LMFDB - Embedded newform 570.2.k.a.77.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.12
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +(2.22222 - 0.248430i) q^{10} -4.73487i q^{11} +(-1.43759 + 0.966096i) q^{12} +(3.07524 - 3.07524i) q^{13} +0.524733 q^{14} +(0.318631 - 3.85985i) q^{15} -1.00000 q^{16} +(2.77446 - 2.77446i) q^{17} +(1.16275 + 2.76550i) q^{18} +1.00000i q^{19} +(1.39568 - 1.74702i) q^{20} +(0.174943 - 0.891868i) q^{21} +(-3.34806 - 3.34806i) q^{22} +(-5.62880 - 5.62880i) q^{23} +(-0.333395 + 1.69966i) q^{24} +(1.10414 + 4.87656i) q^{25} -4.34904i q^{26} +(5.08807 - 1.05428i) q^{27} +(0.371042 - 0.371042i) q^{28} -4.06253 q^{29} +(-2.50402 - 2.95464i) q^{30} +3.53345 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.80679 + 4.57434i) q^{33} -3.92368i q^{34} +(0.130360 + 1.16607i) q^{35} +(2.77770 + 1.13332i) q^{36} +(2.20796 + 2.20796i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-7.39190 - 1.44995i) q^{39} +(-0.248430 - 2.22222i) q^{40} +6.41083i q^{41} +(-0.506942 - 0.754350i) q^{42} +(-6.80047 + 6.80047i) q^{43} -4.73487 q^{44} +(-5.85671 + 3.27093i) q^{45} -7.96032 q^{46} +(5.86781 - 5.86781i) q^{47} +(0.966096 + 1.43759i) q^{48} -6.72466i q^{49} +(4.22899 + 2.66751i) q^{50} +(-6.66893 - 1.30814i) q^{51} +(-3.07524 - 3.07524i) q^{52} +(6.65823 + 6.65823i) q^{53} +(2.85232 - 4.34330i) q^{54} +(6.60838 - 8.27189i) q^{55} -0.524733i q^{56} +(1.43759 - 0.966096i) q^{57} +(-2.87264 + 2.87264i) q^{58} -6.00225 q^{59} +(-3.85985 - 0.318631i) q^{60} -3.00545 q^{61} +(2.49852 - 2.49852i) q^{62} +(-1.45115 + 0.610134i) q^{63} +1.00000i q^{64} +(9.66455 - 1.08043i) q^{65} +(-1.57858 + 8.04767i) q^{66} +(4.01127 + 4.01127i) q^{67} +(-2.77446 - 2.77446i) q^{68} +(-2.65393 + 13.5299i) q^{69} +(0.916717 + 0.732361i) q^{70} +3.67498i q^{71} +(2.76550 - 1.16275i) q^{72} +(7.51659 - 7.51659i) q^{73} +3.12253 q^{74} +(5.94379 - 6.29852i) q^{75} +1.00000 q^{76} +(1.75684 - 1.75684i) q^{77} +(-6.25213 + 4.20159i) q^{78} -7.93390i q^{79} +(-1.74702 - 1.39568i) q^{80} +(-6.43119 - 6.29602i) q^{81} +(4.53314 + 4.53314i) q^{82} +(7.74087 + 7.74087i) q^{83} +(-0.891868 - 0.174943i) q^{84} +(8.71931 - 0.974762i) q^{85} +9.61732i q^{86} +(3.92480 + 5.84025i) q^{87} +(-3.34806 + 3.34806i) q^{88} -7.13257 q^{89} +(-1.82842 + 6.45421i) q^{90} +2.28209 q^{91} +(-5.62880 + 5.62880i) q^{92} +(-3.41365 - 5.07964i) q^{93} -8.29833i q^{94} +(-1.39568 + 1.74702i) q^{95} +(1.69966 + 0.333395i) q^{96} +(5.01544 + 5.01544i) q^{97} +(-4.75505 - 4.75505i) q^{98} +(13.1520 + 5.36611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.966096	−	1.43759i	−0.557776	−	0.829992i
$3$	−0.966096	−	1.43759i	−0.557776	−	0.829992i
$4$		−	1.00000i		−	0.500000i
$5$	1.74702	+	1.39568i	0.781290	+	0.624169i
$5$	1.74702	+	1.39568i	0.781290	+	0.624169i
$6$	−1.69966	−	0.333395i	−0.693884	−	0.136108i
$7$	0.371042	+	0.371042i	0.140241	+	0.140241i	0.773742	−	0.633501i	$-0.218383\pi$
$7$	0.371042	+	0.371042i	0.140241	+	0.140241i	−0.633501	+	0.773742i	$0.718383\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.13332	+	2.77770i	−0.377772	+	0.925899i
$10$	2.22222	−	0.248430i	0.702729	−	0.0785605i
$11$		−	4.73487i		−	1.42762i	−0.700341	−	0.713808i	$-0.746969\pi$
$11$		−	4.73487i		−	1.42762i	0.700341	−	0.713808i	$-0.253031\pi$
$12$	−1.43759	+	0.966096i	−0.414996	+	0.278888i
$13$	3.07524	−	3.07524i	0.852917	−	0.852917i	−0.137574	−	0.990491i	$-0.543931\pi$
$13$	3.07524	−	3.07524i	0.852917	−	0.852917i	0.990491	+	0.137574i	$0.0439305\pi$
$14$	0.524733			0.140241
$15$	0.318631	−	3.85985i	0.0822703	−	0.996610i
$16$	−1.00000			−0.250000
$17$	2.77446	−	2.77446i	0.672906	−	0.672906i	−0.285479	−	0.958385i	$-0.592153\pi$
$17$	2.77446	−	2.77446i	0.672906	−	0.672906i	0.958385	+	0.285479i	$0.0921526\pi$
$18$	1.16275	+	2.76550i	0.274063	+	0.651835i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.39568	−	1.74702i	0.312084	−	0.390645i
$21$	0.174943	−	0.891868i	0.0381758	−	0.194622i
$22$	−3.34806	−	3.34806i	−0.713808	−	0.713808i
$23$	−5.62880	−	5.62880i	−1.17369	−	1.17369i	−0.981324	−	0.192362i	$-0.938385\pi$
$23$	−5.62880	−	5.62880i	−1.17369	−	1.17369i	−0.192362	−	0.981324i	$-0.561615\pi$
$24$	−0.333395	+	1.69966i	−0.0680540	+	0.346942i
$25$	1.10414	+	4.87656i	0.220827	+	0.975313i
$26$		−	4.34904i		−	0.852917i
$27$	5.08807	−	1.05428i	0.979200	−	0.202896i
$28$	0.371042	−	0.371042i	0.0701204	−	0.0701204i
$29$	−4.06253			−0.754393			−0.377197	−	0.926133i	$-0.623112\pi$
$29$	−4.06253			−0.754393			−0.377197	+	0.926133i	$0.623112\pi$
$30$	−2.50402	−	2.95464i	−0.457170	−	0.539440i
$31$	3.53345			0.634625			0.317313	−	0.948321i	$-0.397220\pi$
$31$	3.53345			0.634625			0.317313	+	0.948321i	$0.397220\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−6.80679	+	4.57434i	−1.18491	+	0.796290i
$34$		−	3.92368i		−	0.672906i
$35$	0.130360	+	1.16607i	0.0220348	+	0.197103i
$36$	2.77770	+	1.13332i	0.462949	+	0.188886i
$37$	2.20796	+	2.20796i	0.362987	+	0.362987i	0.864911	−	0.501925i	$-0.167375\pi$
$37$	2.20796	+	2.20796i	0.362987	+	0.362987i	−0.501925	+	0.864911i	$0.667375\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	−7.39190	−	1.44995i	−1.18365	−	0.232178i
$40$	−0.248430	−	2.22222i	−0.0392803	−	0.351365i
$41$			6.41083i			1.00120i	0.865678	+	0.500601i	$0.166888\pi$
$41$			6.41083i			1.00120i	−0.865678	+	0.500601i	$0.833112\pi$
$42$	−0.506942	−	0.754350i	−0.0782229	−	0.116399i
$43$	−6.80047	+	6.80047i	−1.03706	+	1.03706i	−0.0377764	+	0.999286i	$0.512027\pi$
$43$	−6.80047	+	6.80047i	−1.03706	+	1.03706i	−0.999286	+	0.0377764i	$0.987973\pi$
$44$	−4.73487			−0.713808
$45$	−5.85671	+	3.27093i	−0.873066	+	0.487601i
$46$	−7.96032			−1.17369
$47$	5.86781	−	5.86781i	0.855908	−	0.855908i	−0.134945	−	0.990853i	$-0.543086\pi$
$47$	5.86781	−	5.86781i	0.855908	−	0.855908i	0.990853	+	0.134945i	$0.0430859\pi$
$48$	0.966096	+	1.43759i	0.139444	+	0.207498i
$49$		−	6.72466i		−	0.960665i
$50$	4.22899	+	2.66751i	0.598070	+	0.377243i
$51$	−6.66893	−	1.30814i	−0.933837	−	0.183176i
$52$	−3.07524	−	3.07524i	−0.426459	−	0.426459i
$53$	6.65823	+	6.65823i	0.914579	+	0.914579i	0.996628	−	0.0820496i	$-0.0261466\pi$
$53$	6.65823	+	6.65823i	0.914579	+	0.914579i	−0.0820496	+	0.996628i	$0.526147\pi$
$54$	2.85232	−	4.34330i	0.388152	−	0.591048i
$55$	6.60838	−	8.27189i	0.891073	−	1.11538i
$56$		−	0.524733i		−	0.0701204i
$57$	1.43759	−	0.966096i	0.190413	−	0.127963i
$58$	−2.87264	+	2.87264i	−0.377197	+	0.377197i
$59$	−6.00225			−0.781426			−0.390713	−	0.920513i	$-0.627772\pi$
$59$	−6.00225			−0.781426			−0.390713	+	0.920513i	$0.627772\pi$
$60$	−3.85985	−	0.318631i	−0.498305	−	0.0411351i
$61$	−3.00545			−0.384809			−0.192404	−	0.981316i	$-0.561628\pi$
$61$	−3.00545			−0.384809			−0.192404	+	0.981316i	$0.561628\pi$
$62$	2.49852	−	2.49852i	0.317313	−	0.317313i
$63$	−1.45115	+	0.610134i	−0.182828	+	0.0768696i
$64$			1.00000i			0.125000i
$65$	9.66455	−	1.08043i	1.19874	−	0.134011i
$66$	−1.57858	+	8.04767i	−0.194310	+	0.990600i
$67$	4.01127	+	4.01127i	0.490055	+	0.490055i	0.908323	−	0.418269i	$-0.137363\pi$
$67$	4.01127	+	4.01127i	0.490055	+	0.490055i	−0.418269	+	0.908323i	$0.637363\pi$
$68$	−2.77446	−	2.77446i	−0.336453	−	0.336453i
$69$	−2.65393	+	13.5299i	−0.319496	+	1.62880i
$70$	0.916717	+	0.732361i	0.109569	+	0.0875339i
$71$			3.67498i			0.436140i	0.975933	+	0.218070i	$0.0699762\pi$
$71$			3.67498i			0.436140i	−0.975933	+	0.218070i	$0.930024\pi$
$72$	2.76550	−	1.16275i	0.325918	−	0.137032i
$73$	7.51659	−	7.51659i	0.879750	−	0.879750i	−0.113758	−	0.993508i	$-0.536289\pi$
$73$	7.51659	−	7.51659i	0.879750	−	0.879750i	0.993508	+	0.113758i	$0.0362890\pi$
$74$	3.12253			0.362987
$75$	5.94379	−	6.29852i	0.686330	−	0.727291i
$76$	1.00000			0.114708
$77$	1.75684	−	1.75684i	0.200210	−	0.200210i
$78$	−6.25213	+	4.20159i	−0.707914	+	0.475737i
$79$		−	7.93390i		−	0.892633i	−0.894875	−	0.446317i	$-0.852735\pi$
$79$		−	7.93390i		−	0.892633i	0.894875	−	0.446317i	$-0.147265\pi$
$80$	−1.74702	−	1.39568i	−0.195322	−	0.156042i
$81$	−6.43119	−	6.29602i	−0.714576	−	0.699558i
$82$	4.53314	+	4.53314i	0.500601	+	0.500601i
$83$	7.74087	+	7.74087i	0.849671	+	0.849671i	0.990092	−	0.140421i	$-0.0448455\pi$
$83$	7.74087	+	7.74087i	0.849671	+	0.849671i	−0.140421	+	0.990092i	$0.544846\pi$
$84$	−0.891868	−	0.174943i	−0.0973108	−	0.0190879i
$85$	8.71931	−	0.974762i	0.945742	−	0.105728i
