LMFDB - Embedded newform 216.2.t.a.205.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			205.18
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.000955132 + 1.41421i) q^{2} +(0.368292 + 1.69244i) q^{3} +(-2.00000 - 0.00270152i) q^{4} +(-0.355965 + 0.978005i) q^{5} +(-2.39383 + 0.519227i) q^{6} +(-0.272085 + 1.54307i) q^{7} +(0.00573079 - 2.82842i) q^{8} +(-2.72872 + 1.24663i) q^{9} +(-1.38277 - 0.504344i) q^{10} +(-1.44773 - 3.97760i) q^{11} +(-0.732011 - 3.38588i) q^{12} +(4.33941 + 5.17151i) q^{13} +(-2.18198 - 0.386261i) q^{14} +(-1.78632 - 0.242259i) q^{15} +(3.99999 + 0.0108061i) q^{16} +(-0.494959 - 0.857294i) q^{17} +(-1.76039 - 3.86019i) q^{18} +(-2.70129 - 1.55959i) q^{19} +(0.714571 - 1.95505i) q^{20} +(-2.71177 + 0.107812i) q^{21} +(5.62656 - 2.04360i) q^{22} +(1.17888 + 6.68573i) q^{23} +(4.78905 - 1.03199i) q^{24} +(3.00044 + 2.51767i) q^{25} +(-7.31776 + 6.13191i) q^{26} +(-3.11481 - 4.15908i) q^{27} +(0.548339 - 3.08541i) q^{28} +(2.84964 - 3.39607i) q^{29} +(0.344311 - 2.52600i) q^{30} +(-0.409166 - 2.32049i) q^{31} +(-0.0191026 + 5.65682i) q^{32} +(6.19868 - 3.91512i) q^{33} +(1.21287 - 0.699158i) q^{34} +(-1.41228 - 0.815381i) q^{35} +(5.46081 - 2.48588i) q^{36} +(3.19157 - 1.84266i) q^{37} +(2.20817 - 3.81871i) q^{38} +(-7.15431 + 9.24883i) q^{39} +(2.76417 + 1.01242i) q^{40} +(-2.44191 + 2.04900i) q^{41} +(-0.149880 - 3.83512i) q^{42} +(3.71087 + 10.1955i) q^{43} +(2.88471 + 7.95911i) q^{44} +(-0.247877 - 3.11246i) q^{45} +(-9.45618 + 1.66079i) q^{46} +(-0.155220 + 0.880296i) q^{47} +(1.45487 + 6.77372i) q^{48} +(4.27080 + 1.55445i) q^{49} +(-3.56338 + 4.24086i) q^{50} +(1.26863 - 1.15342i) q^{51} +(-8.66484 - 10.3547i) q^{52} +5.00251i q^{53} +(5.88481 - 4.40103i) q^{54} +4.40546 q^{55} +(4.36290 + 0.778415i) q^{56} +(1.64465 - 5.14616i) q^{57} +(4.80005 + 4.03325i) q^{58} +(3.85475 - 10.5908i) q^{59} +(3.57198 + 0.489342i) q^{60} +(5.41575 + 0.954943i) q^{61} +(3.28206 - 0.576431i) q^{62} +(-1.18119 - 4.54981i) q^{63} +(-7.99993 - 0.0324182i) q^{64} +(-6.60244 + 2.40309i) q^{65} +(5.53089 + 8.76999i) q^{66} +(0.467287 + 0.556891i) q^{67} +(0.987601 + 1.71592i) q^{68} +(-10.8810 + 4.45748i) q^{69} +(1.15447 - 1.99649i) q^{70} +(-2.52073 - 4.36603i) q^{71} +(3.51034 + 7.72512i) q^{72} +(7.01816 - 12.1558i) q^{73} +(2.60286 + 4.51532i) q^{74} +(-3.15597 + 6.00531i) q^{75} +(5.39836 + 3.12648i) q^{76} +(6.53164 - 1.15170i) q^{77} +(-13.0730 - 10.1266i) q^{78} +(-6.78017 - 5.68924i) q^{79} +(-1.43442 + 3.90816i) q^{80} +(5.89185 - 6.80339i) q^{81} +(-2.89539 - 3.45533i) q^{82} +(4.03223 - 4.80543i) q^{83} +(5.42383 - 0.208299i) q^{84} +(1.01463 - 0.178906i) q^{85} +(-14.4222 + 5.23823i) q^{86} +(6.79716 + 3.57211i) q^{87} +(-11.2586 + 4.07199i) q^{88} +(4.02279 - 6.96768i) q^{89} +(4.40192 - 0.347578i) q^{90} +(-9.16071 + 5.28894i) q^{91} +(-2.33969 - 13.3746i) q^{92} +(3.77661 - 1.54711i) q^{93} +(-1.24478 - 0.220355i) q^{94} +(2.48685 - 2.08672i) q^{95} +(-9.58088 + 2.05103i) q^{96} +(-10.1365 + 3.68937i) q^{97} +(-2.20240 + 6.03834i) q^{98} +(8.90903 + 9.04900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.000955132		1.41421i	−0.000675380		1.00000i
$2$	−0.000955132		1.41421i	−0.000675380		1.00000i
$3$	0.368292	+	1.69244i	0.212633	+	0.977132i
$3$	0.368292	+	1.69244i	0.212633	+	0.977132i
$4$	−2.00000	−	0.00270152i	−0.999999	−	0.00135076i
$5$	−0.355965	+	0.978005i	−0.159192	+	0.437377i	−0.993488	−	0.113941i	$-0.963653\pi$
$5$	−0.355965	+	0.978005i	−0.159192	+	0.437377i	0.834295	+	0.551318i	$0.185875\pi$
$6$	−2.39383	+	0.519227i	−0.977275	+	0.211973i
$7$	−0.272085	+	1.54307i	−0.102839	+	0.583227i	0.889223	+	0.457474i	$0.151246\pi$
$7$	−0.272085	+	1.54307i	−0.102839	+	0.583227i	−0.992062	+	0.125753i	$0.959865\pi$
$8$	0.00573079	−	2.82842i	0.00202614	−	0.999998i
$9$	−2.72872	+	1.24663i	−0.909574	+	0.415542i
$10$	−1.38277	−	0.504344i	−0.437270	−	0.159488i
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	−0.941750	−	0.336315i	$-0.890819\pi$
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	0.505243	−	0.862977i	$-0.331403\pi$
$12$	−0.732011	−	3.38588i	−0.211313	−	0.977418i
$13$	4.33941	+	5.17151i	1.20354	+	1.43432i	0.871039	+	0.491214i	$0.163447\pi$
$13$	4.33941	+	5.17151i	1.20354	+	1.43432i	0.332497	+	0.943104i	$0.392109\pi$
$14$	−2.18198	−	0.386261i	−0.583157	−	0.103233i
$15$	−1.78632	−	0.242259i	−0.461225	−	0.0625509i
$16$	3.99999	+	0.0108061i	0.999996	+	0.00270152i
$17$	−0.494959	−	0.857294i	−0.120045	−	0.207924i	0.799740	−	0.600346i	$-0.204971\pi$
$17$	−0.494959	−	0.857294i	−0.120045	−	0.207924i	−0.919785	+	0.392422i	$0.871637\pi$
$18$	−1.76039	−	3.86019i	−0.414927	−	0.909855i
$19$	−2.70129	−	1.55959i	−0.619719	−	0.357795i	0.157041	−	0.987592i	$-0.449805\pi$
$19$	−2.70129	−	1.55959i	−0.619719	−	0.357795i	−0.776759	+	0.629797i	$0.783138\pi$
$20$	0.714571	−	1.95505i	0.159783	−	0.437162i
$21$	−2.71177	+	0.107812i	−0.591757	+	0.0235266i
