LMFDB - Embedded newform 532.2.bs.a.67.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(67,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 12, 17]))

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

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

chi := DirichletCharacter("532.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.bs (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$76$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	532.67
Dual form			532.2.bs.a.135.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26336 + 0.635558i) q^{2} +(0.319161 + 1.81005i) q^{3} +(1.19213 - 1.60587i) q^{4} +(-0.215645 - 1.22298i) q^{5} +(-1.55361 - 2.08390i) q^{6} +(1.37354 + 2.26128i) q^{7} +(-0.485462 + 2.78645i) q^{8} +(-0.355354 + 0.129338i) q^{9} +O(q^{10})$	\(q+(-1.26336 + 0.635558i) q^{2} +(0.319161 + 1.81005i) q^{3} +(1.19213 - 1.60587i) q^{4} +(-0.215645 - 1.22298i) q^{5} +(-1.55361 - 2.08390i) q^{6} +(1.37354 + 2.26128i) q^{7} +(-0.485462 + 2.78645i) q^{8} +(-0.355354 + 0.129338i) q^{9} +(1.04971 + 1.40801i) q^{10} -2.47683i q^{11} +(3.28720 + 1.64529i) q^{12} +(-1.84829 + 2.20270i) q^{13} +(-3.17244 - 1.98384i) q^{14} +(2.14484 - 0.780658i) q^{15} +(-1.15764 - 3.82882i) q^{16} +(6.43795 + 2.34322i) q^{17} +(0.366736 - 0.389248i) q^{18} +(-2.55937 + 3.52840i) q^{19} +(-2.22103 - 1.11166i) q^{20} +(-3.65466 + 3.20789i) q^{21} +(1.57417 + 3.12911i) q^{22} +(0.223368 - 0.266200i) q^{23} +(-5.19857 + 0.0106164i) q^{24} +(3.24928 - 1.18264i) q^{25} +(0.935098 - 3.95749i) q^{26} +(2.40944 + 4.17327i) q^{27} +(5.26876 + 0.490023i) q^{28} +(2.86643 + 0.505429i) q^{29} +(-2.21354 + 2.34942i) q^{30} +(2.79716 + 4.84483i) q^{31} +(3.89595 + 4.10141i) q^{32} +(4.48319 - 0.790508i) q^{33} +(-9.62267 + 1.13137i) q^{34} +(2.46931 - 2.16745i) q^{35} +(-0.215928 + 0.724841i) q^{36} +(-8.53498 + 4.92768i) q^{37} +(0.990893 - 6.08425i) q^{38} +(-4.57692 - 2.64248i) q^{39} +(3.51247 - 0.00717307i) q^{40} +(-7.43148 - 8.85649i) q^{41} +(2.57834 - 6.37545i) q^{42} +(-0.515133 + 1.41532i) q^{43} +(-3.97747 - 2.95271i) q^{44} +(0.234809 + 0.406701i) q^{45} +(-0.113008 + 0.478269i) q^{46} +(1.72738 + 4.74594i) q^{47} +(6.56090 - 3.31741i) q^{48} +(-3.22679 + 6.21191i) q^{49} +(-3.35335 + 3.55920i) q^{50} +(-2.18661 + 12.4009i) q^{51} +(1.33385 + 5.59403i) q^{52} +(1.60981 + 0.283853i) q^{53} +(-5.69634 - 3.74099i) q^{54} +(-3.02912 + 0.534115i) q^{55} +(-6.96776 + 2.72953i) q^{56} +(-7.20345 - 3.50647i) q^{57} +(-3.94255 + 1.18325i) q^{58} +(-7.34252 - 2.67246i) q^{59} +(1.30330 - 4.37498i) q^{60} +(4.49719 + 3.77359i) q^{61} +(-6.61298 - 4.34298i) q^{62} +(-0.780562 - 0.625905i) q^{63} +(-7.52865 - 2.70543i) q^{64} +(3.09244 + 1.78542i) q^{65} +(-5.16145 + 3.84802i) q^{66} +(-7.06656 - 5.92955i) q^{67} +(11.4378 - 7.54509i) q^{68} +(0.553127 + 0.319348i) q^{69} +(-1.74208 + 4.30765i) q^{70} +(-2.08340 - 0.758296i) q^{71} +(-0.187884 - 1.05297i) q^{72} +(-1.10817 - 6.28476i) q^{73} +(7.65089 - 11.6499i) q^{74} +(3.17769 + 5.50392i) q^{75} +(2.61505 + 8.31634i) q^{76} +(5.60081 - 3.40201i) q^{77} +(7.46172 + 0.429499i) q^{78} +(7.64259 + 2.78167i) q^{79} +(-4.43294 + 2.24144i) q^{80} +(-7.65391 + 6.42240i) q^{81} +(15.0174 + 6.46576i) q^{82} +(5.98432 + 3.45505i) q^{83} +(0.794617 + 9.69315i) q^{84} +(1.47741 - 8.37881i) q^{85} +(-0.248720 - 2.11544i) q^{86} +5.34971i q^{87} +(6.90157 + 1.20241i) q^{88} +(3.97606 + 0.701086i) q^{89} +(-0.555129 - 0.364573i) q^{90} +(-7.51963 - 1.15400i) q^{91} +(-0.161198 - 0.676046i) q^{92} +(-7.87666 + 6.60930i) q^{93} +(-5.19862 - 4.89796i) q^{94} +(4.86709 + 2.36919i) q^{95} +(-6.18034 + 8.36089i) q^{96} +(8.01712 - 1.41363i) q^{97} +(0.128555 - 9.89866i) q^{98} +(0.320349 + 0.880151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 456 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 15 q^{10} - 36 q^{13} + 15 q^{14} - 3 q^{16} - 6 q^{17} - 24 q^{20} - 18 q^{21} - 6 q^{22} - 12 q^{24} - 6 q^{25} - 6 q^{26} - 27 q^{28} - 24 q^{29} + 3 q^{30} + 12 q^{32} + 66 q^{33} - 12 q^{34} - 81 q^{36} - 72 q^{38} - 33 q^{40} - 36 q^{41} - 87 q^{42} + 12 q^{44} + 6 q^{45} - 45 q^{48} - 6 q^{49} - 45 q^{50} - 3 q^{52} + 6 q^{53} - 39 q^{54} - 24 q^{57} - 42 q^{58} + 66 q^{60} - 18 q^{61} + 3 q^{62} - 6 q^{64} + 18 q^{65} + 75 q^{66} - 39 q^{68} - 36 q^{69} + 9 q^{70} - 54 q^{72} + 30 q^{73} - 57 q^{74} - 84 q^{76} - 18 q^{77} - 9 q^{78} - 3 q^{80} - 24 q^{81} + 117 q^{82} - 9 q^{84} - 78 q^{86} - 9 q^{88} - 30 q^{89} - 48 q^{90} + 30 q^{92} + 42 q^{93} - 57 q^{96} - 24 q^{97} + 60 q^{98}+O(q^{100}) $ 456 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 15 * q^10 - 36 * q^13 + 15 * q^14 - 3 * q^16 - 6 * q^17 - 24 * q^20 - 18 * q^21 - 6 * q^22 - 12 * q^24 - 6 * q^25 - 6 * q^26 - 27 * q^28 - 24 * q^29 + 3 * q^30 + 12 * q^32 + 66 * q^33 - 12 * q^34 - 81 * q^36 - 72 * q^38 - 33 * q^40 - 36 * q^41 - 87 * q^42 + 12 * q^44 + 6 * q^45 - 45 * q^48 - 6 * q^49 - 45 * q^50 - 3 * q^52 + 6 * q^53 - 39 * q^54 - 24 * q^57 - 42 * q^58 + 66 * q^60 - 18 * q^61 + 3 * q^62 - 6 * q^64 + 18 * q^65 + 75 * q^66 - 39 * q^68 - 36 * q^69 + 9 * q^70 - 54 * q^72 + 30 * q^73 - 57 * q^74 - 84 * q^76 - 18 * q^77 - 9 * q^78 - 3 * q^80 - 24 * q^81 + 117 * q^82 - 9 * q^84 - 78 * q^86 - 9 * q^88 - 30 * q^89 - 48 * q^90 + 30 * q^92 + 42 * q^93 - 57 * q^96 - 24 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.26336	+	0.635558i	−0.893327	+	0.449407i
$2$	−1.26336	+	0.635558i	−0.893327	+	0.449407i
$3$	0.319161	+	1.81005i	0.184268	+	1.04504i	0.926892	+	0.375327i	$0.122470\pi$
$3$	0.319161	+	1.81005i	0.184268	+	1.04504i	−0.742624	+	0.669708i	$0.766419\pi$
$4$	1.19213	−	1.60587i	0.596066	−	0.802935i
$5$	−0.215645	−	1.22298i	−0.0964394	−	0.546935i	−0.994297	−	0.106648i	$-0.965988\pi$
$5$	−0.215645	−	1.22298i	−0.0964394	−	0.546935i	0.897857	−	0.440286i	$-0.145123\pi$
$6$	−1.55361	−	2.08390i	−0.634258	−	0.850747i
$7$	1.37354	+	2.26128i	0.519148	+	0.854684i
$7$	1.37354	+	2.26128i	0.519148	+	0.854684i
$8$	−0.485462	+	2.78645i	−0.171637	+	0.985160i
$9$	−0.355354	+	0.129338i	−0.118451	+	0.0431128i
$10$	1.04971	+	1.40801i	0.331948	+	0.445251i
$11$		−	2.47683i		−	0.746792i	−0.927672	−	0.373396i	$-0.878193\pi$
$11$		−	2.47683i		−	0.746792i	0.927672	−	0.373396i	$-0.121807\pi$
$12$	3.28720	+	1.64529i	0.948932	+	0.474955i
$13$	−1.84829	+	2.20270i	−0.512623	+	0.610920i	−0.958820	−	0.284015i	$-0.908334\pi$
$13$	−1.84829	+	2.20270i	−0.512623	+	0.610920i	0.446197	+	0.894935i	$0.352778\pi$
$14$	−3.17244	−	1.98384i	−0.847870	−	0.530203i
$15$	2.14484	−	0.780658i	0.553795	−	0.201565i
$16$	−1.15764	−	3.82882i	−0.289411	−	0.957205i
$17$	6.43795	+	2.34322i	1.56143	+	0.568315i	0.971064	−	0.238819i	$-0.0767602\pi$
$17$	6.43795	+	2.34322i	1.56143	+	0.568315i	0.590368	+	0.807134i	$0.298982\pi$
$18$	0.366736	−	0.389248i	0.0864406	−	0.0917467i
$19$	−2.55937	+	3.52840i	−0.587160	+	0.809471i
$19$	−2.55937	+	3.52840i	−0.587160	+	0.809471i
$20$	−2.22103	−	1.11166i	−0.496638	−	0.248575i
$21$	−3.65466	+	3.20789i	−0.797513	+	0.700019i
$22$	1.57417	+	3.12911i	0.335614	+	0.667129i
$23$	0.223368	−	0.266200i	0.0465755	−	0.0555065i	−0.742254	−	0.670119i	$-0.766243\pi$
$23$	0.223368	−	0.266200i	0.0465755	−	0.0555065i	0.788829	+	0.614612i	$0.210688\pi$
$24$	−5.19857	+	0.0106164i	−1.06115	+	0.00216706i
$25$	3.24928	−	1.18264i	0.649856	−	0.236528i
$26$	0.935098	−	3.95749i	0.183388	−	0.776128i
$27$	2.40944	+	4.17327i	0.463697	+	0.803147i
$28$	5.26876	+	0.490023i	0.995703	+	0.0926057i
$29$	2.86643	+	0.505429i	0.532283	+	0.0938558i	0.433328	−	0.901236i	$-0.357339\pi$
$29$	2.86643	+	0.505429i	0.532283	+	0.0938558i	0.0989545	+	0.995092i	$0.468450\pi$
$30$	−2.21354	+	2.34942i	−0.404136	+	0.428943i
$31$	2.79716	+	4.84483i	0.502386	+	0.870157i	0.999996	+	0.00275688i	$0.000877543\pi$
$31$	2.79716	+	4.84483i	0.502386	+	0.870157i	−0.497611	+	0.867401i	$0.665789\pi$
$32$	3.89595	+	4.10141i	0.688713	+	0.725034i
$33$	4.48319	−	0.790508i	0.780423	−	0.137610i
$34$	−9.62267	+	1.13137i	−1.65027	+	0.194028i
$35$	2.46931	−	2.16745i	0.417390	−	0.366365i
$36$	−0.215928	+	0.724841i	−0.0359881	+	0.120807i
$37$	−8.53498	+	4.92768i	−1.40314	+	0.810105i	−0.994714	−	0.102685i	$-0.967257\pi$
$37$	−8.53498	+	4.92768i	−1.40314	+	0.810105i	−0.408429	+	0.912790i	$0.633923\pi$
$38$	0.990893	−	6.08425i	0.160744	−	0.986996i
$39$	−4.57692	−	2.64248i	−0.732893	−	0.423136i
$40$	3.51247	−	0.00717307i	0.555371	−	0.00113416i
$41$	−7.43148	−	8.85649i	−1.16060	−	1.38315i	−0.909766	−	0.415121i	$-0.863739\pi$
$41$	−7.43148	−	8.85649i	−1.16060	−	1.38315i	−0.250836	−	0.968030i	$-0.580705\pi$
$42$	2.57834	−	6.37545i	0.397846	−	0.983754i
$43$	−0.515133	+	1.41532i	−0.0785570	+	0.215834i	−0.972754	−	0.231840i	$-0.925525\pi$
$43$	−0.515133	+	1.41532i	−0.0785570	+	0.215834i	0.894197	+	0.447674i	$0.147748\pi$
$44$	−3.97747	−	2.95271i	−0.599625	−	0.445137i
$45$	0.234809	+	0.406701i	0.0350032	+	0.0606274i
$46$	−0.113008	+	0.478269i	−0.0166621	+	0.0705169i
$47$	1.72738	+	4.74594i	0.251965	+	0.692267i	0.999603	+	0.0281614i	$0.00896523\pi$
$47$	1.72738	+	4.74594i	0.251965	+	0.692267i	−0.747639	+	0.664106i	$0.768813\pi$
$48$	6.56090	−	3.31741i	0.946984	−	0.478827i
$49$	−3.22679	+	6.21191i	−0.460970	+	0.887416i
$50$	−3.35335	+	3.55920i	−0.474236	+	0.503347i
$51$	−2.18661	+	12.4009i	−0.306187	+	1.73647i
$52$	1.33385	+	5.59403i	0.184972	+	0.775752i
$53$	1.60981	+	0.283853i	0.221124	+	0.0389902i	0.283112	−	0.959087i	$-0.408633\pi$
$53$	1.60981	+	0.283853i	0.221124	+	0.0389902i	−0.0619883	+	0.998077i	$0.519744\pi$
$54$	−5.69634	−	3.74099i	−0.775173	−	0.509084i
$55$	−3.02912	+	0.534115i	−0.408446	+	0.0720201i
$56$	−6.96776	+	2.72953i	−0.931106	+	0.364749i
$57$	−7.20345	−	3.50647i	−0.954120	−	0.464444i
