LMFDB - Embedded newform 630.2.cd.a.137.5

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			137.5
Character	$\chi$	$=$	630.137
Dual form			630.2.cd.a.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.48287 + 0.895033i) q^{3} -1.00000i q^{4} +(1.60407 + 1.55787i) q^{5} +(0.415666 - 1.68143i) q^{6} +(-0.441381 - 2.60867i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.39783 - 2.65444i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.48287 + 0.895033i) q^{3} -1.00000i q^{4} +(1.60407 + 1.55787i) q^{5} +(0.415666 - 1.68143i) q^{6} +(-0.441381 - 2.60867i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.39783 - 2.65444i) q^{9} +(-2.23583 + 0.0326704i) q^{10} +(-5.45229 + 3.14788i) q^{11} +(0.895033 + 1.48287i) q^{12} +(5.72800 + 1.53481i) q^{13} +(2.15671 + 1.53251i) q^{14} +(-3.77298 - 0.874425i) q^{15} -1.00000 q^{16} +(1.12337 + 4.19247i) q^{17} +(0.888559 + 2.86539i) q^{18} +(-1.36418 + 0.787607i) q^{19} +(1.55787 - 1.60407i) q^{20} +(2.98936 + 3.47329i) q^{21} +(1.62946 - 6.08124i) q^{22} +(1.13445 - 0.303976i) q^{23} +(-1.68143 - 0.415666i) q^{24} +(0.146091 + 4.99787i) q^{25} +(-5.13559 + 2.96503i) q^{26} +(0.303009 + 5.18731i) q^{27} +(-2.60867 + 0.441381i) q^{28} +(-0.461965 + 0.800147i) q^{29} +(3.28621 - 2.04959i) q^{30} -3.20319 q^{31} +(0.707107 - 0.707107i) q^{32} +(5.26760 - 9.54789i) q^{33} +(-3.75886 - 2.17018i) q^{34} +(3.35597 - 4.87211i) q^{35} +(-2.65444 - 1.39783i) q^{36} +(-0.625472 + 2.33429i) q^{37} +(0.407696 - 1.52154i) q^{38} +(-9.86762 + 2.85082i) q^{39} +(0.0326704 + 2.23583i) q^{40} +(-5.94493 + 3.43231i) q^{41} +(-4.56978 - 0.342185i) q^{42} +(-0.485278 - 1.81108i) q^{43} +(3.14788 + 5.45229i) q^{44} +(6.37749 - 2.08028i) q^{45} +(-0.587236 + 1.01712i) q^{46} +(-4.13599 + 4.13599i) q^{47} +(1.48287 - 0.895033i) q^{48} +(-6.61037 + 2.30284i) q^{49} +(-3.63733 - 3.43072i) q^{50} +(-5.41821 - 5.21145i) q^{51} +(1.53481 - 5.72800i) q^{52} +(-5.91945 + 1.58611i) q^{53} +(-3.88224 - 3.45372i) q^{54} +(-13.6499 - 3.44453i) q^{55} +(1.53251 - 2.15671i) q^{56} +(1.31797 - 2.38891i) q^{57} +(-0.239131 - 0.892448i) q^{58} +8.32434 q^{59} +(-0.874425 + 3.77298i) q^{60} -12.3608 q^{61} +(2.26500 - 2.26500i) q^{62} +(-7.54155 - 2.47487i) q^{63} +1.00000i q^{64} +(6.79709 + 11.3854i) q^{65} +(3.02662 + 10.4761i) q^{66} +(4.51921 + 4.51921i) q^{67} +(4.19247 - 1.12337i) q^{68} +(-1.41018 + 1.46613i) q^{69} +(1.07208 + 5.81813i) q^{70} +9.47913i q^{71} +(2.86539 - 0.888559i) q^{72} +(-1.54938 - 5.78236i) q^{73} +(-1.20832 - 2.09287i) q^{74} +(-4.68989 - 7.28045i) q^{75} +(0.787607 + 1.36418i) q^{76} +(10.6183 + 12.8338i) q^{77} +(4.96163 - 8.99329i) q^{78} +13.3166i q^{79} +(-1.60407 - 1.55787i) q^{80} +(-5.09214 - 7.42092i) q^{81} +(1.77669 - 6.63071i) q^{82} +(17.4269 - 4.66953i) q^{83} +(3.47329 - 2.98936i) q^{84} +(-4.72935 + 8.47507i) q^{85} +(1.62377 + 0.937485i) q^{86} +(-0.0311222 - 1.59999i) q^{87} +(-6.08124 - 1.62946i) q^{88} +(-6.67816 - 11.5669i) q^{89} +(-3.03859 + 5.98055i) q^{90} +(1.47560 - 15.6199i) q^{91} +(-0.303976 - 1.13445i) q^{92} +(4.74993 - 2.86697i) q^{93} -5.84918i q^{94} +(-3.41522 - 0.861828i) q^{95} +(-0.415666 + 1.68143i) q^{96} +(-0.0834947 + 0.0223723i) q^{97} +(3.04588 - 6.30259i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.48287	+	0.895033i	−0.856138	+	0.516748i
$3$	−1.48287	+	0.895033i	−0.856138	+	0.516748i
$4$		−	1.00000i		−	0.500000i
$5$	1.60407	+	1.55787i	0.717363	+	0.696700i
$5$	1.60407	+	1.55787i	0.717363	+	0.696700i
$6$	0.415666	−	1.68143i	0.169695	−	0.686443i
$7$	−0.441381	−	2.60867i	−0.166826	−	0.985986i
$7$	−0.441381	−	2.60867i	−0.166826	−	0.985986i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.39783	−	2.65444i	0.465944	−	0.884814i
$10$	−2.23583	+	0.0326704i	−0.707031	+	0.0103313i
$11$	−5.45229	+	3.14788i	−1.64393	+	0.949122i	−0.664510	+	0.747280i	$0.731360\pi$
$11$	−5.45229	+	3.14788i	−1.64393	+	0.949122i	−0.979418	+	0.201842i	$0.935307\pi$
$12$	0.895033	+	1.48287i	0.258374	+	0.428069i
$13$	5.72800	+	1.53481i	1.58866	+	0.425681i	0.941594	−	0.336751i	$-0.109328\pi$
$13$	5.72800	+	1.53481i	1.58866	+	0.425681i	0.647069	+	0.762432i	$0.275995\pi$
$14$	2.15671	+	1.53251i	0.576406	+	0.409580i
$15$	−3.77298	−	0.874425i	−0.974179	−	0.225776i
$16$	−1.00000			−0.250000
$17$	1.12337	+	4.19247i	0.272457	+	1.01682i	0.957527	+	0.288345i	$0.0931050\pi$
$17$	1.12337	+	4.19247i	0.272457	+	1.01682i	−0.685070	+	0.728477i	$0.740228\pi$
$18$	0.888559	+	2.86539i	0.209435	+	0.675379i
$19$	−1.36418	+	0.787607i	−0.312963	+	0.180690i	−0.648252	−	0.761426i	$-0.724500\pi$
$19$	−1.36418	+	0.787607i	−0.312963	+	0.180690i	0.335288	+	0.942116i	$0.391166\pi$
$20$	1.55787	−	1.60407i	0.348350	−	0.358681i
$21$	2.98936	+	3.47329i	0.652332	+	0.757933i
$22$	1.62946	−	6.08124i	0.347403	−	1.29652i
$23$	1.13445	−	0.303976i	0.236550	−	0.0633833i	−0.138597	−	0.990349i	$-0.544259\pi$
$23$	1.13445	−	0.303976i	0.236550	−	0.0633833i	0.375146	+	0.926966i	$0.377592\pi$
$24$	−1.68143	−	0.415666i	−0.343221	−	0.0848475i
$25$	0.146091	+	4.99787i	0.0292182	+	0.999573i
$26$	−5.13559	+	2.96503i	−1.00717	+	0.581491i
$27$	0.303009	+	5.18731i	0.0583141	+	0.998298i
$28$	−2.60867	+	0.441381i	−0.492993	+	0.0834131i
$29$	−0.461965	+	0.800147i	−0.0857848	+	0.148584i	−0.905725	−	0.423865i	$-0.860673\pi$
$29$	−0.461965	+	0.800147i	−0.0857848	+	0.148584i	0.819941	+	0.572449i	$0.194006\pi$
$30$	3.28621	−	2.04959i	0.599977	−	0.374202i
$31$	−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
$33$	5.26760	−	9.54789i	0.916972	−	1.66208i
$34$	−3.75886	−	2.17018i	−0.644639	−	0.372183i
$35$	3.35597	−	4.87211i	0.567262	−	0.823537i
$36$	−2.65444	−	1.39783i	−0.442407	−	0.232972i
$37$	−0.625472	+	2.33429i	−0.102827	+	0.383755i	−0.998090	−	0.0617835i	$-0.980321\pi$
$37$	−0.625472	+	2.33429i	−0.102827	+	0.383755i	0.895263	+	0.445539i	$0.146988\pi$
$38$	0.407696	−	1.52154i	0.0661370	−	0.246826i
$39$	−9.86762	+	2.85082i	−1.58008	+	0.456496i
$40$	0.0326704	+	2.23583i	0.00516564	+	0.353516i
$41$	−5.94493	+	3.43231i	−0.928443	+	0.536037i	−0.886319	−	0.463076i	$-0.846746\pi$
$41$	−5.94493	+	3.43231i	−0.928443	+	0.536037i	−0.0421240	+	0.999112i	$0.513412\pi$
$42$	−4.56978	−	0.342185i	−0.705133	−	0.0528003i
$43$	−0.485278	−	1.81108i	−0.0740042	−	0.276187i	0.919001	−	0.394254i	$-0.128997\pi$
$43$	−0.485278	−	1.81108i	−0.0740042	−	0.276187i	−0.993006	+	0.118067i	$0.962330\pi$
$44$	3.14788	+	5.45229i	0.474561	+	0.821964i
$45$	6.37749	−	2.08028i	0.950701	−	0.310110i
$46$	−0.587236	+	1.01712i	−0.0865832	+	0.149966i
$47$	−4.13599	+	4.13599i	−0.603296	+	0.603296i	−0.941186	−	0.337889i	$-0.890287\pi$
$47$	−4.13599	+	4.13599i	−0.603296	+	0.603296i	0.337889	+	0.941186i	$0.390287\pi$
$48$	1.48287	−	0.895033i	0.214034	−	0.129187i
$49$	−6.61037	+	2.30284i	−0.944338	+	0.328977i
$50$	−3.63733	−	3.43072i	−0.514396	−	0.485177i
$51$	−5.41821	−	5.21145i	−0.758701	−	0.729748i
$52$	1.53481	−	5.72800i	0.212840	−	0.794331i
$53$	−5.91945	+	1.58611i	−0.813099	+	0.217869i	−0.641327	−	0.767267i	$-0.721616\pi$
$53$	−5.91945	+	1.58611i	−0.813099	+	0.217869i	−0.171772	+	0.985137i	$0.554949\pi$
$54$	−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
$57$	1.31797	−	2.38891i	0.174569	−	0.316418i
$58$	−0.239131	−	0.892448i	−0.0313994	−	0.117184i
$59$	8.32434			1.08374			0.541868	−	0.840463i	$-0.317717\pi$
$59$	8.32434			1.08374			0.541868	+	0.840463i	$0.317717\pi$
$60$	−0.874425	+	3.77298i	−0.112888	+	0.487090i
$61$	−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
$63$	−7.54155	−	2.47487i	−0.950147	−	0.311804i
$64$			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	$0.622337\pi$
$68$	4.19247	−	1.12337i	0.508411	−	0.136228i
$69$	−1.41018	+	1.46613i	−0.169766	+	0.176501i
$70$	1.07208	+	5.81813i	0.128138	+	0.695400i
$71$			9.47913i			1.12497i	0.826809	+	0.562483i	$0.190154\pi$
$71$			9.47913i			1.12497i	−0.826809	+	0.562483i	$0.809846\pi$
$72$	2.86539	−	0.888559i	0.337689	−	0.104718i
$73$	−1.54938	−	5.78236i	−0.181341	−	0.676774i	−0.995384	−	0.0959699i	$-0.969405\pi$
$73$	−1.54938	−	5.78236i	−0.181341	−	0.676774i	0.814043	−	0.580804i	$-0.197262\pi$
$74$	−1.20832	−	2.09287i	−0.140464	−	0.243291i
$75$	−4.68989	−	7.28045i	−0.541542	−	0.840674i
$76$	0.787607	+	1.36418i	0.0903448	+	0.156482i
$77$	10.6183	+	12.8338i	1.21007	+	1.46255i
$78$	4.96163	−	8.99329i	0.561794	−	1.01829i