$86$			9.61732i			1.03706i
$87$	3.92480	+	5.84025i	0.420782	+	0.626140i
$88$	−3.34806	+	3.34806i	−0.356904	+	0.356904i
$89$	−7.13257			−0.756051			−0.378026	−	0.925795i	$-0.623397\pi$
$89$	−7.13257			−0.756051			−0.378026	+	0.925795i	$0.623397\pi$
$90$	−1.82842	+	6.45421i	−0.192733	+	0.680334i
$91$	2.28209			0.239228
$92$	−5.62880	+	5.62880i	−0.586843	+	0.586843i
$93$	−3.41365	−	5.07964i	−0.353979	−	0.526734i
$94$		−	8.29833i		−	0.855908i
$95$	−1.39568	+	1.74702i	−0.143194	+	0.179240i
$96$	1.69966	+	0.333395i	0.173471	+	0.0340270i
$97$	5.01544	+	5.01544i	0.509241	+	0.509241i	0.914293	−	0.405053i	$-0.132747\pi$
$97$	5.01544	+	5.01544i	0.509241	+	0.509241i	−0.405053	+	0.914293i	$0.632747\pi$
$98$	−4.75505	−	4.75505i	−0.480333	−	0.480333i
$99$	13.1520	+	5.36611i	1.32183	+	0.539314i
$100$	4.87656	−	1.10414i	0.487656	−	0.110414i
$101$			14.1063i			1.40363i	0.712361	+	0.701813i	$0.247626\pi$
$101$			14.1063i			1.40363i	−0.712361	+	0.701813i	$0.752374\pi$
$102$	−5.64064	+	3.79066i	−0.558507	+	0.375331i
$103$	−5.16485	+	5.16485i	−0.508907	+	0.508907i	−0.914191	−	0.405284i	$-0.867173\pi$
$103$	−5.16485	+	5.16485i	−0.508907	+	0.508907i	0.405284	+	0.914191i	$0.367173\pi$
$104$	−4.34904			−0.426459
$105$	1.55039	−	1.31394i	0.151303	−	0.128228i
$106$	9.41616			0.914579
$107$	5.85663	−	5.85663i	0.566182	−	0.566182i	−0.364875	−	0.931057i	$-0.618888\pi$
$107$	5.85663	−	5.85663i	0.566182	−	0.566182i	0.931057	+	0.364875i	$0.118888\pi$
$108$	−1.05428	−	5.08807i	−0.101448	−	0.489600i
$109$			10.5464i			1.01016i	0.863073	+	0.505079i	$0.168537\pi$
$109$			10.5464i			1.01016i	−0.863073	+	0.505079i	$0.831463\pi$
$110$	−1.17628	−	10.5219i	−0.112154	−	1.00323i
$111$	1.04104	−	5.30724i	0.0988107	−	0.503741i
$112$	−0.371042	−	0.371042i	−0.0350602	−	0.0350602i
$113$	11.6877	+	11.6877i	1.09948	+	1.09948i	0.994471	+	0.105011i	$0.0334878\pi$
$113$	11.6877	+	11.6877i	1.09948	+	1.09948i	0.105011	+	0.994471i	$0.466512\pi$
$114$	0.333395	−	1.69966i	0.0312253	−	0.159188i
$115$	−1.97758	−	17.6896i	−0.184411	−	1.64957i
$116$			4.06253i			0.377197i
$117$	5.05685	+	12.0273i	0.467506	+	1.11192i
$118$	−4.24423	+	4.24423i	−0.390713	+	0.390713i
$119$	2.05889			0.188738
$120$	−2.95464	+	2.50402i	−0.269720	+	0.228585i
$121$	−11.4190			−1.03809
$122$	−2.12517	+	2.12517i	−0.192404	+	0.192404i
$123$	9.21612	−	6.19347i	0.830990	−	0.558447i
$124$		−	3.53345i		−	0.317313i
$125$	−4.87720	+	10.0605i	−0.436230	+	0.899835i
$126$	−0.594689	+	1.45755i	−0.0529791	+	0.129849i
$127$	11.5688	+	11.5688i	1.02656	+	1.02656i	0.999637	+	0.0269261i	$0.00857187\pi$
$127$	11.5688	+	11.5688i	1.02656	+	1.02656i	0.0269261	+	0.999637i	$0.491428\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	16.3462	+	3.20637i	1.43920	+	0.282305i
$130$	6.06989	−	7.59785i	0.532364	−	0.666376i
$131$			12.1137i			1.05838i	0.848505	+	0.529188i	$0.177503\pi$
$131$			12.1137i			1.05838i	−0.848505	+	0.529188i	$0.822497\pi$
$132$	4.57434	+	6.80679i	0.398145	+	0.592455i
$133$	−0.371042	+	0.371042i	−0.0321734	+	0.0321734i
$134$	5.67279			0.490055
$135$	10.3604	+	5.25950i	0.891680	+	0.452666i
$136$	−3.92368			−0.336453
$137$	1.08854	−	1.08854i	0.0930002	−	0.0930002i	−0.659076	−	0.752076i	$-0.729052\pi$
$137$	1.08854	−	1.08854i	0.0930002	−	0.0930002i	0.752076	+	0.659076i	$0.229052\pi$
$138$	7.69044	+	11.4437i	0.654653	+	0.974149i
$139$		−	6.34474i		−	0.538154i	−0.963119	−	0.269077i	$-0.913281\pi$
$139$		−	6.34474i		−	0.538154i	0.963119	−	0.269077i	$-0.0867185\pi$
$140$	1.16607	−	0.130360i	0.0985513	−	0.0110174i
$141$	−14.1044	−	2.76662i	−1.18780	−	0.232992i
$142$	2.59861	+	2.59861i	0.218070	+	0.218070i
$143$	−14.5608	−	14.5608i	−1.21764	−	1.21764i
$144$	1.13332	−	2.77770i	0.0944431	−	0.231475i
$145$	−7.09731	−	5.67001i	−0.589400	−	0.470869i
$146$		−	10.6301i		−	0.879750i
$147$	−9.66728	+	6.49666i	−0.797344	+	0.535836i
$148$	2.20796	−	2.20796i	0.181493	−	0.181493i
$149$	−19.2260			−1.57506			−0.787529	−	0.616278i	$-0.788640\pi$
$149$	−19.2260			−1.57506			−0.787529	+	0.616278i	$0.788640\pi$
$150$	−0.250834	−	8.65662i	−0.0204805	−	0.706810i
$151$	5.62170			0.457487			0.228744	−	0.973487i	$-0.426538\pi$
$151$	5.62170			0.457487			0.228744	+	0.973487i	$0.426538\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	4.56227	+	10.8510i	0.368838	+	0.877248i
$154$		−	2.48454i		−	0.200210i
$155$	6.17299	+	4.93157i	0.495826	+	0.396113i
$156$	−1.44995	+	7.39190i	−0.116089	+	0.591825i
$157$	−10.3090	−	10.3090i	−0.822747	−	0.822747i	0.163754	−	0.986501i	$-0.447640\pi$
$157$	−10.3090	−	10.3090i	−0.822747	−	0.822747i	−0.986501	+	0.163754i	$0.947640\pi$
$158$	−5.61011	−	5.61011i	−0.446317	−	0.446317i
$159$	3.13930	−	16.0043i	0.248963	−	1.26922i
$160$	−2.22222	+	0.248430i	−0.175682	+	0.0196401i
$161$		−	4.17704i		−	0.329197i
$162$	−8.99949	+	0.0955769i	−0.707067	+	0.00750923i
$163$	15.8628	−	15.8628i	1.24247	−	1.24247i	0.283497	−	0.958973i	$-0.408505\pi$
$163$	15.8628	−	15.8628i	1.24247	−	1.24247i	0.958973	−	0.283497i	$-0.0914947\pi$
$164$	6.41083			0.500601
$165$	−18.2759	−	1.50868i	−1.42278	−	0.117450i
$166$	10.9472			0.849671
$167$	−16.9172	+	16.9172i	−1.30910	+	1.30910i	−0.387027	+	0.922068i	$0.626498\pi$
$167$	−16.9172	+	16.9172i	−1.30910	+	1.30910i	−0.922068	+	0.387027i	$0.873502\pi$
$168$	−0.754350	+	0.506942i	−0.0581993	+	0.0391115i
$169$		−	5.91417i		−	0.454936i
$170$	5.47622	−	6.85474i	0.420007	−	0.525735i
$171$	−2.77770	−	1.13332i	−0.212416	−	0.0866669i
$172$	6.80047	+	6.80047i	0.518531	+	0.518531i
$173$	−6.04290	−	6.04290i	−0.459433	−	0.459433i	0.439036	−	0.898469i	$-0.355320\pi$
$173$	−6.04290	−	6.04290i	−0.459433	−	0.459433i	−0.898469	+	0.439036i	$0.855320\pi$
$174$	6.90493	+	1.35443i	0.523461	+	0.102679i
$175$	−1.39973	+	2.21909i	−0.105810	+	0.167748i
$176$			4.73487i			0.356904i
$177$	5.79875	+	8.62876i	0.435861	+	0.648577i
$178$	−5.04349	+	5.04349i	−0.378026	+	0.378026i
$179$	−7.72862			−0.577664			−0.288832	−	0.957380i	$-0.593267\pi$
$179$	−7.72862			−0.577664			−0.288832	+	0.957380i	$0.593267\pi$
$180$	3.27093	+	5.85671i	0.243801	+	0.436533i
$181$	−15.5179			−1.15343			−0.576717	−	0.816944i	$-0.695666\pi$
$181$	−15.5179			−1.15343			−0.576717	+	0.816944i	$0.695666\pi$
$182$	1.61368	−	1.61368i	0.119614	−	0.119614i
$183$	2.90355	+	4.32060i	0.214637	+	0.319388i
$184$			7.96032i			0.586843i
$185$	0.775731	+	6.93896i	0.0570328	+	0.510163i
$186$	−6.00566	−	1.17803i	−0.440356	−	0.0863776i
$187$	−13.1367	−	13.1367i	−0.960652	−	0.960652i
$188$	−5.86781	−	5.86781i	−0.427954	−	0.427954i
$189$	2.27907	+	1.49671i	0.165778	+	0.108870i
$190$	0.248430	+	2.22222i	0.0180230	+	0.161217i
$191$			13.5080i			0.977402i	0.872451	+	0.488701i	$0.162529\pi$
$191$			13.5080i			0.977402i	−0.872451	+	0.488701i	$0.837471\pi$
$192$	1.43759	−	0.966096i	0.103749	−	0.0697220i
$193$	−2.95772	+	2.95772i	−0.212901	+	0.212901i	−0.805499	−	0.592597i	$-0.798103\pi$
$193$	−2.95772	+	2.95772i	−0.212901	+	0.212901i	0.592597	+	0.805499i	$0.298103\pi$
$194$	7.09290			0.509241
$195$	−10.8901	−	12.8498i	−0.779856	−	0.920196i
$196$	−6.72466			−0.480333
$197$	14.5718	−	14.5718i	1.03820	−	1.03820i	0.0389574	−	0.999241i	$-0.487596\pi$
$197$	14.5718	−	14.5718i	1.03820	−	1.03820i	0.999241	−	0.0389574i	$-0.0124037\pi$
$198$	13.0943	−	5.50547i	0.930571	−	0.391257i
$199$		−	5.90849i		−	0.418842i	−0.977826	−	0.209421i	$-0.932842\pi$
$199$		−	5.90849i		−	0.418842i	0.977826	−	0.209421i	$-0.0671578\pi$
$200$	2.66751	−	4.22899i	0.188621	−	0.299035i
$201$	1.89128	−	9.64183i	0.133401	−	0.680082i
$202$	9.97464	+	9.97464i	0.701813	+	0.701813i
$203$	−1.50737	−	1.50737i	−0.105797	−	0.105797i
$204$	−1.30814	+	6.66893i	−0.0915879	+	0.466919i
$205$	−8.94748	+	11.1998i	−0.624919	+	0.782229i
$206$			7.30419i			0.508907i
$207$	22.0143	−	9.25588i	1.53010	−	0.643328i
$208$	−3.07524	+	3.07524i	−0.213229	+	0.213229i
$209$	4.73487			0.327518
$210$	0.167196	−	2.02539i	0.0115376	−	0.139765i
$211$	−6.45326			−0.444261			−0.222130	−	0.975017i	$-0.571301\pi$
$211$	−6.45326			−0.444261			−0.222130	+	0.975017i	$0.571301\pi$
$212$	6.65823	−	6.65823i	0.457289	−	0.457289i
$213$	5.28311	−	3.55039i	0.361993	−	0.243268i
$214$		−	8.28252i		−	0.566182i
$215$	−21.3719	+	2.38923i	−1.45755	+	0.162944i
$216$	−4.34330	−	2.85232i	−0.295524	−	0.194076i
$217$	1.31106	+	1.31106i	0.0890004	+	0.0890004i
$218$	7.45740	+	7.45740i	0.505079	+	0.505079i
