LMFDB - Embedded newform 891.2.bb.a.656.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(8,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("891.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.bb (of order $90$, degree $24$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			656.1
Character	$\chi$	$=$	891.656
Dual form			891.2.bb.a.800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90595 + 1.84056i) q^{2} +(0.175206 - 5.01725i) q^{4} +(0.596870 + 0.148816i) q^{5} +(-1.35158 + 1.05597i) q^{7} +(5.35476 + 5.94706i) q^{8} +O(q^{10})$	\(q+(-1.90595 + 1.84056i) q^{2} +(0.175206 - 5.01725i) q^{4} +(0.596870 + 0.148816i) q^{5} +(-1.35158 + 1.05597i) q^{7} +(5.35476 + 5.94706i) q^{8} +(-1.41151 + 0.814937i) q^{10} +(2.02183 - 2.62910i) q^{11} +(1.16895 + 0.570137i) q^{13} +(0.632476 - 4.50030i) q^{14} +(-11.1357 - 0.778681i) q^{16} +(0.422020 + 0.187896i) q^{17} +(0.505207 - 0.454891i) q^{19} +(0.851224 - 2.96857i) q^{20} +(0.985499 + 8.73225i) q^{22} +(1.57794 - 4.33534i) q^{23} +(-4.08063 - 2.16971i) q^{25} +(-3.27734 + 1.06487i) q^{26} +(5.06127 + 6.96624i) q^{28} +(-10.1195 + 1.42220i) q^{29} +(-2.67248 - 3.96211i) q^{31} +(10.3966 - 8.72380i) q^{32} +(-1.15018 + 0.418632i) q^{34} +(-0.963866 + 0.429141i) q^{35} +(4.81972 - 5.35285i) q^{37} +(-0.125649 + 1.79686i) q^{38} +(2.31107 + 4.34650i) q^{40} +(9.35861 + 1.31527i) q^{41} +(3.76508 - 4.48705i) q^{43} +(-12.8366 - 10.6047i) q^{44} +(4.97198 + 11.1672i) q^{46} +(7.78223 - 0.271762i) q^{47} +(-0.981753 + 3.93760i) q^{49} +(11.7710 - 3.37527i) q^{50} +(3.06533 - 5.76504i) q^{52} +(3.92774 - 5.40607i) q^{53} +(1.59803 - 1.26835i) q^{55} +(-13.5173 - 2.38347i) q^{56} +(16.6696 - 21.3362i) q^{58} +(6.29133 - 10.0682i) q^{59} +(4.72808 + 3.18913i) q^{61} +(12.3861 + 2.63275i) q^{62} +(-1.42514 + 13.5593i) q^{64} +(0.612868 + 0.514258i) q^{65} +(0.459764 + 2.60745i) q^{67} +(1.01666 - 2.08446i) q^{68} +(1.04723 - 2.59197i) q^{70} +(-4.57064 + 10.2658i) q^{71} +(3.33968 - 15.7120i) q^{73} +(0.666053 + 19.0733i) q^{74} +(-2.19378 - 2.61445i) q^{76} +(0.0435864 + 5.68846i) q^{77} +(0.817920 + 0.846981i) q^{79} +(-6.53066 - 2.12194i) q^{80} +(-20.2579 + 14.7182i) q^{82} +(7.00971 + 14.3720i) q^{83} +(0.223929 + 0.174953i) q^{85} +(1.08260 + 15.4820i) q^{86} +(26.4619 - 2.05425i) q^{88} +(-11.2798 - 6.51241i) q^{89} +(-2.18199 + 0.463796i) q^{91} +(-21.4750 - 8.67647i) q^{92} +(-14.3324 + 14.8416i) q^{94} +(0.369238 - 0.196328i) q^{95} +(1.89794 + 7.61221i) q^{97} +(-5.37620 - 9.31185i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8}+O(q^{10}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29} - 9 q^{31} - 42 q^{34} + 45 q^{35} - 9 q^{37} + 18 q^{38} - 90 q^{40} + 30 q^{41} + 108 q^{44} - 15 q^{46} + 6 q^{47} - 18 q^{49} + 105 q^{50} - 30 q^{52} - 48 q^{55} - 54 q^{56} - 18 q^{58} - 81 q^{59} - 30 q^{61} + 45 q^{62} + 51 q^{64} + 6 q^{67} + 225 q^{68} - 93 q^{70} + 27 q^{71} - 15 q^{73} + 30 q^{74} + 141 q^{77} - 30 q^{79} - 36 q^{82} - 15 q^{83} - 30 q^{85} - 93 q^{86} - 108 q^{88} - 54 q^{89} - 9 q^{91} - 276 q^{92} - 30 q^{94} - 90 q^{95} - 81 q^{97}+O(q^{100}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	−1.90595	+	1.84056i	−1.34771	+	1.30147i	−0.430763	+	0.902465i	$0.641756\pi$
$2$	−1.90595	+	1.84056i	−1.34771	+	1.30147i	−0.916949	+	0.399005i	$0.869355\pi$
$3$		0			0
$3$		0			0
$4$	0.175206	−	5.01725i	0.0876031	−	2.50862i
$5$	0.596870	+	0.148816i	0.266928	+	0.0665527i	0.373087	−	0.927797i	$-0.378299\pi$
$5$	0.596870	+	0.148816i	0.266928	+	0.0665527i	−0.106158	+	0.994349i	$0.533855\pi$
$6$		0			0
$7$	−1.35158	+	1.05597i	−0.510851	+	0.399120i	−0.837847	−	0.545905i	$-0.816186\pi$
$7$	−1.35158	+	1.05597i	−0.510851	+	0.399120i	0.326996	+	0.945026i	$0.393964\pi$
$8$	5.35476	+	5.94706i	1.89319	+	2.10260i
$9$		0			0
$10$	−1.41151	+	0.814937i	−0.446359	+	0.257706i
$11$	2.02183	−	2.62910i	0.609606	−	0.792705i
$11$	2.02183	−	2.62910i	0.609606	−	0.792705i
$12$		0			0
$13$	1.16895	+	0.570137i	0.324210	+	0.158128i	0.593287	−	0.804991i	$-0.297830\pi$
$13$	1.16895	+	0.570137i	0.324210	+	0.158128i	−0.269077	+	0.963119i	$0.586719\pi$
$14$	0.632476	−	4.50030i	0.169036	−	1.20276i
$15$		0			0
$16$	−11.1357	−	0.778681i	−2.78392	−	0.194670i
$17$	0.422020	+	0.187896i	0.102355	+	0.0455714i	0.457275	−	0.889325i	$-0.348825\pi$
$17$	0.422020	+	0.187896i	0.102355	+	0.0455714i	−0.354920	+	0.934897i	$0.615492\pi$
$18$		0			0
$19$	0.505207	−	0.454891i	0.115902	−	0.104359i	−0.609142	−	0.793061i	$-0.708486\pi$
$19$	0.505207	−	0.454891i	0.115902	−	0.104359i	0.725044	+	0.688702i	$0.241819\pi$
$20$	0.851224	−	2.96857i	0.190340	−	0.663793i
$21$		0			0
$22$	0.985499	+	8.73225i	0.210109	+	1.86172i
$23$	1.57794	−	4.33534i	0.329022	−	0.903982i	−0.659337	−	0.751847i	$-0.729163\pi$
$23$	1.57794	−	4.33534i	0.329022	−	0.903982i	0.988360	−	0.152134i	$-0.0486147\pi$
$24$		0			0
$25$	−4.08063	−	2.16971i	−0.816126	−	0.433942i
$26$	−3.27734	+	1.06487i	−0.642740	+	0.208839i
$27$		0			0
$28$	5.06127	+	6.96624i	0.956491	+	1.31650i
$29$	−10.1195	+	1.42220i	−1.87914	+	0.264096i	−0.983531	−	0.180740i	$-0.942151\pi$
$29$	−10.1195	+	1.42220i	−1.87914	+	0.264096i	−0.895612	+	0.444836i	$0.853262\pi$
$30$		0			0
$31$	−2.67248	−	3.96211i	−0.479991	−	0.711616i	0.508806	−	0.860881i	$-0.330087\pi$
$31$	−2.67248	−	3.96211i	−0.479991	−	0.711616i	−0.988797	+	0.149265i	$0.952309\pi$
$32$	10.3966	−	8.72380i	1.83788	−	1.54216i
$33$		0			0
$34$	−1.15018	+	0.418632i	−0.197255	+	0.0717949i
$35$	−0.963866	+	0.429141i	−0.162923	+	0.0725381i
$36$		0			0
$37$	4.81972	−	5.35285i	0.792358	−	0.880003i	−0.202706	−	0.979240i	$-0.564974\pi$
$37$	4.81972	−	5.35285i	0.792358	−	0.880003i	0.995064	+	0.0992371i	$0.0316402\pi$
$38$	−0.125649	+	1.79686i	−0.0203829	+	0.291490i
$39$		0			0
$40$	2.31107	+	4.34650i	0.365413	+	0.687242i
$41$	9.35861	+	1.31527i	1.46157	+	0.205410i	0.824704	−	0.565565i	$-0.191342\pi$
$41$	9.35861	+	1.31527i	1.46157	+	0.205410i	0.636866	+	0.770975i	$0.280231\pi$
$42$		0			0
$43$	3.76508	−	4.48705i	0.574170	−	0.684269i	−0.398311	−	0.917250i	$-0.630404\pi$
$43$	3.76508	−	4.48705i	0.574170	−	0.684269i	0.972481	+	0.232981i	$0.0748481\pi$
$44$	−12.8366	−	10.6047i	−1.93519	−	1.59871i
$45$		0			0
$46$	4.97198	+	11.1672i	0.733078	+	1.64652i
$47$	7.78223	−	0.271762i	1.13516	−	0.0396405i	0.538852	−	0.842400i	$-0.318858\pi$
$47$	7.78223	−	0.271762i	1.13516	−	0.0396405i	0.596303	+	0.802760i	$0.296636\pi$
$48$		0			0
$49$	−0.981753	+	3.93760i	−0.140250	+	0.562514i
$50$	11.7710	−	3.37527i	1.66467	−	0.477335i
$51$		0			0
$52$	3.06533	−	5.76504i	0.425084	−	0.799468i
$53$	3.92774	−	5.40607i	0.539517	−	0.742581i	−0.449027	−	0.893518i	$-0.648229\pi$
$53$	3.92774	−	5.40607i	0.539517	−	0.742581i	0.988543	+	0.150938i	$0.0482292\pi$
$54$		0			0
$55$	1.59803	−	1.26835i	0.215478	−	0.171025i
$56$	−13.5173	−	2.38347i	−1.80633	−	0.318505i
$57$		0			0
$58$	16.6696	−	21.3362i	2.18883	−	2.80157i
$59$	6.29133	−	10.0682i	0.819061	−	1.31077i	−0.128666	−	0.991688i	$-0.541069\pi$
$59$	6.29133	−	10.0682i	0.819061	−	1.31077i	0.947727	−	0.319083i	$-0.103375\pi$
$60$		0			0
$61$	4.72808	+	3.18913i	0.605369	+	0.408326i	0.823275	−	0.567643i	$-0.192145\pi$
$61$	4.72808	+	3.18913i	0.605369	+	0.408326i	−0.217906	+	0.975970i	$0.569923\pi$
$62$	12.3861	+	2.63275i	1.57304	+	0.334359i
$63$		0			0
$64$	−1.42514	+	13.5593i	−0.178143	+	1.69491i
$65$	0.612868	+	0.514258i	0.0760170	+	0.0637858i
$66$		0			0
$67$	0.459764	+	2.60745i	0.0561691	+	0.318551i	0.999927	−	0.0120867i	$-0.00384742\pi$
$67$	0.459764	+	2.60745i	0.0561691	+	0.318551i	−0.943758	+	0.330637i	$0.892736\pi$
$68$	1.01666	−	2.08446i	0.123288	−	0.252778i
$69$		0			0
$70$	1.04723	−	2.59197i	0.125167	−	0.309800i
$71$	−4.57064	+	10.2658i	−0.542436	+	1.21833i	0.409578	+	0.912275i	$0.365676\pi$
$71$	−4.57064	+	10.2658i	−0.542436	+	1.21833i	−0.952014	+	0.306055i	$0.900991\pi$
$72$		0			0
