LMFDB - Embedded newform 1620.2.x.a.593.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(53,1620)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			593.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1620.593
Dual form			1620.2.x.a.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48356 - 1.67303i) q^{5} +(0.732051 + 2.73205i) q^{7} +O(q^{10})$	$q+(1.48356 - 1.67303i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.44949 - 1.41421i) q^{11} +(1.09808 - 4.09808i) q^{13} +(-1.41421 - 1.41421i) q^{17} -4.00000i q^{19} +(-7.72741 - 2.07055i) q^{23} +(-0.598076 - 4.96410i) q^{25} +(4.94975 - 8.57321i) q^{29} +(4.00000 + 6.92820i) q^{31} +(5.65685 + 2.82843i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-1.22474 + 0.707107i) q^{41} +(11.5911 - 3.10583i) q^{47} +(-0.866025 + 0.500000i) q^{49} +(7.07107 - 7.07107i) q^{53} +(-6.00000 + 2.00000i) q^{55} +(-1.41421 - 2.44949i) q^{59} +(-5.22715 - 7.91688i) q^{65} +(-10.9282 - 2.92820i) q^{67} +5.65685i q^{71} +(7.00000 + 7.00000i) q^{73} +(2.07055 - 7.72741i) q^{77} +(-3.10583 - 11.5911i) q^{83} +(-4.46410 + 0.267949i) q^{85} +1.41421 q^{89} +12.0000 q^{91} +(-6.69213 - 5.93426i) q^{95} +(1.09808 + 4.09808i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$5$	1.48356	−	1.67303i	0.663470	−	0.748203i
$5$	1.48356	−	1.67303i	0.663470	−	0.748203i
$6$		0			0
$7$	0.732051	+	2.73205i	0.276689	+	1.03262i	0.954701	+	0.297567i	$0.0961752\pi$
$7$	0.732051	+	2.73205i	0.276689	+	1.03262i	−0.678012	+	0.735051i	$0.737158\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.44949	−	1.41421i	−0.738549	−	0.426401i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	−2.44949	−	1.41421i	−0.738549	−	0.426401i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	1.09808	−	4.09808i	0.304552	−	1.13660i	−0.628779	−	0.777584i	$-0.716445\pi$
$13$	1.09808	−	4.09808i	0.304552	−	1.13660i	0.933331	−	0.359018i	$-0.116888\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.72741	−	2.07055i	−1.61128	−	0.431740i	−0.662853	−	0.748749i	$-0.730655\pi$
$23$	−7.72741	−	2.07055i	−1.61128	−	0.431740i	−0.948422	+	0.317009i	$0.897321\pi$
$24$		0			0
$25$	−0.598076	−	4.96410i	−0.119615	−	0.992820i
$26$		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	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.22474	+	0.707107i	−0.191273	+	0.110432i	−0.592578	−	0.805513i	$-0.701890\pi$
$41$	−1.22474	+	0.707107i	−0.191273	+	0.110432i	0.401305	+	0.915944i	$0.368557\pi$
$42$		0			0
$43$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$43$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	11.5911	−	3.10583i	1.69074	−	0.453032i	0.720157	−	0.693811i	$-0.244070\pi$
$47$	11.5911	−	3.10583i	1.69074	−	0.453032i	0.970580	+	0.240779i	$0.0774030\pi$
$48$		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	−0.0283132	−	0.999599i	$-0.509014\pi$
$53$	7.07107	−	7.07107i	0.971286	−	0.971286i	0.999599	+	0.0283132i	$0.00901359\pi$
$54$		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
$65$	−5.22715	−	7.91688i	−0.648348	−	0.981968i
$66$		0			0
$67$	−10.9282	−	2.92820i	−1.33509	−	0.357737i	−0.480481	−	0.877005i	$-0.659538\pi$
$67$	−10.9282	−	2.92820i	−1.33509	−	0.357737i	−0.854611	+	0.519268i	$0.826205\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$		0			0
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	0.986005	−	0.166717i	$-0.0533166\pi$
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	−0.166717	+	0.986005i	$0.553317\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.07055	−	7.72741i	0.235961	−	0.880620i
$78$		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
$83$	−3.10583	−	11.5911i	−0.340909	−	1.27229i	−0.897319	−	0.441382i	$-0.854488\pi$
$83$	−3.10583	−	11.5911i	−0.340909	−	1.27229i	0.556410	−	0.830908i	$-0.312178\pi$
$84$		0			0
$85$	−4.46410	+	0.267949i	−0.484200	+	0.0290632i
$86$		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
$95$	−6.69213	−	5.93426i	−0.686598	−	0.608842i
$96$		0			0
$97$	1.09808	+	4.09808i	0.111493	+	0.416097i	0.999001	−	0.0446959i	$-0.0142319\pi$
$97$	1.09808	+	4.09808i	0.111493	+	0.416097i	−0.887508	+	0.460793i	$0.847565\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.22474	−	0.707107i	−0.121867	−	0.0703598i	0.437828	−	0.899059i	$-0.355748\pi$
$101$	−1.22474	−	0.707107i	−0.121867	−	0.0703598i	−0.559694	+	0.828699i	$0.689081\pi$
$102$		0			0
