LMFDB - Embedded newform 637.2.bd.b.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.6
Character	$\chi$	$=$	637.293
Dual form			637.2.bd.b.587.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94658 - 0.521585i) q^{2} +(-1.25027 - 0.721843i) q^{3} +(1.78508 - 1.03062i) q^{4} +(-2.32001 + 2.32001i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 - 0.793083i) q^{9} +O(q^{10})$	\(q+(1.94658 - 0.521585i) q^{2} +(-1.25027 - 0.721843i) q^{3} +(1.78508 - 1.03062i) q^{4} +(-2.32001 + 2.32001i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 - 0.793083i) q^{9} +(-3.30601 + 5.72618i) q^{10} +(1.53889 + 5.74323i) q^{11} -2.97577 q^{12} +(2.81021 + 2.25892i) q^{13} +(4.57532 - 1.22595i) q^{15} +(-1.93689 + 3.35480i) q^{16} +(0.314289 + 0.544364i) q^{17} +(-1.30497 - 1.30497i) q^{18} +(0.712944 + 0.191033i) q^{19} +(-1.75036 + 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +(-3.93752 - 2.27333i) q^{23} +(-0.172073 + 0.0461069i) q^{24} -5.76492i q^{25} +(6.64853 + 2.93140i) q^{26} +5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +(8.26680 - 4.77284i) q^{30} +(-0.781192 + 0.781192i) q^{31} +(-2.08438 + 7.77903i) q^{32} +(2.22168 - 8.29142i) q^{33} +(0.895721 + 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(0.655210 + 2.44528i) q^{37} +1.48744 q^{38} +(-1.88294 - 4.85278i) q^{39} +0.404858i q^{40} +(-0.746755 - 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(8.66611 + 8.66611i) q^{44} +(2.90227 + 0.777660i) q^{45} +(-8.85043 - 2.37147i) q^{46} +(-5.20343 - 5.20343i) q^{47} +(4.84328 - 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} -0.907468i q^{51} +(7.34452 + 1.13609i) q^{52} -7.78083 q^{53} +(2.94859 + 11.0043i) q^{54} +(-16.8946 - 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(-1.39390 + 5.20211i) q^{58} +(0.246488 - 0.919907i) q^{59} +(6.90382 - 6.90382i) q^{60} +(0.943178 - 0.544544i) q^{61} +(-1.11320 + 1.92811i) q^{62} +8.48212i q^{64} +(-11.7604 + 1.27902i) q^{65} -17.2987i q^{66} +(5.21286 - 1.39678i) q^{67} +(1.12206 + 0.647822i) q^{68} +(3.28197 + 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(-0.109151 - 0.0292470i) q^{72} +(4.35215 + 4.35215i) q^{73} +(2.55084 + 4.41818i) q^{74} +(-4.16136 + 7.20769i) q^{75} +(1.46954 - 0.393762i) q^{76} +(-6.19643 - 8.46422i) q^{78} +12.1660 q^{79} +(-3.28956 - 12.2768i) q^{80} +(2.70702 - 4.68870i) q^{81} +(-2.90724 - 5.03549i) q^{82} +(3.59152 - 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(5.74749 - 5.74749i) q^{86} +(3.34126 - 1.92908i) q^{87} +(0.635390 + 0.366843i) q^{88} +(3.94532 - 1.05715i) q^{89} +6.05511 q^{90} -9.37170 q^{92} +(1.54060 - 0.412802i) q^{93} +(-12.8429 - 7.41487i) q^{94} +(-2.09724 + 1.21084i) q^{95} +(8.22127 - 8.22127i) q^{96} +(8.41780 + 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	1.94658	−	0.521585i	1.37644	−	0.368816i	0.506614	−	0.862173i	$-0.330897\pi$
$2$	1.94658	−	0.521585i	1.37644	−	0.368816i	0.869827	+	0.493357i	$0.164230\pi$
$3$	−1.25027	−	0.721843i	−0.721843	−	0.416756i	0.0935879	−	0.995611i	$-0.470166\pi$
$3$	−1.25027	−	0.721843i	−0.721843	−	0.416756i	−0.815430	+	0.578855i	$0.803500\pi$
$4$	1.78508	−	1.03062i	0.892539	−	0.515308i
$5$	−2.32001	+	2.32001i	−1.03754	+	1.03754i	−0.0382739	+	0.999267i	$0.512186\pi$
$5$	−2.32001	+	2.32001i	−1.03754	+	1.03754i	−0.999267	+	0.0382739i	$0.987814\pi$
$6$	−2.81025	−	0.753004i	−1.14728	−	0.307413i
$7$		0			0
$7$		0			0
$8$	0.0872533	−	0.0872533i	0.0308487	−	0.0308487i
$9$	−0.457887	−	0.793083i	−0.152629	−	0.264361i
$10$	−3.30601	+	5.72618i	−1.04545	+	1.81078i
$11$	1.53889	+	5.74323i	0.463994	+	1.73165i	0.660202	+	0.751088i	$0.270471\pi$
$11$	1.53889	+	5.74323i	0.463994	+	1.73165i	−0.196208	+	0.980562i	$0.562863\pi$
$12$	−2.97577			−0.859030
$13$	2.81021	+	2.25892i	0.779413	+	0.626511i
$13$	2.81021	+	2.25892i	0.779413	+	0.626511i
$14$		0			0
$15$	4.57532	−	1.22595i	1.18134	−	0.316540i
$16$	−1.93689	+	3.35480i	−0.484224	+	0.838700i
$17$	0.314289	+	0.544364i	0.0762262	+	0.132028i	0.901619	−	0.432531i	$-0.142380\pi$
$17$	0.314289	+	0.544364i	0.0762262	+	0.132028i	−0.825393	+	0.564559i	$0.809046\pi$
$18$	−1.30497	−	1.30497i	−0.307585	−	0.307585i
$19$	0.712944	+	0.191033i	0.163561	+	0.0438259i	0.339670	−	0.940545i	$-0.389685\pi$
$19$	0.712944	+	0.191033i	0.163561	+	0.0438259i	−0.176109	+	0.984371i	$0.556351\pi$
$20$	−1.75036	+	6.53244i	−0.391393	+	1.46070i
$21$		0			0
$22$	5.99117	+	10.3770i	1.27732	+	2.21239i
$23$	−3.93752	−	2.27333i	−0.821029	−	0.474021i	0.0297422	−	0.999558i	$-0.490531\pi$
$23$	−3.93752	−	2.27333i	−0.821029	−	0.474021i	−0.850771	+	0.525536i	$0.823865\pi$
$24$	−0.172073	+	0.0461069i	−0.0351243	+	0.00941153i
$25$		−	5.76492i		−	1.15298i
$26$	6.64853	+	2.93140i	1.30388	+	0.574895i
$27$			5.65314i			1.08795i
$28$		0			0
$29$	−1.33622	+	2.31439i	−0.248129	+	0.429772i	−0.963007	−	0.269477i	$-0.913149\pi$
$29$	−1.33622	+	2.31439i	−0.248129	+	0.429772i	0.714878	+	0.699250i	$0.246482\pi$
$30$	8.26680	−	4.77284i	1.50930	−	0.871397i
$31$	−0.781192	+	0.781192i	−0.140306	+	0.140306i	−0.773771	−	0.633465i	$-0.781632\pi$
$31$	−0.781192	+	0.781192i	−0.140306	+	0.140306i	0.633465	+	0.773771i	$0.281632\pi$
$32$	−2.08438	+	7.77903i	−0.368471	+	1.37515i
$33$	2.22168	−	8.29142i	0.386745	−	1.44335i
$34$	0.895721	+	0.895721i	0.153615	+	0.153615i
$35$		0			0
$36$	−1.63473	−	0.943810i	−0.272454	−	0.157302i
$37$	0.655210	+	2.44528i	0.107716	+	0.402001i	0.998639	−	0.0521528i	$-0.0166083\pi$
$37$	0.655210	+	2.44528i	0.107716	+	0.402001i	−0.890923	+	0.454154i	$0.849942\pi$
$38$	1.48744			0.241295
$39$	−1.88294	−	4.85278i	−0.301511	−	0.777067i
$40$			0.404858i			0.0640136i
$41$	−0.746755	−	2.78693i	−0.116624	−	0.435245i	0.882780	−	0.469787i	$-0.155669\pi$
$41$	−0.746755	−	2.78693i	−0.116624	−	0.435245i	−0.999403	+	0.0345422i	$0.989003\pi$
$42$		0			0
$43$	3.49297	−	2.01667i	0.532673	−	0.307539i	−0.209431	−	0.977823i	$-0.567161\pi$
$43$	3.49297	−	2.01667i	0.532673	−	0.307539i	0.742104	+	0.670285i	$0.233828\pi$
$44$	8.66611	+	8.66611i	1.30647	+	1.30647i
$45$	2.90227	+	0.777660i	0.432644	+	0.115927i
$46$	−8.85043	−	2.37147i	−1.30492	−	0.349654i
$47$	−5.20343	−	5.20343i	−0.758999	−	0.758999i	0.217141	−	0.976140i	$-0.430327\pi$
$47$	−5.20343	−	5.20343i	−0.758999	−	0.758999i	−0.976140	+	0.217141i	$0.930327\pi$
$48$	4.84328	−	2.79627i	0.699067	−	0.403606i
$49$		0			0
$50$	−3.00689	−	11.2219i	−0.425239	−	1.58701i
$51$		−	0.907468i		−	0.127071i
$52$	7.34452	+	1.13609i	1.01850	+	0.157548i
$53$	−7.78083			−1.06878			−0.534390	−	0.845238i	$-0.679458\pi$
$53$	−7.78083			−1.06878			−0.534390	+	0.845238i	$0.679458\pi$
$54$	2.94859	+	11.0043i	0.401253	+	1.49750i
$55$	−16.8946	−	9.75412i	−2.27807	−	1.31525i
$56$		0			0
$57$	−0.753475	−	0.753475i	−0.0998002	−	0.0998002i
$58$	−1.39390	+	5.20211i	−0.183028	+	0.683070i
$59$	0.246488	−	0.919907i	0.0320901	−	0.119762i	−0.948023	−	0.318202i	$-0.896921\pi$
$59$	0.246488	−	0.919907i	0.0320901	−	0.119762i	0.980113	+	0.198440i	$0.0635876\pi$
$60$	6.90382	−	6.90382i	0.891279	−	0.891279i
$61$	0.943178	−	0.544544i	0.120762	−	0.0697217i	−0.438402	−	0.898779i	$-0.644456\pi$
$61$	0.943178	−	0.544544i	0.120762	−	0.0697217i	0.559164	+	0.829057i	$0.311122\pi$
$62$	−1.11320	+	1.92811i	−0.141376	+	0.244870i
$63$		0			0
$64$			8.48212i			1.06026i
$65$	−11.7604	+	1.27902i	−1.45870	+	0.158642i
$66$		−	17.2987i		−	2.12933i
$67$	5.21286	−	1.39678i	0.636852	−	0.170644i	0.0740750	−	0.997253i	$-0.476400\pi$
$67$	5.21286	−	1.39678i	0.636852	−	0.170644i	0.562777	+	0.826609i	$0.309733\pi$
$68$	1.12206	+	0.647822i	0.136070	+	0.0785599i
$69$	3.28197	+	5.68453i	0.395102	+	0.684338i
$70$		0			0
$71$	0.590023	−	2.20200i	0.0700229	−	0.261329i	−0.922036	−	0.387105i	$-0.873475\pi$
$71$	0.590023	−	2.20200i	0.0700229	−	0.261329i	0.992059	+	0.125776i	$0.0401419\pi$
$72$	−0.109151	−	0.0292470i	−0.0128636	−	0.00344679i
$73$	4.35215	+	4.35215i	0.509381	+	0.509381i	0.914336	−	0.404956i	$-0.132713\pi$
$73$	4.35215	+	4.35215i	0.509381	+	0.509381i	−0.404956	+	0.914336i	$0.632713\pi$
$74$	2.55084	+	4.41818i	0.296529	+	0.513603i
$75$	−4.16136	+	7.20769i	−0.480513	+	0.832273i
$76$	1.46954	−	0.393762i	0.168568	−	0.0451677i
$77$		0			0
$78$	−6.19643	−	8.46422i	−0.701608	−	0.958385i
$79$	12.1660			1.36878			0.684390	−	0.729116i	$-0.260068\pi$
$79$	12.1660			1.36878			0.684390	+	0.729116i	$0.260068\pi$
