LMFDB - Embedded newform 900.2.h.b.899.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(899,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("900.899");

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.h (of order $2$, degree $1$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.5
Root			$0.500000 + 2.10607i$ of defining polynomial
Character	$\chi$	$=$	900.899
Dual form			900.2.h.b.899.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 1.39897i) q^{2} +(-1.91421 - 0.579471i) q^{4} -1.63899 q^{7} +(-1.20711 + 2.55791i) q^{8} +O(q^{10})$	\(q+(0.207107 - 1.39897i) q^{2} +(-1.91421 - 0.579471i) q^{4} -1.63899 q^{7} +(-1.20711 + 2.55791i) q^{8} -3.95687 q^{11} +0.585786i q^{13} +(-0.339446 + 2.29289i) q^{14} +(3.32843 + 2.21846i) q^{16} +4.00000 q^{17} +7.91375i q^{19} +(-0.819496 + 5.53553i) q^{22} -5.59587i q^{23} +(0.819496 + 0.121320i) q^{26} +(3.13738 + 0.949747i) q^{28} +7.65685i q^{29} +5.59587i q^{31} +(3.79289 - 4.19690i) q^{32} +(0.828427 - 5.59587i) q^{34} +9.07107i q^{37} +(11.0711 + 1.63899i) q^{38} +1.41421i q^{41} -7.91375 q^{43} +(7.57430 + 2.29289i) q^{44} +(-7.82843 - 1.15894i) q^{46} -3.27798i q^{47} -4.31371 q^{49} +(0.339446 - 1.12132i) q^{52} +5.17157 q^{53} +(1.97844 - 4.19239i) q^{56} +(10.7117 + 1.58579i) q^{58} -11.8706 q^{59} -0.828427 q^{61} +(7.82843 + 1.15894i) q^{62} +(-5.08579 - 6.17534i) q^{64} +11.1917 q^{67} +(-7.65685 - 2.31788i) q^{68} +4.63577 q^{71} +8.82843i q^{73} +(12.6901 + 1.87868i) q^{74} +(4.58579 - 15.1486i) q^{76} +6.48528 q^{77} +10.2316i q^{79} +(1.97844 + 0.292893i) q^{82} -3.27798i q^{83} +(-1.63899 + 11.0711i) q^{86} +(4.77637 - 10.1213i) q^{88} -5.41421i q^{89} -0.960099i q^{91} +(-3.24264 + 10.7117i) q^{92} +(-4.58579 - 0.678892i) q^{94} -14.4853i q^{97} +(-0.893398 + 6.03473i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 4 q^{16} + 32 q^{17} + 36 q^{32} - 16 q^{34} + 32 q^{38} - 40 q^{46} + 56 q^{49} + 64 q^{53} + 16 q^{61} + 40 q^{62} - 52 q^{64} - 16 q^{68} + 48 q^{76} - 16 q^{77} + 8 q^{92} - 48 q^{94} - 92 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 4 * q^16 + 32 * q^17 + 36 * q^32 - 16 * q^34 + 32 * q^38 - 40 * q^46 + 56 * q^49 + 64 * q^53 + 16 * q^61 + 40 * q^62 - 52 * q^64 - 16 * q^68 + 48 * q^76 - 16 * q^77 + 8 * q^92 - 48 * q^94 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.207107	−	1.39897i	0.146447	−	0.989219i
$2$	0.207107	−	1.39897i	0.146447	−	0.989219i
$3$		0			0
$3$		0			0
$4$	−1.91421	−	0.579471i	−0.957107	−	0.289735i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.63899			−0.619480			−0.309740	−	0.950821i	$-0.600242\pi$
$7$	−1.63899			−0.619480			−0.309740	+	0.950821i	$0.600242\pi$
$8$	−1.20711	+	2.55791i	−0.426777	+	0.904357i
$9$		0			0
$10$		0			0
$11$	−3.95687			−1.19304			−0.596521	−	0.802597i	$-0.703451\pi$
$11$	−3.95687			−1.19304			−0.596521	+	0.802597i	$0.703451\pi$
$12$		0			0
$13$			0.585786i			0.162468i	0.996695	+	0.0812340i	$0.0258861\pi$
$13$			0.585786i			0.162468i	−0.996695	+	0.0812340i	$0.974114\pi$
$14$	−0.339446	+	2.29289i	−0.0907208	+	0.612801i
$15$		0			0
$16$	3.32843	+	2.21846i	0.832107	+	0.554615i
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$			7.91375i			1.81554i	0.419470	+	0.907769i	$0.362216\pi$
$19$			7.91375i			1.81554i	−0.419470	+	0.907769i	$0.637784\pi$
$20$		0			0
$21$		0			0
$22$	−0.819496	+	5.53553i	−0.174717	+	1.18018i
$23$		−	5.59587i		−	1.16682i	−0.812178	−	0.583409i	$-0.801718\pi$
$23$		−	5.59587i		−	1.16682i	0.812178	−	0.583409i	$-0.198282\pi$
$24$		0			0
$25$		0			0
$26$	0.819496	+	0.121320i	0.160716	+	0.0237929i
$27$		0			0
$28$	3.13738	+	0.949747i	0.592909	+	0.179485i
$29$			7.65685i			1.42184i	0.703272	+	0.710921i	$0.251722\pi$
$29$			7.65685i			1.42184i	−0.703272	+	0.710921i	$0.748278\pi$
$30$		0			0
$31$			5.59587i			1.00505i	0.864564	+	0.502524i	$0.167595\pi$
$31$			5.59587i			1.00505i	−0.864564	+	0.502524i	$0.832405\pi$
$32$	3.79289	−	4.19690i	0.670495	−	0.741914i
$33$		0			0
$34$	0.828427	−	5.59587i	0.142074	−	0.959683i
$35$		0			0
$36$		0			0
$37$			9.07107i			1.49127i	0.666352	+	0.745637i	$0.267855\pi$
$37$			9.07107i			1.49127i	−0.666352	+	0.745637i	$0.732145\pi$
$38$	11.0711	+	1.63899i	1.79596	+	0.265879i
$39$		0			0
$40$		0			0
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		0			0
$43$	−7.91375			−1.20684			−0.603418	−	0.797425i	$-0.706195\pi$
$43$	−7.91375			−1.20684			−0.603418	+	0.797425i	$0.706195\pi$
$44$	7.57430	+	2.29289i	1.14187	+	0.345667i
$45$		0			0
$46$	−7.82843	−	1.15894i	−1.15424	−	0.170877i
$47$		−	3.27798i		−	0.478143i	−0.971002	−	0.239071i	$-0.923157\pi$
$47$		−	3.27798i		−	0.478143i	0.971002	−	0.239071i	$-0.0768430\pi$
$48$		0			0
$49$	−4.31371			−0.616244
$50$		0			0
$51$		0			0
$52$	0.339446	−	1.12132i	0.0470727	−	0.155499i
$53$	5.17157			0.710370			0.355185	−	0.934796i	$-0.384418\pi$
$53$	5.17157			0.710370			0.355185	+	0.934796i	$0.384418\pi$
$54$		0			0
$55$		0			0
$56$	1.97844	−	4.19239i	0.264380	−	0.560231i
$57$		0			0
$58$	10.7117	+	1.58579i	1.40651	+	0.208224i
$59$	−11.8706			−1.54542			−0.772712	−	0.634757i	$-0.781100\pi$
$59$	−11.8706			−1.54542			−0.772712	+	0.634757i	$0.781100\pi$
$60$		0			0
$61$	−0.828427			−0.106069			−0.0530346	−	0.998593i	$-0.516889\pi$
$61$	−0.828427			−0.106069			−0.0530346	+	0.998593i	$0.516889\pi$
$62$	7.82843	+	1.15894i	0.994211	+	0.147186i
$63$		0			0
$64$	−5.08579	−	6.17534i	−0.635723	−	0.771917i
$65$		0			0
$66$		0			0
$67$	11.1917			1.36729			0.683644	−	0.729816i	$-0.260394\pi$
$67$	11.1917			1.36729			0.683644	+	0.729816i	$0.260394\pi$
$68$	−7.65685	−	2.31788i	−0.928530	−	0.281085i
$69$		0			0
$70$		0			0
$71$	4.63577			0.550164			0.275082	−	0.961421i	$-0.411295\pi$
$71$	4.63577			0.550164			0.275082	+	0.961421i	$0.411295\pi$
$72$		0			0
$73$			8.82843i			1.03329i	0.856200	+	0.516645i	$0.172819\pi$
$73$			8.82843i			1.03329i	−0.856200	+	0.516645i	$0.827181\pi$
$74$	12.6901	+	1.87868i	1.47520	+	0.218392i
$75$		0			0
$76$	4.58579	−	15.1486i	0.526026	−	1.73766i
$77$	6.48528			0.739066
$78$		0			0
$79$			10.2316i			1.15115i	0.817750	+	0.575574i	$0.195221\pi$
