LMFDB - Embedded newform 900.2.h.c.899.6

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			899.6
Root			$0.500000 - 1.44392i$ of defining polynomial
Character	$\chi$	$=$	900.899
Dual form			900.2.h.c.899.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 - 0.736813i) q^{2} +(0.914214 - 1.77882i) q^{4} +5.03127 q^{7} +(-0.207107 - 2.82083i) q^{8} +O(q^{10})$	\(q+(1.20711 - 0.736813i) q^{2} +(0.914214 - 1.77882i) q^{4} +5.03127 q^{7} +(-0.207107 - 2.82083i) q^{8} +2.08402 q^{11} +3.41421i q^{13} +(6.07328 - 3.70711i) q^{14} +(-2.32843 - 3.25245i) q^{16} -4.00000 q^{17} +4.16804i q^{19} +(2.51564 - 1.53553i) q^{22} -2.94725i q^{23} +(2.51564 + 4.12132i) q^{26} +(4.59966 - 8.94975i) q^{28} +3.65685i q^{29} -2.94725i q^{31} +(-5.20711 - 2.21044i) q^{32} +(-4.82843 + 2.94725i) q^{34} -5.07107i q^{37} +(3.07107 + 5.03127i) q^{38} +1.41421i q^{41} -4.16804 q^{43} +(1.90524 - 3.70711i) q^{44} +(-2.17157 - 3.55765i) q^{46} -10.0625i q^{47} +18.3137 q^{49} +(6.07328 + 3.12132i) q^{52} -10.8284 q^{53} +(-1.04201 - 14.1924i) q^{56} +(2.69442 + 4.41421i) q^{58} +6.25206 q^{59} +4.82843 q^{61} +(-2.17157 - 3.55765i) q^{62} +(-7.91421 + 1.16843i) q^{64} -5.89450 q^{67} +(-3.65685 + 7.11529i) q^{68} -14.2306 q^{71} +3.17157i q^{73} +(-3.73643 - 6.12132i) q^{74} +(7.41421 + 3.81048i) q^{76} +10.4853 q^{77} +11.2833i q^{79} +(1.04201 + 1.70711i) q^{82} -10.0625i q^{83} +(-5.03127 + 3.07107i) q^{86} +(-0.431615 - 5.87868i) q^{88} +2.58579i q^{89} +17.1778i q^{91} +(-5.24264 - 2.69442i) q^{92} +(-7.41421 - 12.1466i) q^{94} +2.48528i q^{97} +(22.1066 - 13.4938i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.20711	−	0.736813i	0.853553	−	0.521005i
$2$	1.20711	−	0.736813i	0.853553	−	0.521005i
$3$		0			0
$3$		0			0
$4$	0.914214	−	1.77882i	0.457107	−	0.889412i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	5.03127			1.90164			0.950821	−	0.309740i	$-0.100242\pi$
$7$	5.03127			1.90164			0.950821	+	0.309740i	$0.100242\pi$
$8$	−0.207107	−	2.82083i	−0.0732233	−	0.997316i
$9$		0			0
$10$		0			0
$11$	2.08402			0.628356			0.314178	−	0.949364i	$-0.398271\pi$
$11$	2.08402			0.628356			0.314178	+	0.949364i	$0.398271\pi$
$12$		0			0
$13$			3.41421i			0.946932i	0.880812	+	0.473466i	$0.156997\pi$
$13$			3.41421i			0.946932i	−0.880812	+	0.473466i	$0.843003\pi$
$14$	6.07328	−	3.70711i	1.62315	−	0.990766i
$15$		0			0
$16$	−2.32843	−	3.25245i	−0.582107	−	0.813112i
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$			4.16804i			0.956215i	0.878301	+	0.478107i	$0.158677\pi$
$19$			4.16804i			0.956215i	−0.878301	+	0.478107i	$0.841323\pi$
$20$		0			0
$21$		0			0
$22$	2.51564	−	1.53553i	0.536336	−	0.327377i
$23$		−	2.94725i		−	0.614544i	−0.951622	−	0.307272i	$-0.900584\pi$
$23$		−	2.94725i		−	0.614544i	0.951622	−	0.307272i	$-0.0994162\pi$
$24$		0			0
$25$		0			0
$26$	2.51564	+	4.12132i	0.493357	+	0.808257i
$27$		0			0
$28$	4.59966	−	8.94975i	0.869254	−	1.69134i
$29$			3.65685i			0.679061i	0.940595	+	0.339530i	$0.110268\pi$
$29$			3.65685i			0.679061i	−0.940595	+	0.339530i	$0.889732\pi$
$30$		0			0
$31$		−	2.94725i		−	0.529342i	−0.964339	−	0.264671i	$-0.914737\pi$
$31$		−	2.94725i		−	0.529342i	0.964339	−	0.264671i	$-0.0852634\pi$
$32$	−5.20711	−	2.21044i	−0.920495	−	0.390754i
$33$		0			0
$34$	−4.82843	+	2.94725i	−0.828068	+	0.505449i
$35$		0			0
$36$		0			0
$37$		−	5.07107i		−	0.833678i	−0.908980	−	0.416839i	$-0.863138\pi$
$37$		−	5.07107i		−	0.833678i	0.908980	−	0.416839i	$-0.136862\pi$
$38$	3.07107	+	5.03127i	0.498193	+	0.816180i
$39$		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
$43$	−4.16804			−0.635621			−0.317810	−	0.948154i	$-0.602948\pi$
$43$	−4.16804			−0.635621			−0.317810	+	0.948154i	$0.602948\pi$
$44$	1.90524	−	3.70711i	0.287226	−	0.558867i
$45$		0			0
$46$	−2.17157	−	3.55765i	−0.320181	−	0.524546i
$47$		−	10.0625i		−	1.46777i	−0.679272	−	0.733887i	$-0.737704\pi$
$47$		−	10.0625i		−	1.46777i	0.679272	−	0.733887i	$-0.262296\pi$
$48$		0			0
$49$	18.3137			2.61624
$50$		0			0
$51$		0			0
$52$	6.07328	+	3.12132i	0.842213	+	0.432849i
$53$	−10.8284			−1.48740			−0.743699	−	0.668514i	$-0.766931\pi$
$53$	−10.8284			−1.48740			−0.743699	+	0.668514i	$0.766931\pi$
$54$		0			0
$55$		0			0
$56$	−1.04201	−	14.1924i	−0.139245	−	1.89654i
$57$		0			0
$58$	2.69442	+	4.41421i	0.353794	+	0.579615i
$59$	6.25206			0.813949			0.406975	−	0.913439i	$-0.366584\pi$
$59$	6.25206			0.813949			0.406975	+	0.913439i	$0.366584\pi$
$60$		0			0
$61$	4.82843			0.618217			0.309108	−	0.951027i	$-0.399969\pi$
$61$	4.82843			0.618217			0.309108	+	0.951027i	$0.399969\pi$
$62$	−2.17157	−	3.55765i	−0.275790	−	0.451822i
$63$		0			0
$64$	−7.91421	+	1.16843i	−0.989277	+	0.146053i
$65$		0			0
$66$		0			0
$67$	−5.89450			−0.720128			−0.360064	−	0.932928i	$-0.617245\pi$
$67$	−5.89450			−0.720128			−0.360064	+	0.932928i	$0.617245\pi$
$68$	−3.65685	+	7.11529i	−0.443459	+	0.862856i
$69$		0			0
$70$		0			0
$71$	−14.2306			−1.68886			−0.844430	−	0.535666i	$-0.820061\pi$
$71$	−14.2306			−1.68886			−0.844430	+	0.535666i	$0.820061\pi$
$72$		0			0
$73$			3.17157i			0.371205i	0.982625	+	0.185602i	$0.0594236\pi$
$73$			3.17157i			0.371205i	−0.982625	+	0.185602i	$0.940576\pi$
$74$	−3.73643	−	6.12132i	−0.434351	−	0.711589i
$75$		0			0
$76$	7.41421	+	3.81048i	0.850469	+	0.437092i
$77$	10.4853			1.19491
$78$		0			0
$79$			11.2833i			1.26947i	0.772728	+	0.634737i	$0.218892\pi$
$79$			11.2833i			1.26947i	−0.772728	+	0.634737i	$0.781108\pi$
$80$		0			0
$81$		0			0
$82$	1.04201	+	1.70711i	0.115071	+	0.188518i
$83$		−	10.0625i		−	1.10451i	−0.833676	−	0.552254i	$-0.813768\pi$
$83$		−	10.0625i		−	1.10451i	0.833676	−	0.552254i	$-0.186232\pi$
$84$		0			0
$85$		0			0
$86$	−5.03127	+	3.07107i	−0.542536	+	0.331162i
$87$		0			0
$88$	−0.431615	−	5.87868i	−0.0460103	−	0.626669i
$89$			2.58579i			0.274093i	0.990565	+	0.137046i	$0.0437609\pi$
$89$			2.58579i			0.274093i	−0.990565	+	0.137046i	$0.956239\pi$