$80$	−3.28956	−	12.2768i	−0.367784	−	1.37259i
$81$	2.70702	−	4.68870i	0.300780	−	0.520966i
$82$	−2.90724	−	5.03549i	−0.321051	−	0.556076i
$83$	3.59152	−	3.59152i	0.394220	−	0.394220i	−0.481968	−	0.876189i	$-0.660078\pi$
$83$	3.59152	−	3.59152i	0.394220	−	0.394220i	0.876189	+	0.481968i	$0.160078\pi$
$84$		0			0
$85$	−1.99209	−	0.533778i	−0.216072	−	0.0578963i
$86$	5.74749	−	5.74749i	0.619768	−	0.619768i
$87$	3.34126	−	1.92908i	0.358220	−	0.206819i
$88$	0.635390	+	0.366843i	0.0677328	+	0.0391055i
$89$	3.94532	−	1.05715i	0.418203	−	0.112057i	−0.0435803	−	0.999050i	$-0.513876\pi$
$89$	3.94532	−	1.05715i	0.418203	−	0.112057i	0.461783	+	0.886993i	$0.347210\pi$
$90$	6.05511			0.638265
$91$		0			0
$92$	−9.37170			−0.977067
$93$	1.54060	−	0.412802i	0.159752	−	0.0428055i
$94$	−12.8429	−	7.41487i	−1.32465	−	0.764786i
$95$	−2.09724	+	1.21084i	−0.215172	+	0.124230i
$96$	8.22127	−	8.22127i	0.839080	−	0.839080i
$97$	8.41780	+	2.25554i	0.854698	+	0.229016i	0.659460	−	0.751740i	$-0.270785\pi$
$97$	8.41780	+	2.25554i	0.854698	+	0.229016i	0.195239	+	0.980756i	$0.437452\pi$
$98$		0			0
$99$	3.85022	−	3.85022i	0.386962	−	0.386962i
$100$	−5.94141	−	10.2908i	−0.594141	−	1.02908i
$101$	−8.58758	+	14.8741i	−0.854496	+	1.48003i	0.0226160	+	0.999744i	$0.492800\pi$
$101$	−8.58758	+	14.8741i	−0.854496	+	1.48003i	−0.877112	+	0.480286i	$0.840533\pi$
$102$	−0.473322	−	1.76646i	−0.0468658	−	0.174906i
$103$	14.3896			1.41785			0.708926	−	0.705283i	$-0.249180\pi$
$103$	14.3896			1.41785			0.708926	+	0.705283i	$0.249180\pi$
$104$	0.442298	−	0.0481025i	0.0433709	−	0.00471684i
$105$		0			0
$106$	−15.1460	+	4.05836i	−1.47111	+	0.394183i
$107$	−1.56036	+	2.70262i	−0.150846	+	0.261272i	−0.931539	−	0.363643i	$-0.881533\pi$
$107$	−1.56036	+	2.70262i	−0.150846	+	0.261272i	0.780693	+	0.624915i	$0.214866\pi$
$108$	5.82622	+	10.0913i	0.560628	+	0.971036i
$109$	6.71811	+	6.71811i	0.643478	+	0.643478i	0.951409	−	0.307931i	$-0.0996364\pi$
$109$	6.71811	+	6.71811i	0.643478	+	0.643478i	−0.307931	+	0.951409i	$0.599636\pi$
$110$	−37.9744	−	10.1752i	−3.62071	−	0.970168i
$111$	0.945917	−	3.53021i	0.0897825	−	0.335073i
$112$		0			0
$113$	1.34080	+	2.32234i	0.126132	+	0.218467i	0.922175	−	0.386773i	$-0.126410\pi$
$113$	1.34080	+	2.32234i	0.126132	+	0.218467i	−0.796043	+	0.605240i	$0.793077\pi$
$114$	−1.85970	−	1.07370i	−0.174177	−	0.100561i
$115$	14.4092	−	3.86094i	1.34367	−	0.360035i
$116$			5.50850i			0.511451i
$117$	0.504749	−	3.26306i	0.0466640	−	0.301670i
$118$		−	1.91924i		−	0.176680i
$119$		0			0
$120$	0.292243	−	0.506181i	0.0266781	−	0.0462077i
$121$	−21.0903	+	12.1765i	−1.91730	+	1.10695i
$122$	1.55195	−	1.55195i	0.140507	−	0.140507i
$123$	−1.07808	+	4.02345i	−0.0972071	+	0.362782i
$124$	−0.589380	+	2.19960i	−0.0529279	+	0.197530i
$125$	1.77462	+	1.77462i	0.158727	+	0.158727i
$126$		0			0
$127$	−4.93218	−	2.84760i	−0.437661	−	0.252683i	0.264944	−	0.964264i	$-0.414646\pi$
$127$	−4.93218	−	2.84760i	−0.437661	−	0.252683i	−0.702605	+	0.711580i	$0.747980\pi$
$128$	0.255376	+	0.953075i	0.0225722	+	0.0842407i
$129$	−5.82286			−0.512675
$130$	−22.2255	+	8.62378i	−1.94931	+	0.756355i
$131$			17.5104i			1.52989i	0.644095	+	0.764946i	$0.277234\pi$
$131$			17.5104i			1.52989i	−0.644095	+	0.764946i	$0.722766\pi$
$132$	−4.57939	−	17.0905i	−0.398585	−	1.48754i
$133$		0			0
$134$	9.41872	−	5.43790i	0.813653	−	0.469763i
$135$	−13.1154	−	13.1154i	−1.12879	−	1.12879i
$136$	0.0749203	+	0.0200748i	0.00642437	+	0.00172140i
$137$	−14.1600	−	3.79415i	−1.20977	−	0.324156i	−0.403097	−	0.915157i	$-0.632066\pi$
$137$	−14.1600	−	3.79415i	−1.20977	−	0.324156i	−0.806671	+	0.591001i	$0.798733\pi$
$138$	9.35358	+	9.35358i	0.796230	+	0.796230i
$139$	3.10457	−	1.79243i	0.263327	−	0.152032i	−0.362525	−	0.931974i	$-0.618085\pi$
$139$	3.10457	−	1.79243i	0.263327	−	0.152032i	0.625851	+	0.779943i	$0.284752\pi$
$140$		0			0
$141$	2.74963	+	10.2617i	0.231560	+	0.864195i
$142$		−	4.59411i		−	0.385530i
$143$	−8.64886	+	19.6159i	−0.723254	+	1.64037i
$144$	3.54751			0.295626
$145$	−2.26939	−	8.46946i	−0.188462	−	0.703351i
$146$	10.7418	+	6.20180i	0.889001	+	0.513265i
$147$		0			0
$148$	3.68974	+	3.68974i	0.303295	+	0.303295i
$149$	3.71462	−	13.8632i	0.304314	−	1.13571i	−0.629221	−	0.777226i	$-0.716626\pi$
$149$	3.71462	−	13.8632i	0.304314	−	1.13571i	0.933535	−	0.358487i	$-0.116707\pi$
$150$	−4.34101	+	16.2009i	−0.354442	+	1.32279i
$151$	16.8160	−	16.8160i	1.36847	−	1.36847i	0.505844	−	0.862625i	$-0.331181\pi$
$151$	16.8160	−	16.8160i	1.36847	−	1.36847i	0.862625	−	0.505844i	$-0.168819\pi$
$152$	0.0788749	−	0.0455385i	0.00639760	−	0.00369366i
$153$	0.287817	−	0.498514i	0.0232687	−	0.0403025i
$154$		0			0
$155$		−	3.62475i		−	0.291147i
$156$	−8.36254	−	6.72201i	−0.669539	−	0.538192i
$157$		−	7.60865i		−	0.607237i	−0.952794	−	0.303618i	$-0.901805\pi$
$157$		−	7.60865i		−	0.607237i	0.952794	−	0.303618i	$-0.0981947\pi$
$158$	23.6821	−	6.34560i	1.88405	−	0.504829i
$159$	9.72812	+	5.61653i	0.771490	+	0.445420i
$160$	−13.2116	−	22.8832i	−1.04447	−	1.80908i
$161$		0			0
$162$	2.82388	−	10.5389i	0.221865	−	0.828012i
$163$	2.48431	+	0.665670i	0.194586	+	0.0521393i	0.354796	−	0.934944i	$-0.384550\pi$
$163$	2.48431	+	0.665670i	0.194586	+	0.0521393i	−0.160210	+	0.987083i	$0.551217\pi$
$164$	−4.20527	−	4.20527i	−0.328376	−	0.328376i
$165$	14.0819	+	24.3905i	1.09627	+	1.89880i
$166$	5.11790	−	8.86446i	0.397226	−	0.688016i
$167$	3.28638	−	0.880582i	0.254308	−	0.0681415i	−0.129413	−	0.991591i	$-0.541309\pi$
$167$	3.28638	−	0.880582i	0.254308	−	0.0681415i	0.383720	+	0.923449i	$0.374643\pi$
$168$		0			0
$169$	2.79460	+	12.6961i	0.214969	+	0.976621i
$170$	−4.15617			−0.318764
$171$	−0.174943	−	0.652895i	−0.0133782	−	0.0499281i
$172$	4.15682	−	7.19982i	0.316954	−	0.548981i
$173$	−7.02517	−	12.1680i	−0.534114	−	0.925113i	−0.999206	−	0.0398501i	$-0.987312\pi$
$173$	−7.02517	−	12.1680i	−0.534114	−	0.925113i	0.465092	−	0.885263i	$-0.346021\pi$
$174$	5.49785	−	5.49785i	0.416791	−	0.416791i
$175$		0			0
$176$	−22.2481	−	5.96136i	−1.67701	−	0.449354i
$177$	−0.972205	+	0.972205i	−0.0730754	+	0.0730754i
$178$	7.12850	−	4.11564i	0.534303	−	0.308480i
$179$	12.9578	+	7.48119i	0.968512	+	0.559170i	0.898782	−	0.438395i	$-0.144453\pi$
$179$	12.9578	+	7.48119i	0.968512	+	0.559170i	0.0697295	+	0.997566i	$0.477786\pi$
$180$	5.98224	−	1.60294i	0.445890	−	0.119476i
$181$	−15.4409			−1.14772			−0.573858	−	0.818955i	$-0.694554\pi$
$181$	−15.4409			−1.14772			−0.573858	+	0.818955i	$0.694554\pi$
$182$		0			0
$183$	−1.57230			−0.116228
$184$	−0.541917	+	0.145206i	−0.0399506	+	0.0107047i
$185$	−7.19317	−	4.15298i	−0.528852	−	0.305333i
$186$	2.78359	−	1.60710i	0.204102	−	0.117839i
$187$	−2.64275	+	2.64275i	−0.193257	+	0.193257i
$188$	−14.6513	−	3.92580i	−1.06855	−	0.286318i
$189$		0			0
$190$	−3.45089	+	3.45089i	−0.250354	+	0.250354i
$191$	8.57746	+	14.8566i	0.620643	+	1.07499i	0.989366	+	0.145446i	$0.0464617\pi$
$191$	8.57746	+	14.8566i	0.620643	+	1.07499i	−0.368723	+	0.929539i	$0.620205\pi$
$192$	6.12275	−	10.6049i	0.441872	−	0.765344i
$193$	−1.58725	−	5.92369i	−0.114253	−	0.426396i	0.884977	−	0.465634i	$-0.154174\pi$
$193$	−1.58725	−	5.92369i	−0.114253	−	0.426396i	−0.999230	+	0.0392377i	$0.987507\pi$
$194$	17.5624			1.26091
$195$	15.6270	+	6.89008i	1.11907	+	0.493409i
$196$		0			0
$197$	24.7906	−	6.64263i	1.76626	−	0.473268i	0.778288	−	0.627908i	$-0.216089\pi$
$197$	24.7906	−	6.64263i	1.76626	−	0.473268i	0.987971	+	0.154640i	$0.0494219\pi$
$198$	5.48655	−	9.50299i	0.389912	−	0.675348i
$199$	−4.36369	−	7.55813i	−0.309334	−	0.535782i	0.668883	−	0.743368i	$-0.266773\pi$
$199$	−4.36369	−	7.55813i	−0.309334	−	0.535782i	−0.978217	+	0.207586i	$0.933439\pi$
$200$	−0.503008	−	0.503008i	−0.0355681	−	0.0355681i
$201$	−7.52573	−	2.01651i	−0.530824	−	0.142234i
$202$	−8.95830	+	33.4328i	−0.630304	+	2.35233i
$203$		0			0
$204$	−0.935251	−	1.61990i	−0.0654806	−	0.113416i
$205$	8.19819	+	4.73323i	0.572586	+	0.330583i
$206$	28.0106	−	7.50541i	1.95159	−	0.522927i
$207$			4.16370i			0.289397i
$208$	−13.0213	+	5.05242i	−0.902865	+	0.350322i
$209$			4.38858i			0.303565i
$210$		0			0
$211$	−5.41370	+	9.37680i	−0.372694	+	0.645525i	−0.989979	−	0.141214i	$-0.954899\pi$
$211$	−5.41370	+	9.37680i	−0.372694	+	0.645525i	0.617285	+	0.786740i	$0.288233\pi$
$212$	−13.8894	+	8.01904i	−0.953927	+	0.550750i
$213$	−2.32718	+	2.32718i	−0.159456	+	0.159456i
