LMFDB - Embedded newform 819.2.ew.a.176.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(176,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 11]))

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

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

chi := DirichletCharacter("819.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ew (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			176.2
Character	$\chi$	$=$	819.176
Dual form			819.2.ew.a.470.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91264 + 1.91264i) q^{2} +(-1.50144 + 0.863523i) q^{3} -5.31637i q^{4} +(0.990693 + 3.69732i) q^{5} +(1.22011 - 4.52332i) q^{6} +(0.258819 + 0.965926i) q^{7} +(6.34303 + 6.34303i) q^{8} +(1.50865 - 2.59306i) q^{9} +O(q^{10})$	\(q+(-1.91264 + 1.91264i) q^{2} +(-1.50144 + 0.863523i) q^{3} -5.31637i q^{4} +(0.990693 + 3.69732i) q^{5} +(1.22011 - 4.52332i) q^{6} +(0.258819 + 0.965926i) q^{7} +(6.34303 + 6.34303i) q^{8} +(1.50865 - 2.59306i) q^{9} +(-8.96647 - 5.17679i) q^{10} +(-0.392511 - 0.392511i) q^{11} +(4.59081 + 7.98223i) q^{12} +(3.10509 - 1.83260i) q^{13} +(-2.34249 - 1.35244i) q^{14} +(-4.68019 - 4.69582i) q^{15} -13.6311 q^{16} +(1.77559 + 3.07541i) q^{17} +(2.07408 + 7.84510i) q^{18} +(-1.43848 + 5.36849i) q^{19} +(19.6563 - 5.26689i) q^{20} +(-1.22270 - 1.22679i) q^{21} +1.50146 q^{22} +(0.405742 + 0.702766i) q^{23} +(-15.0010 - 4.04633i) q^{24} +(-8.35855 + 4.82581i) q^{25} +(-2.43383 + 9.44401i) q^{26} +(-0.0259896 + 5.19609i) q^{27} +(5.13522 - 1.37598i) q^{28} +9.85608i q^{29} +(17.9329 + 0.0298985i) q^{30} +(3.81667 - 1.02267i) q^{31} +(13.3853 - 13.3853i) q^{32} +(0.928275 + 0.250390i) q^{33} +(-9.27821 - 2.48609i) q^{34} +(-3.31492 + 1.91387i) q^{35} +(-13.7857 - 8.02057i) q^{36} +(1.22662 + 4.57779i) q^{37} +(-7.51668 - 13.0193i) q^{38} +(-3.07963 + 5.43285i) q^{39} +(-17.1682 + 29.7362i) q^{40} +(-6.56950 - 1.76029i) q^{41} +(4.68498 + 0.00781100i) q^{42} +(-0.371870 - 0.214699i) q^{43} +(-2.08673 + 2.08673i) q^{44} +(11.0820 + 3.00905i) q^{45} +(-2.12018 - 0.568099i) q^{46} +(2.80600 - 10.4721i) q^{47} +(20.4663 - 11.7708i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(6.75685 - 25.2169i) q^{50} +(-5.32163 - 3.08429i) q^{51} +(-9.74276 - 16.5078i) q^{52} +5.57558i q^{53} +(-9.88853 - 9.98795i) q^{54} +(1.06238 - 1.84009i) q^{55} +(-4.48520 + 7.76859i) q^{56} +(-2.47602 - 9.30263i) q^{57} +(-18.8511 - 18.8511i) q^{58} +(0.279881 + 0.279881i) q^{59} +(-24.9647 + 24.8816i) q^{60} +(-1.72981 + 2.99612i) q^{61} +(-5.34390 + 9.25591i) q^{62} +(2.89517 + 0.786115i) q^{63} +23.9403i q^{64} +(9.85188 + 9.66497i) q^{65} +(-2.25436 + 1.29655i) q^{66} +(2.14711 - 8.01313i) q^{67} +(16.3500 - 9.43969i) q^{68} +(-1.21605 - 0.704794i) q^{69} +(2.67971 - 10.0008i) q^{70} +(-15.0987 - 4.04568i) q^{71} +(26.0173 - 6.87841i) q^{72} +(1.85661 - 1.85661i) q^{73} +(-11.1017 - 6.40959i) q^{74} +(8.38267 - 14.4635i) q^{75} +(28.5409 + 7.64751i) q^{76} +(0.277547 - 0.480726i) q^{77} +(-4.50088 - 16.2813i) q^{78} +(1.53536 + 2.65931i) q^{79} +(-13.5042 - 50.3984i) q^{80} +(-4.44792 - 7.82407i) q^{81} +(15.9319 - 9.19827i) q^{82} +(7.42707 + 1.99008i) q^{83} +(-6.52205 + 6.50034i) q^{84} +(-9.61170 + 9.61170i) q^{85} +(1.12189 - 0.300611i) q^{86} +(-8.51096 - 14.7983i) q^{87} -4.97941i q^{88} +(16.0942 - 4.31242i) q^{89} +(-26.9510 + 15.4406i) q^{90} +(2.57381 + 2.52498i) q^{91} +(3.73617 - 2.15708i) q^{92} +(-4.84740 + 4.83127i) q^{93} +(14.6625 + 25.3963i) q^{94} -21.2741 q^{95} +(-8.53873 + 31.6558i) q^{96} +(13.1512 - 3.52386i) q^{97} +(0.700074 - 2.61271i) q^{98} +(-1.60997 + 0.425641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) $ 336 * q + 24 * q^6 - 36 * q^8	$ 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) $ 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.91264	+	1.91264i	−1.35244	+	1.35244i	−0.469516	+	0.882924i	$0.655571\pi$
$2$	−1.91264	+	1.91264i	−1.35244	+	1.35244i	−0.882924	+	0.469516i	$0.844429\pi$
$3$	−1.50144	+	0.863523i	−0.866858	+	0.498555i
$3$	−1.50144	+	0.863523i	−0.866858	+	0.498555i
$4$		−	5.31637i		−	2.65819i
$5$	0.990693	+	3.69732i	0.443051	+	1.65349i	0.721031	+	0.692903i	$0.243669\pi$
$5$	0.990693	+	3.69732i	0.443051	+	1.65349i	−0.277979	+	0.960587i	$0.589665\pi$
$6$	1.22011	−	4.52332i	0.498107	−	1.84664i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	6.34303	+	6.34303i	2.24260	+	2.24260i
$9$	1.50865	−	2.59306i	0.502885	−	0.864353i
$10$	−8.96647	−	5.17679i	−2.83545	−	1.63705i
$11$	−0.392511	−	0.392511i	−0.118346	−	0.118346i	0.645453	−	0.763800i	$-0.276669\pi$
$11$	−0.392511	−	0.392511i	−0.118346	−	0.118346i	−0.763800	+	0.645453i	$0.776669\pi$
$12$	4.59081	+	7.98223i	1.32525	+	2.30427i
$13$	3.10509	−	1.83260i	0.861197	−	0.508271i
$13$	3.10509	−	1.83260i	0.861197	−	0.508271i
$14$	−2.34249	−	1.35244i	−0.626058	−	0.361455i
$15$	−4.68019	−	4.69582i	−1.20842	−	1.21246i
$16$	−13.6311			−3.40777
$17$	1.77559	+	3.07541i	0.430643	+	0.745896i	0.996929	−	0.0783129i	$-0.0249533\pi$
$17$	1.77559	+	3.07541i	0.430643	+	0.745896i	−0.566285	+	0.824209i	$0.691620\pi$
$18$	2.07408	+	7.84510i	0.488864	+	1.84911i
$19$	−1.43848	+	5.36849i	−0.330010	+	1.23162i	0.579168	+	0.815208i	$0.303378\pi$
$19$	−1.43848	+	5.36849i	−0.330010	+	1.23162i	−0.909178	+	0.416407i	$0.863289\pi$
$20$	19.6563	−	5.26689i	4.39529	−	1.17771i
$21$	−1.22270	−	1.22679i	−0.266815	−	0.267706i
$22$	1.50146			0.320113
$23$	0.405742	+	0.702766i	0.0846031	+	0.146537i	0.905222	−	0.424939i	$-0.139704\pi$
$23$	0.405742	+	0.702766i	0.0846031	+	0.146537i	−0.820619	+	0.571476i	$0.806371\pi$
$24$	−15.0010	−	4.04633i	−3.06207	−	0.825954i
$25$	−8.35855	+	4.82581i	−1.67171	+	0.965162i
$26$	−2.43383	+	9.44401i	−0.477313	+	1.85212i
$27$	−0.0259896	+	5.19609i	−0.00500170	+	0.999987i
$28$	5.13522	−	1.37598i	0.970466	−	0.260036i
$29$			9.85608i			1.83023i	0.403194	+	0.915114i	$0.367900\pi$
$29$			9.85608i			1.83023i	−0.403194	+	0.915114i	$0.632100\pi$
$30$	17.9329	+	0.0298985i	3.27409	+	0.00545869i
$31$	3.81667	−	1.02267i	0.685494	−	0.183677i	0.100770	−	0.994910i	$-0.467869\pi$
$31$	3.81667	−	1.02267i	0.685494	−	0.183677i	0.584724	+	0.811232i	$0.301203\pi$
$32$	13.3853	−	13.3853i	2.36621	−	2.36621i
$33$	0.928275	+	0.250390i	0.161592	+	0.0435873i
$34$	−9.27821	−	2.48609i	−1.59120	−	0.426361i
$35$	−3.31492	+	1.91387i	−0.560324	+	0.323503i
$36$	−13.7857	−	8.02057i	−2.29761	−	1.33676i
$37$	1.22662	+	4.57779i	0.201654	+	0.752585i	0.990443	+	0.137920i	$0.0440418\pi$
$37$	1.22662	+	4.57779i	0.201654	+	0.752585i	−0.788789	+	0.614664i	$0.789292\pi$
$38$	−7.51668	−	13.0193i	−1.21937	−	2.11200i
$39$	−3.07963	+	5.43285i	−0.493135	+	0.869953i
$40$	−17.1682	+	29.7362i	−2.71453	+	4.70170i
$41$	−6.56950	−	1.76029i	−1.02598	−	0.274911i	−0.293690	−	0.955901i	$-0.594883\pi$
$41$	−6.56950	−	1.76029i	−1.02598	−	0.274911i	−0.732293	+	0.680989i	$0.761550\pi$
$42$	4.68498	+	0.00781100i	0.722909	+	0.00120526i
$43$	−0.371870	−	0.214699i	−0.0567096	−	0.0327413i	0.471377	−	0.881932i	$-0.343757\pi$
$43$	−0.371870	−	0.214699i	−0.0567096	−	0.0327413i	−0.528087	+	0.849190i	$0.677090\pi$
$44$	−2.08673	+	2.08673i	−0.314587	+	0.314587i
$45$	11.0820	+	3.00905i	1.65200	+	0.448562i
$46$	−2.12018	−	0.568099i	−0.312603	−	0.0837617i
$47$	2.80600	−	10.4721i	0.409297	−	1.52752i	−0.386693	−	0.922208i	$-0.626383\pi$
$47$	2.80600	−	10.4721i	0.409297	−	1.52752i	0.795991	−	0.605309i	$-0.206950\pi$
$48$	20.4663	−	11.7708i	2.95405	−	1.69896i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	6.75685	−	25.2169i	0.955563	−	3.56621i
$51$	−5.32163	−	3.08429i	−0.745177	−	0.431886i
$52$	−9.74276	−	16.5078i	−1.35108	−	2.28922i
$53$			5.57558i			0.765865i	0.923776	+	0.382933i	$0.125086\pi$
$53$			5.57558i			0.765865i	−0.923776	+	0.382933i	$0.874914\pi$
$54$	−9.88853	−	9.98795i	−1.34566	−	1.35919i
$55$	1.06238	−	1.84009i	0.143251	−	0.248118i
$56$	−4.48520	+	7.76859i	−0.599360	+	1.03812i
$57$	−2.47602	−	9.30263i	−0.327956	−	1.23216i
$58$	−18.8511	−	18.8511i	−2.47527	−	2.47527i
$59$	0.279881	+	0.279881i	0.0364375	+	0.0364375i	0.725091	−	0.688653i	$-0.241798\pi$
$59$	0.279881	+	0.279881i	0.0364375	+	0.0364375i	−0.688653	+	0.725091i	$0.741798\pi$
$60$	−24.9647	+	24.8816i	−3.22293	+	3.21220i
$61$	−1.72981	+	2.99612i	−0.221479	+	0.383614i	−0.955257	−	0.295776i	$-0.904422\pi$
$61$	−1.72981	+	2.99612i	−0.221479	+	0.383614i	0.733778	+	0.679389i	$0.237755\pi$
$62$	−5.34390	+	9.25591i	−0.678676	+	1.17550i
$63$	2.89517	+	0.786115i	0.364757	+	0.0990412i
$64$			23.9403i			2.99254i
$65$	9.85188	+	9.66497i	1.22197	+	1.19879i
$66$	−2.25436	+	1.29655i	−0.277492	+	0.159594i
$67$	2.14711	−	8.01313i	0.262311	−	0.978960i	−0.701564	−	0.712606i	$-0.747515\pi$
$67$	2.14711	−	8.01313i	0.262311	−	0.978960i	0.963875	−	0.266353i	$-0.0858188\pi$
$68$	16.3500	−	9.43969i	1.98273	−	1.14473i
$69$	−1.21605	−	0.704794i	−0.146396	−	0.0848473i
$70$	2.67971	−	10.0008i	0.320286	−	1.19532i
$71$	−15.0987	−	4.04568i	−1.79188	−	0.480134i	−0.799219	−	0.601040i	$-0.794753\pi$
$71$	−15.0987	−	4.04568i	−1.79188	−	0.480134i	−0.992664	+	0.120907i	$0.961420\pi$
$72$	26.0173	−	6.87841i	3.06617	−	0.810628i
$73$	1.85661	−	1.85661i	0.217300	−	0.217300i	−0.590060	−	0.807360i	$-0.700896\pi$