$79$			13.3166i			1.49823i	0.662440	+	0.749115i	$0.269521\pi$
$79$			13.3166i			1.49823i	−0.662440	+	0.749115i	$0.730479\pi$
$80$	−1.60407	−	1.55787i	−0.179341	−	0.174175i
$81$	−5.09214	−	7.42092i	−0.565793	−	0.824547i
$82$	1.77669	−	6.63071i	0.196203	−	0.732240i
$83$	17.4269	−	4.66953i	1.91285	−	0.512547i	0.920216	−	0.391411i	$-0.128013\pi$
$83$	17.4269	−	4.66953i	1.91285	−	0.512547i	0.992636	−	0.121137i	$-0.0386539\pi$
$84$	3.47329	−	2.98936i	0.378967	−	0.326166i
$85$	−4.72935	+	8.47507i	−0.512970	+	0.919251i
$86$	1.62377	+	0.937485i	0.175096	+	0.101092i
$87$	−0.0311222	−	1.59999i	−0.00333666	−	0.171537i
$88$	−6.08124	−	1.62946i	−0.648262	−	0.173701i
$89$	−6.67816	−	11.5669i	−0.707884	−	1.22609i	−0.965641	−	0.259881i	$-0.916317\pi$
$89$	−6.67816	−	11.5669i	−0.707884	−	1.22609i	0.257757	−	0.966210i	$-0.417017\pi$
$90$	−3.03859	+	5.98055i	−0.320295	+	0.630405i
$91$	1.47560	−	15.6199i	0.154685	−	1.63741i
$92$	−0.303976	−	1.13445i	−0.0316916	−	0.118275i
$93$	4.74993	−	2.86697i	0.492545	−	0.297290i
$94$		−	5.84918i		−	0.603296i
$95$	−3.41522	−	0.861828i	−0.350395	−	0.0884217i
$96$	−0.415666	+	1.68143i	−0.0424237	+	0.171611i
$97$	−0.0834947	+	0.0223723i	−0.00847760	+	0.00227157i	−0.263055	−	0.964781i	$-0.584730\pi$
$97$	−0.0834947	+	0.0223723i	−0.00847760	+	0.00227157i	0.254578	+	0.967052i	$0.418064\pi$
$98$	3.04588	−	6.30259i	0.307681	−	0.636657i
$99$	0.734495	+	18.8730i	0.0738195	+	1.89681i
$100$	4.99787	−	0.146091i	0.499787	−	0.0146091i
$101$	9.81937	−	5.66922i	0.977064	−	0.564108i	0.0756817	−	0.997132i	$-0.475887\pi$
$101$	9.81937	−	5.66922i	0.977064	−	0.564108i	0.901383	+	0.433024i	$0.142553\pi$
$102$	7.51630	−	0.146203i	0.744225	−	0.0144763i
$103$	−1.17223	−	4.37483i	−0.115503	−	0.431064i	0.883821	−	0.467826i	$-0.154963\pi$
$103$	−1.17223	−	4.37483i	−0.115503	−	0.431064i	−0.999324	+	0.0367614i	$0.988296\pi$
$104$	2.96503	+	5.13559i	0.290745	+	0.503586i
$105$	−0.615771	+	10.2284i	−0.0600931	+	0.998193i
$106$	3.06413	−	5.30724i	0.297615	−	0.515484i
$107$	1.02305	+	0.274125i	0.0989020	+	0.0265007i	0.307931	−	0.951409i	$-0.400364\pi$
$107$	1.02305	+	0.274125i	0.0989020	+	0.0265007i	−0.209029	+	0.977910i	$0.567030\pi$
$108$	5.18731	−	0.303009i	0.499149	−	0.0291570i
$109$	0.201442	+	0.116303i	0.0192947	+	0.0111398i	0.509616	−	0.860402i	$-0.329787\pi$
$109$	0.201442	+	0.116303i	0.0192947	+	0.0111398i	−0.490322	+	0.871542i	$0.663121\pi$
$110$	12.0876	−	7.21626i	1.15250	−	0.688043i
$111$	−1.16177	−	4.02128i	−0.110271	−	0.381683i
$112$	0.441381	+	2.60867i	0.0417065	+	0.246497i
$113$	−3.94167	+	14.7105i	−0.370801	+	1.38385i	0.488583	+	0.872518i	$0.337514\pi$
$113$	−3.94167	+	14.7105i	−0.370801	+	1.38385i	−0.859384	+	0.511331i	$0.829153\pi$
$114$	0.757268	+	2.62115i	0.0709247	+	0.245494i
$115$	2.29330	+	1.27973i	0.213851	+	0.119335i
$116$	0.800147	+	0.461965i	0.0742918	+	0.0428924i
$117$	12.0809	−	13.0593i	1.11688	−	1.20733i
$118$	−5.88620	+	5.88620i	−0.541868	+	0.541868i
$119$	10.4409	−	4.78097i	0.957120	−	0.438271i
$120$	−2.04959	−	3.28621i	−0.187101	−	0.299989i
$121$	14.3183	−	24.8001i	1.30167	−	2.25455i
$122$	8.74043	−	8.74043i	0.791322	−	0.791322i
$123$	5.74356	−	10.4106i	0.517879	−	0.938692i
$124$			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	0.701261	−	0.712904i	$-0.252621\pi$
$131$	4.97306	+	2.87120i	0.434498	+	0.250858i	−0.266763	+	0.963762i	$0.585954\pi$
$132$	−9.54789	−	5.26760i	−0.831038	−	0.458486i
$133$	2.65673	+	3.21106i	0.230368	+	0.278434i
$134$	−6.39112			−0.552109
$135$	−7.59510	+	8.79286i	−0.653682	+	0.756769i
$136$	−2.17018	+	3.75886i	−0.186091	+	0.322320i
$137$	−3.93655	−	1.05479i	−0.336322	−	0.0901172i	0.0867057	−	0.996234i	$-0.472366\pi$
$137$	−3.93655	−	1.05479i	−0.336322	−	0.0901172i	−0.423028	+	0.906117i	$0.639033\pi$
$138$	−0.0395616	−	2.03386i	−0.00336771	−	0.173134i
$139$	1.39830	−	0.807308i	0.118602	−	0.0684750i	−0.439525	−	0.898230i	$-0.644853\pi$
$139$	1.39830	−	0.807308i	0.118602	−	0.0684750i	0.558127	+	0.829755i	$0.311520\pi$
$140$	−4.87211	−	3.35597i	−0.411769	−	0.283631i
$141$	2.43130	−	9.83501i	0.204753	−	0.828257i
$142$	−6.70276	−	6.70276i	−0.562483	−	0.562483i
$143$	−36.0622	+	9.66283i	−3.01567	+	0.808046i
$144$	−1.39783	+	2.65444i	−0.116486	+	0.221204i
$145$	−1.98755	+	0.563812i	−0.165057	+	0.0468221i
$146$	5.18432	+	2.99317i	0.429058	+	0.247717i
$147$	7.74122	−	9.33131i	0.638485	−	0.769634i
$148$	2.33429	+	0.625472i	0.191878	+	0.0514135i
$149$	3.99291	−	6.91592i	0.327112	−	0.566574i	−0.654826	−	0.755780i	$-0.727258\pi$
$149$	3.99291	−	6.91592i	0.327112	−	0.566574i	0.981937	+	0.189206i	$0.0605913\pi$
$150$	8.46431	+	1.83180i	0.691108	+	0.149566i
$151$	2.67237	+	4.62868i	0.217474	+	0.376677i	0.954035	−	0.299695i	$-0.0968848\pi$
$151$	2.67237	+	4.62868i	0.217474	+	0.376677i	−0.736561	+	0.676371i	$0.763552\pi$
$152$	−1.52154	−	0.407696i	−0.123413	−	0.0330685i
$153$	12.6989	+	2.87844i	1.02665	+	0.232708i
$154$	−16.5832	−	1.56660i	−1.33631	−	0.126240i
$155$	−5.13815	−	4.99016i	−0.412706	−	0.400819i
$156$	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
$160$	2.23583	−	0.0326704i	0.176758	−	0.00258282i
$161$	−1.29370	−	2.82525i	−0.101958	−	0.222661i
$162$	8.84807	+	1.64670i	0.695170	+	0.129377i
$163$	15.5338	+	4.16228i	1.21670	+	0.326015i	0.809389	−	0.587274i	$-0.199799\pi$
$163$	15.5338	+	4.16228i	1.21670	+	0.326015i	0.407314	+	0.913288i	$0.366465\pi$
$164$	3.43231	+	5.94493i	0.268018	+	0.464221i
$165$	23.3240	−	7.10927i	1.81577	−	0.553456i
$166$	−9.02083	+	15.6245i	−0.700152	+	1.21270i
$167$	−3.19541	−	0.856206i	−0.247268	−	0.0662552i	0.133056	−	0.991108i	$-0.457521\pi$
$167$	−3.19541	−	0.856206i	−0.247268	−	0.0662552i	−0.380324	+	0.924853i	$0.624188\pi$
$168$	−0.342185	+	4.56978i	−0.0264002	+	0.352566i
$169$	19.1961	+	11.0828i	1.47662	+	0.852527i
$170$	−2.64863	−	9.33694i	−0.203140	−	0.716110i
$171$	0.183772	+	4.72207i	0.0140534	+	0.361106i
$172$	−1.81108	+	0.485278i	−0.138094	+	0.0370021i
$173$	4.11813	+	4.11813i	0.313096	+	0.313096i	0.846108	−	0.533012i	$-0.178940\pi$
$173$	4.11813	+	4.11813i	0.313096	+	0.313096i	−0.533012	+	0.846108i	$0.678940\pi$
$174$	1.15337	+	1.10936i	0.0874369	+	0.0841002i
$175$	12.9733	−	2.58706i	0.980691	−	0.195564i
$176$	5.45229	−	3.14788i	0.410982	−	0.237281i
$177$	−12.3439	+	7.45056i	−0.927828	+	0.560018i
$178$	12.9012	+	3.45687i	0.966987	+	0.259103i
$179$	−2.90382	+	5.02957i	−0.217042	+	0.375927i	−0.953902	−	0.300117i	$-0.902974\pi$
$179$	−2.90382	+	5.02957i	−0.217042	+	0.375927i	0.736860	+	0.676045i	$0.236307\pi$
$180$	−2.08028	−	6.37749i	−0.155055	−	0.475350i
$181$	5.33095			0.396247			0.198123	−	0.980177i	$-0.436515\pi$
$181$	5.33095			0.396247			0.198123	+	0.980177i	$0.436515\pi$
$182$	10.0016	+	12.0884i	0.741365	+	0.896050i
$183$	18.3296	−	11.0634i	1.35496	−	0.817827i
$184$	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	$-0.984882\pi$
$191$		−	1.31228i		−	0.0949531i	0.998872	−	0.0474766i	$-0.0151179\pi$
$192$	−0.895033	−	1.48287i	−0.0645935	−	0.107017i
$193$	−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
$195$	−20.2696	−	10.7995i	−1.45153	−	0.773371i
$196$	2.30284	+	6.61037i	0.164488	+	0.472169i
$197$	−4.43627	+	4.43627i	−0.316071	+	0.316071i	−0.847256	−	0.531185i	$-0.821747\pi$
$197$	−4.43627	+	4.43627i	−0.316071	+	0.316071i	0.531185	+	0.847256i	$0.321747\pi$
$198$	−13.8646	−	12.8259i	−0.985314	−	0.911494i
$199$	−7.75962	−	4.48002i	−0.550065	−	0.317580i	0.199083	−	0.979983i	$-0.436204\pi$
$199$	−7.75962	−	4.48002i	−0.550065	−	0.317580i	−0.749148	+	0.662403i	$0.769537\pi$
$200$	−3.43072	+	3.63733i	−0.242589	+	0.257198i
$201$	−10.7463	−	2.65657i	−0.757982	−	0.187380i
$202$	−2.93460	+	10.9521i	−0.206478	+	0.770586i
$203$	2.29123	+	0.851948i	0.160813	+	0.0597950i
$204$	−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
$207$	0.778886	−	3.43625i	0.0541363	−	0.238836i
$208$	−5.72800	−	1.53481i	−0.397166	−	0.106420i
$209$	4.95859	−	8.58853i	0.342993	−	0.594081i
$210$	−6.79718	−	7.66801i	−0.469050	−	0.529143i
$211$	−1.30948	−	2.26808i	−0.0901481	−	0.156141i	0.817425	−	0.576035i	$-0.195401\pi$
$211$	−1.30948	−	2.26808i	−0.0901481	−	0.156141i	−0.907573	+	0.419894i	$0.862067\pi$
$212$	1.58611	+	5.91945i	0.108935	+	0.406550i
$213$	−8.48414	−	14.0564i	−0.581323	−	0.963125i
$214$	−0.917241	+	0.529570i	−0.0627013	+	0.0362006i
$215$	2.04301	−	3.66110i	0.139332	−	0.249685i
$216$	−3.45372	+	3.88224i	−0.234996	+	0.264153i
