LMFDB - Embedded newform 300.2.w.a.103.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.14
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.253401 - 1.39133i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.87158 + 0.705127i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(-0.467933 - 1.33456i) q^{6} +(1.04258 + 1.04258i) q^{7} +(1.45532 + 2.42529i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.253401 - 1.39133i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.87158 + 0.705127i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(-0.467933 - 1.33456i) q^{6} +(1.04258 + 1.04258i) q^{7} +(1.45532 + 2.42529i) q^{8} +(0.951057 - 0.309017i) q^{9} +(3.13246 + 0.433253i) q^{10} +(4.52673 + 1.47082i) q^{11} +(-1.73823 + 0.989225i) q^{12} +(2.54390 - 4.99269i) q^{13} +(1.18638 - 1.71477i) q^{14} +(-0.357381 + 2.20732i) q^{15} +(3.00559 - 2.63940i) q^{16} +(0.262171 - 1.65528i) q^{17} +(-0.670942 - 1.24492i) q^{18} +(-2.76811 + 2.01115i) q^{19} +(-0.190971 - 4.46806i) q^{20} +(1.19285 + 0.866653i) q^{21} +(0.899317 - 6.67086i) q^{22} +(3.62217 + 7.10891i) q^{23} +(1.81680 + 2.16777i) q^{24} +(-4.02480 - 2.96664i) q^{25} +(-7.59109 - 2.27425i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-2.68643 - 1.21612i) q^{28} +(-4.76887 + 6.56378i) q^{29} +(3.16167 - 0.0621050i) q^{30} +(-1.29321 - 1.77995i) q^{31} +(-4.43388 - 3.51293i) q^{32} +(4.70108 + 0.744578i) q^{33} +(-2.36947 + 0.0546849i) q^{34} +(-2.94272 + 1.48668i) q^{35} +(-1.56208 + 1.24896i) q^{36} +(1.10983 + 0.565484i) q^{37} +(3.49960 + 3.34171i) q^{38} +(1.73155 - 5.32918i) q^{39} +(-6.16813 + 1.39791i) q^{40} +(-1.73027 - 5.32522i) q^{41} +(0.903528 - 1.87925i) q^{42} +(2.44396 - 2.44396i) q^{43} +(-9.50923 + 0.439160i) q^{44} +(-0.00767928 + 2.23605i) q^{45} +(8.97295 - 6.84103i) q^{46} +(0.899254 + 5.67766i) q^{47} +(2.55570 - 3.07708i) q^{48} -4.82603i q^{49} +(-3.10767 + 6.35156i) q^{50} -1.67591i q^{51} +(-1.24063 + 11.1380i) q^{52} +(-0.680800 - 4.29840i) q^{53} +(-0.857431 - 1.12464i) q^{54} +(-6.28532 + 8.58881i) q^{55} +(-1.01128 + 4.04587i) q^{56} +(-2.41941 + 2.41941i) q^{57} +(10.3408 + 4.97178i) q^{58} +(-3.92044 - 12.0659i) q^{59} +(-0.887578 - 4.38317i) q^{60} +(2.15405 - 6.62949i) q^{61} +(-2.14879 + 2.25032i) q^{62} +(1.31373 + 0.669381i) q^{63} +(-3.76408 + 7.05915i) q^{64} +(8.82932 + 8.89017i) q^{65} +(-0.155308 - 6.72942i) q^{66} +(7.39906 + 1.17190i) q^{67} +(0.676511 + 3.28285i) q^{68} +(4.68966 + 6.45476i) q^{69} +(2.81415 + 3.71756i) q^{70} +(-7.39857 + 10.1833i) q^{71} +(2.13355 + 1.85687i) q^{72} +(-9.08821 + 4.63068i) q^{73} +(0.505542 - 1.68742i) q^{74} +(-4.43934 - 2.30050i) q^{75} +(3.76261 - 5.71588i) q^{76} +(3.18604 + 6.25296i) q^{77} +(-7.85340 - 1.05874i) q^{78} +(-7.49468 - 5.44520i) q^{79} +(3.50796 + 8.22765i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-6.97066 + 3.75678i) q^{82} +(0.974493 - 6.15271i) q^{83} +(-2.84360 - 0.780899i) q^{84} +(3.33315 + 1.71277i) q^{85} +(-4.01965 - 2.78105i) q^{86} +(-3.68335 + 7.22899i) q^{87} +(3.02066 + 13.1192i) q^{88} +(1.92856 + 0.626628i) q^{89} +(3.11303 - 0.555934i) q^{90} +(7.85754 - 2.55307i) q^{91} +(-11.7919 - 10.7508i) q^{92} +(-1.55574 - 1.55574i) q^{93} +(7.67161 - 2.68988i) q^{94} +(-2.33924 - 7.28448i) q^{95} +(-4.92884 - 2.77607i) q^{96} +(-3.36367 + 0.532753i) q^{97} +(-6.71459 + 1.22292i) q^{98} +4.75968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−0.253401	−	1.39133i	−0.179182	−	0.983816i
$2$	−0.253401	−	1.39133i	−0.179182	−	0.983816i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$4$	−1.87158	+	0.705127i	−0.935788	+	0.352563i
$5$	−0.698282	+	2.12424i	−0.312281	+	0.949990i
$5$	−0.698282	+	2.12424i	−0.312281	+	0.949990i
$6$	−0.467933	−	1.33456i	−0.191033	−	0.544830i
$7$	1.04258	+	1.04258i	0.394060	+	0.394060i	0.876132	−	0.482072i	$-0.160116\pi$
$7$	1.04258	+	1.04258i	0.394060	+	0.394060i	−0.482072	+	0.876132i	$0.660116\pi$
$8$	1.45532	+	2.42529i	0.514534	+	0.857470i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	3.13246	+	0.433253i	0.990570	+	0.137007i
$11$	4.52673	+	1.47082i	1.36486	+	0.443470i	0.897663	−	0.440683i	$-0.145264\pi$
$11$	4.52673	+	1.47082i	1.36486	+	0.443470i	0.467197	+	0.884153i	$0.345264\pi$
$12$	−1.73823	+	0.989225i	−0.501783	+	0.285565i
$13$	2.54390	−	4.99269i	0.705552	−	1.38472i	−0.208052	−	0.978118i	$-0.566712\pi$
$13$	2.54390	−	4.99269i	0.705552	−	1.38472i	0.913604	−	0.406606i	$-0.133288\pi$
$14$	1.18638	−	1.71477i	0.317074	−	0.458291i
$15$	−0.357381	+	2.20732i	−0.0922753	+	0.569929i
$16$	3.00559	−	2.63940i	0.751398	−	0.659849i
$17$	0.262171	−	1.65528i	0.0635858	−	0.401465i	−0.935282	−	0.353902i	$-0.884855\pi$
$17$	0.262171	−	1.65528i	0.0635858	−	0.401465i	0.998868	−	0.0475627i	$-0.0151454\pi$
$18$	−0.670942	−	1.24492i	−0.158143	−	0.293431i
$19$	−2.76811	+	2.01115i	−0.635047	+	0.461389i	−0.858145	−	0.513407i	$-0.828383\pi$
$19$	−2.76811	+	2.01115i	−0.635047	+	0.461389i	0.223098	+	0.974796i	$0.428383\pi$
$20$	−0.190971	−	4.46806i	−0.0427025	−	0.999088i
$21$	1.19285	+	0.866653i	0.260300	+	0.189119i
$22$	0.899317	−	6.67086i	0.191735	−	1.42223i
$23$	3.62217	+	7.10891i	0.755275	+	1.48231i	0.872189	+	0.489169i	$0.162700\pi$
$23$	3.62217	+	7.10891i	0.755275	+	1.48231i	−0.116914	+	0.993142i	$0.537300\pi$
$24$	1.81680	+	2.16777i	0.370853	+	0.442494i
$25$	−4.02480	−	2.96664i	−0.804961	−	0.593328i
$26$	−7.59109	−	2.27425i	−1.48874	−	0.446016i
$27$	0.891007	−	0.453990i	0.171474	−	0.0873705i
$28$	−2.68643	−	1.21612i	−0.507688	−	0.229825i
$29$	−4.76887	+	6.56378i	−0.885556	+	1.21886i	0.0892946	+	0.996005i	$0.471539\pi$
$29$	−4.76887	+	6.56378i	−0.885556	+	1.21886i	−0.974851	+	0.222858i	$0.928461\pi$
$30$	3.16167	−	0.0621050i	0.577239	−	0.0113388i
$31$	−1.29321	−	1.77995i	−0.232268	−	0.319689i	0.676935	−	0.736043i	$-0.263308\pi$
$31$	−1.29321	−	1.77995i	−0.232268	−	0.319689i	−0.909203	+	0.416354i	$0.863308\pi$
$32$	−4.43388	−	3.51293i	−0.783807	−	0.621005i
$33$	4.70108	+	0.744578i	0.818354	+	0.129614i
$34$	−2.36947	+	0.0546849i	−0.406361	+	0.00937839i
$35$	−2.94272	+	1.48668i	−0.497411	+	0.251295i
$36$	−1.56208	+	1.24896i	−0.260346	+	0.208161i
$37$	1.10983	+	0.565484i	0.182454	+	0.0929650i	0.542832	−	0.839842i	$-0.317352\pi$
$37$	1.10983	+	0.565484i	0.182454	+	0.0929650i	−0.360378	+	0.932807i	$0.617352\pi$
$38$	3.49960	+	3.34171i	0.567710	+	0.542097i
$39$	1.73155	−	5.32918i	0.277271	−	0.853351i
$40$	−6.16813	+	1.39791i	−0.975267	+	0.221030i
$41$	−1.73027	−	5.32522i	−0.270222	−	0.831659i	−0.990444	−	0.137915i	$-0.955960\pi$
$41$	−1.73027	−	5.32522i	−0.270222	−	0.831659i	0.720222	−	0.693744i	$-0.244040\pi$
$42$	0.903528	−	1.87925i	0.139417	−	0.289974i
$43$	2.44396	−	2.44396i	0.372701	−	0.372701i	−0.495759	−	0.868460i	$-0.665110\pi$
$43$	2.44396	−	2.44396i	0.372701	−	0.372701i	0.868460	+	0.495759i	$0.165110\pi$
$44$	−9.50923	+	0.439160i	−1.43357	+	0.0662059i
$45$	−0.00767928	+	2.23605i	−0.00114476	+	0.333331i
$46$	8.97295	−	6.84103i	1.32299	−	1.00865i
$47$	0.899254	+	5.67766i	0.131170	+	0.828172i	0.962279	+	0.272064i	$0.0877062\pi$
$47$	0.899254	+	5.67766i	0.131170	+	0.828172i	−0.831110	+	0.556109i	$0.812294\pi$
$48$	2.55570	−	3.07708i	0.368883	−	0.444138i
$49$		−	4.82603i		−	0.689433i
$50$	−3.10767	+	6.35156i	−0.439492	+	0.898247i
$51$		−	1.67591i		−	0.234675i
$52$	−1.24063	+	11.1380i	−0.172044	+	1.54456i
$53$	−0.680800	−	4.29840i	−0.0935150	−	0.590431i	−0.989295	−	0.145932i	$-0.953382\pi$
$53$	−0.680800	−	4.29840i	−0.0935150	−	0.590431i	0.895780	−	0.444498i	$-0.146618\pi$
$54$	−0.857431	−	1.12464i	−0.116682	−	0.153044i
$55$	−6.28532	+	8.58881i	−0.847512	+	1.15812i
$56$	−1.01128	+	4.04587i	−0.135138	+	0.540652i
$57$	−2.41941	+	2.41941i	−0.320459	+	0.320459i
$58$	10.3408	+	4.97178i	1.35781	+	0.652826i
$59$	−3.92044	−	12.0659i	−0.510398	−	1.57084i	−0.791502	−	0.611166i	$-0.790701\pi$
$59$	−3.92044	−	12.0659i	−0.510398	−	1.57084i	0.281104	−	0.959677i	$-0.409299\pi$
$60$	−0.887578	−	4.38317i	−0.114586	−	0.565865i
$61$	2.15405	−	6.62949i	0.275798	−	0.848819i	−0.713209	−	0.700951i	$-0.752759\pi$
$61$	2.15405	−	6.62949i	0.275798	−	0.848819i	0.989007	−	0.147867i	$-0.0472409\pi$
$62$	−2.14879	+	2.25032i	−0.272897	+	0.285791i
$63$	1.31373	+	0.669381i	0.165515	+	0.0843340i
$64$	−3.76408	+	7.05915i	−0.470511	+	0.882394i
$65$	8.82932	+	8.89017i	1.09514	+	1.10269i
$66$	−0.155308	−	6.72942i	−0.0191171	−	0.828334i
$67$	7.39906	+	1.17190i	0.903939	+	0.143170i	0.591064	−	0.806625i	$-0.298708\pi$
$67$	7.39906	+	1.17190i	0.903939	+	0.143170i	0.312875	+	0.949794i	$0.398708\pi$
$68$	0.676511	+	3.28285i	0.0820390	+	0.398104i
$69$	4.68966	+	6.45476i	0.564568	+	0.777061i
$70$	2.81415	+	3.71756i	0.336355	+	0.444333i
$71$	−7.39857	+	10.1833i	−0.878049	+	1.20853i	0.0989090	+	0.995096i	$0.468465\pi$
$71$	−7.39857	+	10.1833i	−0.878049	+	1.20853i	−0.976958	+	0.213434i	$0.931535\pi$
$72$	2.13355	+	1.85687i	0.251441	+	0.218834i
$73$	−9.08821	+	4.63068i	−1.06369	+	0.541980i	−0.896089	−	0.443874i	$-0.853604\pi$
$73$	−9.08821	+	4.63068i	−1.06369	+	0.541980i	−0.167606	+	0.985854i	$0.553604\pi$
$74$	0.505542	−	1.68742i	0.0587681	−	0.196159i
$75$	−4.43934	−	2.30050i	−0.512610	−	0.265639i
$76$	3.76261	−	5.71588i	0.431601	−	0.655657i
$77$	3.18604	+	6.25296i	0.363083	+	0.712590i
$78$	−7.85340	−	1.05874i	−0.889223	−	0.119878i
