LMFDB - Embedded newform 630.2.cd.a.23.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.19
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.27109 - 1.17657i) q^{3} +1.00000i q^{4} +(-1.89933 + 1.18006i) q^{5} +(-1.73076 - 0.0668357i) q^{6} +(2.22881 - 1.42562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.231353 - 2.99107i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27109 - 1.17657i) q^{3} +1.00000i q^{4} +(-1.89933 + 1.18006i) q^{5} +(-1.73076 - 0.0668357i) q^{6} +(2.22881 - 1.42562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.231353 - 2.99107i) q^{9} +(2.17746 + 0.508599i) q^{10} +(5.61346 + 3.24093i) q^{11} +(1.17657 + 1.27109i) q^{12} +(-0.473993 + 0.127006i) q^{13} +(-2.58407 - 0.567945i) q^{14} +(-1.02579 + 3.73467i) q^{15} -1.00000 q^{16} +(-0.277357 + 1.03511i) q^{17} +(-2.27859 + 1.95141i) q^{18} +(3.37635 + 1.94934i) q^{19} +(-1.18006 - 1.89933i) q^{20} +(1.15569 - 4.43445i) q^{21} +(-1.67763 - 6.26100i) q^{22} +(-4.36258 - 1.16895i) q^{23} +(0.0668357 - 1.73076i) q^{24} +(2.21491 - 4.48265i) q^{25} +(0.424971 + 0.245357i) q^{26} +(-3.22514 - 4.07413i) q^{27} +(1.42562 + 2.22881i) q^{28} +(-2.04717 - 3.54581i) q^{29} +(3.36616 - 1.91546i) q^{30} +9.78597 q^{31} +(0.707107 + 0.707107i) q^{32} +(10.9484 - 2.48512i) q^{33} +(0.928054 - 0.535813i) q^{34} +(-2.55093 + 5.33786i) q^{35} +(2.99107 + 0.231353i) q^{36} +(-2.13891 - 7.98251i) q^{37} +(-1.00905 - 3.76583i) q^{38} +(-0.453058 + 0.719124i) q^{39} +(-0.508599 + 2.17746i) q^{40} +(1.89525 + 1.09422i) q^{41} +(-3.95283 + 2.31844i) q^{42} +(1.93097 - 7.20646i) q^{43} +(-3.24093 + 5.61346i) q^{44} +(3.09023 + 5.95403i) q^{45} +(2.25824 + 3.91138i) q^{46} +(4.95495 + 4.95495i) q^{47} +(-1.27109 + 1.17657i) q^{48} +(2.93523 - 6.35488i) q^{49} +(-4.73589 + 1.60354i) q^{50} +(0.865336 + 1.64205i) q^{51} +(-0.127006 - 0.473993i) q^{52} +(-5.78474 - 1.55002i) q^{53} +(-0.600327 + 5.16136i) q^{54} +(-14.4863 + 0.468634i) q^{55} +(0.567945 - 2.58407i) q^{56} +(6.58519 - 1.49473i) q^{57} +(-1.05969 + 3.95483i) q^{58} -4.21144 q^{59} +(-3.73467 - 1.02579i) q^{60} -1.00823 q^{61} +(-6.91973 - 6.91973i) q^{62} +(-3.74848 - 6.99635i) q^{63} -1.00000i q^{64} +(0.750394 - 0.800568i) q^{65} +(-9.49894 - 5.98446i) q^{66} +(-3.13264 + 3.13264i) q^{67} +(-1.03511 - 0.277357i) q^{68} +(-6.92059 + 3.64705i) q^{69} +(5.57822 - 1.97065i) q^{70} +9.57780i q^{71} +(-1.95141 - 2.27859i) q^{72} +(-2.67346 + 9.97749i) q^{73} +(-4.13205 + 7.15692i) q^{74} +(-2.45882 - 8.30387i) q^{75} +(-1.94934 + 3.37635i) q^{76} +(17.1317 - 0.779214i) q^{77} +(0.828858 - 0.188138i) q^{78} +1.22295i q^{79} +(1.89933 - 1.18006i) q^{80} +(-8.89295 - 1.38399i) q^{81} +(-0.566412 - 2.11388i) q^{82} +(6.65640 + 1.78358i) q^{83} +(4.43445 + 1.15569i) q^{84} +(-0.694703 - 2.29331i) q^{85} +(-6.46114 + 3.73034i) q^{86} +(-6.77405 - 2.09840i) q^{87} +(6.26100 - 1.67763i) q^{88} +(1.18640 - 2.05491i) q^{89} +(2.02501 - 6.39526i) q^{90} +(-0.875381 + 0.958807i) q^{91} +(1.16895 - 4.36258i) q^{92} +(12.4389 - 11.5139i) q^{93} -7.00736i q^{94} +(-8.71314 + 0.281872i) q^{95} +(1.73076 + 0.0668357i) q^{96} +(8.73148 + 2.33959i) q^{97} +(-6.56909 + 2.41806i) q^{98} +(10.9925 - 16.0404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.27109	−	1.17657i	0.733866	−	0.679295i
$3$	1.27109	−	1.17657i	0.733866	−	0.679295i
$4$			1.00000i			0.500000i
$5$	−1.89933	+	1.18006i	−0.849406	+	0.527740i
$5$	−1.89933	+	1.18006i	−0.849406	+	0.527740i
$6$	−1.73076	−	0.0668357i	−0.706580	−	0.0272856i
$7$	2.22881	−	1.42562i	0.842413	−	0.538833i
$7$	2.22881	−	1.42562i	0.842413	−	0.538833i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.231353	−	2.99107i	0.0771177	−	0.997022i
$10$	2.17746	+	0.508599i	0.688573	+	0.160833i
$11$	5.61346	+	3.24093i	1.69252	+	0.977178i	0.952472	+	0.304625i	$0.0985310\pi$
$11$	5.61346	+	3.24093i	1.69252	+	0.977178i	0.740049	+	0.672553i	$0.234802\pi$
$12$	1.17657	+	1.27109i	0.339647	+	0.366933i
$13$	−0.473993	+	0.127006i	−0.131462	+	0.0352252i	−0.323950	−	0.946074i	$-0.605011\pi$
$13$	−0.473993	+	0.127006i	−0.131462	+	0.0352252i	0.192488	+	0.981299i	$0.438344\pi$
$14$	−2.58407	−	0.567945i	−0.690623	−	0.151790i
$15$	−1.02579	+	3.73467i	−0.264859	+	0.964287i
$16$	−1.00000			−0.250000
$17$	−0.277357	+	1.03511i	−0.0672689	+	0.251051i	−0.991369	−	0.131099i	$-0.958150\pi$
$17$	−0.277357	+	1.03511i	−0.0672689	+	0.251051i	0.924100	+	0.382150i	$0.124816\pi$
$18$	−2.27859	+	1.95141i	−0.537070	+	0.459952i
$19$	3.37635	+	1.94934i	0.774588	+	0.447209i	0.834509	−	0.550995i	$-0.185752\pi$
$19$	3.37635	+	1.94934i	0.774588	+	0.447209i	−0.0599209	+	0.998203i	$0.519085\pi$
$20$	−1.18006	−	1.89933i	−0.263870	−	0.424703i
$21$	1.15569	−	4.43445i	0.252191	−	0.967677i
$22$	−1.67763	−	6.26100i	−0.357672	−	1.33485i
$23$	−4.36258	−	1.16895i	−0.909660	−	0.243743i	−0.226500	−	0.974011i	$-0.572728\pi$
$23$	−4.36258	−	1.16895i	−0.909660	−	0.243743i	−0.683160	+	0.730268i	$0.739395\pi$
$24$	0.0668357	−	1.73076i	0.0136428	−	0.353290i
$25$	2.21491	−	4.48265i	0.442981	−	0.896531i
$26$	0.424971	+	0.245357i	0.0833436	+	0.0481185i
$27$	−3.22514	−	4.07413i	−0.620678	−	0.784066i
$28$	1.42562	+	2.22881i	0.269417	+	0.421206i
$29$	−2.04717	−	3.54581i	−0.380150	−	0.658440i	0.610933	−	0.791682i	$-0.290794\pi$
$29$	−2.04717	−	3.54581i	−0.380150	−	0.658440i	−0.991083	+	0.133242i	$0.957461\pi$
$30$	3.36616	−	1.91546i	0.614573	−	0.349714i
$31$	9.78597			1.75761			0.878806	−	0.477179i	$-0.158341\pi$
$31$	9.78597			1.75761			0.878806	+	0.477179i	$0.158341\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	10.9484	−	2.48512i	1.90587	−	0.432603i
$34$	0.928054	−	0.535813i	0.159160	−	0.0918911i
$35$	−2.55093	+	5.33786i	−0.431187	+	0.902263i
$36$	2.99107	+	0.231353i	0.498511	+	0.0385589i
$37$	−2.13891	−	7.98251i	−0.351634	−	1.31232i	−0.884668	−	0.466222i	$-0.845615\pi$
$37$	−2.13891	−	7.98251i	−0.351634	−	1.31232i	0.533033	−	0.846094i	$-0.321052\pi$
$38$	−1.00905	−	3.76583i	−0.163690	−	0.610898i
$39$	−0.453058	+	0.719124i	−0.0725473	+	0.115152i
$40$	−0.508599	+	2.17746i	−0.0804165	+	0.344286i
$41$	1.89525	+	1.09422i	0.295989	+	0.170889i	0.640640	−	0.767842i	$-0.278669\pi$
$41$	1.89525	+	1.09422i	0.295989	+	0.170889i	−0.344651	+	0.938731i	$0.612003\pi$
$42$	−3.95283	+	2.31844i	−0.609934	+	0.357743i
$43$	1.93097	−	7.20646i	0.294470	−	1.09898i	−0.647168	−	0.762347i	$-0.724047\pi$
$43$	1.93097	−	7.20646i	0.294470	−	1.09898i	0.941638	−	0.336628i	$-0.109286\pi$
$44$	−3.24093	+	5.61346i	−0.488589	+	0.846261i
$45$	3.09023	+	5.95403i	0.460664	+	0.887575i
$46$	2.25824	+	3.91138i	0.332959	+	0.576701i
$47$	4.95495	+	4.95495i	0.722754	+	0.722754i	0.969165	−	0.246411i	$-0.0792514\pi$
$47$	4.95495	+	4.95495i	0.722754	+	0.722754i	−0.246411	+	0.969165i	$0.579251\pi$
$48$	−1.27109	+	1.17657i	−0.183466	+	0.169824i
$49$	2.93523	−	6.35488i	0.419318	−	0.907839i
$50$	−4.73589	+	1.60354i	−0.669756	+	0.226775i
$51$	0.865336	+	1.64205i	0.121171	+	0.229933i
$52$	−0.127006	−	0.473993i	−0.0176126	−	0.0657311i
$53$	−5.78474	−	1.55002i	−0.794595	−	0.212911i	−0.161385	−	0.986891i	$-0.551596\pi$
$53$	−5.78474	−	1.55002i	−0.794595	−	0.212911i	−0.633210	+	0.773980i	$0.718263\pi$
$54$	−0.600327	+	5.16136i	−0.0816941	+	0.702372i
$55$	−14.4863	+	0.468634i	−1.95333	+	0.0631907i
$56$	0.567945	−	2.58407i	0.0758949	−	0.345311i
$57$	6.58519	−	1.49473i	0.872230	−	0.197982i
$58$	−1.05969	+	3.95483i	−0.139145	+	0.519295i
$59$	−4.21144			−0.548283			−0.274142	−	0.961689i	$-0.588394\pi$
$59$	−4.21144			−0.548283			−0.274142	+	0.961689i	$0.588394\pi$
$60$	−3.73467	−	1.02579i	−0.482144	−	0.132429i
$61$	−1.00823			−0.129090			−0.0645452	−	0.997915i	$-0.520560\pi$
$61$	−1.00823			−0.129090			−0.0645452	+	0.997915i	$0.520560\pi$
$62$	−6.91973	−	6.91973i	−0.878806	−	0.878806i
$63$	−3.74848	−	6.99635i	−0.472263	−	0.881457i
$64$		−	1.00000i		−	0.125000i
$65$	0.750394	−	0.800568i	0.0930750	−	0.0992983i
$66$	−9.49894	−	5.98446i	−1.16924	−	0.736636i
$67$	−3.13264	+	3.13264i	−0.382712	+	0.382712i	−0.872078	−	0.489366i	$-0.837228\pi$
$67$	−3.13264	+	3.13264i	−0.382712	+	0.382712i	0.489366	+	0.872078i	$0.337228\pi$
$68$	−1.03511	−	0.277357i	−0.125526	−	0.0336345i
$69$	−6.92059	+	3.64705i	−0.833142	+	0.439053i
$70$	5.57822	−	1.97065i	0.666725	−	0.235538i
$71$			9.57780i			1.13668i	0.822795	+	0.568338i	$0.192413\pi$
$71$			9.57780i			1.13668i	−0.822795	+	0.568338i	$0.807587\pi$
$72$	−1.95141	−	2.27859i	−0.229976	−	0.268535i
$73$	−2.67346	+	9.97749i	−0.312905	+	1.16778i	0.613020	+	0.790068i	$0.289955\pi$
$73$	−2.67346	+	9.97749i	−0.312905	+	1.16778i	−0.925924	+	0.377709i	$0.876712\pi$
$74$	−4.13205	+	7.15692i	−0.480341	+	0.831975i
$75$	−2.45882	−	8.30387i	−0.283920	−	0.958848i
$76$	−1.94934	+	3.37635i	−0.223604	+	0.387294i
$77$	17.1317	−	0.779214i	1.95234	−	0.0887997i
$78$	0.828858	−	0.188138i	0.0938497	−	0.0213024i
$79$			1.22295i			0.137592i	0.997631	+	0.0687962i	$0.0219158\pi$
$79$			1.22295i			0.137592i	−0.997631	+	0.0687962i	$0.978084\pi$
$80$	1.89933	−	1.18006i	0.212351	−	0.131935i
$81$	−8.89295	−	1.38399i	−0.988106	−	0.153776i
$82$	−0.566412	−	2.11388i	−0.0625498	−	0.233439i
$83$	6.65640	+	1.78358i	0.730635	+	0.195773i	0.604912	−	0.796292i	$-0.293208\pi$
