LMFDB - Embedded newform 228.2.v.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17174 - 0.791847i) q^{2} +(0.546697 + 1.64351i) q^{3} +(0.745957 + 1.85568i) q^{4} +(-2.52711 - 3.01169i) q^{5} +(0.660820 - 2.35867i) q^{6} +(-1.60040 - 0.923992i) q^{7} +(0.595347 - 2.76506i) q^{8} +(-2.40224 + 1.79700i) q^{9} +O(q^{10})$	\(q+(-1.17174 - 0.791847i) q^{2} +(0.546697 + 1.64351i) q^{3} +(0.745957 + 1.85568i) q^{4} +(-2.52711 - 3.01169i) q^{5} +(0.660820 - 2.35867i) q^{6} +(-1.60040 - 0.923992i) q^{7} +(0.595347 - 2.76506i) q^{8} +(-2.40224 + 1.79700i) q^{9} +(0.576319 + 5.53000i) q^{10} +(-0.408467 - 0.707485i) q^{11} +(-2.64201 + 2.24048i) q^{12} +(0.986301 - 5.59359i) q^{13} +(1.14360 + 2.34995i) q^{14} +(3.56817 - 5.79980i) q^{15} +(-2.88710 + 2.76851i) q^{16} +(0.175324 - 0.481699i) q^{17} +(4.23776 - 0.203414i) q^{18} +(0.444555 - 4.33617i) q^{19} +(3.70362 - 6.93609i) q^{20} +(0.643655 - 3.13542i) q^{21} +(-0.0816026 + 1.15243i) q^{22} +(-1.99250 - 1.67190i) q^{23} +(4.86988 - 0.533193i) q^{24} +(-1.81576 + 10.2977i) q^{25} +(-5.58496 + 5.77325i) q^{26} +(-4.26669 - 2.96569i) q^{27} +(0.520804 - 3.65909i) q^{28} +(2.32390 + 6.38485i) q^{29} +(-8.77353 + 3.97042i) q^{30} +(-6.46502 - 3.73258i) q^{31} +(5.57517 - 0.957842i) q^{32} +(0.939451 - 1.05810i) q^{33} +(-0.586866 + 0.425596i) q^{34} +(1.26161 + 7.15494i) q^{35} +(-5.12663 - 3.11731i) q^{36} -3.47952 q^{37} +(-3.95449 + 4.72885i) q^{38} +(9.73233 - 1.43701i) q^{39} +(-9.83200 + 5.19460i) q^{40} +(-4.77942 + 0.842740i) q^{41} +(-3.23697 + 3.16422i) q^{42} +(4.25838 + 5.07495i) q^{43} +(1.00817 - 1.28574i) q^{44} +(11.4827 + 2.69359i) q^{45} +(1.01080 + 3.53679i) q^{46} +(4.34889 - 1.58287i) q^{47} +(-6.12845 - 3.23143i) q^{48} +(-1.79248 - 3.10466i) q^{49} +(10.2818 - 10.6284i) q^{50} +(0.887525 + 0.0248033i) q^{51} +(11.1157 - 2.34232i) q^{52} +(4.78294 - 5.70009i) q^{53} +(2.65108 + 6.85359i) q^{54} +(-1.09849 + 3.01806i) q^{55} +(-3.50769 + 3.87511i) q^{56} +(7.36957 - 1.63994i) q^{57} +(2.33282 - 9.32157i) q^{58} +(3.44431 + 1.25363i) q^{59} +(13.4243 + 2.29499i) q^{60} +(5.68183 + 4.76762i) q^{61} +(4.61970 + 9.49293i) q^{62} +(5.50497 - 0.656272i) q^{63} +(-7.29112 - 3.29234i) q^{64} +(-19.3386 + 11.1652i) q^{65} +(-1.93865 + 0.495917i) q^{66} +(2.82204 + 7.75348i) q^{67} +(1.02466 - 0.0339810i) q^{68} +(1.65850 - 4.18871i) q^{69} +(4.18734 - 9.38274i) q^{70} +(-3.25296 + 2.72956i) q^{71} +(3.53866 + 7.71219i) q^{72} +(-0.252680 - 1.43302i) q^{73} +(4.07710 + 2.75525i) q^{74} +(-17.9170 + 2.64549i) q^{75} +(8.37816 - 2.40964i) q^{76} +1.50968i q^{77} +(-12.5417 - 6.02272i) q^{78} +(1.10397 - 0.194660i) q^{79} +(15.6339 + 1.69871i) q^{80} +(2.54156 - 8.63368i) q^{81} +(6.26756 + 2.79709i) q^{82} +(5.35043 - 9.26722i) q^{83} +(6.29847 - 1.14447i) q^{84} +(-1.89379 + 0.689282i) q^{85} +(-0.971146 - 9.31851i) q^{86} +(-9.22310 + 7.30993i) q^{87} +(-2.19942 + 0.708237i) q^{88} +(-8.32500 - 1.46792i) q^{89} +(-11.3219 - 12.2488i) q^{90} +(-6.74692 + 8.04066i) q^{91} +(1.61620 - 4.94461i) q^{92} +(2.60012 - 12.6659i) q^{93} +(-6.34916 - 1.58895i) q^{94} +(-14.1826 + 9.61910i) q^{95} +(4.62215 + 8.63920i) q^{96} +(4.79715 + 1.74602i) q^{97} +(-0.358097 + 5.05723i) q^{98} +(2.25259 + 0.965536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.17174	−	0.791847i	−0.828546	−	0.559920i
$2$	−1.17174	−	0.791847i	−0.828546	−	0.559920i
$3$	0.546697	+	1.64351i	0.315636	+	0.948880i
$3$	0.546697	+	1.64351i	0.315636	+	0.948880i
$4$	0.745957	+	1.85568i	0.372978	+	0.927840i
$5$	−2.52711	−	3.01169i	−1.13016	−	1.34687i	−0.930196	−	0.367063i	$-0.880363\pi$
$5$	−2.52711	−	3.01169i	−1.13016	−	1.34687i	−0.199960	−	0.979804i	$-0.564081\pi$
$6$	0.660820	−	2.35867i	0.269779	−	0.962922i
$7$	−1.60040	−	0.923992i	−0.604895	−	0.349236i	0.166070	−	0.986114i	$-0.446892\pi$
$7$	−1.60040	−	0.923992i	−0.604895	−	0.349236i	−0.770965	+	0.636878i	$0.780226\pi$
$8$	0.595347	−	2.76506i	0.210487	−	0.977597i
$9$	−2.40224	+	1.79700i	−0.800748	+	0.599001i
$10$	0.576319	+	5.53000i	0.182248	+	1.74874i
$11$	−0.408467	−	0.707485i	−0.123157	−	0.213315i	0.797854	−	0.602851i	$-0.205969\pi$
$11$	−0.408467	−	0.707485i	−0.123157	−	0.213315i	−0.921011	+	0.389536i	$0.872635\pi$
$12$	−2.64201	+	2.24048i	−0.762684	+	0.646771i
$13$	0.986301	−	5.59359i	0.273551	−	1.55138i	−0.469977	−	0.882679i	$-0.655738\pi$
$13$	0.986301	−	5.59359i	0.273551	−	1.55138i	0.743528	−	0.668705i	$-0.233151\pi$
$14$	1.14360	+	2.34995i	0.305639	+	0.628052i
$15$	3.56817	−	5.79980i	0.921298	−	1.49750i
$16$	−2.88710	+	2.76851i	−0.721774	+	0.692128i
$17$	0.175324	−	0.481699i	0.0425223	−	0.116829i	−0.916614	−	0.399773i	$-0.869089\pi$
$17$	0.175324	−	0.481699i	0.0425223	−	0.116829i	0.959136	+	0.282944i	$0.0913111\pi$
$18$	4.23776	−	0.203414i	0.998850	−	0.0479450i
$19$	0.444555	−	4.33617i	0.101988	−	0.994786i
$19$	0.444555	−	4.33617i	0.101988	−	0.994786i
$20$	3.70362	−	6.93609i	0.828154	−	1.55096i
$21$	0.643655	−	3.13542i	0.140457	−	0.684204i
$22$	−0.0816026	+	1.15243i	−0.0173977	+	0.245700i
$23$	−1.99250	−	1.67190i	−0.415464	−	0.348616i	0.410970	−	0.911649i	$-0.365190\pi$
$23$	−1.99250	−	1.67190i	−0.415464	−	0.348616i	−0.826435	+	0.563033i	$0.809634\pi$
$24$	4.86988	−	0.533193i	0.994060	−	0.108838i
$25$	−1.81576	+	10.2977i	−0.363151	+	2.05953i
$26$	−5.58496	+	5.77325i	−1.09530	+	1.13223i
$27$	−4.26669	−	2.96569i	−0.821125	−	0.570748i
$28$	0.520804	−	3.65909i	0.0984227	−	0.691503i
$29$	2.32390	+	6.38485i	0.431537	+	1.18564i	0.944869	+	0.327448i	$0.106189\pi$
$29$	2.32390	+	6.38485i	0.431537	+	1.18564i	−0.513332	+	0.858190i	$0.671589\pi$
$30$	−8.77353	+	3.97042i	−1.60182	+	0.724896i
$31$	−6.46502	−	3.73258i	−1.16115	−	0.670392i	−0.209572	−	0.977793i	$-0.567207\pi$
$31$	−6.46502	−	3.73258i	−1.16115	−	0.670392i	−0.951580	+	0.307402i	$0.900541\pi$
$32$	5.57517	−	0.957842i	0.985560	−	0.169324i
$33$	0.939451	−	1.05810i	0.163537	−	0.184191i
$34$	−0.586866	+	0.425596i	−0.100647	+	0.0729892i
$35$	1.26161	+	7.15494i	0.213251	+	1.20940i
$36$	−5.12663	−	3.11731i	−0.854439	−	0.519552i
$37$	−3.47952			−0.572030			−0.286015	−	0.958225i	$-0.592331\pi$
$37$	−3.47952			−0.572030			−0.286015	+	0.958225i	$0.592331\pi$
$38$	−3.95449	+	4.72885i	−0.641502	+	0.767121i
$39$	9.73233	−	1.43701i	1.55842	−	0.230105i
$40$	−9.83200	+	5.19460i	−1.55458	+	0.821339i
$41$	−4.77942	+	0.842740i	−0.746419	+	0.131614i	−0.533905	−	0.845544i	$-0.679276\pi$
$41$	−4.77942	+	0.842740i	−0.746419	+	0.131614i	−0.212514	+	0.977158i	$0.568165\pi$
$42$	−3.23697	+	3.16422i	−0.499475	+	0.488250i
$43$	4.25838	+	5.07495i	0.649398	+	0.773922i	0.985823	−	0.167788i	$-0.0536625\pi$
$43$	4.25838	+	5.07495i	0.649398	+	0.773922i	−0.336426	+	0.941710i	$0.609218\pi$
$44$	1.00817	−	1.28574i	0.151987	−	0.193832i
$45$	11.4827	+	2.69359i	1.71175	+	0.401537i
$46$	1.01080	+	3.53679i	0.149034	+	0.521472i
$47$	4.34889	−	1.58287i	0.634351	−	0.230885i	−0.00477306	−	0.999989i	$-0.501519\pi$
$47$	4.34889	−	1.58287i	0.634351	−	0.230885i	0.639124	+	0.769104i	$0.279297\pi$
$48$	−6.12845	−	3.23143i	−0.884565	−	0.466417i
$49$	−1.79248	−	3.10466i	−0.256068	−	0.443523i
$50$	10.2818	−	10.6284i	1.45406	−	1.50308i
$51$	0.887525	+	0.0248033i	0.124278	+	0.00347315i
$52$	11.1157	−	2.34232i	1.54146	−	0.324821i
$53$	4.78294	−	5.70009i	0.656987	−	0.782967i	−0.329963	−	0.943994i	$-0.607036\pi$
$53$	4.78294	−	5.70009i	0.656987	−	0.782967i	0.986950	+	0.161027i	$0.0514806\pi$
$54$	2.65108	+	6.85359i	0.360767	+	0.932656i
$55$	−1.09849	+	3.01806i	−0.148120	+	0.406956i
$56$	−3.50769	+	3.87511i	−0.468735	+	0.517834i
$57$	7.36957	−	1.63994i	0.976124	−	0.217216i
$58$	2.33282	−	9.32157i	0.306314	−	1.22398i
$59$	3.44431	+	1.25363i	0.448411	+	0.163208i	0.556348	−	0.830950i	$-0.312202\pi$
$59$	3.44431	+	1.25363i	0.448411	+	0.163208i	−0.107937	+	0.994158i	$0.534424\pi$
$60$	13.4243	+	2.29499i	1.73307	+	0.296282i
$61$	5.68183	+	4.76762i	0.727484	+	0.610431i	0.929444	−	0.368962i	$-0.120287\pi$
$61$	5.68183	+	4.76762i	0.727484	+	0.610431i	−0.201961	+	0.979394i	$0.564731\pi$
$62$	4.61970	+	9.49293i	0.586703	+	1.20560i
$63$	5.50497	−	0.656272i	0.693561	−	0.0826825i
$64$	−7.29112	−	3.29234i	−0.911391	−	0.411542i
$65$	−19.3386	+	11.1652i	−2.39866	+	1.38487i
$66$	−1.93865	+	0.495917i	−0.238631	+	0.0610432i
$67$	2.82204	+	7.75348i	0.344767	+	0.947238i	0.983991	+	0.178218i	$0.0570332\pi$
$67$	2.82204	+	7.75348i	0.344767	+	0.947238i	−0.639225	+	0.769020i	$0.720745\pi$
$68$	1.02466	−	0.0339810i	0.124259	−	0.00412080i
$69$	1.65850	−	4.18871i	0.199660	−	0.504262i
$70$	4.18734	−	9.38274i	0.500482	−	1.12145i
$71$	−3.25296	+	2.72956i	−0.386055	+	0.323939i	−0.815074	−	0.579357i	$-0.803304\pi$
$71$	−3.25296	+	2.72956i	−0.386055	+	0.323939i	0.429019	+	0.903296i	$0.358859\pi$
$72$	3.53866	+	7.71219i	0.417035	+	0.908891i
$73$	−0.252680	−	1.43302i	−0.0295739	−	0.167722i	0.966444	−	0.256878i	$-0.0826940\pi$
$73$	−0.252680	−	1.43302i	−0.0295739	−	0.167722i	−0.996018	+	0.0891565i	$0.971583\pi$
$74$	4.07710	+	2.75525i	0.473954	+	0.320291i
$75$	−17.9170	+	2.64549i	−2.06887	+	0.305475i
$76$	8.37816	−	2.40964i	0.961041	−	0.276405i
$77$			1.50968i			0.172044i
$78$	−12.5417	−	6.02272i	−1.42006	−	0.681938i
$79$	1.10397	−	0.194660i	0.124207	−	0.0219010i	−0.111199	−	0.993798i	$-0.535469\pi$
