LMFDB - Embedded newform 375.2.m.b.106.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(16,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.m (of order $25$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [260,0,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$260$
Relative dimension:	$13$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			106.3
Character	$\chi$	$=$	375.106
Dual form			375.2.m.b.46.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.988178 + 1.55712i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.596566 - 1.26777i) q^{4} +(-1.45672 + 1.69646i) q^{5} +(-0.345571 - 1.81155i) q^{6} +(-1.01461 + 0.737161i) q^{7} +(-1.09576 - 0.138427i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(-1.20208 - 3.94469i) q^{10} +(-0.279534 + 0.440475i) q^{11} +(1.30272 + 0.515785i) q^{12} +(0.0551626 - 0.876784i) q^{13} +(-0.145227 - 2.30832i) q^{14} +(-0.0993996 - 2.23386i) q^{15} +(3.08456 - 3.72860i) q^{16} +(-1.20263 + 2.55572i) q^{17} +(1.49200 + 1.08400i) q^{18} +(-0.875284 - 0.821947i) q^{19} +(3.01974 + 0.834736i) q^{20} +(0.235001 - 1.23192i) q^{21} +(-0.409643 - 0.870536i) q^{22} +(-1.25993 - 0.323495i) q^{23} +(0.893534 - 0.649190i) q^{24} +(-0.755925 - 4.94253i) q^{25} +(1.31075 + 0.952313i) q^{26} +(0.637424 + 0.770513i) q^{27} +(1.53983 + 0.846530i) q^{28} +(-1.96529 - 1.08043i) q^{29} +(3.57661 + 2.05267i) q^{30} +(2.24991 - 4.78131i) q^{31} +(2.07517 + 6.38672i) q^{32} +(-0.0977545 - 0.512447i) q^{33} +(-2.79115 - 4.39815i) q^{34} +(0.227450 - 2.79509i) q^{35} +(-1.30272 + 0.515785i) q^{36} +(-2.03738 + 2.46277i) q^{37} +(2.14481 - 0.550693i) q^{38} +(0.559988 + 0.676910i) q^{39} +(1.83105 - 1.65726i) q^{40} +(5.84970 - 1.50195i) q^{41} +(1.68602 + 1.58328i) q^{42} +(0.872719 - 2.68595i) q^{43} +(0.725181 + 0.0916116i) q^{44} +(1.60164 + 1.56037i) q^{45} +(1.74876 - 1.64219i) q^{46} +(-4.29123 + 0.542108i) q^{47} +(0.303850 + 4.82956i) q^{48} +(-1.67708 + 5.16153i) q^{49} +(8.44309 + 3.70703i) q^{50} +(-0.872832 - 2.68630i) q^{51} +(-1.14447 + 0.453126i) q^{52} +(-0.845932 + 4.43453i) q^{53} +(-1.82967 + 0.231141i) q^{54} +(-0.340043 - 1.11587i) q^{55} +(1.21382 - 0.667301i) q^{56} +1.20072 q^{57} +(3.62442 - 1.99254i) q^{58} +(-10.1390 - 4.01432i) q^{59} +(-2.77271 + 1.45866i) q^{60} +(-3.85445 - 0.989654i) q^{61} +(5.22176 + 8.22817i) q^{62} +(0.671998 + 1.05890i) q^{63} +(-2.62138 - 0.673055i) q^{64} +(1.40707 + 1.37081i) q^{65} +(0.894540 + 0.354173i) q^{66} +(-7.65075 + 4.20604i) q^{67} +3.95752 q^{68} +(1.13990 - 0.626664i) q^{69} +(4.12752 + 3.11621i) q^{70} +(-0.342440 + 0.0432603i) q^{71} +(-0.206957 + 1.08491i) q^{72} +(-1.17365 + 0.464680i) q^{73} +(-1.82153 - 5.60610i) q^{74} +(3.93444 + 3.08548i) q^{75} +(-0.519873 + 1.60000i) q^{76} +(-0.0410816 - 0.652974i) q^{77} +(-1.60740 + 0.203061i) q^{78} +(-10.7976 + 10.1396i) q^{79} +(1.83205 + 10.6643i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-3.44183 + 10.5929i) q^{82} +(-10.0862 - 9.47153i) q^{83} +(-1.70198 + 0.436994i) q^{84} +(-2.58377 - 5.76319i) q^{85} +(3.31995 + 4.01313i) q^{86} +(2.17224 - 0.557737i) q^{87} +(0.367276 - 0.443960i) q^{88} +(-3.09405 + 1.22502i) q^{89} +(-4.01239 + 0.952023i) q^{90} +(0.590362 + 0.930261i) q^{91} +(0.341515 + 1.79029i) q^{92} +(1.63292 + 5.02560i) q^{93} +(3.39637 - 7.21765i) q^{94} +(2.66944 - 0.287534i) q^{95} +(-5.88475 - 3.23517i) q^{96} +(-12.7868 - 7.02960i) q^{97} +(-6.37986 - 7.71193i) q^{98} +(0.422054 + 0.306640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 260 q + 10 q^{4} - 20 q^{5} + 10 q^{7} - 15 q^{8} + 10 q^{10} + 10 q^{11} - 40 q^{15} - 10 q^{16} - 5 q^{17} - 5 q^{19} - 25 q^{20} + 5 q^{21} - 25 q^{22} + 75 q^{23} + 20 q^{25} - 90 q^{26} - 15 q^{28}+ \cdots - 20 q^{98}+O(q^{100}) $ 260 * q + 10 * q^4 - 20 * q^5 + 10 * q^7 - 15 * q^8 + 10 * q^10 + 10 * q^11 - 40 * q^15 - 10 * q^16 - 5 * q^17 - 5 * q^19 - 25 * q^20 + 5 * q^21 - 25 * q^22 + 75 * q^23 + 20 * q^25 - 90 * q^26 - 15 * q^28 + 5 * q^29 - 20 * q^30 - 5 * q^31 - 5 * q^33 - 15 * q^34 + 10 * q^35 - 10 * q^37 + 15 * q^38 + 25 * q^40 - 10 * q^41 + 10 * q^42 - 10 * q^43 - 15 * q^44 + 5 * q^45 - 60 * q^46 - 80 * q^47 + 10 * q^48 - 205 * q^49 - 80 * q^50 - 20 * q^51 - 70 * q^52 - 40 * q^53 - 5 * q^55 + 135 * q^56 - 80 * q^57 + 85 * q^58 + 40 * q^59 + 60 * q^60 + 20 * q^61 - 55 * q^62 - 5 * q^63 - 25 * q^64 + 40 * q^65 - 35 * q^66 + 30 * q^67 - 200 * q^68 - 155 * q^70 + 145 * q^71 - 15 * q^72 - 10 * q^73 + 60 * q^74 + 5 * q^75 + 90 * q^76 - 40 * q^77 + 15 * q^78 + 10 * q^79 + 100 * q^80 + 70 * q^82 - 95 * q^83 + 20 * q^84 - 125 * q^85 - 20 * q^86 - 250 * q^88 - 110 * q^89 - 15 * q^90 + 110 * q^91 - 40 * q^92 + 120 * q^93 + 60 * q^94 + 25 * q^95 + 30 * q^96 - 30 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{25}\right)$	$1$

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 $

$2$	−0.988178	+	1.55712i	−0.698747	+	1.10105i	0.290792	+	0.956786i	$0.406081\pi$
$2$	−0.988178	+	1.55712i	−0.698747	+	1.10105i	−0.989539	+	0.144263i	$0.953919\pi$
$3$	−0.728969	+	0.684547i	−0.420870	+	0.395223i
$3$	−0.728969	+	0.684547i	−0.420870	+	0.395223i
$4$	−0.596566	−	1.26777i	−0.298283	−	0.633884i
$5$	−1.45672	+	1.69646i	−0.651466	+	0.758678i
$5$	−1.45672	+	1.69646i	−0.651466	+	0.758678i
$6$	−0.345571	−	1.81155i	−0.141079	−	0.739560i
$7$	−1.01461	+	0.737161i	−0.383488	+	0.278620i	−0.762782	−	0.646656i	$-0.776167\pi$
$7$	−1.01461	+	0.737161i	−0.383488	+	0.278620i	0.379294	+	0.925276i	$0.376167\pi$
$8$	−1.09576	−	0.138427i	−0.387409	−	0.0489412i
$9$	0.0627905	−	0.998027i	0.0209302	−	0.332676i
$10$	−1.20208	−	3.94469i	−0.380132	−	1.24742i
$11$	−0.279534	+	0.440475i	−0.0842827	+	0.132808i	−0.883854	−	0.467763i	$-0.845060\pi$
$11$	−0.279534	+	0.440475i	−0.0842827	+	0.132808i	0.799571	+	0.600571i	$0.205060\pi$
$12$	1.30272	+	0.515785i	0.376064	+	0.148894i
$13$	0.0551626	−	0.876784i	0.0152993	−	0.243176i	−0.982943	−	0.183911i	$-0.941124\pi$
$13$	0.0551626	−	0.876784i	0.0152993	−	0.243176i	0.998242	−	0.0592653i	$-0.0188758\pi$
$14$	−0.145227	−	2.30832i	−0.0388136	−	0.616925i
$15$	−0.0993996	−	2.23386i	−0.0256649	−	0.576780i
$16$	3.08456	−	3.72860i	0.771141	−	0.932149i
$17$	−1.20263	+	2.55572i	−0.291681	+	0.619854i	−0.995933	−	0.0900960i	$-0.971283\pi$
$17$	−1.20263	+	2.55572i	−0.291681	+	0.619854i	0.704252	+	0.709950i	$0.251283\pi$
$18$	1.49200	+	1.08400i	0.351667	+	0.255501i
$19$	−0.875284	−	0.821947i	−0.200804	−	0.188568i	0.577621	−	0.816305i	$-0.303981\pi$
$19$	−0.875284	−	0.821947i	−0.200804	−	0.188568i	−0.778425	+	0.627737i	$0.783981\pi$
$20$	3.01974	+	0.834736i	0.675235	+	0.186653i
$21$	0.235001	−	1.23192i	0.0512814	−	0.268827i
$22$	−0.409643	−	0.870536i	−0.0873362	−	0.185599i
$23$	−1.25993	−	0.323495i	−0.262714	−	0.0674534i	0.115035	−	0.993361i	$-0.463302\pi$
$23$	−1.25993	−	0.323495i	−0.262714	−	0.0674534i	−0.377749	+	0.925908i	$0.623302\pi$
$24$	0.893534	−	0.649190i	0.182392	−	0.132515i
$25$	−0.755925	−	4.94253i	−0.151185	−	0.988505i
$26$	1.31075	+	0.952313i	0.257059	+	0.186764i
$27$	0.637424	+	0.770513i	0.122672	+	0.148285i
$28$	1.53983	+	0.846530i	0.291001	+	0.159979i
$29$	−1.96529	−	1.08043i	−0.364946	−	0.200631i	0.288721	−	0.957413i	$-0.406770\pi$
$29$	−1.96529	−	1.08043i	−0.364946	−	0.200631i	−0.653667	+	0.756783i	$0.726770\pi$
$30$	3.57661	+	2.05267i	0.652996	+	0.374765i
$31$	2.24991	−	4.78131i	0.404097	−	0.858749i	−0.594412	−	0.804160i	$-0.702615\pi$
$31$	2.24991	−	4.78131i	0.404097	−	0.858749i	0.998509	−	0.0545886i	$-0.0173847\pi$
$32$	2.07517	+	6.38672i	0.366842	+	1.12902i
$33$	−0.0977545	−	0.512447i	−0.0170169	−	0.0892055i
$34$	−2.79115	−	4.39815i	−0.478679	−	0.754277i
$35$	0.227450	−	2.79509i	0.0384461	−	0.472456i
$36$	−1.30272	+	0.515785i	−0.217121	+	0.0859642i
$37$	−2.03738	+	2.46277i	−0.334943	+	0.404877i	−0.910916	−	0.412592i	$-0.864624\pi$
$37$	−2.03738	+	2.46277i	−0.334943	+	0.404877i	0.575972	+	0.817469i	$0.304624\pi$
$38$	2.14481	−	0.550693i	0.347933	−	0.0893341i
$39$	0.559988	+	0.676910i	0.0896699	+	0.108392i
$40$	1.83105	−	1.65726i	0.289515	−	0.262036i
$41$	5.84970	−	1.50195i	0.913570	−	0.234565i	0.237487	−	0.971391i	$-0.423676\pi$
$41$	5.84970	−	1.50195i	0.913570	−	0.234565i	0.676083	+	0.736826i	$0.263676\pi$
$42$	1.68602	+	1.58328i	0.260159	+	0.244305i
$43$	0.872719	−	2.68595i	0.133088	−	0.409604i	−0.862199	−	0.506569i	$-0.830914\pi$
$43$	0.872719	−	2.68595i	0.133088	−	0.409604i	0.995288	+	0.0969652i	$0.0309135\pi$
$44$	0.725181	+	0.0916116i	0.109325	+	0.0138110i
$45$	1.60164	+	1.56037i	0.238758	+	0.232606i
$46$	1.74876	−	1.64219i	0.257840	−	0.242128i
$47$	−4.29123	+	0.542108i	−0.625940	+	0.0790746i	−0.431904	−	0.901920i	$-0.642158\pi$
$47$	−4.29123	+	0.542108i	−0.625940	+	0.0790746i	−0.194036	+	0.980994i	$0.562158\pi$
$48$	0.303850	+	4.82956i	0.0438570	+	0.697086i
$49$	−1.67708	+	5.16153i	−0.239583	+	0.737361i
$50$	8.44309	+	3.70703i	1.19403	+	0.524253i
$51$	−0.872832	−	2.68630i	−0.122221	−	0.376157i
$52$	−1.14447	+	0.453126i	−0.158709	+	0.0628373i
$53$	−0.845932	+	4.43453i	−0.116198	+	0.609130i	0.875779	+	0.482712i	$0.160348\pi$
$53$	−0.845932	+	4.43453i	−0.116198	+	0.609130i	−0.991977	+	0.126418i	$0.959652\pi$
$54$	−1.82967	+	0.231141i	−0.248986	+	0.0314543i
$55$	−0.340043	−	1.11587i	−0.0458514	−	0.150463i
$56$	1.21382	−	0.667301i	0.162203	−	0.0891718i
$57$	1.20072			0.159039
$58$	3.62442	−	1.99254i	0.475909	−	0.261633i
$59$	−10.1390	−	4.01432i	−1.31999	−	0.522620i	−0.400702	−	0.916209i	$-0.631234\pi$
$59$	−10.1390	−	4.01432i	−1.31999	−	0.522620i	−0.919287	+	0.393588i	$0.871234\pi$
$60$	−2.77271	+	1.45866i	−0.357956	+	0.188312i
$61$	−3.85445	−	0.989654i	−0.493511	−	0.126712i	−0.00627144	−	0.999980i	$-0.501996\pi$
