LMFDB - Embedded newform 900.2.w.c.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(109,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, degree $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.1
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99921 - 1.00158i) q^{5} -3.80992i q^{7} +O(q^{10})$	$q+(-1.99921 - 1.00158i) q^{5} -3.80992i q^{7} +(-0.0589397 - 0.181398i) q^{11} +(1.59724 + 0.518974i) q^{13} +(-2.70572 + 3.72410i) q^{17} +(-2.13682 - 1.55249i) q^{19} +(-6.04461 + 1.96401i) q^{23} +(2.99369 + 4.00473i) q^{25} +(-2.03878 + 1.48126i) q^{29} +(-3.03331 - 2.20383i) q^{31} +(-3.81593 + 7.61682i) q^{35} +(-11.2820 - 3.66574i) q^{37} +(2.22169 - 6.83765i) q^{41} +9.22619i q^{43} +(-2.67353 - 3.67980i) q^{47} -7.51545 q^{49} +(-5.54285 - 7.62908i) q^{53} +(-0.0638510 + 0.421685i) q^{55} +(2.20656 - 6.79109i) q^{59} +(2.94497 + 9.06368i) q^{61} +(-2.67342 - 2.63729i) q^{65} +(3.55709 - 4.89591i) q^{67} +(10.7586 - 7.81655i) q^{71} +(-4.95645 + 1.61045i) q^{73} +(-0.691110 + 0.224555i) q^{77} +(-2.51740 + 1.82900i) q^{79} +(2.74988 - 3.78488i) q^{83} +(9.13928 - 4.73528i) q^{85} +(4.30840 + 13.2599i) q^{89} +(1.97725 - 6.08534i) q^{91} +(2.71702 + 5.24395i) q^{95} +(-3.93527 - 5.41643i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5}+O(q^{10}) $ 24 * q + 2 * q^5	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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
$5$	−1.99921	−	1.00158i	−0.894074	−	0.447919i
$5$	−1.99921	−	1.00158i	−0.894074	−	0.447919i
$6$		0			0
$7$		−	3.80992i		−	1.44001i	−0.693968	−	0.720006i	$-0.744139\pi$
$7$		−	3.80992i		−	1.44001i	0.693968	−	0.720006i	$-0.255861\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.0589397	−	0.181398i	−0.0177710	−	0.0546935i	0.941778	−	0.336236i	$-0.109154\pi$
$11$	−0.0589397	−	0.181398i	−0.0177710	−	0.0546935i	−0.959549	+	0.281542i	$0.909154\pi$
$12$		0			0
$13$	1.59724	+	0.518974i	0.442994	+	0.143937i	0.522016	−	0.852935i	$-0.325180\pi$
$13$	1.59724	+	0.518974i	0.442994	+	0.143937i	−0.0790227	+	0.996873i	$0.525180\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.70572	+	3.72410i	−0.656233	+	0.903227i	−0.999349	−	0.0360656i	$-0.988517\pi$
$17$	−2.70572	+	3.72410i	−0.656233	+	0.903227i	0.343116	+	0.939293i	$0.388517\pi$
$18$		0			0
$19$	−2.13682	−	1.55249i	−0.490221	−	0.356166i	0.315049	−	0.949076i	$-0.397979\pi$
$19$	−2.13682	−	1.55249i	−0.490221	−	0.356166i	−0.805269	+	0.592909i	$0.797979\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.04461	+	1.96401i	−1.26039	+	0.409525i	−0.861632	−	0.507533i	$-0.830558\pi$
$23$	−6.04461	+	1.96401i	−1.26039	+	0.409525i	−0.398755	+	0.917057i	$0.630558\pi$
$24$		0			0
$25$	2.99369	+	4.00473i	0.598737	+	0.800946i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.03878	+	1.48126i	−0.378593	+	0.275064i	−0.760765	−	0.649027i	$-0.775176\pi$
$29$	−2.03878	+	1.48126i	−0.378593	+	0.275064i	0.382172	+	0.924091i	$0.375176\pi$
$30$		0			0
$31$	−3.03331	−	2.20383i	−0.544798	−	0.395819i	0.281066	−	0.959688i	$-0.409312\pi$
$31$	−3.03331	−	2.20383i	−0.544798	−	0.395819i	−0.825864	+	0.563870i	$0.809312\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.81593	+	7.61682i	−0.645009	+	1.28748i
$36$		0			0
$37$	−11.2820	−	3.66574i	−1.85474	−	0.602643i	−0.995906	−	0.0903980i	$-0.971186\pi$
$37$	−11.2820	−	3.66574i	−1.85474	−	0.602643i	−0.858839	−	0.512245i	$-0.828814\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.22169	−	6.83765i	0.346969	−	1.06786i	−0.613552	−	0.789655i	$-0.710260\pi$
$41$	2.22169	−	6.83765i	0.346969	−	1.06786i	0.960521	−	0.278207i	$-0.0897402\pi$
$42$		0			0
$43$			9.22619i			1.40698i	0.710705	+	0.703491i	$0.248376\pi$
$43$			9.22619i			1.40698i	−0.710705	+	0.703491i	$0.751624\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.67353	−	3.67980i	−0.389975	−	0.536754i	0.568218	−	0.822878i	$-0.307633\pi$
$47$	−2.67353	−	3.67980i	−0.389975	−	0.536754i	−0.958193	+	0.286124i	$0.907633\pi$
$48$		0			0
$49$	−7.51545			−1.07364
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.54285	−	7.62908i	−0.761369	−	1.04793i	−0.997099	−	0.0761162i	$-0.975748\pi$
$53$	−5.54285	−	7.62908i	−0.761369	−	1.04793i	0.235730	−	0.971819i	$-0.424252\pi$
$54$		0			0
$55$	−0.0638510	+	0.421685i	−0.00860967	+	0.0568600i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.20656	−	6.79109i	0.287269	−	0.884124i	−0.698440	−	0.715669i	$-0.746122\pi$
$59$	2.20656	−	6.79109i	0.287269	−	0.884124i	0.985709	−	0.168456i	$-0.0538780\pi$
$60$		0			0
$61$	2.94497	+	9.06368i	0.377064	+	1.16049i	0.942075	+	0.335402i	$0.108872\pi$
$61$	2.94497	+	9.06368i	0.377064	+	1.16049i	−0.565011	+	0.825084i	$0.691128\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.67342	−	2.63729i	−0.331597	−	0.327116i
$66$		0			0
$67$	3.55709	−	4.89591i	0.434567	−	0.598131i	−0.534427	−	0.845215i	$-0.679472\pi$
$67$	3.55709	−	4.89591i	0.434567	−	0.598131i	0.968994	+	0.247084i	$0.0794724\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.7586	−	7.81655i	1.27681	−	0.927654i	0.277355	−	0.960768i	$-0.410542\pi$
$71$	10.7586	−	7.81655i	1.27681	−	0.927654i	0.999452	+	0.0331133i	$0.0105422\pi$
$72$		0			0
$73$	−4.95645	+	1.61045i	−0.580109	+	0.188489i	−0.584349	−	0.811502i	$-0.698650\pi$
$73$	−4.95645	+	1.61045i	−0.580109	+	0.188489i	0.00424038	+	0.999991i	$0.498650\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.691110	+	0.224555i	−0.0787593	+	0.0255904i
$78$		0			0
$79$	−2.51740	+	1.82900i	−0.283230	+	0.205779i	−0.720325	−	0.693637i	$-0.756007\pi$
$79$	−2.51740	+	1.82900i	−0.283230	+	0.205779i	0.437095	+	0.899415i	$0.356007\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.74988	−	3.78488i	0.301838	−	0.415445i	−0.630976	−	0.775802i	$-0.717345\pi$
$83$	2.74988	−	3.78488i	0.301838	−	0.415445i	0.932814	+	0.360358i	$0.117345\pi$
$84$		0			0
$85$	9.13928	−	4.73528i	0.991294	−	0.513613i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.30840	+	13.2599i	0.456690	+	1.40555i	0.869140	+	0.494566i	$0.164673\pi$
