LMFDB - Embedded newform 462.2.s.a.377.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(125,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 2]))

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

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

chi := DirichletCharacter("462.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.s (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			377.11
Character	$\chi$	$=$	462.377
Dual form			462.2.s.a.125.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.582733 - 1.63108i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.793236 - 0.576320i) q^{5} +(-1.66209 + 0.487284i) q^{6} +(0.441911 - 2.60858i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.32084 - 1.90097i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.582733 - 1.63108i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.793236 - 0.576320i) q^{5} +(-1.66209 + 0.487284i) q^{6} +(0.441911 - 2.60858i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.32084 - 1.90097i) q^{9} +0.980494i q^{10} +(2.99024 - 1.43473i) q^{11} +(1.37117 + 1.05824i) q^{12} +(1.73459 + 2.38746i) q^{13} +(-2.37014 + 1.17577i) q^{14} +(-1.40227 + 0.957991i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-6.42518 - 4.66817i) q^{17} +(-0.173757 + 2.99496i) q^{18} +(-1.35562 + 0.440466i) q^{19} +(0.793236 - 0.576320i) q^{20} +(-3.99729 - 2.24090i) q^{21} +(-2.91834 - 1.57584i) q^{22} +6.16882i q^{23} +(0.0501805 - 1.73132i) q^{24} +(-1.24801 - 3.84097i) q^{25} +(0.911930 - 2.80663i) q^{26} +(-4.45306 + 2.67773i) q^{27} +(2.34435 + 1.22638i) q^{28} +(3.54438 + 1.15164i) q^{29} +(1.59926 + 0.571366i) q^{30} +(-3.63781 - 5.00702i) q^{31} +1.00000i q^{32} +(-0.597646 - 5.71339i) q^{33} +7.94196i q^{34} +(-1.85392 + 1.81454i) q^{35} +(2.52511 - 1.61982i) q^{36} +(0.129412 - 0.398290i) q^{37} +(1.15316 + 0.837816i) q^{38} +(4.90495 - 1.43801i) q^{39} +(-0.932505 - 0.302989i) q^{40} +(0.484783 + 1.49201i) q^{41} +(0.536624 + 4.55105i) q^{42} +4.90879 q^{43} +(0.440473 + 3.28725i) q^{44} +(0.745412 + 2.84547i) q^{45} +(4.99068 - 3.62594i) q^{46} +(0.768311 + 2.36462i) q^{47} +(-1.43017 + 0.977050i) q^{48} +(-6.60943 - 2.30553i) q^{49} +(-2.37385 + 3.26732i) q^{50} +(-11.3583 + 7.75969i) q^{51} +(-2.80663 + 0.911930i) q^{52} +(0.386678 + 0.532217i) q^{53} +(4.78377 + 2.02868i) q^{54} +(-3.19883 - 0.585257i) q^{55} +(-0.385814 - 2.61747i) q^{56} +(-0.0715262 + 2.46779i) q^{57} +(-1.15164 - 3.54438i) q^{58} +(-1.67598 + 5.15812i) q^{59} +(-0.477779 - 1.62967i) q^{60} +(6.32934 - 8.71159i) q^{61} +(-1.91251 + 5.88611i) q^{62} +(-5.98444 + 5.21406i) q^{63} +(0.809017 - 0.587785i) q^{64} -2.89350i q^{65} +(-4.27094 + 3.84175i) q^{66} -1.50802 q^{67} +(6.42518 - 4.66817i) q^{68} +(10.0618 + 3.59478i) q^{69} +(2.55770 + 0.433291i) q^{70} +(3.68585 - 5.07313i) q^{71} +(-2.79469 - 1.09075i) q^{72} +(5.22459 + 1.69757i) q^{73} +(-0.398290 + 0.129412i) q^{74} +(-6.99218 - 0.202661i) q^{75} -1.42538i q^{76} +(-2.42119 - 8.43432i) q^{77} +(-4.04643 - 3.12295i) q^{78} +(12.4428 - 9.04020i) q^{79} +(0.302989 + 0.932505i) q^{80} +(1.77264 + 8.82370i) q^{81} +(0.922112 - 1.26918i) q^{82} +(-5.34986 - 3.88690i) q^{83} +(3.36646 - 3.10918i) q^{84} +(2.40633 + 7.40592i) q^{85} +(-2.88531 - 3.97129i) q^{86} +(3.94384 - 5.11007i) q^{87} +(2.40053 - 2.28854i) q^{88} +16.7562 q^{89} +(1.86389 - 2.27557i) q^{90} +(6.99444 - 3.46979i) q^{91} +(-5.86690 - 1.90627i) q^{92} +(-10.2867 + 3.01581i) q^{93} +(1.46142 - 2.01147i) q^{94} +(1.32917 + 0.431874i) q^{95} +(1.63108 + 0.582733i) q^{96} +(5.45812 + 7.51246i) q^{97} +(2.01971 + 6.70229i) q^{98} +(-9.66726 - 2.35457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.582733	−	1.63108i	0.336441	−	0.941705i
$3$	0.582733	−	1.63108i	0.336441	−	0.941705i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.793236	−	0.576320i	−0.354746	−	0.257738i	0.396111	−	0.918203i	$-0.370359\pi$
$5$	−0.793236	−	0.576320i	−0.354746	−	0.257738i	−0.750857	+	0.660464i	$0.770359\pi$
$6$	−1.66209	+	0.487284i	−0.678547	+	0.198933i
$7$	0.441911	−	2.60858i	0.167027	−	0.985952i
$7$	0.441911	−	2.60858i	0.167027	−	0.985952i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−2.32084	−	1.90097i	−0.773615	−	0.633656i
$10$			0.980494i			0.310059i
$11$	2.99024	−	1.43473i	0.901592	−	0.432587i
$11$	2.99024	−	1.43473i	0.901592	−	0.432587i
$12$	1.37117	+	1.05824i	0.395824	+	0.305489i
$13$	1.73459	+	2.38746i	0.481090	+	0.662163i	0.978714	−	0.205230i	$-0.0657941\pi$
$13$	1.73459	+	2.38746i	0.481090	+	0.662163i	−0.497624	+	0.867393i	$0.665794\pi$
$14$	−2.37014	+	1.17577i	−0.633446	+	0.314239i
$15$	−1.40227	+	0.957991i	−0.362064	+	0.247352i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−6.42518	−	4.66817i	−1.55833	−	1.13220i	−0.937358	−	0.348367i	$-0.886736\pi$
$17$	−6.42518	−	4.66817i	−1.55833	−	1.13220i	−0.620976	−	0.783829i	$-0.713264\pi$
$18$	−0.173757	+	2.99496i	−0.0409550	+	0.705920i
$19$	−1.35562	+	0.440466i	−0.311000	+	0.101050i	−0.460358	−	0.887733i	$-0.652279\pi$
$19$	−1.35562	+	0.440466i	−0.311000	+	0.101050i	0.149359	+	0.988783i	$0.452279\pi$
$20$	0.793236	−	0.576320i	0.177373	−	0.128869i
$21$	−3.99729	−	2.24090i	−0.872281	−	0.489005i
$22$	−2.91834	−	1.57584i	−0.622192	−	0.335971i
$23$			6.16882i			1.28629i	0.765745	+	0.643144i	$0.222370\pi$
$23$			6.16882i			1.28629i	−0.765745	+	0.643144i	$0.777630\pi$
$24$	0.0501805	−	1.73132i	0.0102431	−	0.353405i
$25$	−1.24801	−	3.84097i	−0.249601	−	0.768193i
$26$	0.911930	−	2.80663i	0.178844	−	0.550426i
$27$	−4.45306	+	2.67773i	−0.856993	+	0.515329i
$28$	2.34435	+	1.22638i	0.443041	+	0.231764i
$29$	3.54438	+	1.15164i	0.658175	+	0.213854i	0.619015	−	0.785379i	$-0.287532\pi$
$29$	3.54438	+	1.15164i	0.658175	+	0.213854i	0.0391596	+	0.999233i	$0.487532\pi$
$30$	1.59926	+	0.571366i	0.291984	+	0.104317i
$31$	−3.63781	−	5.00702i	−0.653371	−	0.899288i	0.345869	−	0.938283i	$-0.387584\pi$
$31$	−3.63781	−	5.00702i	−0.653371	−	0.899288i	−0.999239	+	0.0389952i	$0.987584\pi$
$32$			1.00000i			0.176777i
$33$	−0.597646	−	5.71339i	−0.104037	−	0.994573i
$34$			7.94196i			1.36203i
$35$	−1.85392	+	1.81454i	−0.313370	+	0.306714i
$36$	2.52511	−	1.61982i	0.420851	−	0.269970i
$37$	0.129412	−	0.398290i	0.0212752	−	0.0654785i	−0.939855	−	0.341573i	$-0.889040\pi$
$37$	0.129412	−	0.398290i	0.0212752	−	0.0654785i	0.961130	+	0.276095i	$0.0890403\pi$
$38$	1.15316	+	0.837816i	0.187067	+	0.135912i
$39$	4.90495	−	1.43801i	0.785420	−	0.230266i
$40$	−0.932505	−	0.302989i	−0.147442	−	0.0479068i
$41$	0.484783	+	1.49201i	0.0757104	+	0.233013i	0.981749	−	0.190183i	$-0.0609082\pi$
$41$	0.484783	+	1.49201i	0.0757104	+	0.233013i	−0.906038	+	0.423196i	$0.860908\pi$
$42$	0.536624	+	4.55105i	0.0828028	+	0.702242i
$43$	4.90879			0.748583			0.374292	−	0.927311i	$-0.377886\pi$
$43$	4.90879			0.748583			0.374292	+	0.927311i	$0.377886\pi$
$44$	0.440473	+	3.28725i	0.0664038	+	0.495571i
$45$	0.745412	+	2.84547i	0.111119	+	0.424177i
$46$	4.99068	−	3.62594i	0.735836	−	0.534616i
$47$	0.768311	+	2.36462i	0.112070	+	0.344915i	0.991325	−	0.131436i	$-0.0419589\pi$
$47$	0.768311	+	2.36462i	0.112070	+	0.344915i	−0.879255	+	0.476352i	$0.841959\pi$
$48$	−1.43017	+	0.977050i	−0.206427	+	0.141025i
$49$	−6.60943	−	2.30553i	−0.944204	−	0.329361i
$50$	−2.37385	+	3.26732i	−0.335713	+	0.462069i
$51$	−11.3583	+	7.75969i	−1.59048	+	1.08657i
$52$	−2.80663	+	0.911930i	−0.389210	+	0.126462i
$53$	0.386678	+	0.532217i	0.0531143	+	0.0731056i	0.834748	−	0.550632i	$-0.185613\pi$
$53$	0.386678	+	0.532217i	0.0531143	+	0.0731056i	−0.781634	+	0.623738i	$0.785613\pi$
$54$	4.78377	+	2.02868i	0.650989	+	0.276068i
$55$	−3.19883	−	0.585257i	−0.431330	−	0.0789160i
$56$	−0.385814	−	2.61747i	−0.0515566	−	0.349774i
$57$	−0.0715262	+	2.46779i	−0.00947388	+	0.326867i
$58$	−1.15164	−	3.54438i	−0.151218	−	0.465400i
$59$	−1.67598	+	5.15812i	−0.218193	+	0.671530i	0.780718	+	0.624883i	$0.214854\pi$
$59$	−1.67598	+	5.15812i	−0.218193	+	0.671530i	−0.998911	+	0.0466468i	$0.985146\pi$
$60$	−0.477779	−	1.62967i	−0.0616810	−	0.210390i
$61$	6.32934	−	8.71159i	0.810389	−	1.11540i	−0.180874	−	0.983506i	$-0.557893\pi$
$61$	6.32934	−	8.71159i	0.810389	−	1.11540i	0.991263	−	0.131898i	$-0.0421072\pi$
$62$	−1.91251	+	5.88611i	−0.242889	+	0.747536i
$63$	−5.98444	+	5.21406i	−0.753969	+	0.656910i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		−	2.89350i		−	0.358895i
$66$	−4.27094	+	3.84175i	−0.525717	+	0.472887i
$67$	−1.50802			−0.184234			−0.0921169	−	0.995748i	$-0.529363\pi$
$67$	−1.50802			−0.184234			−0.0921169	+	0.995748i	$0.529363\pi$
$68$	6.42518	−	4.66817i	0.779167	−	0.566098i
$69$	10.0618	+	3.59478i	1.21130	+	0.432760i
$70$	2.55770	+	0.433291i	0.305704	+	0.0517882i
$71$	3.68585	−	5.07313i	0.437429	−	0.602070i	−0.532209	−	0.846613i	$-0.678638\pi$
$71$	3.68585	−	5.07313i	0.437429	−	0.602070i	0.969638	+	0.244543i	$0.0786380\pi$
$72$	−2.79469	−	1.09075i	−0.329357	−	0.128546i
$73$	5.22459	+	1.69757i	0.611493	+	0.198686i	0.598359	−	0.801228i	$-0.295819\pi$
$73$	5.22459	+	1.69757i	0.611493	+	0.198686i	0.0131331	+	0.999914i	$0.495819\pi$
$74$	−0.398290	+	0.129412i	−0.0463003	+	0.0150439i