$219$	−18.0675	−	3.54401i	−1.22089	−	0.239482i
$220$	−8.27189	−	6.60838i	−0.557691	−	0.445537i
$221$		−	17.0643i		−	1.14787i
$222$	−3.01666	−	4.48891i	−0.202465	−	0.301276i
$223$	−12.4934	+	12.4934i	−0.836618	+	0.836618i	−0.988412	−	0.151794i	$-0.951495\pi$
$223$	−12.4934	+	12.4934i	−0.836618	+	0.836618i	0.151794	+	0.988412i	$0.451495\pi$
$224$	−0.524733			−0.0350602
$225$	−14.7969	−	2.45974i	−0.986463	−	0.163983i
$226$	16.5288			1.09948
$227$	3.12326	−	3.12326i	0.207298	−	0.207298i	−0.595820	−	0.803118i	$-0.703173\pi$
$227$	3.12326	−	3.12326i	0.207298	−	0.207298i	0.803118	+	0.595820i	$0.203173\pi$
$228$	−0.966096	−	1.43759i	−0.0639813	−	0.0952066i
$229$			4.46088i			0.294783i	0.989078	+	0.147392i	$0.0470878\pi$
$229$			4.46088i			0.294783i	−0.989078	+	0.147392i	$0.952912\pi$
$230$	−13.9068	−	11.1101i	−0.916989	−	0.732578i
$231$	−4.22288	−	0.828333i	−0.277845	−	0.0545003i
$232$	2.87264	+	2.87264i	0.188598	+	0.188598i
$233$	−2.29263	−	2.29263i	−0.150195	−	0.150195i	0.628010	−	0.778205i	$-0.283870\pi$
$233$	−2.29263	−	2.29263i	−0.150195	−	0.150195i	−0.778205	+	0.628010i	$0.783870\pi$
$234$	12.0803	+	4.92884i	0.789715	+	0.322209i
$235$	18.4408	−	2.06156i	1.20294	−	0.134481i
$236$			6.00225i			0.390713i
$237$	−11.4057	+	7.66491i	−0.740878	+	0.497889i
$238$	1.45585	−	1.45585i	0.0943689	−	0.0943689i
$239$	4.10728			0.265678			0.132839	−	0.991138i	$-0.457591\pi$
$239$	4.10728			0.265678			0.132839	+	0.991138i	$0.457591\pi$
$240$	−0.318631	+	3.85985i	−0.0205676	+	0.249153i
$241$	25.0963			1.61659			0.808297	−	0.588776i	$-0.200390\pi$
$241$	25.0963			1.61659			0.808297	+	0.588776i	$0.200390\pi$
$242$	−8.07443	+	8.07443i	−0.519044	+	0.519044i
$243$	−2.83794	+	15.3280i	−0.182054	+	0.983289i
$244$			3.00545i			0.192404i
$245$	9.38549	−	11.7481i	0.599617	−	0.750558i
$246$	2.13734	−	10.8962i	0.136272	−	0.694718i
$247$	3.07524	+	3.07524i	0.195673	+	0.195673i
$248$	−2.49852	−	2.49852i	−0.158656	−	0.158656i
$249$	3.64976	−	18.6066i	0.231294	−	1.17915i
$250$	3.66512	+	10.5625i	0.231803	+	0.668033i
$251$			21.3779i			1.34936i	0.738110	+	0.674681i	$0.235719\pi$
$251$			21.3779i			1.34936i	−0.738110	+	0.674681i	$0.764281\pi$
$252$	0.610134	+	1.45115i	0.0384348	+	0.0914139i
$253$	−26.6516	+	26.6516i	−1.67557	+	1.67557i
$254$	16.3607			1.02656
$255$	−9.82499	−	11.5931i	−0.615265	−	0.725985i
$256$	1.00000			0.0625000
$257$	7.08612	−	7.08612i	0.442020	−	0.442020i	−0.450670	−	0.892690i	$-0.648815\pi$
$257$	7.08612	−	7.08612i	0.442020	−	0.442020i	0.892690	+	0.450670i	$0.148815\pi$
$258$	13.8257	−	9.29126i	0.860753	−	0.578448i
$259$			1.63849i			0.101811i
$260$	−1.08043	−	9.66455i	−0.0670056	−	0.599370i
$261$	4.60414	−	11.2845i	0.284989	−	0.698492i
$262$	8.56565	+	8.56565i	0.529188	+	0.529188i
$263$	−10.3710	−	10.3710i	−0.639500	−	0.639500i	0.310932	−	0.950432i	$-0.399359\pi$
$263$	−10.3710	−	10.3710i	−0.639500	−	0.639500i	−0.950432	+	0.310932i	$0.899359\pi$
$264$	8.04767	+	1.57858i	0.495300	+	0.0971549i
$265$	2.33926	+	20.9248i	0.143700	+	1.28540i
$266$			0.524733i			0.0321734i
$267$	6.89075	+	10.2537i	0.421707	+	0.627516i
$268$	4.01127	−	4.01127i	0.245027	−	0.245027i
$269$	13.9150			0.848410			0.424205	−	0.905566i	$-0.360554\pi$
$269$	13.9150			0.848410			0.424205	+	0.905566i	$0.360554\pi$
$270$	11.0449	−	3.60687i	0.672173	−	0.219507i
$271$	9.79499			0.595003			0.297502	−	0.954721i	$-0.403847\pi$
$271$	9.79499			0.595003			0.297502	+	0.954721i	$0.403847\pi$
$272$	−2.77446	+	2.77446i	−0.168227	+	0.168227i
$273$	−2.20471	−	3.28070i	−0.133435	−	0.198557i
$274$		−	1.53943i		−	0.0930002i
$275$	23.0899	−	5.22793i	1.39237	−	0.315256i
$276$	13.5299	+	2.65393i	0.814401	+	0.159748i
$277$	−4.58635	−	4.58635i	−0.275567	−	0.275567i	0.555770	−	0.831336i	$-0.312424\pi$
$277$	−4.58635	−	4.58635i	−0.275567	−	0.275567i	−0.831336	+	0.555770i	$0.812424\pi$
$278$	−4.48641	−	4.48641i	−0.269077	−	0.269077i
$279$	−4.00451	+	9.81484i	−0.239744	+	0.587599i
$280$	0.732361	−	0.916717i	0.0437669	−	0.0547843i
$281$		−	12.1098i		−	0.722412i	−0.932486	−	0.361206i	$-0.882365\pi$
$281$		−	12.1098i		−	0.722412i	0.932486	−	0.361206i	$-0.117635\pi$
$282$	−11.9296	+	8.01699i	−0.710396	+	0.477405i
$283$	−1.32735	+	1.32735i	−0.0789029	+	0.0789029i	−0.745457	−	0.666554i	$-0.767769\pi$
$283$	−1.32735	+	1.32735i	−0.0789029	+	0.0789029i	0.666554	+	0.745457i	$0.267769\pi$
$284$	3.67498			0.218070
$285$	3.85985	+	0.318631i	0.228638	+	0.0188741i
$286$	−20.5921			−1.21764
$287$	−2.37869	+	2.37869i	−0.140409	+	0.140409i
$288$	−1.16275	−	2.76550i	−0.0685158	−	0.162959i
$289$			1.60471i			0.0943944i
$290$	−9.02786	+	1.00926i	−0.530134	+	0.0592655i
$291$	2.36474	−	12.0555i	0.138623	−	0.706708i
$292$	−7.51659	−	7.51659i	−0.439875	−	0.439875i
$293$	12.6506	+	12.6506i	0.739057	+	0.739057i	0.972395	−	0.233339i	$-0.0749651\pi$
$293$	12.6506	+	12.6506i	0.739057	+	0.739057i	−0.233339	+	0.972395i	$0.574965\pi$
$294$	−2.24197	+	11.4296i	−0.130754	+	0.666590i
$295$	−10.4860	−	8.37724i	−0.610520	−	0.487742i
$296$		−	3.12253i		−	0.181493i
$297$	−4.99187	−	24.0914i	−0.289657	−	1.39792i
$298$	−13.5949	+	13.5949i	−0.787529	+	0.787529i
$299$	−34.6198			−2.00211
$300$	−6.29852	−	5.94379i	−0.363645	−	0.343165i
$301$	−5.04653			−0.290877
$302$	3.97514	−	3.97514i	0.228744	−	0.228744i
$303$	20.2790	−	13.6280i	1.16500	−	0.782909i
$304$		−	1.00000i		−	0.0573539i
$305$	−5.25057	−	4.19466i	−0.300647	−	0.240185i
$306$	10.8988	+	4.44678i	0.623043	+	0.254205i
$307$	−16.4288	−	16.4288i	−0.937644	−	0.937644i	0.0605232	−	0.998167i	$-0.480723\pi$
$307$	−16.4288	−	16.4288i	−0.937644	−	0.937644i	−0.998167	+	0.0605232i	$0.980723\pi$
$308$	−1.75684	−	1.75684i	−0.100105	−	0.100105i
$309$	12.4147	+	2.43518i	0.706245	+	0.138533i
$310$	7.85211	−	0.877815i	0.445970	−	0.0498565i
$311$		−	6.49385i		−	0.368232i	−0.982904	−	0.184116i	$-0.941058\pi$
$311$		−	6.49385i		−	0.368232i	0.982904	−	0.184116i	$-0.0589423\pi$
$312$	4.20159	+	6.25213i	0.237868	+	0.353957i
$313$	−15.5616	+	15.5616i	−0.879591	+	0.879591i	−0.993492	−	0.113901i	$-0.963665\pi$
$313$	−15.5616	+	15.5616i	−0.879591	+	0.879591i	0.113901	+	0.993492i	$0.463665\pi$
$314$	−14.5791			−0.822747
$315$	−3.38674	−	0.959433i	−0.190821	−	0.0540579i
$316$	−7.93390			−0.446317
$317$	−21.8274	+	21.8274i	−1.22595	+	1.22595i	−0.260466	+	0.965483i	$0.583876\pi$
$317$	−21.8274	+	21.8274i	−1.22595	+	1.22595i	−0.965483	+	0.260466i	$0.916124\pi$
$318$	−9.09692	−	13.5366i	−0.510130	−	0.759093i
$319$			19.2355i			1.07698i
$320$	−1.39568	+	1.74702i	−0.0780211	+	0.0976612i
$321$	−14.0775	−	2.76135i	−0.785728	−	0.154124i
$322$	−2.95362	−	2.95362i	−0.164599	−	0.164599i
$323$	2.77446	+	2.77446i	0.154375	+	0.154375i
$324$	−6.29602	+	6.43119i	−0.349779	+	0.357288i
$325$	18.3921	+	11.6011i	1.02021	+	0.643514i
$326$		−	22.4334i		−	1.24247i
$327$	15.1613	−	10.1888i	0.838422	−	0.563442i
$328$	4.53314	−	4.53314i	0.250301	−	0.250301i
$329$	4.35441			0.240066
$330$	−13.9898	+	11.8562i	−0.770113	+	0.652663i
$331$	−10.9575			−0.602276			−0.301138	−	0.953581i	$-0.597367\pi$
$331$	−10.9575			−0.602276			−0.301138	+	0.953581i	$0.597367\pi$
$332$	7.74087	−	7.74087i	0.424836	−	0.424836i
$333$	−8.63536	+	3.63072i	−0.473215	+	0.198962i
$334$			23.9246i			1.30910i
$335$	1.40929	+	12.6062i	0.0769979	+	0.688752i
$336$	−0.174943	+	0.891868i	−0.00954394	+	0.0486554i
$337$	−9.98105	−	9.98105i	−0.543702	−	0.543702i	0.380910	−	0.924612i	$-0.375611\pi$
$337$	−9.98105	−	9.98105i	−0.543702	−	0.543702i	−0.924612	+	0.380910i	$0.875611\pi$
$338$	−4.18195	−	4.18195i	−0.227468	−	0.227468i
$339$	5.51063	−	28.0934i	0.299296	−	1.52583i
$340$	−0.974762	−	8.71931i	−0.0528639	−	0.472871i
$341$		−	16.7304i		−	0.906002i
$342$	−2.76550	+	1.16275i	−0.149541	+	0.0628744i
$343$	5.09243	−	5.09243i	0.274965	−	0.274965i
$344$	9.61732			0.518531
$345$	−23.5199	+	19.9328i	−1.26627	+	1.07315i
$346$	−8.54595			−0.459433
$347$	6.53710	−	6.53710i	0.350930	−	0.350930i	−0.509526	−	0.860456i	$-0.670179\pi$
$347$	6.53710	−	6.53710i	0.350930	−	0.350930i	0.860456	+	0.509526i	$0.170179\pi$
$348$	5.84025	−	3.92480i	0.313070	−	0.210391i
$349$		−	16.6692i		−	0.892280i	−0.894963	−	0.446140i	$-0.852798\pi$
$349$		−	16.6692i		−	0.892280i	0.894963	−	0.446140i	$-0.147202\pi$
$350$	0.579376	+	2.55889i	0.0309690	+	0.136779i
$351$	12.4049	−	18.8892i	0.662123	−	1.00823i
$352$	3.34806	+	3.34806i	0.178452	+	0.178452i