$79$			10.2316i			1.15115i	−0.817750	+	0.575574i	$0.804779\pi$
$80$		0			0
$81$		0			0
$82$	1.97844	+	0.292893i	0.218482	+	0.0323446i
$83$		−	3.27798i		−	0.359805i	−0.983684	−	0.179903i	$-0.942422\pi$
$83$		−	3.27798i		−	0.359805i	0.983684	−	0.179903i	$-0.0575783\pi$
$84$		0			0
$85$		0			0
$86$	−1.63899	+	11.0711i	−0.176737	+	1.19382i
$87$		0			0
$88$	4.77637	−	10.1213i	0.509163	−	1.07894i
$89$		−	5.41421i		−	0.573905i	−0.957945	−	0.286953i	$-0.907358\pi$
$89$		−	5.41421i		−	0.573905i	0.957945	−	0.286953i	$-0.0926423\pi$
$90$		0			0
$91$		−	0.960099i		−	0.100646i
$92$	−3.24264	+	10.7117i	−0.338069	+	1.11677i
$93$		0			0
$94$	−4.58579	−	0.678892i	−0.472988	−	0.0700224i
$95$		0			0
$96$		0			0
$97$		−	14.4853i		−	1.47076i	−0.677656	−	0.735379i	$-0.737004\pi$
$97$		−	14.4853i		−	1.47076i	0.677656	−	0.735379i	$-0.262996\pi$
$98$	−0.893398	+	6.03473i	−0.0902469	+	0.609600i
$99$		0			0
$100$		0			0
$101$		−	7.17157i		−	0.713598i	−0.934181	−	0.356799i	$-0.883868\pi$
$101$		−	7.17157i		−	0.713598i	0.934181	−	0.356799i	$-0.116132\pi$
$102$		0			0
$103$	−17.4665			−1.72102			−0.860512	−	0.509430i	$-0.829856\pi$
$103$	−17.4665			−1.72102			−0.860512	+	0.509430i	$0.829856\pi$
$104$	−1.49839	−	0.707107i	−0.146929	−	0.0693375i
$105$		0			0
$106$	1.07107	−	7.23486i	0.104031	−	0.702711i
$107$			3.27798i			0.316894i	0.987367	+	0.158447i	$0.0506488\pi$
$107$			3.27798i			0.316894i	−0.987367	+	0.158447i	$0.949351\pi$
$108$		0			0
$109$	4.82843			0.462479			0.231240	−	0.972897i	$-0.425722\pi$
$109$	4.82843			0.462479			0.231240	+	0.972897i	$0.425722\pi$
$110$		0			0
$111$		0			0
$112$	−5.45526	−	3.63604i	−0.515474	−	0.343573i
$113$	−12.4853			−1.17452			−0.587258	−	0.809400i	$-0.699793\pi$
$113$	−12.4853			−1.17452			−0.587258	+	0.809400i	$0.699793\pi$
$114$		0			0
$115$		0			0
$116$	4.43692	−	14.6569i	0.411958	−	1.36085i
$117$		0			0
$118$	−2.45849	+	16.6066i	−0.226322	+	1.52876i
$119$	−6.55596			−0.600984
$120$		0			0
$121$	4.65685			0.423350
$122$	−0.171573	+	1.15894i	−0.0155335	+	0.104926i
$123$		0			0
$124$	3.24264	−	10.7117i	0.291198	−	0.961937i
$125$		0			0
$126$		0			0
$127$	−1.63899			−0.145437			−0.0727185	−	0.997353i	$-0.523167\pi$
$127$	−1.63899			−0.145437			−0.0727185	+	0.997353i	$0.523167\pi$
$128$	−9.69239	+	5.83589i	−0.856694	+	0.515825i
$129$		0			0
$130$		0			0
$131$	−0.678892			−0.0593151			−0.0296575	−	0.999560i	$-0.509442\pi$
$131$	−0.678892			−0.0593151			−0.0296575	+	0.999560i	$0.509442\pi$
$132$		0			0
$133$		−	12.9706i		−	1.12469i
$134$	2.31788	−	15.6569i	0.200235	−	1.35255i
$135$		0			0
$136$	−4.82843	+	10.2316i	−0.414034	+	0.877355i
$137$	−14.1421			−1.20824			−0.604122	−	0.796892i	$-0.706476\pi$
$137$	−14.1421			−1.20824			−0.604122	+	0.796892i	$0.706476\pi$
$138$		0			0
$139$			2.31788i			0.196600i	0.995157	+	0.0983001i	$0.0313405\pi$
$139$			2.31788i			0.196600i	−0.995157	+	0.0983001i	$0.968659\pi$
$140$		0			0
$141$		0			0
$142$	0.960099	−	6.48528i	0.0805697	−	0.544233i
$143$		−	2.31788i		−	0.193831i
$144$		0			0
$145$		0			0
$146$	12.3507	+	1.82843i	1.02215	+	0.151322i
$147$		0			0
$148$	5.25642	−	17.3640i	0.432075	−	1.42731i
$149$			6.48528i			0.531295i	0.964070	+	0.265647i	$0.0855857\pi$
$149$			6.48528i			0.531295i	−0.964070	+	0.265647i	$0.914414\pi$
$150$		0			0
$151$		−	2.31788i		−	0.188627i	−0.995543	−	0.0943133i	$-0.969934\pi$
$151$		−	2.31788i		−	0.188627i	0.995543	−	0.0943133i	$-0.0300656\pi$
$152$	−20.2426	−	9.55274i	−1.64189	−	0.774829i
$153$		0			0
$154$	1.34315	−	9.07269i	0.108234	−	0.731098i
$155$		0			0
$156$		0			0
$157$			1.75736i			0.140253i	0.997538	+	0.0701263i	$0.0223402\pi$
$157$			1.75736i			0.140253i	−0.997538	+	0.0701263i	$0.977660\pi$
$158$	14.3137	+	2.11904i	1.13874	+	0.168582i
$159$		0			0
$160$		0			0
$161$			9.17157i			0.722821i
$162$		0			0
$163$	7.91375			0.619853			0.309926	−	0.950761i	$-0.399696\pi$
$163$	7.91375			0.619853			0.309926	+	0.950761i	$0.399696\pi$
$164$	0.819496	−	2.70711i	0.0639918	−	0.211390i
$165$		0			0
$166$	−4.58579	−	0.678892i	−0.355926	−	0.0526923i
$167$			16.7876i			1.29906i	0.760335	+	0.649532i	$0.225035\pi$
$167$			16.7876i			1.29906i	−0.760335	+	0.649532i	$0.774965\pi$
$168$		0			0
$169$	12.6569			0.973604
$170$		0			0
$171$		0			0
$172$	15.1486	+	4.58579i	1.15507	+	0.349663i
$173$	4.48528			0.341010			0.170505	−	0.985357i	$-0.445460\pi$
$173$	4.48528			0.341010			0.170505	+	0.985357i	$0.445460\pi$
$174$		0			0
$175$		0			0
$176$	−13.1702	−	8.77817i	−0.992739	−	0.661680i
$177$		0			0
$178$	−7.57430	−	1.12132i	−0.567718	−	0.0840465i
$179$	8.59264			0.642244			0.321122	−	0.947038i	$-0.395940\pi$
$179$	8.59264			0.642244			0.321122	+	0.947038i	$0.395940\pi$
$180$		0			0
$181$	−17.7990			−1.32299			−0.661494	−	0.749950i	$-0.730077\pi$
$181$	−17.7990			−1.32299			−0.661494	+	0.749950i	$0.730077\pi$
$182$	−1.34315	−	0.198843i	−0.0995606	−	0.0147392i
$183$		0			0
$184$	14.3137	+	6.75481i	1.05522	+	0.497971i
$185$		0			0
$186$		0			0
$187$	−15.8275			−1.15742
$188$	−1.89949	+	6.27476i	−0.138535	+	0.457634i
$189$		0			0
$190$		0			0
$191$	−19.1055			−1.38242			−0.691212	−	0.722652i	$-0.742923\pi$
$191$	−19.1055			−1.38242			−0.691212	+	0.722652i	$0.742923\pi$
$192$		0			0
$193$		−	4.34315i		−	0.312626i	−0.987708	−	0.156313i	$-0.950039\pi$
$193$		−	4.34315i		−	0.312626i	0.987708	−	0.156313i	$-0.0499609\pi$
$194$	−20.2644	−	3.00000i	−1.45490	−	0.215387i
$195$		0			0
$196$	8.25736	+	2.49967i	0.589811	+	0.178548i
$197$	−8.34315			−0.594425			−0.297212	−	0.954811i	$-0.596057\pi$
$197$	−8.34315			−0.594425			−0.297212	+	0.954811i	$0.596057\pi$
$198$		0			0
$199$			4.23808i			0.300430i	0.988653	+	0.150215i	$0.0479965\pi$
$199$			4.23808i			0.300430i	−0.988653	+	0.150215i	$0.952003\pi$
$200$		0			0
$201$		0			0
$202$	−10.0328	−	1.48528i	−0.705905	−	0.104504i
$203$		−	12.5495i		−	0.880803i
$204$		0			0
$205$		0			0
$206$	−3.61743	+	24.4350i	−0.252038	+	1.70247i
$207$		0			0
$208$	−1.29954	+	1.94975i	−0.0901072	+	0.135191i
$209$		−	31.3137i		−	2.16601i
$210$		0			0
$211$			8.87385i			0.610901i	0.952208	+	0.305450i	$0.0988070\pi$