$73$	3.33968	−	15.7120i	0.390880	−	1.83895i	−0.138238	−	0.990399i	$-0.544144\pi$
$73$	3.33968	−	15.7120i	0.390880	−	1.83895i	0.529118	−	0.848548i	$-0.322523\pi$
$74$	0.666053	+	19.0733i	0.0774270	+	2.21722i
$75$		0			0
$76$	−2.19378	−	2.61445i	−0.251644	−	0.299898i
$77$	0.0435864	+	5.68846i	0.00496714	+	0.648260i
$78$		0			0
$79$	0.817920	+	0.846981i	0.0920232	+	0.0952928i	0.763772	−	0.645486i	$-0.223345\pi$
$79$	0.817920	+	0.846981i	0.0920232	+	0.0952928i	−0.671749	+	0.740779i	$0.734456\pi$
$80$	−6.53066	−	2.12194i	−0.730151	−	0.237240i
$81$		0			0
$82$	−20.2579	+	14.7182i	−2.23711	+	1.62536i
$83$	7.00971	+	14.3720i	0.769416	+	1.57754i	0.815609	+	0.578604i	$0.196402\pi$
$83$	7.00971	+	14.3720i	0.769416	+	1.57754i	−0.0461928	+	0.998933i	$0.514709\pi$
$84$		0			0
$85$	0.223929	+	0.174953i	0.0242885	+	0.0189763i
$86$	1.08260	+	15.4820i	0.116740	+	1.66946i
$87$		0			0
$88$	26.4619	−	2.05425i	2.82084	−	0.218984i
$89$	−11.2798	−	6.51241i	−1.19566	−	0.690314i	−0.236074	−	0.971735i	$-0.575861\pi$
$89$	−11.2798	−	6.51241i	−1.19566	−	0.690314i	−0.959584	+	0.281422i	$0.909194\pi$
$90$		0			0
$91$	−2.18199	+	0.463796i	−0.228735	+	0.0486191i
$92$	−21.4750	−	8.67647i	−2.23893	−	0.904585i
$93$		0			0
$94$	−14.3324	+	14.8416i	−1.47827	+	1.53079i
$95$	0.369238	−	0.196328i	0.0378831	−	0.0201428i
$96$		0			0
$97$	1.89794	+	7.61221i	0.192706	+	0.772903i	0.986370	+	0.164545i	$0.0526157\pi$
$97$	1.89794	+	7.61221i	0.192706	+	0.772903i	−0.793663	+	0.608357i	$0.791829\pi$
$98$	−5.37620	−	9.31185i	−0.543078	−	0.940639i
$99$		0			0
$100$	−11.6009	+	20.0934i	−1.16009	+	2.00934i
$101$	1.38305	+	0.396583i	0.137619	+	0.0394615i	0.343740	−	0.939065i	$-0.388306\pi$
$101$	1.38305	+	0.396583i	0.137619	+	0.0394615i	−0.206121	+	0.978527i	$0.566084\pi$
$102$		0			0
$103$	4.92884	+	3.07988i	0.485653	+	0.303470i	0.750558	−	0.660805i	$-0.229785\pi$
$103$	4.92884	+	3.07988i	0.485653	+	0.303470i	−0.264905	+	0.964275i	$0.585340\pi$
$104$	2.86883	+	10.0048i	0.281312	+	0.981050i
$105$		0			0
$106$	2.46409	+	17.5329i	0.239334	+	1.70295i
$107$	3.36033	−	10.3420i	0.324856	−	0.999803i	−0.646650	−	0.762787i	$-0.723831\pi$
$107$	3.36033	−	10.3420i	0.324856	−	0.999803i	0.971506	−	0.237016i	$-0.0761694\pi$
$108$		0			0
$109$		−	8.12587i		−	0.778318i	−0.921171	−	0.389159i	$-0.872766\pi$
$109$		−	8.12587i		−	0.778318i	0.921171	−	0.389159i	$-0.127234\pi$
$110$	−0.711287	+	5.35868i	−0.0678186	+	0.510930i
$111$		0			0
$112$	15.8731	−	10.7065i	1.49986	−	1.01167i
$113$	−5.12737	+	2.07159i	−0.482343	+	0.194879i	−0.602883	−	0.797829i	$-0.705982\pi$
$113$	−5.12737	+	2.07159i	−0.482343	+	0.194879i	0.120541	+	0.992708i	$0.461537\pi$
$114$		0			0
$115$	1.58699	−	2.35281i	0.147988	−	0.219401i
$116$	5.36254	+	51.0212i	0.497900	+	4.73720i
$117$		0			0
$118$	6.54018	+	30.7691i	0.602072	+	2.83253i
$119$	−0.768808	+	0.191685i	−0.0704766	+	0.0175718i
$120$		0			0
$121$	−2.82438	−	10.6312i	−0.256762	−	0.966475i
$122$	−14.8813	+	2.62397i	−1.34729	+	0.237563i
$123$		0			0
$124$	−20.3471	+	12.7143i	−1.82723	+	1.14178i
$125$	−4.39842	−	3.96035i	−0.393406	−	0.354225i
$126$		0			0
$127$	14.1913	−	1.49157i	1.25928	−	0.132355i	0.548727	−	0.836001i	$-0.315113\pi$
$127$	14.1913	−	1.49157i	1.25928	−	0.132355i	0.710551	+	0.703646i	$0.248446\pi$
$128$	−5.52915	−	7.07699i	−0.488712	−	0.625523i
$129$		0			0
$130$	−2.11462	+	0.147869i	−0.185464	+	0.0129689i
$131$	14.2204	+	5.17580i	1.24244	+	0.452211i	0.877841	−	0.478953i	$-0.158984\pi$
$131$	14.2204	+	5.17580i	1.24244	+	0.452211i	0.364600	+	0.931164i	$0.381206\pi$
$132$		0			0
$133$	−0.202478	+	1.14831i	−0.0175570	+	0.0995710i
$134$	−5.67545	−	4.12345i	−0.490284	−	0.356212i
$135$		0			0
$136$	1.14239	+	3.51591i	0.0979591	+	0.301487i
$137$	18.5152	−	9.03045i	1.58186	−	0.771524i	0.582705	−	0.812684i	$-0.301994\pi$
$137$	18.5152	−	9.03045i	1.58186	−	0.771524i	0.999153	+	0.0411598i	$0.0131053\pi$
$138$		0			0
$139$	−0.0210034		0.000733455i	−0.00178148		6.22108e-5i	0.0340087	−	0.999422i	$-0.489173\pi$
$139$	−0.0210034		0.000733455i	−0.00178148		6.22108e-5i	−0.0357902	+	0.999359i	$0.511395\pi$
$140$	1.98423	+	4.91114i	0.167698	+	0.415067i
$141$		0			0
$142$	−10.1834	−	27.9787i	−0.854574	−	2.34792i
$143$	3.86238	−	1.92058i	0.322989	−	0.160607i
$144$		0			0
$145$	−6.25167	−	0.657077i	−0.519173	−	0.0545673i
$146$	22.5535	+	36.0931i	1.86654	+	2.98709i
$147$		0			0
$148$	−26.0121	−	25.1196i	−2.13818	−	2.06482i
$149$	−7.00310	−	6.76281i	−0.573716	−	0.554031i	0.350176	−	0.936684i	$-0.386122\pi$
$149$	−7.00310	−	6.76281i	−0.573716	−	0.554031i	−0.923892	+	0.382653i	$0.875011\pi$
$150$		0			0
$151$	0.131974	+	0.211203i	0.0107399	+	0.0171875i	0.853375	−	0.521298i	$-0.174552\pi$
$151$	0.131974	+	0.211203i	0.0107399	+	0.0171875i	−0.842635	+	0.538486i	$0.818997\pi$
$152$	5.41052	+	0.568669i	0.438851	+	0.0461251i
$153$		0			0
$154$	−10.5530	−	10.7617i	−0.850385	−	0.867203i
$155$	−1.00549	−	2.76257i	−0.0807633	−	0.221895i
$156$		0			0
$157$	−1.63793	−	4.05402i	−0.130721	−	0.323546i	0.847601	−	0.530633i	$-0.178046\pi$
$157$	−1.63793	−	4.05402i	−0.130721	−	0.323546i	−0.978322	+	0.207088i	$0.933601\pi$
$158$	−3.11783	−	0.108877i	−0.248042	−	0.00866180i
$159$		0			0
$160$	7.50368	−	3.65979i	0.593218	−	0.289332i
$161$	2.44529	+	7.52584i	0.192716	+	0.593119i
$162$		0			0
$163$	0.657814	+	0.477930i	0.0515240	+	0.0374343i	0.613249	−	0.789890i	$-0.289862\pi$
$163$	0.657814	+	0.477930i	0.0515240	+	0.0374343i	−0.561725	+	0.827324i	$0.689862\pi$
$164$	8.23871	−	46.7240i	0.643335	−	3.64853i
$165$		0			0
$166$	−39.8127	−	14.4907i	−3.09007	−	1.12469i
$167$	−7.70276	+	0.538629i	−0.596057	+	0.0416804i	−0.364599	−	0.931165i	$-0.618794\pi$
$167$	−7.70276	+	0.538629i	−0.596057	+	0.0416804i	−0.231458	+	0.972845i	$0.574350\pi$
$168$		0			0
$169$	−6.96220	−	8.91121i	−0.535554	−	0.685478i
$170$	−0.748809	+	0.0787030i	−0.0574311	+	0.00603625i
$171$		0			0
$172$	−21.8530	−	19.6765i	−1.66627	−	1.50032i
$173$	−1.84933	+	1.15559i	−0.140602	+	0.0878580i	−0.598396	−	0.801200i	$-0.704195\pi$
$173$	−1.84933	+	1.15559i	−0.140602	+	0.0878580i	0.457794	+	0.889058i	$0.348640\pi$
$174$		0			0
$175$	7.80647	−	1.37649i	0.590114	−	0.104053i
$176$	−24.5617	+	27.7025i	−1.85141	+	2.08815i
$177$		0			0
$178$	33.4852	−	8.34881i	2.50983	−	0.625770i
$179$	0.427129	+	2.00948i	0.0319251	+	0.150196i	0.991223	−	0.132200i	$-0.0422041\pi$
$179$	0.427129	+	2.00948i	0.0319251	+	0.150196i	−0.959298	+	0.282396i	$0.908871\pi$
$180$		0			0
$181$	0.101364	+	0.964411i	0.00753430	+	0.0716841i	0.997643	−	0.0686185i	$-0.0218591\pi$
$181$	0.101364	+	0.964411i	0.00753430	+	0.0716841i	−0.990109	+	0.140303i	$0.955192\pi$
$182$	3.30513	−	4.90005i	0.244992	−	0.363216i
$183$		0			0
$184$	34.2320	−	13.8306i	2.52362	−	1.01961i
$185$	3.67334	−	2.47770i	0.270069	−	0.182164i
$186$		0			0
$187$	1.34725	−	0.729642i	0.0985208	−	0.0533567i
$188$		−	39.0930i		−	2.85115i
$189$		0			0
$190$	−0.342399	+	1.05380i	−0.0248402	+	0.0764503i
$191$	−1.11542	−	7.93660i	−0.0807087	−	0.574273i	−0.988080	−	0.153942i	$-0.950803\pi$
$191$	−1.11542	−	7.93660i	−0.0807087	−	0.574273i	0.907371	−	0.420330i	$-0.138086\pi$
$192$		0			0
$193$	−2.47720	−	8.63903i	−0.178313	−	0.621851i	−0.998744	−	0.0501056i	$-0.984044\pi$
$193$	−2.47720	−	8.63903i	−0.178313	−	0.621851i	0.820431	−	0.571746i	$-0.193734\pi$
$194$	−17.6281	−	11.0152i	−1.26562	−	0.790849i
$195$		0			0
$196$	19.5839	+	5.61559i	1.39885	+	0.401114i
$197$	−9.22560	+	15.9792i	−0.657297	+	1.13847i	0.324016	+	0.946052i	$0.394967\pi$
$197$	−9.22560	+	15.9792i	−0.657297	+	1.13847i	−0.981313	+	0.192420i	$0.938366\pi$
$198$		0			0
$199$	0.564555	+	0.977838i	0.0400202	+	0.0693171i	0.885342	−	0.464941i	$-0.153924\pi$
$199$	0.564555	+	0.977838i	0.0400202	+	0.0693171i	−0.845321	+	0.534258i	$0.820591\pi$
$200$	−8.94739	−	35.8860i	−0.632676	−	2.53752i
$201$		0			0
$202$	−3.36596	+	1.78971i	−0.236828	+	0.125924i
