LMFDB - Embedded newform 630.2.cd.a.527.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.32
Character	$\chi$	$=$	630.527
Dual form			630.2.cd.a.263.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.895033 + 1.48287i) q^{3} -1.00000i q^{4} +(2.15119 - 0.610232i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-2.60867 - 0.441381i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.39783 - 2.65444i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.895033 + 1.48287i) q^{3} -1.00000i q^{4} +(2.15119 - 0.610232i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-2.60867 - 0.441381i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.39783 - 2.65444i) q^{9} +(1.08962 - 1.95262i) q^{10} +(-5.45229 - 3.14788i) q^{11} +(1.48287 + 0.895033i) q^{12} +(-1.53481 - 5.72800i) q^{13} +(-2.15671 + 1.53251i) q^{14} +(-1.02049 + 3.73612i) q^{15} -1.00000 q^{16} +(4.19247 + 1.12337i) q^{17} +(-2.86539 - 0.888559i) q^{18} +(1.36418 + 0.787607i) q^{19} +(-0.610232 - 2.15119i) q^{20} +(2.98936 - 3.47329i) q^{21} +(-6.08124 + 1.62946i) q^{22} +(0.303976 - 1.13445i) q^{23} +(1.68143 - 0.415666i) q^{24} +(4.25523 - 2.62545i) q^{25} +(-5.13559 - 2.96503i) q^{26} +(5.18731 + 0.303009i) q^{27} +(-0.441381 + 2.60867i) q^{28} +(0.461965 + 0.800147i) q^{29} +(1.92024 + 3.36343i) q^{30} -3.20319 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.54789 - 5.26760i) q^{33} +(3.75886 - 2.17018i) q^{34} +(-5.88110 + 0.642404i) q^{35} +(-2.65444 + 1.39783i) q^{36} +(2.33429 - 0.625472i) q^{37} +(1.52154 - 0.407696i) q^{38} +(9.86762 + 2.85082i) q^{39} +(-1.95262 - 1.08962i) q^{40} +(-5.94493 - 3.43231i) q^{41} +(-0.342185 - 4.56978i) q^{42} +(1.81108 + 0.485278i) q^{43} +(-3.14788 + 5.45229i) q^{44} +(-4.62683 - 4.85721i) q^{45} +(-0.587236 - 1.01712i) q^{46} +(4.13599 - 4.13599i) q^{47} +(0.895033 - 1.48287i) q^{48} +(6.61037 + 2.30284i) q^{49} +(1.15243 - 4.86538i) q^{50} +(-5.41821 + 5.21145i) q^{51} +(-5.72800 + 1.53481i) q^{52} +(-1.58611 + 5.91945i) q^{53} +(3.88224 - 3.45372i) q^{54} +(-13.6499 - 3.44453i) q^{55} +(1.53251 + 2.15671i) q^{56} +(-2.38891 + 1.31797i) q^{57} +(0.892448 + 0.239131i) q^{58} -8.32434 q^{59} +(3.73612 + 1.02049i) q^{60} -12.3608 q^{61} +(-2.26500 + 2.26500i) q^{62} +(2.47487 + 7.54155i) q^{63} +1.00000i q^{64} +(-6.79709 - 11.3854i) q^{65} +(3.02662 - 10.4761i) q^{66} +(4.51921 + 4.51921i) q^{67} +(1.12337 - 4.19247i) q^{68} +(1.41018 + 1.46613i) q^{69} +(-3.70432 + 4.61281i) q^{70} -9.47913i q^{71} +(-0.888559 + 2.86539i) q^{72} +(5.78236 + 1.54938i) q^{73} +(1.20832 - 2.09287i) q^{74} +(0.0846377 + 8.65984i) q^{75} +(0.787607 - 1.36418i) q^{76} +(12.8338 + 10.6183i) q^{77} +(8.99329 - 4.96163i) q^{78} +13.3166i q^{79} +(-2.15119 + 0.610232i) q^{80} +(-5.09214 + 7.42092i) q^{81} +(-6.63071 + 1.77669i) q^{82} +(4.66953 - 17.4269i) q^{83} +(-3.47329 - 2.98936i) q^{84} +(9.70430 - 0.141801i) q^{85} +(1.62377 - 0.937485i) q^{86} +(-1.59999 - 0.0311222i) q^{87} +(1.62946 + 6.08124i) q^{88} +(6.67816 - 11.5669i) q^{89} +(-6.70623 - 0.162906i) q^{90} +(1.47560 + 15.6199i) q^{91} +(-1.13445 - 0.303976i) q^{92} +(2.86697 - 4.74993i) q^{93} -5.84918i q^{94} +(3.41522 + 0.861828i) q^{95} +(-0.415666 - 1.68143i) q^{96} +(0.0223723 - 0.0834947i) q^{97} +(6.30259 - 3.04588i) q^{98} +(-0.734495 + 18.8730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.895033	+	1.48287i	−0.516748	+	0.856138i
$3$	−0.895033	+	1.48287i	−0.516748	+	0.856138i
$4$		−	1.00000i		−	0.500000i
$5$	2.15119	−	0.610232i	0.962041	−	0.272904i
$5$	2.15119	−	0.610232i	0.962041	−	0.272904i
$6$	0.415666	+	1.68143i	0.169695	+	0.686443i
$7$	−2.60867	−	0.441381i	−0.985986	−	0.166826i
$7$	−2.60867	−	0.441381i	−0.985986	−	0.166826i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.39783	−	2.65444i	−0.465944	−	0.884814i
$10$	1.08962	−	1.95262i	0.344568	−	0.617473i
$11$	−5.45229	−	3.14788i	−1.64393	−	0.949122i	−0.979418	−	0.201842i	$-0.935307\pi$
$11$	−5.45229	−	3.14788i	−1.64393	−	0.949122i	−0.664510	−	0.747280i	$-0.731360\pi$
$12$	1.48287	+	0.895033i	0.428069	+	0.258374i
$13$	−1.53481	−	5.72800i	−0.425681	−	1.58866i	−0.762432	−	0.647069i	$-0.775995\pi$
$13$	−1.53481	−	5.72800i	−0.425681	−	1.58866i	0.336751	−	0.941594i	$-0.390672\pi$
$14$	−2.15671	+	1.53251i	−0.576406	+	0.409580i
$15$	−1.02049	+	3.73612i	−0.263489	+	0.964662i
$16$	−1.00000			−0.250000
$17$	4.19247	+	1.12337i	1.01682	+	0.272457i	0.728477	−	0.685070i	$-0.240228\pi$
$17$	4.19247	+	1.12337i	1.01682	+	0.272457i	0.288345	+	0.957527i	$0.406895\pi$
$18$	−2.86539	−	0.888559i	−0.675379	−	0.209435i
$19$	1.36418	+	0.787607i	0.312963	+	0.180690i	0.648252	−	0.761426i	$-0.275500\pi$
$19$	1.36418	+	0.787607i	0.312963	+	0.180690i	−0.335288	+	0.942116i	$0.608834\pi$
$20$	−0.610232	−	2.15119i	−0.136452	−	0.481021i
$21$	2.98936	−	3.47329i	0.652332	−	0.757933i
$22$	−6.08124	+	1.62946i	−1.29652	+	0.347403i
$23$	0.303976	−	1.13445i	0.0633833	−	0.236550i	−0.926966	−	0.375146i	$-0.877592\pi$
$23$	0.303976	−	1.13445i	0.0633833	−	0.236550i	0.990349	+	0.138597i	$0.0442591\pi$
$24$	1.68143	−	0.415666i	0.343221	−	0.0848475i
$25$	4.25523	−	2.62545i	0.851047	−	0.525090i
$26$	−5.13559	−	2.96503i	−1.00717	−	0.581491i
$27$	5.18731	+	0.303009i	0.998298	+	0.0583141i
$28$	−0.441381	+	2.60867i	−0.0834131	+	0.492993i
$29$	0.461965	+	0.800147i	0.0857848	+	0.148584i	0.905725	−	0.423865i	$-0.139327\pi$
$29$	0.461965	+	0.800147i	0.0857848	+	0.148584i	−0.819941	+	0.572449i	$0.805994\pi$
$30$	1.92024	+	3.36343i	0.350587	+	0.614076i
$31$	−3.20319			−0.575311			−0.287655	−	0.957734i	$-0.592876\pi$
$31$	−3.20319			−0.575311			−0.287655	+	0.957734i	$0.592876\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	9.54789	−	5.26760i	1.66208	−	0.916972i
$34$	3.75886	−	2.17018i	0.644639	−	0.372183i
$35$	−5.88110	+	0.642404i	−0.994087	+	0.108586i
$36$	−2.65444	+	1.39783i	−0.442407	+	0.232972i
$37$	2.33429	−	0.625472i	0.383755	−	0.102827i	−0.0617835	−	0.998090i	$-0.519679\pi$
$37$	2.33429	−	0.625472i	0.383755	−	0.102827i	0.445539	+	0.895263i	$0.353012\pi$
$38$	1.52154	−	0.407696i	0.246826	−	0.0661370i
$39$	9.86762	+	2.85082i	1.58008	+	0.456496i
$40$	−1.95262	−	1.08962i	−0.308736	−	0.172284i
$41$	−5.94493	−	3.43231i	−0.928443	−	0.536037i	−0.0421240	−	0.999112i	$-0.513412\pi$
$41$	−5.94493	−	3.43231i	−0.928443	−	0.536037i	−0.886319	+	0.463076i	$0.846746\pi$
$42$	−0.342185	−	4.56978i	−0.0528003	−	0.705133i
$43$	1.81108	+	0.485278i	0.276187	+	0.0740042i	0.394254	−	0.919001i	$-0.371003\pi$
$43$	1.81108	+	0.485278i	0.276187	+	0.0740042i	−0.118067	+	0.993006i	$0.537670\pi$
$44$	−3.14788	+	5.45229i	−0.474561	+	0.821964i
$45$	−4.62683	−	4.85721i	−0.689726	−	0.724070i
$46$	−0.587236	−	1.01712i	−0.0865832	−	0.149966i
$47$	4.13599	−	4.13599i	0.603296	−	0.603296i	−0.337889	−	0.941186i	$-0.609713\pi$
$47$	4.13599	−	4.13599i	0.603296	−	0.603296i	0.941186	+	0.337889i	$0.109713\pi$
$48$	0.895033	−	1.48287i	0.129187	−	0.214034i
$49$	6.61037	+	2.30284i	0.944338	+	0.328977i
$50$	1.15243	−	4.86538i	0.162978	−	0.688068i
$51$	−5.41821	+	5.21145i	−0.758701	+	0.729748i
$52$	−5.72800	+	1.53481i	−0.794331	+	0.212840i
$53$	−1.58611	+	5.91945i	−0.217869	+	0.813099i	0.767267	+	0.641327i	$0.221616\pi$
$53$	−1.58611	+	5.91945i	−0.217869	+	0.813099i	−0.985137	+	0.171772i	$0.945051\pi$
$54$	3.88224	−	3.45372i	0.528306	−	0.469992i
$55$	−13.6499	−	3.44453i	−1.84055	−	0.464460i
$56$	1.53251	+	2.15671i	0.204790	+	0.288203i
$57$	−2.38891	+	1.31797i	−0.316418	+	0.174569i
$58$	0.892448	+	0.239131i	0.117184	+	0.0313994i
$59$	−8.32434			−1.08374			−0.541868	−	0.840463i	$-0.682283\pi$
$59$	−8.32434			−1.08374			−0.541868	+	0.840463i	$0.682283\pi$
$60$	3.73612	+	1.02049i	0.482331	+	0.131745i
$61$	−12.3608			−1.58264			−0.791322	−	0.611400i	$-0.790607\pi$
$61$	−12.3608			−1.58264			−0.791322	+	0.611400i	$0.790607\pi$
$62$	−2.26500	+	2.26500i	−0.287655	+	0.287655i
$63$	2.47487	+	7.54155i	0.311804	+	0.950147i
$64$			1.00000i			0.125000i
$65$	−6.79709	−	11.3854i	−0.843075	−	1.41219i
$66$	3.02662	−	10.4761i	0.372552	−	1.28952i
$67$	4.51921	+	4.51921i	0.552109	+	0.552109i	0.927049	−	0.374940i	$-0.122337\pi$
$67$	4.51921	+	4.51921i	0.552109	+	0.552109i	−0.374940	+	0.927049i	$0.622337\pi$
$68$	1.12337	−	4.19247i	0.136228	−	0.508411i
$69$	1.41018	+	1.46613i	0.169766	+	0.176501i
$70$	−3.70432	+	4.61281i	−0.442750	+	0.551337i
$71$		−	9.47913i		−	1.12497i	−0.826809	−	0.562483i	$-0.809846\pi$
$71$		−	9.47913i		−	1.12497i	0.826809	−	0.562483i	$-0.190154\pi$
$72$	−0.888559	+	2.86539i	−0.104718	+	0.337689i
$73$	5.78236	+	1.54938i	0.676774	+	0.181341i	0.580804	−	0.814043i	$-0.302738\pi$
$73$	5.78236	+	1.54938i	0.676774	+	0.181341i	0.0959699	+	0.995384i	$0.469405\pi$
$74$	1.20832	−	2.09287i	0.140464	−	0.243291i
$75$	0.0846377	+	8.65984i	0.00977312	+	0.999952i
$76$	0.787607	−	1.36418i	0.0903448	−	0.156482i
$77$	12.8338	+	10.6183i	1.46255	+	1.21007i
$78$	8.99329	−	4.96163i	1.01829	−	0.561794i
$79$			13.3166i			1.49823i	0.662440	+	0.749115i	$0.269521\pi$
$79$			13.3166i			1.49823i	−0.662440	+	0.749115i	$0.730479\pi$
$80$	−2.15119	+	0.610232i	−0.240510	+	0.0682261i
$81$	−5.09214	+	7.42092i	−0.565793	+	0.824547i
$82$	−6.63071	+	1.77669i	−0.732240	+	0.196203i