$211$			8.87385i			0.610901i	−0.952208	+	0.305450i	$0.901193\pi$
$212$	−9.89949	−	2.99678i	−0.679900	−	0.205819i
$213$		0			0
$214$	4.58579	+	0.678892i	0.313478	+	0.0464081i
$215$		0			0
$216$		0			0
$217$		−	9.17157i		−	0.622607i
$218$	1.00000	−	6.75481i	0.0677285	−	0.457493i
$219$		0			0
$220$		0			0
$221$			2.34315i			0.157617i
$222$		0			0
$223$	16.1087			1.07872			0.539359	−	0.842076i	$-0.318666\pi$
$223$	16.1087			1.07872			0.539359	+	0.842076i	$0.318666\pi$
$224$	−6.21652	+	6.87868i	−0.415359	+	0.459601i
$225$		0			0
$226$	−2.58579	+	17.4665i	−0.172004	+	1.16185i
$227$		−	15.8275i		−	1.05051i	−0.850946	−	0.525254i	$-0.823970\pi$
$227$		−	15.8275i		−	1.05051i	0.850946	−	0.525254i	$-0.176030\pi$
$228$		0			0
$229$	1.31371			0.0868123			0.0434062	−	0.999058i	$-0.486179\pi$
$229$	1.31371			0.0868123			0.0434062	+	0.999058i	$0.486179\pi$
$230$		0			0
$231$		0			0
$232$	−19.5855	−	9.24264i	−1.28585	−	0.606809i
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$		0			0
$235$		0			0
$236$	22.7229	+	6.87868i	1.47914	+	0.447764i
$237$		0			0
$238$	−1.35778	+	9.17157i	−0.0880121	+	0.594505i
$239$	−1.35778			−0.0878278			−0.0439139	−	0.999035i	$-0.513983\pi$
$239$	−1.35778			−0.0878278			−0.0439139	+	0.999035i	$0.513983\pi$
$240$		0			0
$241$	20.9706			1.35083			0.675416	−	0.737437i	$-0.263964\pi$
$241$	20.9706			1.35083			0.675416	+	0.737437i	$0.263964\pi$
$242$	0.964466	−	6.51478i	0.0619982	−	0.418786i
$243$		0			0
$244$	1.58579	+	0.480049i	0.101520	+	0.0307320i
$245$		0			0
$246$		0			0
$247$	−4.63577			−0.294967
$248$	−14.3137	−	6.75481i	−0.908921	−	0.428931i
$249$		0			0
$250$		0			0
$251$	7.23486			0.456660			0.228330	−	0.973584i	$-0.426673\pi$
$251$	7.23486			0.456660			0.228330	+	0.973584i	$0.426673\pi$
$252$		0			0
$253$			22.1421i			1.39206i
$254$	−0.339446	+	2.29289i	−0.0212987	+	0.143869i
$255$		0			0
$256$	6.15685	+	14.7680i	0.384803	+	0.922999i
$257$	−22.1421			−1.38119			−0.690594	−	0.723242i	$-0.742651\pi$
$257$	−22.1421			−1.38119			−0.690594	+	0.723242i	$0.742651\pi$
$258$		0			0
$259$		−	14.8674i		−	0.923815i
$260$		0			0
$261$		0			0
$262$	−0.140603	+	0.949747i	−0.00868649	+	0.0586756i
$263$			21.4234i			1.32102i	0.750817	+	0.660511i	$0.229660\pi$
$263$			21.4234i			1.32102i	−0.750817	+	0.660511i	$0.770340\pi$
$264$		0			0
$265$		0			0
$266$	−18.1454	−	2.68629i	−1.11256	−	0.164707i
$267$		0			0
$268$	−21.4234	−	6.48528i	−1.30864	−	0.396152i
$269$			2.00000i			0.121942i	0.998140	+	0.0609711i	$0.0194197\pi$
$269$			2.00000i			0.121942i	−0.998140	+	0.0609711i	$0.980580\pi$
$270$		0			0
$271$			2.31788i			0.140801i	0.997519	+	0.0704007i	$0.0224278\pi$
$271$			2.31788i			0.140801i	−0.997519	+	0.0704007i	$0.977572\pi$
$272$	13.3137	+	8.87385i	0.807262	+	0.538056i
$273$		0			0
$274$	−2.92893	+	19.7844i	−0.176943	+	1.19522i
$275$		0			0
$276$		0			0
$277$			14.2426i			0.855757i	0.903836	+	0.427879i	$0.140739\pi$
$277$			14.2426i			0.855757i	−0.903836	+	0.427879i	$0.859261\pi$
$278$	3.24264	+	0.480049i	0.194481	+	0.0287914i
$279$		0			0
$280$		0			0
$281$			10.3848i			0.619504i	0.950817	+	0.309752i	$0.100246\pi$
$281$			10.3848i			0.619504i	−0.950817	+	0.309752i	$0.899754\pi$
$282$		0			0
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−8.87385	−	2.68629i	−0.526566	−	0.159402i
$285$		0			0
$286$	−3.24264	−	0.480049i	−0.191741	−	0.0283859i
$287$		−	2.31788i		−	0.136820i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$	5.11582	−	16.8995i	0.299380	−	0.988968i
$293$	3.65685			0.213636			0.106818	−	0.994279i	$-0.465934\pi$
$293$	3.65685			0.213636			0.106818	+	0.994279i	$0.465934\pi$
$294$		0			0
$295$		0			0
$296$	−23.2030	−	10.9497i	−1.34864	−	0.636441i
$297$		0			0
$298$	9.07269	+	1.34315i	0.525567	+	0.0778063i
$299$	3.27798			0.189571
$300$		0			0
$301$	12.9706			0.747611
$302$	−3.24264	−	0.480049i	−0.186593	−	0.0276237i
$303$		0			0
$304$	−17.5563	+	26.3403i	−1.00693	+	1.51072i
$305$		0			0
$306$		0			0
$307$	−6.55596			−0.374169			−0.187084	−	0.982344i	$-0.559904\pi$
$307$	−6.55596			−0.374169			−0.187084	+	0.982344i	$0.559904\pi$
$308$	−12.4142	−	3.75803i	−0.707365	−	0.214134i
$309$		0			0
$310$		0			0
$311$	25.6614			1.45513			0.727563	−	0.686040i	$-0.240653\pi$
$311$	25.6614			1.45513			0.727563	+	0.686040i	$0.240653\pi$
$312$		0			0
$313$		−	23.6569i		−	1.33716i	−0.743638	−	0.668582i	$-0.766901\pi$
$313$		−	23.6569i		−	1.33716i	0.743638	−	0.668582i	$-0.233099\pi$
$314$	2.45849	+	0.363961i	0.138740	+	0.0205395i
$315$		0			0
$316$	5.92893	−	19.5855i	0.333528	−	1.10177i
$317$	26.9706			1.51482			0.757409	−	0.652941i	$-0.226465\pi$
$317$	26.9706			1.51482			0.757409	+	0.652941i	$0.226465\pi$
$318$		0			0
$319$		−	30.2972i		−	1.69632i
$320$		0			0
$321$		0			0
$322$	12.8307	+	1.89949i	0.715028	+	0.105855i
$323$			31.6550i			1.76133i
$324$		0			0
$325$		0			0
$326$	1.63899	−	11.0711i	0.0907753	−	0.613170i
$327$		0			0
$328$	−3.61743	−	1.70711i	−0.199739	−	0.0942592i
$329$			5.37258i			0.296200i
$330$		0			0
$331$		−	12.5495i		−	0.689784i	−0.938642	−	0.344892i	$-0.887916\pi$
$331$		−	12.5495i		−	0.689784i	0.938642	−	0.344892i	$-0.112084\pi$
$332$	−1.89949	+	6.27476i	−0.104248	+	0.344372i
$333$		0			0
$334$	23.4853	+	3.47682i	1.28506	+	0.190243i
$335$		0			0
$336$		0			0
$337$		−	20.1421i		−	1.09721i	−0.836081	−	0.548606i	$-0.815159\pi$
$337$		−	20.1421i		−	1.09721i	0.836081	−	0.548606i	$-0.184841\pi$
$338$	2.62132	−	17.7065i	0.142581	−	0.963107i
$339$		0			0
$340$		0			0
$341$		−	22.1421i		−	1.19906i
$342$		0			0
$343$	18.5431			1.00123
$344$	9.55274	−	20.2426i	0.515049	−	1.09141i
$345$		0			0
$346$	0.928932	−	6.27476i	0.0499397	−	0.337333i
$347$			4.63577i			0.248861i	0.992228	+	0.124430i	$0.0397104\pi$
$347$			4.63577i			0.248861i	−0.992228	+	0.124430i	$0.960290\pi$
$348$		0			0
$349$	−30.4853			−1.63184			−0.815920	−	0.578165i	$-0.803769\pi$
$349$	−30.4853			−1.63184			−0.815920	+	0.578165i	$0.803769\pi$
$350$		0			0
$351$		0			0
$352$	−15.0080	+	16.6066i	−0.799929	+	0.885135i
$353$	−11.3137			−0.602168			−0.301084	−	0.953598i	$-0.597348\pi$
$353$	−11.3137			−0.602168			−0.301084	+	0.953598i	$0.597348\pi$
