423	+	12.2942i	−0.262908	+	0.981186i	−0.963518	+	0.267642i	$0.913756\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			22.6274i			1.78329i
$162$		0			0
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	15.4548	+	4.14110i	1.19593	+	0.320448i	0.801227	−	0.598361i	$-0.204181\pi$
$167$	15.4548	+	4.14110i	1.19593	+	0.320448i	0.394702	+	0.918809i	$0.370848\pi$
$168$		0			0
$169$	4.33013	+	2.50000i	0.333087	+	0.192308i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.86370	−	1.03528i	0.293752	−	0.0787106i	−0.108933	−	0.994049i	$-0.534744\pi$
$173$	3.86370	−	1.03528i	0.293752	−	0.0787106i	0.402685	+	0.915338i	$0.368077\pi$
$174$		0			0
$175$	−11.1244	+	8.73205i	−0.840922	+	0.660081i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	14.1421			1.05703			0.528516	−	0.848923i	$-0.322748\pi$
$179$	14.1421			1.05703			0.528516	+	0.848923i	$0.322748\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.91688	+	5.22715i	0.582060	+	0.384308i
$186$		0			0
$187$	−5.46410	+	1.46410i	−0.399575	+	0.107066i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.79796	−	5.65685i	−0.708955	−	0.409316i	0.101719	−	0.994813i	$-0.467566\pi$
$191$	−9.79796	−	5.65685i	−0.708955	−	0.409316i	−0.810674	+	0.585498i	$0.800899\pi$
$192$		0			0
$193$	20.4904	+	5.49038i	1.47493	+	0.395206i	0.904618	−	0.426222i	$-0.140156\pi$
$193$	20.4904	+	5.49038i	1.47493	+	0.395206i	0.570311	+	0.821429i	$0.306823\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	−0.336966	−	0.941517i	$-0.609401\pi$
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	0.941517	+	0.336966i	$0.109401\pi$
$198$		0			0
$199$		−	12.0000i		−	0.850657i	−0.905039	−	0.425329i	$-0.860158\pi$
$199$		−	12.0000i		−	0.850657i	0.905039	−	0.425329i	$-0.139842\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.24693	+	27.0459i	−0.508635	+	1.89825i
$204$		0			0
$205$	−2.36603	+	2.09808i	−0.165250	+	0.146536i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.65685	+	9.79796i	−0.391293	+	0.677739i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−16.0000	−	16.0000i	−1.08615	−	1.08615i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.34847	−	4.24264i	0.494312	−	0.285391i
$222$		0			0
$223$	−2.19615	−	8.19615i	−0.147065	−	0.548855i	−0.999655	−	0.0262738i	$-0.991636\pi$
$223$	−2.19615	−	8.19615i	−0.147065	−	0.548855i	0.852590	−	0.522581i	$-0.175031\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.07055	+	7.72741i	0.137427	+	0.512886i	0.999976	+	0.00691198i	$0.00220017\pi$
$227$	2.07055	+	7.72741i	0.137427	+	0.512886i	−0.862549	+	0.505974i	$0.831133\pi$
$228$		0			0
$229$	5.19615	−	3.00000i	0.343371	−	0.198246i	−0.318390	−	0.947960i	$-0.603142\pi$
$229$	5.19615	−	3.00000i	0.343371	−	0.198246i	0.661762	+	0.749714i	$0.269809\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	0.554343	−	0.832288i	$-0.312969\pi$
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	−0.832288	+	0.554343i	$0.812969\pi$
$234$		0			0
$235$	12.0000	+	24.0000i	0.782794	+	1.56559i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.67303	+	1.48356i	−0.106886	+	0.0947814i
$246$		0			0
$247$	4.39230	−	16.3923i	0.279476	−	1.04302i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	25.4558i		−	1.60676i	−0.595468	−	0.803379i	$-0.703033\pi$
$251$		−	25.4558i		−	1.60676i	0.595468	−	0.803379i	$-0.296967\pi$
$252$		0			0
$253$	16.0000	−	16.0000i	1.00591	−	1.00591i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−19.3185	−	5.17638i	−1.20506	−	0.322894i	−0.400236	−	0.916412i	$-0.631072\pi$
$257$	−19.3185	−	5.17638i	−1.20506	−	0.322894i	−0.804820	+	0.593519i	$0.797738\pi$
$258$		0			0
$259$	10.3923	+	6.00000i	0.645746	+	0.372822i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.4548	+	4.14110i	−0.952985	+	0.255351i	−0.701628	−	0.712543i	$-0.747543\pi$
$263$	−15.4548	+	4.14110i	−0.952985	+	0.255351i	−0.251356	+	0.967895i	$0.580877\pi$
$264$		0			0
$265$	−18.6603	−	12.3205i	−1.14629	−	0.756843i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.3848			−1.12094			−0.560470	−	0.828175i	$-0.689379\pi$
$269$	−18.3848			−1.12094			−0.560470	+	0.828175i	$0.689379\pi$
$270$		0			0
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.0406	+	1.69161i	0.846680	+	0.102008i
$276$		0			0
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.815026	−	0.579424i	$-0.803278\pi$
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.416121	+	0.909309i	$0.636611\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.0227	+	6.36396i	0.657559	+	0.379642i	0.791346	−	0.611368i	$-0.209380\pi$