$83$	4.66953	−	17.4269i	0.512547	−	1.91285i	0.121137	−	0.992636i	$-0.461346\pi$
$83$	4.66953	−	17.4269i	0.512547	−	1.91285i	0.391411	−	0.920216i	$-0.371987\pi$
$84$	−3.47329	−	2.98936i	−0.378967	−	0.326166i
$85$	9.70430	−	0.141801i	1.05258	−	0.0153805i
$86$	1.62377	−	0.937485i	0.175096	−	0.101092i
$87$	−1.59999	−	0.0311222i	−0.171537	−	0.00333666i
$88$	1.62946	+	6.08124i	0.173701	+	0.648262i
$89$	6.67816	−	11.5669i	0.707884	−	1.22609i	−0.257757	−	0.966210i	$-0.582983\pi$
$89$	6.67816	−	11.5669i	0.707884	−	1.22609i	0.965641	−	0.259881i	$-0.0836833\pi$
$90$	−6.70623	−	0.162906i	−0.706898	−	0.0171718i
$91$	1.47560	+	15.6199i	0.154685	+	1.63741i
$92$	−1.13445	−	0.303976i	−0.118275	−	0.0316916i
$93$	2.86697	−	4.74993i	0.297290	−	0.492545i
$94$		−	5.84918i		−	0.603296i
$95$	3.41522	+	0.861828i	0.350395	+	0.0884217i
$96$	−0.415666	−	1.68143i	−0.0424237	−	0.171611i
$97$	0.0223723	−	0.0834947i	0.00227157	−	0.00847760i	−0.964781	−	0.263055i	$-0.915270\pi$
$97$	0.0223723	−	0.0834947i	0.00227157	−	0.00847760i	0.967052	+	0.254578i	$0.0819365\pi$
$98$	6.30259	−	3.04588i	0.636657	−	0.307681i
$99$	−0.734495	+	18.8730i	−0.0738195	+	1.89681i
$100$	−2.62545	−	4.25523i	−0.262545	−	0.425523i
$101$	9.81937	+	5.66922i	0.977064	+	0.564108i	0.901383	−	0.433024i	$-0.142553\pi$
$101$	9.81937	+	5.66922i	0.977064	+	0.564108i	0.0756817	+	0.997132i	$0.475887\pi$
$102$	−0.146203	+	7.51630i	−0.0144763	+	0.744225i
$103$	4.37483	+	1.17223i	0.431064	+	0.115503i	0.467826	−	0.883821i	$-0.345037\pi$
$103$	4.37483	+	1.17223i	0.431064	+	0.115503i	−0.0367614	+	0.999324i	$0.511704\pi$
$104$	−2.96503	+	5.13559i	−0.290745	+	0.503586i
$105$	4.31117	−	9.29590i	0.420728	−	0.907187i
$106$	3.06413	+	5.30724i	0.297615	+	0.515484i
$107$	0.274125	+	1.02305i	0.0265007	+	0.0989020i	0.977910	−	0.209029i	$-0.0670302\pi$
$107$	0.274125	+	1.02305i	0.0265007	+	0.0989020i	−0.951409	+	0.307931i	$0.900364\pi$
$108$	0.303009	−	5.18731i	0.0291570	−	0.499149i
$109$	−0.201442	+	0.116303i	−0.0192947	+	0.0111398i	−0.509616	−	0.860402i	$-0.670213\pi$
$109$	−0.201442	+	0.116303i	−0.0192947	+	0.0111398i	0.490322	+	0.871542i	$0.336879\pi$
$110$	−12.0876	+	7.21626i	−1.15250	+	0.688043i
$111$	−1.16177	+	4.02128i	−0.110271	+	0.381683i
$112$	2.60867	+	0.441381i	0.246497	+	0.0417065i
$113$	−14.7105	+	3.94167i	−1.38385	+	0.370801i	−0.872518	−	0.488583i	$-0.837514\pi$
$113$	−14.7105	+	3.94167i	−1.38385	+	0.370801i	−0.511331	+	0.859384i	$0.670847\pi$
$114$	−0.757268	+	2.62115i	−0.0709247	+	0.245494i
$115$	−0.0383704	−	2.62592i	−0.00357806	−	0.244868i
$116$	0.800147	−	0.461965i	0.0742918	−	0.0428924i
$117$	−13.0593	+	12.0809i	−1.20733	+	1.11688i
$118$	−5.88620	+	5.88620i	−0.541868	+	0.541868i
$119$	−10.4409	−	4.78097i	−0.957120	−	0.438271i
$120$	3.36343	−	1.92024i	0.307038	−	0.175293i
$121$	14.3183	+	24.8001i	1.30167	+	2.25455i
$122$	−8.74043	+	8.74043i	−0.791322	+	0.791322i
$123$	10.4106	−	5.74356i	0.938692	−	0.517879i
$124$			3.20319i			0.287655i
$125$	7.55168	−	8.24452i	0.675443	−	0.737413i
$126$	7.08268	+	3.58269i	0.630975	+	0.319171i
$127$	8.24335	+	8.24335i	0.731479	+	0.731479i	0.970913	−	0.239433i	$-0.0769617\pi$
$127$	8.24335	+	8.24335i	0.731479	+	0.731479i	−0.239433	+	0.970913i	$0.576962\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−2.34058	+	2.25127i	−0.206077	+	0.198213i
$130$	−12.8570	−	3.24445i	−1.12763	−	0.284557i
$131$	4.97306	−	2.87120i	0.434498	−	0.250858i	−0.266763	−	0.963762i	$-0.585954\pi$
$131$	4.97306	−	2.87120i	0.434498	−	0.250858i	0.701261	+	0.712904i	$0.252621\pi$
$132$	−5.26760	−	9.54789i	−0.458486	−	0.831038i
$133$	−3.21106	−	2.65673i	−0.278434	−	0.230368i
$134$	6.39112			0.552109
$135$	11.3438	−	2.51364i	0.976318	−	0.216339i
$136$	−2.17018	−	3.75886i	−0.186091	−	0.322320i
$137$	−1.05479	−	3.93655i	−0.0901172	−	0.336322i	0.906117	−	0.423028i	$-0.139033\pi$
$137$	−1.05479	−	3.93655i	−0.0901172	−	0.336322i	−0.996234	+	0.0867057i	$0.972366\pi$
$138$	2.03386	+	0.0395616i	0.173134	+	0.00336771i
$139$	−1.39830	−	0.807308i	−0.118602	−	0.0684750i	0.439525	−	0.898230i	$-0.355147\pi$
$139$	−1.39830	−	0.807308i	−0.118602	−	0.0684750i	−0.558127	+	0.829755i	$0.688480\pi$
$140$	0.642404	+	5.88110i	0.0542931	+	0.497044i
$141$	2.43130	+	9.83501i	0.204753	+	0.828257i
$142$	−6.70276	−	6.70276i	−0.562483	−	0.562483i
$143$	−9.66283	+	36.0622i	−0.808046	+	3.01567i
$144$	1.39783	+	2.65444i	0.116486	+	0.221204i
$145$	1.48205	+	1.43936i	0.123078	+	0.119533i
$146$	5.18432	−	2.99317i	0.429058	−	0.247717i
$147$	−9.33131	+	7.74122i	−0.769634	+	0.638485i
$148$	−0.625472	−	2.33429i	−0.0514135	−	0.191878i
$149$	−3.99291	−	6.91592i	−0.327112	−	0.566574i	0.654826	−	0.755780i	$-0.272742\pi$
$149$	−3.99291	−	6.91592i	−0.327112	−	0.566574i	−0.981937	+	0.189206i	$0.939409\pi$
$150$	6.18328	+	6.06358i	0.504863	+	0.495090i
$151$	2.67237	−	4.62868i	0.217474	−	0.376677i	−0.736561	−	0.676371i	$-0.763552\pi$
$151$	2.67237	−	4.62868i	0.217474	−	0.376677i	0.954035	+	0.299695i	$0.0968848\pi$
$152$	−0.407696	−	1.52154i	−0.0330685	−	0.123413i
$153$	−2.87844	−	12.6989i	−0.232708	−	1.02665i
$154$	16.5832	−	1.56660i	1.33631	−	0.126240i
$155$	−6.89068	+	1.95469i	−0.553473	+	0.157005i
$156$	2.85082	−	9.86762i	0.228248	−	0.790042i
$157$	16.0894	+	16.0894i	1.28407	+	1.28407i	0.938329	+	0.345744i	$0.112373\pi$
$157$	16.0894	+	16.0894i	1.28407	+	1.28407i	0.345744	+	0.938329i	$0.387627\pi$
$158$	9.41623	+	9.41623i	0.749115	+	0.749115i
$159$	−7.35818	−	7.65011i	−0.583541	−	0.606693i
$160$	−1.08962	+	1.95262i	−0.0861421	+	0.154368i
$161$	−1.29370	+	2.82525i	−0.101958	+	0.222661i
$162$	1.64670	+	8.84807i	0.129377	+	0.695170i
$163$	−4.16228	−	15.5338i	−0.326015	−	1.21670i	−0.913288	−	0.407314i	$-0.866465\pi$
$163$	−4.16228	−	15.5338i	−0.326015	−	1.21670i	0.587274	−	0.809389i	$-0.300201\pi$
$164$	−3.43231	+	5.94493i	−0.268018	+	0.464221i
$165$	17.3249	−	17.1580i	1.34874	−	1.33575i
$166$	−9.02083	−	15.6245i	−0.700152	−	1.21270i
$167$	−0.856206	−	3.19541i	−0.0662552	−	0.247268i	0.924853	−	0.380324i	$-0.124188\pi$
$167$	−0.856206	−	3.19541i	−0.0662552	−	0.247268i	−0.991108	+	0.133056i	$0.957521\pi$
$168$	−4.56978	+	0.342185i	−0.352566	+	0.0264002i
$169$	−19.1961	+	11.0828i	−1.47662	+	0.852527i
$170$	6.76171	−	6.96225i	0.518599	−	0.533980i
$171$	0.183772	−	4.72207i	0.0140534	−	0.361106i
$172$	0.485278	−	1.81108i	0.0370021	−	0.138094i
$173$	−4.11813	−	4.11813i	−0.313096	−	0.313096i	0.533012	−	0.846108i	$-0.321060\pi$
$173$	−4.11813	−	4.11813i	−0.313096	−	0.313096i	−0.846108	+	0.533012i	$0.821060\pi$
$174$	−1.15337	+	1.10936i	−0.0874369	+	0.0841002i
$175$	−12.2593	+	4.97077i	−0.926719	+	0.375755i
$176$	5.45229	+	3.14788i	0.410982	+	0.237281i
$177$	7.45056	−	12.3439i	0.560018	−	0.927828i
$178$	−3.45687	−	12.9012i	−0.259103	−	0.966987i
$179$	2.90382	+	5.02957i	0.217042	+	0.375927i	0.953902	−	0.300117i	$-0.0970259\pi$
$179$	2.90382	+	5.02957i	0.217042	+	0.375927i	−0.736860	+	0.676045i	$0.763693\pi$
$180$	−4.85721	+	4.62683i	−0.362035	+	0.344863i
$181$	5.33095			0.396247			0.198123	−	0.980177i	$-0.436515\pi$
$181$	5.33095			0.396247			0.198123	+	0.980177i	$0.436515\pi$
$182$	12.0884	+	10.0016i	0.896050	+	0.741365i
$183$	11.0634	−	18.3296i	0.817827	−	1.35496i
$184$	−1.01712	+	0.587236i	−0.0749832	+	0.0432916i
$185$	4.63982	−	2.76997i	0.341126	−	0.203652i
$186$	−1.33146	−	5.38596i	−0.0976273	−	0.394918i
$187$	−19.3223	−	19.3223i	−1.41299	−	1.41299i
$188$	−4.13599	−	4.13599i	−0.301648	−	0.301648i
$189$	−13.3983	−	3.08003i	−0.974580	−	0.224039i
$190$	3.02433	−	1.80552i	0.219408	−	0.130986i
$191$			1.31228i			0.0949531i	0.998872	+	0.0474766i	$0.0151179\pi$
$191$			1.31228i			0.0949531i	−0.998872	+	0.0474766i	$0.984882\pi$
$192$	−1.48287	−	0.895033i	−0.107017	−	0.0645935i
$193$	−0.459893	+	0.459893i	−0.0331038	+	0.0331038i	−0.723465	−	0.690361i	$-0.757452\pi$
$193$	−0.459893	+	0.459893i	−0.0331038	+	0.0331038i	0.690361	+	0.723465i	$0.257452\pi$
$194$	−0.0432200	−	0.0748593i	−0.00310302	−	0.00537458i
$195$	22.9668	+	0.111112i	1.64469	+	0.00795687i
$196$	2.30284	−	6.61037i	0.164488	−	0.472169i
$197$	4.43627	−	4.43627i	0.316071	−	0.316071i	−0.531185	−	0.847256i	$-0.678253\pi$
$197$	4.43627	−	4.43627i	0.316071	−	0.316071i	0.847256	+	0.531185i	$0.178253\pi$
$198$	12.8259	+	13.8646i	0.911494	+	0.985314i
$199$	7.75962	−	4.48002i	0.550065	−	0.317580i	−0.199083	−	0.979983i	$-0.563796\pi$
$199$	7.75962	−	4.48002i	0.550065	−	0.317580i	0.749148	+	0.662403i	$0.230463\pi$
$200$	−4.86538	−	1.15243i	−0.344034	−	0.0814891i
$201$	−10.7463	+	2.65657i	−0.757982	+	0.187380i
$202$	10.9521	−	2.93460i	0.770586	−	0.206478i
$203$	−0.851948	−	2.29123i	−0.0597950	−	0.160813i
$204$	5.21145	+	5.41821i	0.364874	+	0.379350i
$205$	−14.8832	−	3.75576i	−1.03949	−	0.262313i
$206$	3.92236	−	2.26458i	0.273284	−	0.157781i
$207$	−3.43625	+	0.778886i	−0.238836	+	0.0541363i
$208$	1.53481	+	5.72800i	0.106420	+	0.397166i
$209$	−4.95859	−	8.58853i	−0.342993	−	0.594081i
$210$	−3.52473	−	9.62166i	−0.243230	−	0.663957i
$211$	−1.30948	+	2.26808i	−0.0901481	+	0.156141i	−0.907573	−	0.419894i	$-0.862067\pi$
$211$	−1.30948	+	2.26808i	−0.0901481	+	0.156141i	0.817425	+	0.576035i	$0.195401\pi$
$212$	5.91945	+	1.58611i	0.406550	+	0.108935i
