LMFDB - Embedded newform 300.2.w.a.103.8

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			103.8
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976661 - 1.02281i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-0.0922667 + 1.99787i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(1.12464 + 0.857431i) q^{6} +(-1.04258 - 1.04258i) q^{7} +(2.13355 - 1.85687i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.976661 - 1.02281i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-0.0922667 + 1.99787i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(1.12464 + 0.857431i) q^{6} +(-1.04258 - 1.04258i) q^{7} +(2.13355 - 1.85687i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.85467 - 1.36046i) q^{10} +(-4.52673 - 1.47082i) q^{11} +(-0.221405 - 1.98771i) q^{12} +(2.54390 - 4.99269i) q^{13} +(-0.0481108 + 2.08461i) q^{14} +(0.357381 - 2.20732i) q^{15} +(-3.98297 - 0.368674i) q^{16} +(0.262171 - 1.65528i) q^{17} +(-1.24492 - 0.670942i) q^{18} +(2.76811 - 2.01115i) q^{19} +(-4.17953 - 1.59107i) q^{20} +(1.19285 + 0.866653i) q^{21} +(2.91671 + 6.06646i) 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} +(2.17915 - 1.98675i) q^{28} +(-4.76887 + 6.56378i) q^{29} +(-2.60671 + 1.79028i) q^{30} +(1.29321 + 1.77995i) q^{31} +(3.51293 + 4.43388i) q^{32} +(4.70108 + 0.744578i) q^{33} +(-1.94908 + 1.34850i) q^{34} +(2.94272 - 1.48668i) q^{35} +(0.529625 + 1.92860i) q^{36} +(1.10983 + 0.565484i) q^{37} +(-4.76052 - 0.867029i) q^{38} +(-1.73155 + 5.32918i) q^{39} +(2.45462 + 5.82879i) q^{40} +(-1.73027 - 5.32522i) q^{41} +(-0.278587 - 2.06648i) q^{42} +(-2.44396 + 2.44396i) q^{43} +(3.35618 - 8.90811i) q^{44} +(-0.00767928 + 2.23605i) q^{45} +(-3.73341 + 10.6478i) q^{46} +(-0.899254 - 5.67766i) q^{47} +(3.99161 - 0.258939i) q^{48} -4.82603i q^{49} +(0.896569 + 7.01400i) q^{50} +1.67591i q^{51} +(9.74003 + 5.54305i) q^{52} +(-0.680800 - 4.29840i) q^{53} +(1.33456 + 0.467933i) q^{54} +(6.28532 - 8.58881i) q^{55} +(-4.16035 - 0.288460i) q^{56} +(-2.41941 + 2.41941i) q^{57} +(11.3710 - 1.53296i) q^{58} +(3.92044 + 12.0659i) q^{59} +(4.37697 + 0.917663i) q^{60} +(2.15405 - 6.62949i) q^{61} +(0.557518 - 3.06112i) q^{62} +(-1.31373 - 0.669381i) q^{63} +(1.10406 - 7.92345i) q^{64} +(8.82932 + 8.89017i) q^{65} +(-3.82980 - 5.53550i) q^{66} +(-7.39906 - 1.17190i) q^{67} +(3.28285 + 0.676511i) q^{68} +(4.68966 + 6.45476i) q^{69} +(-4.39463 - 1.55785i) q^{70} +(7.39857 - 10.1833i) q^{71} +(1.45532 - 2.42529i) 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} +(7.14186 - 3.43375i) q^{78} +(7.49468 + 5.44520i) q^{79} +(3.56439 - 8.20336i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-3.75678 + 6.97066i) q^{82} +(-0.974493 + 6.15271i) q^{83} +(-1.84152 + 2.30319i) q^{84} +(3.33315 + 1.71277i) q^{85} +(4.88663 + 0.112778i) q^{86} +(3.68335 - 7.22899i) q^{87} +(-12.3891 + 5.26748i) q^{88} +(1.92856 + 0.626628i) q^{89} +(2.29455 - 2.17601i) q^{90} +(-7.85754 + 2.55307i) q^{91} +(14.5369 - 6.58071i) q^{92} +(-1.55574 - 1.55574i) q^{93} +(-4.92889 + 6.46492i) q^{94} +(2.33924 + 7.28448i) q^{95} +(-4.16329 - 3.82975i) q^{96} +(-3.36367 + 0.532753i) q^{97} +(-4.93610 + 4.71340i) 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 $

$2$	−0.976661	−	1.02281i	−0.690604	−	0.723233i
$2$	−0.976661	−	1.02281i	−0.690604	−	0.723233i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$4$	−0.0922667	+	1.99787i	−0.0461334	+	0.998935i
$5$	−0.698282	+	2.12424i	−0.312281	+	0.949990i
$5$	−0.698282	+	2.12424i	−0.312281	+	0.949990i
$6$	1.12464	+	0.857431i	0.459132	+	0.350045i
$7$	−1.04258	−	1.04258i	−0.394060	−	0.394060i	0.482072	−	0.876132i	$-0.339884\pi$
$7$	−1.04258	−	1.04258i	−0.394060	−	0.394060i	−0.876132	+	0.482072i	$0.839884\pi$
$8$	2.13355	−	1.85687i	0.754323	−	0.656503i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	2.85467	−	1.36046i	0.902727	−	0.430214i
$11$	−4.52673	−	1.47082i	−1.36486	−	0.443470i	−0.467197	−	0.884153i	$-0.654736\pi$
$11$	−4.52673	−	1.47082i	−1.36486	−	0.443470i	−0.897663	+	0.440683i	$0.854736\pi$
$12$	−0.221405	−	1.98771i	−0.0639141	−	0.573802i
$13$	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	$-0.133288\pi$
$14$	−0.0481108	+	2.08461i	−0.0128581	+	0.557137i
$15$	0.357381	−	2.20732i	0.0922753	−	0.569929i
$16$	−3.98297	−	0.368674i	−0.995743	−	0.0921685i
$17$	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	$-0.0151454\pi$
$18$	−1.24492	−	0.670942i	−0.293431	−	0.158143i
$19$	2.76811	−	2.01115i	0.635047	−	0.461389i	−0.223098	−	0.974796i	$-0.571617\pi$
$19$	2.76811	−	2.01115i	0.635047	−	0.461389i	0.858145	+	0.513407i	$0.171617\pi$
$20$	−4.17953	−	1.59107i	−0.934572	−	0.355775i
$21$	1.19285	+	0.866653i	0.260300	+	0.189119i
$22$	2.91671	+	6.06646i	0.621845	+	1.29337i
$23$	−3.62217	−	7.10891i	−0.755275	−	1.48231i	−0.872189	−	0.489169i	$-0.837300\pi$
$23$	−3.62217	−	7.10891i	−0.755275	−	1.48231i	0.116914	−	0.993142i	$-0.462700\pi$
$24$	−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
$28$	2.17915	−	1.98675i	0.411820	−	0.375461i
$29$	−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	$0.928461\pi$
$30$	−2.60671	+	1.79028i	−0.475917	+	0.326858i
$31$	1.29321	+	1.77995i	0.232268	+	0.319689i	0.909203	−	0.416354i	$-0.136692\pi$
$31$	1.29321	+	1.77995i	0.232268	+	0.319689i	−0.676935	+	0.736043i	$0.736692\pi$
$32$	3.51293	+	4.43388i	0.621005	+	0.783807i
$33$	4.70108	+	0.744578i	0.818354	+	0.129614i
$34$	−1.94908	+	1.34850i	−0.334265	+	0.231266i
$35$	2.94272	−	1.48668i	0.497411	−	0.251295i
$36$	0.529625	+	1.92860i	0.0882708	+	0.321433i
$37$	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	$0.617352\pi$
$38$	−4.76052	−	0.867029i	−0.772258	−	0.140651i
$39$	−1.73155	+	5.32918i	−0.277271	+	0.853351i
$40$	2.45462	+	5.82879i	0.388110	+	0.921613i
$41$	−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	$-0.244040\pi$
$42$	−0.278587	−	2.06648i	−0.0429869	−	0.318864i
$43$	−2.44396	+	2.44396i	−0.372701	+	0.372701i	−0.868460	−	0.495759i	$-0.834890\pi$
$43$	−2.44396	+	2.44396i	−0.372701	+	0.372701i	0.495759	+	0.868460i	$0.334890\pi$
$44$	3.35618	−	8.90811i	0.505963	−	1.34295i
$45$	−0.00767928	+	2.23605i	−0.00114476	+	0.333331i
$46$	−3.73341	+	10.6478i	−0.550461	+	1.56993i
$47$	−0.899254	−	5.67766i	−0.131170	−	0.828172i	−0.962279	−	0.272064i	$-0.912294\pi$
$47$	−0.899254	−	5.67766i	−0.131170	−	0.828172i	0.831110	−	0.556109i	$-0.187706\pi$
$48$	3.99161	−	0.258939i	0.576139	−	0.0373747i
$49$		−	4.82603i		−	0.689433i
$50$	0.896569	+	7.01400i	0.126794	+	0.991929i
$51$			1.67591i			0.234675i
$52$	9.74003	+	5.54305i	1.35070	+	0.768683i
$53$	−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	$-0.146618\pi$
$54$	1.33456	+	0.467933i	0.181610	+	0.0636776i
$55$	6.28532	−	8.58881i	0.847512	−	1.15812i
$56$	−4.16035	−	0.288460i	−0.555950	−	0.0385470i
$57$	−2.41941	+	2.41941i	−0.320459	+	0.320459i
$58$	11.3710	−	1.53296i	1.49309	−	0.201288i
$59$	3.92044	+	12.0659i	0.510398	+	1.57084i	0.791502	+	0.611166i	$0.209299\pi$
$59$	3.92044	+	12.0659i	0.510398	+	1.57084i	−0.281104	+	0.959677i	$0.590701\pi$
$60$	4.37697	+	0.917663i	0.565065	+	0.118470i
$61$	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	$-0.0472409\pi$
$62$	0.557518	−	3.06112i	0.0708049	−	0.388762i
$63$	−1.31373	−	0.669381i	−0.165515	−	0.0843340i
$64$	1.10406	−	7.92345i	0.138007	−	0.990431i
$65$	8.82932	+	8.89017i	1.09514	+	1.10269i
$66$	−3.82980	−	5.53550i	−0.471416	−	0.681373i
$67$	−7.39906	−	1.17190i	−0.903939	−	0.143170i	−0.312875	−	0.949794i	$-0.601292\pi$
$67$	−7.39906	−	1.17190i	−0.903939	−	0.143170i	−0.591064	+	0.806625i	$0.701292\pi$
$68$	3.28285	+	0.676511i	0.398104	+	0.0820390i
$69$	4.68966	+	6.45476i	0.564568	+	0.777061i
$70$	−4.39463	−	1.55785i	−0.525259	−	0.186199i
$71$	7.39857	−	10.1833i	0.878049	−	1.20853i	−0.0989090	−	0.995096i	$-0.531535\pi$
$71$	7.39857	−	10.1833i	0.878049	−	1.20853i	0.976958	−	0.213434i	$-0.0684647\pi$