$281$	11.0227	+	6.36396i	0.657559	+	0.379642i	−0.133787	+	0.991010i	$0.542714\pi$
$282$		0			0
$283$	5.46410	+	1.46410i	0.324807	+	0.0870318i	0.417538	−	0.908659i	$-0.362893\pi$
$283$	5.46410	+	1.46410i	0.324807	+	0.0870318i	−0.0927310	+	0.995691i	$0.529560\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.82843	+	2.82843i	−0.166957	+	0.166957i
$288$		0			0
$289$			13.0000i			0.764706i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.10583	+	11.5911i	−0.181444	+	0.677160i	0.813919	+	0.580978i	$0.197330\pi$
$293$	−3.10583	+	11.5911i	−0.181444	+	0.677160i	−0.995364	+	0.0961820i	$0.969337\pi$
$294$		0			0
$295$	4.19615	+	4.73205i	0.244309	+	0.275511i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16.9706	+	29.3939i	−0.981433	+	1.69989i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	0.276219	−	0.961095i	$-0.410919\pi$
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	−0.961095	+	0.276219i	$0.910919\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.89898	+	2.82843i	−0.277796	+	0.160385i	−0.632425	−	0.774622i	$-0.717940\pi$
$311$	−4.89898	+	2.82843i	−0.277796	+	0.160385i	0.354629	+	0.935007i	$0.384607\pi$
$312$		0			0
$313$	1.09808	+	4.09808i	0.0620669	+	0.231637i	0.989991	−	0.141133i	$-0.0450746\pi$
$313$	1.09808	+	4.09808i	0.0620669	+	0.231637i	−0.927924	+	0.372770i	$0.878408\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.55291	+	5.79555i	0.0872204	+	0.325511i	0.995725	−	0.0923631i	$-0.0294421\pi$
$317$	1.55291	+	5.79555i	0.0872204	+	0.325511i	−0.908505	+	0.417874i	$0.862775\pi$
$318$		0			0
$319$	24.2487	−	14.0000i	1.35767	−	0.783850i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.65685	−	5.65685i	−0.314756	−	0.314756i
$324$		0			0
$325$	−21.0000	+	3.00000i	−1.16487	+	0.166410i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.9706	+	29.3939i	0.935617	+	1.62054i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.51575	+	25.2528i	−0.0828142	+	1.37971i
$336$		0			0
$337$	−1.09808	+	4.09808i	−0.0598160	+	0.223236i	−0.989363	−	0.145467i	$-0.953532\pi$
$337$	−1.09808	+	4.09808i	−0.0598160	+	0.223236i	0.929547	+	0.368703i	$0.120198\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			22.6274i			1.22534i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.72741	+	2.07055i	0.414829	+	0.111153i	0.460196	−	0.887817i	$-0.347779\pi$
$347$	7.72741	+	2.07055i	0.414829	+	0.111153i	−0.0453672	+	0.998970i	$0.514446\pi$
$348$		0			0
$349$	27.7128	+	16.0000i	1.48343	+	0.856460i	0.999823	−	0.0188232i	$-0.00599197\pi$
$349$	27.7128	+	16.0000i	1.48343	+	0.856460i	0.483610	+	0.875284i	$0.339325\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.3867	+	4.65874i	−0.925399	+	0.247960i	−0.689892	−	0.723913i	$-0.742342\pi$
$353$	−17.3867	+	4.65874i	−0.925399	+	0.247960i	−0.235507	+	0.971873i	$0.575675\pi$
$354$		0			0
$355$	2.53590	+	12.3923i	0.134592	+	0.657715i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.3137			−0.597115			−0.298557	−	0.954392i	$-0.596505\pi$
$359$	−11.3137			−0.597115			−0.298557	+	0.954392i	$0.596505\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.1967	+	18.4727i	−0.638403	+	0.966906i
$366$		0			0
$367$	−19.1244	+	5.12436i	−0.998283	+	0.267489i	−0.720726	−	0.693220i	$-0.756191\pi$
$367$	−19.1244	+	5.12436i	−0.998283	+	0.267489i	−0.277557	+	0.960709i	$0.589525\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−24.4949	−	14.1421i	−1.27171	−	0.734223i
$372$		0			0
$373$	6.83013	+	1.83013i	0.353651	+	0.0947604i	0.431271	−	0.902223i	$-0.358065\pi$
$373$	6.83013	+	1.83013i	0.353651	+	0.0947604i	−0.0776200	+	0.996983i	$0.524732\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.6985	+	29.6985i	−1.52955	+	1.52955i
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.31749	−	34.7733i	0.476101	−	1.77683i	−0.141064	−	0.990000i	$-0.545052\pi$
$383$	9.31749	−	34.7733i	0.476101	−	1.77683i	0.617165	−	0.786834i	$-0.288281\pi$
$384$		0			0
$385$	17.8564	+	1.07180i	0.910047	+	0.0546238i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	0.461247	+	0.887272i	$0.347402\pi$
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	−0.999023	+	0.0441839i	$0.985931\pi$
$390$		0			0
$391$	8.00000	+	13.8564i	0.404577	+	0.700749i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.0000	−	17.0000i	−0.853206	−	0.853206i	0.137321	−	0.990527i	$-0.456151\pi$
