LMFDB - Embedded newform 867.2.h.c.712.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			712.2
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.c.688.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{3} -2.00000i q^{4} +(2.77164 - 1.14805i) q^{5} +(-3.69552 - 1.53073i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{3} -2.00000i q^{4} +(2.77164 - 1.14805i) q^{5} +(-3.69552 - 1.53073i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(1.14805 - 2.77164i) q^{11} +(1.84776 - 0.765367i) q^{12} +1.00000i q^{13} +(2.12132 + 2.12132i) q^{15} -4.00000 q^{16} +(0.707107 + 0.707107i) q^{19} +(-2.29610 - 5.54328i) q^{20} -4.00000i q^{21} +(3.44415 - 8.31492i) q^{23} +(2.82843 - 2.82843i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(-3.06147 + 7.39104i) q^{28} +(-5.54328 + 2.29610i) q^{29} +(-0.765367 - 1.84776i) q^{31} +3.00000 q^{33} -12.0000 q^{35} +(1.41421 + 1.41421i) q^{36} +(-1.53073 - 3.69552i) q^{37} +(-0.923880 + 0.382683i) q^{39} +(-2.77164 - 1.14805i) q^{41} +(4.94975 - 4.94975i) q^{43} +(-5.54328 - 2.29610i) q^{44} +(-1.14805 + 2.77164i) q^{45} +6.00000i q^{47} +(-1.53073 - 3.69552i) q^{48} +(6.36396 + 6.36396i) q^{49} +2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} -9.00000i q^{55} +(-0.382683 + 0.923880i) q^{57} +(4.24264 - 4.24264i) q^{59} +(4.24264 - 4.24264i) q^{60} +(-7.39104 - 3.06147i) q^{61} +(3.69552 - 1.53073i) q^{63} +8.00000i q^{64} +(1.14805 + 2.77164i) q^{65} +4.00000 q^{67} +9.00000 q^{69} +(4.59220 + 11.0866i) q^{71} +(1.84776 - 0.765367i) q^{73} +(3.69552 + 1.53073i) q^{75} +(1.41421 - 1.41421i) q^{76} +(-8.48528 + 8.48528i) q^{77} +(3.82683 - 9.23880i) q^{79} +(-11.0866 + 4.59220i) q^{80} -1.00000i q^{81} +(-4.24264 - 4.24264i) q^{83} -8.00000 q^{84} +(-4.24264 - 4.24264i) q^{87} +(1.53073 - 3.69552i) q^{91} +(-16.6298 - 6.88830i) q^{92} +(1.41421 - 1.41421i) q^{93} +(2.77164 + 1.14805i) q^{95} +(14.7821 - 6.12293i) q^{97} +(1.14805 + 2.77164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 32 q^{16} + 24 q^{33} - 96 q^{35} + 16 q^{52} + 32 q^{67} + 72 q^{69} - 64 q^{84}+O(q^{100}) $ 8 * q - 32 * q^16 + 24 * q^33 - 96 * q^35 + 16 * q^52 + 32 * q^67 + 72 * q^69 - 64 * q^84

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$2$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$		−	2.00000i		−	1.00000i
$5$	2.77164	−	1.14805i	1.23951	−	0.513424i	0.335952	−	0.941879i	$-0.390942\pi$
$5$	2.77164	−	1.14805i	1.23951	−	0.513424i	0.903563	+	0.428456i	$0.140942\pi$
$6$		0			0
$7$	−3.69552	−	1.53073i	−1.39677	−	0.578563i	−0.447862	−	0.894103i	$-0.647814\pi$
$7$	−3.69552	−	1.53073i	−1.39677	−	0.578563i	−0.948912	+	0.315540i	$0.897814\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	1.14805	−	2.77164i	0.346150	−	0.835680i	−0.650917	−	0.759149i	$-0.725615\pi$
$11$	1.14805	−	2.77164i	0.346150	−	0.835680i	0.997067	−	0.0765316i	$-0.0243846\pi$
$12$	1.84776	−	0.765367i	0.533402	−	0.220942i
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$	2.12132	+	2.12132i	0.547723	+	0.547723i
$16$	−4.00000			−1.00000
$17$		0			0
$17$		0			0
$18$		0			0
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i	0.783550	−	0.621329i	$-0.213407\pi$
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i	−0.621329	+	0.783550i	$0.713407\pi$
$20$	−2.29610	−	5.54328i	−0.513424	−	1.23951i
$21$		−	4.00000i		−	0.872872i
$22$		0			0
$23$	3.44415	−	8.31492i	0.718155	−	1.73378i	0.0396166	−	0.999215i	$-0.487386\pi$
$23$	3.44415	−	8.31492i	0.718155	−	1.73378i	0.678538	−	0.734565i	$-0.262614\pi$
$24$		0			0
$25$	2.82843	−	2.82843i	0.565685	−	0.565685i
$26$		0			0
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	−3.06147	+	7.39104i	−0.578563	+	1.39677i
$29$	−5.54328	+	2.29610i	−1.02936	+	0.426375i	−0.832482	−	0.554053i	$-0.813081\pi$
$29$	−5.54328	+	2.29610i	−1.02936	+	0.426375i	−0.196879	+	0.980428i	$0.563081\pi$
$30$		0			0
$31$	−0.765367	−	1.84776i	−0.137464	−	0.331867i	0.840124	−	0.542394i	$-0.182482\pi$
$31$	−0.765367	−	1.84776i	−0.137464	−	0.331867i	−0.977588	+	0.210527i	$0.932482\pi$
$32$		0			0
$33$	3.00000			0.522233
$34$		0			0
$35$	−12.0000			−2.02837
$36$	1.41421	+	1.41421i	0.235702	+	0.235702i
$37$	−1.53073	−	3.69552i	−0.251651	−	0.607539i	0.746687	−	0.665176i	$-0.231644\pi$
$37$	−1.53073	−	3.69552i	−0.251651	−	0.607539i	−0.998338	+	0.0576366i	$0.981644\pi$
$38$		0			0
$39$	−0.923880	+	0.382683i	−0.147939	+	0.0612784i
$40$		0			0
$41$	−2.77164	−	1.14805i	−0.432857	−	0.179295i	0.155606	−	0.987819i	$-0.450267\pi$
$41$	−2.77164	−	1.14805i	−0.432857	−	0.179295i	−0.588463	+	0.808524i	$0.700267\pi$
$42$		0			0
$43$	4.94975	−	4.94975i	0.754829	−	0.754829i	−0.220547	−	0.975376i	$-0.570784\pi$
$43$	4.94975	−	4.94975i	0.754829	−	0.754829i	0.975376	+	0.220547i	$0.0707842\pi$
$44$	−5.54328	−	2.29610i	−0.835680	−	0.346150i
$45$	−1.14805	+	2.77164i	−0.171141	+	0.413171i
$46$		0			0
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−1.53073	−	3.69552i	−0.220942	−	0.533402i
$49$	6.36396	+	6.36396i	0.909137	+	0.909137i
$50$		0			0
$51$		0			0
$52$	2.00000			0.277350
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$		−	9.00000i		−	1.21356i
$56$		0			0
$57$	−0.382683	+	0.923880i	−0.0506877	+	0.122371i
$58$		0			0
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	−0.374772	−	0.927117i	$-0.622279\pi$
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	0.927117	+	0.374772i	$0.122279\pi$
$60$	4.24264	−	4.24264i	0.547723	−	0.547723i
$61$	−7.39104	−	3.06147i	−0.946325	−	0.391981i	−0.144477	−	0.989508i	$-0.546150\pi$
$61$	−7.39104	−	3.06147i	−0.946325	−	0.391981i	−0.801848	+	0.597527i	$0.796150\pi$
$62$		0			0
$63$	3.69552	−	1.53073i	0.465592	−	0.192854i
$64$			8.00000i			1.00000i
$65$	1.14805	+	2.77164i	0.142398	+	0.343779i
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	9.00000			1.08347
$70$		0			0
$71$	4.59220	+	11.0866i	0.544994	+	1.31573i	0.921162	+	0.389180i	$0.127242\pi$
$71$	4.59220	+	11.0866i	0.544994	+	1.31573i	−0.376168	+	0.926552i	$0.622758\pi$
$72$		0			0
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	−0.271921	−	0.962319i	$-0.587659\pi$
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	0.488185	+	0.872740i	$0.337659\pi$
$74$		0			0
$75$	3.69552	+	1.53073i	0.426722	+	0.176754i
$76$	1.41421	−	1.41421i	0.162221	−	0.162221i
$77$	−8.48528	+	8.48528i	−0.966988	+	0.966988i
$78$		0			0
$79$	3.82683	−	9.23880i	0.430552	−	1.03945i	−0.548557	−	0.836113i	$-0.684823\pi$
$79$	3.82683	−	9.23880i	0.430552	−	1.03945i	0.979110	−	0.203333i	$-0.0651773\pi$
$80$	−11.0866	+	4.59220i	−1.23951	+	0.513424i
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	0.434825	−	0.900515i	$-0.356810\pi$
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	−0.900515	+	0.434825i	$0.856810\pi$
$84$	−8.00000			−0.872872
$85$		0			0
$86$		0			0
