LMFDB - Embedded newform 630.2.bt.a.473.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

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([2, 3, 4]))

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

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

chi := DirichletCharacter("630.317");

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.bt (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			473.17
Character	$\chi$	$=$	630.473
Dual form			630.2.bt.a.317.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.754597 + 1.55903i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.96329 - 1.07027i) q^{5} +(-1.13239 - 1.31061i) q^{6} +(-2.51410 + 0.824195i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.86117 + 2.35288i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.754597 + 1.55903i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.96329 - 1.07027i) q^{5} +(-1.13239 - 1.31061i) q^{6} +(-2.51410 + 0.824195i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.86117 + 2.35288i) q^{9} +(2.17340 + 0.525664i) q^{10} -4.53586i q^{11} +(1.43302 + 0.972864i) q^{12} +(-3.26064 + 0.873687i) q^{13} +(2.21512 - 1.44681i) q^{14} +(0.187092 - 3.86846i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.71077 - 1.79814i) q^{17} +(1.18878 - 2.75442i) q^{18} +(4.85172 - 2.80114i) q^{19} +(-2.23540 + 0.0547655i) q^{20} +(-3.18208 - 3.29763i) q^{21} +(1.17397 + 4.38130i) q^{22} +(3.83187 - 3.83187i) q^{23} +(-1.63598 - 0.568822i) q^{24} +(2.70904 + 4.20251i) q^{25} +(2.92341 - 1.68783i) q^{26} +(-5.07265 - 1.12614i) q^{27} +(-1.76518 + 1.97082i) q^{28} +(-4.57249 - 7.91979i) q^{29} +(0.820515 + 3.78507i) q^{30} +(-0.880254 - 1.52464i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(7.07156 - 3.42275i) q^{33} +(-6.01671 + 3.47375i) q^{34} +(5.81803 + 1.07263i) q^{35} +(-0.435377 + 2.96824i) q^{36} +(-6.47766 - 1.73568i) q^{37} +(-3.96141 + 3.96141i) q^{38} +(-3.82258 - 4.42417i) q^{39} +(2.14505 - 0.631463i) q^{40} +(-0.832022 - 0.480368i) q^{41} +(3.92714 + 2.36168i) q^{42} +(-0.841255 + 3.13961i) q^{43} +(-2.26793 - 3.92817i) q^{44} +(6.17224 - 2.62745i) q^{45} +(-2.70954 + 4.69306i) q^{46} +(-1.09611 + 0.293702i) q^{47} +(1.72746 + 0.126017i) q^{48} +(5.64141 - 4.14422i) q^{49} +(-3.70442 - 3.35816i) q^{50} +(7.86729 + 9.10543i) q^{51} +(-2.38696 + 2.38696i) q^{52} +(-0.424048 - 1.58257i) q^{53} +(5.19127 - 0.225127i) q^{54} +(-4.85460 + 8.90523i) q^{55} +(1.19494 - 2.36053i) q^{56} +(8.02816 + 5.45026i) q^{57} +(6.46648 + 6.46648i) q^{58} +(-4.00955 - 6.94474i) q^{59} +(-1.77220 - 3.44373i) q^{60} +(2.09403 - 3.62696i) q^{61} +(1.24487 + 1.24487i) q^{62} +(2.73993 - 7.44935i) q^{63} -1.00000i q^{64} +(7.33668 + 1.77447i) q^{65} +(-5.94473 + 5.13637i) q^{66} +(-9.25042 - 2.47864i) q^{67} +(4.91262 - 4.91262i) q^{68} +(8.86552 + 3.08249i) q^{69} +(-5.89740 + 0.469734i) q^{70} +12.8302i q^{71} +(-0.347695 - 2.97978i) q^{72} +(8.08951 - 2.16758i) q^{73} +6.70617 q^{74} +(-4.50762 + 7.39469i) q^{75} +(2.80114 - 4.85172i) q^{76} +(3.73843 + 11.4036i) q^{77} +(4.83738 + 3.28406i) q^{78} +(-5.30665 - 3.06379i) q^{79} +(-1.90853 + 1.16513i) q^{80} +(-2.07211 - 8.75822i) q^{81} +(0.928000 + 0.248657i) q^{82} +(-5.33571 - 1.42970i) q^{83} +(-4.40458 - 1.26479i) q^{84} +(-15.0997 - 3.65205i) q^{85} -3.25036i q^{86} +(8.89682 - 13.1049i) q^{87} +(3.20734 + 3.20734i) q^{88} +(-7.21440 - 12.4957i) q^{89} +(-5.28189 + 4.13541i) q^{90} +(7.47750 - 4.88394i) q^{91} +(1.40256 - 5.23443i) q^{92} +(1.71273 - 2.52284i) q^{93} +(0.982746 - 0.567388i) q^{94} +(-12.5233 + 0.306812i) q^{95} +(-1.70121 + 0.325377i) q^{96} +(12.0791 + 3.23659i) q^{97} +(-4.37658 + 5.46311i) q^{98} +(10.6723 + 8.44200i) 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} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.754597	+	1.55903i	0.435667	+	0.900108i
$3$	0.754597	+	1.55903i	0.435667	+	0.900108i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.96329	−	1.07027i	−0.878012	−	0.478639i
$5$	−1.96329	−	1.07027i	−0.878012	−	0.478639i
$6$	−1.13239	−	1.31061i	−0.462297	−	0.535053i
$7$	−2.51410	+	0.824195i	−0.950241	+	0.311516i
$7$	−2.51410	+	0.824195i	−0.950241	+	0.311516i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.86117	+	2.35288i	−0.620389	+	0.784294i
$10$	2.17340	+	0.525664i	0.687290	+	0.166230i
$11$		−	4.53586i		−	1.36761i	−0.729663	−	0.683807i	$-0.760323\pi$
$11$		−	4.53586i		−	1.36761i	0.729663	−	0.683807i	$-0.239677\pi$
$12$	1.43302	+	0.972864i	0.413676	+	0.280842i
$13$	−3.26064	+	0.873687i	−0.904340	+	0.242317i	−0.680879	−	0.732396i	$-0.738402\pi$
$13$	−3.26064	+	0.873687i	−0.904340	+	0.242317i	−0.223461	+	0.974713i	$0.571735\pi$
$14$	2.21512	−	1.44681i	0.592015	−	0.386676i
$15$	0.187092	−	3.86846i	0.0483069	−	0.998833i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.71077	−	1.79814i	1.62760	−	0.436114i	0.674378	−	0.738386i	$-0.264412\pi$
$17$	6.71077	−	1.79814i	1.62760	−	0.436114i	0.953222	+	0.302272i	$0.0977450\pi$
$18$	1.18878	−	2.75442i	0.280198	−	0.649222i
$19$	4.85172	−	2.80114i	1.11306	−	0.642626i	0.173440	−	0.984844i	$-0.444512\pi$
$19$	4.85172	−	2.80114i	1.11306	−	0.642626i	0.939620	+	0.342218i	$0.111178\pi$
$20$	−2.23540	+	0.0547655i	−0.499850	+	0.0122459i
$21$	−3.18208	−	3.29763i	−0.694387	−	0.719602i
$22$	1.17397	+	4.38130i	0.250291	+	0.934097i
$23$	3.83187	−	3.83187i	0.799000	−	0.799000i	−0.183938	−	0.982938i	$-0.558885\pi$
$23$	3.83187	−	3.83187i	0.799000	−	0.799000i	0.982938	+	0.183938i	$0.0588846\pi$
$24$	−1.63598	−	0.568822i	−0.333944	−	0.116110i
$25$	2.70904	+	4.20251i	0.541809	+	0.840502i
$26$	2.92341	−	1.68783i	0.573328	−	0.331011i
$27$	−5.07265	−	1.12614i	−0.976232	−	0.216727i
$28$	−1.76518	+	1.97082i	−0.333587	+	0.372451i
$29$	−4.57249	−	7.91979i	−0.849090	−	1.47067i	−0.882021	−	0.471210i	$-0.843817\pi$
$29$	−4.57249	−	7.91979i	−0.849090	−	1.47067i	0.0329306	−	0.999458i	$-0.489516\pi$
$30$	0.820515	+	3.78507i	0.149805	+	0.691056i
$31$	−0.880254	−	1.52464i	−0.158098	−	0.273834i	0.776085	−	0.630629i	$-0.217203\pi$
$31$	−0.880254	−	1.52464i	−0.158098	−	0.273834i	−0.934183	+	0.356795i	$0.883870\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	7.07156	−	3.42275i	1.23100	−	0.595823i
$34$	−6.01671	+	3.47375i	−1.03186	+	0.595743i
$35$	5.81803	+	1.07263i	0.983426	+	0.181308i
$36$	−0.435377	+	2.96824i	−0.0725629	+	0.494707i
$37$	−6.47766	−	1.73568i	−1.06492	−	0.285345i	−0.316516	−	0.948587i	$-0.602513\pi$
$37$	−6.47766	−	1.73568i	−1.06492	−	0.285345i	−0.748405	+	0.663242i	$0.769180\pi$
$38$	−3.96141	+	3.96141i	−0.642626	+	0.642626i
$39$	−3.82258	−	4.42417i	−0.612102	−	0.708434i
$40$	2.14505	−	0.631463i	0.339163	−	0.0998430i
$41$	−0.832022	−	0.480368i	−0.129940	−	0.0750209i	0.433621	−	0.901095i	$-0.357236\pi$
$41$	−0.832022	−	0.480368i	−0.129940	−	0.0750209i	−0.563561	+	0.826074i	$0.690569\pi$
$42$	3.92714	+	2.36168i	0.605971	+	0.364416i
$43$	−0.841255	+	3.13961i	−0.128290	+	0.478785i	−0.999936	−	0.0113516i	$-0.996387\pi$
$43$	−0.841255	+	3.13961i	−0.128290	+	0.478785i	0.871645	+	0.490137i	$0.163053\pi$
$44$	−2.26793	−	3.92817i	−0.341903	−	0.592194i
$45$	6.17224	−	2.62745i	0.920103	−	0.391677i
$46$	−2.70954	+	4.69306i	−0.399500	+	0.691954i
$47$	−1.09611	+	0.293702i	−0.159884	+	0.0428408i	−0.337873	−	0.941192i	$-0.609708\pi$
$47$	−1.09611	+	0.293702i	−0.159884	+	0.0428408i	0.177989	+	0.984032i	$0.443041\pi$
$48$	1.72746	+	0.126017i	0.249337	+	0.0181889i
$49$	5.64141	−	4.14422i	0.805915	−	0.592031i
$50$	−3.70442	−	3.35816i	−0.523885	−	0.474916i
$51$	7.86729	+	9.10543i	1.10164	+	1.27502i
$52$	−2.38696	+	2.38696i	−0.331011	+	0.331011i
$53$	−0.424048	−	1.58257i	−0.0582474	−	0.217382i	0.930667	−	0.365866i	$-0.119227\pi$
$53$	−0.424048	−	1.58257i	−0.0582474	−	0.217382i	−0.988915	+	0.148484i	$0.952561\pi$
$54$	5.19127	−	0.225127i	0.706443	−	0.0306359i
$55$	−4.85460	+	8.90523i	−0.654594	+	1.20078i
$56$	1.19494	−	2.36053i	0.159681	−	0.315439i
$57$	8.02816	+	5.45026i	1.06336	+	0.721904i
$58$	6.46648	+	6.46648i	0.849090	+	0.849090i
$59$	−4.00955	−	6.94474i	−0.521999	−	0.904129i	−0.999672	−	0.0255913i	$-0.991853\pi$
$59$	−4.00955	−	6.94474i	−0.521999	−	0.904129i	0.477674	−	0.878537i	$-0.341480\pi$
$60$	−1.77220	−	3.44373i	−0.228791	−	0.444584i
$61$	2.09403	−	3.62696i	0.268113	−	0.464385i	−0.700262	−	0.713886i	$-0.746933\pi$
$61$	2.09403	−	3.62696i	0.268113	−	0.464385i	0.968374	+	0.249501i	$0.0802667\pi$
$62$	1.24487	+	1.24487i	0.158098	+	0.158098i
$63$	2.73993	−	7.44935i	0.345199	−	0.938530i
$64$		−	1.00000i		−	0.125000i
$65$	7.33668	+	1.77447i	0.910003	+	0.220095i
$66$	−5.94473	+	5.13637i	−0.731745	+	0.632244i
$67$	−9.25042	−	2.47864i	−1.13012	−	0.302814i	−0.355147	−	0.934810i	$-0.615569\pi$
$67$	−9.25042	−	2.47864i	−1.13012	−	0.302814i	−0.774972	+	0.631996i	$0.782236\pi$
$68$	4.91262	−	4.91262i	0.595743	−	0.595743i
$69$	8.86552	+	3.08249i	1.06728	+	0.371089i
$70$	−5.89740	+	0.469734i	−0.704874	+	0.0561440i
$71$			12.8302i			1.52266i	0.648363	+	0.761331i	$0.275454\pi$
$71$			12.8302i			1.52266i	−0.648363	+	0.761331i	$0.724546\pi$
$72$	−0.347695	−	2.97978i	−0.0409762	−	0.351171i
$73$	8.08951	−	2.16758i	0.946805	−	0.253696i	0.247799	−	0.968811i	$-0.420293\pi$
$73$	8.08951	−	2.16758i	0.946805	−	0.253696i	0.699006	+	0.715116i	$0.253626\pi$