$22$	5.62656	−	2.04360i	1.19959	−	0.435697i
$23$	1.17888	+	6.68573i	0.245812	+	1.39407i	0.818598	+	0.574367i	$0.194752\pi$
$23$	1.17888	+	6.68573i	0.245812	+	1.39407i	−0.572786	+	0.819705i	$0.694137\pi$
$24$	4.78905	−	1.03199i	0.977561	−	0.210653i
$25$	3.00044	+	2.51767i	0.600088	+	0.503533i
$26$	−7.31776	+	6.13191i	−1.43513	+	1.20257i
$27$	−3.11481	−	4.15908i	−0.599445	−	0.800416i
$28$	0.548339	−	3.08541i	0.103626	−	0.583088i
$29$	2.84964	−	3.39607i	0.529166	−	0.630635i	−0.433557	−	0.901126i	$-0.642742\pi$
$29$	2.84964	−	3.39607i	0.529166	−	0.630635i	0.962722	+	0.270491i	$0.0871861\pi$
$30$	0.344311	−	2.52600i	0.0628624	−	0.461183i
$31$	−0.409166	−	2.32049i	−0.0734883	−	0.416773i	−0.999252	−	0.0386704i	$-0.987688\pi$
$31$	−0.409166	−	2.32049i	−0.0734883	−	0.416773i	0.925764	−	0.378103i	$-0.123423\pi$
$32$	−0.0191026	+	5.65682i	−0.00337689	+	0.999994i
$33$	6.19868	−	3.91512i	1.07905	−	0.681534i
$34$	1.21287	−	0.699158i	0.208005	−	0.119905i
$35$	−1.41228	−	0.815381i	−0.238719	−	0.137825i
$36$	5.46081	−	2.48588i	0.910135	−	0.414313i
$37$	3.19157	−	1.84266i	0.524691	−	0.302931i	−0.214161	−	0.976798i	$-0.568702\pi$
$37$	3.19157	−	1.84266i	0.524691	−	0.302931i	0.738852	+	0.673868i	$0.235368\pi$
$38$	2.20817	−	3.81871i	0.358213	−	0.619477i
$39$	−7.15431	+	9.24883i	−1.14561	+	1.48100i
$40$	2.76417	+	1.01242i	0.437054	+	0.160078i
$41$	−2.44191	+	2.04900i	−0.381362	+	0.320000i	−0.813237	−	0.581933i	$-0.802297\pi$
$41$	−2.44191	+	2.04900i	−0.381362	+	0.320000i	0.431875	+	0.901933i	$0.357852\pi$
$42$	−0.149880	−	3.83512i	−0.0231269	−	0.591772i
$43$	3.71087	+	10.1955i	0.565903	+	1.55481i	0.810841	+	0.585267i	$0.199010\pi$
$43$	3.71087	+	10.1955i	0.565903	+	1.55481i	−0.244938	+	0.969539i	$0.578767\pi$
$44$	2.88471	+	7.95911i	0.434886	+	1.19988i
$45$	−0.247877	−	3.11246i	−0.0369513	−	0.463978i
$46$	−9.45618	+	1.66079i	−1.39424	+	0.244871i
$47$	−0.155220	+	0.880296i	−0.0226411	+	0.128404i	−0.994033	−	0.109077i	$-0.965211\pi$
$47$	−0.155220	+	0.880296i	−0.0226411	+	0.128404i	0.971392	+	0.237481i	$0.0763217\pi$
$48$	1.45487	+	6.77372i	0.209993	+	0.977703i
$49$	4.27080	+	1.55445i	0.610115	+	0.222064i
$50$	−3.56338	+	4.24086i	−0.503939	+	0.599748i
$51$	1.26863	−	1.15342i	0.177644	−	0.161512i
$52$	−8.66484	−	10.3547i	−1.20160	−	1.43594i
$53$			5.00251i			0.687148i	0.939126	+	0.343574i	$0.111638\pi$
$53$			5.00251i			0.687148i	−0.939126	+	0.343574i	$0.888362\pi$
$54$	5.88481	−	4.40103i	0.800821	−	0.598904i
$55$	4.40546			0.594032
$56$	4.36290	+	0.778415i	0.583017	+	0.104020i
$57$	1.64465	−	5.14616i	0.217840	−	0.681626i
$58$	4.80005	+	4.03325i	0.630278	+	0.529591i
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	−0.387625	−	0.921817i	$-0.626704\pi$
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	0.889470	−	0.456993i	$-0.151073\pi$
$60$	3.57198	+	0.489342i	0.461140	+	0.0631738i
$61$	5.41575	+	0.954943i	0.693416	+	0.122268i	0.509239	−	0.860625i	$-0.329927\pi$
$61$	5.41575	+	0.954943i	0.693416	+	0.122268i	0.184177	+	0.982893i	$0.441038\pi$
$62$	3.28206	−	0.576431i	0.416823	−	0.0732068i
$63$	−1.18119	−	4.54981i	−0.148816	−	0.573222i
$64$	−7.99993	−	0.0324182i	−0.999992	−	0.00405227i
$65$	−6.60244	+	2.40309i	−0.818932	+	0.298067i
$66$	5.53089	+	8.76999i	0.680805	+	1.07951i
$67$	0.467287	+	0.556891i	0.0570882	+	0.0680351i	0.793833	−	0.608136i	$-0.208082\pi$
$67$	0.467287	+	0.556891i	0.0570882	+	0.0680351i	−0.736745	+	0.676171i	$0.763638\pi$
$68$	0.987601	+	1.71592i	0.119764	+	0.208086i
$69$	−10.8810	+	4.45748i	−1.30992	+	0.536617i
$70$	1.15447	−	1.99649i	0.137986	−	0.238626i
$71$	−2.52073	−	4.36603i	−0.299155	−	0.518152i	0.676788	−	0.736178i	$-0.263372\pi$
$71$	−2.52073	−	4.36603i	−0.299155	−	0.518152i	−0.975943	+	0.218026i	$0.930038\pi$
$72$	3.51034	+	7.72512i	0.413698	+	0.910414i
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	−0.0832165	−	0.996531i	$-0.526519\pi$
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	0.904630	−	0.426198i	$-0.140147\pi$
$74$	2.60286	+	4.51532i	0.302576	+	0.524896i
$75$	−3.15597	+	6.00531i	−0.364420	+	0.693433i
$76$	5.39836	+	3.12648i	0.619235	+	0.358631i
$77$	6.53164	−	1.15170i	0.744349	−	0.131249i
$78$	−13.0730	−	10.1266i	−1.48022	−	1.14661i
$79$	−6.78017	−	5.68924i	−0.762829	−	0.640090i	0.176032	−	0.984384i	$-0.443674\pi$
$79$	−6.78017	−	5.68924i	−0.762829	−	0.640090i	−0.938862	+	0.344295i	$0.888118\pi$
$80$	−1.43442	+	3.90816i	−0.160373	+	0.436946i
$81$	5.89185	−	6.80339i	0.654650	−	0.755932i
$82$	−2.89539	−	3.45533i	−0.319743	−	0.381578i
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	−0.497917	−	0.867225i	$-0.665902\pi$
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	0.940512	+	0.339760i	$0.110346\pi$
$84$	5.42383	−	0.208299i	0.591788	−	0.0227272i
$85$	1.01463	−	0.178906i	0.110052	−	0.0194051i
$86$	−14.4222	+	5.23823i	−1.55519	+	0.564853i
$87$	6.79716	+	3.57211i	0.728732	+	0.382971i
$88$	−11.2586	+	4.07199i	−1.20017	+	0.434076i