$87$	−4.24264	−	4.24264i	−0.454859	−	0.454859i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	1.53073	−	3.69552i	0.160464	−	0.387396i
$92$	−16.6298	−	6.88830i	−1.73378	−	0.718155i
$93$	1.41421	−	1.41421i	0.146647	−	0.146647i
$94$		0			0
$95$	2.77164	+	1.14805i	0.284364	+	0.117787i
$96$		0			0
$97$	14.7821	−	6.12293i	1.50089	−	0.621690i	0.527238	−	0.849718i	$-0.323228\pi$
$97$	14.7821	−	6.12293i	1.50089	−	0.621690i	0.973655	+	0.228028i	$0.0732278\pi$
$98$		0			0
$99$	1.14805	+	2.77164i	0.115383	+	0.278560i
$100$	−5.65685	−	5.65685i	−0.565685	−	0.565685i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$		0			0
$105$	−4.59220	−	11.0866i	−0.448153	−	1.08194i
$106$		0			0
$107$	8.31492	−	3.44415i	0.803833	−	0.332959i	0.0573426	−	0.998355i	$-0.481737\pi$
$107$	8.31492	−	3.44415i	0.803833	−	0.332959i	0.746491	+	0.665396i	$0.231737\pi$
$108$	−0.765367	+	1.84776i	−0.0736475	+	0.177801i
$109$	18.4776	+	7.65367i	1.76983	+	0.733089i	0.994879	+	0.101069i	$0.0322264\pi$
$109$	18.4776	+	7.65367i	1.76983	+	0.733089i	0.774953	+	0.632019i	$0.217774\pi$
$110$		0			0
$111$	2.82843	−	2.82843i	0.268462	−	0.268462i
$112$	14.7821	+	6.12293i	1.39677	+	0.578563i
$113$	3.44415	−	8.31492i	0.323998	−	0.782201i	−0.675015	−	0.737804i	$-0.735863\pi$
$113$	3.44415	−	8.31492i	0.323998	−	0.782201i	0.999014	−	0.0443979i	$-0.0141369\pi$
$114$		0			0
$115$		−	27.0000i		−	2.51776i
$116$	4.59220	+	11.0866i	0.426375	+	1.02936i
$117$	−0.707107	−	0.707107i	−0.0653720	−	0.0653720i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.41421	+	1.41421i	0.128565	+	0.128565i
$122$		0			0
$123$		−	3.00000i		−	0.270501i
$124$	−3.69552	+	1.53073i	−0.331867	+	0.137464i
$125$	−1.14805	+	2.77164i	−0.102685	+	0.247903i
$126$		0			0
$127$	−9.19239	+	9.19239i	−0.815693	+	0.815693i	−0.985481	−	0.169788i	$-0.945692\pi$
$127$	−9.19239	+	9.19239i	−0.815693	+	0.815693i	0.169788	+	0.985481i	$0.445692\pi$
$128$		0			0
$129$	6.46716	+	2.67878i	0.569401	+	0.235854i
$130$		0			0
$131$	−2.77164	+	1.14805i	−0.242159	+	0.100306i	−0.500462	−	0.865758i	$-0.666837\pi$
$131$	−2.77164	+	1.14805i	−0.242159	+	0.100306i	0.258303	+	0.966064i	$0.416837\pi$
$132$		−	6.00000i		−	0.522233i
$133$	−1.53073	−	3.69552i	−0.132731	−	0.320442i
$134$		0			0
$135$	−3.00000			−0.258199
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	0.765367	+	1.84776i	0.0649176	+	0.156725i	0.953009	−	0.302942i	$-0.0979688\pi$
$139$	0.765367	+	1.84776i	0.0649176	+	0.156725i	−0.888091	+	0.459667i	$0.847969\pi$
$140$			24.0000i			2.02837i
$141$	−5.54328	+	2.29610i	−0.466828	+	0.193367i
$142$		0			0
$143$	2.77164	+	1.14805i	0.231776	+	0.0960048i
$144$	2.82843	−	2.82843i	0.235702	−	0.235702i
$145$	−12.7279	+	12.7279i	−1.05700	+	1.05700i
$146$		0			0
$147$	−3.44415	+	8.31492i	−0.284069	+	0.685803i
$148$	−7.39104	+	3.06147i	−0.607539	+	0.251651i
$149$			18.0000i			1.47462i	0.675556	+	0.737309i	$0.263904\pi$
$149$			18.0000i			1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$150$		0			0
$151$	5.65685	+	5.65685i	0.460348	+	0.460348i	0.898770	−	0.438421i	$-0.144462\pi$
$151$	5.65685	+	5.65685i	0.460348	+	0.460348i	−0.438421	+	0.898770i	$0.644462\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.24264	−	4.24264i	−0.340777	−	0.340777i
$156$	0.765367	+	1.84776i	0.0612784	+	0.147939i
$157$			11.0000i			0.877896i	0.898513	+	0.438948i	$0.144649\pi$
$157$			11.0000i			0.877896i	−0.898513	+	0.438948i	$0.855351\pi$
$158$		0			0
$159$	−2.29610	+	5.54328i	−0.182093	+	0.439610i
$160$		0			0
$161$	−25.4558	+	25.4558i	−2.00620	+	2.00620i
$162$		0			0
$163$	−1.84776	−	0.765367i	−0.144728	−	0.0599482i	0.309144	−	0.951015i	$-0.399958\pi$
$163$	−1.84776	−	0.765367i	−0.144728	−	0.0599482i	−0.453872	+	0.891067i	$0.649958\pi$
$164$	−2.29610	+	5.54328i	−0.179295	+	0.432857i
$165$	8.31492	−	3.44415i	0.647315	−	0.268127i
$166$		0			0
$167$	−8.03635	−	19.4015i	−0.621872	−	1.50133i	−0.849503	−	0.527584i	$-0.823098\pi$
$167$	−8.03635	−	19.4015i	−0.621872	−	1.50133i	0.227632	−	0.973747i	$-0.426902\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−1.00000			−0.0764719
$172$	−9.89949	−	9.89949i	−0.754829	−	0.754829i
$173$	5.74025	+	13.8582i	0.436423	+	1.05362i	0.977175	+	0.212437i	$0.0681399\pi$
$173$	5.74025	+	13.8582i	0.436423	+	1.05362i	−0.540752	+	0.841182i	$0.681860\pi$
$174$		0			0
$175$	−14.7821	+	6.12293i	−1.11742	+	0.462850i
$176$	−4.59220	+	11.0866i	−0.346150	+	0.835680i
$177$	5.54328	+	2.29610i	0.416658	+	0.172585i
$178$		0			0
$179$	4.24264	−	4.24264i	0.317110	−	0.317110i	−0.530546	−	0.847656i	$-0.678013\pi$
$179$	4.24264	−	4.24264i	0.317110	−	0.317110i	0.847656	+	0.530546i	$0.178013\pi$
$180$	5.54328	+	2.29610i	0.413171	+	0.171141i
$181$	−5.35757	+	12.9343i	−0.398225	+	0.961400i	0.589862	+	0.807504i	$0.299182\pi$
$181$	−5.35757	+	12.9343i	−0.398225	+	0.961400i	−0.988087	+	0.153896i	$0.950818\pi$
$182$		0			0
$183$		−	8.00000i		−	0.591377i
$184$		0			0
$185$	−8.48528	−	8.48528i	−0.623850	−	0.623850i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$	2.82843	+	2.82843i	0.205738	+	0.205738i
$190$		0			0
$191$			18.0000i			1.30243i	0.758891	+	0.651217i	$0.225741\pi$
$191$			18.0000i			1.30243i	−0.758891	+	0.651217i	$0.774259\pi$
$192$	−7.39104	+	3.06147i	−0.533402	+	0.220942i
$193$	−8.41904	+	20.3253i	−0.606015	+	1.46305i	0.261283	+	0.965262i	$0.415854\pi$
$193$	−8.41904	+	20.3253i	−0.606015	+	1.46305i	−0.867298	+	0.497788i	$0.834146\pi$
$194$		0			0
$195$	−2.12132	+	2.12132i	−0.151911	+	0.151911i
$196$	12.7279	−	12.7279i	0.909137	−	0.909137i
$197$	−2.77164	−	1.14805i	−0.197471	−	0.0817952i	0.281756	−	0.959486i	$-0.409083\pi$
$197$	−2.77164	−	1.14805i	−0.197471	−	0.0817952i	−0.479227	+	0.877691i	$0.659083\pi$
$198$		0			0
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.208741	−	0.977971i	$-0.433063\pi$
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.839132	+	0.543928i	$0.183063\pi$
$200$		0			0
$201$	1.53073	+	3.69552i	0.107970	+	0.260662i
$202$		0			0
$203$	24.0000			1.68447
$204$		0			0
$205$	−9.00000			−0.628587
$206$		0			0
$207$	3.44415	+	8.31492i	0.239385	+	0.577927i
$208$		−	4.00000i		−	0.277350i
$209$	2.77164	−	1.14805i	0.191718	−	0.0794123i
$210$		0			0
$211$	1.84776	+	0.765367i	0.127205	+	0.0526900i	0.445378	−	0.895343i	$-0.353069\pi$
$211$	1.84776	+	0.765367i	0.127205	+	0.0526900i	−0.318173	+	0.948033i	$0.603069\pi$
$212$	8.48528	−	8.48528i	0.582772	−	0.582772i
$213$	−8.48528	+	8.48528i	−0.581402	+	0.581402i
$214$		0			0
$215$	8.03635	−	19.4015i	0.548075	−	1.32317i
$216$		0			0
$217$			8.00000i			0.543075i
$218$		0			0
$219$	1.41421	+	1.41421i	0.0955637	+	0.0955637i
$220$	−18.0000			−1.21356
$221$		0			0
$222$		0			0
$223$	0.707107	+	0.707107i	0.0473514	+	0.0473514i	0.730386	−	0.683035i	$-0.239340\pi$
$223$	0.707107	+	0.707107i	0.0473514	+	0.0473514i	−0.683035	+	0.730386i	$0.739340\pi$
$224$		0			0
$225$			4.00000i			0.266667i
