LMFDB - Embedded newform 820.2.bw.b.11.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(11,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bw (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [672,0,0,0,0,12,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$42$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.29
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.b.671.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.711492 + 1.22220i) q^{2} +(-0.0905429 + 0.218590i) q^{3} +(-0.987559 + 1.73917i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.331582 + 0.0448632i) q^{6} +(-0.432887 - 1.80311i) q^{7} +(-2.82826 + 0.0304120i) q^{8} +(2.08174 + 2.08174i) q^{9} +(1.41200 - 0.0790756i) q^{10} +(3.05068 - 3.57189i) q^{11} +(-0.290750 - 0.373340i) q^{12} +(2.53852 + 4.14249i) q^{13} +(1.89576 - 1.81197i) q^{14} +(0.153659 + 0.179912i) q^{15} +(-2.04946 - 3.43507i) q^{16} +(0.329588 + 4.18781i) q^{17} +(-1.06317 + 4.02544i) q^{18} +(0.457810 + 0.280547i) q^{19} +(1.10127 + 1.66949i) q^{20} +(0.433336 + 0.0686336i) q^{21} +(6.53611 + 1.18718i) q^{22} +(3.83719 + 2.78788i) q^{23} +(0.249431 - 0.620984i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-3.25683 + 6.04994i) q^{26} +(-1.29930 + 0.538189i) q^{27} +(3.56342 + 1.02781i) q^{28} +(-0.282841 + 3.59383i) q^{29} +(-0.110562 + 0.315809i) q^{30} +(-0.0534206 + 0.164412i) q^{31} +(2.74018 - 4.94888i) q^{32} +(0.504561 + 0.990257i) q^{33} +(-4.88385 + 3.38241i) q^{34} +(-1.80311 - 0.432887i) q^{35} +(-5.67634 + 1.56467i) q^{36} +(0.316858 + 0.975189i) q^{37} +(-0.0171564 + 0.759144i) q^{38} +(-1.13535 + 0.179822i) q^{39} +(-1.25691 + 2.53381i) q^{40} +(-5.08777 - 3.88776i) q^{41} +(0.224431 + 0.578456i) q^{42} +(1.14570 + 7.23365i) q^{43} +(3.19941 + 8.83312i) q^{44} +(2.79993 - 0.909752i) q^{45} +(-0.677226 + 6.67338i) q^{46} +(1.08209 - 4.50722i) q^{47} +(0.936436 - 0.136969i) q^{48} +(3.17325 - 1.61685i) q^{49} +(0.570578 - 1.29400i) q^{50} +(-0.945254 - 0.307132i) q^{51} +(-9.71146 + 0.323980i) q^{52} +(-1.42471 - 0.112127i) q^{53} +(-1.58222 - 1.20509i) q^{54} +(-1.79760 - 4.33978i) q^{55} +(1.27916 + 5.08649i) q^{56} +(-0.102776 + 0.0746713i) q^{57} +(-4.59363 + 2.21129i) q^{58} +(-0.529629 + 0.728971i) q^{59} +(-0.464646 + 0.0895669i) q^{60} +(-0.277918 + 1.75471i) q^{61} +(-0.238953 + 0.0516868i) q^{62} +(2.85243 - 4.65475i) q^{63} +(7.99815 - 0.172026i) q^{64} +(4.84345 - 0.381188i) q^{65} +(-0.851304 + 1.32124i) q^{66} +(1.27157 - 1.08602i) q^{67} +(-7.60882 - 3.56249i) q^{68} +(-0.956833 + 0.586348i) q^{69} +(-0.753819 - 2.51176i) q^{70} +(-8.16399 - 6.97271i) q^{71} +(-5.95101 - 5.82439i) q^{72} +(9.96654 - 9.96654i) q^{73} +(-0.966436 + 1.08110i) q^{74} +(0.230063 - 0.0552332i) q^{75} +(-0.940034 + 0.519156i) q^{76} +(-7.76109 - 3.95447i) q^{77} +(-1.02757 - 1.25969i) q^{78} +(-6.59412 - 2.73137i) q^{79} +(-3.99111 + 0.266588i) q^{80} +8.49932i q^{81} +(1.13172 - 8.98439i) q^{82} -3.27833i q^{83} +(-0.547310 + 0.685866i) q^{84} +(3.88099 + 1.60756i) q^{85} +(-8.02584 + 6.54696i) q^{86} +(-0.759966 - 0.387222i) q^{87} +(-8.51950 + 10.1950i) q^{88} +(15.6432 - 3.75561i) q^{89} +(3.10403 + 2.77480i) q^{90} +(6.37046 - 6.37046i) q^{91} +(-8.63806 + 3.92034i) q^{92} +(-0.0311019 - 0.0265635i) q^{93} +(6.27863 - 1.88432i) q^{94} +(0.457810 - 0.280547i) q^{95} +(0.833671 + 1.04706i) q^{96} +(-8.71928 + 7.44697i) q^{97} +(4.23386 + 2.72798i) q^{98} +(13.7864 - 1.08502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$	$1$

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 $

$2$	0.711492	+	1.22220i	0.503101	+	0.864228i
$2$	0.711492	+	1.22220i	0.503101	+	0.864228i
$3$	−0.0905429	+	0.218590i	−0.0522750	+	0.126203i	−0.947860	−	0.318688i	$-0.896758\pi$
$3$	−0.0905429	+	0.218590i	−0.0522750	+	0.126203i	0.895585	+	0.444891i	$0.146758\pi$
$4$	−0.987559	+	1.73917i	−0.493779	+	0.869587i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$6$	−0.331582	+	0.0448632i	−0.135368	+	0.0183153i
$7$	−0.432887	−	1.80311i	−0.163616	−	0.681510i	−0.992516	−	0.122113i	$-0.961033\pi$
$7$	−0.432887	−	1.80311i	−0.163616	−	0.681510i	0.828900	−	0.559397i	$-0.188967\pi$
$8$	−2.82826	+	0.0304120i	−0.999942	+	0.0107523i
$9$	2.08174	+	2.08174i	0.693912	+	0.693912i
$10$	1.41200	−	0.0790756i	0.446514	−	0.0250059i
$11$	3.05068	−	3.57189i	0.919815	−	1.07696i	−0.0769853	−	0.997032i	$-0.524529\pi$
$11$	3.05068	−	3.57189i	0.919815	−	1.07696i	0.996800	−	0.0799327i	$-0.0254706\pi$
$12$	−0.290750	−	0.373340i	−0.0839322	−	0.107774i
$13$	2.53852	+	4.14249i	0.704060	+	1.14892i	0.982102	+	0.188352i	$0.0603146\pi$
$13$	2.53852	+	4.14249i	0.704060	+	1.14892i	−0.278042	+	0.960569i	$0.589685\pi$
$14$	1.89576	−	1.81197i	0.506664	−	0.484270i
$15$	0.153659	+	0.179912i	0.0396747	+	0.0464531i
$16$	−2.04946	−	3.43507i	−0.512364	−	0.858768i
$17$	0.329588	+	4.18781i	0.0799367	+	1.01569i	0.897836	+	0.440331i	$0.145139\pi$
$17$	0.329588	+	4.18781i	0.0799367	+	1.01569i	−0.817899	+	0.575362i	$0.804861\pi$
$18$	−1.06317	+	4.02544i	−0.250590	+	0.948806i
$19$	0.457810	+	0.280547i	0.105029	+	0.0643618i	0.574021	−	0.818841i	$-0.305383\pi$
$19$	0.457810	+	0.280547i	0.105029	+	0.0643618i	−0.468992	+	0.883202i	$0.655383\pi$
$20$	1.10127	+	1.66949i	0.246252	+	0.373309i
$21$	0.433336	+	0.0686336i	0.0945616	+	0.0149771i
$22$	6.53611	+	1.18718i	1.39350	+	0.253108i
$23$	3.83719	+	2.78788i	0.800109	+	0.581313i	0.910946	−	0.412525i	$-0.135353\pi$
$23$	3.83719	+	2.78788i	0.800109	+	0.581313i	−0.110837	+	0.993839i	$0.535353\pi$
$24$	0.249431	−	0.620984i	0.0509150	−	0.126758i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	−3.25683	+	6.04994i	−0.638716	+	1.18649i
$27$	−1.29930	+	0.538189i	−0.250051	+	0.103575i
$28$	3.56342	+	1.02781i	0.673422	+	0.194237i
$29$	−0.282841	+	3.59383i	−0.0525222	+	0.667358i	0.913155	+	0.407613i	$0.133639\pi$
$29$	−0.282841	+	3.59383i	−0.0525222	+	0.667358i	−0.965677	+	0.259745i	$0.916361\pi$
$30$	−0.110562	+	0.315809i	−0.0201857	+	0.0576586i
$31$	−0.0534206	+	0.164412i	−0.00959462	+	0.0295292i	−0.955739	−	0.294215i	$-0.904942\pi$
$31$	−0.0534206	+	0.164412i	−0.00959462	+	0.0295292i	0.946145	+	0.323744i	$0.104942\pi$
$32$	2.74018	−	4.94888i	0.484401	−	0.874846i
$33$	0.504561	+	0.990257i	0.0878329	+	0.172382i
$34$	−4.88385	+	3.38241i	−0.837573	+	0.580079i
$35$	−1.80311	−	0.432887i	−0.304780	−	0.0731713i
$36$	−5.67634	+	1.56467i	−0.946057	+	0.260778i
$37$	0.316858	+	0.975189i	0.0520911	+	0.160320i	0.973718	−	0.227757i	$-0.0731393\pi$
$37$	0.316858	+	0.975189i	0.0520911	+	0.160320i	−0.921627	+	0.388077i	$0.873139\pi$
$38$	−0.0171564	+	0.759144i	−0.00278313	+	0.123149i
$39$	−1.13535	+	0.179822i	−0.181802	+	0.0287946i
$40$	−1.25691	+	2.53381i	−0.198735	+	0.400630i
$41$	−5.08777	−	3.88776i	−0.794576	−	0.607165i
$41$	−5.08777	−	3.88776i	−0.794576	−	0.607165i
$42$	0.224431	+	0.578456i	0.0346304	+	0.0892577i
$43$	1.14570	+	7.23365i	0.174717	+	1.10312i	0.906693	+	0.421791i	$0.138598\pi$
$43$	1.14570	+	7.23365i	0.174717	+	1.10312i	−0.731976	+	0.681331i	$0.761402\pi$
$44$	3.19941	+	8.83312i	0.482329	+	1.33164i
$45$	2.79993	−	0.909752i	0.417389	−	0.135618i
$46$	−0.677226	+	6.67338i	−0.0998516	+	0.983936i
$47$	1.08209	−	4.50722i	0.157839	−	0.657445i	−0.836201	−	0.548423i	$-0.815228\pi$
$47$	1.08209	−	4.50722i	0.157839	−	0.657445i	0.994039	−	0.109022i	$-0.0347718\pi$
$48$	0.936436	−	0.136969i	0.135163	−	0.0197698i
$49$	3.17325	−	1.61685i	0.453321	−	0.230979i
$50$	0.570578	−	1.29400i	0.0806919	−	0.182999i
$51$	−0.945254	−	0.307132i	−0.132362	−	0.0430071i
$52$	−9.71146	+	0.323980i	−1.34674	+	0.0449280i
$53$	−1.42471	−	0.112127i	−0.195699	−	0.0154019i	−0.0197695	−	0.999805i	$-0.506293\pi$
$53$	−1.42471	−	0.112127i	−0.195699	−	0.0154019i	−0.175930	+	0.984403i	$0.556293\pi$
$54$	−1.58222	−	1.20509i	−0.215313	−	0.163993i
$55$	−1.79760	−	4.33978i	−0.242388	−	0.585176i
$56$	1.27916	+	5.08649i	0.170934	+	0.679711i
$57$	−0.102776	+	0.0746713i	−0.0136130	+	0.00989045i
$58$	−4.59363	+	2.21129i	−0.603173	+	0.290357i
$59$	−0.529629	+	0.728971i	−0.0689518	+	0.0949040i	−0.842100	−	0.539321i	$-0.818681\pi$
$59$	−0.529629	+	0.728971i	−0.0689518	+	0.0949040i	0.773148	+	0.634225i	$0.218681\pi$
$60$	−0.464646	+	0.0895669i	−0.0599856	+	0.0115630i
$61$	−0.277918	+	1.75471i	−0.0355838	+	0.224667i	−0.999071	−	0.0430859i	$-0.986281\pi$
$61$	−0.277918	+	1.75471i	−0.0355838	+	0.224667i	0.963488	+	0.267753i	$0.0862811\pi$
$62$	−0.238953	+	0.0516868i	−0.0303470	+	0.00656423i
$63$	2.85243	−	4.65475i	0.359373	−	0.586443i
$64$	7.99815	−	0.172026i	0.999769	−	0.0215033i
$65$	4.84345	−	0.381188i	0.600757	−	0.0472806i
$66$	−0.851304	+	1.32124i	−0.104788	+	0.162633i
$67$	1.27157	−	1.08602i	0.155347	−	0.132679i	−0.568377	−	0.822768i	$-0.692429\pi$
$67$	1.27157	−	1.08602i	0.155347	−	0.132679i	0.723724	+	0.690089i	$0.242429\pi$
$68$	−7.60882	−	3.56249i	−0.922704	−	0.432016i
$69$	−0.956833	+	0.586348i	−0.115189	+	0.0705880i
$70$	−0.753819	−	2.51176i	−0.0900986	−	0.300212i
$71$	−8.16399	−	6.97271i	−0.968888	−	0.827508i	0.0161462	−	0.999870i	$-0.494860\pi$
$71$	−8.16399	−	6.97271i	−0.968888	−	0.827508i	−0.985034	+	0.172362i	$0.944860\pi$
$72$	−5.95101	−	5.82439i	−0.701333	−	0.686411i
$73$	9.96654	−	9.96654i	1.16650	−	1.16650i	0.183470	−	0.983025i	$-0.441267\pi$
$73$	9.96654	−	9.96654i	1.16650	−	1.16650i	0.983025	−	0.183470i	$-0.0587330\pi$
$74$	−0.966436	+	1.08110i	−0.112346	+	0.125676i
$75$	0.230063	−	0.0552332i	0.0265654	−	0.00637778i