$83$	6.65640	+	1.78358i	0.730635	+	0.195773i	0.125723	+	0.992065i	$0.459875\pi$
$84$	4.43445	+	1.15569i	0.483839	+	0.126096i
$85$	−0.694703	−	2.29331i	−0.0753511	−	0.248745i
$86$	−6.46114	+	3.73034i	−0.696722	+	0.402253i
$87$	−6.77405	−	2.09840i	−0.726254	−	0.224972i
$88$	6.26100	−	1.67763i	0.667425	−	0.178836i
$89$	1.18640	−	2.05491i	0.125758	−	0.217820i	−0.796271	−	0.604940i	$-0.793197\pi$
$89$	1.18640	−	2.05491i	0.125758	−	0.217820i	0.922029	+	0.387120i	$0.126530\pi$
$90$	2.02501	−	6.39526i	0.213455	−	0.674119i
$91$	−0.875381	+	0.958807i	−0.0917649	+	0.100510i
$92$	1.16895	−	4.36258i	0.121871	−	0.454830i
$93$	12.4389	−	11.5139i	1.28985	−	1.19394i
$94$		−	7.00736i		−	0.722754i
$95$	−8.71314	+	0.281872i	−0.893949	+	0.0289194i
$96$	1.73076	+	0.0668357i	0.176645	+	0.00682139i
$97$	8.73148	+	2.33959i	0.886547	+	0.237550i	0.673230	−	0.739433i	$-0.264907\pi$
$97$	8.73148	+	2.33959i	0.886547	+	0.237550i	0.213317	+	0.976983i	$0.431573\pi$
$98$	−6.56909	+	2.41806i	−0.663579	+	0.244261i
$99$	10.9925	−	16.0404i	1.10479	−	1.61212i
$100$	4.48265	+	2.21491i	0.448265	+	0.221491i
$101$	0.601627	+	0.347349i	0.0598641	+	0.0345626i	0.529633	−	0.848227i	$-0.322330\pi$
$101$	0.601627	+	0.347349i	0.0598641	+	0.0345626i	−0.469769	+	0.882789i	$0.655663\pi$
$102$	0.549221	−	1.77299i	0.0543810	−	0.175552i
$103$	2.25370	−	8.41091i	0.222063	−	0.828752i	−0.761496	−	0.648169i	$-0.775535\pi$
$103$	2.25370	−	8.41091i	0.222063	−	0.828752i	0.983560	−	0.180583i	$-0.0577984\pi$
$104$	−0.245357	+	0.424971i	−0.0240592	+	0.0416718i
$105$	3.03791	+	9.78627i	0.296469	+	0.955042i
$106$	2.99440	+	5.18645i	0.290842	+	0.503753i
$107$	−2.38635	+	0.639421i	−0.230697	+	0.0618152i	−0.372316	−	0.928106i	$-0.621436\pi$
$107$	−2.38635	+	0.639421i	−0.230697	+	0.0618152i	0.141618	+	0.989921i	$0.454769\pi$
$108$	4.07413	−	3.22514i	0.392033	−	0.310339i
$109$	−16.6841	+	9.63257i	−1.59805	+	0.922633i	−0.606183	+	0.795325i	$0.707300\pi$
$109$	−16.6841	+	9.63257i	−1.59805	+	0.922633i	−0.991863	+	0.127308i	$0.959366\pi$
$110$	10.5747	+	9.91199i	1.00826	+	0.945071i
$111$	−12.1108	−	7.62993i	−1.14950	−	0.724201i
$112$	−2.22881	+	1.42562i	−0.210603	+	0.134708i
$113$	−0.643964	−	2.40331i	−0.0605790	−	0.226084i	0.928999	−	0.370083i	$-0.120671\pi$
$113$	−0.643964	−	2.40331i	−0.0605790	−	0.226084i	−0.989578	+	0.143999i	$0.954004\pi$
$114$	−5.71337	−	3.59950i	−0.535106	−	0.337124i
$115$	9.66540	−	2.92789i	0.901304	−	0.273028i
$116$	3.54581	−	2.04717i	0.329220	−	0.190075i
$117$	0.270224	+	1.44713i	0.0249822	+	0.133787i
$118$	2.97794	+	2.97794i	0.274142	+	0.274142i
$119$	0.857495	+	2.70247i	0.0786064	+	0.247735i
$120$	1.91546	+	3.36616i	0.174857	+	0.307287i
$121$	15.5073	+	26.8594i	1.40975	+	2.44176i
$122$	0.712925	+	0.712925i	0.0645452	+	0.0645452i
$123$	3.69648	−	0.839042i	0.333300	−	0.0756539i
$124$			9.78597i			0.878806i
$125$	1.08298	+	11.1278i	0.0968645	+	0.995298i
$126$	−2.29660	+	7.59774i	−0.204597	+	0.676860i
$127$	−10.9407	+	10.9407i	−0.970833	+	0.970833i	−0.999587	−	0.0287531i	$-0.990846\pi$
$127$	−10.9407	+	10.9407i	−0.970833	+	0.970833i	0.0287531	+	0.999587i	$0.490846\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−6.02449	−	11.4320i	−0.530427	−	1.00653i
$130$	−1.09670	+	0.0354783i	−0.0961866	+	0.00311165i
$131$	−10.8429	+	6.26018i	−0.947353	+	0.546954i	−0.892258	−	0.451527i	$-0.850880\pi$
$131$	−10.8429	+	6.26018i	−0.947353	+	0.546954i	−0.0550952	+	0.998481i	$0.517546\pi$
$132$	2.48512	+	10.9484i	0.216302	+	0.952937i
$133$	10.3043	−	0.468677i	0.893493	−	0.0406395i
$134$	4.43022			0.382712
$135$	10.9333	+	3.93225i	0.940990	+	0.338434i
$136$	0.535813	+	0.928054i	0.0459455	+	0.0795800i
$137$	−7.85918	+	2.10586i	−0.671455	+	0.179916i	−0.578410	−	0.815746i	$-0.696327\pi$
$137$	−7.85918	+	2.10586i	−0.671455	+	0.179916i	−0.0930450	+	0.995662i	$0.529660\pi$
$138$	7.47245	+	2.31475i	0.636097	+	0.197044i
$139$	−3.75610	−	2.16859i	−0.318588	−	0.183937i	0.332175	−	0.943218i	$-0.392218\pi$
$139$	−3.75610	−	2.16859i	−0.318588	−	0.183937i	−0.650763	+	0.759281i	$0.725551\pi$
$140$	−5.33786	−	2.55093i	−0.451131	−	0.215593i
$141$	12.1281	+	0.468342i	1.02137	+	0.0394415i
$142$	6.77252	−	6.77252i	0.568338	−	0.568338i
$143$	−3.07236	−	0.823237i	−0.256924	−	0.0688425i
$144$	−0.231353	+	2.99107i	−0.0192794	+	0.249255i
$145$	8.07253	+	4.31886i	0.670387	+	0.358662i
$146$	8.94557	−	5.16473i	0.740341	−	0.427436i
$147$	−3.74603	−	11.5311i	−0.308967	−	0.951073i
$148$	7.98251	−	2.13891i	0.656158	−	0.175817i
$149$	−3.03171	−	5.25108i	−0.248368	−	0.430185i	0.714705	−	0.699426i	$-0.246561\pi$
$149$	−3.03171	−	5.25108i	−0.248368	−	0.430185i	−0.963073	+	0.269240i	$0.913227\pi$
$150$	−4.13307	+	7.61037i	−0.337464	+	0.621384i
$151$	−0.169891	+	0.294260i	−0.0138255	+	0.0239465i	−0.872855	−	0.487979i	$-0.837734\pi$
$151$	−0.169891	+	0.294260i	−0.0138255	+	0.0239465i	0.859030	+	0.511925i	$0.171068\pi$
$152$	3.76583	−	1.00905i	0.305449	−	0.0818448i
$153$	3.03192	+	1.06907i	0.245116	+	0.0864291i
$154$	−12.6649	−	11.5629i	−1.02057	−	0.931769i
$155$	−18.5868	+	11.5481i	−1.49293	+	0.927562i
$156$	−0.719124	−	0.453058i	−0.0575760	−	0.0362736i
$157$	−11.4042	+	11.4042i	−0.910155	+	0.910155i	−0.996284	−	0.0861294i	$-0.972550\pi$
$157$	−11.4042	+	11.4042i	−0.910155	+	0.910155i	0.0861294	+	0.996284i	$0.472550\pi$
$158$	0.864755	−	0.864755i	0.0687962	−	0.0687962i
$159$	−9.17664	+	4.83595i	−0.727755	+	0.383516i
$160$	−2.17746	−	0.508599i	−0.172143	−	0.0402082i
$161$	−11.3898	+	3.61400i	−0.897646	+	0.284823i
$162$	5.30964	+	7.26689i	0.417165	+	0.570941i
$163$	19.7737	−	5.29834i	1.54880	−	0.414998i	0.619700	−	0.784839i	$-0.287254\pi$
$163$	19.7737	−	5.29834i	1.54880	−	0.414998i	0.929095	+	0.369841i	$0.120588\pi$
$164$	−1.09422	+	1.89525i	−0.0854446	+	0.147994i
$165$	−17.8621	+	17.6399i	−1.39056	+	1.37326i
$166$	−3.44561	−	5.96797i	−0.267431	−	0.463204i
$167$	−1.45959	+	0.391097i	−0.112947	+	0.0302640i	−0.314850	−	0.949142i	$-0.601954\pi$
$167$	−1.45959	+	0.391097i	−0.112947	+	0.0302640i	0.201903	+	0.979406i	$0.435287\pi$
$168$	−2.31844	−	3.95283i	−0.178872	−	0.304967i
$169$	−11.0498	+	6.37960i	−0.849984	+	0.490738i
$170$	−1.13039	+	2.11285i	−0.0866969	+	0.162048i
$171$	6.61172	−	9.64790i	0.505611	−	0.737793i
$172$	7.20646	+	1.93097i	0.549488	+	0.147235i
$173$	6.57743	−	6.57743i	0.500072	−	0.500072i	−0.411388	−	0.911460i	$-0.634956\pi$
$173$	6.57743	−	6.57743i	0.500072	−	0.500072i	0.911460	+	0.411388i	$0.134956\pi$
$174$	3.30618	+	6.27377i	0.250641	+	0.475613i
$175$	−1.45394	−	13.1486i	−0.109908	−	0.993942i
$176$	−5.61346	−	3.24093i	−0.423130	−	0.244294i
$177$	−5.35313	+	4.95507i	−0.402366	+	0.372446i
$178$	−2.29196	+	0.614128i	−0.171789	+	0.0460308i
$179$	7.35710	+	12.7429i	0.549895	+	0.952447i	0.998281	+	0.0586067i	$0.0186658\pi$
$179$	7.35710	+	12.7429i	0.549895	+	0.952447i	−0.448386	+	0.893840i	$0.648001\pi$
$180$	−5.95403	+	3.09023i	−0.443787	+	0.230332i
$181$	−11.7047			−0.870004			−0.435002	−	0.900429i	$-0.643252\pi$
$181$	−11.7047			−0.870004			−0.435002	+	0.900429i	$0.643252\pi$
$182$	1.29697	−	0.0589910i	0.0961376	−	0.00437270i
$183$	−1.28155	+	1.18625i	−0.0947350	+	0.0876904i
$184$	−3.91138	+	2.25824i	−0.288351	+	0.166479i
$185$	13.4823	+	12.6374i	0.991242	+	0.929118i
$186$	−16.9372	−	0.654052i	−1.24189	−	0.0479574i
$187$	−4.91165	+	4.91165i	−0.359176	+	0.359176i
$188$	−4.95495	+	4.95495i	−0.361377	+	0.361377i
$189$	−12.9964	−	4.48266i	−0.945347	−	0.326065i
$190$	6.36043	+	5.96181i	0.461434	+	0.432515i
$191$		−	15.8390i		−	1.14607i	−0.819530	−	0.573036i	$-0.805765\pi$
$191$		−	15.8390i		−	1.14607i	0.819530	−	0.573036i	$-0.194235\pi$
$192$	−1.17657	−	1.27109i	−0.0849118	−	0.0917332i
$193$	8.34684	+	8.34684i	0.600819	+	0.600819i	0.940530	−	0.339711i	$-0.110329\pi$
$193$	8.34684	+	8.34684i	0.600819	+	0.600819i	−0.339711	+	0.940530i	$0.610329\pi$
$194$	−4.51974	−	7.82843i	−0.324499	−	0.562048i
$195$	0.0118940	−	1.90049i	0.000851746	−	0.136097i
$196$	6.35488	+	2.93523i	0.453920	+	0.209659i
$197$	−17.0101	−	17.0101i	−1.21192	−	1.21192i	−0.970395	−	0.241523i	$-0.922353\pi$
$197$	−17.0101	−	17.0101i	−1.21192	−	1.21192i	−0.241523	−	0.970395i	$-0.577647\pi$
$198$	−19.1152	+	3.56940i	−1.35846	+	0.253666i
$199$	11.2362	−	6.48724i	0.796516	−	0.459868i	−0.0457357	−	0.998954i	$-0.514563\pi$
$199$	11.2362	−	6.48724i	0.796516	−	0.459868i	0.842251	+	0.539085i	$0.181230\pi$
$200$	−1.60354	−	4.73589i	−0.113387	−	0.334878i
$201$	−0.296096	+	7.66764i	−0.0208850	+	0.540834i
$202$	−0.179801	−	0.671027i	−0.0126508	−	0.0472133i
$203$	−9.61774	−	4.98446i	−0.675033	−	0.349840i
$204$	−1.64205	+	0.865336i	−0.114967	+	0.0605856i
$205$	−4.89096	+	0.158223i	−0.341600	+	0.0110508i
$206$	−7.54102	+	4.35381i	−0.525408	+	0.303344i
$207$	−4.50570	+	12.7783i	−0.313168	+	0.888154i
$208$	0.473993	−	0.127006i	0.0328655	−	0.00880629i
$209$	12.6353	+	21.8850i	0.874004	+	1.51382i
$210$	4.77182	−	9.06806i	0.329287	−	0.625756i
$211$	−5.76427	+	9.98401i	−0.396829	+	0.687328i	−0.993333	−	0.115282i	$-0.963223\pi$
$211$	−5.76427	+	9.98401i	−0.396829	+	0.687328i	0.596504	+	0.802610i	$0.296556\pi$
$212$	1.55002	−	5.78474i	0.106456	−	0.397297i