$397$	−17.0000	−	17.0000i	−0.853206	−	0.853206i	−0.990527	+	0.137321i	$0.956151\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.3712	+	10.6066i	−0.917413	+	0.529668i	−0.882809	−	0.469733i	$-0.844350\pi$
$401$	−18.3712	+	10.6066i	−0.917413	+	0.529668i	−0.0346039	+	0.999401i	$0.511017\pi$
$402$		0			0
$403$	−8.78461	−	32.7846i	−0.437593	−	1.63312i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.10583	−	11.5911i	−0.153950	−	0.574550i
$408$		0			0
$409$	−20.7846	+	12.0000i	−1.02773	+	0.593362i	−0.916334	−	0.400414i	$-0.868866\pi$
$409$	−20.7846	+	12.0000i	−1.02773	+	0.593362i	−0.111398	+	0.993776i	$0.535533\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.65685	+	5.65685i	0.278356	+	0.278356i
$414$		0			0
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.7279	+	22.0454i	0.621800	+	1.07699i	0.989150	+	0.146906i	$0.0469315\pi$
$419$	12.7279	+	22.0454i	0.621800	+	1.07699i	−0.367351	+	0.930082i	$0.619735\pi$
$420$		0			0
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.72500	+	9.28032i	−0.180689	+	0.450162i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	28.2843i		−	1.36241i	−0.732095	−	0.681203i	$-0.761457\pi$
$431$		−	28.2843i		−	1.36241i	0.732095	−	0.681203i	$-0.238543\pi$
$432$		0			0
$433$	23.0000	−	23.0000i	1.10531	−	1.10531i	0.111551	−	0.993759i	$-0.464418\pi$
$433$	23.0000	−	23.0000i	1.10531	−	1.10531i	0.993759	−	0.111551i	$-0.0355818\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	30.9096	+	8.28221i	1.47861	+	0.396192i
$438$		0			0
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	0.0260459	−	0.999661i	$-0.491708\pi$
$439$	−17.3205	−	10.0000i	−0.826663	−	0.477274i	−0.852709	+	0.522387i	$0.825042\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.1822	+	6.21166i	−1.10142	+	0.295125i	−0.763343	−	0.645994i	$-0.776443\pi$
$443$	−23.1822	+	6.21166i	−1.10142	+	0.295125i	−0.338078	+	0.941118i	$0.609777\pi$
$444$		0			0
$445$	−3.09808	+	0.633975i	−0.146863	+	0.0300533i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.41421			−0.0667409			−0.0333704	−	0.999443i	$-0.510624\pi$
$449$	−1.41421			−0.0667409			−0.0333704	+	0.999443i	$0.510624\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−26.2880	+	5.37945i	−1.23240	+	0.252193i
$456$		0			0
$457$	−20.4904	+	5.49038i	−0.958500	+	0.256829i	−0.703965	−	0.710235i	$-0.748589\pi$
$457$	−20.4904	+	5.49038i	−0.958500	+	0.256829i	−0.254534	+	0.967064i	$0.581922\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.4722	+	7.77817i	0.627463	+	0.362266i	0.779769	−	0.626068i	$-0.215337\pi$
$461$	13.4722	+	7.77817i	0.627463	+	0.362266i	−0.152306	+	0.988333i	$0.548670\pi$
$462$		0			0
$463$	−35.5167	−	9.51666i	−1.65060	−	0.442277i	−0.690819	−	0.723028i	$-0.742750\pi$
$463$	−35.5167	−	9.51666i	−1.65060	−	0.442277i	−0.959781	+	0.280751i	$0.909416\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	−0.0805616	−	0.996750i	$-0.525671\pi$
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	0.996750	+	0.0805616i	$0.0256714\pi$
$468$		0			0
$469$			32.0000i			1.47762i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	7.85641	+	18.3923i	0.360477	+	0.843897i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.7990	−	34.2929i	0.904639	−	1.56688i	0.0832378	−	0.996530i	$-0.473474\pi$
$479$	19.7990	−	34.2929i	0.904639	−	1.56688i	0.821401	−	0.570351i	$-0.193193\pi$
$480$		0			0
$481$	9.00000	+	15.5885i	0.410365	+	0.710772i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.48528	−	4.24264i	0.385297	−	0.192648i
$486$		0			0
$487$	6.00000	+	6.00000i	0.271886	+	0.271886i	0.829859	−	0.557973i	$-0.188421\pi$
$487$	6.00000	+	6.00000i	0.271886	+	0.271886i	−0.557973	+	0.829859i	$0.688421\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	31.8434	−	18.3848i	1.43707	−	0.829693i	0.439426	−	0.898279i	$-0.355182\pi$
$491$	31.8434	−	18.3848i	1.43707	−	0.829693i	0.997645	+	0.0685856i	$0.0218486\pi$
$492$		0			0
$493$	5.12436	+	19.1244i	0.230789	+	0.861318i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.14110	+	15.4548i	0.185754	+	0.693243i
$498$		0			0
$499$	−3.46410	+	2.00000i	−0.155074	+	0.0895323i	−0.575529	−	0.817781i	$-0.695204\pi$
$499$	−3.46410	+	2.00000i	−0.155074	+	0.0895323i	0.420455	+	0.907314i	$0.361871\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	0.870503	−	0.492163i	$-0.163794\pi$
$503$	8.48528	+	8.48528i	0.378340	+	0.378340i	−0.492163	+	0.870503i	$0.663794\pi$
$504$		0			0