$72$	1.45532	−	2.42529i	0.171511	−	0.285823i
$73$	−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
$78$	7.14186	−	3.43375i	0.808656	−	0.388796i
$79$	7.49468	+	5.44520i	0.843218	+	0.612633i	0.923268	−	0.384157i	$-0.125508\pi$
$79$	7.49468	+	5.44520i	0.843218	+	0.612633i	−0.0800501	+	0.996791i	$0.525508\pi$
$80$	3.56439	−	8.20336i	0.398511	−	0.917163i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	−3.75678	+	6.97066i	−0.414867	+	0.769780i
$83$	−0.974493	+	6.15271i	−0.106965	+	0.675348i	0.874690	+	0.484682i	$0.161065\pi$
$83$	−0.974493	+	6.15271i	−0.106965	+	0.675348i	−0.981655	+	0.190666i	$0.938935\pi$
$84$	−1.84152	+	2.30319i	−0.200926	+	0.251298i
$85$	3.33315	+	1.71277i	0.361531	+	0.185776i
$86$	4.88663	+	0.112778i	0.526938	+	0.0121612i
$87$	3.68335	−	7.22899i	0.394897	−	0.775029i
$88$	−12.3891	+	5.26748i	−1.32068	+	0.561515i
$89$	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	$0.565724\pi$
$90$	2.29455	−	2.17601i	0.241867	−	0.229372i
$91$	−7.85754	+	2.55307i	−0.823694	+	0.267634i
$92$	14.5369	−	6.58071i	1.51558	−	0.686087i
$93$	−1.55574	−	1.55574i	−0.161322	−	0.161322i
$94$	−4.92889	+	6.46492i	−0.508376	+	0.666805i
$95$	2.33924	+	7.28448i	0.240001	+	0.747371i
$96$	−4.16329	−	3.82975i	−0.424914	−	0.390872i
$97$	−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	$0.505312\pi$
$98$	−4.93610	+	4.71340i	−0.498621	+	0.476125i
$99$	−4.75968			−0.478366
$100$	6.29832	−	7.76731i	0.629832	−	0.776731i
$101$	−13.7603			−1.36920			−0.684602	−	0.728917i	$-0.740024\pi$
$101$	−13.7603			−1.36920			−0.684602	+	0.728917i	$0.740024\pi$
$102$	1.71414	−	1.63680i	0.169725	−	0.162067i
$103$	−6.04390	+	0.957260i	−0.595524	+	0.0943217i	−0.446918	−	0.894575i	$-0.647478\pi$
$103$	−6.04390	+	0.957260i	−0.595524	+	0.0943217i	−0.148606	+	0.988897i	$0.547478\pi$
$104$	−3.84324	−	15.3759i	−0.376861	−	1.50773i
$105$	−2.67392	+	1.92872i	−0.260948	+	0.188224i
$106$	−3.73152	+	4.89440i	−0.362437	+	0.475387i
$107$	8.72357	+	8.72357i	0.843339	+	0.843339i	0.989292	−	0.145953i	$-0.0466247\pi$
$107$	8.72357	+	8.72357i	0.843339	+	0.843339i	−0.145953	+	0.989292i	$0.546625\pi$
$108$	−0.824804	−	1.82200i	−0.0793668	−	0.175322i
$109$	−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	$0.633246\pi$
$110$	−14.9233	+	1.95969i	−1.42288	+	0.186849i
$111$	−1.18462	−	0.384907i	−0.112439	−	0.0365338i
$112$	3.76821	+	4.53696i	0.356063	+	0.428703i
$113$	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	$0.0844093\pi$
$114$	4.83754	+	0.111645i	0.453077	+	0.0104566i
$115$	17.6303	−	2.73034i	1.64404	−	0.254605i
$116$	−12.6736	−	10.1332i	−1.17671	−	0.940844i
$117$	0.876569	−	5.53444i	0.0810389	−	0.511659i
$118$	8.51212	−	15.7941i	0.783604	−	1.45397i
$119$	−1.99911	+	1.45244i	−0.183258	+	0.133145i
$120$	−3.33623	−	5.37304i	−0.304554	−	0.490489i
$121$	9.42875	+	6.85039i	0.857159	+	0.622763i
$122$	−8.88446	+	4.27158i	−0.804361	+	0.386731i
$123$	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	−0.313034	−	0.949742i	$-0.601345\pi$
$127$	3.05770	−	1.55798i	0.271327	−	0.138248i	0.584361	+	0.811494i	$0.301345\pi$
$128$	−9.18245	+	6.60929i	−0.811621	+	0.584184i
$129$	2.03155	−	2.79619i	0.178868	−	0.246191i
$130$	0.469677	−	17.7134i	0.0411934	−	1.55357i
$131$	−4.34615	−	5.98196i	−0.379725	−	0.522646i	0.575787	−	0.817600i	$-0.304696\pi$
$131$	−4.34615	−	5.98196i	−0.379725	−	0.522646i	−0.955512	+	0.294954i	$0.904696\pi$
$132$	−1.92132	+	9.32346i	−0.167230	+	0.811503i
$133$	−4.98278	−	0.789194i	−0.432062	−	0.0684318i
$134$	6.02775	+	8.71235i	0.520718	+	0.752632i
$135$	−0.342211	−	2.20973i	−0.0294529	−	0.190183i
$136$	−2.51429	−	4.01844i	−0.215599	−	0.344578i
$137$	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	$0.489140\pi$
$138$	2.02176	−	11.1007i	0.172104	−	0.944956i
$139$	−4.52482	+	13.9260i	−0.383791	+	1.18119i	0.553563	+	0.832807i	$0.313268\pi$
$139$	−4.52482	+	13.9260i	−0.383791	+	1.18119i	−0.937354	+	0.348379i	$0.886732\pi$
$140$	2.69869	+	6.01635i	0.228081	+	0.508474i
$141$	1.77636	+	5.46709i	0.149597	+	0.460412i
$142$	−17.6414	+	2.37828i	−1.48043	+	0.199581i
$143$	−18.8589	+	18.8589i	−1.57706	+	1.57706i
$144$	−3.90196	+	0.880177i	−0.325163	+	0.0733481i
$145$	−10.6130	−	14.7136i	−0.881365	−	1.22190i
$146$	13.6124	+	4.77288i	1.12657	+	0.395007i
$147$	0.754958	+	4.76662i	0.0622679	+	0.393144i
$148$	−1.23216	+	2.16511i	−0.101283	+	0.177971i
$149$		−	7.25270i		−	0.594165i	−0.954852	−	0.297082i	$-0.903986\pi$
$149$		−	7.25270i		−	0.594165i	0.954852	−	0.297082i	$-0.0960136\pi$
$150$	−1.98276	−	6.78739i	−0.161892	−	0.554188i
$151$		−	8.89011i		−	0.723467i	−0.932282	−	0.361733i	$-0.882185\pi$
$151$		−	8.89011i		−	0.723467i	0.932282	−	0.361733i	$-0.117815\pi$
$152$	2.17145	−	9.43090i	0.176128	−	0.764947i
$153$	−0.262171	−	1.65528i	−0.0211953	−	0.133822i
$154$	3.28388	−	9.36572i	0.264623	−	0.754711i
$155$	−4.68408	+	1.50418i	−0.376234	+	0.120819i
$156$	−10.4872	−	3.95113i	−0.839651	−	0.316343i
$157$	−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	$0.306607\pi$
$158$	−1.75037	−	12.9837i	−0.139252	−	1.03293i
$159$	1.34484	+	4.13898i	0.106652	+	0.328242i
$160$	−11.8717	+	4.36622i	−0.938537	+	0.345180i
$161$	−3.63522	+	11.1881i	−0.286496	+	0.881743i
$162$	−1.39133	−	0.253401i	−0.109313	−	0.0199091i
$163$	−3.54660	−	1.80708i	−0.277791	−	0.141542i	0.309545	−	0.950885i	$-0.399823\pi$
$163$	−3.54660	−	1.80708i	−0.277791	−	0.141542i	−0.587336	+	0.809343i	$0.699823\pi$
$164$	10.7987	−	2.96551i	0.843240	−	0.231567i
$165$	−4.86435	+	9.46631i	−0.378689	+	0.736951i
$166$	7.24478	−	5.01239i	0.562304	−	0.389037i
$167$	−20.0096	−	3.16922i	−1.54839	−	0.245241i	−0.677058	−	0.735930i	$-0.736745\pi$
$167$	−20.0096	−	3.16922i	−1.54839	−	0.245241i	−0.871335	+	0.490689i	$0.836745\pi$
$168$	4.15426	−	0.365914i	0.320508	−	0.0282309i
$169$	−10.8143	−	14.8846i	−0.831871	−	1.14497i
$170$	−1.50353	−	5.08196i	−0.115315	−	0.389769i
$171$	2.01115	−	2.76811i	0.153796	−	0.211682i
$172$	−4.65723	−	5.10822i	−0.355110	−	0.389498i
$173$	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
$178$	−1.24263	−	2.58455i	−0.0931393	−	0.193720i
$179$	13.4766	+	9.79134i	1.00729	+	0.731839i	0.963639	−	0.267208i	$-0.0861011\pi$
$179$	13.4766	+	9.79134i	1.00729	+	0.731839i	0.0436509	+	0.999047i	$0.486101\pi$
$180$	−4.46664	−	0.221656i	−0.332924	−	0.0165212i
$181$	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	$0.0713176\pi$
$182$	10.2854	+	5.54326i	0.762408	+	0.410894i
$183$	−1.09045	+	6.88483i	−0.0806084	+	0.508942i
$184$	−20.9284	−	8.44130i	−1.54286	−	0.622301i
$185$	−1.97620	+	1.96267i	−0.145293	+	0.144298i
$186$	−0.0717904	+	3.11064i	−0.00526393	+	0.228083i
$187$	−3.62140	+	7.10740i	−0.264823	+	0.519745i
$188$	11.4262	−	1.27273i	0.833342	−	0.0928236i
$189$	1.40227	+	0.455626i	0.102000	+	0.0331419i
$190$	5.16596	−	9.50706i	0.374778	−	0.689714i
$191$	9.15141	−	2.97347i	0.662173	−	0.215153i	0.0413989	−	0.999143i	$-0.486819\pi$
$191$	9.15141	−	2.97347i	0.662173	−	0.215153i	0.620774	+	0.783990i	$0.286819\pi$
$192$	0.149034	+	7.99861i	0.0107556	+	0.577250i
$193$	−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	$0.885513\pi$
$194$	3.83007	+	2.92007i	0.274983	+	0.209649i
$195$	−10.1113	−	7.39951i	−0.724089	−	0.529890i
$196$	9.64179	+	0.445282i	0.688699	+	0.0318059i
$197$	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	$0.425268\pi$
$198$	4.64860	+	4.86824i	0.330361	+	0.345970i
$199$	−9.69051			−0.686942			−0.343471	−	0.939163i	$-0.611603\pi$
$199$	−9.69051			−0.686942			−0.343471	+	0.939163i	$0.611603\pi$
$200$	−14.0958	+	1.14407i	−0.996722	+	0.0808979i
$201$	7.49129			0.528395
$202$	13.4392	+	14.0742i	0.945577	+	0.990254i
$203$	11.8152	−	1.87135i	0.829268	−	0.131343i
$204$	−3.34826	−	0.154631i	−0.234425	−	0.0108263i
$205$	12.5203	+	0.0429983i	0.874453	+	0.00300313i
$206$	6.88194	+	5.24683i	0.479487	+	0.365564i
$207$	−5.64166	−	5.64166i	−0.392123	−	0.392123i
$208$	−11.9730	+	18.9479i	−0.830177	+	1.31380i
