LMFDB - Embedded newform 637.2.x.a.215.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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			215.2
Character	$\chi$	$=$	637.215
Dual form			637.2.x.a.80.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.521585 + 1.94658i) q^{2} +1.44369i q^{3} +(-1.78508 - 1.03062i) q^{4} +(-0.849184 - 3.16920i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +0.915773 q^{9} +O(q^{10})$	\(q+(-0.521585 + 1.94658i) q^{2} +1.44369i q^{3} +(-1.78508 - 1.03062i) q^{4} +(-0.849184 - 3.16920i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +0.915773 q^{9} +6.61202 q^{10} +(4.20434 - 4.20434i) q^{11} +(1.48788 - 2.57709i) 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} +(-0.477654 + 1.78263i) q^{18} +(-0.521911 + 0.521911i) q^{19} +(-1.75036 + 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +(3.93752 - 2.27333i) q^{23} +(0.125966 + 0.125966i) q^{24} +(-4.99256 + 2.88246i) q^{25} +(-5.86293 + 4.29209i) q^{26} +5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +9.54568i q^{30} +(1.06713 + 0.285936i) q^{31} +(7.77903 - 2.08438i) q^{32} +(6.06974 + 6.06974i) q^{33} +(0.895721 + 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(-2.44528 - 0.655210i) q^{37} +(-0.743721 - 1.28816i) q^{38} +(-3.26116 + 4.05706i) q^{39} +(-0.350617 - 0.202429i) q^{40} +(-0.746755 - 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(-11.8381 + 3.17202i) q^{44} +(-0.777660 - 2.90227i) q^{45} +(2.37147 + 8.85043i) q^{46} +(7.10802 - 1.90459i) q^{47} +(4.84328 - 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} +(0.785891 + 0.453734i) q^{51} +(-2.68838 - 6.92859i) q^{52} +(3.89042 + 6.73840i) q^{53} +(-11.0043 - 2.94859i) q^{54} +(-16.8946 - 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(-3.80821 - 3.80821i) q^{58} +(-0.919907 + 0.246488i) q^{59} +(-9.43079 - 2.52697i) q^{60} +1.08909i q^{61} +(-1.11320 + 1.92811i) q^{62} +8.48212i q^{64} +(4.77256 - 10.8244i) q^{65} +(-14.9811 + 8.64936i) q^{66} +(-3.81608 - 3.81608i) q^{67} +(-1.12206 + 0.647822i) q^{68} +(3.28197 + 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(0.0799043 - 0.0799043i) q^{72} +(1.59300 - 5.94515i) 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} +(-6.08299 + 10.5361i) q^{79} +(-8.98724 + 8.98724i) q^{80} -5.41404 q^{81} +5.81448 q^{82} +(3.59152 - 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(2.10373 + 7.85121i) q^{86} +(-3.34126 - 1.92908i) q^{87} -0.733685i q^{88} +(-1.05715 + 3.94532i) q^{89} +6.05511 q^{90} -9.37170 q^{92} +(-0.412802 + 1.54060i) q^{93} +14.8297i q^{94} +(2.09724 + 1.21084i) q^{95} +(3.00919 + 11.2305i) q^{96} +(8.41780 + 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.521585	+	1.94658i	−0.368816	+	1.37644i	0.493357	+	0.869827i	$0.335770\pi$
$2$	−0.521585	+	1.94658i	−0.368816	+	1.37644i	−0.862173	+	0.506614i	$0.830897\pi$
$3$			1.44369i			0.833512i	0.909018	+	0.416756i	$0.136833\pi$
$3$			1.44369i			0.833512i	−0.909018	+	0.416756i	$0.863167\pi$
$4$	−1.78508	−	1.03062i	−0.892539	−	0.515308i
$5$	−0.849184	−	3.16920i	−0.379766	−	1.41731i	−0.846254	−	0.532780i	$-0.821147\pi$
$5$	−0.849184	−	3.16920i	−0.379766	−	1.41731i	0.466487	−	0.884528i	$-0.345519\pi$
$6$	−2.81025	−	0.753004i	−1.14728	−	0.307413i
$7$		0			0
$7$		0			0
$8$	0.0872533	−	0.0872533i	0.0308487	−	0.0308487i
$9$	0.915773			0.305258
$10$	6.61202			2.09090
$11$	4.20434	−	4.20434i	1.26766	−	1.26766i	0.320360	−	0.947296i	$-0.396196\pi$
$11$	4.20434	−	4.20434i	1.26766	−	1.26766i	0.947296	−	0.320360i	$-0.103804\pi$
$12$	1.48788	−	2.57709i	0.429515	−	0.743942i
$13$	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	−0.825393	−	0.564559i	$-0.809046\pi$
$17$	0.314289	−	0.544364i	0.0762262	−	0.132028i	0.901619	+	0.432531i	$0.142380\pi$
$18$	−0.477654	+	1.78263i	−0.112584	+	0.420169i
$19$	−0.521911	+	0.521911i	−0.119735	+	0.119735i	−0.764435	−	0.644701i	$-0.776982\pi$
$19$	−0.521911	+	0.521911i	−0.119735	+	0.119735i	0.644701	+	0.764435i	$0.276982\pi$
$20$	−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	$-0.509469\pi$
$23$	3.93752	−	2.27333i	0.821029	−	0.474021i	0.850771	+	0.525536i	$0.176135\pi$
$24$	0.125966	+	0.125966i	0.0257128	+	0.0257128i
$25$	−4.99256	+	2.88246i	−0.998513	+	0.576492i
$26$	−5.86293	+	4.29209i	−1.14982	+	0.841749i
$27$			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	$0.246482\pi$
$30$			9.54568i			1.74279i
$31$	1.06713	+	0.285936i	0.191662	+	0.0513556i	0.353373	−	0.935482i	$-0.385035\pi$
$31$	1.06713	+	0.285936i	0.191662	+	0.0513556i	−0.161711	+	0.986838i	$0.551701\pi$
$32$	7.77903	−	2.08438i	1.37515	−	0.368471i
$33$	6.06974	+	6.06974i	1.05661	+	1.05661i
$34$	0.895721	+	0.895721i	0.153615	+	0.153615i
$35$		0			0
$36$	−1.63473	−	0.943810i	−0.272454	−	0.157302i
$37$	−2.44528	−	0.655210i	−0.402001	−	0.107716i	0.0521528	−	0.998639i	$-0.483392\pi$
$37$	−2.44528	−	0.655210i	−0.402001	−	0.107716i	−0.454154	+	0.890923i	$0.650058\pi$
$38$	−0.743721	−	1.28816i	−0.120648	−	0.208968i
$39$	−3.26116	+	4.05706i	−0.522204	+	0.649650i
$40$	−0.350617	−	0.202429i	−0.0554374	−	0.0320068i
$41$	−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	$0.233828\pi$
$44$	−11.8381	+	3.17202i	−1.78467	+	0.478200i
$45$	−0.777660	−	2.90227i	−0.115927	−	0.432644i
$46$	2.37147	+	8.85043i	0.349654	+	1.30492i
$47$	7.10802	−	1.90459i	1.03681	−	0.277813i	0.300020	−	0.953933i	$-0.403007\pi$
$47$	7.10802	−	1.90459i	1.03681	−	0.277813i	0.736791	+	0.676120i	$0.236340\pi$
$48$	4.84328	−	2.79627i	0.699067	−	0.403606i
$49$		0			0
$50$	−3.00689	−	11.2219i	−0.425239	−	1.58701i
$51$	0.785891	+	0.453734i	0.110047	+	0.0635355i
$52$	−2.68838	−	6.92859i	−0.372811	−	0.960823i
$53$	3.89042	+	6.73840i	0.534390	+	0.925590i	0.999193	+	0.0401759i	$0.0127918\pi$
$53$	3.89042	+	6.73840i	0.534390	+	0.925590i	−0.464803	+	0.885414i	$0.653875\pi$
$54$	−11.0043	−	2.94859i	−1.49750	−	0.401253i
$55$	−16.8946	−	9.75412i	−2.27807	−	1.31525i
$56$		0			0
$57$	−0.753475	−	0.753475i	−0.0998002	−	0.0998002i
$58$	−3.80821	−	3.80821i	−0.500042	−	0.500042i
$59$	−0.919907	+	0.246488i	−0.119762	+	0.0320901i	−0.318202	−	0.948023i	$-0.603079\pi$
$59$	−0.919907	+	0.246488i	−0.119762	+	0.0320901i	0.198440	+	0.980113i	$0.436412\pi$
$60$	−9.43079	−	2.52697i	−1.21751	−	0.326231i
$61$			1.08909i			0.139443i	0.997566	+	0.0697217i	$0.0222111\pi$
$61$			1.08909i			0.139443i	−0.997566	+	0.0697217i	$0.977789\pi$
$62$	−1.11320	+	1.92811i	−0.141376	+	0.244870i
$63$		0			0
$64$			8.48212i			1.06026i
$65$	4.77256	−	10.8244i	0.591963	−	1.34260i
$66$	−14.9811	+	8.64936i	−1.84405	+	1.06466i
$67$	−3.81608	−	3.81608i	−0.466208	−	0.466208i	0.434476	−	0.900684i	$-0.356934\pi$
$67$	−3.81608	−	3.81608i	−0.466208	−	0.466208i	−0.900684	+	0.434476i	$0.856934\pi$