$226$		0			0
$227$	1.14805	−	2.77164i	0.0761988	−	0.183960i	−0.881190	−	0.472762i	$-0.843257\pi$
$227$	1.14805	−	2.77164i	0.0761988	−	0.183960i	0.957389	+	0.288802i	$0.0932570\pi$
$228$	1.84776	+	0.765367i	0.122371	+	0.0506877i
$229$	9.89949	−	9.89949i	0.654177	−	0.654177i	−0.299819	−	0.953996i	$-0.596926\pi$
$229$	9.89949	−	9.89949i	0.654177	−	0.654177i	0.953996	+	0.299819i	$0.0969263\pi$
$230$		0			0
$231$	−11.0866	−	4.59220i	−0.729442	−	0.302145i
$232$		0			0
$233$	−19.4015	+	8.03635i	−1.27103	+	0.526479i	−0.913278	−	0.407337i	$-0.866458\pi$
$233$	−19.4015	+	8.03635i	−1.27103	+	0.526479i	−0.357755	+	0.933816i	$0.616458\pi$
$234$		0			0
$235$	6.88830	+	16.6298i	0.449343	+	1.08481i
$236$	−8.48528	−	8.48528i	−0.552345	−	0.552345i
$237$	10.0000			0.649570
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−8.48528	−	8.48528i	−0.547723	−	0.547723i
$241$	3.06147	+	7.39104i	0.197206	+	0.476098i	0.991288	−	0.131713i	$-0.0420477\pi$
$241$	3.06147	+	7.39104i	0.197206	+	0.476098i	−0.794081	+	0.607811i	$0.792048\pi$
$242$		0			0
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	−6.12293	+	14.7821i	−0.391981	+	0.946325i
$245$	24.9447	+	10.3325i	1.59366	+	0.660116i
$246$		0			0
$247$	−0.707107	+	0.707107i	−0.0449921	+	0.0449921i
$248$		0			0
$249$	2.29610	−	5.54328i	0.145509	−	0.351291i
$250$		0			0
$251$		−	24.0000i		−	1.51487i	−0.652913	−	0.757433i	$-0.726453\pi$
$251$		−	24.0000i		−	1.51487i	0.652913	−	0.757433i	$-0.273547\pi$
$252$	−3.06147	−	7.39104i	−0.192854	−	0.465592i
$253$	−19.0919	−	19.0919i	−1.20030	−	1.20030i
$254$		0			0
$255$		0			0
$256$	16.0000			1.00000
$257$	−8.48528	−	8.48528i	−0.529297	−	0.529297i	0.391066	−	0.920363i	$-0.372107\pi$
$257$	−8.48528	−	8.48528i	−0.529297	−	0.529297i	−0.920363	+	0.391066i	$0.872107\pi$
$258$		0			0
$259$			16.0000i			0.994192i
$260$	5.54328	−	2.29610i	0.343779	−	0.142398i
$261$	2.29610	−	5.54328i	0.142125	−	0.343120i
$262$		0			0
$263$	8.48528	−	8.48528i	0.523225	−	0.523225i	−0.395319	−	0.918544i	$-0.629366\pi$
$263$	8.48528	−	8.48528i	0.523225	−	0.523225i	0.918544	+	0.395319i	$0.129366\pi$
$264$		0			0
$265$	16.6298	+	6.88830i	1.02156	+	0.423145i
$266$		0			0
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$	5.74025	+	13.8582i	0.349989	+	0.844949i	0.996620	+	0.0821460i	$0.0261774\pi$
$269$	5.74025	+	13.8582i	0.349989	+	0.844949i	−0.646631	+	0.762803i	$0.723823\pi$
$270$		0			0
$271$	−11.0000			−0.668202			−0.334101	−	0.942537i	$-0.608433\pi$
$271$	−11.0000			−0.668202			−0.334101	+	0.942537i	$0.608433\pi$
$272$		0			0
$273$	4.00000			0.242091
$274$		0			0
$275$	−4.59220	−	11.0866i	−0.276920	−	0.668544i
$276$		−	18.0000i		−	1.08347i
$277$	1.84776	−	0.765367i	0.111021	−	0.0459864i	−0.326482	−	0.945204i	$-0.605863\pi$
$277$	1.84776	−	0.765367i	0.111021	−	0.0459864i	0.437503	+	0.899217i	$0.355863\pi$
$278$		0			0
$279$	1.84776	+	0.765367i	0.110622	+	0.0458213i
$280$		0			0
$281$	−8.48528	+	8.48528i	−0.506189	+	0.506189i	−0.913355	−	0.407165i	$-0.866517\pi$
$281$	−8.48528	+	8.48528i	−0.506189	+	0.506189i	0.407165	+	0.913355i	$0.366517\pi$
$282$		0			0
$283$	3.82683	−	9.23880i	0.227482	−	0.549189i	−0.768388	−	0.639984i	$-0.778941\pi$
$283$	3.82683	−	9.23880i	0.227482	−	0.549189i	0.995870	+	0.0907950i	$0.0289408\pi$
$284$	22.1731	−	9.18440i	1.31573	−	0.544994i
$285$			3.00000i			0.177705i
$286$		0			0
$287$	8.48528	+	8.48528i	0.500870	+	0.500870i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	11.3137	+	11.3137i	0.663221	+	0.663221i
$292$	−1.53073	−	3.69552i	−0.0895794	−	0.216264i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	6.88830	−	16.6298i	0.401052	−	0.968226i
$296$		0			0
$297$	−2.12132	+	2.12132i	−0.123091	+	0.123091i
$298$		0			0
$299$	8.31492	+	3.44415i	0.480864	+	0.199180i
$300$	3.06147	−	7.39104i	0.176754	−	0.426722i
$301$	−25.8686	+	10.7151i	−1.49104	+	0.617610i
$302$		0			0
$303$		0			0
$304$	−2.82843	−	2.82843i	−0.162221	−	0.162221i
$305$	−24.0000			−1.37424
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	16.9706	+	16.9706i	0.966988	+	0.966988i
$309$	1.91342	+	4.61940i	0.108850	+	0.262788i
$310$		0			0
$311$	−22.1731	+	9.18440i	−1.25732	+	0.520800i	−0.909086	−	0.416608i	$-0.863219\pi$
$311$	−22.1731	+	9.18440i	−1.25732	+	0.520800i	−0.348235	+	0.937407i	$0.613219\pi$
$312$		0			0
$313$	−14.7821	−	6.12293i	−0.835532	−	0.346089i	−0.0764418	−	0.997074i	$-0.524356\pi$
$313$	−14.7821	−	6.12293i	−0.835532	−	0.346089i	−0.759090	+	0.650985i	$0.774356\pi$
$314$		0			0
$315$	8.48528	−	8.48528i	0.478091	−	0.478091i
$316$	−18.4776	−	7.65367i	−1.03945	−	0.430552i
$317$	2.29610	−	5.54328i	0.128962	−	0.311341i	−0.846189	−	0.532883i	$-0.821109\pi$
$317$	2.29610	−	5.54328i	0.128962	−	0.311341i	0.975151	+	0.221541i	$0.0711087\pi$
$318$		0			0
$319$			18.0000i			1.00781i
$320$	9.18440	+	22.1731i	0.513424	+	1.23951i
$321$	6.36396	+	6.36396i	0.355202	+	0.355202i
$322$		0			0
$323$		0			0
$324$	−2.00000			−0.111111
$325$	2.82843	+	2.82843i	0.156893	+	0.156893i
$326$		0			0
$327$			20.0000i			1.10600i
$328$		0			0
$329$	9.18440	−	22.1731i	0.506352	−	1.22244i
$330$		0			0
$331$	−9.19239	+	9.19239i	−0.505259	+	0.505259i	−0.913068	−	0.407808i	$-0.866293\pi$
$331$	−9.19239	+	9.19239i	−0.505259	+	0.505259i	0.407808	+	0.913068i	$0.366293\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	3.69552	+	1.53073i	0.202513	+	0.0838837i
$334$		0			0
$335$	11.0866	−	4.59220i	0.605723	−	0.250899i
$336$			16.0000i			0.872872i
$337$	−5.35757	−	12.9343i	−0.291845	−	0.704577i	0.708154	−	0.706058i	$-0.249528\pi$
$337$	−5.35757	−	12.9343i	−0.291845	−	0.704577i	−0.999999	+	0.00148149i	$0.999528\pi$
$338$		0			0
$339$	9.00000			0.488813
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−3.06147	−	7.39104i	−0.165304	−	0.399078i
$344$		0			0
$345$	24.9447	−	10.3325i	1.34298	−	0.556281i
$346$		0			0
$347$	−11.0866	−	4.59220i	−0.595157	−	0.246522i	0.0647103	−	0.997904i	$-0.479388\pi$
$347$	−11.0866	−	4.59220i	−0.595157	−	0.246522i	−0.659868	+	0.751382i	$0.729388\pi$
$348$	−8.48528	+	8.48528i	−0.454859	+	0.454859i
$349$	13.4350	−	13.4350i	0.719161	−	0.719161i	−0.249273	−	0.968433i	$-0.580192\pi$
$349$	13.4350	−	13.4350i	0.719161	−	0.719161i	0.968433	+	0.249273i	$0.0801916\pi$
$350$		0			0
$351$	0.382683	−	0.923880i	0.0204261	−	0.0493130i
$352$		0			0
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$		0			0
$355$	25.4558	+	25.4558i	1.35106	+	1.35106i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$359$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$360$		0			0
$361$		−	18.0000i		−	0.947368i
$362$		0			0
$363$	−0.765367	+	1.84776i	−0.0401713	+	0.0969822i
$364$	−7.39104	−	3.06147i	−0.387396	−	0.160464i
$365$	4.24264	−	4.24264i	0.222070	−	0.222070i
$366$		0			0
$367$	−7.39104	−	3.06147i	−0.385809	−	0.159807i	0.181344	−	0.983420i	$-0.441955\pi$