$217$	1.41383	+	8.35609i	0.0959769	+	0.567248i
$218$	−0.224680	+	0.0602028i	−0.0152172	+	0.00407745i
$219$	7.47294	+	7.18777i	0.504975	+	0.485704i
$220$	−3.44453	+	13.6499i	−0.232230	+	0.920273i
$221$			25.7386i			1.73137i
$222$	3.66497	+	2.02198i	0.245977	+	0.135706i
$223$	−6.49461	−	24.2382i	−0.434911	−	1.62311i	−0.741279	−	0.671197i	$-0.765780\pi$
$223$	−6.49461	−	24.2382i	−0.434911	−	1.62311i	0.306367	−	0.951913i	$-0.400886\pi$
$224$	−2.15671	−	1.53251i	−0.144102	−	0.102395i
$225$	13.4708	+	6.59838i	0.898051	+	0.439892i
$226$	−7.61472	−	13.1891i	−0.506524	−	0.877325i
$227$	−24.1560	−	6.47257i	−1.60329	−	0.429600i	−0.657255	−	0.753669i	$-0.728282\pi$
$227$	−24.1560	−	6.47257i	−1.60329	−	0.429600i	−0.946033	+	0.324069i	$0.894949\pi$
$228$	−2.38891	−	1.31797i	−0.158209	−	0.0872844i
$229$	7.93914	+	4.58366i	0.524633	+	0.302897i	0.738828	−	0.673894i	$-0.235379\pi$
$229$	7.93914	+	4.58366i	0.524633	+	0.302897i	−0.214195	+	0.976791i	$0.568713\pi$
$230$	−2.52651	+	0.716701i	−0.166593	+	0.0472578i
$231$	−27.2324	−	9.52720i	−1.79176	−	0.626844i
$232$	−0.892448	+	0.239131i	−0.0585921	+	0.0156997i
$233$	5.49236	−	20.4978i	0.359817	−	1.34285i	−0.514497	−	0.857492i	$-0.672021\pi$
$233$	5.49236	−	20.4978i	0.359817	−	1.34285i	0.874314	−	0.485362i	$-0.161312\pi$
$234$	0.691830	+	17.7767i	0.0452264	+	1.16210i
$235$	−13.0778	+	0.191095i	−0.853099	+	0.0124657i
$236$		−	8.32434i		−	0.541868i
$237$	−11.9188	−	19.7468i	−0.774207	−	1.28269i
$238$	−4.00220	+	10.7635i	−0.259424	+	0.697695i
$239$	2.96499	+	5.13552i	0.191789	+	0.332189i	0.945843	−	0.324624i	$-0.105238\pi$
$239$	2.96499	+	5.13552i	0.191789	+	0.332189i	−0.754054	+	0.656813i	$0.771904\pi$
$240$	3.77298	+	0.874425i	0.243545	+	0.0564439i
$241$	11.3514	+	19.6612i	0.731209	+	1.26649i	0.956367	+	0.292168i	$0.0943767\pi$
$241$	11.3514	+	19.6612i	0.731209	+	1.26649i	−0.225158	+	0.974322i	$0.572290\pi$
$242$	7.41171	+	27.6609i	0.476443	+	1.77811i
$243$	14.1930	+	6.44666i	0.910480	+	0.413554i
$244$			12.3608i			0.791322i
$245$	−14.1910	−	6.60417i	−0.906631	−	0.421925i
$246$	3.30010	+	11.4227i	0.210406	+	0.728286i
$247$	−9.02284	+	2.41766i	−0.574109	+	0.153832i
$248$	−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	$-0.920070\pi$
$251$		−	7.87318i		−	0.496951i	0.968638	−	0.248475i	$-0.0799295\pi$
$252$	−2.47487	+	7.54155i	−0.155902	+	0.475073i
$253$	−5.22849	+	5.22849i	−0.328712	+	0.328712i
$254$	−11.6579			−0.731479
$255$	−0.572446	−	16.8004i	−0.0358480	−	1.05208i
$256$	1.00000			0.0625000
$257$	3.60224	+	13.4437i	0.224701	+	0.838597i	0.982524	+	0.186136i	$0.0595965\pi$
$257$	3.60224	+	13.4437i	0.224701	+	0.838597i	−0.757823	+	0.652461i	$0.773737\pi$
$258$	−3.24693	+	0.0631577i	−0.202145	+	0.00393202i
$259$	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
$262$	−5.54673	+	1.48624i	−0.342678	+	0.0918203i
$263$	1.40058	−	5.22702i	0.0863633	−	0.322312i	−0.909206	−	0.416347i	$-0.863310\pi$
$263$	1.40058	−	5.22702i	0.0863633	−	0.322312i	0.995569	+	0.0940353i	$0.0299767\pi$
$264$	10.4761	−	3.02662i	0.644762	−	0.186276i
$265$	−11.9662	−	6.67749i	−0.735077	−	0.410195i
$266$	−4.14915	−	0.391967i	−0.254401	−	0.0240330i
$267$	20.2557	+	11.1751i	1.23963	+	0.683905i
$268$	4.51921	−	4.51921i	0.276055	−	0.276055i
$269$	14.0186	−	24.2810i	0.854732	−	1.48044i	−0.0221622	−	0.999754i	$-0.507055\pi$
$269$	14.0186	−	24.2810i	0.854732	−	1.48044i	0.876894	−	0.480684i	$-0.159612\pi$
$270$	−0.846947	−	11.5880i	−0.0515436	−	0.705226i
$271$	−4.39946	−	7.62008i	−0.267248	−	0.462887i	0.700902	−	0.713257i	$-0.252781\pi$
$271$	−4.39946	−	7.62008i	−0.267248	−	0.462887i	−0.968150	+	0.250370i	$0.919448\pi$
$272$	−1.12337	−	4.19247i	−0.0681142	−	0.254206i
$273$	11.7922	+	24.4831i	0.713698	+	1.48179i
$274$	3.52941	−	2.03771i	0.213220	−	0.123102i
$275$	−16.5292	−	26.7899i	−0.996749	−	1.61549i
$276$	1.46613	+	1.41018i	0.0882507	+	0.0848830i
$277$	3.49664	−	13.0496i	0.210092	−	0.784076i	−0.777744	−	0.628581i	$-0.783636\pi$
$277$	3.49664	−	13.0496i	0.210092	−	0.784076i	0.987837	−	0.155495i	$-0.0496972\pi$
$278$	−0.417893	+	1.55960i	−0.0250636	+	0.0935386i
$279$	−4.47752	+	8.50270i	−0.268062	+	0.509043i
$280$	5.81813	−	1.07208i	0.347700	−	0.0640689i
$281$	−14.4482	−	8.34169i	−0.861909	−	0.497623i	0.00274228	−	0.999996i	$-0.499127\pi$
$281$	−14.4482	−	8.34169i	−0.861909	−	0.497623i	−0.864651	+	0.502373i	$0.832460\pi$
$282$	5.23521	+	8.67359i	0.311752	+	0.516505i
$283$	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
$285$	5.83571	−	1.77876i	0.345678	−	0.105364i
$286$	18.6671	−	32.3325i	1.10381	−	1.91186i
$287$	11.5778	+	13.9934i	0.683413	+	0.826007i
$288$	−0.888559	−	2.86539i	−0.0523589	−	0.168845i
$289$	−1.59238	+	0.919360i	−0.0936693	+	0.0540800i
$290$	1.00673	−	1.80409i	0.0591175	−	0.105940i
$291$	0.103788	−	0.107906i	0.00608417	−	0.00632555i
$292$	−5.78236	+	1.54938i	−0.338387	+	0.0906706i
$293$	−1.45533	+	5.43138i	−0.0850215	+	0.317305i	−0.995318	−	0.0966517i	$-0.969187\pi$
$293$	−1.45533	+	5.43138i	−0.0850215	+	0.317305i	0.910297	+	0.413956i	$0.135853\pi$
$294$	1.12436	+	12.0721i	0.0655742	+	0.704060i
$295$	13.3528	+	12.9682i	0.777432	+	0.755039i
$296$	−2.09287	+	1.20832i	−0.121646	+	0.0702321i
$297$	−17.9811	−	27.3289i	−1.04337	−	1.58578i
$298$	2.06688	+	7.71371i	0.119731	+	0.446843i
$299$	6.96469			0.402779
$300$	−7.28045	+	4.68989i	−0.420337	+	0.270771i
$301$	−4.51033	+	2.06531i	−0.259971	+	0.119042i
$302$	−5.16262	−	1.38332i	−0.297075	−	0.0796011i
$303$	−9.48676	+	17.1954i	−0.545000	+	0.987850i
$304$	1.36418	−	0.787607i	0.0782409	−	0.0451724i
$305$	−19.8277	−	19.2566i	−1.13533	−	1.10263i
$306$	−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	$0.689102\pi$
$308$	12.8338	−	10.6183i	0.731276	−	0.605036i
$309$	5.65389	+	5.43813i	0.321638	+	0.309364i
$310$	7.16180	−	0.104650i	0.406763	−	0.00594370i
$311$		−	21.0289i		−	1.19244i	−0.802821	−	0.596220i	$-0.796669\pi$
$311$		−	21.0289i		−	1.19244i	0.802821	−	0.596220i	$-0.203331\pi$
$312$	−8.99329	−	4.96163i	−0.509145	−	0.280897i
$313$	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
$315$	−8.24168	−	15.7186i	−0.464366	−	0.885643i
$316$	13.3166			0.749115
$317$	6.57722	−	6.57722i	0.369413	−	0.369413i	−0.497850	−	0.867263i	$-0.665877\pi$
$317$	6.57722	−	6.57722i	0.369413	−	0.369413i	0.867263	+	0.497850i	$0.165877\pi$
$318$	0.206428	+	10.6125i	0.0115759	+	0.595117i
$319$		−	5.81685i		−	0.325681i
$320$	−1.55787	+	1.60407i	−0.0870875	+	0.0896703i
$321$	−1.76241	+	0.509170i	−0.0983679	+	0.0284191i
$322$	2.91254	+	1.08297i	0.162309	+	0.0603515i
$323$	−4.83449	−	4.83449i	−0.268998	−	0.268998i
$324$	−7.42092	+	5.09214i	−0.412274	+	0.282897i
$325$	−6.83399	+	28.8520i	−0.379081	+	1.60042i
$326$	−13.9272	+	8.04090i	−0.771359	+	0.445344i
$327$	−0.402809	+	0.00783523i	−0.0222754	+	0.000433289i
$328$	−6.63071	−	1.77669i	−0.366120	−	0.0981015i
$329$	12.6150	+	8.96391i	0.695488	+	0.494196i
$330$	−11.4655	+	21.5196i	−0.631156	+	1.18461i
$331$	26.0974			1.43444			0.717222	−	0.696845i	$-0.245414\pi$
$331$	26.0974			1.43444			0.717222	+	0.696845i	$0.245414\pi$
$332$	−4.66953	−	17.4269i	−0.256274	−	0.956426i
$333$	5.32194	+	4.92322i	0.291641	+	0.269791i
$334$	2.86492	−	1.65406i	0.156762	−	0.0905063i
$335$	0.208800	+	14.2895i	0.0114080	+	0.780717i
$336$	−2.98936	−	3.47329i	−0.163083	−	0.189483i
$337$	6.58481	−	24.5748i	0.358697	−	1.33868i	−0.517070	−	0.855943i	$-0.672977\pi$
$337$	6.58481	−	24.5748i	0.358697	−	1.33868i	0.875767	−	0.482733i	$-0.160356\pi$
$338$	−21.4104	+	5.73690i	−1.16457	+	0.312046i
$339$	−7.32140	−	25.3418i	−0.397644	−	1.37638i
$340$	8.47507	+	4.72935i	0.459625	+	0.256485i
$341$	17.4647	−	10.0833i	0.945769	−	0.546040i
$342$	−3.46895	−	3.20906i	−0.187580	−	0.173526i
$343$	8.92504	+	16.2279i	0.481907	+	0.876222i
$344$	0.937485	−	1.62377i	0.0505458	−	0.0875479i
$345$	−4.54607	+	0.154900i	−0.244752	+	0.00833954i
$346$	−5.82392			−0.313096
$347$	−23.7875	+	23.7875i	−1.27698	+	1.27698i	−0.334630	+	0.942350i	$0.608611\pi$
$347$	−23.7875	+	23.7875i	−1.27698	+	1.27698i	−0.942350	+	0.334630i	$0.891389\pi$
$348$	−1.59999	+	0.0311222i	−0.0857686	+	0.00166833i
$349$	−16.9808	−	9.80384i	−0.908959	−	0.524788i	−0.0288628	−	0.999583i	$-0.509189\pi$
$349$	−16.9808	−	9.80384i	−0.908959	−	0.524788i	−0.880096	+	0.474796i	$0.842522\pi$
$350$	−7.34419	+	11.0029i	−0.392564	+	0.588127i
$351$	−6.22592	+	30.1780i	−0.332315	+	1.61078i