$89$	4.30840	+	13.2599i	0.456690	+	1.40555i	−0.412451	+	0.910980i	$0.635327\pi$
$90$		0			0
$91$	1.97725	−	6.08534i	0.207272	−	0.637917i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.71702	+	5.24395i	0.278760	+	0.538018i
$96$		0			0
$97$	−3.93527	−	5.41643i	−0.399566	−	0.549955i	0.561069	−	0.827769i	$-0.310390\pi$
$97$	−3.93527	−	5.41643i	−0.399566	−	0.549955i	−0.960635	+	0.277814i	$0.910390\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−10.5147			−1.04625			−0.523127	−	0.852255i	$-0.675235\pi$
$101$	−10.5147			−1.04625			−0.523127	+	0.852255i	$0.675235\pi$
$102$		0			0
$103$	−7.62055	−	10.4888i	−0.750875	−	1.03349i	−0.997919	−	0.0644861i	$-0.979459\pi$
$103$	−7.62055	−	10.4888i	−0.750875	−	1.03349i	0.247044	−	0.969004i	$-0.420541\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			9.64606i			0.932520i	0.884648	+	0.466260i	$0.154399\pi$
$107$			9.64606i			0.932520i	−0.884648	+	0.466260i	$0.845601\pi$
$108$		0			0
$109$	−6.31798	+	19.4447i	−0.605153	+	1.86247i	−0.109414	+	0.993996i	$0.534898\pi$
$109$	−6.31798	+	19.4447i	−0.605153	+	1.86247i	−0.495738	+	0.868472i	$0.665102\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.84623	−	1.24972i	−0.361823	−	0.117564i	0.122463	−	0.992473i	$-0.460921\pi$
$113$	−3.84623	−	1.24972i	−0.361823	−	0.117564i	−0.484286	+	0.874910i	$0.660921\pi$
$114$		0			0
$115$	14.0515	+	2.12767i	1.31031	+	0.198406i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.1885	+	10.3086i	1.30066	+	0.944984i
$120$		0			0
$121$	8.86976	−	6.44425i	0.806341	−	0.585841i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.97396	−	11.0047i	−0.176556	−	0.984291i
$126$		0			0
$127$	15.9338	−	5.17719i	1.41389	−	0.459401i	0.500236	−	0.865889i	$-0.333247\pi$
$127$	15.9338	−	5.17719i	1.41389	−	0.459401i	0.913656	+	0.406488i	$0.133247\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.67583	−	1.94410i	−0.233788	−	0.169857i	0.464723	−	0.885456i	$-0.346154\pi$
$131$	−2.67583	−	1.94410i	−0.233788	−	0.169857i	−0.698511	+	0.715599i	$0.746154\pi$
$132$		0			0
$133$	−5.91486	+	8.14111i	−0.512884	+	0.705924i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.99642	+	0.648677i	0.170566	+	0.0554202i	0.393055	−	0.919515i	$-0.371418\pi$
$137$	1.99642	+	0.648677i	0.170566	+	0.0554202i	−0.222489	+	0.974935i	$0.571418\pi$
$138$		0			0
$139$	4.10525	+	12.6347i	0.348203	+	1.07166i	0.959847	+	0.280525i	$0.0905087\pi$
$139$	4.10525	+	12.6347i	0.348203	+	1.07166i	−0.611643	+	0.791134i	$0.709491\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	0.320323i		−	0.0267868i
$144$		0			0
$145$	5.55956	−	0.919357i	0.461696	−	0.0763484i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.79913			−0.229313			−0.114657	−	0.993405i	$-0.536577\pi$
$149$	−2.79913			−0.229313			−0.114657	+	0.993405i	$0.536577\pi$
$150$		0			0
$151$	−6.71330			−0.546320			−0.273160	−	0.961969i	$-0.588069\pi$
$151$	−6.71330			−0.546320			−0.273160	+	0.961969i	$0.588069\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.85692	+	7.44401i	0.309795	+	0.597917i
$156$		0			0
$157$		−	13.9495i		−	1.11329i	−0.830750	−	0.556646i	$-0.812088\pi$
$157$		−	13.9495i		−	1.11329i	0.830750	−	0.556646i	$-0.187912\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.48272	+	23.0294i	0.589721	+	1.81497i
$162$		0			0
$163$	−8.44065	−	2.74253i	−0.661123	−	0.214812i	−0.0408107	−	0.999167i	$-0.512994\pi$
$163$	−8.44065	−	2.74253i	−0.661123	−	0.214812i	−0.620312	+	0.784355i	$0.712994\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.4563	−	19.8973i	1.11866	−	1.53970i	0.310655	−	0.950523i	$-0.399452\pi$
$167$	14.4563	−	19.8973i	1.11866	−	1.53970i	0.808003	−	0.589178i	$-0.200548\pi$
$168$		0			0
$169$	−8.23539	−	5.98336i	−0.633492	−	0.460259i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.1062	+	5.23322i	−1.22453	+	0.397874i	−0.848730	−	0.528826i	$-0.822632\pi$
$173$	−16.1062	+	5.23322i	−1.22453	+	0.397874i	−0.375801	+	0.926701i	$0.622632\pi$
$174$		0			0
$175$	15.2577	−	11.4057i	1.15337	−	0.862189i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.9328	+	8.66966i	−0.891897	+	0.648001i	−0.936372	−	0.351010i	$-0.885838\pi$
$179$	−11.9328	+	8.66966i	−0.891897	+	0.648001i	0.0444751	+	0.999010i	$0.485838\pi$
$180$		0			0
$181$	8.89013	+	6.45906i	0.660798	+	0.480098i	0.866932	−	0.498426i	$-0.166088\pi$
$181$	8.89013	+	6.45906i	0.660798	+	0.480098i	−0.206134	+	0.978524i	$0.566088\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.8835	+	18.6283i	1.38834	+	1.36958i
$186$		0			0
$187$	0.835018	+	0.271314i	0.0610625	+	0.0198404i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.42739	−	22.8591i	0.537427	−	1.65403i	−0.200919	−	0.979608i	$-0.564393\pi$
$191$	7.42739	−	22.8591i	0.537427	−	1.65403i	0.738346	−	0.674422i	$-0.235607\pi$
$192$		0			0
$193$		−	7.50843i		−	0.540469i	−0.962795	−	0.270234i	$-0.912899\pi$
$193$		−	7.50843i		−	0.540469i	0.962795	−	0.270234i	$-0.0871012\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.37799	−	10.1549i	−0.525660	−	0.723509i	0.460801	−	0.887503i	$-0.347562\pi$
$197$	−7.37799	−	10.1549i	−0.525660	−	0.723509i	−0.986461	+	0.163995i	$0.947562\pi$
$198$		0			0
$199$	19.7618			1.40088			0.700440	−	0.713711i	$-0.252987\pi$
$199$	19.7618			1.40088			0.700440	+	0.713711i	$0.252987\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.64349	+	7.76760i	0.396095	+	0.545178i
$204$		0			0
$205$	−11.2901	+	11.4447i	−0.788532	+	0.799333i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.155675	+	0.479118i	−0.0107683	+	0.0331413i
$210$		0			0
$211$	−3.47579	−	10.6974i	−0.239283	−	0.736437i	−0.996524	−	0.0833021i	$-0.973453\pi$
$211$	−3.47579	−	10.6974i	−0.239283	−	0.736437i	0.757241	−	0.653135i	$-0.226547\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.24075	−	18.4451i	0.630214	−	1.25795i
$216$		0			0
$217$	−8.39639	+	11.5566i	−0.569984	+	0.784516i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.25438	+	4.54407i	−0.420715	+	0.305668i