$79$	1.10397	−	0.194660i	0.124207	−	0.0219010i	0.235406	+	0.971897i	$0.424358\pi$
$80$	15.6339	+	1.69871i	1.74792	+	0.189922i
$81$	2.54156	−	8.63368i	0.282395	−	0.959298i
$82$	6.26756	+	2.79709i	0.692136	+	0.308887i
$83$	5.35043	−	9.26722i	0.587286	−	1.01721i	−0.407300	−	0.913295i	$-0.633530\pi$
$83$	5.35043	−	9.26722i	0.587286	−	1.01721i	0.994586	−	0.103915i	$-0.0331371\pi$
$84$	6.29847	−	1.14447i	0.687220	−	0.124872i
$85$	−1.89379	+	0.689282i	−0.205410	+	0.0747632i
$86$	−0.971146	−	9.31851i	−0.104721	−	1.00484i
$87$	−9.22310	+	7.30993i	−0.988820	+	0.783707i
$88$	−2.19942	+	0.708237i	−0.234459	+	0.0754983i
$89$	−8.32500	−	1.46792i	−0.882449	−	0.155600i	−0.285980	−	0.958236i	$-0.592319\pi$
$89$	−8.32500	−	1.46792i	−0.882449	−	0.155600i	−0.596469	+	0.802636i	$0.703430\pi$
$90$	−11.3219	−	12.2488i	−1.19343	−	1.29113i
$91$	−6.74692	+	8.04066i	−0.707269	+	0.842890i
$92$	1.61620	−	4.94461i	0.168501	−	0.515511i
$93$	2.60012	−	12.6659i	0.269620	−	1.31339i
$94$	−6.34916	−	1.58895i	−0.654866	−	0.163887i
$95$	−14.1826	+	9.61910i	−1.45511	+	0.986899i
$96$	4.62215	+	8.63920i	0.471747	+	0.881734i
$97$	4.79715	+	1.74602i	0.487076	+	0.177281i	0.573872	−	0.818945i	$-0.305441\pi$
$97$	4.79715	+	1.74602i	0.487076	+	0.177281i	−0.0867959	+	0.996226i	$0.527663\pi$
$98$	−0.358097	+	5.05723i	−0.0361733	+	0.510857i
$99$	2.25259	+	0.965536i	0.226394	+	0.0970401i
$100$	−20.4636	+	4.31215i	−2.04636	+	0.431215i
$101$	−6.89433	−	1.21566i	−0.686011	−	0.120962i	−0.180231	−	0.983624i	$-0.557684\pi$
$101$	−6.89433	−	1.21566i	−0.686011	−	0.120962i	−0.505781	+	0.862662i	$0.668795\pi$
$102$	−1.02031	−	0.731847i	−0.101026	−	0.0724637i
$103$	12.2928	−	7.09723i	1.21124	−	0.699311i	0.248212	−	0.968706i	$-0.420157\pi$
$103$	12.2928	−	7.09723i	1.21124	−	0.699311i	0.963030	+	0.269395i	$0.0868236\pi$
$104$	−14.8794	−	6.05731i	−1.45905	−	0.593968i
$105$	−11.0695	+	5.98505i	−1.08027	+	0.584081i
$106$	−10.1180	+	2.89167i	−0.982744	+	0.280864i
$107$	3.69987	−	6.40836i	0.357680	−	0.619520i	−0.629893	−	0.776682i	$-0.716901\pi$
$107$	3.69987	−	6.40836i	0.357680	−	0.619520i	0.987573	+	0.157162i	$0.0502346\pi$
$108$	2.32061	−	10.1299i	0.223301	−	0.974750i
$109$	−2.64734	+	2.22138i	−0.253569	+	0.212769i	−0.760707	−	0.649095i	$-0.775148\pi$
$109$	−2.64734	+	2.22138i	−0.253569	+	0.212769i	0.507139	+	0.861865i	$0.330703\pi$
$110$	3.67699	−	2.66656i	0.350587	−	0.254246i
$111$	−1.90225	−	5.71863i	−0.180553	−	0.542788i
$112$	7.17860	−	1.76308i	0.678314	−	0.166595i
$113$		−	2.18899i		−	0.205923i	−0.994685	−	0.102961i	$-0.967168\pi$
$113$		−	2.18899i		−	0.205923i	0.994685	−	0.102961i	$-0.0328318\pi$
$114$	−9.93382	−	3.91398i	−0.930387	−	0.366578i
$115$			10.2259i			0.953566i
$116$	−10.1147	+	9.07523i	−0.939128	+	0.842614i
$117$	7.68237	+	15.2096i	0.710235	+	1.40612i
$118$	−3.04316	−	4.19629i	−0.280146	−	0.386300i
$119$	−0.725674	+	0.608913i	−0.0665225	+	0.0558190i
$120$	−13.9125	−	13.3191i	−1.27003	−	1.21586i
$121$	5.16631	−	8.94831i	0.469665	−	0.813483i
$122$	−2.88241	−	10.0856i	−0.260961	−	0.913104i
$123$	−3.99794	−	7.39429i	−0.360482	−	0.666721i
$124$	2.10385	−	14.7814i	0.188932	−	1.32741i
$125$	18.5781	−	10.7261i	1.66168	−	0.959371i
$126$	−6.97007	−	3.59012i	−0.620943	−	0.319833i
$127$	−13.6507	−	2.40698i	−1.21130	−	0.213585i	−0.468723	−	0.883345i	$-0.655286\pi$
$127$	−13.6507	−	2.40698i	−1.21130	−	0.213585i	−0.742577	+	0.669760i	$0.766397\pi$
$128$	5.93628	+	9.63123i	0.524698	+	0.851288i
$129$	−6.01267	+	9.77315i	−0.529386	+	0.860478i
$130$	31.5010	+	2.23055i	2.76282	+	0.195632i
$131$	6.47249	+	2.35579i	0.565504	+	0.205826i	0.608921	−	0.793231i	$-0.291602\pi$
$131$	6.47249	+	2.35579i	0.565504	+	0.205826i	−0.0434178	+	0.999057i	$0.513825\pi$
$132$	2.66428	+	0.954024i	0.231896	+	0.0830372i
$133$	−4.71805	+	6.52885i	−0.409107	+	0.566123i
$134$	2.83287	−	11.3197i	0.244723	−	0.977873i
$135$	1.85064	+	20.3446i	0.159278	+	1.75098i
$136$	−1.22755	−	0.771559i	−0.105261	−	0.0661606i
$137$	3.41574	−	4.07072i	0.291826	−	0.347785i	−0.600134	−	0.799900i	$-0.704886\pi$
$137$	3.41574	−	4.07072i	0.291826	−	0.347785i	0.891960	+	0.452115i	$0.149330\pi$
$138$	−5.26015	+	3.59481i	−0.447774	+	0.306011i
$139$	5.51638	+	0.972686i	0.467893	+	0.0825022i	0.402624	−	0.915366i	$-0.368098\pi$
$139$	5.51638	+	0.972686i	0.467893	+	0.0825022i	0.0652692	+	0.997868i	$0.479209\pi$
$140$	−12.3362	+	7.67841i	−1.04260	+	0.648944i
$141$	4.97898	+	6.28209i	0.419306	+	0.529048i
$142$	5.97302	−	0.622489i	0.501245	−	0.0522381i
$143$	−4.36026	+	1.58700i	−0.364623	+	0.132712i
$144$	1.96049	−	11.8388i	0.163374	−	0.986564i
$145$	13.3565	−	23.1341i	1.10919	−	1.92118i
$146$	−0.838655	+	1.87921i	−0.0694076	+	0.155524i
$147$	4.12260	−	4.64326i	0.340026	−	0.382970i
$148$	−2.59557	−	6.45688i	−0.213355	−	0.530753i
$149$	2.84582	−	0.501794i	0.233138	−	0.0411086i	−0.0558582	−	0.998439i	$-0.517789\pi$
$149$	2.84582	−	0.501794i	0.233138	−	0.0411086i	0.288997	+	0.957330i	$0.406678\pi$
$150$	23.0889	+	11.0877i	1.88520	+	0.905304i
$151$		−	3.31156i		−	0.269491i	−0.990880	−	0.134746i	$-0.956978\pi$
$151$		−	3.31156i		−	0.269491i	0.990880	−	0.134746i	$-0.0430217\pi$
$152$	−11.7251	−	3.81074i	−0.951032	−	0.309092i
$153$	0.444443	+	1.47222i	0.0359311	+	0.119022i
$154$	1.19544	−	1.76896i	0.0963310	−	0.142547i
$155$	5.09642	+	28.9033i	0.409355	+	2.32156i
$156$	9.92652	+	16.9881i	0.794758	+	1.36014i
$157$	8.21209	−	6.89076i	0.655396	−	0.549942i	−0.253307	−	0.967386i	$-0.581518\pi$
$157$	8.21209	−	6.89076i	0.655396	−	0.549942i	0.908703	+	0.417444i	$0.137074\pi$
$158$	−1.44771	−	0.646085i	−0.115174	−	0.0513998i
$159$	11.9830	+	4.74458i	0.950311	+	0.376270i
$160$	−16.9738	−	14.3701i	−1.34189	−	1.13606i
$161$	1.64397	+	4.51677i	0.129563	+	0.355971i
$162$	−9.81460	+	8.10392i	−0.771108	+	0.636704i
$163$	9.60165	−	5.54352i	0.752059	−	0.434202i	−0.0743781	−	0.997230i	$-0.523697\pi$
$163$	9.60165	−	5.54352i	0.752059	−	0.434202i	0.826438	+	0.563028i	$0.190364\pi$
$164$	−5.12909	−	8.24042i	−0.400515	−	0.643469i
$165$	−5.56076	−	0.155404i	−0.432904	−	0.0120982i
$166$	−13.6075	+	6.62207i	−1.05615	+	0.513972i
$167$	−15.7324	−	13.2011i	−1.21741	−	1.02153i	−0.998956	−	0.0456823i	$-0.985454\pi$
$167$	−15.7324	−	13.2011i	−1.21741	−	1.02153i	−0.218455	−	0.975847i	$-0.570102\pi$
$168$	−8.28643	−	3.64641i	−0.639312	−	0.281326i
$169$	−18.0995	−	6.58768i	−1.39227	−	0.506744i
$170$	2.76484	+	0.691929i	0.212053	+	0.0530686i
$171$	6.72418	+	11.2154i	0.514211	+	0.857664i
$172$	−6.24091	+	11.6879i	−0.475865	+	0.891193i
$173$	1.92424	−	5.28679i	0.146297	−	0.401948i	−0.844801	−	0.535080i	$-0.820281\pi$
$173$	1.92424	−	5.28679i	0.146297	−	0.401948i	0.991098	+	0.133133i	$0.0425036\pi$
$174$	16.5954	−	1.26206i	1.25810	−	0.0956767i
$175$	12.4209	−	14.8027i	0.938932	−	1.11898i
$176$	3.13797	+	0.911733i	0.236533	+	0.0687245i
$177$	−0.177352	+	6.34611i	−0.0133306	+	0.477003i
$178$	8.59238	+	8.31216i	0.644026	+	0.623022i
$179$	−11.4019	−	19.7487i	−0.852219	−	1.47609i	−0.879202	−	0.476450i	$-0.841923\pi$
$179$	−11.4019	−	19.7487i	−0.852219	−	1.47609i	0.0269830	−	0.999636i	$-0.491410\pi$
$180$	3.56718	+	23.3176i	0.265882	+	1.73799i
$181$	−16.4902	+	6.00196i	−1.22571	+	0.446122i	−0.872126	−	0.489281i	$-0.837259\pi$
$181$	−16.4902	+	6.00196i	−1.22571	+	0.446122i	−0.353584	+	0.935403i	$0.615037\pi$
$182$	14.2726	−	4.07905i	1.05796	−	0.302359i
$183$	−4.72939	+	11.9446i	−0.349606	+	0.882969i
$184$	−5.80914	+	4.51402i	−0.428256	+	0.332778i
$185$	8.79313	+	10.4792i	0.646483	+	0.770449i
$186$	−13.0761	+	12.7823i	−0.958789	+	0.937242i
$187$	−0.412409	+	0.0727188i	−0.0301583	+	0.00531772i
$188$	6.18138	+	6.88940i	0.450823	+	0.502461i
$189$	4.08814	+	8.68869i	0.297369	+	0.632009i
$190$	24.2352	−	0.0406309i	1.75821	−	0.00294767i
$191$	14.7243			1.06541			0.532707	−	0.846300i	$-0.321175\pi$
$191$	14.7243			1.06541			0.532707	+	0.846300i	$0.321175\pi$
$192$	1.42495	−	13.7829i	0.102837	−	0.994698i
$193$	−0.731757	−	4.15000i	−0.0526730	−	0.298724i	0.947079	−	0.321001i	$-0.104019\pi$
$193$	−0.731757	−	4.15000i	−0.0526730	−	0.298724i	−0.999752	+	0.0222775i	$0.992908\pi$
$194$	−4.23844	−	5.84449i	−0.304302	−	0.419610i
$195$	−28.9224	−	25.6793i	−2.07118	−	1.83893i
$196$	4.42415	−	5.64220i	0.316010	−	0.403015i
$197$	−3.50625	−	2.02433i	−0.249810	−	0.144228i	0.369867	−	0.929085i	$-0.379403\pi$
$197$	−3.50625	−	2.02433i	−0.249810	−	0.144228i	−0.619677	+	0.784857i	$0.712736\pi$
$198$	−1.87490	−	2.91507i	−0.133243	−	0.207165i
$199$	5.28054	+	14.5082i	0.374328	+	1.02846i	0.973670	+	0.227964i	$0.0732068\pi$
$199$	5.28054	+	14.5082i	0.374328	+	1.02846i	−0.599342	+	0.800493i	$0.704571\pi$
$200$	27.3927	+	11.1514i	1.93695	+	0.788520i
$201$	−11.2001	+	8.87685i	−0.789995	+	0.626124i
$202$	7.11576	+	6.88369i	0.500663	+	0.484335i
$203$	2.18039	−	12.3656i	0.153033	−	0.867895i
$204$	0.616028	+	1.66546i	0.0431306	+	0.116606i
$205$	14.6162	+	12.2644i	1.02084	+	0.856584i
$206$	−20.0239	−	1.41787i	−1.39513	−	0.0987876i
$207$	7.79088	+	0.435797i	0.541504	+	0.0302900i
$208$	12.6384	+	18.8798i	0.876315	+	1.30908i
$209$	−3.24936	+	1.45667i	−0.224763	+	0.100760i
$210$	17.7098	+	1.75241i	1.22209	+	0.120928i
$211$	8.50175	−	23.3584i	0.585285	−	1.60806i	−0.193733	−	0.981054i	$-0.562060\pi$
$211$	8.50175	−	23.3584i	0.585285	−	1.60806i	0.779018	−	0.627002i	$-0.215718\pi$
$212$	14.1454	+	4.62359i	0.971510	+	0.317549i