$74$	6.70617			0.779576
$75$	−4.50762	+	7.39469i	−0.520495	+	0.853865i
$76$	2.80114	−	4.85172i	0.321313	−	0.556530i
$77$	3.73843	+	11.4036i	0.426034	+	1.29956i
$78$	4.83738	+	3.28406i	0.547726	+	0.371847i
$79$	−5.30665	−	3.06379i	−0.597045	−	0.344704i	0.170833	−	0.985300i	$-0.445354\pi$
$79$	−5.30665	−	3.06379i	−0.597045	−	0.344704i	−0.767878	+	0.640596i	$0.778687\pi$
$80$	−1.90853	+	1.16513i	−0.213380	+	0.130265i
$81$	−2.07211	−	8.75822i	−0.230234	−	0.973135i
$82$	0.928000	+	0.248657i	0.102480	+	0.0274595i
$83$	−5.33571	−	1.42970i	−0.585671	−	0.156930i	−0.0461968	−	0.998932i	$-0.514710\pi$
$83$	−5.33571	−	1.42970i	−0.585671	−	0.156930i	−0.539474	+	0.842002i	$0.681377\pi$
$84$	−4.40458	−	1.26479i	−0.480579	−	0.138000i
$85$	−15.0997	−	3.65205i	−1.63779	−	0.396120i
$86$		−	3.25036i		−	0.350495i
$87$	8.89682	−	13.1049i	0.953840	−	1.40499i
$88$	3.20734	+	3.20734i	0.341903	+	0.341903i
$89$	−7.21440	−	12.4957i	−0.764725	−	1.32454i	−0.940392	−	0.340093i	$-0.889541\pi$
$89$	−7.21440	−	12.4957i	−0.764725	−	1.32454i	0.175667	−	0.984450i	$-0.443792\pi$
$90$	−5.28189	+	4.13541i	−0.556760	+	0.435911i
$91$	7.47750	−	4.88394i	0.783855	−	0.511976i
$92$	1.40256	−	5.23443i	0.146227	−	0.545727i
$93$	1.71273	−	2.52284i	0.177602	−	0.261606i
$94$	0.982746	−	0.567388i	0.101362	−	0.0585217i
$95$	−12.5233	+	0.306812i	−1.28487	+	0.0314783i
$96$	−1.70121	+	0.325377i	−0.173629	+	0.0332087i
$97$	12.0791	+	3.23659i	1.22645	+	0.328626i	0.813196	−	0.581990i	$-0.197726\pi$
$97$	12.0791	+	3.23659i	1.22645	+	0.328626i	0.413254	+	0.910616i	$0.364392\pi$
$98$	−4.37658	+	5.46311i	−0.442101	+	0.551857i
$99$	10.6723	+	8.44200i	1.07261	+	0.848453i
$100$	4.44735	+	2.28496i	0.444735	+	0.228496i
$101$		−	6.72370i		−	0.669033i	−0.942390	−	0.334516i	$-0.891427\pi$
$101$		−	6.72370i		−	0.669033i	0.942390	−	0.334516i	$-0.108573\pi$
$102$	−9.95588	−	6.75897i	−0.985779	−	0.669238i
$103$	2.71452	+	2.71452i	0.267470	+	0.267470i	0.828080	−	0.560610i	$-0.189433\pi$
$103$	2.71452	+	2.71452i	0.267470	+	0.267470i	−0.560610	+	0.828080i	$0.689433\pi$
$104$	1.68783	−	2.92341i	0.165506	−	0.286664i
$105$	2.71800	+	9.87990i	0.265249	+	0.964180i
$106$	0.819197	+	1.41889i	0.0795675	+	0.137815i
$107$	−0.608330	+	2.27032i	−0.0588095	+	0.219480i	−0.989076	−	0.147403i	$-0.952908\pi$
$107$	−0.608330	+	2.27032i	−0.0588095	+	0.219480i	0.930267	+	0.366883i	$0.119575\pi$
$108$	−4.95612	+	1.56106i	−0.476903	+	0.150213i
$109$	1.56177	+	0.901686i	0.149590	+	0.0863659i	0.572927	−	0.819607i	$-0.305808\pi$
$109$	1.56177	+	0.901686i	0.149590	+	0.0863659i	−0.423337	+	0.905972i	$0.639141\pi$
$110$	2.38434	−	9.85825i	0.227338	−	0.939947i
$111$	−2.18203	−	11.4086i	−0.207109	−	1.08286i
$112$	−0.543277	+	2.58937i	−0.0513348	+	0.244673i
$113$	−0.573987	−	2.14215i	−0.0539961	−	0.201516i	0.933658	−	0.358165i	$-0.116598\pi$
$113$	−0.573987	−	2.14215i	−0.0539961	−	0.201516i	−0.987654	+	0.156649i	$0.949931\pi$
$114$	−9.16524	−	3.18670i	−0.858404	−	0.298462i
$115$	−11.6242	+	3.42195i	−1.08396	+	0.319098i
$116$	−7.91979	−	4.57249i	−0.735334	−	0.424545i
$117$	4.01292	−	9.29799i	0.370995	−	0.859599i
$118$	5.67036	+	5.67036i	0.521999	+	0.521999i
$119$	−15.3895	+	10.0517i	−1.41076	+	0.921438i
$120$	2.60312	+	2.86771i	0.237631	+	0.261785i
$121$	−9.57403			−0.870366
$122$	−1.08395	+	4.04535i	−0.0981361	+	0.366249i
$123$	0.121069	−	1.65963i	0.0109164	−	0.149644i
$124$	−1.52464	−	0.880254i	−0.136917	−	0.0790491i
$125$	−0.820826	−	11.1502i	−0.0734169	−	0.997301i
$126$	−0.718536	+	7.90466i	−0.0640123	+	0.704203i
$127$	−3.36408	+	3.36408i	−0.298514	+	0.298514i	−0.840431	−	0.541918i	$-0.817698\pi$
$127$	−3.36408	+	3.36408i	−0.298514	+	0.298514i	0.541918	+	0.840431i	$0.317698\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−5.52956	+	1.05759i	−0.486850	+	0.0931158i
$130$	−7.54595	+	0.184870i	−0.661824	+	0.0162142i
$131$			22.7170i			1.98479i	0.123080	+	0.992397i	$0.460723\pi$
$131$			22.7170i			1.98479i	−0.123080	+	0.992397i	$0.539277\pi$
$132$	4.41277	−	6.49996i	0.384083	−	0.565749i
$133$	−9.88903	+	11.0411i	−0.857487	+	0.957386i
$134$	9.57674			0.827304
$135$	8.75383	+	7.64006i	0.753409	+	0.657552i
$136$	−3.47375	+	6.01671i	−0.297872	+	0.515929i
$137$	−12.6627	−	12.6627i	−1.08185	−	1.08185i	−0.996337	−	0.0855088i	$-0.972748\pi$
$137$	−12.6627	−	12.6627i	−1.08185	−	1.08185i	−0.0855088	−	0.996337i	$-0.527252\pi$
$138$	−9.36125	−	0.682894i	−0.796882	−	0.0581318i
$139$	−10.4869	−	6.05460i	−0.889484	−	0.513544i	−0.0157106	−	0.999877i	$-0.505001\pi$
$139$	−10.4869	−	6.05460i	−0.889484	−	0.513544i	−0.873774	+	0.486333i	$0.838334\pi$
$140$	5.57488	−	1.98009i	0.471163	−	0.167348i
$141$	−1.28501	−	1.48725i	−0.108218	−	0.125249i
$142$	−3.32069	−	12.3930i	−0.278667	−	1.04000i
$143$	3.96292	+	14.7898i	0.331396	+	1.23679i
$144$	1.10707	+	2.78826i	0.0922560	+	0.232355i
$145$	0.500830	+	20.4427i	0.0415917	+	1.69767i
$146$	−7.25285	+	4.18744i	−0.600250	+	0.346555i
$147$	10.7180	+	5.66793i	0.884002	+	0.467483i
$148$	−6.47766	+	1.73568i	−0.532461	+	0.142672i
$149$	4.46352			0.365666			0.182833	−	0.983144i	$-0.441473\pi$
$149$	4.46352			0.365666			0.182833	+	0.983144i	$0.441473\pi$
$150$	2.44014	−	8.30938i	0.199236	−	0.678458i
$151$	1.78372			0.145157			0.0725784	−	0.997363i	$-0.476877\pi$
$151$	1.78372			0.145157			0.0725784	+	0.997363i	$0.476877\pi$
$152$	−1.44998	+	5.41139i	−0.117609	+	0.438922i
$153$	−8.25904	+	19.1363i	−0.667704	+	1.54708i
$154$	−6.56252	−	10.0475i	−0.528823	−	0.809648i
$155$	0.0964152	+	3.93543i	0.00774425	+	0.316102i
$156$	−5.52253	−	1.92015i	−0.442156	−	0.153735i
$157$	17.2609	+	4.62503i	1.37757	+	0.369118i	0.870237	−	0.492634i	$-0.163966\pi$
$157$	17.2609	+	4.62503i	1.37757	+	0.369118i	0.507330	+	0.861752i	$0.330633\pi$
$158$	5.91880	+	1.58594i	0.470874	+	0.126170i
$159$	2.14729	−	1.85531i	0.170291	−	0.147135i
$160$	1.54194	−	1.61939i	0.121901	−	0.128024i
$161$	−6.47550	+	12.7919i	−0.510341	+	1.00814i
$162$	4.26830	+	7.92349i	0.335349	+	0.622528i
$163$	−2.90984	+	10.8597i	−0.227917	+	0.850596i	0.753298	+	0.657679i	$0.228462\pi$
$163$	−2.90984	+	10.8597i	−0.227917	+	0.850596i	−0.981215	+	0.192917i	$0.938205\pi$
$164$	−0.960736			−0.0750209
$165$	−17.5468	−	0.848622i	−1.36602	−	0.0660651i
$166$	5.52394			0.428741
$167$	−1.67203	+	0.448018i	−0.129385	+	0.0346687i	−0.322931	−	0.946423i	$-0.604668\pi$
$167$	−1.67203	+	0.448018i	−0.129385	+	0.0346687i	0.193545	+	0.981091i	$0.438001\pi$
$168$	4.58185	+	0.0817081i	0.353497	+	0.00630392i
$169$	−1.38987	+	0.802440i	−0.106913	+	0.0617262i
$170$	15.5304	−	0.380483i	1.19113	−	0.0291818i
$171$	−2.43911	+	16.6289i	−0.186523	+	1.27165i
$172$	0.841255	+	3.13961i	0.0641451	+	0.239393i
$173$	4.07091	+	15.1928i	0.309505	+	1.15509i	0.928997	+	0.370086i	$0.120672\pi$
$173$	4.07091	+	15.1928i	0.309505	+	1.15509i	−0.619492	+	0.785003i	$0.712661\pi$
$174$	−5.20187	+	14.9610i	−0.394353	+	1.13419i
$175$	−10.2745	−	8.33275i	−0.776679	−	0.629897i
$176$	−3.92817	−	2.26793i	−0.296097	−	0.170952i
$177$	7.80149	−	11.4915i	0.586396	−	0.863754i
$178$	10.2027	+	10.2027i	0.764725	+	0.764725i
$179$	9.94665	−	17.2281i	0.743448	−	1.28769i	−0.207469	−	0.978242i	$-0.566523\pi$
$179$	9.94665	−	17.2281i	0.743448	−	1.28769i	0.950916	−	0.309448i	$-0.100144\pi$
$180$	4.03159	−	5.36155i	0.300497	−	0.399627i
$181$	−0.333503			−0.0247891			−0.0123946	−	0.999923i	$-0.503945\pi$
$181$	−0.333503			−0.0247891			−0.0123946	+	0.999923i	$0.503945\pi$
$182$	−5.95865	+	6.65284i	−0.441685	+	0.493142i
$183$	7.23470	+	0.527764i	0.534804	+	0.0390135i
$184$			5.41908i			0.399500i
$185$	10.8599	+	10.3405i	0.798436	+	0.760249i
$186$	−1.00142	+	2.88016i	−0.0734274	+	0.211184i
$187$	−8.15613	−	30.4391i	−0.596436	−	2.22593i
$188$	−0.802409	+	0.802409i	−0.0585217	+	0.0585217i
$189$	13.6813	−	1.34961i	0.995170	−	0.0981698i
$190$	12.0172	−	3.53763i	0.871819	−	0.256647i
$191$	3.06504	+	1.76960i	0.221778	+	0.128044i	0.606773	−	0.794875i	$-0.292464\pi$
$191$	3.06504	+	1.76960i	0.221778	+	0.128044i	−0.384995	+	0.922919i	$0.625797\pi$
$192$	1.55903	−	0.754597i	0.112514	−	0.0544583i
$193$	3.98440	−	14.8700i	0.286803	−	1.07037i	−0.660708	−	0.750643i	$-0.729744\pi$
$193$	3.98440	−	14.8700i	0.286803	−	1.07037i	0.947511	−	0.319722i	$-0.103590\pi$
$194$	−12.5052			−0.897824
$195$	2.76978	+	12.7771i	0.198348	+	0.914989i
$196$	2.81349	−	6.40970i	0.200964	−	0.457836i
$197$	−12.2538	−	12.2538i	−0.873044	−	0.873044i	0.119759	−	0.992803i	$-0.461788\pi$
$197$	−12.2538	−	12.2538i	−0.873044	−	0.873044i	−0.992803	+	0.119759i	$0.961788\pi$
$198$	−12.4936	−	5.39214i	−0.887885	−	0.383202i
$199$	7.91723	+	4.57102i	0.561238	+	0.324031i	0.753642	−	0.657285i	$-0.228295\pi$
$199$	7.91723	+	4.57102i	0.561238	+	0.324031i	−0.192404	+	0.981316i	$0.561629\pi$
$200$	−4.88721	−	1.05604i	−0.345578	−	0.0746733i
$201$	−3.11605	−	16.2921i	−0.219789	−	1.14916i
$202$	1.74022	+	6.49459i	0.122442	+	0.456958i
$203$	18.0232	+	16.1425i	1.26498	+	1.13298i
$204$	11.3660	+	3.95189i	0.795779	+	0.276688i
$205$	1.11938	+	1.83359i	0.0781808	+	0.128064i
$206$	−3.32459	−	1.91945i	−0.231635	−	0.133735i
$207$	1.88419	+	16.1477i	0.130960	+	1.12234i
$208$	−0.873687	+	3.26064i	−0.0605793	+	0.226085i
$209$	−12.7056	−	22.0067i	−0.878864	−	1.52224i
$210$	−5.18249	−	8.83978i	−0.357626	−	0.610003i