$79$	−7.49468	−	5.44520i	−0.843218	−	0.612633i	0.0800501	−	0.996791i	$-0.474492\pi$
$79$	−7.49468	−	5.44520i	−0.843218	−	0.612633i	−0.923268	+	0.384157i	$0.874492\pi$
$80$	3.50796	+	8.22765i	0.392202	+	0.919879i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	−6.97066	+	3.75678i	−0.769780	+	0.414867i
$83$	0.974493	−	6.15271i	0.106965	−	0.675348i	−0.874690	−	0.484682i	$-0.838935\pi$
$83$	0.974493	−	6.15271i	0.106965	−	0.675348i	0.981655	−	0.190666i	$-0.0610646\pi$
$84$	−2.84360	−	0.780899i	−0.310262	−	0.0852031i
$85$	3.33315	+	1.71277i	0.361531	+	0.185776i
$86$	−4.01965	−	2.78105i	−0.433450	−	0.299888i
$87$	−3.68335	+	7.22899i	−0.394897	+	0.775029i
$88$	3.02066	+	13.1192i	0.322004	+	1.39851i
$89$	1.92856	+	0.626628i	0.204427	+	0.0664225i	0.409441	−	0.912337i	$-0.365724\pi$
$89$	1.92856	+	0.626628i	0.204427	+	0.0664225i	−0.205013	+	0.978759i	$0.565724\pi$
$90$	3.11303	−	0.555934i	0.328142	−	0.0586006i
$91$	7.85754	−	2.55307i	0.823694	−	0.267634i
$92$	−11.7919	−	10.7508i	−1.22939	−	1.12085i
$93$	−1.55574	−	1.55574i	−0.161322	−	0.161322i
$94$	7.67161	−	2.68988i	0.791266	−	0.277440i
$95$	−2.33924	−	7.28448i	−0.240001	−	0.747371i
$96$	−4.92884	−	2.77607i	−0.503047	−	0.283332i
$97$	−3.36367	+	0.532753i	−0.341529	+	0.0540929i	−0.324843	−	0.945768i	$-0.605312\pi$
$97$	−3.36367	+	0.532753i	−0.341529	+	0.0540929i	−0.0166860	+	0.999861i	$0.505312\pi$
$98$	−6.71459	+	1.22292i	−0.678276	+	0.123534i
$99$	4.75968			0.478366
$100$	9.62458	+	2.71430i	0.962458	+	0.271430i
$101$	−13.7603			−1.36920			−0.684602	−	0.728917i	$-0.740024\pi$
$101$	−13.7603			−1.36920			−0.684602	+	0.728917i	$0.740024\pi$
$102$	−2.33174	+	0.424679i	−0.230877	+	0.0420494i
$103$	6.04390	−	0.957260i	0.595524	−	0.0943217i	0.148606	−	0.988897i	$-0.452522\pi$
$103$	6.04390	−	0.957260i	0.595524	−	0.0943217i	0.446918	+	0.894575i	$0.352522\pi$
$104$	15.8109	−	1.09626i	1.55039	−	0.107497i
$105$	−2.67392	+	1.92872i	−0.260948	+	0.188224i
$106$	−5.80796	+	2.03643i	−0.564119	+	0.197796i
$107$	−8.72357	−	8.72357i	−0.843339	−	0.843339i	0.145953	−	0.989292i	$-0.453375\pi$
$107$	−8.72357	−	8.72357i	−0.843339	−	0.843339i	−0.989292	+	0.145953i	$0.953375\pi$
$108$	−1.34747	+	1.47795i	−0.129660	+	0.142216i
$109$	−13.2840	+	4.31622i	−1.27237	+	0.413419i	−0.865888	−	0.500238i	$-0.833246\pi$
$109$	−13.2840	+	4.31622i	−1.27237	+	0.413419i	−0.406486	+	0.913657i	$0.633246\pi$
$110$	13.5425	+	6.56851i	1.29123	+	0.626283i
$111$	1.18462	+	0.384907i	0.112439	+	0.0365338i
$112$	5.88538	+	0.381790i	0.556116	+	0.0360758i
$113$	1.97483	−	3.87583i	0.185777	−	0.364607i	−0.779269	−	0.626690i	$-0.784409\pi$
$113$	1.97483	−	3.87583i	0.185777	−	0.364607i	0.965045	+	0.262083i	$0.0844093\pi$
$114$	3.97928	+	2.75311i	0.372693	+	0.257853i
$115$	−17.6303	+	2.73034i	−1.64404	+	0.254605i
$116$	4.29700	−	15.6473i	0.398966	−	1.45281i
$117$	0.876569	−	5.53444i	0.0810389	−	0.511659i
$118$	−15.7941	+	8.51212i	−1.45397	+	0.783604i
$119$	1.99911	−	1.45244i	0.183258	−	0.133145i
$120$	−5.87351	+	2.34561i	−0.536176	+	0.214124i
$121$	9.42875	+	6.85039i	0.857159	+	0.622763i
$122$	−9.76961	−	1.31707i	−0.884499	−	0.119242i
$123$	−2.54201	−	4.98898i	−0.229206	−	0.449841i
$124$	3.67544	+	2.41944i	0.330064	+	0.217272i
$125$	9.11231	−	6.47810i	0.815030	−	0.579419i
$126$	0.598425	−	1.99745i	0.0533120	−	0.177947i
$127$	−3.05770	+	1.55798i	−0.271327	+	0.138248i	−0.584361	−	0.811494i	$-0.698655\pi$
$127$	−3.05770	+	1.55798i	−0.271327	+	0.138248i	0.313034	+	0.949742i	$0.398655\pi$
$128$	10.7754	+	3.44827i	0.952421	+	0.304787i
$129$	2.03155	−	2.79619i	0.178868	−	0.246191i
$130$	10.1318	−	14.5372i	0.888615	−	1.27500i
$131$	4.34615	+	5.98196i	0.379725	+	0.522646i	0.955512	−	0.294954i	$-0.0953042\pi$
$131$	4.34615	+	5.98196i	0.379725	+	0.522646i	−0.575787	+	0.817600i	$0.695304\pi$
$132$	−9.32346	+	1.92132i	−0.811503	+	0.167230i
$133$	−4.98278	−	0.789194i	−0.432062	−	0.0684318i
$134$	−0.244440	−	10.5915i	−0.0211164	−	0.914963i
$135$	0.342211	+	2.20973i	0.0294529	+	0.190183i
$136$	4.39608	−	1.77312i	0.376961	−	0.152044i
$137$	10.0977	+	5.14506i	0.862708	+	0.439572i	0.828597	−	0.559846i	$-0.189140\pi$
$137$	10.0977	+	5.14506i	0.862708	+	0.439572i	0.0341118	+	0.999418i	$0.489140\pi$
$138$	7.79231	−	8.16048i	0.663325	−	0.694666i
$139$	4.52482	−	13.9260i	0.383791	−	1.18119i	−0.553563	−	0.832807i	$-0.686732\pi$
$139$	4.52482	−	13.9260i	0.383791	−	1.18119i	0.937354	−	0.348379i	$-0.113268\pi$
$140$	4.45922	−	4.85743i	0.376873	−	0.410528i
$141$	1.77636	+	5.46709i	0.149597	+	0.460412i
$142$	16.0430	+	7.71337i	1.34630	+	0.647292i
$143$	18.8589	−	18.8589i	1.57706	−	1.57706i
$144$	2.04287	−	3.43899i	0.170239	−	0.286583i
$145$	−10.6130	−	14.7136i	−0.881365	−	1.22190i
$146$	8.74574	+	11.4712i	0.723803	+	0.949367i
$147$	−0.754958	−	4.76662i	−0.0622679	−	0.393144i
$148$	−2.47586	−	0.275779i	−0.203514	−	0.0226689i
$149$		−	7.25270i		−	0.594165i	−0.954852	−	0.297082i	$-0.903986\pi$
$149$		−	7.25270i		−	0.594165i	0.954852	−	0.297082i	$-0.0960136\pi$
$150$	−2.07581	+	6.75951i	−0.169489	+	0.551912i
$151$			8.89011i			0.723467i	0.932282	+	0.361733i	$0.117815\pi$
$151$			8.89011i			0.723467i	−0.932282	+	0.361733i	$0.882185\pi$
$152$	−8.90610	−	3.78660i	−0.722380	−	0.307134i
$153$	−0.262171	−	1.65528i	−0.0211953	−	0.133822i
$154$	7.89255	−	6.01733i	0.636000	−	0.484890i
$155$	4.68408	−	1.50418i	0.376234	−	0.120819i
$156$	0.517010	+	11.1949i	0.0413939	+	0.896311i
$157$	−3.13469	+	3.13469i	−0.250175	+	0.250175i	−0.821043	−	0.570867i	$-0.806607\pi$
$157$	−3.13469	+	3.13469i	−0.250175	+	0.250175i	0.570867	+	0.821043i	$0.306607\pi$
$158$	−5.67689	+	11.8074i	−0.451629	+	0.939344i
$159$	−1.34484	−	4.13898i	−0.106652	−	0.328242i
$160$	10.5584	−	6.96562i	0.834716	−	0.550680i
$161$	−3.63522	+	11.1881i	−0.286496	+	0.881743i
$162$	−1.02281	−	0.976661i	−0.0803593	−	0.0767337i
$163$	3.54660	+	1.80708i	0.277791	+	0.141542i	0.587336	−	0.809343i	$-0.300177\pi$
$163$	3.54660	+	1.80708i	0.277791	+	0.141542i	−0.309545	+	0.950885i	$0.600177\pi$
$164$	6.99328	+	8.74649i	0.546083	+	0.682986i
$165$	−4.86435	+	9.46631i	−0.378689	+	0.736951i
$166$	−8.80736	+	0.203265i	−0.683584	+	0.0157764i
$167$	20.0096	+	3.16922i	1.54839	+	0.245241i	0.871335	−	0.490689i	$-0.163255\pi$
$167$	20.0096	+	3.16922i	1.54839	+	0.245241i	0.677058	+	0.735930i	$0.263255\pi$
$168$	−0.365914	+	4.15426i	−0.0282309	+	0.320508i
$169$	−10.8143	−	14.8846i	−0.831871	−	1.14497i
$170$	1.53840	−	5.07151i	0.117990	−	0.388967i
$171$	−2.01115	+	2.76811i	−0.153796	+	0.211682i
$172$	−2.85076	+	6.29737i	−0.217368	+	0.480170i
$173$	6.81344	−	3.47162i	0.518016	−	0.263943i	−0.175377	−	0.984501i	$-0.556115\pi$
$173$	6.81344	−	3.47162i	0.518016	−	0.263943i	0.693394	+	0.720559i	$0.256115\pi$
$174$	10.9912	+	3.29291i	0.833244	+	0.249635i
$175$	−1.10322	−	7.28917i	−0.0833959	−	0.551010i
$176$	17.4876	−	7.52714i	1.31818	−	0.567379i
$177$	−5.75969	−	11.3040i	−0.432925	−	0.849663i
$178$	0.383144	−	2.84205i	0.0287179	−	0.213021i
$179$	−13.4766	−	9.79134i	−1.00729	−	0.731839i	−0.0436509	−	0.999047i	$-0.513899\pi$
$179$	−13.4766	−	9.79134i	−1.00729	−	0.731839i	−0.963639	+	0.267208i	$0.913899\pi$
$180$	−1.56233	−	4.19036i	−0.116449	−	0.312331i
$181$	14.3280	−	10.4099i	1.06499	−	0.773762i	0.0899867	−	0.995943i	$-0.471318\pi$
$181$	14.3280	−	10.4099i	1.06499	−	0.773762i	0.975005	+	0.222181i	$0.0713176\pi$
$182$	−5.54326	−	10.2854i	−0.410894	−	0.762408i
$183$	1.09045	−	6.88483i	0.0806084	−	0.508942i
$184$	−11.9698	+	19.1306i	−0.882423	+	1.41032i
$185$	−1.97620	+	1.96267i	−0.145293	+	0.144298i
$186$	−1.77031	+	2.55876i	−0.129805	+	0.187617i
$187$	3.62140	−	7.10740i	0.264823	−	0.519745i
$188$	−5.68649	−	9.99209i	−0.414730	−	0.728748i
$189$	1.40227	+	0.455626i	0.102000	+	0.0331419i
$190$	−9.54231	+	5.10054i	−0.692272	+	0.370032i
$191$	−9.15141	+	2.97347i	−0.662173	+	0.215153i	−0.620774	−	0.783990i	$-0.713181\pi$
$191$	−9.15141	+	2.97347i	−0.662173	+	0.215153i	−0.0413989	+	0.999143i	$0.513181\pi$
$192$	−2.61345	+	7.56108i	−0.188609	+	0.545674i
$193$	−8.11384	−	8.11384i	−0.584047	−	0.584047i	0.351966	−	0.936013i	$-0.385513\pi$
$193$	−8.11384	−	8.11384i	−0.584047	−	0.584047i	−0.936013	+	0.351966i	$0.885513\pi$
$194$	1.59359	+	4.54497i	0.114413	+	0.326309i
$195$	10.1113	+	7.39951i	0.724089	+	0.529890i
$196$	3.40297	+	9.03229i	0.243069	+	0.645163i
$197$	2.15209	−	0.340857i	0.153330	−	0.0242851i	−0.0792975	−	0.996851i	$-0.525268\pi$
$197$	2.15209	−	0.340857i	0.153330	−	0.0242851i	0.232628	+	0.972566i	$0.425268\pi$
$198$	−1.20611	−	6.62227i	−0.0857144	−	0.470624i
$199$	9.69051			0.686942			0.343471	−	0.939163i	$-0.388397\pi$
$199$	9.69051			0.686942			0.343471	+	0.939163i	$0.388397\pi$
$200$	1.33759	−	14.0787i	0.0945820	−	0.995517i
$201$	7.49129			0.528395
$202$	3.48688	+	19.1451i	0.245336	+	1.34704i
$203$	−11.8152	+	1.87135i	−0.829268	+	0.131343i
$204$	1.18173	+	3.13660i	0.0827378	+	0.219606i
$205$	12.5203	+	0.0429983i	0.874453	+	0.00300313i
$206$	−2.86339	−	8.16647i	−0.199502	−	0.568985i
$207$	5.64166	+	5.64166i	0.392123	+	0.392123i
$208$	−5.53176	−	21.7204i	−0.383558	−	1.50604i
$209$	−15.4885	+	5.03252i	−1.07136	+	0.348107i
$210$	3.36106	+	3.23156i	0.231935	+	0.222999i
$211$	−23.4844	−	7.63053i	−1.61673	−	0.525308i	−0.645563	−	0.763707i	$-0.723377\pi$
$211$	−23.4844	−	7.63053i	−1.61673	−	0.525308i	−0.971167	+	0.238399i	$0.923377\pi$