$90$		0			0
$91$			17.1778i			1.80073i
$92$	−5.24264	−	2.69442i	−0.546583	−	0.280912i
$93$		0			0
$94$	−7.41421	−	12.1466i	−0.764718	−	1.25282i
$95$		0			0
$96$		0			0
$97$			2.48528i			0.252342i	0.992009	+	0.126171i	$0.0402688\pi$
$97$			2.48528i			0.252342i	−0.992009	+	0.126171i	$0.959731\pi$
$98$	22.1066	−	13.4938i	2.23310	−	1.36308i
$99$		0			0
$100$		0			0
$101$			12.8284i			1.27648i	0.769839	+	0.638238i	$0.220336\pi$
$101$			12.8284i			1.27648i	−0.769839	+	0.638238i	$0.779664\pi$
$102$		0			0
$103$	−3.30481			−0.325633			−0.162816	−	0.986656i	$-0.552058\pi$
$103$	−3.30481			−0.325633			−0.162816	+	0.986656i	$0.552058\pi$
$104$	9.63093	−	0.707107i	0.944390	−	0.0693375i
$105$		0			0
$106$	−13.0711	+	7.97852i	−1.26957	+	0.774943i
$107$			10.0625i			0.972783i	0.873741	+	0.486392i	$0.161687\pi$
$107$			10.0625i			0.972783i	−0.873741	+	0.486392i	$0.838313\pi$
$108$		0			0
$109$	−0.828427			−0.0793489			−0.0396745	−	0.999213i	$-0.512632\pi$
$109$	−0.828427			−0.0793489			−0.0396745	+	0.999213i	$0.512632\pi$
$110$		0			0
$111$		0			0
$112$	−11.7150	−	16.3640i	−1.10696	−	1.54625i
$113$	−4.48528			−0.421940			−0.210970	−	0.977493i	$-0.567662\pi$
$113$	−4.48528			−0.421940			−0.210970	+	0.977493i	$0.567662\pi$
$114$		0			0
$115$		0			0
$116$	6.50490	+	3.34315i	0.603965	+	0.310403i
$117$		0			0
$118$	7.54691	−	4.60660i	0.694749	−	0.424072i
$119$	−20.1251			−1.84486
$120$		0			0
$121$	−6.65685			−0.605169
$122$	5.82843	−	3.55765i	0.527681	−	0.322094i
$123$		0			0
$124$	−5.24264	−	2.69442i	−0.470803	−	0.241966i
$125$		0			0
$126$		0			0
$127$	5.03127			0.446453			0.223227	−	0.974767i	$-0.428341\pi$
$127$	5.03127			0.446453			0.223227	+	0.974767i	$0.428341\pi$
$128$	−8.69239	+	7.24171i	−0.768306	+	0.640083i
$129$		0			0
$130$		0			0
$131$	12.1466			1.06125			0.530625	−	0.847607i	$-0.321957\pi$
$131$	12.1466			1.06125			0.530625	+	0.847607i	$0.321957\pi$
$132$		0			0
$133$			20.9706i			1.81838i
$134$	−7.11529	+	4.34315i	−0.614668	+	0.375191i
$135$		0			0
$136$	0.828427	+	11.2833i	0.0710370	+	0.967538i
$137$	−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
$139$			7.11529i			0.603511i	0.953385	+	0.301756i	$0.0975727\pi$
$139$			7.11529i			0.603511i	−0.953385	+	0.301756i	$0.902427\pi$
$140$		0			0
$141$		0			0
$142$	−17.1778	+	10.4853i	−1.44153	+	0.879905i
$143$			7.11529i			0.595011i
$144$		0			0
$145$		0			0
$146$	2.33686	+	3.82843i	0.193400	+	0.316843i
$147$		0			0
$148$	−9.02054	−	4.63604i	−0.741483	−	0.381080i
$149$			10.4853i			0.858988i	0.903070	+	0.429494i	$0.141308\pi$
$149$			10.4853i			0.858988i	−0.903070	+	0.429494i	$0.858692\pi$
$150$		0			0
$151$		−	7.11529i		−	0.579034i	−0.957173	−	0.289517i	$-0.906505\pi$
$151$		−	7.11529i		−	0.579034i	0.957173	−	0.289517i	$-0.0934948\pi$
$152$	11.7574	−	0.863230i	0.953648	−	0.0700172i
$153$		0			0
$154$	12.6569	−	7.72569i	1.01992	−	0.622554i
$155$		0			0
$156$		0			0
$157$			10.2426i			0.817452i	0.912657	+	0.408726i	$0.134027\pi$
$157$			10.2426i			0.817452i	−0.912657	+	0.408726i	$0.865973\pi$
$158$	8.31371	+	13.6202i	0.661403	+	1.08356i
$159$		0			0
$160$		0			0
$161$		−	14.8284i		−	1.16864i
$162$		0			0
$163$	4.16804			0.326466			0.163233	−	0.986588i	$-0.447808\pi$
$163$	4.16804			0.326466			0.163233	+	0.986588i	$0.447808\pi$
$164$	2.51564	+	1.29289i	0.196438	+	0.100958i
$165$		0			0
$166$	−7.41421	−	12.1466i	−0.575455	−	0.942756i
$167$			8.84175i			0.684196i	0.939664	+	0.342098i	$0.111137\pi$
$167$			8.84175i			0.684196i	−0.939664	+	0.342098i	$0.888863\pi$
$168$		0			0
$169$	1.34315			0.103319
$170$		0			0
$171$		0			0
$172$	−3.81048	+	7.41421i	−0.290546	+	0.565328i
$173$	12.4853			0.949238			0.474619	−	0.880191i	$-0.342586\pi$
$173$	12.4853			0.949238			0.474619	+	0.880191i	$0.342586\pi$
$174$		0			0
$175$		0			0
$176$	−4.85249	−	6.77817i	−0.365770	−	0.510924i
$177$		0			0
$178$	1.90524	+	3.12132i	0.142804	+	0.233953i
$179$	−16.3146			−1.21941			−0.609706	−	0.792628i	$-0.708712\pi$
$179$	−16.3146			−1.21941			−0.609706	+	0.792628i	$0.708712\pi$
$180$		0			0
$181$	21.7990			1.62031			0.810153	−	0.586218i	$-0.199384\pi$
$181$	21.7990			1.62031			0.810153	+	0.586218i	$0.199384\pi$
$182$	12.6569	+	20.7355i	0.938188	+	1.53702i
$183$		0			0
$184$	−8.31371	+	0.610396i	−0.612895	+	0.0449990i
$185$		0			0
$186$		0			0
$187$	−8.33609			−0.609595
$188$	−17.8995	−	9.19932i	−1.30545	−	0.670929i
$189$		0			0
$190$		0			0
$191$	−1.72646			−0.124922			−0.0624611	−	0.998047i	$-0.519895\pi$
$191$	−1.72646			−0.124922			−0.0624611	+	0.998047i	$0.519895\pi$
$192$		0			0
$193$		−	15.6569i		−	1.12701i	−0.826114	−	0.563503i	$-0.809454\pi$
$193$		−	15.6569i		−	1.12701i	0.826114	−	0.563503i	$-0.190546\pi$
$194$	1.83119	+	3.00000i	0.131472	+	0.215387i
$195$		0			0
$196$	16.7426	−	32.5769i	1.19590	−	2.32692i
$197$	19.6569			1.40049			0.700246	−	0.713901i	$-0.253073\pi$
$197$	19.6569			1.40049			0.700246	+	0.713901i	$0.253073\pi$
$198$		0			0
$199$		−	27.2404i		−	1.93102i	−0.260366	−	0.965510i	$-0.583843\pi$
$199$		−	27.2404i		−	1.93102i	0.260366	−	0.965510i	$-0.416157\pi$
$200$		0			0
$201$		0			0
$202$	9.45215	+	15.4853i	0.665051	+	1.08954i
$203$			18.3986i			1.29133i
$204$		0			0
$205$		0			0
$206$	−3.98926	+	2.43503i	−0.277945	+	0.169656i
$207$		0			0
$208$	11.1046	−	7.94975i	0.769962	−	0.551216i
$209$			8.68629i			0.600843i
$210$		0			0
$211$		−	13.0098i		−	0.895631i	−0.894126	−	0.447816i	$-0.852202\pi$
$211$		−	13.0098i		−	0.895631i	0.894126	−	0.447816i	$-0.147798\pi$
$212$	−9.89949	+	19.2619i	−0.679900	+	1.32291i
$213$		0			0
$214$	7.41421	+	12.1466i	0.506825	+	0.830322i
$215$		0			0
$216$		0			0
$217$		−	14.8284i		−	1.00662i
$218$	−1.00000	+	0.610396i	−0.0677285	+	0.0413412i
$219$		0			0
$220$		0			0
$221$		−	13.6569i		−	0.918659i
$222$		0			0
$223$	−20.9883			−1.40548			−0.702741	−	0.711446i	$-0.748041\pi$
$223$	−20.9883			−1.40548			−0.702741	+	0.711446i	$0.748041\pi$