$214$	−1.62772	+	6.07473i	−0.111269	+	0.415260i
$215$	−3.42504	+	12.7824i	−0.233586	+	0.871754i
$216$	0.493256	+	0.493256i	0.0335618	+	0.0335618i
$217$		0			0
$218$	16.5814	+	9.57329i	1.12304	+	0.648385i
$219$	−2.29979	−	8.58292i	−0.155405	−	0.579980i
$220$	−40.2110			−2.71102
$221$	−0.346455	+	2.23973i	−0.0233051	+	0.150661i
$222$		−	7.36522i		−	0.494321i
$223$	2.01754	+	7.52957i	0.135105	+	0.504217i	0.999997	+	0.00226068i	$0.000719598\pi$
$223$	2.01754	+	7.52957i	0.135105	+	0.504217i	−0.864893	+	0.501957i	$0.832614\pi$
$224$		0			0
$225$	−4.57206	+	2.63968i	−0.304804	+	0.175979i
$226$	3.82128	+	3.82128i	0.254188	+	0.254188i
$227$	13.7698	+	3.68960i	0.913933	+	0.244888i	0.684990	−	0.728552i	$-0.259806\pi$
$227$	13.7698	+	3.68960i	0.913933	+	0.244888i	0.228943	+	0.973440i	$0.426473\pi$
$228$	−2.12156	−	0.568469i	−0.140503	−	0.0376478i
$229$	8.06915	+	8.06915i	0.533224	+	0.533224i	0.921530	−	0.388306i	$-0.126940\pi$
$229$	8.06915	+	8.06915i	0.533224	+	0.533224i	−0.388306	+	0.921530i	$0.626940\pi$
$230$	26.0349	−	15.0313i	1.71669	−	0.991133i
$231$		0			0
$232$	0.0853493	+	0.318528i	0.00560346	+	0.0209124i
$233$			21.8867i			1.43384i	0.697153	+	0.716922i	$0.254450\pi$
$233$			21.8867i			1.43384i	−0.697153	+	0.716922i	$0.745550\pi$
$234$	−0.719428	−	6.61508i	−0.0470305	−	0.432441i
$235$	24.1441			1.57498
$236$	−0.508069	−	1.89614i	−0.0330725	−	0.123428i
$237$	−15.2107	−	8.78193i	−0.988044	−	0.570448i
$238$		0			0
$239$	3.79044	+	3.79044i	0.245183	+	0.245183i	0.818990	−	0.573807i	$-0.194534\pi$
$239$	3.79044	+	3.79044i	0.245183	+	0.245183i	−0.573807	+	0.818990i	$0.694534\pi$
$240$	−4.74909	+	17.7238i	−0.306552	+	1.14407i
$241$	−4.04063	+	15.0798i	−0.260280	+	0.971377i	0.704797	+	0.709409i	$0.251038\pi$
$241$	−4.04063	+	15.0798i	−0.260280	+	0.971377i	−0.965077	+	0.261968i	$0.915629\pi$
$242$	−34.7028	+	34.7028i	−2.23078	+	2.23078i
$243$	7.91830	−	4.57163i	0.507959	−	0.293270i
$244$	1.12243	−	1.94411i	0.0718563	−	0.124459i
$245$		0			0
$246$			8.39427i			0.535199i
$247$	1.57200	+	2.14732i	0.100024	+	0.136631i
$248$			0.136323i			0.00865653i
$249$	−7.08287	+	1.89785i	−0.448858	+	0.120271i
$250$	4.38005	+	2.52882i	0.277019	+	0.159937i
$251$	−2.30694	−	3.99573i	−0.145612	−	0.252208i	0.783989	−	0.620775i	$-0.213182\pi$
$251$	−2.30694	−	3.99573i	−0.145612	−	0.252208i	−0.929601	+	0.368567i	$0.879849\pi$
$252$		0			0
$253$	6.99682	−	26.1125i	0.439886	−	1.64168i
$254$	−11.0862	−	2.97053i	−0.695608	−	0.186388i
$255$	2.10534	+	2.10534i	0.131841	+	0.131841i
$256$	−7.48790	−	12.9694i	−0.467994	−	0.810589i
$257$	−7.83278	+	13.5668i	−0.488596	+	0.846273i	−0.999914	−	0.0131189i	$-0.995824\pi$
$257$	−7.83278	+	13.5668i	−0.488596	+	0.846273i	0.511318	+	0.859391i	$0.329157\pi$
$258$	−11.3347	+	3.03712i	−0.705666	+	0.189083i
$259$		0			0
$260$	−19.6751	+	14.4036i	−1.22020	+	0.893276i
$261$	2.44734			0.151487
$262$	9.13317	+	34.0854i	0.564249	+	2.10581i
$263$	11.9554	−	20.7074i	0.737203	−	1.27687i	−0.216547	−	0.976272i	$-0.569479\pi$
$263$	11.9554	−	20.7074i	0.737203	−	1.27687i	0.953750	−	0.300601i	$-0.0971872\pi$
$264$	−0.529605	−	0.917303i	−0.0325949	−	0.0564561i
$265$	18.0516	−	18.0516i	1.10890	−	1.10890i
$266$		0			0
$267$	−5.69580	−	1.52618i	−0.348577	−	0.0934010i
$268$	7.86582	−	7.86582i	0.480481	−	0.480481i
$269$	11.7207	−	6.76695i	0.714624	−	0.412588i	−0.0981467	−	0.995172i	$-0.531291\pi$
$269$	11.7207	−	6.76695i	0.714624	−	0.412588i	0.812771	+	0.582584i	$0.197958\pi$
$270$	−32.3709	−	18.6893i	−1.97003	−	1.13740i
$271$	−20.9164	+	5.60453i	−1.27058	+	0.340451i	−0.830253	−	0.557387i	$-0.811804\pi$
$271$	−20.9164	+	5.60453i	−1.27058	+	0.340451i	−0.440327	+	0.897838i	$0.645137\pi$
$272$	−2.43498			−0.147642
$273$		0			0
$274$	−29.5425			−1.78473
$275$	33.1093	−	8.87160i	1.99656	−	0.534978i
$276$	11.7171	+	6.76489i	0.705289	+	0.407199i
$277$	−18.5473	+	10.7083i	−1.11440	+	0.643399i	−0.939965	−	0.341270i	$-0.889143\pi$
$277$	−18.5473	+	10.7083i	−1.11440	+	0.643399i	−0.174434	+	0.984669i	$0.555810\pi$
$278$	5.10840	−	5.10840i	0.306382	−	0.306382i
$279$	0.977247	+	0.261853i	0.0585063	+	0.0156767i
$280$		0			0
$281$	0.874765	−	0.874765i	0.0521841	−	0.0521841i	−0.680533	−	0.732717i	$-0.738252\pi$
$281$	0.874765	−	0.874765i	0.0521841	−	0.0521841i	0.732717	+	0.680533i	$0.238252\pi$
$282$	10.7047	+	18.5412i	0.637458	+	1.10411i
$283$	9.23061	−	15.9879i	0.548703	−	0.950381i	−0.449661	−	0.893199i	$-0.648455\pi$
$283$	9.23061	−	15.9879i	0.548703	−	0.950381i	0.998364	−	0.0571816i	$-0.0182114\pi$
$284$	−1.21617	−	4.53882i	−0.0721667	−	0.269330i
$285$	3.49614			0.207094
$286$	−6.60433	+	42.6952i	−0.390522	+	2.52462i
$287$		0			0
$288$	7.12383	−	1.90882i	0.419775	−	0.112479i
$289$	8.30245	−	14.3803i	0.488379	−	0.845897i
$290$	−8.83509	−	15.3028i	−0.518814	−	0.898613i
$291$	−8.89636	−	8.89636i	−0.521514	−	0.521514i
$292$	12.2543	+	3.28354i	0.717130	+	0.192154i
$293$	−3.21602	+	12.0024i	−0.187882	+	0.701186i	0.806113	+	0.591762i	$0.201567\pi$
$293$	−3.21602	+	12.0024i	−0.187882	+	0.701186i	−0.993995	+	0.109424i	$0.965099\pi$
$294$		0			0
$295$	1.56234	+	2.70605i	0.0909629	+	0.157552i
$296$	0.270528	+	0.156189i	0.0157241	+	0.00907832i
$297$	−32.4673	+	8.69959i	−1.88395	+	0.504802i
$298$		−	28.9232i		−	1.67548i
$299$	−5.93001	−	15.2831i	−0.342941	−	0.883842i
$300$			17.1551i			0.990448i
$301$		0			0
$302$	23.9628	−	41.5048i	1.37890	−	2.38833i
$303$	21.4735	−	12.3978i	1.23362	−	0.712233i
$304$	−2.02177	+	2.02177i	−0.115957	+	0.115957i
$305$	−0.924836	+	3.45154i	−0.0529560	+	0.197634i
$306$	0.300242	−	1.12052i	0.0171637	−	0.0640559i
$307$	3.51390	+	3.51390i	0.200549	+	0.200549i	0.800235	−	0.599686i	$-0.204708\pi$
$307$	3.51390	+	3.51390i	0.200549	+	0.200549i	−0.599686	+	0.800235i	$0.704708\pi$
$308$		0			0
$309$	−17.9909	−	10.3870i	−1.02347	−	0.590898i
$310$	−1.89061	−	7.05587i	−0.107380	−	0.400746i
$311$	18.3661			1.04144			0.520722	−	0.853727i	$-0.325663\pi$
$311$	18.3661			1.04144			0.520722	+	0.853727i	$0.325663\pi$
$312$	−0.587714	−	0.259129i	−0.0332727	−	0.0146703i
$313$			8.99058i			0.508177i	0.967181	+	0.254089i	$0.0817755\pi$
$313$			8.99058i			0.508177i	−0.967181	+	0.254089i	$0.918224\pi$
$314$	−3.96856	−	14.8109i	−0.223959	−	0.835825i
$315$		0			0
$316$	21.7172	−	12.5385i	1.22169	−	0.705343i
$317$	10.1873	+	10.1873i	0.572175	+	0.572175i	0.932736	−	0.360561i	$-0.117415\pi$
$317$	10.1873	+	10.1873i	0.572175	+	0.572175i	−0.360561	+	0.932736i	$0.617415\pi$
$318$	21.8661	+	5.85900i	1.22619	+	0.328556i
$319$	−15.3484	−	4.11259i	−0.859346	−	0.230261i
$320$	−19.6786	−	19.6786i	−1.10007	−	1.10007i
$321$	3.90173	−	2.25267i	0.217773	−	0.125732i
$322$		0			0
$323$	0.120079	+	0.448141i	0.00668137	+	0.0249352i
$324$		−	11.1596i		−	0.619977i
$325$	13.0225	−	16.2006i	0.722356	−	0.898650i
$326$	5.18312			0.287067
$327$	−3.55002	−	13.2489i	−0.196317	−	0.732663i
$328$	−0.308326	−	0.178012i	−0.0170244	−	0.00982906i
$329$		0			0
$330$	40.1333	+	40.1333i	2.20926	+	2.20926i
$331$	2.11818	−	7.90514i	0.116426	−	0.434506i	−0.882964	−	0.469441i	$-0.844456\pi$
$331$	2.11818	−	7.90514i	0.116426	−	0.434506i	0.999390	+	0.0349345i	$0.0111223\pi$
$332$	2.70967	−	10.1126i	0.148712	−	0.555001i
$333$	1.63930	−	1.63930i	0.0898329	−	0.0898329i
$334$	5.93790	−	3.42825i	0.324908	−	0.187586i
$335$	−8.85335	+	15.3345i	−0.483710	+	0.837811i
$336$		0			0
$337$			1.63832i			0.0892447i	0.999004	+	0.0446224i	$0.0142085\pi$
$337$			1.63832i			0.0892447i	−0.999004	+	0.0446224i	$0.985792\pi$
$338$	12.0620	+	23.2563i	0.656086	+	1.26498i
$339$		−	3.87140i		−	0.210265i
$340$	−4.10615	+	1.10024i	−0.222687	+	0.0596688i
$341$	−5.68874	−	3.28439i	−0.308062	−	0.177860i
$342$	−0.681080	−	1.17967i	−0.0368286	−	0.0637890i
$343$		0			0
$344$	0.128812	−	0.480734i	0.00694510	−	0.0259194i
$345$	−20.8024	−	5.57399i	−1.11996	−	0.300093i
$346$	−20.0217	−	20.0217i	−1.07637	−	1.07637i
$347$	4.81567	+	8.34098i	0.258519	+	0.447768i	0.965845	−	0.259119i	$-0.0834323\pi$
$347$	4.81567	+	8.34098i	0.258519	+	0.447768i	−0.707327	+	0.706887i	$0.750099\pi$
$348$	3.97627	−	6.88710i	0.213150	−	0.369187i
$349$	−28.4665	+	7.62758i	−1.52378	+	0.408295i	−0.920983	−	0.389602i	$-0.872613\pi$
$349$	−28.4665	+	7.62758i	−1.52378	+	0.408295i	−0.602794	+	0.797897i	$0.705946\pi$
$350$		0			0
$351$	−12.7700	+	15.8865i	−0.681611	+	0.847961i
$352$	−47.8844			−2.55225