$212$	4.30508	+	7.56473i	0.295674	+	0.519548i
$213$	−5.71447	+	11.2153i	−0.391549	+	0.768458i
$214$	−9.92676	+	14.3479i	−0.678580	+	0.980801i
$215$	3.48499	+	6.89815i	0.237674	+	0.470450i
$216$	2.39776	+	1.50025i	0.163147	+	0.102079i
$217$	0.507469	−	3.20403i	0.0344493	−	0.217504i
$218$	9.37144	+	17.3886i	0.634714	+	1.17770i
$219$	−8.25193	+	5.99537i	−0.557613	+	0.405130i
$220$	5.70725	−	20.5066i	0.384782	−	1.38255i
$221$	−7.59737	−	5.51981i	−0.511055	−	0.371303i
$222$	0.235347	−	1.74573i	0.0157954	−	0.117166i
$223$	8.96950	+	17.6036i	0.600642	+	1.17883i	0.968516	+	0.248951i	$0.0800857\pi$
$223$	8.96950	+	17.6036i	0.600642	+	1.17883i	−0.367874	+	0.929876i	$0.619914\pi$
$224$	−0.960167	−	8.28523i	−0.0641539	−	0.553580i
$225$	−4.74456	−	1.57771i	−0.316304	−	0.105181i
$226$	−5.89296	−	1.76550i	−0.391994	−	0.117439i
$227$	0.147478	−	0.0751436i	0.00978843	−	0.00498746i	−0.449089	−	0.893487i	$-0.648252\pi$
$227$	0.147478	−	0.0751436i	0.00978843	−	0.00498746i	0.458878	+	0.888499i	$0.348252\pi$
$228$	2.82212	−	6.23411i	0.186900	−	0.412864i
$229$	4.40665	−	6.06523i	0.291200	−	0.400802i	−0.638204	−	0.769867i	$-0.720322\pi$
$229$	4.40665	−	6.06523i	0.291200	−	0.400802i	0.929403	+	0.369066i	$0.120322\pi$
$230$	8.26634	+	23.8377i	0.545066	+	1.57181i
$231$	4.12499	+	5.67756i	0.271405	+	0.373556i
$232$	−22.8593	−	2.01349i	−1.50079	−	0.132192i
$233$	10.5449	+	1.67016i	0.690822	+	0.109415i	0.491968	−	0.870614i	$-0.336278\pi$
$233$	10.5449	+	1.67016i	0.690822	+	0.109415i	0.198855	+	0.980029i	$0.436278\pi$
$234$	−7.92234	+	0.182839i	−0.517899	+	0.0119526i
$235$	−12.6887	−	2.05438i	−0.827717	−	0.134013i
$236$	15.8454	+	19.8178i	1.03145	+	1.29003i
$237$	−8.25423	−	4.20574i	−0.536170	−	0.273192i
$238$	−2.52739	−	2.41336i	−0.163826	−	0.156435i
$239$	−6.87021	+	21.1443i	−0.444397	+	1.36771i	0.438746	+	0.898611i	$0.355423\pi$
$239$	−6.87021	+	21.1443i	−0.444397	+	1.36771i	−0.883143	+	0.469103i	$0.844577\pi$
$240$	4.75186	+	7.57759i	0.306731	+	0.489131i
$241$	6.30289	+	19.3983i	0.406005	+	1.24956i	0.920053	+	0.391794i	$0.128145\pi$
$241$	6.30289	+	19.3983i	0.406005	+	1.24956i	−0.514048	+	0.857761i	$0.671855\pi$
$242$	7.14187	−	14.8544i	0.459097	−	0.954875i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	0.643159	+	13.9265i	0.0411741	+	0.891550i
$245$	10.2517	+	3.36993i	0.654955	+	0.215297i
$246$	−6.29715	+	4.80098i	−0.401492	+	0.306099i
$247$	2.99924	+	18.9365i	0.190837	+	1.20490i
$248$	2.43487	−	5.72682i	0.154614	−	0.363653i
$249$		−	6.22940i		−	0.394772i
$250$	−11.3222	−	11.0366i	−0.716080	−	0.698018i
$251$			18.0233i			1.13762i	0.822468	+	0.568811i	$0.192597\pi$
$251$			18.0233i			1.13762i	−0.822468	+	0.568811i	$0.807403\pi$
$252$	−2.93075	−	0.326448i	−0.184620	−	0.0205643i
$253$	5.94063	+	37.5077i	0.373484	+	2.35809i
$254$	2.94248	+	3.85946i	0.184627	+	0.242164i
$255$	3.56005	+	1.17026i	0.222939	+	0.0732846i
$256$	2.06717	−	15.8659i	0.129198	−	0.991619i
$257$	−1.16576	+	1.16576i	−0.0727178	+	0.0727178i	−0.742530	−	0.669812i	$-0.766374\pi$
$257$	−1.16576	+	1.16576i	−0.0727178	+	0.0727178i	0.669812	+	0.742530i	$0.266374\pi$
$258$	−4.40522	−	2.11800i	−0.274257	−	0.131861i
$259$	0.567522	+	1.74665i	0.0352641	+	0.108532i
$260$	−22.7934	−	10.4128i	−1.41359	−	0.645777i
$261$	−2.50714	+	7.71619i	−0.155188	+	0.477620i
$262$	7.22154	−	7.56274i	0.446148	−	0.467228i
$263$	−22.7301	−	11.5815i	−1.40160	−	0.714149i	−0.420431	−	0.907324i	$-0.638121\pi$
$263$	−22.7301	−	11.5815i	−1.40160	−	0.714149i	−0.981164	+	0.193176i	$0.938121\pi$
$264$	5.03576	+	12.4851i	0.309930	+	0.768405i
$265$	9.60623	+	1.55531i	0.590106	+	0.0955422i
$266$	0.164614	+	7.13265i	0.0100931	+	0.437331i
$267$	2.00285	+	0.317220i	0.122572	+	0.0194135i
$268$	−14.6742	+	3.02398i	−0.896371	+	0.184719i
$269$	14.4616	+	19.9047i	0.881740	+	1.21361i	0.975936	+	0.218057i	$0.0699720\pi$
$269$	14.4616	+	19.9047i	0.881740	+	1.21361i	−0.0941958	+	0.995554i	$0.530028\pi$
$270$	2.98773	−	1.03607i	0.181828	−	0.0630535i
$271$	0.554963	−	0.763841i	0.0337116	−	0.0464000i	−0.791828	−	0.610744i	$-0.790871\pi$
$271$	0.554963	−	0.763841i	0.0337116	−	0.0464000i	0.825540	+	0.564344i	$0.190871\pi$
$272$	−3.58097	−	5.66707i	−0.217128	−	0.343617i
$273$	7.36141	−	3.75083i	0.445533	−	0.227010i
$274$	4.59967	−	15.3530i	0.277876	−	0.927509i
$275$	−13.8558	−	19.3489i	−0.835535	−	1.16679i
$276$	−13.3285	−	8.77377i	−0.802280	−	0.528119i
$277$	−5.23893	−	10.2820i	−0.314777	−	0.617784i	0.678362	−	0.734728i	$-0.262690\pi$
$277$	−5.23893	−	10.2820i	−0.314777	−	0.617784i	−0.993139	+	0.116944i	$0.962690\pi$
$278$	−20.5222	−	2.76665i	−1.23084	−	0.165933i
$279$	−1.77995	−	1.29321i	−0.106563	−	0.0774225i
$280$	−7.88824	−	4.97336i	−0.471413	−	0.297215i
$281$	4.14505	−	3.01155i	0.247273	−	0.179654i	−0.457244	−	0.889341i	$-0.651164\pi$
$281$	4.14505	−	3.01155i	0.247273	−	0.179654i	0.704517	+	0.709687i	$0.251164\pi$
$282$	7.15637	−	3.85687i	0.426156	−	0.229673i
$283$	1.43610	−	9.06715i	0.0853670	−	0.538986i	−0.907528	−	0.419992i	$-0.862033\pi$
$283$	1.43610	−	9.06715i	0.0853670	−	0.538986i	0.992895	−	0.118994i	$-0.0379670\pi$
$284$	6.66650	−	24.2757i	0.395584	−	1.44050i
$285$	−3.44999	−	6.82885i	−0.204359	−	0.404506i
$286$	−31.0178	−	21.4600i	−1.83412	−	1.26896i
$287$	3.74804	−	7.35594i	0.221240	−	0.434207i
$288$	−5.30243	−	1.97085i	−0.312449	−	0.116134i
$289$	13.4967	+	4.38536i	0.793926	+	0.257962i
$290$	−17.7821	+	18.4946i	−1.04420	+	1.08604i
$291$	−3.23892	+	1.05239i	−0.189869	+	0.0616921i
$292$	13.7441	−	15.0750i	0.804311	−	0.882198i
$293$	−20.8580	−	20.8580i	−1.21854	−	1.21854i	−0.968145	−	0.250392i	$-0.919441\pi$
$293$	−20.8580	−	20.8580i	−1.21854	−	1.21854i	−0.250392	−	0.968145i	$-0.580559\pi$
$294$	−6.44061	+	2.25826i	−0.375624	+	0.131704i
$295$	28.3684	+	0.0974256i	1.65167	+	0.00567234i
$296$	0.243687	+	3.51461i	0.0141640	+	0.204283i
$297$	4.70108	−	0.744578i	0.272785	−	0.0432048i
$298$	−10.0909	+	1.83784i	−0.584549	+	0.106463i
$299$	44.7071			2.58548
$300$	9.93070	+	1.17526i	0.573349	+	0.0678538i
$301$	5.09608			0.293733
$302$	12.3690	−	2.25276i	0.711758	−	0.129632i
$303$	−13.5909	+	2.15259i	−0.780777	+	0.123663i
$304$	−3.01158	+	13.3508i	−0.172726	+	0.765722i
$305$	12.5785	+	9.20498i	0.720242	+	0.527075i
$306$	−2.23660	+	0.784215i	−0.127858	+	0.0448306i
$307$	1.07224	+	1.07224i	0.0611962	+	0.0611962i	0.737043	−	0.675846i	$-0.236222\pi$
$307$	1.07224	+	1.07224i	0.0611962	+	0.0611962i	−0.675846	+	0.737043i	$0.736222\pi$
$308$	−10.3720	−	9.45632i	−0.591002	−	0.538824i
$309$	5.81975	−	1.89095i	0.331074	−	0.107572i
$310$	−3.27976	−	6.13591i	−0.186278	−	0.348497i
$311$	−0.0825240	−	0.0268137i	−0.00467951	−	0.00152046i	0.306676	−	0.951814i	$-0.400783\pi$
$311$	−0.0825240	−	0.0268137i	−0.00467951	−	0.00152046i	−0.311356	+	0.950293i	$0.600783\pi$
$312$	15.4448	−	3.55614i	0.874388	−	0.201327i
$313$	−10.0594	+	19.7428i	−0.568593	+	1.11593i	0.410375	+	0.911917i	$0.365398\pi$
$313$	−10.0594	+	19.7428i	−0.568593	+	1.11593i	−0.978969	+	0.204011i	$0.934602\pi$
$314$	5.15571	+	3.56704i	0.290953	+	0.201300i
$315$	−2.33928	+	2.32327i	−0.131804	+	0.130901i
$316$	17.8664	+	4.90641i	1.00506	+	0.276007i
$317$	4.98965	−	31.5034i	0.280247	−	1.76941i	−0.298998	−	0.954254i	$-0.596652\pi$
$317$	4.98965	−	31.5034i	0.280247	−	1.76941i	0.579244	−	0.815154i	$-0.303348\pi$
$318$	−5.41789	+	2.91993i	−0.303820	+	0.163741i
$319$	−31.2415	+	22.6983i	−1.74919	+	1.27086i
$320$	−12.3670	−	12.9251i	−0.691334	−	0.722535i
$321$	−9.98083	−	7.25150i	−0.557076	−	0.404739i
$322$	16.4874	+	2.22271i	0.918808	+	0.123867i
$323$	2.60330	+	5.10926i	0.144851	+	0.284287i
$324$	−1.09967	+	1.67054i	−0.0610930	+	0.0928080i
$325$	−25.0502	+	12.5478i	−1.38954	+	0.696024i
$326$	1.61553	−	5.39239i	0.0894759	−	0.298657i
$327$	−12.4452	+	6.34115i	−0.688222	+	0.350667i
$328$	10.3971	−	11.9463i	0.574084	−	0.659624i
$329$	−4.98190	+	6.85700i	−0.274661	+	0.378038i
$330$	14.4034	+	4.36912i	0.792879	+	0.240512i
$331$	11.2987	+	15.5513i	0.621031	+	0.854776i	0.997428	−	0.0716824i	$-0.0228368\pi$
$331$	11.2987	+	15.5513i	0.621031	+	0.854776i	−0.376396	+	0.926459i	$0.622837\pi$
$332$	2.51460	+	12.2024i	0.138007	+	0.669694i
$333$	1.23025	+	0.194853i	0.0674173	+	0.0106779i
$334$	−0.661051	−	28.6430i	−0.0361711	−	1.56728i
$335$	−7.65602	+	14.8991i	−0.418293	+	0.814023i
$336$	5.87265	−	0.543587i	0.320379	−	0.0296551i
$337$	12.8547	+	6.54977i	0.700238	+	0.356789i	0.767591	−	0.640940i	$-0.221455\pi$
$337$	12.8547	+	6.54977i	0.700238	+	0.356789i	−0.0673530	+	0.997729i	$0.521455\pi$
$338$	−17.9690	+	18.8180i	−0.977386	+	1.02357i
$339$	1.34421	−	4.13704i	0.0730072	−	0.224693i
$340$	−7.44596	−	0.855283i	−0.403814	−	0.0463842i
$341$	−3.23602	−	9.95944i	−0.175240	−	0.539334i
$342$	4.36097	+	2.09672i	0.235814	+	0.113378i
$343$	12.3296	−	12.3296i	0.665738	−	0.665738i
$344$	9.48408	+	2.37058i	0.511347	+	0.127813i
$345$	−16.9862	+	5.45472i	−0.914504	+	0.293672i
$346$	−6.55669	−	8.60001i	−0.352490	−	0.462339i
$347$	0.544569	+	3.43827i	0.0292340	+	0.184576i	0.997984	−	0.0634620i	$-0.0202142\pi$
$347$	0.544569	+	3.43827i	0.0292340	+	0.184576i	−0.968750	+	0.248038i	$0.920214\pi$
$348$	1.79632	−	16.1268i	0.0962929	−	0.864489i
$349$		−	1.06294i		−	0.0568981i	−0.999595	−	0.0284490i	$-0.990943\pi$
$349$		−	1.06294i		−	0.0568981i	0.999595	−	0.0284490i	$-0.00905683\pi$