$58$	−3.94255	+	1.18325i	−0.517682	+	0.155368i
$59$	−7.34252	−	2.67246i	−0.955915	−	0.347925i	−0.183483	−	0.983023i	$-0.558737\pi$
$59$	−7.34252	−	2.67246i	−0.955915	−	0.347925i	−0.772431	+	0.635098i	$0.780960\pi$
$60$	1.30330	−	4.37498i	0.168255	−	0.564808i
$61$	4.49719	+	3.77359i	0.575806	+	0.483158i	0.883567	−	0.468305i	$-0.155135\pi$
$61$	4.49719	+	3.77359i	0.575806	+	0.483158i	−0.307761	+	0.951464i	$0.599580\pi$
$62$	−6.61298	−	4.34298i	−0.839850	−	0.551559i
$63$	−0.780562	−	0.625905i	−0.0983416	−	0.0788566i
$64$	−7.52865	−	2.70543i	−0.941082	−	0.338179i
$65$	3.09244	+	1.78542i	0.383570	+	0.221455i
$66$	−5.16145	+	3.84802i	−0.635330	+	0.473659i
$67$	−7.06656	−	5.92955i	−0.863318	−	0.724410i	0.0993623	−	0.995051i	$-0.468320\pi$
$67$	−7.06656	−	5.92955i	−0.863318	−	0.724410i	−0.962680	+	0.270642i	$0.912764\pi$
$68$	11.4378	−	7.54509i	1.38704	−	0.914976i
$69$	0.553127	+	0.319348i	0.0665887	+	0.0384450i
$70$	−1.74208	+	4.30765i	−0.208219	+	0.514862i
$71$	−2.08340	−	0.758296i	−0.247254	−	0.0899932i	0.215420	−	0.976521i	$-0.430888\pi$
$71$	−2.08340	−	0.758296i	−0.247254	−	0.0899932i	−0.462674	+	0.886528i	$0.653110\pi$
$72$	−0.187884	−	1.05297i	−0.0221424	−	0.124093i
$73$	−1.10817	−	6.28476i	−0.129702	−	0.735575i	−0.978404	−	0.206704i	$-0.933726\pi$
$73$	−1.10817	−	6.28476i	−0.129702	−	0.735575i	0.848702	−	0.528872i	$-0.177385\pi$
$74$	7.65089	−	11.6499i	0.889398	−	1.35427i
$75$	3.17769	+	5.50392i	0.366928	+	0.635537i
$76$	2.61505	+	8.31634i	0.299966	+	0.953950i
$77$	5.60081	−	3.40201i	0.638271	−	0.387695i
$78$	7.46172	+	0.429499i	0.844873	+	0.0486312i
$79$	7.64259	+	2.78167i	0.859858	+	0.312963i	0.734053	−	0.679092i	$-0.237626\pi$
$79$	7.64259	+	2.78167i	0.859858	+	0.312963i	0.125805	+	0.992055i	$0.459849\pi$
$80$	−4.43294	+	2.24144i	−0.495618	+	0.250601i
$81$	−7.65391	+	6.42240i	−0.850435	+	0.713600i
$82$	15.0174	+	6.46576i	1.65840	+	0.714023i
$83$	5.98432	+	3.45505i	0.656864	+	0.379241i	0.791081	−	0.611711i	$-0.209519\pi$
$83$	5.98432	+	3.45505i	0.656864	+	0.379241i	−0.134217	+	0.990952i	$0.542852\pi$
$84$	0.794617	+	9.69315i	0.0866999	+	1.05761i
$85$	1.47741	−	8.37881i	0.160248	−	0.908810i
$86$	−0.248720	−	2.11544i	−0.0268201	−	0.228114i
$87$			5.34971i			0.573549i
$88$	6.90157	+	1.20241i	0.735709	+	0.128177i
$89$	3.97606	+	0.701086i	0.421461	+	0.0743150i	0.380357	−	0.924840i	$-0.375801\pi$
$89$	3.97606	+	0.701086i	0.421461	+	0.0743150i	0.0411045	+	0.999155i	$0.486912\pi$
$90$	−0.555129	−	0.364573i	−0.0585157	−	0.0384294i
$91$	−7.51963	−	1.15400i	−0.788271	−	0.120973i
$92$	−0.161198	−	0.676046i	−0.0168061	−	0.0704827i
$93$	−7.87666	+	6.60930i	−0.816772	+	0.685353i
$94$	−5.19862	−	4.89796i	−0.536197	−	0.505186i
$95$	4.86709	+	2.36919i	0.499353	+	0.243074i
$96$	−6.18034	+	8.36089i	−0.630778	+	0.853330i
$97$	8.01712	−	1.41363i	0.814015	−	0.143533i	0.248883	−	0.968534i	$-0.419936\pi$
$97$	8.01712	−	1.41363i	0.814015	−	0.143533i	0.565132	+	0.825001i	$0.308825\pi$
$98$	0.128555	−	9.89866i	0.0129860	−	0.999916i
$99$	0.320349	+	0.880151i	0.0321963	+	0.0884585i
$100$	1.97440	−	6.62778i	0.197440	−	0.662778i
$101$	15.8445	−	5.76694i	1.57659	−	0.573832i	0.602132	−	0.798397i	$-0.294318\pi$
$101$	15.8445	−	5.76694i	1.57659	−	0.573832i	0.974459	+	0.224565i	$0.0720960\pi$
$102$	−5.11903	−	17.0565i	−0.506859	−	1.68884i
$103$	−6.32666	+	10.9581i	−0.623385	+	1.07973i	0.365466	+	0.930825i	$0.380910\pi$
$103$	−6.32666	+	10.9581i	−0.623385	+	1.07973i	−0.988851	+	0.148909i	$0.952424\pi$
$104$	−5.24046	−	6.21950i	−0.513869	−	0.609872i
$105$	4.71131	+	3.77783i	0.459776	+	0.368678i
$106$	−2.21416	+	0.664520i	−0.215059	+	0.0645439i
$107$	15.5431			1.50261			0.751304	−	0.659956i	$-0.229425\pi$
$107$	15.5431			1.50261			0.751304	+	0.659956i	$0.229425\pi$
$108$	9.57411	+	1.10584i	0.921269	+	0.106410i
$109$	2.92685	+	3.48808i	0.280341	+	0.334097i	0.887779	−	0.460269i	$-0.152247\pi$
$109$	2.92685	+	3.48808i	0.280341	+	0.334097i	−0.607438	+	0.794367i	$0.707803\pi$
$110$	3.48739	−	2.59996i	0.332510	−	0.247896i
$111$	−11.6434	−	13.8761i	−1.10514	−	1.31706i
$112$	7.06798	−	7.87678i	0.667861	−	0.744286i
$113$		−	11.6862i		−	1.09935i	−0.835380	−	0.549673i	$-0.814752\pi$
$113$		−	11.6862i		−	1.09935i	0.835380	−	0.549673i	$-0.185248\pi$
$114$	11.3291	−	0.148289i	1.06107	−	0.0138885i
$115$	−0.373726	−	0.215771i	−0.0348502	−	0.0201208i
$116$	4.22882	−	4.00058i	0.392636	−	0.371444i
$117$	0.371903	−	1.02179i	0.0343824	−	0.0944649i
$118$	10.9747	−	1.29033i	1.01030	−	0.118785i
$119$	3.54408	+	17.7765i	0.324885	+	1.62957i
$120$	1.13403	+	6.35548i	0.103522	+	0.580173i
$121$	4.86533			0.442302
$122$	−8.07988	−	1.90916i	−0.731518	−	0.172847i
$123$	13.6589	−	16.2780i	1.23158	−	1.46774i
$124$	11.1148	+	1.28379i	0.998135	+	0.115288i
$125$	−5.25166	−	9.09615i	−0.469723	−	0.813584i
$126$	1.38393	+	0.294647i	0.123290	+	0.0262493i
$127$	−15.7529	−	13.2183i	−1.39785	−	1.17293i	−0.962046	−	0.272888i	$-0.912021\pi$
$127$	−15.7529	−	13.2183i	−1.39785	−	1.17293i	−0.435799	−	0.900044i	$-0.643534\pi$
$128$	11.2308	−	1.36697i	0.992674	−	0.120824i
$129$	−2.72621	−	0.480704i	−0.240029	−	0.0423237i
$130$	−5.04159	−	0.290196i	−0.442177	−	0.0254519i
$131$	−10.7638	−	12.8278i	−0.940435	−	1.12077i	−0.992515	−	0.122124i	$-0.961030\pi$
$131$	−10.7638	−	12.8278i	−0.940435	−	1.12077i	0.0520800	−	0.998643i	$-0.483415\pi$
$132$	4.07510	−	8.14182i	0.354692	−	0.708654i
$133$	−11.4941	−	0.941074i	−0.996665	−	0.0816014i
$134$	12.6961	+	2.99992i	1.09678	+	0.259153i
$135$	4.58426	−	3.84665i	0.394550	−	0.331067i
$136$	−9.65466	+	16.8015i	−0.827880	+	1.44072i
$137$	2.09817	−	11.8993i	0.179258	−	1.01663i	−0.753854	−	0.657042i	$-0.771808\pi$
$137$	2.09817	−	11.8993i	0.179258	−	1.01663i	0.933113	−	0.359584i	$-0.117081\pi$
$138$	−0.901760	−	0.0519056i	−0.0767629	−	0.00441850i
$139$	3.34440	−	3.98570i	0.283668	−	0.338062i	−0.605329	−	0.795975i	$-0.706958\pi$
$139$	3.34440	−	3.98570i	0.283668	−	0.338062i	0.888997	+	0.457913i	$0.151403\pi$
$140$	−0.536892	−	6.54928i	−0.0453757	−	0.553515i
$141$	−8.03910	+	4.64138i	−0.677014	+	0.390874i
$142$	3.11402	−	0.366125i	0.261322	−	0.0307245i
$143$	5.45572	+	4.57789i	0.456230	+	0.382822i
$144$	0.906586	+	1.21086i	0.0755489	+	0.100905i
$145$		−	3.61459i		−	0.300175i
$146$	5.39434	+	7.23557i	0.446439	+	0.598820i
$147$	−12.2738	−	3.85807i	−1.01232	−	0.318208i
$148$	−2.26162	+	19.5805i	−0.185904	+	1.60951i
$149$	−2.85031	−	1.03743i	−0.233507	−	0.0849896i	0.222617	−	0.974906i	$-0.428540\pi$
$149$	−2.85031	−	1.03743i	−0.233507	−	0.0849896i	−0.456123	+	0.889917i	$0.650762\pi$
$150$	−7.51260	−	4.93379i	−0.613402	−	0.402843i
$151$	8.87798	−	15.3771i	0.722479	−	1.25137i	−0.237524	−	0.971382i	$-0.576336\pi$
$151$	8.87798	−	15.3771i	0.722479	−	1.25137i	0.960003	−	0.279989i	$-0.0903309\pi$
$152$	−8.58925	−	8.84448i	−0.696680	−	0.717382i
$153$	−2.59082			−0.209455
$154$	−4.91363	+	7.85759i	−0.395951	+	0.633183i
$155$	5.32195	−	4.46565i	0.427470	−	0.358690i
$156$	−9.69977	+	4.19975i	−0.776603	+	0.336249i
$157$	−2.89399	+	2.42835i	−0.230966	+	0.193803i	−0.750924	−	0.660388i	$-0.770392\pi$
$157$	−2.89399	+	2.42835i	−0.230966	+	0.193803i	0.519959	+	0.854191i	$0.325947\pi$
$158$	−11.4232	+	1.34307i	−0.908782	+	0.106849i
$159$			3.00443i			0.238267i
$160$	4.17581	−	5.64913i	0.330127	−	0.446603i
$161$	0.908758	+	0.139463i	0.0716202	+	0.0109912i
$162$	5.58781	−	12.9783i	0.439019	−	1.01967i
$163$	−9.89774	−	5.71446i	−0.775251	−	0.447591i	0.0594939	−	0.998229i	$-0.481051\pi$
$163$	−9.89774	−	5.71446i	−0.775251	−	0.447591i	−0.834744	+	0.550638i	$0.814385\pi$
$164$	−23.0817	+	1.37589i	−1.80238	+	0.107439i
$165$	−1.93356	−	5.31240i	−0.150527	−	0.413570i
$166$	−9.75620	−	0.561571i	−0.757228	−	0.0435863i
$167$	6.23954	−	2.27101i	0.482830	−	0.175736i	−0.0891253	−	0.996020i	$-0.528407\pi$
$167$	6.23954	−	2.27101i	0.482830	−	0.175736i	0.571956	+	0.820285i	$0.306185\pi$
$168$	−7.16444	−	11.7409i	−0.552749	−	0.905827i
$169$	0.821691	+	4.66004i	0.0632070	+	0.358465i
$170$	3.45873	+	11.5244i	0.265272	+	0.883881i
$171$	0.453126	−	1.58486i	0.0346514	−	0.121197i
$172$	1.65871	+	2.51448i	0.126475	+	0.191727i
$173$	1.53653	+	1.83117i	0.116820	+	0.139221i	0.821285	−	0.570518i	$-0.193257\pi$
$173$	1.53653	+	1.83117i	0.116820	+	0.139221i	−0.704465	+	0.709739i	$0.748813\pi$
$174$	−3.40005	−	6.75858i	−0.257757	−	0.512367i
$175$	7.13729	+	5.72313i	0.539528	+	0.432628i
$176$	−9.48333	+	2.86728i	−0.714833	+	0.216129i
$177$	2.49385	−	14.1433i	0.187449	−	1.06308i
$178$	−5.46875	+	1.64129i	−0.409900	+	0.123020i
$179$	−9.92450			−0.741792			−0.370896	−	0.928674i	$-0.620949\pi$
$179$	−9.92450			−0.741792			−0.370896	+	0.928674i	$0.620949\pi$
$180$	0.933033	+	0.107768i	0.0695441	+	0.00803259i
$181$	15.8427	+	2.79350i	1.17758	+	0.207640i	0.727986	−	0.685592i	$-0.240457\pi$
$181$	15.8427	+	2.79350i	1.17758	+	0.207640i	0.449596	+	0.893232i	$0.351568\pi$
$182$	10.2334	−	3.32124i	0.758550	−	0.246187i
$183$	−5.39507	+	9.34453i	−0.398815	+	0.690768i
$184$	0.633317	+	0.751635i	0.0466888	+	0.0554113i
$185$	7.86699	+	9.37552i	0.578393	+	0.689302i
$186$	5.75042	−	13.3560i	0.421641	−	0.979307i
$187$	5.80376	−	15.9457i	0.424413	−	1.16606i
$188$	9.68064	+	2.88384i	0.706033	+	0.210325i
$189$	−6.12749	+	11.1806i	−0.445710	+	0.813267i
$190$	−7.65462	+	0.100193i	−0.555325	+	0.00726877i
$191$	−7.99183	+	4.61409i	−0.578269	+	0.333864i	−0.760445	−	0.649402i	$-0.775019\pi$
$191$	−7.99183	+	4.61409i	−0.578269	+	0.333864i	0.182176	+	0.983266i	$0.441686\pi$
$192$	2.49413	−	14.4907i	0.179998	−	1.04578i
$193$	18.7058	−	3.29835i	1.34648	−	0.237420i	0.546504	−	0.837457i	$-0.315958\pi$
$193$	18.7058	−	3.29835i	1.34648	−	0.237420i	0.799973	+	0.600037i	$0.204847\pi$
$194$	−9.23002	+	6.88126i	−0.662677	+	0.494046i
$195$	−2.24472	+	6.16733i	−0.160748	+	0.441652i