$353$	−4.13727	−	15.4405i	−0.220205	−	0.821814i	−0.984269	−	0.176675i	$-0.943466\pi$
$353$	−4.13727	−	15.4405i	−0.220205	−	0.821814i	0.764065	−	0.645140i	$-0.223201\pi$
$354$	−1.38539	+	2.39956i	−0.0736326	+	0.127535i
$355$	3.73980	+	6.47752i	0.198488	+	0.343791i
$356$	5.95319	−	5.95319i	0.315519	−	0.315519i
$357$		0			0
$358$	29.1255	+	7.80415i	1.53933	+	0.412462i
$359$	−4.06358	+	4.06358i	−0.214467	+	0.214467i	−0.806162	−	0.591695i	$-0.798459\pi$
$359$	−4.06358	+	4.06358i	−0.214467	+	0.214467i	0.591695	+	0.806162i	$0.298459\pi$
$360$	0.321086	−	0.185379i	0.0169227	−	0.00977033i
$361$	−15.9827	−	9.22761i	−0.841194	−	0.485664i
$362$	−30.0570	+	8.05376i	−1.57976	+	0.423296i
$363$	35.1580			1.84531
$364$		0			0
$365$	−20.1941			−1.05701
$366$	−3.06061	+	0.820088i	−0.159981	+	0.0428667i
$367$	−22.0499	−	12.7305i	−1.15099	−	0.664527i	−0.201865	−	0.979413i	$-0.564700\pi$
$367$	−22.0499	−	12.7305i	−1.15099	−	0.664527i	−0.949129	+	0.314887i	$0.898034\pi$
$368$	15.2531	−	8.80639i	0.795123	−	0.459065i
$369$	−1.86834	+	1.86834i	−0.0972617	+	0.0972617i
$370$	−16.1682	−	4.33226i	−0.840546	−	0.225224i
$371$		0			0
$372$	2.32465	−	2.32465i	0.120527	−	0.120527i
$373$	−9.35778	−	16.2082i	−0.484528	−	0.839227i	0.515314	−	0.857001i	$-0.327675\pi$
$373$	−9.35778	−	16.2082i	−0.484528	−	0.839227i	−0.999842	+	0.0177746i	$0.994342\pi$
$374$	−3.76592	+	6.52276i	−0.194731	+	0.337284i
$375$	−0.937753	−	3.49974i	−0.0484254	−	0.180726i
$376$	−0.908034			−0.0468283
$377$	−8.98308	+	3.48554i	−0.462652	+	0.179515i
$378$		0			0
$379$	−20.5112	+	5.49596i	−1.05359	+	0.282309i	−0.743735	−	0.668475i	$-0.766947\pi$
$379$	−20.5112	+	5.49596i	−1.05359	+	0.282309i	−0.309856	+	0.950784i	$0.600281\pi$
$380$	−2.49582	+	4.32289i	−0.128033	+	0.221760i
$381$	4.11103	+	7.12052i	0.210615	+	0.364795i
$382$	24.4457	+	24.4457i	1.25075	+	1.25075i
$383$	31.3484	+	8.39979i	1.60183	+	0.429209i	0.945595	−	0.325347i	$-0.105481\pi$
$383$	31.3484	+	8.39979i	1.60183	+	0.429209i	0.656236	+	0.754556i	$0.272148\pi$
$384$	0.368682	−	1.37594i	0.0188142	−	0.0702157i
$385$		0			0
$386$	−6.17941	−	10.7031i	−0.314524	−	0.544771i
$387$	−3.19877	−	1.84681i	−0.162603	−	0.0938786i
$388$	17.3510	−	4.64919i	0.880865	−	0.236027i
$389$		−	6.96381i		−	0.353079i	−0.984294	−	0.176540i	$-0.943510\pi$
$389$		−	6.96381i		−	0.353079i	0.984294	−	0.176540i	$-0.0564904\pi$
$390$	34.0129	+	5.26131i	1.72231	+	0.266417i
$391$		−	2.85792i		−	0.144531i
$392$		0			0
$393$	12.6398	−	21.8927i	0.637591	−	1.10434i
$394$	44.7923	−	25.8608i	2.25660	−	1.30285i
$395$	−28.2252	+	28.2252i	−1.42017	+	1.42017i
$396$	2.90485	−	10.8410i	0.145974	−	0.544783i
$397$	3.86677	−	14.4310i	0.194068	−	0.724270i	−0.798439	−	0.602076i	$-0.794340\pi$
$397$	3.86677	−	14.4310i	0.194068	−	0.724270i	0.992506	−	0.122194i	$-0.0389930\pi$
$398$	−12.4365	−	12.4365i	−0.623384	−	0.623384i
$399$		0			0
$400$	19.3401	+	11.1660i	0.967007	+	0.558302i
$401$	6.25695	+	23.3513i	0.312457	+	1.16611i	0.926334	+	0.376704i	$0.122943\pi$
$401$	6.25695	+	23.3513i	0.312457	+	1.16611i	−0.613877	+	0.789402i	$0.710391\pi$
$402$	−15.7012			−0.783106
$403$	−3.95996	+	0.430669i	−0.197260	+	0.0214531i
$404$			35.4020i			1.76131i
$405$	4.59751	+	17.1582i	0.228452	+	0.852595i
$406$		0			0
$407$	−13.0355	+	7.52605i	−0.646146	+	0.373052i
$408$	−0.0791796	−	0.0791796i	−0.00391998	−	0.00391998i
$409$	36.2537	+	9.71416i	1.79263	+	0.480334i	0.992789	−	0.119875i	$-0.0382494\pi$
$409$	36.2537	+	9.71416i	1.79263	+	0.480334i	0.799843	+	0.600209i	$0.204916\pi$
$410$	18.4272	+	4.93756i	0.910056	+	0.243849i
$411$	14.9650	+	14.9650i	0.738168	+	0.738168i
$412$	25.6866	−	14.8302i	1.26549	−	0.730630i
$413$		0			0
$414$	2.17172	+	8.10499i	0.106734	+	0.398338i
$415$			16.6647i			0.818039i
$416$	−23.4297	+	17.1523i	−1.14874	+	0.840960i
$417$	−5.17540			−0.253440
$418$	2.28902	+	8.54273i	0.111960	+	0.417839i
$419$	7.05130	+	4.07107i	0.344478	+	0.198885i	0.662251	−	0.749282i	$-0.269601\pi$
$419$	7.05130	+	4.07107i	0.344478	+	0.198885i	−0.317772	+	0.948167i	$0.602935\pi$
$420$		0			0
$421$	2.46118	+	2.46118i	0.119951	+	0.119951i	0.764534	−	0.644583i	$-0.222969\pi$
$421$	2.46118	+	2.46118i	0.119951	+	0.119951i	−0.644583	+	0.764534i	$0.722969\pi$
$422$	−5.64740	+	21.0764i	−0.274911	+	1.02598i
$423$	−1.74417	+	6.50934i	−0.0848045	+	0.316495i
$424$	−0.678903	+	0.678903i	−0.0329705	+	0.0329705i
$425$	3.13822	−	1.81185i	0.152226	−	0.0878876i
$426$	−3.31623	+	5.74387i	−0.160672	+	0.278292i
$427$		0			0
$428$			6.43252i			0.310927i
$429$	24.9730	−	18.2821i	1.20571	−	0.882667i
$430$			26.6685i			1.28607i
$431$	14.7958	−	3.96452i	0.712688	−	0.190964i	0.115781	−	0.993275i	$-0.463063\pi$
$431$	14.7958	−	3.96452i	0.712688	−	0.190964i	0.596907	+	0.802310i	$0.296396\pi$
$432$	−18.9652	−	10.9495i	−0.912462	−	0.526810i
$433$	−6.16396	−	10.6763i	−0.296221	−	0.513070i	0.679047	−	0.734095i	$-0.262393\pi$
$433$	−6.16396	−	10.6763i	−0.296221	−	0.513070i	−0.975268	+	0.221025i	$0.929060\pi$
$434$		0			0
$435$	−3.27628	+	12.2272i	−0.157086	+	0.586251i
$436$	18.9161	+	5.06856i	0.905919	+	0.242740i
$437$	−2.37295	−	2.37295i	−0.113514	−	0.113514i
$438$	−8.95345	−	15.5078i	−0.427812	−	0.740993i
$439$	3.88598	−	6.73072i	0.185468	−	0.321240i	−0.758266	−	0.651945i	$-0.773953\pi$
$439$	3.88598	−	6.73072i	0.185468	−	0.321240i	0.943734	+	0.330705i	$0.107287\pi$
$440$	−2.32519	+	0.623033i	−0.110849	+	0.0297019i
$441$		0			0
$442$	0.493808	+	4.54053i	0.0234881	+	0.215971i
$443$	6.29900			0.299274			0.149637	−	0.988741i	$-0.452189\pi$
$443$	6.29900			0.299274			0.149637	+	0.988741i	$0.452189\pi$
$444$	−1.94975	−	7.27658i	−0.0925312	−	0.345331i
$445$	−6.70060	+	11.6058i	−0.317639	+	0.550167i
$446$	7.85462	+	13.6046i	0.371927	+	0.644196i
$447$	−14.6513	+	14.6513i	−0.692982	+	0.692982i
$448$		0			0
$449$	14.6362	+	3.92175i	0.690723	+	0.185079i	0.587072	−	0.809535i	$-0.300281\pi$
$449$	14.6362	+	3.92175i	0.690723	+	0.185079i	0.103651	+	0.994614i	$0.466947\pi$
$450$	−7.52307	+	7.52307i	−0.354641	+	0.354641i
$451$	14.8568	−	8.57758i	0.699579	−	0.403902i
$452$	4.78688	+	2.76370i	0.225156	+	0.129994i
$453$	−33.1631	+	8.88602i	−1.55814	+	0.417501i
$454$	28.7285			1.34829
$455$		0			0
$456$	−0.131486			−0.00615742
$457$	−15.0204	+	4.02470i	−0.702623	+	0.188267i	−0.592405	−	0.805640i	$-0.701822\pi$
$457$	−15.0204	+	4.02470i	−0.702623	+	0.188267i	−0.110218	+	0.993907i	$0.535155\pi$
$458$	19.9160	+	11.4985i	0.930613	+	0.537290i
$459$	−3.07737	+	1.77672i	−0.143639	+	0.0829302i
$460$	21.7425	−	21.7425i	1.01375	−	1.01375i
$461$	−29.6778	−	7.95214i	−1.38223	−	0.370368i	−0.510301	−	0.859996i	$-0.670466\pi$
$461$	−29.6778	−	7.95214i	−1.38223	−	0.370368i	−0.871931	+	0.489628i	$0.837133\pi$
$462$		0			0
$463$	−4.11310	+	4.11310i	−0.191152	+	0.191152i	−0.796194	−	0.605042i	$-0.793156\pi$
$463$	−4.11310	+	4.11310i	−0.191152	+	0.191152i	0.605042	+	0.796194i	$0.293156\pi$
$464$	−5.17622	−	8.96548i	−0.240300	−	0.416212i
$465$	−2.61650	+	4.53191i	−0.121337	+	0.210162i
$466$	11.4158	+	42.6042i	0.528825	+	1.97360i
$467$	−8.16491			−0.377827			−0.188913	−	0.981994i	$-0.560497\pi$
$467$	−8.16491			−0.377827			−0.188913	+	0.981994i	$0.560497\pi$
$468$	−2.46194	−	6.34502i	−0.113803	−	0.293299i
$469$		0			0
$470$	46.9984	−	12.5932i	2.16787	−	0.580880i
$471$	−5.49225	+	9.51285i	−0.253069	+	0.438329i
$472$	−0.0587580	−	0.101772i	−0.00270456	−	0.00468443i
$473$	16.9575	+	16.9575i	0.779707	+	0.779707i
$474$	−34.1895	−	9.16104i	−1.57037	−	0.420781i
$475$	1.10129	−	4.11006i	0.0505305	−	0.188583i
$476$		0			0
$477$	3.56274	+	6.17084i	0.163127	+	0.282544i
$478$	9.35544	+	5.40136i	0.427908	+	0.247053i
$479$	−35.3085	+	9.46087i	−1.61328	+	0.432278i	−0.949019	−	0.315218i	$-0.897922\pi$
$479$	−35.3085	+	9.46087i	−1.61328	+	0.432278i	−0.664266	+	0.747497i	$0.731256\pi$
$480$			38.1469i			1.74116i
$481$	−3.68240	+	8.35182i	−0.167903	+	0.380810i
$482$			31.4616i			1.43304i
$483$		0			0
$484$	−25.0985	+	43.4719i	−1.14084	+	1.97599i
$485$	−24.7623	+	14.2965i	−1.12440	+	0.649171i
$486$	13.0291	−	13.0291i	0.591013	−	0.591013i
$487$	4.36001	−	16.2718i	0.197571	−	0.737344i	−0.794016	−	0.607897i	$-0.792013\pi$
$487$	4.36001	−	16.2718i	0.197571	−	0.737344i	0.991586	−	0.129447i	$-0.0413201\pi$
$488$	0.0347821	−	0.129809i	0.00157451	−	0.00587617i
$489$	−2.62555	−	2.62555i	−0.118731	−	0.118731i
$490$		0			0