$505$	−3.00000	−	1.00000i	−0.133498	−	0.0444994i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.707107	+	1.22474i	0.0313420	+	0.0542859i	0.881271	−	0.472611i	$-0.156689\pi$
$509$	0.707107	+	1.22474i	0.0313420	+	0.0542859i	−0.849929	+	0.526897i	$0.823355\pi$
$510$		0			0
$511$	−14.0000	+	24.2487i	−0.619324	+	1.07270i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.31319	−	0.378937i	−0.278193	−	0.0166980i
$516$		0			0
$517$	8.78461	−	32.7846i	0.386347	−	1.44187i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	29.6985i		−	1.30111i	−0.759457	−	0.650557i	$-0.774535\pi$
$521$		−	29.6985i		−	1.30111i	0.759457	−	0.650557i	$-0.225465\pi$
$522$		0			0
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.4548	−	4.14110i	−0.673222	−	0.180389i
$528$		0			0
$529$	−35.5070	−	20.5000i	−1.54378	−	0.891304i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.79555	+	1.55291i	−0.251033	+	0.0672642i
$534$		0			0
$535$	−4.92820	+	7.46410i	−0.213065	+	0.322701i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.82843			0.121829
$540$		0			0
$541$	40.0000			1.71973			0.859867	−	0.510518i	$-0.170546\pi$
$541$	40.0000			1.71973			0.859867	+	0.510518i	$0.170546\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.58630	−	17.5254i	−0.153620	−	0.750704i
$546$		0			0
$547$	16.3923	−	4.39230i	0.700884	−	0.187801i	0.109258	−	0.994013i	$-0.465153\pi$
$547$	16.3923	−	4.39230i	0.700884	−	0.187801i	0.591627	+	0.806212i	$0.298486\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	34.2929	+	19.7990i	1.46092	+	0.843465i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.7279	+	12.7279i	−0.539299	+	0.539299i	−0.923323	−	0.384024i	$-0.874538\pi$
$557$	−12.7279	+	12.7279i	−0.539299	+	0.539299i	0.384024	+	0.923323i	$0.374538\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.21166	+	23.1822i	−0.261790	+	0.977014i	0.702396	+	0.711787i	$0.252114\pi$
$563$	−6.21166	+	23.1822i	−0.261790	+	0.977014i	−0.964186	+	0.265227i	$0.914553\pi$
$564$		0			0
$565$	−0.535898	+	8.92820i	−0.0225454	+	0.375612i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.77817	−	13.4722i	0.326078	−	0.564784i	−0.655652	−	0.755063i	$-0.727606\pi$
$569$	7.77817	−	13.4722i	0.326078	−	0.564784i	0.981730	+	0.190280i	$0.0609394\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.65685	−	39.5980i	−0.235907	−	1.65135i
$576$		0			0
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	0.837639	−	0.546225i	$-0.183936\pi$
$577$	7.00000	+	7.00000i	0.291414	+	0.291414i	−0.546225	+	0.837639i	$0.683936\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−29.3939	+	16.9706i	−1.21946	+	0.704058i
$582$		0			0
$583$	7.32051	+	27.3205i	0.303184	+	1.13150i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.10583	−	11.5911i	−0.128191	−	0.478416i	0.871742	−	0.489965i	$-0.162990\pi$
$587$	−3.10583	−	11.5911i	−0.128191	−	0.478416i	−0.999933	+	0.0115488i	$0.996324\pi$
$588$		0			0
$589$	−27.7128	+	16.0000i	−1.14189	+	0.659269i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.1421	+	14.1421i	0.580748	+	0.580748i	0.935109	−	0.354361i	$-0.115302\pi$
$593$	14.1421	+	14.1421i	0.580748	+	0.580748i	−0.354361	+	0.935109i	$0.615302\pi$
$594$		0			0
$595$	−4.00000	+	12.0000i	−0.163984	+	0.491952i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.1421	−	24.4949i	−0.577832	−	1.00083i	−0.995728	−	0.0923393i	$-0.970566\pi$
$599$	−14.1421	−	24.4949i	−0.577832	−	1.00083i	0.417896	−	0.908495i	$-0.362768\pi$
$600$		0			0
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	−0.0929227	−	0.995673i	$-0.529621\pi$
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	0.908740	−	0.417363i	$-0.137046\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.45069	+	5.01910i	0.180946	+	0.204055i
$606$		0			0
$607$	6.58846	−	24.5885i	0.267417	−	0.998015i	−0.693337	−	0.720614i	$-0.743860\pi$
$607$	6.58846	−	24.5885i	0.267417	−	0.998015i	0.960754	−	0.277401i	$-0.0894731\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			50.9117i			2.05967i
$612$		0			0
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.0950469	+	0.995473i	$0.530300\pi$
$613$	−27.0000	+	27.0000i	−1.09052	+	1.09052i	−0.995473	+	0.0950469i	$0.969700\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.79555	+	1.55291i	0.233320	+	0.0625180i	0.373585	−	0.927596i	$-0.378129\pi$
$617$	5.79555	+	1.55291i	0.233320	+	0.0625180i	−0.140264	+	0.990114i	$0.544795\pi$
$618$		0			0
$619$	20.7846	+	12.0000i	0.835404	+	0.482321i	0.855699	−	0.517473i	$-0.173127\pi$