$367$	−7.39104	−	3.06147i	−0.385809	−	0.159807i	−0.567153	+	0.823612i	$0.691955\pi$
$368$	−13.7766	+	33.2597i	−0.718155	+	1.73378i
$369$	2.77164	−	1.14805i	0.144286	−	0.0597651i
$370$		0			0
$371$	−9.18440	−	22.1731i	−0.476830	−	1.15117i
$372$	−2.82843	−	2.82843i	−0.146647	−	0.146647i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	−2.29610	−	5.54328i	−0.118255	−	0.285493i
$378$		0			0
$379$	29.5641	−	12.2459i	1.51861	−	0.629028i	0.541296	−	0.840832i	$-0.317934\pi$
$379$	29.5641	−	12.2459i	1.51861	−	0.629028i	0.977312	+	0.211804i	$0.0679339\pi$
$380$	2.29610	−	5.54328i	0.117787	−	0.284364i
$381$	−12.0104	−	4.97488i	−0.615313	−	0.254871i
$382$		0			0
$383$	8.48528	−	8.48528i	0.433578	−	0.433578i	−0.456266	−	0.889843i	$-0.650813\pi$
$383$	8.48528	−	8.48528i	0.433578	−	0.433578i	0.889843	+	0.456266i	$0.150813\pi$
$384$		0			0
$385$	−13.7766	+	33.2597i	−0.702121	+	1.69507i
$386$		0			0
$387$			7.00000i			0.355830i
$388$	−12.2459	−	29.5641i	−0.621690	−	1.50089i
$389$	25.4558	+	25.4558i	1.29066	+	1.29066i	0.934377	+	0.356285i	$0.115957\pi$
$389$	25.4558	+	25.4558i	1.29066	+	1.29066i	0.356285	+	0.934377i	$0.384043\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−2.12132	−	2.12132i	−0.107006	−	0.107006i
$394$		0			0
$395$		−	30.0000i		−	1.50946i
$396$	5.54328	−	2.29610i	0.278560	−	0.115383i
$397$	7.65367	−	18.4776i	0.384127	−	0.927364i	−0.607032	−	0.794678i	$-0.707640\pi$
$397$	7.65367	−	18.4776i	0.384127	−	0.927364i	0.991158	−	0.132686i	$-0.0423602\pi$
$398$		0			0
$399$	2.82843	−	2.82843i	0.141598	−	0.141598i
$400$	−11.3137	+	11.3137i	−0.565685	+	0.565685i
$401$	13.8582	+	5.74025i	0.692045	+	0.286654i	0.700852	−	0.713307i	$-0.252803\pi$
$401$	13.8582	+	5.74025i	0.692045	+	0.286654i	−0.00880685	+	0.999961i	$0.502803\pi$
$402$		0			0
$403$	1.84776	−	0.765367i	0.0920434	−	0.0381256i
$404$		0			0
$405$	−1.14805	−	2.77164i	−0.0570471	−	0.137724i
$406$		0			0
$407$	−12.0000			−0.594818
$408$		0			0
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$		0			0
$411$	−2.29610	−	5.54328i	−0.113258	−	0.273430i
$412$		−	10.0000i		−	0.492665i
$413$	−22.1731	+	9.18440i	−1.09107	+	0.451935i
$414$		0			0
$415$	−16.6298	−	6.88830i	−0.816326	−	0.338133i
$416$		0			0
$417$	−1.41421	+	1.41421i	−0.0692543	+	0.0692543i
$418$		0			0
$419$	−4.59220	+	11.0866i	−0.224344	+	0.541614i	−0.995471	−	0.0950676i	$-0.969693\pi$
$419$	−4.59220	+	11.0866i	−0.224344	+	0.541614i	0.771127	+	0.636681i	$0.219693\pi$
$420$	−22.1731	+	9.18440i	−1.08194	+	0.448153i
$421$			25.0000i			1.21843i	0.793007	+	0.609213i	$0.208514\pi$
$421$			25.0000i			1.21843i	−0.793007	+	0.609213i	$0.791486\pi$
$422$		0			0
$423$	−4.24264	−	4.24264i	−0.206284	−	0.206284i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	22.6274	+	22.6274i	1.09502	+	1.09502i
$428$	−6.88830	−	16.6298i	−0.332959	−	0.803833i
$429$			3.00000i			0.144841i
$430$		0			0
$431$	−9.18440	+	22.1731i	−0.442397	+	1.06804i	0.532708	+	0.846299i	$0.321174\pi$
$431$	−9.18440	+	22.1731i	−0.442397	+	1.06804i	−0.975105	+	0.221742i	$0.928826\pi$
$432$	3.69552	+	1.53073i	0.177801	+	0.0736475i
$433$	−0.707107	+	0.707107i	−0.0339814	+	0.0339814i	−0.723893	−	0.689912i	$-0.757649\pi$
$433$	−0.707107	+	0.707107i	−0.0339814	+	0.0339814i	0.689912	+	0.723893i	$0.257649\pi$
$434$		0			0
$435$	−16.6298	−	6.88830i	−0.797339	−	0.330269i
$436$	15.3073	−	36.9552i	0.733089	−	1.76983i
$437$	8.31492	−	3.44415i	0.397756	−	0.164756i
$438$		0			0
$439$	10.7151	+	25.8686i	0.511406	+	1.23464i	0.943066	+	0.332606i	$0.107928\pi$
$439$	10.7151	+	25.8686i	0.511406	+	1.23464i	−0.431660	+	0.902036i	$0.642072\pi$
$440$		0			0
$441$	−9.00000			−0.428571
$442$		0			0
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$	−5.65685	−	5.65685i	−0.268462	−	0.268462i
$445$		0			0
$446$		0			0
$447$	−16.6298	+	6.88830i	−0.786564	+	0.325805i
$448$	12.2459	−	29.5641i	0.578563	−	1.39677i
$449$	−5.54328	−	2.29610i	−0.261603	−	0.108360i	0.248027	−	0.968753i	$-0.420218\pi$
$449$	−5.54328	−	2.29610i	−0.261603	−	0.108360i	−0.509630	+	0.860393i	$0.670218\pi$
$450$		0			0
$451$	−6.36396	+	6.36396i	−0.299667	+	0.299667i
$452$	−16.6298	−	6.88830i	−0.782201	−	0.323998i
$453$	−3.06147	+	7.39104i	−0.143840	+	0.347261i
$454$		0			0
$455$		−	12.0000i		−	0.562569i
$456$		0			0
$457$	−13.4350	−	13.4350i	−0.628464	−	0.628464i	0.319217	−	0.947682i	$-0.396580\pi$
$457$	−13.4350	−	13.4350i	−0.628464	−	0.628464i	−0.947682	+	0.319217i	$0.896580\pi$
$458$		0			0
$459$		0			0
$460$	−54.0000			−2.51776
$461$	−21.2132	−	21.2132i	−0.987997	−	0.987997i	0.0119314	−	0.999929i	$-0.496202\pi$
$461$	−21.2132	−	21.2132i	−0.987997	−	0.987997i	−0.999929	+	0.0119314i	$0.996202\pi$
$462$		0			0
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$	22.1731	−	9.18440i	1.02936	−	0.426375i
$465$	2.29610	−	5.54328i	0.106479	−	0.257063i
$466$		0			0
$467$	29.6985	−	29.6985i	1.37428	−	1.37428i	0.520296	−	0.853986i	$-0.325822\pi$
$467$	29.6985	−	29.6985i	1.37428	−	1.37428i	0.853986	−	0.520296i	$-0.174178\pi$
$468$	−1.41421	+	1.41421i	−0.0653720	+	0.0653720i
$469$	−14.7821	−	6.12293i	−0.682573	−	0.282731i
$470$		0			0
$471$	−10.1627	+	4.20952i	−0.468271	+	0.193964i
$472$		0			0
$473$	−8.03635	−	19.4015i	−0.369512	−	0.892081i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−10.3325	−	24.9447i	−0.472102	−	1.13975i	−0.963233	−	0.268669i	$-0.913416\pi$
$479$	−10.3325	−	24.9447i	−0.472102	−	1.13975i	0.491131	−	0.871086i	$-0.336584\pi$
$480$		0			0
$481$	3.69552	−	1.53073i	0.168501	−	0.0697955i
$482$		0			0
$483$	−33.2597	−	13.7766i	−1.51337	−	0.626857i
$484$	2.82843	−	2.82843i	0.128565	−	0.128565i
$485$	33.9411	−	33.9411i	1.54119	−	1.54119i
$486$		0			0
$487$	8.41904	−	20.3253i	0.381503	−	0.921030i	−0.610173	−	0.792268i	$-0.708900\pi$
$487$	8.41904	−	20.3253i	0.381503	−	0.921030i	0.991676	−	0.128761i	$-0.0411000\pi$
$488$		0			0
$489$		−	2.00000i		−	0.0904431i
$490$		0			0
$491$	−4.24264	−	4.24264i	−0.191468	−	0.191468i	0.604862	−	0.796330i	$-0.293228\pi$
$491$	−4.24264	−	4.24264i	−0.191468	−	0.191468i	−0.796330	+	0.604862i	$0.793228\pi$
$492$	−6.00000			−0.270501
$493$		0			0
$494$		0			0
$495$	6.36396	+	6.36396i	0.286039	+	0.286039i
$496$	3.06147	+	7.39104i	0.137464	+	0.331867i
$497$		−	48.0000i		−	2.15309i
$498$		0			0
$499$	−8.41904	+	20.3253i	−0.376888	+	0.909888i	0.615658	+	0.788014i	$0.288890\pi$
$499$	−8.41904	+	20.3253i	−0.376888	+	0.909888i	−0.992546	+	0.121874i	$0.961110\pi$
$500$	5.54328	+	2.29610i	0.247903	+	0.102685i
$501$	14.8492	−	14.8492i	0.663415	−	0.663415i
$502$		0			0
$503$	−13.8582	−	5.74025i	−0.617906	−	0.255945i	0.0516985	−	0.998663i	$-0.483537\pi$
$503$	−13.8582	−	5.74025i	−0.617906	−	0.255945i	−0.669605	+	0.742718i	$0.733537\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.59220	+	11.0866i	0.203947	+	0.492371i
$508$	18.3848	+	18.3848i	0.815693	+	0.815693i