$61$	−3.85445	−	0.989654i	−0.493511	−	0.126712i	−0.487240	+	0.873268i	$0.661996\pi$
$62$	5.22176	+	8.22817i	0.663164	+	1.04498i
$63$	0.671998	+	1.05890i	0.0846638	+	0.133409i
$64$	−2.62138	−	0.673055i	−0.327672	−	0.0841319i
$65$	1.40707	+	1.37081i	0.174525	+	0.170028i
$66$	0.894540	+	0.354173i	0.110110	+	0.0435957i
$67$	−7.65075	+	4.20604i	−0.934688	+	0.513849i	−0.874869	−	0.484360i	$-0.839053\pi$
$67$	−7.65075	+	4.20604i	−0.934688	+	0.513849i	−0.0598195	+	0.998209i	$0.519053\pi$
$68$	3.95752			0.479919
$69$	1.13990	−	0.626664i	0.137228	−	0.0754415i
$70$	4.12752	+	3.11621i	0.493333	+	0.372458i
$71$	−0.342440	+	0.0432603i	−0.0406402	+	0.00513405i	−0.145627	−	0.989340i	$-0.546520\pi$
$71$	−0.342440	+	0.0432603i	−0.0406402	+	0.00513405i	0.104987	+	0.994474i	$0.466520\pi$
$72$	−0.206957	+	1.08491i	−0.0243901	+	0.127857i
$73$	−1.17365	+	0.464680i	−0.137365	+	0.0543867i	−0.435801	−	0.900043i	$-0.643535\pi$
$73$	−1.17365	+	0.464680i	−0.137365	+	0.0543867i	0.298436	+	0.954430i	$0.403535\pi$
$74$	−1.82153	−	5.60610i	−0.211749	−	0.651696i
$75$	3.93444	+	3.08548i	0.454310	+	0.356281i
$76$	−0.519873	+	1.60000i	−0.0596335	+	0.183533i
$77$	−0.0410816	−	0.652974i	−0.00468169	−	0.0744133i
$78$	−1.60740	+	0.203061i	−0.182002	+	0.0229922i
$79$	−10.7976	+	10.1396i	−1.21482	+	1.14079i	−0.228922	+	0.973445i	$0.573520\pi$
$79$	−10.7976	+	10.1396i	−1.21482	+	1.14079i	−0.985898	+	0.167348i	$0.946480\pi$
$80$	1.83205	+	10.6643i	0.204829	+	1.19231i
$81$	−0.992115	−	0.125333i	−0.110235	−	0.0139259i
$82$	−3.44183	+	10.5929i	−0.380087	+	1.16979i
$83$	−10.0862	−	9.47153i	−1.10710	−	1.03964i	−0.998964	−	0.0454988i	$-0.985512\pi$
$83$	−10.0862	−	9.47153i	−1.10710	−	1.03964i	−0.108134	−	0.994136i	$-0.534488\pi$
$84$	−1.70198	+	0.436994i	−0.185701	+	0.0476800i
$85$	−2.58377	−	5.76319i	−0.280250	−	0.625106i
$86$	3.31995	+	4.01313i	0.357999	+	0.432746i
$87$	2.17224	−	0.557737i	0.232889	−	0.0597957i
$88$	0.367276	−	0.443960i	0.0391517	−	0.0473263i
$89$	−3.09405	+	1.22502i	−0.327969	+	0.129852i	−0.526338	−	0.850275i	$-0.676435\pi$
$89$	−3.09405	+	1.22502i	−0.327969	+	0.129852i	0.198369	+	0.980127i	$0.436435\pi$
$90$	−4.01239	+	0.952023i	−0.422943	+	0.100352i
$91$	0.590362	+	0.930261i	0.0618867	+	0.0975179i
$92$	0.341515	+	1.79029i	0.0356054	+	0.186650i
$93$	1.63292	+	5.02560i	0.169326	+	0.521130i
$94$	3.39637	−	7.21765i	0.350309	−	0.744444i
$95$	2.66944	−	0.287534i	0.273879	−	0.0295003i
$96$	−5.88475	−	3.23517i	−0.600610	−	0.330188i
$97$	−12.7868	−	7.02960i	−1.29830	−	0.713748i	−0.325535	−	0.945530i	$-0.605544\pi$
$97$	−12.7868	−	7.02960i	−1.29830	−	0.713748i	−0.972768	+	0.231782i	$0.925544\pi$
$98$	−6.37986	−	7.71193i	−0.644463	−	0.779022i
$99$	0.422054	+	0.306640i	0.0424180	+	0.0308185i
$100$	−5.81502	+	3.90688i	−0.581502	+	0.390688i
$101$	−10.4964	+	7.62607i	−1.04443	+	0.758823i	−0.971145	−	0.238489i	$-0.923348\pi$
$101$	−10.4964	+	7.62607i	−1.04443	+	0.758823i	−0.0732844	+	0.997311i	$0.523348\pi$
$102$	5.04541	+	1.29544i	0.499570	+	0.128268i
$103$	4.49876	+	9.56035i	0.443276	+	0.942009i	0.994209	+	0.107460i	$0.0342718\pi$
$103$	4.49876	+	9.56035i	0.443276	+	0.942009i	−0.550933	+	0.834549i	$0.685728\pi$
$104$	−0.181815	+	0.953108i	−0.0178284	+	0.0934600i
$105$	1.74756	+	2.19323i	0.170545	+	0.214037i
$106$	−6.06916	−	5.69932i	−0.589489	−	0.553567i
$107$	0.425929	+	0.309456i	0.0411761	+	0.0299162i	0.608183	−	0.793797i	$-0.291899\pi$
$107$	0.425929	+	0.309456i	0.0411761	+	0.0299162i	−0.567007	+	0.823713i	$0.691899\pi$
$108$	0.596566	−	1.26777i	0.0574046	−	0.121991i
$109$	−8.46055	+	10.2270i	−0.810374	+	0.979573i	−0.999997	−	0.00228346i	$-0.999273\pi$
$109$	−8.46055	+	10.2270i	−0.810374	+	0.979573i	0.189624	+	0.981857i	$0.439273\pi$
$110$	2.07356	+	0.573187i	0.197706	+	0.0546512i
$111$	−0.200696	−	3.18997i	−0.0190492	−	0.302778i
$112$	−0.381068	+	6.05690i	−0.0360075	+	0.572324i
$113$	13.2356	+	5.24033i	1.24510	+	0.492969i	0.895973	−	0.444108i	$-0.146479\pi$
$113$	13.2356	+	5.24033i	1.24510	+	0.492969i	0.349124	+	0.937077i	$0.386479\pi$
$114$	−1.18652	+	1.86966i	−0.111128	+	0.175110i
$115$	2.38416	−	1.66617i	0.222324	−	0.155372i
$116$	−0.197306	+	3.13608i	−0.0183194	+	0.291178i
$117$	−0.871590	−	0.110107i	−0.0805786	−	0.0101794i
$118$	16.2699	−	11.8208i	1.49777	−	1.08819i
$119$	−0.663771	−	3.47961i	−0.0608478	−	0.318975i
$120$	−0.200307	+	2.46153i	−0.0182855	+	0.224706i
$121$	4.56769	+	9.70684i	0.415245	+	0.882440i
$122$	5.34989	−	5.02388i	0.484356	−	0.454841i
$123$	−3.23610	+	5.09927i	−0.291789	+	0.459786i
$124$	−7.40382			−0.664882
$125$	9.48595	+	5.91749i	0.848449	+	0.529277i
$126$	−2.31289			−0.206048
$127$	8.45021	−	13.3154i	0.749835	−	1.18155i	−0.228302	−	0.973590i	$-0.573317\pi$
$127$	8.45021	−	13.3154i	0.749835	−	1.18155i	0.978137	−	0.207961i	$-0.0666826\pi$
$128$	−6.15222	+	5.77732i	−0.543784	+	0.510647i
$129$	1.20248	+	2.55539i	0.105872	+	0.224990i
$130$	−3.52495	+	0.836369i	−0.309159	+	0.0733544i
$131$	−2.40192	−	12.5913i	−0.209857	−	1.10011i	−0.918764	−	0.394807i	$-0.870812\pi$
$131$	−2.40192	−	12.5913i	−0.209857	−	1.10011i	0.708907	−	0.705302i	$-0.249188\pi$
$132$	−0.591347	+	0.429638i	−0.0514701	+	0.0373952i
$133$	1.49398	+	0.188734i	0.129545	+	0.0163653i
$134$	1.01100	−	16.0694i	0.0873374	−	1.38819i
$135$	−2.23569	−	0.0410616i	−0.192418	−	0.00353402i
$136$	1.67158	−	2.63398i	0.143336	−	0.225862i
$137$	−2.60987	−	1.03332i	−0.222976	−	0.0882825i	0.253980	−	0.967209i	$-0.418260\pi$
$137$	−2.60987	−	1.03332i	−0.222976	−	0.0882825i	−0.476957	+	0.878927i	$0.658260\pi$
$138$	−0.150631	+	2.39421i	−0.0128226	+	0.203809i
$139$	1.00441	+	15.9647i	0.0851931	+	1.35411i	0.775847	+	0.630921i	$0.217323\pi$
$139$	1.00441	+	15.9647i	0.0851931	+	1.35411i	−0.690654	+	0.723185i	$0.742677\pi$
$140$	−3.67921	+	1.37910i	−0.310950	+	0.116555i
$141$	2.75707	−	3.33273i	0.232187	−	0.280666i
$142$	0.271031	−	0.575969i	0.0227444	−	0.0483343i
$143$	0.370782	+	0.269389i	0.0310063	+	0.0225274i
$144$	−3.52756	−	3.31260i	−0.293963	−	0.276050i
$145$	4.69579	−	1.76015i	0.389964	−	0.146172i
$146$	0.436211	−	2.28670i	0.0361011	−	0.189248i
$147$	−2.31077	−	4.91063i	−0.190589	−	0.405022i
$148$	4.33766	+	1.11372i	0.356553	+	0.0915473i
$149$	10.1644	−	7.38483i	0.832696	−	0.604989i	−0.0876248	−	0.996154i	$-0.527928\pi$
$149$	10.1644	−	7.38483i	0.832696	−	0.604989i	0.920321	+	0.391164i	$0.127928\pi$
$150$	−8.69239	+	3.07739i	−0.709730	+	0.251267i
$151$	1.36993	+	0.995309i	0.111483	+	0.0809971i	0.642130	−	0.766596i	$-0.278051\pi$
$151$	1.36993	+	0.995309i	0.111483	+	0.0809971i	−0.530647	+	0.847593i	$0.678051\pi$
$152$	0.845322	+	1.02182i	0.0685647	+	0.0828804i
$153$	2.47517	+	1.36073i	0.200105	+	0.110009i
$154$	1.05735	+	0.581285i	0.0852040	+	0.0468413i
$155$	4.83379	+	10.7819i	0.388259	+	0.866025i
$156$	0.524094	−	1.11376i	0.0419611	−	0.0891719i
$157$	2.10833	+	6.48878i	0.168263	+	0.517861i	0.999262	−	0.0384133i	$-0.0122304\pi$
$157$	2.10833	+	6.48878i	0.168263	+	0.517861i	−0.830999	+	0.556274i	$0.812230\pi$
$158$	−5.11863	−	26.8328i	−0.407216	−	2.13470i
$159$	−2.41899	−	3.81171i	−0.191838	−	0.302289i
$160$	−13.8577	−	5.78324i	−1.09555	−	0.457205i
$161$	1.51681	−	0.600548i	0.119541	−	0.0473298i
$162$	1.17554	−	1.42099i	0.0923595	−	0.111643i
$163$	14.5250	−	3.72938i	1.13768	−	0.292107i	0.367558	−	0.930000i	$-0.380194\pi$
$163$	14.5250	−	3.72938i	1.13768	−	0.292107i	0.770125	+	0.637893i	$0.220194\pi$
$164$	−5.39386	−	6.52005i	−0.421190	−	0.509131i
$165$	1.01174	+	0.580656i	0.0787642	+	0.0452040i
$166$	24.7152	−	6.34579i	1.91827	−	0.492529i
$167$	−18.7972	−	17.6518i	−1.45457	−	1.36594i	−0.773753	−	0.633487i	$-0.781623\pi$
$167$	−18.7972	−	17.6518i	−1.45457	−	1.36594i	−0.680822	−	0.732449i	$-0.738377\pi$
$168$	−0.428035	+	1.31736i	−0.0330236	+	0.101636i
$169$	12.1318	+	1.53260i	0.933214	+	0.117892i
$170$	11.5272	+	1.67182i	0.884096	+	0.128223i
$171$	−0.875284	+	0.821947i	−0.0669347	+	0.0628558i
$172$	−3.92580	+	0.495944i	−0.299339	+	0.0378153i
$173$	0.638413	+	10.1473i	0.0485376	+	0.771484i	0.944736	+	0.327831i	$0.106318\pi$
$173$	0.638413	+	10.1473i	0.0485376	+	0.771484i	−0.896199	+	0.443653i	$0.853682\pi$
$174$	−1.27810	+	3.93358i	−0.0968924	+	0.298204i
$175$	4.41041	+	4.45752i	0.333396	+	0.336957i
$176$	0.780113	+	2.40094i	0.0588033	+	0.180978i
$177$	10.1390	−	4.01432i	0.762096	−	0.301735i
$178$	1.14997	−	6.02834i	0.0861938	−	0.451844i
$179$	5.63921	−	0.712398i	0.421494	−	0.0532471i	0.0882743	−	0.996096i	$-0.471865\pi$
$179$	5.63921	−	0.712398i	0.421494	−	0.0532471i	0.333220	+	0.942849i	$0.391865\pi$
$180$	1.02270	−	2.96137i	0.0762276	−	0.220728i
$181$	6.04911	−	3.32552i	0.449627	−	0.247184i	−0.240817	−	0.970571i	$-0.577415\pi$
$181$	6.04911	−	3.32552i	0.449627	−	0.247184i	0.690444	+	0.723386i	$0.257415\pi$
$182$	−2.03191			−0.150615
$183$	3.48724	−	1.91712i	0.257784	−	0.141718i
$184$	1.33580	+	0.528881i	0.0984765	+	0.0389896i
$185$	−1.21009	−	7.04390i	−0.0889672	−	0.517878i
$186$	−9.43907	−	2.42354i	−0.692106	−	0.177703i
$187$	−0.789556	−	1.24414i	−0.0577381	−	0.0909807i
$188$	3.24727	+	5.11687i	0.236831	+	0.373186i
$189$	−1.21473	−	0.311890i	−0.0883587	−	0.0226867i
$190$	−2.19016	+	4.44077i	−0.158891	+	0.322168i
$191$	1.86337	+	0.737761i	0.134829	+	0.0533825i	0.434570	−	0.900638i	$-0.356900\pi$
$191$	1.86337	+	0.737761i	0.134829	+	0.0533825i	−0.299741	+	0.954021i	$0.596900\pi$
$192$	2.37164	−	1.30382i	0.171158	−	0.0940951i
$193$	13.1179			0.944247			0.472124	−	0.881532i	$-0.343488\pi$
$193$	13.1179			0.944247			0.472124	+	0.881532i	$0.343488\pi$
$194$	23.5816	−	12.9641i	1.69306	−	0.930766i
$195$	−1.96409	−	0.0360733i	−0.140652	−	0.00258327i
$196$	7.54411	−	0.953043i	0.538865	−	0.0680745i
$197$	0.0816432	−	0.427989i	0.00581684	−	0.0304929i	−0.979261	−	0.202605i	$-0.935059\pi$