$619$	20.7846	+	12.0000i	0.835404	+	0.482321i	−0.0202954	+	0.999794i	$0.506461\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.86370	+	1.03528i	−0.154796	+	0.0414775i
$624$		0			0
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.48528			0.338330
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	26.3896	+	17.4238i	1.04724	+	0.691444i
$636$		0			0
$637$	−4.09808	+	1.09808i	−0.162372	+	0.0435074i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−35.5176	−	20.5061i	−1.40286	−	0.809942i	−0.408176	−	0.912903i	$-0.633835\pi$
$641$	−35.5176	−	20.5061i	−1.40286	−	0.809942i	−0.994685	+	0.102961i	$0.967168\pi$
$642$		0			0
$643$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$643$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.82843	+	2.82843i	−0.111197	+	0.111197i	−0.760516	−	0.649319i	$-0.775054\pi$
$647$	−2.82843	+	2.82843i	−0.111197	+	0.111197i	0.649319	+	0.760516i	$0.275054\pi$
$648$		0			0
$649$		−	8.00000i		−	0.314027i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.55291	−	5.79555i	0.0607702	−	0.226798i	−0.928861	−	0.370428i	$-0.879211\pi$
$653$	1.55291	−	5.79555i	0.0607702	−	0.226798i	0.989631	+	0.143630i	$0.0458777\pi$
$654$		0			0
$655$	4.73205	−	4.19615i	0.184897	−	0.163957i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.41421	−	2.44949i	0.0550899	−	0.0954186i	−0.837165	−	0.546950i	$-0.815789\pi$
$659$	1.41421	−	2.44949i	0.0550899	−	0.0954186i	0.892255	+	0.451531i	$0.149122\pi$
$660$		0			0
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	0.978615	−	0.205702i	$-0.0659478\pi$
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	−0.667451	+	0.744654i	$0.732615\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	11.3137	+	22.6274i	0.438727	+	0.877454i
$666$		0			0
$667$	−56.0000	−	56.0000i	−2.16833	−	2.16833i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.41858	−	31.4186i	−0.324513	−	1.21110i	−0.914801	−	0.403905i	$-0.867653\pi$
$673$	−8.41858	−	31.4186i	−0.324513	−	1.21110i	0.590288	−	0.807192i	$-0.299014\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.62347	−	13.5230i	−0.139261	−	0.519730i	−0.999944	−	0.0105881i	$-0.996630\pi$
$677$	−3.62347	−	13.5230i	−0.139261	−	0.519730i	0.860683	−	0.509142i	$-0.170037\pi$
$678$		0			0
$679$	10.3923	−	6.00000i	0.398820	−	0.230259i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		0			0
$685$	−12.0000	−	24.0000i	−0.458496	−	0.916993i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−21.2132	−	36.7423i	−0.808159	−	1.39977i
$690$		0			0
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	26.7685	−	23.7370i	1.01539	−	0.900397i
$696$		0			0
$697$	−0.732051	+	2.73205i	−0.0277284	+	0.103484i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			9.89949i			0.373899i	0.982370	+	0.186949i	$0.0598600\pi$
$701$			9.89949i			0.373899i	−0.982370	+	0.186949i	$0.940140\pi$
$702$		0			0
$703$	12.0000	−	12.0000i	0.452589	−	0.452589i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.86370	−	1.03528i	−0.145310	−	0.0389356i
$708$		0			0
$709$	−8.66025	−	5.00000i	−0.325243	−	0.187779i	0.328484	−	0.944509i	$-0.393462\pi$
$709$	−8.66025	−	5.00000i	−0.325243	−	0.187779i	−0.653727	+	0.756730i	$0.726796\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	61.8193	−	16.5644i	2.31515	−	0.620342i
$714$		0			0
$715$	22.3923	+	14.7846i	0.837425	+	0.552913i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−39.5980			−1.47676			−0.738378	−	0.674387i	$-0.764408\pi$
$719$	−39.5980			−1.47676			−0.738378	+	0.674387i	$0.764408\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.92065	−	49.1421i	0.219888	−	1.82509i
$726$		0			0
$727$	8.19615	−	2.19615i	0.303978	−	0.0814508i	−0.103606	−	0.994618i	$-0.533038\pi$
$727$	8.19615	−	2.19615i	0.303978	−	0.0814508i	0.407584	+	0.913168i	$0.366371\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	39.6147	+	10.6147i	1.46320	+	0.392064i	0.900595	−	0.434659i	$-0.143131\pi$
$733$	39.6147	+	10.6147i	1.46320	+	0.392064i	0.562609	+	0.826723i	$0.309798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.6274	−	22.6274i	0.833492	−	0.833492i
$738$		0			0
$739$		−	28.0000i		−	1.03000i	−0.857191	−	0.514998i	$-0.827793\pi$
$739$		−	28.0000i		−	1.03000i	0.857191	−	0.514998i	$-0.172207\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.24693	−	27.0459i	0.265864	−	0.992219i	−0.695855	−	0.718182i	$-0.744974\pi$
$743$	7.24693	−	27.0459i	0.265864	−	0.992219i	0.961719	−	0.274036i	$-0.0883589\pi$