$213$	11.2690	+	12.1743i	0.772137	+	0.834167i
$214$	2.13954	+	1.23527i	0.146256	+	0.0844411i
$215$	4.83654	+	15.9661i	0.329849	+	1.08888i
$216$	−5.16136	−	0.600327i	−0.351186	−	0.0408471i
$217$	21.8111	−	13.9511i	1.48063	−	0.947060i
$218$	18.6087	+	4.98618i	1.26034	+	0.337707i
$219$	8.34103	+	15.8278i	0.563634	+	1.06955i
$220$	−0.468634	−	14.4863i	−0.0315953	−	0.976667i
$221$		−	0.525862i		−	0.0353733i
$222$	3.16842	+	13.9588i	0.212650	+	0.936851i
$223$	−5.34791	+	19.9587i	−0.358122	+	1.33653i	0.518387	+	0.855146i	$0.326533\pi$
$223$	−5.34791	+	19.9587i	−0.358122	+	1.33653i	−0.876509	+	0.481385i	$0.840134\pi$
$224$	2.58407	+	0.567945i	0.172656	+	0.0379474i
$225$	−12.8955	−	7.66200i	−0.859699	−	0.510800i
$226$	−1.24404	+	2.15474i	−0.0827525	+	0.143331i
$227$	12.9705	−	3.47544i	0.860883	−	0.230673i	0.198742	−	0.980052i	$-0.436314\pi$
$227$	12.9705	−	3.47544i	0.860883	−	0.230673i	0.662141	+	0.749379i	$0.269648\pi$
$228$	1.49473	+	6.58519i	0.0989912	+	0.436115i
$229$	−18.3143	+	10.5738i	−1.21025	+	0.698736i	−0.962813	−	0.270170i	$-0.912920\pi$
$229$	−18.3143	+	10.5738i	−1.21025	+	0.698736i	−0.247433	+	0.968905i	$0.579587\pi$
$230$	−8.90481	−	4.76414i	−0.587166	−	0.314138i
$231$	20.8592	−	21.1471i	1.37243	−	1.39138i
$232$	−3.95483	−	1.05969i	−0.259648	−	0.0695724i
$233$	−1.65637	−	6.18164i	−0.108512	−	0.404973i	0.890208	−	0.455555i	$-0.150559\pi$
$233$	−1.65637	−	6.18164i	−0.108512	−	0.404973i	−0.998720	+	0.0505818i	$0.983892\pi$
$234$	0.832197	−	1.21435i	0.0544025	−	0.0793847i
$235$	−15.2582	−	3.56393i	−0.995338	−	0.232485i
$236$		−	4.21144i		−	0.274142i
$237$	1.43889	+	1.55448i	0.0934658	+	0.100974i
$238$	1.30460	−	2.51728i	0.0845645	−	0.163171i
$239$	11.4526	−	19.8365i	0.740809	−	1.28312i	−0.211318	−	0.977417i	$-0.567775\pi$
$239$	11.4526	−	19.8365i	0.740809	−	1.28312i	0.952127	−	0.305702i	$-0.0988912\pi$
$240$	1.02579	−	3.73467i	0.0662147	−	0.241072i
$241$	−11.2489	+	19.4837i	−0.724608	+	1.25506i	0.234527	+	0.972110i	$0.424646\pi$
$241$	−11.2489	+	19.4837i	−0.724608	+	1.25506i	−0.959135	+	0.282949i	$0.908687\pi$
$242$	8.02716	−	29.9578i	0.516005	−	1.92576i
$243$	−12.9321	+	8.70403i	−0.829596	+	0.558364i
$244$		−	1.00823i		−	0.0645452i
$245$	1.92419	+	15.5338i	0.122932	+	0.992415i
$246$	−3.20710	−	2.02051i	−0.204477	−	0.128823i
$247$	−1.84795	−	0.495156i	−0.117582	−	0.0315060i
$248$	6.91973	−	6.91973i	0.439403	−	0.439403i
$249$	10.5594	−	5.56465i	0.669175	−	0.352645i
$250$	7.10274	−	8.63430i	0.449217	−	0.546081i
$251$		−	17.6396i		−	1.11340i	−0.830714	−	0.556700i	$-0.812067\pi$
$251$		−	17.6396i		−	1.11340i	0.830714	−	0.556700i	$-0.187933\pi$
$252$	6.99635	−	3.74848i	0.440729	−	0.236132i
$253$	−20.7007	−	20.7007i	−1.30144	−	1.30144i
$254$	15.4725			0.970833
$255$	−3.58128	−	2.09765i	−0.224269	−	0.131360i
$256$	1.00000			0.0625000
$257$	−0.668266	+	2.49400i	−0.0416853	+	0.155572i	−0.983631	−	0.180193i	$-0.942328\pi$
$257$	−0.668266	+	2.49400i	−0.0416853	+	0.155572i	0.941946	+	0.335764i	$0.108995\pi$
$258$	−3.82369	+	12.3436i	−0.238052	+	0.768479i
$259$	−16.1472	−	14.7423i	−1.00334	−	0.916040i
$260$	0.800568	+	0.750394i	0.0496491	+	0.0465375i
$261$	−11.0794	+	5.30290i	−0.685795	+	0.328241i
$262$	12.0937	+	3.24051i	0.747154	+	0.200199i
$263$	−4.28899	−	16.0067i	−0.264470	−	0.987017i	−0.962574	−	0.271020i	$-0.912639\pi$
$263$	−4.28899	−	16.0067i	−0.264470	−	0.987017i	0.698103	−	0.715997i	$-0.254028\pi$
$264$	5.98446	−	9.49894i	0.368318	−	0.584620i
$265$	12.8162	−	3.88236i	0.787295	−	0.238492i
$266$	−7.61762	−	6.95481i	−0.467066	−	0.426427i
$267$	−0.909723	−	4.00787i	−0.0556742	−	0.245278i
$268$	−3.13264	−	3.13264i	−0.191356	−	0.191356i
$269$	3.98942	+	6.90988i	0.243239	+	0.421303i	0.961635	−	0.274332i	$-0.0884567\pi$
$269$	3.98942	+	6.90988i	0.243239	+	0.421303i	−0.718396	+	0.695634i	$0.755123\pi$
$270$	−4.95051	−	10.5115i	−0.301278	−	0.639712i
$271$	13.4683	−	23.3278i	0.818143	−	1.41707i	−0.0889052	−	0.996040i	$-0.528337\pi$
$271$	13.4683	−	23.3278i	0.818143	−	1.41707i	0.907049	−	0.421026i	$-0.138330\pi$
$272$	0.277357	−	1.03511i	0.0168172	−	0.0627628i
$273$	0.0154156	+	2.24868i	0.000932996	+	0.136096i
$274$	7.04635	+	4.06821i	0.425686	+	0.245770i
$275$	26.9613	−	17.9848i	1.62582	−	1.08453i
$276$	−3.64705	−	6.92059i	−0.219526	−	0.416571i
$277$	−2.01344	−	7.51426i	−0.120976	−	0.451488i	0.878689	−	0.477396i	$-0.158419\pi$
$277$	−2.01344	−	7.51426i	−0.120976	−	0.451488i	−0.999664	+	0.0259076i	$0.991752\pi$
$278$	1.12254	+	4.18939i	0.0673256	+	0.251263i
$279$	2.26402	−	29.2705i	0.135543	−	1.75238i
$280$	1.97065	+	5.57822i	0.117769	+	0.333362i
$281$	22.5137	−	12.9983i	1.34305	−	0.775413i	0.355800	−	0.934562i	$-0.384209\pi$
$281$	22.5137	−	12.9983i	1.34305	−	0.775413i	0.987254	+	0.159150i	$0.0508752\pi$
$282$	−8.24467	−	8.90701i	−0.490963	−	0.530404i
$283$	7.16596	+	7.16596i	0.425972	+	0.425972i	0.887254	−	0.461282i	$-0.152610\pi$
$283$	7.16596	+	7.16596i	0.425972	+	0.425972i	−0.461282	+	0.887254i	$0.652610\pi$
$284$	−9.57780			−0.568338
$285$	−10.7436	+	10.6099i	−0.636394	+	0.628478i
$286$	1.59037	+	2.75460i	0.0940406	+	0.162883i
$287$	5.78411	−	0.263083i	0.341425	−	0.0155293i
$288$	2.27859	−	1.95141i	0.134267	−	0.114988i
$289$	13.7279	+	7.92581i	0.807524	+	0.466224i
$290$	−2.65424	−	8.76204i	−0.155862	−	0.514525i
$291$	13.8512	−	7.29938i	0.811973	−	0.427897i
$292$	−9.97749	−	2.67346i	−0.583888	−	0.156452i
$293$	6.32981	+	23.6232i	0.369791	+	1.38008i	0.860808	+	0.508930i	$0.169959\pi$
$293$	6.32981	+	23.6232i	0.369791	+	1.38008i	−0.491016	+	0.871150i	$0.663375\pi$
$294$	−5.50491	+	10.8026i	−0.321053	+	0.630020i
$295$	7.99892	−	4.96976i	0.465715	−	0.289351i
$296$	−7.15692	−	4.13205i	−0.415988	−	0.240171i
$297$	−4.90020	−	33.3224i	−0.284338	−	1.93356i
$298$	−1.56933	+	5.85682i	−0.0909089	+	0.339277i
$299$	2.21630			0.128172
$300$	8.30387	−	2.45882i	0.479424	−	0.141960i
$301$	−5.96990	−	18.8147i	−0.344099	−	1.08446i
$302$	0.328204	−	0.0879420i	0.0188860	−	0.00506049i
$303$	1.17341	−	0.266344i	0.0674104	−	0.0153011i
$304$	−3.37635	−	1.94934i	−0.193647	−	0.111802i
$305$	1.91496	−	1.18977i	0.109650	−	0.0681262i
$306$	−1.38794	−	2.89983i	−0.0793434	−	0.165772i
$307$	−13.3097	+	13.3097i	−0.759626	+	0.759626i	−0.976254	−	0.216628i	$-0.930494\pi$
$307$	−13.3097	+	13.3097i	−0.759626	+	0.759626i	0.216628	+	0.976254i	$0.430494\pi$
$308$	0.779214	+	17.1317i	0.0443999	+	0.976168i
$309$	−7.03139	−	13.3427i	−0.400002	−	0.759039i
$310$	21.3086	+	4.97713i	1.21024	+	0.282682i
$311$			11.2927i			0.640349i	0.947359	+	0.320174i	$0.103741\pi$
$311$			11.2927i			0.640349i	−0.947359	+	0.320174i	$0.896259\pi$
$312$	0.188138	+	0.828858i	0.0106512	+	0.0469248i
$313$	−8.99612	−	8.99612i	−0.508491	−	0.508491i	0.405572	−	0.914063i	$-0.367072\pi$
$313$	−8.99612	−	8.99612i	−0.508491	−	0.508491i	−0.914063	+	0.405572i	$0.867072\pi$
$314$	16.1280			0.910155
$315$	15.3757	+	8.86494i	0.866324	+	0.499483i
$316$	−1.22295			−0.0687962
$317$	1.92613	+	1.92613i	0.108182	+	0.108182i	0.759126	−	0.650944i	$-0.225627\pi$
$317$	1.92613	+	1.92613i	0.108182	+	0.108182i	−0.650944	+	0.759126i	$0.725627\pi$
$318$	9.90840	+	3.06933i	0.555636	+	0.172120i
$319$		−	26.5390i		−	1.48590i
$320$	1.18006	+	1.89933i	0.0659675	+	0.106176i
$321$	−2.28095	+	3.62048i	−0.127310	+	0.202075i
$322$	10.6093	+	5.49836i	0.591234	+	0.306411i
$323$	−2.95423	+	2.95423i	−0.164378	+	0.164378i
$324$	1.38399	−	8.89295i	0.0768881	−	0.494053i
$325$	−0.480526	+	2.40606i	−0.0266548	+	0.133464i
$326$	−17.7286	−	10.2356i	−0.981897	−	0.566898i
$327$	−9.87362	+	31.8739i	−0.546012	+	1.76263i
$328$	2.11388	−	0.566412i	0.116719	−	0.0312749i
$329$	18.1075	+	3.97980i	0.998301	+	0.219413i
$330$	25.1037	+	0.157108i	1.38191	+	0.00864852i
$331$	−32.7441			−1.79978			−0.899889	−	0.436119i	$-0.856353\pi$
$331$	−32.7441			−1.79978			−0.899889	+	0.436119i	$0.856353\pi$
$332$	−1.78358	+	6.65640i	−0.0978865	+	0.365317i
$333$	−24.3711	+	4.55083i	−1.33553	+	0.249384i
$334$	1.30863	+	0.755541i	0.0716053	+	0.0413413i
$335$	2.25320	−	9.64661i	0.123106	−	0.527051i
$336$	−1.15569	+	4.43445i	−0.0630478	+	0.241919i
$337$	2.16627	+	8.08462i	0.118004	+	0.440397i	0.999494	−	0.0318056i	$-0.0101257\pi$
$337$	2.16627	+	8.08462i	0.118004	+	0.440397i	−0.881490	+	0.472203i	$0.843459\pi$
$338$	12.3244	+	3.30232i	0.670361	+	0.179623i
$339$	−3.64620	−	2.29715i	−0.198034	−	0.124764i
$340$	2.29331	−	0.694703i	0.124372	−	0.0376755i
$341$	54.9332	+	31.7157i	2.97480	+	1.71750i
$342$	−11.4973	+	2.14690i	−0.621702	+	0.116091i
$343$	−2.51756	−	18.3483i	−0.135935	−	0.990718i
$344$	−3.73034	−	6.46114i	−0.201126	−	0.348361i
$345$	8.84074	−	15.0937i	0.475970	−	0.812616i
$346$	−9.30188			−0.500072
$347$	−20.6341	−	20.6341i	−1.10769	−	1.10769i	−0.993453	−	0.114242i	$-0.963556\pi$
$347$	−20.6341	−	20.6341i	−1.10769	−	1.10769i	−0.114242	−	0.993453i	$-0.536444\pi$
$348$	2.09840	−	6.77405i	0.112486	−	0.363127i
$349$	−12.1674	+	7.02485i	−0.651306	+	0.376032i	−0.788956	−	0.614449i	$-0.789378\pi$
$349$	−12.1674	+	7.02485i	−0.651306	+	0.376032i	0.137651	+	0.990481i	$0.456045\pi$
$350$	−8.26938	+	10.3256i	−0.442017	+	0.551925i
$351$	2.04613	+	1.52150i	0.109214	+	0.0812115i
$352$	1.67763	+	6.26100i	0.0894180	+	0.333712i