$213$	14.0564	+	8.48414i	0.963125	+	0.581323i
$214$	0.917241	+	0.529570i	0.0627013	+	0.0362006i
$215$	4.19211	−	0.0612560i	0.285900	−	0.00417762i
$216$	−3.45372	−	3.88224i	−0.234996	−	0.264153i
$217$	8.35609	+	1.41383i	0.567248	+	0.0959769i
$218$	−0.0602028	+	0.224680i	−0.00407745	+	0.0152172i
$219$	−7.47294	+	7.18777i	−0.504975	+	0.485704i
$220$	−3.44453	+	13.6499i	−0.232230	+	0.920273i
$221$		−	25.7386i		−	1.73137i
$222$	2.02198	+	3.66497i	0.135706	+	0.245977i
$223$	24.2382	+	6.49461i	1.62311	+	0.434911i	0.951913	−	0.306367i	$-0.0991136\pi$
$223$	24.2382	+	6.49461i	1.62311	+	0.434911i	0.671197	+	0.741279i	$0.265780\pi$
$224$	2.15671	−	1.53251i	0.144102	−	0.102395i
$225$	−12.9172	−	7.62534i	−0.861147	−	0.508356i
$226$	−7.61472	+	13.1891i	−0.506524	+	0.877325i
$227$	−6.47257	−	24.1560i	−0.429600	−	1.60329i	−0.753669	−	0.657255i	$-0.771718\pi$
$227$	−6.47257	−	24.1560i	−0.429600	−	1.60329i	0.324069	−	0.946033i	$-0.394949\pi$
$228$	1.31797	+	2.38891i	0.0872844	+	0.158209i
$229$	−7.93914	+	4.58366i	−0.524633	+	0.302897i	−0.738828	−	0.673894i	$-0.764621\pi$
$229$	−7.93914	+	4.58366i	−0.524633	+	0.302897i	0.214195	+	0.976791i	$0.431287\pi$
$230$	−1.88394	−	1.82967i	−0.124223	−	0.120645i
$231$	−27.2324	+	9.52720i	−1.79176	+	0.626844i
$232$	0.239131	−	0.892448i	0.0156997	−	0.0585921i
$233$	20.4978	−	5.49236i	1.34285	−	0.359817i	0.485362	−	0.874314i	$-0.338688\pi$
$233$	20.4978	−	5.49236i	1.34285	−	0.359817i	0.857492	+	0.514497i	$0.172021\pi$
$234$	−0.691830	+	17.7767i	−0.0452264	+	1.16210i
$235$	6.37339	−	11.4212i	0.415754	−	0.745038i
$236$			8.32434i			0.541868i
$237$	−19.7468	−	11.9188i	−1.28269	−	0.774207i
$238$	−10.7635	+	4.00220i	−0.697695	+	0.259424i
$239$	−2.96499	+	5.13552i	−0.191789	+	0.332189i	−0.945843	−	0.324624i	$-0.894762\pi$
$239$	−2.96499	+	5.13552i	−0.191789	+	0.332189i	0.754054	+	0.656813i	$0.228096\pi$
$240$	1.02049	−	3.73612i	0.0658723	−	0.241166i
$241$	11.3514	−	19.6612i	0.731209	−	1.26649i	−0.225158	−	0.974322i	$-0.572290\pi$
$241$	11.3514	−	19.6612i	0.731209	−	1.26649i	0.956367	−	0.292168i	$-0.0943767\pi$
$242$	27.6609	+	7.41171i	1.77811	+	0.476443i
$243$	−6.44666	−	14.1930i	−0.413554	−	0.910480i
$244$			12.3608i			0.791322i
$245$	15.6254	+	0.919978i	0.998271	+	0.0587753i
$246$	3.30010	−	11.4227i	0.210406	−	0.728286i
$247$	2.41766	−	9.02284i	0.153832	−	0.574109i
$248$	2.26500	+	2.26500i	0.143828	+	0.143828i
$249$	21.6625	+	22.5220i	1.37281	+	1.42727i
$250$	−0.489916	−	11.1696i	−0.0309850	−	0.706428i
$251$			7.87318i			0.496951i	0.968638	+	0.248475i	$0.0799295\pi$
$251$			7.87318i			0.496951i	−0.968638	+	0.248475i	$0.920070\pi$
$252$	7.54155	−	2.47487i	0.475073	−	0.155902i
$253$	−5.22849	+	5.22849i	−0.328712	+	0.328712i
$254$	11.6579			0.731479
$255$	−8.47540	+	14.5172i	−0.530750	+	0.909101i
$256$	1.00000			0.0625000
$257$	13.4437	+	3.60224i	0.838597	+	0.224701i	0.652461	−	0.757823i	$-0.273737\pi$
$257$	13.4437	+	3.60224i	0.838597	+	0.224701i	0.186136	+	0.982524i	$0.440403\pi$
$258$	−0.0631577	+	3.24693i	−0.00393202	+	0.202145i
$259$	−6.36548	+	0.601341i	−0.395532	+	0.0373655i
$260$	−11.3854	+	6.79709i	−0.706094	+	0.421538i
$261$	1.47820	−	2.34473i	0.0914981	−	0.145135i
$262$	1.48624	−	5.54673i	0.0918203	−	0.342678i
$263$	5.22702	−	1.40058i	0.322312	−	0.0863633i	−0.0940353	−	0.995569i	$-0.529977\pi$
$263$	5.22702	−	1.40058i	0.322312	−	0.0863633i	0.416347	+	0.909206i	$0.363310\pi$
$264$	−10.4761	−	3.02662i	−0.644762	−	0.186276i
$265$	0.200213	+	13.7018i	0.0122990	+	0.841692i
$266$	−4.14915	+	0.391967i	−0.254401	+	0.0240330i
$267$	11.1751	+	20.2557i	0.683905	+	1.23963i
$268$	4.51921	−	4.51921i	0.276055	−	0.276055i
$269$	−14.0186	−	24.2810i	−0.854732	−	1.48044i	−0.876894	−	0.480684i	$-0.840388\pi$
$269$	−14.0186	−	24.2810i	−0.854732	−	1.48044i	0.0221622	−	0.999754i	$-0.492945\pi$
$270$	6.24386	−	9.79868i	0.379989	−	0.596329i
$271$	−4.39946	+	7.62008i	−0.267248	+	0.462887i	−0.968150	−	0.250370i	$-0.919448\pi$
$271$	−4.39946	+	7.62008i	−0.267248	+	0.462887i	0.700902	+	0.713257i	$0.252781\pi$
$272$	−4.19247	−	1.12337i	−0.254206	−	0.0681142i
$273$	−24.4831	−	11.7922i	−1.48179	−	0.713698i
$274$	−3.52941	−	2.03771i	−0.213220	−	0.123102i
$275$	−31.4654	+	0.919753i	−1.89743	+	0.0554632i
$276$	1.46613	−	1.41018i	0.0882507	−	0.0848830i
$277$	−13.0496	+	3.49664i	−0.784076	+	0.210092i	−0.628581	−	0.777744i	$-0.716364\pi$
$277$	−13.0496	+	3.49664i	−0.784076	+	0.210092i	−0.155495	+	0.987837i	$0.549697\pi$
$278$	−1.55960	+	0.417893i	−0.0935386	+	0.0250636i
$279$	4.47752	+	8.50270i	0.268062	+	0.509043i
$280$	4.61281	+	3.70432i	0.275668	+	0.221375i
$281$	−14.4482	+	8.34169i	−0.861909	+	0.497623i	−0.864651	−	0.502373i	$-0.832460\pi$
$281$	−14.4482	+	8.34169i	−0.861909	+	0.497623i	0.00274228	+	0.999996i	$0.499127\pi$
$282$	8.67359	+	5.23521i	0.516505	+	0.311752i
$283$	9.71304	−	9.71304i	0.577380	−	0.577380i	−0.356800	−	0.934181i	$-0.616132\pi$
$283$	9.71304	−	9.71304i	0.577380	−	0.577380i	0.934181	+	0.356800i	$0.116132\pi$
$284$	−9.47913			−0.562483
$285$	−4.33472	+	4.29298i	−0.256767	+	0.254294i
$286$	18.6671	+	32.3325i	1.10381	+	1.91186i
$287$	13.9934	+	11.5778i	0.826007	+	0.683413i
$288$	2.86539	+	0.888559i	0.168845	+	0.0523589i
$289$	1.59238	+	0.919360i	0.0936693	+	0.0540800i
$290$	2.06575	−	0.0301852i	0.121305	−	0.00177253i
$291$	0.103788	+	0.107906i	0.00608417	+	0.00632555i
$292$	1.54938	−	5.78236i	0.0906706	−	0.338387i
$293$	−5.43138	+	1.45533i	−0.317305	+	0.0850215i	−0.413956	−	0.910297i	$-0.635853\pi$
$293$	−5.43138	+	1.45533i	−0.317305	+	0.0850215i	0.0966517	+	0.995318i	$0.469187\pi$
$294$	−1.12436	+	12.0721i	−0.0655742	+	0.704060i
$295$	−17.9072	+	5.07978i	−1.04260	+	0.295756i
$296$	−2.09287	−	1.20832i	−0.121646	−	0.0702321i
$297$	−27.3289	−	17.9811i	−1.58578	−	1.04337i
$298$	−7.71371	−	2.06688i	−0.446843	−	0.119731i
$299$	−6.96469			−0.402779
$300$	8.65984	−	0.0846377i	0.499976	−	0.00488656i
$301$	−4.51033	−	2.06531i	−0.259971	−	0.119042i
$302$	−1.38332	−	5.16262i	−0.0796011	−	0.297075i
$303$	−17.1954	+	9.48676i	−0.987850	+	0.545000i
$304$	−1.36418	−	0.787607i	−0.0782409	−	0.0451724i
$305$	−26.5905	+	7.54299i	−1.52257	+	0.431910i
$306$	−11.0149	−	6.94414i	−0.629678	−	0.396970i
$307$	4.71179	+	4.71179i	0.268916	+	0.268916i	0.828663	−	0.559747i	$-0.189102\pi$
$307$	4.71179	+	4.71179i	0.268916	+	0.268916i	−0.559747	+	0.828663i	$0.689102\pi$
$308$	10.6183	−	12.8338i	0.605036	−	0.731276i
$309$	−5.65389	+	5.43813i	−0.321638	+	0.309364i
$310$	−3.49027	+	6.25462i	−0.198234	+	0.355239i
$311$			21.0289i			1.19244i	0.802821	+	0.596220i	$0.203331\pi$
$311$			21.0289i			1.19244i	−0.802821	+	0.596220i	$0.796669\pi$
$312$	−4.96163	−	8.99329i	−0.280897	−	0.509145i
$313$	0.287266	−	0.287266i	0.0162372	−	0.0162372i	−0.698942	−	0.715179i	$-0.746345\pi$
$313$	0.287266	−	0.287266i	0.0162372	−	0.0162372i	0.715179	+	0.698942i	$0.246345\pi$
$314$	22.7538			1.28407
$315$	9.92601	+	14.7131i	0.559267	+	0.828988i
$316$	13.3166			0.749115
$317$	−6.57722	+	6.57722i	−0.369413	+	0.369413i	−0.867263	−	0.497850i	$-0.834123\pi$
$317$	−6.57722	+	6.57722i	−0.369413	+	0.369413i	0.497850	+	0.867263i	$0.334123\pi$
$318$	−10.6125	−	0.206428i	−0.595117	−	0.0115759i
$319$		−	5.81685i		−	0.325681i
$320$	0.610232	+	2.15119i	0.0341130	+	0.120255i
$321$	−1.76241	−	0.509170i	−0.0983679	−	0.0284191i
$322$	1.08297	+	2.91254i	0.0603515	+	0.162309i
$323$	4.83449	+	4.83449i	0.268998	+	0.268998i
$324$	7.42092	+	5.09214i	0.412274	+	0.282897i
$325$	−21.5696	−	20.3444i	−1.19647	−	1.12851i
$326$	−13.9272	−	8.04090i	−0.771359	−	0.445344i
$327$	0.00783523	−	0.402809i	0.000433289	−	0.0222754i
$328$	1.77669	+	6.63071i	0.0981015	+	0.366120i
$329$	−12.6150	+	8.96391i	−0.695488	+	0.494196i
$330$	0.117964	−	24.3831i	0.00649369	−	1.34225i
$331$	26.0974			1.43444			0.717222	−	0.696845i	$-0.245414\pi$
$331$	26.0974			1.43444			0.717222	+	0.696845i	$0.245414\pi$
$332$	−17.4269	−	4.66953i	−0.956426	−	0.256274i
$333$	−4.92322	−	5.32194i	−0.269791	−	0.291641i
$334$	−2.86492	−	1.65406i	−0.156762	−	0.0905063i
$335$	12.4794	+	6.96390i	0.681824	+	0.380479i
$336$	−2.98936	+	3.47329i	−0.163083	+	0.189483i
$337$	−24.5748	+	6.58481i	−1.33868	+	0.358697i	−0.855943	−	0.517070i	$-0.827023\pi$
$337$	−24.5748	+	6.58481i	−1.33868	+	0.358697i	−0.482733	+	0.875767i	$0.660356\pi$
$338$	−5.73690	+	21.4104i	−0.312046	+	1.16457i
$339$	7.32140	−	25.3418i	0.397644	−	1.37638i
$340$	−0.141801	−	9.70430i	−0.00769025	−	0.526290i
$341$	17.4647	+	10.0833i	0.945769	+	0.546040i
$342$	−3.20906	−	3.46895i	−0.173526	−	0.187580i
$343$	−16.2279	−	8.92504i	−0.876222	−	0.481907i
$344$	−0.937485	−	1.62377i	−0.0505458	−	0.0875479i
$345$	3.92825	+	2.29339i	0.211490	+	0.123472i
$346$	−5.82392			−0.313096
$347$	23.7875	−	23.7875i	1.27698	−	1.27698i	0.334630	−	0.942350i	$-0.391389\pi$
$347$	23.7875	−	23.7875i	1.27698	−	1.27698i	0.942350	−	0.334630i	$-0.108611\pi$
$348$	−0.0311222	+	1.59999i	−0.00166833	+	0.0857686i
$349$	16.9808	−	9.80384i	0.908959	−	0.524788i	0.0288628	−	0.999583i	$-0.490811\pi$
$349$	16.9808	−	9.80384i	0.908959	−	0.524788i	0.880096	+	0.474796i	$0.157478\pi$
$350$	−5.15380	+	12.1835i	−0.275482	+	0.651237i
$351$	−6.22592	−	30.1780i	−0.332315	−	1.61078i