$350$	−9.86206	+	3.38203i	−0.527149	+	0.180777i
$351$		−	5.60343i		−	0.299089i
$352$	−14.9041	−	22.4235i	−0.794390	−	1.19518i
$353$	−3.21923	−	20.3254i	−0.171342	−	1.08181i	−0.912078	−	0.410017i	$-0.865523\pi$
$353$	−3.21923	−	20.3254i	−0.171342	−	1.08181i	0.740736	−	0.671797i	$-0.234477\pi$
$354$	−14.2681	+	10.8781i	−0.758340	+	0.578163i
$355$	−16.4654	−	22.8271i	−0.873893	−	1.21154i
$356$	−4.05131	+	0.187100i	−0.214719	+	0.00991626i
$357$	1.74728	−	1.74728i	0.0924760	−	0.0924760i
$358$	−10.2080	+	21.2315i	−0.539507	+	1.12212i
$359$	5.08507	+	15.6502i	0.268380	+	0.825988i	0.990895	+	0.134633i	$0.0429856\pi$
$359$	5.08507	+	15.6502i	0.268380	+	0.825988i	−0.722516	+	0.691354i	$0.757014\pi$
$360$	−5.43426	+	3.23555i	−0.286411	+	0.170529i
$361$	−2.25362	+	6.93593i	−0.118612	+	0.365049i
$362$	−18.1143	−	17.2970i	−0.952066	−	0.909112i
$363$	10.3843	+	5.29107i	0.545035	+	0.277709i
$364$	−12.9057	+	10.3188i	−0.676445	+	0.540853i
$365$	−3.49054	−	22.5391i	−0.182703	−	1.17975i
$366$	−9.85537	+	0.227452i	−0.515148	+	0.0118891i
$367$	18.7851	+	2.97526i	0.980573	+	0.155307i	0.626086	−	0.779754i	$-0.284656\pi$
$367$	18.7851	+	2.97526i	0.980573	+	0.155307i	0.354486	+	0.935061i	$0.384656\pi$
$368$	29.6500	+	11.8061i	1.54561	+	0.615438i
$369$	−3.29116	−	4.52990i	−0.171331	−	0.235817i
$370$	3.23148	+	2.25219i	0.167997	+	0.117086i
$371$	3.77165	−	5.19124i	0.195815	−	0.269516i
$372$	4.00867	+	1.81469i	0.207840	+	0.0940871i
$373$	0.521594	−	0.265765i	0.0270071	−	0.0137608i	−0.440435	−	0.897785i	$-0.645176\pi$
$373$	0.521594	−	0.265765i	0.0270071	−	0.0137608i	0.467442	+	0.884024i	$0.345176\pi$
$374$	−10.8064	−	3.23753i	−0.558785	−	0.167409i
$375$	7.98672	−	7.82382i	0.412433	−	0.404021i
$376$	−12.4613	+	10.4438i	−0.642642	+	0.538597i
$377$	20.6394	+	40.5071i	1.06298	+	2.08622i
$378$	0.278587	−	2.06648i	0.0143290	−	0.106288i
$379$	4.02282	+	2.92275i	0.206639	+	0.150132i	0.686292	−	0.727327i	$-0.259237\pi$
$379$	4.02282	+	2.92275i	0.206639	+	0.150132i	−0.479653	+	0.877458i	$0.659237\pi$
$380$	9.51455	+	11.9840i	0.488086	+	0.614766i
$381$	−2.77633	+	2.01712i	−0.142236	+	0.103340i
$382$	6.45605	+	11.9791i	0.330320	+	0.612905i
$383$	−2.89726	+	18.2926i	−0.148043	+	0.934708i	0.796098	+	0.605167i	$0.206894\pi$
$383$	−2.89726	+	18.2926i	−0.148043	+	0.934708i	−0.944141	+	0.329540i	$0.893106\pi$
$384$	11.1822	+	1.72017i	0.570638	+	0.0877822i
$385$	−15.5075	+	2.40159i	−0.790338	+	0.122396i
$386$	−9.23294	+	13.3451i	−0.469944	+	0.679245i
$387$	1.56912	−	3.07957i	0.0797629	−	0.156544i
$388$	5.91971	−	3.36890i	0.300528	−	0.171030i
$389$	−14.1818	−	4.60795i	−0.719046	−	0.233632i	−0.0734363	−	0.997300i	$-0.523397\pi$
$389$	−14.1818	−	4.60795i	−0.719046	−	0.233632i	−0.645609	+	0.763668i	$0.723397\pi$
$390$	7.73291	−	15.9432i	0.391571	−	0.807316i
$391$	12.7169	−	4.13196i	0.643120	−	0.208962i
$392$	11.7045	−	7.02343i	0.591169	−	0.354737i
$393$	5.22842	+	5.22842i	0.263739	+	0.263739i
$394$	−1.01959	−	2.90788i	−0.0513660	−	0.146497i
$395$	16.8003	−	12.1182i	0.845317	−	0.609734i
$396$	−8.90811	+	3.35618i	−0.447649	+	0.168654i
$397$	17.2952	−	2.73929i	0.868021	−	0.137481i	0.293488	−	0.955963i	$-0.405184\pi$
$397$	17.2952	−	2.73929i	0.868021	−	0.137481i	0.574533	+	0.818482i	$0.305184\pi$
$398$	−2.45558	−	13.4827i	−0.123087	−	0.675825i
$399$	−5.04489			−0.252560
$400$	−19.9271	+	1.70654i	−0.996353	+	0.0853270i
$401$	−23.4783			−1.17245			−0.586226	−	0.810147i	$-0.699387\pi$
$401$	−23.4783			−1.17245			−0.586226	+	0.810147i	$0.699387\pi$
$402$	−1.89830	−	10.4228i	−0.0946786	−	0.519843i
$403$	−12.1766	+	1.92858i	−0.606558	+	0.0960693i
$404$	25.7535	−	9.70277i	1.28128	−	0.482731i
$405$	0.683675	+	2.12899i	0.0339721	+	0.105790i
$406$	5.59766	+	15.9647i	0.277807	+	0.792313i
$407$	4.19215	+	4.19215i	0.207797	+	0.207797i
$408$	4.06458	−	2.43899i	0.201227	−	0.120748i
$409$	36.3503	−	11.8109i	1.79741	−	0.584014i	0.797593	−	0.603196i	$-0.206106\pi$
$409$	36.3503	−	11.8109i	1.79741	−	0.584014i	0.999816	+	0.0191827i	$0.00610643\pi$
$410$	−3.11282	−	17.4307i	−0.153731	−	0.860839i
$411$	10.7783	+	3.50208i	0.531654	+	0.172745i
$412$	−10.6366	+	6.05331i	−0.524029	+	0.298225i
$413$	8.49231	−	16.6671i	0.417879	−	0.820134i
$414$	6.41979	−	9.27900i	0.315516	−	0.456038i
$415$	12.3894	+	6.36639i	0.608170	+	0.312514i
$416$	−28.8184	+	13.2004i	−1.41294	+	0.647205i
$417$	2.29061	−	14.4624i	0.112172	−	0.708225i
$418$	10.9267	+	20.2743i	0.534441	+	0.991649i
$419$	−8.44580	+	6.13623i	−0.412604	+	0.299775i	−0.774655	−	0.632384i	$-0.782077\pi$
$419$	−8.44580	+	6.13623i	−0.412604	+	0.299775i	0.362051	+	0.932158i	$0.382077\pi$
$420$	3.64445	−	5.49521i	0.177831	−	0.268139i
$421$	3.57920	+	2.60044i	0.174439	+	0.126738i	0.671579	−	0.740933i	$-0.265616\pi$
$421$	3.57920	+	2.60044i	0.174439	+	0.126738i	−0.497140	+	0.867671i	$0.665616\pi$
$422$	−4.66560	+	34.6080i	−0.227118	+	1.68469i
$423$	2.60974	+	5.12189i	0.126890	+	0.249035i
$424$	9.43409	−	7.90669i	0.458160	−	0.383983i
$425$	−5.96581	+	5.88442i	−0.289384	+	0.285436i
$426$	17.0522	+	5.10873i	0.826180	+	0.247519i
$427$	9.15758	−	4.66602i	0.443166	−	0.225805i
$428$	22.4780	+	10.1756i	1.08652	+	0.491856i
$429$	15.6766	−	21.5769i	0.756871	−	1.04174i
$430$	8.71447	−	6.59676i	0.420249	−	0.318124i
$431$	−14.7423	−	20.2911i	−0.710114	−	0.977388i	−0.999795	−	0.0202643i	$-0.993549\pi$
$431$	−14.7423	−	20.2911i	−0.710114	−	0.977388i	0.289681	−	0.957123i	$-0.406451\pi$
$432$	1.47974	−	3.71623i	0.0711941	−	0.178797i
$433$	11.9800	+	1.89745i	0.575723	+	0.0911856i	0.437505	−	0.899216i	$-0.355862\pi$
$433$	11.9800	+	1.89745i	0.575723	+	0.0911856i	0.138219	+	0.990402i	$0.455862\pi$
$434$	−4.58645	+	0.105851i	−0.220157	+	0.00508099i
$435$	−12.7841	−	12.8722i	−0.612950	−	0.617175i
$436$	21.8185	−	17.4450i	1.04492	−	0.835465i
$437$	−24.3236	−	12.3935i	−1.16356	−	0.592862i
$438$	10.4326	+	9.96188i	0.498487	+	0.475997i
$439$	−6.68775	+	20.5828i	−0.319189	+	0.982363i	0.654807	+	0.755796i	$0.272750\pi$
$439$	−6.68775	+	20.5828i	−0.319189	+	0.982363i	−0.973996	+	0.226567i	$0.927250\pi$
$440$	−29.9775	−	2.74426i	−1.42912	−	0.130827i
$441$	−1.49133	−	4.58983i	−0.0710155	−	0.218563i
$442$	−5.75468	+	11.9691i	−0.273722	+	0.569314i
$443$	−8.27711	+	8.27711i	−0.393257	+	0.393257i	−0.875847	−	0.482589i	$-0.839696\pi$
$443$	−8.27711	+	8.27711i	−0.393257	+	0.393257i	0.482589	+	0.875847i	$0.339696\pi$
$444$	−2.48852	+	0.114926i	−0.118100	+	0.00545415i
$445$	−2.67779	+	3.65917i	−0.126940	+	0.173461i
$446$	22.2195	−	16.9403i	1.05212	−	0.802145i
$447$	−1.13457	−	7.16341i	−0.0536635	−	0.338818i
$448$	−11.2841	+	3.43539i	−0.533126	+	0.162307i
$449$			15.5833i			0.735422i	0.929940	+	0.367711i	$0.119858\pi$
$449$			15.5833i			0.735422i	−0.929940	+	0.367711i	$0.880142\pi$
$450$	−0.992833	+	7.00102i	−0.0468026	+	0.330031i
$451$		−	26.6507i		−	1.25493i
$452$	−0.963099	+	8.64641i	−0.0453004	+	0.406693i
$453$	1.39072	+	8.78066i	0.0653417	+	0.412551i
$454$	−0.141920	−	0.186148i	−0.00666065	−	0.00873636i
$455$	−0.0634455	+	18.4741i	−0.00297437	+	0.866078i
$456$	−9.38881	−	2.34676i	−0.439671	−	0.109897i
$457$	−1.36886	+	1.36886i	−0.0640324	+	0.0640324i	−0.738398	−	0.674365i	$-0.764417\pi$
$457$	−1.36886	+	1.36886i	−0.0640324	+	0.0640324i	0.674365	+	0.738398i	$0.264417\pi$
$458$	−9.55536	−	4.59415i	−0.446493	−	0.214670i
$459$	−0.517886	−	1.59389i	−0.0241729	−	0.0743964i
$460$	31.0713	−	17.5417i	1.44871	−	0.817884i
$461$	1.20334	−	3.70349i	0.0560450	−	0.172489i	−0.919115	−	0.393988i	$-0.871095\pi$
$461$	1.20334	−	3.70349i	0.0560450	−	0.172489i	0.975161	+	0.221499i	$0.0710951\pi$
$462$	6.85407	−	7.17791i	0.318880	−	0.333947i
$463$	−30.4751	−	15.5278i	−1.41630	−	0.721639i	−0.432618	−	0.901577i	$-0.642410\pi$
$463$	−30.4751	−	15.5278i	−1.41630	−	0.721639i	−0.983678	+	0.179938i	$0.942410\pi$
$464$	2.99116	+	32.3150i	0.138861	+	1.50019i
$465$	4.39110	−	2.21842i	0.203632	−	0.102877i
$466$	−0.348370	−	15.0947i	−0.0161379	−	0.699247i
$467$	−1.58480	−	0.251008i	−0.0733359	−	0.0116153i	0.119659	−	0.992815i	$-0.461820\pi$
$467$	−1.58480	−	0.251008i	−0.0733359	−	0.0116153i	−0.192995	+	0.981200i	$0.561820\pi$
$468$	2.26192	+	10.9762i	0.104557	+	0.507376i
$469$	6.49234	+	8.93595i	0.299789	+	0.412624i
$470$	0.357007	+	18.1746i	0.0164675	+	0.838334i
$471$	−2.60572	+	3.58647i	−0.120065	+	0.165256i
$472$	23.5578	−	27.0679i	1.08433	−	1.24590i
$473$	14.6578	−	7.46852i	0.673966	−	0.343403i
$474$	−3.75992	+	12.5501i	−0.172699	+	0.576443i
$475$	17.1074	+	0.117506i	0.784943	+	0.00539152i
$476$	−2.71733	+	4.12797i	−0.124549	+	0.189205i
$477$	−1.97576	−	3.87764i	−0.0904637	−	0.177545i
$478$	31.1596	+	4.20071i	1.42521	+	0.192136i
$479$	5.24823	+	3.81306i	0.239798	+	0.174223i	0.701193	−	0.712971i	$-0.252651\pi$
$479$	5.24823	+	3.81306i	0.239798	+	0.174223i	−0.461395	+	0.887195i	$0.652651\pi$
$480$	9.33876	−	8.53156i	0.426254	−	0.389411i
$481$	5.64658	−	4.10248i	0.257462	−	0.187057i
$482$	25.3922	−	13.6849i	1.15658	−	0.623332i
$483$	−1.84027	+	11.6190i	−0.0837351	+	0.528683i
$484$	−22.4770	−	6.17256i	−1.02168	−	0.280571i
$485$	1.21710	−	7.51727i	0.0552655	−	0.341341i
$486$	−1.16300	−	0.804634i	−0.0527546	−	0.0364990i
$487$	1.10097	−	2.16077i	0.0498896	−	0.0979138i	−0.864716	−	0.502262i	$-0.832501\pi$
$487$	1.10097	−	2.16077i	0.0498896	−	0.0979138i	0.914605	+	0.404348i	$0.132501\pi$