$203$	12.1755	−	12.6081i	0.854555	−	0.884918i
$204$		0			0
$205$	5.39014	+	2.17776i	0.376464	+	0.152101i
$206$	−15.0628	+	3.20170i	−1.04948	+	0.223073i
$207$		0			0
$208$	−12.5731	−	7.25910i	−0.871790	−	0.503328i
$209$	−0.174510	−	2.24796i	−0.0120711	−	0.155494i
$210$		0			0
$211$	0.824810	+	11.7953i	0.0567823	+	0.812025i	0.939593	+	0.342295i	$0.111204\pi$
$211$	0.824810	+	11.7953i	0.0567823	+	0.812025i	−0.882810	+	0.469730i	$0.844351\pi$
$212$	−26.4354	−	20.6536i	−1.81559	−	1.41850i
$213$		0			0
$214$	12.6305	+	25.8963i	0.863402	+	1.77024i
$215$	2.91501	−	2.11788i	0.198802	−	0.144438i
$216$		0			0
$217$	7.79596	+	2.53306i	0.529224	+	0.171955i
$218$	14.9561	+	15.4875i	1.01296	+	1.04895i
$219$		0			0
$220$	−6.08365	−	8.23991i	−0.410160	−	0.555535i
$221$	0.386196	+	0.460251i	0.0259784	+	0.0309598i
$222$		0			0
$223$	0.943706	+	27.0242i	0.0631952	+	1.80967i	0.455923	+	0.890019i	$0.349309\pi$
$223$	0.943706	+	27.0242i	0.0631952	+	1.80967i	−0.392728	+	0.919655i	$0.628468\pi$
$224$	−4.83981	+	22.7695i	−0.323373	+	1.52135i
$225$		0			0
$226$	5.95964	−	13.3856i	0.396430	−	0.890396i
$227$	4.64921	−	11.5072i	0.308579	−	0.763760i	−0.690599	−	0.723238i	$-0.742653\pi$
$227$	4.64921	−	11.5072i	0.308579	−	0.763760i	0.999179	−	0.0405229i	$-0.0129024\pi$
$228$		0			0
$229$	8.36794	−	17.1568i	0.552969	−	1.13375i	−0.420997	−	0.907062i	$-0.638320\pi$
$229$	8.36794	−	17.1568i	0.552969	−	1.13375i	0.973966	−	0.226693i	$-0.0727913\pi$
$230$	1.30576	+	7.40531i	0.0860989	+	0.488291i
$231$		0			0
$232$	−62.6453	−	52.5657i	−4.11287	−	3.45111i
$233$	−0.583211	+	5.54888i	−0.0382074	+	0.363519i	0.958668	+	0.284528i	$0.0918367\pi$
$233$	−0.583211	+	5.54888i	−0.0382074	+	0.363519i	−0.996875	+	0.0789917i	$0.974830\pi$
$234$		0			0
$235$	4.68543	+	0.995918i	0.305643	+	0.0649665i
$236$	−49.4125	−	33.3292i	−3.21648	−	2.16954i
$237$		0			0
$238$	1.11250	−	1.78038i	0.0721129	−	0.115405i
$239$	3.88440	−	4.97180i	0.251261	−	0.321599i	−0.645800	−	0.763507i	$-0.723476\pi$
$239$	3.88440	−	4.97180i	0.251261	−	0.321599i	0.897061	+	0.441908i	$0.145698\pi$
$240$		0			0
$241$	4.00179	+	0.705624i	0.257778	+	0.0454532i	0.301044	−	0.953610i	$-0.402665\pi$
$241$	4.00179	+	0.705624i	0.257778	+	0.0454532i	−0.0432656	+	0.999064i	$0.513776\pi$
$242$	24.9505	+	15.0642i	1.60388	+	0.968361i
$243$		0			0
$244$	16.8290	−	23.1632i	1.07737	−	1.48287i
$245$	−1.17196	+	2.20413i	−0.0748737	+	0.140817i
$246$		0			0
$247$	0.849914	−	0.243709i	0.0540788	−	0.0155068i
$248$	9.25244	−	37.1095i	0.587531	−	2.35646i
$249$		0			0
$250$	15.6724	−	0.547293i	0.991212	−	0.0346139i
$251$	−7.95464	−	17.8664i	−0.502092	−	1.12772i	−0.969815	−	0.243842i	$-0.921592\pi$
$251$	−7.95464	−	17.8664i	−0.502092	−	1.12772i	0.467723	−	0.883875i	$-0.345075\pi$
$252$		0			0
$253$	−8.20775	−	12.9139i	−0.516017	−	0.811890i
$254$	−24.3027	+	28.9628i	−1.52489	+	1.81729i
$255$		0			0
$256$	−3.43876	−	0.483286i	−0.214922	−	0.0302054i
$257$	0.0826412	+	0.155425i	0.00515502	+	0.00969518i	0.885512	−	0.464617i	$-0.153808\pi$
$257$	0.0826412	+	0.155425i	0.00515502	+	0.00969518i	−0.880357	+	0.474312i	$0.842697\pi$
$258$		0			0
$259$	−0.861801	+	12.3243i	−0.0535497	+	0.765796i
$260$	2.68754	−	2.98481i	0.166674	−	0.185110i
$261$		0			0
$262$	−36.6297	+	16.3086i	−2.26299	+	1.00755i
$263$	−14.6793	+	5.34285i	−0.905167	+	0.329454i	−0.752322	−	0.658796i	$-0.771066\pi$
$263$	−14.6793	+	5.34285i	−0.905167	+	0.329454i	−0.152846	+	0.988250i	$0.548844\pi$
$264$		0			0
$265$	3.14886	−	2.64221i	0.193433	−	0.162310i
$266$	−1.72761	−	2.56129i	−0.105927	−	0.157043i
$267$		0			0
$268$	13.1628	−	1.84991i	0.804044	−	0.113001i
$269$	−3.43294	−	4.72504i	−0.209310	−	0.288091i	0.691435	−	0.722439i	$-0.256979\pi$
$269$	−3.43294	−	4.72504i	−0.209310	−	0.288091i	−0.900745	+	0.434348i	$0.856979\pi$
$270$		0			0
$271$	−0.0396553	+	0.0128848i	−0.00240889	+	0.000782695i	−0.310221	−	0.950664i	$-0.600403\pi$
$271$	−0.0396553	+	0.0128848i	−0.00240889	+	0.000782695i	0.307812	+	0.951447i	$0.400403\pi$
$272$	−4.55316	−	2.42096i	−0.276076	−	0.146792i
$273$		0			0
$274$	−18.6680	+	51.2898i	−1.12777	+	3.09853i
$275$	−13.9547	+	6.34161i	−0.841503	+	0.382414i
$276$		0			0
$277$	1.87811	−	6.54975i	0.112845	−	0.393536i	−0.884485	−	0.466569i	$-0.845490\pi$
$277$	1.87811	−	6.54975i	0.112845	−	0.393536i	0.997330	+	0.0730326i	$0.0232677\pi$
$278$	0.0413814	−	0.0372600i	0.00248189	−	0.00223471i
$279$		0			0
$280$	−7.71340	−	3.43423i	−0.460964	−	0.205234i
$281$	−26.6226	−	1.86163i	−1.58817	−	0.111056i	−0.751863	−	0.659319i	$-0.770845\pi$
$281$	−26.6226	−	1.86163i	−1.58817	−	0.111056i	−0.836305	+	0.548264i	$0.815289\pi$
$282$		0			0
$283$	−2.70610	+	19.2549i	−0.160861	+	1.14459i	0.727723	+	0.685871i	$0.240579\pi$
$283$	−2.70610	+	19.2549i	−0.160861	+	1.14459i	−0.888584	+	0.458714i	$0.848310\pi$
$284$	50.7054	+	24.7307i	3.00881	+	1.46750i
$285$		0			0
$286$	−3.82658	+	10.7695i	−0.226270	+	0.636812i
$287$	−14.0378	+	8.10475i	−0.828627	+	0.478408i
$288$		0			0
$289$	−11.2324	−	12.4749i	−0.660731	−	0.733816i
$290$	13.1248	−	10.2542i	0.770713	−	0.602147i
$291$		0			0
$292$	−78.2457	−	19.5088i	−4.57898	−	1.14167i
$293$	0.667015	−	19.1008i	0.0389674	−	1.11588i	−0.809663	−	0.586895i	$-0.800350\pi$
$293$	0.667015	−	19.1008i	0.0389674	−	1.11588i	0.848630	−	0.528986i	$-0.177428\pi$
$294$		0			0
$295$	5.25342	−	5.07317i	0.305866	−	0.295371i
$296$	57.6422			3.35038
$297$		0			0
$298$	25.7949			1.49426
$299$	4.31628	−	4.16818i	0.249617	−	0.241052i
$300$		0			0
$301$	−0.350620	+	10.0405i	−0.0202094	+	0.578722i
$302$	−0.640268	−	0.159637i	−0.0368433	−	0.00918606i
$303$		0			0
$304$	−5.98003	+	4.67211i	−0.342978	+	0.267964i
$305$	2.34746	+	2.60711i	0.134415	+	0.149283i
$306$		0			0
$307$	0.669905	−	0.386770i	0.0382335	−	0.0220741i	−0.480761	−	0.876851i	$-0.659640\pi$
$307$	0.669905	−	0.386770i	0.0382335	−	0.0220741i	0.518995	+	0.854777i	$0.326306\pi$
$308$	28.5480	+	0.777969i	1.62668	+	0.0443289i
$309$		0			0
$310$	7.00110	+	3.41466i	0.397636	+	0.193940i
$311$	2.25803	−	16.0667i	0.128041	−	0.911060i	−0.815254	−	0.579104i	$-0.803403\pi$
$311$	2.25803	−	16.0667i	0.128041	−	0.911060i	0.943295	−	0.331956i	$-0.107709\pi$
$312$		0			0
$313$	14.3347	+	1.00238i	0.810247	+	0.0566580i	0.468869	−	0.883268i	$-0.344662\pi$
$313$	14.3347	+	1.00238i	0.810247	+	0.0566580i	0.341378	+	0.939926i	$0.389106\pi$
$314$	10.5835	+	4.71206i	0.597259	+	0.265917i
$315$		0			0
$316$	4.39282	−	3.95531i	0.247115	−	0.222504i
$317$	−6.02966	+	21.0279i	−0.338659	+	1.18105i	0.589160	+	0.808016i	$0.299459\pi$
$317$	−6.02966	+	21.0279i	−0.338659	+	1.18105i	−0.927820	+	0.373029i	$0.878319\pi$
$318$		0			0
$319$	−16.7208	+	29.4807i	−0.936186	+	1.65060i
$320$	−2.86847	+	7.88107i	−0.160353	+	0.440565i
$321$		0			0
$322$	−18.5124	−	9.84319i	−1.03165	−	0.548540i
$323$	0.298680	−	0.0970469i	0.0166190	−	0.00539983i
$324$		0			0
$325$	−3.53304	−	4.86281i	−0.195978	−	0.269740i
$326$	−2.13342	+	0.299832i	−0.118159	+	0.0166062i
$327$		0			0
$328$	42.2911	+	62.6992i	2.33514	+	3.46198i
$329$	−10.2314	+	8.58514i	−0.564074	+	0.473314i
$330$		0			0
$331$	8.23558	−	2.99751i	0.452668	−	0.164758i	−0.105617	−	0.994407i	$-0.533682\pi$
$331$	8.23558	−	2.99751i	0.452668	−	0.164758i	0.558285	+	0.829649i	$0.311459\pi$
$332$	73.3362	−	32.6514i	4.02485	−	1.79198i
$333$		0			0
$334$	13.6897	−	15.2040i	0.749068	−	0.831924i
$335$	−0.113612	+	1.62473i	−0.00620729	+	0.0887684i
$336$		0			0
$337$	14.9002	+	28.0232i	0.811665	+	1.52652i	0.849714	+	0.527244i	$0.176775\pi$
$337$	14.9002	+	28.0232i	0.811665	+	1.52652i	−0.0380484	+	0.999276i	$0.512114\pi$
$338$	29.6712	+	4.17002i	1.61390	+	0.226819i
$339$		0			0
$340$	0.917015	−	1.09286i	0.0497321	−	0.0592684i
$341$	−15.8201	−	0.984504i	−0.856707	−	0.0533139i
$342$		0			0
$343$	−7.71447	−	17.3270i	−0.416542	−	0.935570i
$344$	46.8459	−	1.63589i	2.52576	−	0.0882015i
$345$		0			0
$346$	1.39781	−	5.60630i	0.0751467	−	0.301397i