$75$	−6.99218	−	0.202661i	−0.807387	−	0.0234012i
$76$		−	1.42538i		−	0.163502i
$77$	−2.42119	−	8.43432i	−0.275920	−	0.961180i
$78$	−4.04643	−	3.12295i	−0.458168	−	0.353604i
$79$	12.4428	−	9.04020i	1.39992	−	1.01710i	0.405228	−	0.914216i	$-0.367192\pi$
$79$	12.4428	−	9.04020i	1.39992	−	1.01710i	0.994693	−	0.102887i	$-0.0328079\pi$
$80$	0.302989	+	0.932505i	0.0338752	+	0.104257i
$81$	1.77264	+	8.82370i	0.196960	+	0.980412i
$82$	0.922112	−	1.26918i	0.101830	−	0.140157i
$83$	−5.34986	−	3.88690i	−0.587224	−	0.426643i	0.254097	−	0.967179i	$-0.418222\pi$
$83$	−5.34986	−	3.88690i	−0.587224	−	0.426643i	−0.841321	+	0.540536i	$0.818222\pi$
$84$	3.36646	−	3.10918i	0.367310	−	0.339239i
$85$	2.40633	+	7.40592i	0.261003	+	0.803284i
$86$	−2.88531	−	3.97129i	−0.311131	−	0.428236i
$87$	3.94384	−	5.11007i	0.422824	−	0.547857i
$88$	2.40053	−	2.28854i	0.255898	−	0.243960i
$89$	16.7562			1.77615			0.888075	−	0.459699i	$-0.152043\pi$
$89$	16.7562			1.77615			0.888075	+	0.459699i	$0.152043\pi$
$90$	1.86389	−	2.27557i	0.196471	−	0.239867i
$91$	6.99444	−	3.46979i	0.733216	−	0.363733i
$92$	−5.86690	−	1.90627i	−0.611666	−	0.198742i
$93$	−10.2867	+	3.01581i	−1.06668	+	0.312725i
$94$	1.46142	−	2.01147i	0.150733	−	0.207467i
$95$	1.32917	+	0.431874i	0.136370	+	0.0443094i
$96$	1.63108	+	0.582733i	0.166471	+	0.0594749i
$97$	5.45812	+	7.51246i	0.554188	+	0.762774i	0.990573	−	0.136986i	$-0.0437414\pi$
$97$	5.45812	+	7.51246i	0.554188	+	0.762774i	−0.436385	+	0.899760i	$0.643741\pi$
$98$	2.01971	+	6.70229i	0.204022	+	0.677034i
$99$	−9.66726	−	2.35457i	−0.971597	−	0.236643i
$100$	4.03863			0.403863
$101$	12.3242	−	8.95405i	1.22630	−	0.890961i	0.229695	−	0.973263i	$-0.426227\pi$
$101$	12.3242	−	8.95405i	1.22630	−	0.890961i	0.996607	+	0.0823013i	$0.0262270\pi$
$102$	12.9540	+	4.62804i	1.28263	+	0.458244i
$103$	−14.4071	−	4.68114i	−1.41957	−	0.461247i	−0.504106	−	0.863642i	$-0.668178\pi$
$103$	−14.4071	−	4.68114i	−1.41957	−	0.461247i	−0.915466	+	0.402395i	$0.868178\pi$
$104$	2.38746	+	1.73459i	0.234110	+	0.170091i
$105$	1.87932	+	4.08128i	0.183403	+	0.398293i
$106$	0.203289	−	0.625658i	0.0197451	−	0.0607693i
$107$	3.96932	−	1.28971i	0.383729	−	0.124681i	−0.110799	−	0.993843i	$-0.535341\pi$
$107$	3.96932	−	1.28971i	0.383729	−	0.124681i	0.494528	+	0.869162i	$0.335341\pi$
$108$	−1.17060	−	5.06258i	−0.112641	−	0.487147i
$109$	−4.92386			−0.471620			−0.235810	−	0.971799i	$-0.575774\pi$
$109$	−4.92386			−0.471620			−0.235810	+	0.971799i	$0.575774\pi$
$110$	1.40674	+	2.93191i	0.134128	+	0.279547i
$111$	−0.574230	−	0.443178i	−0.0545035	−	0.0420646i
$112$	−1.89080	+	1.85064i	−0.178664	+	0.174869i
$113$	−6.42966	+	2.08912i	−0.604852	+	0.196528i	−0.595403	−	0.803427i	$-0.703008\pi$
$113$	−6.42966	+	2.08912i	−0.604852	+	0.196528i	−0.00944860	+	0.999955i	$0.503008\pi$
$114$	2.03853	−	1.39267i	0.190926	−	0.130435i
$115$	3.55521	−	4.89333i	0.331525	−	0.456306i
$116$	−2.19055	+	3.01503i	−0.203387	+	0.279938i
$117$	0.512770	−	8.83834i	0.0474056	−	0.817105i
$118$	5.15812	−	1.67598i	0.474844	−	0.154286i
$119$	−15.0167	+	14.6977i	−1.37658	+	1.34734i
$120$	−1.03760	+	1.34443i	−0.0947196	+	0.122729i
$121$	6.88310	−	8.58038i	0.625736	−	0.780035i
$122$	−10.7681			−0.974899
$123$	2.71608	+	0.0787227i	0.244901	+	0.00709819i
$124$	5.88611	−	1.91251i	0.528588	−	0.171749i
$125$	−2.73861	+	8.42857i	−0.244949	+	0.753874i
$126$	7.73583	+	1.77677i	0.689163	+	0.158287i
$127$	12.8923	+	9.36680i	1.14401	+	0.831169i	0.987672	−	0.156535i	$-0.0500324\pi$
$127$	12.8923	+	9.36680i	1.14401	+	0.831169i	0.156334	+	0.987704i	$0.450032\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	2.86051	−	8.00663i	0.251854	−	0.704944i
$130$	−2.34089	+	1.70076i	−0.205310	+	0.149166i
$131$	19.2622			1.68295			0.841473	−	0.540299i	$-0.181689\pi$
$131$	19.2622			1.68295			0.841473	+	0.540299i	$0.181689\pi$
$132$	5.61844	+	1.19714i	0.489022	+	0.104198i
$133$	0.549932	+	3.73089i	0.0476851	+	0.323509i
$134$	0.886391	+	1.22001i	0.0765725	+	0.105393i
$135$	5.07556	+	0.442320i	0.436835	+	0.0380688i
$136$	−7.55325	−	2.45420i	−0.647686	−	0.210446i
$137$	−1.41651	+	1.94965i	−0.121020	+	0.166570i	−0.865229	−	0.501377i	$-0.832827\pi$
$137$	−1.41651	+	1.94965i	−0.121020	+	0.166570i	0.744208	+	0.667947i	$0.232827\pi$
$138$	−3.00597	−	10.2532i	−0.255885	−	0.872807i
$139$	12.2983	+	3.99595i	1.04313	+	0.338932i	0.779967	−	0.625821i	$-0.215236\pi$
$139$	12.2983	+	3.99595i	1.04313	+	0.338932i	0.263159	+	0.964753i	$0.415236\pi$
$140$	−1.15284	−	2.32391i	−0.0974327	−	0.196406i
$141$	4.30460	+	0.124764i	0.362513	+	0.0105070i
$142$	−6.27074			−0.526228
$143$	8.61222	+	4.65042i	0.720190	+	0.388888i
$144$	0.760242	+	2.90207i	0.0633535	+	0.241839i
$145$	−2.14782	−	2.95622i	−0.178367	−	0.245501i
$146$	−1.69757	−	5.22459i	−0.140492	−	0.432391i
$147$	−7.61203	+	9.43700i	−0.627830	+	0.778351i
$148$	0.338806	+	0.246157i	0.0278497	+	0.0202340i
$149$	5.61240	−	7.72480i	0.459785	−	0.632840i	−0.514679	−	0.857383i	$-0.672089\pi$
$149$	5.61240	−	7.72480i	0.459785	−	0.632840i	0.974464	+	0.224543i	$0.0720889\pi$
$150$	3.94594	+	5.77591i	0.322185	+	0.471601i
$151$	−3.83642	−	11.8073i	−0.312203	−	0.960862i	−0.976890	−	0.213741i	$-0.931435\pi$
$151$	−3.83642	−	11.8073i	−0.312203	−	0.960862i	0.664687	−	0.747122i	$-0.268565\pi$
$152$	−1.15316	+	0.837816i	−0.0935333	+	0.0679559i
$153$	6.03781	+	23.0481i	0.488128	+	1.86333i
$154$	−5.40037	+	6.91636i	−0.435174	+	0.557336i
$155$			6.06830i			0.487417i
$156$	−0.148086	+	5.10925i	−0.0118564	+	0.409068i
$157$	20.3465	−	6.61098i	1.62383	−	0.527614i	0.650988	−	0.759088i	$-0.274355\pi$
$157$	20.3465	−	6.61098i	1.62383	−	0.527614i	0.972841	+	0.231474i	$0.0743549\pi$
$158$	−14.6274	−	4.75272i	−1.16369	−	0.378106i
$159$	1.09342	−	0.320563i	0.0867137	−	0.0254223i
$160$	0.576320	−	0.793236i	0.0455621	−	0.0627108i
$161$	16.0919	+	2.72607i	1.26822	+	0.214845i
$162$	6.09660	−	6.62054i	0.478994	−	0.520159i
$163$	−16.4475	+	11.9498i	−1.28827	+	0.935982i	−0.999769	−	0.0214976i	$-0.993157\pi$
$163$	−16.4475	+	11.9498i	−1.28827	+	0.935982i	−0.288500	+	0.957480i	$0.593157\pi$
$164$	−1.56879			−0.122502
$165$	−2.81867	+	4.87650i	−0.219433	+	0.379635i
$166$			6.61280i			0.513252i
$167$	−7.12101	+	5.17371i	−0.551040	+	0.400354i	−0.828169	−	0.560479i	$-0.810617\pi$
$167$	−7.12101	+	5.17371i	−0.551040	+	0.400354i	0.277129	+	0.960833i	$0.410617\pi$
$168$	−4.49413	−	0.895992i	−0.346730	−	0.0691273i
$169$	1.32605	−	4.08118i	0.102004	−	0.313937i
$170$	4.57711	−	6.29985i	0.351048	−	0.483176i
$171$	3.98349	+	1.55473i	0.304625	+	0.118893i
$172$	−1.51690	+	4.66854i	−0.115662	+	0.355973i
$173$	−4.10167	−	12.6236i	−0.311844	−	0.959757i	−0.977034	−	0.213083i	$-0.931650\pi$
$173$	−4.10167	−	12.6236i	−0.311844	−	0.959757i	0.665190	−	0.746674i	$-0.268350\pi$
$174$	−6.45227	−	0.187012i	−0.489145	−	0.0141773i
$175$	−10.5710	+	1.55816i	−0.799092	+	0.117786i
$176$	−3.26247	−	0.596900i	−0.245918	−	0.0449930i
$177$	7.43666	+	5.73946i	0.558974	+	0.431404i
$178$	−9.84902	−	13.5560i	−0.738216	−	1.01607i
$179$	−16.8534	+	5.47600i	−1.25968	+	0.409295i	−0.861381	−	0.507960i	$-0.830400\pi$
$179$	−16.8534	+	5.47600i	−1.25968	+	0.409295i	−0.398300	+	0.917255i	$0.630400\pi$
$180$	−2.93654	−	0.170368i	−0.218877	−	0.0126985i
$181$	−8.20517	+	11.2934i	−0.609885	+	0.839435i	−0.996568	−	0.0827777i	$-0.973621\pi$
$181$	−8.20517	+	11.2934i	−0.609885	+	0.839435i	0.386683	+	0.922213i	$0.373621\pi$
$182$	−6.91834	−	3.61913i	−0.512822	−	0.268268i
$183$	−10.5210	−	15.4002i	−0.777733	−	1.13841i
$184$	1.90627	+	5.86690i	0.140532	+	0.432513i
$185$	−0.332197	+	0.241355i	−0.0244236	+	0.0177448i
$186$	8.48623	+	6.54949i	0.622241	+	0.480232i
$187$	−25.9104	−	4.74055i	−1.89476	−	0.346664i
$188$	−2.48631			−0.181333
$189$	5.01722	+	12.7995i	0.364949	+	0.931028i
$190$	−0.431874	−	1.32917i	−0.0313315	−	0.0964283i
$191$	6.88137	+	2.23589i	0.497919	+	0.161784i	0.547201	−	0.837001i	$-0.315693\pi$
$191$	6.88137	+	2.23589i	0.497919	+	0.161784i	−0.0492821	+	0.998785i	$0.515693\pi$
$192$	−0.487284	−	1.66209i	−0.0351667	−	0.119951i
$193$	−5.90383	−	4.28938i	−0.424967	−	0.308756i	0.354666	−	0.934993i	$-0.384594\pi$
$193$	−5.90383	−	4.28938i	−0.424967	−	0.308756i	−0.779633	+	0.626236i	$0.784594\pi$
$194$	2.86950	−	8.83142i	0.206018	−	0.634059i
$195$	−4.71954	−	1.68614i	−0.337973	−	0.120747i
$196$	4.23511	−	5.57349i	0.302508	−	0.398107i
$197$		−	14.1617i		−	1.00898i	−0.863418	−	0.504489i	$-0.831681\pi$
$197$		−	14.1617i		−	1.00898i	0.863418	−	0.504489i	$-0.168319\pi$
$198$	3.77739	+	9.20496i	0.268447	+	0.654168i
$199$			12.9144i			0.915476i	0.889087	+	0.457738i	$0.151340\pi$
$199$			12.9144i			0.915476i	−0.889087	+	0.457738i	$0.848660\pi$
$200$	−2.37385	−	3.26732i	−0.167856	−	0.231035i
$201$	−0.878772	+	2.45970i	−0.0619838	+	0.173494i
$202$	−14.4880	−	4.70742i	−1.01937	−	0.331213i
$203$	4.57045	−	8.73689i	0.320783	−	0.613210i
$204$	−3.86999	−	13.2003i	−0.270953	−	0.924204i
$205$	0.475327	−	1.46291i	0.0331983	−	0.102174i
$206$	4.68114	+	14.4071i	0.326151	+	1.00379i
$207$	11.7267	−	14.3169i	0.815064	−	0.995092i
$208$		−	2.95107i		−	0.204620i
$209$	−3.42167	+	3.26204i	−0.236682	+	0.225640i
$210$	2.19719	−	3.91932i	0.151621	−	0.270459i