$213$	−6.26444	−	3.85403i	−0.429232	−	0.264074i
$214$	−9.40973	+	4.57921i	−0.643236	+	0.313028i
$215$	4.52276	−	25.6498i	0.308450	−	1.74930i
$216$	−10.7405	+	10.0320i	−0.730797	+	0.682594i
$217$	6.89775	+	11.9473i	0.468250	+	0.811033i
$218$	4.86098	−	0.506596i	0.329227	−	0.0343110i
$219$	2.21704	−	1.19871i	0.149813	−	0.0810011i
$220$	−6.41998	+	0.212907i	−0.432835	+	0.0143542i
$221$	−2.52150	−	1.45579i	−0.169615	−	0.0979271i
$222$	−2.29934	+	8.20704i	−0.154322	+	0.550821i
$223$	−5.63487	−	6.71538i	−0.377339	−	0.449695i	0.543634	−	0.839323i	$-0.317048\pi$
$223$	−5.63487	−	6.71538i	−0.377339	−	0.449695i	−0.920972	+	0.389628i	$0.872604\pi$
$224$	−9.80755	−	3.61848i	−0.655295	−	0.241770i
$225$	−14.1430	−	28.0004i	−0.942870	−	1.86669i
$226$	−1.73334	+	2.56493i	−0.115300	+	0.170617i
$227$	−10.4925			−0.696415			−0.348207	−	0.937418i	$-0.613209\pi$
$227$	−10.4925			−0.696415			−0.348207	+	0.937418i	$0.613209\pi$
$228$	8.54059	+	12.4522i	0.565614	+	0.824670i
$229$	−11.3656			−0.751060			−0.375530	−	0.926810i	$-0.622539\pi$
$229$	−11.3656			−0.751060			−0.375530	+	0.926810i	$0.622539\pi$
$230$	8.09732	−	11.9821i	0.533921	−	0.790074i
$231$	−2.48117	+	0.825338i	−0.163249	+	0.0543033i
$232$	19.0380	−	2.62452i	1.24991	−	0.172308i
$233$	11.5311	+	13.7422i	0.755428	+	0.900284i	0.997550	−	0.0699619i	$-0.0222878\pi$
$233$	11.5311	+	13.7422i	0.755428	+	0.900284i	−0.242122	+	0.970246i	$0.577843\pi$
$234$	3.04190	−	23.9049i	0.198855	−	1.56271i
$235$	−15.7572	−	9.09743i	−1.02789	−	0.593451i
$236$	0.242976	+	7.32669i	0.0158164	+	0.476927i
$237$	0.923464	+	1.70797i	0.0599854	+	0.110944i
$238$	1.33247	−	0.138866i	0.0863711	−	0.00900133i
$239$	12.1523	+	21.0485i	0.786070	+	1.36151i	0.928358	+	0.371688i	$0.121221\pi$
$239$	12.1523	+	21.0485i	0.786070	+	1.36151i	−0.142288	+	0.989825i	$0.545446\pi$
$240$	5.75516	+	26.6231i	0.371494	+	1.71852i
$241$	−2.79534	+	15.8532i	−0.180064	+	1.02119i	0.752071	+	0.659082i	$0.229055\pi$
$241$	−2.79534	+	15.8532i	−0.180064	+	1.02119i	−0.932135	+	0.362111i	$0.882056\pi$
$242$	−13.1393	+	6.39418i	−0.844624	+	0.411033i
$243$	15.5790	−	0.542939i	0.999393	−	0.0348295i
$244$	−4.60878	+	14.1001i	−0.295047	+	0.902666i
$245$	−4.82049	+	13.2442i	−0.307970	+	0.846140i
$246$	−1.17059	+	11.8300i	−0.0746341	+	0.754250i
$247$	−23.8163	−	6.76343i	−1.51540	−	0.430347i
$248$	−14.1697	+	15.6540i	−0.899780	+	0.994030i
$249$	18.1558	+	3.72712i	1.15058	+	0.236197i
$250$	−30.2622	−	2.14284i	−1.91395	−	0.135525i
$251$	7.18164	+	6.02611i	0.453301	+	0.380365i	0.840659	−	0.541565i	$-0.182168\pi$
$251$	7.18164	+	6.02611i	0.453301	+	0.380365i	−0.387358	+	0.921929i	$0.626612\pi$
$252$	5.32430	+	9.72592i	0.335399	+	0.612675i
$253$	−0.368978	+	2.09258i	−0.0231975	+	0.131559i
$254$	14.0891	+	13.6296i	0.884028	+	0.855197i
$255$	−2.16817	−	2.73563i	−0.135776	−	0.171312i
$256$	0.670667	−	15.9859i	0.0419167	−	0.999121i
$257$	−5.52550	−	15.1812i	−0.344671	−	0.946976i	−0.984020	−	0.178059i	$-0.943018\pi$
$257$	−5.52550	−	15.1812i	−0.344671	−	0.946976i	0.639349	−	0.768917i	$-0.279204\pi$
$258$	14.7841	−	6.69049i	0.920420	−	0.416532i
$259$	5.56864	+	3.21505i	0.346018	+	0.199774i
$260$	−35.1448	−	27.5576i	−2.17959	−	1.70905i
$261$	−17.0562	−	11.1619i	−1.05575	−	0.690906i
$262$	−5.71865	−	7.88560i	−0.353300	−	0.487174i
$263$	1.95883	+	11.1091i	0.120787	+	0.685016i	0.983721	+	0.179700i	$0.0575128\pi$
$263$	1.95883	+	11.1091i	0.120787	+	0.685016i	−0.862935	+	0.505316i	$0.831376\pi$
$264$	−2.36641	−	3.22757i	−0.145642	−	0.198644i
$265$	−29.2539			−1.79705
$266$	10.6982	−	3.91415i	0.655948	−	0.239992i
$267$	−2.13871	−	14.4847i	−0.130887	−	0.886451i
$268$	−12.2829	+	11.0206i	−0.750295	+	0.673187i
$269$	31.6617	−	5.58281i	1.93045	−	0.340390i	0.930765	−	0.365617i	$-0.119142\pi$
$269$	31.6617	−	5.58281i	1.93045	−	0.340390i	0.999682	+	0.0252273i	$0.00803095\pi$
$270$	13.9413	−	25.3040i	0.848441	−	1.53995i
$271$	11.1445	+	13.2815i	0.676978	+	0.806791i	0.989716	−	0.143049i	$-0.0456905\pi$
$271$	11.1445	+	13.2815i	0.676978	+	0.806791i	−0.312738	+	0.949840i	$0.601246\pi$
$272$	0.827412	+	1.87610i	0.0501692	+	0.113755i
$273$	−16.9034	−	6.69281i	−1.02304	−	0.405067i
$274$	−7.22575	+	2.06509i	−0.436523	+	0.124756i
$275$	8.02712	−	2.92163i	0.484054	−	0.176181i
$276$	9.01008	−	0.0469584i	0.542343	−	0.00282656i
$277$	−7.66188	−	13.2708i	−0.460358	−	0.797363i	0.538621	−	0.842548i	$-0.318946\pi$
$277$	−7.66188	−	13.2708i	−0.460358	−	0.797363i	−0.998979	+	0.0451851i	$0.985612\pi$
$278$	−5.69355	−	5.50786i	−0.341476	−	0.330340i
$279$	22.2380	−	2.65109i	1.33136	−	0.158717i
$280$	20.5349	+	0.771243i	1.22720	+	0.0460906i
$281$	−8.39113	+	10.0002i	−0.500573	+	0.596560i	−0.955874	−	0.293778i	$-0.905087\pi$
$281$	−8.39113	+	10.0002i	−0.500573	+	0.596560i	0.455301	+	0.890338i	$0.349532\pi$
$282$	−0.859624	−	11.3036i	−0.0511898	−	0.673118i
$283$	−2.99418	+	8.22644i	−0.177986	+	0.489011i	−0.996318	−	0.0857338i	$-0.972677\pi$
$283$	−2.99418	+	8.22644i	−0.177986	+	0.489011i	0.818333	+	0.574745i	$0.194899\pi$
$284$	−7.49175	−	4.00032i	−0.444554	−	0.237375i
$285$	−23.5627	−	18.0505i	−1.39573	−	1.06922i
$286$	6.36576	+	1.59310i	0.376415	+	0.0942019i
$287$	8.42767	+	3.06742i	0.497470	+	0.181064i
$288$	−11.6717	+	12.3196i	−0.687760	+	0.725938i
$289$	12.8215	+	10.7585i	0.754204	+	0.632852i
$290$	−33.9689	+	16.5309i	−1.99472	+	0.970726i
$291$	−0.247011	+	8.83870i	−0.0144800	+	0.518134i
$292$	2.47073	−	1.53786i	0.144589	−	0.0899965i
$293$	15.5573	−	8.98199i	0.908865	−	0.524733i	0.0287989	−	0.999585i	$-0.490832\pi$
$293$	15.5573	−	8.98199i	0.908865	−	0.524733i	0.880066	+	0.474852i	$0.157498\pi$
$294$	−8.50737	+	2.17624i	−0.496160	+	0.126921i
$295$	−4.92860	−	13.5412i	−0.286954	−	0.788401i
$296$	−2.07152	+	9.62110i	−0.120405	+	0.559215i
$297$	−0.355383	+	4.23001i	−0.0206214	+	0.245450i
$298$	−3.73191	−	1.66548i	−0.216183	−	0.0964786i
$299$	−11.3172	+	9.49622i	−0.654488	+	0.549181i
$300$	−18.2745	−	31.2747i	−1.05508	−	1.80565i
$301$	−2.12592	−	12.0567i	−0.122536	−	0.694935i
$302$	−2.62225	+	3.88030i	−0.150894	+	0.223286i
$303$	−1.77117	−	11.9955i	−0.101751	−	0.689123i
$304$	10.7213	+	13.7497i	0.614907	+	0.788600i
$305$		−	29.1602i		−	1.66971i
$306$	0.644997	−	2.07699i	0.0368720	−	0.118733i
$307$	7.67258	−	1.35288i	0.437897	−	0.0772131i	0.0496465	−	0.998767i	$-0.484191\pi$
$307$	7.67258	−	1.35288i	0.437897	−	0.0772131i	0.388251	+	0.921554i	$0.373079\pi$
$308$	−2.80149	+	1.12616i	−0.159629	+	0.0641687i
$309$	18.3848	+	16.3232i	1.04587	+	0.928596i
$310$	16.9153	−	37.9027i	0.960722	−	2.15273i
$311$	−9.56080	+	16.5598i	−0.542143	+	0.939020i	0.456637	+	0.889653i	$0.349054\pi$
$311$	−9.56080	+	16.5598i	−0.542143	+	0.939020i	−0.998781	+	0.0493669i	$0.984280\pi$
$312$	1.82070	−	27.7660i	0.103077	−	1.57194i
$313$	11.5650	−	4.20932i	0.653694	−	0.237925i	0.00618244	−	0.999981i	$-0.498032\pi$
$313$	11.5650	−	4.20932i	0.653694	−	0.237925i	0.647511	+	0.762056i	$0.275810\pi$
$314$	−15.0789	+	1.57147i	−0.850950	+	0.0886833i
$315$	−15.8881	−	14.9208i	−0.895195	−	0.840691i
$316$	1.18474	+	1.90341i	0.0666469	+	0.107075i
$317$	16.5656	+	2.92096i	0.930417	+	0.164058i	0.618261	−	0.785973i	$-0.287838\pi$
$317$	16.5656	+	2.92096i	0.930417	+	0.164058i	0.312157	+	0.950031i	$0.398949\pi$
$318$	−10.2839	−	15.0481i	−0.576695	−	0.843856i
$319$	3.56796	−	4.25212i	0.199767	−	0.238073i
$320$	8.50995	+	30.2787i	0.475720	+	1.69263i
$321$	12.5549	+	2.57734i	0.700747	+	0.143853i
$322$	1.65028	−	6.59426i	0.0919667	−	0.367484i
$323$	−2.01079	−	0.974376i	−0.111883	−	0.0542157i
$324$	17.9172	−	1.72404i	0.995403	−	0.0957798i
$325$	55.8101	+	20.3132i	3.09579	+	1.12677i
$326$	−15.6403	−	1.10747i	−0.866235	−	0.0613372i
$327$	−5.09815	−	3.13650i	−0.281928	−	0.173449i
$328$	−0.515182	+	13.7171i	−0.0284461	+	0.757400i
$329$	−8.42253	−	1.48512i	−0.464349	−	0.0818773i
$330$	6.39271	+	4.58536i	0.351907	+	0.252416i
$331$	−8.46976	+	4.89002i	−0.465540	+	0.268780i	−0.714371	−	0.699767i	$-0.753287\pi$
$331$	−8.46976	+	4.89002i	−0.465540	+	0.268780i	0.248831	+	0.968547i	$0.419954\pi$
$332$	21.1882	+	3.01575i	1.16285	+	0.165511i
$333$	8.35867	−	6.25272i	0.458052	−	0.342647i
$334$	7.98110	+	27.9259i	0.436707	+	1.52804i
$335$	16.2195	−	28.0929i	0.886164	−	1.53488i
$336$	6.82215	+	10.8342i	0.372179	+	0.591056i
$337$	−20.6586	+	17.3346i	−1.12534	+	0.944275i	−0.998862	−	0.0476940i	$-0.984813\pi$
$337$	−20.6586	+	17.3346i	−1.12534	+	0.944275i	−0.126481	+	0.991969i	$0.540368\pi$
$338$	15.9915	+	22.0511i	0.869823	+	1.19942i
$339$	3.59762	−	1.19671i	0.195396	−	0.0649966i
$340$	−2.69177	−	3.00009i	−0.145982	−	0.162703i
$341$			6.09854i			0.330255i
$342$	1.00188	−	18.4661i	0.0541755	−	0.998531i
$343$			19.5608i			1.05619i
$344$	16.5677	−	8.75334i	0.893273	−	0.471949i
$345$	−16.8063	+	5.59045i	−0.904820	+	0.300980i
$346$	−6.44104	+	4.67106i	−0.346272	+	0.251118i
$347$	6.85601	−	5.75288i	0.368050	−	0.308831i	−0.439940	−	0.898027i	$-0.645000\pi$
$347$	6.85601	−	5.75288i	0.368050	−	0.308831i	0.807990	+	0.589197i	$0.200556\pi$
$348$	−20.4449	−	11.6622i	−1.09596	−	0.625161i
$349$	0.418101	−	0.724172i	0.0223804	−	0.0387640i	−0.854618	−	0.519257i	$-0.826209\pi$
$349$	0.418101	−	0.724172i	0.0223804	−	0.0387640i	0.876999	+	0.480493i	$0.159542\pi$
$350$	−26.2755	+	7.50943i	−1.40449	+	0.401396i