$68$	−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	$0.0401419\pi$
$72$	0.0799043	−	0.0799043i	0.00941681	−	0.00941681i
$73$	1.59300	−	5.94515i	0.186446	−	0.695827i	−0.807870	−	0.589361i	$-0.799380\pi$
$73$	1.59300	−	5.94515i	0.186446	−	0.695827i	0.994316	−	0.106466i	$-0.0339537\pi$
$74$	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
$79$	−6.08299	+	10.5361i	−0.684390	+	1.18540i	0.289238	+	0.957257i	$0.406598\pi$
$79$	−6.08299	+	10.5361i	−0.684390	+	1.18540i	−0.973628	+	0.228141i	$0.926735\pi$
$80$	−8.98724	+	8.98724i	−1.00480	+	1.00480i
$81$	−5.41404			−0.601560
$82$	5.81448			0.642102
$83$	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
$86$	2.10373	+	7.85121i	0.226851	+	0.846618i
$87$	−3.34126	−	1.92908i	−0.358220	−	0.206819i
$88$		−	0.733685i		−	0.0782111i
$89$	−1.05715	+	3.94532i	−0.112057	+	0.418203i	−0.999050	−	0.0435803i	$-0.986124\pi$
$89$	−1.05715	+	3.94532i	−0.112057	+	0.418203i	0.886993	+	0.461783i	$0.152790\pi$
$90$	6.05511			0.638265
$91$		0			0
$92$	−9.37170			−0.977067
$93$	−0.412802	+	1.54060i	−0.0428055	+	0.159752i
$94$			14.8297i			1.52957i
$95$	2.09724	+	1.21084i	0.215172	+	0.124230i
$96$	3.00919	+	11.2305i	0.307125	+	1.14620i
$97$	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
$100$	11.8828			1.18828
$101$	17.1752			1.70899			0.854496	−	0.519458i	$-0.173866\pi$
$101$	17.1752			1.70899			0.854496	+	0.519458i	$0.173866\pi$
$102$	−1.29314	+	1.29314i	−0.128040	+	0.128040i
$103$	−7.19481	+	12.4618i	−0.708926	+	1.22790i	0.256330	+	0.966589i	$0.417487\pi$
$103$	−7.19481	+	12.4618i	−0.708926	+	1.22790i	−0.965256	+	0.261306i	$0.915847\pi$
$104$	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	0.780693	−	0.624915i	$-0.214866\pi$
$107$	−1.56036	−	2.70262i	−0.150846	−	0.261272i	−0.931539	+	0.363643i	$0.881533\pi$
$108$	5.82622	−	10.0913i	0.560628	−	0.971036i
$109$	2.45900	−	9.17711i	0.235529	−	0.879008i	−0.742380	−	0.669979i	$-0.766303\pi$
$109$	2.45900	−	9.17711i	0.235529	−	0.879008i	0.977909	−	0.209029i	$-0.0670302\pi$
$110$	27.7992	−	27.7992i	2.65055	−	2.65055i
$111$	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
$115$	−10.5483	−	10.5483i	−0.983633	−	0.983633i
$116$	4.77050	−	2.75425i	0.442930	−	0.255726i
$117$	2.57352	+	2.06866i	0.237922	+	0.191247i
$118$		−	1.91924i		−	0.176680i
$119$		0			0
$120$	0.292243	−	0.506181i	0.0266781	−	0.0462077i
$121$		−	24.3529i		−	2.21390i
$122$	−2.12000	−	0.568052i	−0.191936	−	0.0514290i
$123$	4.02345	−	1.07808i	0.362782	−	0.0972071i
$124$	−1.61022	−	1.61022i	−0.144602	−	0.144602i
$125$	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	$0.747980\pi$
$128$	−0.953075	−	0.255376i	−0.0842407	−	0.0225722i
$129$	2.91143	+	5.04275i	0.256337	+	0.443989i
$130$	18.5812	+	14.9360i	1.62968	+	1.30997i
$131$	−15.1645	−	8.75520i	−1.32492	−	0.764946i	−0.340415	−	0.940275i	$-0.610568\pi$
$131$	−15.1645	−	8.75520i	−1.32492	−	0.764946i	−0.984510	+	0.175329i	$0.943901\pi$
$132$	−4.57939	−	17.0905i	−0.398585	−	1.48754i
$133$		0			0
$134$	9.41872	−	5.43790i	0.813653	−	0.469763i
$135$	17.9159	−	4.80056i	1.54196	−	0.413166i
$136$	−0.0200748	−	0.0749203i	−0.00172140	−	0.00642437i
$137$	3.79415	+	14.1600i	0.324156	+	1.20977i	0.915157	+	0.403097i	$0.132066\pi$
$137$	3.79415	+	14.1600i	0.324156	+	1.20977i	−0.591001	+	0.806671i	$0.701267\pi$
$138$	−12.7772	+	3.42365i	−1.08767	+	0.291440i
$139$	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
$142$	3.97862	+	2.29706i	0.333878	+	0.192765i
$143$	21.3123	−	2.31784i	1.78223	−	0.193827i
$144$	−1.77376	−	3.07224i	−0.147813	−	0.256020i
$145$	8.46946	+	2.26939i	0.703351	+	0.188462i
$146$	10.7418	+	6.20180i	0.889001	+	0.513265i
$147$		0			0
$148$	3.68974	+	3.68974i	0.303295	+	0.303295i
$149$	10.1485	+	10.1485i	0.831400	+	0.831400i	0.987708	−	0.156308i	$-0.0499593\pi$
$149$	10.1485	+	10.1485i	0.831400	+	0.831400i	−0.156308	+	0.987708i	$0.549959\pi$
$150$	16.2009	−	4.34101i	1.32279	−	0.354442i
$151$	−22.9711	−	6.15509i	−1.86936	−	0.500894i	−0.999977	−	0.00676075i	$-0.997848\pi$
$151$	−22.9711	−	6.15509i	−1.86936	−	0.500894i	−0.869386	−	0.494134i	$-0.835485\pi$
$152$			0.0910769i			0.00738732i
$153$	0.287817	−	0.498514i	0.0232687	−	0.0403025i
$154$		0			0
$155$		−	3.62475i		−	0.291147i
$156$	10.0027	−	3.88117i	0.800857	−	0.310742i
$157$	−6.58929	+	3.80433i	−0.525882	+	0.303618i	−0.739338	−	0.673334i	$-0.764861\pi$
$157$	−6.58929	+	3.80433i	−0.525882	+	0.303618i	0.213456	+	0.976953i	$0.431528\pi$
$158$	−17.3365	−	17.3365i	−1.37922	−	1.37922i
$159$	−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
$163$	−1.81864	+	1.81864i	−0.142447	+	0.142447i	−0.774734	−	0.632287i	$-0.782116\pi$
$163$	−1.81864	+	1.81864i	−0.142447	+	0.142447i	0.632287	+	0.774734i	$0.282116\pi$
$164$	−1.53923	+	5.74450i	−0.120194	+	0.448570i
$165$	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
$170$	2.07808	−	3.59935i	0.159382	−	0.276057i
$171$	−0.477952	+	0.477952i	−0.0365499	+	0.0365499i
$172$	−8.31363			−0.633908
$173$	14.0503			1.06823			0.534114	−	0.845412i	$-0.320645\pi$
$173$	14.0503			1.06823			0.534114	+	0.845412i	$0.320645\pi$
$174$	5.49785	−	5.49785i	0.416791	−	0.416791i
$175$		0			0
$176$	−22.2481	−	5.96136i	−1.67701	−	0.449354i
$177$	−0.355852	−	1.32806i	−0.0267474	−	0.0998228i
$178$	−7.12850	−	4.11564i	−0.534303	−	0.308480i
$179$		−	14.9624i		−	1.11834i	−0.829053	−	0.559170i	$-0.811120\pi$
$179$		−	14.9624i		−	1.11834i	0.829053	−	0.559170i	$-0.188880\pi$
$180$	−1.60294	+	5.98224i	−0.119476	+	0.445890i
$181$	−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
$184$	0.145206	−	0.541917i	0.0107047	−	0.0399506i
$185$			8.30596i			0.610666i
$186$	−2.78359	−	1.60710i	−0.204102	−	0.117839i
$187$	−0.967315	−	3.61007i	−0.0707371	−	0.263994i
$188$	−14.6513	−	3.92580i	−1.06855	−	0.286318i
$189$		0			0
$190$	−3.45089	+	3.45089i	−0.250354	+	0.250354i
$191$	−17.1549			−1.24129			−0.620643	−	0.784093i	$-0.713128\pi$
$191$	−17.1549			−1.24129			−0.620643	+	0.784093i	$0.713128\pi$
$192$	−12.2455			−0.883743
$193$	−4.33644	+	4.33644i	−0.312144	+	0.312144i	−0.845740	−	0.533596i	$-0.820840\pi$
$193$	−4.33644	+	4.33644i	−0.312144	+	0.312144i	0.533596	+	0.845740i	$0.320840\pi$
$194$	−8.78120	+	15.2095i	−0.630453	+	1.09198i
$195$	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	−0.978217	−	0.207586i	$-0.933439\pi$
$199$	−4.36369	+	7.55813i	−0.309334	+	0.535782i	0.668883	+	0.743368i	$0.266773\pi$
$200$	−0.184114	+	0.687122i	−0.0130188	+	0.0485869i
$201$	5.50921	−	5.50921i	0.388590	−	0.388590i
$202$	−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
$206$	−20.5052	−	20.5052i	−1.42866	−	1.42866i
$207$	3.60587	−	2.08185i	0.250625	−	0.144699i
$208$	2.13513	−	13.8030i	0.148044	−	0.957065i