$76$	−0.940034	+	0.519156i	−0.107829	+	0.0595513i
$77$	−7.76109	−	3.95447i	−0.884459	−	0.450654i
$78$	−1.02757	−	1.25969i	−0.116350	−	0.142632i
$79$	−6.59412	−	2.73137i	−0.741897	−	0.307304i	−0.0204662	−	0.999791i	$-0.506515\pi$
$79$	−6.59412	−	2.73137i	−0.741897	−	0.307304i	−0.721430	+	0.692487i	$0.756515\pi$
$80$	−3.99111	+	0.266588i	−0.446219	+	0.0298055i
$81$			8.49932i			0.944369i
$82$	1.13172	−	8.98439i	0.124978	−	0.992160i
$83$		−	3.27833i		−	0.359843i	−0.983681	−	0.179922i	$-0.942416\pi$
$83$		−	3.27833i		−	0.359843i	0.983681	−	0.179922i	$-0.0575844\pi$
$84$	−0.547310	+	0.685866i	−0.0597164	+	0.0748342i
$85$	3.88099	+	1.60756i	0.420953	+	0.174364i
$86$	−8.02584	+	6.54696i	−0.865448	+	0.705977i
$87$	−0.759966	−	0.387222i	−0.0814770	−	0.0415146i
$88$	−8.51950	+	10.1950i	−0.908182	+	1.08679i
$89$	15.6432	−	3.75561i	1.65818	−	0.398094i	0.707119	−	0.707094i	$-0.249994\pi$
$89$	15.6432	−	3.75561i	1.65818	−	0.398094i	0.951062	+	0.309000i	$0.0999945\pi$
$90$	3.10403	+	2.77480i	0.327193	+	0.292490i
$91$	6.37046	−	6.37046i	0.667805	−	0.667805i
$92$	−8.63806	+	3.92034i	−0.900580	+	0.408724i
$93$	−0.0311019	−	0.0265635i	−0.00322511	−	0.00275451i
$94$	6.27863	−	1.88432i	0.647591	−	0.194353i
$95$	0.457810	−	0.280547i	0.0469704	−	0.0287835i
$96$	0.833671	+	1.04706i	0.0850861	+	0.106865i
$97$	−8.71928	+	7.44697i	−0.885309	+	0.756125i	−0.970718	−	0.240221i	$-0.922780\pi$
$97$	−8.71928	+	7.44697i	−0.885309	+	0.756125i	0.0854096	+	0.996346i	$0.472780\pi$
$98$	4.23386	+	2.72798i	0.427684	+	0.275567i
$99$	13.7864	−	1.08502i	1.38559	−	0.109048i
$100$	1.98749	−	0.223310i	0.198749	−	0.0223310i
$101$	−5.13863	+	8.38548i	−0.511312	+	0.834386i	−0.999259	−	0.0384874i	$-0.987746\pi$
$101$	−5.13863	+	8.38548i	−0.511312	+	0.834386i	0.487947	+	0.872873i	$0.337746\pi$
$102$	−0.297164	−	1.37381i	−0.0294236	−	0.136028i
$103$	−2.34466	+	14.8036i	−0.231026	+	1.45864i	0.550533	+	0.834813i	$0.314424\pi$
$103$	−2.34466	+	14.8036i	−0.231026	+	1.45864i	−0.781560	+	0.623831i	$0.785576\pi$
$104$	−7.30559	−	11.6389i	−0.716372	−	1.14128i
$105$	0.257883	−	0.354946i	0.0251668	−	0.0346392i
$106$	−0.876630	−	1.82107i	−0.0851458	−	0.176878i
$107$	6.72186	−	4.88372i	0.649827	−	0.472127i	−0.213385	−	0.976968i	$-0.568449\pi$
$107$	6.72186	−	4.88372i	0.649827	−	0.472127i	0.863212	+	0.504841i	$0.168449\pi$
$108$	0.347133	−	2.79121i	0.0334029	−	0.268584i
$109$	−5.38061	−	12.9899i	−0.515369	−	1.24421i	−0.940721	−	0.339182i	$-0.889850\pi$
$109$	−5.38061	−	12.9899i	−0.515369	−	1.24421i	0.425352	−	0.905028i	$-0.360150\pi$
$110$	4.02512	−	5.28475i	0.383780	−	0.503881i
$111$	−0.241856	−	0.0190345i	−0.0229559	−	0.00180667i
$112$	−5.30661	+	5.18238i	−0.501428	+	0.489689i
$113$	−2.18095	−	0.708634i	−0.205167	−	0.0666627i	0.204631	−	0.978839i	$-0.434401\pi$
$113$	−2.18095	−	0.708634i	−0.205167	−	0.0666627i	−0.409797	+	0.912177i	$0.634401\pi$
$114$	−0.164388	−	0.0724853i	−0.0153963	−	0.00678887i
$115$	4.22607	−	2.15329i	0.394083	−	0.200795i
$116$	−5.97098	−	4.04103i	−0.554392	−	0.375200i
$117$	−3.33904	+	13.9081i	−0.308695	+	1.28581i
$118$	−1.26778	−	0.128656i	−0.116708	−	0.0118438i
$119$	7.40838	−	2.40713i	0.679125	−	0.220661i
$120$	−0.440061	−	0.504166i	−0.0401719	−	0.0460238i
$121$	−1.73095	−	10.9288i	−0.157359	−	0.993529i
$122$	−2.34234	+	0.908787i	−0.212066	+	0.0822777i
$123$	1.31049	−	0.760126i	0.118162	−	0.0685382i
$124$	−0.233185	−	0.255274i	−0.0209406	−	0.0229243i
$125$	−0.987688	+	0.156434i	−0.0883415	+	0.0139919i
$126$	7.71853	+	0.174436i	0.687621	+	0.0155400i
$127$	4.93660	+	15.1933i	0.438053	+	1.34819i	0.889926	+	0.456105i	$0.150756\pi$
$127$	4.93660	+	15.1933i	0.438053	+	1.34819i	−0.451873	+	0.892082i	$0.649244\pi$
$128$	5.90087	+	9.65296i	0.521568	+	0.853210i
$129$	−1.68494	−	0.404518i	−0.148351	−	0.0356158i
$130$	3.91197	+	5.64847i	0.343102	+	0.495404i
$131$	−6.40214	−	12.5649i	−0.559358	−	1.09780i	−0.981534	−	0.191288i	$-0.938734\pi$
$131$	−6.40214	−	12.5649i	−0.559358	−	1.09780i	0.422176	−	0.906514i	$-0.361266\pi$
$132$	−2.22051	−	0.100417i	−0.193271	−	0.00874017i
$133$	0.307675	−	0.946926i	0.0266788	−	0.0821089i
$134$	2.23205	+	0.781420i	0.192820	+	0.0675044i
$135$	−0.110341	+	1.40202i	−0.00949667	+	0.120667i
$136$	−1.05952	−	11.8342i	−0.0908531	−	1.01477i
$137$	5.32800	−	2.20693i	0.455202	−	0.188551i	−0.143288	−	0.989681i	$-0.545768\pi$
$137$	5.32800	−	2.20693i	0.455202	−	0.188551i	0.598490	+	0.801130i	$0.295768\pi$
$138$	−1.39741	−	0.752262i	−0.118956	−	0.0640368i
$139$	−8.45773	−	11.6411i	−0.717376	−	0.987383i	−0.999607	−	0.0280365i	$-0.991075\pi$
$139$	−8.45773	−	11.6411i	−0.717376	−	0.987383i	0.282231	−	0.959346i	$-0.408925\pi$
$140$	2.53354	−	2.70841i	0.214123	−	0.228903i
$141$	0.887257	+	0.644630i	0.0747205	+	0.0542876i
$142$	2.71345	−	14.9391i	0.227707	−	1.25366i
$143$	22.5407	+	3.57010i	1.88495	+	0.298547i
$144$	2.88449	−	11.4173i	0.240374	−	0.951446i
$145$	3.07372	+	1.88358i	0.255259	+	0.156423i
$146$	19.2722	+	5.09002i	1.59498	+	0.421253i
$147$	0.0661122	+	0.840035i	0.00545284	+	0.0692849i
$148$	−2.00894	−	0.411985i	−0.165134	−	0.0338649i
$149$	1.47901	+	1.73169i	0.121165	+	0.141866i	0.817673	−	0.575683i	$-0.195264\pi$
$149$	1.47901	+	1.73169i	0.121165	+	0.141866i	−0.696508	+	0.717549i	$0.745264\pi$
$150$	0.231194	+	0.241885i	0.0188769	+	0.0197499i
$151$	−8.37533	−	13.6673i	−0.681574	−	1.11223i	−0.987109	−	0.160047i	$-0.948835\pi$
$151$	−8.37533	−	13.6673i	−0.681574	−	1.11223i	0.305535	−	0.952181i	$-0.401165\pi$
$152$	−1.30334	−	0.779537i	−0.105715	−	0.0632288i
$153$	−8.03180	+	9.40403i	−0.649332	+	0.760271i
$154$	−0.688786	−	12.2992i	−0.0555039	−	0.991098i
$155$	0.122239	+	0.122239i	0.00981851	+	0.00981851i
$156$	0.808485	−	2.15216i	0.0647306	−	0.172311i
$157$	−4.69936	−	19.5742i	−0.375050	−	1.56219i	−0.766654	−	0.642060i	$-0.778080\pi$
$157$	−4.69936	−	19.5742i	−0.375050	−	1.56219i	0.391605	−	0.920134i	$-0.371920\pi$
$158$	−1.35337	−	10.0027i	−0.107668	−	0.795772i
$159$	0.153508	−	0.301276i	0.0121739	−	0.0238927i
$160$	−3.16546	−	4.68827i	−0.250252	−	0.370640i
$161$	3.36577	−	8.12569i	0.265260	−	0.640394i
$162$	−10.3879	+	6.04720i	−0.816150	+	0.475113i
$163$	−17.0373			−1.33446			−0.667232	−	0.744850i	$-0.732521\pi$
$163$	−17.0373			−1.33446			−0.667232	+	0.744850i	$0.732521\pi$
$164$	11.7860	−	5.00913i	0.920328	−	0.391147i
$165$	1.11139			0.0865217
$166$	4.00678	−	2.33250i	0.310986	−	0.181037i
$167$	4.63103	−	11.1803i	0.358360	−	0.865158i	−0.637171	−	0.770723i	$-0.719895\pi$
$167$	4.63103	−	11.1803i	0.358360	−	0.865158i	0.995531	−	0.0944354i	$-0.0301046\pi$
$168$	−1.22767	−	0.180935i	−0.0947171	−	0.0139595i
$169$	−4.81427	+	9.44855i	−0.370329	+	0.726811i
$170$	0.796531	+	5.88713i	0.0610912	+	0.451522i
$171$	0.369017	+	1.53707i	0.0282194	+	0.117542i
$172$	−13.7120	−	5.15109i	−1.04553	−	0.392767i
$173$	−0.889666	−	0.889666i	−0.0676401	−	0.0676401i	0.672478	−	0.740118i	$-0.265230\pi$
$173$	−0.889666	−	0.889666i	−0.0676401	−	0.0676401i	−0.740118	+	0.672478i	$0.765230\pi$
$174$	−0.0674459	−	1.20434i	−0.00511306	−	0.0913007i
$175$	−1.20430	+	1.41005i	−0.0910364	+	0.106590i
$176$	−18.5219	−	3.15888i	−1.39614	−	0.238110i
$177$	−0.111392	−	0.181775i	−0.00837271	−	0.0136630i
$178$	15.7202	+	16.4471i	1.17828	+	1.23276i
$179$	8.78662	+	10.2878i	0.656743	+	0.768947i	0.984418	−	0.175844i	$-0.0562653\pi$
$179$	8.78662	+	10.2878i	0.656743	+	0.768947i	−0.327676	+	0.944790i	$0.606265\pi$
$180$	−1.18288	+	5.76800i	−0.0881664	+	0.429921i
$181$	−0.0322671	−	0.409993i	−0.00239840	−	0.0304745i	0.995602	−	0.0936872i	$-0.0298654\pi$
$181$	−0.0322671	−	0.409993i	−0.00239840	−	0.0304745i	−0.998000	+	0.0632127i	$0.979865\pi$
$182$	12.3185	+	3.25346i	0.913109	+	0.241163i
$183$	−0.358397	−	0.219626i	−0.0264935	−	0.0162352i
$184$	−10.9374	−	7.76816i	−0.806313	−	0.572677i
$185$	1.01275	+	0.160404i	0.0744589	+	0.0117931i
$186$	0.0103373	−	0.0569125i	0.000757965	−	0.00417303i
$187$	15.9638	+	11.5984i	1.16739	+	0.848160i
$188$	6.77021	+	6.33308i	0.493768	+	0.461887i
$189$	1.53286	+	2.10980i	0.111499	+	0.153466i
$190$	0.668613	+	0.359931i	0.0485063	+	0.0261121i
$191$	−7.49620	+	3.10503i	−0.542406	+	0.224672i	−0.637027	−	0.770842i	$-0.719836\pi$
$191$	−7.49620	+	3.10503i	−0.542406	+	0.224672i	0.0946212	+	0.995513i	$0.469836\pi$
$192$	−0.686573	+	1.76389i	−0.0495491	+	0.127298i
$193$	0.516392	−	6.56138i	0.0371707	−	0.472299i	−0.949959	−	0.312375i	$-0.898875\pi$
$193$	0.516392	−	6.56138i	0.0371707	−	0.472299i	0.987129	−	0.159923i	$-0.0511247\pi$
$194$	−15.3054	−	5.35827i	−1.09886	−	0.384701i
$195$	−0.355217	+	1.09324i	−0.0254376	+	0.0782888i
$196$	−0.321783	+	7.11557i	−0.0229845	+	0.508255i
$197$	−1.43807	−	2.82238i	−0.102459	−	0.201086i	0.834086	−	0.551634i	$-0.185995\pi$
$197$	−1.43807	−	2.82238i	−0.102459	−	0.201086i	−0.936545	+	0.350548i	$0.885995\pi$
$198$	11.1351	+	16.0779i	0.791334	+	1.14260i
$199$	−12.6498	−	3.03696i	−0.896723	−	0.215284i	−0.241214	−	0.970472i	$-0.577546\pi$
$199$	−12.6498	−	3.03696i	−0.896723	−	0.215284i	−0.655508	+	0.755188i	$0.727546\pi$
$200$	1.68702	+	2.27024i	0.119290	+	0.160530i
$201$	0.122262	+	0.376284i	0.00862371	+	0.0265410i
$202$	−13.9048	−	0.314244i	−0.978341	−	0.0221101i
$203$	6.60250	−	1.04573i	0.463404	−	0.0733960i
$204$	1.46765	−	1.34065i	0.102756	−	0.0938644i
$205$	−5.77381	+	2.76823i	−0.403261	+	0.193341i
$206$	−19.7612	+	7.66700i	−1.37683	+	0.534185i
$207$	2.18438	+	13.7916i	0.151825	+	0.958586i
$208$	9.02718	−	17.2099i	0.625922	−	1.19329i