$73$	1.85661	−	1.85661i	0.217300	−	0.217300i	0.807360	+	0.590060i	$0.200896\pi$
$74$	−11.1017	−	6.40959i	−1.29055	−	0.745100i
$75$	8.38267	−	14.4635i	0.967948	−	1.67010i
$76$	28.5409	+	7.64751i	3.27386	+	0.877229i
$77$	0.277547	−	0.480726i	0.0316294	−	0.0547838i
$78$	−4.50088	−	16.2813i	−0.509624	−	1.84349i
$79$	1.53536	+	2.65931i	0.172741	+	0.299196i	0.939377	−	0.342886i	$-0.111404\pi$
$79$	1.53536	+	2.65931i	0.172741	+	0.299196i	−0.766636	+	0.642082i	$0.778071\pi$
$80$	−13.5042	−	50.3984i	−1.50982	−	5.63472i
$81$	−4.44792	−	7.82407i	−0.494213	−	0.869341i
$82$	15.9319	−	9.19827i	1.75938	−	1.01578i
$83$	7.42707	+	1.99008i	0.815227	+	0.218439i	0.642258	−	0.766488i	$-0.277998\pi$
$83$	7.42707	+	1.99008i	0.815227	+	0.218439i	0.172968	+	0.984927i	$0.444664\pi$
$84$	−6.52205	+	6.50034i	−0.711614	+	0.709245i
$85$	−9.61170	+	9.61170i	−1.04254	+	1.04254i
$86$	1.12189	−	0.300611i	0.120977	−	0.0324157i
$87$	−8.51096	−	14.7983i	−0.912471	−	1.58655i
$88$		−	4.97941i		−	0.530807i
$89$	16.0942	−	4.31242i	1.70598	−	0.457115i	0.731544	−	0.681794i	$-0.238800\pi$
$89$	16.0942	−	4.31242i	1.70598	−	0.457115i	0.974433	+	0.224679i	$0.0721333\pi$
$90$	−26.9510	+	15.4406i	−2.84089	+	1.62758i
$91$	2.57381	+	2.52498i	0.269808	+	0.264690i
$92$	3.73617	−	2.15708i	0.389522	−	0.224891i
$93$	−4.84740	+	4.83127i	−0.502652	+	0.500979i
$94$	14.6625	+	25.3963i	1.51233	+	2.61943i
$95$	−21.2741			−2.18268
$96$	−8.53873	+	31.6558i	−0.871480	+	3.23085i
$97$	13.1512	−	3.52386i	1.33531	−	0.357794i	0.480615	−	0.876931i	$-0.340413\pi$
$97$	13.1512	−	3.52386i	1.33531	−	0.357794i	0.854691	+	0.519137i	$0.173747\pi$
$98$	0.700074	−	2.61271i	0.0707182	−	0.263924i
$99$	−1.60997	+	0.425641i	−0.161808	+	0.0427785i
$100$	25.6558	+	44.4372i	2.56558	+	4.44372i
$101$	−7.19410			−0.715840			−0.357920	−	0.933752i	$-0.616514\pi$
$101$	−7.19410			−0.715840			−0.357920	+	0.933752i	$0.616514\pi$
$102$	16.0775	−	4.27923i	1.59191	−	0.423707i
$103$	−3.55432	−	2.05209i	−0.350217	−	0.202198i	0.314564	−	0.949236i	$-0.398142\pi$
$103$	−3.55432	−	2.05209i	−0.350217	−	0.202198i	−0.664781	+	0.747038i	$0.731475\pi$
$104$	31.3199	+	8.07148i	3.07117	+	0.791473i
$105$	3.32449	−	5.73608i	0.324437	−	0.559784i
$106$	−10.6641	−	10.6641i	−1.03579	−	1.03579i
$107$	−7.06833	−	4.08090i	−0.683321	−	0.394516i	0.117784	−	0.993039i	$-0.462421\pi$
$107$	−7.06833	−	4.08090i	−0.683321	−	0.394516i	−0.801105	+	0.598524i	$0.795754\pi$
$108$	27.6243	+	0.138170i	2.65815	+	0.0132954i
$109$	0.156272	+	0.156272i	0.0149682	+	0.0149682i	0.714551	−	0.699583i	$-0.246631\pi$
$109$	0.156272	+	0.156272i	0.0149682	+	0.0149682i	−0.699583	+	0.714551i	$0.746631\pi$
$110$	1.48749	+	5.55138i	0.141826	+	0.529304i
$111$	−5.79472	−	5.81408i	−0.550011	−	0.551848i
$112$	−3.52798	−	13.1666i	−0.333363	−	1.24413i
$113$			12.3450i			1.16132i	0.814147	+	0.580659i	$0.197205\pi$
$113$			12.3450i			1.16132i	−0.814147	+	0.580659i	$0.802795\pi$
$114$	22.5283	+	13.0568i	2.10997	+	1.22289i
$115$	−2.19638	+	2.19638i	−0.204814	+	0.204814i
$116$	52.3986			4.86509
$117$	−0.0675181	−	10.8164i	−0.00624205	−	0.999981i
$118$	−1.07062			−0.0985590
$119$	−2.51106	+	2.51106i	−0.230189	+	0.230189i
$120$	0.0991546	−	59.4722i	0.00905153	−	5.42905i
$121$		−	10.6919i		−	0.971988i
$122$	−2.42199	−	9.03899i	−0.219277	−	0.818352i
$123$	11.3838	−	3.02994i	1.02644	−	0.273200i
$124$	−5.43691	−	20.2908i	−0.488249	−	1.82217i
$125$	−12.5902	−	12.5902i	−1.12610	−	1.12610i
$126$	−7.04097	+	4.03386i	−0.627260	+	0.359365i
$127$	−1.55831	−	0.899689i	−0.138277	−	0.0798345i	0.429265	−	0.903178i	$-0.358773\pi$
$127$	−1.55831	−	0.899689i	−0.138277	−	0.0798345i	−0.567543	+	0.823344i	$0.692106\pi$
$128$	−19.0185	−	19.0185i	−1.68102	−	1.68102i
$129$	0.743739	+	0.00123999i	0.0654825	+	0.000109175i
$130$	−37.3287	+	0.357492i	−3.27394	+	0.0313541i
$131$	−11.8957	−	6.86797i	−1.03933	−	0.600057i	−0.119686	−	0.992812i	$-0.538189\pi$
$131$	−11.8957	−	6.86797i	−1.03933	−	0.600057i	−0.919643	+	0.392755i	$0.871522\pi$
$132$	1.33117	−	4.93505i	0.115863	−	0.429541i
$133$	−5.55787			−0.481928
$134$	11.2196	+	19.4329i	0.969224	+	1.67874i
$135$	−19.2373	+	5.05164i	−1.65569	+	0.434776i
$136$	−8.24480	+	30.7700i	−0.706986	+	2.63851i
$137$	5.33338	−	1.42908i	0.455662	−	0.122094i	−0.0236856	−	0.999719i	$-0.507540\pi$
$137$	5.33338	−	1.42908i	0.455662	−	0.122094i	0.479347	+	0.877625i	$0.340873\pi$
$138$	3.67389	−	0.977853i	0.312742	−	0.0832404i
$139$	−6.21072			−0.526786			−0.263393	−	0.964689i	$-0.584842\pi$
$139$	−6.21072			−0.526786			−0.263393	+	0.964689i	$0.584842\pi$
$140$	10.1749	+	17.6234i	0.859932	+	1.48945i
$141$	4.82989	+	18.1463i	0.406750	+	1.52820i
$142$	36.6162	−	21.1404i	3.07277	−	1.77406i
$143$	−1.93810	−	0.499469i	−0.162072	−	0.0417677i
$144$	−20.5646	+	35.3462i	−1.71372	+	2.94552i
$145$	−36.4411	+	9.76435i	−3.02627	+	0.810885i
$146$			7.10204i			0.587769i
$147$	0.868525	−	1.49855i	0.0716347	−	0.123599i
$148$	24.3373	−	6.52115i	2.00051	−	0.536035i
$149$	−3.54431	+	3.54431i	−0.290361	+	0.290361i	−0.837223	−	0.546862i	$-0.815822\pi$
$149$	−3.54431	+	3.54431i	−0.290361	+	0.290361i	0.546862	+	0.837223i	$0.315822\pi$
$150$	11.6304	+	43.6964i	0.949616	+	3.56780i
$151$	−1.30863	−	0.350648i	−0.106495	−	0.0285353i	0.205178	−	0.978725i	$-0.434223\pi$
$151$	−1.30863	−	0.350648i	−0.106495	−	0.0285353i	−0.311673	+	0.950189i	$0.600889\pi$
$152$	−43.1768	+	24.9281i	−3.50210	+	2.02194i
$153$	10.6535	+	0.0355239i	0.861282	+	0.00287194i
$154$	0.388607	+	1.45030i	0.0313149	+	0.116869i
$155$	7.56229	+	13.0983i	0.607418	+	1.05208i
$156$	28.8831	+	16.3724i	2.31250	+	1.31084i
$157$	−10.2809	+	17.8071i	−0.820508	+	1.42116i	0.0847960	+	0.996398i	$0.472976\pi$
$157$	−10.2809	+	17.8071i	−0.820508	+	1.42116i	−0.905304	+	0.424764i	$0.860357\pi$
$158$	−8.02289	−	2.14973i	−0.638267	−	0.171023i
$159$	−4.81465	−	8.37142i	−0.381826	−	0.663896i
$160$	62.7504	+	36.2289i	4.96085	+	2.86415i
$161$	−0.573806	+	0.573806i	−0.0452223	+	0.0452223i
$162$	23.4719	+	6.45734i	1.84412	+	0.507337i
$163$	−7.20903	−	1.93165i	−0.564655	−	0.151299i	−0.0348109	−	0.999394i	$-0.511083\pi$
$163$	−7.20903	−	1.93165i	−0.564655	−	0.151299i	−0.529844	+	0.848095i	$0.677750\pi$
$164$	−9.35837	+	34.9259i	−0.730766	+	2.72726i
$165$	−0.00613575	+	3.68018i	−0.000477668	+	0.286502i
$166$	−18.0116	+	10.3990i	−1.39797	+	0.807119i
$167$	0.421605	−	1.57345i	0.0326248	−	0.121757i	−0.947693	−	0.319183i	$-0.896591\pi$
$167$	0.421605	−	1.57345i	0.0326248	−	0.121757i	0.980318	+	0.197426i	$0.0632581\pi$
$168$	0.0259042	−	15.5372i	0.00199855	−	1.19872i
$169$	6.28319	−	11.3808i	0.483322	−	0.875443i
$170$		−	36.7674i		−	2.81993i
$171$	11.7506	+	11.8293i	0.898594	+	0.904606i
$172$	−1.14142	+	1.97700i	−0.0870325	+	0.150745i
$173$	2.90382	−	5.02956i	0.220773	−	0.382390i	−0.734270	−	0.678858i	$-0.762475\pi$
$173$	2.90382	−	5.02956i	0.220773	−	0.382390i	0.955043	+	0.296468i	$0.0958087\pi$
$174$	44.5823	+	12.0255i	3.37977	+	0.911649i
$175$	−6.82473	−	6.82473i	−0.515901	−	0.515901i
$176$	5.35035	+	5.35035i	0.403298	+	0.403298i
$177$	−0.661910	−	0.178542i	−0.0497522	−	0.0134200i
$178$	−22.5342	+	39.0304i	−1.68901	+	2.92545i
$179$	−5.12276	+	8.87289i	−0.382893	+	0.663191i	−0.991474	−	0.130301i	$-0.958406\pi$
$179$	−5.12276	+	8.87289i	−0.382893	+	0.663191i	0.608581	+	0.793492i	$0.291739\pi$
$180$	15.9972	−	58.9159i	1.19236	−	4.39133i
$181$		−	11.5129i		−	0.855747i	−0.903839	−	0.427873i	$-0.859263\pi$
$181$		−	11.5129i		−	0.855747i	0.903839	−	0.427873i	$-0.140737\pi$
$182$	−9.75214	+	0.0933949i	−0.722876	+	0.00692289i
$183$	0.00999049	−	5.99223i	0.000738518	−	0.442958i
$184$	−1.88403	+	7.03130i	−0.138893	+	0.518354i
$185$	−15.7103	+	9.07037i	−1.15505	+	0.666867i
$186$	0.0308636	−	18.5118i	0.00226303	−	1.35735i
$187$	0.510194	−	1.90407i	0.0373091	−	0.139239i
$188$	−55.6738	−	14.9177i	−4.06043	−	1.08799i
$189$	−5.02576	+	1.31974i	−0.365570	+	0.0959971i
$190$	40.6896	−	40.6896i	2.95194	−	2.95194i
$191$	3.39366	+	1.95933i	0.245557	+	0.141772i	0.617728	−	0.786392i	$-0.288053\pi$
$191$	3.39366	+	1.95933i	0.245557	+	0.141772i	−0.372171	+	0.928164i	$0.621387\pi$
$192$	−20.6730	−	35.9449i	−1.49195	−	2.59410i
$193$	−7.62924	−	2.04425i	−0.549165	−	0.147148i	−0.0264410	−	0.999650i	$-0.508417\pi$
$193$	−7.62924	−	2.04425i	−0.549165	−	0.147148i	−0.522724	+	0.852502i	$0.675084\pi$
$194$	−18.4137	+	31.8935i	−1.32203	+	2.28982i
$195$	−23.1379	−	6.00406i	−1.65694	−	0.429960i
$196$	2.65819	+	4.60412i	0.189871	+	0.328865i
$197$	6.84913	+	25.5613i	0.487980	+	1.82117i	0.566248	+	0.824235i	$0.308394\pi$
$197$	6.84913	+	25.5613i	0.487980	+	1.82117i	−0.0782683	+	0.996932i	$0.524939\pi$
$198$	2.26519	−	3.89338i	0.160980	−	0.276691i
$199$	−3.74368	+	2.16141i	−0.265382	+	0.153219i	−0.626787	−	0.779190i	$-0.715631\pi$
$199$	−3.74368	+	2.16141i	−0.265382	+	0.153219i	0.361405	+	0.932409i	$0.382297\pi$
$200$	−83.6287	−	22.4082i	−5.91344	−	1.58450i
$201$	3.69576	+	13.8853i	0.260679	+	0.979396i
$202$	13.7597	−	13.7597i	0.968130	−	0.968130i
$203$	−9.52025	+	2.55094i	−0.668190	+	0.179041i
$204$	−16.3972	+	28.2918i	−1.14804	+	1.98082i
$205$		−	26.0334i		−	1.81825i
$206$	10.7230	−	2.87322i	0.747108	−	0.200187i