$353$	−8.34725	−	31.1524i	−0.444279	−	1.65807i	−0.717832	−	0.696216i	$-0.754865\pi$
$353$	−8.34725	−	31.1524i	−0.444279	−	1.65807i	0.273552	−	0.961857i	$-0.411801\pi$
$354$	7.28900	+	0.281475i	0.387406	+	0.0149602i
$355$	−11.3024	−	18.1914i	−0.599869	−	0.965499i
$356$	2.05491	+	1.18640i	0.108910	+	0.0628792i
$357$	4.26961	+	2.42619i	0.225972	+	0.128408i
$358$	3.80832	−	14.2128i	0.201276	−	0.751171i
$359$	−14.4995	+	25.1138i	−0.765253	+	1.32546i	0.174860	+	0.984593i	$0.444053\pi$
$359$	−14.4995	+	25.1138i	−0.765253	+	1.32546i	−0.940113	+	0.340864i	$0.889280\pi$
$360$	6.39526	+	2.02501i	0.337060	+	0.106728i
$361$	−1.90017	−	3.29120i	−0.100009	−	0.173221i
$362$	8.27648	+	8.27648i	0.435002	+	0.435002i
$363$	51.3132	+	15.8953i	2.69325	+	0.834289i
$364$	−0.958807	−	0.875381i	−0.0502551	−	0.0458824i
$365$	−6.69628	−	22.1054i	−0.350499	−	1.15705i
$366$	1.74500	+	0.0673856i	0.0912127	+	0.00352230i
$367$	−0.536956	−	2.00395i	−0.0280289	−	0.104605i	0.950494	−	0.310742i	$-0.100578\pi$
$367$	−0.536956	−	2.00395i	−0.0280289	−	0.104605i	−0.978523	+	0.206137i	$0.933911\pi$
$368$	4.36258	+	1.16895i	0.227415	+	0.0609357i
$369$	3.71137	−	5.41567i	0.193206	−	0.281929i
$370$	−0.597489	−	18.4694i	−0.0310620	−	0.960180i
$371$	−15.1028	+	4.79213i	−0.784100	+	0.248795i
$372$	11.5139	+	12.4389i	0.596968	+	0.644926i
$373$	−3.69931	+	13.8060i	−0.191543	+	0.714848i	0.801592	+	0.597872i	$0.203987\pi$
$373$	−3.69931	+	13.8060i	−0.191543	+	0.714848i	−0.993135	+	0.116976i	$0.962680\pi$
$374$	6.94613			0.359176
$375$	14.4692	+	12.8702i	0.747186	+	0.664615i
$376$	7.00736			0.361377
$377$	1.42069	+	1.42069i	0.0731690	+	0.0731690i
$378$	6.02011	+	12.3595i	0.309641	+	0.635706i
$379$		−	3.80555i		−	0.195478i	−0.995212	−	0.0977389i	$-0.968839\pi$
$379$		−	3.80555i		−	0.195478i	0.995212	−	0.0977389i	$-0.0311610\pi$
$380$	−0.281872	−	8.71314i	−0.0144597	−	0.446975i
$381$	−1.03412	+	26.7793i	−0.0529795	+	1.37194i
$382$	−11.1999	+	11.1999i	−0.573036	+	0.573036i
$383$	−33.7332	−	9.03878i	−1.72369	−	0.461860i	−0.744973	−	0.667094i	$-0.767538\pi$
$383$	−33.7332	−	9.03878i	−1.72369	−	0.461860i	−0.978713	+	0.205234i	$0.934204\pi$
$384$	−0.0668357	+	1.73076i	−0.00341069	+	0.0883225i
$385$	−31.6192	+	21.6964i	−1.61146	+	1.10575i
$386$		−	11.8042i		−	0.600819i
$387$	−21.1083	−	7.44288i	−1.07299	−	0.378343i
$388$	−2.33959	+	8.73148i	−0.118775	+	0.443274i
$389$	1.58196	−	2.74003i	0.0802085	−	0.138925i	−0.823131	−	0.567852i	$-0.807775\pi$
$389$	1.58196	−	2.74003i	0.0802085	−	0.138925i	0.903339	+	0.428926i	$0.141108\pi$
$390$	−1.35226	+	1.33544i	−0.0684743	+	0.0676226i
$391$	2.41998	−	4.19153i	0.122384	−	0.211975i
$392$	−2.41806	−	6.56909i	−0.122130	−	0.331789i
$393$	−6.41684	+	20.7148i	−0.323687	+	1.04492i
$394$			24.0559i			1.21192i
$395$	−1.44316	−	2.32278i	−0.0726131	−	0.116872i
$396$	16.0404	+	10.9925i	0.806062	+	0.552396i
$397$	−6.39214	−	23.8558i	−0.320812	−	1.19729i	−0.918455	−	0.395525i	$-0.870563\pi$
$397$	−6.39214	−	23.8558i	−0.320812	−	1.19729i	0.597643	−	0.801763i	$-0.296104\pi$
$398$	−12.5324	−	3.35804i	−0.628192	−	0.168324i
$399$	12.5462	−	12.7195i	0.628098	−	0.636769i
$400$	−2.21491	+	4.48265i	−0.110745	+	0.224133i
$401$	−5.69088	+	3.28563i	−0.284189	+	0.164077i	−0.635318	−	0.772250i	$-0.719131\pi$
$401$	−5.69088	+	3.28563i	−0.284189	+	0.164077i	0.351129	+	0.936327i	$0.385798\pi$
$402$	5.63121	−	5.21247i	0.280859	−	0.259974i
$403$	−4.63849	+	1.24288i	−0.231059	+	0.0619122i
$404$	−0.347349	+	0.601627i	−0.0172813	+	0.0299320i
$405$	18.5238	−	7.86559i	0.920457	−	0.390845i
$406$	3.27622	+	10.3253i	0.162596	+	0.512437i
$407$	13.8641	−	51.7415i	0.687218	−	2.56473i
$408$	1.77299	+	0.549221i	0.0877761	+	0.0271905i
$409$		−	11.2186i		−	0.554723i	−0.960766	−	0.277362i	$-0.910540\pi$
$409$		−	11.2186i		−	0.554723i	0.960766	−	0.277362i	$-0.0894600\pi$
$410$	3.57031	+	3.34655i	0.176325	+	0.165274i
$411$	−7.51205	+	11.9236i	−0.370542	+	0.588150i
$412$	8.41091	+	2.25370i	0.414376	+	0.111032i
$413$	−9.38652	+	6.00391i	−0.461881	+	0.295433i
$414$	12.2216	−	5.84962i	0.600661	−	0.287493i
$415$	−14.7474	+	4.46737i	−0.723923	+	0.219294i
$416$	−0.424971	−	0.245357i	−0.0208359	−	0.0120296i
$417$	−7.32585	+	1.66285i	−0.358749	+	0.0814302i
$418$	6.54053	−	24.4096i	0.319908	−	1.19391i
$419$	−15.9568	+	27.6381i	−0.779543	+	1.35021i	0.152663	+	0.988278i	$0.451215\pi$
$419$	−15.9568	+	27.6381i	−0.779543	+	1.35021i	−0.932206	+	0.361929i	$0.882118\pi$
$420$	−9.78627	+	3.03791i	−0.477521	+	0.148235i
$421$	1.82823	+	3.16658i	0.0891023	+	0.154330i	0.907132	−	0.420846i	$-0.138267\pi$
$421$	1.82823	+	3.16658i	0.0891023	+	0.154330i	−0.818030	+	0.575176i	$0.804934\pi$
$422$	11.1357	−	2.98381i	0.542078	−	0.145249i
$423$	15.9669	−	13.6742i	0.776339	−	0.664865i
$424$	−5.18645	+	2.99440i	−0.251876	+	0.145421i
$425$	4.02572	+	3.53597i	0.195276	+	0.171520i
$426$	0.640138	−	16.5769i	0.0310148	−	0.803152i
$427$	−2.24715	+	1.43735i	−0.108747	+	0.0695582i
$428$	−0.639421	−	2.38635i	−0.0309076	−	0.115349i
$429$	−4.87385	+	2.56845i	−0.235312	+	0.124006i
$430$	7.86980	−	14.7097i	0.379515	−	0.709364i
$431$	7.39425	−	4.26907i	0.356169	−	0.205634i	−0.311230	−	0.950335i	$-0.600741\pi$
$431$	7.39425	−	4.26907i	0.356169	−	0.205634i	0.667399	+	0.744701i	$0.267408\pi$
$432$	3.22514	+	4.07413i	0.155169	+	0.196016i
$433$	15.8763	+	15.8763i	0.762964	+	0.762964i	0.976857	−	0.213893i	$-0.0686144\pi$
$433$	15.8763	+	15.8763i	0.762964	+	0.762964i	−0.213893	+	0.976857i	$0.568614\pi$
$434$	−25.2877	−	5.55790i	−1.21385	−	0.266788i
$435$	15.3424	−	4.00824i	0.735611	−	0.192180i
$436$	−9.63257	−	16.6841i	−0.461316	−	0.799023i
$437$	−12.4509	−	12.4509i	−0.595608	−	0.595608i
$438$	5.29397	−	17.0900i	0.252956	−	0.816590i
$439$		−	32.3690i		−	1.54489i	−0.635084	−	0.772443i	$-0.719035\pi$
$439$		−	32.3690i		−	1.54489i	0.635084	−	0.772443i	$-0.280965\pi$
$440$	−9.91199	+	10.5747i	−0.472536	+	0.504131i
$441$	−18.3288	−	10.2497i	−0.872799	−	0.488080i
$442$	−0.371840	+	0.371840i	−0.0176866	+	0.0176866i
$443$	−12.1828	+	12.1828i	−0.578821	+	0.578821i	−0.934578	−	0.355757i	$-0.884223\pi$
$443$	−12.1828	+	12.1828i	−0.578821	+	0.578821i	0.355757	+	0.934578i	$0.384223\pi$
$444$	7.62993	−	12.1108i	0.362100	−	0.574751i
$445$	0.171552	+	5.30298i	0.00813236	+	0.251385i
$446$	17.8945	−	10.3314i	0.847327	−	0.489204i
$447$	−10.0319	−	3.10758i	−0.474491	−	0.146984i
$448$	−1.42562	−	2.22881i	−0.0673541	−	0.105302i
$449$	−22.0446			−1.04035			−0.520176	−	0.854059i	$-0.674133\pi$
$449$	−22.0446			−1.04035			−0.520176	+	0.854059i	$0.674133\pi$
$450$	3.70063	+	14.5363i	0.174450	+	0.685250i
$451$	7.09262	+	12.2848i	0.333978	+	0.578467i
$452$	2.40331	−	0.643964i	0.113042	−	0.0302895i
$453$	0.130271	+	0.573920i	0.00612065	+	0.0269651i
$454$	−11.6290	−	6.71403i	−0.545778	−	0.315105i
$455$	0.531185	−	2.85409i	0.0249023	−	0.133802i
$456$	3.59950	−	5.71337i	0.168562	−	0.267553i
$457$	6.80719	−	6.80719i	0.318427	−	0.318427i	−0.529736	−	0.848163i	$-0.677709\pi$
$457$	6.80719	−	6.80719i	0.318427	−	0.318427i	0.848163	+	0.529736i	$0.177709\pi$
$458$	20.4270	+	5.47340i	0.954491	+	0.255755i
$459$	5.11168	−	2.20838i	0.238593	−	0.103079i
$460$	2.92789	+	9.66540i	0.136514	+	0.450652i
$461$	12.7649	−	7.36980i	0.594519	−	0.343246i	−0.172363	−	0.985033i	$-0.555140\pi$
$461$	12.7649	−	7.36980i	0.594519	−	0.343246i	0.766882	+	0.641788i	$0.221807\pi$
$462$	−29.7029	+	0.203626i	−1.38191	+	0.00947352i
$463$	−17.4273	+	4.66963i	−0.809915	+	0.217016i	−0.639932	−	0.768431i	$-0.721038\pi$
$463$	−17.4273	+	4.66963i	−0.809915	+	0.217016i	−0.169982	+	0.985447i	$0.554371\pi$
$464$	2.04717	+	3.54581i	0.0950376	+	0.164610i
$465$	−10.0384	+	36.5474i	−0.465519	+	1.69484i
$466$	−3.19985	+	5.54231i	−0.148230	+	0.256743i
$467$	8.89319	−	2.38292i	0.411528	−	0.110269i	−0.0471145	−	0.998889i	$-0.515003\pi$
$467$	8.89319	−	2.38292i	0.411528	−	0.110269i	0.458642	+	0.888621i	$0.348336\pi$
$468$	−1.44713	+	0.270224i	−0.0668936	+	0.0124911i
$469$	−2.51612	+	11.4480i	−0.116184	+	0.528620i
$470$	8.26912	+	13.3093i	0.381426	+	0.613912i
$471$	−1.07792	+	27.9137i	−0.0496681	+	1.28619i
$472$	−2.97794	+	2.97794i	−0.137071	+	0.137071i
$473$	34.1950	−	34.1950i	1.57229	−	1.57229i
$474$	0.0817366	−	2.11663i	0.00375429	−	0.0972201i
$475$	16.2165	−	10.8174i	0.744064	−	0.496337i
$476$	−2.70247	+	0.857495i	−0.123868	+	0.0393032i
$477$	−5.97452	+	16.9439i	−0.273554	+	0.775809i
$478$	−22.1248	+	5.92832i	−1.01196	+	0.271155i
$479$	−20.2724	+	35.1129i	−0.926271	+	1.60435i	−0.136767	+	0.990603i	$0.543671\pi$
$479$	−20.2724	+	35.1129i	−0.926271	+	1.60435i	−0.789504	+	0.613745i	$0.789662\pi$
$480$	−3.36616	+	1.91546i	−0.153643	+	0.0874285i
$481$	2.02766	+	3.51200i	0.0924531	+	0.160134i
$482$	21.7313	−	5.82288i	0.989833	−	0.265225i
$483$	−10.2254	+	17.9947i	−0.465273	+	0.818788i
$484$	−26.8594	+	15.5073i	−1.22088	+	0.704876i
$485$	−19.3448	+	5.86003i	−0.878403	+	0.266090i
$486$	15.2991	+	2.98971i	0.693980	+	0.135616i
$487$	−3.40855	−	0.913318i	−0.154456	−	0.0413864i	0.180762	−	0.983527i	$-0.442143\pi$
$487$	−3.40855	−	0.913318i	−0.154456	−	0.0413864i	−0.335219	+	0.942140i	$0.608810\pi$
$488$	−0.712925	+	0.712925i	−0.0322726	+	0.0322726i