$509$	−36.0000			−1.59567			−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000			−1.59567			−0.797836	+	0.602875i	$0.794022\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$		0			0
$513$	−0.382683	−	0.923880i	−0.0168959	−	0.0407903i
$514$		0			0
$515$	13.8582	−	5.74025i	0.610665	−	0.252946i
$516$	5.35757	−	12.9343i	0.235854	−	0.569401i
$517$	16.6298	+	6.88830i	0.731379	+	0.302947i
$518$		0			0
$519$	−10.6066	+	10.6066i	−0.465578	+	0.465578i
$520$		0			0
$521$	−8.03635	+	19.4015i	−0.352079	+	0.849994i	0.644284	+	0.764786i	$0.277155\pi$
$521$	−8.03635	+	19.4015i	−0.352079	+	0.849994i	−0.996363	+	0.0852077i	$0.972845\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	2.29610	+	5.54328i	0.100306	+	0.242159i
$525$	−11.3137	−	11.3137i	−0.493771	−	0.493771i
$526$		0			0
$527$		0			0
$528$	−12.0000			−0.522233
$529$	−41.0122	−	41.0122i	−1.78314	−	1.78314i
$530$		0			0
$531$			6.00000i			0.260378i
$532$	−7.39104	+	3.06147i	−0.320442	+	0.132731i
$533$	1.14805	−	2.77164i	0.0497276	−	0.120053i
$534$		0			0
$535$	19.0919	−	19.0919i	0.825414	−	0.825414i
$536$		0			0
$537$	5.54328	+	2.29610i	0.239210	+	0.0990841i
$538$		0			0
$539$	24.9447	−	10.3325i	1.07445	−	0.445050i
$540$			6.00000i			0.258199i
$541$	6.12293	+	14.7821i	0.263246	+	0.635531i	0.999136	−	0.0415701i	$-0.0132360\pi$
$541$	6.12293	+	14.7821i	0.263246	+	0.635531i	−0.735890	+	0.677101i	$0.763236\pi$
$542$		0			0
$543$	−14.0000			−0.600798
$544$		0			0
$545$	60.0000			2.57012
$546$		0			0
$547$	3.06147	+	7.39104i	0.130899	+	0.316018i	0.975717	−	0.219036i	$-0.0702913\pi$
$547$	3.06147	+	7.39104i	0.130899	+	0.316018i	−0.844818	+	0.535054i	$0.820291\pi$
$548$			12.0000i			0.512615i
$549$	7.39104	−	3.06147i	0.315442	−	0.130660i
$550$		0			0
$551$	−5.54328	−	2.29610i	−0.236152	−	0.0978172i
$552$		0			0
$553$	−28.2843	+	28.2843i	−1.20277	+	1.20277i
$554$		0			0
$555$	4.59220	−	11.0866i	0.194928	−	0.470598i
$556$	3.69552	−	1.53073i	0.156725	−	0.0649176i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$		0			0
$559$	4.94975	+	4.94975i	0.209352	+	0.209352i
$560$	48.0000			2.02837
$561$		0			0
$562$		0			0
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	0.994900	−	0.100870i	$-0.0321625\pi$
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	−0.100870	+	0.994900i	$0.532163\pi$
$564$	4.59220	+	11.0866i	0.193367	+	0.466828i
$565$		−	27.0000i		−	1.13590i
$566$		0			0
$567$	−1.53073	+	3.69552i	−0.0642848	+	0.155197i
$568$		0			0
$569$	−16.9706	+	16.9706i	−0.711443	+	0.711443i	−0.966837	−	0.255394i	$-0.917795\pi$
$569$	−16.9706	+	16.9706i	−0.711443	+	0.711443i	0.255394	+	0.966837i	$0.417795\pi$
$570$		0			0
$571$	−7.39104	−	3.06147i	−0.309305	−	0.128118i	0.222631	−	0.974903i	$-0.428535\pi$
$571$	−7.39104	−	3.06147i	−0.309305	−	0.128118i	−0.531936	+	0.846784i	$0.678535\pi$
$572$	2.29610	−	5.54328i	0.0960048	−	0.231776i
$573$	−16.6298	+	6.88830i	−0.694721	+	0.287763i
$574$		0			0
$575$	−13.7766	−	33.2597i	−0.574524	−	1.38702i
$576$	−5.65685	−	5.65685i	−0.235702	−	0.235702i
$577$	7.00000			0.291414			0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000			0.291414			0.145707	+	0.989328i	$0.453454\pi$
$578$		0			0
$579$	−22.0000			−0.914289
$580$	25.4558	+	25.4558i	1.05700	+	1.05700i
$581$	9.18440	+	22.1731i	0.381033	+	0.919896i
$582$		0			0
$583$	16.6298	−	6.88830i	0.688737	−	0.285284i
$584$		0			0
$585$	−2.77164	−	1.14805i	−0.114593	−	0.0474660i
$586$		0			0
$587$	25.4558	−	25.4558i	1.05068	−	1.05068i	0.0520296	−	0.998646i	$-0.483431\pi$
$587$	25.4558	−	25.4558i	1.05068	−	1.05068i	0.998646	−	0.0520296i	$-0.0165690\pi$
$588$	16.6298	+	6.88830i	0.685803	+	0.284069i
$589$	0.765367	−	1.84776i	0.0315364	−	0.0761356i
$590$		0			0
$591$		−	3.00000i		−	0.123404i
$592$	6.12293	+	14.7821i	0.251651	+	0.607539i
$593$	−12.7279	−	12.7279i	−0.522673	−	0.522673i	0.395705	−	0.918378i	$-0.370500\pi$
$593$	−12.7279	−	12.7279i	−0.522673	−	0.522673i	−0.918378	+	0.395705i	$0.870500\pi$
$594$		0			0
$595$		0			0
$596$	36.0000			1.47462
$597$	11.3137	+	11.3137i	0.463039	+	0.463039i
$598$		0			0
$599$		−	6.00000i		−	0.245153i	−0.992459	−	0.122577i	$-0.960884\pi$
$599$		−	6.00000i		−	0.245153i	0.992459	−	0.122577i	$-0.0391157\pi$
$600$		0			0
$601$	14.5420	−	35.1074i	0.593179	−	1.43206i	−0.287237	−	0.957860i	$-0.592737\pi$
$601$	14.5420	−	35.1074i	0.593179	−	1.43206i	0.880416	−	0.474202i	$-0.157263\pi$
$602$		0			0
$603$	−2.82843	+	2.82843i	−0.115182	+	0.115182i
$604$	11.3137	−	11.3137i	0.460348	−	0.460348i
$605$	5.54328	+	2.29610i	0.225366	+	0.0933498i
$606$		0			0
$607$	−35.1074	+	14.5420i	−1.42497	+	0.590240i	−0.956103	−	0.293030i	$-0.905336\pi$
$607$	−35.1074	+	14.5420i	−1.42497	+	0.590240i	−0.468863	+	0.883271i	$0.655336\pi$
$608$		0			0
$609$	9.18440	+	22.1731i	0.372171	+	0.898500i
$610$		0			0
$611$	−6.00000			−0.242734
$612$		0			0
$613$	11.0000			0.444286			0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000			0.444286			0.222143	+	0.975014i	$0.428695\pi$
$614$		0			0
$615$	−3.44415	−	8.31492i	−0.138882	−	0.335290i
$616$		0			0
$617$	−5.54328	+	2.29610i	−0.223164	+	0.0924375i	−0.491464	−	0.870898i	$-0.663538\pi$
$617$	−5.54328	+	2.29610i	−0.223164	+	0.0924375i	0.268300	+	0.963335i	$0.413538\pi$
$618$		0			0
$619$	−9.23880	−	3.82683i	−0.371339	−	0.153813i	0.189207	−	0.981937i	$-0.439408\pi$
$619$	−9.23880	−	3.82683i	−0.371339	−	0.153813i	−0.560545	+	0.828124i	$0.689408\pi$
$620$	−8.48528	+	8.48528i	−0.340777	+	0.340777i
$621$	−6.36396	+	6.36396i	−0.255377	+	0.255377i
$622$		0			0
$623$		0			0
$624$	3.69552	−	1.53073i	0.147939	−	0.0612784i
$625$			29.0000i			1.16000i
$626$		0			0
$627$	2.12132	+	2.12132i	0.0847174	+	0.0847174i
$628$	22.0000			0.877896
$629$		0			0
$630$		0			0
$631$	26.1630	+	26.1630i	1.04153	+	1.04153i	0.999099	+	0.0424312i	$0.0135103\pi$
$631$	26.1630	+	26.1630i	1.04153	+	1.04153i	0.0424312	+	0.999099i	$0.486490\pi$
$632$		0			0
$633$			2.00000i			0.0794929i
$634$		0			0
$635$	−14.9247	+	36.0313i	−0.592267	+	1.42986i
$636$	11.0866	+	4.59220i	0.439610	+	0.182093i
$637$	−6.36396	+	6.36396i	−0.252149	+	0.252149i
$638$		0			0
$639$	−11.0866	−	4.59220i	−0.438577	−	0.181665i
$640$		0			0
$641$	30.4880	−	12.6286i	1.20420	−	0.498798i	0.311849	−	0.950132i	$-0.399052\pi$
$641$	30.4880	−	12.6286i	1.20420	−	0.498798i	0.892355	+	0.451334i	$0.149052\pi$
$642$		0			0
$643$	−12.2459	−	29.5641i	−0.482930	−	1.16590i	−0.958211	−	0.286062i	$-0.907654\pi$
$643$	−12.2459	−	29.5641i	−0.482930	−	1.16590i	0.475281	−	0.879834i	$-0.342346\pi$
$644$	50.9117	+	50.9117i	2.00620	+	2.00620i
$645$	21.0000			0.826874
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$		0			0
$649$	−6.88830	−	16.6298i	−0.270389	−	0.652778i
$650$		0			0
$651$	−7.39104	+	3.06147i	−0.289678	+	0.119988i
$652$	−1.53073	+	3.69552i	−0.0599482	+	0.144728i
$653$	24.9447	+	10.3325i	0.976163	+	0.404340i	0.813003	−	0.582259i	$-0.197831\pi$