$352$	6.08124	−	1.62946i	0.324131	−	0.0868507i
$353$	18.4779	−	4.95115i	0.983481	−	0.263523i	0.268971	−	0.963148i	$-0.413316\pi$
$353$	18.4779	−	4.95115i	0.983481	−	0.263523i	0.714510	+	0.699625i	$0.246650\pi$
$354$	−3.46015	−	13.9968i	−0.183905	−	0.743923i
$355$	−5.78447	−	20.3914i	−0.307008	−	1.08226i
$356$	−11.5669	−	6.67816i	−0.613045	−	0.353942i
$357$	16.4346	−	11.2035i	0.869810	−	0.592951i
$358$	5.60975	+	1.50313i	0.296485	+	0.0794428i
$359$	−6.21763	+	10.7692i	−0.328154	+	0.568379i	−0.982146	−	0.188123i	$-0.939760\pi$
$359$	−6.21763	+	10.7692i	−0.328154	+	0.568379i	0.653992	+	0.756502i	$0.273093\pi$
$360$	−0.162906	+	6.70623i	−0.00858589	+	0.353449i
$361$	−8.25935	−	14.3056i	−0.434703	−	0.752927i
$362$	3.76955	−	3.76955i	0.198123	−	0.198123i
$363$	−49.5907	−	0.964614i	−2.60284	−	0.0506291i
$364$	15.6199	−	1.47560i	0.818707	−	0.0773425i
$365$	13.3844	−	0.195576i	0.700574	−	0.0102369i
$366$	−5.13798	−	20.7839i	−0.268567	−	1.08639i
$367$	1.69703	−	0.454718i	0.0885843	−	0.0237361i	−0.214255	−	0.976778i	$-0.568732\pi$
$367$	1.69703	−	0.454718i	0.0885843	−	0.0237361i	0.302839	+	0.953042i	$0.402066\pi$
$368$	−0.303976	+	1.13445i	−0.0158458	+	0.0591374i
$369$	−0.800860	+	20.5783i	−0.0416911	+	1.07126i
$370$	1.32219	−	5.23951i	0.0687372	−	0.272389i
$371$	6.75038	−	14.7418i	0.350462	−	0.765358i
$372$	−4.74993	−	2.86697i	−0.246273	−	0.148645i
$373$	−12.2071	−	3.27088i	−0.632060	−	0.169360i	−0.0714555	−	0.997444i	$-0.522764\pi$
$373$	−12.2071	−	3.27088i	−0.632060	−	0.169360i	−0.560604	+	0.828084i	$0.689431\pi$
$374$	−27.3259			−1.41299
$375$	5.46659	+	18.5773i	0.282293	+	0.959328i
$376$	−5.84918			−0.301648
$377$	3.87422	−	3.87422i	0.199532	−	0.199532i
$378$	−11.6519	+	7.29609i	−0.599310	+	0.375271i
$379$		−	23.9709i		−	1.23130i	−0.788019	−	0.615651i	$-0.788893\pi$
$379$		−	23.9709i		−	1.23130i	0.788019	−	0.615651i	$-0.211107\pi$
$380$	0.861828	−	3.41522i	0.0442109	−	0.175197i
$381$	−19.6019	+	4.84578i	−1.00424	+	0.248257i
$382$	0.927921	+	0.927921i	0.0474766	+	0.0474766i
$383$	−3.93430	+	14.6830i	−0.201033	+	0.750266i	0.789589	+	0.613636i	$0.210294\pi$
$383$	−3.93430	+	14.6830i	−0.201033	+	0.750266i	−0.990622	+	0.136630i	$0.956373\pi$
$384$	−1.68143	+	0.415666i	−0.0858053	+	0.0212119i
$385$	34.0877	+	15.0104i	1.73727	+	0.765002i
$386$			0.650387i			0.0331038i
$387$	−1.24344	−	5.48575i	−0.0632078	−	0.278856i
$388$	−0.0834947	−	0.0223723i	−0.00423880	−	0.00113578i
$389$	4.46656	−	7.73631i	0.226464	−	0.392247i	−0.730294	−	0.683133i	$-0.760617\pi$
$389$	4.46656	−	7.73631i	0.226464	−	0.392247i	0.956758	+	0.290887i	$0.0939502\pi$
$390$	16.3185	−	16.1614i	0.826321	−	0.818364i
$391$	2.54881	−	4.41468i	0.128899	−	0.223260i
$392$	−3.04588	−	6.30259i	−0.153840	−	0.318329i
$393$	−0.193430	+	9.94424i	−0.00975728	+	0.501621i
$394$		−	6.27383i		−	0.316071i
$395$	8.12620	+	28.6465i	0.408873	+	1.44136i
$396$	18.8730	+	0.734495i	0.948404	+	0.0369097i
$397$	6.91625	−	1.85320i	0.347116	−	0.0930096i	−0.0810486	−	0.996710i	$-0.525827\pi$
$397$	6.91625	−	1.85320i	0.347116	−	0.0930096i	0.428165	+	0.903701i	$0.359160\pi$
$398$	2.31903	−	8.65473i	0.116242	−	0.433822i
$399$	6.81360	−	2.38373i	0.341107	−	0.119336i
$400$	−4.25523	+	2.62545i	−0.212762	+	0.131273i
$401$	−5.47738	+	3.16237i	−0.273527	+	0.157921i	−0.630489	−	0.776198i	$-0.717146\pi$
$401$	−5.47738	+	3.16237i	−0.273527	+	0.157921i	0.356962	+	0.934119i	$0.383812\pi$
$402$	−5.72027	+	9.47723i	−0.285301	+	0.472681i
$403$	4.91631	+	18.3479i	0.244899	+	0.913975i
$404$	5.66922	−	9.81937i	0.282054	−	0.488532i
$405$	−6.42567	+	19.0712i	−0.319294	+	0.947656i
$406$	−2.22256	−	1.01772i	−0.110304	−	0.0505088i
$407$	−14.6962	−	3.93782i	−0.728461	−	0.195191i
$408$	7.51630	+	0.146203i	0.372112	+	0.00723814i
$409$		−	6.13817i		−	0.303513i	−0.988418	−	0.151757i	$-0.951507\pi$
$409$		−	6.13817i		−	0.303513i	0.988418	−	0.151757i	$-0.0484930\pi$
$410$	−13.1797	+	7.86828i	−0.650900	+	0.388587i
$411$	6.78148	+	1.95921i	0.334506	+	0.0966409i
$412$	1.17223	−	4.37483i	0.0577517	−	0.215532i
$413$	21.7155	+	3.67420i	1.06855	+	0.180796i
$414$	−1.87904	+	2.98055i	−0.0923496	+	0.146486i
$415$	−0.589428	−	40.3381i	−0.0289339	−	1.98012i
$416$	5.13559	+	2.96503i	0.251793	+	0.145373i
$417$	2.44866	−	1.35093i	0.119911	−	0.0661555i
$418$	−9.57926	−	2.56675i	−0.468537	−	0.125544i
$419$	−15.9180	+	27.5708i	−0.777645	+	1.34692i	0.155651	+	0.987812i	$0.450252\pi$
$419$	−15.9180	+	27.5708i	−0.777645	+	1.34692i	−0.933296	+	0.359108i	$0.883081\pi$
$420$	−9.29590	−	4.31117i	−0.453594	−	0.210364i
$421$	4.03625	+	6.99099i	0.196715	+	0.340720i	0.947461	−	0.319870i	$-0.103639\pi$
$421$	4.03625	+	6.99099i	0.196715	+	0.340720i	−0.750747	+	0.660590i	$0.770306\pi$
$422$	0.677835	+	2.52971i	0.0329965	+	0.123145i
$423$	−16.7602	−	5.19734i	−0.814908	−	0.252703i
$424$	5.30724	−	3.06413i	0.257742	−	0.148807i
$425$	20.7893	−	6.22692i	1.00843	−	0.302050i
$426$	15.9385	−	3.94015i	0.772224	−	0.190901i
$427$	32.2454	+	5.45583i	1.56046	+	0.264026i
$428$	1.02305	−	0.274125i	0.0494510	−	0.0132503i
$429$	−44.8271	−	46.6056i	−2.16427	−	2.25014i
$430$	2.92096	−	3.00759i	0.140861	−	0.145039i
$431$	21.0923	−	12.1776i	1.01598	−	0.586576i	0.103042	−	0.994677i	$-0.467142\pi$
$431$	21.0923	−	12.1776i	1.01598	−	0.586576i	0.912937	+	0.408101i	$0.133809\pi$
$432$	−5.18731	−	0.303009i	−0.249575	−	0.0145785i
$433$	18.6284	−	18.6284i	0.895224	−	0.895224i	−0.0997846	−	0.995009i	$-0.531815\pi$
$433$	18.6284	−	18.6284i	0.895224	−	0.895224i	0.995009	+	0.0997846i	$0.0318154\pi$
$434$	6.90838	−	4.90892i	0.331613	−	0.235636i
$435$	−3.46088	+	0.909417i	−0.165936	+	0.0436032i
$436$	0.116303	+	0.201442i	0.00556989	+	0.00964734i
$437$	1.30818	−	1.30818i	0.0625787	−	0.0625787i
$438$	−0.201648	+	10.3667i	−0.00963510	+	0.495339i
$439$		−	13.1054i		−	0.625485i	−0.949838	−	0.312743i	$-0.898752\pi$
$439$		−	13.1054i		−	0.625485i	0.949838	−	0.312743i	$-0.101248\pi$
$440$	7.21626	+	12.0876i	0.344021	+	0.576251i
$441$	−3.12742	−	20.7658i	−0.148925	−	0.988849i
$442$	−18.2000	−	18.2000i	−0.865683	−	0.865683i
$443$	1.88960	+	1.88960i	0.0897778	+	0.0897778i	0.750569	−	0.660792i	$-0.229779\pi$
$443$	1.88960	+	1.88960i	0.0897778	+	0.0897778i	−0.660792	+	0.750569i	$0.729779\pi$
$444$	4.02128	+	1.16177i	0.190841	+	0.0551353i
$445$	7.30749	−	28.9579i	0.346408	−	1.37273i
$446$	21.7314	−	12.5466i	1.02901	−	0.594100i
$447$	13.8292	+	0.268999i	0.654100	+	0.0127232i
$448$	0.441381	−	2.60867i	0.0208533	−	0.123248i
$449$	15.7386			0.742749			0.371374	−	0.928483i	$-0.378887\pi$
$449$	15.7386			0.742749			0.371374	+	0.928483i	$0.378887\pi$
$450$	−14.5258	+	3.74191i	−0.684751	+	0.176396i
$451$	21.6090	+	37.4279i	1.01753	+	1.76241i
$452$	3.94167	+	14.7105i	0.185401	+	0.691924i
$453$	4.47189	+	8.10561i	0.210108	+	0.380835i
$454$	−21.6577	−	12.5041i	−1.01644	−	0.586844i
$455$	12.7061	+	32.7010i	0.595671	+	1.53305i
$456$	2.62115	+	0.757268i	0.122747	+	0.0354623i
$457$	6.59771	+	6.59771i	0.308628	+	0.308628i	0.844377	−	0.535749i	$-0.179971\pi$
$457$	6.59771	+	6.59771i	0.308628	+	0.308628i	−0.535749	+	0.844377i	$0.679971\pi$
$458$	−2.37268	+	8.85496i	−0.110868	+	0.413765i
$459$	21.4072	+	7.09761i	0.999204	+	0.331288i
$460$	−2.62592	+	0.0383704i	−0.122434	+	0.00178903i
$461$	−23.1959	+	13.3922i	−1.08034	+	0.623735i	−0.930988	−	0.365049i	$-0.881052\pi$
$461$	−23.1959	+	13.3922i	−1.08034	+	0.623735i	−0.149352	+	0.988784i	$0.547719\pi$
$462$	−12.5194	+	25.9929i	−0.582457	+	1.20930i
$463$	10.7337	+	40.0588i	0.498838	+	1.86169i	0.507376	+	0.861725i	$0.330616\pi$
$463$	10.7337	+	40.0588i	0.498838	+	1.86169i	−0.00853803	+	0.999964i	$0.502718\pi$
$464$	−0.461965	−	0.800147i	−0.0214462	−	0.0371459i
$465$	3.26882	−	11.9675i	0.151588	−	0.554981i
$466$	10.6104	−	18.3778i	0.491519	−	0.851335i
$467$	6.33527	+	23.6435i	0.293161	+	1.09409i	0.942667	+	0.333736i	$0.108309\pi$
$467$	6.33527	+	23.6435i	0.293161	+	1.09409i	−0.649505	+	0.760357i	$0.725024\pi$
$468$	12.0809	+	13.0593i	0.558438	+	0.603664i
$469$	−9.79445	−	13.7838i	−0.452266	−	0.636478i
$470$	−3.56936	−	12.5827i	−0.164642	−	0.580396i
$471$	−38.2591	+	9.45799i	−1.76288	+	0.435801i
$472$	5.88620	+	5.88620i	0.270934	+	0.270934i
$473$	−8.34695	−	8.34695i	−0.383793	−	0.383793i
$474$	−22.3909	+	5.53524i	−1.02845	+	0.254242i
$475$	7.87271	−	0.230124i	0.361225	−	0.0105588i
$476$	−4.78097	+	10.4409i	−0.219136	+	0.478560i
$477$	17.9300	−	4.06415i	0.820957	−	0.186084i
$478$	1.53479	+	5.72792i	0.0701998	+	0.261989i
$479$	−1.67282	+	2.89742i	−0.0764333	+	0.132386i	−0.901709	−	0.432344i	$-0.857687\pi$
$479$	−1.67282	+	2.89742i	−0.0764333	+	0.132386i	0.825275	+	0.564731i	$0.191020\pi$
$480$	−1.92024	−	3.36343i	−0.0876467	−	0.153519i
$481$	−7.16541	−	12.4109i	−0.326715	−	0.565886i
$482$	−5.87592	−	21.9292i	−0.267641	−	0.998850i
$483$	−3.03158	−	4.44708i	−0.137942	−	0.202349i
$484$	24.8001	−	14.3183i	1.12728	−	0.650833i
$485$	−0.00282403	−	0.193265i	−0.000128233	−	0.00877572i
$486$	−14.5944	−	5.47747i	−0.662017	−	0.248463i
$487$	−3.59947	+	13.4334i	−0.163108	+	0.608726i	0.835166	+	0.549998i	$0.185371\pi$
$487$	−3.59947	+	13.4334i	−0.163108	+	0.608726i	−0.998274	+	0.0587288i	$0.981295\pi$