$488$	19.2133	−	4.42382i	0.869744	−	0.200257i
$489$	3.78563	+	1.23002i	0.171192	+	0.0556236i
$490$	2.09090	−	15.1173i	0.0944570	−	0.682932i
$491$	−12.7330	+	4.13721i	−0.574634	+	0.186710i	−0.581895	−	0.813264i	$-0.697689\pi$
$491$	−12.7330	+	4.13721i	−0.574634	+	0.186710i	0.00726141	+	0.999974i	$0.497689\pi$
$492$	8.27543	+	7.54481i	0.373085	+	0.340146i
$493$	9.61465	+	9.61465i	0.433022	+	0.433022i
$494$	25.5868	−	8.97144i	1.15120	−	0.403644i
$495$	−3.32360	+	10.1107i	−0.149385	+	0.454443i
$496$	−8.58487	−	1.93651i	−0.385472	−	0.0869521i
$497$	−18.3305	+	2.90327i	−0.822237	+	0.130230i
$498$	−8.66713	+	1.57854i	−0.388383	+	0.0707359i
$499$	33.0488			1.47947			0.739734	−	0.672900i	$-0.234951\pi$
$499$	33.0488			1.47947			0.739734	+	0.672900i	$0.234951\pi$
$500$	−12.4865	+	18.5496i	−0.558413	+	0.829563i
$501$	20.2591			0.905108
$502$	25.0763	−	4.56713i	1.11921	−	0.203841i
$503$	−14.8800	+	2.35677i	−0.663468	+	0.105083i	−0.479081	−	0.877771i	$-0.659030\pi$
$503$	−14.8800	+	2.35677i	−0.663468	+	0.105083i	−0.184387	+	0.982854i	$0.559030\pi$
$504$	0.288460	+	4.16035i	0.0128490	+	0.185317i
$505$	9.60859	−	29.2303i	0.427577	−	1.30073i
$506$	50.6800	−	17.7698i	2.25300	−	0.789966i
$507$	−13.0096	−	13.0096i	−0.577779	−	0.577779i
$508$	4.62415	−	5.07194i	0.205163	−	0.225031i
$509$	−15.1212	+	4.91317i	−0.670234	+	0.217772i	−0.624315	−	0.781173i	$-0.714622\pi$
$509$	−15.1212	+	4.91317i	−0.670234	+	0.217772i	−0.0459196	+	0.998945i	$0.514622\pi$
$510$	0.726096	−	5.24973i	0.0321521	−	0.232462i
$511$	−14.3031	−	4.64736i	−0.632732	−	0.205587i
$512$	−22.5985	+	1.14433i	−0.998720	+	0.0505727i
$513$	−1.55336	+	3.04864i	−0.0685825	+	0.134601i
$514$	1.91735	+	1.32654i	0.0845706	+	0.0585113i
$515$	−2.18690	+	13.5072i	−0.0963663	+	0.595196i
$516$	−1.83054	+	6.66579i	−0.0805849	+	0.293445i
$517$	−4.28016	+	27.0239i	−0.188241	+	1.18851i
$518$	2.28635	−	1.23221i	0.100457	−	0.0541402i
$519$	6.18648	−	4.49474i	0.271556	−	0.197297i
$520$	−8.71178	+	34.3517i	−0.382037	+	1.50642i
$521$	−18.9526	−	13.7698i	−0.830327	−	0.603268i	0.0893252	−	0.996003i	$-0.471529\pi$
$521$	−18.9526	−	13.7698i	−0.830327	−	0.603268i	−0.919652	+	0.392735i	$0.871529\pi$
$522$	11.3710	+	1.53296i	0.497697	+	0.0670959i
$523$	18.9802	+	37.2508i	0.829947	+	1.62886i	0.776352	+	0.630300i	$0.217068\pi$
$523$	18.9802	+	37.2508i	0.829947	+	1.62886i	0.0535947	+	0.998563i	$0.482932\pi$
$524$	−12.3522	−	8.13110i	−0.539608	−	0.355209i
$525$	−2.22992	−	7.02685i	−0.0973217	−	0.306677i
$526$	−10.3539	+	34.5597i	−0.451451	+	1.50687i
$527$	−3.28536	+	1.67398i	−0.143113	+	0.0729196i
$528$	16.0948	−	10.1701i	0.700435	−	0.442598i
$529$	−23.8974	+	32.8920i	−1.03902	+	1.43009i
$530$	−0.270280	−	13.7595i	−0.0117402	−	0.597675i
$531$	−7.45712	−	10.2638i	−0.323612	−	0.445413i
$532$	9.88213	−	2.03645i	0.428445	−	0.0882914i
$533$	−30.9888	−	4.90814i	−1.34227	−	0.212595i
$534$	−0.0661673	−	2.86700i	−0.00286334	−	0.124067i
$535$	24.6225	−	12.4394i	1.06452	−	0.537804i
$536$	7.92581	+	19.6504i	0.342343	+	0.848766i
$537$	−14.8424	−	7.56258i	−0.640497	−	0.326349i
$538$	24.0293	−	25.1647i	1.03598	−	1.08493i
$539$	7.09824	−	21.8461i	0.305743	−	0.940980i
$540$	−2.19861	−	3.89437i	−0.0946132	−	0.167587i
$541$	7.36951	+	22.6810i	0.316840	+	0.975133i	0.974990	+	0.222247i	$0.0713391\pi$
$541$	7.36951	+	22.6810i	0.316840	+	0.975133i	−0.658150	+	0.752886i	$0.728661\pi$
$542$	−1.20338	−	0.578576i	−0.0516896	−	0.0248520i
$543$	12.5231	−	12.5231i	0.537419	−	0.537419i
$544$	−6.97733	+	6.41833i	−0.299150	+	0.275184i
$545$	0.107261	−	31.2323i	0.00459456	−	1.33784i
$546$	−7.08401	−	9.29166i	−0.303168	−	0.397646i
$547$	−4.47666	−	28.2645i	−0.191408	−	1.20850i	−0.876990	−	0.480509i	$-0.840452\pi$
$547$	−4.47666	−	28.2645i	−0.191408	−	1.20850i	0.685582	−	0.727996i	$-0.259548\pi$
$548$	−22.5266	−	2.50917i	−0.962289	−	0.107187i
$549$		−	6.97065i		−	0.297500i
$550$	−23.4096	+	24.1810i	−0.998190	+	1.03108i
$551$		−	27.7601i		−	1.18262i
$552$	−8.82972	+	20.7675i	−0.375818	+	0.883925i
$553$	−2.13675	−	13.4909i	−0.0908640	−	0.573693i
$554$	−12.9780	+	9.89452i	−0.551384	+	0.420378i
$555$	−1.64484	+	2.24765i	−0.0698194	+	0.0954074i
$556$	1.35103	+	29.2541i	0.0572964	+	1.24065i
$557$	−19.6252	+	19.6252i	−0.831547	+	0.831547i	−0.987728	−	0.156181i	$-0.950082\pi$
$557$	−19.6252	+	19.6252i	−0.831547	+	0.831547i	0.156181	+	0.987728i	$0.450082\pi$
$558$	−1.34824	+	2.80420i	−0.0570754	+	0.118711i
$559$	−5.98475	−	18.4192i	−0.253128	−	0.779048i
$560$	−4.92067	+	12.2354i	−0.207936	+	0.517039i
$561$	2.46497	−	7.58641i	0.104071	−	0.320298i
$562$	−5.24041	−	5.00398i	−0.221053	−	0.211080i
$563$	−24.2640	−	12.3631i	−1.02261	−	0.521044i	−0.139503	−	0.990222i	$-0.544551\pi$
$563$	−24.2640	−	12.3631i	−1.02261	−	0.521044i	−0.883104	+	0.469177i	$0.844551\pi$
$564$	−7.17959	−	8.97951i	−0.302315	−	0.378105i
$565$	6.85420	+	6.90144i	0.288358	+	0.290346i
$566$	−12.9793	+	0.299548i	−0.545559	+	0.0125909i
$567$	1.45628	+	0.230653i	0.0611582	+	0.00968651i
$568$	−35.4647	−	3.12379i	−1.48806	−	0.131071i
$569$	20.7368	+	28.5418i	0.869333	+	1.19653i	0.979263	+	0.202594i	$0.0649373\pi$
$569$	20.7368	+	28.5418i	0.869333	+	1.19653i	−0.109930	+	0.993939i	$0.535063\pi$
$570$	−8.62693	+	6.53049i	−0.361342	+	0.273532i
$571$	2.29350	−	3.15674i	0.0959802	−	0.132105i	−0.758326	−	0.651876i	$-0.773982\pi$
$571$	2.29350	−	3.15674i	0.0959802	−	0.132105i	0.854306	+	0.519770i	$0.173982\pi$
$572$	−21.9980	+	48.5938i	−0.919781	+	2.03181i
$573$	−8.57359	+	4.36846i	−0.358167	+	0.182495i
$574$	−11.1843	−	3.35074i	−0.466822	−	0.139857i
$575$	6.51106	−	39.3577i	0.271530	−	1.64133i
$576$	−1.39846	+	7.87682i	−0.0582691	+	0.328201i
$577$	−11.1988	−	21.9789i	−0.466213	−	0.914994i	−0.997691	−	0.0679219i	$-0.978363\pi$
$577$	−11.1988	−	21.9789i	−0.466213	−	0.914994i	0.531478	−	0.847072i	$-0.321637\pi$
$578$	2.68137	−	19.8896i	0.111530	−	0.827299i
$579$	−9.28323	−	6.74466i	−0.385798	−	0.280299i
$580$	30.2381	+	20.0541i	1.25557	+	0.832700i
$581$	7.43071	−	5.39873i	0.308278	−	0.223977i
$582$	2.28496	+	4.23972i	0.0947147	+	0.175742i
$583$	3.24039	−	20.4590i	0.134203	−	0.847326i
$584$	−24.4570	−	15.3025i	−1.01204	−	0.633220i
$585$	11.1444	+	5.72665i	0.460764	+	0.236768i
$586$	−23.7348	+	34.3057i	−0.980476	+	1.41715i
$587$	1.15344	−	2.26375i	0.0476076	−	0.0934351i	−0.865977	−	0.500084i	$-0.833303\pi$
$587$	1.15344	−	2.26375i	0.0476076	−	0.0934351i	0.913585	+	0.406648i	$0.133303\pi$
$588$	4.77403	+	8.38874i	0.196878	+	0.345946i
$589$	7.15949	+	2.32626i	0.295002	+	0.0958519i
$590$	−7.05303	−	39.4944i	−0.290369	−	1.62596i
$591$	2.07227	−	0.673322i	0.0852419	−	0.0276968i
$592$	4.82822	−	1.22965i	0.198439	−	0.0505385i
$593$	24.4019	+	24.4019i	1.00206	+	1.00206i	0.999998	+	0.00206677i	$0.000657873\pi$
$593$	24.4019	+	24.4019i	1.00206	+	1.00206i	0.00206677	+	0.999998i	$0.499342\pi$
$594$	−2.22721	−	6.35206i	−0.0913836	−	0.260628i
$595$	1.68938	+	5.26080i	0.0692580	+	0.215672i
$596$	5.11408	+	13.5740i	0.209481	+	0.556012i
$597$	9.57120	−	1.51593i	0.391723	−	0.0620429i
$598$	−11.3288	−	62.2021i	−0.463270	−	2.54363i
$599$	−10.8060			−0.441521			−0.220761	−	0.975328i	$-0.570854\pi$
$599$	−10.8060			−0.441521			−0.220761	+	0.975328i	$0.570854\pi$
$600$	−0.881276	−	14.1147i	−0.0359780	−	0.576228i
$601$	−18.5184			−0.755379			−0.377690	−	0.925932i	$-0.623281\pi$
$601$	−18.5184			−0.755379			−0.377690	+	0.925932i	$0.623281\pi$
$602$	−1.29135	−	7.09031i	−0.0526316	−	0.288979i
$603$	7.39906	−	1.17190i	0.301313	−	0.0477233i
$604$	−6.26866	−	16.6385i	−0.255068	−	0.677012i
$605$	−21.1358	+	15.2454i	−0.859293	+	0.619815i
$606$	6.43890	+	18.3639i	0.261563	+	0.745983i
$607$	−31.2527	−	31.2527i	−1.26851	−	1.26851i	−0.946858	−	0.321651i	$-0.895762\pi$
$607$	−31.2527	−	31.2527i	−1.26851	−	1.26851i	−0.321651	−	0.946858i	$-0.604238\pi$
$608$	19.3385	+	0.806984i	0.784279	+	0.0327275i
$609$	−11.3770	+	3.69662i	−0.461021	+	0.149795i
$610$	9.61972	−	19.8333i	0.389491	−	0.803028i
$611$	30.6344	+	9.95373i	1.23934	+	0.402685i
$612$	1.65786	+	2.91312i	0.0670149	+	0.117756i
$613$	−3.45059	+	6.77216i	−0.139368	+	0.273525i	−0.950132	−	0.311848i	$-0.899052\pi$
$613$	−3.45059	+	6.77216i	−0.139368	+	0.273525i	0.810764	+	0.585373i	$0.199052\pi$
$614$	1.22013	−	1.76355i	0.0492406	−	0.0711711i
$615$	12.3728	−	1.91613i	0.498921	−	0.0772659i
$616$	−10.5285	+	16.8271i	−0.424207	+	0.677984i
$617$	−5.40602	+	34.1323i	−0.217638	+	1.37411i	0.600746	+	0.799440i	$0.294870\pi$
$617$	−5.40602	+	34.1323i	−0.217638	+	1.37411i	−0.818384	+	0.574672i	$0.805130\pi$
$618$	−4.10566	−	7.61799i	−0.165154	−	0.306441i
$619$	−11.1832	+	8.12509i	−0.449492	+	0.326575i	−0.789395	−	0.613885i	$-0.789606\pi$
$619$	−11.1832	+	8.12509i	−0.449492	+	0.326575i	0.339903	+	0.940460i	$0.389606\pi$
$620$	−7.70596	+	6.11806i	−0.309479	+	0.245707i
$621$	6.45476	+	4.68966i	0.259020	+	0.188189i
$622$	−0.0163949	+	0.121612i	−0.000657375	+	0.00487621i
$623$	1.35738	+	2.66400i	0.0543822	+	0.106731i
$624$	−8.86147	−	20.5876i	−0.354743	−	0.824163i
$625$	7.39809	+	23.8803i	0.295923	+	0.955212i
$626$	30.0177	+	8.99313i	1.19975	+	0.359438i
$627$	−14.5106	+	7.39350i	−0.579496	+	0.295268i
$628$	3.65646	−	8.07716i	0.145908	−	0.322314i
$629$	1.22700	−	1.68882i	0.0489237	−	0.0673376i
$630$	3.82520	+	2.66599i	0.152400	+	0.106215i
$631$	−15.1133	−	20.8017i	−0.601652	−	0.828103i	0.394206	−	0.919022i	$-0.371020\pi$