$211$	−13.5298	+	9.82998i	−0.931430	+	0.676723i	−0.946342	−	0.323165i	$-0.895253\pi$
$211$	−13.5298	+	9.82998i	−0.931430	+	0.676723i	0.0149127	+	0.999889i	$0.495253\pi$
$212$	−0.625658	+	0.203289i	−0.0429704	+	0.0139619i
$213$	−6.12682	−	8.96819i	−0.419803	−	0.614490i
$214$	−3.37651	−	2.45318i	−0.230813	−	0.167696i
$215$	−3.89383	−	2.82903i	−0.265557	−	0.192938i
$216$	−3.40765	+	3.92274i	−0.231861	+	0.266909i
$217$	−14.6688	+	7.27689i	−0.995785	+	0.493987i
$218$	2.89417	+	3.98348i	0.196018	+	0.269796i
$219$	5.81342	−	7.53250i	0.392835	−	0.508999i
$220$	1.54511	−	2.86142i	0.104171	−	0.192917i
$221$		−	23.4372i		−	1.57656i
$222$	−0.0210149	+	0.725056i	−0.00141043	+	0.0486626i
$223$	−9.87123	+	3.20736i	−0.661027	+	0.214781i	−0.620270	−	0.784389i	$-0.712977\pi$
$223$	−9.87123	+	3.20736i	−0.661027	+	0.214781i	−0.0407568	+	0.999169i	$0.512977\pi$
$224$	2.60858	+	0.441911i	0.174293	+	0.0295264i
$225$	−4.40513	+	11.2867i	−0.293675	+	0.752447i
$226$	5.46940	+	3.97375i	0.363819	+	0.264330i
$227$	4.16652	−	12.8232i	0.276541	−	0.851107i	−0.712266	−	0.701910i	$-0.752331\pi$
$227$	4.16652	−	12.8232i	0.276541	−	0.851107i	0.988807	−	0.149197i	$-0.0476689\pi$
$228$	−2.32491	−	0.830615i	−0.153971	−	0.0550088i
$229$	2.85639	+	3.93148i	0.188756	+	0.259800i	0.892898	−	0.450259i	$-0.148668\pi$
$229$	2.85639	+	3.93148i	0.188756	+	0.259800i	−0.704142	+	0.710059i	$0.748668\pi$
$230$	−6.04849			−0.398826
$231$	−15.1680	−	0.965801i	−0.997979	−	0.0635450i
$232$	3.72678			0.244675
$233$	8.36558	+	11.5142i	0.548047	+	0.754322i	0.989746	−	0.142841i	$-0.0456239\pi$
$233$	8.36558	+	11.5142i	0.548047	+	0.754322i	−0.441698	+	0.897164i	$0.645624\pi$
$234$	−7.45177	+	4.78021i	−0.487137	+	0.312492i
$235$	0.753325	−	2.31849i	0.0491415	−	0.151242i
$236$	−4.38776	−	3.18789i	−0.285619	−	0.207514i
$237$	−7.49448	−	25.5632i	−0.486819	−	1.66051i
$238$	20.7173	+	3.50964i	1.34290	+	0.227496i
$239$	−7.13874	+	2.31952i	−0.461767	+	0.150037i	−0.530656	−	0.847587i	$-0.678054\pi$
$239$	−7.13874	+	2.31952i	−0.461767	+	0.150037i	0.0688895	+	0.997624i	$0.478054\pi$
$240$	1.69755	+	0.0492017i	0.109577	+	0.00317596i
$241$			27.3955i			1.76470i	0.470596	+	0.882349i	$0.344039\pi$
$241$			27.3955i			1.76470i	−0.470596	+	0.882349i	$0.655961\pi$
$242$	−10.9875	−	0.525125i	−0.706301	−	0.0337563i
$243$	15.4251	+	2.25055i	0.989523	+	0.144373i
$244$	6.32934	+	8.71159i	0.405194	+	0.557702i
$245$	3.91412	+	5.63797i	0.250064	+	0.360197i
$246$	−1.53279	−	2.24363i	−0.0977269	−	0.143049i
$247$	−3.40304	−	2.47245i	−0.216530	−	0.157318i
$248$	−5.00702	−	3.63781i	−0.317946	−	0.231001i
$249$	−9.45739	+	6.46103i	−0.599338	+	0.409451i
$250$	8.42857	−	2.73861i	0.533070	−	0.173205i
$251$	0.834593	−	0.606368i	0.0526791	−	0.0382736i	−0.561134	−	0.827725i	$-0.689635\pi$
$251$	0.834593	−	0.606368i	0.0526791	−	0.0382736i	0.613813	+	0.789451i	$0.289635\pi$
$252$	−3.10957	−	7.30278i	−0.195885	−	0.460032i
$253$	8.85059	+	18.4463i	0.556432	+	1.15971i
$254$		−	15.9358i		−	0.999898i
$255$	13.4819	+	0.390758i	0.844269	+	0.0244702i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.699955	+	2.15424i	−0.0436620	+	0.134378i	−0.970511	−	0.241056i	$-0.922506\pi$
$257$	−0.699955	+	2.15424i	−0.0436620	+	0.134378i	0.926849	+	0.375434i	$0.122506\pi$
$258$	−8.15887	+	2.39197i	−0.507949	+	0.148918i
$259$	−0.981784	−	0.513592i	−0.0610051	−	0.0319130i
$260$	2.75189	+	0.894142i	0.170665	+	0.0554523i
$261$	−6.03673	−	9.41053i	−0.373664	−	0.582497i
$262$	−11.3220	−	15.5834i	−0.699478	−	0.962749i
$263$			23.7116i			1.46212i	0.682313	+	0.731060i	$0.260974\pi$
$263$			23.7116i			1.46212i	−0.682313	+	0.731060i	$0.739026\pi$
$264$	−2.33393	−	5.24907i	−0.143643	−	0.323058i
$265$		−	0.645024i		−	0.0396235i
$266$	2.69511	−	2.63786i	0.165248	−	0.161738i
$267$	9.76437	−	27.3306i	0.597570	−	1.67261i
$268$	0.466003	−	1.43421i	0.0284657	−	0.0876084i
$269$	−10.7921	−	7.84089i	−0.658004	−	0.478068i	0.207985	−	0.978132i	$-0.433310\pi$
$269$	−10.7921	−	7.84089i	−0.658004	−	0.478068i	−0.865988	+	0.500065i	$0.833310\pi$
$270$	−2.62549	−	4.36620i	−0.159783	−	0.265719i
$271$	−0.675524	−	0.219491i	−0.0410352	−	0.0133331i	0.288427	−	0.957502i	$-0.406868\pi$
$271$	−0.675524	−	0.219491i	−0.0410352	−	0.0133331i	−0.329463	+	0.944169i	$0.606868\pi$
$272$	2.45420	+	7.55325i	0.148808	+	0.457983i
$273$	−1.58361	−	13.4304i	−0.0958446	−	0.812848i
$274$	2.40990			0.145588
$275$	−9.24259	−	9.69487i	−0.557349	−	0.584623i
$276$	−6.52811	+	8.45853i	−0.392946	+	0.509144i
$277$	−11.0427	+	8.02301i	−0.663493	+	0.482056i	−0.867841	−	0.496842i	$-0.834493\pi$
$277$	−11.0427	+	8.02301i	−0.663493	+	0.482056i	0.204348	+	0.978898i	$0.434493\pi$
$278$	−3.99595	−	12.2983i	−0.239661	−	0.737601i
$279$	−1.07539	+	18.5359i	−0.0643818	+	1.10971i
$280$	−1.20246	+	2.29862i	−0.0718606	+	0.137369i
$281$	1.52502	−	2.09901i	0.0909751	−	0.125216i	−0.761103	−	0.648631i	$-0.775342\pi$
$281$	1.52502	−	2.09901i	0.0909751	−	0.125216i	0.852078	+	0.523414i	$0.175342\pi$
$282$	−2.42925	−	3.55583i	−0.144660	−	0.211747i
$283$	−23.4572	+	7.62172i	−1.39439	+	0.453064i	−0.907372	−	0.420328i	$-0.861915\pi$
$283$	−23.4572	+	7.62172i	−1.39439	+	0.453064i	−0.487017	+	0.873393i	$0.661915\pi$
$284$	3.68585	+	5.07313i	0.218715	+	0.301035i
$285$	1.47897	−	1.91632i	0.0876069	−	0.113513i
$286$	−1.29987	−	9.70088i	−0.0768627	−	0.573625i
$287$	4.10626	−	0.605262i	0.242385	−	0.0357275i
$288$	1.90097	−	2.32084i	0.112016	−	0.136757i
$289$	14.2379	+	43.8196i	0.837521	+	2.57762i
$290$	−1.12917	+	3.47524i	−0.0663074	+	0.204073i
$291$	15.4340	−	4.52487i	0.904760	−	0.265253i
$292$	−3.22898	+	4.44431i	−0.188962	+	0.260083i
$293$	5.00213	−	15.3950i	0.292228	−	0.899384i	−0.691911	−	0.721983i	$-0.743231\pi$
$293$	5.00213	−	15.3950i	0.292228	−	0.899384i	0.984139	−	0.177401i	$-0.0567691\pi$
$294$	12.1089	+	0.611331i	0.706207	+	0.0356536i
$295$	4.30217	−	3.12571i	0.250482	−	0.181986i
$296$		−	0.418787i		−	0.0243415i
$297$	−9.47393	+	14.3960i	−0.549733	+	0.835340i
$298$	−9.54838			−0.553123
$299$	−14.7278	+	10.7004i	−0.851733	+	0.618820i
$300$	2.35344	−	6.58733i	0.135876	−	0.380320i
$301$	2.16925	−	12.8050i	0.125033	−	0.738068i
$302$	−7.29730	+	10.0439i	−0.419912	+	0.577959i
$303$	−7.42306	−	25.3196i	−0.426444	−	1.45457i
$304$	1.35562	+	0.440466i	0.0777499	+	0.0252625i
$305$	−10.0413	+	3.26262i	−0.574964	+	0.186817i
$306$	15.0974	−	18.4320i	0.863061	−	1.05369i
$307$		−	11.6271i		−	0.663595i	−0.943351	−	0.331798i	$-0.892345\pi$
$307$		−	11.6271i		−	0.663595i	0.943351	−	0.331798i	$-0.107655\pi$
$308$	8.76971	+	0.303659i	0.499701	+	0.0173026i
$309$	−16.0308	+	20.7712i	−0.911961	+	1.18164i
$310$	4.90936	−	3.56686i	0.278833	−	0.202584i
$311$	−2.43573	−	7.49639i	−0.138117	−	0.425081i	0.857945	−	0.513742i	$-0.171741\pi$
$311$	−2.43573	−	7.49639i	−0.138117	−	0.425081i	−0.996062	+	0.0886609i	$0.971741\pi$
$312$	4.22052	−	2.88334i	0.238940	−	0.163237i
$313$	8.44672	−	11.6259i	0.477437	−	0.657136i	−0.500573	−	0.865694i	$-0.666877\pi$
$313$	8.44672	−	11.6259i	0.477437	−	0.657136i	0.978010	+	0.208559i	$0.0668772\pi$
$314$	−17.3078	−	12.5748i	−0.976735	−	0.709639i
$315$	7.75204	−	0.687027i	0.436778	−	0.0387096i
$316$	4.75272	+	14.6274i	0.267361	+	0.822853i
$317$	10.3144	+	14.1966i	0.579316	+	0.797360i	0.993620	−	0.112779i	$-0.0359751\pi$
$317$	10.3144	+	14.1966i	0.579316	+	0.797360i	−0.414304	+	0.910138i	$0.635975\pi$
$318$	−0.902036	−	0.696172i	−0.0505836	−	0.0390394i
$319$	12.2508	−	1.64155i	0.685916	−	0.0919090i
$320$	−0.980494			−0.0548113
$321$	0.209433	−	7.22584i	0.0116894	−	0.403307i
$322$	−7.25314	−	14.6210i	−0.404202	−	0.814794i
$323$	10.7662	+	3.49816i	0.599050	+	0.194643i
$324$	−8.93962	−	1.04079i	−0.496645	−	0.0578219i
$325$	7.00539	−	9.64209i	0.388589	−	0.534847i
$326$	19.3352	+	6.28239i	1.07088	+	0.347950i
$327$	−2.86929	+	8.03121i	−0.158672	+	0.444127i
$328$	0.922112	+	1.26918i	0.0509151	+	0.0700786i
$329$	6.50784	−	0.959253i	0.358789	−	0.0528853i
$330$	5.60194	−	0.585988i	0.308377	−	0.0322576i
$331$	−29.2921			−1.61004			−0.805020	−	0.593248i	$-0.797845\pi$
$331$	−29.2921			−1.61004			−0.805020	+	0.593248i	$0.797845\pi$
$332$	5.34986	−	3.88690i	0.293612	−	0.213322i
$333$	−1.05748	+	0.678361i	−0.0579497	+	0.0371739i
$334$	8.37125	+	2.71998i	0.458054	+	0.148831i
$335$	1.19622	+	0.869101i	0.0653562	+	0.0474841i
$336$	1.91671	+	4.16248i	0.104565	+	0.227082i
$337$	0.174412	−	0.536784i	0.00950081	−	0.0292405i	−0.946194	−	0.323601i	$-0.895107\pi$
$337$	0.174412	−	0.536784i	0.00950081	−	0.0292405i	0.955695	+	0.294360i	$0.0951065\pi$
$338$	−4.08118	+	1.32605i	−0.221987	+	0.0721278i
$339$	−0.339248	+	11.7047i	−0.0184254	+	0.635712i
$340$	−7.78704			−0.422312
$341$	−18.0617	−	9.75293i	−0.978094	−	0.528151i
$342$	−1.08363	−	4.13655i	−0.0585961	−	0.223679i
$343$	−8.93494	+	16.2224i	−0.482442	+	0.875928i
$344$	4.66854	−	1.51690i	0.251711	−	0.0817857i
$345$	−5.90968	−	8.65035i	−0.318166	−	0.465719i
$346$	−7.80183	+	10.7383i	−0.419429	+	0.577295i
$347$	−12.7992	+	17.6166i	−0.687096	+	0.945707i	−0.999992	−	0.00408074i	$-0.998701\pi$
$347$	−12.7992	+	17.6166i	−0.687096	+	0.945707i	0.312895	+	0.949788i	$0.398701\pi$
$348$	3.64125	+	5.32992i	0.195192	+	0.285713i