$207$	2.43444	+	0.00811762i	0.169205	+	0.000564213i
$208$	−42.3258	+	24.9803i	−2.93476	+	1.73207i
$209$	2.67181	−	1.54257i	0.184813	−	0.106702i
$210$	4.61250	+	17.3296i	0.318293	+	1.19586i
$211$	−8.87088	−	15.3648i	−0.610697	−	1.05776i	−0.991123	−	0.132947i	$-0.957556\pi$
$211$	−8.87088	−	15.3648i	−0.610697	−	1.05776i	0.380426	−	0.924811i	$-0.375777\pi$
$212$	29.6419			2.03581
$213$	26.1633	−	6.96371i	1.79268	−	0.477145i
$214$	21.3245	−	5.71387i	1.45771	−	0.390592i
$215$	0.425402	−	1.58762i	0.0290122	−	0.108275i
$216$	−33.1238	+	32.7941i	−2.25379	+	2.23135i
$217$	1.97565	+	3.42193i	0.134116	+	0.232296i
$218$	−0.597785			−0.0404871
$219$	−1.18437	+	4.39082i	−0.0800320	+	0.296704i
$220$	−9.78263	−	5.64800i	−0.659545	−	0.380788i
$221$	11.1493	+	6.29549i	0.749986	+	0.423481i
$222$	22.2034	+	0.0370185i	1.49020	+	0.00248452i
$223$	8.16814	+	8.16814i	0.546979	+	0.546979i	0.925566	−	0.378587i	$-0.123590\pi$
$223$	8.16814	+	8.16814i	0.546979	+	0.546979i	−0.378587	+	0.925566i	$0.623590\pi$
$224$	16.3936	+	9.46483i	1.09534	+	0.632396i
$225$	−0.0965492	+	28.9547i	−0.00643661	+	1.93031i
$226$	−23.6115	−	23.6115i	−1.57061	−	1.57061i
$227$	−0.695510	−	2.59568i	−0.0461626	−	0.172281i	0.938996	−	0.343928i	$-0.111758\pi$
$227$	−0.695510	−	2.59568i	−0.0461626	−	0.172281i	−0.985158	+	0.171647i	$0.945091\pi$
$228$	−49.4563	+	13.1634i	−3.27532	+	0.871770i
$229$	−5.26009	−	19.6309i	−0.347596	−	1.29725i	−0.889550	−	0.456839i	$-0.848982\pi$
$229$	−5.26009	−	19.6309i	−0.347596	−	1.29725i	0.541953	−	0.840409i	$-0.317685\pi$
$230$		−	8.40177i		−	0.553996i
$231$	−0.00160297	+	0.961450i	−0.000105468	+	0.0632588i
$232$	−62.5174	+	62.5174i	−4.10447	+	4.10447i
$233$	8.30662			0.544185			0.272092	−	0.962271i	$-0.412284\pi$
$233$	8.30662			0.544185			0.272092	+	0.962271i	$0.412284\pi$
$234$	20.8171	+	20.5588i	1.36086	+	1.34397i
$235$	41.4987			2.70707
$236$	1.48795	−	1.48795i	0.0968576	−	0.0968576i
$237$	−4.60163	−	2.66699i	−0.298908	−	0.173240i
$238$		−	9.60551i		−	0.622633i
$239$	2.05069	+	7.65327i	0.132648	+	0.495049i	0.999996	−	0.00265252i	$-0.000844323\pi$
$239$	2.05069	+	7.65327i	0.132648	+	0.495049i	−0.867349	+	0.497701i	$0.834178\pi$
$240$	63.7960	+	64.0091i	4.11802	+	4.13177i
$241$	0.741403	+	2.76695i	0.0477579	+	0.178235i	0.985685	−	0.168598i	$-0.0539238\pi$
$241$	0.741403	+	2.76695i	0.0477579	+	0.178235i	−0.937927	+	0.346833i	$0.887257\pi$
$242$	20.4497	+	20.4497i	1.31456	+	1.31456i
$243$	13.4346	+	7.90650i	0.861827	+	0.507202i
$244$	15.9285	+	9.19631i	1.01972	+	0.588734i
$245$	−2.70662	−	2.70662i	−0.172920	−	0.172920i
$246$	−15.9779	+	27.5682i	−1.01871	+	1.75769i
$247$	5.37165	+	19.3058i	0.341790	+	1.22840i
$248$	30.6961	+	17.7224i	1.94920	+	1.12537i
$249$	−12.8698	+	3.42546i	−0.815590	+	0.217080i
$250$	48.1609			3.04597
$251$	7.88859	+	13.6634i	0.497923	+	0.862428i	0.999997	−	0.00239633i	$-0.000762775\pi$
$251$	7.88859	+	13.6634i	0.497923	+	0.862428i	−0.502074	+	0.864825i	$0.667429\pi$
$252$	4.17928	−	15.3918i	0.263270	−	0.969593i
$253$	0.116585	−	0.435102i	0.00732964	−	0.0273546i
$254$	4.70126	−	1.25970i	0.294983	−	0.0790405i
$255$	6.13148	−	22.7313i	0.383968	−	1.42349i
$256$	24.8706			1.55441
$257$	−13.0007	−	22.5178i	−0.810959	−	1.40462i	−0.912193	−	0.409760i	$-0.865612\pi$
$257$	−13.0007	−	22.5178i	−0.810959	−	1.40462i	0.101234	−	0.994863i	$-0.467721\pi$
$258$	−1.42487	+	1.42013i	−0.0887088	+	0.0884135i
$259$	−4.10434	+	2.36964i	−0.255031	+	0.147242i
$260$	51.3826	−	52.3763i	3.18661	−	3.24824i
$261$	25.5574	+	14.8694i	1.58196	+	0.920395i
$262$	35.8881	−	9.61618i	2.21717	−	0.594089i
$263$			2.20690i			0.136083i	0.997682	+	0.0680415i	$0.0216750\pi$
$263$			2.20690i			0.136083i	−0.997682	+	0.0680415i	$0.978325\pi$
$264$	4.29984	+	7.47630i	0.264637	+	0.460134i
$265$	−20.6147	+	5.52369i	−1.26635	+	0.339318i
$266$	10.6302	−	10.6302i	0.651779	−	0.651779i
$267$	−20.4406	+	20.3725i	−1.25094	+	1.24678i
$268$	−42.6008	−	11.4148i	−2.60226	−	0.697273i
$269$	2.77780	−	1.60376i	0.169366	−	0.0977833i	−0.412921	−	0.910767i	$-0.635491\pi$
$269$	2.77780	−	1.60376i	0.169366	−	0.0977833i	0.582287	+	0.812984i	$0.302158\pi$
$270$	27.1321	−	46.4560i	1.65121	−	2.82722i
$271$	6.08749	+	22.7188i	0.369789	+	1.38007i	0.860811	+	0.508924i	$0.169957\pi$
$271$	6.08749	+	22.7188i	0.369789	+	1.38007i	−0.491023	+	0.871147i	$0.663377\pi$
$272$	−24.2032	−	41.9212i	−1.46753	−	2.54184i
$273$	−6.04480	−	1.56856i	−0.365848	−	0.0949338i
$274$	−7.46753	+	12.9341i	−0.451130	+	0.781380i
$275$	5.17500	+	1.38664i	0.312064	+	0.0836174i
$276$	−3.74695	+	6.46499i	−0.225540	+	0.389147i
$277$	8.48784	+	4.90046i	0.509985	+	0.294440i	0.732828	−	0.680414i	$-0.238200\pi$
$277$	8.48784	+	4.90046i	0.509985	+	0.294440i	−0.222842	+	0.974854i	$0.571534\pi$
$278$	11.8789	−	11.8789i	0.712446	−	0.712446i
$279$	3.10618	−	11.4397i	0.185962	−	0.684877i
$280$	−33.1664	−	8.88690i	−1.98207	−	0.531094i
$281$	0.837630	−	3.12608i	0.0499688	−	0.186486i	−0.936430	−	0.350853i	$-0.885892\pi$
$281$	0.837630	−	3.12608i	0.0499688	−	0.186486i	0.986399	+	0.164367i	$0.0525582\pi$
$282$	−43.9452	−	25.4696i	−2.61690	−	1.51669i
$283$	−16.8333	+	9.71870i	−1.00063	+	0.577717i	−0.908436	−	0.418024i	$-0.862723\pi$
$283$	−16.8333	+	9.71870i	−1.00063	+	0.577717i	−0.0921986	+	0.995741i	$0.529389\pi$
$284$	−21.5083	+	80.2702i	−1.27628	+	4.76316i
$285$	31.9418	−	18.3707i	1.89207	−	1.08818i
$286$	4.66218	−	2.75157i	0.275681	−	0.162704i
$287$		−	6.80124i		−	0.401465i
$288$	−14.5151	−	54.9027i	−0.855309	−	3.23517i
$289$	2.19457	−	3.80111i	0.129092	−	0.223595i
$290$	51.0229	−	88.3743i	2.99617	−	5.18952i
$291$	−16.7029	+	16.6473i	−0.979140	+	0.975881i
$292$	−9.87043	−	9.87043i	−0.577623	−	0.577623i
$293$	10.2364	+	10.2364i	0.598020	+	0.598020i	0.939785	−	0.341766i	$-0.111025\pi$
$293$	10.2364	+	10.2364i	0.598020	+	0.598020i	−0.341766	+	0.939785i	$0.611025\pi$
$294$	1.20502	+	4.52737i	0.0702781	+	0.264041i
$295$	−0.757534	+	1.31209i	−0.0441053	+	0.0763927i
$296$	−21.2566	+	36.8175i	−1.23552	+	2.13997i
$297$	2.04972	−	2.02932i	0.118937	−	0.117753i
$298$		−	13.5580i		−	0.785391i
$299$	2.54775	+	1.43859i	0.147340	+	0.0831959i
$300$	−76.8932	−	44.5654i	−4.43943	−	2.57299i
$301$	0.111136	−	0.414767i	0.00640580	−	0.0239068i
$302$	3.17361	−	1.83228i	0.182621	−	0.105436i
$303$	10.8015	−	6.21227i	0.620531	−	0.356886i
$304$	19.6081	−	73.1783i	1.12460	−	4.19706i
$305$	−12.7913	−	3.42742i	−0.732428	−	0.196253i
$306$	−20.4442	+	20.3083i	−1.16872	+	1.16095i
$307$	21.0507	−	21.0507i	1.20142	−	1.20142i	0.227691	−	0.973733i	$-0.426882\pi$
$307$	21.0507	−	21.0507i	1.20142	−	1.20142i	0.973733	−	0.227691i	$-0.0731178\pi$
$308$	−2.55572	−	1.47554i	−0.145626	−	0.0840769i
$309$	7.10862	+	0.0118518i	0.404395	+	0.000674225i
$310$	−39.5162	−	10.5883i	−2.24437	−	0.601377i
$311$	9.25420	−	16.0287i	0.524757	−	0.908906i	−0.474827	−	0.880079i	$-0.657489\pi$
$311$	9.25420	−	16.0287i	0.524757	−	0.908906i	0.999584	−	0.0288273i	$-0.00917727\pi$
$312$	−53.9949	+	14.9266i	−3.05686	+	0.845052i
$313$	−4.51029	−	7.81206i	−0.254937	−	0.441564i	0.709942	−	0.704261i	$-0.248721\pi$
$313$	−4.51029	−	7.81206i	−0.254937	−	0.441564i	−0.964878	+	0.262697i	$0.915388\pi$
$314$	−14.3948	−	53.7223i	−0.812348	−	3.03172i
$315$	−0.0382905	+	11.4832i	−0.00215743	+	0.647003i
$316$	14.1379	−	8.16253i	0.795320	−	0.459178i
$317$	14.5383	+	3.89554i	0.816555	+	0.218795i	0.642840	−	0.766001i	$-0.277756\pi$
$317$	14.5383	+	3.89554i	0.816555	+	0.218795i	0.173715	+	0.984796i	$0.444423\pi$
$318$	25.2202	+	6.80281i	1.41428	+	0.381483i
$319$	3.86862	−	3.86862i	0.216601	−	0.216601i
$320$	−88.5148	+	23.7175i	−4.94813	+	1.32585i
$321$	14.1366	+	0.0235692i	0.789030	+	0.00131550i
$322$		−	2.19497i		−	0.122321i
$323$	−19.0644	+	5.10830i	−1.06077	+	0.284234i
$324$	−41.5957	+	23.6468i	−2.31087	+	1.31371i
$325$	−17.1103	+	30.3024i	−0.949109	+	1.68088i
$326$	17.4828	−	10.0937i	0.968285	−	0.559039i
$327$	−0.369579	−	0.0996891i	−0.0204378	−	0.00551282i
$328$	−30.5049	−	52.8361i	−1.68435	−	2.91738i
$329$	10.8415			0.597714
$330$	−7.02713	−	7.05060i	−0.386831	−	0.388123i
$331$	13.3293	−	3.57156i	0.732642	−	0.196311i	0.126837	−	0.991924i	$-0.459518\pi$
$331$	13.3293	−	3.57156i	0.732642	−	0.196311i	0.605806	+	0.795613i	$0.292851\pi$
$332$	10.5800	−	39.4851i	0.580652	−	2.16702i
$333$	13.7210	+	3.72562i	0.751908	+	0.204163i
$334$	2.20307	+	3.81582i	0.120546	+	0.208793i
$335$	31.7542			1.73492
$336$	16.6667	+	16.7224i	0.909246	+	0.912282i
$337$	22.4580	+	12.9661i	1.22336	+	0.706309i	0.965633	−	0.259908i	$-0.0836924\pi$
$337$	22.4580	+	12.9661i	1.22336	+	0.706309i	0.257729	+	0.966217i	$0.417026\pi$
$338$	9.74980	+	33.7847i	0.530319	+	1.83765i
$339$	−10.6602	−	18.5353i	−0.578981	−	1.00670i
$340$	51.0994	+	51.0994i	2.77125	+	2.77125i
$341$	−1.89949	−	1.09667i	−0.102863	−	0.0593882i
$342$	−45.0998	−	0.150385i	−2.43872	−	0.00813189i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−0.996938	−	3.72062i	−0.0537513	−	0.200603i
$345$	1.40111	−	5.19437i	0.0754334	−	0.279655i
$346$	4.06577	+	15.1737i	0.218577	+	0.815742i
$347$		−	13.1280i		−	0.704750i	−0.935859	−	0.352375i	$-0.885374\pi$
$347$		−	13.1280i		−	0.704750i	0.935859	−	0.352375i	$-0.114626\pi$
$348$	−78.6735	+	45.2474i	−4.21734	+	2.42552i