$222$		0			0
$223$	−6.91605	+	2.24716i	−0.463133	+	0.150481i	−0.531284	−	0.847194i	$-0.678290\pi$
$223$	−6.91605	+	2.24716i	−0.463133	+	0.150481i	0.0681508	+	0.997675i	$0.478290\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.00583	−	2.92617i	0.597738	−	0.194217i	0.00550660	−	0.999985i	$-0.498247\pi$
$227$	9.00583	−	2.92617i	0.597738	−	0.194217i	0.592231	+	0.805768i	$0.298247\pi$
$228$		0			0
$229$	17.1755	−	12.4787i	1.13499	−	0.824617i	0.148575	−	0.988901i	$-0.452531\pi$
$229$	17.1755	−	12.4787i	1.13499	−	0.824617i	0.986413	+	0.164284i	$0.0525315\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.16700	−	5.73538i	0.272989	−	0.375737i	−0.650407	−	0.759586i	$-0.725402\pi$
$233$	4.16700	−	5.73538i	0.272989	−	0.375737i	0.923396	+	0.383849i	$0.125402\pi$
$234$		0			0
$235$	1.65935	+	10.0344i	0.108244	+	0.654575i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.18395	−	19.0323i	−0.400007	−	1.23109i	−0.924993	−	0.379983i	$-0.875930\pi$
$239$	−6.18395	−	19.0323i	−0.400007	−	1.23109i	0.524987	−	0.851110i	$-0.324070\pi$
$240$		0			0
$241$	6.43498	−	19.8048i	0.414513	−	1.27574i	−0.498172	−	0.867078i	$-0.665995\pi$
$241$	6.43498	−	19.8048i	0.414513	−	1.27574i	0.912686	−	0.408662i	$-0.134005\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	15.0250	+	7.52731i	0.959910	+	0.480902i
$246$		0			0
$247$	−2.60731	−	3.58865i	−0.165899	−	0.228340i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	29.7741			1.87932			0.939662	−	0.342104i	$-0.111139\pi$
$251$	29.7741			1.87932			0.939662	+	0.342104i	$0.111139\pi$
$252$		0			0
$253$	0.712534	+	0.980719i	0.0447966	+	0.0616573i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			21.2853i			1.32774i	0.747849	+	0.663869i	$0.231087\pi$
$257$			21.2853i			1.32774i	−0.747849	+	0.663869i	$0.768913\pi$
$258$		0			0
$259$	−13.9661	+	42.9834i	−0.867814	+	2.67086i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.7951	+	6.75674i	1.28228	+	0.416638i	0.869383	−	0.494139i	$-0.164517\pi$
$263$	20.7951	+	6.75674i	1.28228	+	0.416638i	0.412898	+	0.910777i	$0.364517\pi$
$264$		0			0
$265$	3.44021	+	20.8037i	0.211331	+	1.27796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.69018	+	2.68108i	0.224995	+	0.163468i	0.694572	−	0.719423i	$-0.255594\pi$
$269$	3.69018	+	2.68108i	0.224995	+	0.163468i	−0.469578	+	0.882891i	$0.655594\pi$
$270$		0			0
$271$	10.4519	−	7.59377i	0.634909	−	0.461288i	−0.223188	−	0.974775i	$-0.571646\pi$
$271$	10.4519	−	7.59377i	0.634909	−	0.461288i	0.858097	+	0.513487i	$0.171646\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.550002	−	0.779085i	0.0331663	−	0.0469806i
$276$		0			0
$277$	−8.40278	+	2.73023i	−0.504874	+	0.164044i	−0.550370	−	0.834921i	$-0.685513\pi$
$277$	−8.40278	+	2.73023i	−0.504874	+	0.164044i	0.0454957	+	0.998965i	$0.485513\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0247151	+	0.0179566i	0.00147438	+	0.00107120i	0.588522	−	0.808481i	$-0.299710\pi$
$281$	0.0247151	+	0.0179566i	0.00147438	+	0.00107120i	−0.587048	+	0.809552i	$0.699710\pi$
$282$		0			0
$283$	2.82560	−	3.88910i	0.167964	−	0.231183i	−0.716735	−	0.697346i	$-0.754364\pi$
$283$	2.82560	−	3.88910i	0.167964	−	0.231183i	0.884699	+	0.466163i	$0.154364\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−26.0509	−	8.46444i	−1.53773	−	0.499640i
$288$		0			0
$289$	−1.29473	−	3.98478i	−0.0761607	−	0.234399i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			14.9705i			0.874587i	0.899319	+	0.437294i	$0.144063\pi$
$293$			14.9705i			0.874587i	−0.899319	+	0.437294i	$0.855937\pi$
$294$		0			0
$295$	−11.2132	+	11.3668i	−0.652856	+	0.661799i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.6739			−0.617290
$300$		0			0
$301$	35.1510			2.02607
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.19037	−	21.0698i	0.182680	−	1.20645i
$306$		0			0
$307$		−	4.47622i		−	0.255472i	−0.991808	−	0.127736i	$-0.959229\pi$
$307$		−	4.47622i		−	0.255472i	0.991808	−	0.127736i	$-0.0407710\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.0915043	−	0.281621i	−0.00518873	−	0.0159693i	0.948429	−	0.316991i	$-0.102672\pi$
$311$	−0.0915043	−	0.281621i	−0.00518873	−	0.0159693i	−0.953617	+	0.301021i	$0.902672\pi$
$312$		0			0
$313$	−20.1214	−	6.53785i	−1.13733	−	0.369541i	−0.320973	−	0.947088i	$-0.604010\pi$
$313$	−20.1214	−	6.53785i	−1.13733	−	0.369541i	−0.816357	+	0.577547i	$0.804010\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.2334	−	20.9670i	0.855594	−	1.17762i	−0.127008	−	0.991902i	$-0.540537\pi$
$317$	15.2334	−	20.9670i	0.855594	−	1.17762i	0.982602	−	0.185723i	$-0.0594626\pi$
$318$		0			0
$319$	0.388863	+	0.282526i	0.0217722	+	0.0158184i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	11.5633	−	3.75714i	0.643398	−	0.209053i
$324$		0			0
$325$	2.70328	+	7.95014i	0.149951	+	0.440995i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.0197	+	10.1859i	−0.772932	+	0.561568i
$330$		0			0
$331$	2.48400	+	1.80473i	0.136533	+	0.0991969i	0.653955	−	0.756533i	$-0.273108\pi$
$331$	2.48400	+	1.80473i	0.136533	+	0.0991969i	−0.517423	+	0.855730i	$0.673108\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.0150	+	6.22526i	−0.656450	+	0.340122i
$336$		0			0
$337$	−26.8694	−	8.73038i	−1.46367	−	0.475574i	−0.534479	−	0.845182i	$-0.679492\pi$
$337$	−26.8694	−	8.73038i	−1.46367	−	0.475574i	−0.929188	+	0.369607i	$0.879492\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.220987	+	0.680128i	−0.0119671	+	0.0368310i
$342$		0			0
$343$			1.96383i			0.106037i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.9869	−	24.7568i	−0.965586	−	1.32901i	−0.944245	−	0.329242i	$-0.893207\pi$
$347$	−17.9869	−	24.7568i	−0.965586	−	1.32901i	−0.0213401	−	0.999772i	$-0.506793\pi$
$348$		0			0
$349$	16.1178			0.862764			0.431382	−	0.902169i	$-0.358026\pi$
$349$	16.1178			0.862764			0.431382	+	0.902169i	$0.358026\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.253341	−	0.348695i	−0.0134840	−	0.0185591i	0.802222	−	0.597026i	$-0.203651\pi$