$347$	2.59593	−	0.744371i	0.139357	−	0.0399599i	−0.205234	−	0.978713i	$-0.565795\pi$
$347$	2.59593	−	0.744371i	0.139357	−	0.0399599i	0.344591	+	0.938753i	$0.388018\pi$
$348$		0			0
$349$	−8.27583	+	15.5646i	−0.442995	+	0.833153i	0.557001	+	0.830512i	$0.311952\pi$
$349$	−8.27583	+	15.5646i	−0.442995	+	0.833153i	−0.999997	+	0.00264120i	$0.999159\pi$
$350$	−12.3453	+	16.9918i	−0.659881	+	0.908249i
$351$		0			0
$352$	−1.91555	−	44.9719i	−0.102099	−	2.39701i
$353$	−7.87364	−	1.38833i	−0.419071	−	0.0738936i	−0.0398636	−	0.999205i	$-0.512692\pi$
$353$	−7.87364	−	1.38833i	−0.419071	−	0.0738936i	−0.379208	+	0.925312i	$0.623803\pi$
$354$		0			0
$355$	−4.25581	+	5.44718i	−0.225875	+	0.289106i
$356$	−34.6506	+	55.4526i	−1.83648	+	2.93898i
$357$		0			0
$358$	−4.51266	−	3.04383i	−0.238501	−	0.160871i
$359$	−31.1299	−	6.61687i	−1.64297	−	0.349225i	−0.708626	−	0.705584i	$-0.750685\pi$
$359$	−31.1299	−	6.61687i	−1.64297	−	0.349225i	−0.934349	+	0.356359i	$0.884018\pi$
$360$		0			0
$361$	−1.93773	+	18.4363i	−0.101986	+	0.970331i
$362$	−1.96825	−	1.65156i	−0.103449	−	0.0868038i
$363$		0			0
$364$	1.94468	+	11.0288i	0.101929	+	0.578068i
$365$	4.33156	−	8.88101i	0.226724	−	0.464853i
$366$		0			0
$367$	−4.96034	+	12.2773i	−0.258928	+	0.640869i	−0.999517	−	0.0310898i	$-0.990102\pi$
$367$	−4.96034	+	12.2773i	−0.258928	+	0.640869i	0.740589	+	0.671958i	$0.234547\pi$
$368$	−20.9472	+	47.0482i	−1.09195	+	2.45256i
$369$		0			0
$370$	−2.44087	+	11.4834i	−0.126895	+	0.596992i
$371$	0.399995	+	11.4543i	0.0207667	+	0.594680i
$372$		0			0
$373$	−20.1696	−	24.0372i	−1.04434	−	1.24460i	−0.968901	−	0.247448i	$-0.920408\pi$
$373$	−20.1696	−	24.0372i	−1.04434	−	1.24460i	−0.0754405	−	0.997150i	$-0.524036\pi$
$374$	−1.22485	+	3.87036i	−0.0633355	+	0.200131i
$375$		0			0
$376$	43.2881	+	44.8262i	2.23242	+	2.31173i
$377$	−12.6401	−	4.10701i	−0.650997	−	0.211522i
$378$		0			0
$379$	14.3649	−	10.4367i	0.737874	−	0.536097i	−0.154170	−	0.988044i	$-0.549270\pi$
$379$	14.3649	−	10.4367i	0.737874	−	0.536097i	0.892045	+	0.451947i	$0.149270\pi$
$380$	−0.920331	−	1.88696i	−0.0472120	−	0.0967989i
$381$		0			0
$382$	16.7337	+	13.0738i	0.856171	+	0.668914i
$383$	0.256081	+	3.66213i	0.0130851	+	0.187126i	0.999709	+	0.0241141i	$0.00767651\pi$
$383$	0.256081	+	3.66213i	0.0130851	+	0.187126i	−0.986624	+	0.163012i	$0.947879\pi$
$384$		0			0
$385$	−0.820521	+	3.40176i	−0.0418176	+	0.173370i
$386$	20.6221	+	11.9062i	1.04964	+	0.606007i
$387$		0			0
$388$	38.5249	−	8.18871i	1.95580	−	0.415719i
$389$	−2.43583	−	0.984140i	−0.123502	−	0.0498979i	0.312024	−	0.950074i	$-0.398993\pi$
$389$	−2.43583	−	0.984140i	−0.123502	−	0.0498979i	−0.435526	+	0.900176i	$0.643437\pi$
$390$		0			0
$391$	1.48051	−	1.53312i	0.0748727	−	0.0775330i
$392$	−28.6742	+	15.2463i	−1.44826	+	0.770056i
$393$		0			0
$394$	−11.8271	−	47.4359i	−0.595840	−	2.38978i
$395$	0.362147	+	0.627258i	0.0182216	+	0.0315608i
$396$		0			0
$397$	10.4449	−	18.0911i	0.524215	−	0.907968i	−0.475387	−	0.879777i	$-0.657692\pi$
$397$	10.4449	−	18.0911i	0.524215	−	0.907968i	0.999603	−	0.0281909i	$-0.00897464\pi$
$398$	−2.87578	−	0.824617i	−0.144150	−	0.0413343i
$399$		0			0
$400$	43.7510	+	27.3387i	2.18755	+	1.36693i
$401$	7.01147	+	24.4519i	0.350136	+	1.22107i	0.917545	+	0.397633i	$0.130168\pi$
$401$	7.01147	+	24.4519i	0.350136	+	1.22107i	−0.567408	+	0.823436i	$0.692054\pi$
$402$		0			0
$403$	−0.865058	−	6.15521i	−0.0430916	−	0.306613i
$404$	2.23207	−	6.86962i	0.111050	−	0.341776i
$405$		0			0
$406$			46.4403i			2.30479i
$407$	−4.32851	−	23.4941i	−0.214556	−	1.16456i
$408$		0			0
$409$	−23.8243	+	16.0697i	−1.17804	+	0.794596i	−0.982530	−	0.186107i	$-0.940413\pi$
$409$	−23.8243	+	16.0697i	−1.17804	+	0.794596i	−0.195507	+	0.980702i	$0.562635\pi$
$410$	−14.2816	+	5.77016i	−0.705320	+	0.284968i
$411$		0			0
$412$	16.3161	−	24.1896i	0.803836	−	1.19174i
$413$	2.12852	+	20.2515i	0.104738	+	0.996512i
$414$		0			0
$415$	2.04509	+	9.62140i	0.100390	+	0.472296i
$416$	17.1269	−	4.27023i	0.839717	−	0.209365i
$417$		0			0
$418$	4.47010	+	3.96330i	0.218640	+	0.193851i
$419$	16.4329	−	2.89757i	0.802802	−	0.141556i	0.242832	−	0.970068i	$-0.421924\pi$
$419$	16.4329	−	2.89757i	0.802802	−	0.141556i	0.559970	+	0.828513i	$0.310813\pi$
$420$		0			0
$421$	−27.4785	+	17.1705i	−1.33922	+	0.836839i	−0.994787	−	0.101971i	$-0.967485\pi$
$421$	−27.4785	+	17.1705i	−1.33922	+	0.836839i	−0.344435	+	0.938810i	$0.611929\pi$
$422$	−23.2820	−	20.9632i	−1.13335	−	1.02047i
$423$		0			0
$424$	53.1823	−	5.58969i	2.58276	−	0.271459i
$425$	−1.31443	−	1.68239i	−0.0637592	−	0.0816081i
$426$		0			0
$427$	−9.75804	+	0.682348i	−0.472224	+	0.0330212i
$428$	−51.2998	−	18.6716i	−2.47967	−	0.902526i
$429$		0			0
$430$	−1.65780	+	9.40183i	−0.0799460	+	0.453396i
$431$	−7.69080	−	5.58769i	−0.370453	−	0.269150i	0.386946	−	0.922102i	$-0.373530\pi$
$431$	−7.69080	−	5.58769i	−0.370453	−	0.269150i	−0.757399	+	0.652953i	$0.773530\pi$
$432$		0			0
$433$	−7.09353	−	21.8317i	−0.340894	−	1.04916i	−0.963746	−	0.266823i	$-0.914026\pi$
$433$	−7.09353	−	21.8317i	−0.340894	−	1.04916i	0.622852	−	0.782340i	$-0.285974\pi$
$434$	−19.5210	+	9.52101i	−0.937037	+	0.457023i
$435$		0			0
$436$	−40.7695	−	1.42370i	−1.95251	−	0.0681830i
$437$	−1.17492	−	2.90804i	−0.0562042	−	0.139110i
$438$		0			0
$439$	1.91262	+	5.25489i	0.0912845	+	0.250802i	0.976930	−	0.213560i	$-0.0685059\pi$
$439$	1.91262	+	5.25489i	0.0912845	+	0.250802i	−0.885645	+	0.464362i	$0.846284\pi$
$440$	16.1000	+	2.71184i	0.767538	+	0.129282i
$441$		0			0
$442$	−1.58319	−	0.166400i	−0.0753047	−	0.00791484i
$443$	6.04824	+	9.67920i	0.287360	+	0.459873i	0.959961	−	0.280133i	$-0.0903785\pi$
$443$	6.04824	+	9.67920i	0.287360	+	0.459873i	−0.672601	+	0.740005i	$0.734823\pi$
$444$		0			0
$445$	−5.76343	−	5.56568i	−0.273213	−	0.263839i
$446$	−51.5382	−	49.7699i	−2.44041	−	2.35667i
$447$		0			0
$448$	−12.3921	−	19.8315i	−0.585471	−	0.936949i
$449$	13.3876	+	1.40709i	0.631800	+	0.0664049i	0.415015	−	0.909814i	$-0.363776\pi$
$449$	13.3876	+	1.40709i	0.631800	+	0.0664049i	0.216785	+	0.976219i	$0.430443\pi$
$450$		0			0
$451$	22.3795	−	21.9455i	1.05381	−	1.03337i
$452$	9.49535	+	26.0883i	0.446624	+	1.22709i
$453$		0			0
$454$	12.3185	+	30.4893i	0.578136	+	1.43094i
$455$	−1.37139	−	0.0478898i	−0.0642915	−	0.00224511i
$456$		0			0
$457$	2.22758	−	1.08646i	0.104202	−	0.0508226i	−0.385533	−	0.922694i	$-0.625982\pi$
$457$	2.22758	−	1.08646i	0.104202	−	0.0508226i	0.489735	+	0.871871i	$0.337094\pi$
$458$	15.6292	+	48.1018i	0.730305	+	2.24765i
$459$		0			0
$460$	−11.5266	−	8.37457i	−0.537431	−	0.390466i
$461$	−2.24987	+	12.7596i	−0.104787	+	0.594275i	0.886519	+	0.462693i	$0.153117\pi$
$461$	−2.24987	+	12.7596i	−0.104787	+	0.594275i	−0.991305	+	0.131582i	$0.957994\pi$
$462$		0			0
$463$	9.89023	+	3.59975i	0.459638	+	0.167294i	0.561453	−	0.827509i	$-0.310243\pi$
$463$	9.89023	+	3.59975i	0.459638	+	0.167294i	−0.101815	+	0.994803i	$0.532465\pi$
$464$	113.795	−	7.95730i	5.28279	−	0.369408i
$465$		0			0
$466$	−9.10146	−	11.6493i	−0.421617	−	0.539645i
$467$	13.6794	−	1.43777i	0.633008	−	0.0665318i	0.217410	−	0.976080i	$-0.430239\pi$
$467$	13.6794	−	1.43777i	0.633008	−	0.0665318i	0.415598	+	0.909548i	$0.363572\pi$
$468$		0			0
$469$	−3.37481	−	3.03869i	−0.155834	−	0.140314i
$470$	−10.7632	+	6.72562i	−0.496471	+	0.310230i
$471$		0			0
$472$	93.5649	−	16.4980i	4.30667	−	0.759382i
$473$	−4.18456	−	18.9709i	−0.192406	−	0.872281i
$474$		0			0
$475$	−3.04854	+	0.760088i	−0.139877	+	0.0348752i
$476$	0.827033	+	3.89089i	0.0379070	+	0.178338i
$477$		0			0
$478$	1.74741	+	16.6255i	0.0799246	+	0.760432i
$479$	2.91492	−	4.32154i	0.133186	−	0.197456i	−0.756545	−	0.653942i	$-0.773114\pi$
$479$	2.91492	−	4.32154i	0.133186	−	0.197456i	0.889731	+	0.456485i	$0.150892\pi$
$480$		0			0
$481$	8.68590	−	3.50933i	0.396043	−	0.160012i
$482$	−8.92596	+	6.02064i	−0.406567	+	0.274233i
$483$		0			0