$349$	2.95476	−	2.95476i	0.158165	−	0.158165i	−0.623588	−	0.781753i	$-0.714326\pi$
$349$	2.95476	−	2.95476i	0.158165	−	0.158165i	0.781753	+	0.623588i	$0.214326\pi$
$350$	26.1065			1.39545
$351$	9.44163	+	16.1820i	0.503957	+	0.863729i
$352$	−10.5077			−0.560065
$353$	−17.8291	+	17.8291i	−0.948949	+	0.948949i	−0.998759	−	0.0498093i	$-0.984139\pi$
$353$	−17.8291	+	17.8291i	−0.948949	+	0.948949i	0.0498093	+	0.998759i	$0.484139\pi$
$354$	1.60748	−	0.924509i	0.0854366	−	0.0491371i
$355$		−	59.8326i		−	3.17558i
$356$	−22.9264	−	85.5626i	−1.21510	−	4.53481i
$357$	1.60185	−	5.93857i	0.0847790	−	0.314303i
$358$	−7.17263	−	26.7686i	−0.379085	−	1.41477i
$359$	−19.1232	−	19.1232i	−1.00928	−	1.00928i	−0.999957	−	0.00932707i	$-0.997031\pi$
$359$	−19.1232	−	19.1232i	−1.00928	−	1.00928i	−0.00932707	−	0.999957i	$-0.502969\pi$
$360$	51.2068	+	89.3797i	2.69884	+	4.71073i
$361$	−10.2969	−	5.94494i	−0.541944	−	0.312891i
$362$	22.0200	+	22.0200i	1.15735	+	1.15735i
$363$	9.23268	+	16.0532i	0.484590	+	0.842576i
$364$	13.4237	−	13.6833i	0.703594	−	0.717201i
$365$	8.70380	+	5.02514i	0.455578	+	0.263028i
$366$	11.4419	+	11.4801i	0.598075	+	0.600073i
$367$	−15.8747			−0.828653			−0.414326	−	0.910128i	$-0.635983\pi$
$367$	−15.8747			−0.828653			−0.414326	+	0.910128i	$0.635983\pi$
$368$	−5.53071	−	9.57946i	−0.288308	−	0.499364i
$369$	−14.4756	+	14.3794i	−0.753572	+	0.748563i
$370$	12.6999	−	47.3966i	0.660235	−	2.46403i
$371$	−5.38560	+	1.44307i	−0.279606	+	0.0749203i
$372$	25.6848	+	25.7706i	1.33170	+	1.33614i
$373$	−19.3617			−1.00251			−0.501256	−	0.865299i	$-0.667129\pi$
$373$	−19.3617			−1.00251			−0.501256	+	0.865299i	$0.667129\pi$
$374$	2.66598	+	4.61761i	0.137855	+	0.238771i
$375$	29.7753	+	8.03151i	1.53759	+	0.414745i
$376$	84.2235	−	48.6265i	4.34350	−	2.50772i
$377$	18.0622	+	30.6040i	0.930251	+	1.57619i
$378$	7.08828	−	12.1367i	0.364582	−	0.624242i
$379$	13.6147	−	3.64804i	0.699339	−	0.187387i	0.108405	−	0.994107i	$-0.465426\pi$
$379$	13.6147	−	3.64804i	0.699339	−	0.187387i	0.590935	+	0.806720i	$0.298759\pi$
$380$			113.101i			5.80196i
$381$	3.11661	+	0.00519614i	0.159669	+	0.000266206i
$382$	−10.2383	+	2.74336i	−0.523839	+	0.140362i
$383$	−8.70178	+	8.70178i	−0.444640	+	0.444640i	−0.893568	−	0.448928i	$-0.851806\pi$
$383$	−8.70178	+	8.70178i	−0.444640	+	0.444640i	0.448928	+	0.893568i	$0.351806\pi$
$384$	44.9782	+	12.1323i	2.29528	+	0.619123i
$385$	2.05236	+	0.549928i	0.104598	+	0.0280269i
$386$	18.5019	−	10.6821i	0.941722	−	0.543703i
$387$	−1.11775	+	0.640374i	−0.0568185	+	0.0325520i
$388$	−18.7342	−	69.9169i	−0.951084	−	3.54949i
$389$	−11.2520	−	19.4890i	−0.570498	−	0.988132i	−0.996515	−	0.0834163i	$-0.973417\pi$
$389$	−11.2520	−	19.4890i	−0.570498	−	0.988132i	0.426017	−	0.904715i	$-0.359916\pi$
$390$	55.7381	−	32.7709i	2.82241	−	1.65942i
$391$	−1.44086	+	2.49565i	−0.0728675	+	0.126210i
$392$	−8.66473	−	2.32171i	−0.437635	−	0.117264i
$393$	23.7913	+	0.0396658i	1.20011	+	0.00200088i
$394$	−61.9894	−	35.7896i	−3.12298	−	1.80305i
$395$	−8.31126	+	8.31126i	−0.418185	+	0.418185i
$396$	2.26287	+	8.55919i	0.113713	+	0.430116i
$397$	36.1771	+	9.69364i	1.81568	+	0.486510i	0.996238	−	0.0866551i	$-0.0276178\pi$
$397$	36.1771	+	9.69364i	1.81568	+	0.486510i	0.819440	+	0.573165i	$0.194284\pi$
$398$	3.02630	−	11.2943i	0.151695	−	0.566132i
$399$	8.34481	−	4.79935i	0.417763	−	0.240268i
$400$	113.936	−	65.7810i	5.69680	−	3.28905i
$401$	−2.21167	+	8.25406i	−0.110445	+	0.412188i	−0.998906	−	0.0467651i	$-0.985109\pi$
$401$	−2.21167	+	8.25406i	−0.110445	+	0.412188i	0.888460	+	0.458953i	$0.151775\pi$
$402$	−33.6263	−	19.4890i	−1.67713	−	0.972021i
$403$	9.97696	−	10.1699i	0.496988	−	0.506599i
$404$			38.2465i			1.90284i
$405$	24.5215	−	24.1966i	1.21848	−	1.20234i
$406$	13.3298	−	23.0878i	0.661545	−	1.14583i
$407$	1.31537	−	2.27829i	0.0652006	−	0.112931i
$408$	−14.1915	−	53.3189i	−0.702586	−	2.63968i
$409$	13.5827	+	13.5827i	0.671619	+	0.671619i	0.958089	−	0.286470i	$-0.0924819\pi$
$409$	13.5827	+	13.5827i	0.671619	+	0.671619i	−0.286470	+	0.958089i	$0.592482\pi$
$410$	49.7925	+	49.7925i	2.45908	+	2.45908i
$411$	−6.77373	+	6.75118i	−0.334123	+	0.333011i
$412$	−10.9097	+	18.8961i	−0.537480	+	0.930943i
$413$	−0.197906	+	0.342783i	−0.00973832	+	0.0168673i
$414$	−4.67173	+	4.64068i	−0.229603	+	0.228077i
$415$			29.4318i			1.44475i
$416$	17.0327	−	66.0924i	0.835099	−	3.24045i
$417$	9.32503	−	5.36310i	0.456649	−	0.262632i
$418$	−2.15983	+	8.06058i	−0.105641	+	0.394256i
$419$	−16.0742	+	9.28043i	−0.785275	+	0.453379i	−0.838296	−	0.545215i	$-0.816448\pi$
$419$	−16.0742	+	9.28043i	−0.785275	+	0.453379i	0.0530215	+	0.998593i	$0.483115\pi$
$420$	−30.4951	−	17.6742i	−1.48801	−	0.862415i
$421$	−5.37751	+	20.0691i	−0.262084	+	0.978110i	0.701927	+	0.712249i	$0.252323\pi$
$421$	−5.37751	+	20.0691i	−0.262084	+	0.978110i	−0.964011	+	0.265862i	$0.914344\pi$
$422$	46.3542	+	12.4206i	2.25648	+	0.604623i
$423$	−22.9216	−	23.0750i	−1.11449	−	1.12194i
$424$	−35.3661	+	35.3661i	−1.71753	+	1.71753i
$425$	−29.6827	−	17.1373i	−1.43982	−	0.831281i
$426$	−36.7219	+	63.3600i	−1.77918	+	3.06980i
$427$	−3.34173	−	0.895415i	−0.161718	−	0.0433322i
$428$	−21.6956	+	37.5779i	−1.04870	+	1.81640i
$429$	3.34124	−	0.923668i	0.161317	−	0.0445951i
$430$	2.22291	+	3.85019i	0.107198	+	0.185672i
$431$	0.943206	+	3.52009i	0.0454327	+	0.169557i	0.984914	−	0.173042i	$-0.0553596\pi$
$431$	0.943206	+	3.52009i	0.0454327	+	0.169557i	−0.939482	+	0.342599i	$0.888693\pi$
$432$	0.354266	−	70.8283i	0.0170446	−	3.40773i
$433$	−13.9835	+	8.07336i	−0.672003	+	0.387981i	−0.796835	−	0.604197i	$-0.793494\pi$
$433$	−13.9835	+	8.07336i	−0.672003	+	0.387981i	0.124832	+	0.992178i	$0.460161\pi$
$434$	−10.3236	−	2.76621i	−0.495550	−	0.132782i
$435$	46.2824	−	46.1283i	2.21907	−	2.21168i
$436$	0.830803	−	0.830803i	0.0397882	−	0.0397882i
$437$	−4.35644	+	1.16731i	−0.208397	+	0.0558398i
$438$	−6.13278	−	10.6633i	−0.293036	−	0.509513i
$439$			16.0763i			0.767281i	0.923483	+	0.383640i	$0.125330\pi$
$439$			16.0763i			0.767281i	−0.923483	+	0.383640i	$0.874670\pi$
$440$	18.4105	−	4.93307i	0.877685	−	0.235175i
$441$	−0.0100034	+	2.99998i	−0.000476353	+	0.142856i
$442$	−33.3657	+	9.28367i	−1.58704	+	0.441579i
$443$	−14.8546	+	8.57633i	−0.705765	+	0.407474i	−0.809491	−	0.587132i	$-0.800257\pi$
$443$	−14.8546	+	8.57633i	−0.705765	+	0.407474i	0.103726	+	0.994606i	$0.466924\pi$
$444$	−30.9098	+	30.8069i	−1.46691	+	1.46203i
$445$	31.8887	+	55.2329i	1.51167	+	2.61829i
$446$	−31.2454			−1.47951
$447$	2.26098	−	8.38216i	0.106941	−	0.396462i
$448$	−23.1245	+	6.19620i	−1.09253	+	0.292743i
$449$	−4.62197	+	17.2494i	−0.218124	+	0.814051i	0.766919	+	0.641744i	$0.221789\pi$
$449$	−4.62197	+	17.2494i	−0.218124	+	0.814051i	−0.985043	+	0.172307i	$0.944878\pi$
$450$	−55.1952	−	55.5645i	−2.60193	−	2.61934i
$451$	1.88767	+	3.26953i	0.0888867	+	0.153956i
$452$	65.6305			3.08700
$453$	2.26763	−	0.603560i	0.106543	−	0.0283577i
$454$	6.29485	+	3.63434i	0.295432	+	0.170568i
$455$	−6.78579	+	12.0177i	−0.318123	+	0.563397i
$456$	43.3014	−	74.7123i	2.02777	−	3.49872i
$457$	−5.55211	−	5.55211i	−0.259717	−	0.259717i	0.565222	−	0.824939i	$-0.308790\pi$
$457$	−5.55211	−	5.55211i	−0.259717	−	0.259717i	−0.824939	+	0.565222i	$0.808790\pi$
$458$	47.6075	+	27.4862i	2.22455	+	1.28435i
$459$	−16.0262	+	9.14618i	−0.748041	+	0.426907i
$460$	11.6768	+	11.6768i	0.544433	+	0.544433i
$461$	4.02716	+	15.0296i	0.187564	+	0.699997i	0.994067	+	0.108768i	$0.0346904\pi$
$461$	4.02716	+	15.0296i	0.187564	+	0.699997i	−0.806504	+	0.591229i	$0.798643\pi$
$462$	−1.83584	−	1.84197i	−0.0854110	−	0.0856963i
$463$	0.586077	+	2.18727i	0.0272373	+	0.101651i	0.978206	−	0.207635i	$-0.0665766\pi$
$463$	0.586077	+	2.18727i	0.0272373	+	0.101651i	−0.950969	+	0.309286i	$0.899910\pi$
$464$		−	134.349i		−	6.23700i
$465$	−22.6650	−	13.1361i	−1.05106	−	0.609171i
$466$	−15.8876	+	15.8876i	−0.735977	+	0.735977i
$467$	−8.60575			−0.398226			−0.199113	−	0.979976i	$-0.563806\pi$
$467$	−8.60575			−0.398226			−0.199113	+	0.979976i	$0.563806\pi$
$468$	−57.5043	+	0.358952i	−2.65814	+	0.0165925i
$469$	8.29580			0.383065
$470$	−79.3720	+	79.3720i	−3.66116	+	3.66116i
$471$	0.0593774	−	35.6142i	0.00273597	−	1.64101i
$472$			3.55059i			0.163429i
$473$	0.0616912	+	0.230235i	0.00283656	+	0.0105862i
$474$	13.9022	−	3.70026i	0.638551	−	0.169959i
$475$	−13.8837	−	51.8146i	−0.637027	−	2.37742i
$476$	13.3497	+	13.3497i	0.611884	+	0.611884i
$477$	14.4578	+	8.41163i	0.661978	+	0.385142i
$478$	−18.5602	−	10.7157i	−0.848922	−	0.490125i
$479$	−17.3737	−	17.3737i	−0.793825	−	0.793825i	0.188288	−	0.982114i	$-0.439706\pi$
$479$	−17.3737	−	17.3737i	−0.793825	−	0.793825i	−0.982114	+	0.188288i	$0.939706\pi$
$480$	−125.501	−	0.209240i	−5.72829	−	0.00955044i
$481$	12.1980	+	11.9666i	0.556181	+	0.545629i
$482$	−6.71022	−	3.87415i	−0.305642	−	0.176462i
$483$	0.366041	−	1.35703i	0.0166555	−	0.0617471i
$484$	−56.8420			−2.58373
$485$	26.0577	+	45.1332i	1.18322	+	2.04939i
$486$	−40.8177	+	10.5732i	−1.85153	+	0.479609i
$487$	−5.80263	+	21.6557i	−0.262942	+	0.981314i	0.700556	+	0.713598i	$0.252936\pi$
$487$	−5.80263	+	21.6557i	−0.262942	+	0.981314i	−0.963498	+	0.267716i	$0.913731\pi$
