LMFDB - Embedded newform 462.2.s.a.125.19

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			125.19
Character	$\chi$	$=$	462.125
Dual form			462.2.s.a.377.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-1.43017 + 0.977050i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.793236 + 0.576320i) q^{5} +(-0.0501805 + 1.73132i) q^{6} +(1.17577 + 2.37014i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.09075 - 2.79469i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-1.43017 + 0.977050i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.793236 + 0.576320i) q^{5} +(-0.0501805 + 1.73132i) q^{6} +(1.17577 + 2.37014i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.09075 - 2.79469i) q^{9} +0.980494i q^{10} +(-2.99024 - 1.43473i) q^{11} +(1.37117 + 1.05824i) q^{12} +(-1.73459 + 2.38746i) q^{13} +(2.60858 + 0.441911i) q^{14} +(0.571366 - 1.59926i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-6.42518 + 4.66817i) q^{17} +(-1.61982 - 2.52511i) 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} +(1.66209 - 0.487284i) q^{24} +(-1.24801 + 3.84097i) q^{25} +(0.911930 + 2.80663i) q^{26} +(1.17060 + 5.06258i) q^{27} +(1.89080 - 1.85064i) q^{28} +(-3.54438 + 1.15164i) q^{29} +(-0.957991 - 1.40227i) q^{30} +(3.63781 - 5.00702i) q^{31} +1.00000i q^{32} +(5.67834 - 0.869714i) q^{33} +7.94196i q^{34} +(-2.29862 - 1.20246i) q^{35} +(-2.99496 - 0.173757i) q^{36} +(0.129412 + 0.398290i) q^{37} +(1.15316 - 0.837816i) q^{38} +(0.148086 - 5.10925i) q^{39} +(0.932505 - 0.302989i) q^{40} +(0.484783 - 1.49201i) q^{41} +(-4.16248 + 1.91671i) 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} +(0.582733 - 1.63108i) q^{48} +(-4.23511 + 5.57349i) q^{49} +(2.37385 + 3.26732i) q^{50} +(4.62804 - 12.9540i) 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} +(-2.36911 + 0.694564i) q^{57} +(-1.15164 + 3.54438i) q^{58} +(-1.67598 - 5.15812i) q^{59} +(-1.69755 - 0.0492017i) q^{60} +(-6.32934 - 8.71159i) q^{61} +(-1.91251 - 5.88611i) q^{62} +(7.90626 - 0.700695i) q^{63} +(0.809017 + 0.587785i) q^{64} -2.89350i q^{65} +(2.63403 - 5.10508i) q^{66} -1.50802 q^{67} +(6.42518 + 4.66817i) q^{68} +(-6.02724 - 8.82244i) q^{69} +(-2.32391 + 1.15284i) q^{70} +(-3.68585 - 5.07313i) q^{71} +(-1.90097 + 2.32084i) q^{72} +(-5.22459 + 1.69757i) q^{73} +(0.398290 + 0.129412i) q^{74} +(-1.96796 - 6.71258i) q^{75} -1.42538i q^{76} +(-0.115341 - 8.77421i) q^{77} +(-4.04643 - 3.12295i) q^{78} +(12.4428 + 9.04020i) q^{79} +(0.302989 - 0.932505i) q^{80} +(-6.62054 - 6.09660i) q^{81} +(-0.922112 - 1.26918i) q^{82} +(-5.34986 + 3.88690i) q^{83} +(-0.895992 + 4.49413i) 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} +(2.74017 + 1.06947i) q^{90} +(-7.69811 - 1.30411i) q^{91} +(5.86690 - 1.90627i) q^{92} +(-0.310568 + 10.7152i) q^{93} +(-1.46142 - 2.01147i) q^{94} +(-1.32917 + 0.431874i) q^{95} +(-0.977050 - 1.43017i) q^{96} +(-5.45812 + 7.51246i) q^{97} +(2.01971 + 6.70229i) q^{98} +(-7.27122 + 6.79186i) 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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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
$3$	−1.43017	+	0.977050i	−0.825707	+	0.564100i
$3$	−1.43017	+	0.977050i	−0.825707	+	0.564100i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.793236	+	0.576320i	−0.354746	+	0.257738i	−0.750857	−	0.660464i	$-0.770359\pi$
$5$	−0.793236	+	0.576320i	−0.354746	+	0.257738i	0.396111	+	0.918203i	$0.370359\pi$
$6$	−0.0501805	+	1.73132i	−0.0204861	+	0.706810i
$7$	1.17577	+	2.37014i	0.444401	+	0.895828i
$7$	1.17577	+	2.37014i	0.444401	+	0.895828i
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	1.09075	−	2.79469i	0.363583	−	0.931562i
$10$			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	$-0.934206\pi$
$13$	−1.73459	+	2.38746i	−0.481090	+	0.662163i	0.497624	+	0.867393i	$0.334206\pi$
$14$	2.60858	+	0.441911i	0.697174	+	0.118106i
$15$	0.571366	−	1.59926i	0.147526	−	0.412928i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−6.42518	+	4.66817i	−1.55833	+	1.13220i	−0.620976	+	0.783829i	$0.713264\pi$
$17$	−6.42518	+	4.66817i	−1.55833	+	1.13220i	−0.937358	+	0.348367i	$0.886736\pi$
$18$	−1.61982	−	2.52511i	−0.381796	−	0.595174i
$19$	1.35562	+	0.440466i	0.311000	+	0.101050i	0.460358	−	0.887733i	$-0.347721\pi$
$19$	1.35562	+	0.440466i	0.311000	+	0.101050i	−0.149359	+	0.988783i	$0.547721\pi$
$20$	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	$0.777630\pi$
$24$	1.66209	−	0.487284i	0.339273	−	0.0994664i
$25$	−1.24801	+	3.84097i	−0.249601	+	0.768193i
$26$	0.911930	+	2.80663i	0.178844	+	0.550426i
$27$	1.17060	+	5.06258i	0.225281	+	0.974294i
$28$	1.89080	−	1.85064i	0.357328	−	0.349738i
$29$	−3.54438	+	1.15164i	−0.658175	+	0.213854i	−0.619015	−	0.785379i	$-0.712468\pi$
$29$	−3.54438	+	1.15164i	−0.658175	+	0.213854i	−0.0391596	+	0.999233i	$0.512468\pi$
$30$	−0.957991	−	1.40227i	−0.174904	−	0.256018i
$31$	3.63781	−	5.00702i	0.653371	−	0.899288i	−0.345869	−	0.938283i	$-0.612416\pi$
$31$	3.63781	−	5.00702i	0.653371	−	0.899288i	0.999239	+	0.0389952i	$0.0124157\pi$
$32$			1.00000i			0.176777i
$33$	5.67834	−	0.869714i	0.988473	−	0.151398i
$34$			7.94196i			1.36203i
$35$	−2.29862	−	1.20246i	−0.388538	−	0.203252i
$36$	−2.99496	−	0.173757i	−0.499161	−	0.0289596i
$37$	0.129412	+	0.398290i	0.0212752	+	0.0654785i	0.961130	−	0.276095i	$-0.0890403\pi$
$37$	0.129412	+	0.398290i	0.0212752	+	0.0654785i	−0.939855	+	0.341573i	$0.889040\pi$
$38$	1.15316	−	0.837816i	0.187067	−	0.135912i
$39$	0.148086	−	5.10925i	0.0237128	−	0.818135i
$40$	0.932505	−	0.302989i	0.147442	−	0.0479068i
$41$	0.484783	−	1.49201i	0.0757104	−	0.233013i	−0.906038	−	0.423196i	$-0.860908\pi$
$41$	0.484783	−	1.49201i	0.0757104	−	0.233013i	0.981749	+	0.190183i	$0.0609082\pi$
$42$	−4.16248	+	1.91671i	−0.642284	+	0.295755i
$43$	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	−0.879255	−	0.476352i	$-0.841959\pi$
$47$	0.768311	−	2.36462i	0.112070	−	0.344915i	0.991325	+	0.131436i	$0.0419589\pi$
$48$	0.582733	−	1.63108i	0.0841103	−	0.235426i
$49$	−4.23511	+	5.57349i	−0.605016	+	0.796213i
$50$	2.37385	+	3.26732i	0.335713	+	0.462069i
$51$	4.62804	−	12.9540i	0.648055	−	1.81392i
$52$	2.80663	+	0.911930i	0.389210	+	0.126462i
$53$	−0.386678	+	0.532217i	−0.0531143	+	0.0731056i	−0.834748	−	0.550632i	$-0.814387\pi$
$53$	−0.386678	+	0.532217i	−0.0531143	+	0.0731056i	0.781634	+	0.623738i	$0.214387\pi$
$54$	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
$57$	−2.36911	+	0.694564i	−0.313797	+	0.0919973i
$58$	−1.15164	+	3.54438i	−0.151218	+	0.465400i
$59$	−1.67598	−	5.15812i	−0.218193	−	0.671530i	−0.998911	−	0.0466468i	$-0.985146\pi$
$59$	−1.67598	−	5.15812i	−0.218193	−	0.671530i	0.780718	−	0.624883i	$-0.214854\pi$
$60$	−1.69755	−	0.0492017i	−0.219153	−	0.00635191i
$61$	−6.32934	−	8.71159i	−0.810389	−	1.11540i	−0.991263	−	0.131898i	$-0.957893\pi$
$61$	−6.32934	−	8.71159i	−0.810389	−	1.11540i	0.180874	−	0.983506i	$-0.442107\pi$
$62$	−1.91251	−	5.88611i	−0.242889	−	0.747536i
$63$	7.90626	−	0.700695i	0.996096	−	0.0882793i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		−	2.89350i		−	0.358895i
$66$	2.63403	−	5.10508i	0.324227	−	0.628392i
$67$	−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
$69$	−6.02724	−	8.82244i	−0.725595	−	1.06210i
$70$	−2.32391	+	1.15284i	−0.277760	+	0.137791i
$71$	−3.68585	−	5.07313i	−0.437429	−	0.602070i	0.532209	−	0.846613i	$-0.321362\pi$
$71$	−3.68585	−	5.07313i	−0.437429	−	0.602070i	−0.969638	+	0.244543i	$0.921362\pi$
$72$	−1.90097	+	2.32084i	−0.224031	+	0.273514i
$73$	−5.22459	+	1.69757i	−0.611493	+	0.198686i	−0.598359	−	0.801228i	$-0.704181\pi$
$73$	−5.22459	+	1.69757i	−0.611493	+	0.198686i	−0.0131331	+	0.999914i	$0.504181\pi$
$74$	0.398290	+	0.129412i	0.0463003	+	0.0150439i
$75$	−1.96796	−	6.71258i	−0.227240	−	0.775102i
$76$		−	1.42538i		−	0.163502i
$77$	−0.115341	−	8.77421i	−0.0131444	−	0.999914i