$103$	−0.732051	+	2.73205i	−0.0721311	+	0.269197i	−0.992567	−	0.121695i	$-0.961167\pi$
$103$	−0.732051	+	2.73205i	−0.0721311	+	0.269197i	0.920436	+	0.390892i	$0.127834\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	0.830481	−	0.557047i	$-0.188066\pi$
$107$	2.82843	+	2.82843i	0.273434	+	0.273434i	−0.557047	+	0.830481i	$0.688066\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.86370	−	1.03528i	−0.363467	−	0.0973906i	0.0724636	−	0.997371i	$-0.476914\pi$
$113$	−3.86370	−	1.03528i	−0.363467	−	0.0973906i	−0.435930	+	0.899980i	$0.643581\pi$
$114$		0			0
$115$	−14.9282	+	9.85641i	−1.39206	+	0.919115i
$116$		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	−0.994268	−	0.106912i	$-0.965904\pi$
$127$	−10.0000	+	10.0000i	−0.887357	+	0.887357i	0.106912	+	0.994268i	$0.465904\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.44949	−	1.41421i	0.214013	−	0.123560i	−0.389162	−	0.921169i	$-0.627235\pi$
$131$	2.44949	−	1.41421i	0.214013	−	0.123560i	0.603175	+	0.797609i	$0.293902\pi$
$132$		0			0
$133$	10.9282	−	2.92820i	0.947595	−	0.253907i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.5911	+	3.10583i	−0.990295	+	0.265349i	−0.717375	−	0.696688i	$-0.754656\pi$
$137$	−11.5911	+	3.10583i	−0.990295	+	0.265349i	−0.272921	+	0.962037i	$0.587990\pi$
$138$		0			0
$139$	13.8564	−	8.00000i	1.17529	−	0.678551i	0.220366	−	0.975417i	$-0.429275\pi$
$139$	13.8564	−	8.00000i	1.17529	−	0.678551i	0.954919	+	0.296866i	$0.0959415\pi$
$140$		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
$155$	17.5254	+	3.58630i	1.40767	+	0.288059i
$156$		0			0
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.713544	−	0.700610i	$-0.247089\pi$
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.267642	+	0.963518i	$0.413756\pi$
$158$		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	0.532884	−	0.846188i	$-0.321108\pi$
$163$	−4.00000	−	4.00000i	−0.313304	−	0.313304i	−0.846188	+	0.532884i	$0.821108\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.14110	+	15.4548i	−0.320448	+	1.19593i	0.598361	+	0.801227i	$0.295819\pi$
$167$	−4.14110	+	15.4548i	−0.320448	+	1.19593i	−0.918809	+	0.394702i	$0.870848\pi$
$168$		0			0
$169$	−4.33013	−	2.50000i	−0.333087	−	0.192308i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.03528	−	3.86370i	−0.0787106	−	0.293752i	0.915338	−	0.402685i	$-0.131923\pi$
$173$	−1.03528	−	3.86370i	−0.0787106	−	0.293752i	−0.994049	+	0.108933i	$0.965256\pi$
$174$		0			0
$175$	13.1244	−	5.26795i	0.992108	−	0.398220i
$176$		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
$185$	0.568406	+	9.46979i	0.0417900	+	0.696233i
$186$		0			0
$187$	1.46410	+	5.46410i	0.107066	+	0.399575i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.79796	+	5.65685i	0.708955	+	0.409316i	0.810674	−	0.585498i	$-0.199101\pi$
$191$	9.79796	+	5.65685i	0.708955	+	0.409316i	−0.101719	+	0.994813i	$0.532434\pi$
$192$		0			0
$193$	−5.49038	+	20.4904i	−0.395206	+	1.47493i	0.426222	+	0.904618i	$0.359844\pi$
$193$	−5.49038	+	20.4904i	−0.395206	+	1.47493i	−0.821429	+	0.570311i	$0.806823\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.48528	+	8.48528i	0.604551	+	0.604551i	0.941517	−	0.336966i	$-0.109401\pi$
$197$	8.48528	+	8.48528i	0.604551	+	0.604551i	−0.336966	+	0.941517i	$0.609401\pi$
$198$		0			0
$199$			12.0000i			0.850657i	0.905039	+	0.425329i	$0.139842\pi$
$199$			12.0000i			0.850657i	−0.905039	+	0.425329i	$0.860158\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	27.0459	+	7.24693i	1.89825	+	0.508635i
$204$		0			0
$205$	−0.633975	+	3.09808i	−0.0442787	+	0.216379i
$206$		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
$223$	8.19615	−	2.19615i	0.548855	−	0.147065i	0.0262738	−	0.999655i	$-0.491636\pi$
$223$	8.19615	−	2.19615i	0.548855	−	0.147065i	0.522581	+	0.852590i	$0.324969\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.72741	+	2.07055i	−0.512886	+	0.137427i	−0.505974	−	0.862549i	$-0.668867\pi$
$227$	−7.72741	+	2.07055i	−0.512886	+	0.137427i	−0.00691198	+	0.999976i	$0.502200\pi$
$228$		0			0
$229$	−5.19615	+	3.00000i	−0.343371	+	0.198246i	−0.661762	−	0.749714i	$-0.730191\pi$
$229$	−5.19615	+	3.00000i	−0.343371	+	0.198246i	0.318390	+	0.947960i	$0.396858\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	−0.832288	−	0.554343i	$-0.812969\pi$
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	0.554343	+	0.832288i	$0.312969\pi$