$89$	4.02279	−	6.96768i	0.426415	−	0.738573i	−0.570136	−	0.821550i	$-0.693110\pi$
$89$	4.02279	−	6.96768i	0.426415	−	0.738573i	0.996551	+	0.0829775i	$0.0264430\pi$
$90$	4.40192	−	0.347578i	0.464003	−	0.0366380i
$91$	−9.16071	+	5.28894i	−0.960303	+	0.554431i
$92$	−2.33969	−	13.3746i	−0.243929	−	1.39440i
$93$	3.77661	−	1.54711i	0.391616	−	0.160428i
$94$	−1.24478	−	0.220355i	−0.128389	−	0.0227279i
$95$	2.48685	−	2.08672i	0.255146	−	0.214093i
$96$	−9.58088	+	2.05103i	−0.977845	+	0.209333i
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.800777	−	0.598963i	$-0.795580\pi$
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.228425	+	0.973561i	$0.573358\pi$
$98$	−2.20240	+	6.03834i	−0.222476	+	0.609965i
$99$	8.90903	+	9.04900i	0.895391	+	0.909458i
$100$	−5.99407	−	5.04344i	−0.599407	−	0.504344i
$101$	−6.50659	−	1.14729i	−0.647430	−	0.114159i	−0.159716	−	0.987163i	$-0.551058\pi$
$101$	−6.50659	−	1.14729i	−0.647430	−	0.114159i	−0.487714	+	0.873004i	$0.662169\pi$
$102$	1.62998	+	1.79522i	0.161392	+	0.177753i
$103$	−14.9315	−	5.43464i	−1.47125	−	0.535491i	−0.522809	−	0.852450i	$-0.675116\pi$
$103$	−14.9315	−	5.43464i	−1.47125	−	0.535491i	−0.948439	+	0.316959i	$0.897338\pi$
$104$	14.6521	−	12.2440i	1.43675	−	1.20063i
$105$	0.859854	−	2.69050i	0.0839131	−	0.262566i
$106$	−7.07462	−	0.00477806i	−0.687148	−	0.000464086i
$107$		−	3.85513i		−	0.372689i	−0.982484	−	0.186345i	$-0.940336\pi$
$107$		−	3.85513i		−	0.372689i	0.982484	−	0.186345i	$-0.0596641\pi$
$108$	6.21837	+	8.32657i	0.598363	+	0.801225i
$109$		−	3.32803i		−	0.318767i	−0.987217	−	0.159384i	$-0.949049\pi$
$109$		−	3.32803i		−	0.318767i	0.987217	−	0.159384i	$-0.0509507\pi$
$110$	−0.00420779	+	6.23026i	−0.000401197	+	0.594032i
$111$	4.29402	+	4.72292i	0.407570	+	0.448279i
$112$	−1.10501	+	6.16933i	−0.104414	+	0.582947i
$113$	7.85208	+	2.85792i	0.738662	+	0.268851i	0.683827	−	0.729645i	$-0.260314\pi$
$113$	7.85208	+	2.85792i	0.738662	+	0.268851i	0.0548351	+	0.998495i	$0.482537\pi$
$114$	7.27620	+	2.33081i	0.681479	+	0.218300i
$115$	−6.95832	−	1.22694i	−0.648867	−	0.114413i
$116$	−5.70846	+	6.78444i	−0.530017	+	0.629920i
$117$	−18.2880	−	8.70199i	−1.69072	−	0.804499i
$118$	14.9740	+	5.46156i	1.37847	+	0.502777i
$119$	1.45754	−	0.530501i	0.133612	−	0.0486309i
$120$	−0.695446	+	5.05107i	−0.0634853	+	0.461097i
$121$	−5.29891	+	4.44632i	−0.481719	+	0.404211i
$122$	−1.35567	+	7.65811i	−0.122736	+	0.693333i
$123$	−4.36715	−	3.37815i	−0.393773	−	0.304598i
$124$	0.812062	+	4.64209i	0.0729253	+	0.416872i
$125$	−8.03702	+	4.64017i	−0.718853	+	0.415030i
$126$	6.43553	−	1.66611i	0.573322	−	0.148429i
$127$	1.83012	−	3.16986i	0.162397	−	0.281280i	−0.773331	−	0.634003i	$-0.781411\pi$
$127$	1.83012	−	3.16986i	0.162397	−	0.281280i	0.935728	+	0.352723i	$0.114744\pi$
$128$	0.0534872	−	11.3136i	0.00472764	−	0.999989i
$129$	−15.8887	+	10.0354i	−1.39892	+	0.883566i
$130$	−3.39218	−	9.33955i	−0.297514	−	0.819133i
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.578930	−	0.815378i	$-0.696529\pi$
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.265140	+	0.964210i	$0.585418\pi$
$132$	−12.4079	+	7.81348i	−1.07997	+	0.680076i
$133$	3.14155	−	3.74395i	0.272407	−	0.324641i
$134$	−0.788009	+	0.660312i	−0.0680736	+	0.0570423i
$135$	5.17637	−	1.56581i	0.445511	−	0.134764i
$136$	−2.42762	+	1.39504i	−0.208167	+	0.119624i
$137$	−16.9231	−	14.2001i	−1.44583	−	1.21320i	−0.935550	−	0.353193i	$-0.885096\pi$
$137$	−16.9231	−	14.2001i	−1.44583	−	1.21320i	−0.510284	−	0.860006i	$-0.670460\pi$
$138$	−6.29343	−	15.3924i	−0.535733	−	1.31029i
$139$	4.68849	−	0.826707i	0.397672	−	0.0701203i	0.0287641	−	0.999586i	$-0.490843\pi$
$139$	4.68849	−	0.826707i	0.397672	−	0.0701203i	0.368908	+	0.929466i	$0.379732\pi$
$140$	2.82236	+	1.63458i	0.238533	+	0.138147i
$141$	−1.54702	+	0.0615050i	−0.130282	+	0.00517966i
$142$	6.17690	−	3.56068i	0.518354	−	0.298805i
$143$	14.2879	−	24.7474i	1.19482	−	2.06948i
$144$	−10.9283	+	4.95700i	−0.910693	+	0.413083i
$145$	2.30701	+	3.99585i	0.191586	+	0.331837i
$146$	17.1842	+	9.93678i	1.42217	+	0.822374i
$147$	−1.05791	+	7.80058i	−0.0872547	+	0.643381i
$148$	−6.38812	+	3.67668i	−0.525100	+	0.302222i
$149$	14.7916	+	17.6280i	1.21178	+	1.44414i	0.861700	+	0.507418i	$0.169400\pi$
$149$	14.7916	+	17.6280i	1.21178	+	1.44414i	0.350076	+	0.936721i	$0.386156\pi$
$150$	−8.48977	−	4.46895i	−0.693187	−	0.364888i
$151$	18.6779	−	6.79819i	1.51998	−	0.553229i	0.558840	−	0.829276i	$-0.311247\pi$
$151$	18.6779	−	6.79819i	1.51998	−	0.553229i	0.961144	+	0.276047i	$0.0890245\pi$
$152$	−4.42666	+	7.63145i	−0.359050	+	0.618992i
$153$	2.41933	+	1.72229i	0.195591	+	0.139239i
$154$	1.62252	+	9.23823i	0.130746	+	0.744438i
$155$	2.41510	+	0.425848i	0.193986	+	0.0342049i
$156$	14.3336	−	18.4783i	1.14761	−	1.47945i
$157$	1.67263	−	4.59552i	0.133491	−	0.366762i	−0.854880	−	0.518825i	$-0.826369\pi$
$157$	1.67263	−	4.59552i	0.133491	−	0.366762i	0.988371	+	0.152063i	$0.0485917\pi$