$224$	−26.1984	−	11.1213i	−1.75045	−	0.743074i
$225$		0			0
$226$	−5.41421	+	3.30481i	−0.360148	+	0.219833i
$227$			8.33609i			0.553285i	0.960973	+	0.276643i	$0.0892219\pi$
$227$			8.33609i			0.553285i	−0.960973	+	0.276643i	$0.910778\pi$
$228$		0			0
$229$	−21.3137			−1.40845			−0.704225	−	0.709977i	$-0.748705\pi$
$229$	−21.3137			−1.40845			−0.704225	+	0.709977i	$0.748705\pi$
$230$		0			0
$231$		0			0
$232$	10.3154	−	0.757359i	0.677238	−	0.0497231i
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$		0			0
$235$		0			0
$236$	5.71572	−	11.1213i	0.372062	−	0.723936i
$237$		0			0
$238$	−24.2931	+	14.8284i	−1.57469	+	0.961184i
$239$	24.2931			1.57139			0.785696	−	0.618613i	$-0.212305\pi$
$239$	24.2931			1.57139			0.785696	+	0.618613i	$0.212305\pi$
$240$		0			0
$241$	−12.9706			−0.835507			−0.417754	−	0.908560i	$-0.637183\pi$
$241$	−12.9706			−0.835507			−0.417754	+	0.908560i	$0.637183\pi$
$242$	−8.03553	+	4.90486i	−0.516544	+	0.315296i
$243$		0			0
$244$	4.41421	−	8.58892i	0.282591	−	0.549849i
$245$		0			0
$246$		0			0
$247$	−14.2306			−0.905471
$248$	−8.31371	+	0.610396i	−0.527921	+	0.0387602i
$249$		0			0
$250$		0			0
$251$	7.97852			0.503600			0.251800	−	0.967779i	$-0.418977\pi$
$251$	7.97852			0.503600			0.251800	+	0.967779i	$0.418977\pi$
$252$		0			0
$253$		−	6.14214i		−	0.386153i
$254$	6.07328	−	3.70711i	0.381072	−	0.232605i
$255$		0			0
$256$	−5.15685	+	15.1462i	−0.322303	+	0.946636i
$257$	−6.14214			−0.383136			−0.191568	−	0.981479i	$-0.561357\pi$
$257$	−6.14214			−0.383136			−0.191568	+	0.981479i	$0.561357\pi$
$258$		0			0
$259$		−	25.5139i		−	1.58536i
$260$		0			0
$261$		0			0
$262$	14.6622	−	8.94975i	0.905834	−	0.552917i
$263$		−	5.38883i		−	0.332290i	−0.986101	−	0.166145i	$-0.946868\pi$
$263$		−	5.38883i		−	0.332290i	0.986101	−	0.166145i	$-0.0531319\pi$
$264$		0			0
$265$		0			0
$266$	15.4514	+	25.3137i	0.947385	+	1.55208i
$267$		0			0
$268$	−5.38883	+	10.4853i	−0.329175	+	0.640490i
$269$		−	2.00000i		−	0.121942i	−0.998140	−	0.0609711i	$-0.980580\pi$
$269$		−	2.00000i		−	0.121942i	0.998140	−	0.0609711i	$-0.0194197\pi$
$270$		0			0
$271$			7.11529i			0.432223i	0.976369	+	0.216112i	$0.0693375\pi$
$271$			7.11529i			0.432223i	−0.976369	+	0.216112i	$0.930662\pi$
$272$	9.31371	+	13.0098i	0.564727	+	0.788835i
$273$		0			0
$274$	−17.0711	+	10.4201i	−1.03130	+	0.629502i
$275$		0			0
$276$		0			0
$277$			5.75736i			0.345926i	0.984928	+	0.172963i	$0.0553341\pi$
$277$			5.75736i			0.345926i	−0.984928	+	0.172963i	$0.944666\pi$
$278$	5.24264	+	8.58892i	0.314433	+	0.515129i
$279$		0			0
$280$		0			0
$281$			26.3848i			1.57398i	0.616963	+	0.786992i	$0.288363\pi$
$281$			26.3848i			1.57398i	−0.616963	+	0.786992i	$0.711637\pi$
$282$		0			0
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−13.0098	+	25.3137i	−0.771989	+	1.50209i
$285$		0			0
$286$	5.24264	+	8.58892i	0.310004	+	0.507874i
$287$			7.11529i			0.420003i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$	5.64167	+	2.89949i	0.330154	+	0.169680i
$293$	7.65685			0.447318			0.223659	−	0.974667i	$-0.428200\pi$
$293$	7.65685			0.447318			0.223659	+	0.974667i	$0.428200\pi$
$294$		0			0
$295$		0			0
$296$	−14.3046	+	1.05025i	−0.831440	+	0.0610447i
$297$		0			0
$298$	7.72569	+	12.6569i	0.447537	+	0.733192i
$299$	10.0625			0.581932
$300$		0			0
$301$	−20.9706			−1.20872
$302$	−5.24264	−	8.58892i	−0.301680	−	0.494237i
$303$		0			0
$304$	13.5563	−	9.70498i	0.777510	−	0.556619i
$305$		0			0
$306$		0			0
$307$	20.1251			1.14860			0.574300	−	0.818645i	$-0.305274\pi$
$307$	20.1251			1.14860			0.574300	+	0.818645i	$0.305274\pi$
$308$	9.58579	−	18.6515i	0.546201	−	1.06277i
$309$		0			0
$310$		0			0
$311$	21.8516			1.23909			0.619544	−	0.784962i	$-0.287318\pi$
$311$	21.8516			1.23909			0.619544	+	0.784962i	$0.287318\pi$
$312$		0			0
$313$		−	12.3431i		−	0.697676i	−0.937183	−	0.348838i	$-0.886576\pi$
$313$		−	12.3431i		−	0.697676i	0.937183	−	0.348838i	$-0.113424\pi$
$314$	7.54691	+	12.3640i	0.425897	+	0.697739i
$315$		0			0
$316$	20.0711	+	10.3154i	1.12909	+	0.580285i
$317$	6.97056			0.391506			0.195753	−	0.980653i	$-0.437285\pi$
$317$	6.97056			0.391506			0.195753	+	0.980653i	$0.437285\pi$
$318$		0			0
$319$			7.62096i			0.426692i
$320$		0			0
$321$		0			0
$322$	−10.9258	−	17.8995i	−0.608870	−	0.997500i
$323$		−	16.6722i		−	0.927664i
$324$		0			0
$325$		0			0
$326$	5.03127	−	3.07107i	0.278656	−	0.170091i
$327$		0			0
$328$	3.98926	−	0.292893i	0.220270	−	0.0161723i
$329$		−	50.6274i		−	2.79118i
$330$		0			0
$331$		−	18.3986i		−	1.01128i	−0.862744	−	0.505640i	$-0.831256\pi$
$331$		−	18.3986i		−	1.01128i	0.862744	−	0.505640i	$-0.168744\pi$
$332$	−17.8995	−	9.19932i	−0.982362	−	0.504878i
$333$		0			0
$334$	6.51472	+	10.6729i	0.356470	+	0.583997i
$335$		0			0
$336$		0			0
$337$			8.14214i			0.443530i	0.975100	+	0.221765i	$0.0711818\pi$
$337$			8.14214i			0.443530i	−0.975100	+	0.221765i	$0.928818\pi$
$338$	1.62132	−	0.989647i	0.0881882	−	0.0538297i
$339$		0			0
$340$		0			0
$341$		−	6.14214i		−	0.332615i
$342$		0			0
$343$	56.9224			3.07352
$344$	0.863230	+	11.7574i	0.0465422	+	0.633914i
$345$		0			0
$346$	15.0711	−	9.19932i	0.810226	−	0.494558i
$347$		−	14.2306i		−	0.763938i	−0.924175	−	0.381969i	$-0.875246\pi$
$347$		−	14.2306i		−	0.763938i	0.924175	−	0.381969i	$-0.124754\pi$
$348$		0			0
$349$	−13.5147			−0.723426			−0.361713	−	0.932289i	$-0.617808\pi$
$349$	−13.5147			−0.723426			−0.361713	+	0.932289i	$0.617808\pi$
$350$		0			0
$351$		0			0
$352$	−10.8517	−	4.60660i	−0.578399	−	0.245533i
$353$	−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
$356$	4.59966	+	2.36396i	0.243781	+	0.125290i
$357$		0			0
$358$	−19.6935	+	12.0208i	−1.04083	+	0.635320i
$359$	1.72646			0.0911191			0.0455595	−	0.998962i	$-0.485493\pi$
$359$	1.72646			0.0911191			0.0455595	+	0.998962i	$0.485493\pi$
$360$		0			0
$361$	1.62742			0.0856535