$349$	18.2880	−	5.94214i	0.978935	−	0.318075i	0.224517	−	0.974470i	$-0.427919\pi$
$349$	18.2880	−	5.94214i	0.978935	−	0.318075i	0.754418	+	0.656395i	$0.227919\pi$
$350$	7.47406	+	7.63625i	0.399505	+	0.408175i
$351$	−14.1172	−	5.98676i	−0.753522	−	0.319550i
$352$	1.43473	+	2.99024i	0.0764713	+	0.159380i
$353$	33.8151			1.79979			0.899897	−	0.436102i	$-0.143641\pi$
$353$	33.8151			1.79979			0.899897	+	0.436102i	$0.143641\pi$
$354$	0.272158	−	9.38996i	0.0144650	−	0.499071i
$355$	−5.84749	+	1.89997i	−0.310353	+	0.100840i
$356$	−5.17794	+	15.9361i	−0.274430	+	0.844609i
$357$	15.2224	+	33.0582i	0.805657	+	1.74963i
$358$	14.3363	+	10.4160i	0.757699	+	0.550501i
$359$	24.6772	+	8.01810i	1.30241	+	0.423179i	0.876420	−	0.481547i	$-0.159925\pi$
$359$	24.6772	+	8.01810i	1.30241	+	0.423179i	0.425992	+	0.904727i	$0.359925\pi$
$360$	1.58823	+	2.47585i	0.0837069	+	0.130489i
$361$	−13.7276	+	9.97371i	−0.722507	+	0.524932i
$362$	13.9595			0.733693
$363$	−9.98428	−	16.2270i	−0.524039	−	0.851695i
$364$	1.13856	+	7.72433i	0.0596770	+	0.404865i
$365$	−3.16599	−	4.35761i	−0.165716	−	0.228088i
$366$	−6.27494	+	17.5637i	−0.327996	+	0.918067i
$367$	24.8469	+	8.07323i	1.29700	+	0.421419i	0.874535	−	0.484962i	$-0.161167\pi$
$367$	24.8469	+	8.07323i	1.29700	+	0.421419i	0.422460	+	0.906381i	$0.361167\pi$
$368$	3.62594	−	4.99068i	0.189015	−	0.260157i
$369$	1.71115	−	4.38428i	0.0890792	−	0.228236i
$370$	0.390521	+	0.126888i	0.0203022	+	0.00659659i
$371$	1.55921	−	0.773490i	0.0809501	−	0.0401576i
$372$	0.310568	−	10.7152i	0.0161022	−	0.555557i
$373$	21.7018			1.12368			0.561838	−	0.827248i	$-0.310095\pi$
$373$	21.7018			1.12368			0.561838	+	0.827248i	$0.310095\pi$
$374$	11.3946	+	23.7484i	0.589199	+	1.22800i
$375$	12.1518	+	9.37850i	0.627516	+	0.484303i
$376$	1.46142	+	2.01147i	0.0753667	+	0.103733i
$377$	3.39856	+	10.4597i	0.175035	+	0.538702i
$378$	7.40598	−	11.5824i	0.380922	−	0.595733i
$379$	14.3587	+	10.4322i	0.737555	+	0.535865i	0.891944	−	0.452145i	$-0.149341\pi$
$379$	14.3587	+	10.4322i	0.737555	+	0.535865i	−0.154389	+	0.988010i	$0.549341\pi$
$380$	−0.821474	+	1.13066i	−0.0421407	+	0.0580017i
$381$	22.7908	−	15.5700i	1.16761	−	0.797677i
$382$	−2.23589	−	6.88137i	−0.114398	−	0.352082i
$383$	−8.21903	+	5.97147i	−0.419973	+	0.305128i	−0.777627	−	0.628726i	$-0.783577\pi$
$383$	−8.21903	+	5.97147i	−0.419973	+	0.305128i	0.357654	+	0.933854i	$0.383577\pi$
$384$	−1.05824	+	1.37117i	−0.0540033	+	0.0699725i
$385$	−2.94029	+	8.08579i	−0.149851	+	0.412090i
$386$			7.29753i			0.371435i
$387$	−11.3925	−	9.33145i	−0.579115	−	0.474344i
$388$	−8.83142	+	2.86950i	−0.448348	+	0.145677i
$389$	−14.1463	−	4.59643i	−0.717248	−	0.233048i	−0.0724186	−	0.997374i	$-0.523072\pi$
$389$	−14.1463	−	4.59643i	−0.717248	−	0.233048i	−0.644830	+	0.764326i	$0.723072\pi$
$390$	1.40996	+	4.80927i	0.0713960	+	0.243527i
$391$	28.7971	−	39.6358i	1.45633	−	2.00447i
$392$	−6.99839	−	0.150260i	−0.353472	−	0.00758927i
$393$	11.2247	−	31.4182i	0.566212	−	1.58484i
$394$	−11.4570	+	8.32402i	−0.577197	+	0.419358i
$395$	−15.0801			−0.758763
$396$	5.22668	−	8.46651i	0.262651	−	0.425458i
$397$		−	21.7137i		−	1.08978i	−0.838508	−	0.544889i	$-0.816572\pi$
$397$		−	21.7137i		−	1.08978i	0.838508	−	0.544889i	$-0.183428\pi$
$398$	10.4480	−	7.59088i	0.523709	−	0.380497i
$399$	6.40584	+	1.27713i	0.320693	+	0.0639363i
$400$	−1.24801	+	3.84097i	−0.0624003	+	0.192048i
$401$	5.88895	−	8.10545i	0.294080	−	0.404767i	−0.636254	−	0.771480i	$-0.719517\pi$
$401$	5.88895	−	8.10545i	0.294080	−	0.404767i	0.930334	+	0.366713i	$0.119517\pi$
$402$	2.50647	−	0.734833i	0.125011	−	0.0366502i
$403$	5.64395	−	17.3703i	0.281145	−	0.865276i
$404$	4.70742	+	14.4880i	0.234203	+	0.720803i
$405$	3.67915	−	8.02089i	0.182819	−	0.398561i
$406$	−9.75474	+	1.43785i	−0.484120	+	0.0713591i
$407$	−0.184464	−	1.37666i	−0.00914356	−	0.0682383i
$408$	−8.40452	+	10.8898i	−0.416086	+	0.539126i
$409$	7.62011	+	10.4882i	0.376790	+	0.518607i	0.954731	−	0.297472i	$-0.0961435\pi$
$409$	7.62011	+	10.4882i	0.376790	+	0.518607i	−0.577941	+	0.816079i	$0.696143\pi$
$410$	−1.46291	+	0.475327i	−0.0722477	+	0.0234747i
$411$	2.35460	+	3.44656i	0.116144	+	0.170006i
$412$	8.90407	−	12.2554i	0.438672	−	0.603780i
$413$	12.7148	+	6.65136i	0.625653	+	0.327292i
$414$	−18.4754	−	1.07188i	−0.908016	−	0.0526800i
$415$	2.00361	+	6.16647i	0.0983532	+	0.302700i
$416$	−2.38746	+	1.73459i	−0.117055	+	0.0850455i
$417$	13.6843	−	17.7309i	0.670124	−	0.868285i
$418$	4.65025	+	0.850808i	0.227451	+	0.0416144i
$419$	5.43414			0.265475			0.132737	−	0.991151i	$-0.457623\pi$
$419$	5.43414			0.265475			0.132737	+	0.991151i	$0.457623\pi$
$420$	−4.46227	+	0.526156i	−0.217737	+	0.0256738i
$421$	−0.686859	−	2.11393i	−0.0334754	−	0.103027i	0.932923	−	0.360077i	$-0.117250\pi$
$421$	−0.686859	−	2.11393i	−0.0334754	−	0.103027i	−0.966398	+	0.257050i	$0.917250\pi$
$422$	15.9052	+	5.16792i	0.774255	+	0.251571i
$423$	2.71193	−	6.94845i	0.131859	−	0.337845i
$424$	0.532217	+	0.386678i	0.0258467	+	0.0187787i
$425$	−9.91161	+	30.5048i	−0.480784	+	1.47970i
$426$	−3.65416	+	10.2281i	−0.177045	+	0.495552i
$427$	−19.9279	−	20.3604i	−0.964379	−	0.985307i
$428$			4.17359i			0.201738i
$429$	12.6038	−	11.3373i	0.608519	−	0.547368i
$430$			4.81304i			0.232105i
$431$	−3.56552	−	4.90751i	−0.171745	−	0.236387i	0.714464	−	0.699672i	$-0.246670\pi$
$431$	−3.56552	−	4.90751i	−0.171745	−	0.236387i	−0.886209	+	0.463285i	$0.846670\pi$
$432$	5.17653	+	0.451119i	0.249056	+	0.0217045i
$433$	−28.6078	−	9.29522i	−1.37480	−	0.446700i	−0.473844	−	0.880609i	$-0.657134\pi$
$433$	−28.6078	−	9.29522i	−1.37480	−	0.446700i	−0.900957	+	0.433909i	$0.857134\pi$
$434$	14.5093	+	7.59009i	0.696466	+	0.364336i
$435$	−6.07343	+	1.78058i	−0.291199	+	0.0853722i
$436$	1.52156	−	4.68287i	0.0728693	−	0.224269i
$437$	−2.71716	−	8.36255i	−0.129979	−	0.400035i
$438$	−9.51096	−	0.275665i	−0.454451	−	0.0131718i
$439$			8.86186i			0.422954i	0.977383	+	0.211477i	$0.0678273\pi$
$439$			8.86186i			0.422954i	−0.977383	+	0.211477i	$0.932173\pi$
$440$	−3.22312	+	0.431881i	−0.153656	+	0.0205891i
$441$	10.9567	+	17.9151i	0.521749	+	0.853099i
$442$	−18.9611	+	13.7761i	−0.901889	+	0.655261i
$443$	−37.3429	+	12.1334i	−1.77422	+	0.576477i	−0.998507	−	0.0546148i	$-0.982607\pi$
$443$	−37.3429	+	12.1334i	−1.77422	+	0.576477i	−0.775708	+	0.631092i	$0.782607\pi$
$444$	0.598935	−	0.409176i	0.0284242	−	0.0194186i
$445$	−13.2916	−	9.65691i	−0.630082	−	0.457781i
$446$	8.39697	+	6.10076i	0.397608	+	0.288879i
$447$	−9.32924	−	13.6558i	−0.441258	−	0.645895i
$448$	−1.17577	−	2.37014i	−0.0555501	−	0.111979i
$449$	−12.6726	−	17.4423i	−0.598056	−	0.823153i	0.397473	−	0.917614i	$-0.369887\pi$
$449$	−12.6726	−	17.4423i	−0.598056	−	0.823153i	−0.995529	+	0.0944606i	$0.969887\pi$
$450$	11.7204	−	3.07034i	0.552505	−	0.144737i
$451$	3.59025	+	3.76593i	0.169058	+	0.177331i
$452$		−	6.76055i		−	0.317989i
$453$	−21.4942	−	0.622986i	−1.00989	−	0.0292704i
$454$	−12.8232	+	4.16652i	−0.601823	+	0.195544i
$455$	−7.54795	−	1.27867i	−0.353853	−	0.0599451i
$456$	0.694564	+	2.36911i	0.0325259	+	0.110944i
$457$	−13.2050	−	9.59398i	−0.617703	−	0.448787i	0.234416	−	0.972136i	$-0.424682\pi$
$457$	−13.2050	−	9.59398i	−0.617703	−	0.448787i	−0.852118	+	0.523349i	$0.824682\pi$
$458$	1.50169	−	4.62174i	0.0701695	−	0.215960i
$459$	41.1118	+	3.58277i	1.91893	+	0.167229i
$460$	3.55521	+	4.89333i	0.165763	+	0.228153i
$461$	−6.51076			−0.303236			−0.151618	−	0.988439i	$-0.548448\pi$
$461$	−6.51076			−0.303236			−0.151618	+	0.988439i	$0.548448\pi$
$462$	8.13416	+	12.8388i	0.378435	+	0.597316i
$463$	24.2797			1.12838			0.564188	−	0.825647i	$-0.309189\pi$
$463$	24.2797			1.12838			0.564188	+	0.825647i	$0.309189\pi$
$464$	−2.19055	−	3.01503i	−0.101694	−	0.139969i
$465$	9.89788	+	3.53620i	0.459003	+	0.163987i
$466$	4.39804	−	13.5358i	0.203735	−	0.627033i
$467$	23.9109	+	17.3723i	1.10646	+	0.803894i	0.982103	−	0.188343i	$-0.0603117\pi$
$467$	23.9109	+	17.3723i	1.10646	+	0.803894i	0.124362	+	0.992237i	$0.460312\pi$
$468$	8.24731	+	3.21887i	0.381232	+	0.148792i
$469$	−0.666411	+	3.93379i	−0.0307720	+	0.181646i
$470$	−2.31849	+	0.753325i	−0.106944	+	0.0347483i
$471$	1.07354	−	37.0392i	0.0494662	−	1.70668i
$472$			5.42357i			0.249640i
$473$	14.6785	−	7.04279i	0.674917	−	0.323828i
$474$	−16.2759	+	21.0888i	−0.747577	+	0.968642i
$475$	3.38363	+	4.65717i	0.155252	+	0.213686i
$476$	−9.33795	−	18.8235i	−0.428004	−	0.862775i
$477$	0.114307	−	1.97025i	0.00523378	−	0.0902118i
$478$	6.07257	+	4.41198i	0.277753	+	0.201799i
$479$	17.3074	+	12.5745i	0.790794	+	0.574545i	0.908199	−	0.418539i	$-0.137458\pi$
$479$	17.3074	+	12.5745i	0.790794	+	0.574545i	−0.117405	+	0.993084i	$0.537458\pi$
$480$	−0.957991	−	1.40227i	−0.0437261	−	0.0640045i
$481$	1.17538	−	0.381904i	0.0535927	−	0.0174133i
$482$	22.1634	−	16.1027i	1.00952	−	0.733456i
$483$	13.8237	−	24.6586i	0.629001	−	1.12200i
$484$	6.03343	+	9.19770i	0.274247	+	0.418077i
$485$		−	9.10478i		−	0.413427i
$486$	−7.24594	−	13.8020i	−0.328683	−	0.626073i
$487$	2.10828	+	6.48861i	0.0955352	+	0.294027i	0.987393	−	0.158289i	$-0.0505978\pi$
$487$	2.10828	+	6.48861i	0.0955352	+	0.294027i	−0.891858	+	0.452316i	$0.850598\pi$