$489$	18.9003	−	29.9999i	0.854701	−	1.35664i
$490$	9.62341	−	12.3446i	0.434742	−	0.557674i
$491$	−24.3816	−	14.0767i	−1.10033	−	0.635274i	−0.164019	−	0.986457i	$-0.552446\pi$
$491$	−24.3816	−	14.0767i	−1.10033	−	0.635274i	−0.936307	+	0.351184i	$0.885779\pi$
$492$	0.839042	+	3.69648i	0.0378269	+	0.166650i
$493$	4.23810	−	1.13560i	0.190874	−	0.0511446i
$494$	0.956567	+	1.65682i	0.0430380	+	0.0745440i
$495$	−1.94974	+	43.4379i	−0.0876341	+	1.95239i
$496$	−9.78597			−0.439403
$497$	13.6543	+	21.3471i	0.612478	+	0.957549i
$498$	−11.4014	−	3.53183i	−0.510910	−	0.158265i
$499$	25.3627	−	14.6431i	1.13539	−	0.655517i	0.190104	−	0.981764i	$-0.439117\pi$
$499$	25.3627	−	14.6431i	1.13539	−	0.655517i	0.945285	+	0.326247i	$0.105784\pi$
$500$	−11.1278	+	1.08298i	−0.497649	+	0.0484323i
$501$	−1.39512	+	2.21444i	−0.0623295	+	0.0989337i
$502$	−12.4731	+	12.4731i	−0.556700	+	0.556700i
$503$	−2.88421	+	2.88421i	−0.128601	+	0.128601i	−0.768478	−	0.639877i	$-0.778985\pi$
$503$	−2.88421	+	2.88421i	−0.128601	+	0.128601i	0.639877	+	0.768478i	$0.278985\pi$
$504$	−7.59774	−	2.29660i	−0.338430	−	0.102298i
$505$	−1.55258	+	0.0502263i	−0.0690890	+	0.00223504i
$506$			29.2752i			1.30144i
$507$	−6.53925	+	21.1099i	−0.290418	+	0.937526i
$508$	−10.9407	−	10.9407i	−0.485417	−	0.485417i
$509$	12.1113	+	20.9773i	0.536823	+	0.929804i	0.999073	+	0.0430543i	$0.0137089\pi$
$509$	12.1113	+	20.9773i	0.536823	+	0.929804i	−0.462250	+	0.886750i	$0.652958\pi$
$510$	1.04909	+	4.01561i	0.0464544	+	0.177814i
$511$	8.26544	+	26.0493i	0.365642	+	1.15235i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.94734	−	20.0426i	−0.130128	−	0.884900i
$514$	2.23606	−	1.29099i	0.0986285	−	0.0569432i
$515$	5.64489	+	18.6346i	0.248744	+	0.821139i
$516$	11.4320	−	6.02449i	0.503266	−	0.265213i
$517$	11.7558	+	43.8731i	0.517018	+	1.92954i
$518$	0.993465	+	21.8422i	0.0436504	+	0.959690i
$519$	0.621698	−	16.0993i	0.0272895	−	0.706682i
$520$	−0.0354783	−	1.09670i	−0.00155583	−	0.0480933i
$521$	12.6879	−	7.32535i	0.555866	−	0.320929i	−0.195619	−	0.980680i	$-0.562671\pi$
$521$	12.6879	−	7.32535i	0.555866	−	0.320929i	0.751485	+	0.659751i	$0.229338\pi$
$522$	11.5840	+	4.08458i	0.507018	+	0.178777i
$523$	3.19096	−	0.855016i	0.139531	−	0.0373872i	−0.188378	−	0.982097i	$-0.560323\pi$
$523$	3.19096	−	0.855016i	0.139531	−	0.0373872i	0.327909	+	0.944709i	$0.393656\pi$
$524$	−6.26018	−	10.8429i	−0.273477	−	0.473676i
$525$	−17.3184	−	15.0024i	−0.755837	−	0.654760i
$526$	−8.28569	+	14.3512i	−0.361273	+	0.625744i
$527$	−2.71421	+	10.1296i	−0.118233	+	0.441251i
$528$	−10.9484	+	2.48512i	−0.476469	+	0.108151i
$529$	−2.25295	−	1.30074i	−0.0979541	−	0.0565538i
$530$	−11.8077	−	6.31720i	−0.512893	−	0.274402i
$531$	−0.974330	+	12.5967i	−0.0422823	+	0.546650i
$532$	0.468677	+	10.3043i	0.0203197	+	0.446747i
$533$	−1.03731	−	0.277947i	−0.0449309	−	0.0120392i
$534$	−2.19072	+	3.47726i	−0.0948018	+	0.150476i
$535$	3.77791	−	4.03051i	0.163333	−	0.174254i
$536$			4.43022i			0.191356i
$537$	24.3445	+	7.54121i	1.05054	+	0.325427i
$538$	2.06508	−	7.70697i	0.0890317	−	0.332271i
$539$	37.0725	−	26.1600i	1.59682	−	1.12679i
$540$	−3.93225	+	10.9333i	−0.169217	+	0.470495i
$541$	6.03604	−	10.4547i	0.259509	−	0.449484i	−0.706601	−	0.707612i	$-0.749772\pi$
$541$	6.03604	−	10.4547i	0.259509	−	0.449484i	0.966111	+	0.258129i	$0.0831058\pi$
$542$	−26.0188	+	6.97173i	−1.11760	+	0.299461i
$543$	−14.8778	+	13.7714i	−0.638466	+	0.590989i
$544$	−0.928054	+	0.535813i	−0.0397900	+	0.0229728i
$545$	20.3216	−	37.9837i	0.870480	−	1.62704i
$546$	1.57916	−	1.60096i	0.0675817	−	0.0685147i
$547$	33.2030	+	8.89672i	1.41966	+	0.380396i	0.885362	−	0.464902i	$-0.153910\pi$
$547$	33.2030	+	8.89672i	1.41966	+	0.380396i	0.534295	+	0.845298i	$0.320577\pi$
$548$	−2.10586	−	7.85918i	−0.0899579	−	0.335728i
$549$	−0.233257	+	3.01568i	−0.00995516	+	0.128706i
$550$	−31.7817	−	6.34728i	−1.35518	−	0.270649i
$551$		−	15.9625i		−	0.680026i
$552$	−2.31475	+	7.47245i	−0.0985222	+	0.318049i
$553$	1.74346	+	2.72573i	0.0741394	+	0.115910i
$554$	−3.88966	+	6.73710i	−0.165256	+	0.286232i
$555$	32.0061	+	0.200306i	1.35858	+	0.00850253i
$556$	2.16859	−	3.75610i	0.0919685	−	0.159294i
$557$	−0.159929	+	0.596864i	−0.00677642	+	0.0252900i	−0.969231	−	0.246152i	$-0.920834\pi$
$557$	−0.159929	+	0.596864i	−0.00677642	+	0.0252900i	0.962455	+	0.271442i	$0.0875005\pi$
$558$	−22.2983	+	19.0965i	−0.943961	+	0.808418i
$559$			3.66106i			0.154846i
$560$	2.55093	−	5.33786i	0.107797	−	0.225566i
$561$	−0.464249	+	12.0221i	−0.0196006	+	0.507573i
$562$	−25.1108	−	6.72841i	−1.05923	−	0.283821i
$563$	−5.75355	+	5.75355i	−0.242483	+	0.242483i	−0.817877	−	0.575394i	$-0.804849\pi$
$563$	−5.75355	+	5.75355i	−0.242483	+	0.242483i	0.575394	+	0.817877i	$0.304849\pi$
$564$	−0.468342	+	12.1281i	−0.0197207	+	0.510684i
$565$	4.05915	+	3.80475i	0.170770	+	0.160067i
$566$		−	10.1342i		−	0.425972i
$567$	−21.7938	+	9.59331i	−0.915252	+	0.402881i
$568$	6.77252	+	6.77252i	0.284169	+	0.284169i
$569$	25.3384			1.06224			0.531120	−	0.847297i	$-0.321771\pi$
$569$	25.3384			1.06224			0.531120	+	0.847297i	$0.321771\pi$
$570$	15.0992	+	0.0944965i	0.632436	+	0.00395802i
$571$	−12.7408			−0.533187			−0.266593	−	0.963809i	$-0.585898\pi$
$571$	−12.7408			−0.533187			−0.266593	+	0.963809i	$0.585898\pi$
$572$	0.823237	−	3.07236i	0.0344212	−	0.128462i
$573$	−18.6358	−	20.1329i	−0.778521	−	0.841063i
$574$	−4.27601	−	3.90396i	−0.178477	−	0.162948i
$575$	−14.9027	+	16.9668i	−0.621485	+	0.707565i
$576$	−2.99107	−	0.231353i	−0.124628	−	0.00963971i
$577$	38.0173	+	10.1867i	1.58268	+	0.424078i	0.939754	−	0.341851i	$-0.111054\pi$
$577$	38.0173	+	10.1867i	1.58268	+	0.424078i	0.642925	+	0.765929i	$0.277720\pi$
$578$	−4.10270	−	15.3115i	−0.170650	−	0.636874i
$579$	20.4303	+	0.788943i	0.849053	+	0.0327873i
$580$	−4.31886	+	8.07253i	−0.179331	+	0.335194i
$581$	17.3786	−	5.51422i	0.720985	−	0.228769i
$582$	−14.9557	−	4.63285i	−0.619935	−	0.192038i
$583$	−27.4489	−	27.4489i	−1.13682	−	1.13682i
$584$	5.16473	+	8.94557i	0.213718	+	0.370170i
$585$	−2.22095	−	2.42969i	−0.0918248	−	0.100455i
$586$	12.2283	−	21.1800i	0.505144	−	0.874936i
$587$	0.678802	−	2.53332i	0.0280172	−	0.104561i	−0.950501	−	0.310720i	$-0.899430\pi$
$587$	0.678802	−	2.53332i	0.0280172	−	0.104561i	0.978519	+	0.206159i	$0.0660964\pi$
$588$	11.5311	−	3.74603i	0.475536	−	0.154484i
$589$	33.0409	+	19.0762i	1.36143	+	0.786019i
$590$	−9.17024	−	2.14193i	−0.377533	−	0.0881820i
$591$	−41.6350	−	1.60779i	−1.71263	−	0.0661357i
$592$	2.13891	+	7.98251i	0.0879085	+	0.328079i
$593$	−1.42903	−	5.33320i	−0.0586831	−	0.219008i	0.930357	−	0.366655i	$-0.119497\pi$
$593$	−1.42903	−	5.33320i	−0.0586831	−	0.219008i	−0.989040	+	0.147646i	$0.952830\pi$
$594$	−20.0975	+	27.0274i	−0.824611	+	1.10895i
$595$	−4.81775	−	4.12099i	−0.197509	−	0.168944i
$596$	5.25108	−	3.03171i	0.215093	−	0.124184i
$597$	6.64958	−	21.4661i	0.272149	−	0.878550i
$598$	−1.56716	−	1.56716i	−0.0640859	−	0.0640859i
$599$	2.83671			0.115905			0.0579524	−	0.998319i	$-0.481543\pi$
$599$	2.83671			0.115905			0.0579524	+	0.998319i	$0.481543\pi$
$600$	−7.61037	−	4.13307i	−0.310692	−	0.168732i
$601$	−6.30431	−	10.9194i	−0.257158	−	0.445411i	0.708321	−	0.705890i	$-0.249453\pi$
$601$	−6.30431	−	10.9194i	−0.257158	−	0.445411i	−0.965479	+	0.260479i	$0.916119\pi$
$602$	−9.08263	+	17.5253i	−0.370181	+	0.714280i
$603$	8.64517	+	10.0947i	0.352059	+	0.411087i
$604$	−0.294260	−	0.169891i	−0.0119732	−	0.00691276i
$605$	−61.1492	−	32.7153i	−2.48607	−	1.33007i
$606$	−1.01806	−	0.641389i	−0.0413557	−	0.0260546i
$607$	−19.9818	−	5.35410i	−0.811036	−	0.217316i	−0.170612	−	0.985338i	$-0.554574\pi$
$607$	−19.9818	−	5.35410i	−0.811036	−	0.217316i	−0.640423	+	0.768022i	$0.721241\pi$
$608$	1.00905	+	3.76583i	0.0409224	+	0.152725i
$609$	−18.0896	+	4.98026i	−0.733028	+	0.201810i
$610$	−2.19538	−	0.512783i	−0.0888882	−	0.0207620i
$611$	−2.97792	−	1.71931i	−0.120474	−	0.0695557i
$612$	−1.06907	+	3.03192i	−0.0432146	+	0.122558i
$613$	−0.579778	+	2.16376i	−0.0234170	+	0.0873935i	−0.976645	−	0.214857i	$-0.931071\pi$
$613$	−0.579778	+	2.16376i	−0.0234170	+	0.0873935i	0.953228	+	0.302251i	$0.0977380\pi$
$614$	18.8228			0.759626
$615$	−6.03071	+	5.95569i	−0.243182	+	0.240157i
$616$	11.5629	−	12.6649i	0.465884	−	0.510284i
$617$	−38.7840	+	10.3922i	−1.56139	+	0.418372i	−0.933102	−	0.359611i	$-0.882909\pi$
$617$	−38.7840	+	10.3922i	−1.56139	+	0.418372i	−0.628285	+	0.777984i	$0.716243\pi$
$618$	−4.46276	+	14.4067i	−0.179519	+	0.579520i
$619$	14.9205	+	8.61436i	0.599706	+	0.346240i	0.768926	−	0.639338i	$-0.220792\pi$
$619$	14.9205	+	8.61436i	0.599706	+	0.346240i	−0.169220	+	0.985578i	$0.554125\pi$
$620$	−11.5481	−	18.5868i	−0.463781	−	0.746463i
$621$	9.30746	+	21.5437i	0.373495	+	0.864519i
$622$	7.98512	−	7.98512i	0.320174	−	0.320174i
$623$	−0.285246	−	6.27137i	−0.0114281	−	0.251257i
$624$	0.453058	−	0.719124i	0.0181368	−	0.0287880i
$625$	−15.1884	−	19.8573i	−0.607536	−	0.794292i
$626$			12.7224i			0.508491i
$627$	41.8100	+	12.9515i	1.66973	+	0.517234i
$628$	−11.4042	−	11.4042i	−0.455077	−	0.455077i
$629$	8.85602			0.353113
$630$	−4.60382	−	17.1407i	−0.183420	−	0.682903i