$351$	−20.7971	+	20.9411i	−1.11007	+	1.11775i
$352$	−2.95493	−	3.55311i	−0.157498	−	0.189381i
$353$	−14.9057	+	8.60584i	−0.793353	+	0.458043i	−0.841142	−	0.540815i	$-0.818116\pi$
$353$	−14.9057	+	8.60584i	−0.793353	+	0.458043i	0.0477886	+	0.998857i	$0.484783\pi$
$354$	5.23296	−	7.29556i	0.278129	−	0.387755i
$355$	16.4411	+	2.89902i	0.872606	+	0.153864i
$356$	−3.48610	−	16.5436i	−0.184763	−	0.876806i
$357$	−1.39748	−	0.859762i	−0.0739624	−	0.0455034i
$358$	−2.27785	+	32.1689i	−0.120388	+	1.70018i
$359$	−30.0962	−	10.9541i	−1.58842	−	0.578137i	−0.611405	−	0.791318i	$-0.709395\pi$
$359$	−30.0962	−	10.9541i	−1.58842	−	0.578137i	−0.977013	+	0.213181i	$0.931618\pi$
$360$	14.2842	−	30.1468i	0.752841	−	1.58888i
$361$	−18.6047	−	3.85533i	−0.979197	−	0.202912i
$362$	24.0749	+	6.02501i	1.26535	+	0.316667i
$363$	17.5310	+	3.59886i	0.920141	+	0.188891i
$364$	−19.9538	−	6.52213i	−1.04586	−	0.341853i
$365$	−3.67725	+	4.38238i	−0.192476	+	0.229384i
$366$	14.9999	−	10.2510i	0.784057	−	0.535829i
$367$	−10.9145	−	1.92451i	−0.569730	−	0.100459i	−0.118640	−	0.992937i	$-0.537854\pi$
$367$	−10.9145	−	1.92451i	−0.569730	−	0.100459i	−0.451090	+	0.892479i	$0.648965\pi$
$368$	10.3812	−	0.689306i	0.541159	−	0.0359326i
$369$	9.96692	−	10.6131i	0.518857	−	0.552496i
$370$	−2.00532	−	19.2418i	−0.104251	−	1.00033i
$371$	−12.9215	+	4.70303i	−0.670849	+	0.244169i
$372$	25.4435	−	4.62322i	1.31918	−	0.239703i
$373$	6.01501	−	10.4183i	0.311446	−	0.539440i	−0.667230	−	0.744852i	$-0.732520\pi$
$373$	6.01501	−	10.4183i	0.311446	−	0.539440i	0.978676	+	0.205412i	$0.0658535\pi$
$374$	0.540819	+	0.241357i	0.0279651	+	0.0124803i
$375$	27.7851	+	24.6694i	1.43481	+	1.27392i
$376$	−1.78763	−	12.9673i	−0.0921898	−	0.668738i
$377$	38.0063	−	6.70154i	1.95743	−	0.345147i
$378$	2.08987	−	13.4181i	0.107491	−	0.690152i
$379$			15.2025i			0.780898i	0.920625	+	0.390449i	$0.127680\pi$
$379$			15.2025i			0.780898i	−0.920625	+	0.390449i	$0.872320\pi$
$380$	−28.4296	−	19.1430i	−1.45841	−	0.982014i
$381$	−3.50688	−	23.7509i	−0.179663	−	1.21679i
$382$	−17.2531	−	11.6594i	−0.882745	−	0.596547i
$383$	−3.66018	−	20.7579i	−0.187026	−	1.06068i	−0.923324	−	0.384021i	$-0.874539\pi$
$383$	−3.66018	−	20.7579i	−0.187026	−	1.06068i	0.736298	−	0.676657i	$-0.236572\pi$
$384$	−12.5837	+	15.0217i	−0.642157	+	0.766573i
$385$	4.54669	−	3.81512i	0.231721	−	0.194437i
$386$	−2.42874	+	5.44217i	−0.123619	+	0.276999i
$387$	−19.3494	−	4.53893i	−0.983584	−	0.230727i
$388$	0.338411	+	10.2044i	0.0171802	+	0.518051i
$389$	−7.46086	−	20.4985i	−0.378281	−	1.03932i	−0.972069	−	0.234696i	$-0.924591\pi$
$389$	−7.46086	−	20.4985i	−0.378281	−	1.03932i	0.593788	−	0.804621i	$-0.297632\pi$
$390$	13.5556	+	52.9916i	0.686413	+	2.68333i
$391$	−1.15469	+	0.666658i	−0.0583950	+	0.0337144i
$392$	−9.65172	+	3.10796i	−0.487485	+	0.156976i
$393$	−0.333276	+	11.9255i	−0.0168116	+	0.601562i
$394$	2.50546	+	5.14841i	0.126223	+	0.259373i
$395$	−3.37611	−	2.83289i	−0.169870	−	0.142538i
$396$	−0.111392	+	4.90034i	−0.00559765	+	0.246251i
$397$	−18.4059	−	6.69921i	−0.923767	−	0.336224i	−0.164031	−	0.986455i	$-0.552450\pi$
$397$	−18.4059	−	6.69921i	−0.923767	−	0.336224i	−0.759736	+	0.650231i	$0.774672\pi$
$398$	5.30082	−	21.1812i	0.265706	−	1.06172i
$399$	−13.3096	−	4.18486i	−0.666312	−	0.209505i
$400$	−23.2670	−	34.7573i	−1.16335	−	1.73787i
$401$	−11.0270	+	30.2964i	−0.550661	+	1.51293i	0.282150	+	0.959370i	$0.408952\pi$
$401$	−11.0270	+	30.2964i	−0.550661	+	1.51293i	−0.832811	+	0.553558i	$0.813270\pi$
$402$	20.1527	−	1.53259i	1.00513	−	0.0764387i
$403$	−27.2550	+	32.4813i	−1.35767	+	1.61801i
$404$	−2.88700	−	13.7005i	−0.143634	−	0.681625i
$405$	−32.4247	+	14.1639i	−1.61120	+	0.703808i
$406$	−12.3465	+	12.7627i	−0.612747	+	0.633405i
$407$	1.42127	+	2.46171i	0.0704498	+	0.122023i
$408$	0.596968	−	2.43929i	0.0295543	−	0.120763i
$409$	23.1601	−	8.42959i	1.14519	−	0.416817i	0.301407	−	0.953495i	$-0.402544\pi$
$409$	23.1601	−	8.42959i	1.14519	−	0.416817i	0.843787	+	0.536679i	$0.180321\pi$
$410$	−7.41482	−	25.9445i	−0.366192	−	1.28131i
$411$	8.55764	+	3.38835i	0.422117	+	0.167135i
$412$	22.3401	+	17.5172i	1.10062	+	0.863011i
$413$	−4.35394	−	5.18882i	−0.214243	−	0.255325i
$414$	−8.78382	−	6.67983i	−0.431701	−	0.328296i
$415$	−41.4311	+	7.30542i	−2.03377	+	0.358609i
$416$	0.141019	−	32.1300i	0.00691404	−	1.57530i
$417$	1.41717	+	9.59798i	0.0693991	+	0.470015i
$418$	4.96087	+	0.866162i	0.242644	+	0.0423654i
$419$	1.77830			0.0868756			0.0434378	−	0.999056i	$-0.486169\pi$
$419$	1.77830			0.0868756			0.0434378	+	0.999056i	$0.486169\pi$
$420$	−19.3637	−	16.0768i	−0.944851	−	0.784469i
$421$	−6.90800	−	39.1772i	−0.336675	−	1.90938i	−0.410024	−	0.912075i	$-0.634480\pi$
$421$	−6.90800	−	39.1772i	−0.336675	−	1.90938i	0.0733486	−	0.997306i	$-0.476631\pi$
$422$	−28.4581	+	20.6379i	−1.38532	+	1.00464i
$423$	−7.60268	+	11.6174i	−0.369655	+	0.564858i
$424$	−12.9136	−	16.6186i	−0.627139	−	0.807073i
$425$	4.64202	+	2.68007i	0.225171	+	0.130003i
$426$	4.28850	+	9.47640i	0.207779	+	0.459133i
$427$	−4.68796	−	12.8801i	−0.226866	−	0.623310i
$428$	14.6518	+	2.08541i	0.708222	+	0.100802i
$429$	−4.99199	−	6.29851i	−0.241016	−	0.304095i
$430$	−25.6103	+	26.4737i	−1.23504	+	1.27667i
$431$	−5.93788	+	33.6754i	−0.286017	+	1.62209i	0.415611	+	0.909543i	$0.363568\pi$
$431$	−5.93788	+	33.6754i	−0.286017	+	1.62209i	−0.701628	+	0.712543i	$0.747543\pi$
$432$	20.5289	−	3.25015i	0.987698	−	0.156373i
$433$	−0.798545	−	0.670059i	−0.0383756	−	0.0322010i	0.623398	−	0.781905i	$-0.285752\pi$
$433$	−0.798545	−	0.670059i	−0.0383756	−	0.0322010i	−0.661774	+	0.749704i	$0.730196\pi$
$434$	1.37802	−	19.4611i	0.0661470	−	0.934161i
$435$	45.3230	+	9.30413i	2.17307	+	0.446099i
$436$	−6.09696	−	3.25556i	−0.291992	−	0.155913i
$437$	−8.13543	+	7.89656i	−0.389171	+	0.377744i
$438$	−3.54699	−	0.350979i	−0.169482	−	0.0167704i
$439$	6.29001	−	17.2817i	0.300206	−	0.824809i	−0.694258	−	0.719727i	$-0.744267\pi$
$439$	6.29001	−	17.2817i	0.300206	−	0.824809i	0.994464	−	0.105082i	$-0.0335106\pi$
$440$	7.69115	+	4.83417i	0.366661	+	0.230460i
$441$	9.88505	+	4.23707i	0.470717	+	0.201765i
$442$	1.80179	+	3.70246i	0.0857023	+	0.176108i
$443$	−1.01298	+	5.74488i	−0.0481280	+	0.272948i	−0.999370	−	0.0354989i	$-0.988698\pi$
$443$	−1.01298	+	5.74488i	−0.0481280	+	0.272948i	0.951242	+	0.308447i	$0.0998091\pi$
$444$	9.19296	−	7.79581i	0.436278	−	0.369973i
$445$	16.6172	+	28.7819i	0.787733	+	1.36439i
$446$	1.28506	+	12.3306i	0.0608494	+	0.583873i
$447$	2.38050	+	4.40280i	0.112594	+	0.208245i
$448$	8.62663	+	12.0060i	0.407570	+	0.567231i
$449$	−8.02414	−	4.63274i	−0.378683	−	0.218633i	0.298562	−	0.954390i	$-0.403493\pi$
$449$	−8.02414	−	4.63274i	−0.378683	−	0.218633i	−0.677245	+	0.735758i	$0.736826\pi$
$450$	−5.60006	+	44.0084i	−0.263989	+	2.07458i
$451$	2.54846	+	3.03714i	0.120002	+	0.143013i
$452$	4.06206	−	1.63289i	0.191063	−	0.0768047i
$453$	5.44258	−	1.81042i	0.255715	−	0.0850611i
$454$	12.2945	+	8.30849i	0.577012	+	0.389937i
$455$	41.2661			1.93459
$456$	−0.147091	−	21.3536i	−0.00688818	−	0.999976i
$457$	8.67588			0.405841			0.202920	−	0.979195i	$-0.434957\pi$
$457$	8.67588			0.405841			0.202920	+	0.979195i	$0.434957\pi$
$458$	13.3175	+	8.99981i	0.622288	+	0.420534i
$459$	−2.17662	+	1.53530i	−0.101596	+	0.0716618i
$460$	−18.9759	+	7.62805i	−0.884757	+	0.355659i
$461$	2.31241	+	2.75583i	0.107700	+	0.128352i	0.817201	−	0.576352i	$-0.195524\pi$
$461$	2.31241	+	2.75583i	0.107700	+	0.128352i	−0.709502	+	0.704704i	$0.751080\pi$
$462$	3.56084	+	0.997627i	0.165665	+	0.0464138i
$463$	29.8697	+	17.2453i	1.38816	+	0.801456i	0.993108	−	0.117202i	$-0.0373926\pi$
$463$	29.8697	+	17.2453i	1.38816	+	0.801456i	0.395054	+	0.918658i	$0.370726\pi$
$464$	−24.3859	−	12.0000i	−1.13209	−	0.557084i
$465$	−44.7166	+	24.1773i	−2.07368	+	1.12120i
$466$	−2.62973	−	25.2332i	−0.121820	−	1.16891i
$467$	9.10511	+	15.7705i	0.421334	+	0.729772i	0.996070	−	0.0885667i	$-0.0282287\pi$
$467$	9.10511	+	15.7705i	0.421334	+	0.729772i	−0.574736	+	0.818339i	$0.694895\pi$
$468$	−22.4934	+	25.6017i	−1.03976	+	1.18344i
$469$	2.64776	−	15.0162i	0.122262	−	0.693385i
$470$	11.2596	+	23.1371i	0.519367	+	1.06724i
$471$	15.8145	+	9.72948i	0.728696	+	0.448311i
$472$	5.51691	−	8.77738i	0.253936	−	0.404012i
$473$	1.85104	−	5.08569i	0.0851109	−	0.233840i
$474$	0.270388	−	2.73254i	0.0124193	−	0.125510i
$475$	43.8452	+	12.4513i	2.01176	+	0.571305i
$476$	−1.67127	−	0.892397i	−0.0766025	−	0.0409029i
$477$	−1.24672	+	22.2880i	−0.0570832	+	1.02050i
$478$	2.42777	−	34.2862i	0.111044	−	1.56821i
$479$	14.7886	+	12.4091i	0.675711	+	0.566988i	0.914749	−	0.404022i	$-0.132388\pi$
$479$	14.7886	+	12.4091i	0.675711	+	0.566988i	−0.239039	+	0.971010i	$0.576832\pi$
$480$	14.3379	−	35.7526i	0.654432	−	1.63188i
$481$	−3.43186	+	19.4630i	−0.156479	+	0.887439i
$482$	15.8287	−	16.3623i	0.720978	−	0.745284i
$483$	−6.52460	+	5.17119i	−0.296880	+	0.235297i
$484$	20.4590	+	2.91197i	0.929957	+	0.132362i
$485$	−6.86443	−	18.8599i	−0.311698	−	0.856383i
$486$	−18.6845	−	11.7000i	−0.847545	−	0.530723i
$487$	−30.9096	−	17.8457i	−1.40065	−	0.808664i	−0.406188	−	0.913789i	$-0.633142\pi$
$487$	−30.9096	−	17.8457i	−1.40065	−	0.808664i	−0.994459	+	0.105125i	$0.966476\pi$
$488$	16.5654	−	12.8722i	0.749881	−	0.582698i
$489$	14.3600	+	12.7498i	0.649382	+	0.576565i