$352$	−1.62946	+	6.08124i	−0.0868507	+	0.324131i
$353$	4.95115	−	18.4779i	0.263523	−	0.983481i	−0.699625	−	0.714510i	$-0.746650\pi$
$353$	4.95115	−	18.4779i	0.263523	−	0.983481i	0.963148	−	0.268971i	$-0.0866836\pi$
$354$	3.46015	−	13.9968i	0.183905	−	0.743923i
$355$	−14.7672	+	15.2052i	−0.783763	+	0.807008i
$356$	−11.5669	+	6.67816i	−0.613045	+	0.353942i
$357$	−11.2035	+	16.4346i	−0.592951	+	0.869810i
$358$	−1.50313	−	5.60975i	−0.0794428	−	0.296485i
$359$	6.21763	+	10.7692i	0.328154	+	0.568379i	0.982146	−	0.188123i	$-0.0602403\pi$
$359$	6.21763	+	10.7692i	0.328154	+	0.568379i	−0.653992	+	0.756502i	$0.726907\pi$
$360$	5.98055	+	3.03859i	0.315203	+	0.160148i
$361$	−8.25935	+	14.3056i	−0.434703	+	0.752927i
$362$	−3.76955	+	3.76955i	−0.198123	+	0.198123i
$363$	0.964614	+	49.5907i	0.0506291	+	2.60284i
$364$	−15.6199	−	1.47560i	−0.818707	−	0.0773425i
$365$	6.52285	−	11.6891i	0.341421	−	0.611833i
$366$	−5.13798	+	20.7839i	−0.268567	+	1.08639i
$367$	−0.454718	+	1.69703i	−0.0237361	+	0.0885843i	−0.976778	−	0.214255i	$-0.931268\pi$
$367$	−0.454718	+	1.69703i	−0.0237361	+	0.0885843i	0.953042	+	0.302839i	$0.0979344\pi$
$368$	−1.13445	+	0.303976i	−0.0591374	+	0.0158458i
$369$	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
$372$	−2.86697	−	4.74993i	−0.148645	−	0.246273i
$373$	3.27088	+	12.2071i	0.169360	+	0.632060i	0.997444	+	0.0714555i	$0.0227644\pi$
$373$	3.27088	+	12.2071i	0.169360	+	0.632060i	−0.828084	+	0.560604i	$0.810569\pi$
$374$	27.3259			1.41299
$375$	3.81906	−	18.9846i	0.197216	−	0.980360i
$376$	−5.84918			−0.301648
$377$	−3.87422	+	3.87422i	−0.199532	+	0.199532i
$378$	−7.29609	+	11.6519i	−0.375271	+	0.599310i
$379$		−	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
$383$	−14.6830	+	3.93430i	−0.750266	+	0.201033i	−0.613636	−	0.789589i	$-0.710294\pi$
$383$	−14.6830	+	3.93430i	−0.750266	+	0.201033i	−0.136630	+	0.990622i	$0.543627\pi$
$384$	1.68143	+	0.415666i	0.0858053	+	0.0212119i
$385$	−2.96087	+	37.1284i	−0.150900	+	1.89224i
$386$		−	0.650387i		−	0.0331038i
$387$	−5.48575	−	1.24344i	−0.278856	−	0.0632078i
$388$	0.0223723	+	0.0834947i	0.00113578	+	0.00423880i
$389$	−4.46656	−	7.73631i	−0.226464	−	0.392247i	0.730294	−	0.683133i	$-0.239383\pi$
$389$	−4.46656	−	7.73631i	−0.226464	−	0.392247i	−0.956758	+	0.290887i	$0.906050\pi$
$390$	21.9692	−	6.69632i	1.11245	−	0.339082i
$391$	2.54881	+	4.41468i	0.128899	+	0.223260i
$392$	−6.30259	−	3.04588i	−0.318329	−	0.153840i
$393$	−9.94424	+	0.193430i	−0.501621	+	0.00975728i
$394$		−	6.27383i		−	0.316071i
$395$	−20.7455	+	21.3607i	−1.04382	+	1.07477i
$396$	18.8730	−	0.734495i	0.948404	−	0.0369097i
$397$	−1.85320	+	6.91625i	−0.0930096	+	0.347116i	−0.996710	−	0.0810486i	$-0.974173\pi$
$397$	−1.85320	+	6.91625i	−0.0930096	+	0.347116i	0.903701	+	0.428165i	$0.140840\pi$
$398$	8.65473	−	2.31903i	0.433822	−	0.116242i
$399$	−6.81360	−	2.38373i	−0.341107	−	0.119336i
$400$	−0.146091	−	4.99787i	−0.00730454	−	0.249893i
$401$	−5.47738	−	3.16237i	−0.273527	−	0.157921i	0.356962	−	0.934119i	$-0.383812\pi$
$401$	−5.47738	−	3.16237i	−0.273527	−	0.157921i	−0.630489	+	0.776198i	$0.717146\pi$
$402$	9.47723	−	5.72027i	0.472681	−	0.285301i
$403$	−18.3479	−	4.91631i	−0.913975	−	0.244899i
$404$	−5.66922	−	9.81937i	−0.282054	−	0.488532i
$405$	3.39267	−	19.8366i	0.168583	−	0.985687i
$406$	−2.22256	+	1.01772i	−0.110304	+	0.0505088i
$407$	−3.93782	−	14.6962i	−0.195191	−	0.728461i
$408$	−0.146203	−	7.51630i	−0.00723814	−	0.372112i
$409$		−	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
$412$	−4.37483	+	1.17223i	−0.215532	+	0.0577517i
$413$	−3.67420	−	21.7155i	−0.180796	−	1.06855i
$414$	1.87904	+	2.98055i	0.0923496	+	0.146486i
$415$	35.2285	+	19.6586i	1.72930	+	0.965002i
$416$	5.13559	−	2.96503i	0.251793	−	0.145373i
$417$	−1.35093	+	2.44866i	−0.0661555	+	0.119911i
$418$	2.56675	+	9.57926i	0.125544	+	0.468537i
$419$	15.9180	+	27.5708i	0.777645	+	1.34692i	0.933296	+	0.359108i	$0.116919\pi$
$419$	15.9180	+	27.5708i	0.777645	+	1.34692i	−0.155651	+	0.987812i	$0.549748\pi$
$420$	10.2284	+	0.615771i	0.499096	+	0.0300465i
$421$	4.03625	−	6.99099i	0.196715	−	0.340720i	−0.750747	−	0.660590i	$-0.770306\pi$
$421$	4.03625	−	6.99099i	0.196715	−	0.340720i	0.947461	+	0.319870i	$0.103639\pi$
$422$	2.52971	+	0.677835i	0.123145	+	0.0329965i
$423$	5.19734	+	16.7602i	0.252703	+	0.814908i
$424$	−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
$427$	5.45583	+	32.2454i	0.264026	+	1.56046i
$428$	0.274125	−	1.02305i	0.0132503	−	0.0494510i
$429$	44.8271	−	46.6056i	2.16427	−	2.25014i
$430$	1.14417	+	4.03342i	0.0551767	+	0.194509i
$431$	21.0923	+	12.1776i	1.01598	+	0.586576i	0.912937	−	0.408101i	$-0.133809\pi$
$431$	21.0923	+	12.1776i	1.01598	+	0.586576i	0.103042	+	0.994677i	$0.467142\pi$
$432$	−0.303009	−	5.18731i	−0.0145785	−	0.249575i
$433$	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
$435$	2.44265	−	2.61499i	0.117116	−	0.125379i
$436$	0.116303	−	0.201442i	0.00556989	−	0.00964734i
$437$	−1.30818	+	1.30818i	−0.0625787	+	0.0625787i
$438$	−10.3667	+	0.201648i	−0.495339	+	0.00963510i
$439$		−	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	0.660792	−	0.750569i	$-0.270221\pi$
$443$	−1.88960	−	1.88960i	−0.0897778	−	0.0897778i	−0.750569	+	0.660792i	$0.770221\pi$
$444$	−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
$447$	0.268999	+	13.8292i	0.0127232	+	0.654100i
$448$	2.60867	−	0.441381i	0.123248	−	0.0208533i
$449$	−15.7386			−0.742749			−0.371374	−	0.928483i	$-0.621113\pi$
$449$	−15.7386			−0.742749			−0.371374	+	0.928483i	$0.621113\pi$
$450$	−14.1910	+	4.85951i	−0.668971	+	0.229079i
$451$	21.6090	−	37.4279i	1.01753	−	1.76241i
$452$	14.7105	+	3.94167i	0.691924	+	0.185401i
$453$	−8.10561	−	4.47189i	−0.380835	−	0.210108i
$454$	21.6577	−	12.5041i	1.01644	−	0.586844i
$455$	26.7008	−	22.7567i	1.25175	−	1.06685i
$456$	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	$0.679971\pi$
$458$	−8.85496	+	2.37268i	−0.413765	+	0.110868i
$459$	−21.4072	+	7.09761i	−0.999204	+	0.331288i
$460$	1.27973	−	2.29330i	0.0596677	−	0.106926i
$461$	−23.1959	−	13.3922i	−1.08034	−	0.623735i	−0.149352	−	0.988784i	$-0.547719\pi$
$461$	−23.1959	−	13.3922i	−1.08034	−	0.623735i	−0.930988	+	0.365049i	$0.881052\pi$
$462$	25.9929	−	12.5194i	1.20930	−	0.582457i
$463$	−40.0588	−	10.7337i	−1.86169	−	0.498838i	−0.861725	−	0.507376i	$-0.830616\pi$
$463$	−40.0588	−	10.7337i	−1.86169	−	0.498838i	−0.999964	+	0.00853803i	$0.997282\pi$
$464$	0.461965	−	0.800147i	0.0214462	−	0.0371459i
$465$	12.0856	+	2.80095i	0.560456	+	0.129891i
$466$	10.6104	+	18.3778i	0.491519	+	0.851335i
$467$	23.6435	+	6.33527i	1.09409	+	0.293161i	0.760357	−	0.649505i	$-0.225024\pi$
$467$	23.6435	+	6.33527i	1.09409	+	0.293161i	0.333736	+	0.942667i	$0.391691\pi$
$468$	−13.0593	−	12.0809i	−0.603664	−	0.558438i
$469$	9.79445	−	13.7838i	0.452266	−	0.636478i
$470$	9.11225	−	9.38250i	0.420317	−	0.432782i
$471$	−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
$475$	−4.13565	−	6.70291i	−0.189757	−	0.307550i
$476$	−4.78097	−	10.4409i	−0.219136	−	0.478560i
$477$	−4.06415	+	17.9300i	−0.186084	+	0.820957i
$478$	−5.72792	−	1.53479i	−0.261989	−	0.0701998i
$479$	1.67282	+	2.89742i	0.0764333	+	0.132386i	0.901709	−	0.432344i	$-0.142313\pi$
$479$	1.67282	+	2.89742i	0.0764333	+	0.132386i	−0.825275	+	0.564731i	$0.808980\pi$
$480$	−3.28621	+	2.04959i	−0.149994	+	0.0935505i
$481$	−7.16541	+	12.4109i	−0.326715	+	0.565886i
$482$	−21.9292	−	5.87592i	−0.998850	−	0.267641i
$483$	4.44708	+	3.03158i	0.202349	+	0.137942i
$484$	−24.8001	−	14.3183i	−1.12728	−	0.650833i
$485$	−0.168785	−	0.0941869i	−0.00766411	−	0.00427681i
$486$	−14.5944	+	5.47747i	−0.662017	+	0.248463i
$487$	13.4334	−	3.59947i	0.608726	−	0.163108i	0.0587288	−	0.998274i	$-0.481295\pi$
$487$	13.4334	−	3.59947i	0.608726	−	0.163108i	0.549998	+	0.835166i	$0.314629\pi$
$488$	−8.74043	−	8.74043i	−0.395661	−	0.395661i
$489$	−26.7601	+	7.73116i	−1.21013	+	0.349615i
$490$	14.7044	−	5.36471i	0.664278	−	0.242353i
$491$	−31.2490	+	18.0416i	−1.41025	+	0.814207i	−0.995411	−	0.0956893i	$-0.969494\pi$
$491$	−31.2490	+	18.0416i	−1.41025	+	0.814207i	−0.414836	+	0.909896i	$0.636161\pi$
$492$	−10.4106	−	5.74356i	−0.469346	−	0.258940i
$493$	−3.87355	−	1.03791i	−0.174456	−	0.0467453i
$494$	4.67056	−	8.08965i	0.210139	−	0.363971i
$495$	−28.2235	+	31.4179i	−1.26855	+	1.41213i
$496$	3.20319			0.143828
$497$	24.7280	−	4.18390i	1.10920	−	0.187674i