$362$	26.3137	−	16.0618i	1.38302	−	0.844188i
$363$		0			0
$364$	30.5563	+	15.7042i	1.60159	+	0.823125i
$365$		0			0
$366$		0			0
$367$	−12.6522			−0.660441			−0.330221	−	0.943904i	$-0.607123\pi$
$367$	−12.6522			−0.660441			−0.330221	+	0.943904i	$0.607123\pi$
$368$	−9.58579	+	6.86246i	−0.499694	+	0.357730i
$369$		0			0
$370$		0			0
$371$	−54.4808			−2.82850
$372$		0			0
$373$		−	12.5858i		−	0.651667i	−0.945427	−	0.325834i	$-0.894355\pi$
$373$		−	12.5858i		−	0.651667i	0.945427	−	0.325834i	$-0.105645\pi$
$374$	−10.0625	+	6.14214i	−0.520322	+	0.317602i
$375$		0			0
$376$	−28.3848	+	2.08402i	−1.46383	+	0.107475i
$377$	−12.4853			−0.643025
$378$		0			0
$379$			24.7988i			1.27383i	0.770934	+	0.636914i	$0.219790\pi$
$379$			24.7988i			1.27383i	−0.770934	+	0.636914i	$0.780210\pi$
$380$		0			0
$381$		0			0
$382$	−2.08402	+	1.27208i	−0.106628	+	0.0650852i
$383$			10.0625i			0.514172i	0.966389	+	0.257086i	$0.0827624\pi$
$383$			10.0625i			0.514172i	−0.966389	+	0.257086i	$0.917238\pi$
$384$		0			0
$385$		0			0
$386$	−11.5362	−	18.8995i	−0.587176	−	0.961959i
$387$		0			0
$388$	4.42088	+	2.27208i	0.224436	+	0.115347i
$389$		−	5.02944i		−	0.255003i	−0.991838	−	0.127501i	$-0.959304\pi$
$389$		−	5.02944i		−	0.255003i	0.991838	−	0.127501i	$-0.0406957\pi$
$390$		0			0
$391$			11.7890i			0.596196i
$392$	−3.79289	−	51.6599i	−0.191570	−	2.60922i
$393$		0			0
$394$	23.7279	−	14.4834i	1.19540	−	0.729664i
$395$		0			0
$396$		0			0
$397$			33.0711i			1.65979i	0.557920	+	0.829895i	$0.311600\pi$
$397$			33.0711i			1.65979i	−0.557920	+	0.829895i	$0.688400\pi$
$398$	−20.0711	−	32.8821i	−1.00607	−	1.64823i
$399$		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
$403$	10.0625			0.501251
$404$	22.8195	+	11.7279i	1.13531	+	0.583486i
$405$		0			0
$406$	13.5563	+	22.2091i	0.672790	+	1.10222i
$407$		−	10.5682i		−	0.523847i
$408$		0			0
$409$	−14.9706			−0.740247			−0.370123	−	0.928983i	$-0.620685\pi$
$409$	−14.9706			−0.740247			−0.370123	+	0.928983i	$0.620685\pi$
$410$		0			0
$411$		0			0
$412$	−3.02130	+	5.87868i	−0.148849	+	0.289622i
$413$	31.4558			1.54784
$414$		0			0
$415$		0			0
$416$	7.54691	−	17.7782i	0.370018	−	0.871647i
$417$		0			0
$418$	6.40017	+	10.4853i	0.313043	+	0.512852i
$419$	−4.52560			−0.221090			−0.110545	−	0.993871i	$-0.535260\pi$
$419$	−4.52560			−0.221090			−0.110545	+	0.993871i	$0.535260\pi$
$420$		0			0
$421$	−14.9706			−0.729621			−0.364810	−	0.931082i	$-0.618866\pi$
$421$	−14.9706			−0.729621			−0.364810	+	0.931082i	$0.618866\pi$
$422$	−9.58579	−	15.7042i	−0.466629	−	0.764469i
$423$		0			0
$424$	2.24264	+	30.5452i	0.108912	+	1.48341i
$425$		0			0
$426$		0			0
$427$	24.2931			1.17563
$428$	17.8995	+	9.19932i	0.865205	+	0.444666i
$429$		0			0
$430$		0			0
$431$	36.0821			1.73802			0.869008	−	0.494798i	$-0.164758\pi$
$431$	36.0821			1.73802			0.869008	+	0.494798i	$0.164758\pi$
$432$		0			0
$433$		−	31.4558i		−	1.51167i	−0.654761	−	0.755836i	$-0.727231\pi$
$433$		−	31.4558i		−	1.51167i	0.654761	−	0.755836i	$-0.272769\pi$
$434$	−10.9258	−	17.8995i	−0.524454	−	0.859203i
$435$		0			0
$436$	−0.757359	+	1.47363i	−0.0362709	+	0.0705739i
$437$	12.2843			0.587636
$438$		0			0
$439$			13.0098i			0.620924i	0.950586	+	0.310462i	$0.100484\pi$
$439$			13.0098i			0.620924i	−0.950586	+	0.310462i	$0.899516\pi$
$440$		0			0
$441$		0			0
$442$	−10.0625	−	16.4853i	−0.478627	−	0.784125i
$443$			34.3557i			1.63229i	0.577849	+	0.816144i	$0.303892\pi$
$443$			34.3557i			1.63229i	−0.577849	+	0.816144i	$0.696108\pi$
$444$		0			0
$445$		0			0
$446$	−25.3351	+	15.4645i	−1.19965	+	0.732264i
$447$		0			0
$448$	−39.8186	+	5.87868i	−1.88125	+	0.277742i
$449$		−	33.2132i		−	1.56743i	−0.621122	−	0.783714i	$-0.713323\pi$
$449$		−	33.2132i		−	1.56743i	0.621122	−	0.783714i	$-0.286677\pi$
$450$		0			0
$451$			2.94725i			0.138781i
$452$	−4.10051	+	7.97852i	−0.192872	+	0.375278i
$453$		0			0
$454$	6.14214	+	10.0625i	0.288265	+	0.472259i
$455$		0			0
$456$		0			0
$457$		−	39.4558i		−	1.84567i	−0.385200	−	0.922833i	$-0.625867\pi$
$457$		−	39.4558i		−	1.84567i	0.385200	−	0.922833i	$-0.374133\pi$
$458$	−25.7279	+	15.7042i	−1.20219	+	0.733810i
$459$		0			0
$460$		0			0
$461$			5.79899i			0.270086i	0.990840	+	0.135043i	$0.0431172\pi$
$461$			5.79899i			0.270086i	−0.990840	+	0.135043i	$0.956883\pi$
$462$		0			0
$463$	−12.6522			−0.587999			−0.294000	−	0.955806i	$-0.594986\pi$
$463$	−12.6522			−0.587999			−0.294000	+	0.955806i	$0.594986\pi$
$464$	11.8937	−	8.51472i	0.552153	−	0.395286i
$465$		0			0
$466$	4.82843	−	2.94725i	0.223673	−	0.136529i
$467$		−	40.9653i		−	1.89565i	−0.318794	−	0.947824i	$-0.603278\pi$
$467$		−	40.9653i		−	1.89565i	0.318794	−	0.947824i	$-0.396722\pi$
$468$		0			0
$469$	−29.6569			−1.36943
$470$		0			0
$471$		0			0
$472$	−1.29484	−	17.6360i	−0.0596001	−	0.811764i
$473$	−8.68629			−0.399396
$474$		0			0
$475$		0			0
$476$	−18.3986	+	35.7990i	−0.843300	+	1.64084i
$477$		0			0
$478$	29.3244	−	17.8995i	1.34127	−	0.818704i
$479$	34.3557			1.56975			0.784876	−	0.619653i	$-0.212727\pi$
$479$	34.3557			1.56975			0.784876	+	0.619653i	$0.212727\pi$
$480$		0			0
$481$	17.3137			0.789437
$482$	−15.6569	+	9.55688i	−0.713150	+	0.435304i
$483$		0			0
$484$	−6.08579	+	11.8414i	−0.276627	+	0.538244i
$485$		0			0
$486$		0			0
$487$	−5.03127			−0.227989			−0.113994	−	0.993481i	$-0.536365\pi$
$487$	−5.03127			−0.227989			−0.113994	+	0.993481i	$0.536365\pi$
$488$	−1.00000	−	13.6202i	−0.0452679	−	0.616557i
$489$		0			0
$490$		0			0
$491$	−14.5882			−0.658354			−0.329177	−	0.944268i	$-0.606771\pi$
$491$	−14.5882			−0.658354			−0.329177	+	0.944268i	$0.606771\pi$
$492$		0			0
$493$		−	14.6274i		−	0.658786i
$494$	−17.1778	+	10.4853i	−0.772868	+	0.471755i
$495$		0			0
$496$	−9.58579	+	6.86246i	−0.430415	+	0.308134i
$497$	−71.5980			−3.21161
$498$		0			0
$499$		−	30.1876i		−	1.35138i	−0.737184	−	0.675692i	$-0.763845\pi$
$499$		−	30.1876i		−	1.35138i	0.737184	−	0.675692i	$-0.236155\pi$