$488$	−29.9767	+	8.03223i	−1.35698	+	0.363602i
$489$	12.4920	−	3.32490i	0.564907	−	0.150357i
$490$	10.3536			0.467727
$491$	−5.04853	−	8.74430i	−0.227837	−	0.394625i	0.729330	−	0.684162i	$-0.239832\pi$
$491$	−5.04853	−	8.74430i	−0.227837	−	0.394625i	−0.957167	+	0.289537i	$0.906499\pi$
$492$	−16.1083	−	60.5204i	−0.726218	−	2.72847i
$493$	−30.3115	+	17.5003i	−1.36516	+	0.788176i
$494$	−47.1990	−	26.6510i	−2.12358	−	1.19909i
$495$	−3.16871	−	5.53088i	−0.142423	−	0.248595i
$496$	−52.0253	+	13.9401i	−2.33601	+	0.625931i
$497$		−	15.6313i		−	0.701159i
$498$	18.0636	−	31.1669i	0.809448	−	1.39662i
$499$	6.65695	−	1.78372i	0.298006	−	0.0798505i	−0.106718	−	0.994289i	$-0.534034\pi$
$499$	6.65695	−	1.78372i	0.298006	−	0.0798505i	0.404724	+	0.914439i	$0.367368\pi$
$500$	−66.9341	+	66.9341i	−2.99338	+	2.99338i
$501$	0.725697	+	2.72651i	0.0324217	+	0.121812i
$502$	−41.2212	−	11.0452i	−1.83979	−	0.492971i
$503$	−20.5925	+	11.8891i	−0.918176	+	0.530109i	−0.883053	−	0.469274i	$-0.844516\pi$
$503$	−20.5925	+	11.8891i	−0.918176	+	0.530109i	−0.0351230	+	0.999383i	$0.511182\pi$
$504$	13.3778	+	23.3505i	0.595895	+	1.04011i
$505$	−7.12715	−	26.5989i	−0.317154	−	1.18363i
$506$	0.609207	+	1.05518i	0.0270825	+	0.0469084i
$507$	0.393704	+	22.5132i	0.0174850	+	0.999847i
$508$	−4.78308	+	8.28454i	−0.212215	+	0.367567i
$509$	4.86226	+	1.30284i	0.215516	+	0.0577473i	0.364961	−	0.931023i	$-0.381082\pi$
$509$	4.86226	+	1.30284i	0.215516	+	0.0577473i	−0.149446	+	0.988770i	$0.547749\pi$
$510$	31.7495	+	55.2041i	1.40589	+	2.44448i
$511$	2.27387	+	1.31282i	0.100590	+	0.0580758i
$512$	−9.53141	+	9.53141i	−0.421233	+	0.421233i
$513$	−27.8577	−	7.61400i	−1.22995	−	0.336166i
$514$	67.9340	+	18.2029i	2.99644	+	0.802894i
$515$	4.06597	−	15.1744i	0.179168	−	0.668665i
$516$	0.00659226	−	3.95399i	0.000290208	−	0.174065i
$517$	−5.21181	+	3.00904i	−0.229215	+	0.132337i
$518$	3.31785	−	12.3824i	0.145778	−	0.544051i
$519$	−0.0167709	+	10.0591i	−0.000736163	+	0.441545i
$520$	1.18558	+	123.796i	0.0519910	+	5.42881i
$521$		−	22.7492i		−	0.996662i	−0.866987	−	0.498331i	$-0.833946\pi$
$521$		−	22.7492i		−	0.996662i	0.866987	−	0.498331i	$-0.166054\pi$
$522$	−77.3220	+	20.4423i	−3.38429	+	0.894733i
$523$	19.3136	−	33.4522i	0.844526	−	1.46276i	−0.0415066	−	0.999138i	$-0.513216\pi$
$523$	19.3136	−	33.4522i	0.844526	−	1.46276i	0.886032	−	0.463623i	$-0.153451\pi$
$524$	−36.5127	+	63.2418i	−1.59506	+	2.76273i
$525$	16.1402	+	4.35362i	0.704418	+	0.190007i
$526$	−4.22099	−	4.22099i	−0.184044	−	0.184044i
$527$	9.92197	+	9.92197i	0.432208	+	0.432208i
$528$	−12.6534	−	3.41309i	−0.550668	−	0.148536i
$529$	11.1707	−	19.3483i	0.485685	−	0.841230i
$530$	28.8636	−	49.9933i	1.25376	−	2.17157i
$531$	1.14799	−	0.303505i	0.0498187	−	0.0131710i
$532$			29.5477i			1.28106i
$533$	−23.6248	+	6.57336i	−1.02330	+	0.284724i
$534$	0.130146	−	78.0607i	0.00563197	−	3.37802i
$535$	8.08584	−	30.1768i	0.349581	−	1.30466i
$536$	64.4467	−	37.2083i	2.78367	−	1.60715i
$537$	0.0295864	−	17.7457i	0.00127675	−	0.765786i
$538$	−2.24551	+	8.38035i	−0.0968108	+	0.361303i
$539$	0.536180	+	0.143669i	0.0230949	+	0.00618826i
$540$	26.8564	+	102.273i	1.15571	+	4.40112i
$541$	12.0126	−	12.0126i	0.516463	−	0.516463i	−0.400037	−	0.916499i	$-0.631003\pi$
$541$	12.0126	−	12.0126i	0.516463	−	0.516463i	0.916499	+	0.400037i	$0.131003\pi$
$542$	−55.0961	−	31.8097i	−2.36658	−	1.36635i
$543$	9.94166	+	17.2859i	0.426637	+	0.741811i
$544$	64.9320	+	17.3985i	2.78394	+	0.745954i
$545$	−0.422971	+	0.732607i	−0.0181181	+	0.0313814i
$546$	14.5616	−	8.56142i	0.623180	−	0.366395i
$547$	21.9205	+	37.9674i	0.937253	+	1.62337i	0.770566	+	0.637360i	$0.219973\pi$
$547$	21.9205	+	37.9674i	0.937253	+	1.62337i	0.166687	+	0.986010i	$0.446693\pi$
$548$	−7.59750	−	28.3543i	−0.324549	−	1.21123i
$549$	5.15943	+	9.00561i	0.220199	+	0.384350i
$550$	−12.5501	+	7.24578i	−0.535136	+	0.308961i
$551$	−52.9123	−	14.1778i	−2.25414	−	0.603994i
$552$	−3.24293	−	12.1840i	−0.138028	−	0.518585i
$553$	−2.17132	+	2.17132i	−0.0923340	+	0.0923340i
$554$	−25.6070	+	6.86137i	−1.08794	+	0.291512i
$555$	15.7557	−	27.1849i	0.668792	−	1.15393i
$556$			33.0185i			1.40030i
$557$	−29.4225	+	7.88375i	−1.24667	+	0.334045i	−0.821050	−	0.570856i	$-0.806612\pi$
$557$	−29.4225	+	7.88375i	−1.24667	+	0.334045i	−0.425623	+	0.904901i	$0.639945\pi$
$558$	15.9390	+	27.8210i	0.674753	+	1.17776i
$559$	−1.54815	+	0.0148264i	−0.0654796	+	0.000627090i
$560$	45.1860	−	26.0882i	1.90946	−	1.10243i
$561$	0.878182	+	3.29941i	0.0370769	+	0.139301i
$562$	4.37697	+	7.58114i	0.184632	+	0.319791i
$563$	33.3749			1.40659			0.703293	−	0.710900i	$-0.251712\pi$
$563$	33.3749			1.40659			0.703293	+	0.710900i	$0.251712\pi$
$564$	96.4727	−	25.6775i	4.06224	−	1.08122i
$565$	−45.6433	+	12.2301i	−1.92023	+	0.514523i
$566$	13.6076	−	50.7843i	0.571971	−	2.13463i
$567$	6.40626	−	6.32138i	0.269038	−	0.265473i
$568$	−70.1094	−	121.433i	−2.94173	−	5.09522i
$569$	−12.7474			−0.534398			−0.267199	−	0.963641i	$-0.586098\pi$
$569$	−12.7474			−0.534398			−0.267199	+	0.963641i	$0.586098\pi$
$570$	−25.9567	+	96.2296i	−1.08721	+	4.03061i
$571$	−0.650882	−	0.375787i	−0.0272385	−	0.0157262i	0.486319	−	0.873781i	$-0.338339\pi$
$571$	−0.650882	−	0.375787i	−0.0272385	−	0.0157262i	−0.513557	+	0.858055i	$0.671673\pi$
$572$	−2.65536	+	10.3036i	−0.111026	+	0.430817i
$573$	−6.78732	−	0.0113161i	−0.283544	−	0.000472737i
$574$	13.0083	+	13.0083i	0.542957	+	0.542957i
$575$	−6.78283	−	3.91607i	−0.282864	−	0.163311i
$576$	62.0786	+	36.1176i	2.58661	+	1.50490i
$577$	9.95912	+	9.95912i	0.414604	+	0.414604i	0.883339	−	0.468735i	$-0.155290\pi$
$577$	9.95912	+	9.95912i	0.414604	+	0.414604i	−0.468735	+	0.883339i	$0.655290\pi$
$578$	3.07273	+	11.4676i	0.127809	+	0.476988i
$579$	13.2201	−	3.51871i	0.549409	−	0.146232i
$580$	51.9110	+	193.734i	2.15548	+	8.04438i
$581$			7.68907i			0.318996i
$582$	0.106348	−	63.7868i	0.00440827	−	2.64405i
$583$	2.18848	−	2.18848i	0.0906375	−	0.0906375i
$584$	23.5530			0.974632
$585$	39.9249	−	10.9654i	1.65069	−	0.453364i
$586$	−39.1573			−1.61757
$587$	28.5429	−	28.5429i	1.17809	−	1.17809i	0.197860	−	0.980230i	$-0.436601\pi$
$587$	28.5429	−	28.5429i	1.17809	−	1.17809i	0.980230	−	0.197860i	$-0.0633990\pi$
$588$	−7.96687	−	4.61740i	−0.328548	−	0.190419i
$589$			21.9608i			0.904880i
$590$	−1.06066	−	3.95844i	−0.0436667	−	0.162966i
$591$	−32.3563	−	32.4644i	−1.33096	−	1.33541i
$592$	−16.7201	−	62.4003i	−0.687192	−	2.56464i
$593$	−30.1870	−	30.1870i	−1.23963	−	1.23963i	−0.960151	−	0.279482i	$-0.909837\pi$
$593$	−30.1870	−	30.1870i	−1.23963	−	1.23963i	−0.279482	−	0.960151i	$-0.590163\pi$
$594$	−0.0390224	+	7.80173i	−0.00160111	+	0.320109i
$595$	−11.7719	−	6.79650i	−0.482600	−	0.278629i
$596$	18.8429	+	18.8429i	0.771833	+	0.771833i
$597$	3.75448	−	6.47799i	0.153661	−	0.265126i
$598$	−7.62444	+	2.12142i	−0.311786	+	0.0867515i
$599$	2.32795	+	1.34404i	0.0951175	+	0.0549161i	0.546804	−	0.837260i	$-0.315844\pi$
$599$	2.32795	+	1.34404i	0.0951175	+	0.0549161i	−0.451687	+	0.892177i	$0.649178\pi$
$600$	144.914	−	38.5707i	5.91608	−	1.57464i
$601$	11.6444			0.474987			0.237493	−	0.971389i	$-0.423674\pi$
$601$	11.6444			0.474987			0.237493	+	0.971389i	$0.423674\pi$
$602$	0.580735	+	1.00586i	0.0236690	+	0.0409959i
$603$	−17.5393	−	17.6566i	−0.714255	−	0.719034i
$604$	−1.86417	+	6.95719i	−0.0758522	+	0.283084i
$605$	39.5312	−	10.5924i	1.60717	−	0.430641i
$606$	−8.77758	+	32.5413i	−0.356565	+	1.32190i
$607$	44.0481			1.78786			0.893929	−	0.448209i	$-0.147938\pi$
$607$	44.0481			1.78786			0.893929	+	0.448209i	$0.147938\pi$
$608$	52.6043	+	91.1133i	2.13338	+	3.69513i
$609$	12.0913	−	12.0510i	0.489964	−	0.488333i
$610$	31.0206	−	17.9097i	1.25599	−	0.725144i
$611$	−10.4783	−	37.6592i	−0.423906	−	1.52353i
$612$	0.188858	−	56.6378i	0.00763415	−	2.28945i
$613$	22.9340	−	6.14514i	0.926294	−	0.248200i	0.236021	−	0.971748i	$-0.424157\pi$
$613$	22.9340	−	6.14514i	0.926294	−	0.248200i	0.690274	+	0.723548i	$0.257490\pi$
$614$			80.5246i			3.24971i
$615$	22.4805	+	39.0877i	0.906500	+	1.57617i
$616$	4.80974	−	1.28877i	0.193790	−	0.0519259i
$617$	9.14088	−	9.14088i	0.367998	−	0.367998i	−0.498749	−	0.866747i	$-0.666207\pi$
$617$	9.14088	−	9.14088i	0.367998	−	0.367998i	0.866747	+	0.498749i	$0.166207\pi$
$618$	−13.6189	+	13.5736i	−0.547832	+	0.546009i
$619$	10.6783	+	2.86124i	0.429197	+	0.115003i	0.466949	−	0.884284i	$-0.345353\pi$
$619$	10.6783	+	2.86124i	0.429197	+	0.115003i	−0.0377524	+	0.999287i	$0.512020\pi$
$620$	69.6353	−	40.2040i	2.79662	−	1.61463i
$621$	−3.66218	+	2.09001i	−0.146958	+	0.0838691i
$622$	12.9573	+	48.3571i	0.519538	+	1.93894i
$623$	8.33095	+	14.4296i	0.333772	+	0.578111i
$624$	41.9786	−	74.0557i	1.68049	−	2.96460i
$625$	9.94783	−	17.2301i	0.397913	−	0.689206i
$626$	23.5682	+	6.31508i	0.941975	+	0.252401i
$627$	−2.67952	+	4.62325i	−0.107010	+	0.184635i
$628$	94.6693	+	54.6573i	3.77771	+	2.18106i
$629$	−11.9006	+	11.9006i	−0.474509	+	0.474509i
$630$	−21.8899	−	22.0364i	−0.872115	−	0.877951i
$631$	−14.0080	−	3.75343i	−0.557650	−	0.149422i	−0.0310234	−	0.999519i	$-0.509877\pi$
$631$	−14.0080	−	3.75343i	−0.557650	−	0.149422i	−0.526626	+	0.850097i	$0.676543\pi$