$744$		0			0
$745$	18.8827	+	21.2942i	0.691808	+	0.780160i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.65685	+	9.79796i	−0.206697	+	0.358010i
$750$		0			0
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−14.1421	+	42.4264i	−0.514685	+	1.54406i
$756$		0			0
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	0.851487	−	0.524376i	$-0.175701\pi$
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	−0.524376	+	0.851487i	$0.675701\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.2702	−	13.4350i	0.843542	−	0.487019i	−0.0149244	−	0.999889i	$-0.504751\pi$
$761$	23.2702	−	13.4350i	0.843542	−	0.487019i	0.858467	+	0.512869i	$0.171417\pi$
$762$		0			0
$763$	−5.85641	−	21.8564i	−0.212016	−	0.791255i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.10583	+	11.5911i	0.112145	+	0.418531i
$768$		0			0
$769$	6.92820	−	4.00000i	0.249837	−	0.144244i	−0.369852	−	0.929091i	$-0.620592\pi$
$769$	6.92820	−	4.00000i	0.249837	−	0.144244i	0.619690	+	0.784847i	$0.287258\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.7279	−	12.7279i	−0.457792	−	0.457792i	0.440138	−	0.897930i	$-0.354929\pi$
$773$	−12.7279	−	12.7279i	−0.457792	−	0.457792i	−0.897930	+	0.440138i	$0.854929\pi$
$774$		0			0
$775$	32.0000	+	24.0000i	1.14947	+	0.862105i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.82843	+	4.89898i	0.101339	+	0.175524i
$780$		0			0
$781$	8.00000	−	13.8564i	0.286263	−	0.495821i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.70522	−	28.4094i	0.0608618	−	1.01397i
$786$		0			0
$787$	−7.32051	+	27.3205i	−0.260948	+	0.973871i	0.703736	+	0.710461i	$0.251514\pi$
$787$	−7.32051	+	27.3205i	−0.260948	+	0.973871i	−0.964684	+	0.263410i	$0.915153\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			11.3137i			0.402269i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.5911	−	3.10583i	−0.410578	−	0.110014i	0.0476171	−	0.998866i	$-0.484837\pi$
$797$	−11.5911	−	3.10583i	−0.410578	−	0.110014i	−0.458195	+	0.888852i	$0.651504\pi$
$798$		0			0
$799$	20.7846	+	12.0000i	0.735307	+	0.424529i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	27.0459	−	7.24693i	0.954430	−	0.255739i
$804$		0			0
$805$	−10.1436	−	49.5692i	−0.357515	−	1.74709i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	43.8406			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$809$	43.8406			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.96953	−	10.5558i	0.244132	−	0.369755i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.4722	+	7.77817i	0.470183	+	0.271460i	0.716316	−	0.697776i	$-0.245827\pi$
$821$	13.4722	+	7.77817i	0.470183	+	0.271460i	−0.246133	+	0.969236i	$0.579160\pi$
$822$		0			0
$823$	−35.5167	−	9.51666i	−1.23803	−	0.331730i	−0.420331	−	0.907371i	$-0.638086\pi$
$823$	−35.5167	−	9.51666i	−1.23803	−	0.331730i	−0.817702	+	0.575641i	$0.804753\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.9411	−	33.9411i	1.18025	−	1.18025i	0.200569	−	0.979680i	$-0.435721\pi$
$827$	33.9411	−	33.9411i	1.18025	−	1.18025i	0.979680	−	0.200569i	$-0.0642791\pi$
$828$		0			0
$829$			8.00000i			0.277851i	0.990303	+	0.138926i	$0.0443649\pi$
$829$			8.00000i			0.277851i	−0.990303	+	0.138926i	$0.955635\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.517638	+	1.93185i	−0.0179351	+	0.0669347i
$834$		0			0
$835$	−35.7128	−	2.14359i	−1.23589	−	0.0741821i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.65685	−	9.79796i	0.195296	−	0.338263i	−0.751701	−	0.659504i	$-0.770766\pi$
$839$	5.65685	−	9.79796i	0.195296	−	0.338263i	0.946998	+	0.321241i	$0.104100\pi$
$840$		0			0
$841$	−34.5000	−	59.7558i	−1.18966	−	2.06054i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.6066	−	3.53553i	−0.364878	−	0.121626i
$846$		0			0
$847$	6.00000	+	6.00000i	0.206162	+	0.206162i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−29.3939	+	16.9706i	−1.00761	+	0.581743i
$852$		0			0
$853$	−1.83013	−	6.83013i	−0.0626624	−	0.233859i	0.927491	−	0.373845i	$-0.121961\pi$
$853$	−1.83013	−	6.83013i	−0.0626624	−	0.233859i	−0.990153	+	0.139986i	$0.955294\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.8704	−	40.5689i	−0.371326	−	1.38581i	−0.858640	−	0.512580i	$-0.828690\pi$
$857$	−10.8704	−	40.5689i	−0.371326	−	1.38581i	0.487314	−	0.873227i	$-0.337977\pi$
$858$		0			0
$859$	6.92820	−	4.00000i	0.236387	−	0.136478i	−0.377128	−	0.926161i	$-0.623088\pi$