$209$			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	$0.288233\pi$
$212$		−	16.0381i		−	1.10150i
$213$	3.17899	+	0.851808i	0.217821	+	0.0583649i
$214$	6.07473	−	1.62772i	0.415260	−	0.111269i
$215$	−9.35739	−	9.35739i	−0.638168	−	0.638168i
$216$	0.493256	+	0.493256i	0.0335618	+	0.0335618i
$217$		0			0
$218$	16.5814	+	9.57329i	1.12304	+	0.648385i
$219$	8.58292	+	2.29979i	0.579980	+	0.155405i
$220$	20.1055	+	34.8237i	1.35551	+	2.34782i
$221$	2.11289	−	0.819827i	0.142128	−	0.0551476i
$222$	6.37847	+	3.68261i	0.428095	+	0.247161i
$223$	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
$226$	−5.21997	+	1.39869i	−0.347227	+	0.0930392i
$227$	−3.68960	−	13.7698i	−0.244888	−	0.913933i	−0.973440	−	0.228943i	$-0.926473\pi$
$227$	−3.68960	−	13.7698i	−0.244888	−	0.913933i	0.728552	−	0.684990i	$-0.240194\pi$
$228$	0.568469	+	2.12156i	0.0376478	+	0.140503i
$229$	−11.0227	+	2.95351i	−0.728398	+	0.195174i	−0.603916	−	0.797048i	$-0.706394\pi$
$229$	−11.0227	+	2.95351i	−0.728398	+	0.195174i	−0.124482	+	0.992222i	$0.539727\pi$
$230$	26.0349	−	15.0313i	1.71669	−	0.991133i
$231$		0			0
$232$	0.0853493	+	0.318528i	0.00560346	+	0.0209124i
$233$	−18.9544	−	10.9433i	−1.24175	−	0.716922i	−0.272297	−	0.962213i	$-0.587783\pi$
$233$	−18.9544	−	10.9433i	−1.24175	−	0.716922i	−0.969450	+	0.245291i	$0.921117\pi$
$234$	−5.36911	+	3.93058i	−0.350990	+	0.256950i
$235$	−12.0720	−	20.9094i	−0.787492	−	1.36398i
$236$	1.89614	+	0.508069i	0.123428	+	0.0330725i
$237$	−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	$0.694534\pi$
$240$	−12.9747	−	12.9747i	−0.837516	−	0.837516i
$241$	15.0798	−	4.04063i	0.971377	−	0.260280i	0.261968	−	0.965077i	$-0.415629\pi$
$241$	15.0798	−	4.04063i	0.971377	−	0.260280i	0.709409	+	0.704797i	$0.248962\pi$
$242$	47.4050	+	12.7021i	3.04731	+	0.816523i
$243$			9.14326i			0.586541i
$244$	1.12243	−	1.94411i	0.0718563	−	0.124459i
$245$		0			0
$246$			8.39427i			0.535199i
$247$	−2.64563	+	0.287728i	−0.168338	+	0.0183077i
$248$	0.118059	−	0.0681616i	0.00749677	−	0.00432826i
$249$	5.18502	+	5.18502i	0.328587	+	0.328587i
$250$	−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
$254$	8.11563	−	8.11563i	0.509220	−	0.509220i
$255$	0.770607	−	2.87595i	0.0482573	−	0.180099i
$256$	−7.48790	+	12.9694i	−0.467994	+	0.810589i
$257$	−7.83278	−	13.5668i	−0.488596	−	0.846273i	0.511318	−	0.859391i	$-0.329157\pi$
$257$	−7.83278	−	13.5668i	−0.488596	−	0.846273i	−0.999914	+	0.0131189i	$0.995824\pi$
$258$	−11.3347	+	3.03712i	−0.705666	+	0.189083i
$259$		0			0
$260$	−19.6751	+	14.4036i	−1.22020	+	0.893276i
$261$	−1.22367	+	2.11946i	−0.0757434	+	0.131191i
$262$	24.9523	−	24.9523i	1.54156	−	1.54156i
$263$	−23.9108			−1.47441			−0.737203	−	0.675671i	$-0.763854\pi$
$263$	−23.9108			−1.47441			−0.737203	+	0.675671i	$0.763854\pi$
$264$	1.05921			0.0651899
$265$	18.0516	−	18.0516i	1.10890	−	1.10890i
$266$		0			0
$267$	−5.69580	−	1.52618i	−0.348577	−	0.0934010i
$268$	2.87909	+	10.7449i	0.175868	+	0.656350i
$269$	−11.7207	−	6.76695i	−0.714624	−	0.412588i	0.0981467	−	0.995172i	$-0.468709\pi$
$269$	−11.7207	−	6.76695i	−0.714624	−	0.412588i	−0.812771	+	0.582584i	$0.802042\pi$
$270$			37.3787i			2.27480i
$271$	5.60453	−	20.9164i	0.340451	−	1.27058i	−0.557387	−	0.830253i	$-0.688196\pi$
$271$	5.60453	−	20.9164i	0.340451	−	1.27058i	0.897838	−	0.440327i	$-0.145137\pi$
$272$	−2.43498			−0.147642
$273$		0			0
$274$	−29.5425			−1.78473
$275$	−8.87160	+	33.1093i	−0.534978	+	1.99656i
$276$		−	13.5298i		−	0.814397i
$277$	18.5473	+	10.7083i	1.11440	+	0.643399i	0.939965	−	0.341270i	$-0.110857\pi$
$277$	18.5473	+	10.7083i	1.11440	+	0.643399i	0.174434	+	0.984669i	$0.444190\pi$
$278$	1.86981	+	6.97821i	0.112143	+	0.418525i
$279$	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	$0.238252\pi$
$282$	−21.4095			−1.27492
$283$	−18.4612			−1.09741			−0.548703	−	0.836018i	$-0.684878\pi$
$283$	−18.4612			−1.09741			−0.548703	+	0.836018i	$0.684878\pi$
$284$	−3.32265	+	3.32265i	−0.197163	+	0.197163i
$285$	−1.74807	+	3.02775i	−0.103547	+	0.179348i
$286$	−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
$291$	−3.25629	+	12.1527i	−0.190887	+	0.712401i
$292$	−8.97079	+	8.97079i	−0.524976	+	0.524976i
$293$	−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
$297$	23.7677	+	23.7677i	1.37914	+	1.37914i
$298$	−25.0483	+	14.4616i	−1.45101	+	0.837739i
$299$	16.2005	+	2.50599i	0.936900	+	0.144925i
$300$			17.1551i			0.990448i
$301$		0			0
$302$	23.9628	−	41.5048i	1.37890	−	2.38833i
$303$			24.7955i			1.42447i
$304$	2.76179	+	0.740021i	0.158400	+	0.0424431i
$305$	3.45154	−	0.924836i	0.197634	−	0.0529560i
$306$	0.820277	+	0.820277i	0.0468921	+	0.0468921i
$307$	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
$310$	7.05587	+	1.89061i	0.400746	+	0.107380i
$311$	−9.18303	−	15.9055i	−0.520722	−	0.901916i	−0.999710	−	0.0240949i	$-0.992330\pi$
$311$	−9.18303	−	15.9055i	−0.520722	−	0.901916i	0.478988	−	0.877821i	$-0.341004\pi$
$312$	0.0694448	+	0.638540i	0.00393154	+	0.0361502i
$313$	−7.78607	−	4.49529i	−0.440095	−	0.254089i	0.263543	−	0.964648i	$-0.415109\pi$
$313$	−7.78607	−	4.49529i	−0.440095	−	0.254089i	−0.703638	+	0.710559i	$0.748442\pi$
$314$	−3.96856	−	14.8109i	−0.223959	−	0.835825i
$315$		0			0
$316$	21.7172	−	12.5385i	1.22169	−	0.705343i
$317$	−13.9161	+	3.72880i	−0.781605	+	0.209430i	−0.627492	−	0.778623i	$-0.715919\pi$
$317$	−13.9161	+	3.72880i	−0.781605	+	0.209430i	−0.154113	+	0.988053i	$0.549252\pi$
$318$	−5.85900	−	21.8661i	−0.328556	−	1.22619i
$319$	4.11259	+	15.3484i	0.230261	+	0.859346i
$320$	26.8815	−	7.20287i	1.50272	−	0.402653i
$321$	3.90173	−	2.25267i	0.217773	−	0.125732i
$322$		0			0
$323$	0.120079	+	0.448141i	0.00668137	+	0.0249352i
$324$	9.66448	+	5.57979i	0.536916	+	0.309988i
$325$	−20.5414	−	3.17746i	−1.13943	−	0.176254i
$326$	−2.59156	−	4.48871i	−0.143533	−	0.248607i
$327$	13.2489	+	3.55002i	0.732663	+	0.196317i
$328$	−0.308326	−	0.178012i	−0.0170244	−	0.00982906i
$329$		0			0
$330$	40.1333	+	40.1333i	2.20926	+	2.20926i
$331$	5.78697	+	5.78697i	0.318081	+	0.318081i	0.848030	−	0.529949i	$-0.177789\pi$
$331$	5.78697	+	5.78697i	0.318081	+	0.318081i	−0.529949	+	0.848030i	$0.677789\pi$
$332$	−10.1126	+	2.70967i	−0.555001	+	0.148712i
$333$	−2.23932	−	0.600024i	−0.122714	−	0.0328811i
$334$			6.85650i			0.375171i
$335$	−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	$0.985792\pi$
$338$	−26.1716	−	1.18217i	−1.42355	−	0.0643017i
$339$	−3.35273	+	1.93570i	−0.182095	+	0.105133i
$340$	3.00591	+	3.00591i	0.163018	+	0.163018i
$341$	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
$345$	15.2284	−	15.2284i	0.819870	−	0.819870i
$346$	−7.32845	+	27.3501i	−0.393980	+	1.47035i
$347$	4.81567	−	8.34098i	0.258519	−	0.447768i	−0.707327	−	0.706887i	$-0.750099\pi$