$488$	8.74043	+	8.74043i	0.395661	+	0.395661i
$489$	26.7601	+	7.73116i	1.21013	+	0.349615i
$490$	11.6994	−	10.3983i	0.528523	−	0.469748i
$491$	−31.2490	−	18.0416i	−1.41025	−	0.814207i	−0.414836	−	0.909896i	$-0.636161\pi$
$491$	−31.2490	−	18.0416i	−1.41025	−	0.814207i	−0.995411	+	0.0956893i	$0.969494\pi$
$492$	−5.74356	−	10.4106i	−0.258940	−	0.469346i
$493$	1.03791	+	3.87355i	0.0467453	+	0.174456i
$494$	−4.67056	−	8.08965i	−0.210139	−	0.363971i
$495$	9.93688	+	41.0476i	0.446630	+	1.84495i
$496$	3.20319			0.143828
$497$	−4.18390	+	24.7280i	−0.187674	+	1.10920i
$498$	31.2432	+	0.607727i	1.40004	+	0.0272329i
$499$	30.9349	−	17.8603i	1.38484	−	0.799535i	0.392109	−	0.919919i	$-0.371746\pi$
$499$	30.9349	−	17.8603i	1.38484	−	0.799535i	0.992727	+	0.120383i	$0.0384124\pi$
$500$	−8.24452	−	7.55168i	−0.368706	−	0.337721i
$501$	5.50472	+	1.59035i	0.245933	+	0.0710515i
$502$	5.56718	+	5.56718i	0.248475	+	0.248475i
$503$	−18.8085	−	18.8085i	−0.838628	−	0.838628i	0.150050	−	0.988678i	$-0.452056\pi$
$503$	−18.8085	−	18.8085i	−0.838628	−	0.838628i	−0.988678	+	0.150050i	$0.952056\pi$
$504$	3.58269	−	7.08268i	0.159586	−	0.315488i
$505$	24.5829	+	6.20346i	1.09392	+	0.276050i
$506$			7.39420i			0.328712i
$507$	0.746643	−	38.3848i	0.0331596	−	1.70473i
$508$	8.24335	−	8.24335i	0.365740	−	0.365740i
$509$	−13.8762	−	24.0343i	−0.615052	−	1.06530i	−0.990375	−	0.138408i	$-0.955802\pi$
$509$	−13.8762	−	24.0343i	−0.615052	−	1.06530i	0.375323	−	0.926894i	$-0.377532\pi$
$510$	4.27218	+	16.2582i	0.189175	+	0.719925i
$511$	−14.4004	−	6.59405i	−0.637038	−	0.291704i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.83775	+	4.49892i	0.301894	+	0.198632i
$514$	12.0533	−	6.95899i	0.531649	−	0.306948i
$515$	10.1264	−	0.147969i	0.446223	−	0.00652030i
$516$	2.25127	+	2.34058i	0.0991065	+	0.103039i
$517$	−35.5702	+	9.53102i	−1.56438	+	0.419174i
$518$	−4.07586	+	4.92629i	−0.179083	+	0.216449i
$519$	9.79254	−	2.42081i	0.429845	−	0.106262i
$520$	−3.24445	+	12.8570i	−0.142278	+	0.563816i
$521$	31.4799	−	18.1749i	1.37916	−	0.796257i	0.387100	−	0.922038i	$-0.373477\pi$
$521$	31.4799	−	18.1749i	1.37916	−	0.796257i	0.992058	+	0.125780i	$0.0401434\pi$
$522$	−0.612732	−	2.70322i	−0.0268186	−	0.118317i
$523$	−7.62423	−	28.4540i	−0.333384	−	1.24421i	−0.905610	−	0.424111i	$-0.860587\pi$
$523$	−7.62423	−	28.4540i	−0.333384	−	1.24421i	0.572226	−	0.820096i	$-0.306080\pi$
$524$	−2.87120	−	4.97306i	−0.125429	−	0.217249i
$525$	3.60149	−	22.6281i	0.157182	−	0.987570i
$526$	2.70571	−	4.68642i	0.117974	−	0.204338i
$527$	−13.4293	−	3.59836i	−0.584989	−	0.156747i
$528$	−9.54789	+	5.26760i	−0.415519	+	0.229243i
$529$	18.7240	+	10.8103i	0.814087	+	0.470013i
$530$	9.83018	+	9.54704i	0.426996	+	0.414697i
$531$	11.6360	+	22.0965i	0.504960	+	0.958906i
$532$	−2.65673	+	3.21106i	−0.115184	+	0.139217i
$533$	−10.5359	+	39.3206i	−0.456361	+	1.70316i
$534$	22.2249	+	6.42092i	0.961765	+	0.277860i
$535$	1.21399	+	2.03349i	0.0524855	+	0.0879156i
$536$		−	6.39112i		−	0.276055i
$537$	−10.0572	−	0.195628i	−0.434002	−	0.00844198i
$538$	−27.0819	−	7.25658i	−1.16759	−	0.312853i
$539$	−28.7926	−	33.3644i	−1.24018	−	1.43711i
$540$	−2.51364	−	11.3438i	−0.108170	−	0.488159i
$541$	2.92530	−	5.06677i	0.125769	−	0.217838i	−0.796265	−	0.604949i	$-0.793194\pi$
$541$	2.92530	−	5.06677i	0.125769	−	0.217838i	0.922033	+	0.387111i	$0.126527\pi$
$542$	2.27733	+	8.49910i	0.0978196	+	0.365068i
$543$	−4.77138	+	7.90513i	−0.204760	+	0.339242i
$544$	−3.75886	+	2.17018i	−0.161160	+	0.0930457i
$545$	−0.362369	+	0.373116i	−0.0155222	+	0.0159825i
$546$	−25.6505	+	8.97380i	−1.09774	+	0.384043i
$547$	−8.92718	+	33.3167i	−0.381699	+	1.42452i	0.461607	+	0.887085i	$0.347273\pi$
$547$	−8.92718	+	33.3167i	−0.381699	+	1.42452i	−0.843306	+	0.537434i	$0.819394\pi$
$548$	−3.93655	+	1.05479i	−0.168161	+	0.0450586i
$549$	17.2784	+	32.8112i	0.737422	+	1.40035i
$550$	−21.5990	+	22.8997i	−0.920985	+	0.976448i
$551$			1.45539i			0.0620017i
$552$	0.0395616	−	2.03386i	0.00168385	−	0.0865668i
$553$	5.87767	−	34.7386i	0.249944	−	1.47723i
$554$	−6.75498	+	11.7000i	−0.286992	+	0.497084i
$555$	−0.0452805	+	9.35949i	−0.00192205	+	0.397288i
$556$	−0.807308	+	1.39830i	−0.0342375	+	0.0593011i
$557$	−34.9990	−	9.37795i	−1.48295	−	0.397356i	−0.575603	−	0.817729i	$-0.695233\pi$
$557$	−34.9990	−	9.37795i	−1.48295	−	0.397356i	−0.907351	+	0.420373i	$0.861899\pi$
$558$	9.17840	+	2.84623i	0.388553	+	0.120490i
$559$		−	11.1187i		−	0.470271i
$560$	5.88110	−	0.642404i	0.248522	−	0.0271465i
$561$	45.9467	−	11.3584i	1.93987	−	0.479554i
$562$	−4.31797	+	16.1149i	−0.182143	+	0.679766i
$563$	−10.7610	−	10.7610i	−0.453523	−	0.453523i	0.442999	−	0.896522i	$-0.353914\pi$
$563$	−10.7610	−	10.7610i	−0.453523	−	0.453523i	−0.896522	+	0.442999i	$0.853914\pi$
$564$	9.83501	−	2.43130i	0.414128	−	0.102376i
$565$	−29.2398	+	17.4561i	−1.23013	+	0.734384i
$566$		−	13.7363i		−	0.577380i
$567$	16.5592	−	17.1112i	0.695420	−	0.718603i
$568$	−6.70276	+	6.70276i	−0.281241	+	0.281241i
$569$	−13.4096			−0.562160			−0.281080	−	0.959684i	$-0.590693\pi$
$569$	−13.4096			−0.562160			−0.281080	+	0.959684i	$0.590693\pi$
$570$	−0.0295148	+	6.10071i	−0.00123624	+	0.255531i
$571$	12.1254			0.507434			0.253717	−	0.967278i	$-0.418347\pi$
$571$	12.1254			0.507434			0.253717	+	0.967278i	$0.418347\pi$
$572$	36.0622	+	9.66283i	1.50783	+	0.404023i
$573$	−1.94594	−	1.17453i	−0.0812929	−	0.0490668i
$574$	18.0816	−	1.70815i	0.754710	−	0.0712968i
$575$	−1.68496	−	5.62543i	−0.0702678	−	0.234597i
$576$	2.65444	−	1.39783i	0.110602	−	0.0582429i
$577$	−12.1223	+	45.2410i	−0.504657	+	1.88341i	−0.0373702	+	0.999301i	$0.511898\pi$
$577$	−12.1223	+	45.2410i	−0.504657	+	1.88341i	−0.467287	+	0.884106i	$0.654769\pi$
$578$	1.77607	−	0.475896i	0.0738746	−	0.0197946i
$579$	−0.270344	−	1.09358i	−0.0112351	−	0.0454478i
$580$	1.43936	−	1.48205i	0.0597663	−	0.0615388i
$581$	−19.8732	+	43.4001i	−0.824478	+	1.80054i
$582$	0.149690	+	0.00291170i	0.00620486	+	0.000120694i
$583$	27.2817	−	27.2817i	1.12989	−	1.12989i
$584$	−2.99317	−	5.18432i	−0.123858	−	0.214529i
$585$	−20.7208	+	33.9574i	−0.856700	+	1.40397i
$586$	−2.81149	+	4.86964i	−0.116142	+	0.201163i
$587$	6.30235	+	1.68871i	0.260126	+	0.0697005i	0.386525	−	0.922279i	$-0.373675\pi$
$587$	6.30235	+	1.68871i	0.260126	+	0.0697005i	−0.126399	+	0.991979i	$0.540342\pi$
$588$	7.74122	+	9.33131i	0.319243	+	0.384817i
$589$	−4.36972	−	2.52286i	−0.180051	−	0.103953i
$590$	−9.07038	+	16.2543i	−0.373421	+	0.669178i
$591$	2.60782	+	10.5490i	0.107271	+	0.433929i
$592$	−2.33429	+	0.625472i	−0.0959388	+	0.0257067i
$593$	7.98493	−	2.13956i	0.327902	−	0.0878610i	−0.0911127	−	0.995841i	$-0.529042\pi$
$593$	7.98493	−	2.13956i	0.327902	−	0.0878610i	0.419014	+	0.907980i	$0.362376\pi$
$594$	−32.0390	+	6.60986i	−1.31458	+	0.271206i
$595$	−25.3780	−	3.91338i	−1.04039	−	0.160433i
$596$	−6.91592	+	3.99291i	−0.283287	+	0.163556i
$597$	−0.301815	+	15.5163i	−0.0123525	+	0.635040i
$598$	−4.92478	+	4.92478i	−0.201389	+	0.201389i
$599$	−5.64607			−0.230692			−0.115346	−	0.993325i	$-0.536798\pi$
$599$	−5.64607			−0.230692			−0.115346	+	0.993325i	$0.536798\pi$
$600$	6.06358	−	6.18328i	0.247545	−	0.252431i
$601$	6.35844	+	11.0131i	0.259366	+	0.449236i	0.966072	−	0.258272i	$-0.0831530\pi$
$601$	6.35844	+	11.0131i	0.259366	+	0.449236i	−0.706706	+	0.707507i	$0.749820\pi$
$602$	−4.64968	+	1.72889i	−0.189507	+	0.0704644i
$603$	5.67889	−	18.3131i	0.231262	−	0.745766i
$604$	−4.62868	−	2.67237i	−0.188338	−	0.108737i
$605$	45.9352	+	44.6121i	1.86753	+	1.81374i
$606$	−5.45084	+	18.8671i	−0.221425	+	0.766425i
$607$	−4.28953	+	16.0087i	−0.174106	+	0.649774i	0.822596	+	0.568627i	$0.192525\pi$
$607$	−4.28953	+	16.0087i	−0.174106	+	0.649774i	−0.996702	+	0.0811474i	$0.974142\pi$
$608$	−1.52154	+	0.407696i	−0.0617066	+	0.0165342i
$609$	4.16012	+	0.787393i	0.168577	+	0.0319068i
$610$	−13.4686	+	24.1360i	−0.545329	+	0.977239i
$611$	−30.0390	−	17.3430i	−1.21525	−	0.701623i
$612$	−12.6989	+	2.87844i	−0.513324	+	0.116354i
$613$	−28.2077	−	7.55823i	−1.13930	−	0.305274i	−0.360629	−	0.932709i	$-0.617438\pi$
$613$	−28.2077	−	7.55823i	−1.13930	−	0.305274i	−0.778669	+	0.627435i	$0.784105\pi$
$614$	6.66347			0.268916
$615$	18.8903	−	18.7084i	0.761729	−	0.754394i
$616$	−1.56660	−	16.5832i	−0.0631201	−	0.668156i
$617$	4.87605	+	18.1977i	0.196302	+	0.732610i	0.991926	+	0.126819i	$0.0404767\pi$
$617$	4.87605	+	18.1977i	0.196302	+	0.732610i	−0.795624	+	0.605791i	$0.792857\pi$
$618$	−0.152563	+	7.84324i	−0.00613697	+	0.315501i
$619$	3.20771	+	1.85197i	0.128929	+	0.0744370i	0.563077	−	0.826404i	$-0.309617\pi$
$619$	3.20771	+	1.85197i	0.128929	+	0.0744370i	−0.434148	+	0.900841i	$0.642951\pi$
$620$	1.95469	+	6.89068i	0.0785024	+	0.276736i
$621$	1.92056	−	5.79265i	0.0770696	−	0.232451i
$622$	14.8697	+	14.8697i	0.596220	+	0.596220i
$623$	−22.5266	+	27.2267i	−0.902508	+	1.09082i
$624$	−9.86762	−	2.85082i	−0.395021	−	0.114124i
$625$	11.2140	−	22.3438i	0.448561	−	0.893752i
$626$		−	0.406255i		−	0.0162372i
$627$	17.1738	+	0.334056i	0.685856	+	0.0133409i
$628$	16.0894	−	16.0894i	0.642036	−	0.642036i
$629$	10.4891			0.418227
$630$	17.4225	+	3.38497i	0.694127	+	0.134860i
$631$	−21.5905			−0.859502			−0.429751	−	0.902947i	$-0.641399\pi$