$196$	6.12876	+	12.5872i	0.437769	+	0.899088i
$197$	−2.76064	+	4.78157i	−0.196687	+	0.340673i	−0.947452	−	0.319897i	$-0.896352\pi$
$197$	−2.76064	+	4.78157i	−0.196687	+	0.340673i	0.750765	+	0.660569i	$0.229685\pi$
$198$	−0.964101	−	0.908343i	−0.0685157	−	0.0645531i
$199$	4.86150	−	5.79372i	0.344623	−	0.410706i	−0.565696	−	0.824614i	$-0.691392\pi$
$199$	4.86150	−	5.79372i	0.344623	−	0.410706i	0.910318	+	0.413909i	$0.135837\pi$
$200$	1.71797	+	9.62809i	0.121479	+	0.680809i
$201$	8.47743	−	14.6833i	0.597952	−	1.03568i
$202$	−16.3521	+	17.3558i	−1.15053	+	1.22115i
$203$	2.79423	+	7.17603i	0.196117	+	0.503659i
$204$	17.3075	+	18.2949i	1.21177	+	1.28090i
$205$	−9.22878	+	10.9984i	−0.644566	+	0.768164i
$206$	1.02831	−	17.8649i	0.0716459	−	1.24471i
$207$	−0.0449450	+	0.123485i	−0.00312389	+	0.00858282i
$208$	10.5734	+	4.52682i	0.733134	+	0.313878i
$209$	8.73924	+	6.33912i	0.604506	+	0.438486i
$210$	−8.35308	−	1.77843i	−0.576417	−	0.122723i
$211$	−3.67787	−	20.8582i	−0.253195	−	1.43594i	−0.800664	−	0.599113i	$-0.795520\pi$
$211$	−3.67787	−	20.8582i	−0.253195	−	1.43594i	0.547470	−	0.836825i	$-0.315591\pi$
$212$	2.37493	−	2.24675i	0.163111	−	0.154308i
$213$	0.707616	−	4.01309i	0.0484850	−	0.274972i
$214$	−19.6364	+	9.87854i	−1.34232	+	0.675283i
$215$	1.84199	+	0.324793i	0.125623	+	0.0221507i
$216$	−12.7983	+	4.68783i	−0.870816	+	0.318967i
$217$	−7.11352	+	12.9797i	−0.482897	+	0.881122i
$218$	−5.91452	−	2.54650i	−0.400582	−	0.172471i
$219$	11.0221	−	4.01170i	0.744802	−	0.271086i
$220$	−2.75339	+	5.50111i	−0.185633	+	0.370885i
$221$	−17.0606	+	9.84995i	−1.14762	+	0.662579i
$222$	23.5288	+	10.1303i	1.57915	+	0.679904i
$223$	18.9704	+	6.90467i	1.27035	+	0.462371i	0.887230	−	0.461327i	$-0.152626\pi$
$223$	18.9704	+	6.90467i	1.27035	+	0.462371i	0.383122	+	0.923698i	$0.374849\pi$
$224$	−3.92321	+	14.4433i	−0.262131	+	0.965032i
$225$	−1.00168	+	0.840512i	−0.0667789	+	0.0560341i
$226$	7.42727	+	14.7638i	0.494055	+	0.982076i
$227$	1.01116	−	1.75138i	0.0671131	−	0.116243i	−0.830516	−	0.556994i	$-0.811954\pi$
$227$	1.01116	−	1.75138i	0.0671131	−	0.116243i	0.897629	+	0.440751i	$0.145288\pi$
$228$	−14.2184	+	7.38763i	−0.941637	+	0.489258i
$229$	−3.67285	−	6.36156i	−0.242709	−	0.420384i	0.718776	−	0.695242i	$-0.244703\pi$
$229$	−3.67285	−	6.36156i	−0.242709	−	0.420384i	−0.961485	+	0.274858i	$0.911369\pi$
$230$	0.609284	+	0.0350706i	0.0401750	+	0.00231249i
$231$	7.94539	+	9.05197i	0.522768	+	0.595576i
$232$	−2.79990	+	7.74181i	−0.183822	+	0.508275i
$233$	2.34756	+	13.3137i	0.153794	+	0.872206i	0.959881	+	0.280409i	$0.0904702\pi$
$233$	2.34756	+	13.3137i	0.153794	+	0.872206i	−0.806087	+	0.591797i	$0.798419\pi$
$234$	0.179564	+	1.52725i	0.0117385	+	0.0998398i
$235$	5.43171	−	3.13600i	0.354326	−	0.204570i
$236$	−13.0449	+	8.60522i	−0.849149	+	0.560152i
$237$	−2.59576	+	14.7213i	−0.168613	+	0.956251i
$238$	−15.7754	−	20.2056i	−1.02257	−	1.30973i
$239$	−12.1895	+	7.03760i	−0.788472	+	0.455225i	−0.839424	−	0.543476i	$-0.817108\pi$
$239$	−12.1895	+	7.03760i	−0.788472	+	0.455225i	0.0509521	+	0.998701i	$0.483774\pi$
$240$	−5.47196	−	7.30849i	−0.353213	−	0.471761i
$241$	6.05339	+	16.6315i	0.389933	+	1.07133i	0.967031	+	0.254657i	$0.0819627\pi$
$241$	6.05339	+	16.6315i	0.389933	+	1.07133i	−0.577098	+	0.816675i	$0.695815\pi$
$242$	−6.14663	+	3.09220i	−0.395121	+	0.198774i
$243$	−2.99329	−	2.51166i	−0.192019	−	0.161123i
$244$	11.4211	−	2.72329i	0.731163	−	0.174341i
$245$	8.29290	+	2.60675i	0.529814	+	0.166539i
$246$	−6.91039	+	29.2459i	−0.440590	+	1.86465i
$247$	−3.04156	−	12.1590i	−0.193530	−	0.773661i
$248$	−14.8578	+	5.44219i	−0.943472	+	0.345579i
$249$	−4.34386	+	11.9347i	−0.275281	+	0.756328i
$250$	12.4158	+	8.15393i	0.785247	+	0.515700i
$251$	−7.07407	−	19.4358i	−0.446511	−	1.22678i	−0.935137	−	0.354286i	$-0.884724\pi$
$251$	−7.07407	−	19.4358i	−0.446511	−	1.22678i	0.488626	−	0.872493i	$-0.337498\pi$
$252$	−1.93566	+	0.507321i	−0.121935	+	0.0319582i
$253$	−0.659331	−	0.553245i	−0.0414518	−	0.0347822i
$254$	28.3025	+	6.68747i	1.77586	+	0.419609i
$255$	15.6376			0.979267
$256$	−13.3197	+	8.86481i	−0.832483	+	0.554051i
$257$	−10.1881	−	27.9917i	−0.635519	−	1.74607i	−0.665364	−	0.746519i	$-0.731723\pi$
$257$	−10.1881	−	27.9917i	−0.635519	−	1.74607i	0.0298447	−	0.999555i	$-0.490499\pi$
$258$	3.74969	−	1.12536i	0.233445	−	0.0700621i
$259$	−22.8660	−	12.5317i	−1.42082	−	0.778680i
$260$	6.55376	−	2.83761i	0.406447	−	0.175981i
$261$	−1.08397	+	0.191133i	−0.0670960	+	0.0118308i
$262$	21.7512	+	9.36502i	1.34380	+	0.578573i
$263$	−12.4267	+	2.19117i	−0.766266	+	0.135113i	−0.543101	−	0.839667i	$-0.682750\pi$
$263$	−12.4267	+	2.19117i	−0.766266	+	0.135113i	−0.223165	+	0.974781i	$0.571639\pi$
$264$	0.0262949	+	12.8760i	0.00161834	+	0.792461i
$265$		−	2.02998i		−	0.124701i
$266$	15.1192	−	6.11626i	0.927020	−	0.375012i
$267$			7.42064i			0.454136i
$268$	−17.9464	+	4.27918i	−1.09625	+	0.261393i
$269$	7.38107	−	1.30148i	0.450032	−	0.0793527i	0.0559611	−	0.998433i	$-0.482178\pi$
$269$	7.38107	−	1.30148i	0.450032	−	0.0793527i	0.394070	+	0.919080i	$0.371067\pi$
$270$	−3.34678	+	7.77325i	−0.203678	+	0.473065i
$271$	4.30043	−	0.758281i	0.261232	−	0.0460623i	−0.0414980	−	0.999139i	$-0.513213\pi$
$271$	4.30043	−	0.758281i	0.261232	−	0.0460623i	0.302730	+	0.953076i	$0.402102\pi$
$272$	1.51893	−	27.3624i	0.0920987	−	1.65909i
$273$	−0.311163	−	13.9792i	−0.0188324	−	0.846062i
$274$	4.91196	+	16.3665i	0.296743	+	0.988739i
$275$	−2.92920	−	8.04790i	−0.176637	−	0.485307i
$276$	1.17223	−	0.507545i	0.0705601	−	0.0305506i
$277$	−29.9481			−1.79940			−0.899702	−	0.436504i	$-0.856217\pi$
$277$	−29.9481			−1.79940			−0.899702	+	0.436504i	$0.856217\pi$
$278$	−1.69202	+	7.16091i	−0.101481	+	0.429483i
$279$	−1.62061	−	1.35985i	−0.0970232	−	0.0814121i
$280$	4.84073	+	7.93284i	0.289289	+	0.474078i
$281$	−9.46661	−	26.0093i	−0.564730	−	1.55158i	−0.812619	−	0.582796i	$-0.801959\pi$
$281$	−9.46661	−	26.0093i	−0.564730	−	1.55158i	0.247888	−	0.968789i	$-0.420263\pi$
$282$	7.20637	−	10.9730i	0.429133	−	0.653434i
$283$	−3.76708	+	10.3500i	−0.223930	+	0.615242i	−0.999879	−	0.0155536i	$-0.995049\pi$
$283$	−3.76708	+	10.3500i	−0.223930	+	0.615242i	0.775949	+	0.630795i	$0.217271\pi$
$284$	−3.70141	+	2.44168i	−0.219639	+	0.144887i
$285$	−2.73497	+	9.56585i	−0.162006	+	0.566632i
$286$	−9.80202	−	2.31608i	−0.579606	−	0.136952i
$287$	9.81961	−	28.9694i	0.579633	−	1.71001i
$288$	−1.91491	−	0.953557i	−0.112837	−	0.0561889i
$289$	22.9338	+	19.2437i	1.34905	+	1.13198i
$290$	2.29728	+	4.56651i	0.134901	+	0.268155i
$291$	5.11751	+	14.0602i	0.299994	+	0.824226i
$292$	−11.4136	−	5.71268i	−0.667930	−	0.334309i
$293$	−7.37297	+	4.25678i	−0.430733	+	0.248684i	−0.699659	−	0.714477i	$-0.746665\pi$
$293$	−7.37297	+	4.25678i	−0.430733	+	0.248684i	0.268926	+	0.963161i	$0.413331\pi$
$294$	17.9581	−	2.92658i	1.04734	−	0.170682i
$295$	−1.68500	+	9.55608i	−0.0981042	+	0.556377i
$296$	−9.58733	−	26.1745i	−0.557252	−	1.52136i
$297$	10.3365	−	5.96777i	0.599783	−	0.346285i
$298$	4.26031	−	0.500898i	0.246793	−	0.0290163i
$299$	0.173511	+	0.984028i	0.0100344	+	0.0569078i
$300$	12.6268	+	1.45844i	0.729009	+	0.0842030i
$301$	−3.90798	+	0.779128i	−0.225252	+	0.0449082i
$302$	−1.44299	+	25.0692i	−0.0830349	+	1.44257i
$303$	15.4954	+	26.8389i	0.890190	+	1.54185i
$304$	16.4725	+	5.71475i	0.944760	+	0.327763i
$305$	3.64524	−	6.31374i	0.208726	−	0.361524i
$306$	3.27313	−	1.64662i	0.187112	−	0.0941308i
$307$	17.9838	−	15.0902i	1.02639	−	0.861245i	0.0359742	−	0.999353i	$-0.488547\pi$
$307$	17.9838	−	15.0902i	1.02639	−	0.861245i	0.990417	+	0.138108i	$0.0441021\pi$
$308$	1.21370	−	13.0498i	0.0691572	−	0.743582i
$309$	−21.8540	−	7.95420i	−1.24323	−	0.452499i
$310$	−3.88534	+	9.02411i	−0.220672	+	0.512535i
$311$	−5.82967	+	3.36576i	−0.330570	+	0.190855i	−0.656094	−	0.754679i	$-0.727793\pi$
$311$	−5.82967	+	3.36576i	−0.330570	+	0.190855i	0.325524	+	0.945534i	$0.394459\pi$
$312$	9.58508	−	11.4705i	0.542648	−	0.649391i
$313$	−7.18310	+	2.61443i	−0.406013	+	0.147776i	−0.536950	−	0.843614i	$-0.680424\pi$
$313$	−7.18310	+	2.61443i	−0.406013	+	0.147776i	0.130937	+	0.991391i	$0.458201\pi$
$314$	2.11278	−	4.90716i	0.119231	−	0.276927i
$315$	−0.597147	+	1.08959i	−0.0336454	+	0.0613913i
$316$	13.5780	−	8.95689i	0.763821	−	0.503864i
$317$	−30.6702	−	5.40799i	−1.72261	−	0.303743i	−0.777110	−	0.629364i	$-0.783315\pi$
$317$	−30.6702	−	5.40799i	−1.72261	−	0.303743i	−0.945500	+	0.325622i	$0.894426\pi$
$318$	−1.90949	−	3.79567i	−0.107079	−	0.212850i
$319$	1.25186	−	7.09965i	0.0700907	−	0.397504i
$320$	−1.68518	+	9.79083i	−0.0942047	+	0.547324i
$321$	4.96076	+	28.1338i	0.276882	+	1.57028i
$322$	−1.23672	+	0.401377i	−0.0689198	+	0.0223679i
$323$	−24.7449	+	16.7185i	−1.37685	+	0.930242i
$324$	1.18906	+	19.9475i	0.0660591	+	1.10820i
$325$	−3.40059	+	9.34306i	−0.188631	+	0.518260i
$326$	16.1362	+	0.928807i	0.893703	+	0.0514419i
$327$	−5.37948	+	6.41101i	−0.297486	+	0.354530i
$328$	28.2859	−	16.4080i	1.56183	−	0.905979i
$329$	−8.35929	+	10.4248i	−0.460863	+	0.574739i
$330$	5.81911	+	5.48256i	0.320331	+	0.301805i
$331$	1.20437	−	2.08603i	0.0661983	−	0.114659i	−0.831027	−	0.556233i	$-0.812246\pi$
$331$	1.20437	−	2.08603i	0.0661983	−	0.114659i	0.897225	+	0.441574i	$0.145580\pi$
$332$	12.6825	−	5.49117i	0.696040	−	0.301367i
$333$	2.39560	−	2.85497i	0.131278	−	0.156451i
$334$	−6.43940	+	6.83468i	−0.352348	+	0.373977i
$335$	−5.72787	+	9.92096i	−0.312947	+	0.542040i
$336$	16.5132	+	10.2795i	0.900870	+	0.560790i
$337$	−1.00431	+	2.75932i	−0.0547083	+	0.150310i	−0.964037	−	0.265770i	$-0.914374\pi$
$337$	−1.00431	+	2.75932i	−0.0547083	+	0.150310i	0.909328	+	0.416079i	$0.136596\pi$
$338$	−3.99981	−	5.36505i	−0.217561	−	0.291820i
$339$	21.1527	−	3.72979i	1.14886	−	0.202574i