$347$	4.81567	−	8.34098i	0.258519	−	0.447768i	0.965845	+	0.259119i	$0.0834323\pi$
$348$	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
$352$	23.9422	−	41.4691i	1.27612	−	2.21031i
$353$	−11.3032	+	11.3032i	−0.601610	+	0.601610i	−0.940740	−	0.339130i	$-0.889867\pi$
$353$	−11.3032	+	11.3032i	−0.601610	+	0.601610i	0.339130	+	0.940740i	$0.389867\pi$
$354$	2.77078			0.147265
$355$	−7.47960			−0.396976
$356$	5.95319	−	5.95319i	0.315519	−	0.315519i
$357$		0			0
$358$	29.1255	+	7.80415i	1.53933	+	0.412462i
$359$	−1.48737	−	5.55095i	−0.0785005	−	0.292968i	0.915504	−	0.402309i	$-0.131792\pi$
$359$	−1.48737	−	5.55095i	−0.0785005	−	0.292968i	−0.994004	+	0.109342i	$0.965126\pi$
$360$	−0.321086	−	0.185379i	−0.0169227	−	0.00977033i
$361$			18.4552i			0.971327i
$362$	8.05376	−	30.0570i	0.423296	−	1.57976i
$363$	35.1580			1.84531
$364$		0			0
$365$	−20.1941			−1.05701
$366$	0.820088	−	3.06061i	0.0428667	−	0.159981i
$367$			25.4610i			1.32905i	0.747264	+	0.664527i	$0.231367\pi$
$367$			25.4610i			1.32905i	−0.747264	+	0.664527i	$0.768633\pi$
$368$	−15.2531	−	8.80639i	−0.795123	−	0.459065i
$369$	−0.683858	−	2.55219i	−0.0356002	−	0.132862i
$370$	−16.1682	−	4.33226i	−0.840546	−	0.225224i
$371$		0			0
$372$	2.32465	−	2.32465i	0.120527	−	0.120527i
$373$	18.7156			0.969055			0.484528	−	0.874776i	$-0.338991\pi$
$373$	18.7156			0.969055			0.484528	+	0.874776i	$0.338991\pi$
$374$	7.53183			0.389462
$375$	−2.56199	+	2.56199i	−0.132301	+	0.132301i
$376$	0.454017	−	0.786380i	0.0234141	−	0.0405545i
$377$	−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
$382$	8.94774	−	33.3934i	0.457806	−	1.70856i
$383$	−22.9487	+	22.9487i	−1.17262	+	1.17262i	−0.191039	+	0.981582i	$0.561186\pi$
$383$	−22.9487	+	22.9487i	−1.17262	+	1.17262i	−0.981582	+	0.191039i	$0.938814\pi$
$384$	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
$388$	−12.7018	−	12.7018i	−0.644838	−	0.644838i
$389$	−6.03084	+	3.48191i	−0.305776	+	0.176540i	−0.645035	−	0.764153i	$-0.723157\pi$
$389$	−6.03084	+	3.48191i	−0.305776	+	0.176540i	0.339259	+	0.940693i	$0.389824\pi$
$390$	−21.5629	+	26.8254i	−1.09188	+	1.35836i
$391$		−	2.85792i		−	0.144531i
$392$		0			0
$393$	12.6398	−	21.8927i	0.637591	−	1.10434i
$394$			51.7217i			2.60570i
$395$	38.5564	+	10.3312i	1.93998	+	0.519817i
$396$	−10.8410	+	2.90485i	−0.544783	+	0.145974i
$397$	10.5642	+	10.5642i	0.530203	+	0.530203i	0.920633	−	0.390430i	$-0.127674\pi$
$397$	10.5642	+	10.5642i	0.530203	+	0.530203i	−0.390430	+	0.920633i	$0.627674\pi$
$398$	−12.4365	−	12.4365i	−0.623384	−	0.623384i
$399$		0			0
$400$	19.3401	+	11.1660i	0.967007	+	0.558302i
$401$	−23.3513	−	6.25695i	−1.16611	−	0.312457i	−0.376704	−	0.926334i	$-0.622943\pi$
$401$	−23.3513	−	6.25695i	−1.16611	−	0.312457i	−0.789402	+	0.613877i	$0.789609\pi$
$402$	7.85061	+	13.5977i	0.391553	+	0.678190i
$403$	2.35295	+	3.21409i	0.117209	+	0.160105i
$404$	−30.6590	−	17.7010i	−1.52534	−	0.880657i
$405$	4.59751	+	17.1582i	0.228452	+	0.852595i
$406$		0			0
$407$	−13.0355	+	7.52605i	−0.646146	+	0.373052i
$408$	0.108161	−	0.0289818i	0.00535479	−	0.00143481i
$409$	−9.71416	−	36.2537i	−0.480334	−	1.79263i	−0.600209	−	0.799843i	$-0.704916\pi$
$409$	−9.71416	−	36.2537i	−0.480334	−	1.79263i	0.119875	−	0.992789i	$-0.461751\pi$
$410$	−4.93756	−	18.4272i	−0.243849	−	0.910056i
$411$	−20.4425	+	5.47756i	−1.00836	+	0.270188i
$412$	25.6866	−	14.8302i	1.26549	−	0.730630i
$413$		0			0
$414$	2.17172	+	8.10499i	0.106734	+	0.398338i
$415$	−14.4321	−	8.33236i	−0.708443	−	0.409020i
$416$	26.5692	+	11.7146i	1.30266	+	0.574356i
$417$	2.58770	+	4.48203i	0.126720	+	0.219486i
$418$	−8.54273	−	2.28902i	−0.417839	−	0.111960i
$419$	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	$0.722969\pi$
$422$	−15.4290	−	15.4290i	−0.751072	−	0.751072i
$423$	6.50934	−	1.74417i	0.316495	−	0.0848045i
$424$	0.927399	+	0.248496i	0.0450385	+	0.0120680i
$425$			3.62370i			0.175775i
$426$	−3.31623	+	5.74387i	−0.160672	+	0.278292i
$427$		0			0
$428$			6.43252i			0.310927i
$429$	3.34623	+	30.7683i	0.161557	+	1.48551i
$430$	23.0956	−	13.3342i	1.11377	−	0.643034i
$431$	−10.8313	−	10.8313i	−0.521724	−	0.521724i	0.396368	−	0.918092i	$-0.370271\pi$
$431$	−10.8313	−	10.8313i	−0.521724	−	0.521724i	−0.918092	+	0.396368i	$0.870271\pi$
$432$	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
$436$	−13.8476	+	13.8476i	−0.663179	+	0.663179i
$437$	−0.868559	+	3.24151i	−0.0415488	+	0.155062i
$438$	−8.95345	+	15.5078i	−0.427812	+	0.740993i
$439$	3.88598	+	6.73072i	0.185468	+	0.321240i	0.943734	−	0.330705i	$-0.107287\pi$
$439$	3.88598	+	6.73072i	0.185468	+	0.321240i	−0.758266	+	0.651945i	$0.773953\pi$
$440$	−2.32519	+	0.623033i	−0.110849	+	0.0297019i
$441$		0			0
$442$	0.493808	+	4.54053i	0.0234881	+	0.215971i
$443$	−3.14950	+	5.45509i	−0.149637	+	0.259179i	−0.931093	−	0.364781i	$-0.881144\pi$
$443$	−3.14950	+	5.45509i	−0.149637	+	0.259179i	0.781456	+	0.623960i	$0.214477\pi$
$444$	−5.32682	+	5.32682i	−0.252800	+	0.252800i
$445$	13.4012			0.635278
$446$	−15.7092			−0.743854
$447$	−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	$0.466947\pi$
$450$	−2.75363	−	10.2767i	−0.129808	−	0.484448i
$451$	−14.8568	−	8.57758i	−0.699579	−	0.403902i
$452$		−	5.52741i		−	0.259987i
$453$	8.88602	−	33.1631i	0.417501	−	1.55814i
$454$	28.7285			1.34829
$455$		0			0
$456$	−0.131486			−0.00615742
$457$	4.02470	−	15.0204i	0.188267	−	0.702623i	−0.805640	−	0.592405i	$-0.798178\pi$
$457$	4.02470	−	15.0204i	0.188267	−	0.702623i	0.993907	−	0.110218i	$-0.0351549\pi$
$458$		−	22.9970i		−	1.07458i
$459$	3.07737	+	1.77672i	0.143639	+	0.0829302i
$460$	7.95829	+	29.7008i	0.371057	+	1.38480i
$461$	−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	$0.293156\pi$
$464$	10.3524			0.480600
$465$	5.23300			0.242674
$466$	31.1885	−	31.1885i	1.44478	−	1.44478i
$467$	4.08246	−	7.07102i	0.188913	−	0.327208i	−0.755975	−	0.654601i	$-0.772837\pi$
$467$	4.08246	−	7.07102i	0.188913	−	0.327208i	0.944888	+	0.327393i	$0.106170\pi$
$468$	−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
$473$	6.20688	−	23.1644i	0.285393	−	1.06510i
$474$	25.0284	−	25.0284i	1.14959	−	1.14959i
$475$	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
$479$	25.8476	+	25.8476i	1.18101	+	1.18101i	0.979484	+	0.201523i	$0.0645890\pi$
$479$	25.8476	+	25.8476i	1.18101	+	1.18101i	0.201523	+	0.979484i	$0.435411\pi$
$480$	33.0362	−	19.0735i	1.50789	−	0.870580i
$481$	−5.39169	−	7.36496i	−0.245840	−	0.335813i
$482$			31.4616i			1.43304i
$483$		0			0
$484$	−25.0985	+	43.4719i	−1.14084	+	1.97599i
$485$		−	28.5930i		−	1.29834i
$486$	−17.7981	−	4.76899i	−0.807339	−	0.216326i
$487$	−16.2718	+	4.36001i	−0.737344	+	0.197571i	−0.607897	−	0.794016i	$-0.707987\pi$