$234$		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
$245$	−0.448288	+	2.19067i	−0.0286401	+	0.139957i
$246$		0			0
$247$	−16.3923	−	4.39230i	−1.04302	−	0.279476i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			25.4558i			1.60676i	0.595468	+	0.803379i	$0.296967\pi$
$251$			25.4558i			1.60676i	−0.595468	+	0.803379i	$0.703033\pi$
$252$		0			0
$253$	16.0000	+	16.0000i	1.00591	+	1.00591i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.17638	−	19.3185i	0.322894	−	1.20506i	−0.593519	−	0.804820i	$-0.702262\pi$
$257$	5.17638	−	19.3185i	0.322894	−	1.20506i	0.916412	−	0.400236i	$-0.131072\pi$
$258$		0			0
$259$	−10.3923	−	6.00000i	−0.645746	−	0.372822i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.14110	+	15.4548i	0.255351	+	0.952985i	0.967895	+	0.251356i	$0.0808766\pi$
$263$	4.14110	+	15.4548i	0.255351	+	0.952985i	−0.712543	+	0.701628i	$0.752457\pi$
$264$		0			0
$265$	−1.33975	−	22.3205i	−0.0822999	−	1.37114i
$266$		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
$275$	−5.55532	+	13.0053i	−0.334998	+	0.784251i
$276$		0			0
$277$	5.49038	+	20.4904i	0.329885	+	1.23115i	0.909309	+	0.416121i	$0.136611\pi$
$277$	5.49038	+	20.4904i	0.329885	+	1.23115i	−0.579424	+	0.815026i	$0.696722\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.0227	−	6.36396i	−0.657559	−	0.379642i	0.133787	−	0.991010i	$-0.457286\pi$
$281$	−11.0227	−	6.36396i	−0.657559	−	0.379642i	−0.791346	+	0.611368i	$0.790620\pi$
$282$		0			0
$283$	−1.46410	+	5.46410i	−0.0870318	+	0.324807i	−0.995691	−	0.0927310i	$-0.970440\pi$
$283$	−1.46410	+	5.46410i	−0.0870318	+	0.324807i	0.908659	+	0.417538i	$0.137107\pi$
$284$		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
$293$	11.5911	+	3.10583i	0.677160	+	0.181444i	0.580978	−	0.813919i	$-0.302670\pi$
$293$	11.5911	+	3.10583i	0.677160	+	0.181444i	0.0961820	+	0.995364i	$0.469337\pi$
$294$		0			0
$295$	−6.19615	−	1.26795i	−0.360754	−	0.0738229i
$296$		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	−0.961095	−	0.276219i	$-0.910919\pi$
$307$	−12.0000	+	12.0000i	−0.684876	+	0.684876i	0.276219	+	0.961095i	$0.410919\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.89898	−	2.82843i	0.277796	−	0.160385i	−0.354629	−	0.935007i	$-0.615393\pi$
$311$	4.89898	−	2.82843i	0.277796	−	0.160385i	0.632425	+	0.774622i	$0.282060\pi$
$312$		0			0
$313$	−4.09808	+	1.09808i	−0.231637	+	0.0620669i	−0.372770	−	0.927924i	$-0.621592\pi$
$313$	−4.09808	+	1.09808i	−0.231637	+	0.0620669i	0.141133	+	0.989991i	$0.454925\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.79555	+	1.55291i	−0.325511	+	0.0872204i	−0.417874	−	0.908505i	$-0.637225\pi$
$317$	−5.79555	+	1.55291i	−0.325511	+	0.0872204i	0.0923631	+	0.995725i	$0.470558\pi$
$318$		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
$335$	−21.1117	+	13.9391i	−1.15345	+	0.761572i
$336$		0			0
$337$	4.09808	+	1.09808i	0.223236	+	0.0598160i	0.368703	−	0.929547i	$-0.379802\pi$
$337$	4.09808	+	1.09808i	0.223236	+	0.0598160i	−0.145467	+	0.989363i	$0.546468\pi$
$338$		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
$347$	−2.07055	+	7.72741i	−0.111153	+	0.414829i	−0.998970	−	0.0453672i	$-0.985554\pi$
$347$	−2.07055	+	7.72741i	−0.111153	+	0.414829i	0.887817	+	0.460196i	$0.152221\pi$
$348$		0			0
$349$	−27.7128	−	16.0000i	−1.48343	−	0.856460i	−0.483610	−	0.875284i	$-0.660675\pi$
$349$	−27.7128	−	16.0000i	−1.48343	−	0.856460i	−0.999823	+	0.0188232i	$0.994008\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.65874	+	17.3867i	0.247960	+	0.925399i	0.971873	+	0.235507i	$0.0756751\pi$
$353$	4.65874	+	17.3867i	0.247960	+	0.925399i	−0.723913	+	0.689892i	$0.757658\pi$
$354$		0			0
$355$	9.46410	+	8.39230i	0.502302	+	0.445417i
$356$		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
$365$	22.0962	−	1.32628i	1.15657	−	0.0694207i
$366$		0			0
$367$	5.12436	+	19.1244i	0.267489	+	0.998283i	0.960709	+	0.277557i	$0.0895248\pi$
$367$	5.12436	+	19.1244i	0.267489	+	0.998283i	−0.693220	+	0.720726i	$0.743809\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	24.4949	+	14.1421i	1.27171	+	0.734223i
$372$		0			0
$373$	−1.83013	+	6.83013i	−0.0947604	+	0.353651i	−0.996983	−	0.0776200i	$-0.975268\pi$
$373$	−1.83013	+	6.83013i	−0.0947604	+	0.353651i	0.902223	+	0.431271i	$0.141935\pi$
$374$		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	$-0.865203\pi$