$209$	2.39872	−	0.779390i	0.165923	−	0.0539115i
$210$	0.617297	+	0.0626445i	0.0425976	+	0.00432288i
$211$	6.10981	−	25.4492i	0.420616	−	1.75199i	−0.211750	−	0.977324i	$-0.567916\pi$
$211$	6.10981	−	25.4492i	0.420616	−	1.75199i	0.632366	−	0.774670i	$-0.282084\pi$
$212$	1.60200	−	2.36709i	0.110026	−	0.162573i
$213$	2.26336	−	1.15324i	0.155083	−	0.0790185i
$214$	10.7514	+	4.74075i	0.734954	+	0.324071i
$215$	6.96537	+	2.26319i	0.475034	+	0.154348i
$216$	3.65840	−	1.56165i	0.248923	−	0.106257i
$217$	0.319577	+	0.0251512i	0.0216943	+	0.00170738i
$218$	12.0481	−	15.8184i	0.815999	−	1.07136i
$219$	1.27619	+	3.08098i	0.0862366	+	0.208194i
$220$	9.32287	+	1.15945i	0.628548	+	0.0781704i
$221$	−16.5113	+	11.9962i	−1.11067	+	0.806949i
$222$	−0.148814	−	0.309140i	−0.00998777	−	0.0207481i
$223$	−4.95923	+	6.82580i	−0.332095	+	0.457089i	−0.942112	−	0.335299i	$-0.891163\pi$
$223$	−4.95923	+	6.82580i	−0.332095	+	0.457089i	0.610017	+	0.792388i	$0.291163\pi$
$224$	−10.1095	−	2.79853i	−0.675472	−	0.186985i
$225$	0.460546	−	2.90777i	0.0307031	−	0.193852i
$226$	−0.685635	−	3.16975i	−0.0456078	−	0.210849i
$227$	−7.34014	+	11.9780i	−0.487182	+	0.795009i	−0.997902	−	0.0647378i	$-0.979379\pi$
$227$	−7.34014	+	11.9780i	−0.487182	+	0.795009i	0.510720	+	0.859747i	$0.329379\pi$
$228$	−0.0283689	−	0.252488i	−0.00187877	−	0.0167214i
$229$	−6.34675	+	0.499500i	−0.419405	+	0.0330079i	−0.286406	−	0.958108i	$-0.592461\pi$
$229$	−6.34675	+	0.499500i	−0.419405	+	0.0330079i	−0.132999	+	0.991116i	$0.542461\pi$
$230$	5.63857	+	3.63306i	0.371796	+	0.239557i
$231$	1.56712	−	1.33845i	0.103109	−	0.0880633i
$232$	0.690653	−	10.1729i	0.0453436	−	0.667884i
$233$	5.99728	−	3.67514i	0.392895	−	0.240766i	−0.311994	−	0.950084i	$-0.600997\pi$
$233$	5.99728	−	3.67514i	0.392895	−	0.240766i	0.704889	+	0.709318i	$0.250997\pi$
$234$	−19.3742	+	5.81453i	−1.26653	+	0.380107i
$235$	−3.52470	−	3.01038i	−0.229926	−	0.196376i
$236$	−0.744769	−	1.64102i	−0.0484803	−	0.106821i
$237$	1.19410	−	1.19410i	0.0775653	−	0.0775653i
$238$	8.21301	+	7.34189i	0.532370	+	0.475904i
$239$	18.7342	−	4.49769i	1.21182	−	0.290932i	0.423326	−	0.905977i	$-0.360863\pi$
$239$	18.7342	−	4.49769i	1.21182	−	0.290932i	0.788491	+	0.615046i	$0.210863\pi$
$240$	0.303093	−	0.896553i	0.0195646	−	0.0578723i
$241$	8.20463	+	4.18047i	0.528507	+	0.269288i	0.697818	−	0.716275i	$-0.254154\pi$
$241$	8.20463	+	4.18047i	0.528507	+	0.269288i	−0.169311	+	0.985563i	$0.554154\pi$
$242$	12.1257	−	9.89134i	0.779467	−	0.635839i
$243$	−5.75577	−	2.38412i	−0.369233	−	0.152941i
$244$	−2.77728	−	2.21622i	−0.177797	−	0.141879i
$245$		−	3.56142i		−	0.227531i
$246$	1.86143	+	1.06086i	0.118680	+	0.0676377i
$247$			2.60865i			0.165984i
$248$	0.146087	−	0.466624i	0.00927656	−	0.0296307i
$249$	0.716609	+	0.296829i	0.0454133	+	0.0188108i
$250$	−0.893927	−	1.09585i	−0.0565369	−	0.0693079i
$251$	−18.0012	−	9.17206i	−1.13622	−	0.578935i	−0.218376	−	0.975865i	$-0.570076\pi$
$251$	−18.0012	−	9.17206i	−1.13622	−	0.578935i	−0.917849	+	0.396929i	$0.870076\pi$
$252$	5.27847	+	9.55771i	0.332513	+	0.602079i
$253$	21.6640	−	5.20107i	1.36201	−	0.326989i
$254$	−15.0569	+	16.8434i	−0.944756	+	1.05685i
$255$	−0.702793	+	0.702793i	−0.0440106	+	0.0440106i
$256$	−7.59946	+	14.0801i	−0.474966	+	0.880004i
$257$	12.0177	+	10.2641i	0.749641	+	0.640254i	0.939888	−	0.341482i	$-0.110929\pi$
$257$	12.0177	+	10.2641i	0.749641	+	0.640254i	−0.190247	+	0.981736i	$0.560929\pi$
$258$	−0.704417	−	2.34715i	−0.0438551	−	0.146127i
$259$	1.62120	−	0.993475i	0.100737	−	0.0617315i
$260$	−4.12024	+	8.80006i	−0.255527	+	0.545756i
$261$	−8.07021	+	6.89261i	−0.499534	+	0.426642i
$262$	10.8018	−	16.7646i	0.667337	−	1.03572i
$263$	9.68192	−	0.761984i	0.597013	−	0.0469859i	0.223647	−	0.974670i	$-0.428204\pi$
$263$	9.68192	−	0.761984i	0.597013	−	0.0469859i	0.373366	+	0.927684i	$0.378204\pi$
$264$	−1.45715	−	2.78536i	−0.0896813	−	0.171427i
$265$	−0.746713	+	1.21852i	−0.0458702	+	0.0748533i
$266$	1.37624	−	0.297689i	0.0843829	−	0.0182525i
$267$	−0.595446	+	3.75950i	−0.0364407	+	0.230078i
$268$	0.633035	+	3.28399i	0.0386687	+	0.200602i
$269$	−5.31952	+	7.32169i	−0.324337	+	0.446411i	−0.939785	−	0.341766i	$-0.888975\pi$
$269$	−5.31952	+	7.32169i	−0.324337	+	0.446411i	0.615448	+	0.788177i	$0.288975\pi$
$270$	−1.79206	+	0.862666i	−0.109061	+	0.0525002i
$271$	−0.195952	+	0.142367i	−0.0119032	+	0.00864819i	−0.593721	−	0.804671i	$-0.702342\pi$
$271$	−0.195952	+	0.142367i	−0.0119032	+	0.00864819i	0.581818	+	0.813319i	$0.302342\pi$
$272$	13.7100	−	9.71489i	0.831288	−	0.589052i
$273$	0.815718	+	1.96932i	0.0493695	+	0.119189i
$274$	6.48814	+	4.94168i	0.391963	+	0.298538i
$275$	−4.68286	−	0.368549i	−0.282387	−	0.0222244i
$276$	−0.0748330	−	2.24315i	−0.00450441	−	0.135022i
$277$	−27.7860	−	9.02823i	−1.66950	−	0.542454i	−0.686671	−	0.726968i	$-0.740929\pi$
$277$	−27.7860	−	9.02823i	−1.66950	−	0.542454i	−0.982830	+	0.184514i	$0.940929\pi$
$278$	8.21014	−	18.6196i	0.492411	−	1.11673i
$279$	−0.453469	+	0.231054i	−0.0271485	+	0.0138329i
$280$	5.11282	+	1.16948i	0.305550	+	0.0698900i
$281$	3.99855	−	16.6551i	0.238533	−	0.993562i	−0.716623	−	0.697461i	$-0.754313\pi$
$281$	3.99855	−	16.6551i	0.238533	−	0.993562i	0.955156	−	0.296102i	$-0.0956868\pi$
$282$	−0.156592	+	1.54306i	−0.00932493	+	0.0918877i
$283$	−21.2211	+	6.89516i	−1.26147	+	0.409875i	−0.862016	−	0.506880i	$-0.830799\pi$
$283$	−21.2211	+	6.89516i	−1.26147	+	0.409875i	−0.399449	+	0.916755i	$0.630799\pi$
$284$	20.1892	−	7.31265i	1.19801	−	0.433926i
$285$	0.0198732	+	0.125474i	0.00117719	+	0.00743245i
$286$	11.6742	+	30.0895i	0.690308	+	1.77923i
$287$	−4.80760	+	10.8567i	−0.283784	+	0.640853i
$288$	16.0066	−	4.59792i	0.943198	−	0.270935i
$289$	−0.638403	+	0.101113i	−0.0375531	+	0.00594783i
$290$	−0.115187	+	5.09686i	−0.00676402	+	0.299298i
$291$	−0.838363	−	2.58022i	−0.0491457	−	0.151255i
$292$	7.49101	+	27.1761i	0.438378	+	1.59036i
$293$	−24.0756	−	5.78005i	−1.40651	−	0.337674i	−0.542041	−	0.840352i	$-0.682348\pi$
$293$	−24.0756	−	5.78005i	−1.40651	−	0.337674i	−0.864474	+	0.502678i	$0.832348\pi$
$294$	−0.979654	+	0.678480i	−0.0571346	+	0.0395698i
$295$	0.409072	+	0.802849i	0.0238171	+	0.0467437i
$296$	−0.925816	−	2.74845i	−0.0538119	−	0.159751i
$297$	−2.04141	+	6.28281i	−0.118455	+	0.364566i
$298$	−1.06418	+	3.03973i	−0.0616463	+	0.176087i
$299$	−1.80798	+	22.9726i	−0.104558	+	1.32854i
$300$	−0.131140	+	0.454665i	−0.00757139	+	0.0262501i
$301$	12.5471	−	5.19717i	0.723202	−	0.299560i
$302$	10.7452	−	19.9605i	0.618318	−	1.14860i
$303$	−1.36771	−	1.88250i	−0.0785731	−	0.108147i
$304$	0.0254356	−	2.14758i	0.00145883	−	0.123172i
$305$	1.43728	+	1.04425i	0.0822985	+	0.0597934i
$306$	−17.2082	−	3.12560i	−0.983727	−	0.178678i
$307$	−10.9330	−	1.73161i	−0.623978	−	0.0988284i	−0.163564	−	0.986533i	$-0.552299\pi$
$307$	−10.9330	−	1.73161i	−0.623978	−	0.0988284i	−0.460414	+	0.887704i	$0.652299\pi$
$308$	14.5421	−	9.59262i	0.828610	−	0.546590i
$309$	−3.02363	−	1.85288i	−0.172008	−	0.105407i
$310$	−0.0624290	+	0.236374i	−0.00354573	+	0.0134251i
$311$	−0.855207	−	10.8664i	−0.0484944	−	0.616179i	−0.972364	−	0.233471i	$-0.924992\pi$
$311$	−0.855207	−	10.8664i	−0.0484944	−	0.616179i	0.923869	−	0.382708i	$-0.125008\pi$
$312$	3.20561	−	0.543113i	0.181482	−	0.0307477i
$313$	−0.0782841	−	0.0916589i	−0.00442488	−	0.00518087i	0.758189	−	0.652035i	$-0.226084\pi$
$313$	−0.0782841	−	0.0916589i	−0.00442488	−	0.00518087i	−0.762614	+	0.646854i	$0.776084\pi$
$314$	20.5801	−	19.6705i	1.16140	−	1.11007i
$315$	−2.85243	−	4.65475i	−0.160716	−	0.262265i
$316$	11.2624	−	8.77094i	0.633561	−	0.493404i
$317$	13.3536	−	15.6350i	0.750011	−	0.878150i	−0.245825	−	0.969314i	$-0.579059\pi$
$317$	13.3536	−	15.6350i	0.750011	−	0.878150i	0.995836	+	0.0911645i	$0.0290589\pi$
$318$	0.477439	−	0.0267378i	0.0267735	−	0.00149938i
$319$	11.9739	+	11.9739i	0.670410	+	0.670410i
$320$	3.47781	−	7.20450i	0.194415	−	0.402744i
$321$	0.458915	+	1.91152i	0.0256141	+	0.106691i
$322$	12.3260	−	1.66771i	0.686899	−	0.0929378i
$323$	−1.02399	+	2.00969i	−0.0569761	+	0.111822i
$324$	−14.7818	−	8.39357i	−0.821211	−	0.466310i
$325$	1.85924	−	4.48860i	0.103132	−	0.248983i
$326$	−12.1219	−	20.8230i	−0.671370	−	1.15328i
$327$	3.32665			0.183964
$328$	14.5078	+	10.8409i	0.801058	+	0.598587i
$329$	−8.59541			−0.473880
$330$	0.790746	+	1.35835i	0.0435292	+	0.0747745i
$331$	−0.575780	+	1.39006i	−0.0316477	+	0.0764043i	−0.938913	−	0.344154i	$-0.888166\pi$
$331$	−0.575780	+	1.39006i	−0.0316477	+	0.0764043i	0.907266	+	0.420558i	$0.138166\pi$
$332$	5.70158	+	3.23754i	0.312915	+	0.177683i
$333$	−1.37047	+	2.68970i	−0.0751014	+	0.147395i
$334$	16.9595	−	2.29463i	0.927985	−	0.125557i
$335$	−0.390373	−	1.62602i	−0.0213284	−	0.0888391i
$336$	−0.652341	−	1.62920i	−0.0355881	−	0.0888802i
$337$	14.3645	+	14.3645i	0.782483	+	0.782483i	0.980249	−	0.197766i	$-0.0633688\pi$
$337$	14.3645	+	14.3645i	0.782483	+	0.782483i	−0.197766	+	0.980249i	$0.563369\pi$
$338$	−14.9734	+	0.838545i	−0.814443	+	0.0456108i
$339$	0.352370	−	0.412572i	0.0191381	−	0.0224079i
$340$	−6.62854	+	5.16217i	−0.359483	+	0.279958i
$341$	0.424291	+	0.692380i	0.0229766	+	0.0374945i
$342$	−1.61605	+	1.54462i	−0.0873861	+	0.0835236i
$343$	−12.7191	−	14.8921i	−0.686767	−	0.804100i
$344$	−3.46033	−	20.4238i	−0.186568	−	1.10118i
$345$	0.0880468	+	1.11874i	0.00474028	+	0.0602310i
$346$	0.454362	−	1.72034i	0.0244267	−	0.0924862i
$347$	10.3318	+	6.33136i	0.554642	+	0.339885i	0.771410	−	0.636338i	$-0.219552\pi$