$487$	−16.2718	+	4.36001i	−0.737344	+	0.197571i	−0.129447	+	0.991586i	$0.541320\pi$
$488$	0.0950266	+	0.0950266i	0.00430165	+	0.00430165i
$489$	−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	$0.595748\pi$
$492$	−8.29325	−	2.22217i	−0.373889	−	0.100183i
$493$	0.839916	+	1.45478i	0.0378279	+	0.0655199i
$494$	0.819837	−	5.30002i	0.0368862	−	0.238459i
$495$	−15.4717	−	8.93256i	−0.695399	−	0.401489i
$496$	−1.10766	−	4.13383i	−0.0497352	−	0.185614i
$497$		0			0
$498$	−12.7975	+	7.38863i	−0.573469	+	0.331093i
$499$	2.84635	−	0.762677i	0.127420	−	0.0341421i	−0.194545	−	0.980894i	$-0.562323\pi$
$499$	2.84635	−	0.762677i	0.127420	−	0.0341421i	0.321966	+	0.946751i	$0.395656\pi$
$500$	−1.33888	−	4.99678i	−0.0598767	−	0.223463i
$501$	1.27128	+	4.74449i	0.0567968	+	0.211968i
$502$	8.98127	−	2.40653i	0.400854	−	0.107408i
$503$	−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
$506$	47.1807	+	27.2398i	2.09744	+	1.21096i
$507$	−18.3291	+	4.03452i	−0.814025	+	0.179179i
$508$	5.86956	+	10.1664i	0.260419	+	0.451060i
$509$	18.6168	+	4.98837i	0.825177	+	0.221106i	0.646609	−	0.762822i	$-0.276187\pi$
$509$	18.6168	+	4.98837i	0.825177	+	0.221106i	0.178569	+	0.983927i	$0.442853\pi$
$510$	5.19632	+	3.00010i	0.230097	+	0.132847i
$511$		0			0
$512$	−22.7359	−	22.7359i	−1.00479	−	1.00479i
$513$	−2.95044	−	2.95044i	−0.130265	−	0.130265i
$514$	30.4943	−	8.17093i	1.34505	−	0.360404i
$515$	45.6035	+	12.2194i	2.00953	+	0.538452i
$516$		−	12.0023i		−	0.528370i
$517$	21.8770	−	37.8921i	0.962149	−	1.66649i
$518$		0			0
$519$			20.2843i			0.890381i
$520$	−0.528039	−	1.36088i	−0.0231560	−	0.0596786i
$521$	−9.05428	+	5.22749i	−0.396675	+	0.229020i	−0.685048	−	0.728498i	$-0.740219\pi$
$521$	−9.05428	+	5.22749i	−0.396675	+	0.229020i	0.288373	+	0.957518i	$0.406886\pi$
$522$	−3.48746	−	3.48746i	−0.152642	−	0.152642i
$523$	−15.9637	+	9.21666i	−0.698045	+	0.403016i	−0.806619	−	0.591072i	$-0.798705\pi$
$523$	−15.9637	+	9.21666i	−0.698045	+	0.403016i	0.108574	+	0.994088i	$0.465372\pi$
$524$	18.0465	+	31.2574i	0.788365	+	1.36549i
$525$		0			0
$526$	12.4715	−	46.5444i	0.543785	−	2.02943i
$527$	0.491040	−	0.491040i	0.0213900	−	0.0213900i
$528$	8.60632	−	32.1192i	0.374542	−	1.39781i
$529$	−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
$534$	5.94169	−	10.2913i	0.257122	−	0.445348i
$535$	−7.24010	+	7.24010i	−0.313017	+	0.313017i
$536$	−0.665931			−0.0287638
$537$	21.6010			0.932151
$538$	19.2858	−	19.2858i	0.831469	−	0.831469i
$539$		0			0
$540$	−36.9288	−	9.89505i	−1.58916	−	0.425815i
$541$	−10.8498	−	40.4921i	−0.466470	−	1.74089i	−0.651969	−	0.758246i	$-0.726057\pi$
$541$	−10.8498	−	40.4921i	−0.466470	−	1.74089i	0.185499	−	0.982644i	$-0.440610\pi$
$542$	37.7922	+	21.8193i	1.62331	+	0.937221i
$543$		−	22.2919i		−	0.956635i
$544$	1.31020	−	4.88972i	0.0561743	−	0.209645i
$545$	−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	$0.182264\pi$
$548$	7.82062	−	29.1870i	0.334080	−	1.24680i
$549$			0.997358i			0.0425662i
$550$	−59.8226	−	34.5386i	−2.55084	−	1.47273i
$551$	−0.510522	−	1.90529i	−0.0217490	−	0.0811683i
$552$	0.782357	+	0.209632i	0.0332993	+	0.00892253i
$553$		0			0
$554$	−30.5185	+	30.5185i	−1.29661	+	1.29661i
$555$	−11.9912			−0.508998
$556$	−7.38921			−0.313372
$557$	−30.1372	+	30.1372i	−1.27695	+	1.27695i	−0.334587	+	0.942365i	$0.608597\pi$
$557$	−30.1372	+	30.1372i	−1.27695	+	1.27695i	−0.942365	+	0.334587i	$0.891403\pi$
$558$	−1.01943	+	1.76571i	−0.0431561	+	0.0747486i
$559$	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	−0.139263	−	0.990255i	$-0.544473\pi$
$563$	18.6963	−	32.3829i	0.787955	−	1.36478i	0.927218	−	0.374523i	$-0.122193\pi$
$564$	5.66761	−	21.1518i	0.238650	−	0.890652i
$565$	6.22136	−	6.22136i	0.261735	−	0.261735i
$566$	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	$-0.440093\pi$
$569$	26.9875	−	15.5812i	1.13137	−	0.653199i	0.944280	+	0.329143i	$0.106760\pi$
$570$	−4.98199	−	4.98199i	−0.208673	−	0.208673i
$571$	16.5495	−	9.55483i	0.692573	−	0.399857i	−0.112002	−	0.993708i	$-0.535726\pi$
$571$	16.5495	−	9.55483i	0.692573	−	0.399857i	0.804575	+	0.593851i	$0.202393\pi$
$572$	−40.4330	−	17.8273i	−1.69059	−	0.745397i
$573$		−	24.7663i		−	1.03463i
$574$		0			0
$575$	−13.1055	+	22.6995i	−0.546539	+	0.946633i
$576$			7.76770i			0.323654i
$577$	−19.2526	−	5.15872i	−0.801497	−	0.214760i	−0.165256	−	0.986251i	$-0.552845\pi$
$577$	−19.2526	−	5.15872i	−0.801497	−	0.214760i	−0.636241	+	0.771490i	$0.719512\pi$
$578$	−32.3228	+	8.66086i	−1.34445	+	0.360244i
$579$	−6.26045	−	6.26045i	−0.260176	−	0.260176i
$580$	−12.7798	−	12.7798i	−0.530652	−	0.530652i
$581$		0			0
$582$	−21.9577	−	12.6773i	−0.910176	−	0.525490i
$583$	44.6871	+	11.9739i	1.85075	+	0.495907i
$584$	−0.379740	−	0.657728i	−0.0157137	−	0.0272170i
$585$	4.37058	−	9.91265i	0.180701	−	0.409838i
$586$	−21.6861	−	12.5205i	−0.895847	−	0.517217i
$587$	−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
$590$	−6.08244	+	1.62979i	−0.250410	+	0.0670972i
$591$	9.58986	+	35.7898i	0.394474	+	1.47220i
$592$	2.53815	+	9.47249i	0.104317	+	0.389317i
$593$	6.94560	−	1.86107i	0.285222	−	0.0764249i	−0.113372	−	0.993553i	$-0.536165\pi$
$593$	6.94560	−	1.86107i	0.285222	−	0.0764249i	0.398594	+	0.917128i	$0.369498\pi$
$594$	−58.6627	+	33.8689i	−2.40696	+	1.38966i
$595$		0			0
$596$	−7.65669	−	28.5752i	−0.313630	−	1.17048i
$597$	−10.9116	−	6.29979i	−0.446580	−	0.257833i
$598$	−13.3281	+	30.2285i	−0.545025	+	1.23614i
$599$	14.6877	+	25.4398i	0.600123	+	1.03944i	0.992802	+	0.119768i	$0.0382150\pi$
$599$	14.6877	+	25.4398i	0.600123	+	1.03944i	−0.392679	+	0.919676i	$0.628452\pi$
$600$	−0.991988	−	0.265802i	−0.0404977	−	0.0108513i
$601$	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
$604$	34.6617	+	34.6617i	1.41036	+	1.41036i
$605$	−77.1792	+	20.6801i	−3.13778	+	0.840766i
$606$	−48.2665	−	12.9330i	−1.96069	−	0.525366i
$607$			21.4872i			0.872140i	0.899913	+	0.436070i	$0.143630\pi$
$607$			21.4872i			0.872140i	−0.899913	+	0.436070i	$0.856370\pi$
$608$	−2.97210	+	5.14782i	−0.120534	+	0.208772i
$609$		0			0
$610$			7.20107i			0.291563i
$611$	24.2774	+	10.7041i	0.982157	+	0.433043i
$612$	−1.02755	+	0.593258i	−0.0415364	+	0.0239810i
$613$	20.2128	+	20.2128i	0.816389	+	0.816389i	0.985583	−	0.169194i	$-0.0541165\pi$
$613$	20.2128	+	20.2128i	0.816389	+	0.816389i	−0.169194	+	0.985583i	$0.554116\pi$
$614$	−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	$0.945119\pi$
$618$	29.6030	−	29.6030i	1.19081	−	1.19081i
$619$	1.16061	−	4.33146i	0.0466489	−	0.174096i	−0.938671	−	0.344814i	$-0.887942\pi$
$619$	1.16061	−	4.33146i	0.0466489	−	0.174096i	0.985320	+	0.170718i	$0.0546087\pi$
$620$	−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