$631$	−21.5905			−0.859502			−0.429751	+	0.902947i	$0.641399\pi$
$632$	9.41623	−	9.41623i	0.374558	−	0.374558i
$633$	−2.19125	−	3.97180i	−0.0870944	−	0.157865i
$634$			9.30159i			0.369413i
$635$	22.7634	+	12.7027i	0.903337	+	0.504090i
$636$	−7.65011	+	7.35818i	−0.303347	+	0.291771i
$637$	3.04497	−	41.3986i	0.120646	−	1.64027i
$638$	−4.11313	−	4.11313i	−0.162840	−	0.162840i
$639$	−25.1618	+	13.2502i	−0.995386	+	0.524170i
$640$	1.95262	+	1.08962i	0.0771841	+	0.0430711i
$641$	1.34965	+	0.779223i	0.0533081	+	0.0307774i	0.526417	−	0.850226i	$-0.323535\pi$
$641$	1.34965	+	0.779223i	0.0533081	+	0.0307774i	−0.473109	+	0.881004i	$0.656868\pi$
$642$	−1.60625	+	0.886171i	−0.0633935	+	0.0349744i
$643$	−2.26734	−	8.46183i	−0.0894152	−	0.333702i	0.906698	−	0.421780i	$-0.138594\pi$
$643$	−2.26734	−	8.46183i	−0.0894152	−	0.333702i	−0.996114	+	0.0880774i	$0.971928\pi$
$644$	2.82525	+	1.29370i	0.111330	+	0.0509789i
$645$	−3.66125	+	6.27120i	−0.144161	+	0.246928i
$646$	6.83700			0.268998
$647$	14.0566	+	3.76645i	0.552621	+	0.148074i	0.524314	−	0.851525i	$-0.324322\pi$
$647$	14.0566	+	3.76645i	0.552621	+	0.148074i	0.0283070	+	0.999599i	$0.490988\pi$
$648$	8.84807	−	1.64670i	0.347585	−	0.0646885i
$649$	45.3867	+	26.2040i	1.78158	+	1.02860i
$650$	−29.6377	+	0.866328i	−1.16249	+	0.0339802i
$651$	−9.57551	+	11.1256i	−0.375294	+	0.436047i
$652$	−15.5338	+	4.16228i	−0.608351	+	0.163007i
$653$	−7.43262	+	27.7389i	−0.290861	+	1.08551i	0.653588	+	0.756850i	$0.273263\pi$
$653$	−7.43262	+	27.7389i	−0.290861	+	1.08551i	−0.944449	+	0.328657i	$0.893404\pi$
$654$	−0.279288	−	0.290369i	−0.0109210	−	0.0113543i
$655$	8.94590	−	9.21122i	0.349545	−	0.359912i
$656$	5.94493	+	3.43231i	0.232111	+	0.134009i
$657$	−3.97002	−	17.5147i	−0.154885	−	0.683314i
$658$	−2.58171	+	15.2586i	−0.100646	+	0.594842i
$659$	−9.41467	−	16.3067i	−0.366743	−	0.635218i	0.622311	−	0.782770i	$-0.286194\pi$
$659$	−9.41467	−	16.3067i	−0.366743	−	0.635218i	−0.989054	+	0.147552i	$0.952861\pi$
$660$	−17.1580	−	17.3249i	−0.667876	−	0.674370i
$661$	7.26978			0.282762			0.141381	−	0.989955i	$-0.454846\pi$
$661$	7.26978			0.282762			0.141381	+	0.989955i	$0.454846\pi$
$662$	18.4537	−	18.4537i	0.717222	−	0.717222i
$663$	38.1671	+	23.0369i	1.48229	+	0.894680i
$664$	−15.6245	+	9.02083i	−0.606350	+	0.350076i
$665$	−8.52882	−	3.75564i	−0.330733	−	0.145638i
$666$	−7.24443	−	0.281937i	−0.280716	−	0.0109248i
$667$	1.04816	−	0.280852i	0.0405847	−	0.0108746i
$668$	−3.19541	+	0.856206i	−0.123634	+	0.0331276i
$669$	−31.3247	+	30.1293i	−1.21108	+	1.16487i
$670$	13.7485	−	3.90007i	0.531152	−	0.150673i
$671$	67.3949	+	38.9105i	2.60175	+	1.50212i
$672$	0.342185	+	4.56978i	0.0132001	+	0.176283i
$673$	−23.9868	−	6.42725i	−0.924624	−	0.247752i	−0.235063	−	0.971980i	$-0.575530\pi$
$673$	−23.9868	−	6.42725i	−0.924624	−	0.247752i	−0.689561	+	0.724228i	$0.742196\pi$
$674$	−12.7209	+	22.0332i	−0.489990	+	0.848687i
$675$	22.8687	−	12.3297i	0.880218	−	0.474569i
$676$	11.0828	+	19.1961i	0.426263	+	0.738310i
$677$	12.5245	−	12.5245i	0.481355	−	0.481355i	−0.424209	−	0.905564i	$-0.639448\pi$
$677$	12.5245	−	12.5245i	0.481355	−	0.481355i	0.905564	+	0.424209i	$0.139448\pi$
$678$	−12.7423	−	23.0963i	−0.489366	−	0.887010i
$679$	−0.0952151	+	0.207936i	−0.00365402	+	0.00797984i
$680$	−6.96225	−	6.76171i	−0.266990	−	0.259300i
$681$	41.6134	+	12.0224i	1.59463	+	0.460699i
$682$	19.4794	−	5.21949i	0.745905	−	0.199865i
$683$	−5.22405	+	19.4964i	−0.199893	+	0.746010i	0.791053	+	0.611748i	$0.209533\pi$
$683$	−5.22405	+	19.4964i	−0.199893	+	0.746010i	−0.990946	+	0.134262i	$0.957134\pi$
$684$	−4.72207	−	0.183772i	−0.180553	−	0.00702671i
$685$	−4.67127	−	7.82459i	−0.178480	−	0.298962i
$686$	−17.7858	+	5.16388i	−0.679065	+	0.197158i
$687$	0.308798	−	15.8753i	0.0117814	−	0.605680i
$688$	−1.81108	−	0.485278i	−0.0690469	−	0.0185010i
$689$	36.3410			1.38448
$690$	4.39936	−	1.15602i	0.167481	−	0.0440090i
$691$	−34.9314			−1.32885			−0.664427	−	0.747353i	$-0.731324\pi$
$691$	−34.9314			−1.32885			−0.664427	+	0.747353i	$0.731324\pi$
$692$	−4.11813	+	4.11813i	−0.156548	+	0.156548i
$693$	10.2462	−	48.9093i	0.389222	−	1.85791i
$694$		−	33.6406i		−	1.27698i
$695$	−3.50065	−	0.883386i	−0.132787	−	0.0335087i
$696$	1.10936	+	1.15337i	0.0420501	+	0.0437185i
$697$	−21.0682	−	21.0682i	−0.798014	−	0.798014i
$698$	5.07484	−	18.9396i	0.192086	−	0.716873i
$699$	−10.2017	+	35.3115i	−0.385864	+	1.33560i
$700$	4.97077	+	12.2593i	0.187877	+	0.463360i
$701$		−	26.6507i		−	1.00658i	−0.864117	−	0.503292i	$-0.832122\pi$
$701$		−	26.6507i		−	1.00658i	0.864117	−	0.503292i	$-0.167878\pi$
$702$	−25.7415	−	16.9367i	−0.971549	−	0.639234i
$703$	3.67701	+	0.985252i	0.138681	+	0.0371595i
$704$	3.14788	−	5.45229i	0.118640	−	0.205491i
$705$	11.2318	+	19.6733i	0.423015	+	0.740939i
$706$	9.56488	−	16.5669i	0.359979	−	0.623502i
$707$	−23.1133	−	19.1232i	−0.869264	−	0.719203i
$708$	−12.3439	−	7.45056i	−0.463914	−	0.280009i
$709$			51.6335i			1.93914i	0.244817	+	0.969569i	$0.421272\pi$
$709$			51.6335i			1.93914i	−0.244817	+	0.969569i	$0.578728\pi$
$710$	−18.5091	−	10.3287i	−0.694635	−	0.387628i
$711$	35.3481	−	18.6143i	1.32566	−	0.698091i
$712$	−12.9012	+	3.45687i	−0.483494	+	0.129552i
$713$	−0.973693	+	3.63387i	−0.0364651	+	0.136090i
$714$	3.69895	−	19.5431i	0.138430	−	0.731380i
$715$	1.21973	+	83.4731i	0.0456152	+	3.12172i
$716$	5.02957	−	2.90382i	0.187964	−	0.108521i
$717$	−4.96156	−	8.99317i	−0.185293	−	0.335856i
$718$	3.21848	+	12.0115i	0.120113	+	0.448266i
$719$	6.06041	−	10.4969i	0.226015	−	0.391469i	−0.730608	−	0.682797i	$-0.760763\pi$
$719$	6.06041	−	10.4969i	0.226015	−	0.391469i	0.956623	+	0.291327i	$0.0940968\pi$
$720$	4.62683	+	4.85721i	0.172432	+	0.181018i
$721$	−10.8951	−	4.98893i	−0.405755	−	0.185798i
$722$	−15.9558	−	4.27535i	−0.593815	−	0.159112i
$723$	18.9952	+	34.4302i	0.706440	+	1.28047i
$724$		−	5.33095i		−	0.198123i
$725$	4.06652	+	2.19195i	0.151027	+	0.0814068i
$726$	−35.7480	+	34.3839i	−1.32673	+	1.27610i
$727$	7.76423	−	28.9765i	0.287959	−	1.07468i	−0.658690	−	0.752414i	$-0.728889\pi$
$727$	7.76423	−	28.9765i	0.287959	−	1.07468i	0.946649	−	0.322265i	$-0.104444\pi$
$728$	10.0016	−	12.0884i	0.370682	−	0.448025i
$729$	26.8164	+	3.14360i	0.993199	+	0.116430i
$730$	9.32593	−	9.60252i	0.345168	−	0.355405i
$731$	7.04775	+	4.06902i	0.260671	+	0.150498i
$732$	−18.3296	−	11.0634i	−0.677480	−	0.408914i
$733$	−4.19382	−	1.12373i	−0.154902	−	0.0415059i	0.180535	−	0.983569i	$-0.442217\pi$
$733$	−4.19382	−	1.12373i	−0.154902	−	0.0415059i	−0.335437	+	0.942063i	$0.608884\pi$
$734$	0.878448	−	1.52152i	0.0324241	−	0.0561602i
$735$	−15.3495	+	22.3471i	−0.566174	+	0.824286i
$736$	0.587236	+	1.01712i	0.0216458	+	0.0374916i
$737$	−10.4141	−	38.8660i	−0.383608	−	1.43165i
$738$	13.9847	+	15.1173i	0.514786	+	0.556477i
$739$	−18.6590	+	10.7728i	−0.686382	+	0.396283i	−0.802255	−	0.596981i	$-0.796367\pi$
$739$	−18.6590	+	10.7728i	−0.686382	+	0.396283i	0.115873	+	0.993264i	$0.463033\pi$
$740$	−2.76997	−	4.63982i	−0.101826	−	0.170563i
$741$	11.2158	+	11.6608i	0.412024	+	0.428371i
$742$	−5.65082	−	15.1973i	−0.207448	−	0.557910i
$743$	15.9296	−	4.26833i	0.584401	−	0.156590i	0.0455079	−	0.998964i	$-0.485509\pi$
$743$	15.9296	−	4.26833i	0.584401	−	0.156590i	0.538893	+	0.842374i	$0.318843\pi$
$744$	−5.38596	+	1.33146i	−0.197459	+	0.0488137i
$745$	−12.8098	−	12.4409i	−0.469315	−	0.455798i
$746$	−10.9446	+	6.31886i	−0.400710	+	0.231350i
$747$	−52.7860	+	11.9649i	−1.93134	+	0.437772i
$748$	−19.3223	+	19.3223i	−0.706494	+	0.706494i
$749$	−0.263550	−	2.78980i	−0.00962989	−	0.101937i
$750$	17.0016	+	9.27068i	0.620811	+	0.338517i
$751$	−8.13144	−	14.0841i	−0.296721	−	0.513935i	0.678663	−	0.734450i	$-0.262560\pi$
$751$	−8.13144	−	14.0841i	−0.296721	−	0.513935i	−0.975384	+	0.220515i	$0.929226\pi$
$752$	−4.13599	+	4.13599i	−0.150824	+	0.150824i
$753$	−11.6749	−	7.04676i	−0.425458	−	0.256798i
$754$		−	5.47897i		−	0.199532i
$755$	2.92420	−	11.5879i	0.106423	−	0.421728i
$756$	−3.08003	+	13.3983i	−0.112020	+	0.487290i
$757$	17.7496	+	17.7496i	0.645121	+	0.645121i	0.951810	−	0.306689i	$-0.0992212\pi$
$757$	17.7496	+	17.7496i	0.645121	+	0.645121i	−0.306689	+	0.951810i	$0.599221\pi$
$758$	−16.9500	−	16.9500i	−0.615651	−	0.615651i
$759$	−3.07352	−	12.4329i	−0.111562	−	0.451284i
$760$	−1.80552	−	3.02433i	−0.0654932	−	0.109704i
$761$	31.2162	−	18.0227i	1.13159	−	0.653321i	0.187252	−	0.982312i	$-0.440042\pi$
$761$	31.2162	−	18.0227i	1.13159	−	0.653321i	0.944333	+	0.328991i	$0.106709\pi$
$762$	−10.4342	+	17.2871i	−0.377990	+	0.626247i
$763$	0.576831	−	0.214483i	0.0208827	−	0.00776482i
$764$	1.31228			0.0474766
$765$	−13.9414	−	25.5613i	−0.504051	−	0.924171i
$766$	7.60048	+	13.1644i	0.274616	+	0.475650i
$767$	12.7763	+	47.6818i	0.461326	+	1.72169i
$768$	−0.895033	+	1.48287i	−0.0322967	+	0.0535086i
$769$	−8.44111	−	4.87348i	−0.304394	−	0.175742i	0.340021	−	0.940418i	$-0.389566\pi$
$769$	−8.44111	−	4.87348i	−0.304394	−	0.175742i	−0.644415	+	0.764676i	$0.722899\pi$
$770$	34.7176	−	13.4897i	1.25114	−	0.486133i
$771$	−17.3742	+	16.7112i	−0.625718	+	0.601840i
$772$	0.459893	+	0.459893i	0.0165519	+	0.0165519i