$631$	−15.1133	−	20.8017i	−0.601652	−	0.828103i	−0.995858	+	0.0909189i	$0.971020\pi$
$632$	2.29905	−	26.1013i	0.0914513	−	1.03825i
$633$	−24.3889	−	3.86282i	−0.969372	−	0.153533i
$634$	−45.0959	+	1.04077i	−1.79099	+	0.0413341i
$635$	−1.17438	−	7.58320i	−0.0466038	−	0.300930i
$636$	5.43547	+	6.79813i	0.215530	+	0.269563i
$637$	−24.0949	−	12.2770i	−0.954675	−	0.486431i
$638$	39.4974	+	37.7154i	1.56372	+	1.49317i
$639$	−3.88966	+	11.9711i	−0.153872	+	0.473571i
$640$	−14.8492	+	20.4817i	−0.586968	+	0.809610i
$641$	−3.11325	−	9.58161i	−0.122966	−	0.378451i	0.870559	−	0.492064i	$-0.163757\pi$
$641$	−3.11325	−	9.58161i	−0.122966	−	0.378451i	−0.993525	+	0.113613i	$0.963757\pi$
$642$	−7.56005	+	15.7241i	−0.298371	+	0.620582i
$643$	−17.4447	+	17.4447i	−0.687951	+	0.687951i	−0.961779	−	0.273828i	$-0.911710\pi$
$643$	−17.4447	+	17.4447i	−0.687951	+	0.687951i	0.273828	+	0.961779i	$0.411710\pi$
$644$	−1.08541	−	23.5026i	−0.0427711	−	0.926132i
$645$	4.52119	+	6.26805i	0.178022	+	0.246804i
$646$	6.44897	−	4.91673i	0.253731	−	0.193446i
$647$	4.48496	+	28.3169i	0.176322	+	1.11325i	0.904063	+	0.427400i	$0.140570\pi$
$647$	4.48496	+	28.3169i	0.176322	+	1.11325i	−0.727741	+	0.685852i	$0.759430\pi$
$648$	2.60293	+	1.10669i	0.102253	+	0.0434748i
$649$		−	60.3852i		−	2.37033i
$650$	23.8058	+	31.6734i	0.933739	+	1.24233i
$651$		−	3.24397i		−	0.127141i
$652$	−7.91195	−	0.881290i	−0.309856	−	0.0345140i
$653$	−0.257017	−	1.62274i	−0.0100578	−	0.0635027i	0.982149	−	0.188105i	$-0.0602345\pi$
$653$	−0.257017	−	1.62274i	−0.0100578	−	0.0635027i	−0.992207	+	0.124602i	$0.960235\pi$
$654$	11.9762	+	15.7085i	0.468308	+	0.614251i
$655$	−15.7420	+	5.05517i	−0.615089	+	0.197522i
$656$	−19.2558	−	11.4386i	−0.751814	−	0.446601i
$657$	−7.21245	+	7.21245i	−0.281384	+	0.281384i
$658$	10.8027	+	5.19388i	0.421134	+	0.202478i
$659$	6.95495	+	21.4051i	0.270926	+	0.833826i	0.990269	+	0.139170i	$0.0444434\pi$
$659$	6.95495	+	21.4051i	0.270926	+	0.833826i	−0.719342	+	0.694656i	$0.755557\pi$
$660$	2.42905	−	21.1469i	0.0945505	−	0.823142i
$661$	12.2871	−	37.8159i	0.477914	−	1.47087i	−0.364072	−	0.931371i	$-0.618614\pi$
$661$	12.2871	−	37.8159i	0.477914	−	1.47087i	0.841986	−	0.539499i	$-0.181386\pi$
$662$	18.7738	−	19.6609i	0.729665	−	0.764141i
$663$	−8.36733	−	4.26337i	−0.324960	−	0.165575i
$664$	16.3403	−	6.59073i	0.634127	−	0.255770i
$665$	5.15583	−	10.0335i	0.199934	−	0.389084i
$666$	−0.0406433	−	1.76106i	−0.00157490	−	0.0682395i
$667$	−63.9350	−	10.1263i	−2.47557	−	0.392092i
$668$	−39.6843	+	8.17791i	−1.53543	+	0.316413i
$669$	11.6129	+	15.9838i	0.448980	+	0.617968i
$670$	22.6695	+	6.87658i	0.875799	+	0.265665i
$671$	19.5016	−	26.8416i	0.752851	−	1.03621i
$672$	−2.24444	−	8.03302i	−0.0865812	−	0.309880i
$673$	9.74354	−	4.96458i	0.375586	−	0.191371i	−0.255999	−	0.966677i	$-0.582405\pi$
$673$	9.74354	−	4.96458i	0.375586	−	0.191371i	0.631585	+	0.775306i	$0.282405\pi$
$674$	5.85549	−	19.5447i	0.225545	−	0.752835i
$675$	−4.93295	−	0.816074i	−0.189869	−	0.0314107i
$676$	30.7354	+	20.2323i	1.18213	+	0.778164i
$677$	20.7348	+	40.6944i	0.796904	+	1.56401i	0.825488	+	0.564420i	$0.190900\pi$
$677$	20.7348	+	40.6944i	0.796904	+	1.56401i	−0.0285840	+	0.999591i	$0.509100\pi$
$678$	−6.09659	−	0.821898i	−0.234138	−	0.0315648i
$679$	−4.06236	−	2.95147i	−0.155899	−	0.113267i
$680$	0.696836	+	10.5765i	0.0267224	+	0.405590i
$681$	0.133907	−	0.0972891i	0.00513132	−	0.00372812i
$682$	−13.0368	+	7.02609i	−0.499206	+	0.269043i
$683$	−3.21000	+	20.2671i	−0.122827	+	0.775500i	0.846980	+	0.531626i	$0.178419\pi$
$683$	−3.21000	+	20.2671i	−0.122827	+	0.775500i	−0.969807	+	0.243875i	$0.921581\pi$
$684$	1.81215	−	6.59884i	0.0692892	−	0.252313i
$685$	−17.9804	+	17.8573i	−0.686996	+	0.682294i
$686$	−20.2789	−	14.0302i	−0.774252	−	0.535676i
$687$	3.40358	−	6.67991i	0.129855	−	0.254854i
$688$	0.894969	−	13.7961i	0.0341204	−	0.525973i
$689$	−23.1925	−	7.53569i	−0.883563	−	0.287087i
$690$	11.8936	+	22.2511i	0.452782	+	0.847084i
$691$	19.2612	−	6.25835i	0.732731	−	0.238079i	0.0811970	−	0.996698i	$-0.474126\pi$
$691$	19.2612	−	6.25835i	0.732731	−	0.238079i	0.651534	+	0.758619i	$0.274126\pi$
$692$	−10.3039	+	11.3017i	−0.391697	+	0.429628i
$693$	4.96237	+	4.96237i	0.188505	+	0.188505i
$694$	4.64576	−	1.62893i	0.176351	−	0.0618335i
$695$	26.4225	+	19.3361i	1.00226	+	0.733460i
$696$	−22.8929	+	1.58729i	−0.867752	+	0.0601659i
$697$	−9.26836	+	1.46796i	−0.351064	+	0.0556031i
$698$	−1.47890	+	0.269351i	−0.0559772	+	0.0101951i
$699$	10.6764			0.403818
$700$	7.20456	+	12.8643i	0.272307	+	0.486226i
$701$	13.8933			0.524741			0.262370	−	0.964967i	$-0.415496\pi$
$701$	13.8933			0.524741			0.262370	+	0.964967i	$0.415496\pi$
$702$	−7.79620	+	1.41991i	−0.294248	+	0.0535912i
$703$	−4.20939	+	0.666701i	−0.158760	+	0.0251451i
$704$	−27.4218	+	26.4186i	−1.03350	+	0.995687i
$705$	−12.8538	−	0.0441439i	−0.484103	−	0.00166255i
$706$	−27.4635	+	9.62948i	−1.03360	+	0.362410i
$707$	−14.3463	−	14.3463i	−0.539548	−	0.539548i
$708$	18.7505	+	17.0950i	0.704686	+	0.642471i
$709$	15.5492	−	5.05225i	0.583964	−	0.189741i	−0.00211169	−	0.999998i	$-0.500672\pi$
$709$	15.5492	−	5.05225i	0.583964	−	0.189741i	0.586076	+	0.810256i	$0.300672\pi$
$710$	−27.5876	+	28.6932i	−1.03535	+	1.07684i
$711$	−8.81053	−	2.86271i	−0.330421	−	0.107360i
$712$	1.28692	+	5.58928i	0.0482294	+	0.209467i
$713$	7.96929	−	15.6406i	0.298452	−	0.585746i
$714$	−2.87380	−	1.98828i	−0.107549	−	0.0744094i
$715$	26.8921	+	53.2298i	1.00571	+	1.99068i
$716$	32.1266	+	8.82250i	1.20063	+	0.329712i
$717$	−3.47793	+	21.9588i	−0.129886	+	0.820065i
$718$	20.4860	−	11.0408i	0.764531	−	0.412038i
$719$	−6.10365	+	4.43456i	−0.227628	+	0.165381i	−0.695753	−	0.718281i	$-0.744929\pi$
$719$	−6.10365	+	4.43456i	−0.227628	+	0.165381i	0.468126	+	0.883662i	$0.344929\pi$
$720$	5.87875	+	6.74094i	0.219088	+	0.251220i
$721$	7.29931	+	5.30326i	0.271840	+	0.197504i
$722$	10.2212	+	1.37795i	0.380394	+	0.0512820i
$723$	9.25986	+	18.1735i	0.344378	+	0.675880i
$724$	−19.4756	+	29.5860i	−0.723807	+	1.09955i
$725$	38.6661	−	12.2704i	1.43602	−	0.455712i
$726$	4.73021	−	15.7887i	0.175554	−	0.585974i
$727$	−42.6795	+	21.7463i	−1.58289	+	0.806525i	−0.999982	−	0.00600972i	$-0.998087\pi$
$727$	−42.6795	+	21.7463i	−1.58289	+	0.806525i	−0.582913	+	0.812535i	$0.698087\pi$
$728$	17.6272	+	15.3413i	0.653307	+	0.568586i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−30.4747	+	10.5679i	−1.12792	+	0.391135i
$731$	−3.40471	−	4.68618i	−0.125928	−	0.173325i
$732$	2.81382	+	13.6544i	0.104002	+	0.504681i
$733$	12.5781	+	1.99218i	0.464584	+	0.0735829i	0.384339	−	0.923192i	$-0.374430\pi$
$733$	12.5781	+	1.99218i	0.464584	+	0.0735829i	0.0802457	+	0.996775i	$0.474430\pi$
$734$	−0.620596	−	26.8901i	−0.0229066	−	0.992531i
$735$	10.6526	+	1.72473i	0.392928	+	0.0636177i
$736$	8.91285	−	44.2445i	0.328532	−	1.63087i
$737$	31.7699	+	16.1876i	1.17026	+	0.596276i
$738$	−5.46858	+	5.72696i	−0.201301	+	0.210812i
$739$	7.24911	−	22.3105i	0.266663	−	0.820704i	−0.724643	−	0.689125i	$-0.757995\pi$
$739$	7.24911	−	22.3105i	0.266663	−	0.820704i	0.991306	−	0.131579i	$-0.0420048\pi$
$740$	2.31467	−	5.06675i	0.0850890	−	0.186258i
$741$	5.92463	+	18.2341i	0.217647	+	0.669848i
$742$	−8.17844	−	3.93214i	−0.300240	−	0.144353i
$743$	31.2758	−	31.2758i	1.14740	−	1.14740i	0.160337	−	0.987062i	$-0.448742\pi$
$743$	31.2758	−	31.2758i	1.14740	−	1.14740i	0.987062	−	0.160337i	$-0.0512581\pi$
$744$	1.50902	−	6.03721i	0.0553233	−	0.221335i
$745$	15.4065	+	5.06444i	0.564450	+	0.185547i
$746$	−0.501939	−	0.658362i	−0.0183773	−	0.0241043i
$747$	−0.974493	−	6.15271i	−0.0356548	−	0.225116i
$748$	−1.76611	+	15.8556i	−0.0645753	+	0.579738i
$749$		−	18.1901i		−	0.664652i
$750$	−12.9093	−	9.12957i	−0.471382	−	0.333365i
$751$			25.1683i			0.918404i	0.888332	+	0.459202i	$0.151865\pi$
$751$			25.1683i			0.918404i	−0.888332	+	0.459202i	$0.848135\pi$
$752$	17.6884	+	14.6913i	0.645029	+	0.535735i
$753$	2.81947	+	17.8014i	0.102747	+	0.648721i
$754$	51.1285	−	38.9807i	1.86199	−	1.41959i
$755$	−18.8847	−	6.20781i	−0.687286	−	0.225925i
$756$	−2.94574	+	0.136042i	−0.107135	+	0.00494778i
$757$	19.3441	−	19.3441i	0.703072	−	0.703072i	−0.261997	−	0.965069i	$-0.584381\pi$
$757$	19.3441	−	19.3441i	0.703072	−	0.703072i	0.965069	+	0.261997i	$0.0843809\pi$
$758$	3.04711	−	6.33769i	0.110676	−	0.230195i
$759$	11.7350	+	36.1166i	0.425953	+	1.31095i
$760$	14.2626	−	16.2746i	0.517360	−	0.590342i
$761$	−8.59037	+	26.4384i	−0.311401	+	0.958392i	0.665810	+	0.746121i	$0.268086\pi$
$761$	−8.59037	+	26.4384i	−0.311401	+	0.958392i	−0.977211	+	0.212271i	$0.931914\pi$
$762$	3.51000	+	3.35164i	0.127154	+	0.121417i
$763$	−18.3497	−	9.34964i	−0.664304	−	0.338480i
$764$	15.0309	−	12.0180i	0.543798	−	0.434795i
$765$	3.69929	+	0.598940i	0.133748	+	0.0216547i
$766$	26.1851	−	0.604326i	0.946107	−	0.0218352i
$767$	−70.2144	−	11.1209i	−2.53530	−	0.401551i
$768$	−0.440254	−	15.9939i	−0.0158863	−	0.577132i
$769$	−13.5028	−	18.5850i	−0.486923	−	0.670192i	0.492894	−	0.870090i	$-0.335939\pi$
$769$	−13.5028	−	18.5850i	−0.486923	−	0.670192i	−0.979817	+	0.199897i	$0.935939\pi$
$770$	7.27102	+	20.9675i	0.262029	+	0.755616i
$771$	−0.969038	+	1.33377i	−0.0348991	+	0.0480344i
$772$	20.9070	+	9.46438i	0.752458	+	0.340631i
$773$	17.5103	−	8.92192i	0.629800	−	0.320899i	−0.109792	−	0.993955i	$-0.535018\pi$