$498$	−0.607727	−	31.2432i	−0.0272329	−	1.40004i
$499$	−30.9349	−	17.8603i	−1.38484	−	0.799535i	−0.392109	−	0.919919i	$-0.628254\pi$
$499$	−30.9349	−	17.8603i	−1.38484	−	0.799535i	−0.992727	+	0.120383i	$0.961588\pi$
$500$	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	0.988678	−	0.150050i	$-0.0479436\pi$
$503$	18.8085	+	18.8085i	0.838628	+	0.838628i	−0.150050	+	0.988678i	$0.547944\pi$
$504$	−3.58269	−	7.08268i	−0.159586	−	0.315488i
$505$	24.5829	+	6.20346i	1.09392	+	0.276050i
$506$		−	7.39420i		−	0.328712i
$507$	−38.3848	+	0.746643i	−1.70473	+	0.0331596i
$508$	8.24335	−	8.24335i	0.365740	−	0.365740i
$509$	13.8762	−	24.0343i	0.615052	−	1.06530i	−0.375323	−	0.926894i	$-0.622468\pi$
$509$	13.8762	−	24.0343i	0.615052	−	1.06530i	0.990375	−	0.138408i	$-0.0441984\pi$
$510$	12.2845	+	11.4749i	0.543965	+	0.508117i
$511$	−14.4004	+	6.59405i	−0.637038	+	0.291704i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.49892	−	6.83775i	−0.198632	−	0.301894i
$514$	−12.0533	−	6.95899i	−0.531649	−	0.306948i
$515$	4.93506	−	8.84371i	0.217465	−	0.389701i
$516$	2.25127	−	2.34058i	0.0991065	−	0.103039i
$517$	9.53102	−	35.5702i	0.419174	−	1.56438i
$518$	−4.92629	+	4.07586i	−0.216449	+	0.179083i
$519$	−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	0.992058	−	0.125780i	$-0.0401434\pi$
$521$	31.4799	+	18.1749i	1.37916	+	0.796257i	0.387100	+	0.922038i	$0.373477\pi$
$522$	−2.70322	−	0.612732i	−0.118317	−	0.0268186i
$523$	28.4540	+	7.62423i	1.24421	+	0.333384i	0.820096	−	0.572226i	$-0.193920\pi$
$523$	28.4540	+	7.62423i	1.24421	+	0.333384i	0.424111	+	0.905610i	$0.360587\pi$
$524$	2.87120	−	4.97306i	0.125429	−	0.217249i
$525$	−16.9223	+	15.4478i	−0.738549	+	0.674199i
$526$	2.70571	+	4.68642i	0.117974	+	0.204338i
$527$	−3.59836	−	13.4293i	−0.156747	−	0.584989i
$528$	−5.26760	+	9.54789i	−0.229243	+	0.415519i
$529$	−18.7240	+	10.8103i	−0.814087	+	0.470013i
$530$	13.1831	−	3.73967i	0.572636	−	0.162441i
$531$	11.6360	−	22.0965i	0.504960	−	0.958906i
$532$	3.21106	−	2.65673i	0.139217	−	0.115184i
$533$	−39.3206	+	10.5359i	−1.70316	+	0.456361i
$534$	−22.2249	+	6.42092i	−0.961765	+	0.277860i
$535$	1.21399	+	2.03349i	0.0524855	+	0.0879156i
$536$			6.39112i			0.276055i
$537$	−0.195628	−	10.0572i	−0.00844198	−	0.434002i
$538$	7.25658	+	27.0819i	0.312853	+	1.16759i
$539$	28.7926	−	33.3644i	1.24018	−	1.43711i
$540$	8.79286	+	7.59510i	0.378385	+	0.326841i
$541$	2.92530	+	5.06677i	0.125769	+	0.217838i	0.922033	−	0.387111i	$-0.126527\pi$
$541$	2.92530	+	5.06677i	0.125769	+	0.217838i	−0.796265	+	0.604949i	$0.793194\pi$
$542$	8.49910	+	2.27733i	0.365068	+	0.0978196i
$543$	−7.90513	+	4.77138i	−0.339242	+	0.204760i
$544$	3.75886	+	2.17018i	0.161160	+	0.0930457i
$545$	0.141943	+	0.500379i	0.00608019	+	0.0214339i
$546$	−25.6505	−	8.97380i	−1.09774	−	0.384043i
$547$	33.3167	−	8.92718i	1.42452	−	0.381699i	0.537434	−	0.843306i	$-0.319394\pi$
$547$	33.3167	−	8.92718i	1.42452	−	0.381699i	0.887085	+	0.461607i	$0.152727\pi$
$548$	−1.05479	+	3.93655i	−0.0450586	+	0.168161i
$549$	−17.2784	+	32.8112i	−0.737422	+	1.40035i
$550$	30.6313	+	7.25543i	1.30612	+	0.309372i
$551$		−	1.45539i		−	0.0620017i
$552$	−2.03386	+	0.0395616i	−0.0865668	+	0.00168385i
$553$	34.7386	−	5.87767i	1.47723	−	0.249944i
$554$	6.75498	+	11.7000i	0.286992	+	0.497084i
$555$	4.40106	−	8.26031i	0.186814	−	0.350631i
$556$	−0.807308	−	1.39830i	−0.0342375	−	0.0593011i
$557$	−9.37795	−	34.9990i	−0.397356	−	1.48295i	−0.817729	−	0.575603i	$-0.804767\pi$
$557$	−9.37795	−	34.9990i	−0.397356	−	1.48295i	0.420373	−	0.907351i	$-0.361899\pi$
$558$	−2.84623	−	9.17840i	−0.120490	−	0.388553i
$559$		−	11.1187i		−	0.470271i
$560$	−3.35597	+	4.87211i	−0.141815	+	0.205884i
$561$	45.9467	+	11.3584i	1.93987	+	0.479554i
$562$	16.1149	−	4.31797i	0.679766	−	0.182143i
$563$	10.7610	+	10.7610i	0.453523	+	0.453523i	0.896522	−	0.442999i	$-0.146086\pi$
$563$	10.7610	+	10.7610i	0.453523	+	0.453523i	−0.442999	+	0.896522i	$0.646086\pi$
$564$	−9.83501	−	2.43130i	−0.414128	−	0.102376i
$565$	−29.2398	+	17.4561i	−1.23013	+	0.734384i
$566$			13.7363i			0.577380i
$567$	−17.1112	+	16.5592i	−0.718603	+	0.695420i
$568$	−6.70276	+	6.70276i	−0.281241	+	0.281241i
$569$	13.4096			0.562160			0.281080	−	0.959684i	$-0.409307\pi$
$569$	13.4096			0.562160			0.281080	+	0.959684i	$0.409307\pi$
$570$	−2.86870	+	5.38424i	−0.120157	+	0.225521i
$571$	12.1254			0.507434			0.253717	−	0.967278i	$-0.418347\pi$
$571$	12.1254			0.507434			0.253717	+	0.967278i	$0.418347\pi$
$572$	9.66283	+	36.0622i	0.404023	+	1.50783i
$573$	1.17453	+	1.94594i	0.0490668	+	0.0812929i
$574$	−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
$577$	45.2410	−	12.1223i	1.88341	−	0.504657i	0.884106	−	0.467287i	$-0.154769\pi$
$577$	45.2410	−	12.1223i	1.88341	−	0.504657i	0.999301	−	0.0373702i	$-0.0118981\pi$
$578$	0.475896	−	1.77607i	0.0197946	−	0.0738746i
$579$	0.270344	−	1.09358i	0.0112351	−	0.0454478i
$580$	0.563812	+	1.98755i	0.0234110	+	0.0825285i
$581$	−19.8732	−	43.4001i	−0.824478	−	1.80054i
$582$	0.00291170	+	0.149690i	0.000120694	+	0.00620486i
$583$	27.2817	−	27.2817i	1.12989	−	1.12989i
$584$	2.99317	−	5.18432i	0.123858	−	0.214529i
$585$	39.7232	−	2.12759i	1.64235	−	0.0879649i
$586$	−2.81149	−	4.86964i	−0.116142	−	0.201163i
$587$	1.68871	+	6.30235i	0.0697005	+	0.260126i	0.991979	−	0.126399i	$-0.0403420\pi$
$587$	1.68871	+	6.30235i	0.0697005	+	0.260126i	−0.922279	+	0.386525i	$0.873675\pi$
$588$	−9.33131	−	7.74122i	−0.384817	−	0.319243i
$589$	4.36972	−	2.52286i	0.180051	−	0.103953i
$590$	−18.6118	+	0.271959i	−0.766236	+	0.0111964i
$591$	2.60782	−	10.5490i	0.107271	−	0.433929i
$592$	0.625472	−	2.33429i	0.0257067	−	0.0959388i
$593$	2.13956	−	7.98493i	0.0878610	−	0.327902i	−0.907980	−	0.419014i	$-0.862376\pi$
$593$	2.13956	−	7.98493i	0.0878610	−	0.327902i	0.995841	+	0.0911127i	$0.0290423\pi$
$594$	32.0390	+	6.60986i	1.31458	+	0.271206i
$595$	24.1962	+	8.59660i	0.991945	+	0.352426i
$596$	−6.91592	−	3.99291i	−0.283287	−	0.163556i
$597$	15.5163	−	0.301815i	0.635040	−	0.0123525i
$598$	−4.92478	+	4.92478i	−0.201389	+	0.201389i
$599$	5.64607			0.230692			0.115346	−	0.993325i	$-0.463202\pi$
$599$	5.64607			0.230692			0.115346	+	0.993325i	$0.463202\pi$
$600$	1.83180	−	8.46431i	0.0747830	−	0.345554i
$601$	6.35844	−	11.0131i	0.259366	−	0.449236i	−0.706706	−	0.707507i	$-0.749820\pi$
$601$	6.35844	−	11.0131i	0.259366	−	0.449236i	0.966072	+	0.258272i	$0.0831530\pi$
$602$	1.72889	−	4.64968i	0.0704644	−	0.189507i
$603$	18.3131	−	5.67889i	0.745766	−	0.231262i
$604$	4.62868	−	2.67237i	0.188338	−	0.108737i
$605$	61.6028	−	17.4750i	2.50451	−	0.710460i
$606$	−5.45084	−	18.8671i	−0.221425	−	0.766425i
$607$	16.0087	−	4.28953i	0.649774	−	0.174106i	0.0811474	−	0.996702i	$-0.474142\pi$
$607$	16.0087	−	4.28953i	0.649774	−	0.174106i	0.568627	+	0.822596i	$0.307475\pi$
$608$	−0.407696	+	1.52154i	−0.0165342	+	0.0617066i
$609$	−4.16012	+	0.787393i	−0.168577	+	0.0319068i
$610$	27.6367	−	0.403833i	1.11898	−	0.0163507i
$611$	−30.0390	+	17.3430i	−1.21525	+	0.701623i
$612$	2.87844	−	12.6989i	0.116354	−	0.513324i
$613$	7.55823	+	28.2077i	0.305274	+	1.13930i	0.932709	+	0.360629i	$0.117438\pi$
$613$	7.55823	+	28.2077i	0.305274	+	1.13930i	−0.627435	+	0.778669i	$0.715895\pi$
$614$	−6.66347			−0.268916
$615$	25.4314	−	7.75163i	1.02549	−	0.312576i
$616$	−1.56660	+	16.5832i	−0.0631201	+	0.668156i
$617$	18.1977	+	4.87605i	0.732610	+	0.196302i	0.605791	−	0.795624i	$-0.292857\pi$
$617$	18.1977	+	4.87605i	0.732610	+	0.196302i	0.126819	+	0.991926i	$0.459523\pi$
$618$	−7.84324	+	0.152563i	−0.315501	+	0.00613697i
$619$	−3.20771	+	1.85197i	−0.128929	+	0.0744370i	−0.563077	−	0.826404i	$-0.690383\pi$
$619$	−3.20771	+	1.85197i	−0.128929	+	0.0744370i	0.434148	+	0.900841i	$0.357049\pi$
$620$	−4.99016	+	5.13815i	−0.200409	+	0.206353i
$621$	1.92056	+	5.79265i	0.0770696	+	0.232451i
$622$	14.8697	+	14.8697i	0.596220	+	0.596220i
$623$	−27.2267	+	22.5266i	−1.09082	+	0.902508i
$624$	9.86762	−	2.85082i	0.395021	−	0.114124i
$625$	−24.9573	+	1.46028i	−0.998293	+	0.0584114i
$626$			0.406255i			0.0162372i
$627$	0.334056	+	17.1738i	0.0133409	+	0.685856i
$628$	16.0894	−	16.0894i	0.642036	−	0.642036i
$629$	−10.4891			−0.418227
$630$	16.9425	+	5.28699i	0.675005	+	0.210639i
$631$	−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
$633$	3.97180	+	2.19125i	0.157865	+	0.0870944i
$634$			9.30159i			0.369413i