$197$	0.0816432	−	0.427989i	0.00581684	−	0.0304929i	0.985077	+	0.172112i	$0.0550592\pi$
$198$	−0.894540	+	0.354173i	−0.0635722	+	0.0251700i
$199$	3.31901	+	10.2149i	0.235279	+	0.724113i	0.997084	+	0.0763076i	$0.0243131\pi$
$199$	3.31901	+	10.2149i	0.235279	+	0.724113i	−0.761806	+	0.647806i	$0.775687\pi$
$200$	0.144134	+	5.52046i	0.0101918	+	0.390356i
$201$	2.69793	−	8.30337i	0.190297	−	0.585675i
$202$	−1.50241	−	23.8800i	−0.105709	−	1.68019i
$203$	2.79046	−	0.352518i	0.195852	−	0.0247419i
$204$	−2.88490	+	2.70911i	−0.201984	+	0.189675i
$205$	−5.97340	+	12.1117i	−0.417200	+	0.845917i
$206$	−19.3322	−	2.44222i	−1.34694	−	0.170158i
$207$	−0.401969	+	1.23713i	−0.0279387	+	0.0859866i
$208$	−3.09902	−	2.91017i	−0.214878	−	0.201784i
$209$	0.606719	−	0.155779i	0.0419676	−	0.0107755i
$210$	−5.14203	+	0.553863i	−0.354833	+	0.0382202i
$211$	−10.8137	−	13.0715i	−0.744446	−	0.899881i	0.253272	−	0.967395i	$-0.418493\pi$
$211$	−10.8137	−	13.0715i	−0.744446	−	0.899881i	−0.997718	+	0.0675140i	$0.978493\pi$
$212$	6.12661	−	1.57305i	0.420777	−	0.108037i
$213$	0.220015	−	0.265952i	0.0150752	−	0.0182227i
$214$	−0.902753	+	0.357425i	−0.0617109	+	0.0244331i
$215$	3.28529	+	5.39321i	0.224055	+	0.367814i
$216$	−0.591804	−	0.932534i	−0.0402671	−	0.0634509i
$217$	1.24180	+	6.50974i	0.0842988	+	0.441910i
$218$	−7.56420	−	23.2802i	−0.512313	−	1.57674i
$219$	0.537457	−	1.14215i	0.0363180	−	0.0771797i
$220$	−1.21180	+	1.09678i	−0.0816996	+	0.0739452i
$221$	2.17448	+	1.19543i	0.146271	+	0.0804133i
$222$	5.16548	+	2.83975i	0.346684	+	0.190591i
$223$	−14.4707	−	17.4920i	−0.969027	−	1.17135i	−0.985187	−	0.171483i	$-0.945144\pi$
$223$	−14.4707	−	17.4920i	−0.969027	−	1.17135i	0.0161596	−	0.999869i	$-0.494856\pi$
$224$	−6.81354	−	4.95033i	−0.455249	−	0.330758i
$225$	−4.98024	+	0.444089i	−0.332016	+	0.0296059i
$226$	−21.2389	+	15.4310i	−1.41279	+	1.02645i
$227$	−12.1587	−	3.12183i	−0.807003	−	0.207203i	−0.177419	−	0.984135i	$-0.556775\pi$
$227$	−12.1587	−	3.12183i	−0.807003	−	0.207203i	−0.629584	+	0.776932i	$0.716775\pi$
$228$	−0.716307	−	1.52223i	−0.0474386	−	0.100812i
$229$	−5.03525	+	26.3957i	−0.332739	+	1.74428i	0.285584	+	0.958354i	$0.407812\pi$
$229$	−5.03525	+	26.3957i	−0.332739	+	1.74428i	−0.618323	+	0.785924i	$0.712188\pi$
$230$	0.238454	+	5.35890i	0.0157232	+	0.353356i
$231$	0.476939	+	0.447875i	0.0313803	+	0.0294680i
$232$	2.00393	+	1.45594i	0.131564	+	0.0955871i
$233$	2.94077	−	6.24946i	0.192656	−	0.409416i	−0.785038	−	0.619447i	$-0.787357\pi$
$233$	2.94077	−	6.24946i	0.192656	−	0.409416i	0.977695	+	0.210032i	$0.0673568\pi$
$234$	1.03274	−	1.24836i	0.0675121	−	0.0816081i
$235$	5.33146	−	8.06958i	0.347786	−	0.526401i
$236$	0.959369	+	15.2487i	0.0624496	+	0.992608i
$237$	0.930060	−	14.7829i	0.0604139	−	0.960251i
$238$	6.07409	+	2.40490i	0.393725	+	0.155887i
$239$	9.66065	−	15.2228i	0.624896	−	0.984678i	−0.373476	−	0.927640i	$-0.621834\pi$
$239$	9.66065	−	15.2228i	0.624896	−	0.984678i	0.998372	−	0.0570383i	$-0.0181657\pi$
$240$	−8.63575	−	6.51985i	−0.557436	−	0.420855i
$241$	−0.937442	+	14.9002i	−0.0603860	+	0.959808i	0.844878	+	0.534959i	$0.179673\pi$
$241$	−0.937442	+	14.9002i	−0.0603860	+	0.959808i	−0.905264	+	0.424849i	$0.860327\pi$
$242$	−19.6284	−	2.47964i	−1.26176	−	0.159398i
$243$	0.809017	−	0.587785i	0.0518985	−	0.0377064i
$244$	1.04478	+	5.47694i	0.0668853	+	0.350625i
$245$	−6.31326	−	10.3640i	−0.403340	−	0.662132i
$246$	−4.74233	−	10.0780i	−0.302360	−	0.642548i
$247$	−0.768953	+	0.722095i	−0.0489273	+	0.0459458i
$248$	−3.12723	+	4.92772i	−0.198579	+	0.312911i
$249$	13.8362			0.876833
$250$	−18.5881	+	8.92322i	−1.17561	+	0.564354i
$251$	−18.1124			−1.14325			−0.571623	−	0.820516i	$-0.693686\pi$
$251$	−18.1124			−1.14325			−0.571623	+	0.820516i	$0.693686\pi$
$252$	0.941547	−	1.48364i	0.0593119	−	0.0934606i
$253$	0.494685	−	0.464540i	0.0311006	−	0.0292054i
$254$	12.3834	+	26.3160i	0.777001	+	1.65121i
$255$	5.82867	+	2.43247i	0.365005	+	0.152327i
$256$	−3.93074	−	20.6057i	−0.245671	−	1.28785i
$257$	8.99929	−	6.53837i	0.561360	−	0.407852i	−0.270596	−	0.962693i	$-0.587221\pi$
$257$	8.99929	−	6.53837i	0.561360	−	0.407852i	0.831957	+	0.554841i	$0.187221\pi$
$258$	−5.16731	−	0.652783i	−0.321703	−	0.0406405i
$259$	0.251699	−	4.00064i	0.0156398	−	0.248588i
$260$	0.898460	−	2.60162i	0.0557202	−	0.161345i
$261$	−1.20170	+	1.89357i	−0.0743833	+	0.117209i
$262$	21.9797	+	8.70238i	1.35791	+	0.537635i
$263$	0.241994	−	3.84638i	0.0149220	−	0.237178i	−0.983495	−	0.180935i	$-0.942088\pi$
$263$	0.241994	−	3.84638i	0.0149220	−	0.237178i	0.998417	−	0.0562433i	$-0.0179122\pi$
$264$	0.0361791	+	0.575050i	0.00222667	+	0.0353919i
$265$	−6.29070	−	7.89496i	−0.386434	−	0.484984i
$266$	−1.77020	+	2.13981i	−0.108538	+	0.131200i
$267$	1.41688	−	3.01103i	0.0867117	−	0.184272i
$268$	9.89646	+	7.19020i	0.604522	+	0.439211i
$269$	20.3944	+	19.1516i	1.24347	+	1.16770i	0.979123	+	0.203268i	$0.0651564\pi$
$269$	20.3944	+	19.1516i	1.24347	+	1.16770i	0.264347	+	0.964428i	$0.414844\pi$
$270$	2.27320	−	3.44066i	0.138342	−	0.209392i
$271$	−4.42459	+	23.1945i	−0.268775	+	1.40897i	0.550151	+	0.835065i	$0.314570\pi$
$271$	−4.42459	+	23.1945i	−0.268775	+	1.40897i	−0.818925	+	0.573900i	$0.805430\pi$
$272$	5.81967	+	12.3674i	0.352869	+	0.749885i
$273$	−1.06716	−	0.274001i	−0.0645876	−	0.0165833i
$274$	4.18802	−	3.04277i	0.253007	−	0.183821i
$275$	2.38837	+	1.04864i	0.144024	+	0.0632353i
$276$	−1.47449	−	1.07128i	−0.0887538	−	0.0644834i
$277$	−10.7763	−	13.0263i	−0.647486	−	0.782676i	0.339993	−	0.940428i	$-0.389575\pi$
$277$	−10.7763	−	13.0263i	−0.647486	−	0.782676i	−0.987479	+	0.157752i	$0.949575\pi$
$278$	−25.8514	−	14.2120i	−1.55047	−	0.852376i
$279$	−4.63060	−	2.54570i	−0.277227	−	0.152407i
$280$	−0.636145	+	3.03126i	−0.0380169	+	0.181152i
$281$	0.391092	−	0.831113i	0.0233306	−	0.0495801i	−0.892822	−	0.450409i	$-0.851278\pi$
$281$	0.391092	−	0.831113i	0.0233306	−	0.0495801i	0.916153	+	0.400829i	$0.131278\pi$
$282$	2.46498	+	7.58641i	0.146787	+	0.451764i
$283$	2.51929	+	13.2066i	0.149756	+	0.785050i	0.975329	+	0.220755i	$0.0708520\pi$
$283$	2.51929	+	13.2066i	0.149756	+	0.785050i	−0.825573	+	0.564295i	$0.809148\pi$
$284$	0.259132	+	0.408327i	0.0153767	+	0.0242298i
$285$	−1.74911	+	2.03696i	−0.103608	+	0.120659i
$286$	−0.785869	+	0.311147i	−0.0464694	+	0.0183985i
$287$	−4.82802	+	5.83607i	−0.284989	+	0.344492i
$288$	6.50442	−	1.67005i	0.383277	−	0.0984087i
$289$	5.75081	+	6.95153i	0.338283	+	0.408913i
$290$	−1.89951	+	9.05124i	−0.111543	+	0.531507i
$291$	14.1333	−	3.62881i	0.828507	−	0.212724i
$292$	1.28927	+	1.21070i	0.0754486	+	0.0708509i
$293$	−8.20051	+	25.2386i	−0.479079	+	1.47445i	0.361298	+	0.932450i	$0.382334\pi$
$293$	−8.20051	+	25.2386i	−0.479079	+	1.47445i	−0.840377	+	0.542003i	$0.817666\pi$
$294$	9.92989	+	1.25444i	0.579123	+	0.0731603i
$295$	21.5799	−	11.3527i	1.25643	−	0.660977i
$296$	2.57339	−	2.41658i	0.149575	−	0.140461i
$297$	−0.517574	+	0.0653848i	−0.0300327	+	0.00379401i
$298$	1.45488	+	23.1246i	0.0842789	+	1.33957i
$299$	−0.353136	+	1.08684i	−0.0204224	+	0.0628537i
$300$	1.56452	−	6.82865i	0.0903277	−	0.394252i
$301$	1.09450	+	3.36854i	0.0630862	+	0.194159i
$302$	−2.90355	+	1.14960i	−0.167080	+	0.0661518i
$303$	2.43113	−	12.7444i	0.139665	−	0.732149i
$304$	−5.76458	+	0.728235i	−0.330621	+	0.0417672i
$305$	7.29376	−	5.09725i	0.417639	−	0.291868i
$306$	−4.56473	+	2.50948i	−0.260948	+	0.143458i
$307$	6.68931			0.381779			0.190890	−	0.981612i	$-0.438863\pi$
$307$	6.68931			0.381779			0.190890	+	0.981612i	$0.438863\pi$
$308$	−0.803311	+	0.441624i	−0.0457729	+	0.0251639i
$309$	−9.82396	−	3.88958i	−0.558866	−	0.221271i
$310$	−21.5654	−	3.12768i	−1.22483	−	0.177640i
$311$	−3.23196	−	0.829825i	−0.183267	−	0.0470551i	0.155941	−	0.987766i	$-0.450159\pi$
$311$	−3.23196	−	0.829825i	−0.183267	−	0.0470551i	−0.339208	+	0.940711i	$0.610159\pi$
$312$	−0.519910	−	0.819247i	−0.0294341	−	0.0463807i
$313$	−9.10898	−	14.3535i	−0.514870	−	0.811306i	0.483062	−	0.875586i	$-0.339525\pi$
$313$	−9.10898	−	14.3535i	−0.514870	−	0.811306i	−0.997932	+	0.0642808i	$0.979525\pi$
$314$	−12.1872	−	3.12914i	−0.687764	−	0.176588i
$315$	−2.77529	−	0.402506i	−0.156370	−	0.0226787i
$316$	19.2961	+	7.63987i	1.08549	+	0.429776i
$317$	−25.9877	+	14.2869i	−1.45962	+	0.802430i	−0.996478	−	0.0838564i	$-0.973276\pi$
$317$	−25.9877	+	14.2869i	−1.45962	+	0.802430i	−0.463137	+	0.886287i	$0.653276\pi$
$318$	8.32568			0.466881
$319$	1.02527	−	0.563646i	0.0574040	−	0.0315581i
$320$	4.96042	−	3.46659i	0.277296	−	0.193789i
$321$	−0.522326	+	0.0659851i	−0.0291534	+	0.00368293i
$322$	−0.563755	+	2.95530i	−0.0314168	+	0.164693i
$323$	3.15332	−	1.24849i	0.175455	−	0.0694676i
$324$	0.432969	+	1.33254i	0.0240538	+	0.0740300i
$325$	−4.37523	+	0.390140i	−0.242694	+	0.0216411i
$326$	−8.54617	+	26.3024i	−0.473328	+	1.45675i
$327$	−0.833421	−	13.2468i	−0.0460883	−	0.732552i
$328$	−6.61778	+	0.836020i	−0.365406	+	0.0461615i
$329$	3.95432	−	3.71335i	0.218009	−	0.204724i
$330$	−1.90393	+	1.00162i	−0.104808	+	0.0551371i
$331$	1.53224	+	0.193567i	0.0842197	+	0.0106394i	0.167330	−	0.985901i	$-0.446485\pi$
$331$	1.53224	+	0.193567i	0.0842197	+	0.0106394i	−0.0831104	+	0.996540i	$0.526485\pi$
$332$	−5.99064	+	18.4373i	−0.328779	+	1.01188i
$333$	2.32998	+	2.18800i	0.127682	+	0.119902i
$334$	46.0610	−	11.8264i	2.52034	−	0.647114i
$335$	4.00966	−	19.1062i	0.219071	−	1.04388i
$336$	−3.86845	−	4.67615i	−0.211041	−	0.255105i
$337$	25.8444	−	6.63570i	1.40783	−	0.361470i	0.533090	−	0.846059i	$-0.321031\pi$
$337$	25.8444	−	6.63570i	1.40783	−	0.361470i	0.874742	+	0.484589i	$0.161031\pi$
$338$	−14.3748	+	17.3762i	−0.781886	+	0.945138i
$339$	−13.2356	+	5.24033i	−0.718857	+	0.284616i