$490$	16.1357	−	11.7017i	0.728938	−	0.528627i
$491$	−6.54895	−	37.1409i	−0.295550	−	1.67615i	−0.664959	−	0.746879i	$-0.731551\pi$
$491$	−6.54895	−	37.1409i	−0.295550	−	1.67615i	0.369410	−	0.929267i	$-0.379560\pi$
$492$	10.7391	−	12.9347i	0.484158	−	0.583142i
$493$	3.48301			0.156867
$494$	22.5510	+	26.7839i	1.01462	+	1.20506i
$495$	−2.78464	−	9.22411i	−0.125160	−	0.414593i
$496$	28.9989	−	7.12217i	1.30209	−	0.319795i
$497$	7.72813	−	1.36268i	0.346654	−	0.0611245i
$498$	−18.3226	−	18.7439i	−0.821057	−	0.839933i
$499$	12.5295	+	14.9321i	0.560899	+	0.668453i	0.969736	−	0.244154i	$-0.0785102\pi$
$499$	12.5295	+	14.9321i	0.560899	+	0.668453i	−0.408838	+	0.912607i	$0.634066\pi$
$500$	33.7627	+	26.4739i	1.50991	+	1.18395i
$501$	13.0952	−	33.0734i	0.585051	−	1.47761i
$502$	−3.64327	−	12.7478i	−0.162607	−	0.568962i
$503$	−9.58943	+	3.49027i	−0.427571	+	0.155623i	−0.546837	−	0.837239i	$-0.684168\pi$
$503$	−9.58943	+	3.49027i	−0.427571	+	0.155623i	0.119266	+	0.992862i	$0.461946\pi$
$504$	1.46274	−	15.6123i	0.0651554	−	0.695427i
$505$	13.7615	+	23.8356i	0.612379	+	1.06067i
$506$	2.08935	−	2.15979i	0.0928830	−	0.0960143i
$507$	0.931965	−	33.3481i	0.0413900	−	1.48104i
$508$	−5.71621	−	27.1268i	−0.253616	−	1.20356i
$509$	−14.7678	+	17.5996i	−0.654571	+	0.780088i	−0.986596	−	0.163183i	$-0.947824\pi$
$509$	−14.7678	+	17.5996i	−0.654571	+	0.780088i	0.332025	+	0.943271i	$0.392268\pi$
$510$	0.374336	+	4.92231i	0.0165759	+	0.217963i
$511$	−0.919708	+	2.52688i	−0.0406855	+	0.111782i
$512$	−13.4443	+	18.2003i	−0.594158	+	0.804348i
$513$	−14.7565	+	17.1827i	−0.651517	+	0.758634i
$514$	−5.54672	+	22.1638i	−0.244655	+	0.977602i
$515$	−52.4397	−	19.0865i	−2.31077	−	0.841052i
$516$	−22.6210	−	3.86725i	−0.995836	−	0.170246i
$517$	−2.89623	−	2.43023i	−0.127376	−	0.106881i
$518$	−3.97917	−	8.17672i	−0.174835	−	0.359265i
$519$	9.74087	+	0.272224i	0.427577	+	0.0119493i
$520$	19.3592	+	60.1197i	0.848956	+	2.63642i
$521$	17.1402	−	9.89589i	0.750925	−	0.433547i	−0.0751028	−	0.997176i	$-0.523928\pi$
$521$	17.1402	−	9.89589i	0.750925	−	0.433547i	0.826028	+	0.563629i	$0.190595\pi$
$522$	11.1469	+	26.5848i	0.487886	+	1.16358i
$523$	5.62078	+	15.4430i	0.245780	+	0.675274i	0.999830	+	0.0184571i	$0.00587541\pi$
$523$	5.62078	+	15.4430i	0.245780	+	0.675274i	−0.754050	+	0.656817i	$0.771902\pi$
$524$	0.456596	+	13.7682i	0.0199465	+	0.601466i
$525$	31.1188	+	12.3213i	1.35813	+	0.537745i
$526$	6.50146	−	14.5681i	0.283477	−	0.635199i
$527$	−2.93145	+	2.45978i	−0.127696	+	0.107150i
$528$	0.217075	+	5.65572i	0.00944698	+	0.246134i
$529$	−2.81912	−	15.9880i	−0.122571	−	0.695133i
$530$	34.2780	+	23.1646i	1.48894	+	1.00621i
$531$	−10.5268	+	3.17792i	−0.456826	+	0.137910i
$532$	−15.6349	−	3.88496i	−0.677860	−	0.168434i
$533$			27.5653i			1.19399i
$534$	−8.96367	+	18.6659i	−0.387896	+	0.807752i
$535$	−28.6499	+	5.05176i	−1.23864	+	0.218406i
$536$	23.1189	−	3.18709i	0.998586	−	0.137661i
$537$	26.2238	−	29.5357i	1.13164	−	1.27456i
$538$	−41.5200	−	18.5296i	−1.79006	−	0.798868i
$539$	−1.46433	+	2.53630i	−0.0630733	+	0.109246i
$540$	−36.3725	+	18.6104i	−1.56522	+	0.800862i
$541$	−23.2327	+	8.45599i	−0.998850	+	0.363552i	−0.789141	−	0.614212i	$-0.789474\pi$
$541$	−23.2327	+	8.45599i	−0.998850	+	0.363552i	−0.209709	+	0.977764i	$0.567252\pi$
$542$	−2.54155	−	24.3871i	−0.109169	−	1.04752i
$543$	−18.8794	−	23.8206i	−0.810195	−	1.02224i
$544$	0.516070	−	2.85348i	0.0221263	−	0.122342i
$545$	13.3802	+	2.35929i	0.573144	+	0.101061i
$546$	14.5068	+	21.2272i	0.620832	+	0.908439i
$547$	−11.8739	+	14.1508i	−0.507691	+	0.605043i	−0.957625	−	0.288019i	$-0.907003\pi$
$547$	−11.8739	+	14.1508i	−0.507691	+	0.605043i	0.449933	+	0.893062i	$0.351448\pi$
$548$	10.1019	+	3.30194i	0.431534	+	0.141052i
$549$	−22.2166	−	1.24272i	−0.948180	−	0.0530381i
$550$	−11.7192	−	2.93285i	−0.499708	−	0.125057i
$551$	28.7189	−	7.23840i	1.22347	−	0.308366i
$552$	−10.5947	−	7.07958i	−0.450939	−	0.301327i
$553$	−1.94666	−	0.708527i	−0.0827805	−	0.0301296i
$554$	−1.53067	+	21.6169i	−0.0650321	+	0.918416i
$555$	−12.4155	+	20.1806i	−0.527011	+	0.856617i
$556$	2.30998	+	10.9622i	0.0979651	+	0.464901i
$557$	23.9025	+	4.21465i	1.01278	+	0.178580i	0.655322	−	0.755349i	$-0.272533\pi$
$557$	23.9025	+	4.21465i	1.01278	+	0.178580i	0.357457	+	0.933930i	$0.383644\pi$
$558$	−28.1565	−	14.5027i	−1.19196	−	0.613949i
$559$	32.5872	−	18.8142i	1.37829	−	0.795758i
$560$	−23.4509	−	17.1642i	−0.990982	−	0.725321i
$561$	−0.344977	−	0.638042i	−0.0145649	−	0.0269382i
$562$	17.7508	−	5.07311i	0.748774	−	0.213996i
$563$	−9.69314	+	16.7890i	−0.408517	+	0.707573i	−0.994724	−	0.102589i	$-0.967287\pi$
$563$	−9.69314	+	16.7890i	−0.408517	+	0.707573i	0.586207	+	0.810162i	$0.300621\pi$
$564$	−7.94345	+	13.9256i	−0.334480	+	0.586372i
$565$	−6.59255	+	5.53180i	−0.277351	+	0.232725i
$566$	10.0225	−	7.26833i	0.421277	−	0.305511i
$567$	−12.0450	+	11.4690i	−0.505841	+	0.481652i
$568$	5.61075	+	10.6197i	0.235422	+	0.445591i
$569$		−	15.5507i		−	0.651919i	−0.945384	−	0.325959i	$-0.894313\pi$
$569$		−	15.5507i		−	0.651919i	0.945384	−	0.325959i	$-0.105687\pi$
$570$	13.3161	+	39.8086i	0.557750	+	1.66740i
$571$		−	17.2428i		−	0.721587i	−0.932646	−	0.360794i	$-0.882506\pi$
$571$		−	17.2428i		−	0.721587i	0.932646	−	0.360794i	$-0.117494\pi$
$572$	−6.19753	−	6.90741i	−0.259132	−	0.288813i
$573$	8.04974	+	24.1996i	0.336283	+	1.01095i
$574$	−7.44612	−	10.2677i	−0.310795	−	0.428563i
$575$	20.8346	−	17.4823i	0.868863	−	0.729062i
$576$	23.4314	−	5.19317i	0.976309	−	0.216382i
$577$	−0.972885	+	1.68509i	−0.0405017	+	0.0701511i	−0.885566	−	0.464514i	$-0.846229\pi$
$577$	−0.972885	+	1.68509i	−0.0405017	+	0.0701511i	0.845064	+	0.534665i	$0.179562\pi$
$578$	−6.50437	−	22.7588i	−0.270546	−	0.946641i
$579$	6.42052	−	3.47144i	0.266828	−	0.144268i
$580$	52.8927	+	7.52831i	2.19625	+	0.312596i
$581$	−17.1257	+	9.88752i	−0.710493	+	0.410203i
$582$	7.28833	−	10.1611i	0.302111	−	0.421190i
$583$	−5.98640	−	1.05556i	−0.247931	−	0.0437170i
$584$	−4.11281	−	0.154467i	−0.170189	−	0.00639191i
$585$	26.3923	−	61.5731i	1.09119	−	2.54573i
$586$	−25.3414	−	1.79440i	−1.04685	−	0.0741260i
$587$	−21.7221	−	7.90620i	−0.896567	−	0.326324i	−0.147691	−	0.989034i	$-0.547184\pi$
$587$	−21.7221	−	7.90620i	−0.896567	−	0.326324i	−0.748876	+	0.662710i	$0.769406\pi$
$588$	11.6917	+	4.18655i	0.482157	+	0.172650i
$589$	−19.0592	+	26.3741i	−0.785319	+	1.08673i
$590$	−4.94753	+	19.7695i	−0.203687	+	0.813898i
$591$	1.41016	−	6.86925i	0.0580060	−	0.282563i
$592$	10.0457	−	9.63311i	0.412877	−	0.395918i
$593$	−7.15355	+	8.52526i	−0.293761	+	0.350091i	−0.892657	−	0.450736i	$-0.851162\pi$
$593$	−7.15355	+	8.52526i	−0.293761	+	0.350091i	0.598896	+	0.800826i	$0.295606\pi$
$594$	3.76594	−	4.67507i	0.154518	−	0.191820i
$595$	3.66771	+	0.646717i	0.150362	+	0.0265128i
$596$	3.05402	+	4.90661i	0.125098	+	0.200983i
$597$	−20.9575	+	16.6102i	−0.857731	+	0.679810i
$598$	20.7803	−	2.16566i	0.849771	−	0.0885604i
$599$	−9.34469	+	3.40119i	−0.381813	+	0.138969i	−0.525794	−	0.850612i	$-0.676232\pi$
$599$	−9.34469	+	3.40119i	−0.381813	+	0.138969i	0.143981	+	0.989580i	$0.454010\pi$
$600$	−3.35186	+	51.1165i	−0.136839	+	2.08682i
$601$	20.4943	−	35.4971i	0.835979	−	1.44796i	−0.0572511	−	0.998360i	$-0.518234\pi$
$601$	20.4943	−	35.4971i	0.835979	−	1.44796i	0.893230	−	0.449599i	$-0.148433\pi$
$602$	−7.05601	+	15.8107i	−0.287582	+	0.644396i
$603$	−20.7122	−	13.5545i	−0.843468	−	0.551984i
$604$	6.14520	−	2.47028i	0.250045	−	0.100514i
$605$	−40.0053	+	7.05402i	−1.62645	+	0.286787i
$606$	−7.42324	+	15.4581i	−0.301548	+	0.627942i
$607$		−	20.0981i		−	0.815758i	−0.913036	−	0.407879i	$-0.866269\pi$
$607$		−	20.0981i		−	0.815758i	0.913036	−	0.407879i	$-0.133731\pi$
$608$	−1.67490	−	24.6007i	−0.0679261	−	0.997690i
$609$	21.5150	−	3.17675i	0.871831	−	0.128728i
$610$	−23.0904	+	34.1682i	−0.934903	+	1.38343i
$611$	−4.56460	−	25.8871i	−0.184664	−	1.04728i
$612$	−2.40043	+	1.92295i	−0.0970315	+	0.0777308i
$613$	−4.29342	+	3.60261i	−0.173410	+	0.145508i	−0.725362	−	0.688368i	$-0.758328\pi$
$613$	−4.29342	+	3.60261i	−0.173410	+	0.145508i	0.551952	+	0.833876i	$0.313883\pi$
$614$	−10.0616	−	4.49028i	−0.406051	−	0.181213i
$615$	−12.1661	+	30.7267i	−0.490583	+	1.23902i
$616$	4.17436	+	0.898783i	0.168190	+	0.0362130i
$617$	−10.4325	−	28.6630i	−0.419996	−	1.15393i	−0.951708	−	0.307005i	$-0.900673\pi$
$617$	−10.4325	−	28.6630i	−0.419996	−	1.15393i	0.531712	−	0.846925i	$-0.321549\pi$
$618$	−8.61671	−	33.6845i	−0.346615	−	1.35499i
$619$	24.7871	−	14.3109i	0.996279	−	0.575202i	0.0891341	−	0.996020i	$-0.471590\pi$
$619$	24.7871	−	14.3109i	0.996279	−	0.575202i	0.907145	+	0.420817i	$0.138257\pi$
$620$	−49.8335	+	31.0179i	−2.00136	+	1.24571i
$621$	3.54302	+	13.0426i	0.142176	+	0.523383i
$622$	24.3156	−	11.8331i	0.974967	−	0.474464i
$623$	11.9670	+	10.0415i	0.479448	+	0.402304i
$624$	−24.1198	+	31.0929i	−0.965565	+	1.24471i
$625$	−30.1230	−	10.9639i	−1.20492	−	0.438555i
$626$	−16.8844	−	4.22549i	−0.674835	−	0.168885i
$627$	−4.17046	−	4.54400i	−0.166552	−	0.181470i
$628$	18.9129	+	10.0988i	0.754707	+	0.402986i
$629$	−0.610044	+	1.67608i	−0.0243240	+	0.0668298i
$630$	6.80180	+	30.0643i	0.270990	+	1.19779i
$631$	20.9960	−	25.0221i	0.835837	−	0.996112i	−0.164116	−	0.986441i	$-0.552477\pi$