$491$	8.48030	+	4.89611i	0.382711	+	0.220958i	0.678997	−	0.734141i	$-0.262415\pi$
$491$	8.48030	+	4.89611i	0.382711	+	0.220958i	−0.296286	+	0.955099i	$0.595748\pi$
$492$	2.22217	+	8.29325i	0.100183	+	0.373889i
$493$	−1.67983			−0.0756558
$494$	4.18003	+	3.36001i	0.188069	+	0.151174i
$495$			17.8651i			0.802978i
$496$	−1.10766	−	4.13383i	−0.0497352	−	0.185614i
$497$		0			0
$498$	−12.7975	+	7.38863i	−0.573469	+	0.331093i
$499$	−2.08367	−	2.08367i	−0.0932780	−	0.0932780i	0.658928	−	0.752206i	$-0.271010\pi$
$499$	−2.08367	−	2.08367i	−0.0932780	−	0.0932780i	−0.752206	+	0.658928i	$0.771010\pi$
$500$	4.99678	+	1.33888i	0.223463	+	0.0598767i
$501$	−4.74449	−	1.27128i	−0.211968	−	0.0567968i
$502$	−6.57475	−	6.57475i	−0.293445	−	0.293445i
$503$	−24.6898	+	14.2547i	−1.10086	+	0.635584i	−0.936448	−	0.350807i	$-0.885907\pi$
$503$	−24.6898	+	14.2547i	−1.10086	+	0.635584i	−0.164416	+	0.986391i	$0.552574\pi$
$504$		0			0
$505$	−14.5849	−	54.4314i	−0.649018	−	2.42217i
$506$		−	54.4795i		−	2.42191i
$507$	5.67057	−	17.8907i	0.251839	−	0.794556i
$508$	−11.7391			−0.520839
$509$	−4.98837	−	18.6168i	−0.221106	−	0.825177i	−0.983927	−	0.178569i	$-0.942853\pi$
$509$	−4.98837	−	18.6168i	−0.221106	−	0.825177i	0.762822	−	0.646609i	$-0.223813\pi$
$510$	5.19632	+	3.00010i	0.230097	+	0.132847i
$511$		0			0
$512$	−22.7359	−	22.7359i	−1.00479	−	1.00479i
$513$	−1.07994	+	4.03037i	−0.0476803	+	0.177945i
$514$	−8.17093	+	30.4943i	−0.360404	+	1.34505i
$515$	−33.3841	+	33.3841i	−1.47108	+	1.47108i
$516$	−10.3943	+	6.00113i	−0.457582	+	0.264185i
$517$	21.8770	−	37.8921i	0.962149	−	1.66649i
$518$		0			0
$519$			20.2843i			0.890381i
$520$	−0.914539	+	1.13774i	−0.0401052	+	0.0498930i
$521$		−	10.4550i		−	0.458041i	−0.973422	−	0.229020i	$-0.926448\pi$
$521$		−	10.4550i		−	0.458041i	0.973422	−	0.229020i	$-0.0735523\pi$
$522$	4.76395	−	1.27650i	0.208513	−	0.0558708i
$523$	15.9637	+	9.21666i	0.698045	+	0.403016i	0.806619	−	0.591072i	$-0.201295\pi$
$523$	15.9637	+	9.21666i	0.698045	+	0.403016i	−0.108574	+	0.994088i	$0.534628\pi$
$524$	18.0465	+	31.2574i	0.788365	+	1.36549i
$525$		0			0
$526$	12.4715	−	46.5444i	0.543785	−	2.02943i
$527$	−0.670773	−	0.179733i	−0.0292193	−	0.00782929i
$528$	23.5129	+	23.5129i	1.02327	+	1.02327i
$529$	−1.16397	−	2.01606i	−0.0506076	−	0.0876549i
$530$	25.7235	−	44.5544i	1.11736	−	1.93532i
$531$	−0.842426	+	0.225727i	−0.0365582	+	0.00979574i
$532$		0			0
$533$	4.19689	−	9.51872i	0.181788	−	0.412301i
$534$	−11.8834			−0.514244
$535$	−2.65006	−	9.89016i	−0.114572	−	0.427589i
$536$	0.332965	−	0.576713i	0.0143819	−	0.0249102i
$537$	−10.8005	−	18.7070i	−0.466075	−	0.807266i
$538$	19.2858	−	19.2858i	0.831469	−	0.831469i
$539$		0			0
$540$	−36.9288	−	9.89505i	−1.58916	−	0.425815i
$541$	−29.6423	+	29.6423i	−1.27442	+	1.27442i	−0.330676	+	0.943744i	$0.607277\pi$
$541$	−29.6423	+	29.6423i	−1.27442	+	1.27442i	−0.943744	+	0.330676i	$0.892723\pi$
$542$	−37.7922	+	21.8193i	−1.62331	+	0.937221i
$543$	19.3053	+	11.1459i	0.828470	+	0.478317i
$544$	−4.88972	+	1.31020i	−0.209645	+	0.0561743i
$545$	−31.1722			−1.33527
$546$		0			0
$547$	39.3151			1.68099			0.840496	−	0.541818i	$-0.182264\pi$
$547$	39.3151			1.68099			0.840496	+	0.541818i	$0.182264\pi$
$548$	−29.1870	+	7.82062i	−1.24680	+	0.334080i
$549$	−0.863737	−	0.498679i	−0.0368634	−	0.0212831i
$550$	59.8226	−	34.5386i	2.55084	−	1.47273i
$551$	−1.39477	+	1.39477i	−0.0594193	+	0.0594193i
$552$	0.782357	+	0.209632i	0.0332993	+	0.00892253i
$553$		0			0
$554$	−30.5185	+	30.5185i	−1.29661	+	1.29661i
$555$	5.99559	+	10.3847i	0.254499	+	0.440805i
$556$	3.69460	−	6.39924i	0.156686	−	0.271388i
$557$	−11.0310	−	41.1681i	−0.467397	−	1.74435i	−0.648818	−	0.760944i	$-0.724736\pi$
$557$	−11.0310	−	41.1681i	−0.467397	−	1.74435i	0.181421	−	0.983405i	$-0.441930\pi$
$558$	2.03887			0.0863122
$559$	14.3715	+	2.22306i	0.607848	+	0.0940255i
$560$		0			0
$561$	5.21180	−	1.39650i	0.220042	−	0.0589602i
$562$	1.24654	−	2.15907i	0.0525820	−	0.0910747i
$563$	18.6963	+	32.3829i	0.787955	+	1.36478i	0.927218	+	0.374523i	$0.122193\pi$
$563$	18.6963	+	32.3829i	0.787955	+	1.36478i	−0.139263	+	0.990255i	$0.544473\pi$
$564$	15.4842	+	15.4842i	0.652003	+	0.652003i
$565$	−8.49854	−	2.27718i	−0.357536	−	0.0958015i
$566$	9.62909	−	35.9363i	0.404741	−	1.51051i
$567$		0			0
$568$	−0.140650	−	0.243613i	−0.00590155	−	0.0102218i
$569$	−26.9875	−	15.5812i	−1.13137	−	0.653199i	−0.187094	−	0.982342i	$-0.559907\pi$
$569$	−26.9875	−	15.5812i	−1.13137	−	0.653199i	−0.944280	+	0.329143i	$0.893240\pi$
$570$	6.80553	−	1.82354i	0.285052	−	0.0763795i
$571$			19.1097i			0.799714i	0.916577	+	0.399857i	$0.130940\pi$
$571$			19.1097i			0.799714i	−0.916577	+	0.399857i	$0.869060\pi$
$572$	4.77760	+	43.9296i	0.199762	+	1.83679i
$573$		−	24.7663i		−	1.03463i
$574$		0			0
$575$	−13.1055	+	22.6995i	−0.546539	+	0.946633i
$576$	6.72702	−	3.88385i	0.280293	−	0.161827i
$577$	14.0939	−	14.0939i	0.586737	−	0.586737i	−0.350010	−	0.936746i	$-0.613822\pi$
$577$	14.0939	−	14.0939i	0.586737	−	0.586737i	0.936746	+	0.350010i	$0.113822\pi$
$578$	8.66086	−	32.3228i	0.360244	−	1.34445i
$579$	−2.29149	+	8.55194i	−0.0952309	+	0.355406i
$580$	−12.7798	−	12.7798i	−0.530652	−	0.530652i
$581$		0			0
$582$	−21.9577	−	12.6773i	−0.910176	−	0.525490i
$583$	−11.9739	−	44.6871i	−0.495907	−	1.85075i
$584$	0.759479			0.0314275
$585$	6.39932	+	8.74136i	0.264579	+	0.361411i
$586$			25.0410i			1.03443i
$587$	−10.4047	−	38.8308i	−0.429447	−	1.60272i	−0.754016	−	0.656856i	$-0.771886\pi$
$587$	−10.4047	−	38.8308i	−0.429447	−	1.60272i	0.324569	−	0.945862i	$-0.394781\pi$
$588$		0			0
$589$	−0.706179	+	0.407713i	−0.0290976	+	0.0167995i
$590$	4.45266	+	4.45266i	0.183313	+	0.183313i
$591$	−35.7898	−	9.58986i	−1.47220	−	0.394474i
$592$	−9.47249	−	2.53815i	−0.389317	−	0.104317i
$593$	−5.08454	−	5.08454i	−0.208797	−	0.208797i	0.594959	−	0.803756i	$-0.297168\pi$
$593$	−5.08454	−	5.08454i	−0.208797	−	0.208797i	−0.803756	+	0.594959i	$0.797168\pi$
$594$	−58.6627	+	33.8689i	−2.40696	+	1.38966i
$595$		0			0
$596$	−7.65669	−	28.5752i	−0.313630	−	1.17048i
$597$			12.5996i			0.515667i
$598$	−19.5147	−	26.6567i	−0.798013	−	1.09007i
$599$	−29.3754			−1.20025			−0.600123	−	0.799908i	$-0.704882\pi$
$599$	−29.3754			−1.20025			−0.600123	+	0.799908i	$0.704882\pi$
$600$	0.265802	+	0.991988i	0.0108513	+	0.0404977i
$601$	40.3495	+	23.2958i	1.64589	+	0.950255i	0.978682	+	0.205384i	$0.0658442\pi$
$601$	40.3495	+	23.2958i	1.64589	+	0.950255i	0.667208	+	0.744871i	$0.267489\pi$
$602$		0			0
$603$	−3.49466	−	3.49466i	−0.142314	−	0.142314i
$604$	12.6871	−	47.3488i	0.516229	−	1.92659i
$605$	20.6801	−	77.1792i	0.840766	−	3.13778i
$606$	35.3335	−	35.3335i	1.43533	−	1.43533i
$607$	18.6085	−	10.7436i	0.755295	−	0.436070i	−0.0723088	−	0.997382i	$-0.523037\pi$
$607$	18.6085	−	10.7436i	0.755295	−	0.436070i	0.827604	+	0.561312i	$0.189703\pi$
$608$	−2.97210	+	5.14782i	−0.120534	+	0.208772i
$609$		0			0
$610$			7.20107i			0.291563i
$611$	−2.86864	−	26.3769i	−0.116053	−	1.06709i
$612$		−	1.18652i		−	0.0479621i
$613$	−27.6112	+	7.39841i	−1.11521	+	0.298819i	−0.768943	−	0.639318i	$-0.779217\pi$
$613$	−27.6112	+	7.39841i	−1.11521	+	0.298819i	−0.346265	+	0.938137i	$0.612550\pi$
$614$	8.67288	+	5.00729i	0.350009	+	0.202078i
$615$	−6.83329	−	11.8356i	−0.275545	−	0.477257i
$616$		0			0
$617$	−5.40928	+	20.1877i	−0.217769	+	0.812726i	0.767404	+	0.641164i	$0.221548\pi$
$617$	−5.40928	+	20.1877i	−0.217769	+	0.812726i	−0.985173	+	0.171562i	$0.945119\pi$
$618$	−40.4384	−	10.8354i	−1.62667	−	0.435866i
$619$	3.17085	+	3.17085i	0.127447	+	0.127447i	0.767953	−	0.640506i	$-0.221275\pi$
$619$	3.17085	+	3.17085i	0.127447	+	0.127447i	−0.640506	+	0.767953i	$0.721275\pi$
$620$	−3.73572	−	6.47046i	−0.150030	−	0.259860i
$621$	12.8514	−	22.2593i	0.515711	−	0.893237i
$622$	35.7510	−	9.57946i	1.43349	−	0.384101i
$623$		0			0
$624$	19.9272	+	3.08245i	0.797725	+	0.123397i
$625$	20.5903			0.823613
$626$	4.68935	+	17.5009i	0.187424	+	0.699476i
$627$	3.16787	−	5.48690i	0.126512	−	0.219126i
$628$	−7.84159	−	13.5820i	−0.312914	−	0.541982i
$629$	−1.12520	+	1.12520i	−0.0448645	+	0.0448645i
$630$		0			0
$631$	−9.89598	−	2.65162i	−0.393953	−	0.105559i	0.0564039	−	0.998408i	$-0.482037\pi$
$631$	−9.89598	−	2.65162i	−0.393953	−	0.105559i	−0.450357	+	0.892849i	$0.648703\pi$
$632$	1.06152	−	1.06152i	0.0422251	−	0.0422251i