$340$	−5.76500	+	6.71375i	−0.312651	+	0.364104i
$341$	1.47712	+	2.32757i	0.0799906	+	0.126045i
$342$	−0.414932	−	2.17515i	−0.0224370	−	0.117619i
$343$	−4.81612	−	14.8225i	−0.260046	−	0.800339i
$344$	−1.32810	+	2.82235i	−0.0716062	+	0.152171i
$345$	−0.597406	+	2.84666i	−0.0321632	+	0.153259i
$346$	−16.4314	−	9.03324i	−0.883357	−	0.485630i
$347$	2.42951	+	1.33564i	0.130423	+	0.0717007i	0.545629	−	0.838027i	$-0.316291\pi$
$347$	2.42951	+	1.33564i	0.130423	+	0.0717007i	−0.415206	+	0.909727i	$0.636291\pi$
$348$	−2.00297	−	2.42117i	−0.107370	−	0.129788i
$349$	−13.1967	−	9.58796i	−0.706403	−	0.513232i	0.175608	−	0.984460i	$-0.443811\pi$
$349$	−13.1967	−	9.58796i	−0.706403	−	0.513232i	−0.882011	+	0.471228i	$0.843811\pi$
$350$	−11.2992	+	2.46271i	−0.603966	+	0.131637i
$351$	0.710736	−	0.516380i	0.0379363	−	0.0275623i
$352$	−3.39327	−	0.871245i	−0.180862	−	0.0464375i
$353$	12.7939	+	27.1885i	0.680953	+	1.44710i	0.883789	+	0.467885i	$0.154984\pi$
$353$	12.7939	+	27.1885i	0.680953	+	1.44710i	−0.202837	+	0.979213i	$0.565016\pi$
$354$	−3.76838	+	19.7545i	−0.200287	+	1.04994i
$355$	0.425451	−	0.643953i	0.0225806	−	0.0341775i
$356$	3.39885	+	3.19173i	0.180139	+	0.169161i
$357$	2.86582	+	2.08214i	0.151675	+	0.110199i
$358$	−4.46325	+	9.48490i	−0.235890	+	0.501292i
$359$	−21.2209	+	25.6516i	−1.11999	+	1.35384i	−0.191936	+	0.981408i	$0.561476\pi$
$359$	−21.2209	+	25.6516i	−1.11999	+	1.35384i	−0.928059	+	0.372433i	$0.878524\pi$
$360$	−1.53902	−	1.93150i	−0.0811132	−	0.101799i
$361$	−1.10249	−	17.5236i	−0.0580260	−	0.922296i
$362$	−0.799355	+	12.7054i	−0.0420132	+	0.667780i
$363$	−9.97450	−	3.94918i	−0.523525	−	0.207278i
$364$	0.827166	−	1.30340i	0.0433553	−	0.0683170i
$365$	0.921369	−	2.66795i	0.0482267	−	0.139647i
$366$	−0.460819	+	7.32450i	−0.0240874	+	0.382858i
$367$	6.76592	+	0.854734i	0.353178	+	0.0446167i	0.299921	−	0.953964i	$-0.403040\pi$
$367$	6.76592	+	0.854734i	0.353178	+	0.0446167i	0.0532571	+	0.998581i	$0.483040\pi$
$368$	−5.09252	+	3.69993i	−0.265466	+	0.192872i
$369$	−1.13168	−	5.93247i	−0.0589128	−	0.308832i
$370$	12.1640	+	5.07638i	0.632375	+	0.263908i
$371$	−2.41067	−	5.12293i	−0.125156	−	0.265969i
$372$	5.39715	−	5.06826i	0.279829	−	0.262777i
$373$	−18.5058	+	29.1604i	−0.958192	+	1.50987i	−0.100991	+	0.994887i	$0.532201\pi$
$373$	−18.5058	+	29.1604i	−0.958192	+	1.50987i	−0.857201	+	0.514982i	$0.827799\pi$
$374$	2.71750			0.140519
$375$	−10.9658	+	2.17991i	−0.566270	+	0.112570i
$376$	4.77719			0.246365
$377$	−1.05571	+	1.66354i	−0.0543720	+	0.0856766i
$378$	1.68602	−	1.58328i	0.0867196	−	0.0814351i
$379$	−2.19269	−	4.65970i	−0.112631	−	0.239353i	0.840562	−	0.541715i	$-0.182225\pi$
$379$	−2.19269	−	4.65970i	−0.112631	−	0.239353i	−0.953193	+	0.302362i	$0.902225\pi$
$380$	−1.95703	−	3.21270i	−0.100393	−	0.164808i
$381$	2.95508	+	15.4911i	0.151393	+	0.793632i
$382$	−2.99012	+	2.17245i	−0.152988	+	0.111152i
$383$	−2.62171	−	0.331200i	−0.133963	−	0.0169235i	0.0580656	−	0.998313i	$-0.481507\pi$
$383$	−2.62171	−	0.331200i	−0.133963	−	0.0169235i	−0.192029	+	0.981389i	$0.561507\pi$
$384$	0.529928	−	8.42296i	0.0270428	−	0.429833i
$385$	1.16759	+	0.881508i	0.0595057	+	0.0449258i
$386$	−12.9628	+	20.4261i	−0.659790	+	1.03966i
$387$	−2.62585	−	1.03965i	−0.133480	−	0.0528483i
$388$	−1.28373	+	20.4043i	−0.0651716	+	1.03587i
$389$	−2.09440	−	33.2896i	−0.106191	−	1.68785i	−0.585869	−	0.810406i	$-0.699247\pi$
$389$	−2.09440	−	33.2896i	−0.106191	−	1.68785i	0.479678	−	0.877444i	$-0.340753\pi$
$390$	1.99704	−	3.02268i	0.101124	−	0.153059i
$391$	2.34200	−	2.83099i	0.118440	−	0.143169i
$392$	2.55217	−	5.42364i	0.128904	−	0.273935i
$393$	10.3703	+	7.53445i	0.523111	+	0.380063i
$394$	0.585752	+	0.550057i	0.0295097	+	0.0277115i
$395$	−1.47232	−	33.0881i	−0.0740803	−	1.66484i
$396$	0.136965	−	0.717998i	0.00688277	−	0.0360807i
$397$	4.75128	+	10.0970i	0.238460	+	0.506753i	0.987857	−	0.155368i	$-0.0496564\pi$
$397$	4.75128	+	10.0970i	0.238460	+	0.506753i	−0.749397	+	0.662121i	$0.769656\pi$
$398$	−19.1856	−	4.92601i	−0.961685	−	0.246919i
$399$	−1.21826	+	0.885121i	−0.0609895	+	0.0443115i
$400$	−20.7604	−	12.4270i	−1.03802	−	0.621350i
$401$	28.8791	+	20.9819i	1.44215	+	1.04779i	0.987587	+	0.157074i	$0.0502060\pi$
$401$	28.8791	+	20.9819i	1.44215	+	1.04779i	0.454567	+	0.890712i	$0.349794\pi$
$402$	10.2633	+	12.4062i	0.511887	+	0.618765i
$403$	−4.06807	−	2.23644i	−0.202645	−	0.111405i
$404$	15.9299	+	8.75753i	0.792541	+	0.435703i
$405$	1.65786	−	1.50050i	0.0823796	−	0.0745606i
$406$	−2.20856	+	4.69344i	−0.109609	+	0.232931i
$407$	−0.515272	−	1.58584i	−0.0255411	−	0.0786074i
$408$	0.584559	+	3.06436i	0.0289400	+	0.151709i
$409$	−1.80346	−	2.84180i	−0.0891754	−	0.140518i	0.796812	−	0.604227i	$-0.206518\pi$
$409$	−1.80346	−	2.84180i	−0.0891754	−	0.140518i	−0.885987	+	0.463709i	$0.846518\pi$
$410$	−12.9566	−	21.2698i	−0.639879	−	1.05044i
$411$	2.60987	−	1.03332i	0.128735	−	0.0509699i
$412$	9.43650	−	11.4068i	0.464903	−	0.561971i
$413$	13.2464	−	3.40110i	0.651813	−	0.167357i
$414$	−1.52915	−	1.84842i	−0.0751534	−	0.0908449i
$415$	30.7607	−	3.31333i	1.50999	−	0.162645i
$416$	5.71425	−	1.46717i	0.280164	−	0.0719339i
$417$	−11.6608	−	10.9502i	−0.571030	−	0.536233i
$418$	−0.356980	+	1.09867i	−0.0174605	+	0.0537378i
$419$	36.1362	+	4.56506i	1.76537	+	0.223018i	0.939905	−	0.341437i	$-0.110914\pi$
$419$	36.1362	+	4.56506i	1.76537	+	0.223018i	0.825464	+	0.564455i	$0.190914\pi$
$420$	1.73797	−	3.52391i	0.0848042	−	0.171949i
$421$	−24.5810	+	23.0831i	−1.19800	+	1.12500i	−0.208876	+	0.977942i	$0.566981\pi$
$421$	−24.5810	+	23.0831i	−1.19800	+	1.12500i	−0.989128	+	0.147059i	$0.953019\pi$
$422$	31.0398	−	3.92124i	1.51099	−	0.190883i
$423$	0.271590	+	4.31680i	0.0132052	+	0.209890i
$424$	1.54079	−	4.74208i	0.0748276	−	0.230296i
$425$	13.5408	+	4.01211i	0.656827	+	0.194616i
$426$	0.196705	+	0.605397i	0.00953041	+	0.0293316i
$427$	4.64031	−	1.83723i	0.224560	−	0.0889097i
$428$	0.138223	−	0.724590i	0.00668126	−	0.0350244i
$429$	−0.454698	+	0.0574417i	−0.0219530	+	0.00277331i
$430$	−11.6443	−	0.213864i	−0.561539	−	0.0103135i
$431$	17.1844	−	9.44722i	0.827744	−	0.455056i	−0.0107659	−	0.999942i	$-0.503427\pi$
$431$	17.1844	−	9.44722i	0.827744	−	0.455056i	0.838510	+	0.544886i	$0.183427\pi$
$432$	4.83911			0.232822
$433$	−8.22577	+	4.52216i	−0.395305	+	0.217321i	−0.666992	−	0.745065i	$-0.732419\pi$
$433$	−8.22577	+	4.52216i	−0.395305	+	0.217321i	0.271687	+	0.962386i	$0.412419\pi$
$434$	−11.3636	−	4.49915i	−0.545468	−	0.215966i
$435$	−2.21818	+	4.49758i	−0.106353	+	0.215642i
$436$	18.0128	+	4.62490i	0.862657	+	0.221493i
$437$	0.836902	+	1.31875i	0.0400344	+	0.0630842i
$438$	1.24737	+	1.96554i	0.0596015	+	0.0939170i
$439$	−10.1712	−	2.61153i	−0.485447	−	0.124642i	−0.00196872	−	0.999998i	$-0.500627\pi$
$439$	−10.1712	−	2.61153i	−0.485447	−	0.124642i	−0.483478	+	0.875357i	$0.660627\pi$
$440$	0.218140	+	1.26979i	0.0103994	+	0.0605350i
$441$	5.04604	+	1.99787i	0.240288	+	0.0951366i
$442$	−4.01020	+	2.20463i	−0.190746	+	0.104863i
$443$	7.90349			0.375506			0.187753	−	0.982216i	$-0.439880\pi$
$443$	7.90349			0.375506			0.187753	+	0.982216i	$0.439880\pi$
$444$	−3.92441	+	2.15746i	−0.186244	+	0.102389i
$445$	2.42898	−	7.03343i	0.115144	−	0.333417i
$446$	41.5368	−	5.24731i	1.96682	−	0.248468i
$447$	−2.35423	+	12.3413i	−0.111351	+	0.583723i
$448$	3.15584	−	1.24948i	0.149099	−	0.0590326i
$449$	−5.02149	−	15.4545i	−0.236979	−	0.729345i	−0.996853	−	0.0792748i	$-0.974740\pi$
$449$	−5.02149	−	15.4545i	−0.236979	−	0.729345i	0.759874	−	0.650070i	$-0.225260\pi$
$450$	4.22986	−	8.19367i	0.199398	−	0.386253i
$451$	−0.973620	+	2.99649i	−0.0458460	+	0.141099i
$452$	−1.25237	−	19.9058i	−0.0589064	−	0.936291i
$453$	−1.67997	+	0.212229i	−0.0789318	+	0.00997141i
$454$	16.8760	−	15.8477i	0.792032	−	0.743767i
$455$	−2.43814	−	0.353609i	−0.114302	−	0.0165774i
$456$	−1.31570	−	0.166211i	−0.0616131	−	0.00778355i
$457$	5.09123	−	15.6692i	0.238158	−	0.732974i	−0.758529	−	0.651639i	$-0.774082\pi$
$457$	5.09123	−	15.6692i	0.238158	−	0.732974i	0.996687	−	0.0813346i	$-0.0259182\pi$
$458$	−36.1256	−	33.9242i	−1.68804	−	1.58517i
$459$	−2.73581	+	0.702436i	−0.127697	+	0.0327869i
$460$	−3.53463	−	2.02858i	−0.164803	−	0.0945831i
$461$	6.14330	+	7.42598i	0.286122	+	0.345862i	0.893918	−	0.448231i	$-0.147946\pi$
$461$	6.14330	+	7.42598i	0.286122	+	0.345862i	−0.607795	+	0.794094i	$0.707946\pi$
$462$	−1.16870	+	0.300070i	−0.0543726	+	0.0139605i
$463$	−8.20839	+	9.92224i	−0.381476	+	0.461125i	−0.925947	−	0.377655i	$-0.876731\pi$
$463$	−8.20839	+	9.92224i	−0.381476	+	0.461125i	0.544470	+	0.838780i	$0.316731\pi$
$464$	−10.0906	+	3.99513i	−0.468442	+	0.185469i
$465$	−10.9044	−	4.55073i	−0.505680	−	0.211035i
$466$	6.82514	+	10.7547i	0.316169	+	0.498202i
$467$	−1.16634	−	6.11419i	−0.0539720	−	0.282931i	0.945061	−	0.326893i	$-0.106002\pi$
$467$	−1.16634	−	6.11419i	−0.0539720	−	0.282931i	−0.999033	+	0.0439625i	$0.986002\pi$
$468$	0.380371	+	1.17066i	0.0175826	+	0.0541138i
$469$	4.66204	−	9.90734i	0.215273	−	0.457478i
$470$	7.29686	+	16.2759i	0.336579	+	0.750751i
$471$	−5.97878	−	3.28686i	−0.275488	−	0.151451i
$472$	10.5542	+	5.80224i	0.485798	+	0.267070i
$473$	0.939141	+	1.13523i	0.0431817	+	0.0521977i
$474$	22.0996	+	16.0563i	1.01507	+	0.737492i
$475$	−3.40085	+	4.94745i	−0.156041	+	0.227004i
$476$	−4.01535	+	2.91732i	−0.184043	+	0.133715i
$477$	4.37266	+	1.12271i	0.200210	+	0.0514053i
$478$	14.1572	+	30.0856i	0.647535	+	1.37608i
$479$	0.0372997	−	0.195532i	0.00170427	−	0.00893409i	−0.981425	−	0.191846i	$-0.938552\pi$
$479$	0.0372997	−	0.195532i	0.00170427	−	0.00893409i	0.983129	+	0.182912i	$0.0585525\pi$
$480$	14.0608	−	5.27048i	0.641783	−	0.240563i