$353$	−18.7729	−	18.7729i	−0.999178	−	0.999178i	0.000821466	−	1.00000i	$-0.499739\pi$
$353$	−18.7729	−	18.7729i	−0.999178	−	0.999178i	−1.00000		0.000821466i	$0.999739\pi$
$354$	10.2018	+	2.00112i	0.542219	+	0.106358i
$355$	−5.12911	+	6.42026i	−0.272225	+	0.340752i
$356$			7.13257i			0.378026i
$357$	−1.98908	−	2.95983i	−0.105273	−	0.156651i
$358$	−5.46496	+	5.46496i	−0.288832	+	0.288832i
$359$	31.0918			1.64096			0.820480	−	0.571675i	$-0.193706\pi$
$359$	31.0918			1.64096			0.820480	+	0.571675i	$0.193706\pi$
$360$	6.45421	+	1.82842i	0.340167	+	0.0963663i
$361$	−1.00000			−0.0526316
$362$	−10.9728	+	10.9728i	−0.576717	+	0.576717i
$363$	11.0318	+	16.4158i	0.579020	+	0.861604i
$364$		−	2.28209i		−	0.119614i
$365$	23.6224	−	2.64083i	1.23645	−	0.138227i
$366$	5.10825	+	1.00200i	0.267012	+	0.0523755i
$367$	−0.761107	−	0.761107i	−0.0397295	−	0.0397295i	0.686963	−	0.726692i	$-0.258943\pi$
$367$	−0.761107	−	0.761107i	−0.0397295	−	0.0397295i	−0.726692	+	0.686963i	$0.758943\pi$
$368$	5.62880	+	5.62880i	0.293421	+	0.293421i
$369$	−17.8073	−	7.26550i	−0.927012	−	0.378227i
$370$	5.45511	+	4.35806i	0.283598	+	0.226565i
$371$			4.94097i			0.256522i
$372$	−5.07964	+	3.41365i	−0.263367	+	0.176989i
$373$	8.01035	−	8.01035i	0.414760	−	0.414760i	−0.468633	−	0.883393i	$-0.655253\pi$
$373$	8.01035	−	8.01035i	0.414760	−	0.414760i	0.883393	+	0.468633i	$0.155253\pi$
$374$	−18.5781			−0.960652
$375$	19.1746	−	2.70798i	0.990174	−	0.139839i
$376$	−8.29833			−0.427954
$377$	−12.4932	+	12.4932i	−0.643435	+	0.643435i
$378$	2.66988	−	0.553214i	0.137324	−	0.0284543i
$379$		−	15.0607i		−	0.773616i	−0.922160	−	0.386808i	$-0.873578\pi$
$379$		−	15.0607i		−	0.773616i	0.922160	−	0.386808i	$-0.126422\pi$
$380$	1.74702	+	1.39568i	0.0896201	+	0.0715970i
$381$	5.45459	−	27.8077i	0.279447	−	1.42463i
$382$	9.55157	+	9.55157i	0.488701	+	0.488701i
$383$	21.4822	+	21.4822i	1.09769	+	1.09769i	0.994680	+	0.103010i	$0.0328474\pi$
$383$	21.4822	+	21.4822i	1.09769	+	1.09769i	0.103010	+	0.994680i	$0.467153\pi$
$384$	0.333395	−	1.69966i	0.0170135	−	0.0867355i
$385$	5.52121	−	0.617235i	0.281387	−	0.0314572i
$386$			4.18285i			0.212901i
$387$	−11.1826	−	26.5967i	−0.568441	−	1.35199i
$388$	5.01544	−	5.01544i	0.254620	−	0.254620i
$389$	−11.7608			−0.596296			−0.298148	−	0.954520i	$-0.596369\pi$
$389$	−11.7608			−0.596296			−0.298148	+	0.954520i	$0.596369\pi$
$390$	−16.7867	−	1.38574i	−0.850026	−	0.0701697i
$391$	−31.2338			−1.57956
$392$	−4.75505	+	4.75505i	−0.240166	+	0.240166i
$393$	17.4144	−	11.7030i	0.878443	−	0.590336i
$394$		−	20.6076i		−	1.03820i
$395$	11.0732	−	13.8607i	0.557154	−	0.697405i
$396$	5.36611	−	13.1520i	0.269657	−	0.660914i
$397$	6.27425	+	6.27425i	0.314895	+	0.314895i	0.846803	−	0.531907i	$-0.178524\pi$
$397$	6.27425	+	6.27425i	0.314895	+	0.314895i	−0.531907	+	0.846803i	$0.678524\pi$
$398$	−4.17793	−	4.17793i	−0.209421	−	0.209421i
$399$	0.891868	+	0.174943i	0.0446493	+	0.00875812i
$400$	−1.10414	−	4.87656i	−0.0552068	−	0.243828i
$401$		−	28.8320i		−	1.43980i	−0.694076	−	0.719901i	$-0.744187\pi$
$401$		−	28.8320i		−	1.43980i	0.694076	−	0.719901i	$-0.255813\pi$
$402$	−5.48046	−	8.15514i	−0.273341	−	0.406741i
$403$	10.8662	−	10.8662i	0.541283	−	0.541283i
$404$	14.1063			0.701813
$405$	−2.44814	−	19.9751i	−0.121649	−	0.992573i
$406$	−2.13174			−0.105797
$407$	10.4544	−	10.4544i	0.518206	−	0.518206i
$408$	3.79066	+	5.64064i	0.187665	+	0.279253i
$409$			18.6400i			0.921687i	0.887482	+	0.460843i	$0.152453\pi$
$409$			18.6400i			0.921687i	−0.887482	+	0.460843i	$0.847547\pi$
$410$	1.59264	+	14.2463i	0.0786550	+	0.703574i
$411$	−2.61650	−	0.513237i	−0.129063	−	0.0253161i
$412$	5.16485	+	5.16485i	0.254454	+	0.254454i
$413$	−2.22709	−	2.22709i	−0.109588	−	0.109588i
$414$	9.02157	−	22.1114i	0.443386	−	1.08671i
$415$	2.71963	+	24.3272i	0.133501	+	1.19418i
$416$			4.34904i			0.213229i
$417$	−9.12112	+	6.12962i	−0.446663	+	0.300169i
$418$	3.34806	−	3.34806i	0.163759	−	0.163759i
$419$	−33.3598			−1.62974			−0.814868	−	0.579647i	$-0.803190\pi$
$419$	−33.3598			−1.62974			−0.814868	+	0.579647i	$0.803190\pi$
$420$	−1.31394	−	1.55039i	−0.0641139	−	0.0756515i
$421$	−14.3797			−0.700824			−0.350412	−	0.936596i	$-0.613959\pi$
$421$	−14.3797			−0.700824			−0.350412	+	0.936596i	$0.613959\pi$
$422$	−4.56315	+	4.56315i	−0.222130	+	0.222130i
$423$	9.64890	+	22.9491i	0.469145	+	1.11582i
$424$		−	9.41616i		−	0.457289i
$425$	16.5932	+	10.4665i	0.804890	+	0.507698i
$426$	1.22522	−	6.24623i	0.0593622	−	0.302631i
$427$	−1.11515	−	1.11515i	−0.0539658	−	0.0539658i
$428$	−5.85663	−	5.85663i	−0.283091	−	0.283091i
$429$	−6.86532	+	34.9997i	−0.331461	+	1.68980i
$430$	−13.4227	+	16.8016i	−0.647302	+	0.810246i
$431$			13.4317i			0.646980i	0.946232	+	0.323490i	$0.104856\pi$
$431$			13.4317i			0.646980i	−0.946232	+	0.323490i	$0.895144\pi$
$432$	−5.08807	+	1.05428i	−0.244800	+	0.0507240i
$433$	4.59824	−	4.59824i	0.220977	−	0.220977i	−0.587933	−	0.808910i	$-0.700058\pi$
$433$	4.59824	−	4.59824i	0.220977	−	0.220977i	0.808910	+	0.587933i	$0.200058\pi$
$434$	1.85411			0.0890004
$435$	−1.29445	+	15.6808i	−0.0620641	+	0.751836i
$436$	10.5464			0.505079
$437$	5.62880	−	5.62880i	0.269262	−	0.269262i
$438$	−15.2816	+	10.2697i	−0.730185	+	0.490703i
$439$		−	8.50450i		−	0.405898i	−0.979189	−	0.202949i	$-0.934948\pi$
$439$		−	8.50450i		−	0.405898i	0.979189	−	0.202949i	$-0.0650525\pi$
$440$	−10.5219	+	1.17628i	−0.501614	+	0.0560771i
$441$	18.6790	+	7.62117i	0.889478	+	0.362913i
$442$	−12.0663	−	12.0663i	−0.573933	−	0.573933i
$443$	−21.4192	−	21.4192i	−1.01766	−	1.01766i	−0.999841	−	0.0178169i	$-0.994328\pi$
$443$	−21.4192	−	21.4192i	−1.01766	−	1.01766i	−0.0178169	−	0.999841i	$-0.505672\pi$
$444$	−5.30724	−	1.04104i	−0.251871	−	0.0494054i
$445$	−12.4607	−	9.95481i	−0.590695	−	0.471903i
$446$			17.6683i			0.836618i
$447$	18.5742	+	27.6391i	0.878529	+	1.30728i
$448$	−0.371042	+	0.371042i	−0.0175301	+	0.0175301i
$449$	33.6163			1.58645			0.793226	−	0.608927i	$-0.208400\pi$
$449$	33.6163			1.58645			0.793226	+	0.608927i	$0.208400\pi$
$450$	−12.2023	+	8.72372i	−0.575223	+	0.411240i
$451$	30.3544			1.42933
$452$	11.6877	−	11.6877i	0.549741	−	0.549741i
$453$	−5.43110	−	8.08168i	−0.255175	−	0.379710i
$454$		−	4.41695i		−	0.207298i
$455$	3.98684	+	3.18507i	0.186906	+	0.149318i
$456$	−1.69966	−	0.333395i	−0.0795939	−	0.0156127i
$457$	−14.7287	−	14.7287i	−0.688978	−	0.688978i	0.273028	−	0.962006i	$-0.411975\pi$
$457$	−14.7287	−	14.7287i	−0.688978	−	0.688978i	−0.962006	+	0.273028i	$0.911975\pi$
$458$	3.15432	+	3.15432i	0.147392	+	0.147392i
$459$	11.1916	−	17.0417i	0.522380	−	0.795440i
$460$	−17.6896	+	1.97758i	−0.824783	+	0.0922054i
$461$		−	1.22359i		−	0.0569885i	−0.999594	−	0.0284942i	$-0.990929\pi$
$461$		−	1.22359i		−	0.0569885i	0.999594	−	0.0284942i	$-0.00907123\pi$
$462$	−3.57174	+	2.40030i	−0.166173	+	0.111672i
$463$	12.9428	−	12.9428i	0.601501	−	0.601501i	−0.339209	−	0.940711i	$-0.610160\pi$
$463$	12.9428	−	12.9428i	0.601501	−	0.601501i	0.940711	+	0.339209i	$0.110160\pi$
$464$	4.06253			0.188598
$465$	1.12587	−	13.6386i	0.0522108	−	0.632474i
$466$	−3.24227			−0.150195
$467$	8.23017	−	8.23017i	0.380847	−	0.380847i	−0.490560	−	0.871407i	$-0.663208\pi$
$467$	8.23017	−	8.23017i	0.380847	−	0.380847i	0.871407	+	0.490560i	$0.163208\pi$
$468$	12.0273	−	5.05685i	0.555962	−	0.233753i
$469$			2.97670i			0.137451i
$470$	11.5818	−	14.4973i	0.534231	−	0.668712i
$471$	−4.86060	+	24.7796i	−0.223965	+	1.14178i
$472$	4.24423	+	4.24423i	0.195357	+	0.195357i
$473$	32.1993	+	32.1993i	1.48053	+	1.48053i
$474$	−2.64512	+	13.4849i	−0.121494	+	0.619384i
$475$	−4.87656	+	1.10414i	−0.223752	+	0.0506612i
$476$		−	2.05889i		−	0.0943689i
$477$	−26.0404	+	10.9487i	−1.19231	+	0.501304i
$478$	2.90428	−	2.90428i	0.132839	−	0.132839i
$479$	−23.7395			−1.08469			−0.542344	−	0.840157i	$-0.682463\pi$
$479$	−23.7395			−1.08469			−0.542344	+	0.840157i	$0.682463\pi$
$480$	2.50402	+	2.95464i	0.114292	+	0.134860i
$481$	13.5800			0.619195
$482$	17.7457	−	17.7457i	0.808297	−	0.808297i
$483$	−6.00487	+	4.03543i	−0.273231	+	0.183618i
$484$			11.4190i			0.519044i
$485$	1.76209	+	15.7620i	0.0800125	+	0.715717i
$486$	8.83177	+	12.8452i	0.400617	+	0.582671i
$487$	27.2107	+	27.2107i	1.23303	+	1.23303i	0.962793	+	0.270239i	$0.0871028\pi$
$487$	27.2107	+	27.2107i	1.23303	+	1.23303i	0.270239	+	0.962793i	$0.412897\pi$