$158$	8.05228	−	9.58318i	0.640605	−	0.762397i
$159$	−8.46647	+	1.84239i	−0.671435	+	0.146111i
$160$	−5.52560	−	2.03231i	−0.436837	−	0.160668i
$161$	−10.6373			−0.838339
$162$	9.61582	+	8.33883i	0.755490	+	0.655160i
$163$		−	4.18081i		−	0.327466i	−0.986505	−	0.163733i	$-0.947646\pi$
$163$		−	4.18081i		−	0.327466i	0.986505	−	0.163733i	$-0.0523536\pi$
$164$	4.88934	−	4.09140i	0.381794	−	0.319485i
$165$	1.62249	+	7.45598i	0.126311	+	0.580447i
$166$	6.79205	+	5.70703i	0.527165	+	0.442951i
$167$	5.72775	+	2.08473i	0.443227	+	0.161321i	0.553986	−	0.832526i	$-0.313106\pi$
$167$	5.72775	+	2.08473i	0.443227	+	0.161321i	−0.110759	+	0.993847i	$0.535328\pi$
$168$	0.289398	+	7.67065i	0.0223276	+	0.591803i
$169$	−5.65659	+	32.0801i	−0.435122	+	2.46770i
$170$	0.252042	+	1.43507i	0.0193307	+	0.110065i
$171$	9.31530	+	0.888193i	0.712359	+	0.0679218i
$172$	−7.39420	−	20.4011i	−0.563802	−	1.55557i
$173$	0.453627	+	1.24633i	0.0344886	+	0.0947567i	0.955742	−	0.294207i	$-0.0950554\pi$
$173$	0.453627	+	1.24633i	0.0344886	+	0.0947567i	−0.921253	+	0.388964i	$0.872833\pi$
$174$	−5.05822	+	9.60922i	−0.383463	+	0.728473i
$175$	−4.70132	+	3.94488i	−0.355386	+	0.298205i
$176$	−5.74791	−	15.9260i	−0.433265	−	1.20047i
$177$	19.3441	+	2.62342i	1.45399	+	0.197189i
$178$	9.84994	+	5.69574i	0.738284	+	0.426914i
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	−0.0922343	−	0.995737i	$-0.529401\pi$
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	0.816217	+	0.577746i	$0.196068\pi$
$180$	0.487345	+	6.22558i	0.0363246	+	0.464028i
$181$	−3.21058	−	1.85363i	−0.238641	−	0.137779i	0.375911	−	0.926656i	$-0.377330\pi$
$181$	−3.21058	−	1.85363i	−0.238641	−	0.137779i	−0.614552	+	0.788876i	$0.710663\pi$
$182$	−7.47093	−	12.9602i	−0.553783	−	0.960677i
$183$	0.378391	+	9.51754i	0.0279714	+	0.703557i
$184$	18.9168	−	3.29604i	1.39457	−	0.242987i
$185$	0.666039	+	3.77730i	0.0489682	+	0.277712i
$186$	2.18433	+	5.34241i	0.160163	+	0.391725i
$187$	−2.69341	+	3.20988i	−0.196961	+	0.234730i
$188$	0.312818	−	1.76017i	0.0228146	−	0.128374i
$189$	7.26526	−	3.67475i	0.528470	−	0.267299i
$190$	2.94869	+	3.51893i	0.213920	+	0.255290i
$191$	13.8306	+	11.6053i	1.00075	+	0.839729i	0.987088	−	0.160178i	$-0.0512067\pi$
$191$	13.8306	+	11.6053i	1.00075	+	0.839729i	0.0136618	+	0.999907i	$0.495651\pi$
$192$	−2.89144	−	13.5514i	−0.208672	−	0.977986i
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	0.999900	−	0.0141163i	$-0.00449352\pi$
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	−0.944427	+	0.328721i	$0.893382\pi$
$194$	−5.20788	−	14.3386i	−0.373904	−	1.02945i
$195$	−6.49872	−	10.2892i	−0.465383	−	0.736826i
$196$	−8.53740	−	3.12043i	−0.609814	−	0.222888i
$197$	−14.1519	−	8.17063i	−1.00828	−	0.582133i	−0.0975957	−	0.995226i	$-0.531115\pi$
$197$	−14.1519	−	8.17063i	−1.00828	−	0.582133i	−0.910689	+	0.413093i	$0.864449\pi$
$198$	−12.8057	+	12.5906i	−0.910063	+	0.894777i
$199$	−0.458824	−	0.794707i	−0.0325252	−	0.0563353i	0.849305	−	0.527903i	$-0.177022\pi$
$199$	−0.458824	−	0.794707i	−0.0325252	−	0.0563353i	−0.881830	+	0.471568i	$0.843688\pi$
$200$	7.13822	−	8.47208i	0.504748	−	0.599066i
$201$	−0.770408	+	0.995955i	−0.0543404	+	0.0702493i
$202$	1.62872	−	9.20061i	0.114597	−	0.647352i
$203$	4.46504	+	5.32123i	0.313385	+	0.373477i
$204$	−2.54038	+	2.30342i	−0.177862	+	0.161272i
$205$	−1.13470	−	3.11757i	−0.0792511	−	0.217741i
$206$	7.70000	−	21.1112i	0.536484	−	1.47089i
$207$	−11.5514	−	16.7739i	−0.802880	−	1.16587i
$208$	17.3017	+	20.7328i	1.19966	+	1.43756i
$209$	−2.29270	+	13.0025i	−0.158589	+	0.899403i
$210$	3.80412	+	1.21859i	0.262509	+	0.0840904i
$211$	2.09734	−	5.76240i	0.144387	−	0.396700i	−0.846327	−	0.532664i	$-0.821191\pi$
$211$	2.09734	−	5.76240i	0.144387	−	0.396700i	0.990714	+	0.135964i	$0.0434131\pi$
$212$	0.0135144	−	10.0050i	0.000928172	−	0.687148i
$213$	6.46089	−	5.87416i	0.442693	−	0.402491i
$214$	5.45197	+	0.00368215i	0.372689	+	0.000251707i
$215$	−11.2922			−0.770124
$216$	−11.7815	+	8.78615i	−0.801629	+	0.597822i
$217$	3.69202			0.250631
$218$	4.70654	+	0.00317870i	0.318767	+	0.000215289i
$219$	23.1577	+	7.40094i	1.56485	+	0.500109i
$220$	−8.81091	−	0.0119014i	−0.594031	−	0.000802394i
$221$	2.28567	−	6.27983i	0.153751	−	0.422427i
$222$	−6.68331	+	6.06815i	−0.448555	+	0.407267i
$223$	−3.72326	+	21.1156i	−0.249328	+	1.41401i	0.560896	+	0.827887i	$0.310457\pi$
$223$	−3.72326	+	21.1156i	−0.249328	+	1.41401i	−0.810223	+	0.586121i	$0.800654\pi$
$224$	−8.72369	−	1.56862i	−0.582876	−	0.104808i
$225$	−11.3260	−	3.12959i	−0.755063	−	0.208639i
$226$	−4.04921	+	11.1018i	−0.269350	+	0.738480i
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	0.950319	+	0.311279i	$0.100757\pi$
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	−0.527900	+	0.849307i	$0.677020\pi$
$228$	−3.30321	+	10.2879i	−0.218760	+	0.681331i
$229$	−5.70813	−	6.80268i	−0.377204	−	0.449534i	0.543726	−	0.839263i	$-0.317013\pi$