$340$	−11.6940	−	12.3612i	−0.634197	−	0.670379i
$341$	11.9998	−	6.92809i	0.649826	−	0.375177i
$342$	0.434809	+	2.29022i	0.0235118	+	0.123841i
$343$	−18.4790	+	1.23560i	−0.997772	+	0.0667162i
$344$	−3.69364	−	2.12248i	−0.199148	−	0.114436i
$345$	0.271278	−	0.745331i	0.0146051	−	0.0401273i
$346$	−3.10500	−	1.33686i	−0.166926	−	0.0718701i
$347$	12.6418	+	15.0659i	0.678649	+	0.808782i	0.989933	−	0.141534i	$-0.0452036\pi$
$347$	12.6418	+	15.0659i	0.678649	+	0.808782i	−0.311284	+	0.950317i	$0.600759\pi$
$348$	8.59094	+	6.37756i	0.460523	+	0.341873i
$349$	−4.23272	+	7.33128i	−0.226572	+	0.392435i	−0.956790	−	0.290780i	$-0.906085\pi$
$349$	−4.23272	+	7.33128i	−0.226572	+	0.392435i	0.730218	+	0.683214i	$0.239419\pi$
$350$	−12.6543	−	2.69419i	−0.676401	−	0.144010i
$351$	−13.6458	−	2.40613i	−0.728360	−	0.128430i
$352$	10.1585	−	9.64960i	0.541449	−	0.514325i
$353$	−5.71625			−0.304245			−0.152123	−	0.988362i	$-0.548611\pi$
$353$	−5.71625			−0.304245			−0.152123	+	0.988362i	$0.548611\pi$
$354$	5.83828	+	19.4530i	0.310301	+	1.03392i
$355$	−0.478108	+	2.71149i	−0.0253754	+	0.143911i
$356$	5.86584	−	5.54925i	0.310889	−	0.294110i
$357$	−31.0453	+	12.0886i	−1.64309	+	0.639794i
$358$	12.5382	−	6.30760i	0.662663	−	0.333367i
$359$	−18.1526	−	21.6335i	−0.958059	−	1.14177i	−0.989827	−	0.142275i	$-0.954558\pi$
$359$	−18.1526	−	21.6335i	−0.958059	−	1.14177i	0.0317684	−	0.999495i	$-0.489886\pi$
$360$	−1.24724	+	0.456847i	−0.0657356	+	0.0240779i
$361$	−5.89922	−	18.0610i	−0.310486	−	0.950578i
$362$	−21.7904	+	6.53980i	−1.14528	+	0.343724i
$363$	1.55282	+	8.80650i	0.0815021	+	0.462222i
$364$	−10.8176	+	10.6998i	−0.566995	+	0.560823i
$365$	−7.44718	+	2.71055i	−0.389803	+	0.141877i
$366$	0.876894	−	15.2343i	0.0458360	−	0.796312i
$367$	−8.49121	−	23.3294i	−0.443237	−	1.21778i	−0.937351	−	0.348387i	$-0.886729\pi$
$367$	−8.49121	−	23.3294i	−0.443237	−	1.21778i	0.494113	−	0.869397i	$-0.335493\pi$
$368$	−1.27781	−	0.547073i	−0.0666106	−	0.0285181i
$369$	3.78629	+	2.18601i	0.197106	+	0.113799i
$370$	−15.8975	−	6.84468i	−0.826471	−	0.355838i
$371$	1.56926	+	4.03011i	0.0814719	+	0.209233i
$372$	1.22367	+	20.5281i	0.0634442	+	1.06433i
$373$		−	20.0278i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$373$		−	20.0278i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$374$	2.80221	+	23.8337i	0.144899	+	1.23241i
$375$	14.7884	−	12.4089i	0.763669	−	0.640795i
$376$	−14.0629	+	2.50930i	−0.725240	+	0.129407i
$377$	−6.41130	+	5.37972i	−0.330199	+	0.277070i
$378$	0.635297	−	18.0194i	0.0326762	−	0.926818i
$379$	21.1731			1.08759			0.543795	−	0.839218i	$-0.316987\pi$
$379$	21.1731			1.08759			0.543795	+	0.839218i	$0.316987\pi$
$380$	9.60683	−	4.99154i	0.492820	−	0.256060i
$381$	18.8981	−	32.7324i	0.968177	−	1.67693i
$382$	7.16400	−	10.9085i	0.366542	−	0.558128i
$383$	7.58674	+	2.76135i	0.387664	+	0.141098i	0.528497	−	0.848935i	$-0.322756\pi$
$383$	7.58674	+	2.76135i	0.387664	+	0.141098i	−0.140833	+	0.990033i	$0.544978\pi$
$384$	6.05874	+	19.8921i	0.309184	+	1.01512i
$385$	−5.36839	−	6.11606i	−0.273599	−	0.311703i
$386$	−21.5358	+	16.0556i	−1.09615	+	0.817210i
$387$		−	0.569565i		−	0.0289526i
$388$	7.28735	−	14.5597i	0.369959	−	0.739156i
$389$	8.53363	+	7.16056i	0.432672	+	0.363055i	0.832959	−	0.553335i	$-0.186645\pi$
$389$	8.53363	+	7.16056i	0.432672	+	0.363055i	−0.400287	+	0.916390i	$0.631090\pi$
$390$	−1.08381	−	9.21818i	−0.0548809	−	0.466781i
$391$	2.06180	−	1.19038i	0.104270	−	0.0602001i
$392$	−15.7427	−	12.0070i	−0.795127	−	0.606443i
$393$	19.7836	−	23.5771i	0.997949	−	1.18931i
$394$	0.448704	−	7.79536i	0.0226054	−	0.392725i
$395$	1.75386	−	9.94661i	0.0882461	−	0.500468i
$396$	1.79531	+	0.534817i	0.0902175	+	0.0268756i
$397$	−9.76681	+	8.19533i	−0.490182	+	0.411312i	−0.854092	−	0.520123i	$-0.825886\pi$
$397$	−9.76681	+	8.19533i	−0.490182	+	0.411312i	0.363909	+	0.931434i	$0.381442\pi$
$398$	−2.45956	+	10.4093i	−0.123287	+	0.521770i
$399$	−1.96508	−	21.1053i	−0.0983770	−	1.05659i
$400$	−8.28962	−	11.0718i	−0.414481	−	0.553591i
$401$	3.97137	+	4.73289i	0.198321	+	0.236349i	0.856035	−	0.516918i	$-0.172921\pi$
$401$	3.97137	+	4.73289i	0.198321	+	0.236349i	−0.657714	+	0.753268i	$0.728476\pi$
$402$	−1.37789	+	23.9382i	−0.0687229	+	1.19393i
$403$	−15.8417	−	2.79332i	−0.789131	−	0.139145i
$404$	9.62782	−	32.3192i	0.479002	−	1.60794i
$405$	9.50501	+	7.97565i	0.472308	+	0.396313i
$406$	−8.09089	−	7.28998i	−0.401544	−	0.361796i
$407$	12.2050	+	21.1397i	0.604979	+	1.04786i
$408$	−33.4930	−	12.1131i	−1.65815	−	0.599686i
$409$	−2.75968	+	3.28885i	−0.136457	+	0.162623i	−0.829945	−	0.557845i	$-0.811629\pi$
$409$	−2.75968	+	3.28885i	−0.136457	+	0.162623i	0.693488	+	0.720468i	$0.256073\pi$
$410$	4.66908	−	19.7603i	0.230590	−	0.975894i
$411$	22.2080			1.09544
$412$	10.0551	+	23.2233i	0.495378	+	1.14413i
$413$	−4.04204	−	20.2742i	−0.198896	−	0.997630i
$414$	−0.0217006	−	0.184571i	−0.00106653	−	0.00907117i
$415$	2.93498	−	8.06379i	0.144072	−	0.395836i
$416$	−16.2350	+	1.00104i	−0.795988	+	0.0490800i
$417$	8.28173	+	4.78146i	0.405558	+	0.234149i
$418$	−15.0696	−	2.45427i	−0.737080	−	0.120042i
$419$			11.7691i			0.574959i	0.957787	+	0.287479i	$0.0928173\pi$
$419$			11.7691i			0.574959i	−0.957787	+	0.287479i	$0.907183\pi$
$420$	11.6832	−	3.06208i	0.570082	−	0.149414i
$421$	−15.6031	−	18.5951i	−0.760450	−	0.906268i	0.237427	−	0.971405i	$-0.423696\pi$
$421$	−15.6031	−	18.5951i	−0.760450	−	0.906268i	−0.997876	+	0.0651370i	$0.979252\pi$
$422$	17.9031	+	24.0138i	0.871507	+	1.16897i
$423$	−1.22766	−	1.46307i	−0.0596911	−	0.0711371i
$424$	−1.57244	+	4.34786i	−0.0763646	+	0.211151i
$425$	23.6899			1.14913
$426$	1.65658	+	5.51968i	0.0802616	+	0.267430i
$427$	−2.35609	+	15.3526i	−0.114019	+	0.742963i
$428$	18.5294	−	24.9602i	0.895653	−	1.20650i
$429$	−6.54497	+	11.3362i	−0.315994	+	0.547318i
$430$	−2.53352	+	0.760365i	−0.122177	+	0.0366681i
$431$	−12.8671	+	4.68325i	−0.619788	+	0.225584i	−0.632780	−	0.774331i	$-0.718086\pi$
$431$	−12.8671	+	4.68325i	−0.619788	+	0.225584i	0.0129928	+	0.999916i	$0.495864\pi$
$432$	13.1894	−	14.0565i	0.634577	−	0.676293i
$433$	−0.574698	−	1.57897i	−0.0276182	−	0.0758804i	0.925117	−	0.379681i	$-0.123966\pi$
$433$	−0.574698	−	1.57897i	−0.0276182	−	0.0758804i	−0.952735	+	0.303801i	$0.901744\pi$
$434$	0.737528	−	20.9191i	0.0354025	−	1.00415i
$435$	6.54260	−	1.15364i	0.313694	−	0.0553127i
$436$	9.09059	−	0.541886i	0.435360	−	0.0259516i
$437$	0.367578	+	1.46944i	0.0175836	+	0.0702927i
$438$	−11.3751	+	12.0734i	−0.543524	+	0.576888i
$439$	−2.12695	+	1.78473i	−0.101514	+	0.0851804i	−0.692132	−	0.721771i	$-0.743328\pi$
$439$	−2.12695	+	1.78473i	−0.101514	+	0.0851804i	0.590618	+	0.806951i	$0.298884\pi$
$440$	−0.0177664	−	8.69979i	−0.000846982	−	0.414746i
$441$	0.343216	−	2.62478i	0.0163436	−	0.124989i
$442$	15.2934	−	23.2870i	0.727433	−	1.10765i
$443$	−14.7192	−	2.59539i	−0.699330	−	0.123311i	−0.187331	−	0.982297i	$-0.559984\pi$
$443$	−14.7192	−	2.59539i	−0.699330	−	0.123311i	−0.511999	+	0.858986i	$0.671095\pi$
$444$	−36.1636	+	2.15570i	−1.71625	+	0.102305i
$445$		−	5.01384i		−	0.237679i
$446$	−28.3547	+	3.33375i	−1.34263	+	0.157858i
$447$	0.968094	−	5.49033i	0.0457893	−	0.259684i
$448$	−4.22314	−	20.7404i	−0.199524	−	0.979893i
$449$	6.41503	+	3.70372i	0.302744	+	0.174789i	0.643675	−	0.765299i	$-0.277409\pi$
$449$	6.41503	+	3.70372i	0.302744	+	0.174789i	−0.340931	+	0.940088i	$0.610742\pi$
$450$	0.731288	−	1.69849i	0.0344732	−	0.0800677i
$451$	−21.9360	+	18.4065i	−1.03293	+	0.866727i
$452$	−18.7666	−	13.9315i	−0.882705	−	0.655283i
$453$	30.6669	+	11.1618i	1.44086	+	0.524429i
$454$	−0.164350	+	2.85527i	−0.00771334	+	0.134004i
$455$	0.210241	+	9.44523i	0.00985624	+	0.442799i
$456$	13.2676	−	18.3698i	0.621314	−	0.860246i
$457$	8.16811	+	14.1476i	0.382088	+	0.661796i	0.991361	−	0.131165i	$-0.0418718\pi$
$457$	8.16811	+	14.1476i	0.382088	+	0.661796i	−0.609272	+	0.792961i	$0.708538\pi$
$458$	8.68326	+	5.70260i	0.405742	+	0.266465i
$459$	5.73295	+	32.5132i	0.267591	+	1.51759i
$460$	−0.792032	+	0.342929i	−0.0369287	+	0.0159891i
$461$	33.3129	+	12.1249i	1.55154	+	0.564714i	0.968778	−	0.247931i	$-0.0797505\pi$
$461$	33.3129	+	12.1249i	1.55154	+	0.564714i	0.582760	+	0.812644i	$0.301973\pi$
$462$	−15.7909	−	6.38609i	−0.734659	−	0.297108i
$463$	16.0532	+	9.26831i	0.746055	+	0.430735i	0.824267	−	0.566202i	$-0.191588\pi$
$463$	16.0532	+	9.26831i	0.746055	+	0.430735i	−0.0782120	+	0.996937i	$0.524921\pi$
$464$	−1.38311	−	11.5602i	−0.0642091	−	0.536667i
$465$	9.78163	+	8.20776i	0.453612	+	0.380626i
$466$	−11.4274	−	15.3279i	−0.529364	−	0.710050i
$467$	12.4279	+	7.17528i	0.575097	+	0.332032i	0.759182	−	0.650878i	$-0.225599\pi$
$467$	12.4279	+	7.17528i	0.575097	+	0.332032i	−0.184086	+	0.982910i	$0.558932\pi$
$468$	−1.19751	−	1.81534i	−0.0553550	−	0.0839142i
$469$	3.70220	−	24.1239i	0.170952	−	1.11394i
$470$	−4.86907	+	7.41404i	−0.224593	+	0.341984i
$471$	−5.31909	−	4.46324i	−0.245091	−	0.205655i
$472$	11.0112	−	19.1622i	0.506832	−	0.882013i
$473$	3.50549	+	1.27590i	0.161183	+	0.0586657i
$474$	−6.07687	−	20.2480i	−0.279120	−	0.930021i
$475$	−4.14328	+	14.4916i	−0.190107	+	0.664919i
$476$	32.7718	+	15.5006i	1.50209	+	0.710470i
$477$	−0.608765	+	0.107342i	−0.0278734	+	0.00491484i
$478$	10.9268	−	16.6381i	0.499782	−	0.761010i
$479$	−24.0508	−	4.24080i	−1.09891	−	0.193767i	−0.405345	−	0.914164i	$-0.632849\pi$
$479$	−24.0508	−	4.24080i	−1.09891	−	0.193767i	−0.693562	+	0.720397i	$0.743960\pi$
$480$	11.5580	+	5.75546i	0.527548	+	0.262700i
$481$	4.92090	−	27.9078i	0.224374	−	1.27249i
$482$	−18.2179	−	17.1643i	−0.829802	−	0.781811i
$483$	0.0376045	+	1.68941i	0.00171106	+	0.0768709i
$484$	5.80011	−	7.81309i	0.263641	−	0.355140i
$485$	−3.45770	−	9.49996i	−0.157006	−	0.431371i
$486$	5.37789	+	1.27072i	0.243946	+	0.0576409i