$500$		0			0
$501$		0			0
$502$	9.63093	−	5.87868i	0.429849	−	0.262378i
$503$		−	21.8516i		−	0.974313i	−0.873315	−	0.487156i	$-0.838034\pi$
$503$		−	21.8516i		−	0.974313i	0.873315	−	0.487156i	$-0.161966\pi$
$504$		0			0
$505$		0			0
$506$	−4.52560	−	7.41421i	−0.201188	−	0.329602i
$507$		0			0
$508$	4.59966	−	8.94975i	0.204077	−	0.397081i
$509$			40.1421i			1.77927i	0.456673	+	0.889634i	$0.349041\pi$
$509$			40.1421i			1.77927i	−0.456673	+	0.889634i	$0.650959\pi$
$510$		0			0
$511$			15.9570i			0.705898i
$512$	4.93503	+	22.0827i	0.218100	+	0.975927i
$513$		0			0
$514$	−7.41421	+	4.52560i	−0.327027	+	0.199616i
$515$		0			0
$516$		0			0
$517$		−	20.9706i		−	0.922284i
$518$	−18.7990	−	30.7980i	−0.825980	−	1.35319i
$519$		0			0
$520$		0			0
$521$			10.5858i			0.463772i	0.972743	+	0.231886i	$0.0744896\pi$
$521$			10.5858i			0.463772i	−0.972743	+	0.231886i	$0.925510\pi$
$522$		0			0
$523$	−7.62096			−0.333241			−0.166621	−	0.986021i	$-0.553286\pi$
$523$	−7.62096			−0.333241			−0.166621	+	0.986021i	$0.553286\pi$
$524$	11.1046	−	21.6066i	0.485105	−	0.943889i
$525$		0			0
$526$	−3.97056	−	6.50490i	−0.173125	−	0.283627i
$527$			11.7890i			0.513537i
$528$		0			0
$529$	14.3137			0.622335
$530$		0			0
$531$		0			0
$532$	37.3029	+	19.1716i	1.61729	+	0.831193i
$533$	−4.82843			−0.209142
$534$		0			0
$535$		0			0
$536$	1.22079	+	16.6274i	0.0527302	+	0.718195i
$537$		0			0
$538$	−1.47363	−	2.41421i	−0.0635325	−	0.104084i
$539$	38.1662			1.64393
$540$		0			0
$541$	−20.1421			−0.865978			−0.432989	−	0.901399i	$-0.642541\pi$
$541$	−20.1421			−0.865978			−0.432989	+	0.901399i	$0.642541\pi$
$542$	5.24264	+	8.58892i	0.225191	+	0.368926i
$543$		0			0
$544$	20.8284	+	8.84175i	0.893011	+	0.379087i
$545$		0			0
$546$		0			0
$547$	−18.3986			−0.786669			−0.393334	−	0.919396i	$-0.628679\pi$
$547$	−18.3986			−0.786669			−0.393334	+	0.919396i	$0.628679\pi$
$548$	−12.9289	+	25.1564i	−0.552297	+	1.07463i
$549$		0			0
$550$		0			0
$551$	−15.2419			−0.649328
$552$		0			0
$553$			56.7696i			2.41409i
$554$	4.24210	+	6.94975i	0.180229	+	0.295266i
$555$		0			0
$556$	12.6569	+	6.50490i	0.536770	+	0.275869i
$557$	23.1127			0.979316			0.489658	−	0.871914i	$-0.337122\pi$
$557$	23.1127			0.979316			0.489658	+	0.871914i	$0.337122\pi$
$558$		0			0
$559$		−	14.2306i		−	0.601890i
$560$		0			0
$561$		0			0
$562$	19.4406	+	31.8492i	0.820054	+	1.34348i
$563$		−	14.2306i		−	0.599748i	−0.953979	−	0.299874i	$-0.903055\pi$
$563$		−	14.2306i		−	0.599748i	0.953979	−	0.299874i	$-0.0969446\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	2.94725	+	40.1421i	0.123664	+	1.68433i
$569$		−	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
$571$		−	18.3986i		−	0.769959i	−0.922925	−	0.384979i	$-0.874209\pi$
$571$		−	18.3986i		−	0.769959i	0.922925	−	0.384979i	$-0.125791\pi$
$572$	12.6569	+	6.50490i	0.529210	+	0.271983i
$573$		0			0
$574$	5.24264	+	8.58892i	0.218824	+	0.358495i
$575$		0			0
$576$		0			0
$577$		−	37.7990i		−	1.57359i	−0.617213	−	0.786796i	$-0.711738\pi$
$577$		−	37.7990i		−	1.57359i	0.617213	−	0.786796i	$-0.288262\pi$
$578$	−1.20711	+	0.736813i	−0.0502090	+	0.0306474i
$579$		0			0
$580$		0			0
$581$		−	50.6274i		−	2.10038i
$582$		0			0
$583$	−22.5667			−0.934616
$584$	8.94648	−	0.656854i	0.370208	−	0.0271808i
$585$		0			0
$586$	9.24264	−	5.64167i	0.381810	−	0.233055i
$587$		−	41.9766i		−	1.73256i	−0.499557	−	0.866281i	$-0.666504\pi$
$587$		−	41.9766i		−	1.73256i	0.499557	−	0.866281i	$-0.333496\pi$
$588$		0			0
$589$	12.2843			0.506165
$590$		0			0
$591$		0			0
$592$	−16.4934	+	11.8076i	−0.677874	+	0.485290i
$593$	9.85786			0.404814			0.202407	−	0.979301i	$-0.435124\pi$
$593$	9.85786			0.404814			0.202407	+	0.979301i	$0.435124\pi$
$594$		0			0
$595$		0			0
$596$	18.6515	+	9.58579i	0.763994	+	0.392649i
$597$		0			0
$598$	12.1466	−	7.41421i	0.496710	−	0.303190i
$599$	−12.5041			−0.510905			−0.255452	−	0.966822i	$-0.582224\pi$
$599$	−12.5041			−0.510905			−0.255452	+	0.966822i	$0.582224\pi$
$600$		0			0
$601$	15.3137			0.624659			0.312330	−	0.949974i	$-0.398891\pi$
$601$	15.3137			0.624659			0.312330	+	0.949974i	$0.398891\pi$
$602$	−25.3137	+	15.4514i	−1.03171	+	0.629751i
$603$		0			0
$604$	−12.6569	−	6.50490i	−0.515000	−	0.264681i
$605$		0			0
$606$		0			0
$607$	18.5467			0.752789			0.376394	−	0.926460i	$-0.377164\pi$
$607$	18.5467			0.752789			0.376394	+	0.926460i	$0.377164\pi$
$608$	9.21320	−	21.7034i	0.373645	−	0.880191i
$609$		0			0
$610$		0			0
$611$	34.3557			1.38988
$612$		0			0
$613$		−	28.3848i		−	1.14645i	−0.819398	−	0.573225i	$-0.805692\pi$
$613$		−	28.3848i		−	1.14645i	0.819398	−	0.573225i	$-0.194308\pi$
$614$	24.2931	−	14.8284i	0.980391	−	0.598427i
$615$		0			0
$616$	−2.17157	−	29.5772i	−0.0874952	−	1.19170i
$617$	40.0000			1.61034			0.805170	−	0.593045i	$-0.202074\pi$
$617$	40.0000			1.61034			0.805170	+	0.593045i	$0.202074\pi$
$618$		0			0
$619$		−	18.9043i		−	0.759828i	−0.925022	−	0.379914i	$-0.875954\pi$
$619$		−	18.9043i		−	0.759828i	0.925022	−	0.379914i	$-0.124046\pi$
$620$		0			0
$621$		0			0
$622$	26.3772	−	16.1005i	1.05763	−	0.645571i
$623$			13.0098i			0.521227i
$624$		0			0
$625$		0			0
$626$	−9.09459	−	14.8995i	−0.363493	−	0.595504i
$627$		0			0
$628$	18.2199	+	9.36396i	0.727051	+	0.373663i
$629$			20.2843i			0.808787i
$630$		0			0
$631$		−	0.505668i		−	0.0201303i	−0.999949	−	0.0100652i	$-0.996796\pi$
$631$		−	0.505668i		−	0.0201303i	0.999949	−	0.0100652i	$-0.00320390\pi$
$632$	31.8284	−	2.33686i	1.26607	−	0.0929551i
$633$		0			0
$634$	8.41421	−	5.13600i	0.334171	−	0.203977i
$635$		0			0
$636$		0			0
$637$			62.5269i			2.47741i
$638$	5.61522	+	9.19932i	0.222309	+	0.364204i
$639$		0			0
$640$		0			0
$641$			21.8995i			0.864978i	0.901639	+	0.432489i	$0.142365\pi$
$641$			21.8995i			0.864978i	−0.901639	+	0.432489i	$0.857635\pi$
$642$		0			0
$643$	18.3986			0.725571			0.362786	−	0.931873i	$-0.381826\pi$