$773$	17.5103	−	8.92192i	0.629800	−	0.320899i	0.739592	+	0.673055i	$0.235018\pi$
$774$	−4.68231	−	1.40279i	−0.168302	−	0.0504223i
$775$	−0.0755586	+	11.0005i	−0.00271415	+	0.395148i
$776$	−6.18730	−	7.38256i	−0.222111	−	0.265019i
$777$	0.833771	+	1.63637i	0.0299114	+	0.0587044i
$778$	−2.81747	+	20.8992i	−0.101011	+	0.749271i
$779$	15.4994	+	11.2609i	0.555322	+	0.403465i
$780$	−24.1417	−	6.71897i	−0.864413	−	0.240578i
$781$	−48.4691	+	35.2148i	−1.73436	+	1.26009i
$782$	−8.97138	−	16.6463i	−0.320816	−	0.595270i
$783$	−1.26920	+	8.01339i	−0.0453574	+	0.286375i
$784$	−12.7378	−	14.5051i	−0.454922	−	0.518039i
$785$	−4.46994	−	8.84774i	−0.159539	−	0.315789i
$786$	5.94955	−	8.59933i	0.212214	−	0.306728i
$787$	8.24852	−	16.1886i	0.294028	−	0.577062i	−0.695982	−	0.718059i	$-0.745031\pi$
$787$	8.24852	−	16.1886i	0.294028	−	0.577062i	0.990010	+	0.140997i	$0.0450307\pi$
$788$	−3.78745	+	2.15544i	−0.134922	+	0.0767843i
$789$	−24.2620	−	7.88319i	−0.863749	−	0.280649i
$790$	−21.1176	−	20.3040i	−0.751331	−	0.722383i
$791$	6.09981	−	1.98195i	0.216884	−	0.0704699i
$792$	6.92686	+	11.5436i	0.246135	+	0.410185i
$793$	−27.6193	−	27.6193i	−0.980789	−	0.980789i
$794$	−8.19386	−	23.3691i	−0.290789	−	0.829339i
$795$	9.73126	+	0.0334201i	0.345132	+	0.00118529i
$796$	−18.1365	+	6.83304i	−0.642832	+	0.242191i
$797$	12.2393	−	1.93851i	0.433537	−	0.0686655i	0.0641480	−	0.997940i	$-0.479567\pi$
$797$	12.2393	−	1.93851i	0.433537	−	0.0686655i	0.369389	+	0.929275i	$0.379567\pi$
$798$	1.27838	+	7.01908i	0.0452542	+	0.248473i
$799$	9.63389			0.340823
$800$	7.42389	+	27.2926i	0.262474	+	0.964939i
$801$	2.02781			0.0716492
$802$	5.94944	+	32.6660i	0.210082	+	1.15348i
$803$	−47.9508	+	7.59466i	−1.69215	+	0.268010i
$804$	−14.0205	+	5.28231i	−0.494465	+	0.186293i
$805$	−21.2277	−	15.5345i	−0.748180	−	0.547520i
$806$	5.76883	+	16.4529i	0.203198	+	0.579527i
$807$	17.3973	+	17.3973i	0.612416	+	0.612416i
$808$	−20.0257	−	33.3728i	−0.704501	−	1.17405i
$809$	7.78970	−	2.53103i	0.273871	−	0.0889862i	−0.168861	−	0.985640i	$-0.554009\pi$
$809$	7.78970	−	2.53103i	0.273871	−	0.0889862i	0.442733	+	0.896654i	$0.354009\pi$
$810$	2.78887	−	1.49070i	0.0979910	−	0.0523780i
$811$	51.5148	+	16.7382i	1.80893	+	0.587756i	1.00000		0.000151490i	$-4.82209e-5\pi$
$811$	51.5148	+	16.7382i	1.80893	+	0.587756i	0.808928	+	0.587908i	$0.200048\pi$
$812$	20.7936	−	11.8336i	0.729712	−	0.415279i
$813$	0.428639	−	0.841252i	0.0150330	−	0.0295040i
$814$	4.77035	−	6.89494i	0.167201	−	0.241668i
$815$	−6.31521	+	6.27198i	−0.221212	+	0.219698i
$816$	−4.42340	−	5.03712i	−0.154850	−	0.176334i
$817$	−1.84998	+	11.6803i	−0.0647227	+	0.408643i
$818$	−25.6441	−	47.5823i	−0.896624	−	1.66368i
$819$	6.68402	−	4.85623i	0.233559	−	0.169690i
$820$	−23.4629	+	8.74790i	−0.819361	+	0.305490i
$821$	10.9434	+	7.95088i	0.381929	+	0.277487i	0.762140	−	0.647412i	$-0.224149\pi$
$821$	10.9434	+	7.95088i	0.381929	+	0.277487i	−0.380211	+	0.924900i	$0.624149\pi$
$822$	2.14130	−	15.8835i	0.0746865	−	0.554002i
$823$	9.68724	+	19.0123i	0.337676	+	0.662726i	0.995936	−	0.0900643i	$-0.0287073\pi$
$823$	9.68724	+	19.0123i	0.337676	+	0.662726i	−0.658260	+	0.752791i	$0.728707\pi$
$824$	11.1175	+	13.2651i	0.387295	+	0.462112i
$825$	−16.7120	−	16.9432i	−0.581839	−	0.589887i
$826$	−25.3413	−	7.59211i	−0.881737	−	0.264163i
$827$	41.9088	−	21.3536i	1.45731	−	0.742537i	0.467375	−	0.884059i	$-0.345200\pi$
$827$	41.9088	−	21.3536i	1.45731	−	0.742537i	0.989935	+	0.141522i	$0.0451996\pi$
$828$	−14.5369	−	6.58071i	−0.505192	−	0.228696i
$829$	−13.0763	+	17.9979i	−0.454158	+	0.625094i	−0.973284	−	0.229603i	$-0.926257\pi$
$829$	−13.0763	+	17.9979i	−0.454158	+	0.625094i	0.519127	+	0.854697i	$0.326257\pi$
$830$	5.71824	−	18.8509i	0.198483	−	0.654324i
$831$	−6.78288	−	9.33584i	−0.235296	−	0.323857i
$832$	25.6687	+	36.7507i	0.889903	+	1.27410i
$833$	−7.98844	−	1.26525i	−0.276783	−	0.0438381i
$834$	−20.7023	+	0.477788i	−0.716862	+	0.0165444i
$835$	−20.7046	+	40.2923i	−0.716511	+	1.39437i
$836$	25.4393	−	20.3401i	0.879838	−	0.703477i
$837$	−1.96034	−	0.998844i	−0.0677593	−	0.0345251i
$838$	10.6777	+	10.1959i	0.368854	+	0.352213i
$839$	7.78737	−	23.9670i	0.268850	−	0.827434i	−0.721932	−	0.691964i	$-0.756746\pi$
$839$	7.78737	−	23.9670i	0.268850	−	0.827434i	0.990781	−	0.135470i	$-0.0432545\pi$
$840$	−8.56913	−	3.67813i	−0.295663	−	0.126908i
$841$	−11.3796	−	35.0230i	−0.392402	−	1.20769i
$842$	2.71109	−	5.63879i	0.0934302	−	0.194325i
$843$	3.62290	−	3.62290i	0.124779	−	0.124779i
$844$	49.3333	−	2.27834i	1.69812	−	0.0784235i
$845$	39.1700	−	12.5785i	1.34749	−	0.432715i
$846$	6.46492	−	4.92889i	0.222268	−	0.169459i
$847$	2.68816	+	16.9724i	0.0923664	+	0.583178i
$848$	−13.3914	−	11.1223i	−0.459862	−	0.381943i
$849$		−	9.18017i		−	0.315063i
$850$	9.69888	+	6.80927i	0.332669	+	0.233556i
$851$			9.93793i			0.340668i
$852$	2.78687	−	25.0197i	0.0954766	−	0.857159i
$853$	0.162467	+	1.02578i	0.00556276	+	0.0351219i	0.990314	−	0.138849i	$-0.0443402\pi$
$853$	0.162467	+	1.02578i	0.00556276	+	0.0351219i	−0.984751	+	0.173971i	$0.944340\pi$
$854$	−8.81250	−	11.5588i	−0.301557	−	0.395534i
$855$	−4.47578	−	6.20508i	−0.153068	−	0.212209i
$856$	8.46161	−	33.8528i	0.289212	−	1.15706i
$857$	37.1535	−	37.1535i	1.26914	−	1.26914i	0.322604	−	0.946534i	$-0.395442\pi$
$857$	37.1535	−	37.1535i	1.26914	−	1.26914i	0.946534	−	0.322604i	$-0.104558\pi$
$858$	−33.9930	−	16.3436i	−1.16050	−	0.557961i
$859$	3.89611	+	11.9910i	0.132933	+	0.409127i	0.995263	−	0.0972207i	$-0.0309953\pi$
$859$	3.89611	+	11.9910i	0.132933	+	0.409127i	−0.862329	+	0.506348i	$0.830995\pi$
$860$	−11.3865	−	10.4530i	−0.388276	−	0.356446i
$861$	2.55117	−	7.85170i	0.0869437	−	0.267585i
$862$	−24.4958	+	25.6532i	−0.834330	+	0.873751i
$863$	20.6059	+	10.4992i	0.701431	+	0.357397i	0.768058	−	0.640381i	$-0.221223\pi$
$863$	20.6059	+	10.4992i	0.701431	+	0.357397i	−0.0666261	+	0.997778i	$0.521223\pi$
$864$	−5.54546	−	1.11711i	−0.188660	−	0.0380047i
$865$	2.61686	+	16.8976i	0.0889758	+	0.574535i
$866$	−0.395780	−	17.1489i	−0.0134491	−	0.582745i
$867$	14.0166	+	2.22001i	0.476028	+	0.0753955i
$868$	1.30948	+	6.35442i	0.0444468	+	0.215683i
$869$	−25.9174	−	35.6723i	−0.879189	−	1.21010i
$870$	−14.6699	+	21.0487i	−0.497357	+	0.713617i
$871$	24.6734	−	33.9600i	0.836026	−	1.15069i
$872$	−29.8005	−	25.9360i	−1.00917	−	0.878304i
$873$	−3.03441	+	1.54611i	−0.102699	+	0.0523279i
$874$	−11.0798	+	36.9826i	−0.374779	+	1.25096i
$875$	16.2543	+	2.74639i	0.549497	+	0.0928448i
$876$	11.2166	−	17.0395i	0.378974	−	0.575710i
$877$	−9.76273	−	19.1604i	−0.329664	−	0.647002i	0.665373	−	0.746511i	$-0.268273\pi$
$877$	−9.76273	−	19.1604i	−0.329664	−	0.647002i	−0.995037	+	0.0995093i	$0.968273\pi$
$878$	30.3321	+	4.08915i	1.02366	+	0.138002i
$879$	−23.8641	−	17.3383i	−0.804916	−	0.584806i
$880$	3.77818	+	42.4039i	0.127363	+	1.42944i
$881$	−11.5702	+	8.40623i	−0.389809	+	0.283213i	−0.765377	−	0.643582i	$-0.777448\pi$
$881$	−11.5702	+	8.40623i	−0.389809	+	0.283213i	0.375568	+	0.926795i	$0.377448\pi$
$882$	−6.00805	+	3.23799i	−0.202301	+	0.109029i
$883$	−6.44822	+	40.7125i	−0.217000	+	1.37008i	0.603009	+	0.797734i	$0.293968\pi$
$883$	−6.44822	+	40.7125i	−0.217000	+	1.37008i	−0.820009	+	0.572350i	$0.806032\pi$
$884$	18.1112	+	4.97364i	0.609147	+	0.167282i
$885$	28.0344	−	4.34157i	0.942366	−	0.145940i
$886$	13.6136	+	9.41873i	0.457357	+	0.316428i
$887$	3.65750	−	7.17824i	0.122807	−	0.241022i	−0.821416	−	0.570330i	$-0.806815\pi$
$887$	3.65750	−	7.17824i	0.122807	−	0.241022i	0.944223	+	0.329308i	$0.106815\pi$
$888$	0.790493	+	3.43322i	0.0265272	+	0.115211i
$889$	−4.81223	−	1.56359i	−0.161397	−	0.0524411i
$890$	5.76966	+	2.79844i	0.193399	+	0.0938040i
$891$	4.52673	−	1.47082i	0.151651	−	0.0492744i
$892$	−29.1999	−	26.6219i	−0.977684	−	0.891367i
$893$	−13.9078	−	13.9078i	−0.465408	−	0.465408i
$894$	−9.67914	+	3.39378i	−0.323719	+	0.113505i
$895$	30.2096	−	21.7905i	1.00980	−	0.728375i
$896$	7.63916	+	14.8294i	0.255207	+	0.495415i
$897$	44.1566	−	6.99373i	1.47435	−	0.233514i
$898$	21.6815	−	3.94883i	0.723520	−	0.131774i
$899$	17.8504			0.595343
$900$	9.99229	−	0.392711i	0.333076	−	0.0130904i
$901$	−7.29355			−0.242983
$902$	−37.0798	+	6.75332i	−1.23462	+	0.224861i
$903$	5.03334	−	0.797202i	0.167499	−	0.0265292i
$904$	12.2740	−	0.851024i	0.408228	−	0.0283047i
$905$	12.1082	+	37.7052i	0.402489	+	1.25336i
$906$	11.8643	−	4.15997i	0.394167	−	0.138206i
$907$	22.6464	+	22.6464i	0.751962	+	0.751962i	0.974845	−	0.222883i	$-0.0715469\pi$
$907$	22.6464	+	22.6464i	0.751962	+	0.751962i	−0.222883	+	0.974845i	$0.571547\pi$
$908$	−0.223030	+	0.244627i	−0.00740150	+	0.00811825i
$909$	−13.0868	+	4.25217i	−0.434063	+	0.141036i
$910$	25.7195	−	4.59308i	0.852594	−	0.152259i
$911$	−13.8057	−	4.48573i	−0.457402	−	0.148619i	0.0712485	−	0.997459i	$-0.477302\pi$
$911$	−13.8057	−	4.48573i	−0.457402	−	0.148619i	−0.528650	+	0.848840i	$0.677302\pi$
$912$	−0.885979	+	13.6576i	−0.0293377	+	0.452247i
$913$	13.4608	−	26.4183i	0.445488	−	0.874319i
$914$	2.25140	+	1.55766i	0.0744695	+	0.0515227i
$915$	13.8636	+	7.12394i	0.458317	+	0.235510i
$916$	−3.97062	+	14.4588i	−0.131193	+	0.477732i
$917$	−1.70547	+	10.7679i	−0.0563197	+	0.355588i
$918$	−2.08639	+	1.12444i	−0.0688610	+	0.0371121i
$919$	8.34391	−	6.06221i	0.275240	−	0.199974i	−0.441598	−	0.897213i	$-0.645588\pi$