$353$	−0.253341	−	0.348695i	−0.0134840	−	0.0185591i	−0.815706	+	0.578467i	$0.803651\pi$
$354$		0			0
$355$	−29.3375	+	4.85140i	−1.55707	+	0.257486i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.70871	−	17.5696i	0.301294	−	0.927288i	−0.679740	−	0.733453i	$-0.737907\pi$
$359$	5.70871	−	17.5696i	0.301294	−	0.927288i	0.981034	−	0.193835i	$-0.0620925\pi$
$360$		0			0
$361$	−3.71555	−	11.4353i	−0.195555	−	0.601857i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.5220	+	1.74465i	0.603088	+	0.0913189i
$366$		0			0
$367$	−6.03990	+	8.31320i	−0.315280	+	0.433946i	−0.937019	−	0.349279i	$-0.886427\pi$
$367$	−6.03990	+	8.31320i	−0.315280	+	0.433946i	0.621739	+	0.783225i	$0.286427\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−29.0662	+	21.1178i	−1.50904	+	1.09638i
$372$		0			0
$373$	−13.9266	+	4.52503i	−0.721092	+	0.234297i	−0.646497	−	0.762917i	$-0.723767\pi$
$373$	−13.9266	+	4.52503i	−0.721092	+	0.234297i	−0.0745954	+	0.997214i	$0.523767\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.02516	+	1.30785i	−0.207306	+	0.0673579i
$378$		0			0
$379$	−8.66061	+	6.29230i	−0.444866	+	0.323214i	−0.787565	−	0.616231i	$-0.788659\pi$
$379$	−8.66061	+	6.29230i	−0.444866	+	0.323214i	0.342700	+	0.939445i	$0.388659\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.4690	+	21.2912i	−0.790428	+	1.08793i	0.203627	+	0.979049i	$0.434727\pi$
$383$	−15.4690	+	21.2912i	−0.790428	+	1.08793i	−0.994055	+	0.108882i	$0.965273\pi$
$384$		0			0
$385$	1.60658	+	0.243267i	0.0818791	+	0.0123980i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.0901650	+	0.277499i	0.00457155	+	0.0140698i	0.953316	−	0.301974i	$-0.0976455\pi$
$389$	0.0901650	+	0.277499i	0.00457155	+	0.0140698i	−0.948745	+	0.316043i	$0.897645\pi$
$390$		0			0
$391$	9.04082	−	27.8248i	0.457214	−	1.40716i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.86471	−	1.13518i	0.345401	−	0.0571173i
$396$		0			0
$397$	1.18504	+	1.63106i	0.0594753	+	0.0818608i	0.837719	−	0.546102i	$-0.183889\pi$
$397$	1.18504	+	1.63106i	0.0594753	+	0.0818608i	−0.778243	+	0.627963i	$0.783889\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.88760			−0.493763			−0.246882	−	0.969046i	$-0.579406\pi$
$401$	−9.88760			−0.493763			−0.246882	+	0.969046i	$0.579406\pi$
$402$		0			0
$403$	−3.70118	−	5.09424i	−0.184369	−	0.253762i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			2.26258i			0.112152i
$408$		0			0
$409$	11.6440	−	35.8367i	0.575761	−	1.77201i	−0.0578124	−	0.998327i	$-0.518413\pi$
$409$	11.6440	−	35.8367i	0.575761	−	1.77201i	0.633573	−	0.773683i	$-0.281587\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−25.8735	−	8.40680i	−1.27315	−	0.413672i
$414$		0			0
$415$	−9.28843	+	4.81256i	−0.455951	+	0.236239i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.6641	+	9.20102i	0.618682	+	0.449499i	0.852461	−	0.522791i	$-0.175109\pi$
$419$	12.6641	+	9.20102i	0.618682	+	0.449499i	−0.233779	+	0.972290i	$0.575109\pi$
$420$		0			0
$421$	−11.7531	+	8.53916i	−0.572813	+	0.416173i	−0.836126	−	0.548537i	$-0.815185\pi$
$421$	−11.7531	+	8.53916i	−0.572813	+	0.416173i	0.263313	+	0.964711i	$0.415185\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−23.0141	+	0.313121i	−1.11635	+	0.0151886i
$426$		0			0
$427$	34.5318	−	11.2201i	1.67111	−	0.542978i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.2150	−	7.42161i	−0.492038	−	0.357486i	0.313930	−	0.949446i	$-0.398354\pi$
$431$	−10.2150	−	7.42161i	−0.492038	−	0.357486i	−0.805967	+	0.591960i	$0.798354\pi$
$432$		0			0
$433$	−2.05145	+	2.82358i	−0.0985864	+	0.135693i	−0.855460	−	0.517868i	$-0.826726\pi$
$433$	−2.05145	+	2.82358i	−0.0985864	+	0.135693i	0.756874	+	0.653561i	$0.226726\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.9654	+	5.18746i	0.763727	+	0.248150i
$438$		0			0
$439$	6.04528	+	18.6055i	0.288526	+	0.887991i	0.985320	+	0.170719i	$0.0546092\pi$
$439$	6.04528	+	18.6055i	0.288526	+	0.887991i	−0.696794	+	0.717271i	$0.745391\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			2.77485i			0.131837i	0.997825	+	0.0659185i	$0.0209977\pi$
$443$			2.77485i			0.131837i	−0.997825	+	0.0659185i	$0.979002\pi$
$444$		0			0
$445$	4.66741	−	30.8245i	0.221257	−	1.46122i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−38.4261			−1.81344			−0.906721	−	0.421732i	$-0.861422\pi$
$449$	−38.4261			−1.81344			−0.906721	+	0.421732i	$0.861422\pi$
$450$		0			0
$451$	−1.37128			−0.0645710
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−10.0479	+	10.1855i	−0.471051	+	0.477504i
$456$		0			0
$457$			36.0296i			1.68539i	0.538389	+	0.842696i	$0.319033\pi$
$457$			36.0296i			1.68539i	−0.538389	+	0.842696i	$0.680967\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.265011	−	0.815619i	−0.0123428	−	0.0379871i	0.944695	−	0.327949i	$-0.106357\pi$
$461$	−0.265011	−	0.815619i	−0.0123428	−	0.0379871i	−0.957038	+	0.289962i	$0.906357\pi$
$462$		0			0
$463$	9.89742	+	3.21587i	0.459972	+	0.149454i	0.529832	−	0.848103i	$-0.322255\pi$
$463$	9.89742	+	3.21587i	0.459972	+	0.149454i	−0.0698596	+	0.997557i	$0.522255\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.0910	+	16.6419i	−0.559506	+	0.770094i	−0.991264	−	0.131895i	$-0.957894\pi$
$467$	−12.0910	+	16.6419i	−0.559506	+	0.770094i	0.431757	+	0.901990i	$0.357894\pi$
$468$		0			0
$469$	−18.6530	−	13.5522i	−0.861316	−	0.625782i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.67361	−	0.543789i	0.0769527	−	0.0250034i
$474$		0			0
$475$	−0.179663	−	13.2051i	−0.00824351	−	0.605890i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−25.8384	+	18.7727i	−1.18059	+	0.857747i	−0.992238	−	0.124355i	$-0.960314\pi$
$479$	−25.8384	+	18.7727i	−1.18059	+	0.857747i	−0.188350	+	0.982102i	$0.560314\pi$
$480$		0			0
$481$	−16.1176	−	11.7101i	−0.734898	−	0.533934i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.44245	+	14.7701i	0.110906	+	0.670674i
$486$		0			0