$487$	−16.9877	−	29.4236i	−0.769788	−	1.33331i	−0.937678	−	0.347505i	$-0.887029\pi$
$487$	−16.9877	−	29.4236i	−0.769788	−	1.33331i	0.167890	−	0.985806i	$-0.446305\pi$
$488$	−12.6981	+	10.6993i	−0.574818	+	0.484333i
$489$	7.18451	−	19.7393i	0.324895	−	0.892641i
$490$	−12.1336	+	1.97738i	−0.548141	+	0.0893287i
$491$	−2.75589	−	3.28434i	−0.124371	−	0.148220i	0.700265	−	0.713883i	$-0.253065\pi$
$491$	−2.75589	−	3.28434i	−0.124371	−	0.148220i	−0.824637	+	0.565662i	$0.808621\pi$
$492$	−9.85721	−	41.3400i	−0.444397	−	1.86375i
$493$	17.2696	+	9.97061i	0.777784	+	0.449054i
$494$	11.5704	+	13.4281i	0.520575	+	0.604159i
$495$	1.00733	−	0.581581i	0.0452760	−	0.0261401i
$496$	15.3119	−	16.3184i	0.687523	−	0.732719i
$497$	−1.14691	−	5.75270i	−0.0514458	−	0.258044i
$498$	−2.09733	−	17.8385i	−0.0939836	−	0.799362i
$499$	2.23917	−	0.394827i	0.100239	−	0.0176749i	−0.123304	−	0.992369i	$-0.539349\pi$
$499$	2.23917	−	0.394827i	0.100239	−	0.0176749i	0.223543	+	0.974694i	$0.428238\pi$
$500$	−20.8679	−	2.41032i	−0.933242	−	0.107793i
$501$	6.10207	+	10.5691i	0.272620	+	0.472192i
$502$	21.2897	+	20.0584i	0.950204	+	0.895250i
$503$	23.2700	+	4.10313i	1.03756	+	0.182949i	0.666380	−	0.745613i	$-0.267843\pi$
$503$	23.2700	+	4.10313i	1.03756	+	0.182949i	0.371178	+	0.928562i	$0.378954\pi$
$504$	2.12299	−	1.87115i	0.0945654	−	0.0833476i
$505$	−10.4697	−	18.1340i	−0.465894	−	0.806952i
$506$	1.18459	+	0.279901i	0.0526614	+	0.0124431i
$507$	−8.17267	+	2.97461i	−0.362961	+	0.132107i
$508$	−40.0064	+	9.53923i	−1.77500	+	0.423235i
$509$	−14.7112	+	17.5322i	−0.652064	+	0.777099i	−0.986224	−	0.165417i	$-0.947103\pi$
$509$	−14.7112	+	17.5322i	−0.652064	+	0.777099i	0.334160	+	0.942516i	$0.391547\pi$
$510$	−19.7559	+	9.93862i	−0.874805	+	0.440090i
$511$	12.6895	−	11.1382i	0.561350	−	0.492727i
$512$	11.1934	−	19.6649i	0.494685	−	0.869072i
$513$	−20.8916	−	2.17949i	−0.922389	−	0.0962268i
$514$	30.6616	+	28.8883i	1.35242	+	1.27421i
$515$	14.7659	+	5.37434i	0.650663	+	0.236822i
$516$	−4.02195	+	3.80488i	−0.177057	+	0.167500i
$517$	11.7549	−	4.27843i	0.516979	−	0.188165i
$518$	36.8525	+	1.29928i	1.61920	+	0.0570871i
$519$	−2.82411	+	3.36565i	−0.123965	+	0.147735i
$520$	−6.47626	+	7.75020i	−0.284003	+	0.339869i
$521$			20.5235i			0.899151i	0.893242	+	0.449575i	$0.148425\pi$
$521$			20.5235i			0.899151i	−0.893242	+	0.449575i	$0.851575\pi$
$522$	1.24796	−	0.930394i	0.0546218	−	0.0407222i
$523$	22.7519	−	8.28100i	0.994870	−	0.362103i	0.207266	−	0.978285i	$-0.433544\pi$
$523$	22.7519	−	8.28100i	0.994870	−	0.362103i	0.787604	+	0.616182i	$0.211321\pi$
$524$	−33.4316	+	1.99284i	−1.46046	+	0.0870576i
$525$	−8.08123	+	14.7455i	−0.352694	+	0.643545i
$526$	14.3068	−	10.6661i	0.623805	−	0.465066i
$527$	6.65549	+	37.7452i	0.289918	+	1.64421i
$528$	−8.21665	−	16.2502i	−0.357584	−	0.707200i
$529$	3.97294	+	22.5317i	0.172736	+	0.979637i
$530$	1.29017	+	2.56459i	0.0560414	+	0.111398i
$531$	2.95485			0.128229
$532$	−15.2137	+	17.3362i	−0.659599	+	0.751618i
$533$	33.2437			1.43995
$534$	−4.71625	−	9.37490i	−0.204092	−	0.405692i
$535$	−3.35179	−	19.0089i	−0.144911	−	0.821828i
$536$	19.9530	−	16.8121i	0.861837	−	0.726171i
$537$	−3.16752	−	17.9639i	−0.136688	−	0.775199i
$538$	−8.49774	+	6.33533i	−0.366364	+	0.273135i
$539$	15.3858	+	7.99221i	0.662714	+	0.344249i
$540$	−0.712182	−	11.9474i	−0.0306474	−	0.514136i
$541$	18.6150	−	6.77529i	0.800319	−	0.291292i	0.0907006	−	0.995878i	$-0.471089\pi$
$541$	18.6150	−	6.77529i	0.800319	−	0.291292i	0.709619	+	0.704586i	$0.248867\pi$
$542$	−4.95103	+	3.69115i	−0.212665	+	0.158548i
$543$			29.5678i			1.26888i
$544$	15.4714	+	35.5338i	0.663332	+	1.52350i
$545$	3.63470	−	4.33167i	0.155694	−	0.185548i
$546$	9.27773	+	17.4630i	0.397050	+	0.747347i
$547$	−0.938337	+	0.341527i	−0.0401204	+	0.0146026i	−0.362002	−	0.932177i	$-0.617907\pi$
$547$	−0.938337	+	0.341527i	−0.0401204	+	0.0146026i	0.321882	+	0.946780i	$0.395685\pi$
$548$	−16.6074	−	17.5549i	−0.709435	−	0.749909i
$549$	−2.08616	−	0.759301i	−0.0890353	−	0.0324062i
$550$	8.81552	+	8.30568i	0.375895	+	0.354155i
$551$	−9.11962	+	8.82033i	−0.388509	+	0.375759i
$552$	−1.15837	+	1.38623i	−0.0493035	+	0.0590019i
$553$	4.20723	+	21.1028i	0.178909	+	0.897381i
$554$	37.8350	−	19.0337i	1.60746	−	0.808666i
$555$	−14.4594	+	17.2320i	−0.613765	+	0.731457i
$556$	−2.41355	−	10.1221i	−0.102357	−	0.429275i
$557$	28.9858	−	10.5500i	1.22817	−	0.447017i	0.355198	−	0.934791i	$-0.384413\pi$
$557$	28.9858	−	10.5500i	1.22817	−	0.447017i	0.872970	+	0.487774i	$0.162191\pi$
$558$	2.91166	+	0.687984i	0.123261	+	0.0291247i
$559$	−2.16541	−	3.75060i	−0.0915870	−	0.158633i
$560$	−11.1573	−	6.94543i	−0.471484	−	0.293498i
$561$	30.7149	+	5.41587i	1.29678	+	0.228658i
$562$	28.4901	+	26.8424i	1.20178	+	1.13228i
$563$	−13.9176	−	24.1060i	−0.586557	−	1.01595i	−0.994679	−	0.103020i	$-0.967150\pi$
$563$	−13.9176	−	24.1060i	−0.586557	−	1.01595i	0.408122	−	0.912927i	$-0.366184\pi$
$564$	−2.13022	+	18.4429i	−0.0896983	+	0.776586i
$565$	−14.2920	+	2.52007i	−0.601271	+	0.106020i
$566$	−1.81884	−	15.4699i	−0.0764517	−	0.650247i
$567$	−25.0358	−	8.48626i	−1.05140	−	0.356389i
$568$	3.12437	−	5.43718i	0.131096	−	0.228139i
$569$	23.5359	−	13.5884i	0.986675	−	0.569657i	0.0823963	−	0.996600i	$-0.473743\pi$
$569$	23.5359	−	13.5884i	0.986675	−	0.569657i	0.904279	+	0.426943i	$0.140409\pi$
$570$	−2.62441	−	13.8233i	−0.109925	−	0.578994i
$571$	−17.9204	−	10.3464i	−0.749947	−	0.432982i	0.0757279	−	0.997129i	$-0.475872\pi$
$571$	−17.9204	−	10.3464i	−0.749947	−	0.432982i	−0.825675	+	0.564147i	$0.809205\pi$
$572$	13.8554	−	3.30373i	0.579325	−	0.138136i
$573$	−10.9024	−	12.9930i	−0.455456	−	0.542791i
$574$	6.00607	+	42.8395i	0.250688	+	1.78809i
$575$	0.410967	−	1.12912i	0.0171385	−	0.0470876i
$576$	3.02525	−	0.0123562i	0.126052	−	0.000514842i
$577$	18.6099	+	32.2333i	0.774741	+	1.34189i	0.934940	+	0.354806i	$0.115453\pi$
$577$	18.6099	+	32.2333i	0.774741	+	1.34189i	−0.160199	+	0.987085i	$0.551214\pi$
$578$	−41.2040	−	9.73591i	−1.71386	−	0.404960i
$579$	11.9404	+	32.8059i	0.496225	+	1.36337i
$580$	−5.80456	−	4.30907i	−0.241021	−	0.178924i
$581$	0.406846	+	18.2779i	0.0168788	+	0.758294i
$582$	−15.4013	−	14.5106i	−0.638405	−	0.601484i
$583$	0.703054	−	3.98722i	0.0291175	−	0.165134i
$584$	18.0502	−	0.0368615i	0.746921	−	0.00152534i
$585$	−1.32984	−	0.234486i	−0.0549820	−	0.00969480i
$586$	6.60924	−	10.0638i	0.273025	−	0.415731i
$587$	−31.3167	+	5.52198i	−1.29258	+	0.227917i	−0.777313	−	0.629114i	$-0.783418\pi$
$587$	−31.3167	+	5.52198i	−1.29258	+	0.227917i	−0.515266	+	0.857030i	$0.672307\pi$
$588$	−20.8275	+	15.1107i	−0.858912	+	0.623157i
$589$	−24.2535	−	2.53021i	−0.999348	−	0.104255i
$590$	−3.94470	−	13.1436i	−0.162401	−	0.541115i
$591$	−9.53599	−	3.47082i	−0.392258	−	0.142770i
$592$	28.7476	+	26.9744i	1.18152	+	1.10864i
$593$	−21.1240	−	17.7251i	−0.867458	−	0.727883i	0.0961035	−	0.995371i	$-0.469362\pi$
$593$	−21.1240	−	17.7251i	−0.867458	−	0.727883i	−0.963561	+	0.267488i	$0.913806\pi$
$594$	−9.26578	+	14.1088i	−0.380180	+	0.578893i
$595$	20.9761	−	8.16777i	0.859938	−	0.334846i
$596$	−5.06393	+	3.34048i	−0.207427	+	0.136832i
$597$	12.0385	+	6.95046i	0.492705	+	0.284463i
$598$	−0.844613	−	1.13290i	−0.0345388	−	0.0463278i
$599$	19.1784	+	16.0926i	0.783610	+	0.657526i	0.944155	−	0.329502i	$-0.106881\pi$
$599$	19.1784	+	16.0926i	0.783610	+	0.657526i	−0.160545	+	0.987028i	$0.551325\pi$
$600$	−16.8791	+	6.18254i	−0.689084	+	0.252401i
$601$	−6.36407	−	3.67430i	−0.259596	−	0.149878i	0.364554	−	0.931182i	$-0.381221\pi$
$601$	−6.36407	−	3.67430i	−0.259596	−	0.149878i	−0.624150	+	0.781304i	$0.714555\pi$
$602$	4.44199	−	3.46807i	0.181042	−	0.141348i
$603$	3.27805	+	1.19311i	0.133492	+	0.0485873i
$604$	−14.1099	−	32.5884i	−0.574125	−	1.32600i
$605$	−1.04918	−	5.95021i	−0.0426554	−	0.241911i
$606$	−36.6339	−	24.0588i	−1.48815	−	0.977322i
$607$	−5.87529	−	10.1763i	−0.238471	−	0.413043i	0.721805	−	0.692096i	$-0.243313\pi$
$607$	−5.87529	−	10.1763i	−0.238471	−	0.413043i	−0.960276	+	0.279053i	$0.909979\pi$
$608$	−24.4426	+	3.24944i	−0.991279	+	0.131782i
$609$	−12.0972	+	7.34802i	−0.490203	+	0.297757i
$610$	−0.592483	+	10.2933i	−0.0239890	+	0.416762i
$611$	−13.6466	−	4.96696i	−0.552083	−	0.200942i
$612$	−3.08860	+	4.16052i	−0.124849	+	0.168179i
$613$	29.1141	−	24.4296i	1.17591	−	0.986703i	0.175910	−	0.984406i	$-0.443713\pi$
$613$	29.1141	−	24.4296i	1.17591	−	0.986703i	0.999997	−	0.00229668i	$-0.000731058\pi$
$614$	−13.1292	+	30.4941i	−0.529853	+	1.23064i
$615$	−22.8532	−	13.1943i	−0.921531	−	0.532046i
$616$	6.76058	+	17.2579i	0.272392	+	0.695342i
$617$	4.07339	−	23.1013i	0.163988	−	0.930025i	−0.786113	−	0.618083i	$-0.787910\pi$
$617$	4.07339	−	23.1013i	0.163988	−	0.930025i	0.950101	−	0.311942i	$-0.100979\pi$
$618$	32.6647	−	3.84050i	1.31397	−	0.154487i
$619$			9.12235i			0.366658i	0.983052	+	0.183329i	$0.0586874\pi$
$619$			9.12235i			0.366658i	−0.983052	+	0.183329i	$0.941313\pi$
$620$	−0.826785	−	13.8700i	−0.0332045	−	0.557033i
$621$	1.64912	+	0.290784i	0.0661768	+	0.0116688i
$622$	5.22580	−	7.95724i	0.209536	−	0.319056i
$623$	3.87591	+	9.95395i	0.155285	+	0.398797i
$624$	−4.81916	+	20.5832i	−0.192921	+	0.823989i
$625$	3.25223	−	2.72895i	0.130089	−	0.109158i
$626$	7.41318	−	7.86823i	0.296290	−	0.314478i
$627$	−8.68493	+	17.8417i	−0.346843	+	0.712529i
$628$	0.449592	+	7.54228i	0.0179407	+	0.300970i
$629$	−66.4945	+	11.7248i	−2.65131	+	0.467497i
$630$	0.0619120	−	1.75606i	0.00246663	−	0.0699630i
$631$	0.343402	+	0.943490i	0.0136706	+	0.0375597i	0.946340	−	0.323172i	$-0.104749\pi$
$631$	0.343402	+	0.943490i	0.0136706	+	0.0375597i	−0.932670	+	0.360732i	$0.882527\pi$
$632$	−11.4612	+	19.9453i	−0.455902	+	0.793382i
$633$	36.5807	−	13.3143i	1.45395	−	0.529195i