$354$		0			0
$355$		0			0
$356$	−3.13738	+	10.3640i	−0.166281	+	0.549289i
$357$		0			0
$358$	1.77959	−	12.0208i	0.0940545	−	0.635320i
$359$	19.1055			1.00835			0.504174	−	0.863602i	$-0.331797\pi$
$359$	19.1055			1.00835			0.504174	+	0.863602i	$0.331797\pi$
$360$		0			0
$361$	−43.6274			−2.29618
$362$	−3.68629	+	24.9002i	−0.193747	+	1.30872i
$363$		0			0
$364$	−0.556349	+	1.83783i	−0.0291606	+	0.0963287i
$365$		0			0
$366$		0			0
$367$	31.9362			1.66706			0.833528	−	0.552477i	$-0.186317\pi$
$367$	31.9362			1.66706			0.833528	+	0.552477i	$0.186317\pi$
$368$	12.4142	−	18.6254i	0.647136	−	0.970918i
$369$		0			0
$370$		0			0
$371$	−8.47616			−0.440060
$372$		0			0
$373$		−	15.4142i		−	0.798118i	−0.916925	−	0.399059i	$-0.869337\pi$
$373$		−	15.4142i		−	0.798118i	0.916925	−	0.399059i	$-0.130663\pi$
$374$	−3.27798	+	22.1421i	−0.169500	+	1.14494i
$375$		0			0
$376$	8.38478	+	3.95687i	0.432412	+	0.204060i
$377$	−4.48528			−0.231004
$378$		0			0
$379$		−	31.2573i		−	1.60558i	−0.596262	−	0.802790i	$-0.703348\pi$
$379$		−	31.2573i		−	1.60558i	0.596262	−	0.802790i	$-0.296652\pi$
$380$		0			0
$381$		0			0
$382$	−3.95687	+	26.7279i	−0.202451	+	1.36752i
$383$			3.27798i			0.167497i	0.996487	+	0.0837485i	$0.0266892\pi$
$383$			3.27798i			0.167497i	−0.996487	+	0.0837485i	$0.973311\pi$
$384$		0			0
$385$		0			0
$386$	−6.07591	−	0.899495i	−0.309256	−	0.0457831i
$387$		0			0
$388$	−8.39380	+	27.7279i	−0.426131	+	1.40767i
$389$			38.9706i			1.97589i	0.154818	+	0.987943i	$0.450521\pi$
$389$			38.9706i			1.97589i	−0.154818	+	0.987943i	$0.549479\pi$
$390$		0			0
$391$		−	22.3835i		−	1.13198i
$392$	5.20711	−	11.0341i	0.262999	−	0.557305i
$393$		0			0
$394$	−1.72792	+	11.6718i	−0.0870515	+	0.588016i
$395$		0			0
$396$		0			0
$397$			18.9289i			0.950016i	0.879982	+	0.475008i	$0.157555\pi$
$397$			18.9289i			0.950016i	−0.879982	+	0.475008i	$0.842445\pi$
$398$	5.92893	+	0.877735i	0.297191	+	0.0439969i
$399$		0			0
$400$		0			0
$401$		−	21.2132i		−	1.05934i	−0.848205	−	0.529668i	$-0.822316\pi$
$401$		−	21.2132i		−	1.05934i	0.848205	−	0.529668i	$-0.177684\pi$
$402$		0			0
$403$	−3.27798			−0.163288
$404$	−4.15572	+	13.7279i	−0.206755	+	0.682990i
$405$		0			0
$406$	−17.5563	−	2.59909i	−0.871307	−	0.128991i
$407$		−	35.8931i		−	1.77915i
$408$		0			0
$409$	18.9706			0.938034			0.469017	−	0.883189i	$-0.344608\pi$
$409$	18.9706			0.938034			0.469017	+	0.883189i	$0.344608\pi$
$410$		0			0
$411$		0			0
$412$	33.4346	+	10.1213i	1.64720	+	0.498642i
$413$	19.4558			0.957360
$414$		0			0
$415$		0			0
$416$	2.45849	+	2.22183i	0.120537	+	0.108934i
$417$		0			0
$418$	−43.8068	−	6.48528i	−2.14266	−	0.317205i
$419$	30.9761			1.51328			0.756641	−	0.653831i	$-0.226839\pi$
$419$	30.9761			1.51328			0.756641	+	0.653831i	$0.226839\pi$
$420$		0			0
$421$	18.9706			0.924569			0.462284	−	0.886732i	$-0.347030\pi$
$421$	18.9706			0.924569			0.462284	+	0.886732i	$0.347030\pi$
$422$	12.4142	+	1.83783i	0.604314	+	0.0894644i
$423$		0			0
$424$	−6.24264	+	13.2284i	−0.303169	+	0.642428i
$425$		0			0
$426$		0			0
$427$	1.35778			0.0657078
$428$	1.89949	−	6.27476i	0.0918156	−	0.303302i
$429$		0			0
$430$		0			0
$431$	21.0257			1.01277			0.506386	−	0.862307i	$-0.330981\pi$
$431$	21.0257			1.01277			0.506386	+	0.862307i	$0.330981\pi$
$432$		0			0
$433$			19.4558i			0.934988i	0.883996	+	0.467494i	$0.154843\pi$
$433$			19.4558i			0.934988i	−0.883996	+	0.467494i	$0.845157\pi$
$434$	−12.8307	−	1.89949i	−0.615894	−	0.0911787i
$435$		0			0
$436$	−9.24264	−	2.79793i	−0.442642	−	0.133997i
$437$	44.2843			2.11840
$438$		0			0
$439$		−	8.87385i		−	0.423526i	−0.977321	−	0.211763i	$-0.932080\pi$
$439$		−	8.87385i		−	0.423526i	0.977321	−	0.211763i	$-0.0679204\pi$
$440$		0			0
$441$		0			0
$442$	3.27798	+	0.485281i	0.155918	+	0.0230825i
$443$			1.92020i			0.0912313i	0.998959	+	0.0456157i	$0.0145250\pi$
$443$			1.92020i			0.0912313i	−0.998959	+	0.0456157i	$0.985475\pi$
$444$		0			0
$445$		0			0
$446$	3.33622	−	22.5355i	0.157975	−	1.06709i
$447$		0			0
$448$	8.33556	+	10.1213i	0.393818	+	0.478187i
$449$		−	9.21320i		−	0.434798i	−0.976083	−	0.217399i	$-0.930243\pi$
$449$		−	9.21320i		−	0.434798i	0.976083	−	0.217399i	$-0.0697573\pi$
$450$		0			0
$451$		−	5.59587i		−	0.263499i
$452$	23.8995	+	7.23486i	1.12414	+	0.340299i
$453$		0			0
$454$	−22.1421	−	3.27798i	−1.03918	−	0.153843i
$455$		0			0
$456$		0			0
$457$			11.4558i			0.535882i	0.963435	+	0.267941i	$0.0863432\pi$
$457$			11.4558i			0.535882i	−0.963435	+	0.267941i	$0.913657\pi$
$458$	0.272078	−	1.83783i	0.0127134	−	0.0858763i
$459$		0			0
$460$		0			0
$461$			33.7990i			1.57418i	0.616841	+	0.787088i	$0.288412\pi$
$461$			33.7990i			1.57418i	−0.616841	+	0.787088i	$0.711588\pi$
$462$		0			0
$463$	31.9362			1.48420			0.742101	−	0.670289i	$-0.233830\pi$
$463$	31.9362			1.48420			0.742101	+	0.670289i	$0.233830\pi$
$464$	−16.9864	+	25.4853i	−0.788576	+	1.18312i
$465$		0			0
$466$	−0.828427	+	5.59587i	−0.0383761	+	0.259223i
$467$			33.0128i			1.52765i	0.645424	+	0.763825i	$0.276681\pi$
$467$			33.0128i			1.52765i	−0.645424	+	0.763825i	$0.723319\pi$
$468$		0			0
$469$	−18.3431			−0.847008
$470$		0			0
$471$		0			0
$472$	14.3291	−	30.3640i	0.659551	−	1.39761i
$473$	31.3137			1.43981
$474$		0			0
$475$		0			0
$476$	12.5495	+	3.79899i	0.575206	+	0.174126i
$477$		0			0
$478$	−0.281206	+	1.89949i	−0.0128621	+	0.0868809i
$479$	1.92020			0.0877361			0.0438680	−	0.999037i	$-0.486032\pi$
$479$	1.92020			0.0877361			0.0438680	+	0.999037i	$0.486032\pi$
$480$		0			0
$481$	−5.31371			−0.242284
$482$	4.34315	−	29.3371i	0.197825	−	1.33627i
$483$		0			0
$484$	−8.91421	−	2.69851i	−0.405192	−	0.122660i
$485$		0			0
$486$		0			0
$487$	1.63899			0.0742698			0.0371349	−	0.999310i	$-0.488177\pi$
$487$	1.63899			0.0742698			0.0371349	+	0.999310i	$0.488177\pi$
$488$	1.00000	−	2.11904i	0.0452679	−	0.0959244i
$489$		0			0
$490$		0			0
$491$	27.6981			1.25000			0.624999	−	0.780625i	$-0.285099\pi$
$491$	27.6981			1.25000			0.624999	+	0.780625i	$0.285099\pi$
$492$		0			0
$493$			30.6274i			1.37939i
$494$	−0.960099	+	6.48528i	−0.0431969	+	0.291787i