$484$	−53.8343	+	12.3080i	−2.44701	+	0.559453i
$485$			4.82594i			0.219135i
$486$		0			0
$487$	−6.05340	+	18.6304i	−0.274306	+	0.844226i	0.715097	+	0.699025i	$0.246383\pi$
$487$	−6.05340	+	18.6304i	−0.274306	+	0.844226i	−0.989402	+	0.145200i	$0.953617\pi$
$488$	6.35177	+	45.1952i	0.287531	+	2.04589i
$489$		0			0
$490$	−1.82314	−	6.35803i	−0.0823609	−	0.287227i
$491$	2.74180	+	1.71326i	0.123735	+	0.0773185i	0.590375	−	0.807129i	$-0.298980\pi$
$491$	2.74180	+	1.71326i	0.123735	+	0.0773185i	−0.466639	+	0.884448i	$0.654535\pi$
$492$		0			0
$493$	−4.53786	−	1.30121i	−0.204375	−	0.0586035i
$494$	−1.17134	+	2.02881i	−0.0527009	+	0.0912807i
$495$		0			0
$496$	26.6746	+	46.2017i	1.19772	+	2.07452i
$497$	−4.66284	−	18.7016i	−0.209157	−	0.838882i
$498$		0			0
$499$	22.6673	−	12.0524i	1.01473	−	0.539540i	0.123141	−	0.992389i	$-0.460703\pi$
$499$	22.6673	−	12.0524i	1.01473	−	0.539540i	0.891587	+	0.452849i	$0.149592\pi$
$500$	−20.6407	+	21.3741i	−0.923080	+	0.955878i
$501$		0			0
$502$	48.0453	+	19.4116i	2.14437	+	0.866381i
$503$	2.75001	−	0.584533i	0.122617	−	0.0260630i	−0.146194	−	0.989256i	$-0.546703\pi$
$503$	2.75001	−	0.584533i	0.122617	−	0.0260630i	0.268811	+	0.963193i	$0.413369\pi$
$504$		0			0
$505$	0.766483	+	0.442529i	0.0341081	+	0.0196923i
$506$	39.4124	+	9.50645i	1.75209	+	0.422613i
$507$		0			0
$508$	−4.99717	−	71.4628i	−0.221713	−	3.17065i
$509$	4.72478	+	3.69140i	0.209422	+	0.163618i	0.714913	−	0.699214i	$-0.246466\pi$
$509$	4.72478	+	3.69140i	0.209422	+	0.163618i	−0.505491	+	0.862832i	$0.668689\pi$
$510$		0			0
$511$	12.0776	+	24.7627i	0.534280	+	1.09544i
$512$	21.9749	−	15.9657i	0.971163	−	0.705591i
$513$		0			0
$514$	−0.443580	−	0.144128i	−0.0195655	−	0.00635720i
$515$	2.48354	+	2.57178i	0.109438	+	0.113326i
$516$		0			0
$517$	15.0199	−	21.0098i	0.660574	−	0.924008i
$518$	−21.0411	−	25.0758i	−0.924491	−	1.10177i
$519$		0			0
$520$	0.223440	+	6.39849i	0.00979850	+	0.280592i
$521$	1.17636	−	5.53433i	0.0515372	−	0.242463i	−0.944837	−	0.327540i	$-0.893780\pi$
$521$	1.17636	−	5.53433i	0.0515372	−	0.242463i	0.996374	+	0.0850769i	$0.0271136\pi$
$522$		0			0
$523$	−14.7766	+	33.1888i	−0.646136	+	1.45125i	0.231943	+	0.972729i	$0.425492\pi$
$523$	−14.7766	+	33.1888i	−0.646136	+	1.45125i	−0.878079	+	0.478516i	$0.841175\pi$
$524$	28.4597	−	70.4403i	1.24327	−	3.07720i
$525$		0			0
$526$	18.1443	−	37.2014i	0.791130	−	1.62206i
$527$	−0.383377	−	2.17424i	−0.0167001	−	0.0947112i
$528$		0			0
$529$	1.31370	+	1.10232i	0.0571173	+	0.0479271i
$530$	−1.13845	+	10.8316i	−0.0494509	+	0.470494i
$531$		0			0
$532$	5.72587	+	1.21707i	0.248248	+	0.0527667i
$533$	10.1899	+	6.87318i	0.441374	+	0.297710i
$534$		0			0
$535$	3.54475	−	5.67278i	0.153253	−	0.245256i
$536$	−13.0447	+	16.6965i	−0.563447	+	0.721179i
$537$		0			0
$538$	15.2397	+	2.68717i	0.657031	+	0.115852i
$539$	8.36741	+	10.5423i	0.360410	+	0.454089i
$540$		0			0
$541$	−1.17931	+	1.62318i	−0.0507024	+	0.0697858i	−0.833615	−	0.552345i	$-0.813733\pi$
$541$	−1.17931	+	1.62318i	−0.0507024	+	0.0697858i	0.782913	+	0.622131i	$0.213733\pi$
$542$	0.0518659	−	0.0975456i	0.00222783	−	0.00418994i
$543$		0			0
$544$	6.02675	−	1.72814i	0.258395	−	0.0740935i
$545$	1.20926	−	4.85009i	0.0517992	−	0.207755i
$546$		0			0
$547$	−19.8674	+	0.693783i	−0.849467	+	0.0296640i	−0.456324	−	0.889814i	$-0.650834\pi$
$547$	−19.8674	+	0.693783i	−0.849467	+	0.0296640i	−0.393143	+	0.919478i	$0.628612\pi$
$548$	−42.0640	−	94.4774i	−1.79689	−	4.03587i
$549$		0			0
$550$	14.9250	−	37.7713i	0.636404	−	1.61057i
$551$	−4.46550	+	5.32177i	−0.190236	+	0.226715i
$552$		0			0
$553$	−1.99988	−	0.281064i	−0.0850434	−	0.0119521i
$554$	8.47560	+	15.9403i	0.360094	+	0.677238i
$555$		0			0
$556$	−0.00735985	+	0.105251i	−0.000312127	+	0.00446362i
$557$	−2.31027	+	2.56582i	−0.0978893	+	0.108717i	−0.790099	−	0.612980i	$-0.789971\pi$
$557$	−2.31027	+	2.56582i	−0.0978893	+	0.108717i	0.692209	+	0.721697i	$0.256637\pi$
$558$		0			0
$559$	6.95945	−	3.09855i	0.294353	−	0.131055i
$560$	11.0675	−	4.02822i	0.467685	−	0.170224i
$561$		0			0
$562$	54.1678	−	45.4521i	2.28493	−	1.91728i
$563$	24.9444	+	36.9816i	1.05128	+	1.55859i	0.808491	+	0.588508i	$0.200285\pi$
$563$	24.9444	+	36.9816i	1.05128	+	1.55859i	0.242789	+	0.970079i	$0.421938\pi$
$564$		0			0
$565$	−3.36866	+	0.473435i	−0.141721	+	0.0199175i
$566$	−30.2820	−	41.6797i	−1.27285	−	1.75193i
$567$		0			0
$568$	−85.5262	+	27.7891i	−3.58860	+	1.16601i
$569$	−1.76324	−	0.937531i	−0.0739188	−	0.0393033i	0.432101	−	0.901825i	$-0.357773\pi$
$569$	−1.76324	−	0.937531i	−0.0739188	−	0.0393033i	−0.506019	+	0.862522i	$0.668884\pi$
$570$		0			0
$571$	−1.41619	+	3.89096i	−0.0592658	+	0.162832i	−0.965792	−	0.259318i	$-0.916502\pi$
$571$	−1.41619	+	3.89096i	−0.0592658	+	0.162832i	0.906526	+	0.422150i	$0.138724\pi$
$572$	−8.95932	−	19.7150i	−0.374608	−	0.824326i
$573$		0			0
$574$	11.8382	−	41.2847i	0.494117	−	1.72319i
$575$	−15.8454	+	14.2673i	−0.660799	+	0.594986i
$576$		0			0
$577$	−30.8085	−	13.7168i	−1.28258	−	0.571040i	−0.351610	−	0.936146i	$-0.614366\pi$
$577$	−30.8085	−	13.7168i	−1.28258	−	0.571040i	−0.930966	+	0.365107i	$0.881032\pi$
$578$	44.3692	+	3.10260i	1.84551	+	0.129051i
$579$		0			0
$580$	−4.39205	+	31.2511i	−0.182370	+	1.29763i
$581$	−24.6507	−	12.0230i	−1.02268	−	0.498796i
$582$		0			0
$583$	−6.27189	−	21.2566i	−0.259755	−	0.880359i
$584$	111.323	−	64.2725i	4.60659	−	2.65961i
$585$		0			0
$586$	33.8848	+	37.6329i	1.39977	+	1.55460i
$587$	16.5469	−	12.9279i	0.682965	−	0.533591i	−0.213368	−	0.976972i	$-0.568443\pi$
$587$	16.5469	−	12.9279i	0.682965	−	0.533591i	0.896333	+	0.443381i	$0.146221\pi$
$588$		0			0
$589$	−3.15248	−	0.786002i	−0.129896	−	0.0323866i
$590$	−0.675313	+	19.3384i	−0.0278022	+	0.796151i
$591$		0			0
$592$	−57.8390	+	55.8545i	−2.37717	+	2.29560i
$593$	−6.44646			−0.264724			−0.132362	−	0.991201i	$-0.542256\pi$
$593$	−6.44646			−0.264724			−0.132362	+	0.991201i	$0.542256\pi$
$594$		0			0
$595$	−0.487405			−0.0199816
$596$	−35.1577	+	33.9514i	−1.44011	+	1.39070i
$597$		0			0
$598$	−0.554846	+	15.8887i	−0.0226893	+	0.649738i
$599$	38.2527	+	9.53747i	1.56296	+	0.389691i	0.924875	−	0.380272i	$-0.124170\pi$
$599$	38.2527	+	9.53747i	1.56296	+	0.389691i	0.638089	+	0.769963i	$0.279725\pi$
$600$		0			0
$601$	2.99395	−	2.33913i	0.122126	−	0.0954152i	−0.552747	−	0.833349i	$-0.686421\pi$
$601$	2.99395	−	2.33913i	0.122126	−	0.0954152i	0.674873	+	0.737934i	$0.264198\pi$
$602$	−17.8118	−	19.7820i	−0.725953	−	0.806253i
$603$		0			0
$604$	1.08278	−	0.625144i	0.0440577	−	0.0254367i
$605$	−0.103688	−	6.76577i	−0.00421553	−	0.275068i
$606$		0			0
$607$	−29.5372	−	14.4062i	−1.19888	−	0.584731i	−0.272801	−	0.962070i	$-0.587950\pi$
$607$	−29.5372	−	14.4062i	−1.19888	−	0.584731i	−0.926075	+	0.377340i	$0.876839\pi$
$608$	1.28407	−	9.13665i	0.0520760	−	0.370540i
$609$		0			0
$610$	−9.27268	−	0.648409i	−0.375440	−	0.0262533i
$611$	9.25202	+	4.11926i	0.374297	+	0.166648i
$612$		0			0
$613$	−24.0394	+	21.6452i	−0.970943	+	0.874241i	−0.992089	−	0.125536i	$-0.959935\pi$
$613$	−24.0394	+	21.6452i	−0.970943	+	0.874241i	0.0211464	+	0.999776i	$0.493268\pi$
$614$	−0.564936	+	1.97016i	−0.0227989	+	0.0795094i
$615$		0			0
$616$	−33.5962	+	30.7195i	−1.35363	+	1.23772i
$617$	−1.50850	+	4.14458i	−0.0607301	+	0.166855i	−0.966347	−	0.257242i	$-0.917186\pi$
$617$	−1.50850	+	4.14458i	−0.0607301	+	0.166855i	0.905617	+	0.424097i	$0.139408\pi$
$618$		0			0
$619$	−31.8406	−	16.9300i	−1.27978	−	0.680472i	−0.316406	−	0.948624i	$-0.602476\pi$
$619$	−31.8406	−	16.9300i	−1.27978	−	0.680472i	−0.963377	+	0.268152i	$0.913587\pi$
$620$	−14.0367	+	4.56080i	−0.563727	+	0.183166i
$621$		0			0
$622$	25.2680	+	34.7784i	1.01315	+	1.39449i
$623$	22.1225	−	3.10912i	0.886321	−	0.124564i
$624$		0			0
$625$	10.8859	+	16.1390i	0.435436	+	0.645561i
$626$	−29.1663	+	24.4734i	−1.16572	+	0.978154i
$627$		0			0
$628$	−20.6270	+	7.50761i	−0.823106	+	0.299586i