$631$	20.9960	−	25.0221i	0.835837	−	0.996112i	0.999953	−	0.00967104i	$-0.00307844\pi$
$632$	0.118999	−	3.16844i	0.00473353	−	0.126034i
$633$	43.0376	+	1.20275i	1.71059	+	0.0478051i
$634$	−17.0977	−	16.5400i	−0.679035	−	0.656889i
$635$	27.2476	+	47.1942i	1.08129	+	1.87284i
$636$	0.134337	+	25.7758i	0.00532682	+	1.02208i
$637$	−19.1341	+	6.96425i	−0.758122	+	0.275934i
$638$	−7.54776	+	2.15712i	−0.298818	+	0.0854010i
$639$	2.90938	−	12.4026i	0.115093	−	0.490641i
$640$	14.0046	−	42.2174i	0.553581	−	1.66879i
$641$	−1.01808	−	1.21330i	−0.0402117	−	0.0479224i	0.745564	−	0.666434i	$-0.232180\pi$
$641$	−1.01808	−	1.21330i	−0.0402117	−	0.0479224i	−0.785775	+	0.618512i	$0.787736\pi$
$642$	−12.6702	−	12.9615i	−0.500055	−	0.511551i
$643$	44.7260	−	7.88640i	1.76382	−	0.311009i	0.804633	−	0.593773i	$-0.202362\pi$
$643$	44.7260	−	7.88640i	1.76382	−	0.311009i	0.959190	+	0.282764i	$0.0912512\pi$
$644$	−7.15535	+	6.42000i	−0.281960	+	0.252983i
$645$	44.6283	−	6.58950i	1.75724	−	0.259461i
$646$	1.58456	+	2.73395i	0.0623439	+	0.107566i
$647$	−7.91696			−0.311248			−0.155624	−	0.987816i	$-0.549739\pi$
$647$	−7.91696			−0.311248			−0.155624	+	0.987816i	$0.549739\pi$
$648$	−22.3596	−	12.1676i	−0.878366	−	0.477988i
$649$	−0.519964	−	2.94886i	−0.0204104	−	0.115753i
$650$	−49.3100	−	67.9948i	−1.93410	−	2.66698i
$651$	−15.8645	+	17.8681i	−0.621777	+	0.700304i
$652$	17.4494	+	13.6824i	0.683372	+	0.535843i
$653$	5.90597	+	3.40981i	0.231119	+	0.133436i	0.611088	−	0.791563i	$-0.290732\pi$
$653$	5.90597	+	3.40981i	0.231119	+	0.133436i	−0.379969	+	0.924999i	$0.624065\pi$
$654$	3.49008	+	7.71212i	0.136473	+	0.301568i
$655$	−9.26174	−	25.4464i	−0.361886	−	0.994274i
$656$	11.4655	−	15.6649i	0.447653	−	0.611613i
$657$	3.18213	+	2.98839i	0.124147	+	0.116588i
$658$	8.69304	+	8.40953i	0.338890	+	0.327838i
$659$	−2.00685	+	11.3814i	−0.0781759	+	0.443357i	0.920446	+	0.390870i	$0.127826\pi$
$659$	−2.00685	+	11.3814i	−0.0781759	+	0.443357i	−0.998622	+	0.0524870i	$0.983285\pi$
$660$	−3.85970	−	10.4349i	−0.150239	−	0.406178i
$661$	26.8184	+	22.5033i	1.04311	+	0.875276i	0.992353	−	0.123435i	$-0.0393911\pi$
$661$	26.8184	+	22.5033i	1.04311	+	0.875276i	0.0507603	+	0.998711i	$0.483836\pi$
$662$	13.7965	+	0.976917i	0.536217	+	0.0379690i
$663$	1.01411	−	4.93999i	0.0393846	−	0.191853i
$664$	−22.4391	−	20.3115i	−0.870805	−	0.788239i
$665$	31.5859	−	2.28979i	1.22485	−	0.0887942i
$666$	−14.7454	+	0.707782i	−0.571372	+	0.0274260i
$667$	6.04451	−	16.6071i	0.234044	−	0.643031i
$668$	12.7613	−	39.0418i	0.493748	−	1.51057i
$669$	7.95621	−	12.9322i	0.307605	−	0.499989i
$670$	−41.2503	+	20.0743i	−1.59364	+	0.775539i
$671$	1.05218	−	5.96723i	0.0406191	−	0.230362i
$672$	0.585249	−	18.0970i	0.0225765	−	0.698108i
$673$	3.19840	+	5.53979i	0.123289	+	0.213543i	0.921063	−	0.389414i	$-0.127322\pi$
$673$	3.19840	+	5.53979i	0.123289	+	0.213543i	−0.797774	+	0.602957i	$0.793989\pi$
$674$	37.9328	−	3.95324i	1.46112	−	0.152273i
$675$	38.2870	−	38.5520i	1.47367	−	1.48387i
$676$	−1.27681	−	38.5010i	−0.0491082	−	1.48081i
$677$	−33.2915	−	19.2209i	−1.27950	−	0.738718i	−0.302741	−	0.953073i	$-0.597902\pi$
$677$	−33.2915	−	19.2209i	−1.27950	−	0.738718i	−0.976756	+	0.214355i	$0.931235\pi$
$678$	−5.16310	−	1.44653i	−0.198288	−	0.0555535i
$679$	−6.06405	−	7.22686i	−0.232717	−	0.277341i
$680$	0.778447	+	5.64680i	0.0298521	+	0.216545i
$681$	−5.73624	−	17.2446i	−0.219813	−	0.660814i
$682$	4.82911	−	7.14592i	0.184916	−	0.273631i
$683$	29.1486			1.11534			0.557670	−	0.830063i	$-0.311696\pi$
$683$	29.1486			1.11534			0.557670	+	0.830063i	$0.311696\pi$
$684$	−15.7963	+	20.8441i	−0.603985	+	0.796996i
$685$	−20.8917			−0.798229
$686$	15.4892	−	22.9202i	0.591380	−	0.875099i
$687$	−6.21354	−	18.6795i	−0.237061	−	0.712666i
$688$	−26.3444	−	2.86247i	−1.00437	−	0.109131i
$689$	−27.1665	−	32.3758i	−1.03496	−	1.23342i
$690$	24.1194	+	6.75745i	0.918210	+	0.257252i
$691$	−37.4771	−	21.6374i	−1.42570	−	0.823126i	−0.428919	−	0.903343i	$-0.641105\pi$
$691$	−37.4771	−	21.6374i	−1.42570	−	0.823126i	−0.996777	+	0.0802170i	$0.974439\pi$
$692$	11.2460	−	0.372952i	0.427509	−	0.0141775i
$693$	−2.71290	−	3.62662i	−0.103055	−	0.137764i
$694$	−12.5889	+	1.31197i	−0.477867	+	0.0498018i
$695$	−11.0110	−	19.0717i	−0.417673	−	0.723430i
$696$	14.7215	+	29.8544i	0.558015	+	1.13163i
$697$	−0.431999	+	2.44999i	−0.0163631	+	0.0928000i
$698$	−1.06334	+	0.517470i	−0.0402480	+	0.0195865i
$699$	−16.2815	+	26.4643i	−0.615822	+	1.00097i
$700$	36.7344	+	12.0071i	1.38843	+	0.453825i
$701$	1.49048	−	4.09507i	0.0562947	−	0.154668i	−0.908358	−	0.418194i	$-0.862663\pi$
$701$	1.49048	−	4.09507i	0.0562947	−	0.154668i	0.964652	+	0.263526i	$0.0848854\pi$
$702$	40.9510	−	8.06938i	1.54560	−	0.304559i
$703$	−1.54684	+	15.0878i	−0.0583401	+	0.569048i
$704$	0.648901	+	6.50318i	0.0244564	+	0.245098i
$705$	6.33728	−	30.8706i	0.238676	−	1.16266i
$706$	24.2802	+	1.71926i	0.913797	+	0.0647050i
$707$	9.91044	+	8.31584i	0.372720	+	0.312749i
$708$	−11.9086	+	4.40481i	−0.447554	+	0.165543i
$709$	2.34971	−	13.3259i	0.0882454	−	0.500464i	−0.908364	−	0.418181i	$-0.862668\pi$
$709$	2.34971	−	13.3259i	0.0882454	−	0.500464i	0.996609	−	0.0822832i	$-0.0262212\pi$
$710$	−16.9692	−	16.4158i	−0.636843	−	0.616073i
$711$	−2.30220	+	2.45146i	−0.0863394	+	0.0919370i
$712$	−9.01516	+	22.1452i	−0.337857	+	0.829927i
$713$	6.64102	+	18.2461i	0.248708	+	0.683320i
$714$	0.956684	+	2.11401i	0.0358030	+	0.0791147i
$715$	15.7984	+	9.12120i	0.590826	+	0.341114i
$716$	28.1419	−	35.8900i	1.05171	−	1.34127i
$717$	−27.9497	+	31.4796i	−1.04380	+	1.17563i
$718$	26.5910	+	36.6670i	0.992367	+	1.36840i
$719$	5.99951	+	34.0249i	0.223744	+	1.26892i	0.865072	+	0.501649i	$0.167273\pi$
$719$	5.99951	+	34.0249i	0.223744	+	1.26892i	−0.641327	+	0.767267i	$0.721616\pi$
$720$	−40.6090	+	24.0135i	−1.51341	+	0.894929i
$721$	−26.2311			−0.976899
$722$	18.7471	+	19.2496i	0.697696	+	0.716394i
$723$	−27.5830	+	4.07271i	−1.02582	+	0.151466i
$724$	−23.4387	−	26.1234i	−0.871093	−	0.970870i
$725$	−69.9687	+	12.3374i	−2.59857	+	0.458198i
$726$	−17.6921	−	18.0988i	−0.656615	−	0.671711i
$727$	−26.1375	−	31.1495i	−0.969388	−	1.15527i	−0.987845	−	0.155441i	$-0.950320\pi$
$727$	−26.1375	−	31.1495i	−0.969388	−	1.15527i	0.0184575	−	0.999830i	$-0.494124\pi$
$728$	18.2162	+	23.4426i	0.675136	+	0.868841i
$729$	9.40932	+	25.3074i	0.348493	+	0.937311i
$730$	7.77896	−	2.22319i	0.287912	−	0.0822840i
$731$	3.19119	−	1.16150i	0.118030	−	0.0429596i
$732$	−25.6932	+	0.133907i	−0.949650	+	0.00494935i
$733$	−9.42813	−	16.3300i	−0.348236	−	0.603163i	0.637700	−	0.770285i	$-0.279886\pi$
$733$	−9.42813	−	16.3300i	−0.348236	−	0.603163i	−0.985936	+	0.167122i	$0.946553\pi$
$734$	11.2650	+	10.8976i	0.415799	+	0.402238i
$735$	−24.4023	−	0.681959i	−0.900092	−	0.0251544i
$736$	−12.7099	−	7.41265i	−0.468495	−	0.273234i
$737$	4.33276	−	5.16359i	0.159599	−	0.190203i
$738$	−20.0826	+	4.54353i	−0.739251	+	0.167250i
$739$	−12.0726	+	33.1691i	−0.444096	+	1.22014i	0.492679	+	0.870211i	$0.336018\pi$
$739$	−12.0726	+	33.1691i	−0.444096	+	1.22014i	−0.936775	+	0.349933i	$0.886204\pi$
$740$	−12.8868	+	24.1343i	−0.473729	+	0.887194i
$741$	−1.90455	−	42.8399i	−0.0699655	−	1.57376i
$742$	18.8647	+	4.72109i	0.692545	+	0.173317i
$743$	−21.7536	−	7.91768i	−0.798064	−	0.290471i	−0.0893799	−	0.995998i	$-0.528489\pi$
$743$	−21.7536	−	7.91768i	−0.798064	−	0.290471i	−0.708684	+	0.705526i	$0.750711\pi$
$744$	−33.4741	−	14.7301i	−1.22722	−	0.540032i
$745$	−8.70293	−	7.30262i	−0.318851	−	0.267547i
$746$	−15.2977	+	7.44460i	−0.560090	+	0.272566i
$747$	3.80018	+	31.8769i	0.139041	+	1.16631i
$748$	−0.442582	−	0.711054i	−0.0161824	−	0.0259987i
$749$	−11.8426	+	6.83730i	−0.432717	+	0.249830i
$750$	−13.0225	−	50.9077i	−0.475514	−	1.85889i
$751$	−2.21674	−	6.09045i	−0.0808901	−	0.222244i	0.892654	−	0.450742i	$-0.148841\pi$
$751$	−2.21674	−	6.09045i	−0.0808901	−	0.222244i	−0.973544	+	0.228499i	$0.926618\pi$
$752$	−8.17348	+	16.6099i	−0.298056	+	0.605699i
$753$	−5.97778	+	15.0975i	−0.217843	+	0.550185i
$754$	−49.8402	−	22.2427i	−1.81507	−	0.810033i
$755$	−9.97339	+	8.36867i	−0.362969	+	0.304567i
$756$	−13.0739	+	14.0677i	−0.475492	+	0.511636i
$757$	−0.985133	−	5.58697i	−0.0358053	−	0.203062i	0.961657	−	0.274254i	$-0.0884308\pi$
$757$	−0.985133	−	5.58697i	−0.0358053	−	0.203062i	−0.997463	+	0.0711920i	$0.977320\pi$
$758$	12.0380	−	17.8134i	0.437241	−	0.647010i
$759$	−3.64089	+	0.537588i	−0.132156	+	0.0195132i
$760$	18.1538	+	44.9425i	0.658508	+	1.63024i
$761$			47.9592i			1.73852i	0.494356	+	0.869260i	$0.335404\pi$
$761$			47.9592i			1.73852i	−0.494356	+	0.869260i	$0.664596\pi$
$762$	−14.6979	+	30.6068i	−0.532449	+	1.10877i
$763$	6.28934	−	1.10898i	0.227689	−	0.0401478i
$764$	10.9837	+	27.3236i	0.397376	+	0.988534i
$765$	3.31070	−	5.05897i	0.119699	−	0.182907i
$766$	−12.1483	+	27.2212i	−0.438936	+	0.983541i
$767$	10.4094	−	18.0296i	0.375862	−	0.651012i
$768$	26.6397	−	7.63722i	0.961277	−	0.275584i
$769$	36.0153	−	13.1085i	1.29874	−	0.472704i	0.402157	−	0.915571i	$-0.368261\pi$
$769$	36.0153	−	13.1085i	1.29874	−	0.472704i	0.896588	+	0.442866i	$0.146038\pi$
$770$	−8.34854	+	0.870058i	−0.300860	+	0.0313547i
$771$	21.9296	−	17.3807i	0.789777	−	0.625951i
$772$	7.15522	−	4.45363i	0.257522	−	0.160290i
$773$	−33.5684	−	5.91901i	−1.20737	−	0.212892i	−0.466488	−	0.884527i	$-0.654481\pi$