$625$	−10.2952	+	17.8317i	−0.411806	+	0.713269i
$626$	12.8115	−	12.8115i	0.512052	−	0.512052i
$627$	−6.33573			−0.253025
$628$	15.6832			0.625827
$629$	−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	$0.648703\pi$
$632$	0.388544	+	1.45007i	0.0154555	+	0.0576806i
$633$	−13.5371	−	7.81567i	−0.538053	−	0.310645i
$634$		−	29.0337i		−	1.15307i
$635$	−4.83627	+	18.0492i	−0.191921	+	0.716260i
$636$	23.1539			0.918114
$637$		0			0
$638$	−32.0220			−1.26776
$639$	0.540328	−	2.01653i	0.0213750	−	0.0797727i
$640$			3.23734i			0.127967i
$641$	27.7522	+	16.0227i	1.09615	+	0.632860i	0.935206	−	0.354104i	$-0.115214\pi$
$641$	27.7522	+	16.0227i	1.09615	+	0.632860i	0.160940	+	0.986964i	$0.448547\pi$
$642$	2.34991	+	8.77000i	0.0927437	+	0.346124i
$643$	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
$646$	−0.934973			−0.0367860
$647$	−30.7013			−1.20699			−0.603496	−	0.797366i	$-0.706226\pi$
$647$	−30.7013			−1.20699			−0.603496	+	0.797366i	$0.706226\pi$
$648$	−0.472393	+	0.472393i	−0.0185573	+	0.0185573i
$649$	−2.83128	+	4.90392i	−0.111137	+	0.192496i
$650$	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	0.976232	−	0.216730i	$-0.0695392\pi$
$653$	7.67694	+	13.2969i	0.300422	+	0.520346i	−0.675810	+	0.737076i	$0.736206\pi$
$654$	−13.8208	+	23.9383i	−0.540436	+	0.936063i
$655$	−14.8696	+	55.4939i	−0.581001	+	2.16833i
$656$	−7.90320	+	7.90320i	−0.308568	+	0.308568i
$657$	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
$661$	5.84186	+	5.84186i	0.227222	+	0.227222i	0.811531	−	0.584309i	$-0.198634\pi$
$661$	5.84186	+	5.84186i	0.227222	+	0.227222i	−0.584309	+	0.811531i	$0.698634\pi$
$662$	−14.2832	+	8.24641i	−0.555132	+	0.320506i
$663$	1.18357	+	3.05035i	0.0459662	+	0.118466i
$664$		−	0.626743i		−	0.0243224i
$665$		0			0
$666$	2.33599	−	4.04605i	0.0905178	−	0.156781i
$667$			12.1506i			0.470474i
$668$	−6.77398	−	1.81508i	−0.262093	−	0.0702277i
$669$	−10.8703	+	2.91270i	−0.420271	+	0.112611i
$670$	−25.2320	−	25.2320i	−0.974797	−	0.974797i
$671$	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	$0.874134\pi$
$674$	−3.18911	−	0.854521i	−0.122840	−	0.0329149i
$675$	−16.2950	−	28.2237i	−0.627193	−	1.08633i
$676$	8.09619	−	25.5436i	0.311392	−	0.982447i
$677$	40.8799	+	23.6020i	1.57114	+	0.907099i	0.996029	+	0.0890246i	$0.0283750\pi$
$677$	40.8799	+	23.6020i	1.57114	+	0.907099i	0.575112	+	0.818074i	$0.304958\pi$
$678$	−2.01926	−	7.53599i	−0.0775493	−	0.289418i
$679$		0			0
$680$	−0.220390	+	0.127242i	−0.00845157	+	0.00487952i
$681$	19.8792	−	5.32663i	0.761774	−	0.204117i
$682$	3.42618	+	12.7867i	0.131195	+	0.489627i
$683$	−11.7625	−	43.8982i	−0.450079	−	1.67972i	−0.702166	−	0.712013i	$-0.747784\pi$
$683$	−11.7625	−	43.8982i	−0.450079	−	1.67972i	0.252087	−	0.967705i	$-0.418883\pi$
$684$	1.34577	−	0.360597i	0.0514567	−	0.0137878i
$685$	41.6538	−	24.0488i	1.59151	−	0.918858i
$686$		0			0
$687$	−4.26394	−	15.9132i	−0.162680	−	0.607128i
$688$	−13.5310	−	7.81214i	−0.515866	−	0.297835i
$689$	−4.28858	+	27.7245i	−0.163382	+	1.05622i
$690$	21.7004	+	37.5863i	0.826121	+	1.43088i
$691$	18.2526	+	4.89077i	0.694361	+	0.186054i	0.588703	−	0.808349i	$-0.299639\pi$
$691$	18.2526	+	4.89077i	0.694361	+	0.186054i	0.105658	+	0.994403i	$0.466305\pi$
$692$	−25.0810	−	14.4805i	−0.953435	−	0.550466i
$693$		0			0
$694$	13.7246	+	13.7246i	0.520980	+	0.520980i
$695$	−8.31690	−	8.31690i	−0.315478	−	0.315478i
$696$	−0.459854	+	0.123218i	−0.0174307	+	0.00467055i
$697$	−1.75180	−	0.469393i	−0.0663542	−	0.0177795i
$698$		−	59.3908i		−	2.24798i
$699$	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	$0.796431\pi$
$702$	−24.2638	−	33.1440i	−0.915779	−	1.25094i
$703$	1.61818	−	0.934256i	0.0610308	−	0.0352361i
$704$	35.6617	+	35.6617i	1.34405	+	1.34405i
$705$	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
$709$	−13.7245	+	13.7245i	−0.515433	+	0.515433i	−0.916186	−	0.400753i	$-0.868748\pi$
$709$	−13.7245	+	13.7245i	−0.515433	+	0.515433i	0.400753	+	0.916186i	$0.368748\pi$
$710$	3.90125	−	14.5597i	0.146411	−	0.546414i
$711$	−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
$716$	−15.4205	+	26.7090i	−0.576290	+	0.998163i
$717$	−5.47220	+	5.47220i	−0.204363	+	0.204363i
$718$	11.5812			0.432205
$719$	−4.47081			−0.166733			−0.0833665	−	0.996519i	$-0.526567\pi$
$719$	−4.47081			−0.166733			−0.0833665	+	0.996519i	$0.526567\pi$
$720$	−8.23028	+	8.23028i	−0.306724	+	0.306724i
$721$		0			0
$722$	−35.9246	−	9.62596i	−1.33697	−	0.358241i
$723$	5.83339	+	21.7705i	0.216946	+	0.809654i
$724$	27.5633	+	15.9137i	1.02438	+	0.591427i
$725$		−	15.4064i		−	0.572178i
$726$	−18.3379	+	68.4378i	−0.680582	+	2.53997i
$727$	−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
$730$	10.5329	−	39.3095i	0.389841	−	1.45491i
$731$		−	2.53526i		−	0.0937701i
$732$	2.80668	+	1.62044i	0.103738	+	0.0598931i
$733$	12.4133	+	46.3272i	0.458497	+	1.71114i	0.677597	+	0.735433i	$0.263021\pi$
$733$	12.4133	+	46.3272i	0.458497	+	1.71114i	−0.219100	+	0.975703i	$0.570312\pi$
$734$	−49.5619	−	13.2801i	−1.82936	−	0.490177i
$735$		0			0
$736$	25.8916	−	25.8916i	0.954376	−	0.954376i
$737$	−32.0882			−1.18198
$738$	5.32474			0.196007
$739$	−12.3488	+	12.3488i	−0.454258	+	0.454258i	−0.896765	−	0.442507i	$-0.854089\pi$
$739$	−12.3488	+	12.3488i	−0.454258	+	0.454258i	0.442507	+	0.896765i	$0.354089\pi$
$740$	8.56025	−	14.8268i	0.314681	−	0.545043i
$741$	−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
$746$	−9.76176	+	36.4314i	−0.357403	+	1.33385i
$747$	3.28901	−	3.28901i	0.120339	−	0.120339i
$748$	−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	$-0.634292\pi$
$751$	4.81931	−	2.78243i	0.175859	−	0.101532i	0.585346	+	0.810784i	$0.300959\pi$
$752$	−20.1570	−	20.1570i	−0.735050	−	0.735050i
$753$	5.76857	−	3.33049i	0.210219	−	0.121370i
$754$	−2.09945	−	19.3043i	−0.0764576	−	0.703021i
$755$			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	$0.283778\pi$
$758$		−	42.7934i		−	1.55433i
$759$	37.6982	+	10.1012i	1.36836	+	0.366651i
$760$	0.288641	−	0.0773410i	0.0104701	−	0.00280545i
$761$	−23.9987	−	23.9987i	−0.869953	−	0.869953i	0.122514	−	0.992467i	$-0.460904\pi$
$761$	−23.9987	−	23.9987i	−0.869953	−	0.869953i	−0.992467	+	0.122514i	$0.960904\pi$
$762$	11.7164	+	11.7164i	0.424441	+	0.424441i
$763$		0			0
$764$	30.6229	+	17.6801i	1.10790	+	0.639644i
$765$	−1.82430	−	0.488820i	−0.0659577	−	0.0176733i
$766$	−32.7018	−	56.6411i	−1.18156	−	2.04653i
$767$	−3.14193	−	1.38531i	−0.113449	−	0.0500206i
$768$	−18.7238	−	10.8102i	−0.675635	−	0.390078i
$769$	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
$772$	12.2101	−	3.27168i	0.439451	−	0.117750i
$773$	6.00148	+	22.3978i	0.215858	+	0.805594i	0.985863	+	0.167555i	$0.0535873\pi$
$773$	6.00148	+	22.3978i	0.215858	+	0.805594i	−0.770005	+	0.638038i	$0.779746\pi$