$487$	−14.9140	−	4.84587i	−0.675820	−	0.219587i	−0.0490554	−	0.998796i	$-0.515621\pi$
$487$	−14.9140	−	4.84587i	−0.675820	−	0.219587i	−0.626764	+	0.779209i	$0.715621\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.09354	+	15.6763i	−0.229868	+	0.707462i	0.767892	+	0.640579i	$0.221306\pi$
$491$	−5.09354	+	15.6763i	−0.229868	+	0.707462i	−0.997761	+	0.0668834i	$0.978694\pi$
$492$		0			0
$493$		−	11.6005i		−	0.522461i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−29.7804	−	40.9892i	−1.33583	−	1.83862i
$498$		0			0
$499$	−12.4339			−0.556618			−0.278309	−	0.960492i	$-0.589774\pi$
$499$	−12.4339			−0.556618			−0.278309	+	0.960492i	$0.589774\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.54703	+	3.50569i	0.113567	+	0.156311i	0.862016	−	0.506881i	$-0.169201\pi$
$503$	2.54703	+	3.50569i	0.113567	+	0.156311i	−0.748450	+	0.663191i	$0.769201\pi$
$504$		0			0
$505$	21.0211	+	10.5313i	0.935428	+	0.468637i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.32995	−	13.3262i	0.191922	−	0.590674i	−0.808077	−	0.589077i	$-0.799492\pi$
$509$	4.32995	−	13.3262i	0.191922	−	0.590674i	0.999999	−	0.00159734i	$-0.000508450\pi$
$510$		0			0
$511$	6.13568	+	18.8837i	0.271426	+	0.835364i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.72975	+	28.6019i	0.208418	+	1.26035i
$516$		0			0
$517$	−0.509930	+	0.701859i	−0.0224267	+	0.0308677i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.56002	−	1.13342i	0.0683458	−	0.0496561i	−0.553088	−	0.833123i	$-0.686551\pi$
$521$	1.56002	−	1.13342i	0.0683458	−	0.0496561i	0.621434	+	0.783467i	$0.286551\pi$
$522$		0			0
$523$	1.86306	−	0.605344i	0.0814659	−	0.0264699i	−0.268001	−	0.963419i	$-0.586363\pi$
$523$	1.86306	−	0.605344i	0.0814659	−	0.0264699i	0.349466	+	0.936949i	$0.386363\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.4145	−	5.33341i	0.715029	−	0.232327i
$528$		0			0
$529$	14.0725	−	10.2243i	0.611849	−	0.444534i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.09712	−	9.76835i	0.307410	−	0.423114i
$534$		0			0
$535$	9.66128	−	19.2845i	0.417693	−	0.833742i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.442958	+	1.36329i	0.0190796	+	0.0587209i
$540$		0			0
$541$	−10.6961	+	32.9191i	−0.459860	+	1.41530i	0.405473	+	0.914107i	$0.367107\pi$
$541$	−10.6961	+	32.9191i	−0.459860	+	1.41530i	−0.865333	+	0.501197i	$0.832893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	32.1064	−	32.5462i	1.37529	−	1.39413i
$546$		0			0
$547$	9.37482	+	12.9033i	0.400838	+	0.551706i	0.960954	−	0.276708i	$-0.0892434\pi$
$547$	9.37482	+	12.9033i	0.400838	+	0.551706i	−0.560116	+	0.828414i	$0.689243\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.65617			0.283562
$552$		0			0
$553$	6.96834	+	9.59110i	0.296324	+	0.407855i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			43.0343i			1.82342i	0.410831	+	0.911711i	$0.365239\pi$
$557$			43.0343i			1.82342i	−0.410831	+	0.911711i	$0.634761\pi$
$558$		0			0
$559$	−4.78815	+	14.7364i	−0.202517	+	0.623284i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.9331	−	5.82682i	−0.755791	−	0.245571i	−0.0943197	−	0.995542i	$-0.530068\pi$
$563$	−17.9331	−	5.82682i	−0.755791	−	0.245571i	−0.661471	+	0.749971i	$0.730068\pi$
$564$		0			0
$565$	6.43774	+	6.35075i	0.270838	+	0.267178i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	19.7119	+	14.3215i	0.826364	+	0.600389i	0.918528	−	0.395355i	$-0.129379\pi$
$569$	19.7119	+	14.3215i	0.826364	+	0.600389i	−0.0921644	+	0.995744i	$0.529379\pi$
$570$		0			0
$571$	−12.4096	+	9.01612i	−0.519327	+	0.377313i	−0.816350	−	0.577557i	$-0.804006\pi$
$571$	−12.4096	+	9.01612i	−0.519327	+	0.377313i	0.297023	+	0.954870i	$0.404006\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−25.9610	−	18.3274i	−1.08265	−	0.764304i
$576$		0			0
$577$	13.6382	−	4.43133i	0.567767	−	0.184479i	−0.0110462	−	0.999939i	$-0.503516\pi$
$577$	13.6382	−	4.43133i	0.567767	−	0.184479i	0.578813	+	0.815460i	$0.303516\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−14.4201	−	10.4768i	−0.598245	−	0.434651i
$582$		0			0
$583$	−1.05720	+	1.45512i	−0.0437849	+	0.0602648i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1788	−	3.30729i	−0.420123	−	0.136506i	0.0913234	−	0.995821i	$-0.470890\pi$
$587$	−10.1788	−	3.30729i	−0.420123	−	0.136506i	−0.511447	+	0.859315i	$0.670890\pi$
$588$		0			0
$589$	3.06021	+	9.41837i	0.126094	+	0.388077i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	23.5756i		−	0.968135i	−0.875031	−	0.484067i	$-0.839159\pi$
$593$		−	23.5756i		−	0.968135i	0.875031	−	0.484067i	$-0.160841\pi$
$594$		0			0
$595$	−18.0410	−	34.8199i	−0.739609	−	1.42748i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.8055			0.564078			0.282039	−	0.959403i	$-0.408989\pi$
$599$	13.8055			0.564078			0.282039	+	0.959403i	$0.408989\pi$
$600$		0			0
$601$	9.61536			0.392219			0.196109	−	0.980582i	$-0.437169\pi$
$601$	9.61536			0.392219			0.196109	+	0.980582i	$0.437169\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.1869	+	3.99967i	−0.983338	+	0.162610i
$606$		0			0
$607$		−	23.7884i		−	0.965539i	−0.875747	−	0.482770i	$-0.839631\pi$
$607$		−	23.7884i		−	0.965539i	0.875747	−	0.482770i	$-0.160369\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.36054	−	7.26500i	−0.0954973	−	0.293911i
$612$		0			0
$613$	−15.2850	−	4.96640i	−0.617356	−	0.200591i	−0.0163900	−	0.999866i	$-0.505217\pi$
$613$	−15.2850	−	4.96640i	−0.617356	−	0.200591i	−0.600966	+	0.799275i	$0.705217\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.49341	+	7.56104i	−0.221157	+	0.304396i	−0.905150	−	0.425092i	$-0.860242\pi$
$617$	−5.49341	+	7.56104i	−0.221157	+	0.304396i	0.683994	+	0.729488i	$0.260242\pi$
$618$		0			0
$619$	−14.9480	−	10.8604i	−0.600813	−	0.436516i	0.245354	−	0.969433i	$-0.421096\pi$
$619$	−14.9480	−	10.8604i	−0.600813	−	0.436516i	−0.846167	+	0.532917i	$0.821096\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	50.5191	−	16.4146i	2.02400	−	0.657639i
$624$		0			0