$643$	18.3986			0.725571			0.362786	+	0.931873i	$0.381826\pi$
$644$	−26.3772	−	13.5563i	−1.03941	−	0.534195i
$645$		0			0
$646$	−12.2843	−	20.1251i	−0.483318	−	0.791811i
$647$			18.3986i			0.723325i	0.932309	+	0.361662i	$0.117791\pi$
$647$			18.3986i			0.723325i	−0.932309	+	0.361662i	$0.882209\pi$
$648$		0			0
$649$	13.0294			0.511450
$650$		0			0
$651$		0			0
$652$	3.81048	−	7.41421i	0.149230	−	0.290363i
$653$	23.6569			0.925764			0.462882	−	0.886420i	$-0.346815\pi$
$653$	23.6569			0.925764			0.462882	+	0.886420i	$0.346815\pi$
$654$		0			0
$655$		0			0
$656$	4.59966	−	3.29289i	0.179586	−	0.128566i
$657$		0			0
$658$	−37.3029	−	61.1127i	−1.45422	−	2.38242i
$659$	−45.7871			−1.78361			−0.891807	−	0.452417i	$-0.850562\pi$
$659$	−45.7871			−1.78361			−0.891807	+	0.452417i	$0.850562\pi$
$660$		0			0
$661$	26.4853			1.03016			0.515079	−	0.857143i	$-0.327763\pi$
$661$	26.4853			1.03016			0.515079	+	0.857143i	$0.327763\pi$
$662$	−13.5563	−	22.2091i	−0.526882	−	0.863182i
$663$		0			0
$664$	−28.3848	+	2.08402i	−1.10154	+	0.0808757i
$665$		0			0
$666$		0			0
$667$	10.7777			0.417313
$668$	15.7279	+	8.08325i	0.608532	+	0.312750i
$669$		0			0
$670$		0			0
$671$	10.0625			0.388460
$672$		0			0
$673$		−	10.2010i		−	0.393220i	−0.980482	−	0.196610i	$-0.937007\pi$
$673$		−	10.2010i		−	0.393220i	0.980482	−	0.196610i	$-0.0629933\pi$
$674$	5.99923	+	9.82843i	0.231082	+	0.378577i
$675$		0			0
$676$	1.22792	−	2.38922i	0.0472278	−	0.0918931i
$677$	−5.31371			−0.204222			−0.102111	−	0.994773i	$-0.532560\pi$
$677$	−5.31371			−0.204222			−0.102111	+	0.994773i	$0.532560\pi$
$678$		0			0
$679$			12.5041i			0.479864i
$680$		0			0
$681$		0			0
$682$	−4.52560	−	7.41421i	−0.173294	−	0.283905i
$683$		−	15.9570i		−	0.610580i	−0.952260	−	0.305290i	$-0.901247\pi$
$683$		−	15.9570i		−	0.610580i	0.952260	−	0.305290i	$-0.0987533\pi$
$684$		0			0
$685$		0			0
$686$	68.7114	−	41.9411i	2.62341	−	1.60132i
$687$		0			0
$688$	9.70498	+	13.5563i	0.369999	+	0.516831i
$689$		−	36.9706i		−	1.40847i
$690$		0			0
$691$		−	27.7461i		−	1.05551i	−0.849397	−	0.527755i	$-0.823034\pi$
$691$		−	27.7461i		−	1.05551i	0.849397	−	0.527755i	$-0.176966\pi$
$692$	11.4142	−	22.2091i	0.433903	−	0.844264i
$693$		0			0
$694$	−10.4853	−	17.1778i	−0.398016	−	0.652062i
$695$		0			0
$696$		0			0
$697$		−	5.65685i		−	0.214269i
$698$	−16.3137	+	9.95782i	−0.617483	+	0.376909i
$699$		0			0
$700$		0			0
$701$			24.1421i			0.911836i	0.890022	+	0.455918i	$0.150689\pi$
$701$			24.1421i			0.911836i	−0.890022	+	0.455918i	$0.849311\pi$
$702$		0			0
$703$	21.1364			0.797176
$704$	−16.4934	+	2.43503i	−0.621618	+	0.0917736i
$705$		0			0
$706$	−13.6569	+	8.33609i	−0.513982	+	0.313733i
$707$			64.5433i			2.42740i
$708$		0			0
$709$	−1.31371			−0.0493374			−0.0246687	−	0.999696i	$-0.507853\pi$
$709$	−1.31371			−0.0493374			−0.0246687	+	0.999696i	$0.507853\pi$
$710$		0			0
$711$		0			0
$712$	7.29408	−	0.535534i	0.273357	−	0.0200700i
$713$	−8.68629			−0.325304
$714$		0			0
$715$		0			0
$716$	−14.9150	+	29.0208i	−0.557401	+	1.08456i
$717$		0			0
$718$	2.08402	−	1.27208i	0.0777750	−	0.0474735i
$719$	−13.5155			−0.504042			−0.252021	−	0.967722i	$-0.581095\pi$
$719$	−13.5155			−0.504042			−0.252021	+	0.967722i	$0.581095\pi$
$720$		0			0
$721$	−16.6274			−0.619237
$722$	1.96447	−	1.19910i	0.0731099	−	0.0446259i
$723$		0			0
$724$	19.9289	−	38.7766i	0.740653	−	1.44112i
$725$		0			0
$726$		0			0
$727$	25.1564			0.932998			0.466499	−	0.884522i	$-0.345515\pi$
$727$	25.1564			0.932998			0.466499	+	0.884522i	$0.345515\pi$
$728$	48.4558	−	3.55765i	1.79589	−	0.131855i
$729$		0			0
$730$		0			0
$731$	16.6722			0.616643
$732$		0			0
$733$			33.0711i			1.22151i	0.791820	+	0.610754i	$0.209134\pi$
$733$			33.0711i			1.22151i	−0.791820	+	0.610754i	$0.790866\pi$
$734$	−15.2726	+	9.32233i	−0.563722	+	0.344093i
$735$		0			0
$736$	−6.51472	+	15.3467i	−0.240136	+	0.565685i
$737$	−12.2843			−0.452497
$738$		0			0
$739$			38.5237i			1.41712i	0.705652	+	0.708559i	$0.250654\pi$
$739$			38.5237i			1.41712i	−0.705652	+	0.708559i	$0.749346\pi$
$740$		0			0
$741$		0			0
$742$	−65.7641	+	40.1421i	−2.41428	+	1.47366i
$743$		−	6.60963i		−	0.242484i	−0.992623	−	0.121242i	$-0.961312\pi$
$743$		−	6.60963i		−	0.242484i	0.992623	−	0.121242i	$-0.0386877\pi$
$744$		0			0
$745$		0			0
$746$	−9.27337	−	15.1924i	−0.339522	−	0.556233i
$747$		0			0
$748$	−7.62096	+	14.8284i	−0.278650	+	0.542181i
$749$			50.6274i			1.84989i
$750$		0			0
$751$		−	17.1778i		−	0.626828i	−0.949617	−	0.313414i	$-0.898527\pi$
$751$		−	17.1778i		−	0.626828i	0.949617	−	0.313414i	$-0.101473\pi$
$752$	−32.7279	+	23.4299i	−1.19346	+	0.854401i
$753$		0			0
$754$	−15.0711	+	9.19932i	−0.548856	+	0.335019i
$755$		0			0
$756$		0			0
$757$			42.0416i			1.52803i	0.645199	+	0.764015i	$0.276774\pi$
$757$			42.0416i			1.52803i	−0.645199	+	0.764015i	$0.723226\pi$
$758$	18.2721	+	29.9348i	0.663672	+	1.08728i
$759$		0			0
$760$		0			0
$761$			22.3848i			0.811448i	0.913996	+	0.405724i	$0.132980\pi$
$761$			22.3848i			0.811448i	−0.913996	+	0.405724i	$0.867020\pi$
$762$		0			0
$763$	−4.16804			−0.150893
$764$	−1.57835	+	3.07107i	−0.0571028	+	0.111107i
$765$		0			0
$766$	7.41421	+	12.1466i	0.267886	+	0.438873i
$767$			21.3459i			0.770755i
$768$		0			0
$769$	1.37258			0.0494966			0.0247483	−	0.999694i	$-0.492122\pi$
$769$	1.37258			0.0494966			0.0247483	+	0.999694i	$0.492122\pi$
$770$		0			0
$771$		0			0
$772$	−27.8508	−	14.3137i	−1.00237	−	0.515162i
$773$	−42.2843			−1.52086			−0.760430	−	0.649420i	$-0.775012\pi$
$773$	−42.2843			−1.52086			−0.760430	+	0.649420i	$0.775012\pi$
$774$		0			0
$775$		0			0
$776$	7.01057	−	0.514719i	0.251665	−	0.0184773i
$777$		0			0
$778$	−3.70575	−	6.07107i	−0.132858	−	0.217658i
$779$	−5.89450			−0.211192
$780$		0			0
$781$	−29.6569			−1.06121
$782$	8.68629	+	14.2306i	0.310621	+	0.508885i
$783$		0			0
$784$	−42.6421	−	59.5644i	−1.52293	−	2.12730i