$347$	10.3318	+	6.33136i	0.554642	+	0.339885i	−0.216768	+	0.976223i	$0.569552\pi$
$348$	1.42396	−	0.939310i	0.0763322	−	0.0503523i
$349$	−29.8075	−	4.72105i	−1.59556	−	0.252712i	−0.705553	−	0.708657i	$-0.749301\pi$
$349$	−29.8075	−	4.72105i	−1.59556	−	0.252712i	−0.890008	+	0.455945i	$0.849301\pi$
$350$	−2.58022	−	0.468656i	−0.137918	−	0.0250507i
$351$	−5.52775	−	4.01615i	−0.295050	−	0.214366i
$352$	−9.31741	−	24.8851i	−0.496620	−	1.32638i
$353$	2.01158	+	2.76870i	0.107065	+	0.147363i	0.859187	−	0.511661i	$-0.170970\pi$
$353$	2.01158	+	2.76870i	0.107065	+	0.147363i	−0.752122	+	0.659024i	$0.770970\pi$
$354$	0.142911	−	0.265474i	0.00759565	−	0.0141098i
$355$	−9.91910	+	4.10863i	−0.526451	+	0.218063i
$356$	−8.91696	+	30.9152i	−0.472598	+	1.63850i
$357$	−0.144602	+	1.83735i	−0.00765317	+	0.0972427i
$358$	−6.32218	+	18.0587i	−0.334137	+	0.954433i
$359$	−7.72032	+	23.7607i	−0.407463	+	1.25404i	0.511358	+	0.859368i	$0.329142\pi$
$359$	−7.72032	+	23.7607i	−0.407463	+	1.25404i	−0.918821	+	0.394674i	$0.870858\pi$
$360$	−7.89127	+	2.65817i	−0.415907	+	0.140098i
$361$	−8.49494	−	16.6722i	−0.447102	−	0.877487i
$362$	0.478136	−	0.331143i	0.0251303	−	0.0174045i
$363$	2.54565	+	0.611158i	0.133612	+	0.0320775i
$364$	4.78814	+	17.3705i	0.250967	+	0.910463i
$365$	−4.35554	−	13.4050i	−0.227979	−	0.701648i
$366$	0.0134309	−	0.594297i	0.000702043	−	0.0310644i
$367$	−32.9706	+	5.22203i	−1.72105	+	0.272588i	−0.937310	−	0.348498i	$-0.886692\pi$
$367$	−32.9706	+	5.22203i	−1.72105	+	0.272588i	−0.783743	+	0.621086i	$0.786692\pi$
$368$	1.71242	−	18.8947i	0.0892663	−	0.984952i
$369$	−2.49811	−	18.6847i	−0.130046	−	0.972685i
$370$	0.524517	+	1.35191i	0.0272684	+	0.0702826i
$371$	0.414563	+	2.61745i	0.0215230	+	0.135891i
$372$	0.0769135	−	0.0278586i	0.00398778	−	0.00144440i
$373$	20.3725	−	6.61944i	1.05485	−	0.342742i	0.270280	−	0.962782i	$-0.412884\pi$
$373$	20.3725	−	6.61944i	1.05485	−	0.342742i	0.784570	+	0.620040i	$0.212884\pi$
$374$	−2.81746	+	27.7632i	−0.145688	+	1.43560i
$375$	0.0552332	−	0.230063i	0.00285223	−	0.0118804i
$376$	−2.92335	+	12.7805i	−0.150760	+	0.659104i
$377$	−15.6054	+	7.95136i	−0.803720	+	0.409516i
$378$	−1.48799	+	3.37458i	−0.0765339	+	0.173570i
$379$	1.08928	+	0.353929i	0.0559526	+	0.0181801i	0.336860	−	0.941555i	$-0.390635\pi$
$379$	1.08928	+	0.353929i	0.0559526	+	0.0181801i	−0.280907	+	0.959735i	$0.590635\pi$
$380$	0.0358049	+	1.07327i	0.00183675	+	0.0550575i
$381$	−3.76808	−	0.296554i	−0.193044	−	0.0151929i
$382$	−9.12845	−	6.95267i	−0.467052	−	0.355730i
$383$	12.9061	+	31.1581i	0.659471	+	1.59210i	0.798622	+	0.601833i	$0.205563\pi$
$383$	12.9061	+	31.1581i	0.659471	+	1.59210i	−0.139151	+	0.990271i	$0.544437\pi$
$384$	−2.64432	+	0.415863i	−0.134943	+	0.0212219i
$385$	−7.04692	+	5.11989i	−0.359145	+	0.260934i
$386$	8.38675	−	4.03724i	0.426874	−	0.205490i
$387$	−12.6735	+	17.4436i	−0.644231	+	0.886708i
$388$	−4.34078	−	22.5187i	−0.220370	−	1.14321i
$389$	−3.08217	+	19.4601i	−0.156272	+	0.986665i	0.777522	+	0.628855i	$0.216476\pi$
$389$	−3.08217	+	19.4601i	−0.156272	+	0.986665i	−0.933795	+	0.357809i	$0.883524\pi$
$390$	−1.58890	+	0.343688i	−0.0804571	+	0.0174033i
$391$	−10.4104	+	16.9883i	−0.526477	+	0.859133i
$392$	−8.92561	+	4.66939i	−0.450812	+	0.235840i
$393$	3.32623	−	0.261780i	0.167786	−	0.0132051i
$394$	2.42634	−	3.76572i	0.122237	−	0.189714i
$395$	−5.42734	+	4.63539i	−0.273079	+	0.233232i
$396$	−11.7279	+	25.0486i	−0.589349	+	1.25874i
$397$	−25.2885	+	15.4968i	−1.26920	+	0.777764i	−0.983561	−	0.180575i	$-0.942204\pi$
$397$	−25.2885	+	15.4968i	−1.26920	+	0.777764i	−0.285634	+	0.958339i	$0.592204\pi$
$398$	−5.28848	−	17.6214i	−0.265087	−	0.883282i
$399$	0.179131	+	0.152992i	0.00896775	+	0.00765918i
$400$	−1.57439	+	3.67713i	−0.0787196	+	0.183857i
$401$	22.3997	−	22.3997i	1.11859	−	1.11859i	0.126636	−	0.991949i	$-0.459582\pi$
$401$	22.3997	−	22.3997i	1.11859	−	1.11859i	0.991949	−	0.126636i	$-0.0404181\pi$
$402$	−0.372907	+	0.417152i	−0.0185989	+	0.0208057i
$403$	−0.816684	+	0.196068i	−0.0406819	+	0.00976686i
$404$	−9.50911	−	17.2181i	−0.473096	−	0.856633i
$405$	7.57295	+	3.85861i	0.376303	+	0.191736i
$406$	5.97572	+	7.32556i	0.296570	+	0.363561i
$407$	4.44990	+	1.84321i	0.220573	+	0.0913644i
$408$	2.68277	+	0.839903i	0.132817	+	0.0415814i
$409$			18.9909i			0.939041i	0.882922	+	0.469520i	$0.155573\pi$
$409$			18.9909i			0.939041i	−0.882922	+	0.469520i	$0.844427\pi$
$410$	−7.49136	−	5.08720i	−0.369972	−	0.251239i
$411$			1.36447i			0.0673043i
$412$	−23.4306	−	18.6972i	−1.15434	−	0.921146i
$413$	1.54368	+	0.639414i	0.0759596	+	0.0314635i
$414$	−15.3020	+	12.4824i	−0.752053	+	0.613477i
$415$	−2.92101	−	1.48833i	−0.143387	−	0.0730592i
$416$	27.4567	−	1.21165i	1.34618	−	0.0594059i
$417$	3.31041	−	0.794759i	0.162111	−	0.0389195i
$418$	2.65924	+	2.37719i	0.130068	+	0.116272i
$419$	−14.7376	+	14.7376i	−0.719979	+	0.719979i	−0.968601	−	0.248622i	$-0.920022\pi$
$419$	−14.7376	+	14.7376i	−0.719979	+	0.719979i	0.248622	+	0.968601i	$0.420022\pi$
$420$	0.362638	+	0.799034i	0.0176949	+	0.0389888i
$421$	25.4218	+	21.7122i	1.23898	+	1.05819i	0.996109	+	0.0881315i	$0.0280896\pi$
$421$	25.4218	+	21.7122i	1.23898	+	1.05819i	0.242872	+	0.970058i	$0.421910\pi$
$422$	35.4511	−	10.6395i	1.72573	−	0.517921i
$423$	11.6355	−	7.13022i	0.565735	−	0.346683i
$424$	4.03287	+	0.273797i	0.195854	+	0.0132968i
$425$	3.19428	−	2.72817i	0.154945	−	0.132336i
$426$	3.01985	+	1.94576i	0.146312	+	0.0942724i
$427$	3.28423	−	0.258474i	0.158935	−	0.0125084i
$428$	1.85541	+	16.5135i	0.0896845	+	0.798208i
$429$	−2.82129	+	4.60393i	−0.136213	+	0.222280i
$430$	2.18973	+	10.1233i	0.105598	+	0.488190i
$431$	1.01230	−	6.39144i	0.0487610	−	0.307865i	−0.951239	−	0.308455i	$-0.900188\pi$
$431$	1.01230	−	6.39144i	0.0487610	−	0.307865i	1.00000		0.000590588i	$0.000187990\pi$
$432$	4.51158	+	3.36021i	0.217064	+	0.161668i
$433$	−8.71016	+	11.9885i	−0.418583	+	0.576131i	−0.965286	−	0.261196i	$-0.915883\pi$
$433$	−8.71016	+	11.9885i	−0.418583	+	0.576131i	0.546702	+	0.837327i	$0.315883\pi$
$434$	0.196636	+	0.408482i	0.00943884	+	0.0196078i
$435$	−0.690035	+	0.501340i	−0.0330846	+	0.0240374i
$436$	27.9054	+	3.47051i	1.33643	+	0.166207i
$437$	0.974575	+	2.35283i	0.0466202	+	0.112551i
$438$	−2.85759	+	3.75185i	−0.136541	+	0.179270i
$439$	−35.0703	−	2.76010i	−1.67382	−	0.131732i	−0.794276	−	0.607557i	$-0.792150\pi$
$439$	−35.0703	−	2.76010i	−1.67382	−	0.131732i	−0.879540	+	0.475825i	$0.842150\pi$
$440$	5.21606	+	12.2194i	0.248666	+	0.582536i
$441$	9.97173	+	3.24001i	0.474844	+	0.154286i
$442$	−26.4094	−	11.6450i	−1.25617	−	0.553895i
$443$	−7.47924	+	3.81086i	−0.355349	+	0.181059i	−0.622547	−	0.782582i	$-0.713902\pi$
$443$	−7.47924	+	3.81086i	−0.355349	+	0.181059i	0.267198	+	0.963642i	$0.413902\pi$
$444$	0.271951	−	0.401832i	0.0129062	−	0.0190701i
$445$	3.75561	−	15.6432i	0.178033	−	0.741561i
$446$	−11.8710	−	1.20469i	−0.562106	−	0.0570436i
$447$	−0.512444	+	0.166503i	−0.0242378	+	0.00787534i
$448$	−3.77248	−	14.3470i	−0.178233	−	0.677834i
$449$	−0.991377	−	6.25931i	−0.0467860	−	0.295395i	0.953190	−	0.302373i	$-0.0977788\pi$
$449$	−0.991377	−	6.25931i	−0.0467860	−	0.295395i	−0.999976	+	0.00697802i	$0.997779\pi$
$450$	3.88156	−	1.50598i	0.182979	−	0.0709925i
$451$	−29.4078	+	6.31263i	−1.38476	+	0.297250i
$452$	3.38626	−	3.09324i	0.159276	−	0.145494i
$453$	3.74586	−	0.593286i	0.175996	−	0.0278750i
$454$	−19.8620	−	0.448874i	−0.932171	−	0.0210667i
$455$	−2.78399	−	8.56825i	−0.130516	−	0.401686i
$456$	0.288407	−	0.214316i	0.0135059	−	0.0100362i
$457$	23.1504	+	5.55793i	1.08293	+	0.259989i	0.735368	−	0.677668i	$-0.237009\pi$
$457$	23.1504	+	5.55793i	1.08293	+	0.259989i	0.347563	+	0.937657i	$0.387009\pi$
$458$	−5.12615	−	7.40162i	−0.239529	−	0.345855i
$459$	−2.68207	−	5.26385i	−0.125188	−	0.245696i
$460$	−0.428544	+	9.47637i	−0.0199809	+	0.441838i
$461$	7.06182	−	21.7341i	0.328902	−	1.01226i	−0.640746	−	0.767753i	$-0.721375\pi$
$461$	7.06182	−	21.7341i	0.328902	−	1.01226i	0.969648	−	0.244504i	$-0.0786250\pi$
$462$	2.75085	+	0.963044i	0.127981	+	0.0448049i
$463$	−2.31927	+	29.4692i	−0.107786	+	1.36955i	0.670626	+	0.741795i	$0.266025\pi$
$463$	−2.31927	+	29.4692i	−0.107786	+	1.36955i	−0.778412	+	0.627753i	$0.783975\pi$
$464$	12.9247	−	6.39382i	0.600016	−	0.296826i
$465$	−0.0377882	+	0.0156524i	−0.00175239	+	0.000725862i
$466$	8.75877	+	4.71506i	0.405742	+	0.218421i
$467$	13.1254	+	18.0656i	0.607371	+	0.835975i	0.996358	−	0.0852684i	$-0.0271748\pi$
$467$	13.1254	+	18.0656i	0.607371	+	0.835975i	−0.388987	+	0.921243i	$0.627175\pi$
$468$	−20.8911	−	19.5423i	−0.965693	−	0.903341i
$469$	−2.50866	−	1.82265i	−0.115839	−	0.0841621i
$470$	1.17150	−	6.44976i	0.0540371	−	0.297505i
$471$	4.70422	+	0.745076i	0.216759	+	0.0343313i
$472$	1.47576	−	2.07783i	0.0679274	−	0.0956399i
$473$	29.3330	+	17.9753i	1.34873	+	0.826504i
$474$	2.30903	+	0.609841i	0.106057	+	0.0280109i
$475$	−0.0421273	−	0.535278i	−0.00193293	−	0.0245602i
$476$	−3.12979	+	15.2617i	−0.143454	+	0.699517i
$477$	−2.73246	−	3.19930i	−0.125111	−	0.146486i
$478$	18.8264	+	19.6970i	0.861097	+	0.900918i
$479$	−0.526728	−	0.859541i	−0.0240668	−	0.0392734i	0.840381	−	0.541997i	$-0.182331\pi$
$479$	−0.526728	−	0.859541i	−0.0240668	−	0.0392734i	−0.864447	+	0.502723i	$0.832331\pi$
$480$	1.31142	−	0.267450i	0.0598578	−	0.0122073i
$481$	−3.23536	+	3.78812i	−0.147520	+	0.172723i
$482$	0.728150	+	13.0021i	0.0331663	+	0.592229i
$483$	1.47145	+	1.47145i	0.0669532	+	0.0669532i