$625$	−7.07570	+	23.9778i	−0.283028	+	0.959112i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	44.1774	−	32.0968i	1.76147	−	1.27978i
$630$		0			0
$631$	−31.2030	−	22.6703i	−1.24217	−	0.902491i	−0.244431	−	0.969667i	$-0.578601\pi$
$631$	−31.2030	−	22.6703i	−1.24217	−	0.902491i	−0.997741	+	0.0671762i	$0.978601\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−37.0403	−	5.60860i	−1.46990	−	0.222570i
$636$		0			0
$637$	−12.0040	−	3.90032i	−0.475614	−	0.154536i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.96965	−	12.2173i	0.156792	−	0.482556i	−0.841546	−	0.540185i	$-0.818354\pi$
$641$	3.96965	−	12.2173i	0.156792	−	0.482556i	0.998338	+	0.0576293i	$0.0183541\pi$
$642$		0			0
$643$		−	20.1030i		−	0.792784i	−0.918081	−	0.396392i	$-0.870262\pi$
$643$		−	20.1030i		−	0.792784i	0.918081	−	0.396392i	$-0.129738\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.0350	+	31.7050i	0.905600	+	1.24645i	0.968647	+	0.248441i	$0.0799183\pi$
$647$	23.0350	+	31.7050i	0.905600	+	1.24645i	−0.0630466	+	0.998011i	$0.520082\pi$
$648$		0			0
$649$	−1.36194			−0.0534609
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.2762	−	21.0259i	−0.597804	−	0.822806i	0.397701	−	0.917515i	$-0.369808\pi$
$653$	−15.2762	−	21.0259i	−0.597804	−	0.822806i	−0.995505	+	0.0947087i	$0.969808\pi$
$654$		0			0
$655$	3.40237	+	6.56671i	0.132942	+	0.256583i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.98499	+	6.10917i	−0.0773242	+	0.237980i	−0.982246	−	0.187599i	$-0.939929\pi$
$659$	−1.98499	+	6.10917i	−0.0773242	+	0.237980i	0.904921	+	0.425579i	$0.139929\pi$
$660$		0			0
$661$	6.67091	+	20.5310i	0.259468	+	0.798562i	0.992916	+	0.118816i	$0.0379098\pi$
$661$	6.67091	+	20.5310i	0.259468	+	0.798562i	−0.733448	+	0.679746i	$0.762090\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	19.9790	−	10.3516i	0.774753	−	0.401418i
$666$		0			0
$667$	9.41443	−	12.9578i	0.364528	−	0.501730i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.47055	−	1.06842i	0.0567701	−	0.0412459i
$672$		0			0
$673$	5.64965	−	1.83568i	0.217778	−	0.0707604i	−0.198096	−	0.980183i	$-0.563476\pi$
$673$	5.64965	−	1.83568i	0.217778	−	0.0707604i	0.415874	+	0.909422i	$0.363476\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	35.3587	−	11.4888i	1.35895	−	0.441549i	0.463256	−	0.886225i	$-0.346681\pi$
$677$	35.3587	−	11.4888i	1.35895	−	0.441549i	0.895691	+	0.444676i	$0.146681\pi$
$678$		0			0
$679$	−20.6361	+	14.9930i	−0.791942	+	0.575380i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26.5106	+	36.4886i	−1.01440	+	1.39620i	−0.0983404	+	0.995153i	$0.531353\pi$
$683$	−26.5106	+	36.4886i	−1.01440	+	1.39620i	−0.916058	+	0.401046i	$0.868647\pi$
$684$		0			0
$685$	−3.34157	−	3.29641i	−0.127675	−	0.125949i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.89395	−	15.0620i	−0.186445	−	0.573818i
$690$		0			0
$691$	−8.82903	+	27.1730i	−0.335872	+	1.03371i	0.630419	+	0.776255i	$0.282883\pi$
$691$	−8.82903	+	27.1730i	−0.335872	+	1.03371i	−0.966291	+	0.257453i	$0.917117\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.44734	−	29.3711i	0.168697	−	1.11411i
$696$		0			0
$697$	19.4528	+	26.7745i	0.736829	+	1.01416i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	44.2636			1.67181			0.835907	−	0.548871i	$-0.184942\pi$
$701$	44.2636			1.67181			0.835907	+	0.548871i	$0.184942\pi$
$702$		0			0
$703$	18.4165	+	25.3482i	0.694593	+	0.956025i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			40.0602i			1.50662i
$708$		0			0
$709$	−5.25711	+	16.1797i	−0.197435	+	0.607643i	0.802505	+	0.596646i	$0.203500\pi$
$709$	−5.25711	+	16.1797i	−0.197435	+	0.607643i	−0.999940	+	0.0109965i	$0.996500\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.6635	+	7.36381i	0.848754	+	0.275777i
$714$		0			0
$715$	−0.320828	+	0.640393i	−0.0119983	+	0.0239494i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.71076	−	4.87565i	−0.250269	−	0.181831i	0.455577	−	0.890196i	$-0.349433\pi$
$719$	−6.71076	−	4.87565i	−0.250269	−	0.181831i	−0.705846	+	0.708365i	$0.749433\pi$
$720$		0			0
$721$	−39.9614	+	29.0336i	−1.48824	+	1.08127i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.0355	−	3.73034i	−0.446989	−	0.138541i
$726$		0			0
$727$	7.09791	−	2.30625i	0.263247	−	0.0855342i	−0.174420	−	0.984671i	$-0.555805\pi$
$727$	7.09791	−	2.30625i	0.263247	−	0.0855342i	0.437667	+	0.899137i	$0.355805\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−34.3593	−	24.9635i	−1.27082	−	0.923308i
$732$		0			0
$733$	7.06525	−	9.72449i	0.260961	−	0.359182i	−0.658351	−	0.752711i	$-0.728746\pi$
$733$	7.06525	−	9.72449i	0.260961	−	0.359182i	0.919312	+	0.393529i	$0.128746\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.09776	−	0.356684i	−0.0404365	−	0.0131386i
$738$		0			0
$739$	−7.82848	−	24.0936i	−0.287975	−	0.886297i	−0.985491	−	0.169728i	$-0.945711\pi$
$739$	−7.82848	−	24.0936i	−0.287975	−	0.886297i	0.697516	−	0.716570i	$-0.254289\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	21.0959i		−	0.773935i	−0.922093	−	0.386968i	$-0.873523\pi$
$743$		−	21.0959i		−	0.773935i	0.922093	−	0.386968i	$-0.126477\pi$
$744$		0			0
$745$	5.59605	+	2.80354i	0.205023	+	0.102714i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	36.7507			1.34284
$750$		0			0
$751$	−34.3897			−1.25490			−0.627449	−	0.778658i	$-0.715901\pi$
$751$	−34.3897			−1.25490			−0.627449	+	0.778658i	$0.715901\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.4213	+	6.72389i	0.488451	+	0.244707i
$756$		0			0
$757$			33.9762i			1.23488i	0.786616	+	0.617442i	$0.211831\pi$
$757$			33.9762i			1.23488i	−0.786616	+	0.617442i	$0.788169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.13686	+	12.7319i	0.149961	+	0.461533i	0.997616	−	0.0690159i	$-0.0219859\pi$
$761$	4.13686	+	12.7319i	0.149961	+	0.461533i	−0.847654	+	0.530549i	$0.821986\pi$
$762$		0			0
$763$	74.0828	+	24.0710i	2.68198	+	0.871427i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.04879	−	9.70183i	0.254517	−	0.350313i
$768$		0			0