$773$	−33.5684	−	5.91901i	−1.20737	−	0.212892i	−0.740882	+	0.671635i	$0.765592\pi$
$774$	19.0783	+	20.6402i	0.685756	+	0.741896i
$775$	50.1758	−	59.7972i	1.80237	−	2.14798i
$776$	7.68381	−	12.2249i	0.275833	−	0.438849i
$777$	−2.23961	+	10.9098i	−0.0803457	+	0.391386i
$778$	−7.48951	+	29.9268i	−0.268512	+	1.07293i
$779$	1.52955	+	21.0990i	0.0548019	+	0.755950i
$780$	26.0776	−	72.8264i	0.933729	−	2.60760i
$781$	3.25985	+	1.18649i	0.116647	+	0.0424559i
$782$	1.88089	+	0.133184i	0.0672603	+	0.00476263i
$783$	9.02017	−	34.1342i	0.322355	−	1.21986i
$784$	13.7703	+	4.00096i	0.491798	+	0.142892i
$785$	−41.5056	−	7.31856i	−1.48140	−	0.261211i
$786$	9.83368	−	13.7097i	0.350756	−	0.489009i
$787$	−14.2969	+	8.25433i	−0.509630	+	0.294235i	−0.732681	−	0.680572i	$-0.761731\pi$
$787$	−14.2969	+	8.25433i	−0.509630	+	0.294235i	0.223052	+	0.974807i	$0.428398\pi$
$788$	1.14101	−	8.01655i	0.0406467	−	0.285578i
$789$	−17.1870	+	9.29267i	−0.611874	+	0.330828i
$790$	1.71271	+	5.99278i	0.0609355	+	0.213213i
$791$	−2.02261	+	3.50326i	−0.0719157	+	0.124562i
$792$	4.01084	−	5.65372i	0.142519	−	0.200896i
$793$	32.2721	−	27.0795i	1.14602	−	0.961622i
$794$	16.2622	+	22.4244i	0.577125	+	0.795813i
$795$	−15.9930	−	48.0790i	−0.567213	−	1.70519i
$796$	−22.9835	+	20.6215i	−0.814627	+	0.730908i
$797$		−	21.8763i		−	0.774897i	−0.921891	−	0.387449i	$-0.873356\pi$
$797$		−	21.8763i		−	0.774897i	0.921891	−	0.387449i	$-0.126644\pi$
$798$	12.2816	+	15.4427i	0.434764	+	0.546666i
$799$		−	2.37237i		−	0.0839284i
$800$	−0.259613	+	59.1504i	−0.00917870	+	2.09128i
$801$	22.6366	−	11.4338i	0.799823	−	0.403992i
$802$	36.9108	−	26.7678i	1.30337	−	0.945205i
$803$	−0.910627	+	0.764107i	−0.0321353	+	0.0269647i
$804$	−24.8274	−	14.1621i	−0.875594	−	0.499458i
$805$	9.44861	−	16.3655i	0.333020	−	0.576807i
$806$	57.6560	−	16.4778i	2.03085	−	0.580407i
$807$	26.4848	+	48.9842i	0.932307	+	1.72432i
$808$	−7.46588	+	18.3395i	−0.262649	+	0.645181i
$809$	32.0292	−	18.4920i	1.12609	−	0.650145i	0.183138	−	0.983087i	$-0.441375\pi$
$809$	32.0292	−	18.4920i	1.12609	−	0.650145i	0.942947	+	0.332942i	$0.108041\pi$
$810$	49.2090	+	9.07905i	1.72903	+	0.319005i
$811$	−13.9136	−	2.45335i	−0.488574	−	0.0861488i	−0.0760660	−	0.997103i	$-0.524236\pi$
$811$	−13.9136	−	2.45335i	−0.488574	−	0.0861488i	−0.412508	+	0.910954i	$0.635347\pi$
$812$	24.5731	−	5.17809i	0.862346	−	0.181715i
$813$	−15.7355	+	25.5770i	−0.551870	+	0.897023i
$814$	0.283938	−	4.00992i	0.00995203	−	0.140548i
$815$	−40.9597	−	14.9081i	−1.43476	−	0.522209i
$816$	−2.63104	+	2.38552i	−0.0921048	+	0.0835097i
$817$	23.8989	−	16.2090i	0.836117	−	0.567081i
$818$	−33.8126	−	8.46197i	−1.18223	−	0.295866i
$819$	1.75864	−	31.4399i	0.0614520	−	1.09860i
$820$	−11.8558	+	36.2716i	−0.414023	+	1.26666i
$821$	6.90220	−	8.22573i	0.240889	−	0.287080i	−0.632032	−	0.774942i	$-0.717779\pi$
$821$	6.90220	−	8.22573i	0.240889	−	0.287080i	0.872920	+	0.487863i	$0.162223\pi$
$822$	−7.34429	−	10.7466i	−0.256161	−	0.374831i
$823$	−35.9293	−	6.33531i	−1.25242	−	0.220835i	−0.492188	−	0.870489i	$-0.663803\pi$
$823$	−35.9293	−	6.33531i	−1.25242	−	0.220835i	−0.760230	+	0.649654i	$0.774914\pi$
$824$	−12.3058	−	38.2156i	−0.428694	−	1.33130i
$825$	9.19014	+	11.5954i	0.319959	+	0.403700i
$826$	0.992937	+	9.52761i	0.0345487	+	0.331508i
$827$	11.0278	−	4.01381i	0.383476	−	0.139574i	−0.143087	−	0.989710i	$-0.545703\pi$
$827$	11.0278	−	4.01381i	0.383476	−	0.139574i	0.526563	+	0.850136i	$0.323481\pi$
$828$	5.00296	+	14.7825i	0.173865	+	0.513727i
$829$	2.97115	−	5.14618i	0.103192	−	0.178734i	−0.809806	−	0.586698i	$-0.800428\pi$
$829$	2.97115	−	5.14618i	0.103192	−	0.178734i	0.912998	+	0.407964i	$0.133761\pi$
$830$	54.3313	+	24.2470i	1.88587	+	0.841626i
$831$	17.6219	−	19.8475i	0.611297	−	0.688501i
$832$	−25.6073	+	37.5363i	−0.887772	+	1.30134i
$833$	−1.80977	+	0.319112i	−0.0627050	+	0.0110566i
$834$	5.93958	−	12.3685i	0.205671	−	0.428287i
$835$			80.7416i			2.79418i
$836$	−5.12699	−	4.94317i	−0.177321	−	0.170963i
$837$	16.5146	+	35.0991i	0.570827	+	1.21320i
$838$	−2.08371	−	1.40814i	−0.0719804	−	0.0486434i
$839$	2.37420	+	13.4648i	0.0819665	+	0.464855i	0.997970	+	0.0636851i	$0.0202853\pi$
$839$	2.37420	+	13.4648i	0.0819665	+	0.464855i	−0.916004	+	0.401170i	$0.868604\pi$
$840$	9.95884	+	34.1710i	0.343613	+	1.17901i
$841$	−13.1506	+	11.0347i	−0.453468	+	0.380505i
$842$	−22.9280	+	51.3757i	−0.790150	+	1.77052i
$843$	−21.0228	−	8.32384i	−0.724062	−	0.286688i
$844$	49.6876	−	1.64780i	1.71032	−	0.0567195i
$845$	25.8993	+	71.1578i	0.890963	+	2.44790i
$846$	18.1076	−	7.59243i	0.622552	−	0.261033i
$847$	−16.5363	+	9.54726i	−0.568195	+	0.328048i
$848$	1.97195	+	29.6983i	0.0677170	+	1.01985i
$849$	−15.1571	−	0.423590i	−0.520192	−	0.0145376i
$850$	−3.31704	−	6.81613i	−0.113774	−	0.233791i
$851$	6.93294	+	5.81743i	0.237658	+	0.199419i
$852$	2.47885	−	14.4997i	0.0849239	−	0.496753i
$853$	18.3147	+	6.66601i	0.627084	+	0.228240i	0.635961	−	0.771721i	$-0.280604\pi$
$853$	18.3147	+	6.66601i	0.627084	+	0.228240i	−0.00887785	+	0.999961i	$0.502826\pi$
$854$	−4.70597	+	18.8043i	−0.161035	+	0.643469i
$855$	16.7846	−	48.5937i	0.574020	−	1.66187i
$856$	−15.5168	−	14.0456i	−0.530353	−	0.480067i
$857$	−1.18455	+	3.25451i	−0.0404633	+	0.111172i	−0.958279	−	0.285835i	$-0.907729\pi$
$857$	−1.18455	+	3.25451i	−0.0404633	+	0.111172i	0.917815	+	0.397007i	$0.129951\pi$
$858$	0.861870	+	11.3331i	0.0294238	+	0.386906i
$859$	5.35392	−	6.38056i	0.182673	−	0.217702i	−0.666935	−	0.745116i	$-0.732394\pi$
$859$	5.35392	−	6.38056i	0.182673	−	0.217702i	0.849608	+	0.527414i	$0.176838\pi$
$860$	50.9717	−	10.7409i	1.73812	−	0.366261i
$861$	−0.433951	+	15.5279i	−0.0147890	+	0.529190i
$862$	33.6234	−	34.7569i	1.14522	−	1.18383i
$863$	14.7765	+	25.5936i	0.502998	+	0.871218i	0.999994	+	0.00346494i	$0.00110293\pi$
$863$	14.7765	+	25.5936i	0.502998	+	0.871218i	−0.496996	+	0.867753i	$0.665564\pi$
$864$	−26.6282	−	12.4474i	−0.905910	−	0.423470i
$865$	−20.7849	+	7.56509i	−0.706708	+	0.257221i
$866$	0.405104	+	1.41746i	0.0137660	+	0.0481673i
$867$	−10.6722	+	26.9538i	−0.362447	+	0.915400i
$868$	−17.0249	+	21.7122i	−0.577862	+	0.736959i
$869$	−0.588655	−	0.701532i	−0.0199687	−	0.0237978i
$870$	−45.7393	−	46.7909i	−1.55071	−	1.58636i
$871$	46.1532	−	8.13805i	1.56384	−	0.275747i
$872$	4.56616	+	8.64253i	0.154630	+	0.292673i
$873$	−14.6615	+	4.42612i	−0.496217	+	0.149802i
$874$	15.7855	−	2.81070i	0.533952	−	0.0950735i
$875$	−39.6433			−1.34019
$876$	3.87823	+	3.21993i	0.131033	+	0.108791i
$877$	5.31290	+	30.1310i	0.179404	+	1.01745i	0.932937	+	0.360040i	$0.117237\pi$
$877$	5.31290	+	30.1310i	0.179404	+	1.01745i	−0.753533	+	0.657410i	$0.771652\pi$
$878$	−21.0547	+	15.2689i	−0.710562	+	0.515301i
$879$	23.2671	+	20.6581i	0.784779	+	0.696779i
$880$	−5.18412	−	11.7546i	−0.174757	−	0.396248i
$881$	24.6197	+	14.2142i	0.829458	+	0.478888i	0.853667	−	0.520819i	$-0.174373\pi$
$881$	24.6197	+	14.2142i	0.829458	+	0.478888i	−0.0242093	+	0.999707i	$0.507707\pi$
$882$	−8.22762	−	12.7922i	−0.277038	−	0.430736i
$883$	3.07785	+	8.45632i	0.103578	+	0.284578i	0.980646	−	0.195788i	$-0.0627263\pi$
$883$	3.07785	+	8.45632i	0.103578	+	0.284578i	−0.877068	+	0.480365i	$0.840504\pi$
$884$	0.820550	−	5.76506i	0.0275981	−	0.193900i
$885$	19.5607	−	15.5032i	0.657525	−	0.521133i
$886$	5.73602	−	5.92940i	0.192705	−	0.199202i
$887$	−1.62844	+	9.23534i	−0.0546776	+	0.310092i	−0.999865	−	0.0164364i	$-0.994768\pi$
$887$	−1.62844	+	9.23534i	−0.0546776	+	0.310092i	0.945187	+	0.326529i	$0.105879\pi$
$888$	−16.9449	+	1.85526i	−0.568632	+	0.0622584i
$889$	19.6225	+	16.4652i	0.658118	+	0.552226i
$890$	3.31975	−	46.8833i	0.111278	−	1.57153i
$891$	−7.14635	+	1.72846i	−0.239412	+	0.0579056i
$892$	8.25822	−	15.4659i	0.276506	−	0.517836i
$893$	−4.93026	−	19.5612i	−0.164985	−	0.654591i
$894$	0.697006	−	7.04393i	0.0233114	−	0.235584i
$895$	−30.6630	+	84.2460i	−1.02495	+	2.81603i
$896$	−0.601260	−	20.8989i	−0.0200867	−	0.698184i
$897$	−21.7942	−	13.4083i	−0.727687	−	0.447690i
$898$	5.73380	+	11.7823i	0.191339	+	0.393179i
$899$	8.80795	−	49.9524i	0.293762	−	1.66600i
$900$	41.4097	−	47.1321i	1.38032	−	1.57107i
$901$	−1.90716	−	3.30330i	−0.0635367	−	0.110049i
$902$	−0.581189	−	5.57673i	−0.0193515	−	0.185685i
$903$	18.6530	−	10.0853i	0.620733	−	0.335618i
$904$	−6.05269	−	1.30321i	−0.201309	−	0.0433440i
$905$	59.7486	+	34.4959i	1.98611	+	1.14668i
$906$	−7.81088	−	2.18835i	−0.259499	−	0.0727030i
$907$	0.0781550	+	0.0931416i	0.00259510	+	0.00309271i	0.767340	−	0.641240i	$-0.221580\pi$
$907$	0.0781550	+	0.0931416i	0.00259510	+	0.00309271i	−0.764745	+	0.644333i	$0.777135\pi$
$908$	−7.82698	−	19.4708i	−0.259747	−	0.646161i
$909$	18.7464	−	9.46883i	0.621779	−	0.314061i
$910$	−48.3532	−	32.6765i	−1.60289	−	1.08321i
$911$	37.0091			1.22617			0.613083	−	0.790018i	$-0.289929\pi$
$911$	37.0091			1.22617			0.613083	+	0.790018i	$0.289929\pi$
$912$	−16.7365	+	25.1374i	−0.554200	+	0.832384i
$913$	−8.74190			−0.289315
$914$	−10.1659	−	6.86997i	−0.336258	−	0.227238i
$915$	47.9250	−	15.9418i	1.58435	−	0.527019i
$916$	−8.47824	−	21.0909i	−0.280129	−	0.696863i
$917$	−8.18184	−	9.75074i	−0.270188	−	0.321998i
$918$	3.76616	−	0.0754243i	0.124302	−	0.00248937i
$919$	34.1724	+	19.7294i	1.12724	+	0.650814i	0.943240	−	0.332111i	$-0.107761\pi$