$481$	2.04693	+	1.92220i	0.0933320	+	0.0876446i
$482$	−22.2751	−	16.1838i	−1.01460	−	0.737151i
$483$	−0.694605	+	1.47611i	−0.0316056	+	0.0671653i
$484$	9.58109	−	11.5815i	0.435504	−	0.526434i
$485$	30.5522	−	11.4521i	1.38730	−	0.520012i
$486$	0.115799	+	1.84057i	0.00525275	+	0.0834901i
$487$	0.00501030	−	0.0796364i	0.000227038	−	0.00360867i	−0.997912	−	0.0645948i	$-0.979425\pi$
$487$	0.00501030	−	0.0796364i	0.000227038	−	0.00360867i	0.998139	+	0.0609861i	$0.0194245\pi$
$488$	4.08655	+	1.61798i	0.184990	+	0.0732425i
$489$	−8.03531	+	12.6616i	−0.363369	+	0.572578i
$490$	22.3766	+	0.410978i	1.01087	+	0.0185661i
$491$	−1.52579	+	24.2517i	−0.0688580	+	1.09447i	0.800193	+	0.599743i	$0.204730\pi$
$491$	−1.52579	+	24.2517i	−0.0688580	+	1.09447i	−0.869051	+	0.494723i	$0.835270\pi$
$492$	8.39524	+	1.06057i	0.378487	+	0.0478140i
$493$	5.12481	−	3.72339i	0.230810	−	0.167693i
$494$	−0.364525	−	1.91091i	−0.0164008	−	0.0859759i
$495$	−1.13502	+	0.269307i	−0.0510152	+	0.0121044i
$496$	−10.8876	−	23.1373i	−0.488867	−	1.03889i
$497$	0.315555	−	0.296326i	0.0141546	−	0.0132920i
$498$	−13.6726	+	21.5446i	−0.612685	+	0.965437i
$499$	−37.4011			−1.67430			−0.837152	−	0.546971i	$-0.815781\pi$
$499$	−37.4011			−1.67430			−0.837152	+	0.546971i	$0.815781\pi$
$500$	1.84301	−	15.5562i	0.0824219	−	0.695693i
$501$	25.7861			1.15204
$502$	17.8983	−	28.2032i	0.798840	−	1.25877i
$503$	9.57434	−	8.99091i	0.426899	−	0.400885i	−0.441094	−	0.897461i	$-0.645410\pi$
$503$	9.57434	−	8.99091i	0.426899	−	0.400885i	0.867993	+	0.496576i	$0.165410\pi$
$504$	−0.589768	−	1.25332i	−0.0262704	−	0.0558273i
$505$	2.35302	−	28.9157i	0.104708	−	1.28673i
$506$	0.234508	+	1.22933i	0.0104251	+	0.0546505i
$507$	−9.89283	+	7.18756i	−0.439356	+	0.319211i
$508$	−21.9220	−	2.76939i	−0.972629	−	0.122872i
$509$	1.05883	−	16.8296i	0.0469317	−	0.745958i	−0.902247	−	0.431220i	$-0.858083\pi$
$509$	1.05883	−	16.8296i	0.0469317	−	0.745958i	0.949179	−	0.314738i	$-0.101917\pi$
$510$	−9.54741	+	6.67221i	−0.422766	+	0.295451i
$511$	0.848257	−	1.33664i	0.0375247	−	0.0591294i
$512$	20.2759	+	8.02778i	0.896075	+	0.354781i
$513$	0.0753936	−	1.19835i	0.00332871	−	0.0529083i
$514$	1.28812	+	20.4740i	0.0568164	+	0.903071i
$515$	−22.7722	−	6.29482i	−1.00346	−	0.277383i
$516$	2.52229	−	3.04892i	0.111037	−	0.134221i
$517$	0.960759	−	2.04172i	0.0422541	−	0.0897946i
$518$	5.98075	+	4.34527i	0.262779	+	0.190920i
$519$	−7.41168	−	6.96003i	−0.325336	−	0.305511i
$520$	−1.35205	−	1.69686i	−0.0592914	−	0.0744120i
$521$	−1.37375	+	7.20146i	−0.0601852	+	0.315502i	−0.999630	−	0.0271982i	$-0.991341\pi$
$521$	−1.37375	+	7.20146i	−0.0601852	+	0.315502i	0.939445	+	0.342700i	$0.111341\pi$
$522$	−1.76103	−	3.74238i	−0.0770781	−	0.163799i
$523$	−24.5792	−	6.31086i	−1.07477	−	0.275955i	−0.330483	−	0.943812i	$-0.607212\pi$
$523$	−24.5792	−	6.31086i	−1.07477	−	0.275955i	−0.744290	+	0.667857i	$0.767212\pi$
$524$	−14.5300	+	10.5566i	−0.634744	+	0.461169i
$525$	−6.26643	−	0.230261i	−0.273490	−	0.0100494i
$526$	5.75014	+	4.17772i	0.250718	+	0.182157i
$527$	9.51390	+	11.5003i	0.414432	+	0.500962i
$528$	−2.21224	−	1.21619i	−0.0962752	−	0.0529278i
$529$	−18.6723	−	10.2652i	−0.811838	−	0.446312i
$530$	18.5097	−	1.99374i	0.804011	−	0.0866025i
$531$	−4.64304	+	9.86695i	−0.201491	+	0.428189i
$532$	−0.651989	−	2.00662i	−0.0282673	−	0.0869978i
$533$	−0.994200	−	5.21178i	−0.0430636	−	0.225747i
$534$	3.28840	+	5.18168i	0.142303	+	0.224233i
$535$	−1.14544	+	0.271779i	−0.0495216	+	0.0117500i
$536$	8.96561	−	3.54974i	0.387255	−	0.153325i
$537$	−3.62314	+	4.37962i	−0.156350	+	0.188995i
$538$	−49.9747	+	12.8313i	−2.15456	+	0.553198i
$539$	−1.80472	−	2.18154i	−0.0777349	−	0.0939654i
$540$	1.28168	+	2.85883i	0.0551548	+	0.123025i
$541$	−0.214136	+	0.0549807i	−0.00920641	+	0.00236381i	−0.253290	−	0.967390i	$-0.581513\pi$
$541$	−0.214136	+	0.0549807i	−0.00920641	+	0.00236381i	0.244084	+	0.969754i	$0.421513\pi$
$542$	−31.7443	−	29.8099i	−1.36354	−	1.28044i
$543$	−2.13313	+	6.56510i	−0.0915414	+	0.281735i
$544$	−18.8184	−	2.37731i	−0.806831	−	0.101926i
$545$	−5.02507	−	29.2509i	−0.215250	−	1.25297i
$546$	1.48120	−	1.39094i	0.0633895	−	0.0595267i
$547$	−6.27162	+	0.792290i	−0.268155	+	0.0338759i	−0.258261	−	0.966075i	$-0.583149\pi$
$547$	−6.27162	+	0.792290i	−0.268155	+	0.0338759i	−0.00989419	+	0.999951i	$0.503149\pi$
$548$	0.246950	+	3.92515i	0.0105492	+	0.167674i
$549$	−1.22972	+	3.78470i	−0.0524833	+	0.161527i
$550$	−3.99299	+	2.68273i	−0.170262	+	0.114392i
$551$	0.832135	+	2.56105i	0.0354502	+	0.109104i
$552$	−1.33580	+	0.528881i	−0.0568554	+	0.0225107i
$553$	3.48086	−	18.2473i	0.148021	−	0.775954i
$554$	30.9325	−	3.90768i	1.31419	−	0.166021i
$555$	5.70400	+	4.30642i	0.242121	+	0.182797i
$556$	19.6403	−	10.7973i	0.832934	−	0.457910i
$557$	−3.90988			−0.165667			−0.0828336	−	0.996563i	$-0.526397\pi$
$557$	−3.90988			−0.165667			−0.0828336	+	0.996563i	$0.526397\pi$
$558$	8.53981	−	4.69480i	0.361519	−	0.198747i
$559$	−2.30686	−	0.913350i	−0.0975697	−	0.0386306i
$560$	−9.72016	−	9.46969i	−0.410752	−	0.400167i
$561$	1.42724	+	0.366452i	0.0602579	+	0.0154716i
$562$	0.907674	+	1.43027i	0.0382879	+	0.0603321i
$563$	−0.835230	−	1.31611i	−0.0352007	−	0.0554675i	0.826272	−	0.563271i	$-0.190457\pi$
$563$	−0.835230	−	1.31611i	−0.0352007	−	0.0554675i	−0.861473	+	0.507804i	$0.830457\pi$
$564$	−5.86990	−	1.50713i	−0.247167	−	0.0634618i
$565$	−28.1705	+	14.8198i	−1.18514	+	0.623476i
$566$	−23.0537	−	9.12762i	−0.969020	−	0.383662i
$567$	1.09900	−	0.604183i	0.0461539	−	0.0253733i
$568$	0.381221			0.0159957
$569$	9.77498	−	5.37384i	0.409788	−	0.225283i	−0.263506	−	0.964658i	$-0.584879\pi$
$569$	9.77498	−	5.37384i	0.409788	−	0.225283i	0.673294	+	0.739375i	$0.264879\pi$
$570$	−1.44336	−	4.73645i	−0.0604558	−	0.198388i
$571$	−12.9634	+	1.63766i	−0.542502	+	0.0685340i	−0.391809	−	0.920047i	$-0.628151\pi$
$571$	−12.9634	+	1.63766i	−0.542502	+	0.0685340i	−0.150693	+	0.988581i	$0.548151\pi$
$572$	0.120326	−	0.630774i	0.00503110	−	0.0263740i
$573$	−1.86337	+	0.737761i	−0.0778434	+	0.0308204i
$574$	−4.31652	−	13.2849i	−0.180168	−	0.554500i
$575$	−0.646471	+	6.47178i	−0.0269597	+	0.269892i
$576$	−0.836324	+	2.57394i	−0.0348469	+	0.107248i
$577$	−0.236963	−	3.76643i	−0.00986492	−	0.156798i	−0.999875	−	0.0158027i	$-0.994970\pi$
$577$	−0.236963	−	3.76643i	−0.00986492	−	0.156798i	0.990010	−	0.140996i	$-0.0450304\pi$
$578$	−16.5072	+	2.08534i	−0.686608	+	0.0867388i
$579$	−9.56254	+	8.97982i	−0.397406	+	0.373189i
$580$	−5.03281	−	4.90312i	−0.208976	−	0.203591i
$581$	17.2156	+	2.17483i	0.714223	+	0.0902273i
$582$	−8.31570	+	25.5931i	−0.344697	+	1.06087i
$583$	−1.71683	−	1.61221i	−0.0711040	−	0.0667711i
$584$	1.35036	−	0.346714i	0.0558783	−	0.0143471i
$585$	1.45646	−	1.31822i	0.0602171	−	0.0545016i
$586$	−31.1959	−	37.7094i	−1.28869	−	1.55776i
$587$	−10.2826	+	2.64013i	−0.424409	+	0.108970i	−0.454853	−	0.890567i	$-0.650308\pi$
$587$	−10.2826	+	2.64013i	−0.424409	+	0.108970i	0.0304435	+	0.999536i	$0.490308\pi$
$588$	−4.84702	+	5.85904i	−0.199888	+	0.241623i
$589$	−5.89930	+	2.33570i	−0.243076	+	0.0962408i
$590$	−3.64730	+	44.8209i	−0.150157	+	1.84525i
$591$	0.233463	+	0.367879i	0.00960339	+	0.0151325i
$592$	2.89825	+	15.1931i	0.119117	+	0.624434i
$593$	−12.7319	−	39.1847i	−0.522836	−	1.60912i	−0.768556	−	0.639782i	$-0.779025\pi$
$593$	−12.7319	−	39.1847i	−0.522836	−	1.60912i	0.245721	−	0.969341i	$-0.420975\pi$
$594$	0.409643	−	0.870536i	0.0168079	−	0.0357185i
$595$	6.86993	+	3.94276i	0.281640	+	0.161638i
$596$	−15.4260	−	8.48049i	−0.631872	−	0.347375i
$597$	−9.41202	−	5.17430i	−0.385208	−	0.211770i
$598$	−1.34338	−	1.62387i	−0.0549350	−	0.0664049i
$599$	−25.9333	−	18.8417i	−1.05961	−	0.769849i	−0.0855912	−	0.996330i	$-0.527278\pi$
$599$	−25.9333	−	18.8417i	−1.05961	−	0.769849i	−0.974016	+	0.226481i	$0.927278\pi$
$600$	−3.88408	−	3.92558i	−0.158567	−	0.160261i
$601$	−0.806166	+	0.585714i	−0.0328842	+	0.0238918i	−0.604106	−	0.796904i	$-0.706470\pi$
$601$	−0.806166	+	0.585714i	−0.0328842	+	0.0238918i	0.571222	+	0.820796i	$0.306470\pi$
$602$	−6.32678	−	1.62444i	−0.257860	−	0.0662073i
$603$	3.71734	+	7.89976i	0.151382	+	0.321703i
$604$	0.444570	−	2.33052i	0.0180893	−	0.0948273i
$605$	−23.1211	−	6.39128i	−0.940006	−	0.259842i
$606$	17.4422	+	16.3793i	0.708542	+	0.665365i
$607$	16.4108	+	11.9232i	0.666095	+	0.483946i	0.868716	−	0.495311i	$-0.164946\pi$
$607$	16.4108	+	11.9232i	0.666095	+	0.483946i	−0.202621	+	0.979257i	$0.564946\pi$
$608$	3.43318	−	7.29588i	0.139234	−	0.295887i
$609$	−1.79285	+	2.16718i	−0.0726498	+	0.0878185i
$610$	0.729492	+	16.3942i	0.0295363	+	0.663783i
$611$	0.238597	+	3.79238i	0.00965258	+	0.153423i
$612$	0.248494	−	3.94971i	0.0100448	−	0.159657i
$613$	−7.26562	−	2.87666i	−0.293456	−	0.116187i	0.216784	−	0.976220i	$-0.430443\pi$
$613$	−7.26562	−	2.87666i	−0.293456	−	0.116187i	−0.510240	+	0.860032i	$0.670443\pi$
$614$	−6.61023	+	10.4161i	−0.266767	+	0.420358i
$615$	−3.93660	−	12.9181i	−0.158739	−	0.520909i
$616$	−0.0453734	+	0.721189i	−0.00182815	+	0.0290575i
$617$	12.6642	+	1.59986i	0.509841	+	0.0644079i	0.376046	−	0.926601i	$-0.377284\pi$
$617$	12.6642	+	1.59986i	0.509841	+	0.0644079i	0.133795	+	0.991009i	$0.457284\pi$
$618$	15.7644	−	11.4535i	0.634136	−	0.460727i
$619$	0.287948	+	1.50948i	0.0115736	+	0.0606710i	0.987606	−	0.156956i	$-0.0501682\pi$
$619$	0.287948	+	1.50948i	0.0115736	+	0.0606710i	−0.976032	+	0.217627i	$0.930168\pi$
$620$	10.7853	−	12.5602i	0.433148	−	0.504432i
$621$	−0.553853	−	1.17700i	−0.0222253	−	0.0472313i
$622$	4.48588	−	4.21253i	0.179868	−	0.168907i
$623$	2.23623	−	3.52374i	0.0895927	−	0.141175i
$624$	4.25124			0.170186
$625$	−23.8572	+	7.47236i	−0.954286	+	0.298894i
$626$	31.3513			1.25305