$495$		0			0
$496$	−12.4142	+	18.6254i	−0.557415	+	0.836306i
$497$	−7.59798			−0.340816
$498$		0			0
$499$			9.83395i			0.440228i	0.975474	+	0.220114i	$0.0706429\pi$
$499$			9.83395i			0.440228i	−0.975474	+	0.220114i	$0.929357\pi$
$500$		0			0
$501$		0			0
$502$	1.49839	−	10.1213i	0.0668763	−	0.451737i
$503$		−	25.6614i		−	1.14419i	−0.820188	−	0.572094i	$-0.806131\pi$
$503$		−	25.6614i		−	1.14419i	0.820188	−	0.572094i	$-0.193869\pi$
$504$		0			0
$505$		0			0
$506$	30.9761	+	4.58579i	1.37706	+	0.203863i
$507$		0			0
$508$	3.13738	+	0.949747i	0.139199	+	0.0421382i
$509$		−	11.8579i		−	0.525591i	−0.964852	−	0.262795i	$-0.915356\pi$
$509$		−	11.8579i		−	0.525591i	0.964852	−	0.262795i	$-0.0846444\pi$
$510$		0			0
$511$		−	14.4697i		−	0.640102i
$512$	21.9350	−	5.55468i	0.969400	−	0.245485i
$513$		0			0
$514$	−4.58579	+	30.9761i	−0.202270	+	1.36630i
$515$		0			0
$516$		0			0
$517$			12.9706i			0.570445i
$518$	−20.7990	−	3.07914i	−0.913855	−	0.135290i
$519$		0			0
$520$		0			0
$521$		−	13.4142i		−	0.587687i	−0.955853	−	0.293844i	$-0.905065\pi$
$521$		−	13.4142i		−	0.587687i	0.955853	−	0.293844i	$-0.0949345\pi$
$522$		0			0
$523$	30.2972			1.32480			0.662402	−	0.749148i	$-0.269537\pi$
$523$	30.2972			1.32480			0.662402	+	0.749148i	$0.269537\pi$
$524$	1.29954	+	0.393398i	0.0567709	+	0.0171857i
$525$		0			0
$526$	29.9706	+	4.43692i	1.30678	+	0.193459i
$527$			22.3835i			0.975039i
$528$		0			0
$529$	−8.31371			−0.361466
$530$		0			0
$531$		0			0
$532$	−7.51606	+	24.8284i	−0.325863	+	1.07645i
$533$	−0.828427			−0.0358832
$534$		0			0
$535$		0			0
$536$	−13.5096	+	28.6274i	−0.583526	+	1.23652i
$537$		0			0
$538$	2.79793	+	0.414214i	0.120627	+	0.0178580i
$539$	17.0688			0.735205
$540$		0			0
$541$	8.14214			0.350058			0.175029	−	0.984563i	$-0.443998\pi$
$541$	8.14214			0.350058			0.175029	+	0.984563i	$0.443998\pi$
$542$	3.24264	+	0.480049i	0.139283	+	0.0206199i
$543$		0			0
$544$	15.1716	−	16.7876i	0.650476	−	0.719762i
$545$		0			0
$546$		0			0
$547$	−12.5495			−0.536579			−0.268289	−	0.963338i	$-0.586458\pi$
$547$	−12.5495			−0.536579			−0.268289	+	0.963338i	$0.586458\pi$
$548$	27.0711	+	8.19496i	1.15642	+	0.350071i
$549$		0			0
$550$		0			0
$551$	−60.5944			−2.58141
$552$		0			0
$553$		−	16.7696i		−	0.713114i
$554$	19.9250	+	2.94975i	0.846531	+	0.125323i
$555$		0			0
$556$	1.34315	−	4.43692i	0.0569621	−	0.188167i
$557$	39.1127			1.65726			0.828629	−	0.559798i	$-0.189121\pi$
$557$	39.1127			1.65726			0.828629	+	0.559798i	$0.189121\pi$
$558$		0			0
$559$		−	4.63577i		−	0.196072i
$560$		0			0
$561$		0			0
$562$	14.5280	+	2.15076i	0.612825	+	0.0907242i
$563$			4.63577i			0.195374i	0.995217	+	0.0976871i	$0.0311444\pi$
$563$			4.63577i			0.195374i	−0.995217	+	0.0976871i	$0.968856\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−5.59587	+	11.8579i	−0.234797	+	0.497545i
$569$		−	9.89949i		−	0.415008i	−0.978234	−	0.207504i	$-0.933466\pi$
$569$		−	9.89949i		−	0.415008i	0.978234	−	0.207504i	$-0.0665341\pi$
$570$		0			0
$571$		−	12.5495i		−	0.525181i	−0.964907	−	0.262590i	$-0.915423\pi$
$571$		−	12.5495i		−	0.525181i	0.964907	−	0.262590i	$-0.0845768\pi$
$572$	−1.34315	+	4.43692i	−0.0561597	+	0.185517i
$573$		0			0
$574$	−3.24264	−	0.480049i	−0.135345	−	0.0200369i
$575$		0			0
$576$		0			0
$577$			1.79899i			0.0748929i	0.999299	+	0.0374465i	$0.0119224\pi$
$577$			1.79899i			0.0748929i	−0.999299	+	0.0374465i	$0.988078\pi$
$578$	−0.207107	+	1.39897i	−0.00861451	+	0.0581893i
$579$		0			0
$580$		0			0
$581$			5.37258i			0.222892i
$582$		0			0
$583$	−20.4633			−0.847502
$584$	−22.5823	−	10.6569i	−0.934462	−	0.440984i
$585$		0			0
$586$	0.757359	−	5.11582i	0.0312862	−	0.211332i
$587$		−	32.2174i		−	1.32975i	−0.746953	−	0.664877i	$-0.768484\pi$
$587$		−	32.2174i		−	1.32975i	0.746953	−	0.664877i	$-0.231516\pi$
$588$		0			0
$589$	−44.2843			−1.82470
$590$		0			0
$591$		0			0
$592$	−20.1238	+	30.1924i	−0.827084	+	1.24090i
$593$	−38.1421			−1.56631			−0.783155	−	0.621827i	$-0.786391\pi$
$593$	−38.1421			−1.56631			−0.783155	+	0.621827i	$0.786391\pi$
$594$		0			0
$595$		0			0
$596$	3.75803	−	12.4142i	0.153935	−	0.508506i
$597$		0			0
$598$	0.678892	−	4.58579i	0.0277620	−	0.187527i
$599$	23.7412			0.970041			0.485021	−	0.874503i	$-0.338812\pi$
$599$	23.7412			0.970041			0.485021	+	0.874503i	$0.338812\pi$
$600$		0			0
$601$	−7.31371			−0.298332			−0.149166	−	0.988812i	$-0.547659\pi$
$601$	−7.31371			−0.298332			−0.149166	+	0.988812i	$0.547659\pi$
$602$	2.68629	−	18.1454i	0.109485	−	0.739550i
$603$		0			0
$604$	−1.34315	+	4.43692i	−0.0546518	+	0.180536i
$605$		0			0
$606$		0			0
$607$	−43.1279			−1.75051			−0.875254	−	0.483663i	$-0.839306\pi$
$607$	−43.1279			−1.75051			−0.875254	+	0.483663i	$0.839306\pi$
$608$	33.2132	+	30.0160i	1.34697	+	1.21731i
$609$		0			0
$610$		0			0
$611$	1.92020			0.0776829
$612$		0			0
$613$			8.38478i			0.338658i	0.985560	+	0.169329i	$0.0541600\pi$
$613$			8.38478i			0.338658i	−0.985560	+	0.169329i	$0.945840\pi$
$614$	−1.35778	+	9.17157i	−0.0547957	+	0.370135i
$615$		0			0
$616$	−7.82843	+	16.5888i	−0.315416	+	0.668380i
$617$	−40.0000			−1.61034			−0.805170	−	0.593045i	$-0.797926\pi$
$617$	−40.0000			−1.61034			−0.805170	+	0.593045i	$0.797926\pi$
$618$		0			0
$619$			20.0656i			0.806504i	0.915089	+	0.403252i	$0.132120\pi$
$619$			20.0656i			0.806504i	−0.915089	+	0.403252i	$0.867880\pi$
$620$		0			0
$621$		0			0
$622$	5.31466	−	35.8995i	0.213098	−	1.43944i
$623$			8.87385i			0.355523i
$624$		0			0
$625$		0			0
$626$	−33.0951	−	4.89949i	−1.32275	−	0.195823i
$627$		0			0
$628$	1.01834	−	3.36396i	0.0406361	−	0.134237i
$629$			36.2843i			1.44675i
$630$		0			0
$631$			32.6151i			1.29839i	0.760624	+	0.649193i	$0.224893\pi$
$631$			32.6151i			1.29839i	−0.760624	+	0.649193i	$0.775107\pi$
$632$	−26.1716	−	12.3507i	−1.04105	−	0.491283i
$633$		0			0
$634$	5.58579	−	37.7309i	0.221840	−	1.49849i
$635$		0			0
$636$		0			0
$637$		−	2.52691i		−	0.100120i
$638$	−42.3848	−	6.27476i	−1.67803	−	0.248420i
$639$		0			0
$640$		0			0
$641$		−	2.10051i		−	0.0829650i	−0.999139	−	0.0414825i	$-0.986792\pi$