$631$	18.7023			0.744525			0.372263	−	0.928127i	$-0.378582\pi$
$631$	18.7023			0.744525			0.372263	+	0.928127i	$0.378582\pi$
$632$	0.864755	+	0.864755i	0.0343981	+	0.0343981i
$633$	4.41999	+	19.4727i	0.175679	+	0.773970i
$634$		−	2.72395i		−	0.108182i
$635$	7.86931	−	33.6908i	0.312284	−	1.33698i
$636$	−4.83595	−	9.17664i	−0.191758	−	0.363878i
$637$	−0.584169	+	3.38496i	−0.0231456	+	0.134117i
$638$	−18.7659	+	18.7659i	−0.742949	+	0.742949i
$639$	28.6478	+	2.21585i	1.13329	+	0.0876578i
$640$	0.508599	−	2.17746i	0.0201041	−	0.0860716i
$641$	17.3172	+	9.99807i	0.683987	+	0.394900i	0.801356	−	0.598188i	$-0.204113\pi$
$641$	17.3172	+	9.99807i	0.683987	+	0.394900i	−0.117369	+	0.993088i	$0.537446\pi$
$642$	4.17294	−	0.947191i	0.164693	−	0.0373827i
$643$	−29.4027	+	7.87844i	−1.15953	+	0.310695i	−0.786778	−	0.617235i	$-0.788253\pi$
$643$	−29.4027	+	7.87844i	−1.15953	+	0.310695i	−0.372752	+	0.927931i	$0.621586\pi$
$644$	−3.61400	−	11.3898i	−0.142412	−	0.448823i
$645$	24.9330	+	14.6039i	0.981735	+	0.575027i
$646$	4.17792			0.164378
$647$	−8.02593	+	29.9532i	−0.315532	+	1.17758i	0.607962	+	0.793966i	$0.291987\pi$
$647$	−8.02593	+	29.9532i	−0.315532	+	1.17758i	−0.923493	+	0.383614i	$0.874679\pi$
$648$	−7.26689	+	5.30964i	−0.285470	+	0.208582i
$649$	−23.6408	−	13.6490i	−0.927981	−	0.535770i
$650$	2.04112	−	1.36156i	0.0800594	−	0.0534046i
$651$	11.3095	−	43.3955i	0.443255	−	1.70080i
$652$	5.29834	+	19.7737i	0.207499	+	0.774398i
$653$	−15.1223	−	4.05200i	−0.591779	−	0.158567i	−0.0495131	−	0.998773i	$-0.515767\pi$
$653$	−15.1223	−	4.05200i	−0.591779	−	0.158567i	−0.542266	+	0.840207i	$0.682434\pi$
$654$	29.5200	−	15.5566i	1.15432	−	0.608310i
$655$	13.2069	−	24.6855i	0.516037	−	0.964542i
$656$	−1.89525	−	1.09422i	−0.0739972	−	0.0427223i
$657$	29.2248	+	10.3048i	1.14017	+	0.402029i
$658$	−9.98982	−	15.6181i	−0.389444	−	0.608857i
$659$	24.0964	+	41.7361i	0.938661	+	1.62581i	0.767971	+	0.640484i	$0.221266\pi$
$659$	24.0964	+	41.7361i	0.938661	+	1.62581i	0.170690	+	0.985325i	$0.445400\pi$
$660$	−17.6399	−	17.8621i	−0.686631	−	0.695280i
$661$	31.3654			1.21997			0.609986	−	0.792412i	$-0.291175\pi$
$661$	31.3654			1.21997			0.609986	+	0.792412i	$0.291175\pi$
$662$	23.1536	+	23.1536i	0.899889	+	0.899889i
$663$	−0.618714	−	0.668419i	−0.0240289	−	0.0259592i
$664$	5.96797	−	3.44561i	0.231602	−	0.133715i
$665$	−19.0181	+	13.0499i	−0.737491	+	0.506052i
$666$	20.4509	+	14.0150i	0.792455	+	0.543071i
$667$	4.78608	+	17.8619i	0.185318	+	0.691616i
$668$	−0.391097	−	1.45959i	−0.0151320	−	0.0564733i
$669$	16.6851	+	31.6615i	0.645085	+	1.22411i
$670$	−8.41444	+	5.22793i	−0.325078	+	0.201973i
$671$	−5.65965	−	3.26760i	−0.218488	−	0.126144i
$672$	3.95283	−	2.31844i	0.152484	−	0.0894358i
$673$	0.835724	−	3.11897i	0.0322148	−	0.120227i	−0.947946	−	0.318431i	$-0.896844\pi$
$673$	0.835724	−	3.11897i	0.0322148	−	0.120227i	0.980161	+	0.198204i	$0.0635108\pi$
$674$	4.18490	−	7.24847i	0.161197	−	0.279201i
$675$	−25.4063	+	5.43337i	−0.977888	+	0.209130i
$676$	−6.37960	−	11.0498i	−0.245369	−	0.424992i
$677$	4.03029	+	4.03029i	0.154896	+	0.154896i	0.780301	−	0.625404i	$-0.215066\pi$
$677$	4.03029	+	4.03029i	0.154896	+	0.154896i	−0.625404	+	0.780301i	$0.715066\pi$
$678$	0.953921	+	4.20259i	0.0366351	+	0.161399i
$679$	22.7962	−	7.23324i	0.874838	−	0.277586i
$680$	−2.11285	−	1.13039i	−0.0810240	−	0.0433484i
$681$	12.3976	−	19.6784i	0.475078	−	0.754076i
$682$	−16.4172	−	61.2700i	−0.628649	−	2.34615i
$683$	22.9210	+	6.14166i	0.877047	+	0.235004i	0.669132	−	0.743143i	$-0.266666\pi$
$683$	22.9210	+	6.14166i	0.877047	+	0.235004i	0.207914	+	0.978147i	$0.433333\pi$
$684$	9.64790	+	6.61172i	0.368897	+	0.252806i
$685$	12.4421	−	13.2741i	0.475389	−	0.507175i
$686$	−11.1941	+	14.7544i	−0.427391	+	0.563326i
$687$	−10.8384	+	34.9884i	−0.413510	+	1.33489i
$688$	−1.93097	+	7.20646i	−0.0736174	+	0.274744i
$689$	2.93879			0.111959
$690$	−16.9242	+	4.42149i	−0.644293	+	0.168323i
$691$	−6.93893			−0.263970			−0.131985	−	0.991252i	$-0.542135\pi$
$691$	−6.93893			−0.263970			−0.131985	+	0.991252i	$0.542135\pi$
$692$	6.57743	+	6.57743i	0.250036	+	0.250036i
$693$	1.63279	−	51.4223i	0.0620245	−	1.95337i
$694$			29.1810i			1.10769i
$695$	9.69314	−	0.313575i	0.367682	−	0.0118946i
$696$	−6.27377	+	3.30618i	−0.237807	+	0.125320i
$697$	−1.65830	+	1.65830i	−0.0628128	+	0.0628128i
$698$	13.5710	+	3.63633i	0.513669	+	0.137637i
$699$	−9.37855	−	5.90861i	−0.354729	−	0.223484i
$700$	13.1486	−	1.45394i	0.496971	−	0.0549539i
$701$		−	11.4817i		−	0.433658i	−0.976210	−	0.216829i	$-0.930429\pi$
$701$		−	11.4817i		−	0.433658i	0.976210	−	0.216829i	$-0.0695714\pi$
$702$	−0.370973	−	2.52269i	−0.0140015	−	0.0952130i
$703$	8.33890	−	31.1212i	0.314508	−	1.17376i
$704$	3.24093	−	5.61346i	0.122147	−	0.211565i
$705$	−23.5879	+	13.4223i	−0.888370	+	0.505515i
$706$	−16.1257	+	27.9305i	−0.606897	+	1.05118i
$707$	1.83610	−	0.0835129i	0.0690537	−	0.00314083i
$708$	−4.95507	−	5.35313i	−0.186223	−	0.201183i
$709$			17.1318i			0.643399i	0.946842	+	0.321699i	$0.104254\pi$
$709$			17.1318i			0.643399i	−0.946842	+	0.321699i	$0.895746\pi$
$710$	−4.87125	+	20.8553i	−0.182815	+	0.782684i
$711$	3.65792	+	0.282933i	0.137183	+	0.0106108i
$712$	−0.614128	−	2.29196i	−0.0230154	−	0.0858946i
$713$	−42.6921	−	11.4393i	−1.59883	−	0.428405i
$714$	−1.30350	−	4.73465i	−0.0487822	−	0.177190i
$715$	6.80690	−	2.06198i	0.254563	−	0.0771137i
$716$	−12.7429	+	7.35710i	−0.476223	+	0.274948i
$717$	−8.78178	−	38.6889i	−0.327962	−	1.44487i
$718$	28.0108	−	7.50548i	1.04536	−	0.280102i
$719$	19.0194	−	32.9426i	0.709305	−	1.22855i	−0.255811	−	0.966727i	$-0.582342\pi$
$719$	19.0194	−	32.9426i	0.709305	−	1.22855i	0.965115	−	0.261825i	$-0.0843243\pi$
$720$	−3.09023	−	5.95403i	−0.115166	−	0.221894i
$721$	−6.96768	−	21.9593i	−0.259490	−	0.817806i
$722$	−0.983602	+	3.67085i	−0.0366059	+	0.136615i
$723$	8.62559	+	38.0008i	0.320789	+	1.41327i
$724$		−	11.7047i		−	0.435002i
$725$	−20.4289	+	1.32314i	−0.758711	+	0.0491403i
$726$	−25.0442	−	47.5236i	−0.929478	−	1.76377i
$727$	−24.9002	−	6.67199i	−0.923497	−	0.247450i	−0.234418	−	0.972136i	$-0.575318\pi$
$727$	−24.9002	−	6.67199i	−0.923497	−	0.247450i	−0.689080	+	0.724686i	$0.741985\pi$
$728$	0.0589910	+	1.29697i	0.00218635	+	0.0480688i
$729$	−6.19700	+	26.2792i	−0.229519	+	0.973304i
$730$	−10.8959	+	20.3659i	−0.403275	+	0.753774i
$731$	6.92392	+	3.99753i	0.256090	+	0.147854i
$732$	−1.18625	−	1.28155i	−0.0438452	−	0.0473675i
$733$	−9.60051	+	35.8296i	−0.354603	+	1.32340i	0.526380	+	0.850249i	$0.323549\pi$
$733$	−9.60051	+	35.8296i	−0.354603	+	1.32340i	−0.880983	+	0.473147i	$0.843118\pi$
$734$	−1.03732	+	1.79669i	−0.0382882	+	0.0663171i
$735$	20.7224	+	17.4809i	0.764358	+	0.644792i
$736$	−2.25824	−	3.91138i	−0.0832397	−	0.144175i
$737$	−27.7376	+	7.43226i	−1.02173	+	0.273771i
$738$	−6.45380	+	1.20512i	−0.237568	+	0.0443612i
$739$	35.8976	−	20.7255i	1.32051	−	0.762399i	0.336704	−	0.941611i	$-0.390688\pi$
$739$	35.8976	−	20.7255i	1.32051	−	0.762399i	0.983811	+	0.179211i	$0.0573546\pi$
$740$	−12.6374	+	13.4823i	−0.464559	+	0.495621i
$741$	−2.93150	+	1.54485i	−0.107691	+	0.0567516i
$742$	14.0679	+	7.29077i	0.516448	+	0.267653i
$743$	1.99608	+	7.44946i	0.0732289	+	0.273294i	0.992826	−	0.119569i	$-0.0381513\pi$
$743$	1.99608	+	7.44946i	0.0732289	+	0.273294i	−0.919597	+	0.392863i	$0.871485\pi$
$744$	0.654052	−	16.9372i	0.0239787	−	0.620947i
$745$	11.9548	+	6.39592i	0.437991	+	0.234329i
$746$	12.3781	−	7.14652i	0.453196	−	0.261653i
$747$	6.87478	−	19.4971i	0.251535	−	0.713362i
$748$	−4.91165	−	4.91165i	−0.179588	−	0.179588i
$749$	−4.40716	+	4.82718i	−0.161034	+	0.176381i
$750$	−1.13064	−	19.3319i	−0.0412853	−	0.705901i
$751$	2.80897	+	4.86528i	0.102501	+	0.177537i	0.912714	−	0.408598i	$-0.133982\pi$
$751$	2.80897	+	4.86528i	0.102501	+	0.177537i	−0.810214	+	0.586135i	$0.800649\pi$
$752$	−4.95495	−	4.95495i	−0.180689	−	0.180689i
$753$	−20.7542	−	22.4215i	−0.756326	−	0.817086i
$754$		−	2.00915i		−	0.0731690i
$755$	−0.0245660	−	0.759378i	−0.000894048	−	0.0276366i
$756$	4.48266	−	12.9964i	0.163033	−	0.472674i
$757$	−10.9955	+	10.9955i	−0.399638	+	0.399638i	−0.878105	−	0.478468i	$-0.841192\pi$
$757$	−10.9955	+	10.9955i	−0.399638	+	0.399638i	0.478468	+	0.878105i	$0.341192\pi$
$758$	−2.69093	+	2.69093i	−0.0977389	+	0.0977389i
$759$	−50.6683	−	1.95663i	−1.83914	−	0.0710210i
$760$	−5.96181	+	6.36043i	−0.216257	+	0.230717i
$761$	26.5128	−	15.3072i	0.961088	−	0.554884i	0.0645800	−	0.997913i	$-0.479429\pi$
$761$	26.5128	−	15.3072i	0.961088	−	0.554884i	0.896508	+	0.443028i	$0.146096\pi$
$762$	19.6670	−	18.2046i	0.712461	−	0.659482i
$763$	−23.4534	+	45.2544i	−0.849070	+	1.63832i
$764$	15.8390			0.573036
$765$	−7.02018	+	1.54734i	−0.253815	+	0.0559440i
$766$	17.4616	+	30.2444i	0.630913	+	1.09277i
$767$	1.99620	−	0.534879i	0.0720785	−	0.0193134i
$768$	1.27109	−	1.17657i	0.0458666	−	0.0424559i
$769$	−21.6849	−	12.5198i	−0.781976	−	0.451474i	0.0551539	−	0.998478i	$-0.482435\pi$
$769$	−21.6849	−	12.5198i	−0.781976	−	0.451474i	−0.837130	+	0.547004i	$0.815768\pi$
$770$	37.6999	+	7.01644i	1.35861	+	0.252855i
$771$	2.08495	+	3.95637i	0.0750876	+	0.142485i
$772$	−8.34684	+	8.34684i	−0.300409	+	0.300409i