$859$	6.92820	−	4.00000i	0.236387	−	0.136478i	0.613515	+	0.789683i	$0.289755\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.65685	+	5.65685i	0.192562	+	0.192562i	0.796802	−	0.604240i	$-0.206523\pi$
$863$	5.65685	+	5.65685i	0.192562	+	0.192562i	−0.604240	+	0.796802i	$0.706523\pi$
$864$		0			0
$865$	−8.00000	+	4.00000i	−0.272008	+	0.136004i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−24.0000	+	41.5692i	−0.813209	+	1.40852i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.4553	−	24.1160i	0.691516	−	0.815268i
$876$		0			0
$877$	−5.49038	+	20.4904i	−0.185397	+	0.691911i	0.809148	+	0.587605i	$0.199929\pi$
$877$	−5.49038	+	20.4904i	−0.185397	+	0.691911i	−0.994545	+	0.104306i	$0.966738\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	41.0122i		−	1.38174i	−0.722981	−	0.690868i	$-0.757229\pi$
$881$		−	41.0122i		−	1.38174i	0.722981	−	0.690868i	$-0.242771\pi$
$882$		0			0
$883$	−20.0000	+	20.0000i	−0.673054	+	0.673054i	−0.958419	−	0.285365i	$-0.907885\pi$
$883$	−20.0000	+	20.0000i	−0.673054	+	0.673054i	0.285365	+	0.958419i	$0.407885\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−46.3644	−	12.4233i	−1.55677	−	0.417134i	−0.625128	−	0.780522i	$-0.714953\pi$
$887$	−46.3644	−	12.4233i	−1.55677	−	0.417134i	−0.931638	+	0.363388i	$0.881620\pi$
$888$		0			0
$889$	34.6410	+	20.0000i	1.16182	+	0.670778i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	46.3644	−	12.4233i	1.55153	−	0.415730i
$894$		0			0
$895$	−30.9808	+	6.33975i	−1.03557	+	0.211914i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	79.1960			2.64133
$900$		0			0
$901$	−20.0000			−0.666297
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.5254	+	3.58630i	−0.582563	+	0.119213i
$906$		0			0
$907$	−21.8564	+	5.85641i	−0.725730	+	0.194459i	−0.602727	−	0.797948i	$-0.705919\pi$
$907$	−21.8564	+	5.85641i	−0.725730	+	0.194459i	−0.123003	+	0.992406i	$0.539253\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.4949	−	14.1421i	−0.811552	−	0.468550i	0.0359424	−	0.999354i	$-0.488557\pi$
$911$	−24.4949	−	14.1421i	−0.811552	−	0.468550i	−0.847495	+	0.530804i	$0.821890\pi$
$912$		0			0
$913$	32.7846	+	8.78461i	1.08501	+	0.290728i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.65685	−	5.65685i	0.186806	−	0.186806i
$918$		0			0
$919$			32.0000i			1.05558i	0.849374	+	0.527791i	$0.176980\pi$
$919$			32.0000i			1.05558i	−0.849374	+	0.527791i	$0.823020\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.21166	+	23.1822i	−0.204459	+	0.763052i
$924$		0			0
$925$	−19.6865	−	7.90192i	−0.647289	−	0.259814i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.6777	−	30.6186i	0.579986	−	1.00456i	−0.415495	−	0.909596i	$-0.636392\pi$
$929$	17.6777	−	30.6186i	0.579986	−	1.00456i	0.995480	−	0.0949688i	$-0.0302751\pi$
$930$		0			0
$931$	2.00000	+	3.46410i	0.0655474	+	0.113531i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.3137	−	5.65685i	0.369998	−	0.184999i
$936$		0			0
$937$	37.0000	+	37.0000i	1.20874	+	1.20874i	0.971436	+	0.237301i	$0.0762628\pi$
$937$	37.0000	+	37.0000i	1.20874	+	1.20874i	0.237301	+	0.971436i	$0.423737\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	33.0681	−	19.0919i	1.07799	−	0.622378i	0.147636	−	0.989042i	$-0.452834\pi$
$941$	33.0681	−	19.0919i	1.07799	−	0.622378i	0.930353	+	0.366664i	$0.119500\pi$
$942$		0			0
$943$	−2.92820	−	10.9282i	−0.0953554	−	0.355871i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.28221	+	30.9096i	0.269136	+	1.00443i	0.959670	+	0.281128i	$0.0907087\pi$
$947$	8.28221	+	30.9096i	0.269136	+	1.00443i	−0.690535	+	0.723299i	$0.742625\pi$
$948$		0			0
$949$	−36.3731	+	21.0000i	−1.18072	+	0.681689i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−25.4558	−	25.4558i	−0.824596	−	0.824596i	0.162168	−	0.986763i	$-0.448151\pi$
$953$	−25.4558	−	25.4558i	−0.824596	−	0.824596i	−0.986763	+	0.162168i	$0.948151\pi$
$954$		0			0
$955$	24.0000	+	8.00000i	0.776622	+	0.258874i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.9706	−	29.3939i	−0.548008	−	0.949178i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−47.3489	−	2.84203i	−1.52422	−	0.0914882i
$966$		0			0
$967$	−0.732051	+	2.73205i	−0.0235412	+	0.0878568i	−0.976697	−	0.214623i	$-0.931148\pi$
$967$	−0.732051	+	2.73205i	−0.0235412	+	0.0878568i	0.953156	+	0.302480i	$0.0978144\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			53.7401i			1.72460i	0.506396	+	0.862301i	$0.330978\pi$
$971$			53.7401i			1.72460i	−0.506396	+	0.862301i	$0.669022\pi$
$972$		0			0