$634$	42.1845	−	12.6605i	1.67536	−	0.502812i
$635$	−12.7687	+	22.1160i	−0.506710	+	0.877647i
$636$	4.82473	+	3.58168i	0.191313	+	0.142023i
$637$	−7.71895	−	18.5891i	−0.305836	−	0.736526i
$638$	2.93070	+	9.76501i	0.116027	+	0.386601i
$639$	0.838422			0.0331675
$640$	−4.09365	−	13.4403i	−0.161816	−	0.531276i
$641$	12.7219	+	15.1614i	0.502485	+	0.598838i	0.956347	−	0.292234i	$-0.0943986\pi$
$641$	12.7219	+	15.1614i	0.502485	+	0.598838i	−0.453862	+	0.891072i	$0.649954\pi$
$642$	−24.1479	−	32.3902i	−0.953041	−	1.27834i
$643$	21.1966	+	25.2611i	0.835912	+	0.996201i	0.999952	+	0.00974784i	$0.00310288\pi$
$643$	21.1966	+	25.2611i	0.835912	+	0.996201i	−0.164040	+	0.986454i	$0.552453\pi$
$644$	1.30732	−	1.29309i	0.0515156	−	0.0509549i
$645$			3.43777i			0.135362i
$646$	20.6361	−	36.8482i	0.811916	−	1.44977i
$647$	3.35182	+	1.93517i	0.131774	+	0.0760795i	0.564438	−	0.825476i	$-0.309093\pi$
$647$	3.35182	+	1.93517i	0.131774	+	0.0760795i	−0.432664	+	0.901555i	$0.642426\pi$
$648$	−14.1800	−	24.4451i	−0.557044	−	0.960295i
$649$	−6.61922	+	18.1862i	−0.259827	+	0.713869i
$650$	−1.64190	−	13.9649i	−0.0644005	−	0.547747i
$651$	−25.7644	−	8.73323i	−1.00979	−	0.342282i
$652$	−20.9761	+	9.08210i	−0.821487	+	0.355682i
$653$	−11.6327			−0.455225			−0.227612	−	0.973752i	$-0.573092\pi$
$653$	−11.6327			−0.455225			−0.227612	+	0.973752i	$0.573092\pi$
$654$	2.72162	−	11.5184i	0.106424	−	0.450403i
$655$	−13.3670	+	15.9302i	−0.522291	+	0.622443i
$656$	−25.3069	+	38.7064i	−0.988069	+	1.51123i
$657$	1.20665	+	2.08999i	0.0470760	+	0.0815381i
$658$	3.93517	−	18.4831i	0.153409	−	0.720545i
$659$	4.96431	+	4.16555i	0.193382	+	0.162267i	0.734338	−	0.678784i	$-0.237493\pi$
$659$	4.96431	+	4.16555i	0.193382	+	0.162267i	−0.540956	+	0.841051i	$0.681937\pi$
$660$	−10.8361	−	3.22804i	−0.421794	−	0.125651i
$661$	−41.7929	−	7.36921i	−1.62556	−	0.286629i	−0.714723	−	0.699407i	$-0.753447\pi$
$661$	−41.7929	−	7.36921i	−1.62556	−	0.286629i	−0.910832	+	0.412778i	$0.864559\pi$
$662$	−0.195754	+	3.40085i	−0.00760820	+	0.132178i
$663$	−23.2740	−	27.7369i	−0.903888	−	1.07721i
$664$	−12.5325	+	14.9977i	−0.486355	+	0.582025i
$665$	1.32773	+	14.2600i	0.0514871	+	0.552980i
$666$	−1.21200	+	5.12939i	−0.0469640	+	0.198760i
$667$	0.774815	−	0.650147i	0.0300010	−	0.0251738i
$668$	3.79141	−	12.7272i	0.146694	−	0.492432i
$669$	−6.44319	+	36.5412i	−0.249108	+	1.41276i
$670$	0.930987	−	16.1741i	0.0359672	−	0.624860i
$671$	9.34652	−	11.1388i	0.360819	−	0.430007i
$672$	−27.3953	−	2.49149i	−1.05680	−	0.0961112i
$673$	10.7703	−	6.21825i	0.415165	−	0.239696i	−0.277841	−	0.960627i	$-0.589619\pi$
$673$	10.7703	−	6.21825i	0.415165	−	0.239696i	0.693007	+	0.720931i	$0.256286\pi$
$674$	−0.484908	−	4.12430i	−0.0186779	−	0.158862i
$675$	12.7644	+	10.7106i	0.491303	+	0.412252i
$676$	8.46298	+	4.23585i	0.325499	+	0.162917i
$677$			25.0767i			0.963776i	0.876233	+	0.481888i	$0.160049\pi$
$677$			25.0767i			0.963776i	−0.876233	+	0.481888i	$0.839951\pi$
$678$	−24.3529	+	18.1558i	−0.935266	+	0.697270i
$679$	14.2084	+	16.1873i	0.545269	+	0.621211i
$680$	22.6299	+	8.18433i	0.867819	+	0.313855i
$681$	3.49282	+	1.27128i	0.133845	+	0.0487157i
$682$	−10.7568	+	16.3792i	−0.411900	+	0.627193i
$683$	−9.21954	+	15.9687i	−0.352776	+	0.611026i	−0.986735	−	0.162341i	$-0.948095\pi$
$683$	−9.21954	+	15.9687i	−0.352776	+	0.611026i	0.633959	+	0.773367i	$0.281429\pi$
$684$	−2.00489	−	2.61702i	−0.0766589	−	0.100064i
$685$	−15.0051			−0.573315
$686$	22.5602	−	13.3055i	0.861354	−	0.508005i
$687$	10.3425	−	8.67843i	0.394593	−	0.331103i
$688$	6.01533	+	0.333921i	0.229332	+	0.0127306i
$689$	−3.60063	+	3.02129i	−0.137173	+	0.115102i
$690$	0.130980	+	1.11403i	0.00498633	+	0.0424104i
$691$		−	35.9541i		−	1.36776i	−0.729595	−	0.683880i	$-0.760291\pi$
$691$		−	35.9541i		−	1.36776i	0.729595	−	0.683880i	$-0.239709\pi$
$692$	4.77237	−	0.284479i	0.181418	−	0.0108143i
$693$	−1.55026	+	1.93332i	−0.0588894	+	0.0734407i
$694$	−25.5464	−	10.9990i	−0.969728	−	0.417517i
$695$	−5.59564	−	3.23065i	−0.212255	−	0.122545i
$696$	−14.9067	−	2.59708i	−0.565038	−	0.0984420i
$697$	−27.0908	−	74.4312i	−1.02614	−	2.81928i
$698$	0.687970	−	11.9522i	0.0260401	−	0.452396i
$699$	−23.3492	+	8.49841i	−0.883147	+	0.321439i
$700$	17.6992	−	4.63883i	0.668967	−	0.175331i
$701$	−3.13934	−	17.8041i	−0.118571	−	0.672450i	−0.984920	−	0.173011i	$-0.944650\pi$
$701$	−3.13934	−	17.8041i	−0.118571	−	0.672450i	0.866349	−	0.499440i	$-0.166461\pi$
$702$	18.7688	−	5.63292i	0.708381	−	0.212601i
$703$	4.45739	−	42.7266i	0.168114	−	1.61146i
$704$	−6.70089	+	18.6472i	−0.252549	+	0.702792i
$705$	7.40992	+	8.83080i	0.279074	+	0.332587i
$706$	7.22165	−	3.63301i	0.271790	−	0.136730i
$707$	34.8037	+	27.9079i	1.30893	+	1.04958i
$708$	−19.7393	−	20.8655i	−0.741849	−	0.784173i
$709$	−7.10418	+	40.2898i	−0.266803	+	1.51312i	0.497048	+	0.867723i	$0.334417\pi$
$709$	−7.10418	+	40.2898i	−0.266803	+	1.51312i	−0.763851	+	0.645393i	$0.776694\pi$
$710$	−1.11929	−	3.72944i	−0.0420061	−	0.139963i
$711$	−3.07560			−0.115344
$712$	−3.88377	+	10.7388i	−0.145550	+	0.402452i
$713$	1.91449	+	0.337577i	0.0716983	+	0.0126423i
$714$	31.5383	−	35.0033i	1.18029	−	1.30996i
$715$	4.42219	−	7.65945i	0.165380	−	0.286447i
$716$	−11.8313	+	15.9375i	−0.442157	+	0.595611i
$717$	−16.6289	−	19.8175i	−0.621016	−	0.740098i
$718$	36.6825	+	15.7937i	1.36898	+	0.589415i
$719$	14.9134	−	40.9741i	0.556174	−	1.52808i	−0.268966	−	0.963150i	$-0.586682\pi$
$719$	14.9134	−	40.9741i	0.556174	−	1.52808i	0.825141	−	0.564927i	$-0.191096\pi$
$720$	1.28536	−	1.36986i	0.0479025	−	0.0510515i
$721$	−33.4693	+	0.744990i	−1.24646	+	0.0277449i
$722$	18.9316	+	19.0681i	0.704562	+	0.709643i
$723$	−28.1720	+	16.2651i	−1.04773	+	0.604906i
$724$	23.3727	−	22.1112i	0.868638	−	0.821756i
$725$	9.91157	−	1.74768i	0.368106	−	0.0649071i
$726$	−7.55881	−	10.1388i	−0.280534	−	0.376287i
$727$	1.03343	−	2.83934i	0.0383279	−	0.105305i	−0.919052	−	0.394135i	$-0.871044\pi$
$727$	1.03343	−	2.83934i	0.0383279	−	0.105305i	0.957380	+	0.288830i	$0.0932663\pi$
$728$	6.86607	−	20.3929i	0.254474	−	0.755810i
$729$	−11.3963	+	19.7390i	−0.422085	+	0.731073i
$730$	7.68572	−	8.15751i	0.284461	−	0.301923i
$731$	−6.63280	+	7.90467i	−0.245323	+	0.292365i
$732$	8.57448	+	19.8037i	0.316922	+	0.731966i
$733$	−7.51050	+	13.0086i	−0.277407	+	0.480483i	−0.970740	−	0.240135i	$-0.922808\pi$
$733$	−7.51050	+	13.0086i	−0.277407	+	0.480483i	0.693333	+	0.720618i	$0.256142\pi$
$734$	25.5546	+	24.0767i	0.943237	+	0.888686i
$735$	−2.07158	+	15.8426i	−0.0764113	+	0.584362i
$736$	1.96203	−	0.120977i	0.0723213	−	0.00445927i
$737$	−14.6865	+	17.5027i	−0.540983	+	0.644718i
$738$	−6.17277	−	0.355307i	−0.227223	−	0.0130790i
$739$	−0.856224	+	2.35245i	−0.0314967	+	0.0865365i	−0.954444	−	0.298389i	$-0.903551\pi$
$739$	−0.856224	+	2.35245i	−0.0314967	+	0.0865365i	0.922948	+	0.384926i	$0.125773\pi$
$740$	24.4344	−	1.45652i	0.898225	−	0.0535428i
$741$	21.0378	−	9.38609i	0.772842	−	0.344807i
$742$	−4.54390	−	4.09411i	−0.166812	−	0.150299i
$743$	4.48249	+	25.4214i	0.164446	+	0.932622i	0.949633	+	0.313363i	$0.101456\pi$
$743$	4.48249	+	25.4214i	0.164446	+	0.932622i	−0.785187	+	0.619259i	$0.787433\pi$
$744$	−14.5927	−	25.1565i	−0.534994	−	0.922283i
$745$	−0.654103	+	3.70960i	−0.0239645	+	0.135909i
$746$	12.7288	+	25.3022i	0.466034	+	0.926378i
$747$	−2.57342	−	0.453764i	−0.0941566	−	0.0166024i
$748$	−18.6879	−	28.3295i	−0.683297	−	1.03583i
$749$	21.3490	+	35.1473i	0.780076	+	1.28426i
$750$	−10.7964	+	25.0758i	−0.394229	+	0.915638i
$751$	−10.7896	+	3.92709i	−0.393717	+	0.143301i	−0.531290	−	0.847190i	$-0.678292\pi$
$751$	−10.7896	+	3.92709i	−0.393717	+	0.143301i	0.137572	+	0.990492i	$0.456070\pi$
$752$	16.1717	−	12.1079i	0.589720	−	0.441531i
$753$	32.9222	−	19.0076i	1.19975	−	0.692676i
$754$	4.68062	−	10.8712i	0.170458	−	0.395908i
$755$	−20.7204	−	7.54162i	−0.754094	−	0.274468i
$756$	10.6498	+	23.1687i	0.387329	+	0.842637i
$757$	−32.4153	+	27.1996i	−1.17815	+	0.988587i	−0.178163	+	0.984001i	$0.557015\pi$
$757$	−32.4153	+	27.1996i	−1.17815	+	0.988587i	−0.999989	+	0.00458646i	$0.998540\pi$
$758$	−26.7491	+	13.4567i	−0.971573	+	0.488771i
$759$	0.790970	−	1.37000i	0.0287104	−	0.0497278i
$760$	−8.96442	+	12.4118i	−0.325174	+	0.450222i
$761$	3.93678	+	6.81870i	0.142708	+	0.247178i	0.928516	−	0.371294i	$-0.121086\pi$
$761$	3.93678	+	6.81870i	0.142708	+	0.247178i	−0.785807	+	0.618471i	$0.787752\pi$
$762$	−3.07162	+	53.3634i	−0.111273	+	1.93315i
$763$	−3.86740	+	11.4094i	−0.140009	+	0.413049i
$764$	−2.11769	+	18.3345i	−0.0766154	+	0.663317i
$765$	0.558697	+	3.16853i	0.0201998	+	0.114558i
$766$	−11.3397	+	1.33325i	−0.409722	+	0.0481723i
$767$	19.4577	−	11.2339i	0.702578	−	0.405634i
$768$	−20.2969	−	21.2801i	−0.732402	−	0.767880i
$769$	1.12184	−	6.36229i	0.0404547	−	0.229430i	−0.957876	−	0.287181i	$-0.907282\pi$
$769$	1.12184	−	6.36229i	0.0404547	−	0.229430i	0.998331	+	0.0577511i	$0.0183930\pi$
$770$	10.6693	+	4.31484i	0.384495	+	0.155496i
$771$	47.4148	−	27.3750i	1.70760	−	0.985885i
$772$	17.0031	−	33.9712i	0.611956	−	1.22265i
$773$	−3.74295	−	10.2837i	−0.134625	−	0.369878i	0.854002	−	0.520270i	$-0.174169\pi$
$773$	−3.74295	−	10.2837i	−0.134625	−	0.369878i	−0.988626	+	0.150392i	$0.951946\pi$
$774$	0.361992	+	0.719563i	0.0130115	+	0.0258641i
$775$	14.8185	+	12.4342i	0.532295	+	0.446648i
$776$	0.0470222	+	23.0256i	0.00168800	+	0.826570i
$777$	15.3850	−	45.3883i	0.551935	−	1.62830i
$778$	−15.3320	−	3.62272i	−0.549677	−	0.129881i
$779$	50.2692	−	3.55417i	1.80108	−	0.127341i
$780$	7.22793	+	10.9570i	0.258801	+	0.392324i
$781$	−1.87817	+	5.16022i	−0.0672061	+	0.184647i
$782$	−1.84823	+	2.81427i	−0.0660926	+	0.100638i
$783$	4.79720	+	13.1802i	0.171438	+	0.471022i
$784$	27.5198	+	5.16363i	0.982848	+	0.184416i