$209$	−15.4885	+	5.03252i	−1.07136	+	0.348107i
$210$	4.58423	+	0.851197i	0.316342	+	0.0587382i
$211$	23.4844	+	7.63053i	1.61673	+	0.525308i	0.971167	−	0.238399i	$-0.0766227\pi$
$211$	23.4844	+	7.63053i	1.61673	+	0.525308i	0.645563	+	0.763707i	$0.276623\pi$
$212$	8.65046	−	0.963550i	0.594116	−	0.0661769i
$213$	−5.71447	+	11.2153i	−0.391549	+	0.768458i
$214$	0.402555	−	17.4425i	0.0275181	−	1.19234i
$215$	−3.48499	−	6.89815i	−0.237674	−	0.470450i
$216$	−1.05800	+	2.62310i	−0.0719880	+	0.178479i
$217$	0.507469	−	3.20403i	0.0344493	−	0.217504i
$218$	17.3886	+	9.37144i	1.17770	+	0.634714i
$219$	8.25193	−	5.99537i	0.557613	−	0.405130i
$220$	16.5794	+	13.3497i	1.11778	+	0.900037i
$221$	−7.59737	−	5.51981i	−0.511055	−	0.371303i
$222$	0.763289	+	1.58756i	0.0512286	+	0.106550i
$223$	−8.96950	−	17.6036i	−0.600642	−	1.17883i	−0.968516	−	0.248951i	$-0.919914\pi$
$223$	−8.96950	−	17.6036i	−0.600642	−	1.17883i	0.367874	−	0.929876i	$-0.380086\pi$
$224$	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	−0.458878	−	0.888499i	$-0.651748\pi$
$227$	−0.147478	+	0.0751436i	−0.00978843	+	0.00498746i	0.449089	+	0.893487i	$0.351748\pi$
$228$	−4.61044	−	5.05691i	−0.305334	−	0.334902i
$229$	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	$0.120322\pi$
$230$	−20.0115	−	15.3658i	−1.31952	−	1.01319i
$231$	−4.12499	−	5.67756i	−0.271405	−	0.373556i
$232$	2.01349	+	22.8593i	0.132192	+	1.50079i
$233$	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	$0.436278\pi$
$234$	−6.51677	+	4.50871i	−0.426015	+	0.294744i
$235$	12.6887	+	2.05438i	0.827717	+	0.134013i
$236$	−24.4678	+	6.71925i	−1.59272	+	0.437386i
$237$	−8.25423	−	4.20574i	−0.536170	−	0.273192i
$238$	3.43801	+	0.626162i	0.222853	+	0.0405881i
$239$	6.87021	−	21.1443i	0.444397	−	1.36771i	−0.438746	−	0.898611i	$-0.644577\pi$
$239$	6.87021	−	21.1443i	0.444397	−	1.36771i	0.883143	−	0.469103i	$-0.155423\pi$
$240$	−2.23722	+	8.65996i	−0.144412	+	0.558998i
$241$	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	$0.671855\pi$
$242$	−2.20207	−	16.3343i	−0.141554	−	1.05001i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	13.0461	+	4.91519i	0.835191	+	0.314663i
$245$	10.2517	+	3.36993i	0.654955	+	0.215297i
$246$	2.62008	−	7.47253i	0.167050	−	0.476431i
$247$	−2.99924	−	18.9365i	−0.190837	−	1.20490i
$248$	6.06427	+	1.39629i	0.385082	+	0.0886644i
$249$		−	6.22940i		−	0.394772i
$250$	−15.5255	−	2.99322i	−0.981918	−	0.189308i
$251$		−	18.0233i		−	1.13762i	−0.822468	−	0.568811i	$-0.807403\pi$
$251$		−	18.0233i		−	1.13762i	0.822468	−	0.568811i	$-0.192597\pi$
$252$	1.45855	−	2.56291i	0.0918800	−	0.161448i
$253$	5.94063	+	37.5077i	0.373484	+	2.35809i
$254$	−4.57984	−	1.60582i	−0.287365	−	0.100758i
$255$	−3.56005	−	1.17026i	−0.222939	−	0.0732846i
$256$	15.7282	+	2.93684i	0.983010	+	0.183552i
$257$	−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	$0.266374\pi$
$258$	−4.84411	+	0.653047i	−0.301581	+	0.0406569i
$259$	−0.567522	−	1.74665i	−0.0352641	−	0.108532i
$260$	−18.5761	+	16.8196i	−1.15204	+	1.04311i
$261$	−2.50714	+	7.71619i	−0.155188	+	0.477620i
$262$	−1.87367	+	10.2876i	−0.115756	+	0.635571i
$263$	22.7301	+	11.5815i	1.40160	+	0.714149i	0.981164	−	0.193176i	$-0.0618787\pi$
$263$	22.7301	+	11.5815i	1.40160	+	0.714149i	0.420431	+	0.907324i	$0.361879\pi$
$264$	11.4126	−	7.14071i	0.702395	−	0.439480i
$265$	9.60623	+	1.55531i	0.590106	+	0.0955422i
$266$	4.05929	+	5.86719i	0.248891	+	0.359741i
$267$	−2.00285	−	0.317220i	−0.122572	−	0.0194135i
$268$	3.02398	−	14.6742i	0.184719	−	0.896371i
$269$	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	$0.530028\pi$
$270$	−1.92590	+	2.50817i	−0.117206	+	0.152642i
$271$	−0.554963	+	0.763841i	−0.0337116	+	0.0464000i	−0.825540	−	0.564344i	$-0.809129\pi$
$271$	−0.554963	+	0.763841i	−0.0337116	+	0.0464000i	0.791828	+	0.610744i	$0.209129\pi$
$272$	−1.65448	+	6.49629i	−0.100318	+	0.393895i
$273$	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	$0.962690\pi$
$278$	18.6628	−	8.97294i	1.11932	−	0.538161i
$279$	1.77995	+	1.29321i	0.106563	+	0.0774225i
$280$	3.51786	−	8.63616i	0.210232	−	0.516110i
$281$	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	$0.251164\pi$
$282$	3.85687	−	7.15637i	0.229673	−	0.426156i
$283$	−1.43610	+	9.06715i	−0.0853670	+	0.538986i	0.907528	+	0.419992i	$0.137967\pi$
$283$	−1.43610	+	9.06715i	−0.0853670	+	0.538986i	−0.992895	+	0.118994i	$0.962033\pi$
$284$	19.6622	+	15.7210i	1.16674	+	0.932867i
$285$	−3.44999	−	6.82885i	−0.204359	−	0.404506i
$286$	37.7078	+	0.870257i	2.22971	+	0.0514594i
$287$	−3.74804	+	7.35594i	−0.221240	+	0.434207i
$288$	4.71114	+	3.13132i	0.277607	+	0.184515i
$289$	13.4967	+	4.38536i	0.793926	+	0.257962i
$290$	−4.68382	+	25.2253i	−0.275043	+	1.48128i
$291$	3.23892	−	1.05239i	0.189869	−	0.0616921i
$292$	−8.41295	−	18.5843i	−0.492331	−	1.08757i
$293$	−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	$-0.580559\pi$
$294$	4.13799	−	5.42754i	0.241332	−	0.316541i
$295$	−28.3684	−	0.0974256i	−1.65167	−	0.00567234i
$296$	3.41790	−	0.854314i	0.198661	−	0.0496560i
$297$	4.70108	−	0.744578i	0.272785	−	0.0432048i
$298$	−7.41811	+	7.08343i	−0.429720	+	0.410332i
$299$	−44.7071			−2.58548
$300$	−5.00570	+	8.65696i	−0.289004	+	0.499810i
$301$	5.09608			0.293733
$302$	−9.09286	+	8.68262i	−0.523235	+	0.499629i
$303$	13.5909	−	2.15259i	0.780777	−	0.123663i
$304$	−11.7668	+	6.98982i	−0.674870	+	0.400894i
$305$	12.5785	+	9.20498i	0.720242	+	0.527075i
$306$	−1.43698	+	1.88480i	−0.0821467	+	0.107747i
$307$	−1.07224	−	1.07224i	−0.0611962	−	0.0611962i	0.675846	−	0.737043i	$-0.263778\pi$
$307$	−1.07224	−	1.07224i	−0.0611962	−	0.0611962i	−0.737043	+	0.675846i	$0.763778\pi$
$308$	−12.7866	+	5.78836i	−0.728582	+	0.329822i
$309$	5.81975	−	1.89095i	0.331074	−	0.107572i
$310$	6.11324	+	3.32183i	0.347209	+	0.188667i
$311$	0.0825240	+	0.0268137i	0.00467951	+	0.00152046i	0.311356	−	0.950293i	$-0.399217\pi$
$311$	0.0825240	+	0.0268137i	0.00467951	+	0.00152046i	−0.306676	+	0.951814i	$0.599217\pi$
$312$	6.20124	+	14.5853i	0.351076	+	0.825732i
$313$	−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	$0.934602\pi$
$314$	6.26771	+	0.144652i	0.353707	+	0.00816320i
$315$	2.33928	−	2.32327i	0.131804	−	0.130901i
$316$	−11.5703	+	14.4710i	−0.650882	+	0.814057i
$317$	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	$-0.303348\pi$
$318$	2.91993	−	5.41789i	0.163741	−	0.303820i
$319$	31.2415	−	22.6983i	1.74919	−	1.27086i
$320$	16.0604	+	7.87809i	0.897802	+	0.440399i
$321$	−9.98083	−	7.25150i	−0.557076	−	0.404739i
$322$	14.9936	−	7.20882i	0.835561	−	0.401732i
$323$	−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
$328$	−13.5798	−	8.14872i	−0.749822	−	0.449938i
$329$	−4.98190	+	6.85700i	−0.274661	+	0.378038i
$330$	14.4330	−	4.27009i	0.794512	−	0.235061i
$331$	−11.2987	−	15.5513i	−0.621031	−	0.854776i	0.376396	−	0.926459i	$-0.377163\pi$
$331$	−11.2987	−	15.5513i	−0.621031	−	0.854776i	−0.997428	+	0.0716824i	$0.977163\pi$
$332$	−12.2024	−	2.51460i	−0.669694	−	0.138007i
$333$	1.23025	+	0.194853i	0.0674173	+	0.0106779i
$334$	16.3011	+	23.5612i	0.891959	+	1.28921i
$335$	7.65602	−	14.8991i	0.418293	−	0.814023i
$336$	−4.43156	−	3.89163i	−0.241761	−	0.212306i
$337$	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	$0.521455\pi$
$338$	−4.66218	+	25.5982i	−0.253589	+	1.39236i
$339$	−1.34421	+	4.13704i	−0.0730072	+	0.224693i
$340$	−3.72943	+	6.50117i	−0.202257	+	0.352575i
$341$	−3.23602	−	9.95944i	−0.175240	−	0.539334i
$342$	−4.79545	+	0.646487i	−0.259308	+	0.0349580i
$343$	−12.3296	+	12.3296i	−0.665738	+	0.665738i
$344$	−0.676189	+	9.75244i	−0.0364577	+	0.525816i
$345$	−16.9862	+	5.45472i	−0.914504	+	0.293672i
$346$	−10.2052	−	3.57824i	−0.548636	−	0.192367i
$347$	−0.544569	−	3.43827i	−0.0292340	−	0.184576i	0.968750	−	0.248038i	$-0.0797858\pi$
$347$	−0.544569	−	3.43827i	−0.0292340	−	0.184576i	−0.997984	+	0.0634620i	$0.979786\pi$