$633$	13.5371	−	7.81567i	0.538053	−	0.310645i
$634$	25.1439	+	14.5168i	0.998592	+	0.576537i
$635$	18.0492	−	4.83627i	0.716260	−	0.191921i
$636$	23.1539			0.918114
$637$		0			0
$638$	−32.0220			−1.26776
$639$	−2.01653	+	0.540328i	−0.0797727	+	0.0213750i
$640$	−2.80362	−	1.61867i	−0.110823	−	0.0639836i
$641$	−27.7522	+	16.0227i	−1.09615	+	0.632860i	−0.935206	−	0.354104i	$-0.884786\pi$
$641$	−27.7522	+	16.0227i	−1.09615	+	0.632860i	−0.160940	+	0.986964i	$0.551453\pi$
$642$	6.42008	−	6.42008i	0.253380	−	0.253380i
$643$	44.5502	+	11.9372i	1.75689	+	0.470757i	0.986075	−	0.166302i	$-0.0531826\pi$
$643$	44.5502	+	11.9372i	1.75689	+	0.470757i	0.770815	+	0.637059i	$0.219849\pi$
$644$		0			0
$645$	13.5091	−	13.5091i	0.531921	−	0.531921i
$646$	0.467487	+	0.809711i	0.0183930	+	0.0318576i
$647$	15.3506	−	26.5881i	0.603496	−	1.04529i	−0.388792	−	0.921326i	$-0.627107\pi$
$647$	15.3506	−	26.5881i	0.603496	−	1.04529i	0.992287	−	0.123959i	$-0.0395593\pi$
$648$	−0.172908	−	0.645301i	−0.00679246	−	0.0253498i
$649$	5.66256			0.222275
$650$	16.8993	−	38.3282i	0.662844	−	1.50336i
$651$		0			0
$652$	5.12074	−	1.37210i	0.200544	−	0.0537355i
$653$	7.67694	−	13.2969i	0.300422	−	0.520346i	−0.675810	−	0.737076i	$-0.736206\pi$
$653$	7.67694	−	13.2969i	0.300422	−	0.520346i	0.976232	+	0.216730i	$0.0695392\pi$
$654$	−13.8208	−	23.9383i	−0.540436	−	0.936063i
$655$	−40.6244	−	40.6244i	−1.58733	−	1.58733i
$656$	10.7960	+	2.89277i	0.421512	+	0.112944i
$657$	1.45883	−	5.44441i	0.0569142	−	0.212407i
$658$		0			0
$659$	4.71985	+	8.17502i	0.183859	+	0.318454i	0.943192	−	0.332250i	$-0.107808\pi$
$659$	4.71985	+	8.17502i	0.183859	+	0.318454i	−0.759332	+	0.650703i	$0.774474\pi$
$660$	50.2745	+	29.0260i	1.95693	+	1.12984i
$661$	−7.98013	+	2.13827i	−0.310391	+	0.0831691i	−0.410652	−	0.911792i	$-0.634699\pi$
$661$	−7.98013	+	2.13827i	−0.310391	+	0.0831691i	0.100261	+	0.994961i	$0.468032\pi$
$662$		−	16.4928i		−	0.641012i
$663$	2.04989	−	2.55018i	0.0796113	−	0.0990408i
$664$		−	0.626743i		−	0.0243224i
$665$		0			0
$666$	2.33599	−	4.04605i	0.0905178	−	0.156781i
$667$	10.5227	−	6.07531i	0.407442	−	0.235237i
$668$	4.95890	−	4.95890i	0.191866	−	0.191866i
$669$	2.91270	−	10.8703i	0.112611	−	0.420271i
$670$	−9.23555	+	34.4675i	−0.356800	+	1.33160i
$671$	4.57890	+	4.57890i	0.176766	+	0.176766i
$672$		0			0
$673$	−27.2566	−	15.7366i	−1.05067	−	0.606602i	−0.127830	−	0.991796i	$-0.540801\pi$
$673$	−27.2566	−	15.7366i	−1.05067	−	0.606602i	−0.922836	+	0.385194i	$0.874134\pi$
$674$	0.854521	+	3.18911i	0.0329149	+	0.122840i
$675$	32.5899			1.25439
$676$	18.0733	+	19.7833i	0.695128	+	0.760897i
$677$		−	47.2040i		−	1.81420i	−0.420917	−	0.907099i	$-0.638292\pi$
$677$		−	47.2040i		−	1.81420i	0.420917	−	0.907099i	$-0.361708\pi$
$678$	−2.01926	−	7.53599i	−0.0775493	−	0.289418i
$679$		0			0
$680$	−0.220390	+	0.127242i	−0.00845157	+	0.00487952i
$681$	−14.5526	−	14.5526i	−0.557657	−	0.557657i
$682$	−12.7867	−	3.42618i	−0.489627	−	0.131195i
$683$	43.8982	+	11.7625i	1.67972	+	0.450079i	0.967705	−	0.252087i	$-0.0811170\pi$
$683$	43.8982	+	11.7625i	1.67972	+	0.450079i	0.712013	+	0.702166i	$0.247784\pi$
$684$	−0.985170	−	0.985170i	−0.0376689	−	0.0376689i
$685$	41.6538	−	24.0488i	1.59151	−	0.918858i
$686$		0			0
$687$	−4.26394	−	15.9132i	−0.162680	−	0.607128i
$688$			15.6243i			0.595670i
$689$	−21.8658	−	17.5762i	−0.833020	−	0.669602i
$690$	−43.4009			−1.65224
$691$	−4.89077	−	18.2526i	−0.186054	−	0.694361i	−0.994403	−	0.105658i	$-0.966305\pi$
$691$	−4.89077	−	18.2526i	−0.186054	−	0.694361i	0.808349	−	0.588703i	$-0.200361\pi$
$692$	−25.0810	−	14.4805i	−0.953435	−	0.550466i
$693$		0			0
$694$	13.7246	+	13.7246i	0.520980	+	0.520980i
$695$	−3.04420	+	11.3611i	−0.115473	+	0.430951i
$696$	0.123218	−	0.459854i	0.00467055	−	0.0174307i
$697$	1.28241	−	1.28241i	0.0485746	−	0.0485746i
$698$	−51.4340	+	29.6954i	−1.94680	+	1.12399i
$699$	15.7987	−	27.3642i	0.597563	−	1.03501i
$700$		0			0
$701$			31.6032i			1.19364i	0.802377	+	0.596818i	$0.203569\pi$
$701$			31.6032i			1.19364i	−0.802377	+	0.596818i	$0.796431\pi$
$702$	−16.5716	+	37.5851i	−0.625456	+	1.41856i
$703$			1.86851i			0.0704723i
$704$	−48.7148	+	13.0531i	−1.83601	+	0.491957i
$705$	−30.1865	−	17.4282i	−1.13689	−	0.656384i
$706$	−16.1071	−	27.8982i	−0.606197	−	1.04996i
$707$		0			0
$708$	−0.733492	+	2.73743i	−0.0275663	+	0.102879i
$709$	18.7480	+	5.02350i	0.704094	+	0.188661i	0.593064	−	0.805156i	$-0.297918\pi$
$709$	18.7480	+	5.02350i	0.704094	+	0.188661i	0.111030	+	0.993817i	$0.464585\pi$
$710$	10.6584	+	10.6584i	0.400003	+	0.400003i
$711$	−5.57064	−	9.64864i	−0.208915	−	0.361852i
$712$	0.252003	−	0.436482i	0.00944421	−	0.0163578i
$713$	4.85186	−	1.30005i	0.181704	−	0.0486873i
$714$		0			0
$715$	−25.4438	−	65.5747i	−0.951543	−	2.45236i
$716$	30.8409			1.15258
$717$	−2.00296	−	7.47517i	−0.0748021	−	0.279165i
$718$	−5.79058	+	10.0296i	−0.216103	+	0.374301i
$719$	2.23540	+	3.87183i	0.0833665	+	0.144395i	0.904694	−	0.426062i	$-0.140099\pi$
$719$	2.23540	+	3.87183i	0.0833665	+	0.144395i	−0.821327	+	0.570457i	$0.806766\pi$
$720$	−8.23028	+	8.23028i	−0.306724	+	0.306724i
$721$		0			0
$722$	−35.9246	−	9.62596i	−1.33697	−	0.358241i
$723$	15.9371	−	15.9371i	0.592708	−	0.592708i
$724$	−27.5633	+	15.9137i	−1.02438	+	0.591427i
$725$	13.3423	+	7.70318i	0.495520	+	0.286089i
$726$	68.4378	−	18.3379i	2.53997	−	0.680582i
$727$	−25.9080			−0.960874			−0.480437	−	0.877029i	$-0.659522\pi$
$727$	−25.9080			−0.960874			−0.480437	+	0.877029i	$0.659522\pi$
$728$		0			0
$729$	−29.4421			−1.09045
$730$	−39.3095	+	10.5329i	−1.45491	+	0.389841i
$731$	2.19560	+	1.26763i	0.0812073	+	0.0468851i
$732$	−2.80668	+	1.62044i	−0.103738	+	0.0598931i
$733$	33.9139	−	33.9139i	1.25264	−	1.25264i	0.298105	−	0.954533i	$-0.403645\pi$
$733$	33.9139	−	33.9139i	1.25264	−	1.25264i	0.954533	−	0.298105i	$-0.0963547\pi$
$734$	−49.5619	−	13.2801i	−1.82936	−	0.490177i
$735$		0			0
$736$	25.8916	−	25.8916i	0.954376	−	0.954376i
$737$	16.0441	+	27.7892i	0.590991	+	1.02363i
$738$	−2.66237	+	4.61136i	−0.0980033	+	0.169747i
$739$	−4.51998	−	16.8688i	−0.166270	−	0.620529i	−0.997875	−	0.0651605i	$-0.979244\pi$
$739$	−4.51998	−	16.8688i	−0.166270	−	0.620529i	0.831605	−	0.555368i	$-0.187423\pi$
$740$	−17.1205			−0.629362
$741$	−0.415389	−	3.81946i	−0.0152597	−	0.140311i
$742$		0			0
$743$	−33.0523	+	8.85634i	−1.21257	+	0.324908i	−0.807770	−	0.589497i	$-0.799326\pi$
$743$	−33.0523	+	8.85634i	−1.21257	+	0.324908i	−0.404801	+	0.914405i	$0.632659\pi$
$744$	0.0984038	−	0.170440i	0.00360766	−	0.00624865i
$745$	23.5447	+	40.7807i	0.862612	+	1.49409i
$746$	−26.6696	−	26.6696i	−0.976444	−	0.976444i
$747$	−4.49288	−	1.20386i	−0.164386	−	0.0440470i
$748$	−1.99386	+	7.44118i	−0.0729027	+	0.272077i
$749$		0			0
$750$	−3.65083	−	6.32342i	−0.133309	−	0.230899i
$751$	−4.81931	−	2.78243i	−0.175859	−	0.101532i	0.409487	−	0.912316i	$-0.365708\pi$
$751$	−4.81931	−	2.78243i	−0.175859	−	0.101532i	−0.585346	+	0.810784i	$0.699041\pi$
$752$	27.5350	−	7.37798i	1.00410	−	0.269047i
$753$			6.66098i			0.242739i
$754$	−15.6683	+	11.4703i	−0.570605	+	0.417725i
$755$			78.0268i			2.83969i
$756$		0			0
$757$	−9.89589	+	17.1402i	−0.359672	+	0.622971i	−0.987906	−	0.155054i	$-0.950445\pi$
$757$	−9.89589	+	17.1402i	−0.359672	+	0.622971i	0.628234	+	0.778025i	$0.283778\pi$
$758$	−37.0601	+	21.3967i	−1.34609	+	0.777163i
$759$	−27.5970	+	27.5970i	−1.00171	+	1.00171i
$760$	−0.0773410	+	0.288641i	−0.00280545	+	0.0104701i
$761$	−8.78414	+	32.7829i	−0.318425	+	1.18838i	0.602334	+	0.798245i	$0.294238\pi$
$761$	−8.78414	+	32.7829i	−0.318425	+	1.18838i	−0.920758	+	0.390133i	$0.872429\pi$
$762$	11.7164	+	11.7164i	0.424441	+	0.424441i
$763$		0			0
$764$	30.6229	+	17.6801i	1.10790	+	0.639644i
$765$	0.488820	+	1.82430i	0.0176733	+	0.0659577i
$766$	65.4035			2.36312
$767$	2.77068	−	2.02834i	0.100043	−	0.0732391i
$768$			21.6203i			0.780157i
$769$	4.79803	+	17.9065i	0.173021	+	0.645725i	0.996880	+	0.0789297i	$0.0251503\pi$
$769$	4.79803	+	17.9065i	0.173021	+	0.645725i	−0.823859	+	0.566795i	$0.808183\pi$
$770$		0			0
$771$	19.5862	−	11.3081i	0.705378	−	0.407250i
$772$	−8.93840	−	8.93840i	−0.321700	−	0.321700i
$773$	−22.3978	−	6.00148i	−0.805594	−	0.215858i	−0.167555	−	0.985863i	$-0.553587\pi$
$773$	−22.3978	−	6.00148i	−0.805594	−	0.215858i	−0.638038	+	0.770005i	$0.720254\pi$
$774$	−7.18993	−	1.92654i	−0.258437	−	0.0692479i