$484$	20.7165	+	7.78241i	0.941661	+	0.353746i
$485$	2.67683	+	11.1498i	0.121548	+	0.506286i
$486$	−1.18131	−	8.73100i	−0.0535853	−	0.396046i
$487$	−5.65096	+	11.0906i	−0.256069	+	0.502565i	−0.982874	−	0.184280i	$-0.941005\pi$
$487$	−5.65096	+	11.0906i	−0.256069	+	0.502565i	0.726804	+	0.686845i	$0.241005\pi$
$488$	0.732661	−	4.97122i	0.0331660	−	0.225037i
$489$	1.54261	−	3.72418i	0.0697591	−	0.168413i
$490$	4.35278	−	2.53392i	0.196638	−	0.114471i
$491$	39.7260			1.79281			0.896404	−	0.443237i	$-0.146170\pi$
$491$	39.7260			1.79281			0.896404	+	0.443237i	$0.146170\pi$
$492$	0.0278103	+	3.02983i	0.00125379	+	0.136595i
$493$	−15.1435			−0.682029
$494$	−3.18830	+	1.85603i	−0.143448	+	0.0835069i
$495$	5.29216	−	12.7764i	0.237865	−	0.574257i
$496$	0.674249	−	0.153451i	0.0302747	−	0.00689015i
$497$	−9.03844	+	17.7389i	−0.405429	+	0.795700i
$498$	0.147076	+	1.08703i	0.00659064	+	0.0487111i
$499$	8.64447	+	36.0068i	0.386980	+	1.61189i	0.737511	+	0.675335i	$0.236001\pi$
$499$	8.64447	+	36.0068i	0.386980	+	1.61189i	−0.350531	+	0.936551i	$0.613999\pi$
$500$	0.703333	−	1.87225i	0.0314540	−	0.0837296i
$501$	2.02459	+	2.02459i	0.0904522	+	0.0904522i
$502$	−1.59758	−	28.5269i	−0.0713035	−	1.27322i
$503$	20.6398	−	24.1661i	0.920285	−	1.07751i	−0.0764746	−	0.997072i	$-0.524366\pi$
$503$	20.6398	−	24.1661i	0.920285	−	1.07751i	0.996759	−	0.0804433i	$-0.0256336\pi$
$504$	−7.92587	+	13.2516i	−0.353046	+	0.590273i
$505$	5.13863	+	8.38548i	0.228666	+	0.373149i
$506$	21.7706	+	22.7773i	0.967819	+	1.01258i
$507$	−1.62946	−	1.90785i	−0.0723668	−	0.0847306i
$508$	−31.2990	−	6.41866i	−1.38867	−	0.284782i
$509$	−1.18844	−	15.1005i	−0.0526765	−	0.669318i	−0.965406	−	0.260753i	$-0.916029\pi$
$509$	−1.18844	−	15.1005i	−0.0526765	−	0.669318i	0.912729	−	0.408565i	$-0.133971\pi$
$510$	−1.35899	−	0.358924i	−0.0601769	−	0.0158934i
$511$	−22.2851	−	13.6563i	−0.985835	−	0.604120i
$512$	−22.6156	+	0.729776i	−0.999480	+	0.0322518i
$513$	−0.745822	−	0.118127i	−0.0329288	−	0.00521541i
$514$	−3.99428	+	21.9908i	−0.176180	+	0.969973i
$515$	12.1257	+	8.80981i	0.534321	+	0.388207i
$516$	2.36750	−	2.53092i	0.104224	−	0.111417i
$517$	−12.7982	−	17.6152i	−0.562863	−	0.774714i
$518$	2.36770	+	1.27459i	0.104031	+	0.0560023i
$519$	0.275025	−	0.113919i	0.0120723	−	0.00500049i
$520$	−13.6870	+	1.22540i	−0.600213	+	0.0537373i
$521$	1.67275	−	21.2544i	0.0732847	−	0.931170i	−0.844876	−	0.534962i	$-0.820326\pi$
$521$	1.67275	−	21.2544i	0.0732847	−	0.931170i	0.918161	−	0.396208i	$-0.129674\pi$
$522$	−14.1661	−	4.95940i	−0.620032	−	0.217067i
$523$	0.752707	−	2.31659i	0.0329136	−	0.101298i	−0.933250	−	0.359227i	$-0.883040\pi$
$523$	0.752707	−	2.31659i	0.0329136	−	0.101298i	0.966164	+	0.257930i	$0.0830403\pi$
$524$	28.1751	+	1.27414i	1.23083	+	0.0556612i
$525$	−0.199182	−	0.390918i	−0.00869304	−	0.0170610i
$526$	7.81991	+	11.2911i	0.340964	+	0.492316i
$527$	−0.706131	−	0.169527i	−0.0307596	−	0.00738472i
$528$	2.36753	−	3.76269i	0.103034	−	0.163750i
$529$	−0.155655	−	0.479057i	−0.00676761	−	0.0208286i
$530$	−2.02056	−	0.0456640i	−0.0877677	−	0.00198352i
$531$	−2.62007	+	0.414979i	−0.113702	+	0.0180086i
$532$	1.34302	+	1.47024i	0.0582274	+	0.0637432i
$533$	3.18959	−	30.9452i	0.138156	−	1.34039i
$534$	−5.01853	+	1.94710i	−0.217173	+	0.0842592i
$535$	−1.29976	−	8.20639i	−0.0561937	−	0.354793i
$536$	−3.56331	+	3.11023i	−0.153911	+	0.134342i
$537$	−3.04438	+	0.989178i	−0.131375	+	0.0426862i
$538$	−12.7334	−	1.29221i	−0.548975	−	0.0557110i
$539$	3.90536	−	16.2670i	0.168216	−	0.700669i
$540$	−2.32939	−	1.57648i	−0.100241	−	0.0678409i
$541$	−8.98261	+	4.57687i	−0.386192	+	0.196775i	−0.636297	−	0.771444i	$-0.719535\pi$
$541$	−8.98261	+	4.57687i	−0.386192	+	0.196775i	0.250105	+	0.968219i	$0.419535\pi$
$542$	−0.313419	−	0.138199i	−0.0134625	−	0.00593618i
$543$	0.0925418	+	0.0300687i	0.00397135	+	0.00129037i
$544$	21.6281	+	9.84428i	0.927296	+	0.422070i
$545$	−14.0169	−	1.10315i	−0.600416	−	0.0472538i
$546$	−1.82653	+	2.39813i	−0.0781682	+	0.102630i
$547$	−13.6403	−	32.9306i	−0.583218	−	1.40801i	−0.889880	−	0.456194i	$-0.849212\pi$
$547$	−13.6403	−	32.9306i	−0.583218	−	1.40801i	0.306662	−	0.951818i	$-0.400788\pi$
$548$	−1.42348	+	11.4458i	−0.0608079	+	0.488940i
$549$	−4.23139	+	3.07428i	−0.180591	+	0.131207i
$550$	−2.88138	−	5.98563i	−0.122862	−	0.255228i
$551$	−1.13773	+	1.56594i	−0.0484687	+	0.0667115i
$552$	2.68834	−	1.68745i	0.114423	−	0.0718225i
$553$	−2.07044	+	13.0723i	−0.0880443	+	0.555890i
$554$	−8.73521	−	40.3837i	−0.371124	−	1.71574i
$555$	−0.126760	+	0.206854i	−0.00538066	+	0.00878044i
$556$	28.5984	−	3.21324i	1.21284	−	0.136272i
$557$	−28.4954	+	2.24263i	−1.20739	+	0.0950234i	−0.666131	−	0.745835i	$-0.732051\pi$
$557$	−28.4954	+	2.24263i	−1.20739	+	0.0950234i	−0.541256	+	0.840858i	$0.682051\pi$
$558$	−0.605035	−	0.389838i	−0.0256132	−	0.0165032i
$559$	−27.0570	+	23.1088i	−1.14439	+	0.977400i
$560$	2.20839	+	7.08098i	0.0933213	+	0.299226i
$561$	−3.98071	+	2.43938i	−0.168066	+	0.102991i
$562$	23.2009	−	6.96297i	0.978670	−	0.293715i
$563$	8.47262	+	7.23630i	0.357078	+	0.304974i	0.809832	−	0.586662i	$-0.199558\pi$
$563$	8.47262	+	7.23630i	0.357078	+	0.304974i	−0.452754	+	0.891636i	$0.649558\pi$
$564$	−1.99734	+	0.906485i	−0.0841033	+	0.0381699i
$565$	−1.62153	+	1.62153i	−0.0682182	+	0.0682182i
$566$	−23.5260	−	21.0307i	−0.988870	−	0.883985i
$567$	15.3252	−	3.67925i	0.643596	−	0.154514i
$568$	23.3020	+	19.4724i	0.977729	+	0.817043i
$569$	19.9429	+	10.1614i	0.836051	+	0.425989i	0.818950	−	0.573865i	$-0.194556\pi$
$569$	19.9429	+	10.1614i	0.836051	+	0.425989i	0.0171007	+	0.999854i	$0.494556\pi$
$570$	−0.139215	+	0.113563i	−0.00583109	+	0.00475663i
$571$	−20.2619	−	8.39274i	−0.847932	−	0.351225i	−0.0839561	−	0.996469i	$-0.526756\pi$
$571$	−20.2619	−	8.39274i	−0.847932	−	0.351225i	−0.763976	+	0.645244i	$0.776756\pi$
$572$	−28.4693	+	35.6766i	−1.19036	+	1.49171i
$573$		−	1.91973i		−	0.0801979i
$574$	−16.6897	+	1.84862i	−0.696615	+	0.0771597i
$575$		−	4.74303i		−	0.197798i
$576$	17.0082	+	16.2919i	0.708673	+	0.678830i
$577$	−37.3524	−	15.4719i	−1.55500	−	0.644102i	−0.570788	−	0.821098i	$-0.693362\pi$
$577$	−37.3524	−	15.4719i	−1.55500	−	0.644102i	−0.984212	+	0.176996i	$0.943362\pi$
$578$	−0.577799	−	0.708317i	−0.0240333	−	0.0294621i
$579$	1.38750	+	0.706965i	0.0576624	+	0.0293805i
$580$	−6.31135	+	3.48559i	−0.262065	+	0.144731i
$581$	−5.91117	+	1.41915i	−0.245237	+	0.0588761i
$582$	2.55706	−	2.86045i	0.105994	−	0.118570i
$583$	−4.74685	+	4.74685i	−0.196595	+	0.196595i
$584$	−27.8849	+	28.4911i	−1.15389	+	1.17897i
$585$	10.8763	+	9.28926i	0.449681	+	0.384064i
$586$	−10.0652	−	33.5378i	−0.415791	−	1.38543i
$587$	26.5899	−	16.2943i	1.09748	−	0.672539i	0.148833	−	0.988862i	$-0.452448\pi$
$587$	26.5899	−	16.2943i	1.09748	−	0.672539i	0.948651	+	0.316323i	$0.102448\pi$
$588$	−1.52626	−	0.714603i	−0.0629418	−	0.0294697i
$589$	−0.0705816	+	0.0602824i	−0.00290827	+	0.00248389i
$590$	−0.690193	+	1.07119i	−0.0284148	+	0.0441002i
$591$	0.747151	−	0.0588021i	0.0307337	−	0.00241879i
$592$	2.70046	−	3.08704i	0.110988	−	0.126876i
$593$	−3.24970	+	5.30303i	−0.133449	+	0.217769i	−0.912384	−	0.409336i	$-0.865760\pi$
$593$	−3.24970	+	5.30303i	−0.133449	+	0.217769i	0.778934	+	0.627105i	$0.215760\pi$
$594$	−9.13131	+	1.97515i	−0.374662	+	0.0810415i
$595$	1.21857	−	7.69373i	0.0499564	−	0.315412i
$596$	−4.47232	+	0.862101i	−0.183194	+	0.0353130i
$597$	1.80920	−	2.49015i	0.0740456	−	0.101915i
$598$	−29.3636	+	14.1351i	−1.20077	+	0.578028i
$599$	23.9010	−	17.3651i	0.976567	−	0.709517i	0.0196280	−	0.999807i	$-0.493752\pi$
$599$	23.9010	−	17.3651i	0.976567	−	0.709517i	0.956939	+	0.290290i	$0.0937518\pi$
$600$	−0.648998	+	0.163211i	−0.0264952	+	0.00666305i
$601$	15.6901	+	37.8792i	0.640012	+	1.54512i	0.826662	+	0.562698i	$0.190237\pi$
$601$	15.6901	+	37.8792i	0.640012	+	1.54512i	−0.186651	+	0.982426i	$0.559763\pi$
$602$	15.2791	+	11.6373i	0.622731	+	0.474302i
$603$	4.90789	+	0.386259i	0.199865	+	0.0157297i
$604$	32.0409	−	1.06891i	1.30373	−	0.0434931i
$605$	−10.5235	−	3.41929i	−0.427840	−	0.139014i
$606$	1.32768	−	3.01101i	0.0539331	−	0.122314i
$607$	36.9613	−	18.8327i	1.50021	−	0.764396i	0.505091	−	0.863066i	$-0.331459\pi$
$607$	36.9613	−	18.8327i	1.50021	−	0.764396i	0.995120	+	0.0986705i	$0.0314590\pi$
$608$	2.64288	−	1.49690i	0.107183	−	0.0607073i
$609$	−0.369223	+	1.53792i	−0.0149617	+	0.0623198i
$610$	−0.253666	+	2.49962i	−0.0102706	+	0.101207i
$611$	21.4180	−	6.95914i	0.866480	−	0.281536i
$612$	−8.42338	−	23.2557i	−0.340495	−	0.940057i
$613$	4.82576	+	30.4687i	0.194911	+	1.23062i	0.870063	+	0.492940i	$0.164078\pi$
$613$	4.82576	+	30.4687i	0.194911	+	1.23062i	−0.675153	+	0.737678i	$0.735922\pi$
$614$	−5.66234	−	14.5943i	−0.228514	−	0.588980i
$615$	−0.0823291	−	1.51274i	−0.00331983	−	0.0609996i
$616$	22.0707	+	10.9483i	0.889253	+	0.441118i
$617$	38.0325	−	6.02375i	1.53113	−	0.242507i	0.666725	−	0.745304i	$-0.267696\pi$
$617$	38.0325	−	6.02375i	1.53113	−	0.242507i	0.864405	+	0.502797i	$0.167696\pi$
$618$	0.113310	−	5.01380i	0.00455800	−	0.201685i
$619$	3.76763	+	11.5956i	0.151434	+	0.466065i	0.997782	−	0.0665646i	$-0.0212038\pi$
$619$	3.76763	+	11.5956i	0.151434	+	0.466065i	−0.846348	+	0.532630i	$0.821204\pi$
$620$	−0.333314	+	0.0918771i	−0.0133862	+	0.00368987i
$621$	−6.48608	−	1.55717i	−0.260277	−	0.0624870i
$622$	12.6725	−	8.77662i	0.508122	−	0.351910i
$623$	−13.5435	−	26.5807i	−0.542610	−	1.06493i