$629$	3.03980	−	1.35340i	0.121205	−	0.0539638i
$630$		0			0
$631$	−5.68225	+	6.31078i	−0.226207	+	0.251228i	−0.845555	−	0.533888i	$-0.820730\pi$
$631$	−5.68225	+	6.31078i	−0.226207	+	0.251228i	0.619348	+	0.785116i	$0.287397\pi$
$632$	−0.657284	+	9.39960i	−0.0261453	+	0.373896i
$633$		0			0
$634$	−27.2108	−	51.1761i	−1.08068	−	2.03246i
$635$	8.69236	+	1.22163i	0.344946	+	0.0484790i
$636$		0			0
$637$	−3.39260	+	4.04314i	−0.134420	+	0.160195i
$638$	−22.3918	−	86.9644i	−0.886499	−	3.44295i
$639$		0			0
$640$	−2.24701	−	5.04687i	−0.0888209	−	0.199495i
$641$	−24.8086	+	0.866336i	−0.979881	+	0.0342182i	−0.520359	−	0.853948i	$-0.674202\pi$
$641$	−24.8086	+	0.866336i	−0.979881	+	0.0342182i	−0.459523	+	0.888166i	$0.651980\pi$
$642$		0			0
$643$	0.629637	−	2.52534i	0.0248305	−	0.0995896i	−0.956602	−	0.291398i	$-0.905880\pi$
$643$	0.629637	−	2.52534i	0.0248305	−	0.0995896i	0.981432	+	0.191808i	$0.0614352\pi$
$644$	38.1874	−	10.9501i	1.50480	−	0.431493i
$645$		0			0
$646$	−0.390649	+	0.734704i	−0.0153699	+	0.0289065i
$647$	−17.8579	+	24.5794i	−0.702068	+	0.966314i	0.297863	+	0.954609i	$0.403726\pi$
$647$	−17.8579	+	24.5794i	−0.702068	+	0.966314i	−0.999931	+	0.0117056i	$0.996274\pi$
$648$		0			0
$649$	−13.7504	−	36.8968i	−0.539751	−	1.44833i
$650$	15.6841	+	2.76553i	0.615181	+	0.108473i
$651$		0			0
$652$	2.51314	−	3.21668i	0.0984223	−	0.125975i
$653$	−16.0821	+	25.7367i	−0.629340	+	1.00715i	0.367676	+	0.929954i	$0.380154\pi$
$653$	−16.0821	+	25.7367i	−0.629340	+	1.00715i	−0.997016	+	0.0772001i	$0.975402\pi$
$654$		0			0
$655$	7.71748	+	5.20550i	0.301547	+	0.203396i
$656$	−103.190	−	21.9337i	−4.02890	−	0.856369i
$657$		0			0
$658$	3.69907	−	35.1943i	0.144205	−	1.37202i
$659$	4.92089	+	4.12912i	0.191691	+	0.160848i	0.733582	−	0.679601i	$-0.237847\pi$
$659$	4.92089	+	4.12912i	0.191691	+	0.160848i	−0.541891	+	0.840449i	$0.682292\pi$
$660$		0			0
$661$	7.94027	+	45.0315i	0.308841	+	1.75152i	0.604853	+	0.796338i	$0.293232\pi$
$661$	7.94027	+	45.0315i	0.308841	+	1.75152i	−0.296012	+	0.955184i	$0.595657\pi$
$662$	−10.1795	+	20.8712i	−0.395639	+	0.811180i
$663$		0			0
$664$	−47.9361	+	118.646i	−1.86028	+	4.60436i
$665$	−0.291740	+	0.655259i	−0.0113132	+	0.0254099i
$666$		0			0
$667$	−9.80218	+	46.1156i	−0.379542	+	1.78560i
$668$	1.35287	+	38.7410i	0.0523439	+	1.49893i
$669$		0			0
$670$	−2.77387	−	3.30577i	−0.107164	−	0.127713i
$671$	17.9440	−	5.98273i	0.692719	−	0.230961i
$672$		0			0
$673$	−22.2843	−	23.0761i	−0.858997	−	0.889517i	0.135869	−	0.990727i	$-0.456618\pi$
$673$	−22.2843	−	23.0761i	−0.858997	−	0.889517i	−0.994865	+	0.101210i	$0.967729\pi$
$674$	−79.9773	−	25.9862i	−3.08061	−	1.00095i
$675$		0			0
$676$	−45.9296	+	33.3698i	−1.76652	+	1.28345i
$677$	9.78355	+	20.0593i	0.376012	+	0.770940i	0.999944	−	0.0105388i	$-0.00335468\pi$
$677$	9.78355	+	20.0593i	0.376012	+	0.770940i	−0.623932	+	0.781479i	$0.714466\pi$
$678$		0			0
$679$	−10.6035	−	8.28437i	−0.406925	−	0.317925i
$680$	0.158633	+	2.26855i	0.00608328	+	0.0869950i
$681$		0			0
$682$	31.9644	−	27.2414i	1.22398	−	1.04313i
$683$	0.999916	+	0.577302i	0.0382607	+	0.0220898i	0.519008	−	0.854769i	$-0.326301\pi$
$683$	0.999916	+	0.577302i	0.0382607	+	0.0220898i	−0.480748	+	0.876859i	$0.659635\pi$
$684$		0			0
$685$	12.3950	−	2.63465i	0.473590	−	0.100665i
$686$	46.5947	+	18.8255i	1.77900	+	0.718761i
$687$		0			0
$688$	−45.4207	+	47.0345i	−1.73165	+	1.79317i
$689$	7.67355	−	4.08010i	0.292339	−	0.155439i
$690$		0			0
$691$	−0.807116	−	3.23717i	−0.0307042	−	0.123148i	0.952988	−	0.303008i	$-0.0979909\pi$
$691$	−0.807116	−	3.23717i	−0.0307042	−	0.123148i	−0.983692	+	0.179860i	$0.942435\pi$
$692$	5.47387	+	9.48103i	0.208085	+	0.360415i
$693$		0			0
$694$	−3.57766	+	6.19669i	−0.135806	+	0.235223i
$695$	−0.0124272	−	0.00356343i	−0.000471389	−	0.000135169i
$696$		0			0
$697$	3.70239	+	2.31351i	0.140238	+	0.0876304i
$698$	−12.8741	−	44.8975i	−0.487294	−	1.69940i
$699$		0			0
$700$	−5.53846	−	39.4082i	−0.209334	−	1.48949i
$701$	5.28920	−	16.2785i	0.199770	−	0.614829i	−0.800118	−	0.599843i	$-0.795230\pi$
$701$	5.28920	−	16.2785i	0.199770	−	0.614829i	0.999888	−	0.0149862i	$-0.00477042\pi$
$702$		0			0
$703$		−	4.89674i		−	0.184684i
$704$	32.7675	+	31.1615i	1.23497	+	1.17444i
$705$		0			0
$706$	17.5621	−	11.8458i	0.660958	−	0.445822i
$707$	−2.28809	+	0.924448i	−0.0860525	+	0.0347675i
$708$		0			0
$709$	−9.13602	+	13.5447i	−0.343110	+	0.508682i	−0.960614	−	0.277886i	$-0.910366\pi$
$709$	−9.13602	+	13.5447i	−0.343110	+	0.508682i	0.617504	+	0.786568i	$0.288144\pi$
$710$	−1.91449	−	18.2151i	−0.0718494	−	0.683601i
$711$		0			0
$712$	−21.6710	−	101.954i	−0.812155	−	3.82089i
$713$	−21.3941	+	5.33415i	−0.801216	+	0.199765i
$714$		0			0
$715$	2.59115	−	0.571552i	0.0969037	−	0.0213748i
$716$	10.1569	−	1.79094i	0.379582	−	0.0669305i
$717$		0			0
$718$	71.5109	−	44.6850i	2.66876	−	1.66763i
$719$	−17.5280	−	15.7823i	−0.653685	−	0.588581i	0.274098	−	0.961702i	$-0.411621\pi$
$719$	−17.5280	−	15.7823i	−0.653685	−	0.588581i	−0.927783	+	0.373121i	$0.878288\pi$
$720$		0			0
$721$	−9.91401	+	1.04200i	−0.369217	+	0.0388063i
$722$	−30.2398	−	38.7052i	−1.12541	−	1.44046i
$723$		0			0
$724$	4.85645	−	0.339596i	0.180488	−	0.0126210i
$725$	44.3797	+	16.1529i	1.64822	+	0.599903i
$726$		0			0
$727$	5.17861	−	29.3693i	0.192064	−	1.08925i	−0.724474	−	0.689302i	$-0.757917\pi$
$727$	5.17861	−	29.3693i	0.192064	−	1.08925i	0.916538	−	0.399947i	$-0.130971\pi$
$728$	−14.4423	−	10.4929i	−0.535265	−	0.388893i
$729$		0			0
$730$	8.09026	+	24.8993i	0.299434	+	0.921563i
$731$	2.43204	−	1.18618i	0.0899522	−	0.0438726i
$732$		0			0
$733$	−26.9299	−	0.940411i	−0.994677	−	0.0347349i	−0.467067	−	0.884222i	$-0.654689\pi$
$733$	−26.9299	−	0.940411i	−0.994677	−	0.0347349i	−0.527610	+	0.849487i	$0.676912\pi$
$734$	−13.1429	−	32.5297i	−0.485111	−	1.20069i
$735$		0			0
$736$	−21.4155	−	58.8385i	−0.789385	−	2.16882i
$737$	7.78482	+	4.06306i	0.286758	+	0.149665i
$738$		0			0
$739$	8.64270	+	0.908384i	0.317927	+	0.0334155i	0.262148	−	0.965028i	$-0.415569\pi$
$739$	8.64270	+	0.908384i	0.317927	+	0.0334155i	0.0557789	+	0.998443i	$0.482236\pi$
$740$	−11.7876	−	18.8642i	−0.433322	−	0.693461i
$741$		0			0
$742$	−21.8447	−	21.0952i	−0.801946	−	0.774430i
$743$	−5.16550	−	4.98827i	−0.189504	−	0.183002i	0.593854	−	0.804573i	$-0.297606\pi$
$743$	−5.16550	−	4.98827i	−0.189504	−	0.183002i	−0.783358	+	0.621571i	$0.786495\pi$
$744$		0			0
$745$	−3.17352	−	5.07870i	−0.116269	−	0.186069i
$746$	82.6841	+	8.69045i	3.02728	+	0.318180i
$747$		0			0
$748$	−3.42475	−	6.88733i	−0.125221	−	0.251826i
$749$	6.37914	+	17.5266i	0.233089	+	0.640406i
$750$		0			0
$751$	−1.77556	−	4.39466i	−0.0647911	−	0.160364i	0.891315	−	0.453385i	$-0.149784\pi$
$751$	−1.77556	−	4.39466i	−0.0647911	−	0.160364i	−0.956106	+	0.293021i	$0.905339\pi$
$752$	−86.8719	−	3.03363i	−3.16789	−	0.110625i
$753$		0			0
$754$	31.6506	−	15.4370i	1.15265	−	0.562183i
$755$	0.0473410	+	0.145701i	0.00172292	+	0.00530259i
$756$		0			0
$757$	−8.61542	−	6.25947i	−0.313133	−	0.227504i	0.420107	−	0.907475i	$-0.361993\pi$
$757$	−8.61542	−	6.25947i	−0.313133	−	0.227504i	−0.733240	+	0.679970i	$0.761993\pi$
$758$	−8.16944	+	46.3312i	−0.296728	+	1.68283i
$759$		0			0
$760$	3.14475	+	1.14460i	0.114072	+	0.0415189i
$761$	−36.2615	+	2.53565i	−1.31448	+	0.0919174i	−0.709716	−	0.704488i	$-0.751177\pi$
$761$	−36.2615	+	2.53565i	−1.31448	+	0.0919174i	−0.604764	+	0.796405i	$0.706732\pi$
$762$		0			0
$763$	8.58071	+	10.9828i	0.310642	+	0.397604i
$764$	−40.0153	+	4.20578i	−1.44770	+	0.152160i
$765$		0			0
$766$	−7.22844	−	6.50852i	−0.261174	−	0.235162i
$767$	13.0945	−	8.18238i	0.472817	−	0.295449i
$768$		0			0
$769$	21.4421	−	3.78082i	0.773221	−	0.136340i	0.226903	−	0.973917i	$-0.427140\pi$
$769$	21.4421	−	3.78082i	0.773221	−	0.136340i	0.546318	+	0.837578i	$0.316029\pi$
$770$	−4.69725	−	7.99380i	−0.169277	−	0.288077i