$635$	0.380867	+	26.0650i	0.0151142	+	1.03436i
$636$	−7.65011	−	7.35818i	−0.303347	−	0.291771i
$637$	−41.3986	+	3.04497i	−1.64027	+	0.120646i
$638$	4.11313	+	4.11313i	0.162840	+	0.162840i
$639$	25.1618	+	13.2502i	0.995386	+	0.524170i
$640$	−0.0326704	−	2.23583i	−0.00129141	−	0.0883789i
$641$	1.34965	−	0.779223i	0.0533081	−	0.0307774i	−0.473109	−	0.881004i	$-0.656868\pi$
$641$	1.34965	−	0.779223i	0.0533081	−	0.0307774i	0.526417	+	0.850226i	$0.323535\pi$
$642$	0.886171	−	1.60625i	0.0349744	−	0.0633935i
$643$	8.46183	+	2.26734i	0.333702	+	0.0894152i	0.421780	−	0.906698i	$-0.361406\pi$
$643$	8.46183	+	2.26734i	0.333702	+	0.0894152i	−0.0880774	+	0.996114i	$0.528072\pi$
$644$	−2.82525	+	1.29370i	−0.111330	+	0.0509789i
$645$	0.247288	+	7.25752i	0.00973696	+	0.285764i
$646$	6.83700			0.268998
$647$	3.76645	+	14.0566i	0.148074	+	0.552621i	0.999599	+	0.0283070i	$0.00901159\pi$
$647$	3.76645	+	14.0566i	0.148074	+	0.552621i	−0.851525	+	0.524314i	$0.824322\pi$
$648$	1.64670	−	8.84807i	0.0646885	−	0.347585i
$649$	−45.3867	+	26.2040i	−1.78158	+	1.02860i
$650$	−15.5691	−	25.2338i	−0.610670	−	0.989752i
$651$	−9.57551	−	11.1256i	−0.375294	−	0.436047i
$652$	4.16228	−	15.5338i	0.163007	−	0.608351i
$653$	−27.7389	+	7.43262i	−1.08551	+	0.290861i	−0.756850	−	0.653588i	$-0.773263\pi$
$653$	−27.7389	+	7.43262i	−1.08551	+	0.290861i	−0.328657	+	0.944449i	$0.606596\pi$
$654$	0.279288	−	0.290369i	0.0109210	−	0.0113543i
$655$	3.50420	+	12.3530i	0.136920	+	0.482671i
$656$	5.94493	−	3.43231i	0.232111	−	0.134009i
$657$	−17.5147	−	3.97002i	−0.683314	−	0.154885i
$658$	−15.2586	+	2.58171i	−0.594842	+	0.100646i
$659$	9.41467	−	16.3067i	0.366743	−	0.635218i	−0.622311	−	0.782770i	$-0.713806\pi$
$659$	9.41467	−	16.3067i	0.366743	−	0.635218i	0.989054	+	0.147552i	$0.0471393\pi$
$660$	−7.10927	−	23.3240i	−0.276728	−	0.907885i
$661$	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
$663$	−23.0369	−	38.1671i	−0.894680	−	1.48229i
$664$	15.6245	+	9.02083i	0.606350	+	0.350076i
$665$	−0.740816	+	9.28960i	−0.0287276	+	0.360235i
$666$	−7.24443	+	0.281937i	−0.280716	+	0.0109248i
$667$	−0.280852	+	1.04816i	−0.0108746	+	0.0405847i
$668$	−0.856206	+	3.19541i	−0.0331276	+	0.123634i
$669$	31.3247	+	30.1293i	1.21108	+	1.16487i
$670$	−10.2518	−	9.95653i	−0.396062	−	0.384654i
$671$	67.3949	−	38.9105i	2.60175	−	1.50212i
$672$	4.56978	+	0.342185i	0.176283	+	0.0132001i
$673$	6.42725	+	23.9868i	0.247752	+	0.924624i	0.971980	+	0.235063i	$0.0755297\pi$
$673$	6.42725	+	23.9868i	0.247752	+	0.924624i	−0.724228	+	0.689561i	$0.757804\pi$
$674$	12.7209	+	22.0332i	0.489990	+	0.848687i
$675$	−25.8812	+	2.27222i	−0.996168	+	0.0874576i
$676$	11.0828	−	19.1961i	0.426263	−	0.738310i
$677$	−12.5245	+	12.5245i	−0.481355	+	0.481355i	−0.905564	−	0.424209i	$-0.860552\pi$
$677$	−12.5245	+	12.5245i	−0.481355	+	0.481355i	0.424209	+	0.905564i	$0.360552\pi$
$678$	23.0963	+	12.7423i	0.887010	+	0.489366i
$679$	0.0952151	+	0.207936i	0.00365402	+	0.00797984i
$680$	−9.33694	+	2.64863i	−0.358055	+	0.101570i
$681$	41.6134	−	12.0224i	1.59463	−	0.460699i
$682$	−5.21949	+	19.4794i	−0.199865	+	0.745905i
$683$	−19.4964	+	5.22405i	−0.746010	+	0.199893i	−0.611748	−	0.791053i	$-0.709533\pi$
$683$	−19.4964	+	5.22405i	−0.746010	+	0.199893i	−0.134262	+	0.990946i	$0.542866\pi$
$684$	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
$687$	−15.8753	+	0.308798i	−0.605680	+	0.0117814i
$688$	0.485278	+	1.81108i	0.0185010	+	0.0690469i
$689$	−36.3410			−1.38448
$690$	3.10503	−	3.32409i	0.118206	−	0.126546i
$691$	−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
$693$	48.9093	−	10.2462i	1.85791	−	0.389222i
$694$		−	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
$698$	18.9396	−	5.07484i	0.716873	−	0.192086i
$699$	10.2017	+	35.3115i	0.385864	+	1.33560i
$700$	−2.58706	−	12.9733i	−0.0977818	−	0.490346i
$701$			26.6507i			1.00658i	0.864117	+	0.503292i	$0.167878\pi$
$701$			26.6507i			1.00658i	−0.864117	+	0.503292i	$0.832122\pi$
$702$	−16.9367	−	25.7415i	−0.639234	−	0.971549i
$703$	−0.985252	−	3.67701i	−0.0371595	−	0.138681i
$704$	−3.14788	−	5.45229i	−0.118640	−	0.205491i
$705$	19.2216	−	11.9884i	0.723929	−	0.451509i
$706$	9.56488	+	16.5669i	0.359979	+	0.623502i
$707$	−19.1232	−	23.1133i	−0.719203	−	0.869264i
$708$	7.45056	+	12.3439i	0.280009	+	0.463914i
$709$			51.6335i			1.93914i	0.244817	+	0.969569i	$0.421272\pi$
$709$			51.6335i			1.93914i	−0.244817	+	0.969569i	$0.578728\pi$
$710$	−0.309687	−	21.1937i	−0.0116223	−	0.795386i
$711$	35.3481	+	18.6143i	1.32566	+	0.698091i
$712$	3.45687	−	12.9012i	0.129552	−	0.483494i
$713$	−3.63387	+	0.973693i	−0.136090	+	0.0364651i
$714$	−3.69895	−	19.5431i	−0.138430	−	0.731380i
$715$	−72.8997	−	40.6802i	−2.72629	−	1.52135i
$716$	5.02957	+	2.90382i	0.187964	+	0.108521i
$717$	−8.99317	−	4.96156i	−0.335856	−	0.185293i
$718$	−12.0115	−	3.21848i	−0.448266	−	0.120113i
$719$	−6.06041	−	10.4969i	−0.226015	−	0.391469i	0.730608	−	0.682797i	$-0.239237\pi$
$719$	−6.06041	−	10.4969i	−0.226015	−	0.391469i	−0.956623	+	0.291327i	$0.905903\pi$
$720$	−6.37749	+	2.08028i	−0.237675	+	0.0775275i
$721$	−10.8951	+	4.98893i	−0.405755	+	0.185798i
$722$	−4.27535	−	15.9558i	−0.159112	−	0.593815i
$723$	−34.4302	−	18.9952i	−1.28047	−	0.706440i
$724$		−	5.33095i		−	0.198123i
$725$	−4.06652	−	2.19195i	−0.151027	−	0.0814068i
$726$	−35.7480	−	34.3839i	−1.32673	−	1.27610i
$727$	−28.9765	+	7.76423i	−1.07468	+	0.287959i	−0.752414	−	0.658690i	$-0.771111\pi$
$727$	−28.9765	+	7.76423i	−1.07468	+	0.287959i	−0.322265	+	0.946649i	$0.604444\pi$
$728$	12.0884	−	10.0016i	0.448025	−	0.370682i
$729$	−26.8164	+	3.14360i	−0.993199	+	0.116430i
$730$	3.65306	+	12.8778i	0.135206	+	0.476627i
$731$	7.04775	−	4.06902i	0.260671	−	0.150498i
$732$	−11.0634	−	18.3296i	−0.408914	−	0.677480i
$733$	1.12373	+	4.19382i	0.0415059	+	0.154902i	0.983569	−	0.180535i	$-0.0577828\pi$
$733$	1.12373	+	4.19382i	0.0415059	+	0.154902i	−0.942063	+	0.335437i	$0.891116\pi$
$734$	−0.878448	−	1.52152i	−0.0324241	−	0.0561602i
$735$	26.9544	−	2.90829i	0.994230	−	0.107274i
$736$	0.587236	−	1.01712i	0.0216458	−	0.0374916i
$737$	−38.8660	−	10.4141i	−1.43165	−	0.383608i
$738$	−15.1173	−	13.9847i	−0.556477	−	0.514786i
$739$	18.6590	+	10.7728i	0.686382	+	0.396283i	0.802255	−	0.596981i	$-0.203633\pi$
$739$	18.6590	+	10.7728i	0.686382	+	0.396283i	−0.115873	+	0.993264i	$0.536967\pi$
$740$	2.76997	+	4.63982i	0.101826	+	0.170563i
$741$	11.2158	−	11.6608i	0.412024	−	0.428371i
$742$	−15.1973	−	5.65082i	−0.557910	−	0.207448i
$743$	4.26833	−	15.9296i	0.156590	−	0.584401i	−0.842374	−	0.538893i	$-0.818843\pi$
$743$	4.26833	−	15.9296i	0.156590	−	0.584401i	0.998964	−	0.0455079i	$-0.0144906\pi$
$744$	5.38596	+	1.33146i	0.197459	+	0.0488137i
$745$	17.1790	−	4.87320i	0.629390	−	0.178540i
$746$	−10.9446	−	6.31886i	−0.400710	−	0.231350i
$747$	11.9649	−	52.7860i	0.437772	−	1.93134i
$748$	−19.3223	+	19.3223i	−0.706494	+	0.706494i
$749$	0.263550	−	2.78980i	0.00962989	−	0.101937i
$750$	10.7236	+	16.1246i	0.391572	+	0.588788i
$751$	−8.13144	+	14.0841i	−0.296721	+	0.513935i	−0.975384	−	0.220515i	$-0.929226\pi$
$751$	−8.13144	+	14.0841i	−0.296721	+	0.513935i	0.678663	+	0.734450i	$0.262560\pi$
$752$	4.13599	−	4.13599i	0.150824	−	0.150824i
$753$	7.04676	+	11.6749i	0.256798	+	0.425458i
$754$		−	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	0.944333	−	0.328991i	$-0.106709\pi$
$761$	31.2162	+	18.0227i	1.13159	+	0.653321i	0.187252	+	0.982312i	$0.440042\pi$
$762$	17.2871	−	10.4342i	0.626247	−	0.377990i
$763$	0.214483	−	0.576831i	0.00776482	−	0.0208827i
$764$	−1.31228			−0.0474766
$765$	15.8858	+	24.4005i	0.574351	+	0.882202i
$766$	7.60048	−	13.1644i	0.274616	−	0.475650i
$767$	47.6818	+	12.7763i	1.72169	+	0.461326i
$768$	−1.48287	+	0.895033i	−0.0535086	+	0.0322967i
$769$	8.44111	−	4.87348i	0.304394	−	0.175742i	−0.340021	−	0.940418i	$-0.610434\pi$
$769$	8.44111	−	4.87348i	0.304394	−	0.175742i	0.644415	+	0.764676i	$0.277101\pi$
$770$	−24.1601	−	28.3474i	−0.870669	−	1.02157i
$771$	−17.3742	−	16.7112i	−0.625718	−	0.601840i
$772$	0.459893	+	0.459893i	0.0165519	+	0.0165519i
$773$	−18.7358	+	5.02024i	−0.673880	+	0.180566i	−0.579502	−	0.814971i	$-0.696753\pi$
$773$	−18.7358	+	5.02024i	−0.673880	+	0.180566i	−0.0943779	+	0.995536i	$0.530086\pi$
$774$	4.75826	−	2.99976i	0.171032	−	0.107824i
$775$	−0.467957	−	16.0091i	−0.0168095	−	0.575065i
$776$	−0.0748593	−	0.0432200i	−0.00268729	−	0.00155151i