$624$	2.94456	+	3.53148i	0.117877	+	0.141372i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	0.0563273	−	0.160894i	0.00225129	−	0.00643060i
$627$	−0.0468199	+	0.594903i	−0.00186981	+	0.0237581i
$628$	38.6839	+	11.1577i	1.54366	+	0.445241i
$629$	−3.97947	+	1.64835i	−0.158672	+	0.0657240i
$630$	3.65956	−	6.79807i	0.145800	−	0.270841i
$631$	−23.3360	−	32.1192i	−0.928991	−	1.27865i	−0.960252	−	0.279135i	$-0.909952\pi$
$631$	−23.3360	−	32.1192i	−0.928991	−	1.27865i	0.0312612	−	0.999511i	$-0.490048\pi$
$632$	18.7330	+	7.52451i	0.745158	+	0.299309i
$633$	5.00973	+	3.63978i	0.199119	+	0.144668i
$634$	28.6101	+	5.19657i	1.13625	+	0.206382i
$635$	15.7785	+	2.49907i	0.626151	+	0.0991725i
$636$	0.372373	+	0.564504i	0.0147656	+	0.0223840i
$637$	14.7532	+	9.04075i	0.584541	+	0.358207i
$638$	−6.11521	+	23.1539i	−0.242103	+	0.916671i
$639$	−2.47994	−	31.5106i	−0.0981049	−	1.24654i
$640$	11.2798	−	0.875360i	0.445873	−	0.0346016i
$641$	17.0777	+	19.9954i	0.674527	+	0.789770i	0.987097	−	0.160125i	$-0.0511897\pi$
$641$	17.0777	+	19.9954i	0.674527	+	0.789770i	−0.312569	+	0.949895i	$0.601190\pi$
$642$	−2.00975	+	1.92092i	−0.0793184	+	0.0758125i
$643$	−2.00228	−	3.26742i	−0.0789621	−	0.128855i	0.810721	−	0.585432i	$-0.199075\pi$
$643$	−2.00228	−	3.26742i	−0.0789621	−	0.128855i	−0.889684	+	0.456578i	$0.849075\pi$
$644$	10.8081	+	13.8783i	0.425899	+	0.546880i
$645$	−1.12537	+	1.31764i	−0.0443116	+	0.0518822i
$646$	−3.18480	+	0.178357i	−0.125304	+	0.00701736i
$647$	22.9593	+	22.9593i	0.902623	+	0.902623i	0.995662	−	0.0930394i	$-0.0296583\pi$
$647$	22.9593	+	22.9593i	0.902623	+	0.902623i	−0.0930394	+	0.995662i	$0.529658\pi$
$648$	−0.258481	−	24.0383i	−0.0101541	−	0.944314i
$649$	0.988076	+	4.11563i	0.0387854	+	0.161553i
$650$	6.80882	−	0.921237i	0.267064	−	0.0361339i
$651$	−0.0344332	+	0.0675790i	−0.00134954	+	0.00264863i
$652$	16.8253	−	29.6309i	0.658931	−	1.16043i
$653$	−3.90886	+	9.43682i	−0.152965	+	0.369291i	−0.981723	−	0.190317i	$-0.939048\pi$
$653$	−3.90886	+	9.43682i	−0.152965	+	0.369291i	0.828757	+	0.559608i	$0.189048\pi$
$654$	2.36688	+	4.06583i	0.0925524	+	0.158987i
$655$	−14.1019			−0.551008
$656$	−2.92757	+	25.4446i	−0.114302	+	0.993446i
$657$	41.4954			1.61889
$658$	−6.11556	−	10.5053i	−0.238409	−	0.409540i
$659$	−8.08386	+	19.5162i	−0.314903	+	0.760242i	0.684607	+	0.728913i	$0.259974\pi$
$659$	−8.08386	+	19.5162i	−0.314903	+	0.760242i	−0.999509	+	0.0313293i	$0.990026\pi$
$660$	−1.09756	+	1.93290i	−0.0427226	+	0.0752382i
$661$	12.2627	−	24.0668i	0.476962	−	0.936091i	−0.519692	−	0.854354i	$-0.673953\pi$
$661$	12.2627	−	24.0668i	0.476962	−	0.936091i	0.996654	−	0.0817373i	$-0.0260469\pi$
$662$	−2.10859	+	0.285294i	−0.0819528	+	0.0110882i
$663$	−1.12726	−	4.69537i	−0.0437791	−	0.182353i
$664$	0.0997005	+	9.27197i	0.00386913	+	0.359822i
$665$	−0.704035	−	0.704035i	−0.0273013	−	0.0273013i
$666$	−4.26244	+	0.238707i	−0.165166	+	0.00924971i
$667$	−11.1045	+	13.0017i	−0.429968	+	0.503427i
$668$	14.8711	+	19.0954i	0.575380	+	0.738823i
$669$	−1.04303	−	1.70207i	−0.0403258	−	0.0658057i
$670$	1.70958	−	1.63402i	0.0660469	−	0.0631276i
$671$	5.41977	+	6.34574i	0.209228	+	0.244975i
$672$	1.52708	−	1.95646i	0.0589083	−	0.0754719i
$673$	−0.561319	−	7.13223i	−0.0216372	−	0.274927i	−0.998213	−	0.0597540i	$-0.980968\pi$
$673$	−0.561319	−	7.13223i	−0.0216372	−	0.274927i	0.976576	−	0.215173i	$-0.0690316\pi$
$674$	−7.33609	+	27.7765i	−0.282576	+	1.06991i
$675$	1.19912	+	0.734819i	0.0461540	+	0.0282832i
$676$	−11.6783	−	17.7039i	−0.449165	−	0.680917i
$677$	3.71860	+	0.588969i	0.142917	+	0.0226359i	0.227483	−	0.973782i	$-0.426950\pi$
$677$	3.71860	+	0.588969i	0.142917	+	0.0226359i	−0.0845658	+	0.996418i	$0.526950\pi$
$678$	0.754955	+	0.137126i	0.0289939	+	0.00526628i
$679$	17.2021	+	12.4981i	0.660157	+	0.479632i
$680$	−11.0254	−	4.42858i	−0.422803	−	0.169828i
$681$	−1.95368	−	2.68901i	−0.0748651	−	0.103043i
$682$	−0.544349	+	1.01119i	−0.0208442	+	0.0387206i
$683$	1.41653	−	0.586747i	0.0542021	−	0.0224512i	−0.355418	−	0.934708i	$-0.615661\pi$
$683$	1.41653	−	0.586747i	0.0542021	−	0.0224512i	0.409620	+	0.912256i	$0.365661\pi$
$684$	−3.03765	−	0.876157i	−0.116147	−	0.0335007i
$685$	0.452472	−	5.74921i	0.0172881	−	0.219666i
$686$	9.15169	−	26.1410i	0.349413	−	0.998066i
$687$	0.465467	−	1.43256i	0.0177587	−	0.0546556i
$688$	22.5001	−	18.7606i	0.857807	−	0.715242i
$689$	−3.15218	−	6.18650i	−0.120089	−	0.235687i
$690$	−1.30468	+	0.903586i	−0.0496684	+	0.0343989i
$691$	22.9136	+	5.50107i	0.871675	+	0.209271i	0.644520	−	0.764588i	$-0.277057\pi$
$691$	22.9136	+	5.50107i	0.871675	+	0.209271i	0.227156	+	0.973858i	$0.427057\pi$
$692$	2.42588	−	0.668687i	0.0922182	−	0.0254197i
$693$	−7.92438	−	24.3887i	−0.301022	−	0.926451i
$694$	−0.387184	+	17.1323i	−0.0146973	+	0.650333i
$695$	−14.2120	+	2.25096i	−0.539092	+	0.0853838i
$696$	2.16116	+	1.07205i	0.0819186	+	0.0406361i
$697$	14.6043	−	22.5879i	0.553178	−	0.855579i
$698$	−15.4377	−	39.7899i	−0.584327	−	1.50607i
$699$	0.260337	+	1.64370i	0.00984684	+	0.0621705i
$700$	−1.26301	−	3.48699i	−0.0477373	−	0.131796i
$701$	−31.8036	+	10.3336i	−1.20120	+	0.390295i	−0.840204	−	0.542270i	$-0.817565\pi$
$701$	−31.8036	+	10.3336i	−1.20120	+	0.390295i	−0.361001	+	0.932566i	$0.617565\pi$
$702$	0.975595	−	9.61349i	0.0368215	−	0.362838i
$703$	−0.128525	+	0.535345i	−0.00484741	+	0.0201909i
$704$	23.7853	−	29.0933i	0.896444	−	1.09650i
$705$	0.977176	−	0.497896i	0.0368026	−	0.0187518i
$706$	−1.95269	+	4.42846i	−0.0734904	+	0.166667i
$707$	17.3443	+	5.63552i	0.652301	+	0.211945i
$708$	0.426144	−	0.0142164i	0.0160155	−	0.000534286i
$709$	30.1081	+	2.36956i	1.13073	+	0.0889906i	0.629988	−	0.776605i	$-0.283060\pi$
$709$	30.1081	+	2.36956i	1.13073	+	0.0889906i	0.500745	+	0.865595i	$0.333060\pi$
$710$	−12.0789	−	9.19990i	−0.453314	−	0.345266i
$711$	−8.04122	−	19.4132i	−0.301569	−	0.728053i
$712$	−44.1290	+	11.0976i	−1.65380	+	0.415900i
$713$	−0.663345	+	0.481948i	−0.0248425	+	0.0180491i
$714$	−2.34849	+	1.13052i	−0.0878901	+	0.0423088i
$715$	13.4143	−	18.4632i	0.501665	−	0.690483i
$716$	−26.5696	+	5.12165i	−0.992952	+	0.191405i
$717$	−0.713102	+	4.50235i	−0.0266313	+	0.168143i
$718$	−34.5333	+	7.46975i	−1.28877	+	0.278769i
$719$	15.8904	−	25.9307i	0.592610	−	0.967052i	−0.405975	−	0.913884i	$-0.633068\pi$
$719$	15.8904	−	25.9307i	0.592610	−	0.967052i	0.998586	−	0.0531681i	$-0.0169319\pi$
$720$	−8.86340	−	7.75347i	−0.330319	−	0.288955i
$721$	27.7075	−	2.18062i	1.03188	−	0.0812107i
$722$	14.3328	−	22.2447i	0.533411	−	0.827862i
$723$	−1.65668	+	1.41494i	−0.0616126	+	0.0526221i
$724$	0.744914	+	0.348773i	0.0276845	+	0.0129621i
$725$	3.07372	−	1.88358i	0.114155	−	0.0699544i
$726$	1.06425	+	3.54614i	0.0394982	+	0.131610i
$727$	28.5458	+	24.3804i	1.05870	+	0.904218i	0.995592	−	0.0937884i	$-0.0298977\pi$
$727$	28.5458	+	24.3804i	1.05870	+	0.904218i	0.0631112	+	0.998007i	$0.479898\pi$
$728$	−17.8236	+	18.2111i	−0.660586	+	0.674947i
$729$	−16.9875	+	16.9875i	−0.629166	+	0.629166i
$730$	13.2847	−	14.8609i	0.491687	−	0.550026i
$731$	−29.9155	+	7.18209i	−1.10647	+	0.265639i
$732$	0.735907	−	0.406422i	0.0271999	−	0.0150218i
$733$	−30.1645	−	15.3696i	−1.11415	−	0.567688i	−0.202759	−	0.979229i	$-0.564991\pi$
$733$	−30.1645	−	15.3696i	−1.11415	−	0.567688i	−0.911391	+	0.411540i	$0.864991\pi$
$734$	−29.8407	−	36.5813i	−1.10144	−	1.35024i
$735$	0.778491	+	0.322461i	0.0287151	+	0.0118942i
$736$	24.3115	−	11.3505i	0.896133	−	0.418384i
$737$		−	7.85502i		−	0.289343i
$738$	21.0591	−	16.3472i	0.775195	−	0.601748i
$739$		−	30.1397i		−	1.10871i	−0.832281	−	0.554354i	$-0.812965\pi$
$739$		−	30.1397i		−	1.10871i	0.832281	−	0.554354i	$-0.187035\pi$
$740$	−1.27912	+	1.60294i	−0.0470214	+	0.0589253i
$741$	−0.570225	−	0.236195i	−0.0209477	−	0.00867684i
$742$	−2.90409	+	2.36897i	−0.106613	+	0.0869677i
$743$	−14.3263	−	7.29960i	−0.525580	−	0.267797i	0.171005	−	0.985270i	$-0.445298\pi$
$743$	−14.3263	−	7.29960i	−0.525580	−	0.267797i	−0.696586	+	0.717474i	$0.745298\pi$
$744$	0.0887722	+	0.0741828i	0.00325455	+	0.00271967i
$745$	2.21441	−	0.531632i	0.0811296	−	0.0194775i
$746$	22.5852	+	20.1897i	0.826903	+	0.739197i
$747$	6.82461	−	6.82461i	0.249699	−	0.249699i
$748$	−35.9369	+	16.3098i	−1.31398	+	0.596346i
$749$	−11.7157	−	10.0061i	−0.428081	−	0.365616i
$750$	0.320481	−	0.0961817i	0.0117023	−	0.00351206i
$751$	29.7902	−	18.2554i	1.08706	−	0.666151i	0.140956	−	0.990016i	$-0.454982\pi$
$751$	29.7902	−	18.2554i	1.08706	−	0.666151i	0.946103	+	0.323865i	$0.104982\pi$
$752$	−17.7003	+	5.52030i	−0.645464	+	0.201304i
$753$	3.63480	−	3.10441i	0.132459	−	0.113131i
$754$	−20.8213	−	13.4157i	−0.758267	−	0.488570i
$755$	−15.9800	+	1.25765i	−0.581570	+	0.0457706i
$756$	−5.18311	+	0.582360i	−0.188508	+	0.0211802i
$757$	8.01781	−	13.0839i	0.291412	−	0.475542i	−0.673110	−	0.739542i	$-0.735042\pi$
$757$	8.01781	−	13.0839i	0.291412	−	0.475542i	0.964523	+	0.264001i	$0.0850421\pi$
$758$	0.342442	+	1.58314i	0.0124381	+	0.0575023i
$759$	−0.824622	+	5.20646i	−0.0299319	+	0.188983i
$760$	−1.28628	+	0.807383i	−0.0466582	+	0.0292869i
$761$	−1.74448	+	2.40107i	−0.0632374	+	0.0870388i	−0.839464	−	0.543415i	$-0.817131\pi$
$761$	−1.74448	+	2.40107i	−0.0632374	+	0.0870388i	0.776227	+	0.630454i	$0.217131\pi$
$762$	−2.31851	−	4.81635i	−0.0839906	−	0.174478i
$763$	−21.0930	+	15.3250i	−0.763619	+	0.554801i
$764$	2.00275	−	16.1036i	0.0724570	−	0.582607i
$765$	4.73269	+	11.4257i	0.171111	+	0.413098i
$766$	−28.8989	+	37.9426i	−1.04416	+	1.37092i