$211$	−8.68116	+	15.0362i	−0.597636	+	1.03514i	0.395533	+	0.918452i	$0.370560\pi$
$211$	−8.68116	+	15.0362i	−0.597636	+	1.03514i	−0.993169	+	0.116684i	$0.962774\pi$
$212$	−1.15852	−	1.15852i	−0.0795675	−	0.0795675i
$213$	−20.0027	+	9.68161i	−1.37056	+	0.663373i
$214$		−	2.35041i		−	0.160670i
$215$	5.01186	−	5.26360i	0.341806	−	0.358974i
$216$	4.38321	−	2.79060i	0.298240	−	0.189876i
$217$	3.46965	+	3.10761i	0.235535	+	0.210958i
$218$	−1.74192	−	0.466747i	−0.117978	−	0.0316121i
$219$	9.48364	+	10.9762i	0.640845	+	0.741700i
$220$	0.248409	+	10.1394i	0.0167477	+	0.683602i
$221$	−20.3104	+	11.7262i	−1.36623	+	0.788791i
$222$	5.06045	+	10.4551i	0.339635	+	0.701703i
$223$	7.05189	−	26.3180i	0.472229	−	1.76238i	−0.159503	−	0.987197i	$-0.550989\pi$
$223$	7.05189	−	26.3180i	0.472229	−	1.76238i	0.631732	−	0.775187i	$-0.282344\pi$
$224$	−0.145414	−	2.64175i	−0.00971586	−	0.176509i
$225$	−14.9300	−	1.44751i	−0.995333	−	0.0965010i
$226$	1.10886	+	1.92060i	0.0737601	+	0.127756i
$227$	6.45729	+	6.45729i	0.428586	+	0.428586i	0.888146	−	0.459561i	$-0.151993\pi$
$227$	6.45729	+	6.45729i	0.428586	+	0.428586i	−0.459561	+	0.888146i	$0.651993\pi$
$228$	9.67772	+	0.705981i	0.640923	+	0.0467547i
$229$			5.80548i			0.383637i	0.981430	+	0.191819i	$0.0614385\pi$
$229$			5.80548i			0.383637i	−0.981430	+	0.191819i	$0.938561\pi$
$230$	10.3425	−	6.31392i	0.681962	−	0.416327i
$231$	−14.9576	+	14.4335i	−0.984138	+	0.949652i
$232$	8.83338	+	2.36690i	0.579940	+	0.155394i
$233$	−15.0473	−	4.03190i	−0.985779	−	0.264139i	−0.270302	−	0.962775i	$-0.587124\pi$
$233$	−15.0473	−	4.03190i	−0.985779	−	0.264139i	−0.715476	+	0.698637i	$0.753790\pi$
$234$	−1.46969	+	10.0198i	−0.0960765	+	0.655014i
$235$	2.46633	+	0.596511i	0.160885	+	0.0389121i
$236$	−6.94474	−	4.00955i	−0.452064	−	0.260999i
$237$	0.772178	−	10.5852i	0.0501583	−	0.687581i
$238$	12.2636	−	13.6923i	0.794929	−	0.887540i
$239$	−9.13458	+	15.8216i	−0.590867	+	1.02341i	0.403249	+	0.915090i	$0.367881\pi$
$239$	−9.13458	+	15.8216i	−0.590867	+	1.02341i	−0.994116	+	0.108321i	$0.965453\pi$
$240$	−3.25664	−	2.09626i	−0.210215	−	0.135313i
$241$	2.16629			0.139543			0.0697716	−	0.997563i	$-0.477773\pi$
$241$	2.16629			0.139543			0.0697716	+	0.997563i	$0.477773\pi$
$242$	9.24780	−	2.47794i	0.594471	−	0.159288i
$243$	12.0907	−	9.83941i	0.775621	−	0.631198i
$244$		−	4.18805i		−	0.268113i
$245$	−15.5112	+	2.09848i	−0.990972	+	0.134067i
$246$	0.312601	+	1.63442i	0.0199307	+	0.104207i
$247$	−13.3724	+	13.3724i	−0.850866	+	0.850866i
$248$	1.70052	+	0.455653i	0.107983	+	0.0289340i
$249$	−1.79736	−	9.39740i	−0.113903	−	0.595536i
$250$	3.67873	+	10.5578i	0.232663	+	0.667733i
$251$		−	5.86487i		−	0.370187i	−0.982721	−	0.185094i	$-0.940741\pi$
$251$		−	5.86487i		−	0.370187i	0.982721	−	0.185094i	$-0.0592588\pi$
$252$	−1.35182	−	7.82129i	−0.0851570	−	0.492695i
$253$	−17.3808	−	17.3808i	−1.09272	−	1.09272i
$254$	2.37876	−	4.12014i	0.149257	−	0.258520i
$255$	−5.70053	−	26.2968i	−0.356981	−	1.64677i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.63366	−	5.63366i	−0.351418	−	0.351418i	0.509219	−	0.860637i	$-0.329934\pi$
$257$	−5.63366	−	5.63366i	−0.351418	−	0.351418i	−0.860637	+	0.509219i	$0.829934\pi$
$258$	5.06742	−	2.45271i	0.315484	−	0.152699i
$259$	17.7160	−	0.975169i	1.10082	−	0.0605940i
$260$	7.24098	−	2.13161i	0.449067	−	0.132197i
$261$	27.1445	+	3.98152i	1.68020	+	0.246450i
$262$	−5.87959	−	21.9429i	−0.363242	−	1.35564i
$263$	0.409731	−	0.409731i	0.0252651	−	0.0252651i	−0.694361	−	0.719626i	$-0.744313\pi$
$263$	0.409731	−	0.409731i	0.0252651	−	0.0252651i	0.719626	+	0.694361i	$0.244313\pi$
$264$	−2.58010	+	7.42059i	−0.158794	+	0.456706i
$265$	−0.861245	+	3.56089i	−0.0529059	+	0.218744i
$266$	6.69442	−	13.2244i	0.410461	−	0.810838i
$267$	14.0373	−	20.6767i	0.859067	−	1.26539i
$268$	−9.25042	+	2.47864i	−0.565059	+	0.151407i
$269$	9.47581	−	16.4126i	0.577750	−	1.00069i	−0.417986	−	0.908453i	$-0.637264\pi$
$269$	9.47581	−	16.4126i	0.577750	−	1.00069i	0.995737	−	0.0922398i	$-0.0294026\pi$
$270$	−10.4329	−	5.11407i	−0.634929	−	0.311233i
$271$	−8.58035	−	14.8616i	−0.521219	−	0.902778i	−0.999695	−	0.0246775i	$-0.992144\pi$
$271$	−8.58035	−	14.8616i	−0.521219	−	0.902778i	0.478476	−	0.878100i	$-0.341189\pi$
$272$	1.79814	−	6.71077i	0.109029	−	0.406900i
$273$	13.2567	+	7.97226i	0.802333	+	0.482503i
$274$	15.5086	+	8.95387i	0.936906	+	0.540923i
$275$	19.0620	−	12.2878i	1.14948	−	0.740985i
$276$	9.21902	−	1.76324i	0.554920	−	0.106135i
$277$	−5.01888	+	5.01888i	−0.301555	+	0.301555i	−0.841622	−	0.540067i	$-0.818399\pi$
$277$	−5.01888	+	5.01888i	−0.301555	+	0.301555i	0.540067	+	0.841622i	$0.318399\pi$
$278$	11.6966	+	3.13409i	0.701514	+	0.187970i
$279$	5.22561	+	0.766485i	0.312849	+	0.0458883i
$280$	−4.87243	+	3.35550i	−0.291184	+	0.200530i
$281$	4.86305	−	2.80768i	0.290105	−	0.167492i	−0.347884	−	0.937538i	$-0.613100\pi$
$281$	4.86305	−	2.80768i	0.290105	−	0.167492i	0.637989	+	0.770045i	$0.279766\pi$
$282$	1.62615	+	1.10398i	0.0968361	+	0.0657413i
$283$	0.620253	−	2.31482i	0.0368702	−	0.137602i	−0.945037	−	0.326962i	$-0.893975\pi$
$283$	0.620253	−	2.31482i	0.0368702	−	0.137602i	0.981908	+	0.189361i	$0.0606416\pi$
$284$	6.41509	+	11.1113i	0.380666	+	0.659332i
$285$	−9.92839	−	19.2928i	−0.588107	−	1.14280i
$286$	−7.65577	−	13.2602i	−0.452695	−	0.784091i
$287$	2.48770	+	0.521946i	0.146844	+	0.0308095i
$288$	−1.79100	−	2.40672i	−0.105536	−	0.141817i
$289$	27.0787	−	15.6339i	1.59286	−	0.919639i
$290$	−5.77472	−	19.6165i	−0.339103	−	1.15192i
$291$	4.06892	+	21.2741i	0.238524	+	1.24711i
$292$	5.92193	−	5.92193i	0.346555	−	0.346555i
$293$	0.0724535	+	0.270400i	0.00423278	+	0.0157970i	0.968010	−	0.250912i	$-0.0807305\pi$
$293$	0.0724535	+	0.270400i	0.00423278	+	0.0157970i	−0.963777	+	0.266709i	$0.914064\pi$
$294$	−11.8197	−	2.70078i	−0.689340	−	0.157513i
$295$	0.439170	+	17.9259i	0.0255695	+	1.04368i
$296$	5.80771	−	3.35308i	0.337566	−	0.194894i
$297$	−5.10803	+	23.0088i	−0.296398	+	1.33511i
$298$	−4.31143	+	1.15524i	−0.249755	+	0.0669215i
$299$	−9.14650	+	15.8422i	−0.528956	+	0.916178i
$300$	−0.206366	+	8.65779i	−0.0119145	+	0.499858i
$301$	−0.472647	−	8.58664i	−0.0272429	−	0.494926i
$302$	−1.72294	+	0.461660i	−0.0991439	+	0.0265655i
$303$	10.4825	−	5.07368i	0.602202	−	0.291475i
$304$		−	5.60228i		−	0.321313i
$305$	−7.99302	+	4.87961i	−0.457679	+	0.279406i
$306$	3.02478	−	20.6218i	0.172915	−	1.17887i
$307$	6.08955	−	6.08955i	0.347549	−	0.347549i	−0.511647	−	0.859196i	$-0.670964\pi$
$307$	6.08955	−	6.08955i	0.347549	−	0.347549i	0.859196	+	0.511647i	$0.170964\pi$
$308$	8.93938	+	8.00660i	0.509369	+	0.456218i
$309$	−2.18366	+	6.28039i	−0.124224	+	0.357279i
$310$	−1.11170	−	3.77638i	−0.0631401	−	0.214484i
$311$	11.4507	−	6.61106i	0.649309	−	0.374879i	−0.138883	−	0.990309i	$-0.544351\pi$
$311$	11.4507	−	6.61106i	0.649309	−	0.374879i	0.788191	+	0.615430i	$0.211018\pi$
$312$	5.83133	+	0.425390i	0.330134	+	0.0240830i
$313$	17.6329	−	4.72472i	0.996670	−	0.267057i	0.276620	−	0.960979i	$-0.410786\pi$
$313$	17.6329	−	4.72472i	0.996670	−	0.267057i	0.720050	+	0.693922i	$0.244119\pi$
$314$	−17.8698			−1.00845
$315$	−13.3521	+	11.6928i	−0.752306	+	0.658814i
$316$	−6.12759			−0.344704
$317$	−11.2084	+	3.00327i	−0.629524	+	0.168680i	−0.559454	−	0.828862i	$-0.688989\pi$
$317$	−11.2084	+	3.00327i	−0.629524	+	0.168680i	−0.0700701	+	0.997542i	$0.522322\pi$
$318$	−1.59394	+	2.34785i	−0.0893834	+	0.131661i
$319$	−35.9231	+	20.7402i	−2.01130	+	1.16123i
$320$	−1.07027	+	1.96329i	−0.0598299	+	0.109751i
$321$	−3.99855	+	0.764768i	−0.223177	+	0.0426852i
$322$	2.94406	−	14.0320i	0.164066	−	0.781974i
$323$	27.5219	−	27.5219i	1.53136	−	1.53136i
$324$	−6.17361	−	6.54878i	−0.342978	−	0.363821i
$325$	−12.5049	−	11.3360i	−0.693647	−	0.628810i
$326$		−	11.2428i		−	0.622680i
$327$	−0.227255	+	3.11526i	−0.0125672	+	0.172274i
$328$	0.928000	−	0.248657i	0.0512402	−	0.0137298i
$329$	2.51366	−	1.64180i	0.138583	−	0.0905156i
$330$	17.1685	−	3.72174i	0.945097	−	0.204875i
$331$	8.19634	−	14.1965i	0.450511	−	0.780309i	−0.547906	−	0.836540i	$-0.684575\pi$
$331$	8.19634	−	14.1965i	0.450511	−	0.780309i	0.998418	+	0.0562309i	$0.0179083\pi$
$332$	−5.33571	+	1.42970i	−0.292835	+	0.0784650i
$333$	16.1399	−	12.0108i	0.884460	−	0.658186i
$334$	1.49910	−	0.865505i	0.0820270	−	0.0473583i
$335$	15.5085	+	14.7668i	0.847318	+	0.806794i
$336$	−4.44687	+	1.10695i	−0.242597	+	0.0603888i
$337$	4.73687	+	17.6782i	0.258034	+	0.962995i	0.966377	+	0.257128i	$0.0827760\pi$
$337$	4.73687	+	17.6782i	0.258034	+	0.962995i	−0.708344	+	0.705868i	$0.750557\pi$
$338$	1.13482	−	1.13482i	0.0617262	−	0.0617262i
$339$	2.90655	−	2.51132i	0.157862	−	0.136396i
$340$	−14.9028	+	4.38709i	−0.808215	+	0.237923i
$341$	−6.91558	+	3.99271i	−0.374499	+	0.216217i
$342$	−1.94789	−	16.6936i	−0.105330	−	0.902686i
$343$	−10.7674	+	15.0686i	−0.581386	+	0.813628i
$344$	−1.62518	−	2.81489i	−0.0876238	−	0.151769i
$345$	−14.1065	−	15.5403i	−0.759470	−	0.836664i
$346$	−7.86439	−	13.6215i	−0.422792	−	0.732297i
$347$	−7.46690	+	27.8669i	−0.400844	+	1.49597i	0.410749	+	0.911748i	$0.365267\pi$
$347$	−7.46690	+	27.8669i	−0.400844	+	1.49597i	−0.811593	+	0.584223i	$0.801399\pi$
$348$	1.15242	−	15.7976i	0.0617762	−	0.846840i