$774$	1.92654	+	7.18993i	0.0692479	+	0.258437i
$775$	−6.15190	+	1.64840i	−0.220983	+	0.0592122i
$776$	0.931285	−	0.537678i	0.0334312	−	0.0193015i
$777$		0			0
$778$	−3.63222	−	13.5556i	−0.130221	−	0.485993i
$779$	1.84427	+	1.06479i	0.0660778	+	0.0381500i
$780$	−20.7943	−	28.4047i	−0.744556	−	1.01705i
$781$	−6.77729	−	11.7386i	−0.242510	−	0.420040i
$782$	5.56318	+	1.49065i	0.198939	+	0.0533055i
$783$	−13.0836	−	7.55382i	−0.467570	−	0.269952i
$784$		0			0
$785$	17.6522	+	17.6522i	0.630033	+	0.630033i
$786$	36.0232	+	36.0232i	1.28491	+	1.28491i
$787$	−15.1886	+	4.06976i	−0.541414	+	0.145071i	−0.519154	−	0.854681i	$-0.673753\pi$
$787$	−15.1886	+	4.06976i	−0.541414	+	0.145071i	−0.0222599	+	0.999752i	$0.507086\pi$
$788$	−51.0992	−	13.6920i	−1.82033	−	0.487757i
$789$		−	34.5197i		−	1.22894i
$790$	−40.2209	+	69.6646i	−1.43099	+	2.47856i
$791$		0			0
$792$		−	0.671889i		−	0.0238745i
$793$	−2.46016	+	3.06057i	−0.0873628	+	0.108684i
$794$	−26.0742	+	15.0540i	−0.925340	+	0.534245i
$795$	26.0609	+	26.0609i	0.924284	+	0.924284i
$796$	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
$800$	−32.8292	+	32.8292i	−1.16069	+	1.16069i
$801$	−0.968105	+	3.61302i	−0.0342063	+	0.127660i
$802$	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
$807$	9.76935	−	16.9210i	0.343897	−	0.595648i
$808$	1.49859	−	1.49859i	0.0527202	−	0.0527202i
$809$	35.6805			1.25446			0.627229	−	0.778835i	$-0.284189\pi$
$809$	35.6805			1.25446			0.627229	+	0.778835i	$0.284189\pi$
$810$	−35.7977			−1.25780
$811$	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
$814$	−7.85095	−	29.3001i	−0.275176	−	1.02697i
$815$	7.30800	+	4.21928i	0.255988	+	0.147795i
$816$		−	3.51534i		−	0.123062i
$817$	−0.770499	+	2.87554i	−0.0269563	+	0.100602i
$818$	75.6376			2.64461
$819$		0			0
$820$	19.5125			0.681407
$821$	2.86268	−	10.6837i	0.0999084	−	0.372863i	−0.897809	−	0.440384i	$-0.854842\pi$
$821$	2.86268	−	10.6837i	0.0999084	−	0.372863i	0.997718	+	0.0675209i	$0.0215089\pi$
$822$		−	42.6501i		−	1.48759i
$823$	20.4465	+	11.8048i	0.712719	+	0.411488i	0.812067	−	0.583564i	$-0.198342\pi$
$823$	20.4465	+	11.8048i	0.712719	+	0.411488i	−0.0993482	+	0.995053i	$0.531676\pi$
$824$	0.459560	+	1.71510i	0.0160095	+	0.0597484i
$825$	−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	$0.258551\pi$
$828$	−8.58235			−0.298257
$829$	38.2127			1.32718			0.663591	−	0.748095i	$-0.269031\pi$
$829$	38.2127			1.32718			0.663591	+	0.748095i	$0.269031\pi$
$830$	23.7472	−	23.7472i	0.824277	−	0.824277i
$831$	−15.4594	+	26.7765i	−0.536280	+	0.928865i
$832$	−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
$837$	−1.61644	+	6.03263i	−0.0558722	+	0.208518i
$838$	−11.6025	+	11.6025i	−0.400802	+	0.400802i
$839$	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
$843$	1.26288	+	1.26288i	0.0434961	+	0.0434961i
$844$	19.3277	−	11.1589i	0.665288	−	0.384104i
$845$	37.8632	−	19.6379i	1.30253	−	0.675565i
$846$			13.5807i			0.466914i
$847$		0			0
$848$	15.0707	−	26.1031i	0.517528	−	0.896385i
$849$		−	26.6522i		−	0.914700i
$850$	−7.05382	−	1.89007i	−0.241944	−	0.0648288i
$851$	−11.1178	+	2.97901i	−0.381114	+	0.102119i
$852$	−4.79686	−	4.79686i	−0.164338	−	0.164338i
$853$	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
$856$	−0.371959	−	0.0996661i	−0.0127133	−	0.00340652i
$857$	14.7330	+	25.5183i	0.503270	+	0.871689i	0.999993	+	0.00377978i	$0.00120314\pi$
$857$	14.7330	+	25.5183i	0.503270	+	0.871689i	−0.496723	+	0.867909i	$0.665464\pi$
$858$	−61.6384	−	9.53458i	−2.10430	−	0.325505i
$859$	44.5926	+	25.7455i	1.52148	+	0.878426i	0.999678	+	0.0253585i	$0.00807272\pi$
$859$	44.5926	+	25.7455i	1.52148	+	0.878426i	0.521800	+	0.853068i	$0.325261\pi$
$860$	7.05980	+	26.3475i	0.240737	+	0.898443i
$861$		0			0
$862$	26.7334	−	15.4345i	0.910543	−	0.525702i
$863$	−31.1185	+	8.33816i	−1.05928	+	0.283834i	−0.746083	−	0.665852i	$-0.768068\pi$
$863$	−31.1185	+	8.33816i	−1.05928	+	0.283834i	−0.313201	+	0.949687i	$0.601401\pi$
$864$	11.7833	+	43.9760i	0.400877	+	1.49609i
$865$	−11.9313	−	44.5283i	−0.405677	−	1.51401i
$866$	23.9973	−	6.43005i	0.815461	−	0.218502i
$867$	−20.7606	+	11.9861i	−0.705066	+	0.407070i
$868$		0			0
$869$	18.7222	+	69.8721i	0.635106	+	2.37025i
$870$	−22.0925	−	12.7551i	−0.749005	−	0.432438i
$871$	−2.10379	−	19.3442i	−0.0712843	−	0.655453i
$872$	−0.586177	−	1.01529i	−0.0198505	−	0.0343820i
$873$	7.70880	+	2.06557i	0.260903	+	0.0699088i
$874$	−5.85683	−	3.38144i	−0.198110	−	0.114379i
$875$		0			0
$876$	−12.9510	−	12.9510i	−0.437574	−	0.437574i
$877$	17.5437	+	17.5437i	0.592409	+	0.592409i	0.938281	−	0.345873i	$-0.112417\pi$
$877$	17.5437	+	17.5437i	0.592409	+	0.592409i	−0.345873	+	0.938281i	$0.612417\pi$
$878$	−15.1288	+	4.05374i	−0.510571	+	0.136807i
$879$	−17.3276	−	4.64293i	−0.584447	−	0.156602i
$880$			75.5708i			2.54749i
$881$	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	$-0.0721482\pi$
$884$	−4.61660	−	0.714123i	−0.155273	−	0.0240185i
$885$	−3.90669	+	2.25553i	−0.131322	+	0.0758187i
$886$	−8.97605	−	8.97605i	−0.301556	−	0.301556i
$887$	−14.2827	+	8.24614i	−0.479567	+	0.276878i	−0.720236	−	0.693729i	$-0.755967\pi$
$887$	−14.2827	+	8.24614i	−0.479567	+	0.276878i	0.240669	+	0.970607i	$0.422633\pi$
$888$	−0.225488	−	0.390557i	−0.00756689	−	0.0131062i
$889$		0			0
$890$	−6.98987	+	26.0865i	−0.234301	+	0.874423i
$891$	−22.7625	+	22.7625i	−0.762571	+	0.762571i
$892$	4.15862	−	15.5202i	0.139241	−	0.519654i
$893$	−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
$898$	−15.2680	+	26.4450i	−0.509500	+	0.882480i
$899$	−2.08768	+	2.08768i	−0.0696281	+	0.0696281i
$900$	10.8820			0.362732
$901$	4.89086			0.162938
$902$	24.4460	−	24.4460i	0.813964	−	0.813964i
$903$		0			0
$904$	0.319621	+	0.0856423i	0.0106304	+	0.00284842i
$905$	13.1122	+	48.9354i	0.435864	+	1.62667i
$906$	59.9198	+	34.5947i	1.99070	+	1.14933i
$907$			13.0225i			0.432404i	0.976349	+	0.216202i	$0.0693670\pi$
$907$			13.0225i			0.432404i	−0.976349	+	0.216202i	$0.930633\pi$
$908$	−7.60512	+	28.3827i	−0.252385	+	0.941913i
$909$	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	$0.340264\pi$
$912$	−1.06836	+	3.98716i	−0.0353768	+	0.132028i
$913$		−	30.1999i		−	0.999471i
$914$	27.1392	+	15.6688i	0.897683	+	0.518278i
$915$	1.33517	+	4.98293i	0.0441394	+	0.164731i
$916$	22.7202	+	6.08787i	0.750698	+	0.201149i
$917$		0			0
$918$	−5.06364	+	5.06364i	−0.167125	+	0.167125i
$919$	−15.4786			−0.510591			−0.255296	−	0.966863i	$-0.582173\pi$
$919$	−15.4786			−0.510591			−0.255296	+	0.966863i	$0.582173\pi$
$920$	−1.84075			−0.0606876
$921$	−5.07296	+	5.07296i	−0.167160	+	0.167160i
$922$	30.9590	−	53.6225i	1.01958	−	1.76596i
$923$	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