$641$		−	2.10051i		−	0.0829650i	0.999139	−	0.0414825i	$-0.0132081\pi$
$642$		0			0
$643$	12.5495			0.494905			0.247452	−	0.968900i	$-0.420407\pi$
$643$	12.5495			0.494905			0.247452	+	0.968900i	$0.420407\pi$
$644$	5.31466	−	17.5563i	0.209427	−	0.691817i
$645$		0			0
$646$	44.2843	+	6.55596i	1.74234	+	0.257941i
$647$		−	12.5495i		−	0.493372i	−0.969095	−	0.246686i	$-0.920658\pi$
$647$		−	12.5495i		−	0.493372i	0.969095	−	0.246686i	$-0.0793417\pi$
$648$		0			0
$649$	46.9706			1.84376
$650$		0			0
$651$		0			0
$652$	−15.1486	−	4.58579i	−0.593265	−	0.179593i
$653$	−12.3431			−0.483025			−0.241512	−	0.970398i	$-0.577643\pi$
$653$	−12.3431			−0.483025			−0.241512	+	0.970398i	$0.577643\pi$
$654$		0			0
$655$		0			0
$656$	−3.13738	+	4.70711i	−0.122494	+	0.183782i
$657$		0			0
$658$	7.51606	+	1.11270i	0.293007	+	0.0433775i
$659$	−47.3660			−1.84512			−0.922559	−	0.385856i	$-0.873906\pi$
$659$	−47.3660			−1.84512			−0.922559	+	0.385856i	$0.873906\pi$
$660$		0			0
$661$	9.51472			0.370080			0.185040	−	0.982731i	$-0.440759\pi$
$661$	9.51472			0.370080			0.185040	+	0.982731i	$0.440759\pi$
$662$	−17.5563	−	2.59909i	−0.682347	−	0.101016i
$663$		0			0
$664$	8.38478	+	3.95687i	0.325392	+	0.153557i
$665$		0			0
$666$		0			0
$667$	42.8467			1.65903
$668$	9.72792	−	32.1350i	0.376385	−	1.24334i
$669$		0			0
$670$		0			0
$671$	3.27798			0.126545
$672$		0			0
$673$		−	49.7990i		−	1.91961i	−0.280668	−	0.959805i	$-0.590556\pi$
$673$		−	49.7990i		−	1.91961i	0.280668	−	0.959805i	$-0.409444\pi$
$674$	−28.1782	−	4.17157i	−1.08538	−	0.160683i
$675$		0			0
$676$	−24.2279	−	7.33428i	−0.931843	−	0.282088i
$677$	−17.3137			−0.665420			−0.332710	−	0.943029i	$-0.607963\pi$
$677$	−17.3137			−0.665420			−0.332710	+	0.943029i	$0.607963\pi$
$678$		0			0
$679$			23.7412i			0.911105i
$680$		0			0
$681$		0			0
$682$	−30.9761	−	4.58579i	−1.18614	−	0.175599i
$683$		−	14.4697i		−	0.553668i	−0.960918	−	0.276834i	$-0.910715\pi$
$683$		−	14.4697i		−	0.553668i	0.960918	−	0.276834i	$-0.0892852\pi$
$684$		0			0
$685$		0			0
$686$	3.84039	−	25.9411i	0.146627	−	0.990437i
$687$		0			0
$688$	−26.3403	−	17.5563i	−1.00422	−	0.669330i
$689$			3.02944i			0.115412i
$690$		0			0
$691$			36.8532i			1.40196i	0.713181	+	0.700980i	$0.247254\pi$
$691$			36.8532i			1.40196i	−0.713181	+	0.700980i	$0.752746\pi$
$692$	−8.58579	−	2.59909i	−0.326383	−	0.0988026i
$693$		0			0
$694$	6.48528	+	0.960099i	0.246178	+	0.0364448i
$695$		0			0
$696$		0			0
$697$			5.65685i			0.214269i
$698$	−6.31371	+	42.6479i	−0.238977	+	1.61425i
$699$		0			0
$700$		0			0
$701$			4.14214i			0.156446i	0.996936	+	0.0782232i	$0.0249247\pi$
$701$			4.14214i			0.156446i	−0.996936	+	0.0782232i	$0.975075\pi$
$702$		0			0
$703$	−71.7862			−2.70747
$704$	20.1238	+	24.4350i	0.758445	+	0.920930i
$705$		0			0
$706$	−2.34315	+	15.8275i	−0.0881855	+	0.595676i
$707$			11.7541i			0.442060i
$708$		0			0
$709$	21.3137			0.800453			0.400227	−	0.916416i	$-0.368931\pi$
$709$	21.3137			0.800453			0.400227	+	0.916416i	$0.368931\pi$
$710$		0			0
$711$		0			0
$712$	13.8491	+	6.53553i	0.519015	+	0.244929i
$713$	31.3137			1.17271
$714$		0			0
$715$		0			0
$716$	−16.4481	−	4.97918i	−0.614696	−	0.186081i
$717$		0			0
$718$	3.95687	−	26.7279i	0.147669	−	0.997477i
$719$	−41.4889			−1.54728			−0.773638	−	0.633628i	$-0.781565\pi$
$719$	−41.4889			−1.54728			−0.773638	+	0.633628i	$0.781565\pi$
$720$		0			0
$721$	28.6274			1.06614
$722$	−9.03553	+	61.0333i	−0.336268	+	2.27142i
$723$		0			0
$724$	34.0711	+	10.3140i	1.26624	+	0.383317i
$725$		0			0
$726$		0			0
$727$	−8.19496			−0.303934			−0.151967	−	0.988386i	$-0.548561\pi$
$727$	−8.19496			−0.303934			−0.151967	+	0.988386i	$0.548561\pi$
$728$	2.45584	+	1.15894i	0.0910196	+	0.0429532i
$729$		0			0
$730$		0			0
$731$	−31.6550			−1.17080
$732$		0			0
$733$			18.9289i			0.699156i	0.936907	+	0.349578i	$0.113675\pi$
$733$			18.9289i			0.699156i	−0.936907	+	0.349578i	$0.886325\pi$
$734$	6.61420	−	44.6777i	0.244135	−	1.64908i
$735$		0			0
$736$	−23.4853	−	21.2245i	−0.865679	−	0.782346i
$737$	−44.2843			−1.63123
$738$		0			0
$739$			5.99355i			0.220476i	0.993905	+	0.110238i	$0.0351614\pi$
$739$			5.99355i			0.220476i	−0.993905	+	0.110238i	$0.964839\pi$
$740$		0			0
$741$		0			0
$742$	−1.75547	+	11.8579i	−0.0644453	+	0.435316i
$743$			34.9330i			1.28157i	0.767722	+	0.640783i	$0.221390\pi$
$743$			34.9330i			1.28157i	−0.767722	+	0.640783i	$0.778610\pi$
$744$		0			0
$745$		0			0
$746$	−21.5640	−	3.19239i	−0.789513	−	0.116882i
$747$		0			0
$748$	30.2972	+	9.17157i	1.10778	+	0.335346i
$749$		−	5.37258i		−	0.196310i
$750$		0			0
$751$			0.960099i			0.0350345i	0.999847	+	0.0175172i	$0.00557620\pi$
$751$			0.960099i			0.0350345i	−0.999847	+	0.0175172i	$0.994424\pi$
$752$	7.27208	−	10.9105i	0.265185	−	0.397866i
$753$		0			0
$754$	−0.928932	+	6.27476i	−0.0338297	+	0.228513i
$755$		0			0
$756$		0			0
$757$		−	6.04163i		−	0.219587i	−0.993954	−	0.109793i	$-0.964981\pi$
$757$		−	6.04163i		−	0.219587i	0.993954	−	0.109793i	$-0.0350189\pi$
$758$	−43.7279	−	6.47360i	−1.58827	−	0.235132i
$759$		0			0
$760$		0			0
$761$			14.3848i			0.521448i	0.965413	+	0.260724i	$0.0839612\pi$
$761$			14.3848i			0.521448i	−0.965413	+	0.260724i	$0.916039\pi$
$762$		0			0
$763$	−7.91375			−0.286497
$764$	36.5720	+	11.0711i	1.32313	+	0.400537i
$765$		0			0
$766$	4.58579	+	0.678892i	0.165691	+	0.0245294i
$767$		−	6.95365i		−	0.251082i
$768$		0			0
$769$	46.6274			1.68143			0.840714	−	0.541480i	$-0.182136\pi$
$769$	46.6274			1.68143			0.840714	+	0.541480i	$0.182136\pi$
$770$		0			0
$771$		0			0
$772$	−2.51673	+	8.31371i	−0.0905790	+	0.299217i
$773$	−14.2843			−0.513770			−0.256885	−	0.966442i	$-0.582696\pi$
$773$	−14.2843			−0.513770			−0.256885	+	0.966442i	$0.582696\pi$
$774$		0			0
$775$		0			0
$776$	37.0520	+	17.4853i	1.33009	+	0.627685i
$777$		0			0
$778$	54.5185	+	8.07107i	1.95458	+	0.289362i
$779$	−11.1917			−0.400985
$780$		0			0
$781$	−18.3431			−0.656369
$782$	−31.3137	−	4.63577i	−1.11978	−	0.165775i
$783$		0			0
$784$	−14.3579	−	9.56980i	−0.512781	−	0.341778i
$785$		0			0
$786$		0			0
$787$	−12.5495			−0.447342			−0.223671	−	0.974665i	$-0.571804\pi$