$653$	24.9447	+	10.3325i	0.976163	+	0.404340i	0.163160	+	0.986600i	$0.447831\pi$
$654$		0			0
$655$	−6.36396	+	6.36396i	−0.248661	+	0.248661i
$656$	11.0866	+	4.59220i	0.432857	+	0.179295i
$657$	−0.765367	+	1.84776i	−0.0298598	+	0.0720879i
$658$		0			0
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$	−6.88830	−	16.6298i	−0.268127	−	0.647315i
$661$	−21.9203	−	21.9203i	−0.852601	−	0.852601i	0.137852	−	0.990453i	$-0.455980\pi$
$661$	−21.9203	−	21.9203i	−0.852601	−	0.852601i	−0.990453	+	0.137852i	$0.955980\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.48528	−	8.48528i	−0.329045	−	0.329045i
$666$		0			0
$667$			54.0000i			2.09089i
$668$	−38.8029	+	16.0727i	−1.50133	+	0.621872i
$669$	−0.382683	+	0.923880i	−0.0147954	+	0.0357192i
$670$		0			0
$671$	−16.9706	+	16.9706i	−0.655141	+	0.655141i
$672$		0			0
$673$	20.3253	+	8.41904i	0.783485	+	0.324530i	0.738321	−	0.674450i	$-0.235619\pi$
$673$	20.3253	+	8.41904i	0.783485	+	0.324530i	0.0451638	+	0.998980i	$0.485619\pi$
$674$		0			0
$675$	−3.69552	+	1.53073i	−0.142241	+	0.0589180i
$676$		−	24.0000i		−	0.923077i
$677$	10.3325	+	24.9447i	0.397108	+	0.958705i	0.988348	+	0.152209i	$0.0486386\pi$
$677$	10.3325	+	24.9447i	0.397108	+	0.958705i	−0.591240	+	0.806496i	$0.701361\pi$
$678$		0			0
$679$	−64.0000			−2.45609
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	1.14805	+	2.77164i	0.0439289	+	0.106054i	0.944321	−	0.329026i	$-0.106720\pi$
$683$	1.14805	+	2.77164i	0.0439289	+	0.106054i	−0.900392	+	0.435079i	$0.856720\pi$
$684$			2.00000i			0.0764719i
$685$	−16.6298	+	6.88830i	−0.635393	+	0.263188i
$686$		0			0
$687$	12.9343	+	5.35757i	0.493475	+	0.204404i
$688$	−19.7990	+	19.7990i	−0.754829	+	0.754829i
$689$	−4.24264	+	4.24264i	−0.161632	+	0.161632i
$690$		0			0
$691$	−7.65367	+	18.4776i	−0.291159	+	0.702921i	−0.999997	−	0.00245092i	$-0.999220\pi$
$691$	−7.65367	+	18.4776i	−0.291159	+	0.702921i	0.708838	+	0.705372i	$0.249220\pi$
$692$	27.7164	−	11.4805i	1.05362	−	0.436423i
$693$		−	12.0000i		−	0.455842i
$694$		0			0
$695$	4.24264	+	4.24264i	0.160933	+	0.160933i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−14.8492	−	14.8492i	−0.561650	−	0.561650i
$700$	12.2459	+	29.5641i	0.462850	+	1.11742i
$701$			24.0000i			0.906467i	0.891392	+	0.453234i	$0.149730\pi$
$701$			24.0000i			0.906467i	−0.891392	+	0.453234i	$0.850270\pi$
$702$		0			0
$703$	1.53073	−	3.69552i	0.0577327	−	0.139379i
$704$	22.1731	+	9.18440i	0.835680	+	0.346150i
$705$	−12.7279	+	12.7279i	−0.479361	+	0.479361i
$706$		0			0
$707$		0			0
$708$	4.59220	−	11.0866i	0.172585	−	0.416658i
$709$	−12.9343	+	5.35757i	−0.485758	+	0.201208i	−0.612102	−	0.790779i	$-0.709676\pi$
$709$	−12.9343	+	5.35757i	−0.485758	+	0.201208i	0.126344	+	0.991987i	$0.459676\pi$
$710$		0			0
$711$	3.82683	+	9.23880i	0.143517	+	0.346482i
$712$		0			0
$713$	−18.0000			−0.674105
$714$		0			0
$715$	9.00000			0.336581
$716$	−8.48528	−	8.48528i	−0.317110	−	0.317110i
$717$	−4.59220	−	11.0866i	−0.171499	−	0.414035i
$718$		0			0
$719$	2.77164	−	1.14805i	0.103365	−	0.0428151i	−0.330402	−	0.943840i	$-0.607184\pi$
$719$	2.77164	−	1.14805i	0.103365	−	0.0428151i	0.433767	+	0.901025i	$0.357184\pi$
$720$	4.59220	−	11.0866i	0.171141	−	0.413171i
$721$	−18.4776	−	7.65367i	−0.688141	−	0.285038i
$722$		0			0
$723$	−5.65685	+	5.65685i	−0.210381	+	0.210381i
$724$	25.8686	+	10.7151i	0.961400	+	0.398225i
$725$	−9.18440	+	22.1731i	−0.341100	+	0.823489i
$726$		0			0
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$		0			0
$732$	−16.0000			−0.591377
$733$	−1.41421	−	1.41421i	−0.0522352	−	0.0522352i	0.680507	−	0.732742i	$-0.261760\pi$
$733$	−1.41421	−	1.41421i	−0.0522352	−	0.0522352i	−0.732742	+	0.680507i	$0.761760\pi$
$734$		0			0
$735$			27.0000i			0.995910i
$736$		0			0
$737$	4.59220	−	11.0866i	0.169156	−	0.408378i
$738$		0			0
$739$	−0.707107	+	0.707107i	−0.0260113	+	0.0260113i	−0.719993	−	0.693981i	$-0.755855\pi$
$739$	−0.707107	+	0.707107i	−0.0260113	+	0.0260113i	0.693981	+	0.719993i	$0.255855\pi$
$740$	−16.9706	+	16.9706i	−0.623850	+	0.623850i
$741$	−0.923880	−	0.382683i	−0.0339396	−	0.0140582i
$742$		0			0
$743$	−22.1731	+	9.18440i	−0.813452	+	0.336943i	−0.750331	−	0.661063i	$-0.770106\pi$
$743$	−22.1731	+	9.18440i	−0.813452	+	0.336943i	−0.0631219	+	0.998006i	$0.520106\pi$
$744$		0			0
$745$	20.6649	+	49.8895i	0.757104	+	1.82781i
$746$		0			0
$747$	6.00000			0.219529
$748$		0			0
$749$	−36.0000			−1.31541
$750$		0			0
$751$	−17.6034	−	42.4985i	−0.642359	−	1.55079i	−0.823489	−	0.567332i	$-0.807976\pi$
$751$	−17.6034	−	42.4985i	−0.642359	−	1.55079i	0.181131	−	0.983459i	$-0.442024\pi$
$752$		−	24.0000i		−	0.875190i
$753$	22.1731	−	9.18440i	0.808033	−	0.334698i
$754$		0			0
$755$	22.1731	+	9.18440i	0.806962	+	0.334255i
$756$	5.65685	−	5.65685i	0.205738	−	0.205738i
$757$	30.4056	−	30.4056i	1.10511	−	1.10511i	0.111326	−	0.993784i	$-0.464490\pi$
$757$	30.4056	−	30.4056i	1.10511	−	1.10511i	0.993784	−	0.111326i	$-0.0355098\pi$
$758$		0			0
$759$	10.3325	−	24.9447i	0.375044	−	0.905437i
$760$		0			0
$761$		−	30.0000i		−	1.08750i	−0.839248	−	0.543750i	$-0.817004\pi$
$761$		−	30.0000i		−	1.08750i	0.839248	−	0.543750i	$-0.182996\pi$
$762$		0			0
$763$	−56.5685	−	56.5685i	−2.04792	−	2.04792i
$764$	36.0000			1.30243
$765$		0			0
$766$		0			0
$767$	4.24264	+	4.24264i	0.153193	+	0.153193i
$768$	6.12293	+	14.7821i	0.220942	+	0.533402i
$769$			41.0000i			1.47850i	0.673432	+	0.739249i	$0.264819\pi$
$769$			41.0000i			1.47850i	−0.673432	+	0.739249i	$0.735181\pi$
$770$		0			0
$771$	4.59220	−	11.0866i	0.165384	−	0.399273i
$772$	40.6507	+	16.8381i	1.46305	+	0.606015i
$773$	16.9706	−	16.9706i	0.610389	−	0.610389i	−0.332659	−	0.943047i	$-0.607946\pi$
$773$	16.9706	−	16.9706i	0.610389	−	0.610389i	0.943047	+	0.332659i	$0.107946\pi$
$774$		0			0
$775$	−7.39104	−	3.06147i	−0.265494	−	0.109971i
$776$		0			0
$777$	−14.7821	+	6.12293i	−0.530304	+	0.219659i
$778$		0			0
$779$	−1.14805	−	2.77164i	−0.0411332	−	0.0993043i
$780$	4.24264	+	4.24264i	0.151911	+	0.151911i
$781$	36.0000			1.28818
$782$		0			0
$783$	6.00000			0.214423
$784$	−25.4558	−	25.4558i	−0.909137	−	0.909137i
$785$	12.6286	+	30.4880i	0.450732	+	1.08816i
$786$		0			0
$787$	−36.9552	+	15.3073i	−1.31731	+	0.545648i	−0.927009	−	0.375040i	$-0.877629\pi$
$787$	−36.9552	+	15.3073i	−1.31731	+	0.545648i	−0.390301	+	0.920687i	$0.627629\pi$
$788$	−2.29610	+	5.54328i	−0.0817952	+	0.197471i
$789$	11.0866	+	4.59220i	0.394692	+	0.163487i
$790$		0			0
$791$	−25.4558	+	25.4558i	−0.905106	+	0.905106i
$792$		0			0
$793$	3.06147	−	7.39104i	0.108716	−	0.262463i
$794$		0			0
$795$			18.0000i			0.638394i
$796$	−12.2459	−	29.5641i	−0.434043	−	1.04787i
$797$	−33.9411	−	33.9411i	−1.20226	−	1.20226i	−0.973479	−	0.228778i	$-0.926527\pi$