$632$	−7.12930	+	26.6069i	−0.283588	+	1.05837i
$633$	26.5870	+	15.4092i	1.05674	+	0.612460i
$634$	−35.2573	+	20.3558i	−1.40025	+	0.808434i
$635$	1.78263	−	6.65287i	0.0707416	−	0.264011i
$636$	−44.5056	+	25.5965i	−1.76476	+	1.01497i
$637$	−1.77279	+	3.13962i	−0.0702405	+	0.124396i
$638$			14.7985i			0.585880i
$639$	−33.2694	+	33.0482i	−1.31612	+	1.30737i
$640$	51.4760	−	89.1591i	2.03477	−	3.52432i
$641$	−12.5660	+	21.7650i	−0.496328	+	0.859666i	−0.999991	−	0.00423448i	$-0.998652\pi$
$641$	−12.5660	+	21.7650i	−0.496328	+	0.859666i	0.503663	+	0.863900i	$0.331985\pi$
$642$	−27.0834	+	26.9932i	−1.06890	+	1.06534i
$643$	−2.69314	−	2.69314i	−0.106207	−	0.106207i	0.652006	−	0.758213i	$-0.273928\pi$
$643$	−2.69314	−	2.69314i	−0.106207	−	0.106207i	−0.758213	+	0.652006i	$0.773928\pi$
$644$	3.05057	+	3.05057i	0.120209	+	0.120209i
$645$	0.732232	+	2.75107i	0.0288316	+	0.108323i
$646$	26.6931	−	46.2337i	1.05022	−	1.81904i
$647$	−0.187816	+	0.325307i	−0.00738381	+	0.0127891i	−0.869694	−	0.493592i	$-0.835684\pi$
$647$	−0.187816	+	0.325307i	−0.00738381	+	0.0127891i	0.862310	+	0.506381i	$0.169017\pi$
$648$	21.4150	−	77.8415i	0.841260	−	3.05790i
$649$		−	0.219713i		−	0.00862449i
$650$	−25.2318	−	90.6834i	−0.989671	−	3.55690i
$651$	−5.92124	−	3.43181i	−0.232072	−	0.134503i
$652$	−10.2694	+	38.3259i	−0.402181	+	1.50096i
$653$	22.7714	−	13.1471i	0.891115	−	0.514486i	0.0168082	−	0.999859i	$-0.494650\pi$
$653$	22.7714	−	13.1471i	0.891115	−	0.514486i	0.874307	+	0.485373i	$0.161316\pi$
$654$	0.897540	−	0.516202i	0.0350966	−	0.0201851i
$655$	13.6081	−	50.7861i	0.531712	−	1.98438i
$656$	89.5494	+	23.9947i	3.49632	+	0.936835i
$657$	−2.01332	−	7.61528i	−0.0785470	−	0.297100i
$658$	−20.7360	+	20.7360i	−0.808372	+	0.808372i
$659$	36.4174	+	21.0256i	1.41862	+	0.819040i	0.996178	−	0.0873504i	$-0.0278400\pi$
$659$	36.4174	+	21.0256i	1.41862	+	0.819040i	0.422441	+	0.906390i	$0.361173\pi$
$660$	19.5652	+	0.0326200i	0.761576	+	0.00126973i
$661$	5.30746	+	1.42213i	0.206436	+	0.0553145i	0.360555	−	0.932738i	$-0.382587\pi$
$661$	5.30746	+	1.42213i	0.206436	+	0.0553145i	−0.154119	+	0.988052i	$0.549254\pi$
$662$	−18.6629	+	32.3252i	−0.725356	+	1.25635i
$663$	−22.1764	+	0.175404i	−0.861260	+	0.00681214i
$664$	34.4870	+	59.7332i	1.33835	+	2.31810i
$665$	−5.50614	−	20.5492i	−0.213519	−	0.796863i
$666$	−33.3691	+	19.1176i	−1.29303	+	0.740792i
$667$	−6.92652	+	3.99903i	−0.268196	+	0.154843i
$668$	−8.36506	−	2.24141i	−0.323654	−	0.0867228i
$669$	−19.3174	−	5.21060i	−0.746852	−	0.201454i
$670$	−60.7343	+	60.7343i	−2.34637	+	2.34637i
$671$	1.85498	−	0.497040i	0.0716106	−	0.0191880i
$672$	−32.7871	−	0.0546640i	−1.26479	−	0.00210871i
$673$			22.2820i			0.858906i	0.903089	+	0.429453i	$0.141294\pi$
$673$			22.2820i			0.858906i	−0.903089	+	0.429453i	$0.858706\pi$
$674$	−67.7534	+	18.1545i	−2.60976	+	0.699284i
$675$	−24.8581	−	43.5572i	−0.956788	−	1.67652i
$676$	−60.5043	−	33.4038i	−2.32709	−	1.28476i
$677$	19.0883	−	11.0206i	0.733621	−	0.423556i	−0.0861242	−	0.996284i	$-0.527448\pi$
$677$	19.0883	−	11.0206i	0.733621	−	0.423556i	0.819746	+	0.572728i	$0.194115\pi$
$678$	55.8403	+	15.0622i	2.14453	+	0.578460i
$679$	6.80758	+	11.7911i	0.261251	+	0.452500i
$680$	−121.935			−4.67597
$681$	3.28570	+	3.29667i	0.125908	+	0.126329i
$682$	5.73059	−	1.53551i	0.219435	−	0.0587976i
$683$	−1.54801	+	5.77726i	−0.0592331	+	0.221061i	−0.989198	−	0.146589i	$-0.953171\pi$
$683$	−1.54801	+	5.77726i	−0.0592331	+	0.221061i	0.929964	+	0.367649i	$0.119837\pi$
$684$	62.8888	−	62.4708i	2.40461	−	2.38863i
$685$	10.5675	+	18.3034i	0.403763	+	0.699338i
$686$	2.70488			0.103273
$687$	24.8495	+	24.9325i	0.948066	+	0.951233i
$688$	5.06899	+	2.92658i	0.193253	+	0.111575i
$689$	10.2178	+	17.3127i	0.389267	+	0.659561i
$690$	7.25513	+	12.6148i	0.276198	+	0.480236i
$691$	−2.89478	−	2.89478i	−0.110123	−	0.110123i	0.649898	−	0.760021i	$-0.274811\pi$
$691$	−2.89478	−	2.89478i	−0.110123	−	0.110123i	−0.760021	+	0.649898i	$0.774811\pi$
$692$	−26.7390	−	15.4378i	−1.01646	−	0.586856i
$693$	−0.827828	−	1.44495i	−0.0314466	−	0.0548889i
$694$	25.1092	+	25.1092i	0.953131	+	0.953131i
$695$	−6.15291	−	22.9630i	−0.233393	−	0.871035i
$696$	39.8810	−	147.851i	1.51169	−	5.60430i
$697$	−6.25111	−	23.3294i	−0.236778	−	0.883666i
$698$			11.3028i			0.427817i
$699$	−12.4719	+	7.17296i	−0.471731	+	0.271306i
$700$	−36.2828	+	36.2828i	−1.37136	+	1.37136i
$701$	−7.25263			−0.273928			−0.136964	−	0.990576i	$-0.543734\pi$
$701$	−7.25263			−0.273928			−0.136964	+	0.990576i	$0.543734\pi$
$702$	−49.0087	−	12.8918i	−1.84971	−	0.486570i
$703$	−26.3403			−0.993443
$704$	9.39682	−	9.39682i	0.354156	−	0.354156i
$705$	−62.3078	+	35.8351i	−2.34665	+	1.34963i
$706$		−	68.2014i		−	2.56679i
$707$	−1.86197	−	6.94897i	−0.0700266	−	0.261343i
$708$	−0.949194	+	3.51896i	−0.0356729	+	0.132251i
$709$	−4.54348	−	16.9565i	−0.170634	−	0.636815i	−0.997254	−	0.0740549i	$-0.976406\pi$
$709$	−4.54348	−	16.9565i	−0.170634	−	0.636815i	0.826620	−	0.562760i	$-0.190261\pi$
$710$	114.438	+	114.438i	4.29479	+	4.29479i
$711$	9.21208	+	0.0307176i	0.345480	+	0.00115200i
$712$	129.439	+	74.7319i	4.85095	+	2.80070i
$713$	2.26728	+	2.26728i	0.0849104	+	0.0849104i
$714$	8.29458	+	14.4221i	0.310417	+	0.539734i
$715$	−0.0733643	−	7.66057i	−0.00274367	−	0.286489i
$716$	47.1716	+	27.2345i	1.76288	+	1.01780i
$717$	−9.68776	−	9.72012i	−0.361796	−	0.363004i
$718$	73.1515			2.72999
$719$	9.60321	+	16.6332i	0.358139	+	0.620315i	0.987650	−	0.156676i	$-0.0500780\pi$
$719$	9.60321	+	16.6332i	0.358139	+	0.620315i	−0.629511	+	0.776992i	$0.716745\pi$
$720$	−151.059	−	41.0166i	−5.62965	−	1.52860i
$721$	1.06224	−	3.96432i	0.0395598	−	0.147639i
$722$	31.0648	−	8.32380i	1.15611	−	0.309780i
$723$	−3.50250	−	3.51420i	−0.130259	−	0.130694i
$724$	−61.2069			−2.27474
$725$	−47.5636	−	82.3825i	−1.76647	−	3.05961i
$726$	−48.3628	−	13.0452i	−1.79491	−	0.484154i
$727$	21.1099	−	12.1878i	0.782923	−	0.452021i	−0.0545425	−	0.998511i	$-0.517370\pi$
$727$	21.1099	−	12.1878i	0.782923	−	0.452021i	0.837465	+	0.546491i	$0.184037\pi$
$728$	0.309732	+	32.3417i	0.0114794	+	1.19866i
$729$	−26.9986	−	0.270088i	−0.999950	−	0.0100033i
$730$	−26.2585	+	7.03595i	−0.971871	+	0.260412i
$731$		−	1.52487i		−	0.0563993i
$732$	−31.8569	−	0.0531132i	−1.17747	−	0.00196312i
$733$	31.5713	−	8.45951i	1.16611	−	0.312459i	0.376709	−	0.926332i	$-0.377056\pi$
$733$	31.5713	−	8.45951i	1.16611	−	0.312459i	0.789405	+	0.613873i	$0.210389\pi$
$734$	30.3626	−	30.3626i	1.12070	−	1.12070i
$735$	6.40107	+	1.72660i	0.236107	+	0.0636868i
$736$	14.8377	+	3.97575i	0.546925	+	0.146548i
$737$	−3.98801	+	2.30248i	−0.146900	+	0.0848128i
$738$	0.184028	−	55.1893i	0.00677418	−	2.03155i
$739$	3.92560	+	14.6505i	0.144406	+	0.538929i	0.999781	+	0.0209207i	$0.00665975\pi$
$739$	3.92560	+	14.6505i	0.144406	+	0.538929i	−0.855376	+	0.518008i	$0.826674\pi$
$740$	48.2215	+	83.5221i	1.77266	+	3.07033i
$741$	−24.7362	−	24.3480i	−0.908708	−	0.894446i
$742$	7.54064	−	13.0608i	0.276826	−	0.479476i
$743$	40.5956	+	10.8775i	1.48931	+	0.399058i	0.909503	−	0.415698i	$-0.136463\pi$
$743$	40.5956	+	10.8775i	1.48931	+	0.399058i	0.579804	+	0.814756i	$0.303129\pi$
$744$	−61.3920	−	0.102355i	−2.25074	−	0.00375253i
$745$	−16.6157	−	9.59310i	−0.608753	−	0.351464i
$746$	37.0320	−	37.0320i	1.35584	−	1.35584i
$747$	16.3653	−	16.2565i	0.598774	−	0.594794i
$748$	−10.1227	−	2.71238i	−0.370124	−	0.0991745i
$749$	2.11243	−	7.88370i	0.0771865	−	0.288064i
$750$	−72.3108	+	41.5881i	−2.64042	+	1.51858i
$751$	−38.8475	+	22.4286i	−1.41757	+	0.818432i	−0.996085	−	0.0884043i	$-0.971823\pi$
$751$	−38.8475	+	22.4286i	−1.41757	+	0.818432i	−0.421482	+	0.906837i	$0.638490\pi$
$752$	−38.2488	+	142.747i	−1.39479	+	5.20543i
$753$	−23.6430	−	13.7029i	−0.861597	−	0.499360i
$754$	−93.0810	−	23.9880i	−3.38981	−	0.873591i
$755$		−	5.18582i		−	0.188731i
$756$	7.01624	+	26.7188i	0.255178	+	0.971754i
$757$	1.10985	−	1.92232i	0.0403383	−	0.0698680i	−0.845151	−	0.534527i	$-0.820490\pi$
$757$	1.10985	−	1.92232i	0.0403383	−	0.0698680i	0.885490	+	0.464659i	$0.153823\pi$
$758$	−19.0626	+	33.0174i	−0.692384	+	1.19924i
$759$	0.200675	+	0.753954i	0.00728403	+	0.0273668i
$760$	−134.942	−	134.942i	−4.89486	−	4.89486i
$761$	38.2614	+	38.2614i	1.38697	+	1.38697i	0.831600	+	0.555374i	$0.187425\pi$
$761$	38.2614	+	38.2614i	1.38697	+	1.38697i	0.555374	+	0.831600i	$0.312575\pi$
$762$	−5.97089	+	5.95101i	−0.216302	+	0.215582i
$763$	−0.110501	+	0.191394i	−0.00400042	+	0.00692892i
$764$	10.4165	−	18.0420i	0.376857	−	0.652736i
$765$	10.4230	+	39.4244i	0.376843	+	1.42539i
$766$		−	33.2867i		−	1.20270i
$767$	1.38197	+	0.356148i	0.0498999	+	0.0128598i
$768$	−37.3418	+	21.4763i	−1.34745	+	0.774961i
$769$	7.56780	−	28.2434i	0.272902	−	1.01848i	−0.684333	−	0.729170i	$-0.739906\pi$
$769$	7.56780	−	28.2434i	0.272902	−	1.01848i	0.957235	−	0.289313i	$-0.0934269\pi$
$770$	−4.97723	+	2.87361i	−0.179367	+	0.103558i
$771$	38.9644	+	22.5828i	1.40327	+	0.813300i
$772$	−10.8680	+	40.5599i	−0.391148	+	1.45978i
$773$	30.6689	+	8.21770i	1.10308	+	0.295570i	0.764019	−	0.645193i	$-0.223223\pi$
$773$	30.6689	+	8.21770i	1.10308	+	0.295570i	0.339064	+	0.940763i	$0.389890\pi$