$775$	4.50351	+	4.50351i	0.161771	+	0.161771i
$776$	0.931285	−	0.537678i	0.0334312	−	0.0193015i
$777$		0			0
$778$	−3.63222	−	13.5556i	−0.130221	−	0.485993i
$779$		−	2.12958i		−	0.0763000i
$780$	34.9964	−	3.80605i	1.25307	−	0.136279i
$781$	13.5546			0.485021
$782$	−1.49065	−	5.56318i	−0.0533055	−	0.198939i
$783$	−13.0836	−	7.55382i	−0.467570	−	0.269952i
$784$		0			0
$785$	17.6522	+	17.6522i	0.630033	+	0.630033i
$786$	13.1854	−	49.2086i	0.470308	−	1.75521i
$787$	4.06976	−	15.1886i	0.145071	−	0.541414i	−0.854681	−	0.519154i	$-0.826247\pi$
$787$	4.06976	−	15.1886i	0.145071	−	0.541414i	0.999752	−	0.0222599i	$-0.00708612\pi$
$788$	37.4072	−	37.4072i	1.33258	−	1.33258i
$789$	−29.8950	+	17.2599i	−1.06429	+	0.614468i
$790$	−40.2209	+	69.6646i	−1.43099	+	2.47856i
$791$		0			0
$792$		−	0.671889i		−	0.0238745i
$793$	3.88061	+	0.600275i	0.137805	+	0.0213164i
$794$		−	30.1079i		−	1.06849i
$795$	−35.5998	+	9.53894i	−1.26259	+	0.338311i
$796$	−15.5790	−	8.99457i	−0.552185	−	0.318804i
$797$	10.8696	+	18.8267i	0.385021	+	0.666876i	0.991772	−	0.128016i	$-0.0408608\pi$
$797$	10.8696	+	18.8267i	0.385021	+	0.666876i	−0.606751	+	0.794892i	$0.707527\pi$
$798$		0			0
$799$	1.19718	−	4.46794i	0.0423533	−	0.158064i
$800$	44.8455	+	12.0163i	1.58553	+	0.424840i
$801$	−2.64491	−	2.64491i	−0.0934534	−	0.0934534i
$802$	24.3593	+	42.1916i	0.860158	+	1.48984i
$803$	−18.2979	+	31.6929i	−0.645720	+	1.11842i
$804$	−15.5123	+	4.15650i	−0.547075	+	0.146588i
$805$		0			0
$806$	−7.48376	+	2.90379i	−0.263604	+	0.102282i
$807$	−19.5387			−0.687795
$808$	0.548522	+	2.04711i	0.0192969	+	0.0720171i
$809$	−17.8402	+	30.9002i	−0.627229	+	1.08639i	0.360876	+	0.932614i	$0.382478\pi$
$809$	−17.8402	+	30.9002i	−0.627229	+	1.08639i	−0.988105	+	0.153779i	$0.950856\pi$
$810$	17.8989	+	31.0018i	0.628902	+	1.08929i
$811$	0.747882	−	0.747882i	0.0262617	−	0.0262617i	−0.693854	−	0.720116i	$-0.744089\pi$
$811$	0.747882	−	0.747882i	0.0262617	−	0.0262617i	0.720116	+	0.693854i	$0.244089\pi$
$812$		0			0
$813$	30.1967	+	8.09117i	1.05904	+	0.283770i
$814$	−21.4492	+	21.4492i	−0.751794	+	0.751794i
$815$	−7.30800	+	4.21928i	−0.255988	+	0.147795i
$816$	3.04437	+	1.75767i	0.106574	+	0.0615308i
$817$	2.87554	−	0.770499i	0.100602	−	0.0269563i
$818$	75.6376			2.64461
$819$		0			0
$820$	19.5125			0.681407
$821$	−10.6837	+	2.86268i	−0.372863	+	0.0999084i	−0.440384	−	0.897809i	$-0.645158\pi$
$821$	−10.6837	+	2.86268i	−0.372863	+	0.0999084i	0.0675209	+	0.997718i	$0.478491\pi$
$822$	36.9360	+	21.3250i	1.28829	+	0.743796i
$823$	−20.4465	+	11.8048i	−0.712719	+	0.411488i	−0.812067	−	0.583564i	$-0.801658\pi$
$823$	−20.4465	+	11.8048i	−0.712719	+	0.411488i	0.0993482	+	0.995053i	$0.468324\pi$
$824$	1.25554	−	1.25554i	0.0437389	−	0.0437389i
$825$	−47.7994	−	12.8078i	−1.66416	−	0.445910i
$826$		0			0
$827$	−1.09240	+	1.09240i	−0.0379865	+	0.0379865i	−0.725845	−	0.687858i	$-0.758551\pi$
$827$	−1.09240	+	1.09240i	−0.0379865	+	0.0379865i	0.687858	+	0.725845i	$0.258551\pi$
$828$	4.29118	+	7.43253i	0.149129	+	0.258298i
$829$	−19.1064	+	33.0932i	−0.663591	+	1.14937i	0.316074	+	0.948735i	$0.397635\pi$
$829$	−19.1064	+	33.0932i	−0.663591	+	1.14937i	−0.979665	+	0.200639i	$0.935698\pi$
$830$	8.69207	+	32.4392i	0.301706	+	1.12598i
$831$	30.9188			1.07256
$832$	−19.1604	+	23.8366i	−0.664267	+	0.826384i
$833$		0			0
$834$	−10.0743	+	2.69941i	−0.348846	+	0.0934729i
$835$	−5.58148	+	9.66740i	−0.193155	+	0.334554i
$836$	4.52294	+	7.83396i	0.156429	+	0.270943i
$837$	−4.41619	−	4.41619i	−0.152646	−	0.152646i
$838$	15.8493	+	4.24682i	0.547506	+	0.146704i
$839$	10.2082	−	38.0974i	0.352425	−	1.31527i	−0.531268	−	0.847204i	$-0.678284\pi$
$839$	10.2082	−	38.0974i	0.352425	−	1.31527i	0.883694	−	0.468066i	$-0.155049\pi$
$840$		0			0
$841$	10.9291	+	18.9297i	0.376864	+	0.652747i
$842$	6.07460	+	3.50717i	0.209345	+	0.120865i
$843$	−1.72513	+	0.462248i	−0.0594167	+	0.0159207i
$844$			22.3177i			0.768209i
$845$	−35.9385	−	22.9716i	−1.23632	−	0.790245i
$846$			13.5807i			0.466914i
$847$		0			0
$848$	15.0707	−	26.1031i	0.517528	−	0.896385i
$849$	−23.0815	+	13.3261i	−0.792154	+	0.457350i
$850$	5.16376	−	5.16376i	0.177115	−	0.177115i
$851$	2.97901	−	11.1178i	0.102119	−	0.381114i
$852$	−1.75577	+	6.55263i	−0.0601518	+	0.224490i
$853$	2.18217	+	2.18217i	0.0747162	+	0.0747162i	0.743477	−	0.668761i	$-0.233175\pi$
$853$	2.18217	+	2.18217i	0.0747162	+	0.0747162i	−0.668761	+	0.743477i	$0.733175\pi$
$854$		0			0
$855$	1.92059	+	1.10886i	0.0656829	+	0.0379220i
$856$	0.0996661	+	0.371959i	0.00340652	+	0.0127133i
$857$	−29.4660			−1.00654			−0.503270	−	0.864129i	$-0.667870\pi$
$857$	−29.4660			−1.00654			−0.503270	+	0.864129i	$0.667870\pi$
$858$	39.0764	−	48.6131i	1.33405	−	1.65962i
$859$		−	51.4911i		−	1.75685i	−0.477878	−	0.878426i	$-0.658594\pi$
$859$		−	51.4911i		−	1.75685i	0.477878	−	0.878426i	$-0.341406\pi$
$860$	7.05980	+	26.3475i	0.240737	+	0.898443i
$861$		0			0
$862$	26.7334	−	15.4345i	0.910543	−	0.525702i
$863$	22.7803	+	22.7803i	0.775450	+	0.775450i	0.979053	−	0.203603i	$-0.0652653\pi$
$863$	22.7803	+	22.7803i	0.775450	+	0.775450i	−0.203603	+	0.979053i	$0.565265\pi$
$864$	−43.9760	−	11.7833i	−1.49609	−	0.400877i
$865$	44.5283	+	11.9313i	1.51401	+	0.405677i
$866$	−17.5672	−	17.5672i	−0.596959	−	0.596959i
$867$	−20.7606	+	11.9861i	−0.705066	+	0.407070i
$868$		0			0
$869$	18.7222	+	69.8721i	0.635106	+	2.37025i
$870$			25.5102i			0.864876i
$871$	17.8045	+	7.85016i	0.603281	+	0.265992i
$872$	1.17235			0.0397009
$873$	−2.06557	−	7.70880i	−0.0699088	−	0.260903i
$874$	−5.85683	−	3.38144i	−0.198110	−	0.114379i
$875$		0			0
$876$	−12.9510	−	12.9510i	−0.437574	−	0.437574i
$877$	6.42144	−	23.9651i	0.216837	−	0.809245i	−0.768675	−	0.639639i	$-0.779084\pi$
$877$	6.42144	−	23.9651i	0.216837	−	0.809245i	0.985512	−	0.169606i	$-0.0542496\pi$
$878$	4.05374	−	15.1288i	0.136807	−	0.510571i
$879$	12.6847	−	12.6847i	0.427845	−	0.427845i
$880$	65.4462	−	37.7854i	2.20619	−	1.27375i
$881$	8.18440	−	14.1758i	0.275740	−	0.477595i	−0.694582	−	0.719414i	$-0.744411\pi$
$881$	8.18440	−	14.1758i	0.275740	−	0.477595i	0.970321	+	0.241819i	$0.0777439\pi$
$882$		0			0
$883$		−	13.3555i		−	0.449449i	−0.974422	−	0.224724i	$-0.927852\pi$
$883$		−	13.3555i		−	0.449449i	0.974422	−	0.224724i	$-0.0721482\pi$
$884$	1.68985	+	4.35516i	0.0568359	+	0.146480i
$885$		−	4.51105i		−	0.151637i
$886$	12.2615	−	3.28546i	0.411934	−	0.110377i
$887$	14.2827	+	8.24614i	0.479567	+	0.276878i	0.720236	−	0.693729i	$-0.244033\pi$
$887$	14.2827	+	8.24614i	0.479567	+	0.276878i	−0.240669	+	0.970607i	$0.577367\pi$
$888$	−0.225488	−	0.390557i	−0.00756689	−	0.0131062i
$889$		0			0
$890$	−6.98987	+	26.0865i	−0.234301	+	0.874423i
$891$	31.0941	+	8.33164i	1.04169	+	0.279120i
$892$	11.3616	+	11.3616i	0.380413	+	0.380413i
$893$	−2.71573	−	4.70378i	−0.0908784	−	0.157406i
$894$	−20.8780	+	36.1618i	−0.698266	+	1.20943i
$895$	−47.4187	+	12.7058i	−1.58503	+	0.424708i
$896$		0			0
$897$	−3.61786	+	23.3884i	−0.120797	+	0.780917i
$898$	30.5360			1.01900
$899$	−0.764145	−	2.85183i	−0.0254857	−	0.0951138i
$900$	−5.44099	+	9.42407i	−0.181366	+	0.314136i
$901$	−2.44543	−	4.23561i	−0.0814690	−	0.141108i
$902$	24.4460	−	24.4460i	0.813964	−	0.813964i
$903$		0			0
$904$	0.319621	+	0.0856423i	0.0106304	+	0.00284842i
$905$	35.8232	−	35.8232i	1.19080	−	1.19080i
$906$	−59.9198	+	34.5947i	−1.99070	+	1.14933i
$907$	−11.2778	−	6.51123i	−0.374473	−	0.216202i	0.300938	−	0.953644i	$-0.402700\pi$
$907$	−11.2778	−	6.51123i	−0.374473	−	0.216202i	−0.675411	+	0.737442i	$0.736034\pi$
$908$	28.3827	−	7.60512i	0.941913	−	0.252385i
$909$	15.7285			0.521683
$910$		0			0
$911$	29.0374			0.962053			0.481026	−	0.876706i	$-0.340264\pi$
$911$	29.0374			0.962053			0.481026	+	0.876706i	$0.340264\pi$
$912$	3.98716	−	1.06836i	0.132028	−	0.0353768i
$913$	26.1539	+	15.1000i	0.865567	+	0.499735i
$914$	−27.1392	+	15.6688i	−0.897683	+	0.518278i
$915$	3.64776	−	3.64776i	0.120591	−	0.120591i
$916$	22.7202	+	6.08787i	0.750698	+	0.201149i
$917$		0			0
$918$	−5.06364	+	5.06364i	−0.167125	+	0.167125i
$919$	7.73929	+	13.4048i	0.255296	+	0.442185i	0.964976	−	0.262339i	$-0.0844939\pi$
$919$	7.73929	+	13.4048i	0.255296	+	0.442185i	−0.709680	+	0.704524i	$0.751161\pi$
$920$	0.920373	−	1.59413i	0.0303438	−	0.0525570i
$921$	−1.85683	−	6.92979i	−0.0611847	−	0.228345i
$922$	−61.9179			−2.03916