$767$	−4.36423	−	0.343473i	−0.157583	−	0.0124021i
$768$	−2.38968	−	2.93602i	−0.0862303	−	0.105944i
$769$	−32.0189	−	10.4036i	−1.15463	−	0.375162i	−0.331745	−	0.943369i	$-0.607637\pi$
$769$	−32.0189	−	10.4036i	−1.15463	−	0.375162i	−0.822886	+	0.568207i	$0.807637\pi$
$770$	−11.2714	−	4.97001i	−0.406192	−	0.179107i
$771$	−3.33173	+	1.69760i	−0.119989	+	0.0611377i
$772$	10.9014	+	7.37785i	0.392351	+	0.265535i
$773$	0.472096	−	1.96642i	0.0169801	−	0.0707272i	−0.963237	−	0.268655i	$-0.913421\pi$
$773$	0.472096	−	1.96642i	0.0169801	−	0.0707272i	0.980217	+	0.197927i	$0.0634210\pi$
$774$	−30.3367	−	3.07863i	−1.09043	−	0.110659i
$775$	0.164412	−	0.0534206i	0.00590584	−	0.00191892i
$776$	24.4339	−	21.3272i	0.877127	−	0.765600i
$777$	0.0703751	+	0.444331i	0.00252469	+	0.0159403i
$778$	−25.9771	+	10.0786i	−0.931324	+	0.361337i
$779$	−1.23854	−	3.20721i	−0.0443752	−	0.114910i
$780$	−1.55055	−	1.69743i	−0.0555184	−	0.0607776i
$781$	−49.8115	+	7.88936i	−1.78239	+	0.282304i
$782$	−28.1700	−	0.636632i	−1.00736	−	0.0227659i
$783$	−1.56667	−	4.82170i	−0.0559880	−	0.172313i
$784$	−12.0574	−	7.58668i	−0.430623	−	0.270953i
$785$	−19.5742	−	4.69936i	−0.698634	−	0.167727i
$786$	2.68654	+	3.87908i	0.0958256	+	0.138362i
$787$	19.9000	+	39.0559i	0.709358	+	1.39219i	0.910864	+	0.412707i	$0.135417\pi$
$787$	19.9000	+	39.0559i	0.709358	+	1.39219i	−0.201506	+	0.979487i	$0.564583\pi$
$788$	6.32879	+	0.286203i	0.225454	+	0.0101956i
$789$	−0.710067	+	2.18536i	−0.0252791	+	0.0778010i
$790$	−9.52689	−	3.33527i	−0.338952	−	0.118664i
$791$	−0.333636	+	4.23924i	−0.0118627	+	0.150730i
$792$	−38.9587	+	3.48799i	−1.38434	+	0.123940i
$793$	−7.97436	+	3.30309i	−0.283178	+	0.117296i
$794$	−36.9329	−	19.8818i	−1.31070	−	0.705580i
$795$	−0.198748	−	0.273553i	−0.00704885	−	0.00970191i
$796$	17.7742	−	19.0011i	0.629991	−	0.673476i
$797$	0.0157212	+	0.0114221i	0.000556873	+	0.000404592i	0.588064	−	0.808815i	$-0.299890\pi$
$797$	0.0157212	+	0.0114221i	0.000556873	+	0.000404592i	−0.587507	+	0.809219i	$0.699890\pi$
$798$	−0.0595372	+	0.327786i	−0.00210760	+	0.0116035i
$799$	19.2320	+	3.04605i	0.680379	+	0.107761i
$800$	−5.61437	+	0.692022i	−0.198498	+	0.0244667i
$801$	40.3833	+	24.7469i	1.42687	+	0.874390i
$802$	43.3141	+	11.4397i	1.52947	+	0.403951i
$803$	−5.19464	−	66.0041i	−0.183315	−	2.32923i
$804$	−0.775165	−	0.158967i	−0.0273380	−	0.00560635i
$805$	−5.71202	−	6.68791i	−0.201322	−	0.235718i
$806$	−0.820699	−	0.858652i	−0.0289079	−	0.0302447i
$807$	−1.11880	−	1.82572i	−0.0393837	−	0.0642684i
$808$	14.2784	−	23.8726i	0.502311	−	0.839836i
$809$	27.4058	−	32.0880i	0.963536	−	1.12816i	−0.0281671	−	0.999603i	$-0.508967\pi$
$809$	27.4058	−	32.0880i	0.963536	−	1.12816i	0.991703	−	0.128552i	$-0.0410329\pi$
$810$	0.672088	+	12.0010i	0.0236148	+	0.421674i
$811$	4.76698	+	4.76698i	0.167391	+	0.167391i	0.785832	−	0.618440i	$-0.212235\pi$
$811$	4.76698	+	4.76698i	0.167391	+	0.167391i	−0.618440	+	0.785832i	$0.712235\pi$
$812$	−4.70164	+	12.5156i	−0.164995	+	0.439212i
$813$	−0.0133780	−	0.0557234i	−0.000469187	−	0.00195430i
$814$	0.913293	+	6.75011i	0.0320109	+	0.236591i
$815$	−7.73478	+	15.1804i	−0.270937	+	0.531745i
$816$	0.882237	+	3.87647i	0.0308845	+	0.135704i
$817$	−1.50486	+	3.63306i	−0.0526485	+	0.127105i
$818$	−23.2108	+	13.5119i	−0.811545	+	0.472432i
$819$	26.5232			0.926797
$820$	0.887545	−	12.7755i	0.0309944	−	0.446138i
$821$	−38.1934			−1.33296			−0.666480	−	0.745523i	$-0.732200\pi$
$821$	−38.1934			−1.33296			−0.666480	+	0.745523i	$0.732200\pi$
$822$	−1.66766	+	0.970808i	−0.0581662	+	0.0338608i
$823$	−7.77963	+	18.7817i	−0.271181	+	0.654689i	−0.999534	−	0.0305129i	$-0.990286\pi$
$823$	−7.77963	+	18.7817i	−0.271181	+	0.654689i	0.728353	+	0.685202i	$0.240286\pi$
$824$	6.18112	−	41.9398i	0.215329	−	1.46104i
$825$	0.504561	−	0.990257i	0.0175666	−	0.0344763i
$826$	0.316824	+	2.34163i	0.0110237	+	0.0814757i
$827$	−12.0454	−	50.1729i	−0.418861	−	1.74468i	−0.638995	−	0.769211i	$-0.720649\pi$
$827$	−12.0454	−	50.1729i	−0.418861	−	1.74468i	0.220134	−	0.975470i	$-0.429351\pi$
$828$	−26.1433	−	9.82104i	−0.908542	−	0.341305i
$829$	16.8001	+	16.8001i	0.583491	+	0.583491i	0.935861	−	0.352370i	$-0.114624\pi$
$829$	16.8001	+	16.8001i	0.583491	+	0.583491i	−0.352370	+	0.935861i	$0.614624\pi$
$830$	−0.259235	−	4.62900i	−0.00899819	−	0.160675i
$831$	4.48931	−	5.25631i	0.155732	−	0.182339i
$832$	21.0161	+	32.6956i	0.728602	+	1.13352i
$833$	7.81692	+	12.7561i	0.270840	+	0.441971i
$834$	3.32669	+	3.48053i	0.115194	+	0.120521i
$835$	−7.85928	−	9.20203i	−0.271982	−	0.318450i
$836$	−1.01338	+	4.94148i	−0.0350484	+	0.170905i
$837$	−0.0190750	−	0.242371i	−0.000659329	−	0.00837757i
$838$	−28.4980	−	7.52665i	−0.984447	−	0.260004i
$839$	−0.741135	−	0.454168i	−0.0255868	−	0.0156796i	0.509646	−	0.860384i	$-0.329776\pi$
$839$	−0.741135	−	0.454168i	−0.0255868	−	0.0156796i	−0.535233	+	0.844704i	$0.679776\pi$
$840$	−0.718567	+	1.01172i	−0.0247929	+	0.0349078i
$841$	15.8073	+	2.50363i	0.545080	+	0.0863322i
$842$	−8.44938	+	46.5186i	−0.291185	+	1.60314i
$843$	3.27861	+	2.38205i	0.112921	+	0.0820420i
$844$	38.2268	+	35.7586i	1.31582	+	1.23086i
$845$	6.23308	+	8.57910i	0.214424	+	0.295130i
$846$	16.9931	+	9.14780i	0.584235	+	0.314508i
$847$	−18.9565	+	7.85204i	−0.651353	+	0.269799i
$848$	2.53472	+	5.12379i	0.0870427	+	0.175952i
$849$	0.414210	−	5.26303i	0.0142156	−	0.180627i
$850$	5.60709	+	1.96299i	0.192321	+	0.0673298i
$851$	−1.50287	+	4.62535i	−0.0515176	+	0.158555i
$852$	−0.229515	+	5.07526i	−0.00786306	+	0.173876i
$853$	−18.1993	−	35.7181i	−0.623131	−	1.22296i	−0.959626	−	0.281279i	$-0.909241\pi$
$853$	−18.1993	−	35.7181i	−0.623131	−	1.22296i	0.336495	−	0.941685i	$-0.390759\pi$
$854$	2.65261	+	3.83009i	0.0907704	+	0.131063i
$855$	1.53707	+	0.369017i	0.0525665	+	0.0126201i
$856$	−18.8627	+	14.0169i	−0.644713	+	0.479087i
$857$	6.70360	+	20.6316i	0.228991	+	0.704761i	0.997862	+	0.0653573i	$0.0208187\pi$
$857$	6.70360	+	20.6316i	0.228991	+	0.704761i	−0.768871	+	0.639404i	$0.779181\pi$
$858$	−7.63427	−	0.172532i	−0.260630	−	0.00589013i
$859$	19.6495	−	3.11218i	0.670432	−	0.106186i	0.188067	−	0.982156i	$-0.439778\pi$
$859$	19.6495	−	3.11218i	0.670432	−	0.106186i	0.482365	+	0.875970i	$0.339778\pi$
$860$	−10.8148	+	9.87896i	−0.368781	+	0.336870i
$861$	−1.93788	−	2.03389i	−0.0660427	−	0.0693149i
$862$	8.53188	−	3.31021i	0.290597	−	0.112746i
$863$	−3.58930	−	22.6619i	−0.122181	−	0.771422i	−0.970352	−	0.241698i	$-0.922296\pi$
$863$	−3.58930	−	22.6619i	−0.122181	−	0.771422i	0.848170	−	0.529724i	$-0.177704\pi$
$864$	−0.896898	+	7.90483i	−0.0305131	+	0.268928i
$865$	−1.19660	+	0.388798i	−0.0406856	+	0.0132195i
$866$	−20.8496	−	2.11585i	−0.708498	−	0.0718997i
$867$	0.0357006	−	0.148704i	0.00121246	−	0.00505024i
$868$	−0.359343	+	0.530961i	−0.0121969	+	0.0180220i
$869$	−29.8727	+	15.2209i	−1.01336	+	0.516334i
$870$	−1.10369	−	0.486663i	−0.0374187	−	0.0164994i
$871$	7.72676	+	2.51058i	0.261811	+	0.0850676i
$872$	15.6128	+	36.5753i	0.528717	+	1.23860i
$873$	−33.6539	−	2.64862i	−1.13901	−	0.0896421i
$874$	−2.18223	+	2.86515i	−0.0738152	+	0.0969151i
$875$	0.709625	+	1.71319i	0.0239897	+	0.0579163i
$876$	−6.61868	−	0.823143i	−0.223624	−	0.0278114i
$877$	5.08786	−	3.69654i	0.171805	−	0.124823i	−0.498560	−	0.866855i	$-0.666138\pi$
$877$	5.08786	−	3.69654i	0.171805	−	0.124823i	0.670365	+	0.742032i	$0.266138\pi$
$878$	−21.5789	−	44.8269i	−0.728252	−	1.51283i
$879$	3.44334	−	4.73935i	0.116141	−	0.159854i
$880$	−11.2234	+	15.0691i	−0.378340	+	0.507978i
$881$	5.04986	−	31.8836i	0.170134	−	1.07418i	−0.743824	−	0.668376i	$-0.766990\pi$
$881$	5.04986	−	31.8836i	0.170134	−	1.07418i	0.913958	−	0.405809i	$-0.133010\pi$
$882$	3.13485	+	14.4927i	0.105556	+	0.487995i
$883$	18.7993	−	30.6777i	0.632648	−	1.03239i	−0.362306	−	0.932059i	$-0.618011\pi$
$883$	18.7993	−	30.6777i	0.632648	−	1.03239i	0.994954	−	0.100329i	$-0.0319895\pi$
$884$	−4.55754	−	40.5629i	−0.153287	−	1.36428i
$885$	−0.212533	+	0.0167267i	−0.00714423	+	0.000562263i
$886$	−9.97906	−	6.42975i	−0.335253	−	0.216012i
$887$	−7.59829	+	6.48956i	−0.255126	+	0.217898i	−0.767807	−	0.640681i	$-0.778652\pi$
$887$	−7.59829	+	6.48956i	−0.255126	+	0.217898i	0.512682	+	0.858579i	$0.328652\pi$
$888$	0.684611	+	0.0464791i	0.0229740	+	0.00155974i
$889$	25.2581	−	15.4782i	0.847130	−	0.519122i
$890$	21.7913	−	6.53993i	0.730446	−	0.219219i
$891$	30.3586	+	25.9287i	1.01705	+	0.868644i
$892$	−6.97372	−	15.3658i	−0.233497	−	0.514487i
$893$	1.75988	−	1.75988i	0.0588920	−	0.0588920i
$894$	−0.568101	−	0.507845i	−0.0190001	−	0.0169849i
$895$	13.1555	−	3.15837i	0.439741	−	0.105573i
$896$	14.8509	−	14.8185i	0.496134	−	0.495053i
$897$	−4.85788	−	2.47522i	−0.162200	−	0.0826450i
$898$	6.94478	−	5.66511i	0.231750	−	0.189047i
$899$	−0.575759	−	0.238487i	−0.0192026	−	0.00795399i
$900$	4.60231	+	3.67257i	0.153410	+	0.122419i
$901$		−	6.00338i		−	0.200002i
$902$	−28.6387	−	31.4509i	−0.953565	−	1.04720i
$903$			3.21323i			0.106930i
$904$	6.18986	+	1.93788i	0.205872	+	0.0644528i
$905$	−0.379955	−	0.157383i	−0.0126301	−	0.00523157i
$906$	3.39026	+	4.15608i	0.112634	+	0.138077i
$907$	−46.8994	−	23.8965i	−1.55727	−	0.793469i	−0.557934	−	0.829886i	$-0.688406\pi$
$907$	−46.8994	−	23.8965i	−1.55727	−	0.793469i	−0.999337	+	0.0364167i	$0.988406\pi$
$908$	−13.5831	−	24.5948i	−0.450769	−	0.816207i
$909$	−28.1536	+	6.75909i	−0.933797	+	0.224185i
$910$	8.49134	−	9.49884i	0.281485	−	0.314883i
$911$	32.0671	−	32.0671i	1.06243	−	1.06243i	0.0645119	−	0.997917i	$-0.479451\pi$