$488$	2.12517	+	2.12517i	0.0962021	+	0.0962021i
$489$	−38.1292	−	7.47918i	−1.72426	−	0.338220i
$490$	−1.67061	−	14.9437i	−0.0754704	−	0.675087i
$491$			40.4871i			1.82716i	0.406662	+	0.913579i	$0.366693\pi$
$491$			40.4871i			1.82716i	−0.406662	+	0.913579i	$0.633307\pi$
$492$	−6.19347	−	9.21612i	−0.279223	−	0.415495i
$493$	−11.2713	+	11.2713i	−0.507636	+	0.507636i
$494$	4.34904			0.195673
$495$	15.4874	+	27.7307i	0.696108	+	1.24640i
$496$	−3.53345			−0.158656
$497$	−1.36357	+	1.36357i	−0.0611646	+	0.0611646i
$498$	−10.5761	−	15.7376i	−0.473926	−	0.705220i
$499$			5.75646i			0.257695i	0.991664	+	0.128847i	$0.0411277\pi$
$499$			5.75646i			0.257695i	−0.991664	+	0.128847i	$0.958872\pi$
$500$	10.0605	+	4.87720i	0.449918	+	0.218115i
$501$	40.6637	+	7.97634i	1.81672	+	0.356357i
$502$	15.1165	+	15.1165i	0.674681	+	0.674681i
$503$	−25.9616	−	25.9616i	−1.15757	−	1.15757i	−0.984997	−	0.172573i	$-0.944792\pi$
$503$	−25.9616	−	25.9616i	−1.15757	−	1.15757i	−0.172573	−	0.984997i	$-0.555208\pi$
$504$	1.45755	+	0.594689i	0.0649244	+	0.0264895i
$505$	−19.6879	+	24.6439i	−0.876100	+	1.09664i
$506$			37.6911i			1.67557i
$507$	−8.50213	+	5.71365i	−0.377593	+	0.253752i
$508$	11.5688	−	11.5688i	0.513282	−	0.513282i
$509$	5.27569			0.233841			0.116920	−	0.993141i	$-0.462698\pi$
$509$	5.27569			0.233841			0.116920	+	0.993141i	$0.462698\pi$
$510$	−15.1448	−	1.25021i	−0.670625	−	0.0553602i
$511$	5.57794			0.246754
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.05428	+	5.08807i	0.0465475	+	0.224644i
$514$		−	10.0213i		−	0.442020i
$515$	−16.2316	+	1.81458i	−0.715248	+	0.0799601i
$516$	3.20637	−	16.3462i	0.141152	−	0.719601i
$517$	−27.7833	−	27.7833i	−1.22191	−	1.22191i
$518$	1.15859	+	1.15859i	0.0509055	+	0.0509055i
$519$	−2.84918	+	14.5252i	−0.125065	+	0.637586i
$520$	−7.59785	−	6.06989i	−0.333188	−	0.266182i
$521$			1.12070i			0.0490988i	0.999699	+	0.0245494i	$0.00781510\pi$
$521$			1.12070i			0.0490988i	−0.999699	+	0.0245494i	$0.992185\pi$
$522$	−4.72371	−	11.2349i	−0.206751	−	0.491740i
$523$	−3.66564	+	3.66564i	−0.160287	+	0.160287i	−0.782694	−	0.622407i	$-0.786155\pi$
$523$	−3.66564	+	3.66564i	−0.160287	+	0.160287i	0.622407	+	0.782694i	$0.286155\pi$
$524$	12.1137			0.529188
$525$	4.54241	−	0.131621i	0.198247	−	0.00574440i
$526$	−14.6667			−0.639500
$527$	9.80341	−	9.80341i	0.427043	−	0.427043i
$528$	6.80679	−	4.57434i	0.296227	−	0.199072i
$529$			40.3668i			1.75508i
$530$	16.4502	+	13.1420i	0.714551	+	0.570851i
$531$	6.80245	−	16.6724i	0.295201	−	0.723521i
$532$	0.371042	+	0.371042i	0.0160867	+	0.0160867i
$533$	19.7148	+	19.7148i	0.853943	+	0.853943i
$534$	12.1230	+	2.37796i	0.524612	+	0.102905i
$535$	18.4056	−	2.05763i	0.795745	−	0.0889591i
$536$		−	5.67279i		−	0.245027i
$537$	7.46659	+	11.1106i	0.322207	+	0.479456i
$538$	9.83936	−	9.83936i	0.424205	−	0.424205i
$539$	−31.8403			−1.37146
$540$	5.25950	−	10.3604i	0.226333	−	0.445840i
$541$	35.1833			1.51265			0.756324	−	0.654197i	$-0.226993\pi$
$541$	35.1833			1.51265			0.756324	+	0.654197i	$0.226993\pi$
$542$	6.92611	−	6.92611i	0.297502	−	0.297502i
$543$	14.9917	+	22.3083i	0.643357	+	0.957340i
$544$			3.92368i			0.168227i
$545$	−14.7194	+	18.4247i	−0.630509	+	0.789226i
$546$	−3.87877	−	0.760836i	−0.165996	−	0.0325608i
$547$	−11.8492	−	11.8492i	−0.506635	−	0.506635i	0.406857	−	0.913492i	$-0.366625\pi$
$547$	−11.8492	−	11.8492i	−0.506635	−	0.506635i	−0.913492	+	0.406857i	$0.866625\pi$
$548$	−1.08854	−	1.08854i	−0.0465001	−	0.0465001i
$549$	3.40613	−	8.34823i	0.145370	−	0.356294i
$550$	12.6303	−	20.0237i	0.538558	−	0.853814i
$551$		−	4.06253i		−	0.173070i
$552$	11.4437	−	7.69044i	0.487075	−	0.327327i
$553$	2.94381	−	2.94381i	0.125184	−	0.125184i
$554$	−6.48607			−0.275567
$555$	9.22593	−	7.81888i	0.391619	−	0.331893i
$556$	−6.34474			−0.269077
$557$	−10.8257	+	10.8257i	−0.458701	+	0.458701i	−0.898229	−	0.439528i	$-0.855146\pi$
$557$	−10.8257	+	10.8257i	−0.458701	+	0.458701i	0.439528	+	0.898229i	$0.355146\pi$
$558$	4.10852	+	9.77176i	0.173927	+	0.413671i
$559$			41.8261i			1.76906i
$560$	−0.130360	−	1.16607i	−0.00550869	−	0.0492756i
$561$	−6.19385	+	31.5765i	−0.261505	+	1.33316i
$562$	−8.56294	−	8.56294i	−0.361206	−	0.361206i
$563$	−15.9790	−	15.9790i	−0.673433	−	0.673433i	0.285073	−	0.958506i	$-0.407982\pi$
$563$	−15.9790	−	15.9790i	−0.673433	−	0.673433i	−0.958506	+	0.285073i	$0.907982\pi$
$564$	−2.76662	+	14.1044i	−0.116496	+	0.593900i
$565$	4.10626	+	36.7308i	0.172752	+	1.54528i
$566$			1.87716i			0.0789029i
$567$	−0.0501524	−	4.72233i	−0.00210620	−	0.198319i
$568$	2.59861	−	2.59861i	0.109035	−	0.109035i
$569$	18.1067			0.759073			0.379536	−	0.925177i	$-0.376084\pi$
$569$	18.1067			0.759073			0.379536	+	0.925177i	$0.376084\pi$
$570$	2.95464	−	2.50402i	0.123756	−	0.104882i
$571$	−19.9248			−0.833826			−0.416913	−	0.908946i	$-0.636888\pi$
$571$	−19.9248			−0.833826			−0.416913	+	0.908946i	$0.636888\pi$
$572$	−14.5608	+	14.5608i	−0.608819	+	0.608819i
$573$	19.4189	−	13.0500i	0.811235	−	0.545171i
$574$			3.36397i			0.140409i
$575$	21.2342	−	33.6642i	0.885529	−	1.40389i
$576$	−2.77770	−	1.13332i	−0.115737	−	0.0472215i
$577$	−9.32107	−	9.32107i	−0.388041	−	0.388041i	0.485947	−	0.873988i	$-0.338475\pi$
$577$	−9.32107	−	9.32107i	−0.388041	−	0.388041i	−0.873988	+	0.485947i	$0.838475\pi$
$578$	1.13470	+	1.13470i	0.0471972	+	0.0471972i
$579$	7.10943	+	1.39454i	0.295458	+	0.0579552i
$580$	−5.67001	+	7.09731i	−0.235434	+	0.294700i
$581$			5.74438i			0.238317i
$582$	−6.85243	−	10.1967i	−0.284042	−	0.422666i
$583$	31.5258	−	31.5258i	1.30567	−	1.30567i
$584$	−10.6301			−0.439875
$585$	−7.95188	+	28.0696i	−0.328770	+	1.16054i
$586$	17.8907			0.739057
$587$	29.1721	−	29.1721i	1.20406	−	1.20406i	0.231141	−	0.972920i	$-0.425754\pi$
$587$	29.1721	−	29.1721i	1.20406	−	1.20406i	0.972920	−	0.231141i	$-0.0742458\pi$
$588$	6.49666	+	9.66728i	0.267918	+	0.398672i
$589$			3.53345i			0.145593i
$590$	−13.3383	+	1.49114i	−0.549131	+	0.0613893i
$591$	−35.0260	−	6.87049i	−1.44078	−	0.282614i
$592$	−2.20796	−	2.20796i	−0.0907467	−	0.0907467i
$593$	−3.55825	−	3.55825i	−0.146120	−	0.146120i	0.630262	−	0.776382i	$-0.282947\pi$
$593$	−3.55825	−	3.55825i	−0.146120	−	0.146120i	−0.776382	+	0.630262i	$0.782947\pi$
$594$	−20.5649	−	13.5054i	−0.843790	−	0.554132i
$595$	3.59691	+	2.87355i	0.147459	+	0.117804i
$596$			19.2260i			0.787529i
$597$	−8.49397	+	5.70817i	−0.347635	+	0.233620i
$598$	−24.4799	+	24.4799i	−1.00106	+	1.00106i
$599$	−30.7070			−1.25466			−0.627328	−	0.778755i	$-0.715851\pi$
$599$	−30.7070			−1.25466			−0.627328	+	0.778755i	$0.715851\pi$
$600$	−8.65662	+	0.250834i	−0.353405	+	0.0102403i
$601$	40.1017			1.63578			0.817891	−	0.575373i	$-0.195143\pi$
$601$	40.1017			1.63578			0.817891	+	0.575373i	$0.195143\pi$
$602$	−3.56843	+	3.56843i	−0.145438	+	0.145438i
$603$	−15.6881	+	6.59605i	−0.638870	+	0.268612i
$604$		−	5.62170i		−	0.228744i
$605$	−19.9491	−	15.9373i	−0.811047	−	0.647942i
$606$	4.70296	−	23.9759i	0.191045	−	0.973954i
$607$	−19.8610	−	19.8610i	−0.806134	−	0.806134i	0.177912	−	0.984046i	$-0.443066\pi$
$607$	−19.8610	−	19.8610i	−0.806134	−	0.806134i	−0.984046	+	0.177912i	$0.943066\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	−0.710713	+	3.62324i	−0.0287995	+	0.146821i
$610$	−6.67879	+	0.746645i	−0.270416	+	0.0302308i
$611$		−	36.0898i		−	1.46004i
$612$	10.8510	−	4.56227i	0.438624	−	0.184419i
$613$	22.6569	−	22.6569i	0.915102	−	0.915102i	−0.0815658	−	0.996668i	$-0.525992\pi$
$613$	22.6569	−	22.6569i	0.915102	−	0.915102i	0.996668	+	0.0815658i	$0.0259921\pi$
$614$	−23.2339			−0.937644
$615$	24.7449	+	2.04269i	0.997809	+	0.0823692i
$616$	−2.48454			−0.100105
$617$	15.5110	−	15.5110i	0.624451	−	0.624451i	−0.322215	−	0.946666i	$-0.604427\pi$
$617$	15.5110	−	15.5110i	0.624451	−	0.624451i	0.946666	+	0.322215i	$0.104427\pi$
$618$	10.5004	−	7.05655i	0.422389	−	0.283856i
$619$			15.5862i			0.626463i	0.949677	+	0.313232i	$0.101412\pi$
$619$			15.5862i			0.626463i	−0.949677	+	0.313232i	$0.898588\pi$
$620$	4.93157	−	6.17299i	0.198057	−	0.247913i
$621$	−34.5741	−	22.7054i	−1.38741	−	0.911137i
$622$	−4.59184	−	4.59184i	−0.184116	−	0.184116i
$623$	−2.64649	−	2.64649i	−0.106029	−	0.106029i
$624$	7.39190	+	1.44995i	0.295913	+	0.0580444i
$625$	−22.5618	+	10.7688i	−0.902471	+	0.430751i
$626$			22.0074i			0.879591i
$627$	−4.57434	−	6.80679i	−0.182681	−	0.271837i