$973$	32.0000	−	32.0000i	1.02587	−	1.02587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.3867	+	4.65874i	0.556249	+	0.149046i	0.525982	−	0.850495i	$-0.323698\pi$
$977$	17.3867	+	4.65874i	0.556249	+	0.149046i	0.0302663	+	0.999542i	$0.490364\pi$
$978$		0			0
$979$	3.46410	+	2.00000i	0.110713	+	0.0639203i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.3185	−	5.17638i	0.616165	−	0.165101i	0.0627812	−	0.998027i	$-0.480003\pi$
$983$	19.3185	−	5.17638i	0.616165	−	0.165101i	0.553384	+	0.832926i	$0.313336\pi$
$984$		0			0
$985$	−14.7846	+	22.3923i	−0.471077	+	0.713478i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.37945	+	26.2880i	0.170540	+	0.833387i
$996$		0			0
$997$	15.0263	−	4.02628i	0.475887	−	0.127514i	−0.0128998	−	0.999917i	$-0.504106\pi$
$997$	15.0263	−	4.02628i	0.475887	−	0.127514i	0.488787	+	0.872403i	$0.337440\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.x.a.917.1		8
3.2	odd	2	inner	1620.2.x.a.917.2		8
5.3	odd	4	inner	1620.2.x.a.593.1		8
9.2	odd	6		180.2.j.a.17.1	✓	4
9.4	even	3	inner	1620.2.x.a.377.2		8
9.5	odd	6	inner	1620.2.x.a.377.1		8
9.7	even	3		180.2.j.a.17.2	yes	4
15.8	even	4	inner	1620.2.x.a.593.2		8
36.7	odd	6		720.2.w.b.17.2		4
36.11	even	6		720.2.w.b.17.1		4
45.2	even	12		900.2.j.a.593.2		4
45.7	odd	12		900.2.j.a.593.1		4
45.13	odd	12	inner	1620.2.x.a.53.2		8
45.23	even	12	inner	1620.2.x.a.53.1		8
45.29	odd	6		900.2.j.a.557.2		4
45.34	even	6		900.2.j.a.557.1		4
45.38	even	12		180.2.j.a.53.2	yes	4
45.43	odd	12		180.2.j.a.53.1	yes	4
72.11	even	6		2880.2.w.a.2177.2		4
72.29	odd	6		2880.2.w.j.2177.2		4
72.43	odd	6		2880.2.w.a.2177.1		4
72.61	even	6		2880.2.w.j.2177.1		4
180.7	even	12		3600.2.w.f.593.2		4
180.43	even	12		720.2.w.b.593.1		4
180.47	odd	12		3600.2.w.f.593.1		4
180.79	odd	6		3600.2.w.f.1457.2		4
180.83	odd	12		720.2.w.b.593.2		4
180.119	even	6		3600.2.w.f.1457.1		4
360.43	even	12		2880.2.w.a.2753.2		4
360.83	odd	12		2880.2.w.a.2753.1		4
360.133	odd	12		2880.2.w.j.2753.2		4
360.173	even	12		2880.2.w.j.2753.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.j.a.17.1	✓	4	9.2	odd	6
180.2.j.a.17.2	yes	4	9.7	even	3
180.2.j.a.53.1	yes	4	45.43	odd	12
180.2.j.a.53.2	yes	4	45.38	even	12
720.2.w.b.17.1		4	36.11	even	6
720.2.w.b.17.2		4	36.7	odd	6
720.2.w.b.593.1		4	180.43	even	12
720.2.w.b.593.2		4	180.83	odd	12
900.2.j.a.557.1		4	45.34	even	6
900.2.j.a.557.2		4	45.29	odd	6
900.2.j.a.593.1		4	45.7	odd	12
900.2.j.a.593.2		4	45.2	even	12
1620.2.x.a.53.1		8	45.23	even	12	inner
1620.2.x.a.53.2		8	45.13	odd	12	inner
1620.2.x.a.377.1		8	9.5	odd	6	inner
1620.2.x.a.377.2		8	9.4	even	3	inner
1620.2.x.a.593.1		8	5.3	odd	4	inner
1620.2.x.a.593.2		8	15.8	even	4	inner
1620.2.x.a.917.1		8	1.1	even	1	trivial
1620.2.x.a.917.2		8	3.2	odd	2	inner
2880.2.w.a.2177.1		4	72.43	odd	6
2880.2.w.a.2177.2		4	72.11	even	6
2880.2.w.a.2753.1		4	360.83	odd	12
2880.2.w.a.2753.2		4	360.43	even	12
2880.2.w.j.2177.1		4	72.61	even	6
2880.2.w.j.2177.2		4	72.29	odd	6
2880.2.w.j.2753.1		4	360.173	even	12
2880.2.w.j.2753.2		4	360.133	odd	12
3600.2.w.f.593.1		4	180.47	odd	12
3600.2.w.f.593.2		4	180.7	even	12
3600.2.w.f.1457.1		4	180.119	even	6
3600.2.w.f.1457.2		4	180.79	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.19067 + 0.448288i) q^{5} +(-2.73205 + 0.732051i) q^{7} +(2.44949 + 1.41421i) q^{11} +(-4.09808 - 1.09808i) q^{13} +(-1.41421 + 1.41421i) q^{17} +4.00000i q^{19} +(2.07055 - 7.72741i) q^{23} +(4.59808 - 1.96410i) q^{25} +(4.94975 - 8.57321i) q^{29} +(4.00000 + 6.92820i) q^{31} +(5.65685 - 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(1.22474 - 0.707107i) q^{41} +(-3.10583 - 11.5911i) q^{47} +(0.866025 - 0.500000i) q^{49} +(7.07107 + 7.07107i) q^{53} +(-6.00000 - 2.00000i) q^{55} +(-1.41421 - 2.44949i) q^{59} +(9.46979 + 0.568406i) q^{65} +(2.92820 - 10.9282i) q^{67} -5.65685i q^{71} +(7.00000 - 7.00000i) q^{73} +(-7.72741 - 2.07055i) q^{77} +(11.5911 - 3.10583i) q^{83} +(2.46410 - 3.73205i) q^{85} +1.41421 q^{89} +12.0000 q^{91} +(-1.79315 - 8.76268i) q^{95} +(-4.09808 + 1.09808i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} - 12 q^{13} + 16 q^{25} + 32 q^{31} - 24 q^{37} - 48 q^{55} - 32 q^{67} + 56 q^{73} - 8 q^{85} + 96 q^{91} - 12 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 - 12 * q^13 + 16 * q^25 + 32 * q^31 - 24 * q^37 - 48 * q^55 - 32 * q^67 + 56 * q^73 - 8 * q^85 + 96 * q^91 - 12 * q^97

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