$923$	6.63222	−	4.85527i	0.218302	−	0.159813i
$924$		0			0
$925$	14.0968	−	3.77723i	0.463501	−	0.124195i
$926$	−5.86115	+	10.1518i	−0.192609	+	0.333609i
$927$	−6.58882	−	11.4122i	−0.216405	−	0.374825i
$928$	−15.2186	−	15.2186i	−0.499574	−	0.499574i
$929$	43.6835	+	11.7050i	1.43321	+	0.384028i	0.890151	−	0.455666i	$-0.150599\pi$
$929$	43.6835	+	11.7050i	1.43321	+	0.384028i	0.543060	+	0.839694i	$0.317266\pi$
$930$	−2.72945	+	10.1865i	−0.0895023	+	0.334027i
$931$		0			0
$932$	22.5568	+	39.0695i	0.738871	+	1.27976i
$933$	−22.9625	−	13.2574i	−0.751758	−	0.434028i
$934$	−15.8937	+	4.25869i	−0.520057	+	0.139349i
$935$		−	12.2624i		−	0.401025i
$936$	−0.240672	−	0.328754i	−0.00786660	−	0.0107457i
$937$		−	26.8615i		−	0.877526i	−0.898603	−	0.438763i	$-0.855417\pi$
$937$		−	26.8615i		−	0.877526i	0.898603	−	0.438763i	$-0.144583\pi$
$938$		0			0
$939$	6.48978	−	11.2406i	0.211786	−	0.366824i
$940$	43.0990	−	24.8832i	1.40574	−	0.811602i
$941$	1.02826	−	1.02826i	0.0335203	−	0.0335203i	−0.690148	−	0.723668i	$-0.742455\pi$
$941$	1.02826	−	1.02826i	0.0335203	−	0.0335203i	0.723668	+	0.690148i	$0.242455\pi$
$942$	−5.72935	+	21.3822i	−0.186672	+	0.696670i
$943$	−3.39524	+	12.6712i	−0.110564	+	0.412631i
$944$	2.60868	+	2.60868i	0.0849054	+	0.0849054i
$945$		0			0
$946$	41.8539	+	24.1644i	1.36079	+	0.785652i
$947$	−10.0347	−	37.4500i	−0.326084	−	1.21696i	−0.913218	−	0.407472i	$-0.866410\pi$
$947$	−10.0347	−	37.4500i	−0.326084	−	1.21696i	0.587133	−	0.809490i	$-0.300256\pi$
$948$	−36.2032			−1.17582
$949$	2.39933	+	22.0616i	0.0778855	+	0.716151i
$950$		−	8.57499i		−	0.278209i
$951$	−5.38322	−	20.0904i	−0.174563	−	0.651477i
$952$		0			0
$953$	20.6259	−	11.9084i	0.668138	−	0.385750i	−0.127233	−	0.991873i	$-0.540609\pi$
$953$	20.6259	−	11.9084i	0.668138	−	0.385750i	0.795371	+	0.606123i	$0.207276\pi$
$954$	10.1538	+	10.1538i	0.328741	+	0.328741i
$955$	−54.3673	−	14.5677i	−1.75928	−	0.471399i
$956$	10.6727	+	2.85975i	0.345180	+	0.0924908i
$957$	16.2210	+	16.2210i	0.524350	+	0.524350i
$958$	−63.7962	+	36.8327i	−2.06116	+	1.19001i
$959$		0			0
$960$	10.3987	+	38.8084i	0.335616	+	1.25254i
$961$			29.7795i			0.960628i
$962$	−2.81190	+	18.1782i	−0.0906594	+	0.586088i
$963$	2.85787			0.0920935
$964$	8.32866	+	31.0830i	0.268248	+	1.00112i
$965$	17.4255	+	10.0606i	0.560946	+	0.323862i
$966$		0			0
$967$	5.04001	+	5.04001i	0.162076	+	0.162076i	0.783486	−	0.621410i	$-0.213440\pi$
$967$	5.04001	+	5.04001i	0.162076	+	0.162076i	−0.621410	+	0.783486i	$0.713440\pi$
$968$	−0.777758	+	2.90263i	−0.0249981	+	0.0932941i
$969$	0.173356	−	0.646974i	0.00556900	−	0.0207838i
$970$	−40.7450	+	40.7450i	−1.30824	+	1.30824i
$971$	−14.4726	+	8.35573i	−0.464446	+	0.268148i	−0.713912	−	0.700235i	$-0.753078\pi$
$971$	−14.4726	+	8.35573i	−0.464446	+	0.268148i	0.249466	+	0.968384i	$0.419745\pi$
$972$	9.42319	−	16.3214i	0.302249	−	0.523510i
$973$		0			0
$974$		−	33.9484i		−	1.08778i
$975$	−27.9759	+	10.8550i	−0.895945	+	0.347638i
$976$			4.21890i			0.135044i
$977$	47.5599	−	12.7436i	1.52157	−	0.407705i	0.601315	−	0.799012i	$-0.294644\pi$
$977$	47.5599	−	12.7436i	1.52157	−	0.407705i	0.920260	+	0.391308i	$0.127977\pi$
$978$	−6.48029	−	3.74140i	−0.207217	−	0.119637i
$979$	12.1429	+	21.0321i	0.388088	+	0.672188i
$980$		0			0
$981$	2.25189	−	8.40415i	0.0718972	−	0.268324i
$982$	19.0613	+	5.10747i	0.608272	+	0.162986i
$983$	24.9769	+	24.9769i	0.796638	+	0.796638i	0.982564	−	0.185926i	$-0.0595285\pi$
$983$	24.9769	+	24.9769i	0.796638	+	0.796638i	−0.185926	+	0.982564i	$0.559528\pi$
$984$	0.256993	+	0.445125i	0.00819264	+	0.0141901i
$985$	−42.1036	+	72.9255i	−1.34153	+	2.32360i
$986$	−3.26993	+	0.876175i	−0.104136	+	0.0279031i
$987$		0			0
$988$	5.01920	+	2.21301i	0.159682	+	0.0704054i
$989$	−18.3382			−0.583120
$990$	9.31818	+	34.7759i	0.296151	+	1.10525i
$991$	−3.41914	+	5.92212i	−0.108613	+	0.188122i	−0.915208	−	0.402981i	$-0.867974\pi$
$991$	−3.41914	+	5.92212i	−0.108613	+	0.188122i	0.806596	+	0.591103i	$0.201307\pi$
$992$	−4.44861	−	7.70522i	−0.141243	−	0.244641i
$993$	−8.35456	+	8.35456i	−0.265124	+	0.265124i
$994$		0			0
$995$	27.6588	+	7.41114i	0.876842	+	0.234949i
$996$	−10.6875	+	10.6875i	−0.338647	+	0.338647i
$997$	−42.8521	+	24.7407i	−1.35714	+	0.783545i	−0.989237	−	0.146319i	$-0.953257\pi$
$997$	−42.8521	+	24.7407i	−1.35714	+	0.783545i	−0.367903	+	0.929864i	$0.619924\pi$
$998$	−5.14285	−	2.96923i	−0.162794	−	0.0939892i
$999$	−13.8235	+	3.70400i	−0.437356	+	0.117189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.293.6		28
7.2	even	3		91.2.ba.a.59.2	yes	28
7.3	odd	6		91.2.w.a.33.2	✓	28
7.4	even	3		637.2.x.a.215.2		28
7.5	odd	6		637.2.bb.a.423.2		28
7.6	odd	2		637.2.bd.a.293.6		28
13.2	odd	12		637.2.bd.a.587.6		28
21.2	odd	6		819.2.et.b.514.6		28
21.17	even	6		819.2.gh.b.397.6		28
91.2	odd	12		91.2.w.a.80.2	yes	28
91.41	even	12	inner	637.2.bd.b.587.6		28
91.54	even	12		637.2.x.a.80.2		28
91.67	odd	12		637.2.bb.a.509.2		28
91.80	even	12		91.2.ba.a.54.2	yes	28
273.2	even	12		819.2.gh.b.262.6		28
273.80	odd	12		819.2.et.b.145.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.2	✓	28	7.3	odd	6
91.2.w.a.80.2	yes	28	91.2	odd	12
91.2.ba.a.54.2	yes	28	91.80	even	12
91.2.ba.a.59.2	yes	28	7.2	even	3
637.2.x.a.80.2		28	91.54	even	12
637.2.x.a.215.2		28	7.4	even	3
637.2.bb.a.423.2		28	7.5	odd	6
637.2.bb.a.509.2		28	91.67	odd	12
637.2.bd.a.293.6		28	7.6	odd	2
637.2.bd.a.587.6		28	13.2	odd	12
637.2.bd.b.293.6		28	1.1	even	1	trivial
637.2.bd.b.587.6		28	91.41	even	12	inner
819.2.et.b.145.6		28	273.80	odd	12
819.2.et.b.514.6		28	21.2	odd	6
819.2.gh.b.262.6		28	273.2	even	12
819.2.gh.b.397.6		28	21.17	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94658 - 0.521585i) q^{2} +(-1.25027 - 0.721843i) q^{3} +(1.78508 - 1.03062i) q^{4} +(-2.32001 + 2.32001i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 - 0.793083i) q^{9} +O(q^{10})\)	\(q+(1.94658 - 0.521585i) q^{2} +(-1.25027 - 0.721843i) q^{3} +(1.78508 - 1.03062i) q^{4} +(-2.32001 + 2.32001i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 - 0.793083i) q^{9} +(-3.30601 + 5.72618i) q^{10} +(1.53889 + 5.74323i) q^{11} -2.97577 q^{12} +(2.81021 + 2.25892i) q^{13} +(4.57532 - 1.22595i) q^{15} +(-1.93689 + 3.35480i) q^{16} +(0.314289 + 0.544364i) q^{17} +(-1.30497 - 1.30497i) q^{18} +(0.712944 + 0.191033i) q^{19} +(-1.75036 + 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +(-3.93752 - 2.27333i) q^{23} +(-0.172073 + 0.0461069i) q^{24} -5.76492i q^{25} +(6.64853 + 2.93140i) q^{26} +5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +(8.26680 - 4.77284i) q^{30} +(-0.781192 + 0.781192i) q^{31} +(-2.08438 + 7.77903i) q^{32} +(2.22168 - 8.29142i) q^{33} +(0.895721 + 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(0.655210 + 2.44528i) q^{37} +1.48744 q^{38} +(-1.88294 - 4.85278i) q^{39} +0.404858i q^{40} +(-0.746755 - 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(8.66611 + 8.66611i) q^{44} +(2.90227 + 0.777660i) q^{45} +(-8.85043 - 2.37147i) q^{46} +(-5.20343 - 5.20343i) q^{47} +(4.84328 - 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} -0.907468i q^{51} +(7.34452 + 1.13609i) q^{52} -7.78083 q^{53} +(2.94859 + 11.0043i) q^{54} +(-16.8946 - 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(-1.39390 + 5.20211i) q^{58} +(0.246488 - 0.919907i) q^{59} +(6.90382 - 6.90382i) q^{60} +(0.943178 - 0.544544i) q^{61} +(-1.11320 + 1.92811i) q^{62} +8.48212i q^{64} +(-11.7604 + 1.27902i) q^{65} -17.2987i q^{66} +(5.21286 - 1.39678i) q^{67} +(1.12206 + 0.647822i) q^{68} +(3.28197 + 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(-0.109151 - 0.0292470i) q^{72} +(4.35215 + 4.35215i) q^{73} +(2.55084 + 4.41818i) q^{74} +(-4.16136 + 7.20769i) q^{75} +(1.46954 - 0.393762i) q^{76} +(-6.19643 - 8.46422i) q^{78} +12.1660 q^{79} +(-3.28956 - 12.2768i) q^{80} +(2.70702 - 4.68870i) q^{81} +(-2.90724 - 5.03549i) q^{82} +(3.59152 - 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(5.74749 - 5.74749i) q^{86} +(3.34126 - 1.92908i) q^{87} +(0.635390 + 0.366843i) q^{88} +(3.94532 - 1.05715i) q^{89} +6.05511 q^{90} -9.37170 q^{92} +(1.54060 - 0.412802i) q^{93} +(-12.8429 - 7.41487i) q^{94} +(-2.09724 + 1.21084i) q^{95} +(8.22127 - 8.22127i) q^{96} +(8.41780 + 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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