$78$	−4.04643	−	3.12295i	−0.458168	−	0.353604i
$79$	12.4428	+	9.04020i	1.39992	+	1.01710i	0.994693	+	0.102887i	$0.0328079\pi$
$79$	12.4428	+	9.04020i	1.39992	+	1.01710i	0.405228	+	0.914216i	$0.367192\pi$
$80$	0.302989	−	0.932505i	0.0338752	−	0.104257i
$81$	−6.62054	−	6.09660i	−0.735615	−	0.677399i
$82$	−0.922112	−	1.26918i	−0.101830	−	0.140157i
$83$	−5.34986	+	3.88690i	−0.587224	+	0.426643i	−0.841321	−	0.540536i	$-0.818222\pi$
$83$	−5.34986	+	3.88690i	−0.587224	+	0.426643i	0.254097	+	0.967179i	$0.418222\pi$
$84$	−0.895992	+	4.49413i	−0.0977607	+	0.490350i
$85$	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	$0.152043\pi$
$90$	2.74017	+	1.06947i	0.288840	+	0.112732i
$91$	−7.69811	−	1.30411i	−0.806981	−	0.136708i
$92$	5.86690	−	1.90627i	0.611666	−	0.198742i
$93$	−0.310568	+	10.7152i	−0.0322044	+	1.11111i
$94$	−1.46142	−	2.01147i	−0.150733	−	0.207467i
$95$	−1.32917	+	0.431874i	−0.136370	+	0.0443094i
$96$	−0.977050	−	1.43017i	−0.0997197	−	0.145966i
$97$	−5.45812	+	7.51246i	−0.554188	+	0.762774i	−0.990573	−	0.136986i	$-0.956259\pi$
$97$	−5.45812	+	7.51246i	−0.554188	+	0.762774i	0.436385	+	0.899760i	$0.356259\pi$
$98$	2.01971	+	6.70229i	0.204022	+	0.677034i
$99$	−7.27122	+	6.79186i	−0.730785	+	0.682608i
$100$	4.03863			0.403863
$101$	12.3242	+	8.95405i	1.22630	+	0.890961i	0.996607	−	0.0823013i	$-0.0262270\pi$
$101$	12.3242	+	8.95405i	1.22630	+	0.890961i	0.229695	+	0.973263i	$0.426227\pi$
$102$	−7.75969	−	11.3583i	−0.768323	−	1.12464i
$103$	14.4071	−	4.68114i	1.41957	−	0.461247i	0.504106	−	0.863642i	$-0.331822\pi$
$103$	14.4071	−	4.68114i	1.41957	−	0.461247i	0.915466	+	0.402395i	$0.131822\pi$
$104$	2.38746	−	1.73459i	0.234110	−	0.170091i
$105$	4.46227	−	0.526156i	0.435473	−	0.0513476i
$106$	0.203289	+	0.625658i	0.0197451	+	0.0607693i
$107$	−3.96932	−	1.28971i	−0.383729	−	0.124681i	0.110799	−	0.993843i	$-0.464659\pi$
$107$	−3.96932	−	1.28971i	−0.383729	−	0.124681i	−0.494528	+	0.869162i	$0.664659\pi$
$108$	4.45306	−	2.67773i	0.428496	−	0.257664i
$109$	−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
$112$	−2.34435	−	1.22638i	−0.221521	−	0.115882i
$113$	6.42966	+	2.08912i	0.604852	+	0.196528i	0.595403	−	0.803427i	$-0.296992\pi$
$113$	6.42966	+	2.08912i	0.604852	+	0.196528i	0.00944860	+	0.999955i	$0.496992\pi$
$114$	−0.830615	+	2.32491i	−0.0777942	+	0.217747i
$115$	−3.55521	−	4.89333i	−0.331525	−	0.456306i
$116$	2.19055	+	3.01503i	0.203387	+	0.279938i
$117$	4.78021	+	7.45177i	0.441930	+	0.688916i
$118$	−5.15812	−	1.67598i	−0.474844	−	0.154286i
$119$	−18.6188	−	9.73985i	−1.70678	−	0.892851i
$120$	−1.03760	+	1.34443i	−0.0947196	+	0.122729i
$121$	6.88310	+	8.58038i	0.625736	+	0.780035i
$122$	−10.7681			−0.974899
$123$	0.764446	+	2.60748i	0.0689278	+	0.235108i
$124$	−5.88611	−	1.91251i	−0.528588	−	0.171749i
$125$	−2.73861	−	8.42857i	−0.244949	−	0.753874i
$126$	4.08031	−	6.80816i	0.363503	−	0.606519i
$127$	12.8923	−	9.36680i	1.14401	−	0.831169i	0.156334	−	0.987704i	$-0.450032\pi$
$127$	12.8923	−	9.36680i	1.14401	−	0.831169i	0.987672	+	0.156535i	$0.0500324\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−7.02038	+	4.79613i	−0.618110	+	0.422276i
$130$	−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	$0.181689\pi$
$132$	−2.58185	−	5.13167i	−0.224721	−	0.446655i
$133$	0.549932	+	3.73089i	0.0476851	+	0.323509i
$134$	−0.886391	+	1.22001i	−0.0765725	+	0.105393i
$135$	−3.84622	−	3.34118i	−0.331030	−	0.287563i
$136$	7.55325	−	2.45420i	0.647686	−	0.210446i
$137$	1.41651	+	1.94965i	0.121020	+	0.166570i	0.865229	−	0.501377i	$-0.167173\pi$
$137$	1.41651	+	1.94965i	0.121020	+	0.166570i	−0.744208	+	0.667947i	$0.767173\pi$
$138$	−10.6802	−	0.309555i	−0.909161	−	0.0263510i
$139$	−12.2983	+	3.99595i	−1.04313	+	0.338932i	−0.779967	−	0.625821i	$-0.784764\pi$
$139$	−12.2983	+	3.99595i	−1.04313	+	0.338932i	−0.263159	+	0.964753i	$0.584764\pi$
$140$	−0.433291	+	2.55770i	−0.0366198	+	0.216165i
$141$	1.21154	+	4.13248i	0.102030	+	0.348017i
$142$	−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
$147$	0.611331	−	12.1089i	0.0504218	−	0.998728i
$148$	0.338806	−	0.246157i	0.0278497	−	0.0202340i
$149$	−5.61240	−	7.72480i	−0.459785	−	0.632840i	0.514679	−	0.857383i	$-0.327911\pi$
$149$	−5.61240	−	7.72480i	−0.459785	−	0.632840i	−0.974464	+	0.224543i	$0.927911\pi$
$150$	−6.58733	−	2.35344i	−0.537853	−	0.192158i
$151$	−3.83642	+	11.8073i	−0.312203	+	0.960862i	0.664687	+	0.747122i	$0.268565\pi$
$151$	−3.83642	+	11.8073i	−0.312203	+	0.960862i	−0.976890	+	0.213741i	$0.931435\pi$
$152$	−1.15316	−	0.837816i	−0.0935333	−	0.0679559i
$153$	6.03781	+	23.0481i	0.488128	+	1.86333i
$154$	−7.16628	−	5.06404i	−0.577475	−	0.408072i
$155$			6.06830i			0.487417i
$156$	−4.90495	+	1.43801i	−0.392710	+	0.115133i
$157$	−20.3465	−	6.61098i	−1.62383	−	0.527614i	−0.650988	−	0.759088i	$-0.725645\pi$
$157$	−20.3465	−	6.61098i	−1.62383	−	0.527614i	−0.972841	+	0.231474i	$0.925645\pi$
$158$	14.6274	−	4.75272i	1.16369	−	0.378106i
$159$	0.0330116	−	1.13896i	0.00261799	−	0.0903255i
$160$	−0.576320	−	0.793236i	−0.0455621	−	0.0627108i
$161$	−14.6210	+	7.25314i	−1.15229	+	0.571627i
$162$	−8.82370	+	1.77264i	−0.693256	+	0.139272i
$163$	−16.4475	−	11.9498i	−1.28827	−	0.935982i	−0.288500	−	0.957480i	$-0.593157\pi$
$163$	−16.4475	−	11.9498i	−1.28827	−	0.935982i	−0.999769	+	0.0214976i	$0.993157\pi$
$164$	−1.56879			−0.122502
$165$	−4.00304	+	3.96243i	−0.311636	+	0.308475i
$166$			6.61280i			0.513252i
$167$	−7.12101	−	5.17371i	−0.551040	−	0.400354i	0.277129	−	0.960833i	$-0.410617\pi$
$167$	−7.12101	−	5.17371i	−0.551040	−	0.400354i	−0.828169	+	0.560479i	$0.810617\pi$
$168$	3.10918	+	3.36646i	0.239878	+	0.259728i
$169$	1.32605	+	4.08118i	0.102004	+	0.313937i
$170$	−4.57711	−	6.29985i	−0.351048	−	0.483176i
$171$	2.70960	−	3.30808i	0.207208	−	0.252975i
$172$	−1.51690	−	4.66854i	−0.115662	−	0.355973i
$173$	−4.10167	+	12.6236i	−0.311844	+	0.959757i	0.665190	+	0.746674i	$0.268350\pi$
$173$	−4.10167	+	12.6236i	−0.311844	+	0.959757i	−0.977034	+	0.213083i	$0.931650\pi$
$174$	−1.81600	−	6.19426i	−0.137671	−	0.469586i
$175$	−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	$-0.169600\pi$
$179$	16.8534	+	5.47600i	1.25968	+	0.409295i	0.398300	+	0.917255i	$0.369600\pi$
$180$	2.47585	−	1.58823i	0.184539	−	0.118379i
$181$	8.20517	+	11.2934i	0.609885	+	0.839435i	0.996568	−	0.0827777i	$-0.0263791\pi$
$181$	8.20517	+	11.2934i	0.609885	+	0.839435i	−0.386683	+	0.922213i	$0.626379\pi$
$182$	−5.57988	+	5.46136i	−0.413608	+	0.404823i
$183$	17.5637	+	6.27494i	1.29834	+	0.463857i
$184$	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
$189$	−10.6227	+	8.72692i	−0.772684	+	0.634790i
$190$	−0.431874	+	1.32917i	−0.0313315	+	0.0964283i
$191$	−6.88137	+	2.23589i	−0.497919	+	0.161784i	−0.547201	−	0.837001i	$-0.684307\pi$
$191$	−6.88137	+	2.23589i	−0.497919	+	0.161784i	0.0492821	+	0.998785i	$0.484307\pi$
$192$	−1.73132	−	0.0501805i	−0.124948	−	0.00362147i
$193$	−5.90383	+	4.28938i	−0.424967	+	0.308756i	−0.779633	−	0.626236i	$-0.784594\pi$
$193$	−5.90383	+	4.28938i	−0.424967	+	0.308756i	0.354666	+	0.934993i	$0.384594\pi$
$194$	2.86950	+	8.83142i	0.206018	+	0.634059i
$195$	2.82710	+	4.13819i	0.202453	+	0.296342i
$196$	6.60943	+	2.30553i	0.472102	+	0.164680i
$197$		−	14.1617i		−	1.00898i	−0.863418	−	0.504489i	$-0.831681\pi$
$197$		−	14.1617i		−	1.00898i	0.863418	−	0.504489i	$-0.168319\pi$
$198$	1.22081	+	9.87470i	0.0867595	+	0.701764i
$199$			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
$201$	2.15672	−	1.47341i	0.152123	−	0.103926i
$202$	14.4880	−	4.70742i	1.01937	−	0.331213i
$203$	−6.89693	−	7.04660i	−0.484070	−	0.494575i
$204$	−13.7501	−	0.398532i	−0.962699	−	0.0279028i
$205$	0.475327	+	1.46291i	0.0331983	+	0.102174i
$206$	4.68114	−	14.4071i	0.326151	−	1.00379i
$207$	17.2399	+	6.72863i	1.19826	+	0.467672i
$208$		−	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	0.0149127	−	0.999889i	$-0.495253\pi$