$379$		−	16.0000i		−	0.821865i	0.911666	−	0.410932i	$-0.134797\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−34.7733	−	9.31749i	−1.77683	−	0.476101i	−0.786834	−	0.617165i	$-0.788281\pi$
$383$	−34.7733	−	9.31749i	−1.77683	−	0.476101i	−0.990000	+	0.141064i	$0.954948\pi$
$384$		0			0
$385$	−9.85641	−	14.9282i	−0.502329	−	0.760812i
$386$		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	−0.990527	−	0.137321i	$-0.956151\pi$
$397$	−17.0000	+	17.0000i	−0.853206	+	0.853206i	0.137321	+	0.990527i	$0.456151\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.3712	−	10.6066i	0.917413	−	0.529668i	0.0346039	−	0.999401i	$-0.488983\pi$
$401$	18.3712	−	10.6066i	0.917413	−	0.529668i	0.882809	+	0.469733i	$0.155650\pi$
$402$		0			0
$403$	32.7846	−	8.78461i	1.63312	−	0.437593i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.5911	−	3.10583i	0.574550	−	0.153950i
$408$		0			0
$409$	20.7846	−	12.0000i	1.02773	−	0.593362i	0.111398	−	0.993776i	$-0.464467\pi$
$409$	20.7846	−	12.0000i	1.02773	−	0.593362i	0.916334	+	0.400414i	$0.131134\pi$
$410$		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
$425$	−6.17449	+	7.86611i	−0.299507	+	0.381562i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$			28.2843i			1.36241i	0.732095	+	0.681203i	$0.238543\pi$
$431$			28.2843i			1.36241i	−0.732095	+	0.681203i	$0.761457\pi$
$432$		0			0
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.993759	+	0.111551i	$0.0355818\pi$
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.111551	+	0.993759i	$0.464418\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.28221	+	30.9096i	−0.396192	+	1.47861i
$438$		0			0
$439$	17.3205	+	10.0000i	0.826663	+	0.477274i	0.852709	−	0.522387i	$-0.174958\pi$
$439$	17.3205	+	10.0000i	0.826663	+	0.477274i	−0.0260459	+	0.999661i	$0.508292\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.21166	+	23.1822i	0.295125	+	1.10142i	0.941118	+	0.338078i	$0.109777\pi$
$443$	6.21166	+	23.1822i	0.295125	+	1.10142i	−0.645994	+	0.763343i	$0.723557\pi$
$444$		0			0
$445$	2.09808	−	2.36603i	0.0994584	−	0.112160i
$446$		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
$455$	17.8028	−	20.0764i	0.834607	−	0.941196i
$456$		0			0
$457$	5.49038	+	20.4904i	0.256829	+	0.958500i	0.967064	+	0.254534i	$0.0819222\pi$
$457$	5.49038	+	20.4904i	0.256829	+	0.958500i	−0.710235	+	0.703965i	$0.751411\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.4722	−	7.77817i	−0.627463	−	0.362266i	0.152306	−	0.988333i	$-0.451330\pi$
$461$	−13.4722	−	7.77817i	−0.627463	−	0.362266i	−0.779769	+	0.626068i	$0.784663\pi$
$462$		0			0
$463$	9.51666	−	35.5167i	0.442277	−	1.65060i	−0.280751	−	0.959781i	$-0.590584\pi$
$463$	9.51666	−	35.5167i	0.442277	−	1.65060i	0.723028	−	0.690819i	$-0.242750\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.7990	+	19.7990i	0.916188	+	0.916188i	0.996750	−	0.0805616i	$-0.0256714\pi$
$467$	19.7990	+	19.7990i	0.916188	+	0.916188i	−0.0805616	+	0.996750i	$0.525671\pi$
$468$		0			0
$469$		−	32.0000i		−	1.47762i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−19.8564	+	2.39230i	−0.911074	+	0.109766i
$476$		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	−0.557973	−	0.829859i	$-0.688421\pi$
$487$	6.00000	−	6.00000i	0.271886	−	0.271886i	0.829859	+	0.557973i	$0.188421\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−31.8434	+	18.3848i	−1.43707	+	0.829693i	−0.997645	−	0.0685856i	$-0.978151\pi$
$491$	−31.8434	+	18.3848i	−1.43707	+	0.829693i	−0.439426	+	0.898279i	$0.644818\pi$
$492$		0			0
$493$	−19.1244	+	5.12436i	−0.861318	+	0.230789i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.4548	+	4.14110i	−0.693243	+	0.185754i
$498$		0			0
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	−0.420455	−	0.907314i	$-0.638129\pi$
$499$	3.46410	−	2.00000i	0.155074	−	0.0895323i	0.575529	+	0.817781i	$0.304796\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	−0.492163	−	0.870503i	$-0.663794\pi$
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	0.870503	+	0.492163i	$0.163794\pi$
$504$		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
$515$	3.48477	+	5.27792i	0.153557	+	0.232573i
$516$		0			0
$517$	−32.7846	−	8.78461i	−1.44187	−	0.386347i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			29.6985i			1.30111i	0.759457	+	0.650557i	$0.225465\pi$
$521$			29.6985i			1.30111i	−0.759457	+	0.650557i	$0.774535\pi$
$522$		0			0