$785$	3.59390	+	3.01564i	0.128272	+	0.107633i
$786$	−10.0090	+	42.3599i	−0.357010	+	1.51093i
$787$	5.62597			0.200544			0.100272	−	0.994960i	$-0.468029\pi$
$787$	5.62597			0.200544			0.100272	+	0.994960i	$0.468029\pi$
$788$	4.38753	+	10.1335i	0.156299	+	0.360991i
$789$	−7.93227	−	21.7937i	−0.282396	−	0.775878i
$790$	4.10591	+	13.6808i	0.146082	+	0.486740i
$791$	26.4258	−	16.0515i	0.939594	−	0.570724i
$792$	−2.60802	+	0.465357i	−0.0926718	+	0.0165358i
$793$	−16.6242	+	2.93129i	−0.590342	+	0.104093i
$794$	7.13034	−	16.5610i	0.253046	−	0.587727i
$795$	3.67437	−	0.647891i	0.130317	−	0.0229783i
$796$	−3.50840	−	14.7138i	−0.124352	−	0.521518i
$797$			26.3659i			0.933929i	0.884276	+	0.466965i	$0.154652\pi$
$797$			26.3659i			0.933929i	−0.884276	+	0.466965i	$0.845348\pi$
$798$	15.8962	+	25.4146i	0.562721	+	0.899666i
$799$			34.6018i			1.22412i
$800$	17.5095	+	8.71911i	0.619055	+	0.308267i
$801$	−1.50359	+	0.265123i	−0.0531266	+	0.00936765i
$802$	−8.02528	−	3.45529i	−0.283382	−	0.122011i
$803$	−15.5663	+	2.74475i	−0.549321	+	0.0968602i
$804$	−13.4733	−	31.1181i	−0.475168	−	1.09745i
$805$	−0.0254079	−	1.14147i	−0.000895511	−	0.0402315i
$806$	21.7890	−	6.53936i	0.767485	−	0.230339i
$807$	4.71150	+	12.9447i	0.165853	+	0.455677i
$808$	8.37740	+	46.9497i	0.294716	+	1.65169i
$809$	−39.7346			−1.39700			−0.698498	−	0.715612i	$-0.746148\pi$
$809$	−39.7346			−1.39700			−0.698498	+	0.715612i	$0.746148\pi$
$810$	−17.0772	−	4.03509i	−0.600031	−	0.141779i
$811$	1.80915	+	1.51806i	0.0635278	+	0.0533062i	0.673999	−	0.738733i	$-0.264575\pi$
$811$	1.80915	+	1.51806i	0.0635278	+	0.0533062i	−0.610471	+	0.792039i	$0.709020\pi$
$812$	14.8549	+	4.06760i	0.521304	+	0.142745i
$813$	2.74506	+	7.54199i	0.0962734	+	0.264509i
$814$	−28.8547	−	18.9499i	−1.01136	−	0.664195i
$815$	−4.85429	+	13.3371i	−0.170038	+	0.467177i
$816$	50.0122	−	5.98367i	1.75078	−	0.209470i
$817$	−3.67539	−	5.43992i	−0.128585	−	0.190319i
$818$	1.39619	−	5.90892i	0.0488168	−	0.206601i
$819$	2.82139	−	0.562495i	0.0985872	−	0.0196552i
$820$	6.66014	+	27.9318i	0.232582	+	0.975421i
$821$	−13.4973	−	11.3256i	−0.471060	−	0.395266i	0.376121	−	0.926570i	$-0.377258\pi$
$821$	−13.4973	−	11.3256i	−0.471060	−	0.395266i	−0.847181	+	0.531304i	$0.821702\pi$
$822$	−28.0566	+	14.1145i	−0.978587	+	0.492299i
$823$	5.69327	+	15.6421i	0.198455	+	0.545250i	0.998504	−	0.0546848i	$-0.0174154\pi$
$823$	5.69327	+	15.6421i	0.198455	+	0.545250i	−0.800049	+	0.599935i	$0.795193\pi$
$824$	−27.4629	−	22.9487i	−0.956715	−	0.799456i
$825$	13.6322	−	7.87058i	0.474614	−	0.274018i
$826$	17.9920	+	23.0446i	0.626021	+	0.801824i
$827$	5.18960	−	29.4317i	0.180460	−	1.02344i	−0.751191	−	0.660085i	$-0.770520\pi$
$827$	5.18960	−	29.4317i	0.180460	−	1.02344i	0.931651	−	0.363355i	$-0.118369\pi$
$828$	0.144721	+	0.219387i	0.00502941	+	0.00762421i
$829$	21.7959	−	12.5839i	0.757004	−	0.437057i	−0.0712149	−	0.997461i	$-0.522688\pi$
$829$	21.7959	−	12.5839i	0.757004	−	0.437057i	0.828219	+	0.560404i	$0.189354\pi$
$830$	1.41708	+	12.0528i	0.0491877	+	0.418358i
$831$	−9.55827	−	54.2076i	−0.331573	−	1.88044i
$832$	19.8744	−	11.5830i	0.689021	−	0.401567i
$833$	−35.3298	+	32.4309i	−1.22411	+	1.12366i
$834$	−13.5017	−	0.777160i	−0.467524	−	0.0269109i
$835$	−4.12293	−	7.14113i	−0.142680	−	0.247129i
$836$	20.5981	−	6.47702i	0.712402	−	0.224012i
$837$	−13.4792	+	23.3467i	−0.465910	+	0.806979i
$838$	−7.47995	−	14.8686i	−0.258391	−	0.513626i
$839$	9.84582	−	8.26163i	0.339916	−	0.285223i	−0.456810	−	0.889564i	$-0.651008\pi$
$839$	9.84582	−	8.26163i	0.339916	−	0.285223i	0.796726	+	0.604341i	$0.206564\pi$
$840$	−12.8139	+	11.2938i	−0.442122	+	0.389675i
$841$	−19.2901	−	7.02103i	−0.665177	−	0.242104i
$842$	31.5305	+	13.5755i	1.08661	+	0.467842i
$843$	44.0568	−	25.4362i	1.51740	−	0.876070i
$844$	−37.8801	−	18.9596i	−1.30389	−	0.652615i
$845$	5.52196	−	2.00983i	0.189961	−	0.0691402i
$846$	2.48084	+	1.06813i	0.0852932	+	0.0367230i
$847$	6.68271	+	11.0019i	0.229620	+	0.378029i
$848$	−0.776762	−	6.49227i	−0.0266741	−	0.222945i
$849$	−19.9363	−	3.51531i	−0.684212	−	0.120645i
$850$	−29.9287	+	15.0563i	−1.02655	+	0.516427i
$851$	−0.594698	+	3.37270i	−0.0203860	+	0.115615i
$852$	−5.60093	−	5.92047i	−0.191885	−	0.202832i
$853$	−0.383358	−	2.17413i	−0.0131259	−	0.0744409i	0.977541	−	0.210745i	$-0.0675888\pi$
$853$	−0.383358	−	2.17413i	−0.0131259	−	0.0744409i	−0.990667	+	0.136304i	$0.956478\pi$
$854$	−6.78087	−	20.8932i	−0.232036	−	0.714950i
$855$	−2.03597	−	0.212399i	−0.0696286	−	0.00726390i
$856$	−7.54558	+	43.3101i	−0.257903	+	1.48031i
$857$	−4.92482	+	13.5308i	−0.168229	+	0.462204i	−0.994946	−	0.100413i	$-0.967983\pi$
$857$	−4.92482	+	13.5308i	−0.168229	+	0.462204i	0.826717	+	0.562618i	$0.190206\pi$
$858$	1.06380	−	18.4814i	0.0363174	−	0.630944i
$859$	−12.3071	+	14.6670i	−0.419912	+	0.500432i	−0.933984	−	0.357316i	$-0.883692\pi$
$859$	−12.3071	+	14.6670i	−0.419912	+	0.500432i	0.514072	+	0.857747i	$0.328137\pi$
$860$	2.71748	−	2.57081i	0.0926652	−	0.0876638i
$861$	55.5702	+	8.52812i	1.89383	+	0.290637i
$862$	13.2793	−	14.0944i	0.452294	−	0.480058i
$863$	21.5161	−	37.2669i	0.732416	−	1.26858i	−0.223432	−	0.974720i	$-0.571726\pi$
$863$	21.5161	−	37.2669i	0.732416	−	1.26858i	0.955848	−	0.293862i	$-0.0949406\pi$
$864$	−7.72925	+	26.1410i	−0.262954	+	0.889334i
$865$	1.90814	−	2.27404i	0.0648788	−	0.0773196i
$866$	1.72957	+	1.62955i	0.0587733	+	0.0553742i
$867$	−27.5126	+	47.6532i	−0.934377	+	1.61839i
$868$	12.3635	+	26.8970i	0.419645	+	0.912942i
$869$	6.88973	−	18.9294i	0.233718	−	0.642135i
$870$	−7.53243	+	5.61566i	−0.255373	+	0.190389i
$871$	26.1221	−	4.60603i	0.885113	−	0.156069i
$872$	−11.1402	+	6.46219i	−0.377256	+	0.218838i
$873$	−2.66608	+	1.53926i	−0.0902331	+	0.0520961i
$874$	−1.39829	−	1.62280i	−0.0472980	−	0.0548922i
$875$	13.3556	−	24.3694i	0.451502	−	0.823836i
$876$	6.69748	−	22.4825i	0.226287	−	0.759613i
$877$	−4.75504	+	13.0644i	−0.160566	+	0.441152i	−0.993721	−	0.111888i	$-0.964310\pi$
$877$	−4.75504	+	13.0644i	−0.160566	+	0.441152i	0.833155	+	0.553040i	$0.186532\pi$
$878$	1.55280	−	3.60655i	0.0524045	−	0.121715i
$879$	−10.0582	−	11.9869i	−0.339254	−	0.404307i
$880$	5.55167	+	10.9796i	0.187147	+	0.370123i
$881$	6.78340	−	11.7492i	0.228539	−	0.395840i	−0.728837	−	0.684688i	$-0.759939\pi$
$881$	6.78340	−	11.7492i	0.228539	−	0.395840i	0.957375	+	0.288847i	$0.0932720\pi$
$882$	1.23459	+	3.53416i	0.0415709	+	0.119001i
$883$	−52.0537	−	9.17847i	−1.75175	−	0.308880i	−0.796489	−	0.604653i	$-0.793312\pi$
$883$	−52.0537	−	9.17847i	−1.75175	−	0.308880i	−0.955258	+	0.295773i	$0.904423\pi$
$884$	−4.52076	+	39.1396i	−0.152049	+	1.31641i
$885$	−17.8348			−0.599511
$886$	20.2451	−	6.07600i	0.680147	−	0.204127i
$887$	−0.194420	+	1.10261i	−0.00652798	+	0.0370220i	−0.987898	−	0.155106i	$-0.950428\pi$
$887$	−0.194420	+	1.10261i	−0.00652798	+	0.0370220i	0.981370	+	0.192129i	$0.0615390\pi$
$888$	44.3174	−	25.7075i	1.48720	−	0.862687i
$889$	8.25301	−	53.7776i	0.276797	−	1.80364i
$890$	3.18658	+	6.33426i	0.106815	+	0.212325i
$891$	15.9072	+	18.9574i	0.532910	+	0.635098i
$892$	33.7032	−	22.2328i	1.12847	−	0.744408i
$893$	−21.1666	−	6.05174i	−0.708313	−	0.202514i
$894$	2.26638	+	7.55152i	0.0757990	+	0.252561i
$895$	2.14017	+	12.1375i	0.0715379	+	0.405712i
$896$	18.5171	+	23.5185i	0.618612	+	0.785697i
$897$	−1.72577	+	0.628128i	−0.0576217	+	0.0209726i
$898$	−10.4584	−	0.601988i	−0.349001	−	0.0200886i
$899$	5.56916	+	15.3011i	0.185742	+	0.510322i
$900$	0.155615	+	2.61058i	0.00518717	+	0.0870192i
$901$	9.69874	+	5.59957i	0.323112	+	0.186549i
$902$	16.0146	−	37.1955i	0.533227	−	1.23848i
$903$	−2.65754	−	6.82499i	−0.0884375	−	0.227122i
$904$	32.5631	+	5.67321i	1.08303	+	0.188688i
$905$		−	19.9778i		−	0.664085i
$906$	−45.8372	+	5.38923i	−1.52284	+	0.179045i
$907$	33.6729	−	28.2549i	1.11809	−	0.938189i	0.119584	−	0.992824i	$-0.461844\pi$
$907$	33.6729	−	28.2549i	1.11809	−	0.938189i	0.998506	+	0.0546351i	$0.0173995\pi$
$908$	−1.60706	−	3.71167i	−0.0533320	−	0.123176i
$909$	−4.88454	+	4.09861i	−0.162010	+	0.135942i
$910$	−6.26860	−	11.7991i	−0.207802	−	0.391135i
$911$	12.1465			0.402430			0.201215	−	0.979547i	$-0.435511\pi$
$911$	12.1465			0.402430			0.201215	+	0.979547i	$0.435511\pi$
$912$	−5.08664	+	31.6400i	−0.168435	+	1.04770i
$913$	8.55756	−	14.8221i	0.283214	−	0.490541i
$914$	−19.3108	−	12.6821i	−0.638746	−	0.419487i
$915$	12.5916	+	4.58298i	0.416266	+	0.151509i
$916$	−14.5944	−	1.68570i	−0.482212	−	0.0556971i
$917$	14.2227	−	41.9593i	0.469676	−	1.38562i
$918$	−27.9068	−	37.4321i	−0.921061	−	1.23544i
$919$			31.8205i			1.04966i	0.851207	+	0.524830i	$0.175871\pi$
$919$			31.8205i			1.04966i	−0.851207	+	0.524830i	$0.824129\pi$
$920$	0.782666	−	0.936623i	0.0258037	−	0.0308795i
$921$	33.0539	+	27.7355i	1.08916	+	0.913915i
$922$	−49.7921	+	5.85423i	−1.63982	+	0.192799i
$923$	5.52103	−	3.18757i	0.181727	−	0.104920i
$924$	24.0082	−	1.96813i	0.789813	−	0.0647467i
$925$	−21.9049	+	26.1052i	−0.720228	+	0.858334i
$926$	−26.1714	−	1.50644i	−0.860046	−	0.0495046i
$927$	0.830903	−	4.71229i	0.0272904	−	0.154772i
$928$	9.09450	+	13.7255i	0.298542	+	0.450563i
$929$	−21.2913	+	17.8656i	−0.698546	+	0.586150i	−0.921360	−	0.388711i	$-0.872920\pi$
$929$	−21.2913	+	17.8656i	−0.698546	+	0.586150i	0.222813	+	0.974861i	$0.428476\pi$
$930$	−17.5742	−	4.15252i	−0.576280	−	0.136167i
$931$	−13.6595	−	27.2840i	−0.447673	−	0.894197i
$932$	24.1786	+	12.1018i	0.791997	+	0.396406i
$933$	−7.95281	−	9.47779i	−0.260363	−	0.310289i
$934$	−20.2612	−	1.16624i	−0.662967	−	0.0381606i
$935$	−20.7529	−	3.65929i	−0.678691	−	0.119672i
$936$	2.66664	+	1.53233i	0.0871618	+	0.0500858i
$937$	−36.0450	−	30.2454i	−1.17754	−	0.988073i	−0.999992	−	0.00396077i	$-0.998739\pi$
$937$	−36.0450	−	30.2454i	−1.17754	−	0.988073i	−0.177547	−	0.984112i	$-0.556816\pi$