$628$	−10.3090	+	10.3090i	−0.411374	+	0.411374i
$629$	12.2518			0.488512
$630$	−3.07321	+	1.71636i	−0.122440	+	0.0683816i
$631$	25.8671			1.02975			0.514876	−	0.857264i	$-0.327838\pi$
$631$	25.8671			1.02975			0.514876	+	0.857264i	$0.327838\pi$
$632$	−5.61011	+	5.61011i	−0.223158	+	0.223158i
$633$	6.23447	+	9.27713i	0.247798	+	0.368733i
$634$			30.8686i			1.22595i
$635$	4.06450	+	36.3572i	0.161295	+	1.44279i
$636$	−16.0043	−	3.13930i	−0.634611	−	0.124481i
$637$	−20.6799	−	20.6799i	−0.819368	−	0.819368i
$638$	13.6016	+	13.6016i	0.538492	+	0.538492i
$639$	−10.2080	−	4.16492i	−0.403822	−	0.164762i
$640$	0.248430	+	2.22222i	0.00982007	+	0.0878411i
$641$		−	1.67735i		−	0.0662515i	−0.999451	−	0.0331258i	$-0.989454\pi$
$641$		−	1.67735i		−	0.0662515i	0.999451	−	0.0331258i	$-0.0105462\pi$
$642$	−11.9069	+	8.00171i	−0.469926	+	0.315802i
$643$	−23.1508	+	23.1508i	−0.912978	+	0.912978i	−0.996505	−	0.0835277i	$-0.973381\pi$
$643$	−23.1508	+	23.1508i	−0.912978	+	0.912978i	0.0835277	+	0.996505i	$0.473381\pi$
$644$	−4.17704			−0.164599
$645$	24.0820	+	28.4157i	0.948228	+	1.11887i
$646$	3.92368			0.154375
$647$	−1.87972	+	1.87972i	−0.0738993	+	0.0738993i	−0.743090	−	0.669191i	$-0.766641\pi$
$647$	−1.87972	+	1.87972i	−0.0738993	+	0.0738993i	0.669191	+	0.743090i	$0.266641\pi$
$648$	0.0955769	+	8.99949i	0.00375462	+	0.353533i
$649$			28.4198i			1.11558i
$650$	21.2084	−	4.80193i	0.831861	−	0.188347i
$651$	0.618153	−	3.15137i	0.0242273	−	0.123512i
$652$	−15.8628	−	15.8628i	−0.621235	−	0.621235i
$653$	4.68423	+	4.68423i	0.183308	+	0.183308i	0.792796	−	0.609488i	$-0.208625\pi$
$653$	4.68423	+	4.68423i	0.183308	+	0.183308i	−0.609488	+	0.792796i	$0.708625\pi$
$654$	3.51610	−	17.9252i	0.137490	−	0.700932i
$655$	−16.9068	+	21.1628i	−0.660605	+	0.826898i
$656$		−	6.41083i		−	0.250301i
$657$	12.3601	+	29.3975i	0.482214	+	1.14690i
$658$	3.07903	−	3.07903i	0.120033	−	0.120033i
$659$	−29.9598			−1.16707			−0.583533	−	0.812089i	$-0.698330\pi$
$659$	−29.9598			−1.16707			−0.583533	+	0.812089i	$0.698330\pi$
$660$	−1.50868	+	18.2759i	−0.0587252	+	0.711388i
$661$	25.1252			0.977257			0.488629	−	0.872492i	$-0.337497\pi$
$661$	25.1252			0.977257			0.488629	+	0.872492i	$0.337497\pi$
$662$	−7.74809	+	7.74809i	−0.301138	+	0.301138i
$663$	−24.5314	+	16.4857i	−0.952720	+	0.640252i
$664$		−	10.9472i		−	0.424836i
$665$	−1.16607	+	0.130360i	−0.0452184	+	0.00505513i
$666$	−3.53882	+	8.67343i	−0.137126	+	0.336089i
$667$	22.8672	+	22.8672i	0.885421	+	0.885421i
$668$	16.9172	+	16.9172i	0.654548	+	0.654548i
$669$	30.0301	+	5.89052i	1.16103	+	0.227741i
$670$	9.91047	+	7.91742i	0.382875	+	0.305877i
$671$			14.2304i			0.549359i
$672$	0.506942	+	0.754350i	0.0195557	+	0.0290997i
$673$	31.2587	−	31.2587i	1.20493	−	1.20493i	0.232285	−	0.972648i	$-0.425380\pi$
$673$	31.2587	−	31.2587i	1.20493	−	1.20493i	0.972648	−	0.232285i	$-0.0746201\pi$
$674$	−14.1153			−0.543702
$675$	10.7592	+	23.6483i	0.414121	+	0.910222i
$676$	−5.91417			−0.227468
$677$	−23.6302	+	23.6302i	−0.908182	+	0.908182i	−0.996125	−	0.0879438i	$-0.971970\pi$
$677$	−23.6302	+	23.6302i	−0.908182	+	0.908182i	0.0879438	+	0.996125i	$0.471970\pi$
$678$	−15.9684	−	23.7617i	−0.613265	−	0.912561i
$679$			3.72188i			0.142833i
$680$	−6.85474	−	5.47622i	−0.262867	−	0.210003i
$681$	−7.50733	−	1.47259i	−0.287681	−	0.0564298i
$682$	−11.8302	−	11.8302i	−0.453001	−	0.453001i
$683$	18.9685	+	18.9685i	0.725809	+	0.725809i	0.969782	−	0.243973i	$-0.0784507\pi$
$683$	18.9685	+	18.9685i	0.725809	+	0.725809i	−0.243973	+	0.969782i	$0.578451\pi$
$684$	−1.13332	+	2.77770i	−0.0433335	+	0.106208i
$685$	3.42095	−	0.382440i	0.130708	−	0.0146123i
$686$		−	7.20178i		−	0.274965i
$687$	6.41291	−	4.30964i	0.244668	−	0.164423i
$688$	6.80047	−	6.80047i	0.259266	−	0.259266i
$689$	40.9513			1.56012
$690$	−2.53641	+	30.7257i	−0.0965594	+	1.16971i
$691$	4.36817			0.166173			0.0830866	−	0.996542i	$-0.473522\pi$
$691$	4.36817			0.166173			0.0830866	+	0.996542i	$0.473522\pi$
$692$	−6.04290	+	6.04290i	−0.229717	+	0.229717i
$693$	2.88890	+	6.87101i	0.109740	+	0.261008i
$694$		−	9.24486i		−	0.350930i
$695$	8.85524	−	11.0844i	0.335899	−	0.420454i
$696$	1.35443	−	6.90493i	0.0513395	−	0.261731i
$697$	17.7866	+	17.7866i	0.673716	+	0.673716i
$698$	−11.7869	−	11.7869i	−0.446140	−	0.446140i
$699$	−1.08096	+	5.51077i	−0.0408856	+	0.208436i
$700$	2.21909	+	1.39973i	0.0838738	+	0.0529048i
$701$			20.9191i			0.790102i	0.918659	+	0.395051i	$0.129273\pi$
$701$			20.9191i			0.790102i	−0.918659	+	0.395051i	$0.870727\pi$
$702$	−4.58510	−	22.1282i	−0.173053	−	0.835177i
$703$	−2.20796	+	2.20796i	−0.0832748	+	0.0832748i
$704$	4.73487			0.178452
$705$	−20.7792	−	24.5185i	−0.782590	−	0.923422i
$706$	−26.5488			−0.999178
$707$	−5.23402	+	5.23402i	−0.196846	+	0.196846i
$708$	8.62876	−	5.79875i	0.324289	−	0.217930i
$709$		−	46.0079i		−	1.72786i	−0.503610	−	0.863931i	$-0.667995\pi$
$709$		−	46.0079i		−	1.72786i	0.503610	−	0.863931i	$-0.332005\pi$
$710$	0.912977	+	8.16664i	0.0342634	+	0.306488i
$711$	22.0380	+	8.99162i	0.826488	+	0.337212i
$712$	5.04349	+	5.04349i	0.189013	+	0.189013i
$713$	−19.8891	−	19.8891i	−0.744851	−	0.744851i
$714$	−3.49941	−	0.686422i	−0.130962	−	0.0256887i
$715$	−5.11571	−	45.7604i	−0.191317	−	1.71134i
$716$			7.72862i			0.288832i
$717$	−3.96803	−	5.90457i	−0.148189	−	0.220510i
$718$	21.9852	−	21.9852i	0.820480	−	0.820480i
$719$	25.7542			0.960468			0.480234	−	0.877140i	$-0.340552\pi$
$719$	25.7542			0.960468			0.480234	+	0.877140i	$0.340552\pi$
$720$	5.85671	−	3.27093i	0.218267	−	0.121900i
$721$	−3.83275			−0.142739
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	−24.2454	−	36.0781i	−0.901697	−	1.34176i
$724$			15.5179i			0.576717i
$725$	−4.48559	−	19.8112i	−0.166590	−	0.735770i
$726$	19.4084	+	3.80703i	0.720312	+	0.141292i
$727$	−11.1708	−	11.1708i	−0.414302	−	0.414302i	0.468932	−	0.883234i	$-0.344639\pi$
$727$	−11.1708	−	11.1708i	−0.414302	−	0.414302i	−0.883234	+	0.468932i	$0.844639\pi$
$728$	−1.61368	−	1.61368i	−0.0598069	−	0.0598069i
$729$	24.7770	−	10.7285i	0.917667	−	0.397351i
$730$	14.8362	−	18.5709i	0.549112	−	0.687340i
$731$			37.7353i			1.39569i
$732$	4.32060	−	2.90355i	0.159694	−	0.107318i
$733$	9.70478	−	9.70478i	0.358454	−	0.358454i	−0.504789	−	0.863243i	$-0.668430\pi$
$733$	9.70478	−	9.70478i	0.358454	−	0.358454i	0.863243	+	0.504789i	$0.168430\pi$
$734$	−1.07637			−0.0397295
$735$	−25.9562	−	2.14269i	−0.957408	−	0.0790342i
$736$	7.96032			0.293421
$737$	18.9928	−	18.9928i	0.699610	−	0.699610i
$738$	−17.7292	+	7.45420i	−0.652619	+	0.274393i
$739$			31.4666i			1.15752i	0.815499	+	0.578759i	$0.196463\pi$
$739$			31.4666i			1.15752i	−0.815499	+	0.578759i	$0.803537\pi$
$740$	6.93896	−	0.775731i	0.255081	−	0.0285164i
$741$	1.44995	−	7.39190i	0.0532652	−	0.271548i
$742$	3.49379	+	3.49379i	0.128261	+	0.128261i
$743$	−0.387245	−	0.387245i	−0.0142066	−	0.0142066i	0.699968	−	0.714174i	$-0.253198\pi$
$743$	−0.387245	−	0.387245i	−0.0142066	−	0.0142066i	−0.714174	+	0.699968i	$0.753198\pi$
$744$	−1.17803	+	6.00566i	−0.0431888	+	0.220178i
$745$	−33.5882	−	26.8334i	−1.23058	−	0.983101i
$746$		−	11.3284i		−	0.414760i
$747$	−30.2747	+	12.7289i	−1.10769	+	0.465727i
$748$	−13.1367	+	13.1367i	−0.480326	+	0.480326i
$749$	4.34611			0.158803
$750$	11.6437	−	15.4733i	0.425167	−	0.565007i
$751$	8.65270			0.315742			0.157871	−	0.987460i	$-0.449537\pi$
$751$	8.65270			0.315742			0.157871	+	0.987460i	$0.449537\pi$
$752$	−5.86781	+	5.86781i	−0.213977	+	0.213977i
$753$	30.7326	−	20.6531i	1.11996	−	0.752641i
$754$			17.6681i			0.643435i
$755$	9.82120	+	7.84611i	0.357430	+	0.285549i
$756$	1.49671	−	2.27907i	0.0544348	−	0.0828890i
$757$	−2.24043	−	2.24043i	−0.0814299	−	0.0814299i	0.665219	−	0.746649i	$-0.268338\pi$
$757$	−2.24043	−	2.24043i	−0.0814299	−	0.0814299i	−0.746649	+	0.665219i	$0.768338\pi$
$758$	−10.6495	−	10.6495i	−0.386808	−	0.386808i
$759$	64.0621	+	12.5660i	2.32531	+	0.456117i
$760$	2.22222	−	0.248430i	0.0806086	−	0.00901151i
$761$		−	9.75042i		−	0.353452i	−0.984260	−	0.176726i	$-0.943449\pi$
$761$		−	9.75042i		−	0.353452i	0.984260	−	0.176726i	$-0.0565507\pi$
$762$	−15.8060	−	23.5200i	−0.572592	−	0.852039i
$763$	−3.91314	+	3.91314i	−0.141665	+	0.141665i
$764$	13.5080			0.488701
$765$	−7.17415	+	25.3243i	−0.259382	+	0.915602i
$766$	30.3805			1.09769
$767$	−18.4583	+	18.4583i	−0.666492	+	0.666492i