$211$	−13.5298	−	9.82998i	−0.931430	−	0.676723i	−0.946342	+	0.323165i	$0.895253\pi$
$212$	0.625658	+	0.203289i	0.0429704	+	0.0139619i
$213$	10.2281	+	3.65416i	0.700816	+	0.250379i
$214$	−3.37651	+	2.45318i	−0.230813	+	0.167696i
$215$	−3.89383	+	2.82903i	−0.265557	+	0.192938i
$216$	0.451119	−	5.17653i	0.0306948	−	0.352218i
$217$	16.1446	+	2.73500i	1.09597	+	0.185664i
$218$	−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
$222$	−0.696063	+	0.204068i	−0.0467167	+	0.0136962i
$223$	9.87123	+	3.20736i	0.661027	+	0.214781i	0.620270	−	0.784389i	$-0.287023\pi$
$223$	9.87123	+	3.20736i	0.661027	+	0.214781i	0.0407568	+	0.999169i	$0.487023\pi$
$224$	−2.37014	+	1.17577i	−0.158362	+	0.0785597i
$225$	9.37304	+	7.67731i	0.624869	+	0.511821i
$226$	5.46940	−	3.97375i	0.363819	−	0.264330i
$227$	4.16652	+	12.8232i	0.276541	+	0.851107i	0.988807	+	0.149197i	$0.0476689\pi$
$227$	4.16652	+	12.8232i	0.276541	+	0.851107i	−0.712266	+	0.701910i	$0.752331\pi$
$228$	1.39267	+	2.03853i	0.0922315	+	0.135005i
$229$	−2.85639	+	3.93148i	−0.188756	+	0.259800i	−0.892898	−	0.450259i	$-0.851332\pi$
$229$	−2.85639	+	3.93148i	−0.188756	+	0.259800i	0.704142	+	0.710059i	$0.251332\pi$
$230$	−6.04849			−0.398826
$231$	8.73779	+	12.4359i	0.574905	+	0.818220i
$232$	3.72678			0.244675
$233$	−8.36558	+	11.5142i	−0.548047	+	0.754322i	−0.989746	−	0.142841i	$-0.954376\pi$
$233$	−8.36558	+	11.5142i	−0.548047	+	0.754322i	0.441698	+	0.897164i	$0.354376\pi$
$234$	8.83834	+	0.512770i	0.577780	+	0.0335208i
$235$	0.753325	+	2.31849i	0.0491415	+	0.151242i
$236$	−4.38776	+	3.18789i	−0.285619	+	0.207514i
$237$	−26.6280	−	0.771782i	−1.72967	−	0.0501326i
$238$	−18.8235	+	9.33795i	−1.22015	+	0.605289i
$239$	7.13874	+	2.31952i	0.461767	+	0.150037i	0.530656	−	0.847587i	$-0.321946\pi$
$239$	7.13874	+	2.31952i	0.461767	+	0.150037i	−0.0688895	+	0.997624i	$0.521946\pi$
$240$	0.477779	+	1.62967i	0.0308405	+	0.105195i
$241$			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
$245$	0.147329	−	6.86188i	0.00941250	−	0.438389i
$246$	2.55882	+	0.914186i	0.163145	+	0.0582864i
$247$	−3.40304	+	2.47245i	−0.216530	+	0.157318i
$248$	−5.00702	+	3.63781i	−0.317946	+	0.231001i
$249$	3.85349	−	10.7860i	0.244205	−	0.683535i
$250$	−8.42857	−	2.73861i	−0.533070	−	0.173205i
$251$	0.834593	+	0.606368i	0.0526791	+	0.0382736i	0.613813	−	0.789451i	$-0.289635\pi$
$251$	0.834593	+	0.606368i	0.0526791	+	0.0382736i	−0.561134	+	0.827725i	$0.689635\pi$
$252$	−3.10957	−	7.30278i	−0.195885	−	0.460032i
$253$	8.85059	−	18.4463i	0.556432	−	1.15971i
$254$		−	15.9358i		−	0.999898i
$255$	3.79450	+	12.9428i	0.237621	+	0.810509i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.699955	−	2.15424i	−0.0436620	−	0.134378i	0.926849	−	0.375434i	$-0.122506\pi$
$257$	−0.699955	−	2.15424i	−0.0436620	−	0.134378i	−0.970511	+	0.241056i	$0.922506\pi$
$258$	−0.246326	+	8.49870i	−0.0153356	+	0.529106i
$259$	−0.791843	+	0.775024i	−0.0492027	+	0.0481576i
$260$	−2.75189	+	0.894142i	−0.170665	+	0.0554523i
$261$	−0.647556	+	11.1616i	−0.0400827	+	0.690884i
$262$	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	$0.739026\pi$
$264$	−5.66918	−	0.927557i	−0.348914	−	0.0570872i
$265$		−	0.645024i		−	0.0396235i
$266$	3.34159	+	1.74806i	0.204886	+	0.107180i
$267$	−23.9641	+	16.3716i	−1.46658	+	1.00193i
$268$	0.466003	+	1.43421i	0.0284657	+	0.0876084i
$269$	−10.7921	+	7.84089i	−0.658004	+	0.478068i	−0.865988	−	0.500065i	$-0.833310\pi$
$269$	−10.7921	+	7.84089i	−0.658004	+	0.478068i	0.207985	+	0.978132i	$0.433310\pi$
$270$	−4.96383	+	1.14776i	−0.302089	+	0.0698506i
$271$	0.675524	−	0.219491i	0.0410352	−	0.0133331i	−0.288427	−	0.957502i	$-0.593132\pi$
$271$	0.675524	−	0.219491i	0.0410352	−	0.0133331i	0.329463	+	0.944169i	$0.393132\pi$
$272$	2.45420	−	7.55325i	0.148808	−	0.457983i
$273$	12.2838	−	5.65634i	0.743446	−	0.342337i
$274$	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	0.204348	−	0.978898i	$-0.434493\pi$
$277$	−11.0427	−	8.02301i	−0.663493	−	0.482056i	−0.867841	+	0.496842i	$0.834493\pi$
$278$	−3.99595	+	12.2983i	−0.239661	+	0.737601i
$279$	−10.0251	−	15.6279i	−0.600188	−	0.935621i
$280$	1.81454	+	1.85392i	0.108440	+	0.110793i
$281$	−1.52502	−	2.09901i	−0.0909751	−	0.125216i	0.761103	−	0.648631i	$-0.224658\pi$
$281$	−1.52502	−	2.09901i	−0.0909751	−	0.125216i	−0.852078	+	0.523414i	$0.824658\pi$
$282$	4.05537	+	1.44885i	0.241494	+	0.0862780i
$283$	23.4572	+	7.62172i	1.39439	+	0.453064i	0.907372	−	0.420328i	$-0.138085\pi$
$283$	23.4572	+	7.62172i	1.39439	+	0.453064i	0.487017	+	0.873393i	$0.338085\pi$
$284$	−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
$288$	2.79469	+	1.09075i	0.164678	+	0.0642729i
$289$	14.2379	−	43.8196i	0.837521	−	2.57762i
$290$	−1.12917	−	3.47524i	−0.0663074	−	0.204073i
$291$	0.465972	−	16.0769i	0.0273157	−	0.942445i
$292$	3.22898	+	4.44431i	0.188962	+	0.260083i
$293$	5.00213	+	15.3950i	0.292228	+	0.899384i	0.984139	+	0.177401i	$0.0567691\pi$
$293$	5.00213	+	15.3950i	0.292228	+	0.899384i	−0.691911	+	0.721983i	$0.743231\pi$
$294$	−9.43700	−	7.61203i	−0.550377	−	0.443943i
$295$	4.30217	+	3.12571i	0.250482	+	0.181986i
$296$		−	0.418787i		−	0.0243415i
$297$	3.76306	−	16.8178i	0.218355	−	0.975869i
$298$	−9.54838			−0.553123
$299$	−14.7278	−	10.7004i	−0.851733	−	0.618820i
$300$	−5.77591	+	3.94594i	−0.333472	+	0.227819i
$301$	5.77163	+	11.6345i	0.332671	+	0.670602i
$302$	7.29730	+	10.0439i	0.419912	+	0.577959i
$303$	−26.3742	−	0.764427i	−1.51516	−	0.0439152i
$304$	−1.35562	+	0.440466i	−0.0777499	+	0.0252625i
$305$	10.0413	+	3.26262i	0.574964	+	0.186817i
$306$	22.1953	+	8.66267i	1.26882	+	0.495212i
$307$		−	11.6271i		−	0.663595i	−0.943351	−	0.331798i	$-0.892345\pi$
$307$		−	11.6271i		−	0.663595i	0.943351	−	0.331798i	$-0.107655\pi$
$308$	−8.30912	+	2.82107i	−0.473456	+	0.160746i
$309$	−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	−0.996062	−	0.0886609i	$-0.971741\pi$
$311$	−2.43573	+	7.49639i	−0.138117	+	0.425081i	0.857945	+	0.513742i	$0.171741\pi$
$312$	−1.71968	+	4.81343i	−0.0973579	+	0.272507i
$313$	−8.44672	−	11.6259i	−0.477437	−	0.657136i	0.500573	−	0.865694i	$-0.333123\pi$
$313$	−8.44672	−	11.6259i	−0.477437	−	0.657136i	−0.978010	+	0.208559i	$0.933123\pi$
$314$	−17.3078	+	12.5748i	−0.976735	+	0.709639i
$315$	−5.86771	+	5.11235i	−0.330608	+	0.288049i
$316$	4.75272	−	14.6274i	0.267361	−	0.822853i
$317$	−10.3144	+	14.1966i	−0.579316	+	0.797360i	−0.993620	−	0.112779i	$-0.964025\pi$
$317$	−10.3144	+	14.1966i	−0.579316	+	0.797360i	0.414304	+	0.910138i	$0.364025\pi$
$318$	−0.902036	−	0.696172i	−0.0505836	−	0.0390394i
$319$	12.2508	+	1.64155i	0.685916	+	0.0919090i
$320$	−0.980494			−0.0548113
$321$	6.93690	−	2.03373i	0.387180	−	0.113511i
$322$	−2.72607	+	16.0919i	−0.151918	+	0.896766i
$323$	−10.7662	+	3.49816i	−0.599050	+	0.194643i
$324$	−3.75235	+	8.18046i	−0.208464	+	0.454470i
$325$	−7.00539	−	9.64209i	−0.388589	−	0.534847i
$326$	−19.3352	+	6.28239i	−1.07088	+	0.347950i
$327$	7.04193	−	4.81085i	0.389420	−	0.266041i
$328$	−0.922112	+	1.26918i	−0.0509151	+	0.0700786i
$329$	6.50784	−	0.959253i	0.358789	−	0.0528853i
$330$	0.852750	+	5.56758i	0.0469423	+	0.306485i
$331$	−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
$333$	1.25425	+	0.0727673i	0.0687326	+	0.00398763i
$334$	−8.37125	+	2.71998i	−0.458054	+	0.148831i
$335$	1.19622	−	0.869101i	0.0653562	−	0.0474841i
$336$	4.55105	−	0.536624i	0.248280	−	0.0292752i
$337$	0.174412	+	0.536784i	0.00950081	+	0.0292405i	0.955695	−	0.294360i	$-0.0951065\pi$
$337$	0.174412	+	0.536784i	0.00950081	+	0.0292405i	−0.946194	+	0.323601i	$0.895107\pi$
$338$	4.08118	+	1.32605i	0.221987	+	0.0721278i
$339$	−11.2367	+	3.29431i	−0.610292	+	0.178922i
$340$	−7.78704			−0.422312
$341$	−18.0617	+	9.75293i	−0.978094	+	0.528151i
$342$	−1.08363	−	4.13655i	−0.0585961	−	0.223679i
$343$	−18.1895	−	3.48463i	−0.982140	−	0.188152i
$344$	−4.66854	−	1.51690i	−0.251711	−	0.0817857i
$345$	9.86557	+	3.52466i	0.531145	+	0.189761i