$349$	21.0629	−	12.1607i	1.12747	−	0.650945i	0.184172	−	0.982894i	$-0.441040\pi$
$349$	21.0629	−	12.1607i	1.12747	−	0.650945i	0.943297	+	0.331949i	$0.107706\pi$
$350$	12.0811	+	5.38959i	0.645761	+	0.288086i
$351$	17.5240	−	0.759954i	0.935362	−	0.0405633i
$352$	4.38130	+	1.17397i	0.233524	+	0.0625727i
$353$	4.46580	−	4.46580i	0.237691	−	0.237691i	−0.578203	−	0.815893i	$-0.696246\pi$
$353$	4.46580	−	4.46580i	0.237691	−	0.237691i	0.815893	+	0.578203i	$0.196246\pi$
$354$	−4.56144	+	13.1191i	−0.242438	+	0.697273i
$355$	13.7318	−	25.1894i	0.728806	−	1.33692i
$356$	−12.4957	−	7.21440i	−0.662271	−	0.382363i
$357$	−27.2838	−	16.4078i	−1.44401	−	0.868393i
$358$	−5.14877	+	19.2155i	−0.272121	+	1.01557i
$359$	5.82034	+	10.0811i	0.307186	+	0.532062i	0.977746	−	0.209794i	$-0.0672793\pi$
$359$	5.82034	+	10.0811i	0.307186	+	0.532062i	−0.670560	+	0.741856i	$0.733946\pi$
$360$	−2.50655	+	6.22232i	−0.132107	+	0.327945i
$361$	6.19279	−	10.7262i	0.325936	−	0.564538i
$362$	0.322140	−	0.0863170i	0.0169313	−	0.00453672i
$363$	−7.22453	−	14.9262i	−0.379189	−	0.783424i
$364$	4.03373	−	7.96837i	0.211425	−	0.417656i
$365$	−18.2020	−	4.40237i	−0.952734	−	0.230430i
$366$	−7.12478	+	1.36270i	−0.372418	+	0.0712293i
$367$	−5.06100	+	5.06100i	−0.264182	+	0.264182i	−0.826751	−	0.562569i	$-0.809813\pi$
$367$	−5.06100	+	5.06100i	−0.264182	+	0.264182i	0.562569	+	0.826751i	$0.309813\pi$
$368$	−1.40256	−	5.23443i	−0.0731135	−	0.272863i
$369$	2.67878	−	1.06360i	0.139452	−	0.0553690i
$370$	−13.1662	−	7.17741i	−0.684477	−	0.373136i
$371$	2.37044	+	3.62924i	0.123067	+	0.188421i
$372$	0.221853	−	3.04121i	0.0115026	−	0.157679i
$373$	−9.86036	−	9.86036i	−0.510550	−	0.510550i	0.404145	−	0.914695i	$-0.367569\pi$
$373$	−9.86036	−	9.86036i	−0.510550	−	0.510550i	−0.914695	+	0.404145i	$0.867569\pi$
$374$	15.7564	+	27.2910i	0.814746	+	1.41118i
$375$	16.7641	−	9.69357i	0.865694	−	0.500574i
$376$	0.567388	−	0.982746i	0.0292608	−	0.0506812i
$377$	21.8287	+	21.8287i	1.12423	+	1.12423i
$378$	−12.8658	+	4.84461i	−0.661747	+	0.249180i
$379$			8.26773i			0.424685i	0.977195	+	0.212342i	$0.0681092\pi$
$379$			8.26773i			0.424685i	−0.977195	+	0.212342i	$0.931891\pi$
$380$	−10.6921	+	6.52737i	−0.548494	+	0.334847i
$381$	−7.78323	−	2.70619i	−0.398747	−	0.138642i
$382$	−3.41861	−	0.916013i	−0.174911	−	0.0468673i
$383$	−19.5292	+	19.5292i	−0.997896	+	0.997896i	−0.999998	−	0.00210188i	$-0.999331\pi$
$383$	−19.5292	+	19.5292i	−0.997896	+	0.997896i	0.00210188	+	0.999998i	$0.499331\pi$
$384$	−1.31061	+	1.13239i	−0.0668816	+	0.0577871i
$385$	4.86531	−	26.3898i	0.247959	−	1.34495i
$386$			15.3945i			0.783562i
$387$	−5.82141	−	7.82271i	−0.295919	−	0.397650i
$388$	12.0791	−	3.23659i	0.613225	−	0.164313i
$389$	35.5388			1.80189			0.900944	−	0.433935i	$-0.142875\pi$
$389$	35.5388			1.80189			0.900944	+	0.433935i	$0.142875\pi$
$390$	−5.98237	−	11.6249i	−0.302929	−	0.588649i
$391$	18.8245	−	32.6050i	0.951997	−	1.64891i
$392$	−1.05867	+	6.91948i	−0.0534711	+	0.349487i
$393$	−35.4166	+	17.1422i	−1.78653	+	0.864708i
$394$	15.0077	+	8.66471i	0.756078	+	0.436522i
$395$	7.13942	+	11.6947i	0.359223	+	0.588423i
$396$	13.4635	+	1.97481i	0.676567	+	0.0992380i
$397$	−13.3703	−	3.58256i	−0.671036	−	0.179804i	−0.0928145	−	0.995683i	$-0.529586\pi$
$397$	−13.3703	−	3.58256i	−0.671036	−	0.179804i	−0.578221	+	0.815880i	$0.696253\pi$
$398$	−8.83053	−	2.36613i	−0.442634	−	0.118604i
$399$	−24.6757	−	7.08573i	−1.23533	−	0.354730i
$400$	4.99400	−	0.244845i	0.249700	−	0.0122423i
$401$			28.0533i			1.40091i	0.713695	+	0.700457i	$0.247020\pi$
$401$			28.0533i			1.40091i	−0.713695	+	0.700457i	$0.752980\pi$
$402$	7.22658	+	14.9305i	0.360429	+	0.744663i
$403$	4.20226	+	4.20226i	0.209329	+	0.209329i
$404$	−3.36185	−	5.82289i	−0.167258	−	0.289700i
$405$	−5.30550	+	19.4127i	−0.263632	+	0.964623i
$406$	−21.5870	−	10.9277i	−1.07135	−	0.542335i
$407$	−7.87282	+	29.3818i	−0.390241	+	1.45640i
$408$	−12.0015	−	0.875500i	−0.594164	−	0.0433437i
$409$	16.8543	−	9.73086i	0.833394	−	0.481160i	−0.0216194	−	0.999766i	$-0.506882\pi$
$409$	16.8543	−	9.73086i	0.833394	−	0.481160i	0.855013	+	0.518606i	$0.173549\pi$
$410$	−1.55581	−	1.48140i	−0.0768358	−	0.0731610i
$411$	10.1863	−	29.2968i	0.502454	−	1.44510i
$412$	3.70810	+	0.993583i	0.182685	+	0.0489503i
$413$	15.8042	+	14.1551i	0.777676	+	0.696529i
$414$	−5.99931	−	15.1098i	−0.294850	−	0.742606i
$415$	8.94541	+	8.51758i	0.439113	+	0.418111i
$416$		−	3.37567i		−	0.165506i
$417$	1.52596	−	20.9181i	0.0747265	−	1.02437i
$418$	17.9684	+	17.9684i	0.878864	+	0.878864i
$419$	−5.32527	+	9.22364i	−0.260156	+	0.450604i	−0.966283	−	0.257481i	$-0.917107\pi$
$419$	−5.32527	+	9.22364i	−0.260156	+	0.450604i	0.706127	+	0.708085i	$0.250441\pi$
$420$	7.29381	+	7.19725i	0.355901	+	0.351190i
$421$	−4.96458	−	8.59891i	−0.241959	−	0.419085i	0.719313	−	0.694686i	$-0.244457\pi$
$421$	−4.96458	−	8.59891i	−0.241959	−	0.419085i	−0.961272	+	0.275601i	$0.911123\pi$
$422$	4.49370	−	16.7707i	0.218750	−	0.816386i
$423$	1.34900	−	3.12565i	0.0655906	−	0.151974i
$424$	1.41889	+	0.819197i	0.0689075	+	0.0397837i
$425$	25.7365	+	23.3308i	1.24840	+	1.13171i
$426$	16.8153	−	14.5288i	0.814705	−	0.703922i
$427$	−2.27527	+	10.8444i	−0.110108	+	0.524799i
$428$	0.608330	+	2.27032i	0.0294047	+	0.109740i
$429$	−20.0674	+	17.3387i	−0.968864	+	0.837119i
$430$	−3.47876	+	6.38141i	−0.167761	+	0.307739i
$431$	20.6535	+	11.9243i	0.994846	+	0.574375i	0.906719	−	0.421734i	$-0.138579\pi$
$431$	20.6535	+	11.9243i	0.994846	+	0.574375i	0.0881270	+	0.996109i	$0.471912\pi$
$432$	−3.51160	+	3.82997i	−0.168952	+	0.184270i
$433$	−1.79372	−	1.79372i	−0.0862009	−	0.0862009i	0.662692	−	0.748892i	$-0.269414\pi$
$433$	−1.79372	−	1.79372i	−0.0862009	−	0.0862009i	−0.748892	+	0.662692i	$0.769414\pi$
$434$	−4.15573	−	2.10371i	−0.199482	−	0.100981i
$435$	−31.4929	+	16.2068i	−1.50997	+	0.777056i
$436$	1.80337			0.0863659
$437$	7.85754	−	29.3248i	0.375877	−	1.40279i
$438$	−12.0013	−	8.14761i	−0.573446	−	0.389308i
$439$	32.3637	+	18.6852i	1.54464	+	0.891796i	0.998537	+	0.0540764i	$0.0172215\pi$
$439$	32.3637	+	18.6852i	1.54464	+	0.891796i	0.546100	+	0.837720i	$0.316112\pi$
$440$	−2.86423	−	9.72966i	−0.136547	−	0.463843i
$441$	−0.748748	+	20.9866i	−0.0356547	+	0.999364i
$442$	16.5834	−	16.5834i	0.788791	−	0.788791i
$443$	−7.14394	−	26.6615i	−0.339419	−	1.26673i	−0.898999	−	0.437951i	$-0.855704\pi$
$443$	−7.14394	−	26.6615i	−0.339419	−	1.26673i	0.559580	−	0.828776i	$-0.310962\pi$
$444$	−7.59401	−	8.78915i	−0.360396	−	0.417114i
$445$	0.790201	+	32.2541i	0.0374591	+	1.52899i
$446$			27.2464i			1.29015i
$447$	3.36816	+	6.95878i	0.159309	+	0.329139i
$448$	0.824195	+	2.51410i	0.0389395	+	0.118780i
$449$	14.3732			0.678315			0.339157	−	0.940730i	$-0.389858\pi$
$449$	14.3732			0.678315			0.339157	+	0.940730i	$0.389858\pi$
$450$	14.7959	−	2.46597i	0.697486	−	0.116247i
$451$	−2.17888	+	3.77393i	−0.102600	+	0.177708i
$452$	−1.56816	−	1.56816i	−0.0737601	−	0.0737601i
$453$	1.34599	+	2.78087i	0.0632399	+	0.130657i
$454$	−7.90853	−	4.56599i	−0.371166	−	0.214293i
$455$	−19.9077	+	1.58567i	−0.933285	+	0.0743372i
$456$	−9.53068	+	1.82285i	−0.446315	+	0.0853630i
$457$	0.992067	+	3.70244i	0.0464069	+	0.173193i	0.985240	−	0.171180i	$-0.0547581\pi$
$457$	0.992067	+	3.70244i	0.0464069	+	0.173193i	−0.938833	+	0.344373i	$0.888091\pi$
$458$	−1.50257	−	5.60767i	−0.0702105	−	0.262029i
$459$	−36.0664	+	1.56407i	−1.68343	+	0.0730045i
$460$	−8.35589	+	8.77560i	−0.389596	+	0.409165i
$461$	22.0854	−	12.7510i	1.02862	−	0.593873i	0.112029	−	0.993705i	$-0.464265\pi$
$461$	22.0854	−	12.7510i	1.02862	−	0.593873i	0.916588	+	0.399832i	$0.130932\pi$
$462$	10.7123	−	17.8130i	0.498380	−	0.828734i
$463$	−10.3691	+	2.77838i	−0.481891	+	0.129122i	−0.491583	−	0.870831i	$-0.663582\pi$
$463$	−10.3691	+	2.77838i	−0.481891	+	0.129122i	0.00969205	+	0.999953i	$0.496915\pi$
$464$	−9.14498			−0.424545
$465$	−6.06272	+	3.11998i	−0.281152	+	0.144686i
$466$	15.5781			0.721640
$467$	−1.86404	+	6.95671i	−0.0862577	+	0.321918i	−0.995549	−	0.0942413i	$-0.969957\pi$
$467$	−1.86404	+	6.95671i	−0.0862577	+	0.321918i	0.909292	+	0.416159i	$0.136624\pi$
$468$	−1.17370	−	10.0588i	−0.0542544	−	0.464966i
$469$	25.2994	−	1.39259i	1.16822	−	0.0643038i
$470$	−2.53668	+	0.0621467i	−0.117008	+	0.00286661i
$471$	5.81441	+	30.4003i	0.267914	+	1.40077i
$472$	7.74586	+	2.07550i	0.356532	+	0.0955324i
$473$	14.2408	+	3.81581i	0.654793	+	0.175451i
$474$	1.99378	+	10.4243i	0.0915772	+	0.478806i
$475$	24.9153	+	12.8010i	1.14319	+	0.587349i
$476$	−8.30187	+	16.3998i	−0.380516	+	0.751683i
$477$	4.51282	+	1.94769i	0.206628	+	0.0891786i
$478$	4.72840	−	17.6466i	0.216272	−	0.807139i
$479$	4.14428			0.189357			0.0946784	−	0.995508i	$-0.469818\pi$
$479$	4.14428			0.189357			0.0946784	+	0.995508i	$0.469818\pi$
$480$	3.68822	+	1.18195i	0.168344	+	0.0539483i
$481$	22.6378			1.03219
$482$	−2.09248	+	0.560678i	−0.0953097	+	0.0255382i
$483$	−24.8294	−	0.442783i	−1.12978	−	0.0201473i
$484$	−8.29135	+	4.78701i	−0.376880	+	0.217592i
$485$	−20.2509	−	19.2823i	−0.919544	−	0.875565i
$486$	−9.13213	+	12.6335i	−0.414242	+	0.573065i
$487$	7.09430	+	26.4763i	0.321473	+	1.19976i	0.917810	+	0.397021i	$0.129956\pi$
$487$	7.09430	+	26.4763i	0.321473	+	1.19976i	−0.596336	+	0.802735i	$0.703377\pi$