$488$	3.32753	−	10.2411i	0.150630	−	0.463592i
$489$	9.90660	+	33.7908i	0.447992	+	1.52807i
$490$	2.26055	−	6.48050i	0.102121	−	0.292759i
$491$	−5.55085	−	1.80358i	−0.250506	−	0.0813945i	0.181072	−	0.983470i	$-0.442043\pi$
$491$	−5.55085	−	1.80358i	−0.250506	−	0.0813945i	−0.431579	+	0.902075i	$0.642043\pi$
$492$	−0.914186	+	2.55882i	−0.0412147	+	0.115361i
$493$	−17.3972	−	23.9452i	−0.783532	−	1.07844i
$494$			4.20639i			0.189254i
$495$	6.31144	+	7.43917i	0.283678	+	0.334366i
$496$			6.18902i			0.277895i
$497$	−11.6049	−	11.8567i	−0.520550	−	0.531846i
$498$	10.7860	+	3.85349i	0.483332	+	0.172679i
$499$	4.92304	−	15.1516i	0.220386	−	0.678277i	−0.778342	−	0.627841i	$-0.783939\pi$
$499$	4.92304	−	15.1516i	0.220386	−	0.678277i	0.998727	−	0.0504361i	$-0.0160611\pi$
$500$	−7.16977	−	5.20914i	−0.320642	−	0.232960i
$501$	4.28910	+	14.6298i	0.191623	+	0.653613i
$502$	−0.981123	−	0.318786i	−0.0437897	−	0.0142281i
$503$	−7.82390	−	24.0795i	−0.348851	−	1.07365i	−0.959490	−	0.281743i	$-0.909088\pi$
$503$	−7.82390	−	24.0795i	−0.348851	−	1.07365i	0.610639	−	0.791909i	$-0.290912\pi$
$504$	−4.08031	+	6.80816i	−0.181752	+	0.303260i
$505$	−14.9364			−0.664661
$506$	9.72110	−	18.0027i	0.432156	−	0.800319i
$507$	−5.88399	−	4.54114i	−0.261317	−	0.201679i
$508$	−12.8923	+	9.36680i	−0.572003	+	0.415585i
$509$	−3.88519	−	11.9574i	−0.172208	−	0.530001i	0.827287	−	0.561779i	$-0.189883\pi$
$509$	−3.88519	−	11.9574i	−0.172208	−	0.530001i	−0.999495	+	0.0317781i	$0.989883\pi$
$510$	−7.60833	−	11.1368i	−0.336902	−	0.493144i
$511$	6.73707	−	12.8786i	0.298031	−	0.569717i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	4.85720	−	5.59139i	0.214450	−	0.246866i
$514$	2.15424	−	0.699955i	0.0950195	−	0.0308737i
$515$	8.73038	+	12.0163i	0.384707	+	0.529503i
$516$	6.73081	+	5.19469i	0.296307	+	0.228684i
$517$	5.69003	+	5.96847i	0.250247	+	0.262493i
$518$	0.161574	+	1.09616i	0.00709915	+	0.0481626i
$519$	−22.9803	−	0.666060i	−1.00872	−	0.0292368i
$520$	−0.894142	−	2.75189i	−0.0392107	−	0.120678i
$521$	0.323545	−	0.995769i	0.0141748	−	0.0436254i	−0.943719	−	0.330748i	$-0.892699\pi$
$521$	0.323545	−	0.995769i	0.0141748	−	0.0436254i	0.957894	+	0.287123i	$0.0926988\pi$
$522$	−4.06498	+	10.4152i	−0.177919	+	0.455860i
$523$	2.04864	−	2.81972i	0.0895809	−	0.123298i	−0.761874	−	0.647725i	$-0.775721\pi$
$523$	2.04864	−	2.81972i	0.0895809	−	0.123298i	0.851455	+	0.524427i	$0.175721\pi$
$524$	−5.95235	+	18.3194i	−0.260030	+	0.800289i
$525$	−3.61858	+	18.1501i	−0.157928	+	0.792137i
$526$	19.1831	−	13.9373i	0.836423	−	0.607697i
$527$			49.1529i			2.14114i
$528$	−2.87474	+	4.97352i	−0.125107	+	0.216445i
$529$	−15.0544			−0.654537
$530$	−0.521835	+	0.379135i	−0.0226671	+	0.0164686i
$531$	13.6951	−	8.78522i	0.594317	−	0.381246i
$532$	−3.71822	−	0.629891i	−0.161205	−	0.0273092i
$533$	−2.72121	+	3.74543i	−0.117869	+	0.162233i
$534$	−27.8503	+	8.16501i	−1.20520	+	0.353334i
$535$	−3.89190	−	1.26455i	−0.168261	−	0.0546714i
$536$	−1.43421	+	0.466003i	−0.0619485	+	0.0201283i
$537$	−0.889234	+	30.6803i	−0.0383733	+	1.32395i
$538$			13.3397i			0.575116i
$539$	−23.0716	+	2.58866i	−0.993764	+	0.111502i
$540$	−1.98911	+	4.69046i	−0.0855975	+	0.201845i
$541$	19.8341	−	14.4103i	0.852735	−	0.619548i	−0.0731639	−	0.997320i	$-0.523310\pi$
$541$	19.8341	−	14.4103i	0.852735	−	0.619548i	0.925899	+	0.377772i	$0.123310\pi$
$542$	0.219491	+	0.675524i	0.00942795	+	0.0290163i
$543$	13.6391	+	19.9643i	0.585309	+	0.856752i
$544$	4.66817	−	6.42518i	0.200146	−	0.275477i
$545$	3.90578	+	2.83772i	0.167305	+	0.121554i
$546$	−9.93464	+	9.17539i	−0.425163	+	0.392670i
$547$	−1.55651	−	4.79045i	−0.0665516	−	0.204825i	0.912251	−	0.409633i	$-0.134343\pi$
$547$	−1.55651	−	4.79045i	−0.0665516	−	0.204825i	−0.978802	+	0.204808i	$0.934343\pi$
$548$	−1.41651	−	1.94965i	−0.0605102	−	0.0832851i
$549$	−31.2499	+	8.18637i	−1.33371	+	0.349386i
$550$	−2.41066	+	13.1759i	−0.102791	+	0.561823i
$551$	−5.31207			−0.226302
$552$	10.6802	+	0.309555i	0.454581	+	0.0131755i
$553$	−18.0835	−	36.4530i	−0.768990	−	1.55014i
$554$	12.9815	+	4.21795i	0.551531	+	0.179203i
$555$	0.200088	+	0.682485i	0.00849324	+	0.0289699i
$556$	−7.60075	+	10.4615i	−0.322344	+	0.443668i
$557$	31.8805	+	10.3586i	1.35082	+	0.438908i	0.892968	−	0.450120i	$-0.148619\pi$
$557$	31.8805	+	10.3586i	1.35082	+	0.438908i	0.457853	+	0.889028i	$0.348619\pi$
$558$	15.6279	−	10.0251i	0.661584	−	0.424397i
$559$	8.51476	+	11.7196i	0.360136	+	0.495684i
$560$	2.56641	−	0.378289i	0.108451	−	0.0159856i
$561$	−22.8311	+	39.4995i	−0.963928	+	1.66767i
$562$	−2.59452			−0.109443
$563$	−19.3252	+	14.0405i	−0.814458	+	0.591738i	−0.915120	−	0.403182i	$-0.867904\pi$
$563$	−19.3252	+	14.0405i	−0.814458	+	0.591738i	0.100662	+	0.994921i	$0.467904\pi$
$564$	−1.44885	+	4.05537i	−0.0610077	+	0.170762i
$565$	6.30424	+	2.04837i	0.265222	+	0.0861757i
$566$	19.9539	+	14.4974i	0.838726	+	0.609370i
$567$	23.8007	−	0.724784i	0.999537	−	0.0304381i
$568$	1.93776	−	5.96382i	0.0813068	−	0.250236i
$569$	−37.0388	+	12.0346i	−1.55275	+	0.504518i	−0.954858	−	0.297062i	$-0.903993\pi$
$569$	−37.0388	+	12.0346i	−1.55275	+	0.504518i	−0.597887	+	0.801580i	$0.703993\pi$
$570$	−2.41965	−	0.0701310i	−0.101348	−	0.00293747i
$571$	17.4116			0.728651			0.364325	−	0.931272i	$-0.381300\pi$
$571$	17.4116			0.728651			0.364325	+	0.931272i	$0.381300\pi$
$572$	−7.08414	+	6.75365i	−0.296203	+	0.282384i
$573$	7.65693	−	9.92114i	0.319873	−	0.414462i
$574$	−2.90327	−	2.96627i	−0.121180	−	0.123810i
$575$	23.6942	−	7.69872i	0.988118	−	0.321059i
$576$	−2.99496	−	0.173757i	−0.124790	−	0.00723989i
$577$	7.30337	−	10.0522i	0.304043	−	0.418480i	−0.629469	−	0.777026i	$-0.716727\pi$
$577$	7.30337	−	10.0522i	0.304043	−	0.418480i	0.933512	+	0.358546i	$0.116727\pi$
$578$	27.0820	−	37.2752i	1.12646	−	1.55044i
$579$	−10.4367	+	7.13005i	−0.433734	+	0.296315i
$580$	3.47524	−	1.12917i	0.144302	−	0.0468864i
$581$	−12.5035	+	12.2379i	−0.518732	+	0.507714i
$582$	−12.7326	−	9.82675i	−0.527783	−	0.407332i
$583$	1.91985	+	1.03668i	0.0795120	+	0.0429348i
$584$	5.49346			0.227321
$585$	−5.50046	+	6.71537i	−0.227416	+	0.277646i
$586$	−15.3950	+	5.00213i	−0.635961	+	0.206636i
$587$	0.0736050	−	0.226533i	0.00303800	−	0.00935002i	−0.949526	−	0.313688i	$-0.898435\pi$
$587$	0.0736050	−	0.226533i	0.00303800	−	0.00935002i	0.952564	+	0.304338i	$0.0984353\pi$
$588$	−6.62288	−	10.1557i	−0.273123	−	0.418813i
$589$	7.13690	+	5.18526i	0.294071	+	0.213655i
$590$	−5.05751	−	1.64328i	−0.208214	−	0.0676529i
$591$	−23.0988	−	8.25247i	−0.950159	−	0.339461i
$592$	−0.338806	+	0.246157i	−0.0139248	+	0.0101170i
$593$	−20.2150			−0.830133			−0.415066	−	0.909791i	$-0.636242\pi$
$593$	−20.2150			−0.830133			−0.415066	+	0.909791i	$0.636242\pi$
$594$	17.2152	−	0.797184i	0.706350	−	0.0327089i
$595$	20.3823	−	3.00435i	0.835595	−	0.123166i
$596$	5.61240	+	7.72480i	0.229893	+	0.316420i
$597$	21.0644	+	7.52564i	0.862108	+	0.308004i
$598$	17.3136	+	5.62553i	0.708006	+	0.230045i
$599$	2.46742	−	3.39611i	0.100816	−	0.138761i	−0.755629	−	0.655000i	$-0.772668\pi$
$599$	2.46742	−	3.39611i	0.100816	−	0.138761i	0.856444	+	0.516239i	$0.172668\pi$
$600$	−6.71258	+	1.96796i	−0.274040	+	0.0803416i
$601$	−38.2778	−	12.4372i	−1.56139	−	0.507325i	−0.604208	−	0.796826i	$-0.706511\pi$
$601$	−38.2778	−	12.4372i	−1.56139	−	0.507325i	−0.957178	+	0.289501i	$0.906511\pi$
$602$	−11.6345	+	5.77163i	−0.474187	+	0.235234i
$603$	3.49988	+	2.86670i	0.142526	+	0.116741i
$604$	12.4149			0.505155
$605$	−10.4050	+	2.83940i	−0.423022	+	0.115438i
$606$	−16.1208	+	20.8878i	−0.654862	+	0.848511i
$607$	24.5908	+	33.8463i	0.998109	+	1.37378i	0.926479	+	0.376348i	$0.122820\pi$
$607$	24.5908	+	33.8463i	0.998109	+	1.37378i	0.0716301	+	0.997431i	$0.477180\pi$
$608$	−0.440466	−	1.35562i	−0.0178633	−	0.0549775i
$609$	−11.5872	−	12.5460i	−0.469538	−	0.508391i
$610$	8.54166	+	6.20588i	0.345842	+	0.251269i
$611$	−4.31273	+	5.93597i	−0.174475	+	0.240144i
$612$	−23.7859	−	1.37997i	−0.961487	−	0.0557822i
$613$	6.15484	+	18.9427i	0.248592	+	0.765087i	0.995025	+	0.0996263i	$0.0317647\pi$
$613$	6.15484	+	18.9427i	0.248592	+	0.765087i	−0.746433	+	0.665460i	$0.768235\pi$
$614$	−9.40654	+	6.83425i	−0.379617	+	0.275808i
$615$	−2.10913	−	1.62778i	−0.0850482	−	0.0656384i
$616$	−4.90904	−	7.27333i	−0.197791	−	0.293051i
$617$		−	31.7385i		−	1.27774i	−0.769313	−	0.638871i	$-0.779402\pi$
$617$		−	31.7385i		−	1.27774i	0.769313	−	0.638871i	$-0.220598\pi$
$618$	26.2270	+	0.760160i	1.05500	+	0.0305781i
$619$	15.5378	−	5.04855i	0.624518	−	0.202918i	0.0203728	−	0.999792i	$-0.493515\pi$
$619$	15.5378	−	5.04855i	0.624518	−	0.202918i	0.604145	+	0.796874i	$0.293515\pi$
$620$	−5.77129	−	1.87521i	−0.231781	−	0.0753101i
$621$	−16.5184	−	27.4702i	−0.662861	−	1.10234i
$622$	−4.63302	+	6.37681i	−0.185767	+	0.255687i
$623$	7.40474	−	43.7099i	0.296664	−	1.75120i
$624$	−4.81343	−	1.71968i	−0.192691	−	0.0688425i
$625$	−9.30669	+	6.76171i	−0.372268	+	0.270468i
$626$	−14.3704			−0.574358
$627$	3.32673	+	7.48192i	0.132857	+	0.298799i
$628$			21.3936i			0.853697i
$629$	−2.69078	+	1.95497i	−0.107288	+	0.0779496i
$630$	−5.11235	−	5.86771i	−0.203681	−	0.233775i