$919$	8.34391	−	6.06221i	0.275240	−	0.199974i	0.716839	+	0.697239i	$0.245588\pi$
$920$	−32.2797	−	38.7852i	−1.06423	−	1.27871i
$921$	1.22678	+	0.891308i	0.0404238	+	0.0293696i
$922$	−5.45769	−	0.735766i	−0.179740	−	0.0242312i
$923$	32.0206	+	62.8440i	1.05397	+	2.06854i
$924$	−11.7236	−	7.71735i	−0.385679	−	0.253882i
$925$	−2.78924	−	5.56841i	−0.0917096	−	0.183088i
$926$	−13.8818	+	46.3355i	−0.456186	+	1.52268i
$927$	5.45229	−	2.77808i	0.179077	−	0.0912441i
$928$	44.2027	−	12.3503i	1.45103	−	0.405419i
$929$	1.79123	−	2.46542i	0.0587683	−	0.0808877i	−0.778621	−	0.627494i	$-0.784081\pi$
$929$	1.79123	−	2.46542i	0.0587683	−	0.0808877i	0.837390	+	0.546606i	$0.184081\pi$
$930$	−4.19925	−	5.54730i	−0.137699	−	0.181903i
$931$	9.70586	+	13.3590i	0.318097	+	0.437823i
$932$	−20.9133	+	4.30970i	−0.685039	+	0.141169i
$933$	−0.0857026	−	0.0135740i	−0.00280578	−	0.000444391i
$934$	0.0523566	+	2.26858i	0.00171316	+	0.0742303i
$935$	12.5691	+	12.6557i	0.411053	+	0.413886i
$936$	14.6983	−	5.92845i	0.480430	−	0.193777i
$937$	−22.1391	−	11.2805i	−0.723254	−	0.368516i	0.0532902	−	0.998579i	$-0.483029\pi$
$937$	−22.1391	−	11.2805i	−0.723254	−	0.368516i	−0.776544	+	0.630063i	$0.783029\pi$
$938$	10.7876	−	11.2973i	0.352229	−	0.368871i
$939$	−6.84715	+	21.0733i	−0.223448	+	0.687703i
$940$	25.1964	−	5.10219i	0.821816	−	0.166415i
$941$	−17.5113	−	53.8942i	−0.570851	−	1.75690i	−0.649890	−	0.760028i	$-0.725185\pi$
$941$	−17.5113	−	53.8942i	−0.570851	−	1.75690i	0.0790384	−	0.996872i	$-0.474815\pi$
$942$	5.65024	+	2.71659i	0.184095	+	0.0885114i
$943$	31.5892	−	31.5892i	1.02868	−	1.02868i
$944$	−43.6299	−	25.9175i	−1.42003	−	0.843543i
$945$	−1.94704	+	2.66061i	−0.0633373	+	0.0865497i
$946$	−14.1054	−	18.5012i	−0.458608	−	0.601527i
$947$	−4.35758	−	27.5127i	−0.141602	−	0.894042i	−0.951540	−	0.307526i	$-0.900499\pi$
$947$	−4.35758	−	27.5127i	−0.141602	−	0.894042i	0.809937	−	0.586516i	$-0.199501\pi$
$948$	18.4140	+	2.05108i	0.598059	+	0.0666160i
$949$			57.1546i			1.85532i
$950$	−4.17155	−	23.8318i	−0.135343	−	0.773206i
$951$		−	31.8961i		−	1.03430i
$952$	6.43192	+	2.73466i	0.208460	+	0.0886308i
$953$	8.63132	+	54.4960i	0.279596	+	1.76530i	0.583034	+	0.812447i	$0.301865\pi$
$953$	8.63132	+	54.4960i	0.279596	+	1.76530i	−0.303439	+	0.952851i	$0.598135\pi$
$954$	−4.89440	+	3.73152i	−0.158462	+	0.120812i
$955$	0.0738928	−	21.5161i	0.00239112	−	0.696245i
$956$	−2.05132	−	44.4176i	−0.0663444	−	1.43657i
$957$	−27.3061	+	27.3061i	−0.882680	+	0.882680i
$958$	3.97531	−	8.26824i	0.128436	−	0.267135i
$959$	5.16360	+	15.8919i	0.166741	+	0.513177i
$960$	−14.2366	−	10.8314i	−0.459485	−	0.349581i
$961$	8.08369	−	24.8790i	0.260764	−	0.802550i
$962$	−7.13873	−	6.81666i	−0.230162	−	0.219778i
$963$	−10.9923	−	5.60087i	−0.354223	−	0.180486i
$964$	−25.4746	−	31.8611i	−0.820482	−	1.02618i
$965$	22.9015	−	11.5700i	0.737226	−	0.372452i
$966$	16.6321	−	0.383853i	0.535130	−	0.0123503i
$967$	42.4566	+	6.72446i	1.36531	+	0.216244i	0.795710	−	0.605677i	$-0.207098\pi$
$967$	42.4566	+	6.72446i	1.36531	+	0.216244i	0.569601	+	0.821921i	$0.307098\pi$
$968$	−2.89234	+	32.8370i	−0.0929633	+	1.05542i
$969$	3.37051	+	4.63911i	0.108276	+	0.149030i
$970$	−10.7674	+	0.211505i	−0.345720	+	0.00679101i
$971$	0.810009	−	1.11488i	0.0259944	−	0.0357783i	−0.795822	−	0.605531i	$-0.792961\pi$
$971$	0.810009	−	1.11488i	0.0259944	−	0.0357783i	0.821816	+	0.569752i	$0.192961\pi$
$972$	−0.824804	+	1.82200i	−0.0264556	+	0.0584408i
$973$	19.2365	−	9.80150i	0.616695	−	0.314222i
$974$	−3.28532	−	0.984263i	−0.105268	−	0.0315378i
$975$	−22.7789	+	16.3120i	−0.729509	+	0.522402i
$976$	−11.0236	−	25.6109i	−0.352858	−	0.819786i
$977$	−9.92504	−	19.4790i	−0.317530	−	0.623188i	0.675982	−	0.736919i	$-0.263720\pi$
$977$	−9.92504	−	19.4790i	−0.317530	−	0.623188i	−0.993512	+	0.113731i	$0.963720\pi$
$978$	0.752083	−	5.57873i	0.0240490	−	0.178388i
$979$	7.80842	+	5.67315i	0.249558	+	0.181315i
$980$	−21.5630	+	0.921634i	−0.688804	+	0.0294405i
$981$	−11.3000	+	8.20994i	−0.360782	+	0.262123i
$982$	8.98278	+	16.6674i	0.286652	+	0.531879i
$983$	1.68880	−	10.6627i	0.0538643	−	0.340086i	−0.946009	−	0.324142i	$-0.894925\pi$
$983$	1.68880	−	10.6627i	0.0538643	−	0.340086i	0.999873	−	0.0159443i	$-0.00507544\pi$
$984$	8.40029	−	13.4257i	0.267791	−	0.427995i
$985$	−0.778703	+	4.80957i	−0.0248115	+	0.153246i
$986$	10.9407	−	15.8135i	0.348424	−	0.503604i
$987$	−3.84789	+	7.55191i	−0.122480	+	0.240380i
$988$	−18.9659	−	33.3262i	−0.603386	−	1.06025i
$989$	26.2264	+	8.52147i	0.833950	+	0.270967i
$990$	14.9095	+	2.06215i	0.473855	+	0.0655394i
$991$	−38.6911	+	12.5715i	−1.22906	+	0.399347i	−0.850375	−	0.526178i	$-0.823625\pi$
$991$	−38.6911	+	12.5715i	−1.22906	+	0.399347i	−0.378688	+	0.925524i	$0.623625\pi$
$992$	−0.518908	+	12.4351i	−0.0164754	+	0.394814i
$993$	13.5923	+	13.5923i	0.431340	+	0.431340i
$994$	8.68438	+	24.7681i	0.275452	+	0.785595i
$995$	−6.76671	+	20.5850i	−0.214519	+	0.652588i
$996$	4.39252	+	11.6588i	0.139182	+	0.369423i
$997$	−8.40429	+	1.33111i	−0.266167	+	0.0421567i	−0.288091	−	0.957603i	$-0.593021\pi$
$997$	−8.40429	+	1.33111i	−0.266167	+	0.0421567i	0.0219246	+	0.999760i	$0.493021\pi$
$998$	−8.37460	−	45.9816i	−0.265093	−	1.45552i
$999$	1.24559			0.0394086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.14	yes	240
3.2	odd	2		900.2.bj.f.703.17		240
4.3	odd	2	inner	300.2.w.a.103.8	yes	240
12.11	even	2		900.2.bj.f.703.23		240
25.17	odd	20	inner	300.2.w.a.67.8	✓	240
75.17	even	20		900.2.bj.f.667.23		240
100.67	even	20	inner	300.2.w.a.67.14	yes	240
300.167	odd	20		900.2.bj.f.667.17		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.8	✓	240	25.17	odd	20	inner
300.2.w.a.67.14	yes	240	100.67	even	20	inner
300.2.w.a.103.8	yes	240	4.3	odd	2	inner
300.2.w.a.103.14	yes	240	1.1	even	1	trivial
900.2.bj.f.667.17		240	300.167	odd	20
900.2.bj.f.667.23		240	75.17	even	20
900.2.bj.f.703.17		240	3.2	odd	2
900.2.bj.f.703.23		240	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.253401 - 1.39133i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.87158 + 0.705127i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(-0.467933 - 1.33456i) q^{6} +(1.04258 + 1.04258i) q^{7} +(1.45532 + 2.42529i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.253401 - 1.39133i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.87158 + 0.705127i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(-0.467933 - 1.33456i) q^{6} +(1.04258 + 1.04258i) q^{7} +(1.45532 + 2.42529i) q^{8} +(0.951057 - 0.309017i) q^{9} +(3.13246 + 0.433253i) q^{10} +(4.52673 + 1.47082i) q^{11} +(-1.73823 + 0.989225i) q^{12} +(2.54390 - 4.99269i) q^{13} +(1.18638 - 1.71477i) q^{14} +(-0.357381 + 2.20732i) q^{15} +(3.00559 - 2.63940i) q^{16} +(0.262171 - 1.65528i) q^{17} +(-0.670942 - 1.24492i) q^{18} +(-2.76811 + 2.01115i) q^{19} +(-0.190971 - 4.46806i) q^{20} +(1.19285 + 0.866653i) q^{21} +(0.899317 - 6.67086i) q^{22} +(3.62217 + 7.10891i) q^{23} +(1.81680 + 2.16777i) q^{24} +(-4.02480 - 2.96664i) q^{25} +(-7.59109 - 2.27425i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-2.68643 - 1.21612i) q^{28} +(-4.76887 + 6.56378i) q^{29} +(3.16167 - 0.0621050i) q^{30} +(-1.29321 - 1.77995i) q^{31} +(-4.43388 - 3.51293i) q^{32} +(4.70108 + 0.744578i) q^{33} +(-2.36947 + 0.0546849i) q^{34} +(-2.94272 + 1.48668i) q^{35} +(-1.56208 + 1.24896i) q^{36} +(1.10983 + 0.565484i) q^{37} +(3.49960 + 3.34171i) q^{38} +(1.73155 - 5.32918i) q^{39} +(-6.16813 + 1.39791i) q^{40} +(-1.73027 - 5.32522i) q^{41} +(0.903528 - 1.87925i) q^{42} +(2.44396 - 2.44396i) q^{43} +(-9.50923 + 0.439160i) q^{44} +(-0.00767928 + 2.23605i) q^{45} +(8.97295 - 6.84103i) q^{46} +(0.899254 + 5.67766i) q^{47} +(2.55570 - 3.07708i) q^{48} -4.82603i q^{49} +(-3.10767 + 6.35156i) q^{50} -1.67591i q^{51} +(-1.24063 + 11.1380i) q^{52} +(-0.680800 - 4.29840i) q^{53} +(-0.857431 - 1.12464i) q^{54} +(-6.28532 + 8.58881i) q^{55} +(-1.01128 + 4.04587i) q^{56} +(-2.41941 + 2.41941i) q^{57} +(10.3408 + 4.97178i) q^{58} +(-3.92044 - 12.0659i) q^{59} +(-0.887578 - 4.38317i) q^{60} +(2.15405 - 6.62949i) q^{61} +(-2.14879 + 2.25032i) q^{62} +(1.31373 + 0.669381i) q^{63} +(-3.76408 + 7.05915i) q^{64} +(8.82932 + 8.89017i) q^{65} +(-0.155308 - 6.72942i) q^{66} +(7.39906 + 1.17190i) q^{67} +(0.676511 + 3.28285i) q^{68} +(4.68966 + 6.45476i) q^{69} +(2.81415 + 3.71756i) q^{70} +(-7.39857 + 10.1833i) q^{71} +(2.13355 + 1.85687i) q^{72} +(-9.08821 + 4.63068i) q^{73} +(0.505542 - 1.68742i) q^{74} +(-4.43934 - 2.30050i) q^{75} +(3.76261 - 5.71588i) q^{76} +(3.18604 + 6.25296i) q^{77} +(-7.85340 - 1.05874i) q^{78} +(-7.49468 - 5.44520i) q^{79} +(3.50796 + 8.22765i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-6.97066 + 3.75678i) q^{82} +(0.974493 - 6.15271i) q^{83} +(-2.84360 - 0.780899i) q^{84} +(3.33315 + 1.71277i) q^{85} +(-4.01965 - 2.78105i) q^{86} +(-3.68335 + 7.22899i) q^{87} +(3.02066 + 13.1192i) q^{88} +(1.92856 + 0.626628i) q^{89} +(3.11303 - 0.555934i) q^{90} +(7.85754 - 2.55307i) q^{91} +(-11.7919 - 10.7508i) q^{92} +(-1.55574 - 1.55574i) q^{93} +(7.67161 - 2.68988i) q^{94} +(-2.33924 - 7.28448i) q^{95} +(-4.92884 - 2.77607i) q^{96} +(-3.36367 + 0.532753i) q^{97} +(-6.71459 + 1.22292i) q^{98} +4.75968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more