$346$	7.80183	+	10.7383i	0.419429	+	0.577295i
$347$	12.7992	+	17.6166i	0.687096	+	0.945707i	0.999992	−	0.00408074i	$-0.00129894\pi$
$347$	12.7992	+	17.6166i	0.687096	+	0.945707i	−0.312895	+	0.949788i	$0.601299\pi$
$348$	−6.07868	−	2.17172i	−0.325851	−	0.116416i
$349$	−18.2880	−	5.94214i	−0.978935	−	0.318075i	−0.224517	−	0.974470i	$-0.572081\pi$
$349$	−18.2880	−	5.94214i	−0.978935	−	0.318075i	−0.754418	+	0.656395i	$0.772081\pi$
$350$	−4.95290	+	9.46798i	−0.264743	+	0.506085i
$351$	−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	$0.143641\pi$
$354$	9.01448	−	2.64282i	0.479114	−	0.140464i
$355$	5.84749	+	1.89997i	0.310353	+	0.100840i
$356$	−5.17794	−	15.9361i	−0.274430	−	0.844609i
$357$	36.1442	−	4.26184i	1.91296	−	0.225561i
$358$	14.3363	−	10.4160i	0.757699	−	0.550501i
$359$	−24.6772	+	8.01810i	−1.30241	+	0.423179i	−0.876420	−	0.481547i	$-0.840075\pi$
$359$	−24.6772	+	8.01810i	−1.30241	+	0.423179i	−0.425992	+	0.904727i	$0.640075\pi$
$360$	0.170368	−	2.93654i	0.00897919	−	0.154769i
$361$	−13.7276	−	9.97371i	−0.722507	−	0.524932i
$362$	13.9595			0.733693
$363$	−18.2274	−	5.54623i	−0.956692	−	0.291102i
$364$	1.13856	+	7.72433i	0.0596770	+	0.404865i
$365$	3.16599	−	4.35761i	0.165716	−	0.228088i
$366$	15.4002	−	10.5210i	0.804981	−	0.549941i
$367$	−24.8469	+	8.07323i	−1.29700	+	0.421419i	−0.874535	−	0.484962i	$-0.838833\pi$
$367$	−24.8469	+	8.07323i	−1.29700	+	0.421419i	−0.422460	+	0.906381i	$0.638833\pi$
$368$	−3.62594	−	4.99068i	−0.189015	−	0.260157i
$369$	−3.64092	−	2.98222i	−0.189539	−	0.155248i
$370$	−0.390521	+	0.126888i	−0.0203022	+	0.00659659i
$371$	−1.71607	−	0.290714i	−0.0890941	−	0.0150931i
$372$	10.2867	−	3.01581i	0.533342	−	0.156362i
$373$	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
$378$	0.816390	+	13.7235i	0.0419906	+	0.705859i
$379$	14.3587	−	10.4322i	0.737555	−	0.535865i	−0.154389	−	0.988010i	$-0.549341\pi$
$379$	14.3587	−	10.4322i	0.737555	−	0.535865i	0.891944	+	0.452145i	$0.149341\pi$
$380$	0.821474	+	1.13066i	0.0421407	+	0.0580017i
$381$	−9.28629	+	25.9925i	−0.475751	+	1.33164i
$382$	−2.23589	+	6.88137i	−0.114398	+	0.352082i
$383$	−8.21903	−	5.97147i	−0.419973	−	0.305128i	0.357654	−	0.933854i	$-0.383577\pi$
$383$	−8.21903	−	5.97147i	−0.419973	−	0.305128i	−0.777627	+	0.628726i	$0.783577\pi$
$384$	−1.05824	+	1.37117i	−0.0540033	+	0.0699725i
$385$	5.14824	+	6.89355i	0.262379	+	0.351328i
$386$			7.29753i			0.371435i
$387$	5.35425	−	13.7185i	0.272172	−	0.697352i
$388$	8.83142	+	2.86950i	0.448348	+	0.145677i
$389$	14.1463	−	4.59643i	0.717248	−	0.233048i	0.0724186	−	0.997374i	$-0.476928\pi$
$389$	14.1463	−	4.59643i	0.717248	−	0.233048i	0.644830	+	0.764326i	$0.276928\pi$
$390$	5.00959	+	0.145198i	0.253671	+	0.00735236i
$391$	−28.7971	−	39.6358i	−1.45633	−	2.00447i
$392$	5.75013	−	3.99199i	0.290426	−	0.201626i
$393$	−27.5481	+	18.8201i	−1.38962	+	0.949350i
$394$	−11.4570	−	8.32402i	−0.577197	−	0.419358i
$395$	−15.0801			−0.758763
$396$	8.70637	+	4.81654i	0.437512	+	0.242040i
$397$		−	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
$399$	−4.43175	−	4.79847i	−0.221865	−	0.240224i
$400$	−1.24801	−	3.84097i	−0.0624003	−	0.192048i
$401$	−5.88895	−	8.10545i	−0.294080	−	0.404767i	0.636254	−	0.771480i	$-0.280483\pi$
$401$	−5.88895	−	8.10545i	−0.294080	−	0.404767i	−0.930334	+	0.366713i	$0.880483\pi$
$402$	0.0756732	−	2.61087i	0.00377423	−	0.130218i
$403$	5.64395	+	17.3703i	0.281145	+	0.865276i
$404$	4.70742	−	14.4880i	0.234203	−	0.720803i
$405$	8.76524	+	1.02049i	0.435548	+	0.0507087i
$406$	−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	$-0.903857\pi$
$409$	−7.62011	+	10.4882i	−0.376790	+	0.518607i	0.577941	+	0.816079i	$0.303857\pi$
$410$	1.46291	+	0.475327i	0.0722477	+	0.0234747i
$411$	−3.93075	−	1.40433i	−0.193889	−	0.0692705i
$412$	−8.90407	−	12.2554i	−0.438672	−	0.603780i
$413$	10.2549	−	10.0371i	0.504610	−	0.493892i
$414$	15.5769	−	9.99240i	0.765565	−	0.491100i
$415$	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	$0.457623\pi$
$420$	−1.87932	−	4.08128i	−0.0917016	−	0.199146i
$421$	−0.686859	+	2.11393i	−0.0334754	+	0.103027i	−0.966398	−	0.257050i	$-0.917250\pi$
$421$	−0.686859	+	2.11393i	−0.0334754	+	0.103027i	0.932923	+	0.360077i	$0.117250\pi$
$422$	−15.9052	+	5.16792i	−0.774255	+	0.251571i
$423$	−5.77033	−	4.72639i	−0.280563	−	0.229805i
$424$	0.532217	−	0.386678i	0.0258467	−	0.0187787i
$425$	−9.91161	−	30.5048i	−0.480784	−	1.47970i
$426$	8.96819	−	6.12682i	0.434510	−	0.296845i
$427$	13.2058	−	25.2443i	0.639073	−	1.22166i
$428$			4.17359i			0.201738i
$429$	−7.77321	+	15.0654i	−0.375294	+	0.727366i
$430$			4.81304i			0.232105i
$431$	3.56552	−	4.90751i	0.171745	−	0.236387i	−0.714464	−	0.699672i	$-0.753330\pi$
$431$	3.56552	−	4.90751i	0.171745	−	0.236387i	0.886209	+	0.463285i	$0.153330\pi$
$432$	−3.92274	−	3.40765i	−0.188733	−	0.163951i
$433$	28.6078	−	9.29522i	1.37480	−	0.446700i	0.473844	−	0.880609i	$-0.342866\pi$
$433$	28.6078	−	9.29522i	1.37480	−	0.446700i	0.900957	+	0.433909i	$0.142866\pi$
$434$	11.7022	−	11.4537i	0.561724	−	0.549793i
$435$	−0.183364	+	6.32641i	−0.00879163	+	0.303328i
$436$	1.52156	+	4.68287i	0.0728693	+	0.224269i
$437$	−2.71716	+	8.36255i	−0.129979	+	0.400035i
$438$	−2.67688	−	9.13065i	−0.127906	−	0.436279i
$439$			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	$-0.0173931\pi$
$443$	37.3429	+	12.1334i	1.77422	+	0.576477i	0.775708	+	0.631092i	$0.217393\pi$
$444$	−0.244041	+	0.683075i	−0.0115817	+	0.0324173i
$445$	−13.2916	+	9.65691i	−0.630082	+	0.457781i
$446$	8.39697	−	6.10076i	0.397608	−	0.288879i
$447$	15.5742	+	5.56415i	0.736633	+	0.263175i
$448$	−0.441911	+	2.60858i	−0.0208783	+	0.123244i
$449$	12.6726	−	17.4423i	0.598056	−	0.823153i	−0.397473	−	0.917614i	$-0.630113\pi$
$449$	12.6726	−	17.4423i	0.598056	−	0.823153i	0.995529	+	0.0944606i	$0.0301126\pi$
$450$	11.7204	−	3.07034i	0.552505	−	0.144737i
$451$	−3.59025	+	3.76593i	−0.169058	+	0.177331i
$452$		−	6.76055i		−	0.317989i
$453$	−6.04958	−	20.6347i	−0.284234	−	0.969504i
$454$	12.8232	+	4.16652i	0.601823	+	0.195544i
$455$	6.85800	−	3.40211i	0.321508	−	0.159493i
$456$	2.46779	+	0.0715262i	0.115565	+	0.00334952i
$457$	−13.2050	+	9.59398i	−0.617703	+	0.448787i	−0.852118	−	0.523349i	$-0.824682\pi$
$457$	−13.2050	+	9.59398i	−0.617703	+	0.448787i	0.234416	+	0.972136i	$0.424682\pi$
$458$	1.50169	+	4.62174i	0.0701695	+	0.215960i
$459$	−31.1542	−	27.0634i	−1.45416	−	1.26321i
$460$	−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	$0.548448\pi$
$462$	15.1968	+	0.240601i	0.707018	+	0.0111938i
$463$	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
$465$	−5.92903	−	8.67867i	−0.274952	−	0.402464i
$466$	4.39804	+	13.5358i	0.203735	+	0.627033i
$467$	23.9109	−	17.3723i	1.10646	−	0.803894i	0.124362	−	0.992237i	$-0.460312\pi$
$467$	23.9109	−	17.3723i	1.10646	−	0.803894i	0.982103	+	0.188343i	$0.0603117\pi$
$468$	5.60989	−	6.84897i	0.259317	−	0.316594i
$469$	−1.77309	−	3.57421i	−0.0818736	−	0.165042i
$470$	2.31849	+	0.753325i	0.106944	+	0.0347483i
$471$	35.5581	−	10.4248i	1.63843	−	0.480347i
$472$			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
$476$	−3.50964	+	20.7173i	−0.160864	+	0.949574i
$477$	1.06561	+	1.66116i	0.0487909	+	0.0760592i
$478$	6.07257	−	4.41198i	0.277753	−	0.201799i
$479$	17.3074	−	12.5745i	0.790794	−	0.574545i	−0.117405	−	0.993084i	$-0.537458\pi$
$479$	17.3074	−	12.5745i	0.790794	−	0.574545i	0.908199	+	0.418539i	$0.137458\pi$
$480$	1.59926	+	0.571366i	0.0729961	+	0.0260792i
$481$	−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
$486$	10.8874	−	11.1564i	0.493863	−	0.506063i
$487$	2.10828	−	6.48861i	0.0955352	−	0.294027i	−0.891858	−	0.452316i	$-0.850598\pi$
$487$	2.10828	−	6.48861i	0.0955352	−	0.294027i	0.987393	+	0.158289i	$0.0505978\pi$
$488$	3.32753	+	10.2411i	0.150630	+	0.463592i
$489$	35.1982	+	1.02018i	1.59172	+	0.0461343i
$490$	−5.46478	−	4.15250i	−0.246873	−	0.187591i