$229$	−5.70813	−	6.80268i	−0.377204	−	0.449534i	−0.920930	+	0.389729i	$0.872569\pi$
$230$	1.74180	−	9.83938i	0.114851	−	0.648789i
$231$	4.35474	+	10.6303i	0.286521	+	0.699420i
$232$	−9.58920	−	8.07946i	−0.629562	−	0.530442i
$233$	9.39731	+	16.2766i	0.615638	+	1.06632i	0.990272	+	0.139144i	$0.0444350\pi$
$233$	9.39731	+	16.2766i	0.615638	+	1.06632i	−0.374634	+	0.927173i	$0.622232\pi$
$234$	12.3239	−	25.8548i	0.805641	−	1.69018i
$235$	−0.805681	−	0.465160i	−0.0525568	−	0.0303437i
$236$	−7.73811	+	21.1712i	−0.503708	+	1.37813i
$237$	7.13163	−	13.5704i	0.463249	−	0.881489i
$238$	0.748849	+	2.06178i	0.0485407	+	0.133645i
$239$	3.56653	+	20.2268i	0.230700	+	1.30836i	0.851483	+	0.524382i	$0.175703\pi$
$239$	3.56653	+	20.2268i	0.230700	+	1.30836i	−0.620784	+	0.783982i	$0.713185\pi$
$240$	−7.14262	−	0.988334i	−0.461054	−	0.0637967i
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	0.236166	−	0.971713i	$-0.424109\pi$
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	−0.915941	+	0.401314i	$0.868554\pi$
$242$	−6.28298	−	7.49804i	−0.403885	−	0.481992i
$243$	13.6843	+	7.46598i	0.877846	+	0.478943i
$244$	−10.8289	−	1.92451i	−0.693250	−	0.123204i
$245$	−3.04051	+	3.62354i	−0.194251	+	0.231499i
$246$	4.78160	−	6.17286i	0.304864	−	0.393567i
$247$	−3.65657	−	20.7374i	−0.232662	−	1.31949i
$248$	−6.56568	+	1.14399i	−0.416921	+	0.0726437i
$249$	9.61795	+	5.05452i	0.609513	+	0.320317i
$250$	−6.55452	−	11.3705i	−0.414544	−	0.719133i
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	0.513168	−	0.858288i	$-0.328472\pi$
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	−0.486715	+	0.873561i	$0.661805\pi$
$252$	2.35008	+	9.10280i	0.148041	+	0.573422i
$253$	24.8865	−	14.3682i	1.56460	−	0.903323i
$254$	4.48111	+	2.59121i	0.281170	+	0.162587i
$255$	0.676466	+	1.65131i	0.0423620	+	0.103409i
$256$	15.9998	+	0.0864482i	0.999985	+	0.00540301i
$257$	13.5896	−	11.4030i	0.847695	−	0.711300i	−0.111586	−	0.993755i	$-0.535593\pi$
$257$	13.5896	−	11.4030i	0.847695	−	0.711300i	0.959281	+	0.282454i	$0.0911486\pi$
$258$	−14.1770	−	22.4796i	−0.882621	−	1.39952i
$259$	1.97497	+	5.42619i	0.122719	+	0.337167i
$260$	13.2114	−	4.78834i	0.819334	−	0.296960i
$261$	−3.54226	+	12.8194i	−0.219260	+	0.793500i
$262$	−2.39983	−	13.6641i	−0.148262	−	0.844170i
$263$	1.39832	−	7.93029i	0.0862243	−	0.489002i	−0.910861	−	0.412712i	$-0.864581\pi$
$263$	1.39832	−	7.93029i	0.0862243	−	0.489002i	0.997086	−	0.0762899i	$-0.0243074\pi$
$264$	−11.0381	−	17.5549i	−0.679347	−	1.08043i
$265$	−4.89249	−	1.78072i	−0.300543	−	0.109389i
$266$	5.29174	+	4.44639i	0.324457	+	0.272626i
$267$	13.2740	+	4.24220i	0.812353	+	0.259619i
$268$	−0.933069	−	1.11504i	−0.0569963	−	0.0681121i
$269$			6.56538i			0.400298i	0.979765	+	0.200149i	$0.0641426\pi$
$269$			6.56538i			0.400298i	−0.979765	+	0.200149i	$0.935857\pi$
$270$	2.20945	+	7.32198i	0.134463	+	0.445602i
$271$	10.8623			0.659839			0.329919	−	0.944009i	$-0.392978\pi$
$271$	10.8623			0.659839			0.329919	+	0.944009i	$0.392978\pi$
$272$	−1.97056	−	3.43451i	−0.119483	−	0.208248i
$273$	−12.3250	−	13.5561i	−0.745945	−	0.820452i
$274$	20.0982	−	23.9193i	1.21418	−	1.44501i
$275$	5.67046	−	15.5795i	0.341941	−	0.939476i
$276$	21.7741	−	8.88555i	1.31065	−	0.534847i
$277$	−31.2235	−	5.50555i	−1.87604	−	0.330796i	−0.885131	−	0.465342i	$-0.845931\pi$
$277$	−31.2235	−	5.50555i	−1.87604	−	0.330796i	−0.990907	+	0.134546i	$0.957043\pi$
$278$	1.16466	+	6.63131i	0.0698517	+	0.397719i
$279$	4.00929	+	5.82191i	0.240030	+	0.348549i
$280$	−2.31433	+	3.98985i	−0.138308	+	0.238439i
$281$	−18.4488	+	6.71481i	−1.10056	+	0.400572i	−0.827523	−	0.561431i	$-0.810251\pi$
$281$	−18.4488	+	6.71481i	−1.10056	+	0.400572i	−0.273039	+	0.962003i	$0.588029\pi$
$282$	−0.0855036	−	2.18787i	−0.00509166	−	0.130286i
$283$	−12.6768	−	15.1076i	−0.753556	−	0.898053i	0.243866	−	0.969809i	$-0.421584\pi$
$283$	−12.6768	−	15.1076i	−0.753556	−	0.898053i	−0.997422	+	0.0717558i	$0.977140\pi$
$284$	5.02965	+	8.73886i	0.298455	+	0.518556i
$285$	4.44754	+	3.44033i	0.263449	+	0.203788i
$286$	34.9844	+	20.2298i	2.06867	+	1.19621i
$287$	−2.49735	−	4.32554i	−0.147414	−	0.255329i
$288$	−6.99981	−	15.4597i	−0.412468	−	0.910972i
$289$	8.01003	−	13.8738i	0.471178	−	0.816105i
$290$	−5.65319	+	3.25878i	−0.331967	+	0.191362i
$291$	−9.97723	−	15.7966i	−0.584875	−	0.926014i
$292$	−14.0691	+	24.2926i	−0.823334	+	1.42162i
$293$	−26.1866	+	4.61741i	−1.52984	+	0.269752i	−0.874292	−	0.485401i	$-0.838674\pi$
$293$	−26.1866	+	4.61741i	−1.52984	+	0.269752i	−0.655549	+	0.755153i	$0.727563\pi$
$294$	−11.0307	−	1.50356i	−0.643322	−	0.0876892i
$295$	8.98574	+	7.53993i	0.523170	+	0.438992i
$296$	−5.19351	−	9.03767i	−0.301867	−	0.525304i
$297$	−12.0338	+	18.4107i	−0.698271	+	1.06830i
$298$	−24.9438	+	20.9017i	−1.44496	+	1.21080i
$299$	−29.4597	+	35.1087i	−1.70370	+	2.03039i
$300$	6.32816	−	12.0021i	0.365356	−	0.692940i
$301$	−16.7421	+	2.95209i	−0.965001	+	0.170156i