$631$	−3.45819	+	10.6432i	−0.137668	+	0.423700i	−0.995996	−	0.0894031i	$-0.971504\pi$
$631$	−3.45819	+	10.6432i	−0.137668	+	0.423700i	0.858327	+	0.513103i	$0.171504\pi$
$632$	9.04020	−	12.4428i	0.359600	−	0.494947i
$633$	8.14922	+	27.7964i	0.323902	+	1.10481i
$634$	5.42261	−	16.6891i	0.215359	−	0.662808i
$635$	−4.82836	−	14.8602i	−0.191608	−	0.589708i
$636$	−0.0330116	+	1.13896i	−0.00130899	+	0.0451628i
$637$	−5.96031	−	19.7789i	−0.236156	−	0.783669i
$638$	−8.52891	−	8.94627i	−0.337663	−	0.354186i
$639$	−18.1981	+	4.76727i	−0.719907	+	0.188590i
$640$	0.576320	+	0.793236i	0.0227810	+	0.0313554i
$641$	11.3985	−	3.70361i	0.450215	−	0.146284i	−0.0751285	−	0.997174i	$-0.523937\pi$
$641$	11.3985	−	3.70361i	0.450215	−	0.146284i	0.525344	+	0.850890i	$0.323937\pi$
$642$	−5.96893	+	4.07781i	−0.235575	+	0.160938i
$643$	−25.5731	+	35.1984i	−1.00851	+	1.38809i	−0.0885491	+	0.996072i	$0.528223\pi$
$643$	−25.5731	+	35.1984i	−1.00851	+	1.38809i	−0.919957	+	0.392018i	$0.871777\pi$
$644$	−7.56532	+	14.4619i	−0.298115	+	0.569879i
$645$	−6.88344	+	4.70258i	−0.271035	+	0.185164i
$646$	−3.49816	−	10.7662i	−0.137633	−	0.423592i
$647$	14.5630	−	10.5806i	0.572531	−	0.415968i	−0.263493	−	0.964661i	$-0.584875\pi$
$647$	14.5630	−	10.5806i	0.572531	−	0.415968i	0.836024	+	0.548693i	$0.184875\pi$
$648$	4.41255	+	7.84407i	0.173342	+	0.308144i
$649$	2.38894	+	17.8286i	0.0937740	+	0.699834i
$650$	−11.9183			−0.467473
$651$	3.32117	+	28.1665i	0.130167	+	1.10393i
$652$	−6.28239	−	19.3352i	−0.246037	−	0.757226i
$653$	−19.0613	−	6.19338i	−0.745925	−	0.242366i	−0.0886982	−	0.996059i	$-0.528271\pi$
$653$	−19.0613	−	6.19338i	−0.745925	−	0.242366i	−0.657227	+	0.753693i	$0.728271\pi$
$654$	8.18391	−	2.39932i	0.320016	−	0.0938207i
$655$	−15.2795	−	11.1012i	−0.597019	−	0.433759i
$656$	0.484783	−	1.49201i	0.0189276	−	0.0582531i
$657$	−8.89844	−	13.8716i	−0.347161	−	0.541182i
$658$	−4.60126	−	4.70111i	−0.179376	−	0.183269i
$659$			16.9352i			0.659703i	0.944033	+	0.329852i	$0.106999\pi$
$659$			16.9352i			0.659703i	−0.944033	+	0.329852i	$0.893001\pi$
$660$	−3.76681	−	4.18763i	−0.146623	−	0.163003i
$661$		−	25.7582i		−	1.00188i	−0.865483	−	0.500938i	$-0.832988\pi$
$661$		−	25.7582i		−	1.00188i	0.865483	−	0.500938i	$-0.167012\pi$
$662$	17.2175	+	23.6978i	0.669176	+	0.921042i
$663$	−38.2280	−	13.6577i	−1.48465	−	0.530419i
$664$	−6.28914	−	2.04347i	−0.244066	−	0.0793019i
$665$	1.71396	−	3.27641i	0.0664644	−	0.127054i
$666$	1.17038	+	0.456791i	0.0453512	+	0.0177003i
$667$	−7.10425	+	21.8646i	−0.275078	+	0.846602i
$668$	−2.71998	−	8.37125i	−0.105239	−	0.323893i
$669$	−0.520835	+	17.9698i	−0.0201367	+	0.694753i
$670$		−	1.47860i		−	0.0571234i
$671$	6.42749	−	35.1307i	0.248130	−	1.35620i
$672$	2.24090	−	3.99729i	0.0864446	−	0.154199i
$673$	29.9531	−	21.7622i	1.15461	−	0.838871i	0.165520	−	0.986206i	$-0.447070\pi$
$673$	29.9531	−	21.7622i	1.15461	−	0.838871i	0.989087	+	0.147335i	$0.0470697\pi$
$674$	−0.536784	+	0.174412i	−0.0206761	+	0.00671809i
$675$	15.8425	+	13.7623i	0.609778	+	0.529709i
$676$	3.47166	+	2.52231i	0.133525	+	0.0970117i
$677$	−22.3901	−	16.2674i	−0.860523	−	0.625206i	0.0675045	−	0.997719i	$-0.478496\pi$
$677$	−22.3901	−	16.2674i	−0.860523	−	0.625206i	−0.928027	+	0.372513i	$0.878496\pi$
$678$	9.66870	−	6.60539i	0.371324	−	0.253678i
$679$	22.0089	−	10.9181i	0.844623	−	0.418999i
$680$	4.57711	+	6.29985i	0.175524	+	0.241588i
$681$	−18.4877	−	14.2684i	−0.708451	−	0.546767i
$682$	2.72610	+	20.3448i	0.104388	+	0.779044i
$683$		−	37.9246i		−	1.45115i	−0.688145	−	0.725573i	$-0.741575\pi$
$683$		−	37.9246i		−	1.45115i	0.688145	−	0.725573i	$-0.258425\pi$
$684$	−2.70960	+	3.30808i	−0.103604	+	0.126488i
$685$	2.24725	−	0.730175i	0.0858629	−	0.0278986i
$686$	18.3760	−	2.30678i	0.701600	−	0.0880732i
$687$	8.07708	−	2.36800i	0.308160	−	0.0903447i
$688$	−3.97129	−	2.88531i	−0.151404	−	0.110002i
$689$	−0.599919	+	1.84636i	−0.0228551	+	0.0703407i
$690$	−3.52466	+	9.86557i	−0.134181	+	0.375576i
$691$	20.8099	+	28.6424i	0.791648	+	1.08961i	0.993901	+	0.110276i	$0.0351736\pi$
$691$	20.8099	+	28.6424i	0.791648	+	1.08961i	−0.202253	+	0.979333i	$0.564826\pi$
$692$	13.2733			0.504574
$693$	−10.4142	+	24.1774i	−0.395602	+	0.918422i
$694$	21.7753			0.826578
$695$	−7.45249	−	10.2575i	−0.282689	−	0.389088i
$696$	2.17172	−	6.07868i	0.0823188	−	0.230412i
$697$	3.85012	−	11.8495i	0.145834	−	0.448831i
$698$	−15.5567	−	11.3026i	−0.588830	−	0.427810i
$699$	23.6555	−	6.93521i	0.894734	−	0.262314i
$700$	1.78472	−	10.5351i	0.0674560	−	0.398190i
$701$	−9.31719	+	3.02734i	−0.351905	+	0.114341i	−0.479635	−	0.877468i	$-0.659231\pi$
$701$	−9.31719	+	3.02734i	−0.351905	+	0.114341i	0.127730	+	0.991809i	$0.459231\pi$
$702$	3.45451	+	14.9400i	0.130382	+	0.563874i
$703$			0.596930i			0.0225136i
$704$	1.57584	−	2.91834i	0.0593919	−	0.109989i
$705$	−3.34266	−	2.57980i	−0.125892	−	0.0971607i
$706$	−19.8760	−	27.3570i	−0.748043	−	1.02959i
$707$	−17.9112	−	36.1056i	−0.673620	−	1.35789i
$708$	−7.75660	+	5.29910i	−0.291511	+	0.199152i
$709$	−25.2904	−	18.3746i	−0.949802	−	0.690072i	0.000957708	−	1.00000i	$-0.499695\pi$
$709$	−25.2904	−	18.3746i	−0.949802	−	0.690072i	−0.950760	+	0.309928i	$0.899695\pi$
$710$	4.97417	+	3.61395i	0.186677	+	0.135629i
$711$	−46.0629	−	2.67241i	−1.72749	−	0.100223i
$712$	15.9361	−	5.17794i	0.597229	−	0.194051i
$713$	30.8874	−	22.4410i	1.15674	−	0.840423i
$714$	17.7971	−	31.7463i	0.666041	−	1.18808i
$715$	−4.15140	−	8.65228i	−0.155253	−	0.323577i
$716$		−	17.7207i		−	0.662253i
$717$	−0.376661	+	12.9955i	−0.0140667	+	0.485326i
$718$	−8.01810	−	24.6772i	−0.299233	−	0.920944i
$719$	−5.08235	+	15.6419i	−0.189540	+	0.583343i	−0.999997	−	0.00245449i	$-0.999219\pi$
$719$	−5.08235	+	15.6419i	−0.189540	+	0.583343i	0.810457	+	0.585798i	$0.199219\pi$
$720$	1.06947	−	2.74017i	0.0398569	−	0.102120i
$721$	−18.5778	+	35.5134i	−0.691874	+	1.32259i
$722$	16.1378	+	5.24349i	0.600587	+	0.195143i
$723$	44.6842	+	15.9642i	1.66182	+	0.593717i
$724$	−8.20517	−	11.2934i	−0.304943	−	0.419718i
$725$		−	15.0511i		−	0.558984i
$726$	−7.25928	+	17.6154i	−0.269417	+	0.653769i
$727$		−	21.5954i		−	0.800930i	−0.916312	−	0.400465i	$-0.868849\pi$
$727$		−	21.5954i		−	0.800930i	0.916312	−	0.400465i	$-0.131151\pi$
$728$	5.57988	−	5.46136i	0.206804	−	0.202412i
$729$	12.6596	−	23.8482i	0.468873	−	0.883266i
$730$	−1.66446	+	5.12268i	−0.0616045	+	0.189599i
$731$	−31.5398	−	22.9150i	−1.16654	−	0.847543i
$732$	17.8976	−	5.24713i	0.661515	−	0.193939i
$733$	−7.40470	−	2.40593i	−0.273499	−	0.0888652i	0.169056	−	0.985606i	$-0.445928\pi$
$733$	−7.40470	−	2.40593i	−0.273499	−	0.0888652i	−0.442555	+	0.896741i	$0.645928\pi$
$734$	−8.07323	−	24.8469i	−0.297989	−	0.917114i
$735$	11.4769	−	3.09881i	0.423331	−	0.114301i
$736$	−6.16882			−0.227386
$737$	−4.50934	+	2.16360i	−0.166104	+	0.0796972i
$738$	−4.55275	+	1.19266i	−0.167589	+	0.0439024i
$739$	32.5390	−	23.6410i	1.19697	−	0.869647i	0.202984	−	0.979182i	$-0.434936\pi$
$739$	32.5390	−	23.6410i	1.19697	−	0.869647i	0.993983	+	0.109535i	$0.0349360\pi$
$740$	−0.126888	−	0.390521i	−0.00466449	−	0.0143558i
$741$	−6.01583	+	4.10985i	−0.220997	+	0.150979i
$742$	−1.54225	−	0.806781i	−0.0566177	−	0.0296179i
$743$	−7.24522	+	9.97219i	−0.265801	+	0.365844i	−0.920967	−	0.389641i	$-0.872599\pi$
$743$	−7.24522	+	9.97219i	−0.265801	+	0.365844i	0.655165	+	0.755486i	$0.272599\pi$
$744$	−8.85132	+	6.04698i	−0.324505	+	0.221693i
$745$	−8.90391	+	2.89306i	−0.326214	+	0.105993i
$746$	−12.7560	−	17.5571i	−0.467030	−	0.642811i
$747$	5.02732	+	19.1908i	0.183940	+	0.702155i
$748$	12.5153	−	23.1773i	0.457604	−	0.847447i
$749$	−1.61023	−	10.9243i	−0.0588366	−	0.399164i
$750$	0.444716	−	15.3436i	0.0162387	−	0.560267i
$751$	5.59622	+	17.2234i	0.204209	+	0.628491i	0.999745	+	0.0225844i	$0.00718944\pi$
$751$	5.59622	+	17.2234i	0.204209	+	0.628491i	−0.795536	+	0.605906i	$0.792811\pi$
$752$	0.768311	−	2.36462i	0.0280174	−	0.0862288i
$753$	−0.502689	−	1.71464i	−0.0183190	−	0.0624849i
$754$	6.46445	−	8.89756i	0.235421	−	0.324030i
$755$	−3.76158	+	11.5770i	−0.136898	+	0.421329i
$756$	−13.7235	+	0.816390i	−0.499118	+	0.0296918i
$757$	5.24019	−	3.80722i	0.190458	−	0.138376i	−0.488470	−	0.872581i	$-0.662445\pi$
$757$	5.24019	−	3.80722i	0.190458	−	0.138376i	0.678928	+	0.734205i	$0.262445\pi$
$758$		−	17.7483i		−	0.644647i
$759$	35.2449	−	3.68677i	1.27931	−	0.133821i
$760$	1.39758			0.0506954
$761$	−11.7456	+	8.53367i	−0.425777	+	0.309345i	−0.779958	−	0.625832i	$-0.784760\pi$
$761$	−11.7456	+	8.53367i	−0.425777	+	0.309345i	0.354181	+	0.935177i	$0.384760\pi$
$762$	−25.9925	−	9.28629i	−0.941609	−	0.336407i
$763$	−2.17591	+	12.8443i	−0.0787732	+	0.464995i
$764$	−4.25292	+	5.85365i	−0.153865	+	0.211778i
$765$	8.49370	−	21.7623i	0.307090	−	0.786819i
$766$	9.66205	+	3.13939i	0.349104	+	0.113431i
$767$	−15.2220	+	4.94592i	−0.549633	+	0.178587i
$768$	1.73132	+	0.0501805i	0.0624738	+	0.00181073i
$769$			8.43623i			0.304218i	0.988364	+	0.152109i	$0.0486065\pi$
$769$			8.43623i			0.304218i	−0.988364	+	0.152109i	$0.951393\pi$
$770$	8.26980	−	2.37396i	0.298023	−	0.0855517i
$771$	3.10585	+	2.39703i	0.111855	+	0.0863269i
$772$	5.90383	−	4.28938i	0.212483	−	0.154378i