$491$	5.55085	−	1.80358i	0.250506	−	0.0813945i	−0.181072	−	0.983470i	$-0.557957\pi$
$491$	5.55085	−	1.80358i	0.250506	−	0.0813945i	0.431579	+	0.902075i	$0.357957\pi$
$492$	2.24363	−	1.53279i	0.101151	−	0.0691033i
$493$	17.3972	−	23.9452i	0.783532	−	1.07844i
$494$			4.20639i			0.189254i
$495$	1.85351	−	9.57810i	0.0833091	−	0.430503i
$496$			6.18902i			0.277895i
$497$	7.69030	−	14.7008i	0.344957	−	0.659422i
$498$	−6.46103	−	9.45739i	−0.289526	−	0.423796i
$499$	4.92304	+	15.1516i	0.220386	+	0.678277i	0.998727	+	0.0504361i	$0.0160611\pi$
$499$	4.92304	+	15.1516i	0.220386	+	0.678277i	−0.778342	+	0.627841i	$0.783939\pi$
$500$	−7.16977	+	5.20914i	−0.320642	+	0.232960i
$501$	15.2392	+	0.441691i	0.680837	+	0.0197333i
$502$	0.981123	−	0.318786i	0.0437897	−	0.0142281i
$503$	−7.82390	+	24.0795i	−0.348851	+	1.07365i	0.610639	+	0.791909i	$0.290912\pi$
$503$	−7.82390	+	24.0795i	−0.348851	+	1.07365i	−0.959490	+	0.281743i	$0.909088\pi$
$504$	−7.73583	−	1.77677i	−0.344581	−	0.0791436i
$505$	−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	−0.999495	−	0.0317781i	$-0.989883\pi$
$509$	−3.88519	+	11.9574i	−0.172208	+	0.530001i	0.827287	+	0.561779i	$0.189883\pi$
$510$	12.7013	+	4.53777i	0.562422	+	0.200936i
$511$	−10.1664	−	10.3870i	−0.449736	−	0.459496i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−0.643016	+	7.37852i	−0.0283898	+	0.325770i
$514$	−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
$519$	−6.46785	−	22.0614i	−0.283907	−	0.968389i
$520$	−0.894142	+	2.75189i	−0.0392107	+	0.120678i
$521$	0.323545	+	0.995769i	0.0141748	+	0.0436254i	0.957894	−	0.287123i	$-0.0926988\pi$
$521$	0.323545	+	0.995769i	0.0141748	+	0.0436254i	−0.943719	+	0.330748i	$0.892699\pi$
$522$	8.64928	+	7.08449i	0.378569	+	0.310080i
$523$	−2.04864	−	2.81972i	−0.0895809	−	0.123298i	0.761874	−	0.647725i	$-0.224279\pi$
$523$	−2.04864	−	2.81972i	−0.0895809	−	0.123298i	−0.851455	+	0.524427i	$0.824279\pi$
$524$	−5.95235	−	18.3194i	−0.260030	−	0.800289i
$525$	13.5959	−	12.5568i	0.593373	−	0.548024i
$526$	19.1831	+	13.9373i	0.836423	+	0.607697i
$527$			49.1529i			2.14114i
$528$	−4.08267	+	4.04126i	−0.177675	+	0.175873i
$529$	−15.0544			−0.654537
$530$	−0.521835	−	0.379135i	−0.0226671	−	0.0164686i
$531$	−16.2434	−	0.942386i	−0.704903	−	0.0408961i
$532$	3.37834	−	1.67592i	0.146470	−	0.0726605i
$533$	2.72121	+	3.74543i	0.117869	+	0.162233i
$534$	−0.840833	+	29.0103i	−0.0363864	+	1.25540i
$535$	3.89190	−	1.26455i	0.168261	−	0.0546714i
$536$	1.43421	+	0.466003i	0.0619485	+	0.0201283i
$537$	−29.4534	+	8.63501i	−1.27101	+	0.372628i
$538$			13.3397i			0.575116i
$539$	20.6605	−	10.5899i	0.889909	−	0.456137i
$540$	−1.98911	+	4.69046i	−0.0855975	+	0.201845i
$541$	19.8341	+	14.4103i	0.852735	+	0.619548i	0.925899	−	0.377772i	$-0.123310\pi$
$541$	19.8341	+	14.4103i	0.852735	+	0.619548i	−0.0731639	+	0.997320i	$0.523310\pi$
$542$	0.219491	−	0.675524i	0.00942795	−	0.0290163i
$543$	−22.7690	−	8.13464i	−0.977112	−	0.349091i
$544$	−4.66817	−	6.42518i	−0.200146	−	0.275477i
$545$	3.90578	−	2.83772i	0.167305	−	0.121554i
$546$	2.64413	−	13.2625i	0.113158	−	0.567582i
$547$	−1.55651	+	4.79045i	−0.0665516	+	0.204825i	−0.978802	−	0.204808i	$-0.934343\pi$
$547$	−1.55651	+	4.79045i	−0.0665516	+	0.204825i	0.912251	+	0.409633i	$0.134343\pi$
$548$	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
$552$	3.00597	+	10.2532i	0.127942	+	0.436403i
$553$	−6.79665	+	40.1203i	−0.289023	+	1.70609i
$554$	−12.9815	+	4.21795i	−0.551531	+	0.179203i
$555$	0.710913	+	0.0206050i	0.0301766	+	0.000874635i
$556$	7.60075	+	10.4615i	0.322344	+	0.443668i
$557$	−31.8805	+	10.3586i	−1.35082	+	0.438908i	−0.892968	−	0.450120i	$-0.851381\pi$
$557$	−31.8805	+	10.3586i	−1.35082	+	0.438908i	−0.457853	+	0.889028i	$0.651381\pi$
$558$	−18.5359	−	1.07539i	−0.784687	−	0.0455248i
$559$	−8.51476	+	11.7196i	−0.360136	+	0.495684i
$560$	2.56641	−	0.378289i	0.108451	−	0.0159856i
$561$	−32.4244	+	32.0955i	−1.36896	+	1.35507i
$562$	−2.59452			−0.109443
$563$	−19.3252	−	14.0405i	−0.814458	−	0.591738i	0.100662	−	0.994921i	$-0.467904\pi$
$563$	−19.3252	−	14.0405i	−0.814458	−	0.591738i	−0.915120	+	0.403182i	$0.867904\pi$
$564$	3.55583	−	2.42925i	0.149728	−	0.102290i
$565$	−6.30424	+	2.04837i	−0.265222	+	0.0861757i
$566$	19.9539	−	14.4974i	0.838726	−	0.609370i
$567$	6.66552	−	22.8598i	0.279925	−	0.960022i
$568$	1.93776	+	5.96382i	0.0813068	+	0.250236i
$569$	37.0388	+	12.0346i	1.55275	+	0.504518i	0.954858	−	0.297062i	$-0.0960069\pi$
$569$	37.0388	+	12.0346i	1.55275	+	0.504518i	0.597887	+	0.801580i	$0.296007\pi$
$570$	−0.681016	−	2.32290i	−0.0285246	−	0.0972956i
$571$	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
$574$	1.92393	−	3.67780i	0.0803034	−	0.153508i
$575$	−23.6942	−	7.69872i	−0.988118	−	0.321059i
$576$	2.52511	−	1.61982i	0.105213	−	0.0674926i
$577$	−7.30337	−	10.0522i	−0.304043	−	0.418480i	0.629469	−	0.777026i	$-0.283273\pi$
$577$	−7.30337	−	10.0522i	−0.304043	−	0.418480i	−0.933512	+	0.358546i	$0.883273\pi$
$578$	−27.0820	−	37.2752i	−1.12646	−	1.55044i
$579$	4.25251	−	11.9029i	0.176728	−	0.494666i
$580$	−3.47524	−	1.12917i	−0.144302	−	0.0468864i
$581$	−15.5027	−	8.10980i	−0.643162	−	0.336451i
$582$	−12.7326	−	9.82675i	−0.527783	−	0.407332i
$583$	1.91985	−	1.03668i	0.0795120	−	0.0429348i
$584$	5.49346			0.227321
$585$	−8.08643	−	3.15608i	−0.334333	−	0.130488i
$586$	15.3950	+	5.00213i	0.635961	+	0.206636i
$587$	0.0736050	+	0.226533i	0.00303800	+	0.00935002i	0.952564	−	0.304338i	$-0.0984353\pi$
$587$	0.0736050	+	0.226533i	0.00303800	+	0.00935002i	−0.949526	+	0.313688i	$0.898435\pi$
$588$	−11.7052	+	3.16046i	−0.482714	+	0.130335i
$589$	7.13690	−	5.18526i	0.294071	−	0.213655i
$590$	5.05751	−	1.64328i	0.208214	−	0.0676529i
$591$	13.8367	+	20.2535i	0.569164	+	0.833119i
$592$	−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	$0.636242\pi$
$594$	−11.3940	−	12.9297i	−0.467503	−	0.530510i
$595$	20.3823	−	3.00435i	0.835595	−	0.123166i
$596$	−5.61240	+	7.72480i	−0.229893	+	0.316420i
$597$	−12.6180	−	18.4697i	−0.516420	−	0.755915i
$598$	−17.3136	+	5.62553i	−0.708006	+	0.230045i
$599$	−2.46742	−	3.39611i	−0.100816	−	0.138761i	0.755629	−	0.655000i	$-0.227332\pi$
$599$	−2.46742	−	3.39611i	−0.100816	−	0.138761i	−0.856444	+	0.516239i	$0.827332\pi$
$600$	−0.202661	+	6.99218i	−0.00827359	+	0.285455i
$601$	38.2778	−	12.4372i	1.56139	−	0.507325i	0.604208	−	0.796826i	$-0.293489\pi$
$601$	38.2778	−	12.4372i	1.56139	−	0.507325i	0.957178	+	0.289501i	$0.0934895\pi$
$602$	12.8050	+	2.16925i	0.521893	+	0.0884120i
$603$	−1.64487	+	4.21444i	−0.0669842	+	0.171625i
$604$	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	−0.0716301	+	0.997431i	$0.522820\pi$
$607$	−24.5908	+	33.8463i	−0.998109	+	1.37378i	−0.926479	+	0.376348i	$0.877180\pi$
$608$	−0.440466	+	1.35562i	−0.0178633	+	0.0549775i
$609$	16.7486	+	3.33917i	0.678689	+	0.135310i
$610$	8.54166	−	6.20588i	0.345842	−	0.251269i
$611$	4.31273	+	5.93597i	0.174475	+	0.240144i
$612$	20.0543	−	12.8646i	0.810647	−	0.520019i
$613$	6.15484	−	18.9427i	0.248592	−	0.765087i	−0.746433	−	0.665460i	$-0.768235\pi$
$613$	6.15484	−	18.9427i	0.248592	−	0.765087i	0.995025	−	0.0996263i	$-0.0317647\pi$
$614$	−9.40654	−	6.83425i	−0.379617	−	0.275808i
$615$	−2.10913	−	1.62778i	−0.0850482	−	0.0656384i
$616$	−2.60168	+	8.38041i	−0.104825	+	0.337656i
$617$		−	31.7385i		−	1.27774i	−0.769313	−	0.638871i	$-0.779402\pi$
$617$		−	31.7385i		−	1.27774i	0.769313	−	0.638871i	$-0.220598\pi$
$618$	7.38162	+	25.1782i	0.296932	+	1.01282i
$619$	−15.5378	−	5.04855i	−0.624518	−	0.202918i	−0.0203728	−	0.999792i	$-0.506485\pi$
$619$	−15.5378	−	5.04855i	−0.624518	−	0.202918i	−0.604145	+	0.796874i	$0.706485\pi$
$620$	5.77129	−	1.87521i	0.231781	−	0.0753101i
$621$	−31.2301	+	7.22120i	−1.25322	+	0.289777i
$622$	4.63302	+	6.37681i	0.185767	+	0.255687i
$623$	19.7015	+	39.7144i	0.789322	+	1.59112i
$624$	2.88334	+	4.22052i	0.115426	+	0.168956i
$625$	−9.30669	−	6.76171i	−0.372268	−	0.270468i