$911$	32.0671	−	32.0671i	1.06243	−	1.06243i	0.997917	−	0.0645119i	$-0.0205490\pi$
$912$	0.467136	+	0.200008i	0.0154684	+	0.00662293i
$913$	−11.7098	−	10.0011i	−0.387538	−	0.330989i
$914$	9.67843	+	32.2489i	0.320134	+	1.06670i
$915$	−0.358397	+	0.219626i	−0.0118483	+	0.00726062i
$916$	5.39907	−	11.5314i	0.178390	−	0.381008i
$917$	−19.8845	+	16.9829i	−0.656643	+	0.560826i
$918$	4.52522	−	7.02322i	0.149355	−	0.231801i
$919$	−1.09554	+	0.0862208i	−0.0361385	+	0.00284416i	−0.0965155	−	0.995331i	$-0.530770\pi$
$919$	−1.09554	+	0.0862208i	−0.0361385	+	0.00284416i	0.0603770	+	0.998176i	$0.480770\pi$
$920$	−11.8869	+	6.21859i	−0.391901	+	0.205021i
$921$	1.36842	−	2.23305i	0.0450909	−	0.0735816i
$922$	31.5879	−	6.83263i	1.04029	−	0.225021i
$923$	8.15991	−	51.5197i	0.268587	−	1.69579i
$924$	0.780170	+	4.04729i	0.0256657	+	0.133146i
$925$	0.602700	−	0.829545i	0.0198166	−	0.0272753i
$926$	−37.6674	+	18.1325i	−1.23783	+	0.595869i
$927$	−35.6982	+	25.9363i	−1.17248	+	0.851859i
$928$	17.0104	+	11.2475i	0.558394	+	0.369218i
$929$	−14.9547	−	36.1039i	−0.490648	−	1.18453i	−0.954391	−	0.298560i	$-0.903494\pi$
$929$	−14.9547	−	36.1039i	−0.490648	−	1.18453i	0.463743	−	0.885970i	$-0.346506\pi$
$930$	−0.0460164	−	0.0350483i	−0.00150894	−	0.00114928i
$931$	1.90635	+	0.150033i	0.0624781	+	0.00491713i
$932$	0.469041	+	14.0597i	0.0153640	+	0.460542i
$933$	2.45273	+	0.796939i	0.0802987	+	0.0260906i
$934$	−12.7412	+	28.8954i	−0.416904	+	0.945487i
$935$	17.5817	−	8.95832i	0.574983	−	0.292969i
$936$	9.02072	−	39.4374i	0.294852	−	1.28905i
$937$	9.89311	−	41.2078i	0.323194	−	1.34620i	−0.540144	−	0.841573i	$-0.681630\pi$
$937$	9.89311	−	41.2078i	0.323194	−	1.34620i	0.863338	−	0.504626i	$-0.168370\pi$
$938$	0.442754	−	4.36289i	0.0144564	−	0.142454i
$939$	0.0271238	−	0.00881305i	0.000885151	−	0.000287603i
$940$	8.71643	−	3.15715i	0.284298	−	0.102975i
$941$	−0.764791	−	4.82870i	−0.0249315	−	0.157411i	0.972082	−	0.234643i	$-0.0753920\pi$
$941$	−0.764791	−	4.82870i	−0.0249315	−	0.157411i	−0.997013	+	0.0772315i	$0.975392\pi$
$942$	2.43638	+	6.27963i	0.0793817	+	0.204601i
$943$	−8.68412	−	29.1021i	−0.282794	−	0.947696i
$944$	3.58952	+	0.325318i	0.116829	+	0.0105882i
$945$	2.57576	−	0.407960i	0.0837893	−	0.0132709i
$946$	−1.09925	+	48.6401i	−0.0357396	+	1.58143i
$947$	8.14669	+	25.0729i	0.264732	+	0.814761i	0.991755	+	0.128148i	$0.0409033\pi$
$947$	8.14669	+	25.0729i	0.264732	+	0.814761i	−0.727023	+	0.686613i	$0.759097\pi$
$948$	0.897506	+	3.25600i	0.0291496	+	0.105750i
$949$	66.5866	+	15.9860i	2.16149	+	0.518929i
$950$	0.624245	−	0.432334i	0.0202532	−	0.0140268i
$951$	2.20859	+	4.33459i	0.0716183	+	0.140559i
$952$	−20.8797	+	7.03330i	−0.676714	+	0.227951i
$953$	−14.9121	+	45.8947i	−0.483050	+	1.48668i	0.351734	+	0.936100i	$0.385592\pi$
$953$	−14.9121	+	45.8947i	−0.483050	+	1.48668i	−0.834785	+	0.550577i	$0.814408\pi$
$954$	1.96607	−	5.61589i	0.0636538	−	0.181821i
$955$	−0.636603	+	8.08881i	−0.0206000	+	0.261748i
$956$	−10.6789	+	37.0238i	−0.345380	+	1.19744i
$957$	−3.70153	+	1.53322i	−0.119653	+	0.0495621i
$958$	0.675771	−	1.25532i	0.0218332	−	0.0405577i
$959$	−6.28575	−	8.65159i	−0.202977	−	0.279374i
$960$	1.25994	+	1.41253i	0.0406644	+	0.0455892i
$961$	25.0553	+	18.2038i	0.808237	+	0.587219i
$962$	−6.93179	−	1.25905i	−0.223490	−	0.0405934i
$963$	24.1598	+	3.82653i	0.778538	+	0.123308i
$964$	−15.3731	+	10.1408i	−0.495135	+	0.326614i
$965$	−5.61180	−	3.43891i	−0.180650	−	0.110703i
$966$	−0.751484	+	2.84533i	−0.0241786	+	0.0915470i
$967$	−2.36085	−	29.9975i	−0.0759199	−	0.964654i	−0.910430	−	0.413662i	$-0.864249\pi$
$967$	−2.36085	−	29.9975i	−0.0759199	−	0.964654i	0.834510	−	0.550992i	$-0.185751\pi$
$968$	5.22796	+	30.8569i	0.168033	+	0.991779i
$969$	−0.346583	−	0.405796i	−0.0111338	−	0.0130360i
$970$	−11.7228	+	11.2046i	−0.376395	+	0.359758i
$971$	−3.96838	−	6.47581i	−0.127351	−	0.207819i	0.782609	−	0.622513i	$-0.213888\pi$
$971$	−3.96838	−	6.47581i	−0.127351	−	0.207819i	−0.909961	+	0.414695i	$0.863888\pi$
$972$	9.83056	−	7.65584i	0.315315	−	0.245561i
$973$	−17.3288	+	20.2895i	−0.555537	+	0.650450i
$974$	−17.5756	+	0.984278i	−0.563159	+	0.0315383i
$975$	0.812823	+	0.812823i	0.0260312	+	0.0260312i
$976$	6.59712	−	2.64152i	0.211169	−	0.0845531i
$977$	−7.11768	−	29.6473i	−0.227715	−	0.948500i	−0.962733	−	0.270453i	$-0.912827\pi$
$977$	−7.11768	−	29.6473i	−0.227715	−	0.948500i	0.735018	−	0.678047i	$-0.237173\pi$
$978$	5.64926	−	0.764348i	0.180643	−	0.0244411i
$979$	34.3079	−	67.3331i	1.09649	−	2.15198i
$980$	6.19393	+	3.51711i	0.197858	+	0.112350i
$981$	15.8406	−	38.2426i	0.505752	−	1.22099i
$982$	28.2647	+	48.5532i	0.901963	+	1.54939i
$983$	16.9042			0.539160			0.269580	−	0.962978i	$-0.413115\pi$
$983$	16.9042			0.539160			0.269580	+	0.962978i	$0.413115\pi$
$984$	−3.68328	+	2.18969i	−0.117419	+	0.0698048i
$985$	−3.16763			−0.100929
$986$	−10.7745	−	18.5084i	−0.343129	−	0.589428i
$987$	0.778253	−	1.87887i	0.0247721	−	0.0598051i
$988$	−4.53690	−	2.57620i	−0.144338	−	0.0819597i
$989$	−15.7703	+	30.9510i	−0.501466	+	0.984183i
$990$	19.3807	−	2.62222i	0.615958	−	0.0833395i
$991$	9.87335	+	41.1254i	0.313637	+	1.30639i	0.877122	+	0.480267i	$0.159460\pi$
$991$	9.87335	+	41.1254i	0.313637	+	1.30639i	−0.563485	+	0.826126i	$0.690540\pi$
$992$	0.667271	+	0.714890i	0.0211859	+	0.0226978i
$993$	−0.251719	−	0.251719i	−0.00798807	−	0.00798807i
$994$	−28.1113	+	1.57430i	−0.891638	+	0.0499339i
$995$	−8.44885	+	9.89233i	−0.267847	+	0.313608i
$996$	−1.22393	+	0.953172i	−0.0387817	+	0.0302024i
$997$	13.1078	+	21.3900i	0.415129	+	0.677429i	0.990040	−	0.140787i	$-0.0449633\pi$
$997$	13.1078	+	21.3900i	0.415129	+	0.677429i	−0.574911	+	0.818216i	$0.694963\pi$
$998$	−37.8572	+	36.1839i	−1.19835	+	1.14538i
$999$	−0.936530	−	1.09654i	−0.0296305	−	0.0346929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.b.11.29	yes	672
4.3	odd	2	inner	820.2.bw.b.11.24	✓	672
41.15	odd	40	inner	820.2.bw.b.671.24	yes	672
164.15	even	40	inner	820.2.bw.b.671.29	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.b.11.24	✓	672	4.3	odd	2	inner
820.2.bw.b.11.29	yes	672	1.1	even	1	trivial
820.2.bw.b.671.24	yes	672	41.15	odd	40	inner
820.2.bw.b.671.29	yes	672	164.15	even	40	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bw (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.711492 + 1.22220i) q^{2} +(-0.0905429 + 0.218590i) q^{3} +(-0.987559 + 1.73917i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.331582 + 0.0448632i) q^{6} +(-0.432887 - 1.80311i) q^{7} +(-2.82826 + 0.0304120i) q^{8} +(2.08174 + 2.08174i) q^{9} +(1.41200 - 0.0790756i) q^{10} +(3.05068 - 3.57189i) q^{11} +(-0.290750 - 0.373340i) q^{12} +(2.53852 + 4.14249i) q^{13} +(1.89576 - 1.81197i) q^{14} +(0.153659 + 0.179912i) q^{15} +(-2.04946 - 3.43507i) q^{16} +(0.329588 + 4.18781i) q^{17} +(-1.06317 + 4.02544i) q^{18} +(0.457810 + 0.280547i) q^{19} +(1.10127 + 1.66949i) q^{20} +(0.433336 + 0.0686336i) q^{21} +(6.53611 + 1.18718i) q^{22} +(3.83719 + 2.78788i) q^{23} +(0.249431 - 0.620984i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-3.25683 + 6.04994i) q^{26} +(-1.29930 + 0.538189i) q^{27} +(3.56342 + 1.02781i) q^{28} +(-0.282841 + 3.59383i) q^{29} +(-0.110562 + 0.315809i) q^{30} +(-0.0534206 + 0.164412i) q^{31} +(2.74018 - 4.94888i) q^{32} +(0.504561 + 0.990257i) q^{33} +(-4.88385 + 3.38241i) q^{34} +(-1.80311 - 0.432887i) q^{35} +(-5.67634 + 1.56467i) q^{36} +(0.316858 + 0.975189i) q^{37} +(-0.0171564 + 0.759144i) q^{38} +(-1.13535 + 0.179822i) q^{39} +(-1.25691 + 2.53381i) q^{40} +(-5.08777 - 3.88776i) q^{41} +(0.224431 + 0.578456i) q^{42} +(1.14570 + 7.23365i) q^{43} +(3.19941 + 8.83312i) q^{44} +(2.79993 - 0.909752i) q^{45} +(-0.677226 + 6.67338i) q^{46} +(1.08209 - 4.50722i) q^{47} +(0.936436 - 0.136969i) q^{48} +(3.17325 - 1.61685i) q^{49} +(0.570578 - 1.29400i) q^{50} +(-0.945254 - 0.307132i) q^{51} +(-9.71146 + 0.323980i) q^{52} +(-1.42471 - 0.112127i) q^{53} +(-1.58222 - 1.20509i) q^{54} +(-1.79760 - 4.33978i) q^{55} +(1.27916 + 5.08649i) q^{56} +(-0.102776 + 0.0746713i) q^{57} +(-4.59363 + 2.21129i) q^{58} +(-0.529629 + 0.728971i) q^{59} +(-0.464646 + 0.0895669i) q^{60} +(-0.277918 + 1.75471i) q^{61} +(-0.238953 + 0.0516868i) q^{62} +(2.85243 - 4.65475i) q^{63} +(7.99815 - 0.172026i) q^{64} +(4.84345 - 0.381188i) q^{65} +(-0.851304 + 1.32124i) q^{66} +(1.27157 - 1.08602i) q^{67} +(-7.60882 - 3.56249i) q^{68} +(-0.956833 + 0.586348i) q^{69} +(-0.753819 - 2.51176i) q^{70} +(-8.16399 - 6.97271i) q^{71} +(-5.95101 - 5.82439i) q^{72} +(9.96654 - 9.96654i) q^{73} +(-0.966436 + 1.08110i) q^{74} +(0.230063 - 0.0552332i) q^{75} +(-0.940034 + 0.519156i) q^{76} +(-7.76109 - 3.95447i) q^{77} +(-1.02757 - 1.25969i) q^{78} +(-6.59412 - 2.73137i) q^{79} +(-3.99111 + 0.266588i) q^{80} +8.49932i q^{81} +(1.13172 - 8.98439i) q^{82} -3.27833i q^{83} +(-0.547310 + 0.685866i) q^{84} +(3.88099 + 1.60756i) q^{85} +(-8.02584 + 6.54696i) q^{86} +(-0.759966 - 0.387222i) q^{87} +(-8.51950 + 10.1950i) q^{88} +(15.6432 - 3.75561i) q^{89} +(3.10403 + 2.77480i) q^{90} +(6.37046 - 6.37046i) q^{91} +(-8.63806 + 3.92034i) q^{92} +(-0.0311019 - 0.0265635i) q^{93} +(6.27863 - 1.88432i) q^{94} +(0.457810 - 0.280547i) q^{95} +(0.833671 + 1.04706i) q^{96} +(-8.71928 + 7.44697i) q^{97} +(4.23386 + 2.72798i) q^{98} +(13.7864 - 1.08502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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