$774$	0.913050	−	3.36266i	0.0328189	−	0.120868i
$775$	−26.9666	+	26.9666i	−0.968668	+	0.968668i
$776$	105.771	+	61.0667i	3.79694	+	2.19217i
$777$	4.11618	−	7.10207i	0.147667	−	0.254785i
$778$	58.7964	+	15.7544i	2.10795	+	0.564824i
$779$	18.9002	−	32.7361i	0.677170	−	1.17289i
$780$	−31.9198	+	123.010i	−1.14291	+	4.40446i
$781$	4.33842	+	7.51437i	0.155241	+	0.268885i
$782$	−2.01742	−	7.52912i	−0.0721428	−	0.269241i
$783$	−51.2131	−	0.256156i	−1.83021	−	0.00915425i
$784$	11.8049	−	6.81554i	0.421602	−	0.243412i
$785$	−76.0238	−	20.3705i	−2.71340	−	0.727055i
$786$	−45.5800	+	45.4283i	−1.62579	+	1.62037i
$787$	−10.7359	+	10.7359i	−0.382695	+	0.382695i	−0.872072	−	0.489378i	$-0.837224\pi$
$787$	−10.7359	+	10.7359i	−0.382695	+	0.382695i	0.489378	+	0.872072i	$0.337224\pi$
$788$	135.893	−	36.4125i	4.84100	−	1.29714i
$789$	−1.90571	−	3.31352i	−0.0678449	−	0.117965i
$790$		−	31.7929i		−	1.13114i
$791$	−11.9243	+	3.19511i	−0.423980	+	0.113605i
$792$	−12.9119	−	7.51222i	−0.458805	−	0.266935i
$793$	0.119455	+	12.4733i	0.00424196	+	0.442938i
$794$	−87.7342	+	50.6534i	−3.11357	+	1.79762i
$795$	26.1819	−	26.0948i	0.928577	−	0.925486i
$796$	11.4909	+	19.9028i	0.407283	+	0.705436i
$797$	−43.4100			−1.53766			−0.768830	−	0.639453i	$-0.779161\pi$
$797$	−43.4100			−1.53766			−0.768830	+	0.639453i	$0.779161\pi$
$798$	−6.78119	+	25.1400i	−0.240052	+	0.889947i
$799$	37.1884	−	9.96460i	1.31563	−	0.352522i
$800$	−47.2867	+	176.476i	−1.67184	+	6.23939i
$801$	13.0982	−	48.2391i	0.462801	−	1.70444i
$802$	−11.5569	−	20.0172i	−0.408089	−	0.706831i
$803$	−1.45748			−0.0514333
$804$	73.8196	−	19.6481i	2.60342	−	0.692933i
$805$	−2.69001	−	1.55308i	−0.0948103	−	0.0547388i
$806$	0.369032	+	38.5337i	0.0129986	+	1.35729i
$807$	−2.78582	+	4.80666i	−0.0980655	+	0.169202i
$808$	−45.6324	−	45.6324i	−1.60534	−	1.60534i
$809$	−37.2392	−	21.5001i	−1.30926	−	0.755902i	−0.327288	−	0.944925i	$-0.606135\pi$
$809$	−37.2392	−	21.5001i	−1.30926	−	0.755902i	−0.981973	+	0.189023i	$0.939468\pi$
$810$	−0.621424	+	93.1802i	−0.0218346	+	3.27402i
$811$	28.5179	+	28.5179i	1.00140	+	1.00140i	0.999999	+	0.00139900i	$0.000445317\pi$
$811$	28.5179	+	28.5179i	1.00140	+	1.00140i	0.00139900	+	0.999999i	$0.499555\pi$
$812$	13.5618	+	50.6132i	0.475925	+	1.77617i
$813$	−28.7583	−	28.8543i	−1.00860	−	1.01196i
$814$	1.84172	+	6.87339i	0.0645522	+	0.240912i
$815$		−	28.5678i		−	1.00068i
$816$	72.5396	+	42.0422i	2.53939	+	1.47177i
$817$	1.68754	−	1.68754i	0.0590395	−	0.0590395i
$818$	−51.9574			−1.81665
$819$	10.4304	−	2.86472i	0.364468	−	0.100101i
$820$	−138.403			−4.83326
$821$	−19.2631	+	19.2631i	−0.672288	+	0.672288i	−0.958243	−	0.285955i	$-0.907689\pi$
$821$	−19.2631	+	19.2631i	−0.672288	+	0.672288i	0.285955	+	0.958243i	$0.407689\pi$
$822$	0.0431286	−	25.8683i	0.00150428	−	0.902259i
$823$			29.8652i			1.04104i	0.853850	+	0.520518i	$0.174261\pi$
$823$			29.8652i			1.04104i	−0.853850	+	0.520518i	$0.825739\pi$
$824$	−9.52869	−	35.5616i	−0.331948	−	1.23885i
$825$	−8.96736	+	2.38678i	−0.312203	+	0.0830970i
$826$	−0.277098	−	1.03414i	−0.00964147	−	0.0359825i
$827$	18.0192	+	18.0192i	0.626588	+	0.626588i	0.947208	−	0.320620i	$-0.103891\pi$
$827$	18.0192	+	18.0192i	0.626588	+	0.626588i	−0.320620	+	0.947208i	$0.603891\pi$
$828$	0.0431563	−	12.9424i	0.00149978	−	0.449779i
$829$	14.8744	+	8.58773i	0.516609	+	0.298264i	0.735546	−	0.677475i	$-0.236926\pi$
$829$	14.8744	+	8.58773i	0.516609	+	0.298264i	−0.218937	+	0.975739i	$0.570259\pi$
$830$	−56.2923	−	56.2923i	−1.95394	−	1.95394i
$831$	−16.9757	−	0.0283025i	−0.588879	−	0.000981804i
$832$	43.8729	+	74.3368i	1.52102	+	2.57716i
$833$	−3.07541	−	1.77559i	−0.106557	−	0.0615205i
$834$	−7.57774	+	28.0931i	−0.262396	+	0.972784i
$835$	6.23523			0.215779
$836$	−8.20088	−	14.2043i	−0.283633	−	0.491267i
$837$	5.21470	+	19.8583i	0.180247	+	0.686404i
$838$	12.9940	−	48.4942i	0.448870	−	1.67520i
$839$	32.0944	−	8.59968i	1.10802	−	0.296894i	0.341995	−	0.939702i	$-0.388897\pi$
$839$	32.0944	−	8.59968i	1.10802	−	0.296894i	0.766028	+	0.642808i	$0.222231\pi$
$840$	57.4714	−	15.2968i	1.98295	−	0.527789i
$841$	−68.1424			−2.34974
$842$	−28.0998	−	48.6703i	−0.968383	−	1.67729i
$843$	1.44179	+	5.41694i	0.0496578	+	0.186569i
$844$	−81.6851	+	47.1609i	−2.81172	+	1.62335i
$845$	48.3030	+	11.9561i	1.66167	+	0.411302i
$846$	87.9748	+	0.293351i	3.02463	+	0.0100856i
$847$	10.3276	−	2.76726i	0.354859	−	0.0950842i
$848$		−	76.0013i		−	2.60989i
$849$	16.8819	−	29.1280i	0.579384	−	0.999670i
$850$	89.5497	−	23.9948i	3.07153	−	0.823014i
$851$	−2.71943	+	2.71943i	−0.0932208	+	0.0932208i
$852$	−37.0217	−	139.094i	−1.26834	−	4.76528i
$853$	40.6754	+	10.8989i	1.39270	+	0.373172i	0.875717	−	0.482825i	$-0.160389\pi$
$853$	40.6754	+	10.8989i	1.39270	+	0.373172i	0.516981	+	0.855997i	$0.327056\pi$
$854$	8.10414	−	4.67893i	0.277318	−	0.160110i
$855$	−32.0953	+	55.1650i	−1.09763	+	1.88660i
$856$	−18.9493	−	70.7199i	−0.647675	−	2.41716i
$857$	28.2838	+	48.9890i	0.966157	+	1.67343i	0.706475	+	0.707738i	$0.250284\pi$
$857$	28.2838	+	48.9890i	0.966157	+	1.67343i	0.259682	+	0.965694i	$0.416382\pi$
$858$	−4.62394	+	8.15723i	−0.157859	+	0.278483i
$859$	8.86893	−	15.3614i	0.302604	−	0.524126i	−0.674121	−	0.738621i	$-0.735477\pi$
$859$	8.86893	−	15.3614i	0.302604	−	0.524126i	0.976725	+	0.214495i	$0.0688107\pi$
$860$	−8.44039	−	2.26160i	−0.287815	−	0.0771198i
$861$	5.87303	+	10.2117i	0.200152	+	0.348013i
$862$	−8.53668	−	4.92866i	−0.290761	−	0.167871i
$863$	38.0070	−	38.0070i	1.29377	−	1.29377i	0.361338	−	0.932435i	$-0.382320\pi$
$863$	38.0070	−	38.0070i	1.29377	−	1.29377i	0.932435	−	0.361338i	$-0.117680\pi$
$864$	69.2033	+	69.8990i	2.35434	+	2.37801i
$865$	21.4727	+	5.75358i	0.730092	+	0.195628i
$866$	11.3039	−	42.1867i	0.384122	−	1.43356i
$867$	−0.0126747	+	7.60221i	−0.000430456	+	0.258184i
$868$	18.1923	−	10.5033i	0.617486	−	0.356506i
$869$	0.441166	−	1.64645i	0.0149655	−	0.0558521i
$870$	−0.294682	+	176.748i	−0.00999066	+	5.99233i
$871$	−8.01785	−	28.8163i	−0.271674	−	0.976403i
$872$			1.98248i			0.0671352i
$873$	10.7031	−	39.4183i	0.362245	−	1.33411i
$874$	6.09967	−	10.5649i	0.206324	−	0.357364i
$875$	8.90260	−	15.4198i	0.300963	−	0.521283i
$876$	23.3432	+	6.29653i	0.788694	+	0.212740i
$877$	34.4476	+	34.4476i	1.16321	+	1.16321i	0.983768	+	0.179446i	$0.0574304\pi$
$877$	34.4476	+	34.4476i	1.16321	+	1.16321i	0.179446	+	0.983768i	$0.442570\pi$
$878$	−30.7482	−	30.7482i	−1.03770	−	1.03770i
$879$	−24.2088	−	6.53002i	−0.816544	−	0.220252i
$880$	−14.4814	+	25.0825i	−0.488167	+	0.845531i
$881$	2.93287	−	5.07987i	0.0988107	−	0.171145i	−0.812382	−	0.583126i	$-0.801829\pi$
$881$	2.93287	−	5.07987i	0.0988107	−	0.171145i	0.911193	+	0.411981i	$0.135163\pi$
$882$	−5.71875	−	5.75702i	−0.192560	−	0.193849i
$883$			40.6676i			1.36857i	0.729213	+	0.684287i	$0.239887\pi$
$883$			40.6676i			1.36857i	−0.729213	+	0.684287i	$0.760113\pi$
$884$	33.4692	−	59.2741i	1.12569	−	1.99360i
$885$	0.00437512	−	2.62417i	0.000147068	−	0.0882105i
$886$	12.0081	−	44.8150i	0.403421	−	1.50559i
$887$	−9.33186	+	5.38775i	−0.313333	+	0.180903i	−0.648417	−	0.761285i	$-0.724569\pi$
$887$	−9.33186	+	5.38775i	−0.313333	+	0.180903i	0.335084	+	0.942188i	$0.391235\pi$
$888$	0.122767	−	73.6349i	0.00411980	−	2.47103i
$889$	0.465713	−	1.73807i	0.0156195	−	0.0582929i
$890$	−166.632	−	44.6490i	−5.58552	−	1.49664i
$891$	−1.32517	+	4.81689i	−0.0443950	+	0.161372i
$892$	43.4249	−	43.4249i	1.45397	−	1.45397i
$893$	52.1831	+	30.1279i	1.74624	+	1.00819i
$894$	11.7076	+	20.3565i	0.391561	+	0.680822i
$895$	−37.8810	−	10.1502i	−1.26622	−	0.339283i
$896$	13.4481	−	23.2929i	0.449271	−	0.778160i
$897$	−5.06756	+	0.0400819i	−0.169201	+	0.00133829i
$898$	−24.1518	−	41.8321i	−0.805955	−	1.39596i
$899$	10.0796	+	37.6174i	0.336172	+	1.25461i
$900$	153.934	+	0.513292i	5.13113	+	0.0171097i
$901$	−17.1472	+	9.89994i	−0.571256	+	0.329815i
$902$	−9.86386	−	2.64301i	−0.328431	−	0.0880027i
$903$	0.191296	+	0.718717i	0.00636593	+	0.0239174i
$904$	−78.3045	+	78.3045i	−2.60437	+	2.60437i
$905$	42.5668	−	11.4057i	1.41497	−	0.379140i
$906$	−3.18277	+	5.49155i	−0.105740	+	0.182445i
$907$			14.8149i			0.491920i	0.969280	+	0.245960i	$0.0791031\pi$
$907$			14.8149i			0.491920i	−0.969280	+	0.245960i	$0.920897\pi$
$908$	−13.7996	+	3.69759i	−0.457956	+	0.122709i
$909$	−10.8534	+	18.6547i	−0.359985	+	0.618739i
$910$	−10.0067	−	35.9642i	−0.331718	−	1.19220i
$911$	37.0713	−	21.4031i	1.22823	−	0.709117i	0.261568	−	0.965185i	$-0.415761\pi$
$911$	37.0713	−	21.4031i	1.22823	−	0.709117i	0.966659	+	0.256068i	$0.0824272\pi$
$912$	33.7508	+	126.805i	1.11760	+	4.19893i
$913$	−2.13408	−	3.69633i	−0.0706277	−	0.122331i
$914$	21.2383			0.702502
$915$	22.1651	−	5.89952i	0.732754	−	0.195032i
$916$	−104.365	+	27.9646i	−3.44833	+	0.923976i
$917$	3.55512	−	13.2679i	0.117400	−	0.438145i
$918$	13.1591	−	48.1458i	0.434314	−	1.58905i
$919$	23.3079	+	40.3704i	0.768856	+	1.33170i	0.938184	+	0.346138i	$0.112507\pi$
$919$	23.3079	+	40.3704i	0.768856	+	1.33170i	−0.169327	+	0.985560i	$0.554160\pi$
$920$	−27.8634			−0.918630
$921$	−13.4286	+	49.7841i	−0.442488	+	1.64044i
$922$	−36.4486	−	21.0436i	−1.20037	−	0.693035i
$923$	−54.2968	+	15.1076i	−1.78720	+	0.497271i