$773$	18.8786	+	5.05850i	0.679015	+	0.181942i	0.581812	−	0.813323i	$-0.302344\pi$
$773$	18.8786	+	5.05850i	0.679015	+	0.181942i	0.0972027	+	0.995265i	$0.469011\pi$
$774$	9.66289	+	20.1887i	0.347325	+	0.725668i
$775$	21.6750	−	43.8671i	0.778589	−	1.57575i
$776$	7.82843	−	4.51974i	0.281024	−	0.162249i
$777$	−37.8700	+	0.259614i	−1.35858	+	0.00931360i
$778$	−3.05611	+	0.818882i	−0.109567	+	0.0293583i
$779$	4.26603	+	7.38897i	0.152846	+	0.264737i
$780$	1.90049	+	0.0118940i	0.0680485	+	0.000425873i
$781$	−31.0410	+	53.7646i	−1.11073	+	1.92385i
$782$	−4.67505	+	1.25268i	−0.167179	+	0.0447956i
$783$	−7.84366	+	19.7762i	−0.280309	+	0.706742i
$784$	−2.93523	+	6.35488i	−0.104829	+	0.226960i
$785$	8.20267	−	35.1180i	0.292766	−	1.25342i
$786$	19.1850	−	10.1102i	0.684305	−	0.360618i
$787$	7.50525	−	7.50525i	0.267533	−	0.267533i	−0.560572	−	0.828105i	$-0.689419\pi$
$787$	7.50525	−	7.50525i	0.267533	−	0.267533i	0.828105	+	0.560572i	$0.189419\pi$
$788$	17.0101	−	17.0101i	0.605959	−	0.605959i
$789$	−24.2848	−	15.2997i	−0.864561	−	0.544685i
$790$	−0.621990	+	2.66292i	−0.0221294	+	0.0947425i
$791$	−4.86147	−	4.43847i	−0.172854	−	0.157814i
$792$	−3.56940	−	19.1152i	−0.126833	−	0.679229i
$793$	0.477894	−	0.128051i	0.0169705	−	0.00454723i
$794$	−12.3487	+	21.3885i	−0.438238	+	0.759050i
$795$	11.7227	−	20.0141i	0.415763	−	0.709826i
$796$	6.48724	+	11.2362i	0.229934	+	0.398258i
$797$	20.0083	−	5.36120i	0.708729	−	0.189903i	0.113592	−	0.993528i	$-0.463764\pi$
$797$	20.0083	−	5.36120i	0.708729	−	0.189903i	0.595137	+	0.803624i	$0.297098\pi$
$798$	−17.8655	+	0.122476i	−0.632433	+	0.00433559i
$799$	−6.50321	+	3.75463i	−0.230067	+	0.132829i
$800$	4.73589	−	1.60354i	0.167439	−	0.0566937i
$801$	−5.87190	−	4.02402i	−0.207473	−	0.142182i
$802$	6.34735	+	1.70077i	0.224133	+	0.0600562i
$803$	−47.3437	+	47.3437i	−1.67072	+	1.67072i
$804$	−7.66764	−	0.296096i	−0.270417	−	0.0104425i
$805$	17.3683	−	20.3049i	0.612153	−	0.715654i
$806$	4.15875	+	2.40106i	0.146486	+	0.0845736i
$807$	13.2009	+	4.08925i	0.464693	+	0.143948i
$808$	0.671027	−	0.179801i	0.0236067	−	0.00632539i
$809$	−9.63149	−	16.6822i	−0.338625	−	0.586516i	0.645549	−	0.763719i	$-0.276629\pi$
$809$	−9.63149	−	16.6822i	−0.338625	−	0.586516i	−0.984174	+	0.177203i	$0.943295\pi$
$810$	−18.6601	−	7.53651i	−0.655651	−	0.264806i
$811$	−15.3346			−0.538471			−0.269235	−	0.963074i	$-0.586771\pi$
$811$	−15.3346			−0.538471			−0.269235	+	0.963074i	$0.586771\pi$
$812$	4.98446	−	9.61774i	0.174920	−	0.337516i
$813$	−10.3274	−	45.4983i	−0.362198	−	1.59570i
$814$	−46.3902	+	26.7834i	−1.62598	+	0.938757i
$815$	−31.3044	+	33.3975i	−1.09654	+	1.16986i
$816$	−0.865336	−	1.64205i	−0.0302928	−	0.0574833i
$817$	20.5674	−	20.5674i	0.719564	−	0.719564i
$818$	−7.93273	+	7.93273i	−0.277362	+	0.277362i
$819$	2.66533	+	2.84015i	0.0931342	+	0.0992427i
$820$	−0.158223	−	4.89096i	−0.00552540	−	0.170800i
$821$		−	10.8808i		−	0.379744i	−0.981809	−	0.189872i	$-0.939193\pi$
$821$		−	10.8808i		−	0.379744i	0.981809	−	0.189872i	$-0.0608073\pi$
$822$	13.7431	−	3.11947i	0.479346	−	0.108804i
$823$	30.1966	+	30.1966i	1.05259	+	1.05259i	0.998538	+	0.0540493i	$0.0172128\pi$
$823$	30.1966	+	30.1966i	1.05259	+	1.05259i	0.0540493	+	0.998538i	$0.482787\pi$
$824$	−4.35381	−	7.54102i	−0.151672	−	0.262704i
$825$	13.1098	−	54.5823i	0.456424	−	1.90031i
$826$	10.8827	+	2.39187i	0.378657	+	0.0832238i
$827$	−20.7184	−	20.7184i	−0.720450	−	0.720450i	0.248247	−	0.968697i	$-0.420146\pi$
$827$	−20.7184	−	20.7184i	−0.720450	−	0.720450i	−0.968697	+	0.248247i	$0.920146\pi$
$828$	−12.7783	−	4.50570i	−0.444077	−	0.156584i
$829$	−27.1725	+	15.6881i	−0.943741	+	0.544869i	−0.891131	−	0.453746i	$-0.850087\pi$
$829$	−27.1725	+	15.6881i	−0.943741	+	0.544869i	−0.0526102	+	0.998615i	$0.516754\pi$
$830$	13.5869	+	7.26910i	0.471609	+	0.252314i
$831$	−11.4003	−	7.18236i	−0.395473	−	0.249153i
$832$	0.127006	+	0.473993i	0.00440315	+	0.0164328i
$833$	5.76389	+	4.80085i	0.199707	+	0.166340i
$834$	6.35597	+	4.00435i	0.220089	+	0.138659i
$835$	2.31073	−	2.46523i	0.0799661	−	0.0853129i
$836$	−21.8850	+	12.6353i	−0.756910	+	0.437002i
$837$	−31.5611	−	39.8693i	−1.09091	−	1.37808i
$838$	30.8263	−	8.25987i	1.06488	−	0.285332i
$839$	10.1837	+	17.6387i	0.351581	+	0.608956i	0.986527	−	0.163601i	$-0.0523108\pi$
$839$	10.1837	+	17.6387i	0.351581	+	0.608956i	−0.634946	+	0.772557i	$0.718977\pi$
$840$	9.06806	+	4.77182i	0.312878	+	0.164643i
$841$	6.11817	−	10.5970i	0.210971	−	0.365413i
$842$	0.946359	−	3.53186i	0.0326137	−	0.121716i
$843$	13.3236	−	43.0110i	0.458888	−	1.48138i
$844$	−9.98401	−	5.76427i	−0.343664	−	0.198414i
$845$	13.4589	−	25.1564i	0.462999	−	0.865407i
$846$	−20.9595	−	1.62118i	−0.720602	−	0.0557372i
$847$	72.8541	+	37.7571i	2.50330	+	1.29735i
$848$	5.78474	+	1.55002i	0.198649	+	0.0532278i
$849$	17.5399	+	0.677326i	0.601967	+	0.0232458i
$850$	−0.346310	−	5.34692i	−0.0118783	−	0.183398i
$851$			37.3246i			1.27947i
$852$	−12.1743	+	11.2690i	−0.417083	+	0.386069i
$853$	−1.87011	+	6.97936i	−0.0640315	+	0.238969i	−0.990523	−	0.137347i	$-0.956142\pi$
$853$	−1.87011	+	6.97936i	−0.0640315	+	0.238969i	0.926492	+	0.376316i	$0.122809\pi$
$854$	2.60534	+	0.572618i	0.0891528	+	0.0195946i
$855$	−1.17272	+	26.1268i	−0.0401060	+	0.893517i
$856$	−1.23527	+	2.13954i	−0.0422205	+	0.0731281i
$857$	41.2989	−	11.0660i	1.41074	−	0.378008i	0.528554	−	0.848900i	$-0.322735\pi$
$857$	41.2989	−	11.0660i	1.41074	−	0.378008i	0.882191	+	0.470892i	$0.156068\pi$
$858$	5.26250	+	1.63017i	0.179659	+	0.0556530i
$859$	−29.2669	+	16.8973i	−0.998574	+	0.576527i	−0.907826	−	0.419347i	$-0.862259\pi$
$859$	−29.2669	+	16.8973i	−0.998574	+	0.576527i	−0.0907481	+	0.995874i	$0.528926\pi$
$860$	−15.9661	+	4.83654i	−0.544440	+	0.164925i
$861$	7.04261	−	7.13983i	0.240011	−	0.243325i
$862$	−8.24721	−	2.20983i	−0.280901	−	0.0752673i
$863$	−11.9152	−	44.4680i	−0.405597	−	1.51371i	−0.802952	−	0.596044i	$-0.796738\pi$
$863$	−11.9152	−	44.4680i	−0.405597	−	1.51371i	0.397355	−	0.917665i	$-0.369928\pi$
$864$	0.600327	−	5.16136i	0.0204235	−	0.175593i
$865$	−4.73092	+	20.2545i	−0.160856	+	0.688673i
$866$		−	22.4524i		−	0.762964i
$867$	26.7747	−	6.07744i	0.909318	−	0.206401i
$868$	13.9511	+	21.8111i	0.473530	+	0.740317i
$869$	−3.96349	+	6.86497i	−0.134452	+	0.232878i
$870$	−13.6830	−	8.01446i	−0.463896	−	0.271715i
$871$	1.08698	−	1.88271i	0.0368311	−	0.0637933i
$872$	−4.98618	+	18.6087i	−0.168853	+	0.630170i
$873$	9.01793	−	25.5751i	0.305211	−	0.865588i
$874$			17.6083i			0.595608i
$875$	18.2777	+	23.2578i	0.617899	+	0.786257i
$876$	−15.8278	+	8.34103i	−0.534773	+	0.281817i
$877$	46.9887	+	12.5906i	1.58669	+	0.425153i	0.940990	−	0.338434i	$-0.109897\pi$
$877$	46.9887	+	12.5906i	1.58669	+	0.425153i	0.645704	+	0.763588i	$0.276564\pi$
$878$	−22.8883	+	22.8883i	−0.772443	+	0.772443i
$879$	35.8402	+	22.5798i	1.20886	+	0.761596i
$880$	14.4863	−	0.468634i	0.488333	−	0.0157977i
$881$		−	34.5512i		−	1.16406i	−0.813168	−	0.582029i	$-0.802259\pi$
$881$		−	34.5512i		−	1.16406i	0.813168	−	0.582029i	$-0.197741\pi$
$882$	5.71279	+	20.2080i	0.192360	+	0.680439i
$883$	−19.2523	−	19.2523i	−0.647893	−	0.647893i	0.304590	−	0.952483i	$-0.401480\pi$
$883$	−19.2523	−	19.2523i	−0.647893	−	0.647893i	−0.952483	+	0.304590i	$0.901480\pi$
$884$	0.525862			0.0176866
$885$	4.32007	−	15.7283i	0.145218	−	0.528702i
$886$	17.2290			0.578821
$887$	−8.37592	+	31.2594i	−0.281236	+	1.04959i	0.670310	+	0.742081i	$0.266161\pi$
$887$	−8.37592	+	31.2594i	−0.281236	+	1.04959i	−0.951546	+	0.307506i	$0.900506\pi$
$888$	−13.9588	+	3.16842i	−0.468426	+	0.106325i
$889$	−8.78755	+	39.9822i	−0.294725	+	1.34096i
$890$	3.62847	−	3.87108i	0.121627	−	0.129759i
$891$	−45.4348	−	36.5904i	−1.52212	−	1.22582i
$892$	−19.9587	−	5.34791i	−0.668266	−	0.179061i
$893$	7.07078	+	26.3885i	0.236615	+	0.883058i
$894$	4.89621	+	9.29099i	0.163754	+	0.310737i
$895$	−29.0109	−	15.5211i	−0.969729	−	0.518812i
$896$	−0.567945	+	2.58407i	−0.0189737	+	0.0863279i
$897$	2.81712	−	2.60763i	0.0940608	−	0.0870664i
$898$	15.5879	+	15.5879i	0.520176	+	0.520176i
$899$	−20.0336	−	34.6992i	−0.668157	−	1.15728i
$900$	7.66200	−	12.8955i	0.255400	−	0.429850i
$901$	3.20887	−	5.55793i	0.106903	−	0.185162i
$902$	3.67141	−	13.7019i	0.122245	−	0.456223i
$903$	−29.7251	−	16.8912i	−0.989191	−	0.562104i
$904$	−2.15474	−	1.24404i	−0.0716657	−	0.0413762i
$905$	22.2311	−	13.8123i	0.738987	−	0.459136i
$906$	0.313707	−	0.497938i	0.0104222	−	0.0165429i
$907$	−2.89279	−	10.7960i	−0.0960535	−	0.358477i	0.901124	−	0.433562i	$-0.142744\pi$
$907$	−2.89279	−	10.7960i	−0.0960535	−	0.358477i	−0.997177	+	0.0750857i	$0.976077\pi$
$908$	3.47544	+	12.9705i	0.115337	+	0.430442i
$909$	1.17813	−	1.71914i	0.0390762	−	0.0570204i
$910$	−2.39375	+	1.64254i	−0.0793522	+	0.0544498i
$911$	42.5170	−	24.5472i	1.40865	−	0.813285i	0.413392	−	0.910553i	$-0.364344\pi$
$911$	42.5170	−	24.5472i	1.40865	−	0.813285i	0.995258	+	0.0972684i	$0.0310105\pi$
$912$	−6.58519	+	1.49473i	−0.218057	+	0.0494956i
$913$	31.5850	+	31.5850i	1.04531	+	1.04531i
$914$	−9.62682			−0.318427
$915$	1.03423	−	3.76540i	0.0341908	−	0.124480i
$916$	−10.5738	−	18.3143i	−0.349368	−	0.605123i
$917$	−15.2423	+	29.4107i	−0.503345	+	0.971226i