$787$	−12.5495			−0.447342			−0.223671	+	0.974665i	$0.571804\pi$
$788$	15.9706	+	4.83461i	0.568928	+	0.172226i
$789$		0			0
$790$		0			0
$791$	20.4633			0.727590
$792$		0			0
$793$		−	0.485281i		−	0.0172328i
$794$	26.4809	+	3.92031i	0.939773	+	0.139127i
$795$		0			0
$796$	2.45584	−	8.11259i	0.0870451	−	0.287543i
$797$	37.4558			1.32675			0.663377	−	0.748285i	$-0.269123\pi$
$797$	37.4558			1.32675			0.663377	+	0.748285i	$0.269123\pi$
$798$		0			0
$799$		−	13.1119i		−	0.463867i
$800$		0			0
$801$		0			0
$802$	−29.6766	−	4.39340i	−1.04792	−	0.155136i
$803$		−	34.9330i		−	1.23276i
$804$		0			0
$805$		0			0
$806$	−0.678892	+	4.58579i	−0.0239130	+	0.161527i
$807$		0			0
$808$	18.3442	+	8.65685i	0.645348	+	0.304547i
$809$		−	46.8701i		−	1.64786i	−0.566689	−	0.823932i	$-0.691776\pi$
$809$		−	46.8701i		−	1.64786i	0.566689	−	0.823932i	$-0.308224\pi$
$810$		0			0
$811$			27.4169i			0.962738i	0.876518	+	0.481369i	$0.159860\pi$
$811$			27.4169i			0.962738i	−0.876518	+	0.481369i	$0.840140\pi$
$812$	−7.27208	+	24.0225i	−0.255200	+	0.843023i
$813$		0			0
$814$	−50.2132	−	7.43370i	−1.75997	−	0.260551i
$815$		0			0
$816$		0			0
$817$		−	62.6274i		−	2.19106i
$818$	3.92893	−	26.5392i	0.137372	−	0.927921i
$819$		0			0
$820$		0			0
$821$		−	47.6569i		−	1.66324i	−0.555348	−	0.831618i	$-0.687415\pi$
$821$		−	47.6569i		−	1.66324i	0.555348	−	0.831618i	$-0.312585\pi$
$822$		0			0
$823$	3.55919			0.124066			0.0620328	−	0.998074i	$-0.480242\pi$
$823$	3.55919			0.124066			0.0620328	+	0.998074i	$0.480242\pi$
$824$	21.0839	−	44.6777i	0.734493	−	1.55642i
$825$		0			0
$826$	4.02944	−	27.2181i	0.140202	−	0.947038i
$827$			8.47616i			0.294745i	0.989081	+	0.147373i	$0.0470816\pi$
$827$			8.47616i			0.294745i	−0.989081	+	0.147373i	$0.952918\pi$
$828$		0			0
$829$	−21.1127			−0.733274			−0.366637	−	0.930364i	$-0.619491\pi$
$829$	−21.1127			−0.733274			−0.366637	+	0.930364i	$0.619491\pi$
$830$		0			0
$831$		0			0
$832$	3.61743	−	2.97918i	0.125412	−	0.103285i
$833$	−17.2548			−0.597845
$834$		0			0
$835$		0			0
$836$	−18.1454	+	59.9411i	−0.627571	+	2.07311i
$837$		0			0
$838$	6.41536	−	43.3345i	0.221615	−	1.49697i
$839$	−25.6614			−0.885931			−0.442966	−	0.896539i	$-0.646074\pi$
$839$	−25.6614			−0.885931			−0.442966	+	0.896539i	$0.646074\pi$
$840$		0			0
$841$	−29.6274			−1.02164
$842$	3.92893	−	26.5392i	0.135400	−	0.914600i
$843$		0			0
$844$	5.14214	−	16.9864i	0.177000	−	0.584697i
$845$		0			0
$846$		0			0
$847$	−7.63254			−0.262257
$848$	17.2132	+	11.4729i	0.591104	+	0.393982i
$849$		0			0
$850$		0			0
$851$	50.7605			1.74005
$852$		0			0
$853$			20.1005i			0.688228i	0.938928	+	0.344114i	$0.111821\pi$
$853$			20.1005i			0.688228i	−0.938928	+	0.344114i	$0.888179\pi$
$854$	0.281206	−	1.89949i	0.00962268	−	0.0649994i
$855$		0			0
$856$	−8.38478	−	3.95687i	−0.286586	−	0.135243i
$857$	−32.9706			−1.12625			−0.563126	−	0.826371i	$-0.690402\pi$
$857$	−32.9706			−1.12625			−0.563126	+	0.826371i	$0.690402\pi$
$858$		0			0
$859$			35.8931i			1.22466i	0.790604	+	0.612328i	$0.209767\pi$
$859$			35.8931i			1.22466i	−0.790604	+	0.612328i	$0.790233\pi$
$860$		0			0
$861$		0			0
$862$	4.35456	−	29.4142i	0.148317	−	1.00185i
$863$		−	19.5032i		−	0.663895i	−0.943298	−	0.331948i	$-0.892294\pi$
$863$		−	19.5032i		−	0.663895i	0.943298	−	0.331948i	$-0.107706\pi$
$864$		0			0
$865$		0			0
$866$	27.2181	+	4.02944i	0.924908	+	0.136926i
$867$		0			0
$868$	−5.31466	+	17.5563i	−0.180391	+	0.595901i
$869$		−	40.4853i		−	1.37337i
$870$		0			0
$871$			6.55596i			0.222140i
$872$	−5.82843	+	12.3507i	−0.197375	+	0.418247i
$873$		0			0
$874$	9.17157	−	61.9522i	0.310233	−	2.09556i
$875$		0			0
$876$		0			0
$877$		−	21.0711i		−	0.711519i	−0.934577	−	0.355760i	$-0.884222\pi$
$877$		−	21.0711i		−	0.711519i	0.934577	−	0.355760i	$-0.115778\pi$
$878$	−12.4142	−	1.83783i	−0.418959	−	0.0620239i
$879$		0			0
$880$		0			0
$881$			39.7574i			1.33946i	0.742605	+	0.669730i	$0.233590\pi$
$881$			39.7574i			1.33946i	−0.742605	+	0.669730i	$0.766410\pi$
$882$		0			0
$883$	−48.8403			−1.64361			−0.821803	−	0.569772i	$-0.807032\pi$
$883$	−48.8403			−1.64361			−0.821803	+	0.569772i	$0.807032\pi$
$884$	1.35778	−	4.48528i	0.0456672	−	0.150856i
$885$		0			0
$886$	2.68629	+	0.397686i	0.0902477	+	0.0133605i
$887$			10.2316i			0.343545i	0.985137	+	0.171772i	$0.0549493\pi$
$887$			10.2316i			0.343545i	−0.985137	+	0.171772i	$0.945051\pi$
$888$		0			0
$889$	2.68629			0.0900953
$890$		0			0
$891$		0			0
$892$	−30.8355	−	9.33452i	−1.03245	−	0.312543i
$893$	25.9411			0.868087
$894$		0			0
$895$		0			0
$896$	15.8857	−	9.56497i	0.530705	−	0.319543i
$897$		0			0
$898$	−12.8890	−	1.90812i	−0.430110	−	0.0636747i
$899$	−42.8467			−1.42902
$900$		0			0
$901$	20.6863			0.689160
$902$	−7.82843	−	1.15894i	−0.260658	−	0.0385885i
$903$		0			0
$904$	15.0711	−	31.9362i	0.501256	−	1.06218i
$905$		0			0
$906$		0			0
$907$	25.6614			0.852074			0.426037	−	0.904706i	$-0.359909\pi$
$907$	25.6614			0.852074			0.426037	+	0.904706i	$0.359909\pi$
$908$	−9.17157	+	30.2972i	−0.304369	+	1.00545i
$909$		0			0
$910$		0			0
$911$	−13.1119			−0.434418			−0.217209	−	0.976125i	$-0.569695\pi$
$911$	−13.1119			−0.434418			−0.217209	+	0.976125i	$0.569695\pi$
$912$		0			0
$913$			12.9706i			0.429263i
$914$	16.0263	+	2.37258i	0.530104	+	0.0784781i
$915$		0			0
$916$	−2.51472	−	0.761256i	−0.0830886	−	0.0251526i
$917$	1.11270			0.0367445
$918$		0			0
$919$			18.7078i			0.617113i	0.951206	+	0.308557i	$0.0998459\pi$
$919$			18.7078i			0.617113i	−0.951206	+	0.308557i	$0.900154\pi$
$920$		0			0
$921$		0			0
$922$	47.2836	+	7.00000i	1.55720	+	0.230533i
$923$			2.71557i			0.0893840i
$924$		0			0
$925$		0			0
$926$	6.61420	−	44.6777i	0.217356	−	1.46820i
$927$		0			0
$928$	32.1350	+	29.0416i	1.05488	+	0.953338i
$929$			4.04163i			0.132602i	0.997800	+	0.0663008i	$0.0211197\pi$
$929$			4.04163i			0.132602i	−0.997800	+	0.0663008i	$0.978880\pi$
$930$		0			0
$931$		−	34.1376i		−	1.11881i
$932$	7.65685	+	2.31788i	0.250809	+	0.0759248i
$933$		0			0
$934$	46.1838	+	6.83717i	1.51118	+	0.223719i
$935$		0			0
$936$		0			0
$937$			11.6569i			0.380813i	0.981705	+	0.190406i	$0.0609806\pi$