$626$	−14.3704			−0.574358
$627$	8.08073	+	1.32212i	0.322713	+	0.0528004i
$628$			21.3936i			0.853697i
$629$	−2.69078	−	1.95497i	−0.107288	−	0.0779496i
$630$	0.687027	+	7.75204i	0.0273718	+	0.308849i
$631$	−3.45819	−	10.6432i	−0.137668	−	0.423700i	0.858327	−	0.513103i	$-0.171504\pi$
$631$	−3.45819	−	10.6432i	−0.137668	−	0.423700i	−0.995996	+	0.0894031i	$0.971504\pi$
$632$	−9.04020	−	12.4428i	−0.359600	−	0.494947i
$633$	28.9542	+	0.839207i	1.15083	+	0.0333555i
$634$	5.42261	+	16.6891i	0.215359	+	0.662808i
$635$	−4.82836	+	14.8602i	−0.191608	+	0.589708i
$636$	−1.09342	+	0.320563i	−0.0433568	+	0.0127111i
$637$	−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	$-0.476063\pi$
$641$	−11.3985	−	3.70361i	−0.450215	−	0.146284i	−0.525344	+	0.850890i	$0.676063\pi$
$642$	2.43209	−	6.80747i	0.0959870	−	0.268669i
$643$	25.5731	+	35.1984i	1.00851	+	1.38809i	0.919957	+	0.392018i	$0.128223\pi$
$643$	25.5731	+	35.1984i	1.00851	+	1.38809i	0.0885491	+	0.996072i	$0.471777\pi$
$644$	11.4163	+	11.6640i	0.449864	+	0.459627i
$645$	2.80472	−	7.85045i	0.110436	−	0.309111i
$646$	−3.49816	+	10.7662i	−0.137633	+	0.423592i
$647$	14.5630	+	10.5806i	0.572531	+	0.415968i	0.836024	−	0.548693i	$-0.184875\pi$
$647$	14.5630	+	10.5806i	0.572531	+	0.415968i	−0.263493	+	0.964661i	$0.584875\pi$
$648$	4.41255	+	7.84407i	0.173342	+	0.308144i
$649$	−2.38894	+	17.8286i	−0.0937740	+	0.699834i
$650$	−11.9183			−0.467473
$651$	−25.7617	+	11.8626i	−1.00968	+	0.464930i
$652$	−6.28239	+	19.3352i	−0.246037	+	0.757226i
$653$	19.0613	−	6.19338i	0.745925	−	0.242366i	0.0886982	−	0.996059i	$-0.471729\pi$
$653$	19.0613	−	6.19338i	0.745925	−	0.242366i	0.657227	+	0.753693i	$0.271729\pi$
$654$	0.247082	−	8.52479i	0.00966166	−	0.333346i
$655$	−15.2795	+	11.1012i	−0.597019	+	0.433759i
$656$	0.484783	+	1.49201i	0.0189276	+	0.0582531i
$657$	−0.954530	+	16.4527i	−0.0372398	+	0.641882i
$658$	3.04916	−	5.82878i	0.118869	−	0.227230i
$659$			16.9352i			0.659703i	0.944033	+	0.329852i	$0.106999\pi$
$659$			16.9352i			0.659703i	−0.944033	+	0.329852i	$0.893001\pi$
$660$	5.00550	+	2.58265i	0.194839	+	0.100530i
$661$		−	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
$663$	22.8994	+	33.5191i	0.889337	+	1.30178i
$664$	6.28914	−	2.04347i	0.244066	−	0.0793019i
$665$	−2.58641	−	2.64254i	−0.100297	−	0.102473i
$666$	0.796101	−	0.971939i	0.0308483	−	0.0376619i
$667$	−7.10425	−	21.8646i	−0.275078	−	0.846602i
$668$	−2.71998	+	8.37125i	−0.105239	+	0.323893i
$669$	−17.2512	+	5.05763i	−0.666972	+	0.195539i
$670$		−	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	0.989087	−	0.147335i	$-0.0470697\pi$
$673$	29.9531	+	21.7622i	1.15461	+	0.838871i	0.165520	+	0.986206i	$0.447070\pi$
$674$	0.536784	+	0.174412i	0.0206761	+	0.00671809i
$675$	−20.9061	−	1.82190i	−0.804677	−	0.0701251i
$676$	3.47166	−	2.52231i	0.133525	−	0.0970117i
$677$	−22.3901	+	16.2674i	−0.860523	+	0.625206i	−0.928027	−	0.372513i	$-0.878496\pi$
$677$	−22.3901	+	16.2674i	−0.860523	+	0.625206i	0.0675045	+	0.997719i	$0.478496\pi$
$678$	−3.93959	+	11.0270i	−0.151299	+	0.423489i
$679$	−24.2231	−	4.10355i	−0.929596	−	0.157480i
$680$	−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	$-0.258425\pi$
$684$	−3.98349	−	1.55473i	−0.152312	−	0.0594465i
$685$	−2.24725	−	0.730175i	−0.0858629	−	0.0278986i
$686$	−13.5106	+	12.6674i	−0.515839	+	0.483643i
$687$	0.243856	−	8.41351i	0.00930370	−	0.320995i
$688$	−3.97129	+	2.88531i	−0.151404	+	0.110002i
$689$	−0.599919	−	1.84636i	−0.0228551	−	0.0703407i
$690$	8.65035	−	5.90968i	0.329313	−	0.224978i
$691$	−20.8099	+	28.6424i	−0.791648	+	1.08961i	0.202253	+	0.979333i	$0.435174\pi$
$691$	−20.8099	+	28.6424i	−0.791648	+	1.08961i	−0.993901	+	0.110276i	$0.964826\pi$
$692$	13.2733			0.504574
$693$	−24.6470	−	9.24810i	−0.936261	−	0.351306i
$694$	21.7753			0.826578
$695$	7.45249	−	10.2575i	0.282689	−	0.389088i
$696$	−5.32992	+	3.64125i	−0.202030	+	0.138021i
$697$	3.85012	+	11.8495i	0.145834	+	0.448831i
$698$	−15.5567	+	11.3026i	−0.588830	+	0.427810i
$699$	0.714188	−	24.6408i	0.0270131	−	0.932002i
$700$	4.74852	+	9.57212i	0.179477	+	0.361792i
$701$	9.31719	+	3.02734i	0.351905	+	0.114341i	0.479635	−	0.877468i	$-0.340769\pi$
$701$	9.31719	+	3.02734i	0.351905	+	0.114341i	−0.127730	+	0.991809i	$0.540769\pi$
$702$	−13.1413	+	7.90215i	−0.495986	+	0.298247i
$703$			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
$707$	−6.73187	+	39.7380i	−0.253178	+	1.49450i
$708$	3.16049	−	8.84628i	0.118779	−	0.332463i
$709$	−25.2904	+	18.3746i	−0.949802	+	0.690072i	−0.950760	−	0.309928i	$-0.899695\pi$
$709$	−25.2904	+	18.3746i	−0.949802	+	0.690072i	0.000957708		1.00000i	$0.499695\pi$
$710$	4.97417	−	3.61395i	0.186677	−	0.135629i
$711$	38.8365	−	24.9131i	1.45648	−	0.934313i
$712$	−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
$717$	−12.4759	+	3.65761i	−0.465920	+	0.136596i
$718$	−8.01810	+	24.6772i	−0.299233	+	0.920944i
$719$	−5.08235	−	15.6419i	−0.189540	−	0.583343i	0.810457	−	0.585798i	$-0.199219\pi$
$719$	−5.08235	−	15.6419i	−0.189540	−	0.583343i	−0.999997	+	0.00245449i	$0.999219\pi$
$720$	−2.27557	−	1.86389i	−0.0848056	−	0.0694630i
$721$	28.0344	+	28.6428i	1.04406	+	1.06671i
$722$	−16.1378	+	5.24349i	−0.600587	+	0.195143i
$723$	−26.7667	−	39.1801i	−0.995466	−	1.45712i
$724$	8.20517	−	11.2934i	0.304943	−	0.419718i
$725$		−	15.0511i		−	0.558984i
$726$	−15.2008	+	11.4863i	−0.564155	+	0.426297i
$727$		−	21.5954i		−	0.800930i	−0.916312	−	0.400465i	$-0.868849\pi$
$727$		−	21.5954i		−	0.800930i	0.916312	−	0.400465i	$-0.131151\pi$
$728$	6.91834	+	3.61913i	0.256411	+	0.134134i
$729$	−24.2594	+	11.8525i	−0.898497	+	0.438981i
$730$	−1.66446	−	5.12268i	−0.0616045	−	0.189599i
$731$	−31.5398	+	22.9150i	−1.16654	+	0.847543i
$732$	0.540350	−	18.6431i	0.0199719	−	0.689069i
$733$	7.40470	−	2.40593i	0.273499	−	0.0888652i	−0.169056	−	0.985606i	$-0.554072\pi$
$733$	7.40470	−	2.40593i	0.273499	−	0.0888652i	0.442555	+	0.896741i	$0.354072\pi$
$734$	−8.07323	+	24.8469i	−0.297989	+	0.917114i
$735$	6.49369	+	9.95757i	0.239523	+	0.367290i
$736$	−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	0.993983	−	0.109535i	$-0.0349360\pi$
$739$	32.5390	+	23.6410i	1.19697	+	0.869647i	0.202984	+	0.979182i	$0.434936\pi$
$740$	−0.126888	+	0.390521i	−0.00466449	+	0.0143558i
$741$	2.45120	−	6.86096i	0.0900471	−	0.252044i
$742$	−1.24387	+	1.21745i	−0.0456641	+	0.0446942i
$743$	7.24522	+	9.97219i	0.265801	+	0.365844i	0.920967	−	0.389641i	$-0.127401\pi$
$743$	7.24522	+	9.97219i	0.265801	+	0.365844i	−0.655165	+	0.755486i	$0.727401\pi$
$744$	3.60655	−	10.0948i	0.132222	−	0.370093i
$745$	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
$750$	14.7300	−	4.31847i	0.537864	−	0.157688i
$751$	5.59622	−	17.2234i	0.204209	−	0.628491i	−0.795536	−	0.605906i	$-0.792811\pi$
$751$	5.59622	−	17.2234i	0.204209	−	0.628491i	0.999745	−	0.0225844i	$-0.00718944\pi$
$752$	0.768311	+	2.36462i	0.0280174	+	0.0862288i
$753$	−1.78606	−	0.0517669i	−0.0650876	−	0.00188649i
$754$	−6.46445	−	8.89756i	−0.235421	−	0.324030i
$755$	−3.76158	−	11.5770i	−0.136898	−	0.421329i
$756$	11.5824	+	7.40598i	0.421247	+	0.269353i
$757$	5.24019	+	3.80722i	0.190458	+	0.138376i	0.678928	−	0.734205i	$-0.262445\pi$
$757$	5.24019	+	3.80722i	0.190458	+	0.138376i	−0.488470	+	0.872581i	$0.662445\pi$
$758$		−	17.7483i		−	0.644647i
$759$	5.36511	+	35.0287i	0.194741	+	1.27146i
$760$	1.39758			0.0506954
$761$	−11.7456	−	8.53367i	−0.425777	−	0.309345i	0.354181	−	0.935177i	$-0.384760\pi$
$761$	−11.7456	−	8.53367i	−0.425777	−	0.309345i	−0.779958	+	0.625832i	$0.784760\pi$
$762$	15.5700	+	22.7908i	0.564042	+	0.825623i
$763$	−5.78934	−	11.6702i	−0.209588	−	0.422491i
$764$	4.25292	+	5.85365i	0.153865	+	0.211778i
$765$	−18.0725	−	14.8029i	−0.653413	−	0.535201i
$766$	−9.66205	+	3.13939i	−0.349104	+	0.113431i
$767$	15.2220	+	4.94592i	0.549633	+	0.178587i
$768$	0.487284	+	1.66209i	0.0175833	+	0.0599756i