$773$	10.6163	+	32.6737i	0.381843	+	1.17519i	0.938744	+	0.344614i	$0.111990\pi$
$773$	10.6163	+	32.6737i	0.381843	+	1.17519i	−0.556901	+	0.830579i	$0.688010\pi$
$774$	−0.852939	+	14.7016i	−0.0306583	+	0.528440i
$775$	−14.6918	+	20.2215i	−0.527745	+	0.726378i
$776$	7.51246	+	5.45812i	0.269681	+	0.195935i
$777$	−1.40983	+	1.30208i	−0.0505773	+	0.0467119i
$778$	4.59643	+	14.1463i	0.164790	+	0.507171i
$779$	−1.31436	−	1.80906i	−0.0470918	−	0.0648163i
$780$	3.06203	−	3.96750i	0.109638	−	0.142059i
$781$	3.74300	−	20.4581i	0.133935	−	0.732048i
$782$	−48.9925			−1.75197
$783$	−18.8671	+	4.36256i	−0.674256	+	0.155905i
$784$	3.99199	+	5.75013i	0.142571	+	0.205362i
$785$	−19.9496	−	6.48203i	−0.712033	−	0.231354i
$786$	−32.0156	+	9.38616i	−1.14196	+	0.334793i
$787$	−25.1697	+	34.6431i	−0.897203	+	1.23489i	0.0741492	+	0.997247i	$0.476376\pi$
$787$	−25.1697	+	34.6431i	−0.897203	+	1.23489i	−0.971352	+	0.237646i	$0.923624\pi$
$788$	13.4686	+	4.37620i	0.479797	+	0.155896i
$789$	38.6755	+	13.8175i	1.37689	+	0.491917i
$790$	8.86386	+	12.2001i	0.315362	+	0.434059i
$791$	2.60832	+	17.6955i	0.0927410	+	0.629180i
$792$	−9.92172	+	0.748018i	−0.352553	+	0.0265797i
$793$	31.7774			1.12845
$794$	−17.5667	+	12.7630i	−0.623420	+	0.452941i
$795$	−1.05209	−	0.375877i	−0.0373136	−	0.0133310i
$796$	−12.2823	−	3.99076i	−0.435335	−	0.141449i
$797$	24.5882	+	17.8644i	0.870960	+	0.632789i	0.930844	−	0.365416i	$-0.119073\pi$
$797$	24.5882	+	17.8644i	0.870960	+	0.632789i	−0.0598844	+	0.998205i	$0.519073\pi$
$798$	−2.73204	−	5.93311i	−0.0967131	−	0.210030i
$799$	6.10190	−	18.7797i	0.215870	−	0.664378i
$800$	3.84097	−	1.24801i	0.135799	−	0.0441237i
$801$	−38.8884	−	31.8529i	−1.37406	−	1.12547i
$802$	−10.0189			−0.353779
$803$	18.0584	−	2.41972i	0.637266	−	0.0853902i
$804$	−2.06776	−	1.59585i	−0.0729242	−	0.0562813i
$805$	−11.1936	−	11.4365i	−0.394522	−	0.403084i
$806$	−17.3703	+	5.64395i	−0.611843	+	0.198800i
$807$	−19.0780	+	13.0336i	−0.671578	+	0.458803i
$808$	8.95405	−	12.3242i	0.315002	−	0.433564i
$809$	−28.8637	+	39.7274i	−1.01479	+	1.39674i	−0.0990006	+	0.995087i	$0.531565\pi$
$809$	−28.8637	+	39.7274i	−1.01479	+	1.39674i	−0.915791	+	0.401654i	$0.868435\pi$
$810$	−8.65159	+	1.73806i	−0.303986	+	0.0610693i
$811$	8.48149	−	2.75580i	0.297825	−	0.0967693i	−0.156293	−	0.987711i	$-0.549954\pi$
$811$	8.48149	−	2.75580i	0.297825	−	0.0967693i	0.454118	+	0.890941i	$0.349954\pi$
$812$	6.89693	+	7.04660i	0.242035	+	0.247287i
$813$	−0.751658	+	0.973930i	−0.0263618	+	0.0341572i
$814$	−1.00531	+	0.958413i	−0.0352362	+	0.0335923i
$815$	19.9337			0.698247
$816$	13.7501	+	0.398532i	0.481350	+	0.0139514i
$817$	−6.65443	+	2.16216i	−0.232809	+	0.0756443i
$818$	4.00613	−	12.3296i	0.140071	−	0.431094i
$819$	−22.8290	−	5.24337i	−0.797708	−	0.183218i
$820$	1.24442	+	0.904125i	0.0434571	+	0.0315734i
$821$	−20.0322	−	6.50887i	−0.699130	−	0.227161i	−0.0621783	−	0.998065i	$-0.519805\pi$
$821$	−20.0322	−	6.50887i	−0.699130	−	0.227161i	−0.636951	+	0.770904i	$0.719805\pi$
$822$	1.40433	−	3.93075i	0.0489817	−	0.137101i
$823$	−26.8396	+	19.5001i	−0.935571	+	0.679732i	−0.947351	−	0.320198i	$-0.896250\pi$
$823$	−26.8396	+	19.5001i	−0.935571	+	0.679732i	0.0117793	+	0.999931i	$0.496250\pi$
$824$	−15.1485			−0.527723
$825$	−21.1991	+	9.42588i	−0.738057	+	0.328167i
$826$	−2.09249	−	14.1960i	−0.0728071	−	0.493943i
$827$	−6.91009	−	9.51092i	−0.240287	−	0.330727i	0.671793	−	0.740739i	$-0.265525\pi$
$827$	−6.91009	−	9.51092i	−0.240287	−	0.330727i	−0.912080	+	0.410012i	$0.865525\pi$
$828$	9.99240	+	15.5769i	0.347260	+	0.541336i
$829$	27.8383	+	9.04521i	0.966864	+	0.314153i	0.749549	−	0.661948i	$-0.230270\pi$
$829$	27.8383	+	9.04521i	0.966864	+	0.314153i	0.217315	+	0.976102i	$0.430270\pi$
$830$	3.81109	−	5.24551i	0.132285	−	0.182074i
$831$	6.65121	+	22.6868i	0.230728	+	0.786998i
$832$	2.80663	+	0.911930i	0.0973024	+	0.0316155i
$833$	31.7042	+	45.6673i	1.09848	+	1.58228i
$834$	−22.3880	−	0.648893i	−0.775234	−	0.0224693i
$835$	8.63036			0.298666
$836$	−2.04503	−	4.26223i	−0.0707289	−	0.147412i
$837$	29.6069	+	12.5555i	1.02336	+	0.433982i
$838$	−3.19411	−	4.39631i	−0.110339	−	0.151868i
$839$	7.98646	+	24.5798i	0.275723	+	0.848588i	0.989027	+	0.147734i	$0.0471978\pi$
$839$	7.98646	+	24.5798i	0.275723	+	0.848588i	−0.713304	+	0.700855i	$0.752802\pi$
$840$	3.04853	+	3.30079i	0.105184	+	0.113888i
$841$	−12.2251	−	8.88208i	−0.421556	−	0.306279i
$842$	−1.30648	+	1.79822i	−0.0450244	+	0.0619707i
$843$	−2.53498	−	3.71059i	−0.0873092	−	0.127800i
$844$	−5.16792	−	15.9052i	−0.177887	−	0.547481i
$845$	−3.40394	+	2.47311i	−0.117099	+	0.0850774i
$846$	−7.21545	+	1.89019i	−0.248072	+	0.0649862i
$847$	−19.3409	−	21.7469i	−0.664562	−	0.747233i
$848$		−	0.657856i		−	0.0225909i
$849$	−1.23767	+	42.7021i	−0.0424768	+	1.46553i
$850$	30.5048	−	9.91161i	1.04631	−	0.339965i
$851$	2.45698	+	0.798321i	0.0842242	+	0.0273661i
$852$	10.4225	−	3.05563i	0.357071	−	0.104684i
$853$	−12.3782	+	17.0371i	−0.423820	+	0.583338i	−0.966521	−	0.256588i	$-0.917402\pi$
$853$	−12.3782	+	17.0371i	−0.423820	+	0.583338i	0.542701	+	0.839926i	$0.317402\pi$
$854$	−4.75855	+	28.0895i	−0.162834	+	0.961204i
$855$	−2.26382	−	3.52903i	−0.0774211	−	0.120690i
$856$	3.37651	−	2.45318i	0.115407	−	0.0838479i
$857$	−44.6368			−1.52476			−0.762381	−	0.647128i	$-0.775970\pi$
$857$	−44.6368			−1.52476			−0.762381	+	0.647128i	$0.775970\pi$
$858$	−16.5804	−	3.53284i	−0.566045	−	0.120609i
$859$			13.9455i			0.475814i	0.971288	+	0.237907i	$0.0764613\pi$
$859$			13.9455i			0.475814i	−0.971288	+	0.237907i	$0.923539\pi$
$860$	3.89383	−	2.82903i	0.132779	−	0.0964692i
$861$	1.40562	−	7.05035i	0.0479035	−	0.240275i
$862$	−1.87450	+	5.76913i	−0.0638458	+	0.196497i
$863$	12.1910	−	16.7794i	0.414985	−	0.571178i	−0.549440	−	0.835533i	$-0.685159\pi$
$863$	12.1910	−	16.7794i	0.414985	−	0.571178i	0.964425	+	0.264355i	$0.0851591\pi$
$864$	−2.67773	−	4.45306i	−0.0910981	−	0.151496i
$865$	−4.02166	+	12.3774i	−0.136741	+	0.420844i
$866$	9.29522	+	28.6078i	0.315865	+	0.972131i
$867$	79.7702	+	2.31205i	2.70914	+	0.0785214i
$868$	−2.38781	−	16.1996i	−0.0810477	−	0.549849i
$869$	24.2367	−	44.8844i	0.822172	−	1.52260i
$870$	5.01039	+	3.86691i	0.169868	+	0.131101i
$871$	−2.61580	−	3.60034i	−0.0886330	−	0.121993i
$872$	−4.68287	+	1.52156i	−0.158582	+	0.0515264i
$873$	1.61350	−	27.8110i	0.0546086	−	0.941258i
$874$	−5.16834	+	7.11361i	−0.174822	+	0.240621i
$875$	20.7764	+	10.8686i	0.702371	+	0.367425i
$876$	5.36739	+	7.85656i	0.181347	+	0.265449i
$877$	−12.6246	−	38.8545i	−0.426302	−	1.31202i	−0.901742	−	0.432275i	$-0.857711\pi$
$877$	−12.6246	−	38.8545i	−0.426302	−	1.31202i	0.475439	−	0.879749i	$-0.342289\pi$
$878$	7.16940	−	5.20887i	0.241955	−	0.175791i
$879$	−22.1955	−	17.1300i	−0.748637	−	0.577782i
$880$	2.24390	+	2.35371i	0.0756420	+	0.0793435i
$881$	28.6159			0.964095			0.482048	−	0.876145i	$-0.339893\pi$
$881$	28.6159			0.964095			0.482048	+	0.876145i	$0.339893\pi$
$882$	8.05341	−	19.3944i	0.271172	−	0.653043i
$883$	5.87712	+	18.0879i	0.197781	+	0.608706i	0.999933	+	0.0115868i	$0.00368826\pi$
$883$	5.87712	+	18.0879i	0.197781	+	0.608706i	−0.802152	+	0.597120i	$0.796312\pi$
$884$	22.2901	+	7.24251i	0.749699	+	0.243592i
$885$	−2.59127	−	8.83864i	−0.0871045	−	0.297108i
$886$	31.7658	+	23.0792i	1.06719	+	0.775360i
$887$	−12.2419	+	37.6767i	−0.411043	+	1.26506i	0.504700	+	0.863295i	$0.331603\pi$
$887$	−12.2419	+	37.6767i	−0.411043	+	1.26506i	−0.915743	+	0.401765i	$0.868397\pi$
$888$	−0.683075	−	0.244041i	−0.0229225	−	0.00818948i
$889$	30.1313	−	29.4914i	1.01057	−	0.989108i
$890$			16.4293i			0.550712i
$891$	17.9603	+	23.8418i	0.601691	+	0.798729i
$892$		−	10.3792i		−	0.347522i
$893$	−2.08307	−	2.86710i	−0.0697073	−	0.0959438i
$894$	−5.56415	+	15.5742i	−0.186093	+	0.520878i
$895$	16.5246	+	5.36918i	0.552358	+	0.179472i
$896$	−1.22638	+	2.34435i	−0.0409705	+	0.0783194i
$897$	8.87081	+	30.2578i	0.296188	+	1.01028i
$898$	−6.66237	+	20.5047i	−0.222326	+	0.684250i
$899$	−7.12752	−	21.9362i	−0.237716	−	0.731615i
$900$	−9.37304	−	7.67731i	−0.312435	−	0.255910i
$901$		−	5.22466i		−	0.174059i
$902$	0.936411	−	5.11813i	0.0311791	−	0.170415i
$903$	−19.6219	−	11.0001i	−0.652975	−	0.366061i
$904$	−5.46940	+	3.97375i	−0.181909	+	0.132165i
$905$	13.0173	−	4.22957i	0.432709	−	0.140596i
$906$	12.1300	+	17.7554i	0.402991	+	0.589882i
$907$	−26.4488	−	19.2162i	−0.878219	−	0.638064i	0.0545606	−	0.998510i	$-0.482624\pi$
$907$	−26.4488	−	19.2162i	−0.878219	−	0.638064i	−0.932780	+	0.360447i	$0.882624\pi$
$908$	10.9081	+	7.92518i	0.361997	+	0.263006i
$909$	−45.6239	−	2.64694i	−1.51325	−	0.0877935i
$910$	3.40211	+	6.85800i	0.112779	+	0.227341i
$911$	34.4831	+	47.4619i	1.14248	+	1.57248i	0.761851	+	0.647752i	$0.224291\pi$
$911$	34.4831	+	47.4619i	1.14248	+	1.57248i	0.380624	+	0.924730i	$0.375709\pi$
$912$	1.50840	−	1.95444i	0.0499480	−	0.0647181i
$913$	−21.5740	−	3.94718i	−0.713997	−	0.130632i
$914$			16.3222i			0.539892i
$915$	−0.529810	+	18.2794i	−0.0175150	+	0.604300i
$916$	−4.62174	+	1.50169i	−0.152706	+	0.0496173i
$917$	8.51219	−	50.2471i	0.281097	−	1.65931i
$918$	−21.2664	−	35.3660i	−0.701895	−	1.16725i