$919$	34.1724	+	19.7294i	1.12724	+	0.650814i	0.184003	+	0.982926i	$0.441094\pi$
$920$	28.2751	+	6.08793i	0.932203	+	0.200713i
$921$	6.41805	+	11.8703i	0.211482	+	0.391141i
$922$	−0.527357	−	5.06019i	−0.0173676	−	0.166649i
$923$	12.0596	+	20.8879i	0.396948	+	0.687534i
$924$	−3.38241	−	3.98860i	−0.111273	−	0.131215i
$925$	6.31797	−	35.8310i	0.207733	−	1.17812i
$926$	−21.3439	−	43.8592i	−0.701405	−	1.44130i
$927$	−16.7765	+	39.1394i	−0.551012	+	1.28551i
$928$	19.0718	+	33.3707i	0.626063	+	1.09545i
$929$	15.8720	−	43.6079i	0.520743	−	1.43073i	−0.348952	−	0.937141i	$-0.613462\pi$
$929$	15.8720	−	43.6079i	0.520743	−	1.43073i	0.869695	−	0.493589i	$-0.164315\pi$
$930$	71.5410	+	7.07908i	2.34592	+	0.232132i
$931$	−14.2592	+	6.39229i	−0.467326	+	0.209499i
$932$	−16.8995	+	31.6492i	−0.553561	+	1.03670i
$933$	−32.4430	−	6.66007i	−1.06214	−	0.218041i
$934$	1.81900	−	25.6888i	0.0595194	−	0.840564i
$935$	1.26121	+	1.05828i	0.0412459	+	0.0346094i
$936$	46.6291	−	12.1873i	1.52412	−	0.398353i
$937$	−6.38508	+	36.2116i	−0.208591	+	1.18298i	0.683096	+	0.730329i	$0.260633\pi$
$937$	−6.38508	+	36.2116i	−0.208591	+	1.18298i	−0.891687	+	0.452652i	$0.850478\pi$
$938$	−14.9930	+	15.4985i	−0.489540	+	0.506044i
$939$	13.2406	+	16.7060i	0.432092	+	0.545180i
$940$	5.12772	−	36.0266i	0.167248	−	1.17506i
$941$	17.6722	+	48.5541i	0.576098	+	1.58282i	0.794700	+	0.607003i	$0.207628\pi$
$941$	17.6722	+	48.5541i	0.576098	+	1.58282i	−0.218601	+	0.975814i	$0.570149\pi$
$942$	−10.8263	−	23.9231i	−0.352740	−	0.779458i
$943$	10.9320	+	6.31157i	0.355993	+	0.205533i
$944$	−13.4147	+	5.91628i	−0.436613	+	0.192558i
$945$	15.8365	−	34.2694i	0.515160	−	1.11479i
$946$	−6.19603	+	4.49338i	−0.201450	+	0.146092i
$947$	0.208972	+	1.18514i	0.00679067	+	0.0385118i	0.988015	−	0.154359i	$-0.0493313\pi$
$947$	0.208972	+	1.18514i	0.00679067	+	0.0385118i	−0.981224	+	0.192871i	$0.938220\pi$
$948$	−2.48058	+	2.98772i	−0.0805654	+	0.0970367i
$949$	−8.26493			−0.268291
$950$	−41.5157	−	49.3084i	−1.34695	−	1.59978i
$951$	4.25574	+	28.8226i	0.138002	+	0.934637i
$952$	1.25165	+	2.36905i	0.0405663	+	0.0767813i
$953$	−8.13061	+	1.43365i	−0.263376	+	0.0464404i	−0.303777	−	0.952743i	$-0.598248\pi$
$953$	−8.13061	+	1.43365i	−0.263376	+	0.0464404i	0.0404005	+	0.999184i	$0.487137\pi$
$954$	19.1095	−	25.1285i	0.618692	−	0.813566i
$955$	−37.2099	−	44.3450i	−1.20408	−	1.43497i
$956$	−29.9941	+	38.2521i	−0.970080	+	1.23716i
$957$	8.93900	+	3.53934i	0.288957	+	0.114411i
$958$	−7.50232	−	26.2507i	−0.242389	−	0.848120i
$959$	−9.22786	+	3.35867i	−0.297983	+	0.108457i
$960$	−45.1109	+	30.5394i	−1.45595	+	0.985656i
$961$	12.3643	+	21.4157i	0.398850	+	0.690828i
$962$	19.4330	−	20.0882i	0.626545	−	0.647668i
$963$	2.62786	+	22.0431i	0.0846815	+	0.710330i
$964$	−31.5036	+	6.63852i	−1.01466	+	0.213812i
$965$	−10.6493	+	12.6913i	−0.342812	+	0.408548i
$966$	11.7399	−	0.892808i	0.377726	−	0.0287256i
$967$	−1.37427	+	3.77577i	−0.0441934	+	0.121420i	−0.959826	−	0.280595i	$-0.909468\pi$
$967$	−1.37427	+	3.77577i	−0.0441934	+	0.121420i	0.915633	+	0.402016i	$0.131690\pi$
$968$	−21.6669	−	19.6125i	−0.696400	−	0.630370i
$969$	0.502104	−	3.83743i	0.0161299	−	0.123276i
$970$	−6.89079	+	27.5345i	−0.221250	+	0.884079i
$971$	23.1113	+	8.41181i	0.741675	+	0.269948i	0.685098	−	0.728451i	$-0.259759\pi$
$971$	23.1113	+	8.41181i	0.741675	+	0.269948i	0.0565769	+	0.998398i	$0.481981\pi$
$972$	12.6288	+	28.5046i	0.405068	+	0.914286i
$973$	−7.92967	−	6.65378i	−0.254213	−	0.213310i
$974$	22.0870	+	45.3862i	0.707714	+	1.45427i
$975$	−2.87373	+	102.830i	−0.0920330	+	3.29318i
$976$	−29.6032	+	1.96563i	−0.947576	+	0.0629184i
$977$	−27.6979	+	15.9914i	−0.886133	+	0.511609i	−0.872676	−	0.488300i	$-0.837617\pi$
$977$	−27.6979	+	15.9914i	−0.886133	+	0.511609i	−0.0134576	+	0.999909i	$0.504284\pi$
$978$	−6.73035	−	26.3104i	−0.215213	−	0.841313i
$979$	2.36195	+	6.48942i	0.0754884	+	0.207403i
$980$	−28.1728	+	0.934300i	−0.899948	+	0.0298451i
$981$	2.36772	−	10.0936i	0.0755955	−	0.322263i
$982$	−21.7363	+	48.7053i	−0.693632	+	1.55425i
$983$	32.1387	−	26.9676i	1.02506	−	0.860131i	0.0348091	−	0.999394i	$-0.488918\pi$
$983$	32.1387	−	26.9676i	1.02506	−	0.860131i	0.990255	+	0.139263i	$0.0444732\pi$
$984$	−22.8258	+	6.65239i	−0.727661	+	0.212071i
$985$	2.76400	+	15.6754i	0.0880684	+	0.499461i
$986$	−4.08119	−	2.75801i	−0.129971	−	0.0878330i
$987$	−2.16377	−	14.6544i	−0.0688734	−	0.466455i
$988$	−5.21517	−	49.2407i	−0.165917	−	1.56655i
$989$		−	17.2314i		−	0.547928i
$990$	−4.04120	+	13.0133i	−0.128438	+	0.413589i
$991$	−9.01443	+	1.58949i	−0.286353	+	0.0504917i	−0.314980	−	0.949098i	$-0.601998\pi$
$991$	−9.01443	+	1.58949i	−0.286353	+	0.0504917i	0.0286268	+	0.999590i	$0.490887\pi$
$992$	−39.6188	−	14.6173i	−1.25790	−	0.464100i
$993$	−12.6672	−	11.2468i	−0.401981	−	0.356906i
$994$	−10.1344	−	4.52279i	−0.321444	−	0.143454i
$995$	30.3496	−	52.5670i	0.962146	−	1.66649i
$996$	6.62712	+	36.4717i	0.209988	+	1.15565i
$997$	−20.8455	+	7.58714i	−0.660183	+	0.240287i	−0.650316	−	0.759664i	$-0.725363\pi$
$997$	−20.8455	+	7.58714i	−0.660183	+	0.240287i	−0.00986789	+	0.999951i	$0.503141\pi$
$998$	−2.85742	−	27.4180i	−0.0904501	−	0.867903i
$999$	14.8461	+	10.3192i	0.469709	+	0.326485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.7	yes	216
3.2	odd	2	inner	228.2.v.a.23.30	yes	216
4.3	odd	2	inner	228.2.v.a.23.35	yes	216
12.11	even	2	inner	228.2.v.a.23.2	✓	216
19.5	even	9	inner	228.2.v.a.119.2	yes	216
57.5	odd	18	inner	228.2.v.a.119.35	yes	216
76.43	odd	18	inner	228.2.v.a.119.30	yes	216
228.119	even	18	inner	228.2.v.a.119.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.2	✓	216	12.11	even	2	inner
228.2.v.a.23.7	yes	216	1.1	even	1	trivial
228.2.v.a.23.30	yes	216	3.2	odd	2	inner
228.2.v.a.23.35	yes	216	4.3	odd	2	inner
228.2.v.a.119.2	yes	216	19.5	even	9	inner
228.2.v.a.119.7	yes	216	228.119	even	18	inner
228.2.v.a.119.30	yes	216	76.43	odd	18	inner
228.2.v.a.119.35	yes	216	57.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17174 - 0.791847i) q^{2} +(0.546697 + 1.64351i) q^{3} +(0.745957 + 1.85568i) q^{4} +(-2.52711 - 3.01169i) q^{5} +(0.660820 - 2.35867i) q^{6} +(-1.60040 - 0.923992i) q^{7} +(0.595347 - 2.76506i) q^{8} +(-2.40224 + 1.79700i) q^{9} +O(q^{10})\)	\(q+(-1.17174 - 0.791847i) q^{2} +(0.546697 + 1.64351i) q^{3} +(0.745957 + 1.85568i) q^{4} +(-2.52711 - 3.01169i) q^{5} +(0.660820 - 2.35867i) q^{6} +(-1.60040 - 0.923992i) q^{7} +(0.595347 - 2.76506i) q^{8} +(-2.40224 + 1.79700i) q^{9} +(0.576319 + 5.53000i) q^{10} +(-0.408467 - 0.707485i) q^{11} +(-2.64201 + 2.24048i) q^{12} +(0.986301 - 5.59359i) q^{13} +(1.14360 + 2.34995i) q^{14} +(3.56817 - 5.79980i) q^{15} +(-2.88710 + 2.76851i) q^{16} +(0.175324 - 0.481699i) q^{17} +(4.23776 - 0.203414i) q^{18} +(0.444555 - 4.33617i) q^{19} +(3.70362 - 6.93609i) q^{20} +(0.643655 - 3.13542i) q^{21} +(-0.0816026 + 1.15243i) q^{22} +(-1.99250 - 1.67190i) q^{23} +(4.86988 - 0.533193i) q^{24} +(-1.81576 + 10.2977i) q^{25} +(-5.58496 + 5.77325i) q^{26} +(-4.26669 - 2.96569i) q^{27} +(0.520804 - 3.65909i) q^{28} +(2.32390 + 6.38485i) q^{29} +(-8.77353 + 3.97042i) q^{30} +(-6.46502 - 3.73258i) q^{31} +(5.57517 - 0.957842i) q^{32} +(0.939451 - 1.05810i) q^{33} +(-0.586866 + 0.425596i) q^{34} +(1.26161 + 7.15494i) q^{35} +(-5.12663 - 3.11731i) q^{36} -3.47952 q^{37} +(-3.95449 + 4.72885i) q^{38} +(9.73233 - 1.43701i) q^{39} +(-9.83200 + 5.19460i) q^{40} +(-4.77942 + 0.842740i) q^{41} +(-3.23697 + 3.16422i) q^{42} +(4.25838 + 5.07495i) q^{43} +(1.00817 - 1.28574i) q^{44} +(11.4827 + 2.69359i) q^{45} +(1.01080 + 3.53679i) q^{46} +(4.34889 - 1.58287i) q^{47} +(-6.12845 - 3.23143i) q^{48} +(-1.79248 - 3.10466i) q^{49} +(10.2818 - 10.6284i) q^{50} +(0.887525 + 0.0248033i) q^{51} +(11.1157 - 2.34232i) q^{52} +(4.78294 - 5.70009i) q^{53} +(2.65108 + 6.85359i) q^{54} +(-1.09849 + 3.01806i) q^{55} +(-3.50769 + 3.87511i) q^{56} +(7.36957 - 1.63994i) q^{57} +(2.33282 - 9.32157i) q^{58} +(3.44431 + 1.25363i) q^{59} +(13.4243 + 2.29499i) q^{60} +(5.68183 + 4.76762i) q^{61} +(4.61970 + 9.49293i) q^{62} +(5.50497 - 0.656272i) q^{63} +(-7.29112 - 3.29234i) q^{64} +(-19.3386 + 11.1652i) q^{65} +(-1.93865 + 0.495917i) q^{66} +(2.82204 + 7.75348i) q^{67} +(1.02466 - 0.0339810i) q^{68} +(1.65850 - 4.18871i) q^{69} +(4.18734 - 9.38274i) q^{70} +(-3.25296 + 2.72956i) q^{71} +(3.53866 + 7.71219i) q^{72} +(-0.252680 - 1.43302i) q^{73} +(4.07710 + 2.75525i) q^{74} +(-17.9170 + 2.64549i) q^{75} +(8.37816 - 2.40964i) q^{76} +1.50968i q^{77} +(-12.5417 - 6.02272i) q^{78} +(1.10397 - 0.194660i) q^{79} +(15.6339 + 1.69871i) q^{80} +(2.54156 - 8.63368i) q^{81} +(6.26756 + 2.79709i) q^{82} +(5.35043 - 9.26722i) q^{83} +(6.29847 - 1.14447i) q^{84} +(-1.89379 + 0.689282i) q^{85} +(-0.971146 - 9.31851i) q^{86} +(-9.22310 + 7.30993i) q^{87} +(-2.19942 + 0.708237i) q^{88} +(-8.32500 - 1.46792i) q^{89} +(-11.3219 - 12.2488i) q^{90} +(-6.74692 + 8.04066i) q^{91} +(1.61620 - 4.94461i) q^{92} +(2.60012 - 12.6659i) q^{93} +(-6.34916 - 1.58895i) q^{94} +(-14.1826 + 9.61910i) q^{95} +(4.62215 + 8.63920i) q^{96} +(4.79715 + 1.74602i) q^{97} +(-0.358097 + 5.05723i) q^{98} +(2.25259 + 0.965536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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