$769$	−4.80948	−	3.49429i	−0.173434	−	0.126007i	0.497682	−	0.867360i	$-0.334185\pi$
$769$	−4.80948	−	3.49429i	−0.173434	−	0.126007i	−0.671116	+	0.741352i	$0.734185\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−32.4278	+	10.5364i	−1.16635	+	0.378969i	−0.827278	−	0.561793i	$-0.810112\pi$
$773$	−32.4278	+	10.5364i	−1.16635	+	0.378969i	−0.339068	+	0.940762i	$0.610112\pi$
$774$		0			0
$775$	−0.255039	−	18.7451i	−0.00916127	−	0.673345i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.3628	+	11.1617i	−0.550428	+	0.399909i
$780$		0			0
$781$	−2.05201	−	1.49087i	−0.0734267	−	0.0533476i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13.9715	+	27.8880i	−0.498665	+	0.995365i
$786$		0			0
$787$	−1.87644	−	0.609693i	−0.0668879	−	0.0217332i	0.275382	−	0.961335i	$-0.411196\pi$
$787$	−1.87644	−	0.609693i	−0.0668879	−	0.0217332i	−0.342270	+	0.939602i	$0.611196\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.76132	+	14.6538i	−0.169293	+	0.521030i
$792$		0			0
$793$			16.0052i			0.568361i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.3698	+	23.9075i	0.615269	+	0.846845i	0.996998	−	0.0774291i	$-0.0246711\pi$
$797$	17.3698	+	23.9075i	0.615269	+	0.846845i	−0.381729	+	0.924274i	$0.624671\pi$
$798$		0			0
$799$	20.9378			0.740725
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.584264	+	0.804170i	0.0206182	+	0.0283785i
$804$		0			0
$805$	8.10624	−	53.5352i	0.285707	−	1.88687i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.45516	−	7.55621i	0.0863189	−	0.265662i	−0.898575	−	0.438819i	$-0.855397\pi$
$809$	2.45516	−	7.55621i	0.0863189	−	0.265662i	0.984894	+	0.173157i	$0.0553968\pi$
$810$		0			0
$811$	5.71747	+	17.5966i	0.200768	+	0.617899i	0.999861	+	0.0166920i	$0.00531347\pi$
$811$	5.71747	+	17.5966i	0.200768	+	0.617899i	−0.799093	+	0.601207i	$0.794687\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	14.1278	+	13.9369i	0.494874	+	0.488187i
$816$		0			0
$817$	14.3236	−	19.7147i	0.501119	−	0.689731i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.4784	+	9.06610i	−0.435500	+	0.316409i	−0.783844	−	0.620958i	$-0.786744\pi$
$821$	−12.4784	+	9.06610i	−0.435500	+	0.316409i	0.348345	+	0.937367i	$0.386744\pi$
$822$		0			0
$823$	39.5494	−	12.8504i	1.37860	−	0.447936i	0.476394	−	0.879232i	$-0.341944\pi$
$823$	39.5494	−	12.8504i	1.37860	−	0.447936i	0.902210	+	0.431296i	$0.141944\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.1783	−	10.7803i	1.15372	−	0.374867i	0.331177	−	0.943569i	$-0.392554\pi$
$827$	33.1783	−	10.7803i	1.15372	−	0.374867i	0.822544	+	0.568702i	$0.192554\pi$
$828$		0			0
$829$	37.7079	−	27.3964i	1.30965	−	0.951516i	0.309649	−	0.950851i	$-0.399788\pi$
$829$	37.7079	−	27.3964i	1.30965	−	0.951516i	1.00000		0.000664954i	$-0.000211661\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20.3347	−	27.9883i	0.704555	−	0.969737i
$834$		0			0
$835$	−48.8298	+	25.2999i	−1.68982	+	0.875538i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.1009	+	40.3203i	0.452292	+	1.39201i	0.874285	+	0.485414i	$0.161331\pi$
$839$	13.1009	+	40.3203i	0.452292	+	1.39201i	−0.421992	+	0.906599i	$0.638669\pi$
$840$		0			0
$841$	−6.99899	+	21.5407i	−0.241345	+	0.742782i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.4715	+	20.2104i	0.360230	+	0.695258i
$846$		0			0
$847$	−24.5521	−	33.7930i	−0.843619	−	1.16114i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	75.3946			2.58449
$852$		0			0
$853$	2.20116	+	3.02964i	0.0753663	+	0.103733i	0.845036	−	0.534710i	$-0.179579\pi$
$853$	2.20116	+	3.02964i	0.0753663	+	0.103733i	−0.769670	+	0.638442i	$0.779579\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			39.9648i			1.36517i	0.730806	+	0.682586i	$0.239145\pi$
$857$			39.9648i			1.36517i	−0.730806	+	0.682586i	$0.760855\pi$
$858$		0			0
$859$	17.3383	−	53.3617i	0.591574	−	1.82068i	0.0204824	−	0.999790i	$-0.493480\pi$
$859$	17.3383	−	53.3617i	0.591574	−	1.82068i	0.571091	−	0.820887i	$-0.306520\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−17.6827	−	5.74547i	−0.601927	−	0.195578i	−0.00782756	−	0.999969i	$-0.502492\pi$
$863$	−17.6827	−	5.74547i	−0.601927	−	0.195578i	−0.594100	+	0.804391i	$0.702492\pi$
$864$		0			0
$865$	37.4411	+	5.66929i	1.27304	+	0.192762i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.480152	+	0.348851i	0.0162880	+	0.0118339i
$870$		0			0
$871$	8.22236	−	5.97389i	0.278604	−	0.202418i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−41.9270	+	7.52062i	−1.41739	+	0.254243i
$876$		0			0
$877$	10.3467	−	3.36186i	0.349385	−	0.113522i	−0.129067	−	0.991636i	$-0.541198\pi$
$877$	10.3467	−	3.36186i	0.349385	−	0.113522i	0.478452	+	0.878114i	$0.341198\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	27.5016	+	19.9811i	0.926552	+	0.673180i	0.945146	−	0.326647i	$-0.105919\pi$
$881$	27.5016	+	19.9811i	0.926552	+	0.673180i	−0.0185939	+	0.999827i	$0.505919\pi$
$882$		0			0
$883$	8.96658	−	12.3414i	0.301749	−	0.415322i	−0.631037	−	0.775753i	$-0.717370\pi$
$883$	8.96658	−	12.3414i	0.301749	−	0.415322i	0.932786	+	0.360431i	$0.117370\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−27.1095	−	8.80840i	−0.910247	−	0.295757i	−0.183787	−	0.982966i	$-0.558836\pi$
$887$	−27.1095	−	8.80840i	−0.910247	−	0.295757i	−0.726460	+	0.687209i	$0.758836\pi$
$888$		0			0
$889$	−19.7247	−	60.7063i	−0.661544	−	2.03602i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			12.0137i			0.402024i
$894$		0			0
$895$	32.5394	−	5.38089i	1.08767	−	0.179863i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.44871			0.315132
$900$		0			0
$901$	43.4089			1.44616
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.3040	−	21.8172i	−0.375757	−	0.725227i
$906$		0			0
$907$			22.1919i			0.736868i	0.929654	+	0.368434i	$0.120106\pi$
$907$			22.1919i			0.736868i	−0.929654	+	0.368434i	$0.879894\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.5476	−	38.6174i	−0.415719	−	1.27945i	−0.911606	−	0.411064i	$-0.865157\pi$