$523$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$523$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.14110	−	15.4548i	0.180389	−	0.673222i
$528$		0			0
$529$	35.5070	+	20.5000i	1.54378	+	0.891304i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.55291	+	5.79555i	0.0672642	+	0.251033i
$534$		0			0
$535$	8.92820	−	0.535898i	0.386000	−	0.0231689i
$536$		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
$545$	−13.3843	−	11.8685i	−0.573319	−	0.508391i
$546$		0			0
$547$	−4.39230	−	16.3923i	−0.187801	−	0.700884i	−0.994013	−	0.109258i	$-0.965153\pi$
$547$	−4.39230	−	16.3923i	−0.187801	−	0.700884i	0.806212	−	0.591627i	$-0.201514\pi$
$548$		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	0.384024	−	0.923323i	$-0.374538\pi$
$557$	−12.7279	−	12.7279i	−0.539299	−	0.539299i	−0.923323	+	0.384024i	$0.874538\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	23.1822	+	6.21166i	0.977014	+	0.261790i	0.711787	−	0.702396i	$-0.247886\pi$
$563$	23.1822	+	6.21166i	0.977014	+	0.261790i	0.265227	+	0.964186i	$0.414553\pi$
$564$		0			0
$565$	−7.46410	+	4.92820i	−0.314017	+	0.207331i
$566$		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	−0.546225	−	0.837639i	$-0.683936\pi$
$577$	7.00000	−	7.00000i	0.291414	−	0.291414i	0.837639	+	0.546225i	$0.183936\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	29.3939	−	16.9706i	1.21946	−	0.704058i
$582$		0			0
$583$	−27.3205	+	7.32051i	−1.13150	+	0.303184i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.5911	−	3.10583i	0.478416	−	0.128191i	−0.0115488	−	0.999933i	$-0.503676\pi$
$587$	11.5911	−	3.10583i	0.478416	−	0.128191i	0.489965	+	0.871742i	$0.337010\pi$
$588$		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	−0.354361	−	0.935109i	$-0.615302\pi$
$593$	14.1421	−	14.1421i	0.580748	−	0.580748i	0.935109	+	0.354361i	$0.115302\pi$
$594$		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
$605$	−6.57201	−	1.34486i	−0.267190	−	0.0546765i
$606$		0			0
$607$	−24.5885	−	6.58846i	−0.998015	−	0.267417i	−0.277401	−	0.960754i	$-0.589473\pi$
$607$	−24.5885	−	6.58846i	−0.998015	−	0.267417i	−0.720614	+	0.693337i	$0.756140\pi$
$608$		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	−0.995473	−	0.0950469i	$-0.969700\pi$
$613$	−27.0000	−	27.0000i	−1.09052	−	1.09052i	−0.0950469	−	0.995473i	$-0.530300\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.55291	+	5.79555i	−0.0625180	+	0.233320i	−0.990114	−	0.140264i	$-0.955205\pi$
$617$	−1.55291	+	5.79555i	−0.0625180	+	0.233320i	0.927596	+	0.373585i	$0.121871\pi$
$618$		0			0
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	0.0202954	−	0.999794i	$-0.493539\pi$
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	−0.855699	+	0.517473i	$0.826873\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.03528	+	3.86370i	0.0414775	+	0.154796i
$624$		0			0
$625$	−24.2846	+	5.93782i	−0.971384	+	0.237513i
$626$		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
$635$	1.89469	+	31.5660i	0.0751884	+	1.25266i
$636$		0			0
$637$	1.09808	+	4.09808i	0.0435074	+	0.162372i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.5176	+	20.5061i	1.40286	+	0.809942i	0.994685	−	0.102961i	$-0.0328318\pi$
$641$	35.5176	+	20.5061i	1.40286	+	0.809942i	0.408176	+	0.912903i	$0.366165\pi$
$642$		0			0
$643$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$643$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.82843	−	2.82843i	−0.111197	−	0.111197i	0.649319	−	0.760516i	$-0.275054\pi$
$647$	−2.82843	−	2.82843i	−0.111197	−	0.111197i	−0.760516	+	0.649319i	$0.775054\pi$
$648$		0			0
$649$			8.00000i			0.314027i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.79555	−	1.55291i	−0.226798	−	0.0607702i	0.143630	−	0.989631i	$-0.454122\pi$
$653$	−5.79555	−	1.55291i	−0.226798	−	0.0607702i	−0.370428	+	0.928861i	$0.620789\pi$
$654$		0			0
$655$	1.26795	−	6.19615i	0.0495429	−	0.242104i
$656$		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
$673$	31.4186	−	8.41858i	1.21110	−	0.324513i	0.403905	−	0.914801i	$-0.367653\pi$
$673$	31.4186	−	8.41858i	1.21110	−	0.324513i	0.807192	+	0.590288i	$0.200986\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5230	−	3.62347i	0.519730	−	0.139261i	0.0105881	−	0.999944i	$-0.496630\pi$
$677$	13.5230	−	3.62347i	0.519730	−	0.139261i	0.509142	+	0.860683i	$0.329963\pi$
$678$		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	−0.850559	−	0.525879i	$-0.823736\pi$