$627$	−0.335641	+	0.528886i	−0.0134042	+	0.0211217i
$628$	6.96851	−	6.54386i	0.278074	−	0.261129i
$629$	−3.84394	−	8.16880i	−0.153268	−	0.325711i
$630$	3.36923	−	3.92371i	0.134233	−	0.156324i
$631$	−1.23961	−	6.49828i	−0.0493482	−	0.258692i	0.949060	−	0.315096i	$-0.102037\pi$
$631$	−1.23961	−	6.49828i	−0.0493482	−	0.258692i	−0.998408	+	0.0564035i	$0.982037\pi$
$632$	13.2351	−	9.61587i	0.526465	−	0.382499i
$633$	16.8309	+	2.12624i	0.668969	+	0.0845105i
$634$	3.43413	−	54.5839i	0.136387	−	2.16780i
$635$	10.2794	+	33.7323i	0.407925	+	1.33862i
$636$	−3.38928	+	5.34065i	−0.134394	+	0.211771i
$637$	4.43303	+	1.75516i	0.175643	+	0.0695421i
$638$	−0.135483	+	2.15345i	−0.00536384	+	0.0852558i
$639$	0.0216729	+	0.344481i	0.000857367	+	0.0136275i
$640$	−0.838895	−	18.8529i	−0.0331602	−	0.745226i
$641$	1.84995	−	2.23621i	0.0730687	−	0.0883249i	−0.732712	−	0.680539i	$-0.761746\pi$
$641$	1.84995	−	2.23621i	0.0730687	−	0.0883249i	0.805781	+	0.592214i	$0.201746\pi$
$642$	0.413404	−	0.878529i	0.0163158	−	0.0346728i
$643$	−5.89104	−	4.28009i	−0.232320	−	0.168790i	0.465535	−	0.885030i	$-0.345862\pi$
$643$	−5.89104	−	4.28009i	−0.232320	−	0.168790i	−0.697855	+	0.716239i	$0.745862\pi$
$644$	−1.66623	−	1.56470i	−0.0656588	−	0.0616577i
$645$	−6.08678	−	1.68255i	−0.239667	−	0.0662502i
$646$	−1.17200	+	6.14381i	−0.0461115	+	0.241725i
$647$	19.0419	+	40.4660i	0.748613	+	1.59088i	0.805565	+	0.592507i	$0.201862\pi$
$647$	19.0419	+	40.4660i	0.748613	+	1.59088i	−0.0569517	+	0.998377i	$0.518138\pi$
$648$	1.06977	+	0.274670i	0.0420245	+	0.0107901i
$649$	4.60241	−	3.34385i	0.180660	−	0.131258i
$650$	3.71601	−	7.19828i	0.145754	−	0.282340i
$651$	−5.36145	−	3.89532i	−0.210132	−	0.152670i
$652$	−13.3931	−	16.1895i	−0.524514	−	0.634028i
$653$	37.1204	+	20.4071i	1.45263	+	0.798593i	0.995852	−	0.0909860i	$-0.0290019\pi$
$653$	37.1204	+	20.4071i	1.45263	+	0.798593i	0.456782	+	0.889579i	$0.349002\pi$
$654$	21.4505	+	11.7925i	0.838780	+	0.461123i
$655$	24.8595	+	14.2673i	0.971343	+	0.557469i
$656$	12.4436	−	26.4440i	0.485842	−	1.03247i
$657$	0.390069	+	1.20051i	0.0152181	+	0.0468364i
$658$	1.87456	+	9.82680i	0.0730780	+	0.383089i
$659$	18.0505	+	28.4431i	0.703149	+	1.10799i	0.988741	+	0.149635i	$0.0478098\pi$
$659$	18.0505	+	28.4431i	0.703149	+	1.10799i	−0.285592	+	0.958351i	$0.592190\pi$
$660$	0.132565	−	1.62906i	0.00516007	−	0.0634110i
$661$	−1.08020	+	0.427681i	−0.0420148	+	0.0166349i	−0.389038	−	0.921222i	$-0.627193\pi$
$661$	−1.08020	+	0.427681i	−0.0420148	+	0.0166349i	0.347023	+	0.937857i	$0.387193\pi$
$662$	−1.81554	+	2.19461i	−0.0705628	+	0.0852958i
$663$	−2.40345	+	0.617102i	−0.0933424	+	0.0239663i
$664$	9.74088	+	11.7747i	0.378020	+	0.456947i
$665$	−2.49650	+	2.25954i	−0.0968100	+	0.0876213i
$666$	−5.70942	+	1.46593i	−0.221235	+	0.0568036i
$667$	2.12662	+	1.99703i	0.0823430	+	0.0773253i
$668$	−11.1646	+	34.3610i	−0.431970	+	1.32947i
$669$	22.5228	+	2.84529i	0.870781	+	0.110005i
$670$	25.7884	+	25.1238i	0.996291	+	0.970618i
$671$	1.51337	−	1.42115i	0.0584229	−	0.0548627i
$672$	8.35559	−	1.05556i	0.322324	−	0.0407190i
$673$	−1.56974	−	24.9503i	−0.0605091	−	0.961765i	−0.904788	−	0.425861i	$-0.859971\pi$
$673$	−1.56974	−	24.9503i	−0.0605091	−	0.961765i	0.844279	−	0.535903i	$-0.180029\pi$
$674$	−15.2062	+	46.8000i	−0.585723	+	1.80267i
$675$	3.32644	−	3.73294i	0.128035	−	0.143681i
$676$	−5.29443	−	16.2946i	−0.203632	−	0.626715i
$677$	−6.63443	+	2.62676i	−0.254982	+	0.100954i	−0.492138	−	0.870517i	$-0.663785\pi$
$677$	−6.63443	+	2.62676i	−0.254982	+	0.100954i	0.237156	+	0.971471i	$0.423785\pi$
$678$	4.91927	−	25.7877i	0.188924	−	0.990372i
$679$	18.1556	−	2.29359i	0.696749	−	0.0880198i
$680$	2.03341	+	6.67273i	0.0779779	+	0.255888i
$681$	11.0004	−	6.04750i	0.421535	−	0.231741i
$682$	−5.08396			−0.194675
$683$	35.1332	−	19.3146i	1.34433	−	0.739053i	0.363077	−	0.931759i	$-0.381726\pi$
$683$	35.1332	−	19.3146i	1.34433	−	0.739053i	0.981257	+	0.192706i	$0.0617263\pi$
$684$	1.56420	+	0.619312i	0.0598088	+	0.0236800i
$685$	5.55484	−	2.92227i	0.212239	−	0.111654i
$686$	27.8396	+	7.14799i	1.06292	+	0.272911i
$687$	−14.3986	−	22.6885i	−0.549340	−	0.865621i
$688$	−7.32287	−	11.5390i	−0.279182	−	0.439920i
$689$	3.84146	+	0.986320i	0.146348	+	0.0375758i
$690$	−3.84225	−	3.74324i	−0.146272	−	0.142503i
$691$	5.38613	+	2.13252i	0.204898	+	0.0811249i	0.468332	−	0.883553i	$-0.344855\pi$
$691$	5.38613	+	2.13252i	0.204898	+	0.0811249i	−0.263434	+	0.964677i	$0.584855\pi$
$692$	12.4835	−	6.86289i	0.474553	−	0.260888i
$693$	−0.654265			−0.0248535
$694$	−4.48054	+	2.46320i	−0.170079	+	0.0935017i
$695$	−28.5465	−	21.5521i	−1.08283	−	0.817519i
$696$	−2.45746	+	0.310449i	−0.0931498	+	0.0117676i
$697$	−3.19648	+	16.7565i	−0.121075	+	0.634699i
$698$	27.9703	−	11.0742i	1.05869	−	0.419165i
$699$	2.13432	+	6.56875i	0.0807273	+	0.248453i
$700$	3.02000	−	8.25058i	0.114145	−	0.311843i
$701$	−10.2656	+	31.5941i	−0.387725	+	1.19329i	0.546760	+	0.837290i	$0.315861\pi$
$701$	−10.2656	+	31.5941i	−0.387725	+	1.19329i	−0.934484	+	0.356004i	$0.884139\pi$
$702$	0.101731	+	1.61698i	0.00383961	+	0.0610288i
$703$	3.80756	−	0.481006i	0.143605	−	0.0181415i
$704$	1.02923	−	0.966509i	0.0387905	−	0.0364267i
$705$	1.63754	+	9.53210i	0.0616733	+	0.359000i
$706$	−54.9784	−	6.94539i	−2.06914	−	0.261393i
$707$	5.02815	−	15.4750i	0.189103	−	0.581999i
$708$	−11.1378	−	10.4591i	−0.418585	−	0.393078i
$709$	31.8499	−	8.17766i	1.19615	−	0.307118i	0.402456	−	0.915439i	$-0.368157\pi$
$709$	31.8499	−	8.17766i	1.19615	−	0.307118i	0.793691	+	0.608321i	$0.208157\pi$
$710$	0.582290	+	1.29882i	0.0218530	+	0.0487438i
$711$	9.44159	+	11.4129i	0.354087	+	0.428018i
$712$	3.55991	−	0.914030i	0.133413	−	0.0342547i
$713$	−4.38147	+	5.29628i	−0.164087	+	0.198347i
$714$	−6.07409	+	2.40490i	−0.227317	+	0.0900012i
$715$	−0.997132	+	0.236591i	−0.0372906	+	0.00884799i
$716$	−4.26732	−	6.72422i	−0.159477	−	0.251296i
$717$	3.37838	+	17.7101i	0.126168	+	0.661395i
$718$	−18.9726	−	58.3918i	−0.708053	−	2.17916i
$719$	−17.1181	+	36.3778i	−0.638398	+	1.35666i	0.279614	+	0.960112i	$0.409793\pi$
$719$	−17.1181	+	36.3778i	−0.638398	+	1.35666i	−0.918012	+	0.396552i	$0.870207\pi$
$720$	10.7583	−	1.15881i	0.400940	−	0.0431864i
$721$	−11.6120	−	6.38376i	−0.432454	−	0.237744i
$722$	28.3758	+	15.5998i	1.05604	+	0.580563i
$723$	−9.51654	−	11.5035i	−0.353924	−	0.427820i
$724$	−7.82469	−	5.68497i	−0.290802	−	0.211280i
$725$	−3.85444	+	10.5302i	−0.143150	+	0.391083i
$726$	16.0059	−	11.6290i	0.594036	−	0.431592i
$727$	40.7073	+	10.4519i	1.50975	+	0.387638i	0.910698	−	0.413073i	$-0.135545\pi$
$727$	40.7073	+	10.4519i	1.50975	+	0.387638i	0.599051	+	0.800711i	$0.295545\pi$
$728$	−0.518122	−	1.10106i	−0.0192029	−	0.0408082i
$729$	−0.187381	+	0.982287i	−0.00694005	+	0.0363810i
$730$	3.24384	+	4.07109i	0.120060	+	0.150678i
$731$	5.81499	+	5.46064i	0.215075	+	0.201969i
$732$	−4.51084	−	3.27731i	−0.166725	−	0.121133i
$733$	−16.8729	+	35.8567i	−0.623213	+	1.32440i	0.305002	+	0.952352i	$0.401343\pi$
$733$	−16.8729	+	35.8567i	−0.623213	+	1.32440i	−0.928215	+	0.372044i	$0.878657\pi$
$734$	−8.01685	+	9.69071i	−0.295907	+	0.357691i
$735$	11.6968	+	3.23331i	0.431444	+	0.119262i
$736$	−0.548499	−	8.71814i	−0.0202179	−	0.321355i
$737$	0.285991	−	4.54570i	0.0105346	−	0.167443i
$738$	10.3559	+	4.10018i	0.381205	+	0.150930i
$739$	−1.07646	+	1.69623i	−0.0395982	+	0.0623967i	−0.863550	−	0.504263i	$-0.831764\pi$
$739$	−1.07646	+	1.69623i	−0.0395982	+	0.0623967i	0.823952	+	0.566659i	$0.191764\pi$
$740$	−8.20813	+	5.73626i	−0.301737	+	0.210869i
$741$	0.0662346	−	1.05277i	0.00243319	−	0.0386744i
$742$	10.3592	+	1.30867i	0.380297	+	0.0480427i
$743$	−7.87719	+	5.72312i	−0.288986	+	0.209961i	−0.722827	−	0.691029i	$-0.757158\pi$
$743$	−7.87719	+	5.72312i	−0.288986	+	0.209961i	0.433841	+	0.900989i	$0.357158\pi$
$744$	−1.09361	−	5.73289i	−0.0400936	−	0.210178i
$745$	−2.27859	+	28.0010i	−0.0834809	+	1.02588i
$746$	−27.1193	−	57.6314i	−0.992907	−	2.11003i
$747$	−10.0862	+	9.47153i	−0.369033	+	0.346545i
$748$	−1.10626	+	1.74319i	−0.0404489	+	0.0637372i
$749$	−0.660272			−0.0241258
$750$	7.44174	−	19.2291i	0.271734	−	0.702149i
$751$	23.6869			0.864348			0.432174	−	0.901790i	$-0.357747\pi$
$751$	23.6869			0.864348			0.432174	+	0.901790i	$0.357747\pi$
$752$	−11.2153	+	17.6724i	−0.408978	+	0.644446i
$753$	13.2034	−	12.3988i	0.481158	−	0.451838i
$754$	−1.54710	−	3.28774i	−0.0563419	−	0.119733i
$755$	−3.68410	+	0.874130i	−0.134078	+	0.0318128i
$756$	0.329264	+	1.72606i	0.0119752	+	0.0627762i
$757$	−5.39202	+	3.91753i	−0.195976	+	0.142385i	−0.681446	−	0.731868i	$-0.738649\pi$
$757$	−5.39202	+	3.91753i	−0.195976	+	0.142385i	0.485470	+	0.874253i	$0.338649\pi$
$758$	9.42247	+	1.19033i	0.342240	+	0.0432349i
$759$	−0.0426102	+	0.677270i	−0.00154665	+	0.0245834i
$760$	−2.96487	−	0.0544540i	−0.107547	−	0.00197525i
$761$	−18.3414	+	28.9014i	−0.664874	+	1.04767i	0.329745	+	0.944070i	$0.393037\pi$
$761$	−18.3414	+	28.9014i	−0.664874	+	1.04767i	−0.994619	+	0.103603i	$0.966963\pi$
$762$	−27.0416	−	10.7065i	−0.979614	−	0.387857i
$763$	1.04522	−	16.6133i	0.0378395	−	0.601441i
$764$	−0.176315	−	2.80244i	−0.00637885	−	0.101389i
$765$	−5.91406	+	2.21680i	−0.213823	+	0.0801486i
$766$	3.10644	−	3.75504i	0.112240	−	0.135675i
$767$	−4.07899	+	8.66829i	−0.147284	+	0.312994i
$768$	16.9709	+	12.3301i	0.612386	+	0.444925i
$769$	3.34650	+	3.14257i	0.120678	+	0.113324i	0.742537	−	0.669805i	$-0.233622\pi$
$769$	3.34650	+	3.14257i	0.120678	+	0.113324i	−0.621859	+	0.783129i	$0.713622\pi$
$770$	−2.52640	+	0.946984i	−0.0910450	+	0.0341269i
$771$	−2.08438	+	10.9267i	−0.0750671	+	0.393516i
$772$	−7.82570	−	16.6305i	−0.281653	−	0.598543i
$773$	−16.6580	−	4.27705i	−0.599147	−	0.153835i	−0.0630773	−	0.998009i	$-0.520091\pi$