$302$	9.59625	+	26.4210i	0.552202	+	1.52036i
$303$	−0.454606	−	11.4346i	−0.0261164	−	0.656898i
$304$	−10.7883	−	6.26753i	−0.618750	−	0.359468i
$305$	−2.86175	+	4.95671i	−0.163864	+	0.283820i
$306$	−2.43799	+	3.41980i	−0.139371	+	0.195497i
$307$	−20.0407	+	11.5705i	−1.14379	+	0.660365i	−0.947365	−	0.320155i	$-0.896265\pi$
$307$	−20.0407	+	11.5705i	−1.14379	+	0.660365i	−0.196420	+	0.980520i	$0.562932\pi$
$308$	−13.0664	+	2.28576i	−0.744526	+	0.130243i
$309$	3.69864	−	27.2723i	0.210409	−	1.55147i
$310$	−0.604547	+	3.41507i	−0.0343359	+	0.193963i
$311$	−18.6806	+	15.6749i	−1.05928	+	0.888842i	−0.994039	−	0.109027i	$-0.965227\pi$
$311$	−18.6806	+	15.6749i	−1.05928	+	0.888842i	−0.0652424	+	0.997869i	$0.520782\pi$
$312$	26.1186	+	20.2884i	1.47867	+	1.14860i
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.450000	−	0.893028i	$-0.351424\pi$
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.918748	+	0.394845i	$0.129202\pi$
$314$	6.49745	+	2.36985i	0.366672	+	0.133738i
$315$	4.87020	+	0.464362i	0.274405	+	0.0261639i
$316$	13.5450	+	11.3968i	0.761964	+	0.641120i
$317$	18.1371	+	3.19806i	1.01868	+	0.179621i	0.657960	−	0.753053i	$-0.271420\pi$
$317$	18.1371	+	3.19806i	1.01868	+	0.179621i	0.360721	+	0.932674i	$0.382531\pi$
$318$	−2.59744	−	11.9752i	−0.145657	−	0.671533i
$319$	−17.6337	−	6.41816i	−0.987300	−	0.359348i
$320$	2.87940	−	7.81244i	0.160963	−	0.436729i
$321$	6.52458	−	1.41981i	0.364167	−	0.0792462i
$322$	0.0101601	−	15.0435i	0.000566198	−	0.838339i
$323$			3.08773i			0.171806i
$324$	−11.8021	+	13.5908i	−0.655671	+	0.755047i
$325$			26.4420i			1.46674i
$326$	5.91256	+	0.00399322i	0.327466	+	0.000221164i
$327$	5.63249	−	1.22568i	0.311478	−	0.0677805i
$328$	5.78145	+	6.91848i	0.319227	+	0.382009i
$329$	−1.31613	−	0.479031i	−0.0725605	−	0.0264099i
$330$	−10.5459	+	2.28743i	−0.580533	+	0.125919i
$331$	15.2370	+	2.68670i	0.837502	+	0.147674i	0.575919	−	0.817507i	$-0.304644\pi$
$331$	15.2370	+	2.68670i	0.837502	+	0.147674i	0.261583	+	0.965181i	$0.415755\pi$
$332$	−8.07744	+	9.59995i	−0.443307	+	0.526866i
$333$	−6.41181	+	9.00679i	−0.351365	+	0.493569i
$334$	−2.95372	+	8.09827i	−0.161621	+	0.443118i
$335$	−0.710980	+	0.258776i	−0.0388450	+	0.0141384i
$336$	−10.8482	+	0.401944i	−0.591818	+	0.0219279i
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	−0.352424	−	0.935840i	$-0.614643\pi$
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	0.860425	+	0.509577i	$0.170198\pi$
$338$	−45.3627	−	8.03026i	−2.46740	−	0.436788i
$339$	−1.94501	+	14.3417i	−0.105639	+	0.778937i
$340$	−2.02973	+	0.355070i	−0.110078	+	0.0192564i
$341$	−8.63764	+	4.98695i	−0.467755	+	0.270058i
$342$	−1.26499	+	13.1730i	−0.0684029	+	0.712313i
$343$	−9.04472	+	15.6659i	−0.488369	+	0.845880i
$344$	28.8586	−	10.4375i	1.55595	−	0.562752i
$345$	−0.486168	−	12.2284i	−0.0261744	−	0.658356i
$346$	−1.76301	+	0.640335i	−0.0947800	+	0.0344246i
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.757576	−	0.652747i	$-0.773616\pi$
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.488636	+	0.872488i	$0.662505\pi$
$348$	−13.5847	−	7.16258i	−0.728214	−	0.383955i
$349$	14.7087	−	17.5291i	0.787338	−	0.938312i	−0.211902	−	0.977291i	$-0.567966\pi$
$349$	14.7087	−	17.5291i	0.787338	−	0.938312i	0.999240	+	0.0389784i	$0.0124104\pi$
$350$	−5.57441	−	6.65244i	−0.297965	−	0.355588i
$351$	7.99230	−	34.1562i	0.426598	−	1.82312i
$352$	22.5282	−	8.11356i	1.20076	−	0.432454i
$353$	0.541929	+	0.454733i	0.0288440	+	0.0242030i	0.657096	−	0.753807i	$-0.271785\pi$
$353$	0.541929	+	0.454733i	0.0288440	+	0.0242030i	−0.628252	+	0.778010i	$0.716229\pi$
$354$	−3.72856	+	27.3541i	−0.198171	+	1.45386i
$355$	5.16729	−	0.911132i	0.274251	−	0.0483579i
$356$	−8.06440	+	13.9245i	−0.427412	+	0.737996i
$357$	1.43464	+	2.27142i	0.0759293	+	0.120216i
$358$	7.89952	+	13.7037i	0.417502	+	0.724265i
$359$	−5.07907	+	8.79721i	−0.268063	+	0.464299i	−0.968362	−	0.249551i	$-0.919717\pi$
$359$	−5.07907	+	8.79721i	−0.268063	+	0.464299i	0.700298	+	0.713850i	$0.253050\pi$
$360$	−8.80477	+	0.683264i	−0.464052	+	0.0360112i
$361$	−4.63535	−	8.02867i	−0.243966	−	0.422561i
$362$	2.62450	−	4.53868i	0.137940	−	0.238548i
$363$	−9.47668	−	7.33056i	−0.497397	−	0.384755i
$364$	18.3357	−	10.5531i	0.961051	−	0.553134i
$365$	9.39023	+	11.1908i	0.491507	+	0.585755i
$366$	−13.4602	+	0.526035i	−0.703576	+	0.0274963i
$367$	−1.79478	+	0.653245i	−0.0936866	+	0.0340991i	−0.388438	−	0.921475i	$-0.626985\pi$
$367$	−1.79478	+	0.653245i	−0.0936866	+	0.0340991i	0.294752	+	0.955574i	$0.404763\pi$
$368$	4.64324	+	26.7556i	0.242045	+	1.39473i
$369$	4.10894	−	8.63530i	0.213903	−	0.449536i
$370$	−5.34254	+	0.938313i	−0.277745	+	0.0487806i
$371$	−7.71925	−	1.36111i	−0.400763	−	0.0706654i
$372$	−7.55739	+	3.08401i	−0.391833	+	0.159899i
$373$	−11.8307	+	32.5046i	−0.612571	+	1.68303i	0.111899	+	0.993720i	$0.464307\pi$
$373$	−11.8307	+	32.5046i	−0.612571	+	1.68303i	−0.724470	+	0.689306i	$0.757916\pi$