$348$	14.1027	+	8.02586i	0.755985	+	0.430231i
$349$		−	1.06294i		−	0.0568981i	−0.999595	−	0.0284490i	$-0.990943\pi$
$349$		−	1.06294i		−	0.0568981i	0.999595	−	0.0284490i	$-0.00905683\pi$
$350$	6.37794	−	8.24744i	0.340915	−	0.440844i
$351$			5.60343i			0.299089i
$352$	−9.38063	−	25.2379i	−0.499990	−	1.34518i
$353$	−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	$-0.234477\pi$
$354$	−5.93657	+	16.9313i	−0.315525	+	0.899886i
$355$	16.4654	+	22.8271i	0.873893	+	1.21154i
$356$	−1.42986	+	3.79520i	−0.0757827	+	0.201145i
$357$	1.74728	−	1.74728i	0.0924760	−	0.0924760i
$358$	−3.14744	−	23.3468i	−0.166348	−	1.23392i
$359$	−5.08507	−	15.6502i	−0.268380	−	0.825988i	−0.990895	−	0.134633i	$-0.957014\pi$
$359$	−5.08507	−	15.6502i	−0.268380	−	0.825988i	0.722516	−	0.691354i	$-0.242986\pi$
$360$	4.13568	+	4.78499i	0.217970	+	0.252191i
$361$	−2.25362	+	6.93593i	−0.118612	+	0.365049i
$362$	−24.6409	−	4.48783i	−1.29510	−	0.235875i
$363$	−10.3843	−	5.29107i	−0.545035	−	0.277709i
$364$	−4.37571	−	15.9339i	−0.229350	−	0.835164i
$365$	−3.49054	−	22.5391i	−0.182703	−	1.17975i
$366$	8.10685	−	5.60883i	0.423752	−	0.293178i
$367$	−18.7851	−	2.97526i	−0.980573	−	0.155307i	−0.354486	−	0.935061i	$-0.615344\pi$
$367$	−18.7851	−	2.97526i	−0.980573	−	0.155307i	−0.626086	+	0.779754i	$0.715344\pi$
$368$	11.8061	+	29.6500i	0.615438	+	1.54561i
$369$	−3.29116	−	4.52990i	−0.171331	−	0.235817i
$370$	3.93750	+	0.104404i	0.204701	+	0.00542773i
$371$	−3.77165	+	5.19124i	−0.195815	+	0.269516i
$372$	3.25170	−	2.96462i	0.168593	−	0.153708i
$373$	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
$378$	−0.903528	−	1.87925i	−0.0464725	−	0.0966580i
$379$	−4.02282	−	2.92275i	−0.206639	−	0.150132i	0.479653	−	0.877458i	$-0.340763\pi$
$379$	−4.02282	−	2.92275i	−0.206639	−	0.150132i	−0.686292	+	0.727327i	$0.740763\pi$
$380$	−14.7693	+	4.00139i	−0.757648	+	0.205267i
$381$	−2.77633	+	2.01712i	−0.142236	+	0.103340i
$382$	−11.9791	−	6.45605i	−0.612905	−	0.330320i
$383$	2.89726	−	18.2926i	0.148043	−	0.934708i	−0.796098	−	0.605167i	$-0.793106\pi$
$383$	2.89726	−	18.2926i	0.148043	−	0.934708i	0.944141	−	0.329540i	$-0.106894\pi$
$384$	8.03548	−	7.96437i	0.410059	−	0.406430i
$385$	−15.5075	+	2.40159i	−0.790338	+	0.122396i
$386$	−0.374419	+	16.2234i	−0.0190574	+	0.825748i
$387$	−1.56912	+	3.07957i	−0.0797629	+	0.156544i
$388$	−0.754017	−	6.76934i	−0.0382794	−	0.343661i
$389$	−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	$0.723397\pi$
$390$	2.30709	+	17.5688i	0.116824	+	0.889629i
$391$	−12.7169	+	4.13196i	−0.643120	+	0.208962i
$392$	−8.96132	−	10.2966i	−0.452615	−	0.520056i
$393$	5.22842	+	5.22842i	0.263739	+	0.263739i
$394$	−2.45049	−	1.86827i	−0.123454	−	0.0941220i
$395$	−16.8003	+	12.1182i	−0.845317	+	0.609734i
$396$	0.439160	−	9.50923i	0.0220686	−	0.477857i
$397$	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	$0.305184\pi$
$398$	9.46434	+	9.91152i	0.474405	+	0.496819i
$399$	5.04489			0.252560
$400$	14.9370	+	13.2999i	0.746848	+	0.664995i
$401$	−23.4783			−1.17245			−0.586226	−	0.810147i	$-0.699387\pi$
$401$	−23.4783			−1.17245			−0.586226	+	0.810147i	$0.699387\pi$
$402$	−7.31645	−	7.66214i	−0.364911	−	0.382153i
$403$	12.1766	−	1.92858i	0.606558	−	0.0960693i
$404$	1.26962	−	27.4913i	0.0631660	−	1.36775i
$405$	0.683675	+	2.12899i	0.0339721	+	0.105790i
$406$	−13.4535	−	10.2570i	−0.667687	−	0.509048i
$407$	−4.19215	−	4.19215i	−0.207797	−	0.207797i
$408$	3.11196	+	3.57565i	0.154065	+	0.177021i
$409$	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	$0.00610643\pi$
$410$	−12.1841	−	12.8478i	−0.601728	−	0.634507i
$411$	−10.7783	−	3.50208i	−0.531654	−	0.172745i
$412$	−1.35483	−	12.1633i	−0.0667477	−	0.599241i
$413$	8.49231	−	16.6671i	0.417879	−	0.820134i
$414$	−0.260338	+	11.2803i	−0.0127949	+	0.554398i
$415$	−12.3894	−	6.36639i	−0.608170	−	0.312514i
$416$	31.0736	−	6.25962i	1.52351	−	0.306903i
$417$	2.29061	−	14.4624i	0.112172	−	0.708225i
$418$	20.2743	+	10.9267i	0.991649	+	0.534441i
$419$	8.44580	−	6.13623i	0.412604	−	0.299775i	−0.362051	−	0.932158i	$-0.617923\pi$
$419$	8.44580	−	6.13623i	0.412604	−	0.299775i	0.774655	+	0.632384i	$0.217923\pi$
$420$	−3.60662	−	5.52011i	−0.175985	−	0.269354i
$421$	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	$0.665616\pi$
$422$	−15.1317	−	31.4724i	−0.736600	−	1.53205i
$423$	−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
$428$	−18.2335	+	16.6237i	−0.881347	+	0.803535i
$429$	15.6766	−	21.5769i	0.756871	−	1.04174i
$430$	−3.65181	+	10.3016i	−0.176106	+	0.496788i
$431$	14.7423	+	20.2911i	0.710114	+	0.977388i	0.999795	+	0.0202643i	$0.00645078\pi$
$431$	14.7423	+	20.2911i	0.710114	+	0.977388i	−0.289681	+	0.957123i	$0.593549\pi$
$432$	3.71623	−	1.47974i	0.178797	−	0.0711941i
$433$	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	$0.455862\pi$
$434$	−3.77273	+	2.61021i	−0.181097	+	0.125294i
$435$	12.7841	+	12.8722i	0.612950	+	0.617175i
$436$	−7.39759	−	26.9379i	−0.354280	−	1.29009i
$437$	−24.3236	−	12.3935i	−1.16356	−	0.592862i
$438$	−14.1914	−	2.58468i	−0.678093	−	0.123501i
$439$	6.68775	−	20.5828i	0.319189	−	0.982363i	−0.654807	−	0.755796i	$-0.727250\pi$
$439$	6.68775	−	20.5828i	0.319189	−	0.982363i	0.973996	−	0.226567i	$-0.0727501\pi$
$440$	−2.53829	−	29.9957i	−0.121008	−	1.42999i
$441$	−1.49133	−	4.58983i	−0.0710155	−	0.218563i
$442$	1.77435	+	13.1616i	0.0843974	+	0.626035i
$443$	8.27711	−	8.27711i	0.393257	−	0.393257i	−0.482589	−	0.875847i	$-0.660304\pi$
$443$	8.27711	−	8.27711i	0.393257	−	0.393257i	0.875847	+	0.482589i	$0.160304\pi$
$444$	0.878296	−	2.33121i	0.0416821	−	0.110634i
$445$	−2.67779	+	3.65917i	−0.126940	+	0.173461i
$446$	−9.24495	+	26.3668i	−0.437761	+	1.24851i
$447$	1.13457	+	7.16341i	0.0536635	+	0.338818i
$448$	−9.41194	+	7.10979i	−0.444673	+	0.335906i
$449$			15.5833i			0.735422i	0.929940	+	0.367711i	$0.119858\pi$
$449$			15.5833i			0.735422i	−0.929940	+	0.367711i	$0.880142\pi$
$450$	3.02013	+	6.39365i	0.142370	+	0.301400i
$451$			26.6507i			1.25493i
$452$	7.56119	+	4.30307i	0.355648	+	0.202399i
$453$	1.39072	+	8.78066i	0.0653417	+	0.412551i
$454$	0.220893	+	0.0774513i	0.0103670	+	0.00363497i
$455$	0.0634455	−	18.4741i	0.00297437	−	0.866078i
$456$	−0.669397	+	9.65448i	−0.0313474	+	0.452112i
$457$	−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	$0.264417\pi$
$458$	−10.5074	+	1.41653i	−0.490977	+	0.0661899i
$459$	0.517886	+	1.59389i	0.0241729	+	0.0743964i
$460$	3.82817	+	35.4751i	0.178489	+	1.65403i
$461$	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	$0.0710951\pi$
$462$	−1.77833	+	9.76413i	−0.0827355	+	0.454268i
$463$	30.4751	+	15.5278i	1.41630	+	0.721639i	0.983678	−	0.179938i	$-0.0575898\pi$
$463$	30.4751	+	15.5278i	1.41630	+	0.721639i	0.432618	+	0.901577i	$0.357590\pi$
$464$	21.4142	−	24.3852i	0.994128	−	1.13206i
$465$	4.39110	−	2.21842i	0.203632	−	0.102877i
$466$	−8.59059	−	12.4166i	−0.397951	−	0.575189i
$467$	1.58480	+	0.251008i	0.0733359	+	0.0116153i	0.192995	−	0.981200i	$-0.438180\pi$
$467$	1.58480	+	0.251008i	0.0733359	+	0.0116153i	−0.119659	+	0.992815i	$0.538180\pi$
$468$	10.9762	+	2.26192i	0.507376	+	0.104557i
$469$	6.49234	+	8.93595i	0.299789	+	0.412624i
$470$	−10.2913	−	14.9845i	−0.474702	−	0.691183i
$471$	2.60572	−	3.58647i	0.120065	−	0.165256i
$472$	30.7692	+	18.4634i	1.41627	+	0.849846i
$473$	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
$478$	−28.3364	+	13.6240i	−1.29608	+	0.623145i
$479$	−5.24823	−	3.81306i	−0.239798	−	0.174223i	0.461395	−	0.887195i	$-0.347349\pi$
$479$	−5.24823	−	3.81306i	−0.239798	−	0.174223i	−0.701193	+	0.712971i	$0.747349\pi$
$480$	11.0425	−	6.16960i	0.504017	−	0.281602i
$481$	5.64658	−	4.10248i	0.257462	−	0.187057i
$482$	13.6849	−	25.3922i	0.623332	−	1.15658i
$483$	1.84027	−	11.6190i	0.0837351	−	0.528683i
$484$	−14.5562	+	18.2054i	−0.661643	+	0.827517i
$485$	1.21710	−	7.51727i	0.0552655	−	0.341341i
$486$	1.41384	+	0.0326299i	0.0641330	+	0.00148012i