$773$	−16.6580	−	4.27705i	−0.599147	−	0.153835i	−0.536069	+	0.844174i	$0.680091\pi$
$774$	4.21367	−	3.06141i	0.151457	−	0.110040i
$775$	−25.3325	−	7.50595i	−0.909971	−	0.269622i
$776$	13.0382	+	9.47279i	0.468043	+	0.340053i
$777$	2.55515	+	3.08864i	0.0916654	+	0.110804i
$778$	53.9055	+	29.6348i	1.93261	+	1.06246i
$779$	−6.35468	−	3.49351i	−0.227680	−	0.125168i
$780$	1.12598	+	2.51154i	0.0403165	+	0.0899274i
$781$	0.0766687	−	0.162929i	0.00274342	−	0.00583007i
$782$	2.09388	+	6.44429i	0.0748769	+	0.230447i
$783$	−0.420240	−	2.20298i	−0.0150182	−	0.0787279i
$784$	14.0722	+	22.1742i	0.502578	+	0.791936i
$785$	−14.0792	−	5.87565i	−0.502508	−	0.209711i
$786$	−21.9797	+	8.70238i	−0.783990	+	0.310404i
$787$	9.41552	−	11.3814i	0.335627	−	0.405703i	−0.575518	−	0.817789i	$-0.695200\pi$
$787$	9.41552	−	11.3814i	0.335627	−	0.405703i	0.911145	+	0.412086i	$0.135200\pi$
$788$	−0.591296	+	0.151819i	−0.0210641	+	0.00540833i
$789$	2.45662	+	2.96955i	0.0874581	+	0.105719i
$790$	52.9771	+	30.4044i	1.88484	+	1.08174i
$791$	−17.2920	+	4.43982i	−0.614831	+	0.157862i
$792$	−0.420022	−	0.394427i	−0.0149248	−	0.0140154i
$793$	−1.08033	+	3.32493i	−0.0383638	+	0.118072i
$794$	−20.4173	−	2.57931i	−0.724583	−	0.0915362i
$795$	9.99019	+	1.44890i	0.354316	+	0.0513872i
$796$	10.9701	−	10.3016i	0.388824	−	0.365130i
$797$	3.75722	−	0.474648i	0.133088	−	0.0168129i	−0.0585072	−	0.998287i	$-0.518634\pi$
$797$	3.75722	−	0.474648i	0.133088	−	0.0168129i	0.191595	+	0.981474i	$0.438634\pi$
$798$	−0.174377	−	2.77164i	−0.00617287	−	0.0981150i
$799$	3.77529	−	11.6191i	0.133560	−	0.411056i
$800$	29.9979	−	15.0845i	1.06059	−	0.533317i
$801$	1.02833	+	3.16486i	0.0363341	+	0.111825i
$802$	−61.2090	+	24.2344i	−2.16137	+	0.855745i
$803$	0.123395	−	0.646857i	0.00435450	−	0.0228271i
$804$	−12.1362	+	1.53316i	−0.428012	+	0.0540705i
$805$	−1.19077	+	3.44804i	−0.0419691	+	0.121527i
$806$	7.50238	−	4.12447i	0.264260	−	0.145278i
$807$	−27.9771			−0.984840
$808$	12.5572	−	6.90336i	0.441760	−	0.242859i
$809$	−19.7221	−	7.80852i	−0.693391	−	0.274533i	−0.00512022	−	0.999987i	$-0.501630\pi$
$809$	−19.7221	−	7.80852i	−0.693391	−	0.274533i	−0.688271	+	0.725454i	$0.741630\pi$
$810$	0.698205	+	4.06425i	0.0245324	+	0.142803i
$811$	−28.1888	−	7.23766i	−0.989844	−	0.254149i	−0.281149	−	0.959664i	$-0.590716\pi$
$811$	−28.1888	−	7.23766i	−0.989844	−	0.254149i	−0.708695	+	0.705515i	$0.750716\pi$
$812$	−2.11161	−	3.32736i	−0.0741029	−	0.116767i
$813$	−12.6523	−	19.9369i	−0.443737	−	0.699218i
$814$	2.97853	+	0.764756i	0.104397	+	0.0268047i
$815$	−14.8321	+	30.0736i	−0.519546	+	1.05343i
$816$	−12.7084	−	5.03163i	−0.444884	−	0.176142i
$817$	−2.97159	+	1.63364i	−0.103963	+	0.0571540i
$818$	6.20716			0.217028
$819$	0.965495	−	0.530785i	0.0337371	−	0.0185471i
$820$	18.9183	+	0.347462i	0.660657	+	0.0121339i
$821$	8.16769	−	1.03182i	0.285054	−	0.0360107i	0.0184940	−	0.999829i	$-0.494113\pi$
$821$	8.16769	−	1.03182i	0.285054	−	0.0360107i	0.266560	+	0.963818i	$0.414113\pi$
$822$	−0.970012	+	5.08498i	−0.0338331	+	0.177359i
$823$	40.7068	−	16.1170i	1.41895	−	0.561802i	0.471546	−	0.881841i	$-0.343696\pi$
$823$	40.7068	−	16.1170i	1.41895	−	0.561802i	0.947404	+	0.320039i	$0.103696\pi$
$824$	−3.60615	−	11.0986i	−0.125626	−	0.386638i
$825$	−2.45889	+	0.870525i	−0.0856075	+	0.0303078i
$826$	−7.79389	+	23.9871i	−0.271184	+	0.834618i
$827$	2.84158	+	45.1657i	0.0988116	+	1.57056i	0.665351	+	0.746530i	$0.268282\pi$
$827$	2.84158	+	45.1657i	0.0988116	+	1.57056i	−0.566540	+	0.824034i	$0.691718\pi$
$828$	1.80820	−	0.228428i	0.0628392	−	0.00793844i
$829$	34.2241	−	32.1386i	1.18865	−	1.11622i	0.197945	−	0.980213i	$-0.436573\pi$
$829$	34.2241	−	32.1386i	1.18865	−	1.11622i	0.990708	−	0.136006i	$-0.0434267\pi$
$830$	−25.2378	+	51.1723i	−0.876018	+	1.77622i
$831$	16.7727	+	2.11889i	0.581839	+	0.0735034i
$832$	−0.734726	+	2.26125i	−0.0254720	+	0.0783949i
$833$	−11.1745	−	10.4936i	−0.387175	−	0.363581i
$834$	28.5736	−	7.33646i	0.989424	−	0.254041i
$835$	57.3278	−	6.17496i	1.98391	−	0.213693i
$836$	−0.559440	−	0.676246i	−0.0193486	−	0.0233885i
$837$	5.11821	−	1.31413i	0.176911	−	0.0454231i
$838$	−42.8173	+	51.7573i	−1.47910	+	1.78793i
$839$	−11.9120	+	4.71628i	−0.411246	+	0.162824i	−0.564633	−	0.825342i	$-0.690982\pi$
$839$	−11.9120	+	4.71628i	−0.411246	+	0.162824i	0.153386	+	0.988166i	$0.450982\pi$
$840$	−1.61131	−	2.64516i	−0.0555954	−	0.0912668i
$841$	−12.8439	−	20.2388i	−0.442894	−	0.697889i
$842$	−11.6527	−	61.0857i	−0.401580	−	2.10515i
$843$	0.283842	+	0.873577i	0.00977605	+	0.0300876i
$844$	−10.1206	+	21.5073i	−0.348364	+	0.740312i
$845$	−20.2726	+	18.3485i	−0.697399	+	0.631206i
$846$	−6.99015	−	3.84287i	−0.240326	−	0.132120i
$847$	−11.7899	−	6.48158i	−0.405107	−	0.222710i
$848$	13.9252	+	16.8327i	0.478195	+	0.578038i
$849$	−10.8770	−	7.90261i	−0.373298	−	0.271217i
$850$	−19.6281	+	17.1200i	−0.673238	+	0.587212i
$851$	3.36365	−	2.44384i	0.115305	−	0.0837737i
$852$	−0.468419	−	0.120269i	−0.0160478	−	0.00412036i
$853$	13.2141	+	28.0813i	0.452441	+	0.961487i	0.992770	+	0.120033i	$0.0382999\pi$
$853$	13.2141	+	28.0813i	0.452441	+	0.961487i	−0.540329	+	0.841454i	$0.681700\pi$
$854$	−1.72467	+	9.04103i	−0.0590169	+	0.309378i
$855$	−0.119351	−	2.68223i	−0.00408171	−	0.0917303i
$856$	−0.423879	−	0.398049i	−0.0144879	−	0.0136050i
$857$	−14.5819	−	10.5944i	−0.498110	−	0.361898i	0.310185	−	0.950676i	$-0.399609\pi$
$857$	−14.5819	−	10.5944i	−0.498110	−	0.361898i	−0.808294	+	0.588778i	$0.799609\pi$
$858$	0.359879	−	0.764781i	0.0122861	−	0.0261092i
$859$	−20.0082	+	24.1858i	−0.682672	+	0.825209i	−0.992065	−	0.125726i	$-0.959874\pi$
$859$	−20.0082	+	24.1858i	−0.682672	+	0.825209i	0.309393	+	0.950934i	$0.399874\pi$
$860$	4.87745	−	7.38239i	0.166320	−	0.251738i
$861$	−0.475592	−	7.55932i	−0.0162081	−	0.257621i
$862$	−2.27082	+	36.0937i	−0.0773446	+	1.22936i
$863$	42.4400	+	16.8032i	1.44467	+	0.571987i	0.954120	−	0.299423i	$-0.0967943\pi$
$863$	42.4400	+	16.8032i	1.44467	+	0.571987i	0.490554	+	0.871411i	$0.336794\pi$
$864$	−3.59829	+	5.67000i	−0.122416	+	0.192897i
$865$	−18.1444	−	13.6987i	−0.616928	−	0.465771i
$866$	1.08699	−	17.2772i	0.0369374	−	0.587103i
$867$	−8.95081	−	1.13075i	−0.303985	−	0.0384023i
$868$	7.51202	−	5.45780i	0.254975	−	0.185250i
$869$	−1.44795	−	7.59042i	−0.0491183	−	0.257487i
$870$	−4.81132	−	7.89837i	−0.163119	−	0.267780i
$871$	3.26575	+	6.94007i	0.110656	+	0.235155i
$872$	10.6864	−	10.0352i	0.361888	−	0.339835i
$873$	−7.81862	+	12.3202i	−0.264620	+	0.416975i
$874$	−2.88045			−0.0974328
$875$	−13.9867	+	0.988695i	−0.472838	+	0.0334240i
$876$	−1.76862			−0.0597560
$877$	14.0533	−	22.1445i	0.474547	−	0.747766i	−0.519761	−	0.854312i	$-0.673979\pi$
$877$	14.0533	−	22.1445i	0.474547	−	0.747766i	0.994308	+	0.106546i	$0.0339790\pi$
$878$	14.1175	−	13.2572i	0.476441	−	0.447408i
$879$	−11.2991	−	24.0118i	−0.381108	−	0.809897i
$880$	−5.20950	−	2.17408i	−0.175612	−	0.0732881i
$881$	0.213970	+	1.12167i	0.00720884	+	0.0377900i	0.985710	−	0.168452i	$-0.0538767\pi$
$881$	0.213970	+	1.12167i	0.00720884	+	0.0377900i	−0.978501	+	0.206242i	$0.933877\pi$
$882$	−8.09730	+	5.88303i	−0.272650	+	0.198092i
$883$	31.1305	+	3.93269i	1.04762	+	0.132346i	0.630252	−	0.776390i	$-0.282952\pi$
$883$	31.1305	+	3.93269i	1.04762	+	0.132346i	0.417371	+	0.908736i	$0.362952\pi$
$884$	0.218307	−	3.46989i	0.00734245	−	0.116705i
$885$	−7.95961	+	23.0482i	−0.267559	+	0.774755i
$886$	−7.81005	+	12.3067i	−0.262384	+	0.413451i
$887$	−25.7939	−	10.2125i	−0.866075	−	0.342903i	−0.107277	−	0.994229i	$-0.534213\pi$
$887$	−25.7939	−	10.2125i	−0.866075	−	0.342903i	−0.758798	+	0.651326i	$0.774213\pi$
$888$	−0.221662	+	3.52322i	−0.00743849	+	0.118231i
$889$	1.24188	+	19.7392i	0.0416514	+	0.662030i
$890$	8.55164	+	10.7325i	0.286652	+	0.359754i
$891$	0.332536	−	0.401967i	0.0111404	−	0.0134664i
$892$	−13.5431	+	28.7806i	−0.453457	+	0.963646i
$893$	4.20163	+	3.05266i	0.140602	+	0.102153i
$894$	−16.8905	−	15.8612i	−0.564902	−	0.530478i
$895$	−7.00621	+	10.6044i	−0.234192	+	0.354467i
$896$	1.98332	−	10.3969i	0.0662580	−	0.347337i
$897$	−0.486569	−	1.03401i	−0.0162461	−	0.0345247i
$898$	29.0267	+	7.45279i	0.968633	+	0.248703i
$899$	−9.58761	+	6.96581i	−0.319765	+	0.232323i
$900$	3.53404	+	6.04886i	0.117801	+	0.201629i
$901$	−10.3161	−	7.49508i	−0.343679	−	0.249697i
$902$	−3.70379	−	4.47711i	−0.123323	−	0.149072i
$903$	−3.10378	−	1.70632i	−0.103287	−	0.0567828i
$904$	−13.7776	−	7.57429i	−0.458236	−	0.251917i
$905$	−3.17026	+	15.1064i	−0.105383	+	0.502154i
$906$	1.32964	−	2.82563i	0.0441744	−	0.0938754i
$907$	−3.90164	−	12.0080i	−0.129552	−	0.398720i	0.865151	−	0.501511i	$-0.167222\pi$
$907$	−3.90164	−	12.0080i	−0.129552	−	0.398720i	−0.994703	+	0.102792i	$0.967222\pi$
$908$	3.29573	+	17.2768i	0.109373	+	0.573351i
$909$	6.95195	+	10.9545i	0.230582	+	0.363339i
$910$	2.95993	−	3.44705i	0.0981207	−	0.114268i
$911$	−36.6993	+	14.5303i	−1.21590	+	0.481409i	−0.886477	−	0.462773i	$-0.846855\pi$
$911$	−36.6993	+	14.5303i	−1.21590	+	0.481409i	−0.329424	+	0.944182i	$0.606855\pi$
$912$	3.70368	−	4.47698i	0.122641	−	0.148248i
$913$	6.99139	−	1.79508i	0.231381	−	0.0594086i
$914$	19.3678	+	23.4116i	0.640628	+	0.774387i
$915$	−1.82761	+	8.70866i	−0.0604191	+	0.287899i
$916$	36.4675	−	9.36326i	1.20492	−	0.309371i
$917$	11.7188	+	11.0047i	0.386990	+	0.363408i
$918$	1.60969	−	4.95411i	0.0531276	−	0.163510i
$919$	−12.7960	−	1.61650i	−0.422100	−	0.0533236i	−0.0885852	−	0.996069i	$-0.528235\pi$
$919$	−12.7960	−	1.61650i	−0.422100	−	0.0533236i	−0.333514	+	0.942745i	$0.608235\pi$
$920$	−2.84311	+	1.49569i	−0.0937346	+	0.0493116i
$921$	−4.87630	+	4.57915i	−0.160679	+	0.150888i
$922$	−17.6338	+	2.22767i	−0.580738	+	0.0733643i