$919$	12.2402	+	8.89300i	0.403766	+	0.293353i	0.771073	−	0.636747i	$-0.219720\pi$
$919$	12.2402	+	8.89300i	0.403766	+	0.293353i	−0.367307	+	0.930100i	$0.619720\pi$
$920$	1.86909	−	5.75246i	0.0616220	−	0.189653i
$921$	−18.9648	−	6.77551i	−0.624910	−	0.223261i
$922$	3.82693	+	5.26732i	0.126033	+	0.173470i
$923$	18.5054			0.609111
$924$	5.60569	−	14.1271i	0.184414	−	0.464749i
$925$	−1.69133			−0.0556105
$926$	−14.2713	−	19.6427i	−0.468983	−	0.645500i
$927$	24.5379	+	38.2516i	0.805930	+	1.25635i
$928$	−1.15164	+	3.54438i	−0.0378044	+	0.116350i
$929$	15.4855	+	11.2509i	0.508063	+	0.369130i	0.812088	−	0.583534i	$-0.198331\pi$
$929$	15.4855	+	11.2509i	0.508063	+	0.369130i	−0.304025	+	0.952664i	$0.598331\pi$
$930$	−2.95698	−	10.0861i	−0.0969633	−	0.330735i
$931$	9.97535	+	0.214177i	0.326929	+	0.00701938i
$932$	−13.5358	+	4.39804i	−0.443380	+	0.144063i
$933$	−13.6466	−	0.395532i	−0.446769	−	0.0129491i
$934$		−	29.5555i		−	0.967086i
$935$	17.8210	+	18.6931i	0.582809	+	0.611328i
$936$	−2.24352	−	8.56422i	−0.0733319	−	0.279930i
$937$	−2.34154	−	3.22286i	−0.0764949	−	0.105286i	0.769055	−	0.639183i	$-0.220727\pi$
$937$	−2.34154	−	3.22286i	−0.0764949	−	0.105286i	−0.845550	+	0.533896i	$0.820727\pi$
$938$	3.57421	−	1.77309i	0.116702	−	0.0578934i
$939$	−14.0406	−	20.5521i	−0.458198	−	0.670692i
$940$	1.97223	+	1.43291i	0.0643270	+	0.0467363i
$941$	10.4322	+	7.57940i	0.340078	+	0.247081i	0.744695	−	0.667405i	$-0.232595\pi$
$941$	10.4322	+	7.57940i	0.340078	+	0.247081i	−0.404616	+	0.914486i	$0.632595\pi$
$942$	−30.5964	+	20.9026i	−0.996884	+	0.681044i
$943$	−9.20393	+	2.99054i	−0.299721	+	0.0973854i
$944$	4.38776	−	3.18789i	0.142809	−	0.103757i
$945$	3.39678	−	13.0446i	0.110497	−	0.424340i
$946$	−14.3255	−	7.73549i	−0.465763	−	0.251502i
$947$			42.7939i			1.39062i	0.718712	+	0.695308i	$0.244732\pi$
$947$			42.7939i			1.39062i	−0.718712	+	0.695308i	$0.755268\pi$
$948$	26.6280	+	0.771782i	0.864836	+	0.0250663i
$949$	5.00965	+	15.4181i	0.162620	+	0.500494i
$950$	1.77888	−	5.47483i	0.0577145	−	0.177627i
$951$	29.1663	−	8.55083i	0.945783	−	0.277280i
$952$	−9.73985	+	18.6188i	−0.315670	+	0.603437i
$953$	49.9841	+	16.2408i	1.61914	+	0.526092i	0.971740	−	0.236054i	$-0.0758543\pi$
$953$	49.9841	+	16.2408i	1.61914	+	0.526092i	0.647405	+	0.762146i	$0.275854\pi$
$954$	−1.66116	+	1.06561i	−0.0537820	+	0.0345004i
$955$	−4.16997	−	5.73947i	−0.134937	−	0.185725i
$956$		−	7.50611i		−	0.242765i
$957$	4.46148	−	20.9387i	0.144219	−	0.676852i
$958$		−	21.3931i		−	0.691179i
$959$	4.45987	+	4.55665i	0.144017	+	0.147142i
$960$	−0.571366	+	1.59926i	−0.0184408	+	0.0516160i
$961$	−2.25705	+	6.94649i	−0.0728081	+	0.224080i
$962$	−0.999838	−	0.726425i	−0.0322361	−	0.0234209i
$963$	−11.6639	−	4.55234i	−0.375863	−	0.146697i
$964$	−26.0546	−	8.46567i	−0.839164	−	0.272661i
$965$	2.21107	+	6.80499i	0.0711770	+	0.219060i
$966$	−28.0746	+	3.31033i	−0.903285	+	0.106508i
$967$	−13.4095			−0.431222			−0.215611	−	0.976479i	$-0.569174\pi$
$967$	−13.4095			−0.431222			−0.215611	+	0.976479i	$0.569174\pi$
$968$	3.89474	−	10.2874i	0.125182	−	0.330650i
$969$	11.9796	−	15.5221i	0.384841	−	0.498642i
$970$	−7.36592	+	5.35165i	−0.236505	+	0.171831i
$971$	−0.827815	−	2.54775i	−0.0265658	−	0.0817612i	0.936895	−	0.349612i	$-0.113687\pi$
$971$	−0.827815	−	2.54775i	−0.0265658	−	0.0817612i	−0.963460	+	0.267851i	$0.913687\pi$
$972$	−6.90703	+	13.9747i	−0.221543	+	0.448240i
$973$	15.8585	−	30.3152i	0.508401	−	0.971861i
$974$	4.01018	−	5.51954i	0.128495	−	0.176858i
$975$	−11.6447	−	17.0451i	−0.372930	−	0.545880i
$976$	−10.2411	+	3.32753i	−0.327809	+	0.106512i
$977$	−3.93600	−	5.41743i	−0.125924	−	0.173319i	0.741400	−	0.671063i	$-0.234162\pi$
$977$	−3.93600	−	5.41743i	−0.125924	−	0.173319i	−0.867324	+	0.497744i	$0.834162\pi$
$978$	21.5144	−	27.8763i	0.687953	−	0.891387i
$979$	50.1050	−	24.0406i	1.60136	−	0.768340i
$980$	−6.57156	+	1.98032i	−0.209921	+	0.0632589i
$981$	11.4275	+	9.36010i	0.364852	+	0.298845i
$982$	1.80358	+	5.55085i	0.0575546	+	0.177135i
$983$	−8.60736	+	26.4907i	−0.274532	+	0.844923i	0.714811	+	0.699318i	$0.246513\pi$
$983$	−8.60736	+	26.4907i	−0.274532	+	0.844923i	−0.989343	+	0.145605i	$0.953487\pi$
$984$	2.60748	−	0.764446i	0.0831233	−	0.0243697i
$985$	−8.16165	+	11.2336i	−0.260052	+	0.357931i
$986$	−9.14627	+	28.1493i	−0.291276	+	0.896457i
$987$	2.22771	−	11.1738i	0.0709088	−	0.355666i
$988$	3.40304	−	2.47245i	0.108265	−	0.0786592i
$989$			30.2814i			0.962894i
$990$	2.30864	−	9.47869i	0.0733735	−	0.301253i
$991$	−12.6410			−0.401554			−0.200777	−	0.979637i	$-0.564347\pi$
$991$	−12.6410			−0.401554			−0.200777	+	0.979637i	$0.564347\pi$
$992$	5.00702	−	3.63781i	0.158973	−	0.115501i
$993$	−17.0695	+	47.7778i	−0.541683	+	1.51618i
$994$	−2.77111	+	16.3577i	−0.0878942	+	0.518836i
$995$	7.44282	−	10.2442i	0.235953	−	0.324762i
$996$	−3.22231	−	10.9911i	−0.102103	−	0.348266i
$997$	8.53124	+	2.77197i	0.270187	+	0.0877892i	0.440977	−	0.897518i	$-0.354632\pi$
$997$	8.53124	+	2.77197i	0.270187	+	0.0877892i	−0.170790	+	0.985307i	$0.554632\pi$
$998$	−15.1516	+	4.92304i	−0.479614	+	0.155836i
$999$	0.490231	+	2.12014i	0.0155102	+	0.0670783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.s.a.377.11	yes	128
3.2	odd	2	inner	462.2.s.a.377.30	yes	128
7.6	odd	2	inner	462.2.s.a.377.6	yes	128
11.4	even	5	inner	462.2.s.a.125.19	yes	128
21.20	even	2	inner	462.2.s.a.377.19	yes	128
33.26	odd	10	inner	462.2.s.a.125.6	✓	128
77.48	odd	10	inner	462.2.s.a.125.30	yes	128
231.125	even	10	inner	462.2.s.a.125.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.s.a.125.6	✓	128	33.26	odd	10	inner
462.2.s.a.125.11	yes	128	231.125	even	10	inner
462.2.s.a.125.19	yes	128	11.4	even	5	inner
462.2.s.a.125.30	yes	128	77.48	odd	10	inner
462.2.s.a.377.6	yes	128	7.6	odd	2	inner
462.2.s.a.377.11	yes	128	1.1	even	1	trivial
462.2.s.a.377.19	yes	128	21.20	even	2	inner
462.2.s.a.377.30	yes	128	3.2	odd	2	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.582733 - 1.63108i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.793236 - 0.576320i) q^{5} +(-1.66209 + 0.487284i) q^{6} +(0.441911 - 2.60858i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.32084 - 1.90097i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.582733 - 1.63108i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.793236 - 0.576320i) q^{5} +(-1.66209 + 0.487284i) q^{6} +(0.441911 - 2.60858i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-2.32084 - 1.90097i) q^{9} +0.980494i q^{10} +(2.99024 - 1.43473i) q^{11} +(1.37117 + 1.05824i) q^{12} +(1.73459 + 2.38746i) q^{13} +(-2.37014 + 1.17577i) q^{14} +(-1.40227 + 0.957991i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-6.42518 - 4.66817i) q^{17} +(-0.173757 + 2.99496i) q^{18} +(-1.35562 + 0.440466i) q^{19} +(0.793236 - 0.576320i) q^{20} +(-3.99729 - 2.24090i) q^{21} +(-2.91834 - 1.57584i) q^{22} +6.16882i q^{23} +(0.0501805 - 1.73132i) q^{24} +(-1.24801 - 3.84097i) q^{25} +(0.911930 - 2.80663i) q^{26} +(-4.45306 + 2.67773i) q^{27} +(2.34435 + 1.22638i) q^{28} +(3.54438 + 1.15164i) q^{29} +(1.59926 + 0.571366i) q^{30} +(-3.63781 - 5.00702i) q^{31} +1.00000i q^{32} +(-0.597646 - 5.71339i) q^{33} +7.94196i q^{34} +(-1.85392 + 1.81454i) q^{35} +(2.52511 - 1.61982i) q^{36} +(0.129412 - 0.398290i) q^{37} +(1.15316 + 0.837816i) q^{38} +(4.90495 - 1.43801i) q^{39} +(-0.932505 - 0.302989i) q^{40} +(0.484783 + 1.49201i) q^{41} +(0.536624 + 4.55105i) q^{42} +4.90879 q^{43} +(0.440473 + 3.28725i) q^{44} +(0.745412 + 2.84547i) q^{45} +(4.99068 - 3.62594i) q^{46} +(0.768311 + 2.36462i) q^{47} +(-1.43017 + 0.977050i) q^{48} +(-6.60943 - 2.30553i) q^{49} +(-2.37385 + 3.26732i) q^{50} +(-11.3583 + 7.75969i) q^{51} +(-2.80663 + 0.911930i) q^{52} +(0.386678 + 0.532217i) q^{53} +(4.78377 + 2.02868i) q^{54} +(-3.19883 - 0.585257i) q^{55} +(-0.385814 - 2.61747i) q^{56} +(-0.0715262 + 2.46779i) q^{57} +(-1.15164 - 3.54438i) q^{58} +(-1.67598 + 5.15812i) q^{59} +(-0.477779 - 1.62967i) q^{60} +(6.32934 - 8.71159i) q^{61} +(-1.91251 + 5.88611i) q^{62} +(-5.98444 + 5.21406i) q^{63} +(0.809017 - 0.587785i) q^{64} -2.89350i q^{65} +(-4.27094 + 3.84175i) q^{66} -1.50802 q^{67} +(6.42518 - 4.66817i) q^{68} +(10.0618 + 3.59478i) q^{69} +(2.55770 + 0.433291i) q^{70} +(3.68585 - 5.07313i) q^{71} +(-2.79469 - 1.09075i) q^{72} +(5.22459 + 1.69757i) q^{73} +(-0.398290 + 0.129412i) q^{74} +(-6.99218 - 0.202661i) q^{75} -1.42538i q^{76} +(-2.42119 - 8.43432i) q^{77} +(-4.04643 - 3.12295i) q^{78} +(12.4428 - 9.04020i) q^{79} +(0.302989 + 0.932505i) q^{80} +(1.77264 + 8.82370i) q^{81} +(0.922112 - 1.26918i) q^{82} +(-5.34986 - 3.88690i) q^{83} +(3.36646 - 3.10918i) q^{84} +(2.40633 + 7.40592i) q^{85} +(-2.88531 - 3.97129i) q^{86} +(3.94384 - 5.11007i) q^{87} +(2.40053 - 2.28854i) q^{88} +16.7562 q^{89} +(1.86389 - 2.27557i) q^{90} +(6.99444 - 3.46979i) q^{91} +(-5.86690 - 1.90627i) q^{92} +(-10.2867 + 3.01581i) q^{93} +(1.46142 - 2.01147i) q^{94} +(1.32917 + 0.431874i) q^{95} +(1.63108 + 0.582733i) q^{96} +(5.45812 + 7.51246i) q^{97} +(2.01971 + 6.70229i) q^{98} +(-9.66726 - 2.35457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

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