$785$		0			0
$786$		0			0
$787$	−18.3986			−0.655840			−0.327920	−	0.944705i	$-0.606348\pi$
$787$	−18.3986			−0.655840			−0.327920	+	0.944705i	$0.606348\pi$
$788$	17.9706	−	34.9661i	0.640175	−	1.24561i
$789$		0			0
$790$		0			0
$791$	−22.5667			−0.802379
$792$		0			0
$793$			16.4853i			0.585410i
$794$	24.3672	+	39.9203i	0.864759	+	1.41672i
$795$		0			0
$796$	−48.4558	−	24.9035i	−1.71747	−	0.882682i
$797$	13.4558			0.476630			0.238315	−	0.971188i	$-0.423405\pi$
$797$	13.4558			0.476630			0.238315	+	0.971188i	$0.423405\pi$
$798$		0			0
$799$			40.2502i			1.42395i
$800$		0			0
$801$		0			0
$802$	−15.6302	−	25.6066i	−0.551920	−	0.904201i
$803$			6.60963i			0.233249i
$804$		0			0
$805$		0			0
$806$	12.1466	−	7.41421i	0.427845	−	0.261155i
$807$		0			0
$808$	36.1869	−	2.65685i	1.27305	−	0.0934678i
$809$		−	6.87006i		−	0.241538i	−0.992681	−	0.120769i	$-0.961464\pi$
$809$		−	6.87006i		−	0.241538i	0.992681	−	0.120769i	$-0.0385361\pi$
$810$		0			0
$811$			43.9126i			1.54198i	0.636848	+	0.770989i	$0.280238\pi$
$811$			43.9126i			1.54198i	−0.636848	+	0.770989i	$0.719762\pi$
$812$	32.7279	+	16.8203i	1.14852	+	0.590276i
$813$		0			0
$814$	−7.78680	−	12.7570i	−0.272927	−	0.447131i
$815$		0			0
$816$		0			0
$817$		−	17.3726i		−	0.607790i
$818$	−18.0711	+	11.0305i	−0.631840	+	0.385673i
$819$		0			0
$820$		0			0
$821$			36.3431i			1.26838i	0.773175	+	0.634192i	$0.218667\pi$
$821$			36.3431i			1.26838i	−0.773175	+	0.634192i	$0.781333\pi$
$822$		0			0
$823$	−39.3870			−1.37294			−0.686471	−	0.727157i	$-0.740841\pi$
$823$	−39.3870			−1.37294			−0.686471	+	0.727157i	$0.740841\pi$
$824$	0.684449	+	9.32233i	0.0238439	+	0.324759i
$825$		0			0
$826$	37.9706	−	23.1771i	1.32116	−	0.806433i
$827$			54.4808i			1.89448i	0.320522	+	0.947241i	$0.396142\pi$
$827$			54.4808i			1.89448i	−0.320522	+	0.947241i	$0.603858\pi$
$828$		0			0
$829$	41.1127			1.42790			0.713952	−	0.700195i	$-0.246904\pi$
$829$	41.1127			1.42790			0.713952	+	0.700195i	$0.246904\pi$
$830$		0			0
$831$		0			0
$832$	−3.98926	−	27.0208i	−0.138303	−	0.936778i
$833$	−73.2548			−2.53813
$834$		0			0
$835$		0			0
$836$	15.4514	+	7.94113i	0.534397	+	0.274650i
$837$		0			0
$838$	−5.46289	+	3.33452i	−0.188712	+	0.115189i
$839$	−21.8516			−0.754399			−0.377200	−	0.926132i	$-0.623113\pi$
$839$	−21.8516			−0.754399			−0.377200	+	0.926132i	$0.623113\pi$
$840$		0			0
$841$	15.6274			0.538876
$842$	−18.0711	+	11.0305i	−0.622770	+	0.380136i
$843$		0			0
$844$	−23.1421	−	11.8937i	−0.796585	−	0.409399i
$845$		0			0
$846$		0			0
$847$	−33.4925			−1.15081
$848$	25.2132	+	35.2189i	0.865825	+	1.20942i
$849$		0			0
$850$		0			0
$851$	−14.9457			−0.512332
$852$		0			0
$853$			39.8995i			1.36613i	0.730356	+	0.683066i	$0.239354\pi$
$853$			39.8995i			1.36613i	−0.730356	+	0.683066i	$0.760646\pi$
$854$	29.3244	−	17.8995i	1.00346	−	0.612508i
$855$		0			0
$856$	28.3848	−	2.08402i	0.970172	−	0.0712304i
$857$	−0.970563			−0.0331538			−0.0165769	−	0.999863i	$-0.505277\pi$
$857$	−0.970563			−0.0331538			−0.0165769	+	0.999863i	$0.505277\pi$
$858$		0			0
$859$		−	10.5682i		−	0.360583i	−0.983613	−	0.180291i	$-0.942296\pi$
$859$		−	10.5682i		−	0.360583i	0.983613	−	0.180291i	$-0.0577041\pi$
$860$		0			0
$861$		0			0
$862$	43.5550	−	26.5858i	1.48349	−	0.905515i
$863$			39.7445i			1.35292i	0.736480	+	0.676460i	$0.236487\pi$
$863$			39.7445i			1.35292i	−0.736480	+	0.676460i	$0.763513\pi$
$864$		0			0
$865$		0			0
$866$	−23.1771	−	37.9706i	−0.787589	−	1.29029i
$867$		0			0
$868$	−26.3772	−	13.5563i	−0.895299	−	0.460132i
$869$			23.5147i			0.797682i
$870$		0			0
$871$		−	20.1251i		−	0.681913i
$872$	0.171573	+	2.33686i	0.00581019	+	0.0791359i
$873$		0			0
$874$	14.8284	−	9.05121i	0.501579	−	0.306162i
$875$		0			0
$876$		0			0
$877$		−	6.92893i		−	0.233973i	−0.993133	−	0.116987i	$-0.962677\pi$
$877$		−	6.92893i		−	0.233973i	0.993133	−	0.116987i	$-0.0373235\pi$
$878$	9.58579	+	15.7042i	0.323505	+	0.529992i
$879$		0			0
$880$		0			0
$881$		−	48.2426i		−	1.62534i	−0.582727	−	0.812668i	$-0.698014\pi$
$881$		−	48.2426i		−	1.62534i	0.582727	−	0.812668i	$-0.301986\pi$
$882$		0			0
$883$	−49.3014			−1.65912			−0.829562	−	0.558415i	$-0.811410\pi$
$883$	−49.3014			−1.65912			−0.829562	+	0.558415i	$0.811410\pi$
$884$	−24.2931	−	12.4853i	−0.817067	−	0.419925i
$885$		0			0
$886$	25.3137	+	41.4710i	0.850431	+	1.39324i
$887$		−	11.2833i		−	0.378857i	−0.981894	−	0.189429i	$-0.939336\pi$
$887$		−	11.2833i		−	0.378857i	0.981894	−	0.189429i	$-0.0606636\pi$
$888$		0			0
$889$	25.3137			0.848995
$890$		0			0
$891$		0			0
$892$	−19.1878	+	37.3345i	−0.642455	+	1.25005i
$893$	41.9411			1.40351
$894$		0			0
$895$		0			0
$896$	−43.7338	+	36.4350i	−1.46104	+	1.21721i
$897$		0			0
$898$	−24.4719	−	40.0919i	−0.816638	−	1.33788i
$899$	10.7777			0.359455
$900$		0			0
$901$	43.3137			1.44299
$902$	2.17157	+	3.55765i	0.0723055	+	0.118457i
$903$		0			0
$904$	0.928932	+	12.6522i	0.0308958	+	0.420807i
$905$		0			0
$906$		0			0
$907$	−21.8516			−0.725569			−0.362784	−	0.931873i	$-0.618174\pi$
$907$	−21.8516			−0.725569			−0.362784	+	0.931873i	$0.618174\pi$
$908$	14.8284	+	7.62096i	0.492099	+	0.252911i
$909$		0			0
$910$		0			0
$911$	−40.2502			−1.33355			−0.666774	−	0.745260i	$-0.732325\pi$
$911$	−40.2502			−1.33355			−0.666774	+	0.745260i	$0.732325\pi$
$912$		0			0
$913$		−	20.9706i		−	0.694024i
$914$	−29.0716	−	47.6274i	−0.961602	−	1.57537i
$915$		0			0
$916$	−19.4853	+	37.9133i	−0.643812	+	1.25269i
$917$	61.1127			2.01812
$918$		0			0
$919$		−	43.1974i		−	1.42495i	−0.701697	−	0.712476i	$-0.747574\pi$
$919$		−	43.1974i		−	1.42495i	0.701697	−	0.712476i	$-0.252426\pi$
$920$		0			0
$921$		0			0
$922$	4.27277	+	7.00000i	0.140716	+	0.230533i
$923$		−	48.5863i		−	1.59924i
$924$		0			0
$925$		0			0
$926$	−15.2726	+	9.32233i	−0.501889	+	0.306351i
$927$		0			0
$928$	8.08325	−	19.0416i	0.265346	−	0.625072i
$929$			44.0416i			1.44496i	0.691392	+	0.722480i	$0.256998\pi$