$924$	5.11143	+	0.00852198i	0.168154	+	0.000280353i
$925$	−32.3443	−	32.3443i	−1.06347	−	1.06347i
$926$	−5.30441	−	3.06250i	−0.174314	−	0.100640i
$927$	−10.6834	+	6.12067i	−0.350889	+	0.201029i
$928$	131.927	+	131.927i	4.33070	+	4.33070i
$929$	9.43066	+	35.1957i	0.309410	+	1.15473i	0.929082	+	0.369873i	$0.120599\pi$
$929$	9.43066	+	35.1957i	0.309410	+	1.15473i	−0.619672	+	0.784861i	$0.712734\pi$
$930$	68.4745	−	18.2254i	2.24537	−	0.597634i
$931$	−1.43848	−	5.36849i	−0.0471443	−	0.175945i
$932$		−	44.1611i		−	1.44655i
$933$	−0.0534475	+	32.0574i	−0.00174979	+	1.04951i
$934$	16.4597	−	16.4597i	0.538577	−	0.538577i
$935$	7.54539			0.246761
$936$	68.1807	−	69.0372i	2.22856	−	2.25655i
$937$	−32.0225			−1.04613			−0.523065	−	0.852293i	$-0.675211\pi$
$937$	−32.0225			−1.04613			−0.523065	+	0.852293i	$0.675211\pi$
$938$	−15.8669	+	15.8669i	−0.518072	+	0.518072i
$939$	13.5178	+	7.83461i	0.441138	+	0.255673i
$940$		−	220.622i		−	7.19591i
$941$	−2.89332	−	10.7980i	−0.0943196	−	0.352006i	0.902596	−	0.430489i	$-0.141659\pi$
$941$	−2.89332	−	10.7980i	−0.0943196	−	0.352006i	−0.996915	+	0.0784835i	$0.974992\pi$
$942$	68.0035	+	68.2306i	2.21567	+	2.22307i
$943$	−1.42845	−	5.33104i	−0.0465167	−	0.173603i
$944$	−3.81509	−	3.81509i	−0.124171	−	0.124171i
$945$	−9.85849	−	17.2744i	−0.320697	−	0.561935i
$946$	−0.558349	−	0.322363i	−0.0181535	−	0.0104809i
$947$	22.2540	+	22.2540i	0.723158	+	0.723158i	0.969247	−	0.246089i	$-0.0791455\pi$
$947$	22.2540	+	22.2540i	0.723158	+	0.723158i	−0.246089	+	0.969247i	$0.579146\pi$
$948$	−14.1787	+	24.4640i	−0.460503	+	0.794553i
$949$	2.36253	−	9.16735i	0.0766909	−	0.297585i
$950$	125.657	+	72.5481i	4.07685	+	2.35377i
$951$	−25.1924	+	6.70527i	−0.816918	+	0.217433i
$952$	−31.8555			−1.03244
$953$	−29.8043	−	51.6225i	−0.965455	−	1.67222i	−0.708388	−	0.705823i	$-0.750577\pi$
$953$	−29.8043	−	51.6225i	−0.965455	−	1.67222i	−0.257067	−	0.966394i	$-0.582756\pi$
$954$	−43.7410	+	11.5642i	−1.41617	+	0.374404i
$955$	−3.88219	+	14.4885i	−0.125625	+	0.468838i
$956$	40.6876	−	10.9022i	1.31593	−	0.352603i
$957$	−2.46786	+	9.14915i	−0.0797747	+	0.295750i
$958$	66.4593			2.14720
$959$	2.76076	+	4.78178i	0.0891497	+	0.154412i
$960$	112.419	−	112.045i	3.62832	−	3.61624i
$961$	−13.3257	+	7.69359i	−0.429861	+	0.248180i
$962$	−46.2181	+	0.442625i	−1.49013	+	0.0142708i
$963$	−21.2457	+	12.1719i	−0.684633	+	0.392235i
$964$	14.7102	−	3.94157i	0.473782	−	0.126950i
$965$		−	30.2329i		−	0.973233i
$966$	1.89541	+	3.29562i	0.0609837	+	0.106035i
$967$	−12.1999	+	3.26895i	−0.392321	+	0.105122i	−0.449586	−	0.893237i	$-0.648429\pi$
$967$	−12.1999	+	3.26895i	−0.392321	+	0.105122i	0.0572651	+	0.998359i	$0.481762\pi$
$968$	67.8188	−	67.8188i	2.17978	−	2.17978i
$969$	24.2130	−	24.1324i	0.777834	−	0.775245i
$970$	−136.163	−	36.4846i	−4.37191	−	1.17145i
$971$	−12.5469	+	7.24395i	−0.402649	+	0.232469i	−0.687626	−	0.726065i	$-0.741347\pi$
$971$	−12.5469	+	7.24395i	−0.402649	+	0.232469i	0.284977	+	0.958534i	$0.408014\pi$
$972$	42.0339	−	71.4231i	1.34824	−	2.29090i
$973$	−1.60745	−	5.99909i	−0.0515325	−	0.192322i
$974$	−30.3212	−	52.5179i	−0.971554	−	1.68278i
$975$	−0.476725	−	60.2725i	−0.0152674	−	1.93026i
$976$	23.5792	−	40.8403i	0.754751	−	1.30727i
$977$	−32.8560	−	8.80374i	−1.05116	−	0.281656i	−0.308427	−	0.951248i	$-0.599802\pi$
$977$	−32.8560	−	8.80374i	−1.05116	−	0.281656i	−0.742729	+	0.669592i	$0.766469\pi$
$978$	−17.5333	+	30.2520i	−0.560653	+	0.967351i
$979$	−8.00980	−	4.62446i	−0.255994	−	0.147798i
$980$	−14.3894	+	14.3894i	−0.459653	+	0.459653i
$981$	0.640985	−	0.169463i	0.0204651	−	0.00541053i
$982$	26.3807	+	7.06869i	0.841842	+	0.225571i
$983$	3.50838	−	13.0935i	0.111900	−	0.417616i	−0.887136	−	0.461507i	$-0.847309\pi$
$983$	3.50838	−	13.0935i	0.111900	−	0.417616i	0.999036	+	0.0438910i	$0.0139754\pi$
$984$	91.4265	+	52.9886i	2.91457	+	1.68921i
$985$	−87.7228	+	50.6468i	−2.79508	+	1.61374i
$986$	24.5031	−	91.4468i	0.780337	−	2.91226i
$987$	−16.2780	+	9.36193i	−0.518133	+	0.297994i
$988$	102.637	−	28.5577i	3.26531	−	0.908541i
$989$		−	0.348450i		−	0.0110801i
$990$	16.6392	+	4.51797i	0.528828	+	0.143591i
$991$	7.85552	−	13.6062i	0.249539	−	0.432214i	−0.713859	−	0.700289i	$-0.753054\pi$
$991$	7.85552	−	13.6062i	0.249539	−	0.432214i	0.963398	+	0.268076i	$0.0863877\pi$
$992$	37.3984	−	64.7760i	1.18740	−	2.05664i
$993$	−16.9290	+	16.8726i	−0.537225	+	0.535436i
$994$	29.8970	+	29.8970i	0.948276	+	0.948276i
$995$	−11.7003	−	11.7003i	−0.370923	−	0.370923i
$996$	18.2110	+	68.4206i	0.577039	+	2.16799i
$997$	−5.23688	+	9.07054i	−0.165854	+	0.287267i	−0.936958	−	0.349442i	$-0.886371\pi$
$997$	−5.23688	+	9.07054i	−0.165854	+	0.287267i	0.771104	+	0.636709i	$0.219705\pi$
$998$	−9.32072	+	16.1440i	−0.295042	+	0.511028i
$999$	−23.8185	+	6.25463i	−0.753584	+	0.197888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ew.a.176.2	✓	336
9.2	odd	6		819.2.fy.a.722.2	yes	336
13.2	odd	12		819.2.fy.a.743.2	yes	336
117.2	even	12	inner	819.2.ew.a.470.2	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.176.2	✓	336	1.1	even	1	trivial
819.2.ew.a.470.2	yes	336	117.2	even	12	inner
819.2.fy.a.722.2	yes	336	9.2	odd	6
819.2.fy.a.743.2	yes	336	13.2	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ew (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91264 + 1.91264i) q^{2} +(-1.50144 + 0.863523i) q^{3} -5.31637i q^{4} +(0.990693 + 3.69732i) q^{5} +(1.22011 - 4.52332i) q^{6} +(0.258819 + 0.965926i) q^{7} +(6.34303 + 6.34303i) q^{8} +(1.50865 - 2.59306i) q^{9} +O(q^{10})\)	\(q+(-1.91264 + 1.91264i) q^{2} +(-1.50144 + 0.863523i) q^{3} -5.31637i q^{4} +(0.990693 + 3.69732i) q^{5} +(1.22011 - 4.52332i) q^{6} +(0.258819 + 0.965926i) q^{7} +(6.34303 + 6.34303i) q^{8} +(1.50865 - 2.59306i) q^{9} +(-8.96647 - 5.17679i) q^{10} +(-0.392511 - 0.392511i) q^{11} +(4.59081 + 7.98223i) q^{12} +(3.10509 - 1.83260i) q^{13} +(-2.34249 - 1.35244i) q^{14} +(-4.68019 - 4.69582i) q^{15} -13.6311 q^{16} +(1.77559 + 3.07541i) q^{17} +(2.07408 + 7.84510i) q^{18} +(-1.43848 + 5.36849i) q^{19} +(19.6563 - 5.26689i) q^{20} +(-1.22270 - 1.22679i) q^{21} +1.50146 q^{22} +(0.405742 + 0.702766i) q^{23} +(-15.0010 - 4.04633i) q^{24} +(-8.35855 + 4.82581i) q^{25} +(-2.43383 + 9.44401i) q^{26} +(-0.0259896 + 5.19609i) q^{27} +(5.13522 - 1.37598i) q^{28} +9.85608i q^{29} +(17.9329 + 0.0298985i) q^{30} +(3.81667 - 1.02267i) q^{31} +(13.3853 - 13.3853i) q^{32} +(0.928275 + 0.250390i) q^{33} +(-9.27821 - 2.48609i) q^{34} +(-3.31492 + 1.91387i) q^{35} +(-13.7857 - 8.02057i) q^{36} +(1.22662 + 4.57779i) q^{37} +(-7.51668 - 13.0193i) q^{38} +(-3.07963 + 5.43285i) q^{39} +(-17.1682 + 29.7362i) q^{40} +(-6.56950 - 1.76029i) q^{41} +(4.68498 + 0.00781100i) q^{42} +(-0.371870 - 0.214699i) q^{43} +(-2.08673 + 2.08673i) q^{44} +(11.0820 + 3.00905i) q^{45} +(-2.12018 - 0.568099i) q^{46} +(2.80600 - 10.4721i) q^{47} +(20.4663 - 11.7708i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(6.75685 - 25.2169i) q^{50} +(-5.32163 - 3.08429i) q^{51} +(-9.74276 - 16.5078i) q^{52} +5.57558i q^{53} +(-9.88853 - 9.98795i) q^{54} +(1.06238 - 1.84009i) q^{55} +(-4.48520 + 7.76859i) q^{56} +(-2.47602 - 9.30263i) q^{57} +(-18.8511 - 18.8511i) q^{58} +(0.279881 + 0.279881i) q^{59} +(-24.9647 + 24.8816i) q^{60} +(-1.72981 + 2.99612i) q^{61} +(-5.34390 + 9.25591i) q^{62} +(2.89517 + 0.786115i) q^{63} +23.9403i q^{64} +(9.85188 + 9.66497i) q^{65} +(-2.25436 + 1.29655i) q^{66} +(2.14711 - 8.01313i) q^{67} +(16.3500 - 9.43969i) q^{68} +(-1.21605 - 0.704794i) q^{69} +(2.67971 - 10.0008i) q^{70} +(-15.0987 - 4.04568i) q^{71} +(26.0173 - 6.87841i) q^{72} +(1.85661 - 1.85661i) q^{73} +(-11.1017 - 6.40959i) q^{74} +(8.38267 - 14.4635i) q^{75} +(28.5409 + 7.64751i) q^{76} +(0.277547 - 0.480726i) q^{77} +(-4.50088 - 16.2813i) q^{78} +(1.53536 + 2.65931i) q^{79} +(-13.5042 - 50.3984i) q^{80} +(-4.44792 - 7.82407i) q^{81} +(15.9319 - 9.19827i) q^{82} +(7.42707 + 1.99008i) q^{83} +(-6.52205 + 6.50034i) q^{84} +(-9.61170 + 9.61170i) q^{85} +(1.12189 - 0.300611i) q^{86} +(-8.51096 - 14.7983i) q^{87} -4.97941i q^{88} +(16.0942 - 4.31242i) q^{89} +(-26.9510 + 15.4406i) q^{90} +(2.57381 + 2.52498i) q^{91} +(3.73617 - 2.15708i) q^{92} +(-4.84740 + 4.83127i) q^{93} +(14.6625 + 25.3963i) q^{94} -21.2741 q^{95} +(-8.53873 + 31.6558i) q^{96} +(13.1512 - 3.52386i) q^{97} +(0.700074 - 2.61271i) q^{98} +(-1.60997 + 0.425641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) 336 * q + 24 * q^6 - 36 * q^8	\( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) 336 * q + 24 * q^6 - 36 * q^8 + 16 * q^15 - 336 * q^16 + 20 * q^18 + 8 * q^21 + 8 * q^24 + 96 * q^26 + 24 * q^27 - 96 * q^30 - 72 * q^32 - 36 * q^33 - 12 * q^36 - 72 * q^38 - 16 * q^39 - 48 * q^41 - 28 * q^45 + 60 * q^47 - 48 * q^48 + 132 * q^50 - 36 * q^52 - 108 * q^54 + 68 * q^57 - 72 * q^58 - 44 * q^60 - 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 72 * q^69 + 48 * q^71 - 104 * q^72 + 12 * q^74 + 104 * q^78 - 12 * q^79 + 96 * q^80 - 68 * q^81 - 120 * q^83 - 12 * q^84 + 36 * q^85 + 48 * q^86 - 24 * q^87 - 60 * q^89 - 72 * q^92 - 172 * q^93 - 48 * q^94 - 152 * q^96 + 48 * q^97

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