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	0.525879	+	0.850559i	$0.323736\pi$
$684$		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
$695$	7.17260	−	35.0507i	0.272072	−	1.32955i
$696$		0			0
$697$	2.73205	+	0.732051i	0.103484	+	0.0277284i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	9.89949i		−	0.373899i	−0.982370	−	0.186949i	$-0.940140\pi$
$701$		−	9.89949i		−	0.373899i	0.982370	−	0.186949i	$-0.0598600\pi$
$702$		0			0
$703$	12.0000	+	12.0000i	0.452589	+	0.452589i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.03528	−	3.86370i	0.0389356	−	0.145310i
$708$		0			0
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	0.653727	−	0.756730i	$-0.273204\pi$
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	−0.328484	+	0.944509i	$0.606538\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.5644	−	61.8193i	−0.620342	−	2.31515i
$714$		0			0
$715$	1.60770	+	26.7846i	0.0601244	+	1.00169i
$716$		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
$725$	−45.5186	−	19.4436i	−1.69052	−	0.722118i
$726$		0			0
$727$	−2.19615	−	8.19615i	−0.0814508	−	0.303978i	0.913168	−	0.407584i	$-0.133629\pi$
$727$	−2.19615	−	8.19615i	−0.0814508	−	0.303978i	−0.994618	+	0.103606i	$0.966962\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−10.6147	+	39.6147i	−0.392064	+	1.46320i	0.434659	+	0.900595i	$0.356869\pi$
$733$	−10.6147	+	39.6147i	−0.392064	+	1.46320i	−0.826723	+	0.562609i	$0.809798\pi$
$734$		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	$0.172207\pi$
$739$			28.0000i			1.03000i	−0.857191	+	0.514998i	$0.827793\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.0459	−	7.24693i	−0.992219	−	0.265864i	−0.274036	−	0.961719i	$-0.588359\pi$
$743$	−27.0459	−	7.24693i	−0.992219	−	0.265864i	−0.718182	+	0.695855i	$0.755026\pi$
$744$		0			0
$745$	−27.8827	−	5.70577i	−1.02154	−	0.209043i
$746$		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	−0.524376	−	0.851487i	$-0.675701\pi$
$757$	9.00000	−	9.00000i	0.327111	−	0.327111i	0.851487	+	0.524376i	$0.175701\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.2702	+	13.4350i	−0.843542	+	0.487019i	−0.858467	−	0.512869i	$-0.828583\pi$
$761$	−23.2702	+	13.4350i	−0.843542	+	0.487019i	0.0149244	+	0.999889i	$0.495249\pi$
$762$		0			0
$763$	21.8564	−	5.85641i	0.791255	−	0.212016i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.5911	+	3.10583i	−0.418531	+	0.112145i
$768$		0			0
$769$	−6.92820	+	4.00000i	−0.249837	+	0.144244i	−0.619690	−	0.784847i	$-0.712742\pi$
$769$	−6.92820	+	4.00000i	−0.249837	+	0.144244i	0.369852	+	0.929091i	$0.379408\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.7279	+	12.7279i	−0.457792	+	0.457792i	−0.897930	−	0.440138i	$-0.854929\pi$
$773$	−12.7279	+	12.7279i	−0.457792	+	0.457792i	0.440138	+	0.897930i	$0.354929\pi$
$774$		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
$785$	23.7506	−	15.6814i	0.847696	−	0.559695i
$786$		0			0
$787$	27.3205	+	7.32051i	0.973871	+	0.260948i	0.710461	−	0.703736i	$-0.248486\pi$
$787$	27.3205	+	7.32051i	0.973871	+	0.260948i	0.263410	+	0.964684i	$0.415153\pi$
$788$		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
$797$	3.10583	−	11.5911i	0.110014	−	0.410578i	−0.888852	−	0.458195i	$-0.848496\pi$
$797$	3.10583	−	11.5911i	0.110014	−	0.410578i	0.998866	+	0.0476171i	$0.0151627\pi$
$798$		0			0
$799$	−20.7846	−	12.0000i	−0.735307	−	0.424529i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.24693	−	27.0459i	−0.255739	−	0.954430i
$804$		0			0
$805$	−37.8564	−	33.5692i	−1.33426	−	1.18316i
$806$		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
$815$	−12.6264	+	0.757875i	−0.442283	+	0.0265472i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.4722	−	7.77817i	−0.470183	−	0.271460i	0.246133	−	0.969236i	$-0.420840\pi$
$821$	−13.4722	−	7.77817i	−0.470183	−	0.271460i	−0.716316	+	0.697776i	$0.754173\pi$
$822$		0			0
$823$	9.51666	−	35.5167i	0.331730	−	1.23803i	−0.575641	−	0.817702i	$-0.695247\pi$
$823$	9.51666	−	35.5167i	0.331730	−	1.23803i	0.907371	−	0.420331i	$-0.138086\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.9411	+	33.9411i	1.18025	+	1.18025i	0.979680	+	0.200569i	$0.0642791\pi$
$827$	33.9411	+	33.9411i	1.18025	+	1.18025i	0.200569	+	0.979680i	$0.435721\pi$
$828$		0			0
$829$		−	8.00000i		−	0.277851i	−0.990303	−	0.138926i	$-0.955635\pi$