$777$	−9.97742	+	4.80560i	−0.357938	+	0.172400i
$778$	8.62873	+	2.31206i	0.309355	+	0.0828915i
$779$	5.40662	−	9.36455i	0.193712	−	0.335520i
$780$	−10.7995	+	20.2696i	−0.386685	+	0.725767i
$781$	−29.8392	−	51.6830i	−1.06773	−	1.84936i
$782$	−4.92393	−	1.31936i	−0.176079	−	0.0471803i
$783$	−4.29059	−	2.15391i	−0.153333	−	0.0769743i
$784$	6.61037	−	2.30284i	0.236085	−	0.0822442i
$785$	0.743376	+	50.8737i	0.0265322	+	1.81576i
$786$	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
$790$	−0.435057	−	29.7736i	−0.0154786	−	1.05930i
$791$	40.1147	+	3.78960i	1.42632	+	0.134743i
$792$	−12.8259	+	13.8646i	−0.455747	+	0.492657i
$793$	−70.8029	−	18.9716i	−2.51429	−	0.673701i
$794$	−3.58011	−	6.20094i	−0.127053	−	0.220063i
$795$	23.7209	−	0.808252i	0.841294	−	0.0286657i
$796$	−4.48002	+	7.75962i	−0.158790	+	0.275032i
$797$	−25.4066	−	6.80768i	−0.899948	−	0.241140i	−0.220954	−	0.975284i	$-0.570917\pi$
$797$	−25.4066	−	6.80768i	−0.899948	−	0.241140i	−0.678994	+	0.734144i	$0.737584\pi$
$798$	6.50349	−	3.13239i	0.230221	−	0.110886i
$799$	−21.9862	−	12.6938i	−0.777817	−	0.449073i
$800$	3.63733	+	3.43072i	0.128599	+	0.121294i
$801$	−40.0387	+	1.55821i	−1.41470	+	0.0550568i
$802$	6.10922	−	1.63696i	0.215724	−	0.0578031i
$803$	26.6499	+	26.6499i	0.940453	+	0.940453i
$804$	−2.65657	+	10.7463i	−0.0936901	+	0.378991i
$805$	2.32618	−	6.54731i	0.0819871	−	0.230762i
$806$	16.4503	−	9.49758i	0.579437	−	0.334538i
$807$	0.944425	+	48.5528i	0.0332453	+	1.70914i
$808$	10.9521	+	2.93460i	0.385293	+	0.103239i
$809$	−21.7494	+	37.6710i	−0.764667	+	1.32444i	0.175755	+	0.984434i	$0.443763\pi$
$809$	−21.7494	+	37.6710i	−0.764667	+	1.32444i	−0.940422	+	0.340009i	$0.889570\pi$
$810$	11.6276	+	16.4256i	0.408552	+	0.577135i
$811$	−0.175349			−0.00615732			−0.00307866	−	0.999995i	$-0.500980\pi$
$811$	−0.175349			−0.00615732			−0.00307866	+	0.999995i	$0.500980\pi$
$812$	0.851948	−	2.29123i	0.0298975	−	0.0804063i
$813$	13.3441	+	7.36196i	0.467997	+	0.258195i
$814$	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	$0.0539097\pi$
$821$			9.65918i			0.337108i	−0.985692	+	0.168554i	$0.946090\pi$
$822$	−3.40986	+	6.18061i	−0.118932	+	0.215573i
$823$	−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
$825$	48.4886	+	24.9319i	1.68816	+	0.868018i
$826$	17.9532	+	12.7571i	0.624672	+	0.443877i
$827$	−10.0375	+	10.0375i	−0.349039	+	0.349039i	−0.859751	−	0.510713i	$-0.829382\pi$
$827$	−10.0375	+	10.0375i	−0.349039	+	0.349039i	0.510713	+	0.859751i	$0.329382\pi$
$828$	−3.43625	−	0.778886i	−0.119418	−	0.0270682i
$829$	−10.9598	−	6.32766i	−0.380651	−	0.219769i	0.297451	−	0.954737i	$-0.403864\pi$
$829$	−10.9598	−	6.32766i	−0.380651	−	0.219769i	−0.678101	+	0.734968i	$0.737197\pi$
$830$	−38.8110	+	11.0096i	−1.34715	+	0.382149i
$831$	6.49478	+	22.4805i	0.225301	+	0.779842i
$832$	−1.53481	+	5.72800i	−0.0532101	+	0.198583i
$833$	−17.0804	−	25.1268i	−0.591802	−	0.870592i
$834$	−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
$837$	−0.970596	−	16.6160i	−0.0335487	−	0.574332i
$838$	−30.7512	−	8.23976i	−1.06228	−	0.284638i
$839$	27.0536	−	46.8582i	0.933994	−	1.61772i	0.157575	−	0.987507i	$-0.449632\pi$
$839$	27.0536	−	46.8582i	0.933994	−	1.61772i	0.776419	−	0.630217i	$-0.217034\pi$
$840$	−7.66801	+	6.79718i	−0.264571	+	0.234525i
$841$	14.0732	+	24.3755i	0.485282	+	0.840533i
$842$	2.08932	+	7.79743i	0.0720026	+	0.268717i
$843$	28.8910	−	0.561973i	0.995058	−	0.0193554i
$844$	−2.26808	+	1.30948i	−0.0780705	+	0.0450740i
$845$	13.5262	+	47.6826i	0.465316	+	1.64033i
$846$	−15.5263	−	8.17616i	−0.533805	−	0.281102i
$847$	−71.0151	−	26.4056i	−2.44011	−	0.907306i
$848$	5.91945	−	1.58611i	0.203275	−	0.0544673i
$849$	−5.70972	+	23.0967i	−0.195957	+	0.792677i
$850$	10.2971	−	19.1033i	0.353189	−	0.655239i
$851$			2.83827i			0.0972947i
$852$	−14.0564	+	8.48414i	−0.481563	+	0.290662i
$853$	9.62299	+	35.9135i	0.329485	+	1.22965i	0.909726	+	0.415210i	$0.136292\pi$
$853$	9.62299	+	35.9135i	0.329485	+	1.22965i	−0.580241	+	0.814445i	$0.697042\pi$
$854$	−26.6588	−	18.9431i	−0.912246	−	0.648219i
$855$	−7.06158	+	7.86083i	−0.241501	+	0.268835i
$856$	0.529570	+	0.917241i	0.0181003	+	0.0313507i
$857$	−29.6840	−	7.95381i	−1.01399	−	0.271697i	−0.286693	−	0.958023i	$-0.592556\pi$
$857$	−29.6840	−	7.95381i	−1.01399	−	0.271697i	−0.727294	+	0.686326i	$0.759222\pi$
$858$	1.25759	+	64.6527i	0.0429335	+	2.20721i
$859$	−32.1032	−	18.5348i	−1.09535	−	0.632398i	−0.160351	−	0.987060i	$-0.551263\pi$
$859$	−32.1032	−	18.5348i	−1.09535	−	0.632398i	−0.934995	+	0.354662i	$0.884596\pi$
$860$	−3.66110	−	2.04301i	−0.124843	−	0.0696660i
$861$	−29.6930	−	10.3880i	−1.01193	−	0.354023i
$862$	−23.5254	+	6.30361i	−0.801278	+	0.214702i
$863$	−0.0278709	+	0.104015i	−0.000948735	+	0.00354073i	−0.966399	−	0.257048i	$-0.917250\pi$
$863$	−0.0278709	+	0.104015i	−0.000948735	+	0.00354073i	0.965450	+	0.260589i	$0.0839167\pi$
$864$	3.88224	+	3.45372i	0.132077	+	0.117498i
$865$	0.190270	+	13.0213i	0.00646937	+	0.442737i
$866$			26.3446i			0.895224i
$867$	1.53844	−	2.78853i	0.0522481	−	0.0947033i
$868$	8.35609	−	1.41383i	0.283624	−	0.0479884i
$869$	−41.9190	−	72.6058i	−1.42200	−	2.46298i
$870$	0.121856	+	3.57629i	0.00413132	+	0.121248i
$871$	18.9499	+	32.8222i	0.642093	+	1.11214i
$872$	0.0602028	+	0.224680i	0.00203872	+	0.00760862i
$873$	−0.0573253	+	0.252905i	−0.00194017	+	0.00855953i
$874$		−	1.85004i		−	0.0625787i
$875$	24.8404	+	16.0609i	0.839760	+	0.542957i
$876$	7.18777	−	7.47294i	0.242852	−	0.252487i
$877$	37.6779	−	10.0958i	1.27229	−	0.340910i	0.441384	−	0.897318i	$-0.354488\pi$
$877$	37.6779	−	10.0958i	1.27229	−	0.340910i	0.830909	+	0.556408i	$0.187821\pi$
$878$	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	$-0.788601\pi$
$881$		−	36.5900i		−	1.23275i	0.787454	−	0.616374i	$-0.211399\pi$
$882$	−12.4722	−	16.8951i	−0.419962	−	0.568887i
$883$	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
$885$	−31.4076	−	7.27901i	−1.05575	−	0.244681i
$886$	2.67230			0.0897778
$887$	1.04693	+	3.90720i	0.0351525	+	0.131191i	0.981272	−	0.192626i	$-0.0617004\pi$
$887$	1.04693	+	3.90720i	0.0351525	+	0.131191i	−0.946120	+	0.323817i	$0.895034\pi$
$888$	2.02198	−	3.66497i	0.0678531	−	0.122988i
$889$	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
$892$	−24.2382	+	6.49461i	−0.811555	+	0.217456i
$893$	2.38468	−	8.89976i	0.0798004	−	0.297819i
$894$	−9.96895	−	9.58853i	−0.333412	−	0.320688i
$895$	−12.4933	+	3.54401i	−0.417606	+	0.118463i
$896$	−1.53251	+	2.15671i	−0.0511975	+	0.0720508i
$897$	−10.3278	+	6.23363i	−0.344834	+	0.208135i
$898$	11.1288	−	11.1288i	0.371374	−	0.371374i
$899$	1.47976	−	2.56303i	0.0493529	−	0.0854817i
$900$	6.59838	−	13.4708i	0.219946	−	0.449025i
$901$	−13.2994	−	23.0353i	−0.443069	−	0.767417i
$902$	11.1856	+	41.7454i	0.372441	+	1.38997i
$903$	4.83973	−	7.09949i	0.161056	−	0.236256i
$904$	−13.1891	+	7.61472i	−0.438662	+	0.253262i
$905$	8.55123	+	8.30492i	0.284252	+	0.276065i
$906$	8.89363	−	2.56943i	0.295471	−	0.0853635i
$907$	14.0850	−	52.5659i	0.467685	−	1.74542i	−0.180147	−	0.983640i	$-0.557657\pi$
$907$	14.0850	−	52.5659i	0.467685	−	1.74542i	0.647832	−	0.761783i	$-0.275676\pi$
$908$	−6.47257	+	24.1560i	−0.214800	+	0.801644i
$909$	−1.32280	−	33.9896i	−0.0438744	−	1.12736i
$910$	−2.78888	+	34.9717i	−0.0924505	+	1.15930i
$911$	−22.5707	−	13.0312i	−0.747800	−	0.431743i	0.0770981	−	0.997024i	$-0.475435\pi$
$911$	−22.5707	−	13.0312i	−0.747800	−	0.431743i	−0.824899	+	0.565281i	$0.808768\pi$
$912$	−1.31797	+	2.38891i	−0.0436422	+	0.0791046i
$913$	−80.3175	+	80.3175i	−2.65812	+	2.65812i
$914$	−9.33057			−0.308628
$915$	46.6372	+	10.8086i	1.54178	+	0.357322i
$916$	4.58366	−	7.93914i	0.151449	−	0.262317i
$917$	5.29501	−	14.2404i	0.174857	−	0.470259i
$918$	10.1184	−	20.1560i	0.333958	−	0.665246i
$919$	−25.4695	+	14.7048i	−0.840160	+	0.485067i	−0.857319	−	0.514786i	$-0.827871\pi$
$919$	−25.4695	+	14.7048i	−0.840160	+	0.485067i	0.0171585	+	0.999853i	$0.494538\pi$
$920$	0.716701	+	2.52651i	0.0236289	+	0.0832966i
$921$	−11.2042	−	2.76978i	−0.369191	−	0.0912674i
$922$	25.8717	−	6.93229i	0.852038	−	0.228303i
$923$	−14.5487	+	54.2965i	−0.478876	+	1.78719i
$924$	−9.52720	+	27.2324i	−0.313422	+	0.895879i
$925$	−11.7579	−	2.78500i	−0.386596	−	0.0915704i
$926$	35.9157	−	20.7359i	1.18026	−	0.681425i
$927$	−13.2513	−	3.00364i	−0.435230	−	0.0986526i
$928$	0.239131	+	0.892448i	0.00784985	+	0.0292961i