$773$	−5.02024	+	18.7358i	−0.180566	+	0.673880i	0.814971	+	0.579502i	$0.196753\pi$
$773$	−5.02024	+	18.7358i	−0.180566	+	0.673880i	−0.995536	+	0.0943779i	$0.969914\pi$
$774$	−4.75826	−	2.99976i	−0.171032	−	0.107824i
$775$	−13.6303	+	8.40983i	−0.489616	+	0.302090i
$776$	−0.0748593	+	0.0432200i	−0.00268729	+	0.00155151i
$777$	4.80560	−	9.97742i	0.172400	−	0.357938i
$778$	−2.31206	−	8.62873i	−0.0828915	−	0.309355i
$779$	−5.40662	−	9.36455i	−0.193712	−	0.335520i
$780$	0.111112	−	22.9668i	0.00397843	−	0.822343i
$781$	−29.8392	+	51.6830i	−1.06773	+	1.84936i
$782$	−1.31936	−	4.92393i	−0.0471803	−	0.176079i
$783$	2.15391	+	4.29059i	0.0769743	+	0.153333i
$784$	−6.61037	−	2.30284i	−0.236085	−	0.0822442i
$785$	44.4296	+	24.7931i	1.58576	+	0.884902i
$786$	6.89487	+	7.16842i	0.245932	+	0.255689i
$787$	4.70519	+	4.70519i	0.167722	+	0.167722i	0.785977	−	0.618255i	$-0.212160\pi$
$787$	4.70519	+	4.70519i	0.167722	+	0.167722i	−0.618255	+	0.785977i	$0.712160\pi$
$788$	−4.43627	−	4.43627i	−0.158036	−	0.158036i
$789$	−2.60148	+	9.00458i	−0.0926152	+	0.320572i
$790$	26.0022	+	14.5100i	0.925116	+	0.516243i
$791$	40.1147	−	3.78960i	1.42632	−	0.134743i
$792$	13.8646	−	12.8259i	0.492657	−	0.455747i
$793$	18.9716	+	70.8029i	0.673701	+	2.51429i
$794$	3.58011	−	6.20094i	0.127053	−	0.220063i
$795$	−20.4972	−	11.9666i	−0.726960	−	0.424413i
$796$	−4.48002	−	7.75962i	−0.158790	−	0.275032i
$797$	−6.80768	−	25.4066i	−0.241140	−	0.899948i	−0.975284	−	0.220954i	$-0.929083\pi$
$797$	−6.80768	−	25.4066i	−0.241140	−	0.899948i	0.734144	−	0.678994i	$-0.237584\pi$
$798$	3.13239	−	6.50349i	0.110886	−	0.230221i
$799$	21.9862	−	12.6938i	0.777817	−	0.449073i
$800$	−1.15243	+	4.86538i	−0.0407445	+	0.172017i
$801$	−40.0387	−	1.55821i	−1.41470	−	0.0550568i
$802$	−1.63696	+	6.10922i	−0.0578031	+	0.215724i
$803$	−26.6499	−	26.6499i	−0.940453	−	0.940453i
$804$	2.65657	+	10.7463i	0.0936901	+	0.378991i
$805$	−1.05893	+	6.86710i	−0.0373225	+	0.242034i
$806$	16.4503	+	9.49758i	0.579437	+	0.334538i
$807$	48.5528	+	0.944425i	1.70914	+	0.0332453i
$808$	−2.93460	−	10.9521i	−0.103239	−	0.385293i
$809$	21.7494	+	37.6710i	0.764667	+	1.32444i	0.940422	+	0.340009i	$0.110430\pi$
$809$	21.7494	+	37.6710i	0.764667	+	1.32444i	−0.175755	+	0.984434i	$0.556237\pi$
$810$	8.94174	+	18.0290i	0.314181	+	0.633475i
$811$	−0.175349			−0.00615732			−0.00307866	−	0.999995i	$-0.500980\pi$
$811$	−0.175349			−0.00615732			−0.00307866	+	0.999995i	$0.500980\pi$
$812$	−2.29123	+	0.851948i	−0.0804063	+	0.0298975i
$813$	−7.36196	−	13.3441i	−0.258195	−	0.467997i
$814$	−13.1762	+	7.60729i	−0.461826	+	0.266635i
$815$	−18.4331	−	30.8762i	−0.645683	−	1.08155i
$816$	5.41821	−	5.21145i	0.189675	−	0.182437i
$817$	2.08843	+	2.08843i	0.0730648	+	0.0730648i
$818$	−4.34034	−	4.34034i	−0.151757	−	0.151757i
$819$	39.3996	−	25.7509i	1.37673	−	0.899810i
$820$	−3.75576	+	14.8832i	−0.131157	+	0.519743i
$821$		−	9.65918i		−	0.337108i	−0.985692	−	0.168554i	$-0.946090\pi$
$821$		−	9.65918i		−	0.337108i	0.985692	−	0.168554i	$-0.0539097\pi$
$822$	6.18061	−	3.40986i	0.215573	−	0.118932i
$823$	−0.382332	+	0.382332i	−0.0133273	+	0.0133273i	−0.713739	−	0.700412i	$-0.753000\pi$
$823$	−0.382332	+	0.382332i	−0.0133273	+	0.0133273i	0.700412	+	0.713739i	$0.253000\pi$
$824$	−2.26458	−	3.92236i	−0.0788903	−	0.136642i
$825$	26.7987	−	47.4824i	0.933010	−	1.65313i
$826$	17.9532	−	12.7571i	0.624672	−	0.443877i
$827$	10.0375	−	10.0375i	0.349039	−	0.349039i	−0.510713	−	0.859751i	$-0.670618\pi$
$827$	10.0375	−	10.0375i	0.349039	−	0.349039i	0.859751	+	0.510713i	$0.170618\pi$
$828$	0.778886	+	3.43625i	0.0270682	+	0.119418i
$829$	10.9598	−	6.32766i	0.380651	−	0.219769i	−0.297451	−	0.954737i	$-0.596136\pi$
$829$	10.9598	−	6.32766i	0.380651	−	0.219769i	0.678101	+	0.734968i	$0.262803\pi$
$830$	−28.9401	−	28.1065i	−1.00453	−	0.975592i
$831$	6.49478	−	22.4805i	0.225301	−	0.779842i
$832$	5.72800	−	1.53481i	0.198583	−	0.0532101i
$833$	25.1268	+	17.0804i	0.870592	+	0.591802i
$834$	0.776210	−	2.68672i	0.0268780	−	0.0930334i
$835$	−3.79180	−	6.35144i	−0.131221	−	0.219801i
$836$	−8.58853	+	4.95859i	−0.297041	+	0.171496i
$837$	−16.6160	−	0.970596i	−0.574332	−	0.0335487i
$838$	8.23976	+	30.7512i	0.284638	+	1.06228i
$839$	−27.0536	−	46.8582i	−0.933994	−	1.61772i	−0.776419	−	0.630217i	$-0.782966\pi$
$839$	−27.0536	−	46.8582i	−0.933994	−	1.61772i	−0.157575	−	0.987507i	$-0.550368\pi$
$840$	−9.62166	+	3.52473i	−0.331979	+	0.121615i
$841$	14.0732	−	24.3755i	0.485282	−	0.840533i
$842$	7.79743	+	2.08932i	0.268717	+	0.0720026i
$843$	0.561973	−	28.8910i	0.0193554	−	0.995058i
$844$	2.26808	+	1.30948i	0.0780705	+	0.0450740i
$845$	−34.5312	+	35.5554i	−1.18791	+	1.22314i
$846$	−15.5263	+	8.17616i	−0.533805	+	0.281102i
$847$	−26.4056	−	71.0151i	−0.907306	−	2.44011i
$848$	1.58611	−	5.91945i	0.0544673	−	0.203275i
$849$	5.70972	+	23.0967i	0.195957	+	0.792677i
$850$	10.2971	−	19.1033i	0.353189	−	0.655239i
$851$		−	2.83827i		−	0.0972947i
$852$	8.48414	−	14.0564i	0.290662	−	0.481563i
$853$	−35.9135	−	9.62299i	−1.22965	−	0.329485i	−0.415210	−	0.909726i	$-0.636292\pi$
$853$	−35.9135	−	9.62299i	−1.22965	−	0.329485i	−0.814445	+	0.580241i	$0.802958\pi$
$854$	26.6588	−	18.9431i	0.912246	−	0.648219i
$855$	−2.48623	−	10.2702i	−0.0850273	−	0.351234i
$856$	0.529570	−	0.917241i	0.0181003	−	0.0313507i
$857$	−7.95381	−	29.6840i	−0.271697	−	1.01399i	−0.958023	−	0.286693i	$-0.907444\pi$
$857$	−7.95381	−	29.6840i	−0.271697	−	1.01399i	0.686326	−	0.727294i	$-0.259222\pi$
$858$	−64.6527	−	1.25759i	−2.20721	−	0.0429335i
$859$	32.1032	−	18.5348i	1.09535	−	0.632398i	0.160351	−	0.987060i	$-0.448737\pi$
$859$	32.1032	−	18.5348i	1.09535	−	0.632398i	0.934995	+	0.354662i	$0.115404\pi$
$860$	−0.0612560	−	4.19211i	−0.00208881	−	0.142950i
$861$	−29.6930	+	10.3880i	−1.01193	+	0.354023i
$862$	6.30361	−	23.5254i	0.214702	−	0.801278i
$863$	−0.104015	+	0.0278709i	−0.00354073	+	0.000948735i	−0.260589	−	0.965450i	$-0.583917\pi$
$863$	−0.104015	+	0.0278709i	−0.00354073	+	0.000948735i	0.257048	+	0.966399i	$0.417250\pi$
$864$	−3.88224	+	3.45372i	−0.132077	+	0.117498i
$865$	−11.3719	−	6.34587i	−0.386656	−	0.215766i
$866$		−	26.3446i		−	0.895224i
$867$	−2.78853	+	1.53844i	−0.0947033	+	0.0522481i
$868$	1.41383	−	8.35609i	0.0479884	−	0.283624i
$869$	41.9190	−	72.6058i	1.42200	−	2.46298i
$870$	−1.80416	+	3.09027i	−0.0611666	+	0.104770i
$871$	18.9499	−	32.8222i	0.642093	−	1.11214i
$872$	0.224680	+	0.0602028i	0.00760862	+	0.00203872i
$873$	−0.252905	+	0.0573253i	−0.00855953	+	0.00194017i
$874$		−	1.85004i		−	0.0625787i
$875$	−23.3388	+	18.1741i	−0.788997	+	0.614397i
$876$	7.18777	+	7.47294i	0.242852	+	0.252487i
$877$	−10.0958	+	37.6779i	−0.340910	+	1.27229i	0.556408	+	0.830909i	$0.312179\pi$
$877$	−10.0958	+	37.6779i	−0.340910	+	1.27229i	−0.897318	+	0.441384i	$0.854488\pi$
$878$	−9.26690	−	9.26690i	−0.312743	−	0.312743i
$879$	2.70319	−	9.35662i	0.0911763	−	0.315591i
$880$	13.6499	+	3.44453i	0.460136	+	0.116115i
$881$			36.5900i			1.23275i	0.787454	+	0.616374i	$0.211399\pi$
$881$			36.5900i			1.23275i	−0.787454	+	0.616374i	$0.788601\pi$
$882$	−16.8951	−	12.4722i	−0.568887	−	0.419962i
$883$	11.2799	−	11.2799i	0.379597	−	0.379597i	−0.491360	−	0.870957i	$-0.663500\pi$
$883$	11.2799	−	11.2799i	0.379597	−	0.379597i	0.870957	+	0.491360i	$0.163500\pi$
$884$	−25.7386			−0.865683
$885$	8.49489	−	31.1007i	0.285553	−	1.04544i
$886$	2.67230			0.0897778
$887$	3.90720	+	1.04693i	0.131191	+	0.0351525i	0.323817	−	0.946120i	$-0.395034\pi$
$887$	3.90720	+	1.04693i	0.131191	+	0.0351525i	−0.192626	+	0.981272i	$0.561700\pi$
$888$	3.66497	−	2.02198i	0.122988	−	0.0678531i
$889$	−17.8658	−	25.1427i	−0.599199	−	0.843259i
$890$	−15.3091	−	25.6435i	−0.513163	−	0.859571i
$891$	51.1240	−	24.4316i	1.71272	−	0.818489i
$892$	6.49461	−	24.2382i	0.217456	−	0.811555i
$893$	8.89976	−	2.38468i	0.297819	−	0.0798004i
$894$	9.96895	−	9.58853i	0.333412	−	0.320688i
$895$	9.31588	+	9.04755i	0.311395	+	0.302426i
$896$	−1.53251	−	2.15671i	−0.0511975	−	0.0720508i
$897$	6.23363	−	10.3278i	0.208135	−	0.344834i
$898$	11.1288	−	11.1288i	0.371374	−	0.371374i
$899$	−1.47976	−	2.56303i	−0.0493529	−	0.0854817i
$900$	−7.62534	+	12.9172i	−0.254178	+	0.430574i
$901$	−13.2994	+	23.0353i	−0.443069	+	0.767417i
$902$	41.7454	+	11.1856i	1.38997	+	0.372441i
$903$	7.09949	−	4.83973i	0.236256	−	0.161056i
$904$	13.1891	+	7.61472i	0.438662	+	0.253262i
$905$	11.4679	−	3.25312i	0.381206	−	0.108137i
$906$	8.89363	+	2.56943i	0.295471	+	0.0853635i
$907$	−52.5659	+	14.0850i	−1.74542	+	0.467685i	−0.983640	−	0.180147i	$-0.942343\pi$
$907$	−52.5659	+	14.0850i	−1.74542	+	0.467685i	−0.761783	+	0.647832i	$0.775676\pi$
$908$	−24.1560	+	6.47257i	−0.801644	+	0.214800i
$909$	1.32280	−	33.9896i	0.0438744	−	1.12736i
$910$	32.1076	+	14.1385i	1.06436	+	0.468688i
$911$	−22.5707	+	13.0312i	−0.747800	+	0.431743i	−0.824899	−	0.565281i	$-0.808768\pi$
$911$	−22.5707	+	13.0312i	−0.747800	+	0.431743i	0.0770981	+	0.997024i	$0.475435\pi$
$912$	2.38891	−	1.31797i	0.0791046	−	0.0436422i
$913$	−80.3175	+	80.3175i	−2.65812	+	2.65812i
$914$	9.33057			0.308628
$915$	12.6141	−	46.1816i	0.417009	−	1.52672i
$916$	4.58366	+	7.93914i	0.151449	+	0.262317i
$917$	−14.2404	+	5.29501i	−0.470259	+	0.174857i