$829$		−	8.00000i		−	0.277851i	0.990303	−	0.138926i	$-0.0443649\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.93185	+	0.517638i	0.0669347	+	0.0179351i
$834$		0			0
$835$	19.7128	+	29.8564i	0.682190	+	1.03322i
$836$		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
$853$	6.83013	−	1.83013i	0.233859	−	0.0626624i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	6.83013	−	1.83013i	0.233859	−	0.0626624i	0.373845	+	0.927491i	$0.378039\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	40.5689	−	10.8704i	1.38581	−	0.371326i	0.512580	−	0.858640i	$-0.328690\pi$
$857$	40.5689	−	10.8704i	1.38581	−	0.371326i	0.873227	+	0.487314i	$0.162023\pi$
$858$		0			0
$859$	−6.92820	+	4.00000i	−0.236387	+	0.136478i	−0.613515	−	0.789683i	$-0.710245\pi$
$859$	−6.92820	+	4.00000i	−0.236387	+	0.136478i	0.377128	+	0.926161i	$0.376912\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.65685	−	5.65685i	0.192562	−	0.192562i	−0.604240	−	0.796802i	$-0.706523\pi$
$863$	5.65685	−	5.65685i	0.192562	−	0.192562i	0.796802	+	0.604240i	$0.206523\pi$
$864$		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
$875$	10.6574	−	29.7728i	0.360285	−	1.00650i
$876$		0			0
$877$	20.4904	+	5.49038i	0.691911	+	0.185397i	0.587605	−	0.809148i	$-0.300071\pi$
$877$	20.4904	+	5.49038i	0.691911	+	0.185397i	0.104306	+	0.994545i	$0.466738\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			41.0122i			1.38174i	0.722981	+	0.690868i	$0.242771\pi$
$881$			41.0122i			1.38174i	−0.722981	+	0.690868i	$0.757229\pi$
$882$		0			0
$883$	−20.0000	−	20.0000i	−0.673054	−	0.673054i	0.285365	−	0.958419i	$-0.407885\pi$
$883$	−20.0000	−	20.0000i	−0.673054	−	0.673054i	−0.958419	+	0.285365i	$0.907885\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.4233	−	46.3644i	0.417134	−	1.55677i	−0.363388	−	0.931638i	$-0.618380\pi$
$887$	12.4233	−	46.3644i	0.417134	−	1.55677i	0.780522	−	0.625128i	$-0.214953\pi$
$888$		0			0
$889$	−34.6410	−	20.0000i	−1.16182	−	0.670778i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.4233	−	46.3644i	−0.415730	−	1.55153i
$894$		0			0
$895$	20.9808	−	23.6603i	0.701310	−	0.790875i
$896$		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
$905$	11.8685	−	13.3843i	0.394523	−	0.444908i
$906$		0			0
$907$	5.85641	+	21.8564i	0.194459	+	0.725730i	0.992406	+	0.123003i	$0.0392525\pi$
$907$	5.85641	+	21.8564i	0.194459	+	0.725730i	−0.797948	+	0.602727i	$0.794081\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.4949	+	14.1421i	0.811552	+	0.468550i	0.847495	−	0.530804i	$-0.178110\pi$
$911$	24.4949	+	14.1421i	0.811552	+	0.468550i	−0.0359424	+	0.999354i	$0.511443\pi$
$912$		0			0
$913$	−8.78461	+	32.7846i	−0.290728	+	1.08501i
$914$		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	$-0.823020\pi$
$919$		−	32.0000i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	23.1822	+	6.21166i	0.763052	+	0.204459i
$924$		0			0
$925$	16.6865	+	13.0981i	0.548650	+	0.430662i
$926$		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	0.237301	−	0.971436i	$-0.423737\pi$
$937$	37.0000	−	37.0000i	1.20874	−	1.20874i	0.971436	−	0.237301i	$-0.0762628\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−33.0681	+	19.0919i	−1.07799	+	0.622378i	−0.930353	−	0.366664i	$-0.880500\pi$
$941$	−33.0681	+	19.0919i	−1.07799	+	0.622378i	−0.147636	+	0.989042i	$0.547166\pi$
$942$		0			0
$943$	10.9282	−	2.92820i	0.355871	−	0.0953554i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.9096	+	8.28221i	−1.00443	+	0.269136i	−0.723299	−	0.690535i	$-0.757375\pi$
$947$	−30.9096	+	8.28221i	−1.00443	+	0.269136i	−0.281128	+	0.959670i	$0.590709\pi$
$948$		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	−0.986763	−	0.162168i	$-0.948151\pi$
$953$	−25.4558	+	25.4558i	−0.824596	+	0.824596i	0.162168	+	0.986763i	$0.448151\pi$
$954$		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
$965$	26.1357	+	39.5844i	0.841339	+	1.27427i
$966$		0			0
$967$	2.73205	+	0.732051i	0.0878568	+	0.0235412i	0.302480	−	0.953156i	$-0.402186\pi$
$967$	2.73205	+	0.732051i	0.0878568	+	0.0235412i	−0.214623	+	0.976697i	$0.568852\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	53.7401i		−	1.72460i	−0.506396	−	0.862301i	$-0.669022\pi$
$971$		−	53.7401i		−	1.72460i	0.506396	−	0.862301i	$-0.330978\pi$
$972$		0			0
$973$	32.0000	+	32.0000i	1.02587	+	1.02587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.65874	+	17.3867i	−0.149046	+	0.556249i	0.850495	+	0.525982i	$0.176302\pi$