$911$	−12.5476	−	38.6174i	−0.415719	−	1.27945i	0.495887	−	0.868387i	$-0.334843\pi$
$912$		0			0
$913$	−0.848645	−	0.275742i	−0.0280861	−	0.00912572i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.40686	+	10.1947i	−0.244596	+	0.336658i
$918$		0			0
$919$	10.1543	+	7.37751i	0.334958	+	0.243361i	0.742532	−	0.669811i	$-0.233625\pi$
$919$	10.1543	+	7.37751i	0.334958	+	0.243361i	−0.407573	+	0.913173i	$0.633625\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.2406	−	6.90148i	0.699141	−	0.227165i
$924$		0			0
$925$	−19.0944	−	56.1553i	−0.627820	−	1.84637i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	45.6390	−	33.1587i	1.49737	−	1.08790i	0.525953	−	0.850513i	$-0.323709\pi$
$929$	45.6390	−	33.1587i	1.49737	−	1.08790i	0.971415	−	0.237388i	$-0.0762913\pi$
$930$		0			0
$931$	16.0592	+	11.6677i	0.526319	+	0.382393i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.39763	−	1.37875i	−0.0457075	−	0.0450899i
$936$		0			0
$937$	40.0630	+	13.0173i	1.30880	+	0.425255i	0.878635	−	0.477494i	$-0.158455\pi$
$937$	40.0630	+	13.0173i	1.30880	+	0.425255i	0.430166	+	0.902750i	$0.358455\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.51260	−	29.2768i	0.310102	−	0.954395i	−0.667622	−	0.744500i	$-0.732688\pi$
$941$	9.51260	−	29.2768i	0.310102	−	0.954395i	0.977724	−	0.209895i	$-0.0673122\pi$
$942$		0			0
$943$			45.6943i			1.48801i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.435973	−	0.600065i	−0.0141672	−	0.0194995i	0.801875	−	0.597492i	$-0.203836\pi$
$947$	−0.435973	−	0.600065i	−0.0141672	−	0.0194995i	−0.816042	+	0.577993i	$0.803836\pi$
$948$		0			0
$949$	−8.75241			−0.284115
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.1037	+	31.7995i	0.748401	+	1.03009i	0.998091	+	0.0617601i	$0.0196714\pi$
$953$	23.1037	+	31.7995i	0.748401	+	1.03009i	−0.249690	+	0.968326i	$0.580329\pi$
$954$		0			0
$955$	−37.7441	+	38.2611i	−1.22137	+	1.23810i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.47140	−	7.60620i	0.0798058	−	0.245617i
$960$		0			0
$961$	−5.23543	−	16.1130i	−0.168885	−	0.519774i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.52028	+	15.0109i	−0.242086	+	0.483219i
$966$		0			0
$967$	−28.6718	+	39.4633i	−0.922022	+	1.26905i	0.0408691	+	0.999165i	$0.486987\pi$
$967$	−28.6718	+	39.4633i	−0.922022	+	1.26905i	−0.962891	+	0.269890i	$0.913013\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−49.5659	+	36.0118i	−1.59065	+	1.15567i	−0.687635	+	0.726056i	$0.741351\pi$
$971$	−49.5659	+	36.0118i	−1.59065	+	1.15567i	−0.903011	+	0.429616i	$0.858649\pi$
$972$		0			0
$973$	48.1370	−	15.6407i	1.54320	−	0.501417i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6181	+	3.45004i	−0.339704	+	0.110377i	−0.473901	−	0.880578i	$-0.657155\pi$
$977$	−10.6181	+	3.45004i	−0.339704	+	0.110377i	0.134197	+	0.990955i	$0.457155\pi$
$978$		0			0
$979$	2.15138	−	1.56307i	0.0687583	−	0.0499559i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.2257	−	25.0855i	0.581310	−	0.800104i	−0.412528	−	0.910945i	$-0.635354\pi$
$983$	18.2257	−	25.0855i	0.581310	−	0.800104i	0.993838	+	0.110840i	$0.0353543\pi$
$984$		0			0
$985$	4.57920	+	27.6915i	0.145906	+	0.882323i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−18.1203	−	55.7687i	−0.576194	−	1.77334i
$990$		0			0
$991$	9.13378	−	28.1109i	0.290144	−	0.892972i	−0.694665	−	0.719333i	$-0.744447\pi$
$991$	9.13378	−	28.1109i	0.290144	−	0.892972i	0.984809	−	0.173639i	$-0.0555526\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−39.5081	−	19.7930i	−1.25249	−	0.627481i
$996$		0			0
$997$	−31.7701	−	43.7278i	−1.00617	−	1.38487i	−0.921462	−	0.388469i	$-0.873004\pi$
$997$	−31.7701	−	43.7278i	−1.00617	−	1.38487i	−0.0847083	−	0.996406i	$-0.526996\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.469.1		24
3.2	odd	2		300.2.o.a.169.3	✓	24
15.2	even	4		1500.2.m.c.901.5		24
15.8	even	4		1500.2.m.d.901.2		24
15.14	odd	2		1500.2.o.c.349.4		24
25.4	even	10	inner	900.2.w.c.829.1		24
75.2	even	20		7500.2.a.n.1.10		12
75.11	odd	10		7500.2.d.g.1249.15		24
75.14	odd	10		7500.2.d.g.1249.10		24
75.23	even	20		7500.2.a.m.1.3		12
75.29	odd	10		300.2.o.a.229.3	yes	24
75.47	even	20		1500.2.m.c.601.5		24
75.53	even	20		1500.2.m.d.601.2		24
75.71	odd	10		1500.2.o.c.649.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.3	✓	24	3.2	odd	2
300.2.o.a.229.3	yes	24	75.29	odd	10
900.2.w.c.469.1		24	1.1	even	1	trivial
900.2.w.c.829.1		24	25.4	even	10	inner
1500.2.m.c.601.5		24	75.47	even	20
1500.2.m.c.901.5		24	15.2	even	4
1500.2.m.d.601.2		24	75.53	even	20
1500.2.m.d.901.2		24	15.8	even	4
1500.2.o.c.349.4		24	15.14	odd	2
1500.2.o.c.649.4		24	75.71	odd	10
7500.2.a.m.1.3		12	75.23	even	20
7500.2.a.n.1.10		12	75.2	even	20
7500.2.d.g.1249.10		24	75.14	odd	10
7500.2.d.g.1249.15		24	75.11	odd	10

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99921 - 1.00158i) q^{5} -3.80992i q^{7} +O(q^{10})\)	\(q+(-1.99921 - 1.00158i) q^{5} -3.80992i q^{7} +(-0.0589397 - 0.181398i) q^{11} +(1.59724 + 0.518974i) q^{13} +(-2.70572 + 3.72410i) q^{17} +(-2.13682 - 1.55249i) q^{19} +(-6.04461 + 1.96401i) q^{23} +(2.99369 + 4.00473i) q^{25} +(-2.03878 + 1.48126i) q^{29} +(-3.03331 - 2.20383i) q^{31} +(-3.81593 + 7.61682i) q^{35} +(-11.2820 - 3.66574i) q^{37} +(2.22169 - 6.83765i) q^{41} +9.22619i q^{43} +(-2.67353 - 3.67980i) q^{47} -7.51545 q^{49} +(-5.54285 - 7.62908i) q^{53} +(-0.0638510 + 0.421685i) q^{55} +(2.20656 - 6.79109i) q^{59} +(2.94497 + 9.06368i) q^{61} +(-2.67342 - 2.63729i) q^{65} +(3.55709 - 4.89591i) q^{67} +(10.7586 - 7.81655i) q^{71} +(-4.95645 + 1.61045i) q^{73} +(-0.691110 + 0.224555i) q^{77} +(-2.51740 + 1.82900i) q^{79} +(2.74988 - 3.78488i) q^{83} +(9.13928 - 4.73528i) q^{85} +(4.30840 + 13.2599i) q^{89} +(1.97725 - 6.08534i) q^{91} +(2.71702 + 5.24395i) q^{95} +(-3.93527 - 5.41643i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 24 * q + 2 * q^5	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

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