$769$			8.43623i			0.304218i	0.988364	+	0.152109i	$0.0486065\pi$
$769$			8.43623i			0.304218i	−0.988364	+	0.152109i	$0.951393\pi$
$770$	8.60306	−	0.113091i	0.310033	−	0.00407553i
$771$	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	−0.556901	−	0.830579i	$-0.688010\pi$
$773$	10.6163	−	32.6737i	0.381843	−	1.17519i	0.938744	−	0.344614i	$-0.111990\pi$
$774$	−7.95137	−	12.3952i	−0.285806	−	0.445537i
$775$	14.6918	+	20.2215i	0.527745	+	0.726378i
$776$	7.51246	−	5.45812i	0.269681	−	0.195935i
$777$	0.375230	−	1.88208i	0.0134613	−	0.0675193i
$778$	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
$783$	−9.97930	−	16.5956i	−0.356631	−	0.593078i
$784$	0.150260	−	6.99839i	0.00536643	−	0.249942i
$785$	19.9496	−	6.48203i	0.712033	−	0.231354i
$786$	−0.966587	+	33.3491i	−0.0344770	+	1.18952i
$787$	25.1697	+	34.6431i	0.897203	+	1.23489i	0.971352	+	0.237646i	$0.0763759\pi$
$787$	25.1697	+	34.6431i	0.897203	+	1.23489i	−0.0741492	+	0.997247i	$0.523624\pi$
$788$	−13.4686	+	4.37620i	−0.479797	+	0.155896i
$789$	−23.1674	−	33.9115i	−0.824782	−	1.20728i
$790$	−8.86386	+	12.2001i	−0.315362	+	0.434059i
$791$	2.60832	+	17.6955i	0.0927410	+	0.629180i
$792$	9.01414	−	4.21251i	0.320304	−	0.149685i
$793$	31.7774			1.12845
$794$	−17.5667	−	12.7630i	−0.623420	−	0.452941i
$795$	0.630220	+	0.922491i	0.0223516	+	0.0327174i
$796$	12.2823	−	3.99076i	0.435335	−	0.141449i
$797$	24.5882	−	17.8644i	0.870960	−	0.632789i	−0.0598844	−	0.998205i	$-0.519073\pi$
$797$	24.5882	−	17.8644i	0.870960	−	0.632789i	0.930844	+	0.365416i	$0.119073\pi$
$798$	−6.48697	+	0.764892i	−0.229636	+	0.0270769i
$799$	6.10190	+	18.7797i	0.215870	+	0.664378i
$800$	−3.84097	−	1.24801i	−0.135799	−	0.0441237i
$801$	18.2767	−	46.8282i	0.645777	−	1.65459i
$802$	−10.0189			−0.353779
$803$	18.0584	+	2.41972i	0.637266	+	0.0853902i
$804$	−2.06776	−	1.59585i	−0.0729242	−	0.0562813i
$805$	7.41775	−	14.1798i	0.261441	−	0.499772i
$806$	17.3703	+	5.64395i	0.611843	+	0.198800i
$807$	7.77350	−	21.7582i	0.273640	−	0.765923i
$808$	−8.95405	−	12.3242i	−0.315002	−	0.433564i
$809$	28.8637	+	39.7274i	1.01479	+	1.39674i	0.915791	+	0.401654i	$0.131565\pi$
$809$	28.8637	+	39.7274i	1.01479	+	1.39674i	0.0990006	+	0.995087i	$0.468435\pi$
$810$	5.97767	−	6.49140i	0.210034	−	0.228084i
$811$	−8.48149	−	2.75580i	−0.297825	−	0.0967693i	0.156293	−	0.987711i	$-0.450046\pi$
$811$	−8.48149	−	2.75580i	−0.297825	−	0.0967693i	−0.454118	+	0.890941i	$0.650046\pi$
$812$	−4.57045	+	8.73689i	−0.160391	+	0.306605i
$813$	−0.751658	+	0.973930i	−0.0263618	+	0.0341572i
$814$	−1.00531	−	0.958413i	−0.0352362	−	0.0335923i
$815$	19.9337			0.698247
$816$	3.86999	+	13.2003i	0.135477	+	0.462102i
$817$	6.65443	+	2.16216i	0.232809	+	0.0756443i
$818$	4.00613	+	12.3296i	0.140071	+	0.431094i
$819$	−12.0413	+	20.0913i	−0.420756	+	0.702048i
$820$	1.24442	−	0.904125i	0.0434571	−	0.0315734i
$821$	20.0322	−	6.50887i	0.699130	−	0.227161i	0.0621783	−	0.998065i	$-0.480195\pi$
$821$	20.0322	−	6.50887i	0.699130	−	0.227161i	0.636951	+	0.770904i	$0.280195\pi$
$822$	−3.44656	+	2.35460i	−0.120213	+	0.0821260i
$823$	−26.8396	−	19.5001i	−0.935571	−	0.679732i	0.0117793	−	0.999931i	$-0.496250\pi$
$823$	−26.8396	−	19.5001i	−0.935571	−	0.679732i	−0.947351	+	0.320198i	$0.896250\pi$
$824$	−15.1485			−0.527723
$825$	−3.74606	+	22.8957i	−0.130421	+	0.797127i
$826$	−2.09249	−	14.1960i	−0.0728071	−	0.493943i
$827$	6.91009	−	9.51092i	0.240287	−	0.330727i	−0.671793	−	0.740739i	$-0.734475\pi$
$827$	6.91009	−	9.51092i	0.240287	−	0.330727i	0.912080	+	0.410012i	$0.134475\pi$
$828$	1.07188	−	18.4754i	0.0372504	−	0.642064i
$829$	−27.8383	+	9.04521i	−0.966864	+	0.314153i	−0.749549	−	0.661948i	$-0.769730\pi$
$829$	−27.8383	+	9.04521i	−0.966864	+	0.314153i	−0.217315	+	0.976102i	$0.569730\pi$
$830$	−3.81109	−	5.24551i	−0.132285	−	0.182074i
$831$	23.6318	+	0.684942i	0.819778	+	0.0237604i
$832$	−2.80663	+	0.911930i	−0.0973024	+	0.0316155i
$833$	1.19336	−	55.5809i	0.0413474	−	1.92576i
$834$	−6.30115	−	21.4928i	−0.218191	−	0.744235i
$835$	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	−0.713304	−	0.700855i	$-0.752802\pi$
$839$	7.98646	−	24.5798i	0.275723	−	0.848588i	0.989027	−	0.147734i	$-0.0471978\pi$
$840$	−4.40647	−	0.878514i	−0.152038	−	0.0303116i
$841$	−12.2251	+	8.88208i	−0.421556	+	0.306279i
$842$	1.30648	+	1.79822i	0.0450244	+	0.0619707i
$843$	4.23187	+	1.51191i	0.145753	+	0.0520730i
$844$	−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
$847$	−12.2437	+	26.4025i	−0.420699	+	0.907200i
$848$		−	0.657856i		−	0.0225909i
$849$	−40.9946	+	12.0186i	−1.40693	+	0.412476i
$850$	−30.5048	−	9.91161i	−1.04631	−	0.339965i
$851$	−2.45698	+	0.798321i	−0.0842242	+	0.0273661i
$852$	0.314669	−	10.8567i	0.0107804	−	0.371943i
$853$	12.3782	+	17.0371i	0.423820	+	0.583338i	0.966521	−	0.256588i	$-0.0825982\pi$
$853$	12.3782	+	17.0371i	0.423820	+	0.583338i	−0.542701	+	0.839926i	$0.682598\pi$
$854$	−12.6609	−	25.5219i	−0.433246	−	0.873342i
$855$	−0.242839	+	4.18569i	−0.00830492	+	0.143147i
$856$	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	$0.775970\pi$
$858$	7.61922	+	15.1439i	0.260116	+	0.517004i
$859$			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
$861$	−5.28126	+	4.87765i	−0.179985	+	0.166230i
$862$	−1.87450	−	5.76913i	−0.0638458	−	0.196497i
$863$	−12.1910	−	16.7794i	−0.414985	−	0.571178i	0.549440	−	0.835533i	$-0.314841\pi$
$863$	−12.1910	−	16.7794i	−0.414985	−	0.571178i	−0.964425	+	0.264355i	$0.914841\pi$
$864$	−5.06258	+	1.17060i	−0.172232	+	0.0398245i
$865$	−4.02166	−	12.3774i	−0.136741	−	0.420844i
$866$	9.29522	−	28.6078i	0.315865	−	0.972131i
$867$	22.4515	+	76.5804i	0.762491	+	2.60081i
$868$	−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
$873$	15.0415	+	23.4479i	0.509078	+	0.793592i
$874$	5.16834	+	7.11361i	0.174822	+	0.240621i
$875$	16.7569	−	16.4010i	0.566486	−	0.554454i
$876$	−8.96028	−	3.20122i	−0.302740	−	0.108159i
$877$	−12.6246	+	38.8545i	−0.426302	+	1.31202i	0.475439	+	0.879749i	$0.342289\pi$
$877$	−12.6246	+	38.8545i	−0.426302	+	1.31202i	−0.901742	+	0.432275i	$0.857711\pi$
$878$	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	$0.339893\pi$
$882$	20.9338	+	1.66605i	0.704878	+	0.0560987i
$883$	5.87712	−	18.0879i	0.197781	−	0.608706i	−0.802152	−	0.597120i	$-0.796312\pi$
$883$	5.87712	−	18.0879i	0.197781	−	0.608706i	0.999933	−	0.0115868i	$-0.00368826\pi$
$884$	−22.2901	+	7.24251i	−0.749699	+	0.243592i
$885$	−9.20679	−	0.266849i	−0.309483	−	0.00897003i
$886$	31.7658	−	23.0792i	1.06719	−	0.775360i
$887$	−12.2419	−	37.6767i	−0.411043	−	1.26506i	−0.915743	−	0.401765i	$-0.868397\pi$
$887$	−12.2419	−	37.6767i	−0.411043	−	1.26506i	0.504700	−	0.863295i	$-0.331603\pi$
$888$	0.409176	+	0.598935i	0.0137310	+	0.0200989i
$889$	37.3590	+	19.5433i	1.25298	+	0.655461i
$890$			16.4293i			0.550712i
$891$	11.0500	+	27.7290i	0.370191	+	0.928956i
$892$		−	10.3792i		−	0.347522i
$893$	2.08307	−	2.86710i	0.0697073	−	0.0959438i
$894$	13.6558	−	9.32924i	0.456717	−	0.312016i
$895$	−16.5246	+	5.36918i	−0.552358	+	0.179472i
$896$	1.85064	+	1.89080i	0.0618256	+	0.0631672i
$897$	31.5181	+	0.913517i	1.05236	+	0.0305014i
$898$	−6.66237	−	20.5047i	−0.222326	−	0.684250i
$899$	−7.12752	+	21.9362i	−0.237716	+	0.731615i
$900$	4.40513	−	11.2867i	0.146838	−	0.376224i
$901$		−	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
$906$	−20.2497	−	7.23457i	−0.672751	−	0.240353i
$907$	−26.4488	+	19.2162i	−0.878219	+	0.638064i	−0.932780	−	0.360447i	$-0.882624\pi$
$907$	−26.4488	+	19.2162i	−0.878219	+	0.638064i	0.0545606	+	0.998510i	$0.482624\pi$
$908$	10.9081	−	7.92518i	0.361997	−	0.263006i
$909$	38.4663	−	24.6756i	1.27585	−	0.818439i
$910$	1.27867	−	7.54795i	0.0423876	−	0.250212i
$911$	−34.4831	+	47.4619i	−1.14248	+	1.57248i	−0.380624	+	0.924730i	$0.624291\pi$
$911$	−34.4831	+	47.4619i	−1.14248	+	1.57248i	−0.761851	+	0.647752i	$0.775709\pi$
$912$	1.50840	−	1.95444i	0.0499480	−	0.0647181i
$913$	21.5740	−	3.94718i	0.713997	−	0.130632i