$918$	−5.17607	−	2.05294i	−0.170836	−	0.0677572i
$919$	−15.1966	−	8.77378i	−0.501291	−	0.289420i	0.227956	−	0.973671i	$-0.426796\pi$
$919$	−15.1966	−	8.77378i	−0.501291	−	0.289420i	−0.729246	+	0.684251i	$0.760129\pi$
$920$	4.76414	−	8.90481i	0.157069	−	0.293583i
$921$	−1.25803	+	32.5777i	−0.0414536	+	1.07347i
$922$	−14.2374	−	3.81489i	−0.468882	−	0.125637i
$923$	−1.21644	−	4.53981i	−0.0400396	−	0.149430i
$924$	21.1471	+	20.8592i	0.695689	+	0.686216i
$925$	−40.5203	−	8.09252i	−1.33230	−	0.266080i
$926$	15.6249	+	9.02103i	0.513465	+	0.296449i
$927$	−24.6362	−	8.68685i	−0.809159	−	0.285314i
$928$	1.05969	−	3.95483i	0.0347862	−	0.129824i
$929$	−15.3457			−0.503476			−0.251738	−	0.967795i	$-0.581002\pi$
$929$	−15.3457			−0.503476			−0.251738	+	0.967795i	$0.581002\pi$
$930$	32.9411	−	18.7447i	1.08018	−	0.614662i
$931$	22.2981	−	15.7345i	0.730792	−	0.515679i
$932$	6.18164	−	1.65637i	0.202486	−	0.0542561i
$933$	13.2866	+	14.3540i	0.434985	+	0.469930i
$934$	−7.97342	−	4.60345i	−0.260898	−	0.150630i
$935$	3.53279	−	15.1249i	0.115535	−	0.494637i
$936$	1.21435	+	0.832197i	0.0396923	+	0.0272012i
$937$	18.6587	−	18.6587i	0.609554	−	0.609554i	−0.333275	−	0.942830i	$-0.608154\pi$
$937$	18.6587	−	18.6587i	0.609554	−	0.609554i	0.942830	+	0.333275i	$0.108154\pi$
$938$	9.87413	−	6.31580i	0.322402	−	0.206218i
$939$	−22.0195	−	0.850313i	−0.718579	−	0.0277489i
$940$	3.56393	−	15.2582i	0.116243	−	0.497669i
$941$		−	8.62838i		−	0.281277i	−0.990061	−	0.140639i	$-0.955084\pi$
$941$		−	8.62838i		−	0.281277i	0.990061	−	0.140639i	$-0.0449156\pi$
$942$	20.5002	−	18.9757i	0.667931	−	0.618263i
$943$	−6.98909	−	6.98909i	−0.227596	−	0.227596i
$944$	4.21144			0.137071
$945$	29.9742	−	6.82249i	0.975061	−	0.221936i
$946$	−48.3591			−1.57229
$947$	5.10771	+	5.10771i	0.165978	+	0.165978i	0.785209	−	0.619231i	$-0.212555\pi$
$947$	5.10771	+	5.10771i	0.165978	+	0.165978i	−0.619231	+	0.785209i	$0.712555\pi$
$948$	−1.55448	+	1.43889i	−0.0504872	+	0.0467329i
$949$		−	5.06881i		−	0.164541i
$950$	−19.1159	−	3.81773i	−0.620201	−	0.123863i
$951$	4.71451	+	0.182057i	0.152879	+	0.00590361i
$952$	2.51728	+	1.30460i	0.0815854	+	0.0422822i
$953$	27.2128	−	27.2128i	0.881508	−	0.881508i	−0.112179	−	0.993688i	$-0.535783\pi$
$953$	27.2128	−	27.2128i	0.881508	−	0.881508i	0.993688	+	0.112179i	$0.0357832\pi$
$954$	16.2058	−	7.75655i	0.524682	−	0.251127i
$955$	18.6911	+	30.0836i	0.604828	+	0.973481i
$956$	19.8365	+	11.4526i	0.641560	+	0.370405i
$957$	−31.2251	−	33.7335i	−1.00936	−	1.09045i
$958$	39.1633	−	10.4938i	1.26531	−	0.339039i
$959$	−14.5145	+	15.8978i	−0.468698	+	0.513366i
$960$	3.73467	+	1.02579i	0.120536	+	0.0331074i
$961$	64.7653			2.08920
$962$	1.04959	−	3.91713i	0.0338402	−	0.126293i
$963$	1.36046	+	7.28567i	0.0438402	+	0.234777i
$964$	−19.4837	−	11.2489i	−0.627529	−	0.362304i
$965$	−25.7032	−	6.00361i	−0.827415	−	0.193263i
$966$	19.9546	−	5.49372i	0.642030	−	0.176758i
$967$	9.42113	+	35.1601i	0.302963	+	1.13067i	0.934685	+	0.355478i	$0.115682\pi$
$967$	9.42113	+	35.1601i	0.302963	+	1.13067i	−0.631721	+	0.775196i	$0.717651\pi$
$968$	29.9578	+	8.02716i	0.962879	+	0.258003i
$969$	−0.279234	+	7.23097i	−0.00897028	+	0.232292i
$970$	17.8225	+	9.53518i	0.572247	+	0.306156i
$971$	−13.4424	−	7.76096i	−0.431386	−	0.249061i	0.268551	−	0.963266i	$-0.413455\pi$
$971$	−13.4424	−	7.76096i	−0.431386	−	0.249061i	−0.699937	+	0.714205i	$0.746789\pi$
$972$	−8.70403	−	12.9321i	−0.279182	−	0.414798i
$973$	−11.4632	+	0.521391i	−0.367494	+	0.0167150i
$974$	1.76440	+	3.05602i	0.0565349	+	0.0979213i
$975$	2.22011	+	3.62369i	0.0711003	+	0.116051i
$976$	1.00823			0.0322726
$977$	1.98640	+	1.98640i	0.0635505	+	0.0635505i	0.738168	−	0.674617i	$-0.235691\pi$
$977$	1.98640	+	1.98640i	0.0635505	+	0.0635505i	−0.674617	+	0.738168i	$0.735691\pi$
$978$	−34.5776	+	7.84858i	−1.10567	+	0.250970i
$979$	13.3197	−	7.69010i	0.425698	−	0.245777i
$980$	−15.5338	+	1.92419i	−0.496208	+	0.0614660i
$981$	24.9517	+	52.1318i	0.796647	+	1.66444i
$982$	7.28665	+	27.1941i	0.232526	+	0.867800i
$983$	6.00666	+	22.4172i	0.191583	+	0.714997i	0.993125	+	0.117059i	$0.0373466\pi$
$983$	6.00666	+	22.4172i	0.191583	+	0.714997i	−0.801542	+	0.597938i	$0.795987\pi$
$984$	2.02051	−	3.20710i	0.0644116	−	0.102238i
$985$	52.3807	+	12.2348i	1.66899	+	0.389833i
$986$	−3.79978	−	2.19380i	−0.121010	−	0.0698649i
$987$	27.6989	−	16.2461i	0.881665	−	0.517121i
$988$	0.495156	−	1.84795i	0.0157530	−	0.0587910i
$989$	−16.8480	+	29.1815i	−0.535734	+	0.927919i
$990$	32.0939	−	29.3366i	1.02001	−	0.932378i
$991$	−0.776473	−	1.34489i	−0.0246655	−	0.0427219i	0.853429	−	0.521209i	$-0.174519\pi$
$991$	−0.776473	−	1.34489i	−0.0246655	−	0.0427219i	−0.878095	+	0.478487i	$0.841185\pi$
$992$	6.91973	+	6.91973i	0.219702	+	0.219702i
$993$	−41.6208	+	38.5258i	−1.32080	+	1.22258i
$994$	5.43966	−	24.7497i	0.172536	−	0.785014i
$995$	−13.6860	+	25.5809i	−0.433874	+	0.810968i
$996$	5.56465	+	10.5594i	0.176323	+	0.334588i
$997$	4.48960	+	16.7554i	0.142187	+	0.530649i	0.999865	+	0.0164611i	$0.00523997\pi$
$997$	4.48960	+	16.7554i	0.142187	+	0.530649i	−0.857678	+	0.514188i	$0.828093\pi$
$998$	−28.2884	−	7.57985i	−0.895453	−	0.239936i
$999$	−25.6235	+	34.4589i	−0.810691	+	1.09023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.19	yes	192
5.2	odd	4	inner	630.2.cd.a.527.30	yes	192
7.4	even	3		630.2.bt.a.473.26	yes	192
9.2	odd	6		630.2.bt.a.443.34	yes	192
35.32	odd	12		630.2.bt.a.347.34	yes	192
45.2	even	12		630.2.bt.a.317.26	✓	192
63.11	odd	6	inner	630.2.cd.a.263.30	yes	192
315.137	even	12	inner	630.2.cd.a.137.19	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.26	✓	192	45.2	even	12
630.2.bt.a.347.34	yes	192	35.32	odd	12
630.2.bt.a.443.34	yes	192	9.2	odd	6
630.2.bt.a.473.26	yes	192	7.4	even	3
630.2.cd.a.23.19	yes	192	1.1	even	1	trivial
630.2.cd.a.137.19	yes	192	315.137	even	12	inner
630.2.cd.a.263.30	yes	192	63.11	odd	6	inner
630.2.cd.a.527.30	yes	192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27109 - 1.17657i) q^{3} +1.00000i q^{4} +(-1.89933 + 1.18006i) q^{5} +(-1.73076 - 0.0668357i) q^{6} +(2.22881 - 1.42562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.231353 - 2.99107i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.27109 - 1.17657i) q^{3} +1.00000i q^{4} +(-1.89933 + 1.18006i) q^{5} +(-1.73076 - 0.0668357i) q^{6} +(2.22881 - 1.42562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.231353 - 2.99107i) q^{9} +(2.17746 + 0.508599i) q^{10} +(5.61346 + 3.24093i) q^{11} +(1.17657 + 1.27109i) q^{12} +(-0.473993 + 0.127006i) q^{13} +(-2.58407 - 0.567945i) q^{14} +(-1.02579 + 3.73467i) q^{15} -1.00000 q^{16} +(-0.277357 + 1.03511i) q^{17} +(-2.27859 + 1.95141i) q^{18} +(3.37635 + 1.94934i) q^{19} +(-1.18006 - 1.89933i) q^{20} +(1.15569 - 4.43445i) q^{21} +(-1.67763 - 6.26100i) q^{22} +(-4.36258 - 1.16895i) q^{23} +(0.0668357 - 1.73076i) q^{24} +(2.21491 - 4.48265i) q^{25} +(0.424971 + 0.245357i) q^{26} +(-3.22514 - 4.07413i) q^{27} +(1.42562 + 2.22881i) q^{28} +(-2.04717 - 3.54581i) q^{29} +(3.36616 - 1.91546i) q^{30} +9.78597 q^{31} +(0.707107 + 0.707107i) q^{32} +(10.9484 - 2.48512i) q^{33} +(0.928054 - 0.535813i) q^{34} +(-2.55093 + 5.33786i) q^{35} +(2.99107 + 0.231353i) q^{36} +(-2.13891 - 7.98251i) q^{37} +(-1.00905 - 3.76583i) q^{38} +(-0.453058 + 0.719124i) q^{39} +(-0.508599 + 2.17746i) q^{40} +(1.89525 + 1.09422i) q^{41} +(-3.95283 + 2.31844i) q^{42} +(1.93097 - 7.20646i) q^{43} +(-3.24093 + 5.61346i) q^{44} +(3.09023 + 5.95403i) q^{45} +(2.25824 + 3.91138i) q^{46} +(4.95495 + 4.95495i) q^{47} +(-1.27109 + 1.17657i) q^{48} +(2.93523 - 6.35488i) q^{49} +(-4.73589 + 1.60354i) q^{50} +(0.865336 + 1.64205i) q^{51} +(-0.127006 - 0.473993i) q^{52} +(-5.78474 - 1.55002i) q^{53} +(-0.600327 + 5.16136i) q^{54} +(-14.4863 + 0.468634i) q^{55} +(0.567945 - 2.58407i) q^{56} +(6.58519 - 1.49473i) q^{57} +(-1.05969 + 3.95483i) q^{58} -4.21144 q^{59} +(-3.73467 - 1.02579i) q^{60} -1.00823 q^{61} +(-6.91973 - 6.91973i) q^{62} +(-3.74848 - 6.99635i) q^{63} -1.00000i q^{64} +(0.750394 - 0.800568i) q^{65} +(-9.49894 - 5.98446i) q^{66} +(-3.13264 + 3.13264i) q^{67} +(-1.03511 - 0.277357i) q^{68} +(-6.92059 + 3.64705i) q^{69} +(5.57822 - 1.97065i) q^{70} +9.57780i q^{71} +(-1.95141 - 2.27859i) q^{72} +(-2.67346 + 9.97749i) q^{73} +(-4.13205 + 7.15692i) q^{74} +(-2.45882 - 8.30387i) q^{75} +(-1.94934 + 3.37635i) q^{76} +(17.1317 - 0.779214i) q^{77} +(0.828858 - 0.188138i) q^{78} +1.22295i q^{79} +(1.89933 - 1.18006i) q^{80} +(-8.89295 - 1.38399i) q^{81} +(-0.566412 - 2.11388i) q^{82} +(6.65640 + 1.78358i) q^{83} +(4.43445 + 1.15569i) q^{84} +(-0.694703 - 2.29331i) q^{85} +(-6.46114 + 3.73034i) q^{86} +(-6.77405 - 2.09840i) q^{87} +(6.26100 - 1.67763i) q^{88} +(1.18640 - 2.05491i) q^{89} +(2.02501 - 6.39526i) q^{90} +(-0.875381 + 0.958807i) q^{91} +(1.16895 - 4.36258i) q^{92} +(12.4389 - 11.5139i) q^{93} -7.00736i q^{94} +(-8.71314 + 0.281872i) q^{95} +(1.73076 + 0.0668357i) q^{96} +(8.73148 + 2.33959i) q^{97} +(-6.56909 + 2.41806i) q^{98} +(10.9925 - 16.0404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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