$487$	−1.10097	+	2.16077i	−0.0498896	+	0.0979138i	−0.914605	−	0.404348i	$-0.867499\pi$
$487$	−1.10097	+	2.16077i	−0.0498896	+	0.0979138i	0.864716	+	0.502262i	$0.167499\pi$
$488$	−7.71433	−	18.1441i	−0.349211	−	0.821346i
$489$	3.78563	+	1.23002i	0.171192	+	0.0556236i
$490$	−6.56561	−	13.7767i	−0.296604	−	0.622370i
$491$	12.7330	−	4.13721i	0.574634	−	0.186710i	−0.00726141	−	0.999974i	$-0.502311\pi$
$491$	12.7330	−	4.13721i	0.574634	−	0.186710i	0.581895	+	0.813264i	$0.302311\pi$
$492$	−10.2019	+	4.61829i	−0.459936	+	0.208209i
$493$	9.61465	+	9.61465i	0.433022	+	0.433022i
$494$	−16.4391	+	21.5622i	−0.739630	+	0.970127i
$495$	3.32360	−	10.1107i	0.149385	−	0.454443i
$496$	−4.49460	−	7.56628i	−0.201814	−	0.339736i
$497$	−18.3305	+	2.90327i	−0.822237	+	0.130230i
$498$	−6.37147	+	6.08401i	−0.285513	+	0.272631i
$499$	−33.0488			−1.47947			−0.739734	−	0.672900i	$-0.765049\pi$
$499$	−33.0488			−1.47947			−0.739734	+	0.672900i	$0.765049\pi$
$500$	12.1016	+	18.8029i	0.541202	+	0.840893i
$501$	20.2591			0.905108
$502$	−18.4344	+	17.6027i	−0.822767	+	0.785647i
$503$	14.8800	−	2.35677i	0.663468	−	0.105083i	0.184387	−	0.982854i	$-0.440970\pi$
$503$	14.8800	−	2.35677i	0.663468	−	0.105083i	0.479081	+	0.877771i	$0.340970\pi$
$504$	−4.04587	+	1.01128i	−0.180217	+	0.0450459i
$505$	9.60859	−	29.2303i	0.427577	−	1.30073i
$506$	32.5611	−	42.7084i	1.44752	−	1.89862i
$507$	13.0096	+	13.0096i	0.577779	+	0.577779i
$508$	2.83051	+	6.25264i	0.125584	+	0.277416i
$509$	−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	$0.514622\pi$
$510$	2.28001	+	4.78419i	0.100960	+	0.211847i
$511$	14.3031	+	4.64736i	0.632732	+	0.205587i
$512$	−12.3573	−	18.9552i	−0.546119	−	0.837708i
$513$	−1.55336	+	3.04864i	−0.0685825	+	0.134601i
$514$	2.33089	+	0.0537945i	0.102811	+	0.00237278i
$515$	2.18690	−	13.5072i	0.0963663	−	0.595196i
$516$	5.39899	+	4.31678i	0.237677	+	0.190036i
$517$	−4.28016	+	27.0239i	−0.188241	+	1.18851i
$518$	−1.23221	+	2.28635i	−0.0541402	+	0.100457i
$519$	−6.18648	+	4.49474i	−0.271556	+	0.197297i
$520$	35.3457	+	2.57271i	1.55001	+	0.112821i
$521$	−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	$0.871529\pi$
$522$	10.3408	−	4.97178i	0.452604	−	0.217609i
$523$	−18.9802	−	37.2508i	−0.829947	−	1.62886i	−0.776352	−	0.630300i	$-0.782932\pi$
$523$	−18.9802	−	37.2508i	−0.829947	−	1.62886i	−0.0535947	−	0.998563i	$-0.517068\pi$
$524$	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
$528$	−18.4498	−	4.69880i	−0.802924	−	0.204489i
$529$	−23.8974	+	32.8920i	−1.03902	+	1.43009i
$530$	−7.79124	−	11.3443i	−0.338430	−	0.492766i
$531$	7.45712	+	10.2638i	0.323612	+	0.445413i
$532$	2.03645	−	9.88213i	0.0882914	−	0.428445i
$533$	−30.9888	−	4.90814i	−1.34227	−	0.212595i
$534$	1.63165	+	2.35834i	0.0706083	+	0.102055i
$535$	−24.6225	+	12.4394i	−1.06452	+	0.537804i
$536$	−17.9623	+	11.2388i	−0.775853	+	0.485442i
$537$	−14.8424	−	7.56258i	−0.640497	−	0.326349i
$538$	6.23457	−	34.2316i	0.268791	−	1.47583i
$539$	−7.09824	+	21.8461i	−0.305743	+	0.940980i
$540$	4.44632	−	0.479810i	0.191339	−	0.0206477i
$541$	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	$0.728661\pi$
$542$	1.32327	−	0.178394i	0.0568394	−	0.00766267i
$543$	−12.5231	+	12.5231i	−0.537419	+	0.537419i
$544$	8.26031	−	4.65246i	0.354158	−	0.199473i
$545$	0.107261	−	31.2323i	0.00459456	−	1.33784i
$546$	−11.0260	−	3.86602i	−0.471868	−	0.165450i
$547$	4.47666	+	28.2645i	0.191408	+	1.20850i	0.876990	+	0.480509i	$0.159548\pi$
$547$	4.47666	+	28.2645i	0.191408	+	1.20850i	−0.685582	+	0.727996i	$0.740452\pi$
$548$	−11.2108	+	19.6993i	−0.478903	+	0.841511i
$549$		−	6.97065i		−	0.297500i
$550$	6.25783	−	33.0692i	0.266835	−	1.41007i
$551$			27.7601i			1.18262i
$552$	21.9913	+	5.06345i	0.936010	+	0.215515i
$553$	−2.13675	−	13.4909i	−0.0908640	−	0.573693i
$554$	−5.39982	+	15.4004i	−0.229416	+	0.654301i
$555$	1.64484	−	2.24765i	0.0698194	−	0.0954074i
$556$	−27.4048	−	10.3249i	−1.16222	−	0.437874i
$557$	−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	$0.450082\pi$
$558$	−0.415705	−	3.08358i	−0.0175982	−	0.130538i
$559$	5.98475	+	18.4192i	0.253128	+	0.779048i
$560$	−12.2689	+	4.83652i	−0.518455	+	0.204380i
$561$	2.46497	−	7.58641i	0.104071	−	0.320298i
$562$	−7.12854	−	1.29832i	−0.300699	−	0.0547661i
$563$	24.2640	+	12.3631i	1.02261	+	0.521044i	0.883104	−	0.469177i	$-0.155449\pi$
$563$	24.2640	+	12.3631i	1.02261	+	0.521044i	0.139503	+	0.990222i	$0.455449\pi$
$564$	−11.0864	+	3.04452i	−0.466823	+	0.128197i
$565$	6.85420	+	6.90144i	0.288358	+	0.290346i
$566$	10.6765	−	7.38668i	0.448767	−	0.310485i
$567$	−1.45628	−	0.230653i	−0.0611582	−	0.00968651i
$568$	−3.12379	−	35.4647i	−0.131071	−	1.48806i
$569$	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	$0.535063\pi$
$570$	−3.61513	+	10.1981i	−0.151421	+	0.427153i
$571$	−2.29350	+	3.15674i	−0.0959802	+	0.132105i	−0.854306	−	0.519770i	$-0.826018\pi$
$571$	−2.29350	+	3.15674i	−0.0959802	+	0.132105i	0.758326	+	0.651876i	$0.226018\pi$
$572$	−35.9376	−	39.4177i	−1.50263	−	1.64814i
$573$	−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	$-0.321637\pi$
$578$	−8.69637	−	18.0876i	−0.361721	−	0.752343i
$579$	9.28323	+	6.74466i	0.385798	+	0.280299i
$580$	30.3751	−	19.8459i	1.26126	−	0.824056i
$581$	7.43071	−	5.39873i	0.308278	−	0.223977i
$582$	−4.23972	−	2.28496i	−0.175742	−	0.0947147i
$583$	−3.24039	+	20.4590i	−0.134203	+	0.847326i
$584$	−10.7916	+	26.7554i	−0.446559	+	1.10715i
$585$	11.1444	+	5.72665i	0.460764	+	0.236768i
$586$	−0.962505	+	41.7049i	−0.0397607	+	1.72281i
$587$	−1.15344	+	2.26375i	−0.0476076	+	0.0934351i	−0.913585	−	0.406648i	$-0.866697\pi$
$587$	−1.15344	+	2.26375i	−0.0476076	+	0.0934351i	0.865977	+	0.500084i	$0.166697\pi$
$588$	−9.59274	+	1.06851i	−0.395598	+	0.0440645i
$589$	7.15949	+	2.32626i	0.295002	+	0.0958519i
$590$	27.6067	+	29.1105i	1.13655	+	1.19846i
$591$	−2.07227	+	0.673322i	−0.0852419	+	0.0276968i
$592$	−4.21192	−	2.66147i	−0.173109	−	0.109386i
$593$	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	$0.499342\pi$
$594$	−5.35292	−	4.08110i	−0.219633	−	0.167449i
$595$	−1.68938	−	5.26080i	−0.0692580	−	0.215672i
$596$	14.4900	+	0.669183i	0.593532	+	0.0274108i
$597$	9.57120	−	1.51593i	0.391723	−	0.0620429i
$598$	43.6636	+	45.7267i	1.78554	+	1.86990i
$599$	10.8060			0.441521			0.220761	−	0.975328i	$-0.429146\pi$
$599$	10.8060			0.441521			0.220761	+	0.975328i	$0.429146\pi$
$600$	13.7433	−	3.33505i	0.561067	−	0.136153i
$601$	−18.5184			−0.755379			−0.377690	−	0.925932i	$-0.623281\pi$
$601$	−18.5184			−0.755379			−0.377690	+	0.925932i	$0.623281\pi$
$602$	−4.97714	−	5.21230i	−0.202853	−	0.212438i
$603$	−7.39906	+	1.17190i	−0.301313	+	0.0477233i
$604$	17.7613	+	0.820261i	0.722697	+	0.0333760i
$605$	−21.1358	+	15.2454i	−0.859293	+	0.619815i
$606$	−15.4754	−	11.7985i	−0.628645	−	0.479282i
$607$	31.2527	+	31.2527i	1.26851	+	1.26851i	0.946858	+	0.321651i	$0.104238\pi$
$607$	31.2527	+	31.2527i	1.26851	+	1.26851i	0.321651	+	0.946858i	$0.395762\pi$
$608$	18.6414	+	5.20843i	0.756007	+	0.211230i
$609$	−11.3770	+	3.69662i	−0.461021	+	0.149795i
$610$	−2.87001	−	21.8555i	−0.116203	−	0.884904i
$611$	−30.6344	−	9.95373i	−1.23934	−	0.402685i
$612$	3.33123	−	0.371056i	0.134657	−	0.0149990i
$613$	−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	$0.199052\pi$
$614$	−0.0494794	+	2.14392i	−0.00199683	+	0.0865215i
$615$	−12.3728	+	1.91613i	−0.498921	+	0.0772659i
$616$	18.4085	+	7.42492i	0.741700	+	0.299158i
$617$	−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	$0.805130\pi$
$618$	−7.61799	−	4.10566i	−0.306441	−	0.165154i
$619$	11.1832	−	8.12509i	0.449492	−	0.326575i	−0.339903	−	0.940460i	$-0.610394\pi$
$619$	11.1832	−	8.12509i	0.449492	−	0.326575i	0.789395	+	0.613885i	$0.210394\pi$
$620$	−2.57298	−	9.49696i	−0.103333	−	0.381407i
$621$	6.45476	+	4.68966i	0.259020	+	0.188189i
$622$	−0.0531728	−	0.110594i	−0.00213203	−	0.00443441i