$914$			16.3222i			0.539892i
$915$	−17.5485	+	5.14478i	−0.580136	+	0.170081i
$916$	4.62174	+	1.50169i	0.152706	+	0.0496173i
$917$	22.6480	+	45.6541i	0.747903	+	1.50763i
$918$	−40.2068	+	9.29683i	−1.32702	+	0.306841i
$919$	12.2402	−	8.89300i	0.403766	−	0.293353i	−0.367307	−	0.930100i	$-0.619720\pi$
$919$	12.2402	−	8.89300i	0.403766	−	0.293353i	0.771073	+	0.636747i	$0.219720\pi$
$920$	1.86909	+	5.75246i	0.0616220	+	0.189653i
$921$	11.3603	+	16.6287i	0.374334	+	0.547935i
$922$	−3.82693	+	5.26732i	−0.126033	+	0.173470i
$923$	18.5054			0.609111
$924$	9.12709	−	12.1530i	0.300259	−	0.399805i
$925$	−1.69133			−0.0556105
$926$	14.2713	−	19.6427i	0.468983	−	0.645500i
$927$	2.63217	−	45.3692i	0.0864517	−	1.49012i
$928$	−1.15164	−	3.54438i	−0.0378044	−	0.116350i
$929$	15.4855	−	11.2509i	0.508063	−	0.369130i	−0.304025	−	0.952664i	$-0.598331\pi$
$929$	15.4855	−	11.2509i	0.508063	−	0.369130i	0.812088	+	0.583534i	$0.198331\pi$
$930$	−10.5062	−	0.304510i	−0.344511	−	0.00998529i
$931$	−8.19612	+	5.69009i	−0.268617	+	0.186485i
$932$	13.5358	+	4.39804i	0.443380	+	0.144063i
$933$	−3.84086	−	13.1009i	−0.125744	−	0.428904i
$934$		−	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	$-0.779273\pi$
$937$	2.34154	−	3.22286i	0.0764949	−	0.105286i	0.845550	+	0.533896i	$0.179273\pi$
$938$	−3.93379	−	0.666411i	−0.128443	−	0.0217591i
$939$	23.4393	+	8.37412i	0.764913	+	0.273279i
$940$	1.97223	−	1.43291i	0.0643270	−	0.0467363i
$941$	10.4322	−	7.57940i	0.340078	−	0.247081i	−0.404616	−	0.914486i	$-0.632595\pi$
$941$	10.4322	−	7.57940i	0.340078	−	0.247081i	0.744695	+	0.667405i	$0.232595\pi$
$942$	12.4668	−	34.8947i	0.406189	−	1.13693i
$943$	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	$0.755268\pi$
$948$	7.49448	+	25.5632i	0.243409	+	0.830254i
$949$	5.00965	−	15.4181i	0.162620	−	0.500494i
$950$	1.77888	+	5.47483i	0.0577145	+	0.177627i
$951$	0.880565	−	30.3812i	0.0285543	−	0.985177i
$952$	14.6977	+	15.0167i	0.476355	+	0.486693i
$953$	−49.9841	+	16.2408i	−1.61914	+	0.526092i	−0.971740	−	0.236054i	$-0.924146\pi$
$953$	−49.9841	+	16.2408i	−1.61914	+	0.526092i	−0.647405	+	0.762146i	$0.724146\pi$
$954$	1.97025	+	0.114307i	0.0637894	+	0.00370084i
$955$	4.16997	−	5.73947i	0.134937	−	0.185725i
$956$		−	7.50611i		−	0.242765i
$957$	−19.1246	+	9.62200i	−0.618211	+	0.311035i
$958$		−	21.3931i		−	0.691179i
$959$	−2.95546	+	5.64967i	−0.0954367	+	0.182437i
$960$	1.40227	−	0.957991i	0.0452580	−	0.0309190i
$961$	−2.25705	−	6.94649i	−0.0728081	−	0.224080i
$962$	−0.999838	+	0.726425i	−0.0322361	+	0.0234209i
$963$	−7.93387	+	9.68626i	−0.255665	+	0.312135i
$964$	26.0546	−	8.46567i	0.839164	−	0.272661i
$965$	2.21107	−	6.80499i	0.0711770	−	0.219060i
$966$	−11.8238	−	25.6776i	−0.380426	−	0.826163i
$967$	−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	−0.963460	−	0.267851i	$-0.913687\pi$
$971$	−0.827815	+	2.54775i	−0.0265658	+	0.0817612i	0.936895	+	0.349612i	$0.113687\pi$
$972$	−2.62623	−	15.3656i	−0.0842365	−	0.492853i
$973$	−23.9309	−	24.4503i	−0.767191	−	0.783840i
$974$	−4.01018	−	5.51954i	−0.128495	−	0.176858i
$975$	19.4397	+	6.94517i	0.622567	+	0.222423i
$976$	10.2411	+	3.32753i	0.327809	+	0.106512i
$977$	3.93600	−	5.41743i	0.125924	−	0.173319i	−0.741400	−	0.671063i	$-0.765838\pi$
$977$	3.93600	−	5.41743i	0.125924	−	0.173319i	0.867324	+	0.497744i	$0.165838\pi$
$978$	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
$981$	−5.37069	+	13.7606i	−0.171473	+	0.439343i
$982$	1.80358	−	5.55085i	0.0575546	−	0.177135i
$983$	−8.60736	−	26.4907i	−0.274532	−	0.844923i	−0.989343	−	0.145605i	$-0.953487\pi$
$983$	−8.60736	−	26.4907i	−0.274532	−	0.844923i	0.714811	−	0.699318i	$-0.246513\pi$
$984$	0.0787227	−	2.71608i	0.00250959	−	0.0865856i
$985$	8.16165	+	11.2336i	0.260052	+	0.357931i
$986$	−9.14627	−	28.1493i	−0.291276	−	0.896457i
$987$	−8.37004	+	7.73037i	−0.266421	+	0.246060i
$988$	3.40304	+	2.47245i	0.108265	+	0.0786592i
$989$			30.2814i			0.962894i
$990$	−6.65938	−	7.12939i	−0.211649	−	0.226587i
$991$	−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
$993$	41.8926	−	28.6198i	1.32942	−	0.908223i
$994$	−7.37297	−	14.8625i	−0.233856	−	0.471410i
$995$	−7.44282	−	10.2442i	−0.235953	−	0.324762i
$996$	−11.4489	−	0.331834i	−0.362772	−	0.0105145i
$997$	−8.53124	+	2.77197i	−0.270187	+	0.0877892i	−0.440977	−	0.897518i	$-0.645368\pi$
$997$	−8.53124	+	2.77197i	−0.270187	+	0.0877892i	0.170790	+	0.985307i	$0.445368\pi$
$998$	15.1516	+	4.92304i	0.479614	+	0.155836i
$999$	−1.86488	+	1.12140i	−0.0590023	+	0.0354794i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.s.a.125.6	✓	128	3.2	odd	2	inner
462.2.s.a.125.11	yes	128	21.20	even	2	inner
462.2.s.a.125.19	yes	128	1.1	even	1	trivial
462.2.s.a.125.30	yes	128	7.6	odd	2	inner
462.2.s.a.377.6	yes	128	77.69	odd	10	inner
462.2.s.a.377.11	yes	128	11.3	even	5	inner
462.2.s.a.377.19	yes	128	231.146	even	10	inner
462.2.s.a.377.30	yes	128	33.14	odd	10	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)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.43017 + 0.977050i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.793236 + 0.576320i) q^{5} +(-0.0501805 + 1.73132i) q^{6} +(1.17577 + 2.37014i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.09075 - 2.79469i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.43017 + 0.977050i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.793236 + 0.576320i) q^{5} +(-0.0501805 + 1.73132i) q^{6} +(1.17577 + 2.37014i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.09075 - 2.79469i) q^{9} +0.980494i q^{10} +(-2.99024 - 1.43473i) q^{11} +(1.37117 + 1.05824i) q^{12} +(-1.73459 + 2.38746i) q^{13} +(2.60858 + 0.441911i) q^{14} +(0.571366 - 1.59926i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-6.42518 + 4.66817i) q^{17} +(-1.61982 - 2.52511i) 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} +(1.66209 - 0.487284i) q^{24} +(-1.24801 + 3.84097i) q^{25} +(0.911930 + 2.80663i) q^{26} +(1.17060 + 5.06258i) q^{27} +(1.89080 - 1.85064i) q^{28} +(-3.54438 + 1.15164i) q^{29} +(-0.957991 - 1.40227i) q^{30} +(3.63781 - 5.00702i) q^{31} +1.00000i q^{32} +(5.67834 - 0.869714i) q^{33} +7.94196i q^{34} +(-2.29862 - 1.20246i) q^{35} +(-2.99496 - 0.173757i) q^{36} +(0.129412 + 0.398290i) q^{37} +(1.15316 - 0.837816i) q^{38} +(0.148086 - 5.10925i) q^{39} +(0.932505 - 0.302989i) q^{40} +(0.484783 - 1.49201i) q^{41} +(-4.16248 + 1.91671i) 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} +(0.582733 - 1.63108i) q^{48} +(-4.23511 + 5.57349i) q^{49} +(2.37385 + 3.26732i) q^{50} +(4.62804 - 12.9540i) 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} +(-2.36911 + 0.694564i) q^{57} +(-1.15164 + 3.54438i) q^{58} +(-1.67598 - 5.15812i) q^{59} +(-1.69755 - 0.0492017i) q^{60} +(-6.32934 - 8.71159i) q^{61} +(-1.91251 - 5.88611i) q^{62} +(7.90626 - 0.700695i) q^{63} +(0.809017 + 0.587785i) q^{64} -2.89350i q^{65} +(2.63403 - 5.10508i) q^{66} -1.50802 q^{67} +(6.42518 + 4.66817i) q^{68} +(-6.02724 - 8.82244i) q^{69} +(-2.32391 + 1.15284i) q^{70} +(-3.68585 - 5.07313i) q^{71} +(-1.90097 + 2.32084i) q^{72} +(-5.22459 + 1.69757i) q^{73} +(0.398290 + 0.129412i) q^{74} +(-1.96796 - 6.71258i) q^{75} -1.42538i q^{76} +(-0.115341 - 8.77421i) q^{77} +(-4.04643 - 3.12295i) q^{78} +(12.4428 + 9.04020i) q^{79} +(0.302989 - 0.932505i) q^{80} +(-6.62054 - 6.09660i) q^{81} +(-0.922112 - 1.26918i) q^{82} +(-5.34986 + 3.88690i) q^{83} +(-0.895992 + 4.49413i) 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} +(2.74017 + 1.06947i) q^{90} +(-7.69811 - 1.30411i) q^{91} +(5.86690 - 1.90627i) q^{92} +(-0.310568 + 10.7152i) q^{93} +(-1.46142 - 2.01147i) q^{94} +(-1.32917 + 0.431874i) q^{95} +(-0.977050 - 1.43017i) q^{96} +(-5.45812 + 7.51246i) q^{97} +(2.01971 + 6.70229i) q^{98} +(-7.27122 + 6.79186i) 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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