$488$	1.08395	+	4.04535i	0.0490680	+	0.183124i
$489$	−19.1264	+	3.65814i	−0.864924	+	0.165427i
$490$	14.4395	−	6.04157i	0.652311	−	0.272930i
$491$	1.47373	+	0.850857i	0.0665084	+	0.0383986i	0.532885	−	0.846187i	$-0.321108\pi$
$491$	1.47373	+	0.850857i	0.0665084	+	0.0383986i	−0.466377	+	0.884586i	$0.654441\pi$
$492$	−0.724968	−	1.49782i	−0.0326841	−	0.0675269i
$493$	−44.9259	−	44.9259i	−2.02336	−	2.02336i
$494$	9.45572	−	16.3778i	0.425433	−	0.736871i
$495$	−11.9177	−	27.9964i	−0.535662	−	1.25835i
$496$	−1.76051			−0.0790491
$497$	−10.5746	−	32.2564i	−0.474334	−	1.44690i
$498$	4.16834	+	8.61200i	0.186788	+	0.385913i
$499$		−	25.7993i		−	1.15493i	−0.816414	−	0.577467i	$-0.804041\pi$
$499$		−	25.7993i		−	1.15493i	0.816414	−	0.577467i	$-0.195959\pi$
$500$	−6.28594	−	9.24592i	−0.281116	−	0.413490i
$501$	−1.96018	−	2.26867i	−0.0875744	−	0.101357i
$502$	1.51794	+	5.66503i	0.0677490	+	0.252843i
$503$	6.90078	−	6.90078i	0.307691	−	0.307691i	−0.536322	−	0.844013i	$-0.680187\pi$
$503$	6.90078	−	6.90078i	0.307691	−	0.307691i	0.844013	+	0.536322i	$0.180187\pi$
$504$	3.33006	+	7.20491i	0.148333	+	0.320932i
$505$	−7.19617	+	13.2006i	−0.320226	+	0.587419i
$506$	21.2871	+	12.2901i	0.946326	+	0.546361i
$507$	−2.29982	−	1.56133i	−0.102139	−	0.0693411i
$508$	−1.23134	+	4.59542i	−0.0546318	+	0.203889i
$509$	−6.64849			−0.294689			−0.147345	−	0.989085i	$-0.547073\pi$
$509$	−6.64849			−0.294689			−0.147345	+	0.989085i	$0.547073\pi$
$510$	12.3124	+	23.9253i	0.545202	+	1.05943i
$511$	−18.5513	+	12.1168i	−0.820662	+	0.536017i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−27.7656	+	8.74548i	−1.22588	+	0.386122i
$514$	6.89980	+	3.98360i	0.304337	+	0.175709i
$515$	−2.42413	−	8.23467i	−0.106820	−	0.362863i
$516$	−4.25994	+	3.68068i	−0.187533	+	0.162033i
$517$	1.33219	+	4.97180i	0.0585897	+	0.218660i
$518$	−16.8600	+	5.52719i	−0.740785	+	0.242851i
$519$	−20.6142	+	17.8111i	−0.904864	+	0.781822i
$520$	−6.44255	+	3.93308i	−0.282525	+	0.172477i
$521$	29.5138	+	17.0398i	1.29302	+	0.746527i	0.979189	−	0.202951i	$-0.0650531\pi$
$521$	29.5138	+	17.0398i	1.29302	+	0.746527i	0.313834	+	0.949478i	$0.398386\pi$
$522$	−27.2501	+	3.17966i	−1.19270	+	0.139170i
$523$	−3.66444	+	13.6759i	−0.160235	+	0.598004i	0.838365	+	0.545109i	$0.183512\pi$
$523$	−3.66444	+	13.6759i	−0.160235	+	0.598004i	−0.998600	+	0.0528955i	$0.983155\pi$
$524$	11.3585	+	19.6735i	0.496198	+	0.859441i
$525$	5.23794	−	22.3061i	0.228602	−	0.973520i
$526$	−0.289723	+	0.501816i	−0.0126325	+	0.0218802i
$527$	−8.64871	−	8.64871i	−0.376744	−	0.376744i
$528$	0.571593	−	7.83552i	0.0248754	−	0.340997i
$529$		−	6.36642i		−	0.276801i
$530$	−0.0897276	−	3.66246i	−0.00389752	−	0.159087i
$531$	23.8026	+	3.49133i	1.03295	+	0.151511i
$532$	−3.04359	+	14.5064i	−0.131956	+	0.628932i
$533$	3.13262	+	0.839382i	0.135689	+	0.0363577i
$534$	−8.20743	+	23.6053i	−0.355170	+	1.02150i
$535$	3.62418	−	3.80622i	0.156687	−	0.164557i
$536$	8.29370	−	4.78837i	0.358233	−	0.206826i
$537$	34.3649	+	2.50689i	1.48295	+	0.108180i
$538$	−4.90504	+	18.3059i	−0.211471	+	0.789222i
$539$	−18.7976	−	25.5886i	−0.809669	−	1.10218i
$540$	11.4011	+	2.23957i	0.490624	+	0.0963759i
$541$	−8.72599	−	15.1139i	−0.375160	−	0.649796i	0.615191	−	0.788378i	$-0.289079\pi$
$541$	−8.72599	−	15.1139i	−0.375160	−	0.649796i	−0.990351	+	0.138582i	$0.955745\pi$
$542$	12.1344	+	12.1344i	0.521219	+	0.521219i
$543$	−0.251661	−	0.519943i	−0.0107998	−	0.0223129i
$544$			6.94750i			0.297872i
$545$	−2.10116	−	3.44179i	−0.0900037	−	0.147430i
$546$	−14.8684	−	4.26952i	−0.636308	−	0.182719i
$547$	−38.5893	−	10.3400i	−1.64996	−	0.442105i	−0.690357	−	0.723469i	$-0.742546\pi$
$547$	−38.5893	−	10.3400i	−1.64996	−	0.442105i	−0.959601	+	0.281364i	$0.909213\pi$
$548$	−17.2976	−	4.63486i	−0.738915	−	0.197992i
$549$	4.63648	+	11.6774i	0.197880	+	0.498379i
$550$	−15.2321	+	16.8028i	−0.649501	+	0.716472i
$551$	−44.3689	−	25.6164i	−1.89018	−	1.09130i
$552$	−8.44852	+	4.08922i	−0.359593	+	0.174049i
$553$	15.8666	+	3.32898i	0.674717	+	0.141563i
$554$	3.54889	−	6.14685i	0.150778	−	0.261155i
$555$	−7.92635	+	24.7339i	−0.336455	+	1.04989i
$556$	−12.1092			−0.513544
$557$	−37.9144	+	10.1591i	−1.60648	+	0.430456i	−0.946992	−	0.321256i	$-0.895895\pi$
$557$	−37.9144	+	10.1591i	−1.60648	+	0.430456i	−0.659492	+	0.751712i	$0.729228\pi$
$558$	−5.24593	+	0.612120i	−0.222078	+	0.0259131i
$559$		−	10.9721i		−	0.464071i
$560$	3.83794	−	4.50225i	0.162183	−	0.190255i
$561$	41.3010	−	35.6849i	1.74373	−	1.50662i
$562$	−3.97066	+	3.97066i	−0.167492	+	0.167492i
$563$	9.31834	+	2.49684i	0.392721	+	0.105229i	0.449775	−	0.893142i	$-0.351504\pi$
$563$	9.31834	+	2.49684i	0.392721	+	0.105229i	−0.0570541	+	0.998371i	$0.518171\pi$
$564$	−1.85648	−	0.645486i	−0.0781717	−	0.0271799i
$565$	−1.16577	+	4.81998i	−0.0490444	+	0.202778i
$566$			2.39647i			0.100731i
$567$	12.4280	+	20.3112i	0.521926	+	0.852991i
$568$	−9.07231	−	9.07231i	−0.380666	−	0.380666i
$569$	−9.96323	+	17.2568i	−0.417680	+	0.723444i	−0.995706	−	0.0925751i	$-0.970490\pi$
$569$	−9.96323	+	17.2568i	−0.417680	+	0.723444i	0.578025	+	0.816019i	$0.303823\pi$
$570$	14.5834	+	16.0657i	0.610833	+	0.672919i
$571$	19.2027	+	33.2600i	0.803607	+	1.39189i	0.917227	+	0.398364i	$0.130422\pi$
$571$	19.2027	+	33.2600i	0.803607	+	1.39189i	−0.113620	+	0.993524i	$0.536245\pi$
$572$	10.8269	+	10.8269i	0.452695	+	0.452695i
$573$	−0.445998	+	6.11383i	−0.0186318	+	0.255409i
$574$	−2.53803	+	0.139704i	−0.105935	+	0.00583114i
$575$	26.4842	+	5.72277i	1.10447	+	0.238656i
$576$	2.35288	+	1.86117i	0.0980368	+	0.0775486i
$577$	−5.79484	−	21.6266i	−0.241242	−	0.900329i	−0.975235	−	0.221171i	$-0.929012\pi$
$577$	−5.79484	−	21.6266i	−0.241242	−	0.900329i	0.733993	−	0.679157i	$-0.237655\pi$
$578$	−22.1096	+	22.1096i	−0.919639	+	0.919639i
$579$	26.1894	−	5.00903i	1.08839	−	0.208168i
$580$	10.6551	+	17.4535i	0.442428	+	0.724715i
$581$	14.5929	−	0.803256i	0.605414	−	0.0333247i
$582$	−9.43641	−	19.4961i	−0.391152	−	0.808138i
$583$	−7.17831	+	1.92342i	−0.297295	+	0.0796600i
$584$	−4.18744	+	7.25285i	−0.173277	+	0.300125i
$585$	−17.8299	+	13.9598i	−0.737176	+	0.577165i
$586$	−0.139969	−	0.242434i	−0.00578209	−	0.0100149i
$587$	0.789364	−	2.94595i	0.0325805	−	0.121592i	−0.947720	−	0.319102i	$-0.896619\pi$
$587$	0.789364	−	2.94595i	0.0325805	−	0.121592i	0.980301	+	0.197510i	$0.0632854\pi$
$588$	12.1160	−	0.450411i	0.499655	−	0.0185746i
$589$	−8.54149	−	4.93143i	−0.351946	−	0.203196i
$590$	−5.06376	−	17.2014i	−0.208472	−	0.708170i
$591$	9.85736	−	28.3506i	0.405478	−	1.16619i
$592$	−4.74198	+	4.74198i	−0.194894	+	0.194894i
$593$	−30.8678	−	8.27099i	−1.26759	−	0.339649i	−0.438481	−	0.898740i	$-0.644483\pi$
$593$	−30.8678	−	8.27099i	−1.26759	−	0.339649i	−0.829106	+	0.559091i	$0.811150\pi$
$594$	−1.02114	−	23.5469i	−0.0418981	−	0.966141i
$595$	40.9722	−	3.26348i	1.67970	−	0.133790i
$596$	3.86552	−	2.23176i	0.158338	−	0.0914165i
$597$	−1.15205	+	15.7925i	−0.0471502	+	0.646344i
$598$	4.73458	−	17.6697i	0.193611	−	0.722567i
$599$	−20.3018	−	35.1637i	−0.829508	−	1.43675i	−0.898425	−	0.439128i	$-0.855288\pi$
$599$	−20.3018	−	35.1637i	−0.829508	−	1.43675i	0.0689167	−	0.997622i	$-0.478046\pi$
$600$	−2.04147	−	8.41620i	−0.0833426	−	0.343590i
$601$	18.7510	+	32.4776i	0.764868	+	1.32479i	0.940316	+	0.340302i	$0.110529\pi$
$601$	18.7510	+	32.4776i	0.764868	+	1.32479i	−0.175448	+	0.984489i	$0.556137\pi$
$602$	2.67893	+	8.17173i	0.109185	+	0.333055i
$603$	23.0485	−	17.1520i	0.938609	−	0.698483i
$604$	1.54474	−	0.891858i	0.0628547	−	0.0362892i
$605$	18.7966	+	10.2468i	0.764192	+	0.416592i
$606$	−8.81212	+	7.61386i	−0.357968	+	0.309292i
$607$	15.3001	−	15.3001i	0.621012	−	0.621012i	−0.324778	−	0.945790i	$-0.605290\pi$
$607$	15.3001	−	15.3001i	0.621012	−	0.621012i	0.945790	+	0.324778i	$0.105290\pi$
$608$	1.44998	+	5.41139i	0.0588044	+	0.219461i
$609$	−11.5665	+	40.2798i	−0.468699	+	1.63222i
$610$	6.45773	−	6.78209i	0.261466	−	0.274599i
$611$	3.31742	−	1.91531i	0.134208	−	0.0774853i
$612$	2.41561	+	20.7020i	0.0976452	+	0.836830i
$613$	−2.94788	+	0.789882i	−0.119064	+	0.0319030i	−0.317859	−	0.948138i	$-0.602964\pi$
$613$	−2.94788	+	0.789882i	−0.119064	+	0.0319030i	0.198795	+	0.980041i	$0.436297\pi$
$614$	−4.30596	+	7.45815i	−0.173775	+	0.300986i
$615$	−2.01395	+	3.12877i	−0.0812103	+	0.126164i
$616$	−10.7070	−	5.42010i	−0.431399	−	0.218382i
$617$	14.5691	−	3.90378i	0.586530	−	0.157160i	0.0466633	−	0.998911i	$-0.485141\pi$
$617$	14.5691	−	3.90378i	0.586530	−	0.157160i	0.539867	+	0.841750i	$0.318475\pi$
$618$	0.483766	−	6.63157i	0.0194599	−	0.266761i
$619$			14.5003i			0.582818i	0.956599	+	0.291409i	$0.0941240\pi$
$619$			14.5003i			0.582818i	−0.956599	+	0.291409i	$0.905876\pi$
$620$	2.05122	+	3.35998i	0.0823788	+	0.134940i
$621$	−23.7530	+	15.1225i	−0.953174	+	0.606845i
$622$	−9.34944	+	9.34944i	−0.374879	+	0.374879i
$623$	28.4366	+	25.4694i	1.13929	+	1.02041i
$624$	−5.74273	+	1.09836i	−0.229893	+	0.0439698i
$625$	−10.3222	+	22.7696i	−0.412887	+	0.910782i
$626$	−15.8092	+	9.12746i	−0.631864	+	0.364807i
$627$	24.7216	−	36.4146i	0.987286	−	1.45426i
$628$	17.2609	−	4.62503i	0.688783	−	0.184559i
$629$	−46.5911			−1.85771
$630$	9.87082	−	14.7501i	0.393263	−	0.587660i
$631$	1.86099			0.0740847			0.0370424	−	0.999314i	$-0.488206\pi$