$374$	−4.53688	−	3.81212i	−0.234596	−	0.197120i
$375$	−10.8132	−	11.8932i	−0.558391	−	0.614165i
$376$	2.48896	+	0.444072i	0.128358	+	0.0229013i
$377$	29.9286			1.54140
$378$	5.18994	+	10.2781i	0.266942	+	0.528651i
$379$		−	27.1937i		−	1.39685i	−0.715685	−	0.698423i	$-0.753886\pi$
$379$		−	27.1937i		−	1.39685i	0.715685	−	0.698423i	$-0.246114\pi$
$380$	−4.97934	+	4.16671i	−0.255435	+	0.213748i
$381$	6.03883	+	1.92994i	0.309378	+	0.0988738i
$382$	−16.4256	+	19.5484i	−0.840405	+	1.00018i
$383$	−5.67775	−	2.06653i	−0.290120	−	0.105595i	0.192861	−	0.981226i	$-0.438223\pi$
$383$	−5.67775	−	2.06653i	−0.290120	−	0.105595i	−0.482980	+	0.875631i	$0.660446\pi$
$384$	19.1673	−	4.07618i	0.978126	−	0.208011i
$385$	−1.19866	+	6.79794i	−0.0610894	+	0.346455i
$386$	−6.18174	+	1.08570i	−0.314642	+	0.0552608i
$387$	−22.8360	−	23.1947i	−1.16082	−	1.17905i
$388$	20.2829	−	7.35135i	1.02971	−	0.373208i
$389$	−3.99747	−	10.9830i	−0.202680	−	0.556858i	0.796156	−	0.605091i	$-0.206863\pi$
$389$	−3.99747	−	10.9830i	−0.202680	−	0.556858i	−0.998836	+	0.0482330i	$0.984641\pi$
$390$	14.5573	−	9.18075i	0.737140	−	0.464885i
$391$	5.14814	−	4.31980i	0.260353	−	0.218462i
$392$	4.42110	−	12.0707i	0.223299	−	0.609664i
$393$	−6.44102	−	15.7230i	−0.324906	−	0.793121i
$394$	11.5685	−	20.0061i	0.582814	−	1.00789i
$395$	7.97761	−	4.60588i	0.401397	−	0.231747i
$396$	−17.7936	−	18.1220i	−0.894162	−	0.910667i
$397$	2.31327	+	1.33556i	0.116099	+	0.0670301i	0.556925	−	0.830563i	$-0.311981\pi$
$397$	2.31327	+	1.33556i	0.116099	+	0.0670301i	−0.440826	+	0.897593i	$0.645314\pi$
$398$	1.12432	−	0.648116i	0.0563572	−	0.0324871i
$399$	7.49342	+	3.93802i	0.375140	+	0.197148i
$400$	11.9745	+	10.1031i	0.598725	+	0.505153i
$401$	−2.15776	−	12.2372i	−0.107753	−	0.611099i	−0.990085	−	0.140470i	$-0.955138\pi$
$401$	−2.15776	−	12.2372i	−0.107753	−	0.611099i	0.882332	−	0.470628i	$-0.155973\pi$
$402$	−1.40776	−	1.09047i	−0.0702125	−	0.0543878i
$403$	10.2249	−	12.1856i	0.509339	−	0.607007i
$404$	13.0101	+	2.31215i	0.647275	+	0.115034i
$405$	4.55646	+	8.18403i	0.226412	+	0.406668i
$406$	−7.52962	+	6.30944i	−0.373689	+	0.313132i
$407$	−11.9499	−	10.0271i	−0.592334	−	0.497027i
$408$	−3.25510	−	3.59483i	−0.161151	−	0.177971i
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	0.954651	−	0.297728i	$-0.0962288\pi$
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	−0.998907	+	0.0467370i	$0.985118\pi$
$410$	4.40999	−	1.60173i	0.217794	−	0.0791040i
$411$	17.8003	−	33.8711i	0.878023	−	1.67074i
$412$	29.8484	+	10.9096i	1.47052	+	0.537478i
$413$	15.2936	+	8.82978i	0.752550	+	0.434485i
$414$	23.7329	−	16.3202i	1.16641	−	0.802092i
$415$	3.26440	+	5.65411i	0.160243	+	0.277549i
$416$	−29.3372	+	24.4485i	−1.43837	+	1.19869i
$417$	3.12588	+	7.63052i	0.153075	+	0.373668i
$418$	−18.3862	−	3.25478i	−0.899296	−	0.159196i
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	0.719097	−	0.694909i	$-0.244556\pi$
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	−0.809222	+	0.587503i	$0.800111\pi$
$420$	−1.72697	+	5.37868i	−0.0842677	+	0.262453i
$421$	−4.61049	−	12.6672i	−0.224701	−	0.617362i	0.775195	−	0.631721i	$-0.217651\pi$
$421$	−4.61049	−	12.6672i	−0.224701	−	0.617362i	−0.999897	+	0.0143594i	$0.995429\pi$
$422$	8.14726	+	2.97159i	0.396603	+	0.144655i
$423$	−0.673847	−	2.59558i	−0.0327636	−	0.126202i
$424$	14.1492	+	0.0286683i	0.687147	+	0.00139226i
$425$	0.673287	−	3.81840i	0.0326592	−	0.185220i
$426$	8.30114	+	9.14268i	0.402192	+	0.442964i
$427$	−2.94709	+	8.09707i	−0.142620	+	0.391845i
$428$	−0.0104147	+	7.71025i	−0.000503414	+	0.372689i
$429$	47.1457	+	15.0672i	2.27621	+	0.727452i
$430$	0.0107856	−	15.9696i	0.000520126	−	0.770124i
$431$	25.2153			1.21458			0.607290	−	0.794480i	$-0.292257\pi$
$431$	25.2153			1.21458			0.607290	+	0.794480i	$0.292257\pi$
$432$	−12.4142	−	16.6699i	−0.597281	−	0.802032i
$433$	−15.5658			−0.748046			−0.374023	−	0.927419i	$-0.622022\pi$
$433$	−15.5658			−0.748046			−0.374023	+	0.927419i	$0.622022\pi$
$434$	−0.00352637	+	5.22131i	−0.000169271	+	0.250631i
$435$	−5.91309	+	5.37611i	−0.283511	+	0.257765i
$436$	−0.00899073	+	6.65605i	−0.000430578	+	0.318767i
$437$	7.24252	−	19.8987i	0.346457	−	0.951882i
$438$	−10.4886	+	32.7429i	−0.501166	+	1.56452i
$439$	5.53290	−	31.3787i	0.264071	−	1.49762i	−0.507596	−	0.861595i	$-0.669466\pi$
$439$	5.53290	−	31.3787i	0.264071	−	1.49762i	0.771667	−	0.636026i	$-0.219423\pi$
$440$	0.0252467	−	12.4605i	0.00120359	−	0.594030i
$441$	−13.5916	+	1.08244i	−0.647221	+	0.0515449i
$442$	8.87884	+	3.23843i	0.422323	+	0.154036i
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	0.877634	−	0.479332i	$-0.159121\pi$
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	−0.980415	+	0.196942i	$0.936899\pi$
$444$	−8.57527	−	9.45743i	−0.406964	−	0.448830i
$445$	5.38246	+	6.41456i	0.255153	+	0.304079i
$446$	−29.8585	−	5.28565i	−1.41384	−	0.250283i
$447$	−24.3867	+	31.5262i	−1.15345	+	1.49114i