$623$	−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
$628$	−5.97348	−	6.55193i	−0.238368	−	0.261451i
$629$	1.22700	−	1.68882i	0.0489237	−	0.0673376i
$630$	−4.66094	−	0.123587i	−0.185696	−	0.00492381i
$631$	15.1133	+	20.8017i	0.601652	+	0.828103i	0.995858	−	0.0909189i	$-0.0289804\pi$
$631$	15.1133	+	20.8017i	0.601652	+	0.828103i	−0.394206	+	0.919022i	$0.628980\pi$
$632$	26.1013	−	2.29905i	1.03825	−	0.0914513i
$633$	−24.3889	−	3.86282i	−0.969372	−	0.153533i
$634$	−37.0951	+	25.6647i	−1.47323	+	1.01928i
$635$	1.17438	+	7.58320i	0.0466038	+	0.300930i
$636$	−8.39323	+	2.30492i	−0.332813	+	0.0913959i
$637$	−24.0949	−	12.2770i	−0.954675	−	0.486431i
$638$	−53.7283	−	9.78550i	−2.12713	−	0.387411i
$639$	3.88966	−	11.9711i	0.153872	−	0.473571i
$640$	−7.62778	−	24.1209i	−0.301514	−	0.953462i
$641$	−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	$0.963757\pi$
$642$	2.33101	+	17.2907i	0.0919975	+	0.682410i
$643$	17.4447	−	17.4447i	0.687951	−	0.687951i	−0.273828	−	0.961779i	$-0.588290\pi$
$643$	17.4447	−	17.4447i	0.687951	−	0.687951i	0.961779	+	0.273828i	$0.0882899\pi$
$644$	−22.0169	−	8.29499i	−0.867587	−	0.326868i
$645$	4.52119	+	6.26805i	0.178022	+	0.246804i
$646$	−2.68325	+	7.65269i	−0.105571	+	0.301091i
$647$	−4.48496	−	28.3169i	−0.176322	−	1.11325i	−0.904063	−	0.427400i	$-0.859430\pi$
$647$	−4.48496	−	28.3169i	−0.176322	−	1.11325i	0.727741	−	0.685852i	$-0.240570\pi$
$648$	0.634636	−	2.75631i	0.0249308	−	0.108278i
$649$		−	60.3852i		−	2.37033i
$650$	37.2995	+	13.3666i	1.46301	+	0.524283i
$651$			3.24397i			0.127141i
$652$	3.93755	−	6.91891i	0.154206	−	0.270966i
$653$	−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	$0.960235\pi$
$654$	−18.6405	−	6.53589i	−0.728902	−	0.255574i
$655$	15.7420	−	5.05517i	0.615089	−	0.197522i
$656$	4.92834	+	21.8481i	0.192419	+	0.853025i
$657$	−7.21245	+	7.21245i	−0.281384	+	0.281384i
$658$	11.8790	−	1.60144i	0.463092	−	0.0624307i
$659$	−6.95495	−	21.4051i	−0.270926	−	0.833826i	−0.990269	−	0.139170i	$-0.955557\pi$
$659$	−6.95495	−	21.4051i	−0.270926	−	0.833826i	0.719342	−	0.694656i	$-0.244443\pi$
$660$	−18.4636	−	10.5918i	−0.718696	−	0.412284i
$661$	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	$-0.181386\pi$
$662$	−4.87099	+	26.7447i	−0.189316	+	1.03946i
$663$	8.36733	+	4.26337i	0.324960	+	0.165575i
$664$	9.34566	+	14.9366i	0.362682	+	0.579653i
$665$	5.15583	−	10.0335i	0.199934	−	0.389084i
$666$	−1.00224	−	1.44861i	−0.0388361	−	0.0561326i
$667$	63.9350	+	10.1263i	2.47557	+	0.392092i
$668$	8.17791	−	39.6843i	0.316413	−	1.53543i
$669$	11.6129	+	15.9838i	0.448980	+	0.617968i
$670$	−22.7162	+	6.72071i	−0.877603	+	0.259644i
$671$	−19.5016	+	26.8416i	−0.752851	+	1.03621i
$672$	0.347749	+	8.33343i	0.0134147	+	0.321469i
$673$	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	$0.509100\pi$
$678$	5.54422	−	2.66562i	0.212925	−	0.102373i
$679$	4.06236	+	2.95147i	0.155899	+	0.113267i
$680$	10.2918	−	2.53495i	0.394673	−	0.0972110i
$681$	0.133907	−	0.0972891i	0.00513132	−	0.00372812i
$682$	−7.02609	+	13.0368i	−0.269043	+	0.499206i
$683$	3.21000	−	20.2671i	0.122827	−	0.775500i	−0.846980	−	0.531626i	$-0.821581\pi$
$683$	3.21000	−	20.2671i	0.122827	−	0.775500i	0.969807	−	0.243875i	$-0.0784186\pi$
$684$	5.34476	+	4.27342i	0.204362	+	0.163398i
$685$	−17.9804	+	17.8573i	−0.686996	+	0.682294i
$686$	24.6527	+	0.568959i	0.941245	+	0.0217230i
$687$	−3.40358	+	6.67991i	−0.129855	+	0.254854i
$688$	10.6353	−	8.83322i	0.405466	−	0.336763i
$689$	−23.1925	−	7.53569i	−0.883563	−	0.287087i
$690$	22.1688	+	12.0462i	0.843954	+	0.458589i
$691$	−19.2612	+	6.25835i	−0.732731	+	0.238079i	−0.651534	−	0.758619i	$-0.725874\pi$
$691$	−19.2612	+	6.25835i	−0.732731	+	0.238079i	−0.0811970	+	0.996698i	$0.525874\pi$
$692$	6.30720	+	13.9327i	0.239764	+	0.529641i
$693$	4.96237	+	4.96237i	0.188505	+	0.188505i
$694$	−2.98483	+	3.91501i	−0.113303	+	0.148612i
$695$	−26.4225	−	19.3361i	−1.00226	−	0.733460i
$696$	−5.56468	−	22.2629i	−0.210929	−	0.843873i
$697$	−9.26836	+	1.46796i	−0.351064	+	0.0556031i
$698$	−1.08719	+	1.03814i	−0.0411506	+	0.0392940i
$699$	−10.6764			−0.403818
$700$	−14.6646	+	1.53155i	−0.554270	+	0.0578872i
$701$	13.8933			0.524741			0.262370	−	0.964967i	$-0.415496\pi$
$701$	13.8933			0.524741			0.262370	+	0.964967i	$0.415496\pi$
$702$	5.73122	−	5.47265i	0.216311	−	0.206552i
$703$	4.20939	−	0.666701i	0.158760	−	0.0251451i
$704$	−16.6518	+	34.2434i	−0.627587	+	1.29060i
$705$	−12.8538	−	0.0441439i	−0.484103	−	0.00166255i
$706$	−17.6449	+	23.1437i	−0.664074	+	0.871025i
$707$	14.3463	+	14.3463i	0.539548	+	0.539548i
$708$	23.1154	−	10.4641i	0.868731	−	0.393266i
$709$	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	$0.300672\pi$
$710$	7.26663	−	39.1353i	0.272712	−	1.46872i
$711$	8.81053	+	2.86271i	0.330421	+	0.107360i
$712$	5.27825	−	2.24415i	0.197811	−	0.0841032i
$713$	7.96929	−	15.6406i	0.298452	−	0.585746i
$714$	−3.49364	−	0.0806295i	−0.130746	−	0.00301748i
$715$	−26.8921	−	53.2298i	−1.00571	−	1.99068i
$716$	−20.8053	+	26.0211i	−0.777529	+	0.972455i
$717$	−3.47793	+	21.9588i	−0.129886	+	0.820065i
$718$	−11.0408	+	20.4860i	−0.412038	+	0.764531i
$719$	6.10365	−	4.43456i	0.227628	−	0.165381i	−0.468126	−	0.883662i	$-0.655071\pi$
$719$	6.10365	−	4.43456i	0.227628	−	0.165381i	0.695753	+	0.718281i	$0.255071\pi$
$720$	0.854962	−	8.90332i	0.0318625	−	0.331807i
$721$	7.29931	+	5.30326i	0.271840	+	0.197504i
$722$	9.29514	−	4.46904i	0.345929	−	0.166320i
$723$	−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	0.582913	−	0.812535i	$-0.301913\pi$
$727$	42.6795	−	21.7463i	1.58289	−	0.806525i	0.999982	+	0.00600972i	$0.00191296\pi$
$728$	−12.0237	+	20.0375i	−0.445629	+	0.742641i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−19.6441	+	25.5832i	−0.727059	+	0.946876i
$731$	3.40471	+	4.68618i	0.125928	+	0.173325i
$732$	−13.6544	−	2.81382i	−0.504681	−	0.104002i
$733$	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	$0.474430\pi$
$734$	15.3035	+	22.1193i	0.564863	+	0.816439i
$735$	−10.6526	−	1.72473i	−0.392928	−	0.0636177i
$736$	18.7956	−	41.0334i	0.692816	−	1.51251i
$737$	31.7699	+	16.1876i	1.17026	+	0.596276i
$738$	−1.41886	+	7.79040i	−0.0522289	+	0.286769i
$739$	−7.24911	+	22.3105i	−0.266663	+	0.820704i	0.724643	+	0.689125i	$0.242005\pi$
$739$	−7.24911	+	22.3105i	−0.266663	+	0.820704i	−0.991306	+	0.131579i	$0.957995\pi$
$740$	−3.73882	−	4.12927i	−0.137442	−	0.151795i
$741$	5.92463	+	18.2341i	0.217647	+	0.669848i
$742$	8.99326	−	1.21241i	0.330153	−	0.0445088i
$743$	−31.2758	+	31.2758i	−1.14740	+	1.14740i	−0.160337	+	0.987062i	$0.551258\pi$
$743$	−31.2758	+	31.2758i	−1.14740	+	1.14740i	−0.987062	+	0.160337i	$0.948742\pi$
$744$	−6.20804	−	0.430437i	−0.227598	−	0.0157806i
$745$	15.4065	+	5.06444i	0.564450	+	0.185547i
$746$	−0.781247	−	0.273927i	−0.0286035	−	0.0100292i
$747$	0.974493	+	6.15271i	0.0356548	+	0.225116i
$748$	−13.8655	−	7.89087i	−0.506974	−	0.288519i
$749$		−	18.1901i		−	0.664652i
$750$	15.8026	+	0.527650i	0.577029	+	0.0192671i
$751$		−	25.1683i		−	0.918404i	−0.888332	−	0.459202i	$-0.848135\pi$
$751$		−	25.1683i		−	0.918404i	0.888332	−	0.459202i	$-0.151865\pi$
$752$	1.48850	+	22.9455i	0.0542799	+	0.836737i
$753$	2.81947	+	17.8014i	0.102747	+	0.648721i
$754$	21.2732	−	60.6718i	0.774726	−	2.20954i
$755$	18.8847	+	6.20781i	0.687286	+	0.225925i
$756$	−1.03967	+	2.75952i	−0.0378123	+	0.100363i
$757$	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	$0.0843809\pi$
$758$	0.939524	+	6.96911i	0.0341251	+	0.253129i
$759$	−11.7350	−	36.1166i	−0.425953	−	1.31095i
$760$	18.5172	+	11.1981i	0.671690	+	0.406198i
$761$	−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	$0.931914\pi$
$762$	4.77466	+	0.869605i	0.172968	+	0.0315025i
$763$	18.3497	+	9.34964i	0.664304	+	0.338480i
$764$	5.09624	+	18.5577i	0.184376	+	0.671393i
$765$	3.69929	+	0.598940i	0.133748	+	0.0216547i
$766$	−21.5394	+	14.9023i	−0.778251	+	0.538443i