$918$	20.1560	−	10.1184i	0.665246	−	0.333958i
$919$	25.4695	+	14.7048i	0.840160	+	0.485067i	0.857319	−	0.514786i	$-0.172129\pi$
$919$	25.4695	+	14.7048i	0.840160	+	0.485067i	−0.0171585	+	0.999853i	$0.505462\pi$
$920$	−1.82967	+	1.88394i	−0.0603225	+	0.0621115i
$921$	−11.2042	+	2.76978i	−0.369191	+	0.0912674i
$922$	−6.93229	+	25.8717i	−0.228303	+	0.852038i
$923$	−54.2965	+	14.5487i	−1.78719	+	0.478876i
$924$	9.52720	+	27.2324i	0.313422	+	0.895879i
$925$	8.29081	−	8.79010i	0.272600	−	0.289017i
$926$	35.9157	+	20.7359i	1.18026	+	0.681425i
$927$	−3.00364	−	13.2513i	−0.0986526	−	0.435230i
$928$	−0.892448	−	0.239131i	−0.0292961	−	0.00784985i
$929$	57.0607			1.87210			0.936051	−	0.351865i	$-0.114452\pi$
$929$	57.0607			1.87210			0.936051	+	0.351865i	$0.114452\pi$
$930$	−6.15091	−	10.7737i	−0.201696	−	0.353284i
$931$	7.20397	+	8.34785i	0.236101	+	0.273590i
$932$	−5.49236	−	20.4978i	−0.179908	−	0.671427i
$933$	−31.1832	−	18.8216i	−1.02089	−	0.616191i
$934$	21.1982	+	12.2388i	0.693627	+	0.400466i
$935$	−53.3571	−	29.7749i	−1.74496	−	0.973742i
$936$	17.7767	+	0.691830i	0.581051	+	0.0226132i
$937$	31.6113	+	31.6113i	1.03270	+	1.03270i	0.999447	+	0.0332500i	$0.0105857\pi$
$937$	31.6113	+	31.6113i	1.03270	+	1.03270i	0.0332500	+	0.999447i	$0.489414\pi$
$938$	−16.6724	−	2.82092i	−0.544372	−	0.0921062i
$939$	0.168866	+	0.683091i	0.00551074	+	0.0222918i
$940$	−11.4212	−	6.37339i	−0.372519	−	0.207877i
$941$			0.882115i			0.0287561i	0.999897	+	0.0143781i	$0.00457684\pi$
$941$			0.882115i			0.0287561i	−0.999897	+	0.0143781i	$0.995423\pi$
$942$	−20.3654	+	33.7411i	−0.663542	+	1.09934i
$943$	−5.70091	+	5.70091i	−0.185647	+	0.185647i
$944$	8.32434			0.270934
$945$	−30.7017	+	1.55033i	−0.998727	+	0.0504321i
$946$	−11.8044			−0.383793
$947$	3.71719	−	3.71719i	0.120793	−	0.120793i	−0.644126	−	0.764919i	$-0.722779\pi$
$947$	3.71719	−	3.71719i	0.120793	−	0.120793i	0.764919	+	0.644126i	$0.222779\pi$
$948$	−11.9188	+	19.7468i	−0.387104	+	0.641346i
$949$		−	35.4994i		−	1.15236i
$950$	5.40412	−	5.72957i	0.175333	−	0.185892i
$951$	−3.86636	−	15.6400i	−0.125375	−	0.507162i
$952$	4.00220	+	10.7635i	0.129712	+	0.348848i
$953$	3.95814	+	3.95814i	0.128217	+	0.128217i	0.768303	−	0.640086i	$-0.221101\pi$
$953$	3.95814	+	3.95814i	0.128217	+	0.128217i	−0.640086	+	0.768303i	$0.721101\pi$
$954$	9.80462	−	15.5522i	0.317436	−	0.503521i
$955$	0.800795	+	2.82296i	0.0259131	+	0.0913488i
$956$	5.13552	+	2.96499i	0.166094	+	0.0958947i
$957$	8.62565	+	5.20627i	0.278828	+	0.168295i
$958$	0.865918	+	3.23165i	0.0279765	+	0.104410i
$959$	1.01410	+	10.7347i	0.0327470	+	0.346643i
$960$	−3.73612	−	1.02049i	−0.120583	−	0.0329361i
$961$	−20.7395			−0.669018
$962$	−13.8425	−	3.70909i	−0.446300	−	0.119586i
$963$	2.33245	−	2.15770i	0.0751621	−	0.0695309i
$964$	−19.6612	−	11.3514i	−0.633245	−	0.365604i
$965$	−0.708676	+	1.26996i	−0.0228131	+	0.0408814i
$966$	−5.28822	−	1.00091i	−0.170146	−	0.0322037i
$967$	9.67174	−	2.59154i	0.311022	−	0.0833382i	−0.0999316	−	0.994994i	$-0.531862\pi$
$967$	9.67174	−	2.59154i	0.311022	−	0.0833382i	0.410954	+	0.911656i	$0.365196\pi$
$968$	7.41171	−	27.6609i	0.238221	−	0.889054i
$969$	−11.4960	+	2.84191i	−0.369304	+	0.0912952i
$970$	−0.138656	−	0.134662i	−0.00445198	−	0.00432374i
$971$	−35.9311	−	20.7448i	−1.15308	−	0.665733i	−0.203447	−	0.979086i	$-0.565214\pi$
$971$	−35.9311	−	20.7448i	−1.15308	−	0.665733i	−0.949637	+	0.313353i	$0.898548\pi$
$972$	−14.1930	+	6.44666i	−0.455240	+	0.206777i
$973$	3.29138	+	2.72319i	0.105517	+	0.0873013i
$974$	6.95365	+	12.0441i	0.222809	+	0.385917i
$975$	49.4737	−	13.7761i	1.58443	−	0.441187i
$976$	12.3608			0.395661
$977$	−22.6090	+	22.6090i	−0.723327	+	0.723327i	−0.969281	−	0.245955i	$-0.920899\pi$
$977$	−22.6090	+	22.6090i	−0.723327	+	0.723327i	0.245955	+	0.969281i	$0.420899\pi$
$978$	24.3890	−	13.4555i	0.779874	−	0.430259i
$979$	−72.8226	+	42.0441i	−2.32742	+	1.34374i
$980$	0.919978	−	15.6254i	0.0293876	−	0.499136i
$981$	0.590302	+	0.372146i	0.0188469	+	0.0118817i
$982$	−34.8537	+	9.33903i	−1.11223	+	0.298020i
$983$	16.1552	−	4.32878i	0.515271	−	0.138067i	0.00819281	−	0.999966i	$-0.497392\pi$
$983$	16.1552	−	4.32878i	0.515271	−	0.138067i	0.507078	+	0.861900i	$0.330725\pi$
$984$	−11.4227	−	3.30010i	−0.364143	−	0.105203i
$985$	6.83610	−	12.2504i	0.217816	−	0.390331i
$986$	3.47293	+	2.00510i	0.110601	+	0.0638552i
$987$	−2.00150	−	26.7295i	−0.0637085	−	0.850808i
$988$	−9.02284	−	2.41766i	−0.287055	−	0.0769161i
$989$	1.10105	−	1.90707i	0.0350113	−	0.0606414i
$990$	36.0515	+	21.9986i	1.14579	+	0.699162i
$991$	−20.4353	−	35.3951i	−0.649150	−	1.12436i	−0.983326	−	0.181850i	$-0.941791\pi$
$991$	−20.4353	−	35.3951i	−0.649150	−	1.12436i	0.334176	−	0.942511i	$-0.391542\pi$
$992$	2.26500	−	2.26500i	0.0719138	−	0.0719138i
$993$	−23.3580	+	38.6992i	−0.741245	+	1.22808i
$994$	14.5268	+	20.4438i	0.460763	+	0.648437i
$995$	13.9586	−	14.3725i	0.442516	−	0.455640i
$996$	22.5220	−	21.6625i	0.713636	−	0.686404i
$997$	2.81002	−	0.752943i	0.0889943	−	0.0238459i	−0.214047	−	0.976823i	$-0.568665\pi$
$997$	2.81002	−	0.752943i	0.0889943	−	0.0238459i	0.303041	+	0.952977i	$0.401998\pi$
$998$	9.24516	−	34.5034i	0.292650	−	1.09219i
$999$	12.2982	−	2.53720i	0.389098	−	0.0802736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.527.32	yes	192
5.3	odd	4	inner	630.2.cd.a.23.5	yes	192
7.4	even	3		630.2.bt.a.347.48	yes	192
9.2	odd	6		630.2.bt.a.317.36	✓	192
35.18	odd	12		630.2.bt.a.473.36	yes	192
45.38	even	12		630.2.bt.a.443.48	yes	192
63.11	odd	6	inner	630.2.cd.a.137.5	yes	192
315.263	even	12	inner	630.2.cd.a.263.32	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.36	✓	192	9.2	odd	6
630.2.bt.a.347.48	yes	192	7.4	even	3
630.2.bt.a.443.48	yes	192	45.38	even	12
630.2.bt.a.473.36	yes	192	35.18	odd	12
630.2.cd.a.23.5	yes	192	5.3	odd	4	inner
630.2.cd.a.137.5	yes	192	63.11	odd	6	inner
630.2.cd.a.263.32	yes	192	315.263	even	12	inner
630.2.cd.a.527.32	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.895033 + 1.48287i) q^{3} -1.00000i q^{4} +(2.15119 - 0.610232i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-2.60867 - 0.441381i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.39783 - 2.65444i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.895033 + 1.48287i) q^{3} -1.00000i q^{4} +(2.15119 - 0.610232i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-2.60867 - 0.441381i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.39783 - 2.65444i) q^{9} +(1.08962 - 1.95262i) q^{10} +(-5.45229 - 3.14788i) q^{11} +(1.48287 + 0.895033i) q^{12} +(-1.53481 - 5.72800i) q^{13} +(-2.15671 + 1.53251i) q^{14} +(-1.02049 + 3.73612i) q^{15} -1.00000 q^{16} +(4.19247 + 1.12337i) q^{17} +(-2.86539 - 0.888559i) q^{18} +(1.36418 + 0.787607i) q^{19} +(-0.610232 - 2.15119i) q^{20} +(2.98936 - 3.47329i) q^{21} +(-6.08124 + 1.62946i) q^{22} +(0.303976 - 1.13445i) q^{23} +(1.68143 - 0.415666i) q^{24} +(4.25523 - 2.62545i) q^{25} +(-5.13559 - 2.96503i) q^{26} +(5.18731 + 0.303009i) q^{27} +(-0.441381 + 2.60867i) q^{28} +(0.461965 + 0.800147i) q^{29} +(1.92024 + 3.36343i) q^{30} -3.20319 q^{31} +(-0.707107 + 0.707107i) q^{32} +(9.54789 - 5.26760i) q^{33} +(3.75886 - 2.17018i) q^{34} +(-5.88110 + 0.642404i) q^{35} +(-2.65444 + 1.39783i) q^{36} +(2.33429 - 0.625472i) q^{37} +(1.52154 - 0.407696i) q^{38} +(9.86762 + 2.85082i) q^{39} +(-1.95262 - 1.08962i) q^{40} +(-5.94493 - 3.43231i) q^{41} +(-0.342185 - 4.56978i) q^{42} +(1.81108 + 0.485278i) q^{43} +(-3.14788 + 5.45229i) q^{44} +(-4.62683 - 4.85721i) q^{45} +(-0.587236 - 1.01712i) q^{46} +(4.13599 - 4.13599i) q^{47} +(0.895033 - 1.48287i) q^{48} +(6.61037 + 2.30284i) q^{49} +(1.15243 - 4.86538i) q^{50} +(-5.41821 + 5.21145i) q^{51} +(-5.72800 + 1.53481i) q^{52} +(-1.58611 + 5.91945i) q^{53} +(3.88224 - 3.45372i) q^{54} +(-13.6499 - 3.44453i) q^{55} +(1.53251 + 2.15671i) q^{56} +(-2.38891 + 1.31797i) q^{57} +(0.892448 + 0.239131i) q^{58} -8.32434 q^{59} +(3.73612 + 1.02049i) q^{60} -12.3608 q^{61} +(-2.26500 + 2.26500i) q^{62} +(2.47487 + 7.54155i) q^{63} +1.00000i q^{64} +(-6.79709 - 11.3854i) q^{65} +(3.02662 - 10.4761i) q^{66} +(4.51921 + 4.51921i) q^{67} +(1.12337 - 4.19247i) q^{68} +(1.41018 + 1.46613i) q^{69} +(-3.70432 + 4.61281i) q^{70} -9.47913i q^{71} +(-0.888559 + 2.86539i) q^{72} +(5.78236 + 1.54938i) q^{73} +(1.20832 - 2.09287i) q^{74} +(0.0846377 + 8.65984i) q^{75} +(0.787607 - 1.36418i) q^{76} +(12.8338 + 10.6183i) q^{77} +(8.99329 - 4.96163i) q^{78} +13.3166i q^{79} +(-2.15119 + 0.610232i) q^{80} +(-5.09214 + 7.42092i) q^{81} +(-6.63071 + 1.77669i) q^{82} +(4.66953 - 17.4269i) q^{83} +(-3.47329 - 2.98936i) q^{84} +(9.70430 - 0.141801i) q^{85} +(1.62377 - 0.937485i) q^{86} +(-1.59999 - 0.0311222i) q^{87} +(1.62946 + 6.08124i) q^{88} +(6.67816 - 11.5669i) q^{89} +(-6.70623 - 0.162906i) q^{90} +(1.47560 + 15.6199i) q^{91} +(-1.13445 - 0.303976i) q^{92} +(2.86697 - 4.74993i) q^{93} -5.84918i q^{94} +(3.41522 + 0.861828i) q^{95} +(-0.415666 - 1.68143i) q^{96} +(0.0223723 - 0.0834947i) q^{97} +(6.30259 - 3.04588i) q^{98} +(-0.734495 + 18.8730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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