$928$	−5.57038	+	20.7889i	−0.182857	+	0.682430i
$929$	−31.9786	+	31.9786i	−1.04918	+	1.04918i	−0.0504568	+	0.998726i	$0.516068\pi$
$929$	−31.9786	+	31.9786i	−1.04918	+	1.04918i	−0.998726	+	0.0504568i	$0.983932\pi$
$930$	−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
$934$	11.6350	+	11.6350i	0.380708	+	0.380708i
$935$	−10.6196	+	6.13122i	−0.347298	+	0.200512i
$936$	0.405045	−	0.0440510i	0.0132393	−	0.00143985i
$937$		−	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
$940$			49.7665i			1.62320i
$941$	−1.40463	−	0.376369i	−0.0457896	−	0.0122693i	0.235852	−	0.971789i	$-0.424212\pi$
$941$	−1.40463	−	0.376369i	−0.0457896	−	0.0122693i	−0.281641	+	0.959520i	$0.590879\pi$
$942$	21.3822	−	5.72935i	0.696670	−	0.186672i
$943$	−9.27596	−	9.27596i	−0.302067	−	0.302067i
$944$	2.60868	+	2.60868i	0.0849054	+	0.0849054i
$945$		0			0
$946$	41.8539	+	24.1644i	1.36079	+	0.785652i
$947$	37.4500	+	10.0347i	1.21696	+	0.326084i	0.809490	−	0.587133i	$-0.199744\pi$
$947$	37.4500	+	10.0347i	1.21696	+	0.326084i	0.407472	+	0.913218i	$0.366410\pi$
$948$	18.1016	+	31.3529i	0.587912	+	1.01829i
$949$	17.9063	−	13.1087i	0.581262	−	0.425526i
$950$	7.42616	+	4.28749i	0.240936	+	0.139105i
$951$	−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	$0.207276\pi$
$954$	−13.8703	+	3.71654i	−0.449068	+	0.120327i
$955$	14.5677	+	54.3673i	0.471399	+	1.75928i
$956$	−2.85975	−	10.6727i	−0.0924908	−	0.345180i
$957$	−22.1583	+	5.93729i	−0.716275	+	0.191925i
$958$	−63.7962	+	36.8327i	−2.06116	+	1.19001i
$959$		0			0
$960$	10.3987	+	38.8084i	0.335616	+	1.25254i
$961$	−25.7898	−	14.8897i	−0.831929	−	0.480314i
$962$	17.1487	−	6.65391i	0.552897	−	0.214531i
$963$	−1.42893	−	2.47499i	−0.0460468	−	0.0797553i
$964$	−31.0830	−	8.32866i	−1.00112	−	0.268248i
$965$	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	$0.713440\pi$
$968$	−2.12487	−	2.12487i	−0.0682960	−	0.0682960i
$969$	−0.646974	+	0.173356i	−0.0207838	+	0.00556900i
$970$	55.6587	+	14.9137i	1.78709	+	0.478850i
$971$		−	16.7115i		−	0.536296i	−0.963378	−	0.268148i	$-0.913588\pi$
$971$		−	16.7115i		−	0.536296i	0.963378	−	0.268148i	$-0.0864117\pi$
$972$	9.42319	−	16.3214i	0.302249	−	0.523510i
$973$		0			0
$974$		−	33.9484i		−	1.08778i
$975$	4.58726	−	29.6553i	0.146910	−	0.949730i
$976$	3.65367	−	2.10945i	0.116951	−	0.0675218i
$977$	−34.8162	−	34.8162i	−1.11387	−	1.11387i	−0.992622	−	0.121248i	$-0.961310\pi$
$977$	−34.8162	−	34.8162i	−1.11387	−	1.11387i	−0.121248	−	0.992622i	$-0.538690\pi$
$978$	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
$982$	−13.9539	+	13.9539i	−0.445286	+	0.445286i
$983$	9.14216	−	34.1190i	0.291590	−	1.08823i	−0.652298	−	0.757962i	$-0.726195\pi$
$983$	9.14216	−	34.1190i	0.291590	−	1.08823i	0.943888	−	0.330265i	$-0.107138\pi$
$984$	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
$989$	9.16909	−	15.8813i	0.291560	−	0.504997i
$990$	25.4577	−	25.4577i	0.809100	−	0.809100i
$991$	6.83828			0.217225			0.108613	−	0.994084i	$-0.465359\pi$
$991$	6.83828			0.217225			0.108613	+	0.994084i	$0.465359\pi$
$992$	8.89722			0.282487
$993$	−8.35456	+	8.35456i	−0.265124	+	0.265124i
$994$		0			0
$995$	27.6588	+	7.41114i	0.876842	+	0.234949i
$996$	−3.91190	−	14.5994i	−0.123953	−	0.462600i
$997$	42.8521	+	24.7407i	1.35714	+	0.783545i	0.989237	−	0.146319i	$-0.0467425\pi$
$997$	42.8521	+	24.7407i	1.35714	+	0.783545i	0.367903	+	0.929864i	$0.380076\pi$
$998$			5.93845i			0.187978i
$999$	3.70400	−	13.8235i	0.117189	−	0.437356i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.2	✓	28	7.6	odd	2
91.2.w.a.80.2	yes	28	91.67	odd	12
91.2.ba.a.54.2	yes	28	91.41	even	12
91.2.ba.a.59.2	yes	28	7.4	even	3
637.2.x.a.80.2		28	91.80	even	12	inner
637.2.x.a.215.2		28	1.1	even	1	trivial
637.2.bb.a.423.2		28	7.3	odd	6
637.2.bb.a.509.2		28	13.2	odd	12
637.2.bd.a.293.6		28	7.5	odd	6
637.2.bd.a.587.6		28	91.2	odd	12
637.2.bd.b.293.6		28	7.2	even	3
637.2.bd.b.587.6		28	91.54	even	12
819.2.et.b.145.6		28	273.41	odd	12
819.2.et.b.514.6		28	21.11	odd	6
819.2.gh.b.262.6		28	273.158	even	12
819.2.gh.b.397.6		28	21.20	even	2

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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.521585 + 1.94658i) q^{2} +1.44369i q^{3} +(-1.78508 - 1.03062i) q^{4} +(-0.849184 - 3.16920i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +0.915773 q^{9} +O(q^{10})\)	\(q+(-0.521585 + 1.94658i) q^{2} +1.44369i q^{3} +(-1.78508 - 1.03062i) q^{4} +(-0.849184 - 3.16920i) q^{5} +(-2.81025 - 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +0.915773 q^{9} +6.61202 q^{10} +(4.20434 - 4.20434i) q^{11} +(1.48788 - 2.57709i) 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} +(-0.477654 + 1.78263i) q^{18} +(-0.521911 + 0.521911i) q^{19} +(-1.75036 + 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +(3.93752 - 2.27333i) q^{23} +(0.125966 + 0.125966i) q^{24} +(-4.99256 + 2.88246i) q^{25} +(-5.86293 + 4.29209i) q^{26} +5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +9.54568i q^{30} +(1.06713 + 0.285936i) q^{31} +(7.77903 - 2.08438i) q^{32} +(6.06974 + 6.06974i) q^{33} +(0.895721 + 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(-2.44528 - 0.655210i) q^{37} +(-0.743721 - 1.28816i) q^{38} +(-3.26116 + 4.05706i) q^{39} +(-0.350617 - 0.202429i) q^{40} +(-0.746755 - 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(-11.8381 + 3.17202i) q^{44} +(-0.777660 - 2.90227i) q^{45} +(2.37147 + 8.85043i) q^{46} +(7.10802 - 1.90459i) q^{47} +(4.84328 - 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} +(0.785891 + 0.453734i) q^{51} +(-2.68838 - 6.92859i) q^{52} +(3.89042 + 6.73840i) q^{53} +(-11.0043 - 2.94859i) q^{54} +(-16.8946 - 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(-3.80821 - 3.80821i) q^{58} +(-0.919907 + 0.246488i) q^{59} +(-9.43079 - 2.52697i) q^{60} +1.08909i q^{61} +(-1.11320 + 1.92811i) q^{62} +8.48212i q^{64} +(4.77256 - 10.8244i) q^{65} +(-14.9811 + 8.64936i) q^{66} +(-3.81608 - 3.81608i) q^{67} +(-1.12206 + 0.647822i) q^{68} +(3.28197 + 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(0.0799043 - 0.0799043i) q^{72} +(1.59300 - 5.94515i) 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} +(-6.08299 + 10.5361i) q^{79} +(-8.98724 + 8.98724i) q^{80} -5.41404 q^{81} +5.81448 q^{82} +(3.59152 - 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(2.10373 + 7.85121i) q^{86} +(-3.34126 - 1.92908i) q^{87} -0.733685i q^{88} +(-1.05715 + 3.94532i) q^{89} +6.05511 q^{90} -9.37170 q^{92} +(-0.412802 + 1.54060i) q^{93} +14.8297i q^{94} +(2.09724 + 1.21084i) q^{95} +(3.00919 + 11.2305i) q^{96} +(8.41780 + 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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