$631$	1.86099			0.0740847			0.0370424	+	0.999314i	$0.488206\pi$
$632$	5.91880	−	1.58594i	0.235437	−	0.0630852i
$633$	−29.9927	−	2.18794i	−1.19210	−	0.0869628i
$634$	10.0491	−	5.80187i	0.399102	−	0.230422i
$635$	10.2051	−	3.00420i	0.404979	−	0.119218i
$636$	0.931956	−	2.68039i	0.0369544	−	0.106284i
$637$	−14.7739	+	18.4416i	−0.585362	+	0.730684i
$638$	29.3310	−	29.3310i	1.16123	−	1.16123i
$639$	−30.1879	−	23.8791i	−1.19422	−	0.944643i
$640$	0.525664	−	2.17340i	0.0207787	−	0.0859113i
$641$			3.11956i			0.123215i	0.998100	+	0.0616077i	$0.0196228\pi$
$641$			3.11956i			0.123215i	−0.998100	+	0.0616077i	$0.980377\pi$
$642$	3.66436	−	1.77361i	0.144621	−	0.0699988i
$643$	13.5618	−	3.63388i	0.534826	−	0.143306i	0.0187099	−	0.999825i	$-0.494044\pi$
$643$	13.5618	−	3.63388i	0.534826	−	0.143306i	0.516116	+	0.856519i	$0.327377\pi$
$644$	0.788008	+	14.3159i	0.0310519	+	0.564124i
$645$	11.9881	+	3.84176i	0.472029	+	0.151269i
$646$	−19.4609	+	33.7073i	−0.765680	+	1.32620i
$647$	−25.9680	+	6.95811i	−1.02091	+	0.273551i	−0.730180	−	0.683255i	$-0.760564\pi$
$647$	−25.9680	+	6.95811i	−1.02091	+	0.273551i	−0.290727	+	0.956806i	$0.593897\pi$
$648$	7.65820	+	4.72779i	0.300842	+	0.185725i
$649$	−31.5004	+	18.1868i	−1.23650	+	0.713893i
$650$	15.0128	+	7.71326i	0.588850	+	0.302539i
$651$	−2.22668	+	7.75429i	−0.0872704	+	0.303915i
$652$	2.90984	+	10.8597i	0.113958	+	0.425298i
$653$	33.3283	−	33.3283i	1.30424	−	1.30424i	0.378732	−	0.925506i	$-0.376360\pi$
$653$	33.3283	−	33.3283i	1.30424	−	1.30424i	0.925506	−	0.378732i	$-0.123640\pi$
$654$	−0.586776	−	3.06792i	−0.0229448	−	0.119965i
$655$	24.3133	−	44.6001i	0.950000	−	1.74267i
$656$	−0.832022	+	0.480368i	−0.0324850	+	0.0187552i
$657$	−9.95587	+	23.0679i	−0.388416	+	0.899964i
$658$	−2.00308	+	2.23645i	−0.0780883	+	0.0871857i
$659$	−18.1584	−	31.4512i	−0.707349	−	1.22516i	−0.965837	−	0.259150i	$-0.916558\pi$
$659$	−18.1584	−	31.4512i	−0.707349	−	1.22516i	0.258488	−	0.966014i	$-0.416776\pi$
$660$	−15.6203	+	8.03847i	−0.608019	+	0.312897i
$661$	−16.7977	−	29.0945i	−0.653356	−	1.13165i	−0.982303	−	0.187298i	$-0.940027\pi$
$661$	−16.7977	−	29.0945i	−0.653356	−	1.13165i	0.328947	−	0.944348i	$-0.393306\pi$
$662$	−4.24274	+	15.8341i	−0.164899	+	0.615410i
$663$	−33.6077	−	22.8160i	−1.30522	−	0.886101i
$664$	4.78387	−	2.76197i	0.185650	−	0.107185i
$665$	31.2320	−	11.0930i	1.21113	−	0.430169i
$666$	−12.4813	+	15.7788i	−0.483641	+	0.611417i
$667$	−47.8688	−	12.8264i	−1.85349	−	0.496640i
$668$	−1.22401	+	1.22401i	−0.0473583	+	0.0473583i
$669$	46.3520	−	8.86535i	1.79207	−	0.342754i
$670$	−18.8020	−	10.2497i	−0.726383	−	0.395980i
$671$	−16.4514	−	9.49821i	−0.635099	−	0.366674i
$672$	4.00885	−	2.22016i	0.154645	−	0.0856446i
$673$	−5.99342	+	22.3677i	−0.231029	+	0.862213i	0.748869	+	0.662718i	$0.230597\pi$
$673$	−5.99342	+	22.3677i	−0.231029	+	0.862213i	−0.979899	+	0.199495i	$0.936070\pi$
$674$	−9.15093	−	15.8499i	−0.352481	−	0.610515i
$675$	−9.00940	−	24.3686i	−0.346772	−	0.937949i
$676$	−0.802440	+	1.38987i	−0.0308631	+	0.0534564i
$677$	1.88264	−	0.504453i	0.0723559	−	0.0193877i	−0.222460	−	0.974942i	$-0.571409\pi$
$677$	1.88264	−	0.504453i	0.0723559	−	0.0193877i	0.294815	+	0.955554i	$0.404742\pi$
$678$	−2.15753	+	3.17802i	−0.0828596	+	0.122051i
$679$	−33.0357	+	1.81843i	−1.26780	+	0.0697850i
$680$	13.2595	−	8.09472i	0.508478	−	0.310418i
$681$	−5.19448	+	14.9398i	−0.199053	+	0.572494i
$682$	5.64654	−	5.64654i	0.216217	−	0.216217i
$683$	−11.5608	−	43.1455i	−0.442361	−	1.65092i	−0.722811	−	0.691046i	$-0.757150\pi$
$683$	−11.5608	−	43.1455i	−0.442361	−	1.65092i	0.280449	−	0.959869i	$-0.409517\pi$
$684$	6.20213	+	15.6206i	0.237144	+	0.597269i
$685$	11.3081	+	38.4131i	0.432059	+	1.46769i
$686$	6.50049	−	17.3420i	0.248190	−	0.662119i
$687$	−9.05094	+	4.38080i	−0.345315	+	0.167138i
$688$	2.29835	+	2.29835i	0.0876238	+	0.0876238i
$689$	2.76534	+	4.78970i	0.105351	+	0.182473i
$690$	17.6480	+	11.3598i	0.671848	+	0.432460i
$691$	−12.6103	+	21.8417i	−0.479719	+	0.830897i	−0.999729	−	0.0232627i	$-0.992595\pi$
$691$	−12.6103	+	21.8417i	−0.479719	+	0.830897i	0.520011	+	0.854160i	$0.325928\pi$
$692$	11.1219	+	11.1219i	0.422792	+	0.422792i
$693$	−33.7892	−	12.4279i	−1.28355	−	0.472098i
$694$		−	28.8499i		−	1.09513i
$695$	14.1087	+	23.1107i	0.535175	+	0.876640i
$696$	2.97557	+	15.5576i	0.112789	+	0.589708i
$697$	−6.44728	−	1.72754i	−0.244208	−	0.0654353i
$698$	−17.1978	+	17.1978i	−0.650945	+	0.650945i
$699$	−5.06875	−	26.5016i	−0.191718	−	1.00238i
$700$	−13.0643	−	2.07913i	−0.493786	−	0.0785837i
$701$		−	41.2316i		−	1.55730i	−0.627461	−	0.778648i	$-0.715906\pi$
$701$		−	41.2316i		−	1.55730i	0.627461	−	0.778648i	$-0.284094\pi$
$702$	−16.7302	+	5.26960i	−0.631441	+	0.198888i
$703$	−36.2897	+	9.72380i	−1.36869	+	0.366740i
$704$	−4.53586			−0.170952
$705$	0.931101	+	4.29521i	0.0350673	+	0.161767i
$706$	−3.15780	+	5.46947i	−0.118845	+	0.205846i
$707$	5.54164	+	16.9041i	0.208415	+	0.635742i
$708$	1.01054	−	13.8527i	0.0379784	−	0.520616i
$709$	45.9744	+	26.5433i	1.72660	+	0.996856i	0.902921	+	0.429806i	$0.141418\pi$
$709$	45.9744	+	26.5433i	1.72660	+	0.996856i	0.823684	+	0.567050i	$0.191915\pi$
$710$	−6.74436	+	27.8851i	−0.253111	+	1.04651i
$711$	17.0853	−	6.78368i	0.640749	−	0.254408i
$712$	13.9372	+	3.73445i	0.522317	+	0.139954i
$713$	−9.21525	−	2.46922i	−0.345114	−	0.0924730i
$714$	30.6008	+	8.78715i	1.14521	+	0.328851i
$715$	8.04873	−	33.2782i	0.301005	−	1.24453i
$716$		−	19.8933i		−	0.743448i
$717$	−31.5592	−	2.30222i	−1.17860	−	0.0859778i
$718$	−8.23121	−	8.23121i	−0.307186	−	0.307186i
$719$	9.27141	+	16.0585i	0.345765	+	0.598883i	0.985492	−	0.169719i	$-0.0542861\pi$
$719$	9.27141	+	16.0585i	0.345765	+	0.598883i	−0.639727	+	0.768602i	$0.720953\pi$
$720$	0.810684	−	6.65904i	0.0302124	−	0.248168i
$721$	−9.06187	−	4.58728i	−0.337482	−	0.170839i
$722$	−3.20562	+	11.9636i	−0.119301	+	0.445237i
$723$	1.63468	+	3.37732i	0.0607943	+	0.125604i
$724$	−0.288822	+	0.166752i	−0.0107340	+	0.00619728i
$725$	20.8959	−	40.6710i	0.776054	−	1.51048i
$726$	10.8416	+	12.5478i	0.402368	+	0.465692i
$727$	−26.3498	−	7.06041i	−0.977261	−	0.261856i	−0.265370	−	0.964147i	$-0.585494\pi$
$727$	−26.3498	−	7.06041i	−0.977261	−	0.261856i	−0.711891	+	0.702290i	$0.752161\pi$
$728$	−1.83392	+	8.74086i	−0.0679697	+	0.323958i
$729$	24.4636	+	11.4251i	0.906059	+	0.423151i
$730$	18.7212	−	0.458654i	0.692901	−	0.0169756i
$731$			22.5819i			0.835220i
$732$	6.52931	−	3.16029i	0.241330	−	0.116808i
$733$	30.8243	+	30.8243i	1.13852	+	1.13852i	0.988715	+	0.149806i	$0.0478650\pi$
$733$	30.8243	+	30.8243i	1.13852	+	1.13852i	0.149806	+	0.988715i	$0.452135\pi$
$734$	3.57867	−	6.19843i	0.132091	−	0.228788i
$735$	−14.9763	−	22.5989i	−0.552409	−	0.833574i
$736$	2.70954	+	4.69306i	0.0998750	+	0.172989i
$737$	−11.2428	+	41.9586i	−0.414133	+	1.54557i
$738$	−2.31222	+	1.72068i	−0.0851141	+	0.0633392i
$739$	30.5762	+	17.6532i	1.12476	+	0.649383i	0.942613	−	0.333888i	$-0.108361\pi$
$739$	30.5762	+	17.6532i	1.12476	+	0.649383i	0.182151	+	0.983271i	$0.441694\pi$
$740$	14.5752	+	3.52519i	0.535795	+	0.129589i
$741$	−30.9388	−	10.7572i	−1.13657	−	0.395177i
$742$	−3.22899	−	2.89206i	−0.118540	−	0.106171i
$743$	−1.64433	−	6.13672i	−0.0603246	−	0.225134i	0.929182	−	0.369623i	$-0.120513\pi$
$743$	−1.64433	−	6.13672i	−0.0603246	−	0.225134i	−0.989507	+	0.144488i	$0.953846\pi$
$744$	0.572829	+	2.99500i	0.0210009	+	0.109802i
$745$	−8.76321	−	4.77718i	−0.321059	−	0.175022i
$746$	12.0764	+	6.97233i	0.442150	+	0.255275i
$747$	13.2946	−	9.89339i	0.486423	−	0.361980i
$748$	−22.2830	−	22.2830i	−0.814746	−	0.814746i
$749$	−0.341781	−	6.20919i	−0.0124884	−	0.226879i
$750$	−13.6840	+	13.7021i	−0.499668	+	0.500331i
$751$	33.5844			1.22551			0.612757	−	0.790271i	$-0.290060\pi$
$751$	33.5844			1.22551			0.612757	+	0.790271i	$0.290060\pi$
$752$	−0.293702	+	1.09611i	−0.0107102	+	0.0399710i
$753$	9.14352	−	4.42561i	0.333208	−	0.161278i
$754$	−26.7346	−	15.4352i	−0.973615	−	0.562117i
$755$	−3.50196	−	1.90906i	−0.127449	−	0.0694777i
$756$	11.1736	−	8.00946i	0.406379	−	0.291301i
$757$	21.7514	−	21.7514i	0.790569	−	0.790569i	−0.191017	−	0.981587i	$-0.561179\pi$
$757$	21.7514	−	21.7514i	0.790569	−	0.790569i	0.981587	+	0.191017i	$0.0611787\pi$
$758$	−2.13984	−	7.98601i	−0.0777227	−	0.290065i
$759$	13.9818	−	40.2128i	0.507506	−	1.45963i
$760$	8.63838	−	9.07228i	0.313347	−	0.329086i
$761$			13.7097i			0.496977i	0.968635	+	0.248488i	$0.0799338\pi$
$761$			13.7097i			0.496977i	−0.968635	+	0.248488i	$0.920066\pi$
$762$	8.21844	+	0.599527i	0.297723	+	0.0217186i
$763$	−4.66960	−	0.979731i	−0.169051	−	0.0354686i
$764$	3.53920			0.128044
$765$	36.6959	−	28.7308i	1.32674	−	1.03876i
$766$	13.8092	−	23.9183i	0.498948	−	0.864203i
$767$	19.1412	+	19.1412i	0.691150	+	0.691150i
$768$	0.972864	−	1.43302i	0.0351052	−	0.0517095i
$769$	5.68725	+	3.28354i	0.205088	+	0.118407i	0.599026	−	0.800729i	$-0.295554\pi$
$769$	5.68725	+	3.28354i	0.205088	+	0.118407i	−0.393939	+	0.919137i	$0.628888\pi$
$770$	2.13065	+	26.7498i	0.0767833	+	0.963996i
$771$	4.53192	−	13.0342i	0.163213	−	0.469415i
$772$	−3.98440	−	14.8700i	−0.143402	−	0.535183i
$773$	9.84097	+	36.7270i	0.353955	+	1.32098i	0.881794	+	0.471634i	$0.156336\pi$