$797$	−33.9411	−	33.9411i	−1.20226	−	1.20226i	−0.228778	−	0.973479i	$-0.573473\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		−	6.00000i		−	0.211735i
$804$	7.39104	−	3.06147i	0.260662	−	0.107970i
$805$	−41.3298	+	99.7790i	−1.45668	+	3.51675i
$806$		0			0
$807$	−10.6066	+	10.6066i	−0.373370	+	0.373370i
$808$		0			0
$809$	47.1179	+	19.5169i	1.65658	+	0.686176i	0.997808	−	0.0661707i	$-0.0210782\pi$
$809$	47.1179	+	19.5169i	1.65658	+	0.686176i	0.658767	+	0.752347i	$0.271078\pi$
$810$		0			0
$811$	9.23880	−	3.82683i	0.324418	−	0.134378i	−0.214530	−	0.976717i	$-0.568822\pi$
$811$	9.23880	−	3.82683i	0.324418	−	0.134378i	0.538948	+	0.842339i	$0.318822\pi$
$812$		−	48.0000i		−	1.68447i
$813$	−4.20952	−	10.1627i	−0.147634	−	0.356421i
$814$		0			0
$815$	−6.00000			−0.210171
$816$		0			0
$817$	7.00000			0.244899
$818$		0			0
$819$	1.53073	+	3.69552i	0.0534882	+	0.129132i
$820$			18.0000i			0.628587i
$821$	−19.4015	+	8.03635i	−0.677116	+	0.280471i	−0.694621	−	0.719376i	$-0.744428\pi$
$821$	−19.4015	+	8.03635i	−0.677116	+	0.280471i	0.0175047	+	0.999847i	$0.494428\pi$
$822$		0			0
$823$	−25.8686	−	10.7151i	−0.901724	−	0.373506i	−0.116841	−	0.993151i	$-0.537277\pi$
$823$	−25.8686	−	10.7151i	−0.901724	−	0.373506i	−0.784883	+	0.619644i	$0.787277\pi$
$824$		0			0
$825$	8.48528	−	8.48528i	0.295420	−	0.295420i
$826$		0			0
$827$	8.03635	−	19.4015i	0.279451	−	0.674655i	−0.720369	−	0.693591i	$-0.756028\pi$
$827$	8.03635	−	19.4015i	0.279451	−	0.674655i	0.999821	+	0.0189354i	$0.00602769\pi$
$828$	16.6298	−	6.88830i	0.577927	−	0.239385i
$829$		−	14.0000i		−	0.486240i	−0.969996	−	0.243120i	$-0.921829\pi$
$829$		−	14.0000i		−	0.486240i	0.969996	−	0.243120i	$-0.0781709\pi$
$830$		0			0
$831$	1.41421	+	1.41421i	0.0490585	+	0.0490585i
$832$	−8.00000			−0.277350
$833$		0			0
$834$		0			0
$835$	−44.5477	−	44.5477i	−1.54164	−	1.54164i
$836$	−2.29610	−	5.54328i	−0.0794123	−	0.191718i
$837$			2.00000i			0.0691301i
$838$		0			0
$839$	−21.8130	+	52.6611i	−0.753067	+	1.81806i	−0.211567	+	0.977364i	$0.567857\pi$
$839$	−21.8130	+	52.6611i	−0.753067	+	1.81806i	−0.541500	+	0.840701i	$0.682143\pi$
$840$		0			0
$841$	4.94975	−	4.94975i	0.170681	−	0.170681i
$842$		0			0
$843$	−11.0866	−	4.59220i	−0.381841	−	0.158164i
$844$	1.53073	−	3.69552i	0.0526900	−	0.127205i
$845$	33.2597	−	13.7766i	1.14417	−	0.473930i
$846$		0			0
$847$	−3.06147	−	7.39104i	−0.105193	−	0.253959i
$848$	−16.9706	−	16.9706i	−0.582772	−	0.582772i
$849$	10.0000			0.343199
$850$		0			0
$851$	−36.0000			−1.23406
$852$	16.9706	+	16.9706i	0.581402	+	0.581402i
$853$	9.94977	+	24.0209i	0.340674	+	0.822459i	0.997648	+	0.0685459i	$0.0218360\pi$
$853$	9.94977	+	24.0209i	0.340674	+	0.822459i	−0.656974	+	0.753913i	$0.728164\pi$
$854$		0			0
$855$	−2.77164	+	1.14805i	−0.0947880	+	0.0392625i
$856$		0			0
$857$	−16.6298	−	6.88830i	−0.568064	−	0.235300i	0.0801177	−	0.996785i	$-0.474470\pi$
$857$	−16.6298	−	6.88830i	−0.568064	−	0.235300i	−0.648182	+	0.761486i	$0.724470\pi$
$858$		0			0
$859$	−14.1421	+	14.1421i	−0.482523	+	0.482523i	−0.905937	−	0.423413i	$-0.860832\pi$
$859$	−14.1421	+	14.1421i	−0.482523	+	0.482523i	0.423413	+	0.905937i	$0.360832\pi$
$860$	−38.8029	−	16.0727i	−1.32317	−	0.548075i
$861$	−4.59220	+	11.0866i	−0.156502	+	0.377829i
$862$		0			0
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$	31.8198	+	31.8198i	1.08191	+	1.08191i
$866$		0			0
$867$		0			0
$868$	16.0000			0.543075
$869$	−21.2132	−	21.2132i	−0.719609	−	0.719609i
$870$		0			0
$871$			4.00000i			0.135535i
$872$		0			0
$873$	−6.12293	+	14.7821i	−0.207230	+	0.500297i
$874$		0			0
$875$	8.48528	−	8.48528i	0.286855	−	0.286855i
$876$	2.82843	−	2.82843i	0.0955637	−	0.0955637i
$877$	−12.9343	−	5.35757i	−0.436761	−	0.180912i	0.153459	−	0.988155i	$-0.450959\pi$
$877$	−12.9343	−	5.35757i	−0.436761	−	0.180912i	−0.590219	+	0.807243i	$0.700959\pi$
$878$		0			0
$879$	22.1731	−	9.18440i	0.747880	−	0.309782i
$880$			36.0000i			1.21356i
$881$	−6.88830	−	16.6298i	−0.232073	−	0.560273i	0.764348	−	0.644804i	$-0.223061\pi$
$881$	−6.88830	−	16.6298i	−0.232073	−	0.560273i	−0.996421	+	0.0845306i	$0.973061\pi$
$882$		0			0
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$		0			0
$887$	14.9247	+	36.0313i	0.501121	+	1.20981i	0.948874	+	0.315655i	$0.102224\pi$
$887$	14.9247	+	36.0313i	0.501121	+	1.20981i	−0.447753	+	0.894157i	$0.647776\pi$
$888$		0			0
$889$	48.0417	−	19.8995i	1.61127	−	0.667409i
$890$		0			0
$891$	−2.77164	−	1.14805i	−0.0928534	−	0.0384611i
$892$	1.41421	−	1.41421i	0.0473514	−	0.0473514i
$893$	−4.24264	+	4.24264i	−0.141975	+	0.141975i
$894$		0			0
$895$	6.88830	−	16.6298i	0.230251	−	0.555874i
$896$		0			0
$897$			9.00000i			0.300501i
$898$		0			0
$899$	8.48528	+	8.48528i	0.283000	+	0.283000i
$900$	8.00000			0.266667
$901$		0			0
$902$		0			0
$903$	−19.7990	−	19.7990i	−0.658869	−	0.658869i
$904$		0			0
$905$			42.0000i			1.39613i
$906$		0			0
$907$	0.765367	−	1.84776i	0.0254136	−	0.0613538i	−0.910663	−	0.413149i	$-0.864429\pi$
$907$	0.765367	−	1.84776i	0.0254136	−	0.0613538i	0.936077	+	0.351795i	$0.114429\pi$
$908$	−5.54328	−	2.29610i	−0.183960	−	0.0761988i
$909$		0			0
$910$		0			0
$911$	24.9447	+	10.3325i	0.826456	+	0.342329i	0.755499	−	0.655150i	$-0.227395\pi$
$911$	24.9447	+	10.3325i	0.826456	+	0.342329i	0.0709574	+	0.997479i	$0.477395\pi$
$912$	1.53073	−	3.69552i	0.0506877	−	0.122371i
$913$	−16.6298	+	6.88830i	−0.550367	+	0.227970i
$914$		0			0
$915$	−9.18440	−	22.1731i	−0.303627	−	0.733020i
$916$	−19.7990	−	19.7990i	−0.654177	−	0.654177i
$917$	12.0000			0.396275
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$		0			0
$921$	7.65367	+	18.4776i	0.252197	+	0.608857i
$922$		0			0
$923$	−11.0866	+	4.59220i	−0.364918	+	0.151154i
$924$	−9.18440	+	22.1731i	−0.302145	+	0.729442i
$925$	−14.7821	−	6.12293i	−0.486032	−	0.201321i
$926$		0			0
$927$	−3.53553	+	3.53553i	−0.116122	+	0.116122i
$928$		0			0
$929$	−5.74025	+	13.8582i	−0.188332	+	0.454673i	−0.989639	−	0.143581i	$-0.954138\pi$
$929$	−5.74025	+	13.8582i	−0.188332	+	0.454673i	0.801307	+	0.598253i	$0.204138\pi$
$930$		0			0
$931$			9.00000i			0.294963i
$932$	16.0727	+	38.8029i	0.526479	+	1.27103i
$933$	−16.9706	−	16.9706i	−0.555591	−	0.555591i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	15.5563	+	15.5563i	0.508204	+	0.508204i	0.913975	−	0.405771i	$-0.132997\pi$
$937$	15.5563	+	15.5563i	0.508204	+	0.508204i	−0.405771	+	0.913975i	$0.632997\pi$
$938$		0			0
$939$		−	16.0000i		−	0.522140i
$940$	33.2597	−	13.7766i	1.08481	−	0.449343i
$941$	6.88830	−	16.6298i	0.224552	−	0.542117i	−0.770946	−	0.636901i	$-0.780216\pi$
$941$	6.88830	−	16.6298i	0.224552	−	0.542117i	0.995498	+	0.0947839i	$0.0302160\pi$
$942$		0			0
$943$	−19.0919	+	19.0919i	−0.621717	+	0.621717i
$944$	−16.9706	+	16.9706i	−0.552345	+	0.552345i
$945$	11.0866	+	4.59220i	0.360646	+	0.149384i
$946$		0			0
$947$	−33.2597	+	13.7766i	−1.08079	+	0.447679i	−0.850788	−	0.525510i	$-0.823875\pi$