$977$	−4.65874	+	17.3867i	−0.149046	+	0.556249i	−0.999542	+	0.0302663i	$0.990364\pi$
$978$		0			0
$979$	−3.46410	−	2.00000i	−0.110713	−	0.0639203i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.17638	−	19.3185i	−0.165101	−	0.616165i	−0.998027	−	0.0627812i	$-0.980003\pi$
$983$	−5.17638	−	19.3185i	−0.165101	−	0.616165i	0.832926	−	0.553384i	$-0.186664\pi$
$984$		0			0
$985$	26.7846	−	1.60770i	0.853429	−	0.0512254i
$986$		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
$995$	20.0764	+	17.8028i	0.636464	+	0.564386i
$996$		0			0
$997$	−4.02628	−	15.0263i	−0.127514	−	0.475887i	0.872403	−	0.488787i	$-0.162560\pi$
$997$	−4.02628	−	15.0263i	−0.127514	−	0.475887i	−0.999917	+	0.0128998i	$0.995894\pi$
$998$		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.593.2		8
3.2	odd	2	inner	1620.2.x.a.593.1		8
5.2	odd	4	inner	1620.2.x.a.917.2		8
9.2	odd	6		180.2.j.a.53.1	yes	4
9.4	even	3	inner	1620.2.x.a.53.1		8
9.5	odd	6	inner	1620.2.x.a.53.2		8
9.7	even	3		180.2.j.a.53.2	yes	4
15.2	even	4	inner	1620.2.x.a.917.1		8
36.7	odd	6		720.2.w.b.593.2		4
36.11	even	6		720.2.w.b.593.1		4
45.2	even	12		180.2.j.a.17.2	yes	4
45.7	odd	12		180.2.j.a.17.1	✓	4
45.22	odd	12	inner	1620.2.x.a.377.1		8
45.29	odd	6		900.2.j.a.593.1		4
45.32	even	12	inner	1620.2.x.a.377.2		8
45.34	even	6		900.2.j.a.593.2		4
45.38	even	12		900.2.j.a.557.1		4
45.43	odd	12		900.2.j.a.557.2		4
72.11	even	6		2880.2.w.a.2753.2		4
72.29	odd	6		2880.2.w.j.2753.2		4
72.43	odd	6		2880.2.w.a.2753.1		4
72.61	even	6		2880.2.w.j.2753.1		4
180.7	even	12		720.2.w.b.17.1		4
180.43	even	12		3600.2.w.f.1457.1		4
180.47	odd	12		720.2.w.b.17.2		4
180.79	odd	6		3600.2.w.f.593.1		4
180.83	odd	12		3600.2.w.f.1457.2		4
180.119	even	6		3600.2.w.f.593.2		4
360.187	even	12		2880.2.w.a.2177.2		4
360.227	odd	12		2880.2.w.a.2177.1		4
360.277	odd	12		2880.2.w.j.2177.2		4
360.317	even	12		2880.2.w.j.2177.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.j.a.17.1	✓	4	45.7	odd	12
180.2.j.a.17.2	yes	4	45.2	even	12
180.2.j.a.53.1	yes	4	9.2	odd	6
180.2.j.a.53.2	yes	4	9.7	even	3
720.2.w.b.17.1		4	180.7	even	12
720.2.w.b.17.2		4	180.47	odd	12
720.2.w.b.593.1		4	36.11	even	6
720.2.w.b.593.2		4	36.7	odd	6
900.2.j.a.557.1		4	45.38	even	12
900.2.j.a.557.2		4	45.43	odd	12
900.2.j.a.593.1		4	45.29	odd	6
900.2.j.a.593.2		4	45.34	even	6
1620.2.x.a.53.1		8	9.4	even	3	inner
1620.2.x.a.53.2		8	9.5	odd	6	inner
1620.2.x.a.377.1		8	45.22	odd	12	inner
1620.2.x.a.377.2		8	45.32	even	12	inner
1620.2.x.a.593.1		8	3.2	odd	2	inner
1620.2.x.a.593.2		8	1.1	even	1	trivial
1620.2.x.a.917.1		8	15.2	even	4	inner
1620.2.x.a.917.2		8	5.2	odd	4	inner
2880.2.w.a.2177.1		4	360.227	odd	12
2880.2.w.a.2177.2		4	360.187	even	12
2880.2.w.a.2753.1		4	72.43	odd	6
2880.2.w.a.2753.2		4	72.11	even	6
2880.2.w.j.2177.1		4	360.317	even	12
2880.2.w.j.2177.2		4	360.277	odd	12
2880.2.w.j.2753.1		4	72.61	even	6
2880.2.w.j.2753.2		4	72.29	odd	6
3600.2.w.f.593.1		4	180.79	odd	6
3600.2.w.f.593.2		4	180.119	even	6
3600.2.w.f.1457.1		4	180.43	even	12
3600.2.w.f.1457.2		4	180.83	odd	12

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

\(f(q)\)	\(=\)	\(q+(1.48356 - 1.67303i) q^{5} +(0.732051 + 2.73205i) q^{7} +O(q^{10})\)	\(q+(1.48356 - 1.67303i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-2.44949 - 1.41421i) q^{11} +(1.09808 - 4.09808i) q^{13} +(-1.41421 - 1.41421i) q^{17} -4.00000i q^{19} +(-7.72741 - 2.07055i) q^{23} +(-0.598076 - 4.96410i) q^{25} +(4.94975 - 8.57321i) q^{29} +(4.00000 + 6.92820i) q^{31} +(5.65685 + 2.82843i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-1.22474 + 0.707107i) q^{41} +(11.5911 - 3.10583i) q^{47} +(-0.866025 + 0.500000i) q^{49} +(7.07107 - 7.07107i) q^{53} +(-6.00000 + 2.00000i) q^{55} +(-1.41421 - 2.44949i) q^{59} +(-5.22715 - 7.91688i) q^{65} +(-10.9282 - 2.92820i) q^{67} +5.65685i q^{71} +(7.00000 + 7.00000i) q^{73} +(2.07055 - 7.72741i) q^{77} +(-3.10583 - 11.5911i) q^{83} +(-4.46410 + 0.267949i) q^{85} +1.41421 q^{89} +12.0000 q^{91} +(-6.69213 - 5.93426i) q^{95} +(1.09808 + 4.09808i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 12 q^{13} + 16 q^{25} + 32 q^{31} - 24 q^{37} - 48 q^{55} - 32 q^{67} + 56 q^{73} - 8 q^{85} + 96 q^{91} - 12 q^{97}+O(q^{100}) \) 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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