$937$			11.6569i			0.380813i	−0.981705	+	0.190406i	$0.939019\pi$
$938$	−3.79899	+	25.6614i	−0.124041	+	0.837876i
$939$		0			0
$940$		0			0
$941$			27.6569i			0.901588i	0.892628	+	0.450794i	$0.148859\pi$
$941$			27.6569i			0.901588i	−0.892628	+	0.450794i	$0.851141\pi$
$942$		0			0
$943$	7.91375			0.257707
$944$	−39.5105	−	26.3345i	−1.28596	−	0.857116i
$945$		0			0
$946$	6.48528	−	43.8068i	0.210855	−	1.42428i
$947$		−	17.7477i		−	0.576723i	−0.957522	−	0.288361i	$-0.906890\pi$
$947$		−	17.7477i		−	0.576723i	0.957522	−	0.288361i	$-0.0931104\pi$
$948$		0			0
$949$	−5.17157			−0.167876
$950$		0			0
$951$		0			0
$952$	7.91375	−	16.7696i	0.256486	−	0.543504i
$953$	−14.1421			−0.458109			−0.229054	−	0.973414i	$-0.573563\pi$
$953$	−14.1421			−0.458109			−0.229054	+	0.973414i	$0.573563\pi$
$954$		0			0
$955$		0			0
$956$	2.59909	+	0.786797i	0.0840606	+	0.0254468i
$957$		0			0
$958$	0.397686	−	2.68629i	0.0128486	−	0.0867901i
$959$	23.1788			0.748484
$960$		0			0
$961$	−0.313708			−0.0101196
$962$	−1.10051	+	7.43370i	−0.0354817	+	0.239672i
$963$		0			0
$964$	−40.1421	−	12.1518i	−1.29289	−	0.391384i
$965$		0			0
$966$		0			0
$967$	51.0417			1.64139			0.820695	−	0.571367i	$-0.193587\pi$
$967$	51.0417			1.64139			0.820695	+	0.571367i	$0.193587\pi$
$968$	−5.62132	+	11.9118i	−0.180676	+	0.382860i
$969$		0			0
$970$		0			0
$971$	−45.4458			−1.45843			−0.729213	−	0.684287i	$-0.760114\pi$
$971$	−45.4458			−1.45843			−0.729213	+	0.684287i	$0.760114\pi$
$972$		0			0
$973$		−	3.79899i		−	0.121790i
$974$	0.339446	−	2.29289i	0.0108766	−	0.0734690i
$975$		0			0
$976$	−2.75736	−	1.83783i	−0.0882609	−	0.0588276i
$977$	−21.6569			−0.692864			−0.346432	−	0.938075i	$-0.612607\pi$
$977$	−21.6569			−0.692864			−0.346432	+	0.938075i	$0.612607\pi$
$978$		0			0
$979$			21.4234i			0.684694i
$980$		0			0
$981$		0			0
$982$	5.73647	−	38.7487i	0.183058	−	1.23652i
$983$		−	41.4889i		−	1.32329i	−0.749816	−	0.661646i	$-0.769858\pi$
$983$		−	41.4889i		−	1.32329i	0.749816	−	0.661646i	$-0.230142\pi$
$984$		0			0
$985$		0			0
$986$	42.8467	+	6.34315i	1.36452	+	0.202007i
$987$		0			0
$988$	8.87385	+	2.68629i	0.282315	+	0.0854623i
$989$			44.2843i			1.40816i
$990$		0			0
$991$		−	18.1454i		−	0.576407i	−0.957569	−	0.288204i	$-0.906942\pi$
$991$		−	18.1454i		−	0.576407i	0.957569	−	0.288204i	$-0.0930580\pi$
$992$	23.4853	+	21.2245i	0.745658	+	0.673879i
$993$		0			0
$994$	−1.57359	+	10.6293i	−0.0499113	+	0.337141i
$995$		0			0
$996$		0			0
$997$			17.0711i			0.540646i	0.962770	+	0.270323i	$0.0871305\pi$
$997$			17.0711i			0.540646i	−0.962770	+	0.270323i	$0.912869\pi$
$998$	13.7574	+	2.03668i	0.435482	+	0.0644699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.h.b.899.5		8
3.2	odd	2		900.2.h.c.899.3		8
4.3	odd	2	inner	900.2.h.b.899.8		8
5.2	odd	4		180.2.e.a.71.8	yes	8
5.3	odd	4		900.2.e.d.251.1		8
5.4	even	2		900.2.h.c.899.4		8
12.11	even	2		900.2.h.c.899.2		8
15.2	even	4		180.2.e.a.71.1	✓	8
15.8	even	4		900.2.e.d.251.8		8
15.14	odd	2	inner	900.2.h.b.899.6		8
20.3	even	4		900.2.e.d.251.7		8
20.7	even	4		180.2.e.a.71.2	yes	8
20.19	odd	2		900.2.h.c.899.1		8
40.27	even	4		2880.2.h.e.1151.3		8
40.37	odd	4		2880.2.h.e.1151.2		8
60.23	odd	4		900.2.e.d.251.2		8
60.47	odd	4		180.2.e.a.71.7	yes	8
60.59	even	2	inner	900.2.h.b.899.7		8
120.77	even	4		2880.2.h.e.1151.6		8
120.107	odd	4		2880.2.h.e.1151.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.e.a.71.1	✓	8	15.2	even	4
180.2.e.a.71.2	yes	8	20.7	even	4
180.2.e.a.71.7	yes	8	60.47	odd	4
180.2.e.a.71.8	yes	8	5.2	odd	4
900.2.e.d.251.1		8	5.3	odd	4
900.2.e.d.251.2		8	60.23	odd	4
900.2.e.d.251.7		8	20.3	even	4
900.2.e.d.251.8		8	15.8	even	4
900.2.h.b.899.5		8	1.1	even	1	trivial
900.2.h.b.899.6		8	15.14	odd	2	inner
900.2.h.b.899.7		8	60.59	even	2	inner
900.2.h.b.899.8		8	4.3	odd	2	inner
900.2.h.c.899.1		8	20.19	odd	2
900.2.h.c.899.2		8	12.11	even	2
900.2.h.c.899.3		8	3.2	odd	2
900.2.h.c.899.4		8	5.4	even	2
2880.2.h.e.1151.2		8	40.37	odd	4
2880.2.h.e.1151.3		8	40.27	even	4
2880.2.h.e.1151.6		8	120.77	even	4
2880.2.h.e.1151.7		8	120.107	odd	4

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.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 1.39897i) q^{2} +(-1.91421 - 0.579471i) q^{4} -1.63899 q^{7} +(-1.20711 + 2.55791i) q^{8} +O(q^{10})\)	\(q+(0.207107 - 1.39897i) q^{2} +(-1.91421 - 0.579471i) q^{4} -1.63899 q^{7} +(-1.20711 + 2.55791i) q^{8} -3.95687 q^{11} +0.585786i q^{13} +(-0.339446 + 2.29289i) q^{14} +(3.32843 + 2.21846i) q^{16} +4.00000 q^{17} +7.91375i q^{19} +(-0.819496 + 5.53553i) q^{22} -5.59587i q^{23} +(0.819496 + 0.121320i) q^{26} +(3.13738 + 0.949747i) q^{28} +7.65685i q^{29} +5.59587i q^{31} +(3.79289 - 4.19690i) q^{32} +(0.828427 - 5.59587i) q^{34} +9.07107i q^{37} +(11.0711 + 1.63899i) q^{38} +1.41421i q^{41} -7.91375 q^{43} +(7.57430 + 2.29289i) q^{44} +(-7.82843 - 1.15894i) q^{46} -3.27798i q^{47} -4.31371 q^{49} +(0.339446 - 1.12132i) q^{52} +5.17157 q^{53} +(1.97844 - 4.19239i) q^{56} +(10.7117 + 1.58579i) q^{58} -11.8706 q^{59} -0.828427 q^{61} +(7.82843 + 1.15894i) q^{62} +(-5.08579 - 6.17534i) q^{64} +11.1917 q^{67} +(-7.65685 - 2.31788i) q^{68} +4.63577 q^{71} +8.82843i q^{73} +(12.6901 + 1.87868i) q^{74} +(4.58579 - 15.1486i) q^{76} +6.48528 q^{77} +10.2316i q^{79} +(1.97844 + 0.292893i) q^{82} -3.27798i q^{83} +(-1.63899 + 11.0711i) q^{86} +(4.77637 - 10.1213i) q^{88} -5.41421i q^{89} -0.960099i q^{91} +(-3.24264 + 10.7117i) q^{92} +(-4.58579 - 0.678892i) q^{94} -14.4853i q^{97} +(-0.893398 + 6.03473i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 4 q^{16} + 32 q^{17} + 36 q^{32} - 16 q^{34} + 32 q^{38} - 40 q^{46} + 56 q^{49} + 64 q^{53} + 16 q^{61} + 40 q^{62} - 52 q^{64} - 16 q^{68} + 48 q^{76} - 16 q^{77} + 8 q^{92} - 48 q^{94} - 92 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 4 * q^16 + 32 * q^17 + 36 * q^32 - 16 * q^34 + 32 * q^38 - 40 * q^46 + 56 * q^49 + 64 * q^53 + 16 * q^61 + 40 * q^62 - 52 * q^64 - 16 * q^68 + 48 * q^76 - 16 * q^77 + 8 * q^92 - 48 * q^94 - 92 * q^98

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