$768$	−0.966096	−	1.43759i	−0.0348610	−	0.0518745i
$769$		−	49.3395i		−	1.77923i	−0.456714	−	0.889614i	$-0.650974\pi$
$769$		−	49.3395i		−	1.77923i	0.456714	−	0.889614i	$-0.349026\pi$
$770$	3.46763	−	4.34053i	0.124965	−	0.156422i
$771$	−17.0328	−	3.34105i	−0.613421	−	0.120325i
$772$	2.95772	+	2.95772i	0.106451	+	0.106451i
$773$	−22.1512	−	22.1512i	−0.796725	−	0.796725i	0.185853	−	0.982578i	$-0.440495\pi$
$773$	−22.1512	−	22.1512i	−0.796725	−	0.796725i	−0.982578	+	0.185853i	$0.940495\pi$
$774$	−26.7140	−	10.8995i	−0.960215	−	0.391774i
$775$	3.90140	+	17.2311i	0.140143	+	0.618958i
$776$		−	7.09290i		−	0.254620i
$777$	2.35548	−	1.58294i	0.0845023	−	0.0567877i
$778$	−8.31614	+	8.31614i	−0.298148	+	0.298148i
$779$	−6.41083			−0.229692
$780$	−12.8498	+	10.8901i	−0.460098	+	0.389928i
$781$	17.4006			0.622641
$782$	−22.0856	+	22.0856i	−0.789780	+	0.789780i
$783$	−20.6705	+	4.28304i	−0.738702	+	0.153063i
$784$			6.72466i			0.240166i
$785$	−3.62189	−	32.3981i	−0.129271	−	1.15634i
$786$	4.03863	−	20.5891i	0.144053	−	0.734389i
$787$	−9.86758	−	9.86758i	−0.351741	−	0.351741i	0.509016	−	0.860757i	$-0.330009\pi$
$787$	−9.86758	−	9.86758i	−0.351741	−	0.351741i	−0.860757	+	0.509016i	$0.830009\pi$
$788$	−14.5718	−	14.5718i	−0.519099	−	0.519099i
$789$	−4.88982	+	24.9285i	−0.174082	+	0.887478i
$790$	−1.97102	−	17.6309i	−0.0701258	−	0.627280i
$791$			8.67323i			0.308384i
$792$	−5.50547	−	13.0943i	−0.195628	−	0.465285i
$793$	−9.24247	+	9.24247i	−0.328210	+	0.328210i
$794$	8.87312			0.314895
$795$	27.8213	−	23.5783i	0.986721	−	0.836236i
$796$	−5.90849			−0.209421
$797$	3.60992	−	3.60992i	0.127870	−	0.127870i	−0.640275	−	0.768145i	$-0.721180\pi$
$797$	3.60992	−	3.60992i	0.127870	−	0.127870i	0.768145	+	0.640275i	$0.221180\pi$
$798$	0.754350	−	0.506942i	0.0267037	−	0.0179456i
$799$		−	32.5600i		−	1.15189i
$800$	−4.22899	−	2.66751i	−0.149518	−	0.0943107i
$801$	8.08347	−	19.8121i	0.285615	−	0.700027i
$802$	−20.3873	−	20.3873i	−0.719901	−	0.719901i
$803$	−35.5900	−	35.5900i	−1.25595	−	1.25595i
$804$	−9.64183	−	1.89128i	−0.340041	−	0.0667003i
$805$	5.82983	−	7.29737i	0.205475	−	0.257198i
$806$		−	15.3671i		−	0.541283i
$807$	−13.4432	−	20.0040i	−0.473223	−	0.704173i
$808$	9.97464	−	9.97464i	0.350907	−	0.350907i
$809$	5.63069			0.197964			0.0989822	−	0.995089i	$-0.468441\pi$
$809$	5.63069			0.197964			0.0989822	+	0.995089i	$0.468441\pi$
$810$	−15.8557	−	12.3935i	−0.557111	−	0.435462i
$811$	−4.93429			−0.173266			−0.0866332	−	0.996240i	$-0.527611\pi$
$811$	−4.93429			−0.173266			−0.0866332	+	0.996240i	$0.527611\pi$
$812$	−1.50737	+	1.50737i	−0.0528983	+	0.0528983i
$813$	−9.46290	−	14.0812i	−0.331879	−	0.493848i
$814$		−	14.7848i		−	0.518206i
$815$	49.8520	−	5.57313i	1.74624	−	0.195218i
$816$	6.66893	+	1.30814i	0.233459	+	0.0457939i
$817$	−6.80047	−	6.80047i	−0.237918	−	0.237918i
$818$	13.1804	+	13.1804i	0.460843	+	0.460843i
$819$	−2.58633	+	6.33894i	−0.0903736	+	0.221500i
$820$	11.1998	+	8.94748i	0.391115	+	0.312460i
$821$			33.4852i			1.16864i	0.811522	+	0.584321i	$0.198639\pi$
$821$			33.4852i			1.16864i	−0.811522	+	0.584321i	$0.801361\pi$
$822$	−2.21306	+	1.48723i	−0.0771894	+	0.0518733i
$823$	−1.29986	+	1.29986i	−0.0453102	+	0.0453102i	−0.729399	−	0.684089i	$-0.760200\pi$
$823$	−1.29986	+	1.29986i	−0.0453102	+	0.0453102i	0.684089	+	0.729399i	$0.260200\pi$
$824$	7.30419			0.254454
$825$	−29.8227	−	28.1430i	−1.03829	−	0.979815i
$826$	−3.14958			−0.109588
$827$	−10.5401	+	10.5401i	−0.366514	+	0.366514i	−0.866204	−	0.499690i	$-0.833447\pi$
$827$	−10.5401	+	10.5401i	−0.366514	+	0.366514i	0.499690	+	0.866204i	$0.333447\pi$
$828$	−9.25588	−	22.0143i	−0.321664	−	0.765050i
$829$		−	26.4052i		−	0.917089i	−0.888671	−	0.458545i	$-0.848371\pi$
$829$		−	26.4052i		−	0.917089i	0.888671	−	0.458545i	$-0.151629\pi$
$830$	19.1250	+	15.2789i	0.663839	+	0.530338i
$831$	−2.16242	+	11.0241i	−0.0750137	+	0.382423i
$832$	3.07524	+	3.07524i	0.106615	+	0.106615i
$833$	−18.6573	−	18.6573i	−0.646437	−	0.646437i
$834$	−2.11530	+	10.7839i	−0.0732470	+	0.373416i
$835$	−53.1658	+	5.94359i	−1.83988	+	0.205686i
$836$		−	4.73487i		−	0.163759i
$837$	17.9784	−	3.72523i	0.621425	−	0.128763i
$838$	−23.5890	+	23.5890i	−0.814868	+	0.814868i
$839$	−16.4354			−0.567412			−0.283706	−	0.958911i	$-0.591564\pi$
$839$	−16.4354			−0.567412			−0.283706	+	0.958911i	$0.591564\pi$
$840$	−2.02539	−	0.167196i	−0.0698827	−	0.00576882i
$841$	−12.4958			−0.430891
$842$	−10.1680	+	10.1680i	−0.350412	+	0.350412i
$843$	−17.4089	+	11.6993i	−0.599596	+	0.402944i
$844$			6.45326i			0.222130i
$845$	8.25431	−	10.3322i	0.283957	−	0.355437i
$846$	23.0502	+	9.40464i	0.792484	+	0.323338i
$847$	−4.23692	−	4.23692i	−0.145582	−	0.145582i
$848$	−6.65823	−	6.65823i	−0.228645	−	0.228645i
$849$	3.19054	+	0.625836i	0.109499	+	0.0214786i
$850$	19.1341	−	4.33228i	0.656294	−	0.148596i
$851$		−	24.8563i		−	0.852064i
$852$	−3.55039	−	5.28311i	−0.121634	−	0.180996i
$853$	−0.541057	+	0.541057i	−0.0185254	+	0.0185254i	−0.716309	−	0.697783i	$-0.754170\pi$
$853$	−0.541057	+	0.541057i	−0.0185254	+	0.0185254i	0.697783	+	0.716309i	$0.254170\pi$
$854$	−1.57706			−0.0539658
$855$	−3.27093	−	5.85671i	−0.111863	−	0.200295i
$856$	−8.28252			−0.283091
$857$	12.6475	−	12.6475i	0.432029	−	0.432029i	−0.457289	−	0.889318i	$-0.651180\pi$
$857$	12.6475	−	12.6475i	0.432029	−	0.432029i	0.889318	+	0.457289i	$0.151180\pi$
$858$	19.8940	+	29.6030i	0.679169	+	1.01063i
$859$		−	4.30216i		−	0.146788i	−0.997303	−	0.0733939i	$-0.976617\pi$
$859$		−	4.30216i		−	0.146788i	0.997303	−	0.0733939i	$-0.0233830\pi$
$860$	2.38923	+	21.3719i	0.0814722	+	0.728774i
$861$	5.71761	+	1.12153i	0.194856	+	0.0382217i
$862$	9.49762	+	9.49762i	0.323490	+	0.323490i
$863$	−29.8424	−	29.8424i	−1.01585	−	1.01585i	−0.999872	−	0.0159756i	$-0.994915\pi$
$863$	−29.8424	−	29.8424i	−1.01585	−	1.01585i	−0.0159756	−	0.999872i	$-0.505085\pi$
$864$	−2.85232	+	4.34330i	−0.0970381	+	0.147762i
$865$	−2.12307	−	18.9910i	−0.0721866	−	0.645714i
$866$		−	6.50290i		−	0.220977i
$867$	2.30690	−	1.55030i	0.0783466	−	0.0526509i
$868$	1.31106	−	1.31106i	0.0445002	−	0.0445002i
$869$	−37.5660			−1.27434
$870$	10.1727	+	12.0033i	0.344886	+	0.406950i
$871$	24.6712			0.835952
$872$	7.45740	−	7.45740i	0.252539	−	0.252539i
$873$	−19.6155	+	8.24728i	−0.663882	+	0.279128i
$874$		−	7.96032i		−	0.269262i
$875$	−5.54250	+	1.92321i	−0.187371	+	0.0650164i
$876$	−3.54401	+	18.0675i	−0.119741	+	0.610444i
$877$	30.6993	+	30.6993i	1.03664	+	1.03664i	0.999303	+	0.0373388i	$0.0118881\pi$
$877$	30.6993	+	30.6993i	1.03664	+	1.03664i	0.0373388	+	0.999303i	$0.488112\pi$
$878$	−6.01359	−	6.01359i	−0.202949	−	0.202949i
$879$	5.96466	−	30.4081i	0.201183	−	1.02564i
$880$	−6.60838	+	8.27189i	−0.222768	+	0.278845i
$881$		−	27.9951i		−	0.943179i	−0.881818	−	0.471590i	$-0.843680\pi$
$881$		−	27.9951i		−	0.943179i	0.881818	−	0.471590i	$-0.156320\pi$
$882$	18.5971	−	7.81910i	0.626196	−	0.263283i
$883$	16.3149	−	16.3149i	0.549041	−	0.549041i	−0.377123	−	0.926163i	$-0.623086\pi$
$883$	16.3149	−	16.3149i	0.549041	−	0.549041i	0.926163	+	0.377123i	$0.123086\pi$
$884$	−17.0643			−0.573933
$885$	−1.91250	+	23.1678i	−0.0642881	+	0.778777i
$886$	−30.2914			−1.01766
$887$	−6.91467	+	6.91467i	−0.232172	+	0.232172i	−0.813599	−	0.581427i	$-0.802495\pi$
$887$	−6.91467	+	6.91467i	−0.232172	+	0.232172i	0.581427	+	0.813599i	$0.302495\pi$
$888$	−4.48891	+	3.01666i	−0.150638	+	0.101233i
$889$			8.58501i			0.287932i
$890$	−15.8502	+	1.77195i	−0.531299	+	0.0593958i
$891$	−29.8108	+	30.4508i	−0.998700	+	1.02014i
$892$	12.4934	+	12.4934i	0.418309	+	0.418309i
$893$	5.86781	+	5.86781i	0.196359	+	0.196359i
$894$	32.6777	+	6.40986i	1.09291	+	0.214378i
$895$	−13.5020	−	10.7867i	−0.451323	−	0.360560i
$896$			0.524733i			0.0175301i
$897$	33.4460	+	49.7690i	1.11673	+	1.66174i
$898$	23.7703	−	23.7703i	0.793226	−	0.793226i
$899$	−14.3547			−0.478757
$900$	−2.45974	+	14.7969i	−0.0819914	+	0.493232i
$901$	36.9460			1.23085
$902$	21.4638	−	21.4638i	0.714667	−	0.714667i
$903$	4.87543	+	7.25482i	0.162244	+	0.241425i
$904$		−	16.5288i		−	0.549741i
$905$	−27.1100	−	21.6580i	−0.901165	−	0.719937i
$906$	−9.55498	−	1.87425i	−0.317443	−	0.0622676i
$907$	−30.4082	−	30.4082i	−1.00969	−	1.00969i	−0.999953	−	0.00973481i	$-0.996901\pi$
$907$	−30.4082	−	30.4082i	−1.00969	−	1.00969i	−0.00973481	−	0.999953i	$-0.503099\pi$