$767$	70.2144	+	11.1209i	2.53530	+	0.401551i
$768$	−15.9939	−	0.440254i	−0.577132	−	0.0158863i
$769$	−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	$0.935939\pi$
$770$	17.6020	+	13.5157i	0.634331	+	0.487071i
$771$	0.969038	−	1.33377i	0.0348991	−	0.0480344i
$772$	16.9590	−	15.4618i	0.610369	−	0.556481i
$773$	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
$778$	9.13777	+	19.0056i	0.327605	+	0.681385i
$779$	−15.4994	−	11.2609i	−0.555322	−	0.403465i
$780$	15.7162	−	19.5184i	0.562730	−	0.698872i
$781$	−48.4691	+	35.2148i	−1.73436	+	1.26009i
$782$	16.6463	+	8.97138i	0.595270	+	0.320816i
$783$	1.26920	−	8.01339i	0.0453574	−	0.286375i
$784$	−1.77923	+	19.2220i	−0.0635440	+	0.686499i
$785$	−4.46994	−	8.84774i	−0.159539	−	0.315789i
$786$	0.241269	−	10.4541i	0.00860578	−	0.372884i
$787$	−8.24852	+	16.1886i	−0.294028	+	0.577062i	−0.990010	−	0.140997i	$-0.954969\pi$
$787$	−8.24852	+	16.1886i	−0.294028	+	0.577062i	0.695982	+	0.718059i	$0.254969\pi$
$788$	0.482423	+	4.33105i	0.0171856	+	0.154287i
$789$	−24.2620	−	7.88319i	−0.863749	−	0.280649i
$790$	28.8028	+	5.34810i	1.02476	+	0.190277i
$791$	−6.09981	+	1.98195i	−0.216884	+	0.0704699i
$792$	−10.1550	+	8.83812i	−0.360843	+	0.314049i
$793$	−27.6193	−	27.6193i	−0.980789	−	0.980789i
$794$	−19.6933	−	15.0143i	−0.698889	−	0.532837i
$795$	−9.73126	−	0.0334201i	−0.345132	−	0.00118529i
$796$	0.894112	−	19.3604i	0.0316909	−	0.686211i
$797$	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	$0.379567\pi$
$798$	−4.92715	−	5.15995i	−0.174419	−	0.182660i
$799$	−9.63389			−0.340823
$800$	−0.985131	−	28.2671i	−0.0348296	−	0.999393i
$801$	2.02781			0.0716492
$802$	22.9304	+	24.0138i	0.809700	+	0.847957i
$803$	47.9508	−	7.59466i	1.69215	−	0.268010i
$804$	−0.691197	+	14.9666i	−0.0243766	+	0.527832i
$805$	−21.2277	−	15.5345i	−0.748180	−	0.547520i
$806$	−13.8649	−	10.5707i	−0.488371	−	0.372337i
$807$	−17.3973	−	17.3973i	−0.612416	−	0.612416i
$808$	−29.3583	+	25.5511i	−1.03282	+	0.898886i
$809$	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	$0.354009\pi$
$810$	1.50982	−	2.77857i	0.0530498	−	0.0976289i
$811$	−51.5148	−	16.7382i	−1.80893	−	0.587756i	−0.808928	−	0.587908i	$-0.799952\pi$
$811$	−51.5148	−	16.7382i	−1.80893	−	0.587756i	−1.00000		0.000151490i	$0.999952\pi$
$812$	2.64856	+	23.7780i	0.0929464	+	0.834444i
$813$	0.428639	−	0.841252i	0.0150330	−	0.0295040i
$814$	−0.193449	+	8.38206i	−0.00678040	+	0.293791i
$815$	6.31521	−	6.27198i	0.221212	−	0.219698i
$816$	0.617866	−	6.67512i	0.0216296	−	0.233676i
$817$	−1.84998	+	11.6803i	−0.0647227	+	0.408643i
$818$	−47.5823	−	25.6441i	−1.66368	−	0.896624i
$819$	−6.68402	+	4.85623i	−0.233559	+	0.169690i
$820$	−1.24111	+	25.0099i	−0.0433414	+	0.873383i
$821$	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	$0.624149\pi$
$822$	6.94478	+	14.4444i	0.242227	+	0.503808i
$823$	−9.68724	−	19.0123i	−0.337676	−	0.662726i	0.658260	−	0.752791i	$-0.271293\pi$
$823$	−9.68724	−	19.0123i	−0.337676	−	0.662726i	−0.995936	+	0.0900643i	$0.971293\pi$
$824$	−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	−0.989935	−	0.141522i	$-0.954800\pi$
$827$	−41.9088	+	21.3536i	−1.45731	+	0.742537i	−0.467375	+	0.884059i	$0.654800\pi$
$828$	11.7919	−	10.7508i	0.409795	−	0.373615i
$829$	−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	$0.326257\pi$
$830$	5.58863	+	18.8897i	0.193984	+	0.655672i
$831$	6.78288	+	9.33584i	0.235296	+	0.323857i
$832$	−36.7507	−	25.6687i	−1.27410	−	0.889903i
$833$	−7.98844	−	1.26525i	−0.276783	−	0.0438381i
$834$	−17.0294	+	11.7820i	−0.589678	+	0.407976i
$835$	20.7046	−	40.2923i	0.716511	−	1.39437i
$836$	−8.62525	−	31.4084i	−0.298311	−	1.08628i
$837$	−1.96034	−	0.998844i	−0.0677593	−	0.0345251i
$838$	−14.5249	−	2.64540i	−0.501753	−	0.0913839i
$839$	−7.78737	+	23.9670i	−0.268850	+	0.827434i	0.721932	+	0.691964i	$0.243254\pi$
$839$	−7.78737	+	23.9670i	−0.268850	+	0.827434i	−0.990781	+	0.135470i	$0.956746\pi$
$840$	−2.12355	+	9.08015i	−0.0732696	+	0.313295i
$841$	−11.3796	−	35.0230i	−0.392402	−	1.20769i
$842$	−0.835916	−	6.20058i	−0.0288076	−	0.213686i
$843$	−3.62290	+	3.62290i	−0.124779	+	0.124779i
$844$	−17.4116	+	46.2147i	−0.599333	+	1.59077i
$845$	39.1700	−	12.5785i	1.34749	−	0.432715i
$846$	−2.68988	+	7.67161i	−0.0924800	+	0.263755i
$847$	−2.68816	−	16.9724i	−0.0923664	−	0.583178i
$848$	1.12690	+	17.3714i	0.0386979	+	0.596536i
$849$		−	9.18017i		−	0.315063i
$850$	11.8452	+	0.354792i	0.406287	+	0.0121693i
$851$		−	9.93793i		−	0.340668i
$852$	−21.8794	−	12.4516i	−0.749576	−	0.426584i
$853$	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	$0.944340\pi$
$854$	13.7163	+	4.80931i	0.469362	+	0.164571i
$855$	4.47578	+	6.20508i	0.153068	+	0.212209i
$856$	34.8107	+	2.41361i	1.18981	+	0.0824956i
$857$	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	$-0.104558\pi$
$858$	−37.3797	+	5.03926i	−1.27612	+	0.172037i
$859$	−3.89611	−	11.9910i	−0.132933	−	0.409127i	0.862329	−	0.506348i	$-0.169005\pi$
$859$	−3.89611	−	11.9910i	−0.132933	−	0.409127i	−0.995263	+	0.0972207i	$0.969005\pi$
$860$	14.1032	−	6.32609i	0.480913	−	0.215718i
$861$	2.55117	−	7.85170i	0.0869437	−	0.267585i
$862$	6.35559	−	34.8961i	0.216472	−	1.18857i
$863$	−20.6059	−	10.4992i	−0.701431	−	0.357397i	0.0666261	−	0.997778i	$-0.478777\pi$
$863$	−20.6059	−	10.4992i	−0.701431	−	0.357397i	−0.768058	+	0.640381i	$0.778777\pi$
$864$	−5.14299	−	2.35578i	−0.174968	−	0.0801452i
$865$	2.61686	+	16.8976i	0.0889758	+	0.574535i
$866$	−9.75970	−	14.1064i	−0.331648	−	0.479355i
$867$	−14.0166	−	2.22001i	−0.476028	−	0.0753955i
$868$	6.35442	+	1.30948i	0.215683	+	0.0444468i
$869$	−25.9174	−	35.6723i	−0.879189	−	1.21010i
$870$	0.680051	−	25.6474i	0.0230559	−	0.869529i
$871$	−24.6734	+	33.9600i	−0.836026	+	1.15069i
$872$	−20.3273	+	33.8755i	−0.688370	+	1.14717i
$873$	−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	$0.968273\pi$
$878$	−27.5839	+	13.2621i	−0.930911	+	0.447575i
$879$	23.8641	+	17.3383i	0.804916	+	0.584806i
$880$	−28.2007	+	31.8918i	−0.950646	+	1.07507i
$881$	−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	$0.377448\pi$
$882$	−3.23799	+	6.00805i	−0.109029	+	0.202301i
$883$	6.44822	−	40.7125i	0.217000	−	1.37008i	−0.603009	−	0.797734i	$-0.706032\pi$
$883$	6.44822	−	40.7125i	0.217000	−	1.37008i	0.820009	−	0.572350i	$-0.193968\pi$
$884$	11.7289	−	14.6693i	0.394484	−	0.493381i
$885$	28.0344	−	4.34157i	0.942366	−	0.145940i
$886$	−16.5498	−	0.381952i	−0.556002	−	0.0128319i
$887$	−3.65750	+	7.17824i	−0.122807	+	0.241022i	−0.944223	−	0.329308i	$-0.893185\pi$
$887$	−3.65750	+	7.17824i	−0.122807	+	0.241022i	0.821416	+	0.570330i	$0.193185\pi$
$888$	−3.24217	+	1.37847i	−0.108800	+	0.0462585i
$889$	−4.81223	−	1.56359i	−0.161397	−	0.0524411i
$890$	6.35792	−	0.834907i	0.213118	−	0.0279861i
$891$	−4.52673	+	1.47082i	−0.151651	+	0.0492744i
$892$	35.9974	−	16.2957i	1.20528	−	0.545619i
$893$	−13.9078	−	13.9078i	−0.465408	−	0.465408i
$894$	6.21869	−	8.15667i	0.207984	−	0.272800i
$895$	−30.2096	+	21.7905i	−1.00980	+	0.728375i
$896$	16.4642	+	2.68274i	0.550031	+	0.0896241i
$897$	44.1566	−	6.99373i	1.47435	−	0.233514i
$898$	15.9387	−	15.2196i	0.531882	−	0.507885i
$899$	−17.8504			−0.595343
$900$	3.58983	−	9.33344i	0.119661	−	0.311115i
$901$	−7.29355			−0.242983
$902$	27.2585	−	26.0287i	0.907610	−	0.866661i
$903$	−5.03334	+	0.797202i	−0.167499	+	0.0265292i
$904$	−2.98351	−	11.9363i	−0.0992300	−	0.396994i
$905$	12.1082	+	37.7052i	0.402489	+	1.25336i
$906$	7.62265	−	9.99816i	0.253246	−	0.332167i
$907$	−22.6464	−	22.6464i	−0.751962	−	0.751962i	0.222883	−	0.974845i	$-0.428453\pi$
$907$	−22.6464	−	22.6464i	−0.751962	−	0.751962i	−0.974845	+	0.222883i	$0.928453\pi$
$908$	−0.136520	−	0.301574i	−0.00453057	−	0.0100081i
$909$	−13.0868	+	4.25217i	−0.434063	+	0.141036i
$910$	−18.9574	+	17.9780i	−0.628431	+	0.595965i
$911$	13.8057	+	4.48573i	0.457402	+	0.148619i	0.528650	−	0.848840i	$-0.322698\pi$