$947$	−33.2597	+	13.7766i	−1.08079	+	0.447679i	−0.230006	+	0.973189i	$0.573875\pi$
$948$		−	20.0000i		−	0.649570i
$949$	0.765367	+	1.84776i	0.0248449	+	0.0599808i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	20.6649	+	49.8895i	0.668701	+	1.61439i
$956$			24.0000i			0.776215i
$957$	−16.6298	+	6.88830i	−0.537566	+	0.222667i
$958$		0			0
$959$	22.1731	+	9.18440i	0.716007	+	0.296580i
$960$	−16.9706	+	16.9706i	−0.547723	+	0.547723i
$961$	19.0919	−	19.0919i	0.615867	−	0.615867i
$962$		0			0
$963$	−3.44415	+	8.31492i	−0.110986	+	0.267944i
$964$	14.7821	−	6.12293i	0.476098	−	0.197206i
$965$			66.0000i			2.12462i
$966$		0			0
$967$	28.9914	+	28.9914i	0.932300	+	0.932300i	0.997849	−	0.0655495i	$-0.0208800\pi$
$967$	28.9914	+	28.9914i	0.932300	+	0.932300i	−0.0655495	+	0.997849i	$0.520880\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.24264	−	4.24264i	−0.136153	−	0.136153i	0.635746	−	0.771899i	$-0.280693\pi$
$971$	−4.24264	−	4.24264i	−0.136153	−	0.136153i	−0.771899	+	0.635746i	$0.780693\pi$
$972$	−0.765367	−	1.84776i	−0.0245492	−	0.0592669i
$973$		−	8.00000i		−	0.256468i
$974$		0			0
$975$	−1.53073	+	3.69552i	−0.0490227	+	0.118351i
$976$	29.5641	+	12.2459i	0.946325	+	0.391981i
$977$	−21.2132	+	21.2132i	−0.678671	+	0.678671i	−0.959699	−	0.281029i	$-0.909324\pi$
$977$	−21.2132	+	21.2132i	−0.678671	+	0.678671i	0.281029	+	0.959699i	$0.409324\pi$
$978$		0			0
$979$		0			0
$980$	20.6649	−	49.8895i	0.660116	−	1.59366i
$981$	−18.4776	+	7.65367i	−0.589944	+	0.244363i
$982$		0			0
$983$	3.44415	+	8.31492i	0.109851	+	0.265205i	0.969240	−	0.246119i	$-0.0791554\pi$
$983$	3.44415	+	8.31492i	0.109851	+	0.265205i	−0.859388	+	0.511324i	$0.829155\pi$
$984$		0			0
$985$	−9.00000			−0.286764
$986$		0			0
$987$	24.0000			0.763928
$988$	1.41421	+	1.41421i	0.0449921	+	0.0449921i
$989$	−24.1091	−	58.2044i	−0.766623	−	1.85079i
$990$		0			0
$991$	−48.0417	+	19.8995i	−1.52610	+	0.632130i	−0.978802	−	0.204811i	$-0.934342\pi$
$991$	−48.0417	+	19.8995i	−1.52610	+	0.632130i	−0.547294	+	0.836940i	$0.684342\pi$
$992$		0			0
$993$	−12.0104	−	4.97488i	−0.381140	−	0.157873i
$994$		0			0
$995$	33.9411	−	33.9411i	1.07601	−	1.07601i
$996$	−11.0866	−	4.59220i	−0.351291	−	0.145509i
$997$	−23.7264	+	57.2805i	−0.751422	+	1.81409i	−0.200154	+	0.979765i	$0.564144\pi$
$997$	−23.7264	+	57.2805i	−0.751422	+	1.81409i	−0.551268	+	0.834328i	$0.685856\pi$
$998$		0			0
$999$			4.00000i			0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.c.712.2		8
17.2	even	8	inner	867.2.h.c.757.2		8
17.3	odd	16		867.2.d.a.577.2		2
17.4	even	4	inner	867.2.h.c.733.2		8
17.5	odd	16		867.2.a.c.1.1		1
17.6	odd	16		867.2.e.e.829.2		4
17.7	odd	16		867.2.e.e.616.2		4
17.8	even	8	inner	867.2.h.c.688.2		8
17.9	even	8	inner	867.2.h.c.688.1		8
17.10	odd	16		867.2.e.e.616.1		4
17.11	odd	16		867.2.e.e.829.1		4
17.12	odd	16		51.2.a.a.1.1	✓	1
17.13	even	4	inner	867.2.h.c.733.1		8
17.14	odd	16		867.2.d.a.577.1		2
17.15	even	8	inner	867.2.h.c.757.1		8
17.16	even	2	inner	867.2.h.c.712.1		8
51.5	even	16		2601.2.a.f.1.1		1
51.29	even	16		153.2.a.b.1.1		1
68.63	even	16		816.2.a.g.1.1		1
85.12	even	16		1275.2.b.b.1174.1		2
85.29	odd	16		1275.2.a.d.1.1		1
85.63	even	16		1275.2.b.b.1174.2		2
119.97	even	16		2499.2.a.d.1.1		1
136.29	odd	16		3264.2.a.a.1.1		1
136.131	even	16		3264.2.a.r.1.1		1
187.131	even	16		6171.2.a.e.1.1		1
204.131	odd	16		2448.2.a.c.1.1		1
221.12	odd	16		8619.2.a.g.1.1		1
255.29	even	16		3825.2.a.i.1.1		1
357.335	odd	16		7497.2.a.j.1.1		1
408.29	even	16		9792.2.a.by.1.1		1
408.131	odd	16		9792.2.a.cd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.a.1.1	✓	1	17.12	odd	16
153.2.a.b.1.1		1	51.29	even	16
816.2.a.g.1.1		1	68.63	even	16
867.2.a.c.1.1		1	17.5	odd	16
867.2.d.a.577.1		2	17.14	odd	16
867.2.d.a.577.2		2	17.3	odd	16
867.2.e.e.616.1		4	17.10	odd	16
867.2.e.e.616.2		4	17.7	odd	16
867.2.e.e.829.1		4	17.11	odd	16
867.2.e.e.829.2		4	17.6	odd	16
867.2.h.c.688.1		8	17.9	even	8	inner
867.2.h.c.688.2		8	17.8	even	8	inner
867.2.h.c.712.1		8	17.16	even	2	inner
867.2.h.c.712.2		8	1.1	even	1	trivial
867.2.h.c.733.1		8	17.13	even	4	inner
867.2.h.c.733.2		8	17.4	even	4	inner
867.2.h.c.757.1		8	17.15	even	8	inner
867.2.h.c.757.2		8	17.2	even	8	inner
1275.2.a.d.1.1		1	85.29	odd	16
1275.2.b.b.1174.1		2	85.12	even	16
1275.2.b.b.1174.2		2	85.63	even	16
2448.2.a.c.1.1		1	204.131	odd	16
2499.2.a.d.1.1		1	119.97	even	16
2601.2.a.f.1.1		1	51.5	even	16
3264.2.a.a.1.1		1	136.29	odd	16
3264.2.a.r.1.1		1	136.131	even	16
3825.2.a.i.1.1		1	255.29	even	16
6171.2.a.e.1.1		1	187.131	even	16
7497.2.a.j.1.1		1	357.335	odd	16
8619.2.a.g.1.1		1	221.12	odd	16
9792.2.a.by.1.1		1	408.29	even	16
9792.2.a.cd.1.1		1	408.131	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{3} -2.00000i q^{4} +(2.77164 - 1.14805i) q^{5} +(-3.69552 - 1.53073i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{3} -2.00000i q^{4} +(2.77164 - 1.14805i) q^{5} +(-3.69552 - 1.53073i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(1.14805 - 2.77164i) q^{11} +(1.84776 - 0.765367i) q^{12} +1.00000i q^{13} +(2.12132 + 2.12132i) q^{15} -4.00000 q^{16} +(0.707107 + 0.707107i) q^{19} +(-2.29610 - 5.54328i) q^{20} -4.00000i q^{21} +(3.44415 - 8.31492i) q^{23} +(2.82843 - 2.82843i) q^{25} +(-0.923880 - 0.382683i) q^{27} +(-3.06147 + 7.39104i) q^{28} +(-5.54328 + 2.29610i) q^{29} +(-0.765367 - 1.84776i) q^{31} +3.00000 q^{33} -12.0000 q^{35} +(1.41421 + 1.41421i) q^{36} +(-1.53073 - 3.69552i) q^{37} +(-0.923880 + 0.382683i) q^{39} +(-2.77164 - 1.14805i) q^{41} +(4.94975 - 4.94975i) q^{43} +(-5.54328 - 2.29610i) q^{44} +(-1.14805 + 2.77164i) q^{45} +6.00000i q^{47} +(-1.53073 - 3.69552i) q^{48} +(6.36396 + 6.36396i) q^{49} +2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} -9.00000i q^{55} +(-0.382683 + 0.923880i) q^{57} +(4.24264 - 4.24264i) q^{59} +(4.24264 - 4.24264i) q^{60} +(-7.39104 - 3.06147i) q^{61} +(3.69552 - 1.53073i) q^{63} +8.00000i q^{64} +(1.14805 + 2.77164i) q^{65} +4.00000 q^{67} +9.00000 q^{69} +(4.59220 + 11.0866i) q^{71} +(1.84776 - 0.765367i) q^{73} +(3.69552 + 1.53073i) q^{75} +(1.41421 - 1.41421i) q^{76} +(-8.48528 + 8.48528i) q^{77} +(3.82683 - 9.23880i) q^{79} +(-11.0866 + 4.59220i) q^{80} -1.00000i q^{81} +(-4.24264 - 4.24264i) q^{83} -8.00000 q^{84} +(-4.24264 - 4.24264i) q^{87} +(1.53073 - 3.69552i) q^{91} +(-16.6298 - 6.88830i) q^{92} +(1.41421 - 1.41421i) q^{93} +(2.77164 + 1.14805i) q^{95} +(14.7821 - 6.12293i) q^{97} +(1.14805 + 2.77164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 32 q^{16} + 24 q^{33} - 96 q^{35} + 16 q^{52} + 32 q^{67} + 72 q^{69} - 64 q^{84}+O(q^{100}) \) 8 * q - 32 * q^16 + 24 * q^33 - 96 * q^35 + 16 * q^52 + 32 * q^67 + 72 * q^69 - 64 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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