$938$	10.6550	+	32.8301i	0.347897	+	1.07194i
$939$	−7.02483	−	12.1674i	−0.229247	−	0.397067i
$940$	1.43930	−	12.4611i	0.0469449	−	0.406438i
$941$	−6.62632	+	7.89694i	−0.216012	+	0.257433i	−0.863159	−	0.504932i	$-0.831518\pi$
$941$	−6.62632	+	7.89694i	−0.216012	+	0.257433i	0.647147	+	0.762365i	$0.275962\pi$
$942$	9.55655	+	2.25807i	0.311369	+	0.0735720i
$943$	−4.01755			−0.130830
$944$	−1.73235	+	31.2069i	−0.0563832	+	1.01570i
$945$	14.9950	+	5.08279i	0.487788	+	0.165343i
$946$	−5.23959	+	0.616036i	−0.170354	+	0.0200291i
$947$	−0.907362	+	2.49296i	−0.0294853	+	0.0810102i	−0.953562	−	0.301197i	$-0.902614\pi$
$947$	−0.907362	+	2.49296i	−0.0294853	+	0.0810102i	0.924077	+	0.382207i	$0.124836\pi$
$948$	20.5460	+	21.7182i	0.667304	+	0.705374i
$949$	15.8917	+	9.17507i	0.515866	+	0.297835i
$950$	−3.97580	−	20.9413i	−0.128992	−	0.679425i
$951$		−	57.2408i		−	1.85616i
$952$	−51.2540	+	1.24559i	−1.66115	+	0.0403696i
$953$	38.2830	+	45.6239i	1.24011	+	1.47790i	0.821981	+	0.569515i	$0.192869\pi$
$953$	38.2830	+	45.6239i	1.24011	+	1.47790i	0.418127	+	0.908389i	$0.362687\pi$
$954$	0.700864	−	0.522516i	0.0226913	−	0.0169171i
$955$	7.36635	+	8.77888i	0.238370	+	0.284078i
$956$	−3.22999	+	27.9645i	−0.104465	+	0.904436i
$957$	13.2503			0.428321
$958$	33.0799	−	9.92802i	1.06876	−	0.320760i
$959$	29.7896	−	11.5996i	0.961955	−	0.374570i
$960$	−18.2598	+	0.0745794i	−0.589332	+	0.00240704i
$961$	−0.148262	+	0.256797i	−0.00478263	+	0.00828377i
$962$	11.5202	+	38.3850i	0.371426	+	1.23758i
$963$	−5.52330	+	2.01032i	−0.177986	+	0.0647816i
$964$	33.9246	+	10.1060i	1.09264	+	0.325494i
$965$	−8.06764	−	22.1657i	−0.259707	−	0.713538i
$966$	−1.12123	−	2.11043i	−0.0360749	−	0.0679019i
$967$	−38.1191	+	6.72142i	−1.22583	+	0.216146i	−0.748832	−	0.662760i	$-0.769385\pi$
$967$	−38.1191	+	6.72142i	−1.22583	+	0.216146i	−0.476995	+	0.878906i	$0.658274\pi$
$968$	−2.36193	+	13.5570i	−0.0759153	+	0.435739i
$969$	−38.1590	−	39.4538i	−1.22584	−	1.26744i
$970$	10.4061	+	9.80425i	0.334119	+	0.314795i
$971$	−6.35657	+	5.33380i	−0.203992	+	0.171170i	−0.739061	−	0.673639i	$-0.764730\pi$
$971$	−6.35657	+	5.33380i	−0.203992	+	0.171170i	0.535068	+	0.844809i	$0.320286\pi$
$972$	−7.60180	+	1.81259i	−0.243828	+	0.0581390i
$973$	13.6064	+	2.08812i	0.436202	+	0.0669421i
$974$	40.1619	+	26.3758i	1.28687	+	0.845135i
$975$	−17.9968	−	3.17332i	−0.576358	−	0.101627i
$976$	9.24225	−	21.5874i	0.295837	−	0.690995i
$977$			51.5536i			1.64935i	0.565609	+	0.824673i	$0.308641\pi$
$977$			51.5536i			1.64935i	−0.565609	+	0.824673i	$0.691359\pi$
$978$	3.46887	+	29.5039i	0.110922	+	0.943430i
$979$	1.73647	−	9.84801i	0.0554978	−	0.314744i
$980$	14.0723	−	10.2097i	0.449524	−	0.326138i
$981$	−1.49121	−	0.860950i	−0.0476107	−	0.0274880i
$982$	5.56905	+	2.39776i	0.177716	+	0.0765156i
$983$	−43.3756	+	36.3965i	−1.38347	+	1.16087i	−0.415559	+	0.909566i	$0.636414\pi$
$983$	−43.3756	+	36.3965i	−1.38347	+	1.16087i	−0.967909	+	0.251301i	$0.919141\pi$
$984$	38.7271	+	45.9622i	1.23457	+	1.46522i
$985$	6.44310	+	2.34510i	0.205294	+	0.0747209i
$986$	−28.1546	−	1.62059i	−0.896624	−	0.0516100i
$987$	−21.5375	−	11.8036i	−0.685545	−	0.375712i
$988$	−23.1518	−	9.61082i	−0.736557	−	0.305761i
$989$	0.261693	+	0.453265i	0.00832135	+	0.0144130i
$990$	−0.902985	+	1.37496i	−0.0286987	+	0.0436991i
$991$	−0.281984	−	1.59921i	−0.00895750	−	0.0508005i	0.980001	−	0.198991i	$-0.0637663\pi$
$991$	−0.281984	−	1.59921i	−0.00895750	−	0.0508005i	−0.988959	+	0.148190i	$0.952655\pi$
$992$	−8.97302	+	30.3475i	−0.284894	+	0.963536i
$993$	4.16022	+	1.51420i	0.132021	+	0.0480516i
$994$	5.10513	+	6.53878i	0.161925	+	0.207398i
$995$	−8.13398	−	4.69615i	−0.257864	−	0.148878i
$996$	13.9871	+	21.2034i	0.443197	+	0.671854i
$997$	17.5272	+	14.7070i	0.555091	+	0.465776i	0.876661	−	0.481109i	$-0.159766\pi$
$997$	17.5272	+	14.7070i	0.555091	+	0.465776i	−0.321570	+	0.946886i	$0.604210\pi$
$998$	−2.57794	+	1.92193i	−0.0816032	+	0.0608377i
$999$	−41.1291	−	23.7459i	−1.30127	−	0.751287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.bs.a.67.11	✓	456
4.3	odd	2	inner	532.2.bs.a.67.55	yes	456
7.2	even	3		532.2.ce.a.219.63	yes	456
19.2	odd	18		532.2.ce.a.515.3	yes	456
28.23	odd	6		532.2.ce.a.219.3	yes	456
76.59	even	18		532.2.ce.a.515.63	yes	456
133.2	odd	18	inner	532.2.bs.a.135.55	yes	456
532.135	even	18	inner	532.2.bs.a.135.11	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.bs.a.67.11	✓	456	1.1	even	1	trivial
532.2.bs.a.67.55	yes	456	4.3	odd	2	inner
532.2.bs.a.135.11	yes	456	532.135	even	18	inner
532.2.bs.a.135.55	yes	456	133.2	odd	18	inner
532.2.ce.a.219.3	yes	456	28.23	odd	6
532.2.ce.a.219.63	yes	456	7.2	even	3
532.2.ce.a.515.3	yes	456	19.2	odd	18
532.2.ce.a.515.63	yes	456	76.59	even	18

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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.bs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26336 + 0.635558i) q^{2} +(0.319161 + 1.81005i) q^{3} +(1.19213 - 1.60587i) q^{4} +(-0.215645 - 1.22298i) q^{5} +(-1.55361 - 2.08390i) q^{6} +(1.37354 + 2.26128i) q^{7} +(-0.485462 + 2.78645i) q^{8} +(-0.355354 + 0.129338i) q^{9} +O(q^{10})\)	\(q+(-1.26336 + 0.635558i) q^{2} +(0.319161 + 1.81005i) q^{3} +(1.19213 - 1.60587i) q^{4} +(-0.215645 - 1.22298i) q^{5} +(-1.55361 - 2.08390i) q^{6} +(1.37354 + 2.26128i) q^{7} +(-0.485462 + 2.78645i) q^{8} +(-0.355354 + 0.129338i) q^{9} +(1.04971 + 1.40801i) q^{10} -2.47683i q^{11} +(3.28720 + 1.64529i) q^{12} +(-1.84829 + 2.20270i) q^{13} +(-3.17244 - 1.98384i) q^{14} +(2.14484 - 0.780658i) q^{15} +(-1.15764 - 3.82882i) q^{16} +(6.43795 + 2.34322i) q^{17} +(0.366736 - 0.389248i) q^{18} +(-2.55937 + 3.52840i) q^{19} +(-2.22103 - 1.11166i) q^{20} +(-3.65466 + 3.20789i) q^{21} +(1.57417 + 3.12911i) q^{22} +(0.223368 - 0.266200i) q^{23} +(-5.19857 + 0.0106164i) q^{24} +(3.24928 - 1.18264i) q^{25} +(0.935098 - 3.95749i) q^{26} +(2.40944 + 4.17327i) q^{27} +(5.26876 + 0.490023i) q^{28} +(2.86643 + 0.505429i) q^{29} +(-2.21354 + 2.34942i) q^{30} +(2.79716 + 4.84483i) q^{31} +(3.89595 + 4.10141i) q^{32} +(4.48319 - 0.790508i) q^{33} +(-9.62267 + 1.13137i) q^{34} +(2.46931 - 2.16745i) q^{35} +(-0.215928 + 0.724841i) q^{36} +(-8.53498 + 4.92768i) q^{37} +(0.990893 - 6.08425i) q^{38} +(-4.57692 - 2.64248i) q^{39} +(3.51247 - 0.00717307i) q^{40} +(-7.43148 - 8.85649i) q^{41} +(2.57834 - 6.37545i) q^{42} +(-0.515133 + 1.41532i) q^{43} +(-3.97747 - 2.95271i) q^{44} +(0.234809 + 0.406701i) q^{45} +(-0.113008 + 0.478269i) q^{46} +(1.72738 + 4.74594i) q^{47} +(6.56090 - 3.31741i) q^{48} +(-3.22679 + 6.21191i) q^{49} +(-3.35335 + 3.55920i) q^{50} +(-2.18661 + 12.4009i) q^{51} +(1.33385 + 5.59403i) q^{52} +(1.60981 + 0.283853i) q^{53} +(-5.69634 - 3.74099i) q^{54} +(-3.02912 + 0.534115i) q^{55} +(-6.96776 + 2.72953i) q^{56} +(-7.20345 - 3.50647i) q^{57} +(-3.94255 + 1.18325i) q^{58} +(-7.34252 - 2.67246i) q^{59} +(1.30330 - 4.37498i) q^{60} +(4.49719 + 3.77359i) q^{61} +(-6.61298 - 4.34298i) q^{62} +(-0.780562 - 0.625905i) q^{63} +(-7.52865 - 2.70543i) q^{64} +(3.09244 + 1.78542i) q^{65} +(-5.16145 + 3.84802i) q^{66} +(-7.06656 - 5.92955i) q^{67} +(11.4378 - 7.54509i) q^{68} +(0.553127 + 0.319348i) q^{69} +(-1.74208 + 4.30765i) q^{70} +(-2.08340 - 0.758296i) q^{71} +(-0.187884 - 1.05297i) q^{72} +(-1.10817 - 6.28476i) q^{73} +(7.65089 - 11.6499i) q^{74} +(3.17769 + 5.50392i) q^{75} +(2.61505 + 8.31634i) q^{76} +(5.60081 - 3.40201i) q^{77} +(7.46172 + 0.429499i) q^{78} +(7.64259 + 2.78167i) q^{79} +(-4.43294 + 2.24144i) q^{80} +(-7.65391 + 6.42240i) q^{81} +(15.0174 + 6.46576i) q^{82} +(5.98432 + 3.45505i) q^{83} +(0.794617 + 9.69315i) q^{84} +(1.47741 - 8.37881i) q^{85} +(-0.248720 - 2.11544i) q^{86} +5.34971i q^{87} +(6.90157 + 1.20241i) q^{88} +(3.97606 + 0.701086i) q^{89} +(-0.555129 - 0.364573i) q^{90} +(-7.51963 - 1.15400i) q^{91} +(-0.161198 - 0.676046i) q^{92} +(-7.87666 + 6.60930i) q^{93} +(-5.19862 - 4.89796i) q^{94} +(4.86709 + 2.36919i) q^{95} +(-6.18034 + 8.36089i) q^{96} +(8.01712 - 1.41363i) q^{97} +(0.128555 - 9.89866i) q^{98} +(0.320349 + 0.880151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 456 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 15 q^{10} - 36 q^{13} + 15 q^{14} - 3 q^{16} - 6 q^{17} - 24 q^{20} - 18 q^{21} - 6 q^{22} - 12 q^{24} - 6 q^{25} - 6 q^{26} - 27 q^{28} - 24 q^{29} + 3 q^{30} + 12 q^{32} + 66 q^{33} - 12 q^{34} - 81 q^{36} - 72 q^{38} - 33 q^{40} - 36 q^{41} - 87 q^{42} + 12 q^{44} + 6 q^{45} - 45 q^{48} - 6 q^{49} - 45 q^{50} - 3 q^{52} + 6 q^{53} - 39 q^{54} - 24 q^{57} - 42 q^{58} + 66 q^{60} - 18 q^{61} + 3 q^{62} - 6 q^{64} + 18 q^{65} + 75 q^{66} - 39 q^{68} - 36 q^{69} + 9 q^{70} - 54 q^{72} + 30 q^{73} - 57 q^{74} - 84 q^{76} - 18 q^{77} - 9 q^{78} - 3 q^{80} - 24 q^{81} + 117 q^{82} - 9 q^{84} - 78 q^{86} - 9 q^{88} - 30 q^{89} - 48 q^{90} + 30 q^{92} + 42 q^{93} - 57 q^{96} - 24 q^{97} + 60 q^{98}+O(q^{100}) \) 456 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 15 * q^10 - 36 * q^13 + 15 * q^14 - 3 * q^16 - 6 * q^17 - 24 * q^20 - 18 * q^21 - 6 * q^22 - 12 * q^24 - 6 * q^25 - 6 * q^26 - 27 * q^28 - 24 * q^29 + 3 * q^30 + 12 * q^32 + 66 * q^33 - 12 * q^34 - 81 * q^36 - 72 * q^38 - 33 * q^40 - 36 * q^41 - 87 * q^42 + 12 * q^44 + 6 * q^45 - 45 * q^48 - 6 * q^49 - 45 * q^50 - 3 * q^52 + 6 * q^53 - 39 * q^54 - 24 * q^57 - 42 * q^58 + 66 * q^60 - 18 * q^61 + 3 * q^62 - 6 * q^64 + 18 * q^65 + 75 * q^66 - 39 * q^68 - 36 * q^69 + 9 * q^70 - 54 * q^72 + 30 * q^73 - 57 * q^74 - 84 * q^76 - 18 * q^77 - 9 * q^78 - 3 * q^80 - 24 * q^81 + 117 * q^82 - 9 * q^84 - 78 * q^86 - 9 * q^88 - 30 * q^89 - 48 * q^90 + 30 * q^92 + 42 * q^93 - 57 * q^96 - 24 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more