$771$		0			0
$772$	−43.7782	+	10.9151i	−1.57561	+	0.392844i
$773$	10.8130	+	50.8713i	0.388917	+	1.82971i	0.540596	+	0.841282i	$0.318199\pi$
$773$	10.8130	+	50.8713i	0.388917	+	1.82971i	−0.151679	+	0.988430i	$0.548468\pi$
$774$		0			0
$775$	2.30876	+	21.9664i	0.0829332	+	0.789057i
$776$	−35.1073	+	52.0487i	−1.26028	+	1.86844i
$777$		0			0
$778$	6.45395	−	2.60756i	0.231385	−	0.0934857i
$779$	5.32634	−	3.59266i	0.190836	−	0.128720i
$780$		0			0
$781$	17.7489	+	32.7725i	0.635104	+	1.17269i
$782$			5.64701i			0.201937i
$783$		0			0
$784$	13.9986	−	43.0833i	0.499950	−	1.53869i
$785$	−0.374327	−	2.66347i	−0.0133603	−	0.0950634i
$786$		0			0
$787$	−9.24426	−	32.2386i	−0.329522	−	1.14918i	−0.935391	−	0.353616i	$-0.884952\pi$
$787$	−9.24426	−	32.2386i	−0.329522	−	1.14918i	0.605868	−	0.795565i	$-0.292826\pi$
$788$	78.5553	+	49.0868i	2.79841	+	1.74864i
$789$		0			0
$790$	−1.84474	−	0.528970i	−0.0656329	−	0.0188199i
$791$	4.74253	−	8.21430i	0.168625	−	0.292067i
$792$		0			0
$793$	3.70867	+	6.42361i	0.131699	+	0.228109i
$794$	13.3902	+	53.7053i	0.475202	+	1.90593i
$795$		0			0
$796$	5.00497	−	2.66119i	0.177396	−	0.0943233i
$797$	27.1186	−	28.0821i	0.960589	−	0.994719i	−0.0394010	−	0.999223i	$-0.512545\pi$
$797$	27.1186	−	28.0821i	0.960589	−	0.994719i	0.999990	+	0.00450455i	$0.00143385\pi$
$798$		0			0
$799$	3.33532	+	1.34756i	0.117995	+	0.0476732i
$800$	−61.3529	+	13.0410i	−2.16915	+	0.461067i
$801$		0			0
$802$	−58.3686	−	33.6991i	−2.06107	−	1.18996i
$803$	−34.5561	−	40.5474i	−1.21946	−	1.43089i
$804$		0			0
$805$	0.339554	+	4.85585i	0.0119677	+	0.171146i
$806$	12.9778	+	10.1393i	0.457122	+	0.357143i
$807$		0			0
$808$	5.04739	+	10.3487i	0.177567	+	0.364066i
$809$	2.83436	−	2.05928i	0.0996507	−	0.0724004i	−0.536844	−	0.843681i	$-0.680384\pi$
$809$	2.83436	−	2.05928i	0.0996507	−	0.0724004i	0.636495	+	0.771281i	$0.280384\pi$
$810$		0			0
$811$	9.72074	+	3.15846i	0.341342	+	0.110909i	0.474671	−	0.880163i	$-0.342567\pi$
$811$	9.72074	+	3.15846i	0.341342	+	0.110909i	−0.133330	+	0.991072i	$0.542567\pi$
$812$	−61.1249	−	63.2967i	−2.14506	−	2.22128i
$813$		0			0
$814$	51.4922	+	36.8118i	1.80480	+	1.29025i
$815$	0.321506	+	0.383156i	0.0112619	+	0.0134214i
$816$		0			0
$817$	−0.138970	−	3.97959i	−0.00486196	−	0.139228i
$818$	15.8308	−	74.4781i	0.553511	−	2.60407i
$819$		0			0
$820$	11.8707	−	26.6621i	0.414544	−	0.931082i
$821$	−3.54449	+	8.77292i	−0.123704	+	0.306177i	−0.976310	−	0.216377i	$-0.930576\pi$
$821$	−3.54449	+	8.77292i	−0.123704	+	0.306177i	0.852606	+	0.522554i	$0.175021\pi$
$822$		0			0
$823$	7.02589	−	14.4052i	0.244907	−	0.502134i	−0.740562	−	0.671988i	$-0.765441\pi$
$823$	7.02589	−	14.4052i	0.244907	−	0.502134i	0.985469	+	0.169854i	$0.0543296\pi$
$824$	8.07650	+	45.8041i	0.281358	+	1.59566i
$825$		0			0
$826$	−41.3309	−	34.6808i	−1.43809	−	1.20670i
$827$	−2.36548	+	22.5061i	−0.0822559	+	0.782613i	0.873177	+	0.487404i	$0.162056\pi$
$827$	−2.36548	+	22.5061i	−0.0822559	+	0.782613i	−0.955433	+	0.295209i	$0.904611\pi$
$828$		0			0
$829$	13.8865	+	2.95167i	0.482299	+	0.102516i	0.442644	−	0.896698i	$-0.354041\pi$
$829$	13.8865	+	2.95167i	0.482299	+	0.102516i	0.0396555	+	0.999213i	$0.487374\pi$
$830$	−21.6066	−	14.5738i	−0.749976	−	0.505865i
$831$		0			0
$832$	−9.39660	+	15.0377i	−0.325768	+	0.521339i
$833$	−1.15418	+	1.47728i	−0.0399898	+	0.0511847i
$834$		0			0
$835$	−4.67770	−	0.824805i	−0.161879	−	0.0285436i
$836$	−11.3091	+	0.481706i	−0.391134	+	0.0166601i
$837$		0			0
$838$	−25.9873	+	35.7684i	−0.897716	+	1.23560i
$839$	−0.648782	+	1.22018i	−0.0223985	+	0.0421254i	−0.893896	−	0.448275i	$-0.852038\pi$
$839$	−0.648782	+	1.22018i	−0.0223985	+	0.0421254i	0.871497	+	0.490401i	$0.163150\pi$
$840$		0			0
$841$	72.5049	−	20.7904i	2.50017	−	0.716912i
$842$	20.7695	−	83.3020i	0.715765	−	2.87078i
$843$		0			0
$844$	59.3246	−	2.07166i	2.04204	−	0.0713095i
$845$	−2.82940	−	6.35493i	−0.0973342	−	0.218616i
$846$		0			0
$847$	15.0437	+	11.3865i	0.516907	+	0.391245i
$848$	−47.9476	+	57.1417i	−1.64653	+	1.96225i
$849$		0			0
$850$	5.60178	+	0.787279i	0.192140	+	0.0270035i
$851$	−15.6012	−	29.3416i	−0.534803	−	1.00582i
$852$		0			0
$853$	1.86451	−	26.6638i	0.0638397	−	0.912951i	−0.855077	−	0.518500i	$-0.826490\pi$
$853$	1.86451	−	26.6638i	0.0638397	−	0.912951i	0.918917	−	0.394451i	$-0.129065\pi$
$854$	17.3425	−	19.2607i	0.593447	−	0.659089i
$855$		0			0
$856$	79.4985	−	35.3950i	2.71720	−	1.20978i
$857$	15.8178	−	5.75720i	0.540325	−	0.196662i	−0.0574176	−	0.998350i	$-0.518287\pi$
$857$	15.8178	−	5.75720i	0.540325	−	0.196662i	0.597743	+	0.801688i	$0.296064\pi$
$858$		0			0
$859$	−14.7210	+	12.3524i	−0.502275	+	0.421459i	−0.858401	−	0.512979i	$-0.828542\pi$
$859$	−14.7210	+	12.3524i	−0.502275	+	0.421459i	0.356126	+	0.934438i	$0.384097\pi$
$860$	−10.1152	−	14.9964i	−0.344926	−	0.511373i
$861$		0			0
$862$	24.9428	−	3.50548i	0.849554	−	0.119397i
$863$	27.5578	+	37.9300i	0.938078	+	1.29115i	0.956624	+	0.291325i	$0.0940961\pi$
$863$	27.5578	+	37.9300i	0.938078	+	1.29115i	−0.0185466	+	0.999828i	$0.505904\pi$
$864$		0			0
$865$	−1.27578	+	0.414527i	−0.0433779	+	0.0140943i
$866$	53.7023	+	28.5540i	1.82488	+	0.970306i
$867$		0			0
$868$	14.0749	−	38.6704i	0.477733	−	1.31256i
$869$	3.88050	−	0.437943i	0.131637	−	0.0148562i
$870$		0			0
$871$	−0.949161	+	3.31012i	−0.0321611	+	0.112159i
$872$	48.3251	−	43.5121i	1.63649	−	1.47350i
$873$		0			0
$874$	7.59175	+	3.38007i	0.256795	+	0.114332i
$875$	10.1269	+	0.708139i	0.342350	+	0.0239395i
$876$		0			0
$877$	0.259749	−	1.84821i	0.00877109	−	0.0624095i	−0.985391	−	0.170309i	$-0.945523\pi$
$877$	0.259749	−	1.84821i	0.00877109	−	0.0624095i	0.994162	+	0.107899i	$0.0344124\pi$
$878$	−13.3173	−	6.49527i	−0.449437	−	0.219205i
$879$		0			0
$880$	−18.7827	+	12.8796i	−0.633165	+	0.434171i
$881$	44.4271	−	25.6500i	1.49679	−	0.864171i	0.496795	−	0.867868i	$-0.334510\pi$
$881$	44.4271	−	25.6500i	1.49679	−	0.864171i	0.999993	+	0.00369717i	$0.00117685\pi$
$882$		0			0
$883$	−6.74628	−	7.49250i	−0.227030	−	0.252143i	0.618858	−	0.785503i	$-0.287596\pi$
$883$	−6.74628	−	7.49250i	−0.227030	−	0.252143i	−0.845888	+	0.533360i	$0.820929\pi$
$884$	2.37686	−	1.85700i	0.0799423	−	0.0624578i
$885$		0			0
$886$	−29.3428	−	7.31598i	−0.985790	−	0.245785i
$887$	−1.82039	+	52.1291i	−0.0611226	+	1.75032i	0.452009	+	0.892013i	$0.350708\pi$
$887$	−1.82039	+	52.1291i	−0.0611226	+	1.75032i	−0.513132	+	0.858310i	$0.671515\pi$
$888$		0			0
$889$	−17.6057	+	17.0017i	−0.590477	+	0.570217i
$890$	21.2288			0.711591
$891$		0			0
$892$	135.752			4.54533
$893$	3.80802	−	3.67736i	0.127430	−	0.123058i
$894$		0			0
$895$	−0.0441037	+	1.26296i	−0.00147422	+	0.0422163i
$896$	14.9462	+	3.72651i	0.499318	+	0.124494i
$897$		0			0
$898$	−28.1060	+	21.9588i	−0.937909	+	0.732775i
$899$	32.6790	+	36.2937i	1.08991	+	1.21046i
$900$		0			0
$901$	2.67336	−	1.54347i	0.0890626	−	0.0514203i
$902$	−2.26234	+	83.0179i	−0.0753276	+	2.76419i
$903$		0			0
$904$	−39.7757	−	19.3999i	−1.32292	−	0.645232i
$905$	−0.0830192	+	0.590713i	−0.00275965	+	0.0196359i
$906$		0			0
$907$	15.6258	+	1.09266i	0.518845	+	0.0362812i	0.326779	−	0.945101i	$-0.394037\pi$
$907$	15.6258	+	1.09266i	0.518845	+	0.0362812i	0.192066	+	0.981382i	$0.438481\pi$
$908$	−56.9199	−	25.3424i	−1.88895	−	0.841017i
$909$		0			0
$910$	2.70194	−	2.43284i	0.0895684	−	0.0806478i
$911$	10.8960	−	37.9990i	0.361002	−	1.25896i	−0.545981	−	0.837797i	$-0.683843\pi$
$911$	10.8960	−	37.9990i	0.361002	−	1.25896i	0.906983	−	0.421166i	$-0.138379\pi$
$912$		0			0
$913$	51.9581	+	10.6286i	1.71956	+	0.351755i
$914$	−2.24596	+	6.17073i	−0.0742899	+	0.204110i
$915$		0			0
$916$	−84.6139	−	44.9900i	−2.79572	−	1.48651i
$917$	−24.6855	+	8.02082i	−0.815188	+	0.264871i
$918$		0			0
$919$	−12.2576	−	16.8711i	−0.404340	−	0.556527i	0.557486	−	0.830186i	$-0.311766\pi$
$919$	−12.2576	−	16.8711i	−0.404340	−	0.556527i	−0.961827	+	0.273659i	$0.911766\pi$