$911$	13.8057	+	4.48573i	0.457402	+	0.148619i	−0.0712485	+	0.997459i	$0.522698\pi$
$912$	10.5284	−	8.74449i	0.348631	−	0.289559i
$913$	13.4608	−	26.4183i	0.445488	−	0.874319i
$914$	2.73698	+	0.0631668i	0.0905314	+	0.00208937i
$915$	−13.8636	−	7.12394i	−0.458317	−	0.235510i
$916$	11.7110	+	9.36353i	0.386941	+	0.309380i
$917$	−1.70547	+	10.7679i	−0.0563197	+	0.355588i
$918$	1.12444	−	2.08639i	0.0371121	−	0.0688610i
$919$	−8.34391	+	6.06221i	−0.275240	+	0.199974i	−0.716839	−	0.697239i	$-0.754412\pi$
$919$	−8.34391	+	6.06221i	−0.275240	+	0.199974i	0.441598	+	0.897213i	$0.354412\pi$
$920$	32.5453	−	38.5626i	1.07299	−	1.27137i
$921$	1.22678	+	0.891308i	0.0404238	+	0.0293696i
$922$	−4.96321	+	2.38628i	−0.163455	+	0.0785878i
$923$	−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
$928$	−45.8557	+	1.91353i	−1.50529	+	0.0628149i
$929$	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	$0.184081\pi$
$930$	−6.55763	−	2.32461i	−0.215033	−	0.0762269i
$931$	−9.70586	−	13.3590i	−0.318097	−	0.437823i
$932$	−4.30970	+	20.9133i	−0.141169	+	0.685039i
$933$	−0.0857026	−	0.0135740i	−0.00280578	−	0.000444391i
$934$	−1.29108	−	1.86610i	−0.0422455	−	0.0610606i
$935$	−12.5691	−	12.6557i	−0.411053	−	0.413886i
$936$	−8.40654	−	13.4357i	−0.274776	−	0.439159i
$937$	−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	$0.783029\pi$
$938$	2.79892	−	15.3678i	0.0913881	−	0.501777i
$939$	6.84715	−	21.0733i	0.223448	−	0.687703i
$940$	−5.27513	+	25.1608i	−0.172056	+	0.820653i
$941$	−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	$-0.474815\pi$
$942$	−6.21317	+	0.837614i	−0.202436	+	0.0272910i
$943$	−31.5892	+	31.5892i	−1.02868	+	1.02868i
$944$	−11.1666	−	49.5034i	−0.363443	−	1.61120i
$945$	−1.94704	+	2.66061i	−0.0633373	+	0.0865497i
$946$	−21.9545	−	7.69788i	−0.713804	−	0.250280i
$947$	4.35758	+	27.5127i	0.141602	+	0.894042i	0.951540	+	0.307526i	$0.0995010\pi$
$947$	4.35758	+	27.5127i	0.141602	+	0.894042i	−0.809937	+	0.586516i	$0.800499\pi$
$948$	9.16411	−	16.1028i	0.297637	−	0.522996i
$949$			57.1546i			1.85532i
$950$	16.5880	+	17.6124i	0.538185	+	0.571420i
$951$			31.8961i			1.03430i
$952$	−1.56820	+	6.81093i	−0.0508258	+	0.220743i
$953$	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	$0.598135\pi$
$954$	−2.03643	+	5.80796i	−0.0659319	+	0.188040i
$955$	−0.0738928	+	21.5161i	−0.00239112	+	0.696245i
$956$	41.6098	+	15.6767i	1.34576	+	0.507021i
$957$	−27.3061	+	27.3061i	−0.882680	+	0.882680i
$958$	1.22572	+	9.09200i	0.0396011	+	0.293749i
$959$	−5.16360	−	15.8919i	−0.166741	−	0.513177i
$960$	−17.0951	−	5.26870i	−0.551740	−	0.170047i
$961$	8.08369	−	24.8790i	0.260764	−	0.802550i
$962$	−9.71083	−	1.76863i	−0.313090	−	0.0570228i
$963$	10.9923	+	5.60087i	0.354223	+	0.180486i
$964$	−39.3369	+	10.8025i	−1.26696	+	0.347927i
$965$	22.9015	−	11.5700i	0.737226	−	0.372452i
$966$	−13.6813	+	9.46558i	−0.440189	+	0.304550i
$967$	−42.4566	−	6.72446i	−1.36531	−	0.216244i	−0.569601	−	0.821921i	$-0.692902\pi$
$967$	−42.4566	−	6.72446i	−1.36531	−	0.216244i	−0.795710	+	0.605677i	$0.792902\pi$
$968$	32.8370	−	2.89234i	1.05542	−	0.0929633i
$969$	3.37051	+	4.63911i	0.108276	+	0.149030i
$970$	−8.87740	+	6.09697i	−0.285036	+	0.195762i
$971$	−0.810009	+	1.11488i	−0.0259944	+	0.0357783i	−0.821816	−	0.569752i	$-0.807039\pi$
$971$	−0.810009	+	1.11488i	−0.0259944	+	0.0357783i	0.795822	+	0.605531i	$0.207039\pi$
$972$	−1.34747	−	1.47795i	−0.0432200	−	0.0474053i
$973$	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	$0.963720\pi$
$978$	−2.43920	−	5.07328i	−0.0779969	−	0.162226i
$979$	−7.80842	−	5.67315i	−0.249558	−	0.181315i
$980$	−7.67858	+	20.1706i	−0.245283	+	0.644325i
$981$	−11.3000	+	8.20994i	−0.360782	+	0.262123i
$982$	−16.6674	−	8.98278i	−0.531879	−	0.286652i
$983$	−1.68880	+	10.6627i	−0.0538643	+	0.340086i	0.946009	+	0.324142i	$0.105075\pi$
$983$	−1.68880	+	10.6627i	−0.0538643	+	0.340086i	−0.999873	+	0.0159443i	$0.994925\pi$
$984$	14.6874	+	5.92404i	0.468217	+	0.188852i
$985$	−0.778703	+	4.80957i	−0.0248115	+	0.153246i
$986$	0.443674	−	19.2242i	0.0141295	−	0.612223i
$987$	3.84789	−	7.55191i	0.122480	−	0.240380i
$988$	38.1093	−	4.24489i	1.21242	−	0.135048i
$989$	26.2264	+	8.52147i	0.833950	+	0.270967i
$990$	−13.5873	+	6.47534i	−0.431834	+	0.205800i
$991$	38.6911	−	12.5715i	1.22906	−	0.399347i	0.378688	−	0.925524i	$-0.376375\pi$
$991$	38.6911	−	12.5715i	1.22906	−	0.399347i	0.850375	+	0.526178i	$0.176375\pi$
$992$	−3.34913	+	11.9868i	−0.106335	+	0.380581i
$993$	13.5923	+	13.5923i	0.431340	+	0.431340i
$994$	20.8722	+	15.9131i	0.662026	+	0.504733i
$995$	6.76671	−	20.5850i	0.214519	−	0.652588i
$996$	12.4455	+	0.574767i	0.394352	+	0.0182122i
$997$	−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	$0.493021\pi$
$998$	32.2775	+	33.8025i	1.02173	+	1.07000i
$999$	−1.24559			−0.0394086

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.976661 - 1.02281i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-0.0922667 + 1.99787i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(1.12464 + 0.857431i) q^{6} +(-1.04258 - 1.04258i) q^{7} +(2.13355 - 1.85687i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.976661 - 1.02281i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-0.0922667 + 1.99787i) q^{4} +(-0.698282 + 2.12424i) q^{5} +(1.12464 + 0.857431i) q^{6} +(-1.04258 - 1.04258i) q^{7} +(2.13355 - 1.85687i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.85467 - 1.36046i) q^{10} +(-4.52673 - 1.47082i) q^{11} +(-0.221405 - 1.98771i) q^{12} +(2.54390 - 4.99269i) q^{13} +(-0.0481108 + 2.08461i) q^{14} +(0.357381 - 2.20732i) q^{15} +(-3.98297 - 0.368674i) q^{16} +(0.262171 - 1.65528i) q^{17} +(-1.24492 - 0.670942i) q^{18} +(2.76811 - 2.01115i) q^{19} +(-4.17953 - 1.59107i) q^{20} +(1.19285 + 0.866653i) q^{21} +(2.91671 + 6.06646i) 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} +(2.17915 - 1.98675i) q^{28} +(-4.76887 + 6.56378i) q^{29} +(-2.60671 + 1.79028i) q^{30} +(1.29321 + 1.77995i) q^{31} +(3.51293 + 4.43388i) q^{32} +(4.70108 + 0.744578i) q^{33} +(-1.94908 + 1.34850i) q^{34} +(2.94272 - 1.48668i) q^{35} +(0.529625 + 1.92860i) q^{36} +(1.10983 + 0.565484i) q^{37} +(-4.76052 - 0.867029i) q^{38} +(-1.73155 + 5.32918i) q^{39} +(2.45462 + 5.82879i) q^{40} +(-1.73027 - 5.32522i) q^{41} +(-0.278587 - 2.06648i) q^{42} +(-2.44396 + 2.44396i) q^{43} +(3.35618 - 8.90811i) q^{44} +(-0.00767928 + 2.23605i) q^{45} +(-3.73341 + 10.6478i) q^{46} +(-0.899254 - 5.67766i) q^{47} +(3.99161 - 0.258939i) q^{48} -4.82603i q^{49} +(0.896569 + 7.01400i) q^{50} +1.67591i q^{51} +(9.74003 + 5.54305i) q^{52} +(-0.680800 - 4.29840i) q^{53} +(1.33456 + 0.467933i) q^{54} +(6.28532 - 8.58881i) q^{55} +(-4.16035 - 0.288460i) q^{56} +(-2.41941 + 2.41941i) q^{57} +(11.3710 - 1.53296i) q^{58} +(3.92044 + 12.0659i) q^{59} +(4.37697 + 0.917663i) q^{60} +(2.15405 - 6.62949i) q^{61} +(0.557518 - 3.06112i) q^{62} +(-1.31373 - 0.669381i) q^{63} +(1.10406 - 7.92345i) q^{64} +(8.82932 + 8.89017i) q^{65} +(-3.82980 - 5.53550i) q^{66} +(-7.39906 - 1.17190i) q^{67} +(3.28285 + 0.676511i) q^{68} +(4.68966 + 6.45476i) q^{69} +(-4.39463 - 1.55785i) q^{70} +(7.39857 - 10.1833i) q^{71} +(1.45532 - 2.42529i) 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} +(7.14186 - 3.43375i) q^{78} +(7.49468 + 5.44520i) q^{79} +(3.56439 - 8.20336i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-3.75678 + 6.97066i) q^{82} +(-0.974493 + 6.15271i) q^{83} +(-1.84152 + 2.30319i) q^{84} +(3.33315 + 1.71277i) q^{85} +(4.88663 + 0.112778i) q^{86} +(3.68335 - 7.22899i) q^{87} +(-12.3891 + 5.26748i) q^{88} +(1.92856 + 0.626628i) q^{89} +(2.29455 - 2.17601i) q^{90} +(-7.85754 + 2.55307i) q^{91} +(14.5369 - 6.58071i) q^{92} +(-1.55574 - 1.55574i) q^{93} +(-4.92889 + 6.46492i) q^{94} +(2.33924 + 7.28448i) q^{95} +(-4.16329 - 3.82975i) q^{96} +(-3.36367 + 0.532753i) q^{97} +(-4.93610 + 4.71340i) 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