$773$	9.84097	+	36.7270i	0.353955	+	1.32098i	−0.527839	+	0.849344i	$0.676998\pi$
$774$	7.64771	+	6.04946i	0.274891	+	0.217443i
$775$	4.02269	−	7.82960i	0.144499	−	0.281248i
$776$	−10.8299	+	6.25262i	−0.388769	+	0.224456i
$777$	14.8888	+	26.8840i	0.534132	+	0.964459i
$778$	−34.3278	+	9.19812i	−1.23071	+	0.329768i
$779$	−5.38232			−0.192841
$780$	8.78727	+	9.68043i	0.314635	+	0.346615i
$781$	58.1959			2.08241
$782$	−9.74429	+	36.3662i	−0.348455	+	1.30045i
$783$	14.2758	+	45.3236i	0.510177	+	1.61973i
$784$	−0.768294	−	6.95771i	−0.0274391	−	0.248490i
$785$	−28.9381	−	27.5541i	−1.03285	−	0.983447i
$786$	29.7730	−	25.7245i	1.06197	−	0.917564i
$787$	−14.7717	−	3.95807i	−0.526555	−	0.141090i	−0.0142579	−	0.999898i	$-0.504539\pi$
$787$	−14.7717	−	3.95807i	−0.526555	−	0.141090i	−0.512297	+	0.858808i	$0.671205\pi$
$788$	−16.7389	−	4.48518i	−0.596300	−	0.159778i
$789$	0.947965	+	0.329602i	0.0337485	+	0.0117342i
$790$	−9.92295	−	9.44837i	−0.353043	−	0.336158i
$791$	3.20861	+	4.91250i	0.114085	+	0.174668i
$792$	−13.5159	+	1.57710i	−0.480266	+	0.0560396i
$793$	−3.65905	+	13.6557i	−0.129937	+	0.484930i
$794$	13.8420			0.491232
$795$	−6.20144	+	1.34433i	−0.219942	+	0.0476784i
$796$	9.14203			0.324031
$797$	6.73920	−	1.80576i	0.238715	−	0.0639635i	−0.137478	−	0.990505i	$-0.543900\pi$
$797$	6.73920	−	1.80576i	0.238715	−	0.0639635i	0.376193	+	0.926541i	$0.377233\pi$
$798$	25.6688	+	0.457752i	0.908666	+	0.0162043i
$799$	−6.82762	+	3.94193i	−0.241544	+	0.139455i
$800$	−4.76046	+	1.52905i	−0.168308	+	0.0540599i
$801$	42.8282	+	6.28197i	1.51326	+	0.221963i
$802$	−7.26072	−	27.0974i	−0.256385	−	0.956842i
$803$	−9.83182	−	36.6929i	−0.346958	−	1.29486i
$804$	−10.8446	−	12.5513i	−0.382460	−	0.442651i
$805$	26.4041	−	18.1837i	0.930622	−	0.640893i
$806$	−5.14669	−	2.97144i	−0.181284	−	0.104665i
$807$	32.7382	+	2.38822i	1.15244	+	0.0840693i
$808$	4.75437	+	4.75437i	0.167258	+	0.167258i
$809$	−0.387759	+	0.671617i	−0.0136329	+	0.0236128i	−0.872761	−	0.488147i	$-0.837673\pi$
$809$	−0.387759	+	0.671617i	−0.0136329	+	0.0236128i	0.859128	+	0.511760i	$0.171006\pi$
$810$	0.100349	−	20.1244i	0.00352591	−	0.707098i
$811$	−39.9217			−1.40184			−0.700921	−	0.713239i	$-0.747228\pi$
$811$	−39.9217			−1.40184			−0.700921	+	0.713239i	$0.747228\pi$
$812$	23.6798	+	4.96826i	0.830997	+	0.174352i
$813$	16.6950	−	24.5916i	0.585520	−	0.862464i
$814$		−	30.4182i		−	1.06616i
$815$	17.3357	−	18.2064i	0.607242	−	0.637743i
$816$	11.8192	−	2.26056i	0.413754	−	0.0791353i
$817$	4.71295	+	17.5890i	0.164885	+	0.615360i
$818$	−13.7615	+	13.7615i	−0.481160	+	0.481160i
$819$	−2.42554	+	26.6835i	−0.0847552	+	0.932397i
$820$	1.88621	+	1.02825i	0.0658692	+	0.0359079i
$821$	−36.3901	−	21.0098i	−1.27002	−	0.733248i	−0.295031	−	0.955488i	$-0.595330\pi$
$821$	−36.3901	−	21.0098i	−1.27002	−	0.733248i	−0.974992	+	0.222239i	$0.928663\pi$
$822$	−2.25667	+	30.9349i	−0.0787105	+	1.07898i
$823$	5.62098	−	20.9778i	0.195935	−	0.731239i	−0.796088	−	0.605181i	$-0.793101\pi$
$823$	5.62098	−	20.9778i	0.195935	−	0.731239i	0.992023	−	0.126058i	$-0.0402326\pi$
$824$	−3.83891			−0.133735
$825$	33.5413	+	20.4459i	1.16776	+	0.711835i
$826$	−18.9293	−	9.58238i	−0.658636	−	0.333414i
$827$	11.3282	+	11.3282i	0.393920	+	0.393920i	0.876082	−	0.482162i	$-0.160148\pi$
$827$	11.3282	+	11.3282i	0.393920	+	0.393920i	−0.482162	+	0.876082i	$0.660148\pi$
$828$	9.70559	+	13.0422i	0.337293	+	0.453248i
$829$	6.04221	+	3.48847i	0.209855	+	0.121160i	0.601244	−	0.799066i	$-0.294672\pi$
$829$	6.04221	+	3.48847i	0.209855	+	0.121160i	−0.391389	+	0.920225i	$0.628005\pi$
$830$	−10.8451	−	5.91211i	−0.376439	−	0.205212i
$831$	−11.6118	−	4.03737i	−0.402810	−	0.140055i
$832$	0.873687	+	3.26064i	0.0302896	+	0.113042i
$833$	30.4063	−	37.9549i	1.05351	−	1.31506i
$834$	3.94005	+	20.6003i	0.136433	+	0.713331i
$835$	3.76218	+	0.909929i	0.130196	+	0.0314894i
$836$	−22.0067	−	12.7056i	−0.761118	−	0.439432i
$837$	2.74825	+	8.72529i	0.0949935	+	0.301590i
$838$	2.75656	−	10.2876i	0.0952239	−	0.355380i
$839$	−1.68892	−	2.92530i	−0.0583081	−	0.100993i	0.835398	−	0.549646i	$-0.185237\pi$
$839$	−1.68892	−	2.92530i	−0.0583081	−	0.100993i	−0.893706	+	0.448653i	$0.851904\pi$
$840$	−8.90806	−	5.06423i	−0.307357	−	0.174733i
$841$	−27.3154	+	47.3116i	−0.941909	+	1.63143i
$842$	7.02098	+	7.02098i	0.241959	+	0.241959i
$843$	8.04690	+	5.46298i	0.277150	+	0.188155i
$844$			17.3623i			0.597636i
$845$	3.58754	−	0.0878921i	0.123415	−	0.00302358i
$846$	−0.494056	+	3.36829i	−0.0169860	+	0.115804i
$847$	24.0701	−	7.89086i	0.827057	−	0.271133i
$848$	−1.58257	−	0.424048i	−0.0543456	−	0.0145619i
$849$	4.07692	−	0.779758i	0.139919	−	0.0267612i
$850$	−30.8980	−	15.8747i	−1.05979	−	0.544499i
$851$	−31.4725	+	18.1706i	−1.07886	+	0.622881i
$852$	−12.4820	+	18.3859i	−0.427627	+	0.629889i
$853$	−7.16419	+	26.7371i	−0.245297	+	0.915462i	0.727936	+	0.685645i	$0.240480\pi$
$853$	−7.16419	+	26.7371i	−0.245297	+	0.915462i	−0.973234	+	0.229817i	$0.926187\pi$
$854$	−0.609000	−	11.0638i	−0.0208396	−	0.378595i
$855$	22.5861	−	30.0369i	0.772429	−	1.02724i
$856$	−1.17520	−	2.03551i	−0.0401676	−	0.0695724i
$857$	−7.99006	−	7.99006i	−0.272935	−	0.272935i	0.557345	−	0.830281i	$-0.311820\pi$
$857$	−7.99006	−	7.99006i	−0.272935	−	0.272935i	−0.830281	+	0.557345i	$0.811820\pi$
$858$	14.8961	−	21.9417i	0.508543	−	0.749077i
$859$			0.210995i			0.00719907i	0.999994	+	0.00359953i	$0.00114577\pi$
$859$			0.210995i			0.00719907i	−0.999994	+	0.00359953i	$0.998854\pi$
$860$	1.70860	−	7.06434i	0.0582627	−	0.240892i
$861$	1.06348	+	4.27227i	0.0362434	+	0.145599i
$862$	−23.0360	−	6.17249i	−0.784611	−	0.210236i
$863$	5.32968	+	1.42808i	0.181424	+	0.0486125i	0.348387	−	0.937351i	$-0.386729\pi$
$863$	5.32968	+	1.42808i	0.181424	+	0.0486125i	−0.166963	+	0.985963i	$0.553396\pi$
$864$	2.40067	−	4.60834i	0.0816725	−	0.156779i
$865$	8.26805	−	34.1850i	0.281122	−	1.16232i
$866$	2.19685	+	1.26835i	0.0746521	+	0.0431004i
$867$	44.8072	+	30.4192i	1.52173	+	1.03309i
$868$	4.55861	+	0.956443i	0.154729	+	0.0324638i
$869$	−13.8969	+	24.0702i	−0.471422	+	0.816526i
$870$	26.2252	−	23.8055i	0.889116	−	0.807082i
$871$	32.3279			1.09539
$872$	−1.74192	+	0.466747i	−0.0589890	+	0.0158061i
$873$	−30.0966	+	22.3969i	−1.01862	+	0.758021i
$874$			30.3592i			1.02692i
$875$	11.2535	+	27.3561i	0.380439	+	0.924806i
$876$	13.7012	+	4.76381i	0.462919	+	0.160954i
$877$	−0.245844	+	0.245844i	−0.00830155	+	0.00830155i	−0.711245	−	0.702944i	$-0.751869\pi$
$877$	−0.245844	+	0.245844i	−0.00830155	+	0.00830155i	0.702944	+	0.711245i	$0.251869\pi$
$878$	−36.0971	−	9.67218i	−1.21822	−	0.326420i
$879$	−0.366890	+	0.317001i	−0.0123749	+	0.0106922i
$880$	5.28485	+	8.65682i	0.178152	+	0.291821i
$881$		−	38.6704i		−	1.30284i	−0.758718	−	0.651420i	$-0.774174\pi$
$881$		−	38.6704i		−	1.30284i	0.758718	−	0.651420i	$-0.225826\pi$
$882$	−4.70851	−	20.4653i	−0.158544	−	0.689104i
$883$	16.3598	+	16.3598i	0.550550	+	0.550550i	0.926599	−	0.376050i	$-0.122718\pi$
$883$	16.3598	+	16.3598i	0.550550	+	0.550550i	−0.376050	+	0.926599i	$0.622718\pi$
$884$	−11.7262	+	20.3104i	−0.394395	+	0.683113i
$885$	−27.6156	+	14.2115i	−0.928289	+	0.477714i
$886$	13.8010	+	23.9041i	0.463654	+	0.803073i
$887$	6.30183	+	6.30183i	0.211595	+	0.211595i	0.804945	−	0.593350i	$-0.202195\pi$
$887$	6.30183	+	6.30183i	0.211595	+	0.211595i	−0.593350	+	0.804945i	$0.702195\pi$
$888$	9.61005	+	6.52419i	0.322492	+	0.218937i
$889$	5.68498	−	11.2303i	0.190668	−	0.376652i
$890$	−9.11125	−	30.9506i	−0.305410	−	1.03747i
$891$	−39.7260	+	9.39880i	−1.33087	+	0.314872i
$892$	−7.05189	−	26.3180i	−0.236115	−	0.881192i
$893$	−4.49532	+	4.49532i	−0.150430	+	0.150430i
$894$	−5.05446	−	5.84992i	−0.169046	−	0.195651i
$895$	−37.9669	+	23.1782i	−1.26909	+	0.774763i
$896$	−1.44681	−	2.21512i	−0.0483345	−	0.0740019i
$897$	−31.6004	−	2.30522i	−1.05511	−	0.0769691i
$898$	−13.8835	+	3.72007i	−0.463298	+	0.124140i
$899$	−8.04991	+	13.9429i	−0.268479	+	0.465020i
$900$	−13.6535	+	6.21141i	−0.455117	+	0.207047i
$901$	−5.69137	−	9.85775i	−0.189607	−	0.328409i
$902$	1.12787	−	4.20928i	0.0375540	−	0.140154i
$903$	13.0302	−	7.21632i	0.433618	−	0.240144i
$904$	1.92060	+	1.10886i	0.0638781	+	0.0368800i
$905$	0.654765	+	0.356939i	0.0217651	+	0.0118650i
$906$	−2.01986	−	2.33775i	−0.0671055	−	0.0776665i
$907$	7.83939	−	7.83939i	0.260303	−	0.260303i	−0.564874	−	0.825177i	$-0.691075\pi$
$907$	7.83939	−	7.83939i	0.260303	−	0.260303i	0.825177	+	0.564874i	$0.191075\pi$
$908$	8.82082	+	2.36353i	0.292729	+	0.0784366i
$909$	15.8201	+	12.5139i	0.524719	+	0.415061i
$910$	18.8189	−	6.68412i	0.623841	−	0.221576i
$911$	−28.8620	+	16.6635i	−0.956239	+	0.552085i	−0.895014	−	0.446039i	$-0.852834\pi$
$911$	−28.8620	+	16.6635i	−0.956239	+	0.552085i	−0.0612258	+	0.998124i	$0.519501\pi$
$912$	8.73415	−	4.22746i	0.289216	−	0.139985i
$913$	−6.48492	+	24.2021i	−0.214620	+	0.800971i
$914$	−1.91653	−	3.31952i	−0.0633930	−	0.109800i
$915$	−13.6390	−	8.77924i	−0.450891	−	0.290233i
$916$	2.90274	+	5.02770i	0.0959093	+	0.166120i
$917$	−18.7232	−	57.1128i	−0.618295	−	1.88603i
$918$	34.4326	−	10.8454i	1.13645	−	0.357953i
$919$	−11.2804	+	6.51272i	−0.372105	+	0.214835i	−0.674378	−	0.738387i	$-0.735588\pi$
$919$	−11.2804	+	6.51272i	−0.372105	+	0.214835i	0.302273	+	0.953221i	$0.402255\pi$