$920$	22.4903	−	3.16080i	0.741483	−	0.104209i
$921$		0			0
$922$	−19.1967	−	28.4602i	−0.632209	−	0.937288i
$923$	−11.1958	+	9.39440i	−0.368514	+	0.309220i
$924$		0			0
$925$	−31.2816	+	11.3856i	−1.02853	+	0.374356i
$926$	−25.4758	+	11.3426i	−0.837188	+	0.372740i
$927$		0			0
$928$	−92.8015	+	103.067i	−3.04636	+	3.38333i
$929$	3.65114	−	52.2138i	0.119790	−	1.71308i	−0.451450	−	0.892296i	$-0.649093\pi$
$929$	3.65114	−	52.2138i	0.119790	−	1.71308i	0.571240	−	0.820783i	$-0.306462\pi$
$930$		0			0
$931$	1.29519	+	2.43589i	0.0424480	+	0.0798332i
$932$	27.7379	+	3.89831i	0.908586	+	0.127693i
$933$		0			0
$934$	−23.4260	+	27.9181i	−0.766524	+	0.913507i
$935$	0.912717	−	0.235008i	0.0298490	−	0.00768559i
$936$		0			0
$937$	16.2224	+	36.4362i	0.529963	+	1.19032i	0.958056	+	0.286582i	$0.0925192\pi$
$937$	16.2224	+	36.4362i	0.529963	+	1.19032i	−0.428092	+	0.903735i	$0.640814\pi$
$938$	12.0251	−	0.419926i	0.392633	−	0.0137111i
$939$		0			0
$940$	5.81768	−	23.3334i	0.189752	−	0.761053i
$941$	−40.5143	+	11.6173i	−1.32073	+	0.378713i	−0.860665	−	0.509172i	$-0.829952\pi$
$941$	−40.5143	+	11.6173i	−1.32073	+	0.378713i	−0.460065	+	0.887885i	$0.652174\pi$
$942$		0			0
$943$	20.4694	−	38.4974i	0.666576	−	1.25365i
$944$	−77.8980	+	107.217i	−2.53536	+	3.48963i
$945$		0			0
$946$	42.8925	+	28.4557i	1.39456	+	0.925173i
$947$	−32.7602	−	5.77651i	−1.06456	−	0.187711i	−0.386183	−	0.922422i	$-0.626207\pi$
$947$	−32.7602	−	5.77651i	−1.06456	−	0.187711i	−0.678381	+	0.734711i	$0.737318\pi$
$948$		0			0
$949$	12.8619	−	16.4625i	0.417515	−	0.534395i
$950$	4.41140	−	7.05971i	0.143125	−	0.229047i
$951$		0			0
$952$	−5.25675	−	3.54572i	−0.170372	−	0.114917i
$953$	−23.8326	−	5.06577i	−0.772013	−	0.164097i	−0.194969	−	0.980809i	$-0.562461\pi$
$953$	−23.8326	−	5.06577i	−0.772013	−	0.164097i	−0.577044	+	0.816713i	$0.695794\pi$
$954$		0			0
$955$	0.515338	−	4.90312i	0.0166760	−	0.158661i
$956$	−24.2642	−	20.3601i	−0.784760	−	0.658492i
$957$		0			0
$958$	2.39835	+	13.6017i	0.0774872	+	0.439452i
$959$	−15.4889	+	31.7569i	−0.500163	+	1.02549i
$960$		0			0
$961$	3.05662	−	7.56541i	0.0986007	−	0.244045i
$962$	−10.0958	+	22.6755i	−0.325501	+	0.731088i
$963$		0			0
$964$	4.24143	−	19.9543i	0.136607	−	0.642686i
$965$	−0.192938	−	5.52503i	−0.00621090	−	0.177857i
$966$		0			0
$967$	27.4619	+	32.7278i	0.883115	+	1.05246i	0.998252	+	0.0591061i	$0.0188250\pi$
$967$	27.4619	+	32.7278i	0.883115	+	1.05246i	−0.115136	+	0.993350i	$0.536731\pi$
$968$	48.1006	−	73.7244i	1.54601	−	2.36959i
$969$		0			0
$970$	−8.88242	−	9.19802i	−0.285197	−	0.295331i
$971$	30.4399	+	9.89052i	0.976863	+	0.317402i	0.753583	−	0.657352i	$-0.228324\pi$
$971$	30.4399	+	9.89052i	0.976863	+	0.317402i	0.223280	+	0.974754i	$0.428324\pi$
$972$		0			0
$973$	0.0291624	−	0.0211877i	0.000934902	−	0.000679246i
$974$	−22.7529	−	46.6503i	−0.729050	−	1.49477i
$975$		0			0
$976$	−50.1670	−	39.1948i	−1.60581	−	1.25459i
$977$	−2.37190	−	33.9197i	−0.0758837	−	1.08519i	−0.875036	−	0.484059i	$-0.839162\pi$
$977$	−2.37190	−	33.9197i	−0.0758837	−	1.08519i	0.799152	−	0.601129i	$-0.205282\pi$
$978$		0			0
$979$	−39.9277	+	16.4888i	−1.27609	+	0.526985i
$980$	10.8533	+	6.26618i	0.346697	+	0.200166i
$981$		0			0
$982$	−8.37909	+	1.78103i	−0.267388	+	0.0568350i
$983$	32.8951	+	13.2905i	1.04919	+	0.423900i	0.833475	−	0.552557i	$-0.186348\pi$
$983$	32.8951	+	13.2905i	1.04919	+	0.423900i	0.215714	+	0.976457i	$0.430792\pi$
$984$		0			0
$985$	−7.88445	+	8.16459i	−0.251220	+	0.260146i
$986$	11.0439	−	5.87214i	0.351709	−	0.187007i
$987$		0			0
$988$	−1.07384	−	4.30693i	−0.0341633	−	0.137022i
$989$	−13.5119	−	23.4032i	−0.429652	−	0.744179i
$990$		0			0
$991$	24.1598	−	41.8460i	0.767461	−	1.32928i	−0.171475	−	0.985189i	$-0.554853\pi$
$991$	24.1598	−	41.8460i	0.767461	−	1.32928i	0.938936	−	0.344093i	$-0.111813\pi$
$992$	−62.3494	−	17.8784i	−1.97960	−	0.567640i
$993$		0			0
$994$	43.3085	+	27.0622i	1.37366	+	0.858360i
$995$	0.191448	+	0.667657i	0.00606930	+	0.0211662i
$996$		0			0
$997$	−1.11975	−	7.96742i	−0.0354628	−	0.252331i	0.964467	−	0.264204i	$-0.0851093\pi$
$997$	−1.11975	−	7.96742i	−0.0354628	−	0.252331i	−0.999930	+	0.0118736i	$0.996220\pi$
$998$	−21.0196	+	64.6918i	−0.665365	+	2.04778i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.656.1		816
3.2	odd	2		297.2.x.a.29.34	✓	816
11.8	odd	10	inner	891.2.bb.a.8.1		816
27.13	even	9		297.2.x.a.95.34	yes	816
27.14	odd	18	inner	891.2.bb.a.557.1		816
33.8	even	10		297.2.x.a.272.34	yes	816
297.41	even	90	inner	891.2.bb.a.800.1		816
297.283	odd	90		297.2.x.a.41.34	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.29.34	✓	816	3.2	odd	2
297.2.x.a.41.34	yes	816	297.283	odd	90
297.2.x.a.95.34	yes	816	27.13	even	9
297.2.x.a.272.34	yes	816	33.8	even	10
891.2.bb.a.8.1		816	11.8	odd	10	inner
891.2.bb.a.557.1		816	27.14	odd	18	inner
891.2.bb.a.656.1		816	1.1	even	1	trivial
891.2.bb.a.800.1		816	297.41	even	90	inner

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bb (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.90595 + 1.84056i) q^{2} +(0.175206 - 5.01725i) q^{4} +(0.596870 + 0.148816i) q^{5} +(-1.35158 + 1.05597i) q^{7} +(5.35476 + 5.94706i) q^{8} +O(q^{10})\)	\(q+(-1.90595 + 1.84056i) q^{2} +(0.175206 - 5.01725i) q^{4} +(0.596870 + 0.148816i) q^{5} +(-1.35158 + 1.05597i) q^{7} +(5.35476 + 5.94706i) q^{8} +(-1.41151 + 0.814937i) q^{10} +(2.02183 - 2.62910i) q^{11} +(1.16895 + 0.570137i) q^{13} +(0.632476 - 4.50030i) q^{14} +(-11.1357 - 0.778681i) q^{16} +(0.422020 + 0.187896i) q^{17} +(0.505207 - 0.454891i) q^{19} +(0.851224 - 2.96857i) q^{20} +(0.985499 + 8.73225i) q^{22} +(1.57794 - 4.33534i) q^{23} +(-4.08063 - 2.16971i) q^{25} +(-3.27734 + 1.06487i) q^{26} +(5.06127 + 6.96624i) q^{28} +(-10.1195 + 1.42220i) q^{29} +(-2.67248 - 3.96211i) q^{31} +(10.3966 - 8.72380i) q^{32} +(-1.15018 + 0.418632i) q^{34} +(-0.963866 + 0.429141i) q^{35} +(4.81972 - 5.35285i) q^{37} +(-0.125649 + 1.79686i) q^{38} +(2.31107 + 4.34650i) q^{40} +(9.35861 + 1.31527i) q^{41} +(3.76508 - 4.48705i) q^{43} +(-12.8366 - 10.6047i) q^{44} +(4.97198 + 11.1672i) q^{46} +(7.78223 - 0.271762i) q^{47} +(-0.981753 + 3.93760i) q^{49} +(11.7710 - 3.37527i) q^{50} +(3.06533 - 5.76504i) q^{52} +(3.92774 - 5.40607i) q^{53} +(1.59803 - 1.26835i) q^{55} +(-13.5173 - 2.38347i) q^{56} +(16.6696 - 21.3362i) q^{58} +(6.29133 - 10.0682i) q^{59} +(4.72808 + 3.18913i) q^{61} +(12.3861 + 2.63275i) q^{62} +(-1.42514 + 13.5593i) q^{64} +(0.612868 + 0.514258i) q^{65} +(0.459764 + 2.60745i) q^{67} +(1.01666 - 2.08446i) q^{68} +(1.04723 - 2.59197i) q^{70} +(-4.57064 + 10.2658i) q^{71} +(3.33968 - 15.7120i) q^{73} +(0.666053 + 19.0733i) q^{74} +(-2.19378 - 2.61445i) q^{76} +(0.0435864 + 5.68846i) q^{77} +(0.817920 + 0.846981i) q^{79} +(-6.53066 - 2.12194i) q^{80} +(-20.2579 + 14.7182i) q^{82} +(7.00971 + 14.3720i) q^{83} +(0.223929 + 0.174953i) q^{85} +(1.08260 + 15.4820i) q^{86} +(26.4619 - 2.05425i) q^{88} +(-11.2798 - 6.51241i) q^{89} +(-2.18199 + 0.463796i) q^{91} +(-21.4750 - 8.67647i) q^{92} +(-14.3324 + 14.8416i) q^{94} +(0.369238 - 0.196328i) q^{95} +(1.89794 + 7.61221i) q^{97} +(-5.37620 - 9.31185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8}+O(q^{10}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29} - 9 q^{31} - 42 q^{34} + 45 q^{35} - 9 q^{37} + 18 q^{38} - 90 q^{40} + 30 q^{41} + 108 q^{44} - 15 q^{46} + 6 q^{47} - 18 q^{49} + 105 q^{50} - 30 q^{52} - 48 q^{55} - 54 q^{56} - 18 q^{58} - 81 q^{59} - 30 q^{61} + 45 q^{62} + 51 q^{64} + 6 q^{67} + 225 q^{68} - 93 q^{70} + 27 q^{71} - 15 q^{73} + 30 q^{74} + 141 q^{77} - 30 q^{79} - 36 q^{82} - 15 q^{83} - 30 q^{85} - 93 q^{86} - 108 q^{88} - 54 q^{89} - 9 q^{91} - 276 q^{92} - 30 q^{94} - 90 q^{95} - 81 q^{97}+O(q^{100}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Introduction

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