$929$	−57.0607			−1.87210			−0.936051	−	0.351865i	$-0.885548\pi$
$929$	−57.0607			−1.87210			−0.936051	+	0.351865i	$0.885548\pi$
$930$	−10.5264	+	6.56523i	−0.345173	+	0.215282i
$931$	7.20397	−	8.34785i	0.236101	−	0.273590i
$932$	−20.4978	−	5.49236i	−0.671427	−	0.179908i
$933$	18.8216	+	31.1832i	0.616191	+	1.02089i
$934$	−21.1982	+	12.2388i	−0.693627	+	0.400466i
$935$	−0.892747	−	61.0960i	−0.0291959	−	1.99805i
$936$	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	$0.489414\pi$
$938$	2.82092	+	16.6724i	0.0921062	+	0.544372i
$939$	−0.168866	+	0.683091i	−0.00551074	+	0.0222918i
$940$	0.191095	+	13.0778i	0.00623283	+	0.426549i
$941$		−	0.882115i		−	0.0287561i	−0.999897	−	0.0143781i	$-0.995423\pi$
$941$		−	0.882115i		−	0.0287561i	0.999897	−	0.0143781i	$-0.00457684\pi$
$942$	33.7411	−	20.3654i	1.09934	−	0.663542i
$943$	−5.70091	+	5.70091i	−0.185647	+	0.185647i
$944$	−8.32434			−0.270934
$945$	26.2901	+	15.9321i	0.855215	+	0.518273i
$946$	−11.8044			−0.383793
$947$	−3.71719	+	3.71719i	−0.120793	+	0.120793i	−0.764919	−	0.644126i	$-0.777221\pi$
$947$	−3.71719	+	3.71719i	−0.120793	+	0.120793i	0.644126	+	0.764919i	$0.277221\pi$
$948$	−19.7468	+	11.9188i	−0.641346	+	0.387104i
$949$		−	35.4994i		−	1.15236i
$950$	7.66402	+	1.81532i	0.248653	+	0.0588969i
$951$	−3.86636	+	15.6400i	−0.125375	+	0.507162i
$952$	10.7635	+	4.00220i	0.348848	+	0.129712i
$953$	−3.95814	−	3.95814i	−0.128217	−	0.128217i	0.640086	−	0.768303i	$-0.278899\pi$
$953$	−3.95814	−	3.95814i	−0.128217	−	0.128217i	−0.768303	+	0.640086i	$0.778899\pi$
$954$	−9.80462	−	15.5522i	−0.317436	−	0.503521i
$955$	2.04436	−	2.10499i	0.0661538	−	0.0681158i
$956$	5.13552	−	2.96499i	0.166094	−	0.0958947i
$957$	5.20627	+	8.62565i	0.168295	+	0.278828i
$958$	−3.23165	−	0.865918i	−0.104410	−	0.0279765i
$959$	−1.01410	+	10.7347i	−0.0327470	+	0.346643i
$960$	0.874425	−	3.77298i	0.0282220	−	0.121772i
$961$	−20.7395			−0.669018
$962$	−3.70909	−	13.8425i	−0.119586	−	0.446300i
$963$	2.15770	−	2.33245i	0.0695309	−	0.0751621i
$964$	19.6612	−	11.3514i	0.633245	−	0.365604i
$965$	−1.45415	+	0.0212484i	−0.0468109	+	0.000684010i
$966$	−5.28822	+	1.00091i	−0.170146	+	0.0322037i
$967$	−2.59154	+	9.67174i	−0.0833382	+	0.311022i	−0.994994	−	0.0999316i	$-0.968138\pi$
$967$	−2.59154	+	9.67174i	−0.0833382	+	0.311022i	0.911656	+	0.410954i	$0.134804\pi$
$968$	27.6609	−	7.41171i	0.889054	−	0.238221i
$969$	11.4960	+	2.84191i	0.369304	+	0.0912952i
$970$	0.185949	−	0.0527485i	0.00597046	−	0.00169365i
$971$	−35.9311	+	20.7448i	−1.15308	+	0.665733i	−0.949637	−	0.313353i	$-0.898548\pi$
$971$	−35.9311	+	20.7448i	−1.15308	+	0.665733i	−0.203447	+	0.979086i	$0.565214\pi$
$972$	6.44666	−	14.1930i	0.206777	−	0.455240i
$973$	−2.72319	−	3.29138i	−0.0873013	−	0.105517i
$974$	−6.95365	+	12.0441i	−0.222809	+	0.385917i
$975$	−15.6896	−	48.9006i	−0.502469	−	1.56607i
$976$	12.3608			0.395661
$977$	22.6090	−	22.6090i	0.723327	−	0.723327i	−0.245955	−	0.969281i	$-0.579101\pi$
$977$	22.6090	−	22.6090i	0.723327	−	0.723327i	0.969281	+	0.245955i	$0.0791014\pi$
$978$	13.4555	−	24.3890i	0.430259	−	0.779874i
$979$	72.8226	+	42.0441i	2.32742	+	1.34374i
$980$	−6.60417	+	14.1910i	−0.210962	+	0.453315i
$981$	0.590302	−	0.372146i	0.0188469	−	0.0118817i
$982$	9.33903	−	34.8537i	0.298020	−	1.11223i
$983$	4.32878	−	16.1552i	0.138067	−	0.515271i	−0.861900	−	0.507078i	$-0.830725\pi$
$983$	4.32878	−	16.1552i	0.138067	−	0.515271i	0.999966	−	0.00819281i	$-0.00260788\pi$
$984$	11.4227	−	3.30010i	0.364143	−	0.105203i
$985$	−14.0272	+	0.204969i	−0.446944	+	0.00653084i
$986$	3.47293	−	2.00510i	0.110601	−	0.0638552i
$987$	−26.7295	−	2.00150i	−0.850808	−	0.0637085i
$988$	2.41766	+	9.02284i	0.0769161	+	0.287055i
$989$	−1.10105	−	1.90707i	−0.0350113	−	0.0606414i
$990$	−2.25879	−	42.1728i	−0.0717891	−	1.34034i
$991$	−20.4353	+	35.3951i	−0.649150	+	1.12436i	0.334176	+	0.942511i	$0.391542\pi$
$991$	−20.4353	+	35.3951i	−0.649150	+	1.12436i	−0.983326	+	0.181850i	$0.941791\pi$
$992$	−2.26500	+	2.26500i	−0.0719138	+	0.0719138i
$993$	−38.6992	+	23.3580i	−1.22808	+	0.741245i
$994$	−14.5268	+	20.4438i	−0.460763	+	0.648437i
$995$	−5.46770	−	19.2747i	−0.173338	−	0.611050i
$996$	22.5220	+	21.6625i	0.713636	+	0.686404i
$997$	−0.752943	+	2.81002i	−0.0238459	+	0.0889943i	−0.976823	−	0.214047i	$-0.931335\pi$
$997$	−0.752943	+	2.81002i	−0.0238459	+	0.0889943i	0.952977	+	0.303041i	$0.0980021\pi$
$998$	34.5034	−	9.24516i	1.09219	−	0.292650i
$999$	−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.137.5	yes	192
5.3	odd	4	inner	630.2.cd.a.263.32	yes	192
7.2	even	3		630.2.bt.a.317.36	✓	192
9.5	odd	6		630.2.bt.a.347.48	yes	192
35.23	odd	12		630.2.bt.a.443.48	yes	192
45.23	even	12		630.2.bt.a.473.36	yes	192
63.23	odd	6	inner	630.2.cd.a.527.32	yes	192
315.23	even	12	inner	630.2.cd.a.23.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.36	✓	192	7.2	even	3
630.2.bt.a.347.48	yes	192	9.5	odd	6
630.2.bt.a.443.48	yes	192	35.23	odd	12
630.2.bt.a.473.36	yes	192	45.23	even	12
630.2.cd.a.23.5	yes	192	315.23	even	12	inner
630.2.cd.a.137.5	yes	192	1.1	even	1	trivial
630.2.cd.a.263.32	yes	192	5.3	odd	4	inner
630.2.cd.a.527.32	yes	192	63.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.48287 + 0.895033i) q^{3} -1.00000i q^{4} +(1.60407 + 1.55787i) q^{5} +(0.415666 - 1.68143i) q^{6} +(-0.441381 - 2.60867i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.39783 - 2.65444i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.48287 + 0.895033i) q^{3} -1.00000i q^{4} +(1.60407 + 1.55787i) q^{5} +(0.415666 - 1.68143i) q^{6} +(-0.441381 - 2.60867i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.39783 - 2.65444i) q^{9} +(-2.23583 + 0.0326704i) q^{10} +(-5.45229 + 3.14788i) q^{11} +(0.895033 + 1.48287i) q^{12} +(5.72800 + 1.53481i) q^{13} +(2.15671 + 1.53251i) q^{14} +(-3.77298 - 0.874425i) q^{15} -1.00000 q^{16} +(1.12337 + 4.19247i) q^{17} +(0.888559 + 2.86539i) q^{18} +(-1.36418 + 0.787607i) q^{19} +(1.55787 - 1.60407i) q^{20} +(2.98936 + 3.47329i) q^{21} +(1.62946 - 6.08124i) q^{22} +(1.13445 - 0.303976i) q^{23} +(-1.68143 - 0.415666i) q^{24} +(0.146091 + 4.99787i) q^{25} +(-5.13559 + 2.96503i) q^{26} +(0.303009 + 5.18731i) q^{27} +(-2.60867 + 0.441381i) q^{28} +(-0.461965 + 0.800147i) q^{29} +(3.28621 - 2.04959i) q^{30} -3.20319 q^{31} +(0.707107 - 0.707107i) q^{32} +(5.26760 - 9.54789i) q^{33} +(-3.75886 - 2.17018i) q^{34} +(3.35597 - 4.87211i) q^{35} +(-2.65444 - 1.39783i) q^{36} +(-0.625472 + 2.33429i) q^{37} +(0.407696 - 1.52154i) q^{38} +(-9.86762 + 2.85082i) q^{39} +(0.0326704 + 2.23583i) q^{40} +(-5.94493 + 3.43231i) q^{41} +(-4.56978 - 0.342185i) q^{42} +(-0.485278 - 1.81108i) q^{43} +(3.14788 + 5.45229i) q^{44} +(6.37749 - 2.08028i) q^{45} +(-0.587236 + 1.01712i) q^{46} +(-4.13599 + 4.13599i) q^{47} +(1.48287 - 0.895033i) q^{48} +(-6.61037 + 2.30284i) q^{49} +(-3.63733 - 3.43072i) q^{50} +(-5.41821 - 5.21145i) q^{51} +(1.53481 - 5.72800i) q^{52} +(-5.91945 + 1.58611i) q^{53} +(-3.88224 - 3.45372i) q^{54} +(-13.6499 - 3.44453i) q^{55} +(1.53251 - 2.15671i) q^{56} +(1.31797 - 2.38891i) q^{57} +(-0.239131 - 0.892448i) q^{58} +8.32434 q^{59} +(-0.874425 + 3.77298i) q^{60} -12.3608 q^{61} +(2.26500 - 2.26500i) q^{62} +(-7.54155 - 2.47487i) q^{63} +1.00000i q^{64} +(6.79709 + 11.3854i) q^{65} +(3.02662 + 10.4761i) q^{66} +(4.51921 + 4.51921i) q^{67} +(4.19247 - 1.12337i) q^{68} +(-1.41018 + 1.46613i) q^{69} +(1.07208 + 5.81813i) q^{70} +9.47913i q^{71} +(2.86539 - 0.888559i) q^{72} +(-1.54938 - 5.78236i) q^{73} +(-1.20832 - 2.09287i) q^{74} +(-4.68989 - 7.28045i) q^{75} +(0.787607 + 1.36418i) q^{76} +(10.6183 + 12.8338i) q^{77} +(4.96163 - 8.99329i) q^{78} +13.3166i q^{79} +(-1.60407 - 1.55787i) q^{80} +(-5.09214 - 7.42092i) q^{81} +(1.77669 - 6.63071i) q^{82} +(17.4269 - 4.66953i) q^{83} +(3.47329 - 2.98936i) q^{84} +(-4.72935 + 8.47507i) q^{85} +(1.62377 + 0.937485i) q^{86} +(-0.0311222 - 1.59999i) q^{87} +(-6.08124 - 1.62946i) q^{88} +(-6.67816 - 11.5669i) q^{89} +(-3.03859 + 5.98055i) q^{90} +(1.47560 - 15.6199i) q^{91} +(-0.303976 - 1.13445i) q^{92} +(4.74993 - 2.86697i) q^{93} -5.84918i q^{94} +(-3.41522 - 0.861828i) q^{95} +(-0.415666 + 1.68143i) q^{96} +(-0.0834947 + 0.0223723i) q^{97} +(3.04588 - 6.30259i) 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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