$929$			44.0416i			1.44496i	−0.691392	+	0.722480i	$0.743002\pi$
$930$		0			0
$931$			76.3323i			2.50169i
$932$	3.65685	−	7.11529i	0.119784	−	0.233069i
$933$		0			0
$934$	−30.1838	−	49.4495i	−0.987643	−	1.61804i
$935$		0			0
$936$		0			0
$937$			0.343146i			0.0112101i	0.999984	+	0.00560504i	$0.00178415\pi$
$937$			0.343146i			0.0112101i	−0.999984	+	0.00560504i	$0.998216\pi$
$938$	−35.7990	+	21.8516i	−1.16888	+	0.713478i
$939$		0			0
$940$		0			0
$941$		−	16.3431i		−	0.532771i	−0.963867	−	0.266386i	$-0.914171\pi$
$941$		−	16.3431i		−	0.532771i	0.963867	−	0.266386i	$-0.0858295\pi$
$942$		0			0
$943$	4.16804			0.135730
$944$	−14.5575	−	20.3345i	−0.473806	−	0.661832i
$945$		0			0
$946$	−10.4853	+	6.40017i	−0.340906	+	0.208088i
$947$		−	26.0196i		−	0.845523i	−0.906241	−	0.422762i	$-0.861061\pi$
$947$		−	26.0196i		−	0.845523i	0.906241	−	0.422762i	$-0.138939\pi$
$948$		0			0
$949$	−10.8284			−0.351506
$950$		0			0
$951$		0			0
$952$	4.16804	+	56.7696i	0.135087	+	1.83991i
$953$	−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
$956$	22.2091	−	43.2132i	0.718294	−	1.39761i
$957$		0			0
$958$	41.4710	−	25.3137i	1.33987	−	0.817849i
$959$	−71.1529			−2.29765
$960$		0			0
$961$	22.3137			0.719797
$962$	20.8995	−	12.7570i	0.673827	−	0.411301i
$963$		0			0
$964$	−11.8579	+	23.0723i	−0.381916	+	0.743110i
$965$		0			0
$966$		0			0
$967$	−14.3787			−0.462388			−0.231194	−	0.972908i	$-0.574263\pi$
$967$	−14.3787			−0.462388			−0.231194	+	0.972908i	$0.574263\pi$
$968$	1.37868	+	18.7779i	0.0443124	+	0.603544i
$969$		0			0
$970$		0			0
$971$	−11.4314			−0.366853			−0.183426	−	0.983033i	$-0.558719\pi$
$971$	−11.4314			−0.366853			−0.183426	+	0.983033i	$0.558719\pi$
$972$		0			0
$973$			35.7990i			1.14766i
$974$	−6.07328	+	3.70711i	−0.194601	+	0.118783i
$975$		0			0
$976$	−11.2426	−	15.7042i	−0.359868	−	0.502680i
$977$	10.3431			0.330907			0.165453	−	0.986218i	$-0.447091\pi$
$977$	10.3431			0.330907			0.165453	+	0.986218i	$0.447091\pi$
$978$		0			0
$979$			5.38883i			0.172228i
$980$		0			0
$981$		0			0
$982$	−17.6095	+	10.7487i	−0.561940	+	0.343006i
$983$		−	13.5155i		−	0.431076i	−0.976495	−	0.215538i	$-0.930849\pi$
$983$		−	13.5155i		−	0.431076i	0.976495	−	0.215538i	$-0.0691506\pi$
$984$		0			0
$985$		0			0
$986$	−10.7777	−	17.6569i	−0.343231	−	0.562309i
$987$		0			0
$988$	−13.0098	+	25.3137i	−0.413897	+	0.805336i
$989$			12.2843i			0.390617i
$990$		0			0
$991$		−	15.4514i		−	0.490829i	−0.969418	−	0.245415i	$-0.921076\pi$
$991$		−	15.4514i		−	0.490829i	0.969418	−	0.245415i	$-0.0789241\pi$
$992$	−6.51472	+	15.3467i	−0.206843	+	0.487257i
$993$		0			0
$994$	−86.4264	+	52.7543i	−2.74128	+	1.67327i
$995$		0			0
$996$		0			0
$997$			2.92893i			0.0927602i	0.998924	+	0.0463801i	$0.0147685\pi$
$997$			2.92893i			0.0927602i	−0.998924	+	0.0463801i	$0.985231\pi$
$998$	−22.2426	−	36.4397i	−0.704078	−	1.15348i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.h.c.899.6		8
3.2	odd	2		900.2.h.b.899.4		8
4.3	odd	2	inner	900.2.h.c.899.7		8
5.2	odd	4		180.2.e.a.71.6	yes	8
5.3	odd	4		900.2.e.d.251.3		8
5.4	even	2		900.2.h.b.899.3		8
12.11	even	2		900.2.h.b.899.1		8
15.2	even	4		180.2.e.a.71.3	✓	8
15.8	even	4		900.2.e.d.251.6		8
15.14	odd	2	inner	900.2.h.c.899.5		8
20.3	even	4		900.2.e.d.251.5		8
20.7	even	4		180.2.e.a.71.4	yes	8
20.19	odd	2		900.2.h.b.899.2		8
40.27	even	4		2880.2.h.e.1151.5		8
40.37	odd	4		2880.2.h.e.1151.8		8
60.23	odd	4		900.2.e.d.251.4		8
60.47	odd	4		180.2.e.a.71.5	yes	8
60.59	even	2	inner	900.2.h.c.899.8		8
120.77	even	4		2880.2.h.e.1151.4		8
120.107	odd	4		2880.2.h.e.1151.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.e.a.71.3	✓	8	15.2	even	4
180.2.e.a.71.4	yes	8	20.7	even	4
180.2.e.a.71.5	yes	8	60.47	odd	4
180.2.e.a.71.6	yes	8	5.2	odd	4
900.2.e.d.251.3		8	5.3	odd	4
900.2.e.d.251.4		8	60.23	odd	4
900.2.e.d.251.5		8	20.3	even	4
900.2.e.d.251.6		8	15.8	even	4
900.2.h.b.899.1		8	12.11	even	2
900.2.h.b.899.2		8	20.19	odd	2
900.2.h.b.899.3		8	5.4	even	2
900.2.h.b.899.4		8	3.2	odd	2
900.2.h.c.899.5		8	15.14	odd	2	inner
900.2.h.c.899.6		8	1.1	even	1	trivial
900.2.h.c.899.7		8	4.3	odd	2	inner
900.2.h.c.899.8		8	60.59	even	2	inner
2880.2.h.e.1151.1		8	120.107	odd	4
2880.2.h.e.1151.4		8	120.77	even	4
2880.2.h.e.1151.5		8	40.27	even	4
2880.2.h.e.1151.8		8	40.37	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)

\(f(q)\)	\(=\)	\(q+(1.20711 - 0.736813i) q^{2} +(0.914214 - 1.77882i) q^{4} +5.03127 q^{7} +(-0.207107 - 2.82083i) q^{8} +O(q^{10})\)	\(q+(1.20711 - 0.736813i) q^{2} +(0.914214 - 1.77882i) q^{4} +5.03127 q^{7} +(-0.207107 - 2.82083i) q^{8} +2.08402 q^{11} +3.41421i q^{13} +(6.07328 - 3.70711i) q^{14} +(-2.32843 - 3.25245i) q^{16} -4.00000 q^{17} +4.16804i q^{19} +(2.51564 - 1.53553i) q^{22} -2.94725i q^{23} +(2.51564 + 4.12132i) q^{26} +(4.59966 - 8.94975i) q^{28} +3.65685i q^{29} -2.94725i q^{31} +(-5.20711 - 2.21044i) q^{32} +(-4.82843 + 2.94725i) q^{34} -5.07107i q^{37} +(3.07107 + 5.03127i) q^{38} +1.41421i q^{41} -4.16804 q^{43} +(1.90524 - 3.70711i) q^{44} +(-2.17157 - 3.55765i) q^{46} -10.0625i q^{47} +18.3137 q^{49} +(6.07328 + 3.12132i) q^{52} -10.8284 q^{53} +(-1.04201 - 14.1924i) q^{56} +(2.69442 + 4.41421i) q^{58} +6.25206 q^{59} +4.82843 q^{61} +(-2.17157 - 3.55765i) q^{62} +(-7.91421 + 1.16843i) q^{64} -5.89450 q^{67} +(-3.65685 + 7.11529i) q^{68} -14.2306 q^{71} +3.17157i q^{73} +(-3.73643 - 6.12132i) q^{74} +(7.41421 + 3.81048i) q^{76} +10.4853 q^{77} +11.2833i q^{79} +(1.04201 + 1.70711i) q^{82} -10.0625i q^{83} +(-5.03127 + 3.07107i) q^{86} +(-0.431615 - 5.87868i) q^{88} +2.58579i q^{89} +17.1778i q^{91} +(-5.24264 - 2.69442i) q^{92} +(-7.41421 - 12.1466i) q^{94} +2.48528i q^{97} +(22.1066 - 13.4938i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) \) 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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