$923$	0.0190400	+	0.302633i	0.000626710	+	0.00996127i
$924$	0.283276	−	0.871835i	0.00931910	−	0.0286813i
$925$	13.7124	+	8.20814i	0.450862	+	0.269882i
$926$	−7.33876	−	22.5864i	−0.241167	−	0.742234i
$927$	9.82396	−	3.88958i	0.322661	−	0.127751i
$928$	2.82208	−	14.7939i	0.0926393	−	0.485632i
$929$	26.0280	−	3.28810i	0.853950	−	0.107879i	0.313842	−	0.949475i	$-0.398384\pi$
$929$	26.0280	−	3.28810i	0.853950	−	0.107879i	0.540107	+	0.841596i	$0.318384\pi$
$930$	17.8615	−	12.4825i	0.585703	−	0.409319i
$931$	5.71043	−	3.13933i	0.187152	−	0.102887i
$932$	−9.67722			−0.316988
$933$	2.92405	−	1.60751i	0.0957290	−	0.0526275i
$934$	10.6731	+	4.22577i	0.349234	+	0.138271i
$935$	3.26080	+	0.472921i	0.106639	+	0.0154662i
$936$	0.939811	+	0.241303i	0.0307187	+	0.00788722i
$937$	−29.0416	−	45.7623i	−0.948748	−	1.49499i	−0.866984	−	0.498336i	$-0.833945\pi$
$937$	−29.0416	−	45.7623i	−0.948748	−	1.49499i	−0.0817643	−	0.996652i	$-0.526055\pi$
$938$	10.8200	+	17.0496i	0.353285	+	0.556688i
$939$	16.4658	+	4.22769i	0.537340	+	0.137966i
$940$	−13.4109	−	1.94502i	−0.437416	−	0.0634394i
$941$	−45.1248	−	17.8662i	−1.47103	−	0.582421i	−0.510320	−	0.859985i	$-0.670473\pi$
$941$	−45.1248	−	17.8662i	−1.47103	−	0.582421i	−0.960707	+	0.277564i	$0.910473\pi$
$942$	11.0261	−	6.06167i	0.359251	−	0.197500i
$943$	−7.85609			−0.255830
$944$	−46.2422	+	25.4219i	−1.50506	+	0.827412i
$945$	2.29863	−	1.60640i	0.0747745	−	0.0522562i
$946$	−2.69572	+	0.340549i	−0.0876454	+	0.0110722i
$947$	1.37082	−	7.18611i	0.0445458	−	0.233517i	−0.953050	−	0.302811i	$-0.902075\pi$
$947$	1.37082	−	7.18611i	0.0445458	−	0.233517i	0.997596	+	0.0692943i	$0.0220748\pi$
$948$	−19.2961	+	7.63987i	−0.626708	+	0.248131i
$949$	0.342683	+	1.05467i	0.0111240	+	0.0342360i
$950$	−4.34313	−	10.1845i	−0.140910	−	0.330428i
$951$	9.16419	−	28.2045i	0.297169	−	0.914593i
$952$	0.245663	+	3.90470i	0.00796197	+	0.126552i
$953$	5.03475	−	0.636036i	0.163091	−	0.0206032i	−0.0433634	−	0.999059i	$-0.513807\pi$
$953$	5.03475	−	0.636036i	0.163091	−	0.0206032i	0.206455	+	0.978456i	$0.433807\pi$
$954$	−6.06916	+	5.69932i	−0.196496	+	0.184522i
$955$	−3.96599	+	2.08641i	−0.128336	+	0.0675148i
$956$	−25.0621	−	3.16608i	−0.810567	−	0.102398i
$957$	−0.361546	+	1.11272i	−0.0116871	+	0.0359693i
$958$	0.267608	+	0.251301i	0.00864602	+	0.00811916i
$959$	3.40973	−	0.875471i	0.110106	−	0.0282704i
$960$	−1.24295	+	5.92268i	−0.0401159	+	0.191154i
$961$	1.96131	+	2.37082i	0.0632681	+	0.0764780i
$962$	−5.01582	+	1.28784i	−0.161717	+	0.0415218i
$963$	0.335589	−	0.405658i	0.0108142	−	0.0130721i
$964$	19.4493	−	7.70051i	0.626419	−	0.248017i
$965$	−19.1091	+	22.2539i	−0.615145	+	0.716380i
$966$	−1.61209	−	2.54024i	−0.0518680	−	0.0817309i
$967$	8.74872	+	45.8624i	0.281340	+	1.47484i	0.789595	+	0.613629i	$0.210291\pi$
$967$	8.74872	+	45.8624i	0.281340	+	1.47484i	−0.508255	+	0.861207i	$0.669709\pi$
$968$	−3.66141	−	11.2687i	−0.117682	−	0.362188i
$969$	−1.44402	+	3.06870i	−0.0463886	+	0.0985808i
$970$	−12.3588	+	58.8901i	−0.396817	+	1.89085i
$971$	−44.8933	−	24.6803i	−1.44069	−	0.792028i	−0.446012	−	0.895027i	$-0.647156\pi$
$971$	−44.8933	−	24.6803i	−1.44069	−	0.792028i	−0.994681	+	0.102999i	$0.967156\pi$
$972$	−1.22781	−	0.674993i	−0.0393819	−	0.0216504i
$973$	−12.7876	−	15.4576i	−0.409952	−	0.495547i
$974$	0.119052	+	0.0864966i	0.00381468	+	0.00277153i
$975$	2.92233	−	3.27945i	0.0935896	−	0.105026i
$976$	−15.5793	+	11.3190i	−0.498681	+	0.362313i
$977$	−28.5468	−	7.32957i	−0.913293	−	0.234494i	−0.237330	−	0.971429i	$-0.576272\pi$
$977$	−28.5468	−	7.32957i	−0.913293	−	0.234494i	−0.675963	+	0.736935i	$0.736272\pi$
$978$	−11.7753	−	25.0239i	−0.376534	−	0.800175i
$979$	0.325301	−	1.70529i	0.0103967	−	0.0545012i
$980$	−9.37287	+	14.1866i	−0.299405	+	0.453173i
$981$	9.67562	+	9.08601i	0.308919	+	0.290094i
$982$	−36.2551	−	26.3409i	−1.15695	−	0.840571i
$983$	−5.00625	+	10.6388i	−0.159674	+	0.339326i	−0.968615	−	0.248564i	$-0.920041\pi$
$983$	−5.00625	+	10.6388i	−0.159674	+	0.339326i	0.808941	+	0.587890i	$0.200041\pi$
$984$	4.25186	−	5.13961i	0.135544	−	0.163845i
$985$	0.607133	+	0.761965i	0.0193449	+	0.0242782i
$986$	0.733541	+	11.6593i	0.0233607	+	0.371308i
$987$	−0.340610	+	5.41384i	−0.0108417	+	0.172324i
$988$	1.37418	+	0.544076i	0.0437185	+	0.0173094i
$989$	−1.96846	+	3.10179i	−0.0625933	+	0.0986313i
$990$	0.702256	−	2.03348i	0.0223192	−	0.0646282i
$991$	0.694187	−	11.0338i	0.0220516	−	0.350500i	−0.971494	−	0.237065i	$-0.923815\pi$
$991$	0.694187	−	11.0338i	0.0220516	−	0.350500i	0.993545	−	0.113435i	$-0.0361854\pi$
$992$	35.2059	+	4.44754i	1.11779	+	0.141209i
$993$	−1.24946	+	0.907788i	−0.0396505	+	0.0288078i
$994$	0.149590	+	0.784180i	0.00474472	+	0.0248727i
$995$	−22.1640	−	9.24967i	−0.702645	−	0.293234i
$996$	−8.25421	−	17.5411i	−0.261545	−	0.555810i
$997$	−6.51706	+	6.11993i	−0.206398	+	0.193820i	−0.780851	−	0.624717i	$-0.785214\pi$
$997$	−6.51706	+	6.11993i	−0.206398	+	0.193820i	0.574454	+	0.818537i	$0.305214\pi$
$998$	36.9589	−	58.2380i	1.16992	−	1.84349i
$999$	−3.19627			−0.101126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.m.b.106.3	yes	260
125.46	even	25	inner	375.2.m.b.46.3	✓	260

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.2.m.b.46.3	✓	260	125.46	even	25	inner
375.2.m.b.106.3	yes	260	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988178 + 1.55712i) q^{2} +(-0.728969 + 0.684547i) q^{3} +(-0.596566 - 1.26777i) q^{4} +(-1.45672 + 1.69646i) q^{5} +(-0.345571 - 1.81155i) q^{6} +(-1.01461 + 0.737161i) q^{7} +(-1.09576 - 0.138427i) q^{8} +(0.0627905 - 0.998027i) q^{9} +(-1.20208 - 3.94469i) q^{10} +(-0.279534 + 0.440475i) q^{11} +(1.30272 + 0.515785i) q^{12} +(0.0551626 - 0.876784i) q^{13} +(-0.145227 - 2.30832i) q^{14} +(-0.0993996 - 2.23386i) q^{15} +(3.08456 - 3.72860i) q^{16} +(-1.20263 + 2.55572i) q^{17} +(1.49200 + 1.08400i) q^{18} +(-0.875284 - 0.821947i) q^{19} +(3.01974 + 0.834736i) q^{20} +(0.235001 - 1.23192i) q^{21} +(-0.409643 - 0.870536i) q^{22} +(-1.25993 - 0.323495i) q^{23} +(0.893534 - 0.649190i) q^{24} +(-0.755925 - 4.94253i) q^{25} +(1.31075 + 0.952313i) q^{26} +(0.637424 + 0.770513i) q^{27} +(1.53983 + 0.846530i) q^{28} +(-1.96529 - 1.08043i) q^{29} +(3.57661 + 2.05267i) q^{30} +(2.24991 - 4.78131i) q^{31} +(2.07517 + 6.38672i) q^{32} +(-0.0977545 - 0.512447i) q^{33} +(-2.79115 - 4.39815i) q^{34} +(0.227450 - 2.79509i) q^{35} +(-1.30272 + 0.515785i) q^{36} +(-2.03738 + 2.46277i) q^{37} +(2.14481 - 0.550693i) q^{38} +(0.559988 + 0.676910i) q^{39} +(1.83105 - 1.65726i) q^{40} +(5.84970 - 1.50195i) q^{41} +(1.68602 + 1.58328i) q^{42} +(0.872719 - 2.68595i) q^{43} +(0.725181 + 0.0916116i) q^{44} +(1.60164 + 1.56037i) q^{45} +(1.74876 - 1.64219i) q^{46} +(-4.29123 + 0.542108i) q^{47} +(0.303850 + 4.82956i) q^{48} +(-1.67708 + 5.16153i) q^{49} +(8.44309 + 3.70703i) q^{50} +(-0.872832 - 2.68630i) q^{51} +(-1.14447 + 0.453126i) q^{52} +(-0.845932 + 4.43453i) q^{53} +(-1.82967 + 0.231141i) q^{54} +(-0.340043 - 1.11587i) q^{55} +(1.21382 - 0.667301i) q^{56} +1.20072 q^{57} +(3.62442 - 1.99254i) q^{58} +(-10.1390 - 4.01432i) q^{59} +(-2.77271 + 1.45866i) q^{60} +(-3.85445 - 0.989654i) q^{61} +(5.22176 + 8.22817i) q^{62} +(0.671998 + 1.05890i) q^{63} +(-2.62138 - 0.673055i) q^{64} +(1.40707 + 1.37081i) q^{65} +(0.894540 + 0.354173i) q^{66} +(-7.65075 + 4.20604i) q^{67} +3.95752 q^{68} +(1.13990 - 0.626664i) q^{69} +(4.12752 + 3.11621i) q^{70} +(-0.342440 + 0.0432603i) q^{71} +(-0.206957 + 1.08491i) q^{72} +(-1.17365 + 0.464680i) q^{73} +(-1.82153 - 5.60610i) q^{74} +(3.93444 + 3.08548i) q^{75} +(-0.519873 + 1.60000i) q^{76} +(-0.0410816 - 0.652974i) q^{77} +(-1.60740 + 0.203061i) q^{78} +(-10.7976 + 10.1396i) q^{79} +(1.83205 + 10.6643i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-3.44183 + 10.5929i) q^{82} +(-10.0862 - 9.47153i) q^{83} +(-1.70198 + 0.436994i) q^{84} +(-2.58377 - 5.76319i) q^{85} +(3.31995 + 4.01313i) q^{86} +(2.17224 - 0.557737i) q^{87} +(0.367276 - 0.443960i) q^{88} +(-3.09405 + 1.22502i) q^{89} +(-4.01239 + 0.952023i) q^{90} +(0.590362 + 0.930261i) q^{91} +(0.341515 + 1.79029i) q^{92} +(1.63292 + 5.02560i) q^{93} +(3.39637 - 7.21765i) q^{94} +(2.66944 - 0.287534i) q^{95} +(-5.88475 - 3.23517i) q^{96} +(-12.7868 - 7.02960i) q^{97} +(-6.37986 - 7.71193i) q^{98} +(0.422054 + 0.306640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 260 q + 10 q^{4} - 20 q^{5} + 10 q^{7} - 15 q^{8} + 10 q^{10} + 10 q^{11} - 40 q^{15} - 10 q^{16} - 5 q^{17} - 5 q^{19} - 25 q^{20} + 5 q^{21} - 25 q^{22} + 75 q^{23} + 20 q^{25} - 90 q^{26} - 15 q^{28}+ \cdots - 20 q^{98}+O(q^{100}) \) 260 * q + 10 * q^4 - 20 * q^5 + 10 * q^7 - 15 * q^8 + 10 * q^10 + 10 * q^11 - 40 * q^15 - 10 * q^16 - 5 * q^17 - 5 * q^19 - 25 * q^20 + 5 * q^21 - 25 * q^22 + 75 * q^23 + 20 * q^25 - 90 * q^26 - 15 * q^28 + 5 * q^29 - 20 * q^30 - 5 * q^31 - 5 * q^33 - 15 * q^34 + 10 * q^35 - 10 * q^37 + 15 * q^38 + 25 * q^40 - 10 * q^41 + 10 * q^42 - 10 * q^43 - 15 * q^44 + 5 * q^45 - 60 * q^46 - 80 * q^47 + 10 * q^48 - 205 * q^49 - 80 * q^50 - 20 * q^51 - 70 * q^52 - 40 * q^53 - 5 * q^55 + 135 * q^56 - 80 * q^57 + 85 * q^58 + 40 * q^59 + 60 * q^60 + 20 * q^61 - 55 * q^62 - 5 * q^63 - 25 * q^64 + 40 * q^65 - 35 * q^66 + 30 * q^67 - 200 * q^68 - 155 * q^70 + 145 * q^71 - 15 * q^72 - 10 * q^73 + 60 * q^74 + 5 * q^75 + 90 * q^76 - 40 * q^77 + 15 * q^78 + 10 * q^79 + 100 * q^80 + 70 * q^82 - 95 * q^83 + 20 * q^84 - 125 * q^85 - 20 * q^86 - 250 * q^88 - 110 * q^89 - 15 * q^90 + 110 * q^91 - 40 * q^92 + 120 * q^93 + 60 * q^94 + 25 * q^95 + 30 * q^96 - 30 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

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