$908$	−3.12326	−	3.12326i	−0.103649	−	0.103649i
$909$	−39.1829	−	15.9869i	−1.29962	−	0.530251i
$910$	5.07131	−	0.566939i	0.168112	−	0.0187938i
$911$		−	23.5754i		−	0.781089i	−0.920584	−	0.390544i	$-0.872287\pi$
$911$		−	23.5754i		−	0.781089i	0.920584	−	0.390544i	$-0.127713\pi$
$912$	−1.43759	+	0.966096i	−0.0476033	+	0.0319906i
$913$	36.6520	−	36.6520i	1.21300	−	1.21300i
$914$	−20.8295			−0.688978
$915$	−0.957631	+	11.6006i	−0.0316583	+	0.383504i
$916$	4.46088			0.147392
$917$	−4.49468	+	4.49468i	−0.148427	+	0.148427i
$918$	−4.13665	−	19.9640i	−0.136530	−	0.658910i
$919$			27.2929i			0.900308i	0.892951	+	0.450154i	$0.148631\pi$
$919$			27.2929i			0.900308i	−0.892951	+	0.450154i	$0.851369\pi$
$920$	−11.1101	+	13.9068i	−0.366289	+	0.458494i
$921$	−7.74606	+	39.4897i	−0.255241	+	1.30123i
$922$	−0.865212	−	0.865212i	−0.0284942	−	0.0284942i
$923$	11.3014	+	11.3014i	0.371992	+	0.371992i
$924$	−0.828333	+	4.22288i	−0.0272502	+	0.138922i
$925$	−8.32938	+	13.2052i	−0.273868	+	0.434183i
$926$		−	18.3038i		−	0.601501i
$927$	−8.49296	−	20.1998i	−0.278945	−	0.663448i
$928$	2.87264	−	2.87264i	0.0942992	−	0.0942992i
$929$	−41.8662			−1.37359			−0.686793	−	0.726853i	$-0.740982\pi$
$929$	−41.8662			−1.37359			−0.686793	+	0.726853i	$0.740982\pi$
$930$	−8.84783	−	10.4400i	−0.290132	−	0.342342i
$931$	6.72466			0.220392
$932$	−2.29263	+	2.29263i	−0.0750977	+	0.0750977i
$933$	−9.33548	+	6.27368i	−0.305630	+	0.205391i
$934$		−	11.6392i		−	0.380847i
$935$	−4.61537	−	41.2848i	−0.150939	−	1.35016i
$936$	4.92884	−	12.0803i	0.161104	−	0.394857i
$937$	30.2246	+	30.2246i	0.987396	+	0.987396i	0.999922	−	0.0125256i	$-0.00398713\pi$
$937$	30.2246	+	30.2246i	0.987396	+	0.987396i	−0.0125256	+	0.999922i	$0.503987\pi$
$938$	2.10485	+	2.10485i	0.0687257	+	0.0687257i
$939$	37.4051	+	7.33715i	1.22067	+	0.239439i
$940$	−2.06156	−	18.4408i	−0.0672406	−	0.601471i
$941$		−	26.6531i		−	0.868868i	−0.900704	−	0.434434i	$-0.856948\pi$
$941$		−	26.6531i		−	0.868868i	0.900704	−	0.434434i	$-0.143052\pi$
$942$	14.0848	+	20.9588i	0.458908	+	0.682873i
$943$	36.0852	−	36.0852i	1.17510	−	1.17510i
$944$	6.00225			0.195357
$945$	1.89265	+	5.79564i	0.0615678	+	0.188532i
$946$	45.5367			1.48053
$947$	8.48716	−	8.48716i	0.275796	−	0.275796i	−0.555632	−	0.831428i	$-0.687524\pi$
$947$	8.48716	−	8.48716i	0.275796	−	0.275796i	0.831428	+	0.555632i	$0.187524\pi$
$948$	7.66491	+	11.4057i	0.248945	+	0.370439i
$949$		−	46.2306i		−	1.50071i
$950$	−2.66751	+	4.22899i	−0.0865455	+	0.137207i
$951$	52.4662	+	10.2914i	1.70133	+	0.333723i
$952$	−1.45585	−	1.45585i	−0.0471844	−	0.0471844i
$953$	1.79756	+	1.79756i	0.0582288	+	0.0582288i	0.735622	−	0.677393i	$-0.236890\pi$
$953$	1.79756	+	1.79756i	0.0582288	+	0.0582288i	−0.677393	+	0.735622i	$0.736890\pi$
$954$	−10.6715	+	26.1552i	−0.345502	+	0.846807i
$955$	−18.8528	+	23.5986i	−0.610063	+	0.763634i
$956$		−	4.10728i		−	0.132839i
$957$	27.6528	−	18.5834i	0.893888	−	0.600716i
$958$	−16.7864	+	16.7864i	−0.542344	+	0.542344i
$959$	0.807788			0.0260848
$960$	3.85985	+	0.318631i	0.124576	+	0.0102838i
$961$	−18.5148			−0.597250
$962$	9.60252	−	9.60252i	0.309598	−	0.309598i
$963$	9.63051	+	22.9053i	0.310339	+	0.738114i
$964$		−	25.0963i		−	0.808297i
$965$	−9.29523	+	1.03915i	−0.299224	+	0.0334513i
$966$	−1.39261	+	7.09956i	−0.0448063	+	0.228425i
$967$	39.2936	+	39.2936i	1.26360	+	1.26360i	0.949337	+	0.314260i	$0.101757\pi$
$967$	39.2936	+	39.2936i	1.26360	+	1.26360i	0.314260	+	0.949337i	$0.398243\pi$
$968$	8.07443	+	8.07443i	0.259522	+	0.259522i
$969$	1.30814	−	6.66893i	0.0420234	−	0.214237i
$970$	12.3914	+	9.89945i	0.397865	+	0.317852i
$971$			3.89501i			0.124997i	0.998045	+	0.0624984i	$0.0199068\pi$
$971$			3.89501i			0.124997i	−0.998045	+	0.0624984i	$0.980093\pi$
$972$	15.3280	+	2.83794i	0.491644	+	0.0910269i
$973$	2.35416	−	2.35416i	0.0754711	−	0.0754711i
$974$	38.4817			1.23303
$975$	−1.09089	−	37.6480i	−0.0349364	−	1.20570i
$976$	3.00545			0.0962021
$977$	38.4514	−	38.4514i	1.23017	−	1.23017i	0.266273	−	0.963898i	$-0.414208\pi$
$977$	38.4514	−	38.4514i	1.23017	−	1.23017i	0.963898	−	0.266273i	$-0.0857922\pi$
$978$	−32.2500	+	21.6728i	−1.03124	+	0.693020i
$979$			33.7718i			1.07935i
$980$	−11.7481	−	9.38549i	−0.375279	−	0.299808i
$981$	−29.2946	−	11.9524i	−0.935304	−	0.381610i
$982$	28.6287	+	28.6287i	0.913579	+	0.913579i
$983$	4.51390	+	4.51390i	0.143971	+	0.143971i	0.775419	−	0.631448i	$-0.217539\pi$
$983$	4.51390	+	4.51390i	0.143971	+	0.143971i	−0.631448	+	0.775419i	$0.717539\pi$
$984$	−10.8962	−	2.13734i	−0.347359	−	0.0681358i
$985$	45.7948	−	5.11956i	1.45914	−	0.163123i
$986$			15.9401i			0.507636i
$987$	−4.20678	−	6.25984i	−0.133903	−	0.199253i
$988$	3.07524	−	3.07524i	0.0978363	−	0.0978363i
$989$	76.5570			2.43437
$990$	30.5598	+	8.65733i	0.971256	+	0.275148i
$991$	2.37283			0.0753756			0.0376878	−	0.999290i	$-0.488001\pi$
$991$	2.37283			0.0753756			0.0376878	+	0.999290i	$0.488001\pi$
$992$	−2.49852	+	2.49852i	−0.0793282	+	0.0793282i
$993$	10.5860	+	15.7523i	0.335935	+	0.499884i
$994$			1.92838i			0.0611646i
$995$	8.24638	−	10.3222i	0.261428	−	0.327237i
$996$	−18.6066	−	3.64976i	−0.589573	−	0.115647i
$997$	−39.9605	−	39.9605i	−1.26556	−	1.26556i	−0.948357	−	0.317206i	$-0.897255\pi$
$997$	−39.9605	−	39.9605i	−1.26556	−	1.26556i	−0.317206	−	0.948357i	$-0.602745\pi$
$998$	4.07043	+	4.07043i	0.128847	+	0.128847i
$999$	13.5621	+	8.90647i	0.429085	+	0.281788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.77.12	yes	36
3.2	odd	2	inner	570.2.k.a.77.7	✓	36
5.3	odd	4	inner	570.2.k.a.533.7	yes	36
15.8	even	4	inner	570.2.k.a.533.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.7	✓	36	3.2	odd	2	inner
570.2.k.a.77.12	yes	36	1.1	even	1	trivial
570.2.k.a.533.7	yes	36	5.3	odd	4	inner
570.2.k.a.533.12	yes	36	15.8	even	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +(2.22222 - 0.248430i) q^{10} -4.73487i q^{11} +(-1.43759 + 0.966096i) q^{12} +(3.07524 - 3.07524i) q^{13} +0.524733 q^{14} +(0.318631 - 3.85985i) q^{15} -1.00000 q^{16} +(2.77446 - 2.77446i) q^{17} +(1.16275 + 2.76550i) q^{18} +1.00000i q^{19} +(1.39568 - 1.74702i) q^{20} +(0.174943 - 0.891868i) q^{21} +(-3.34806 - 3.34806i) q^{22} +(-5.62880 - 5.62880i) q^{23} +(-0.333395 + 1.69966i) q^{24} +(1.10414 + 4.87656i) q^{25} -4.34904i q^{26} +(5.08807 - 1.05428i) q^{27} +(0.371042 - 0.371042i) q^{28} -4.06253 q^{29} +(-2.50402 - 2.95464i) q^{30} +3.53345 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.80679 + 4.57434i) q^{33} -3.92368i q^{34} +(0.130360 + 1.16607i) q^{35} +(2.77770 + 1.13332i) q^{36} +(2.20796 + 2.20796i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-7.39190 - 1.44995i) q^{39} +(-0.248430 - 2.22222i) q^{40} +6.41083i q^{41} +(-0.506942 - 0.754350i) q^{42} +(-6.80047 + 6.80047i) q^{43} -4.73487 q^{44} +(-5.85671 + 3.27093i) q^{45} -7.96032 q^{46} +(5.86781 - 5.86781i) q^{47} +(0.966096 + 1.43759i) q^{48} -6.72466i q^{49} +(4.22899 + 2.66751i) q^{50} +(-6.66893 - 1.30814i) q^{51} +(-3.07524 - 3.07524i) q^{52} +(6.65823 + 6.65823i) q^{53} +(2.85232 - 4.34330i) q^{54} +(6.60838 - 8.27189i) q^{55} -0.524733i q^{56} +(1.43759 - 0.966096i) q^{57} +(-2.87264 + 2.87264i) q^{58} -6.00225 q^{59} +(-3.85985 - 0.318631i) q^{60} -3.00545 q^{61} +(2.49852 - 2.49852i) q^{62} +(-1.45115 + 0.610134i) q^{63} +1.00000i q^{64} +(9.66455 - 1.08043i) q^{65} +(-1.57858 + 8.04767i) q^{66} +(4.01127 + 4.01127i) q^{67} +(-2.77446 - 2.77446i) q^{68} +(-2.65393 + 13.5299i) q^{69} +(0.916717 + 0.732361i) q^{70} +3.67498i q^{71} +(2.76550 - 1.16275i) q^{72} +(7.51659 - 7.51659i) q^{73} +3.12253 q^{74} +(5.94379 - 6.29852i) q^{75} +1.00000 q^{76} +(1.75684 - 1.75684i) q^{77} +(-6.25213 + 4.20159i) q^{78} -7.93390i q^{79} +(-1.74702 - 1.39568i) q^{80} +(-6.43119 - 6.29602i) q^{81} +(4.53314 + 4.53314i) q^{82} +(7.74087 + 7.74087i) q^{83} +(-0.891868 - 0.174943i) q^{84} +(8.71931 - 0.974762i) q^{85} +9.61732i q^{86} +(3.92480 + 5.84025i) q^{87} +(-3.34806 + 3.34806i) q^{88} -7.13257 q^{89} +(-1.82842 + 6.45421i) q^{90} +2.28209 q^{91} +(-5.62880 + 5.62880i) q^{92} +(-3.41365 - 5.07964i) q^{93} -8.29833i q^{94} +(-1.39568 + 1.74702i) q^{95} +(1.69966 + 0.333395i) q^{96} +(5.01544 + 5.01544i) q^{97} +(-4.75505 - 4.75505i) q^{98} +(13.1520 + 5.36611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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