$920$	5.79988	−	10.6392i	0.191216	−	0.350765i
$921$	14.0890	+	4.89866i	0.464247	+	0.161416i
$922$	−18.0326	+	18.0326i	−0.593873	+	0.593873i
$923$	−11.2096	−	41.8346i	−0.368967	−	1.37700i
$924$	−5.73693	+	19.9785i	−0.188731	+	0.657246i
$925$	−10.2540	−	31.9245i	−0.337151	−	1.04967i
$926$	9.29664	−	5.36742i	0.305507	−	0.176384i
$927$	−11.4391	+	1.33477i	−0.375710	+	0.0438396i
$928$	8.83338	−	2.36690i	0.289970	−	0.0776972i
$929$	22.4989	−	38.9693i	0.738166	−	1.27854i	−0.215154	−	0.976580i	$-0.569025\pi$
$929$	22.4989	−	38.9693i	0.738166	−	1.27854i	0.953320	−	0.301961i	$-0.0976413\pi$
$930$	5.04863	−	4.58282i	0.165551	−	0.150276i
$931$	15.7620	−	35.9090i	0.516578	−	1.17687i
$932$	−15.0473	+	4.03190i	−0.492889	+	0.132069i
$933$	18.9475	+	12.8633i	0.620313	+	0.421126i
$934$		−	7.20211i		−	0.235660i
$935$	−16.5652	+	68.4902i	−0.541739	+	2.23987i
$936$	3.73711	+	9.41223i	0.122151	+	0.307648i
$937$	19.8244	−	19.8244i	0.647635	−	0.647635i	−0.304786	−	0.952421i	$-0.598585\pi$
$937$	19.8244	−	19.8244i	0.647635	−	0.647635i	0.952421	+	0.304786i	$0.0985850\pi$
$938$	−24.0769	+	7.89310i	−0.786138	+	0.257719i
$939$	20.6717	+	23.9250i	0.674596	+	0.780763i
$940$	2.43416	−	0.716569i	0.0793935	−	0.0233719i
$941$	6.47476	−	3.73820i	0.211071	−	0.121862i	−0.390738	−	0.920502i	$-0.627780\pi$
$941$	6.47476	−	3.73820i	0.211071	−	0.121862i	0.601809	+	0.798640i	$0.294447\pi$
$942$	−13.4845	−	27.8595i	−0.439347	−	0.907713i
$943$	−5.02890	+	1.34749i	−0.163764	+	0.0438803i
$944$	−8.01910			−0.260999
$945$	−28.3049	−	11.9930i	−0.920758	−	0.390133i
$946$	−14.7432			−0.479342
$947$	14.3434	−	3.84331i	0.466099	−	0.124891i	−0.0181237	−	0.999836i	$-0.505769\pi$
$947$	14.3434	−	3.84331i	0.466099	−	0.124891i	0.484222	+	0.874945i	$0.339103\pi$
$948$	−4.62386	−	9.55311i	−0.150176	−	0.310271i
$949$	−24.4832	+	14.1354i	−0.794758	+	0.458854i
$950$	−27.3795	−	5.91624i	−0.888309	−	0.191948i
$951$	−13.1400	−	15.2079i	−0.426093	−	0.493151i
$952$	3.77442	−	17.9897i	0.122330	−	0.583048i
$953$	−0.687841	+	0.687841i	−0.0222814	+	0.0222814i	−0.718160	−	0.695878i	$-0.755015\pi$
$953$	−0.687841	+	0.687841i	−0.0222814	+	0.0222814i	0.695878	+	0.718160i	$0.255015\pi$
$954$	−4.86315	−	0.713320i	−0.157450	−	0.0230946i
$955$	−4.12362	−	6.75466i	−0.133437	−	0.218576i
$956$			18.2692i			0.590867i
$957$	−59.4420	−	40.3547i	−1.92149	−	1.30448i
$958$	−4.00306	+	1.07262i	−0.129333	+	0.0346547i
$959$	42.2718	+	21.3988i	1.36503	+	0.691002i
$960$	−3.86846	−	0.187092i	−0.124854	−	0.00603836i
$961$	13.9503	−	24.1626i	0.450010	−	0.779440i
$962$	−21.8664	+	5.85909i	−0.705002	+	0.188905i
$963$	−4.20959	−	5.65677i	−0.135652	−	0.182287i
$964$	1.87606	−	1.08315i	0.0604239	−	0.0348858i
$965$	−23.7375	+	24.9298i	−0.764136	+	0.802517i
$966$	24.0980	−	5.99862i	0.775339	−	0.193003i
$967$	−1.53678	−	5.73533i	−0.0494194	−	0.184436i	0.936804	−	0.349855i	$-0.113769\pi$
$967$	−1.53678	−	5.73533i	−0.0494194	−	0.184436i	−0.986223	+	0.165419i	$0.947102\pi$
$968$	6.76986	−	6.76986i	0.217592	−	0.217592i
$969$	63.6755	+	22.1396i	2.04555	+	0.711227i
$970$	24.5515	+	13.3840i	0.788300	+	0.429734i
$971$	−46.1246	+	26.6300i	−1.48021	+	0.854598i	−0.999749	−	0.0224188i	$-0.992863\pi$
$971$	−46.1246	+	26.6300i	−1.48021	+	0.854598i	−0.480459	+	0.877017i	$0.659530\pi$
$972$	5.55118	−	14.5665i	0.178054	−	0.467222i
$973$	31.3552	+	6.57864i	1.00520	+	0.210902i
$974$	−13.7051	−	23.7380i	−0.439141	−	0.760614i
$975$	8.23709	−	28.0497i	0.263798	−	0.898309i
$976$	−2.09403	−	3.62696i	−0.0670282	−	0.116096i
$977$	9.70468	−	36.2184i	0.310480	−	1.15873i	−0.617644	−	0.786458i	$-0.711913\pi$
$977$	9.70468	−	36.2184i	0.310480	−	1.15873i	0.928124	−	0.372271i	$-0.121421\pi$
$978$	17.5279	−	8.48376i	0.560479	−	0.271281i
$979$	−56.6788	+	32.7235i	−1.81146	+	1.04585i
$980$	−12.3838	+	9.57293i	−0.395587	+	0.305796i
$981$	−5.02827	+	1.99646i	−0.160540	+	0.0637422i
$982$	−1.64373	−	0.440436i	−0.0524535	−	0.0140549i
$983$	33.1315	−	33.1315i	1.05673	−	1.05673i	0.0584388	−	0.998291i	$-0.481388\pi$
$983$	33.1315	−	33.1315i	1.05673	−	1.05673i	0.998291	−	0.0584388i	$-0.0186123\pi$
$984$	1.08793	+	1.25915i	0.0346819	+	0.0401401i
$985$	10.9429	+	37.1725i	0.348669	+	1.18442i
$986$	55.0227	+	31.7674i	1.75228	+	1.01168i
$987$	4.45643	+	2.67999i	0.141850	+	0.0853049i
$988$	−4.89464	+	18.2670i	−0.155719	+	0.581152i
$989$	8.80698	+	15.2541i	0.280046	+	0.485053i
$990$	18.7576	+	23.9579i	0.596157	+	0.761433i
$991$	−25.1130	+	43.4970i	−0.797741	+	1.38173i	0.123344	+	0.992364i	$0.460638\pi$
$991$	−25.1130	+	43.4970i	−0.797741	+	1.38173i	−0.921084	+	0.389363i	$0.872695\pi$
$992$	1.70052	−	0.455653i	0.0539916	−	0.0144670i
$993$	28.3177	+	2.06575i	0.898635	+	0.0655546i
$994$	18.5628	+	28.4204i	0.588777	+	0.901439i
$995$	−10.6516	−	17.4478i	−0.337679	−	0.553133i
$996$	−6.25526	−	7.23971i	−0.198206	−	0.229399i
$997$	−30.3348	+	30.3348i	−0.960714	+	0.960714i	−0.999257	−	0.0385428i	$-0.987728\pi$
$997$	−30.3348	+	30.3348i	−0.960714	+	0.960714i	0.0385428	+	0.999257i	$0.487728\pi$
$998$	6.67734	+	24.9202i	0.211368	+	0.788835i
$999$	30.9043	+	16.0993i	0.977769	+	0.509359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.473.17	yes	192
5.2	odd	4	inner	630.2.bt.a.347.20	yes	192
7.2	even	3		630.2.cd.a.23.25	yes	192
9.2	odd	6		630.2.cd.a.263.14	yes	192
35.2	odd	12		630.2.cd.a.527.14	yes	192
45.2	even	12		630.2.cd.a.137.25	yes	192
63.2	odd	6	inner	630.2.bt.a.443.20	yes	192
315.2	even	12	inner	630.2.bt.a.317.17	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.17	✓	192	315.2	even	12	inner
630.2.bt.a.347.20	yes	192	5.2	odd	4	inner
630.2.bt.a.443.20	yes	192	63.2	odd	6	inner
630.2.bt.a.473.17	yes	192	1.1	even	1	trivial
630.2.cd.a.23.25	yes	192	7.2	even	3
630.2.cd.a.137.25	yes	192	45.2	even	12
630.2.cd.a.263.14	yes	192	9.2	odd	6
630.2.cd.a.527.14	yes	192	35.2	odd	12

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.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.754597 + 1.55903i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.96329 - 1.07027i) q^{5} +(-1.13239 - 1.31061i) q^{6} +(-2.51410 + 0.824195i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.86117 + 2.35288i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.754597 + 1.55903i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.96329 - 1.07027i) q^{5} +(-1.13239 - 1.31061i) q^{6} +(-2.51410 + 0.824195i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.86117 + 2.35288i) q^{9} +(2.17340 + 0.525664i) q^{10} -4.53586i q^{11} +(1.43302 + 0.972864i) q^{12} +(-3.26064 + 0.873687i) q^{13} +(2.21512 - 1.44681i) q^{14} +(0.187092 - 3.86846i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.71077 - 1.79814i) q^{17} +(1.18878 - 2.75442i) q^{18} +(4.85172 - 2.80114i) q^{19} +(-2.23540 + 0.0547655i) q^{20} +(-3.18208 - 3.29763i) q^{21} +(1.17397 + 4.38130i) q^{22} +(3.83187 - 3.83187i) q^{23} +(-1.63598 - 0.568822i) q^{24} +(2.70904 + 4.20251i) q^{25} +(2.92341 - 1.68783i) q^{26} +(-5.07265 - 1.12614i) q^{27} +(-1.76518 + 1.97082i) q^{28} +(-4.57249 - 7.91979i) q^{29} +(0.820515 + 3.78507i) q^{30} +(-0.880254 - 1.52464i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(7.07156 - 3.42275i) q^{33} +(-6.01671 + 3.47375i) q^{34} +(5.81803 + 1.07263i) q^{35} +(-0.435377 + 2.96824i) q^{36} +(-6.47766 - 1.73568i) q^{37} +(-3.96141 + 3.96141i) q^{38} +(-3.82258 - 4.42417i) q^{39} +(2.14505 - 0.631463i) q^{40} +(-0.832022 - 0.480368i) q^{41} +(3.92714 + 2.36168i) q^{42} +(-0.841255 + 3.13961i) q^{43} +(-2.26793 - 3.92817i) q^{44} +(6.17224 - 2.62745i) q^{45} +(-2.70954 + 4.69306i) q^{46} +(-1.09611 + 0.293702i) q^{47} +(1.72746 + 0.126017i) q^{48} +(5.64141 - 4.14422i) q^{49} +(-3.70442 - 3.35816i) q^{50} +(7.86729 + 9.10543i) q^{51} +(-2.38696 + 2.38696i) q^{52} +(-0.424048 - 1.58257i) q^{53} +(5.19127 - 0.225127i) q^{54} +(-4.85460 + 8.90523i) q^{55} +(1.19494 - 2.36053i) q^{56} +(8.02816 + 5.45026i) q^{57} +(6.46648 + 6.46648i) q^{58} +(-4.00955 - 6.94474i) q^{59} +(-1.77220 - 3.44373i) q^{60} +(2.09403 - 3.62696i) q^{61} +(1.24487 + 1.24487i) q^{62} +(2.73993 - 7.44935i) q^{63} -1.00000i q^{64} +(7.33668 + 1.77447i) q^{65} +(-5.94473 + 5.13637i) q^{66} +(-9.25042 - 2.47864i) q^{67} +(4.91262 - 4.91262i) q^{68} +(8.86552 + 3.08249i) q^{69} +(-5.89740 + 0.469734i) q^{70} +12.8302i q^{71} +(-0.347695 - 2.97978i) q^{72} +(8.08951 - 2.16758i) q^{73} +6.70617 q^{74} +(-4.50762 + 7.39469i) q^{75} +(2.80114 - 4.85172i) q^{76} +(3.73843 + 11.4036i) q^{77} +(4.83738 + 3.28406i) q^{78} +(-5.30665 - 3.06379i) q^{79} +(-1.90853 + 1.16513i) q^{80} +(-2.07211 - 8.75822i) q^{81} +(0.928000 + 0.248657i) q^{82} +(-5.33571 - 1.42970i) q^{83} +(-4.40458 - 1.26479i) q^{84} +(-15.0997 - 3.65205i) q^{85} -3.25036i q^{86} +(8.89682 - 13.1049i) q^{87} +(3.20734 + 3.20734i) q^{88} +(-7.21440 - 12.4957i) q^{89} +(-5.28189 + 4.13541i) q^{90} +(7.47750 - 4.88394i) q^{91} +(1.40256 - 5.23443i) q^{92} +(1.71273 - 2.52284i) q^{93} +(0.982746 - 0.567388i) q^{94} +(-12.5233 + 0.306812i) q^{95} +(-1.70121 + 0.325377i) q^{96} +(12.0791 + 3.23659i) q^{97} +(-4.37658 + 5.46311i) q^{98} +(10.6723 + 8.44200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

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Database

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