$448$	2.22669	−	12.3357i	0.105201	−	0.582805i
$449$	−4.18149	−	7.24256i	−0.197337	−	0.341797i	0.750327	−	0.661067i	$-0.229896\pi$
$449$	−4.18149	−	7.24256i	−0.197337	−	0.341797i	−0.947664	+	0.319269i	$0.896563\pi$
$450$	4.43673	−	16.0143i	0.209149	−	0.754922i
$451$	11.6853	+	6.74653i	0.550241	+	0.317682i
$452$	−15.6964	−	5.73706i	−0.738298	−	0.269848i
$453$	18.3845	+	29.1075i	0.863777	+	1.36759i
$454$	−24.7350	+	8.98389i	−1.16087	+	0.421635i
$455$	−1.91172	−	10.8419i	−0.0896228	−	0.508276i
$456$	−14.5461	−	4.68127i	−0.681183	−	0.219220i
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.0209605	−	0.999780i	$-0.506672\pi$
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.988231	+	0.152968i	$0.951117\pi$
$458$	9.62589	−	8.06601i	0.449788	−	0.376900i
$459$	−2.02385	+	4.72888i	−0.0944655	+	0.220725i
$460$	13.9133	+	2.47267i	0.648712	+	0.115289i
$461$	16.8013	−	20.0230i	0.782513	−	0.932563i	−0.216531	−	0.976276i	$-0.569474\pi$
$461$	16.8013	−	20.0230i	0.782513	−	0.932563i	0.999044	+	0.0437126i	$0.0139186\pi$
$462$	−15.0376	+	6.14838i	−0.699613	+	0.286049i
$463$	3.84612	+	21.8124i	0.178744	+	1.01371i	0.933733	+	0.357971i	$0.116531\pi$
$463$	3.84612	+	21.8124i	0.178744	+	1.01371i	−0.754988	+	0.655738i	$0.772358\pi$
$464$	11.4352	−	13.5535i	0.530867	−	0.629203i
$465$	0.168740	+	4.24426i	0.00782513	+	0.196823i
$466$	−23.0276	+	13.2743i	−1.06673	+	0.614918i
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.872930	−	0.487845i	$-0.162217\pi$
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.0139792	+	0.999902i	$0.495550\pi$
$468$	36.5524	+	17.4534i	1.68964	+	0.806782i
$469$	−0.986466	+	0.569536i	−0.0455508	+	0.0262987i
$470$	0.658605	−	1.13896i	0.0303792	−	0.0525363i
$471$	8.39367	+	1.13834i	0.386760	+	0.0524520i
$472$	−29.9333	−	10.9636i	−1.37779	−	0.504638i
$473$	35.1815	−	29.5208i	1.61765	−	1.35737i
$474$	19.1846	+	10.0986i	0.881176	+	0.463844i
$475$	−4.17853	−	11.4804i	−0.191724	−	0.526757i
$476$	−2.91651	+	1.05706i	−0.133678	+	0.0484504i
$477$	−6.23626	−	13.6505i	−0.285539	−	0.625012i
$478$	−28.6084	+	5.02452i	−1.30852	+	0.229816i
$479$	−2.06488	+	11.7105i	−0.0943470	+	0.535068i	0.900599	+	0.434652i	$0.143129\pi$
$479$	−2.06488	+	11.7105i	−0.0943470	+	0.535068i	−0.994946	+	0.100416i	$0.967983\pi$
$480$	1.40454	−	10.1002i	0.0641080	−	0.461011i
$481$	23.3788	+	8.50920i	1.06598	+	0.387986i
$482$	12.5329	−	14.9157i	0.570858	−	0.679389i
$483$	−3.91764	−	18.0031i	−0.178259	−	0.819168i
$484$	10.6098	−	8.87831i	0.482265	−	0.403560i
$485$		−	11.2268i		−	0.509783i
$486$	−10.5716	+	19.3453i	−0.479536	+	0.877522i
$487$	22.1183			1.00228			0.501138	−	0.865367i	$-0.332915\pi$
$487$	22.1183			1.00228			0.501138	+	0.865367i	$0.332915\pi$
$488$	2.73202	−	15.3125i	0.123673	−	0.693166i
$489$	7.07578	−	1.53976i	0.319978	−	0.0696303i
$490$	−5.12155	−	4.30339i	−0.231368	−	0.194407i
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	−0.983877	−	0.178845i	$-0.942764\pi$
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	0.868653	+	0.495421i	$0.164986\pi$
$492$	8.72517	+	6.76810i	0.393361	+	0.305130i
$493$	−4.32189	−	0.762066i	−0.194648	−	0.0343217i
$494$	29.3307	−	5.15137i	1.31965	−	0.231771i
$495$	−12.0213	+	5.49195i	−0.540316	+	0.246845i
$496$	−1.61158	−	9.28636i	−0.0723622	−	0.416970i
$497$	7.42295	−	2.70173i	0.332965	−	0.121189i
$498$	−7.15736	+	13.5970i	−0.320729	+	0.609296i
$499$	6.65452	+	7.93054i	0.297897	+	0.355020i	0.894143	−	0.447782i	$-0.147786\pi$
$499$	6.65452	+	7.93054i	0.297897	+	0.355020i	−0.596246	+	0.802802i	$0.703342\pi$
$500$	16.0866	−	9.25863i	0.719412	−	0.414058i
$501$	−1.41880	+	10.4617i	−0.0633874	+	0.467393i
$502$	−0.342595	+	0.592467i	−0.0152908	+	0.0264431i
$503$	−16.9435	−	29.3471i	−0.755475	−	1.30852i	−0.945138	−	0.326672i	$-0.894073\pi$
$503$	−16.9435	−	29.3471i	−0.755475	−	1.30852i	0.189663	−	0.981849i	$-0.439261\pi$
$504$	−12.8755	+	3.31483i	−0.573522	+	0.147654i
$505$	3.43817	−	5.95508i	0.152997	−	0.264998i
$506$	20.2960	+	35.2085i	0.902266	+	1.56521i
$507$	−56.3770	+	2.24139i	−2.50379	+	0.0995436i
$508$	−3.66880	+	6.33477i	−0.162777	+	0.281060i
$509$	−16.7517	+	2.95378i	−0.742508	+	0.130924i	−0.532090	−	0.846688i	$-0.678593\pi$
$509$	−16.7517	+	2.95378i	−0.742508	+	0.130924i	−0.210417	+	0.977612i	$0.567482\pi$
$510$	−2.33595	+	0.955090i	−0.103437	+	0.0422921i
$511$	16.8478	+	14.1370i	0.745301	+	0.625382i
$512$	−0.137538	+	22.6270i	−0.00607838	+	0.999982i
$513$	1.92753	+	16.0927i	0.0851026	+	0.710511i
$514$	16.1133	+	19.2295i	0.710728	+	0.848175i
$515$	10.6302	−	12.6686i	0.468423	−	0.558245i
$516$	31.8045	−	20.0278i	1.40011	−	0.881675i
$517$	3.72618	−	0.657026i	0.163877	−	0.0288960i
$518$	−7.67568	+	2.78785i	−0.337250	+	0.122491i
$519$	−1.94227	+	1.22675i	−0.0852564	+	0.0538484i
$520$	6.75912	+	18.6883i	0.296407	+	0.819534i
$521$	−14.6553	+	25.3837i	−0.642060	+	1.11208i	0.342912	+	0.939368i	$0.388587\pi$
$521$	−14.6553	+	25.3837i	−0.642060	+	1.11208i	−0.984972	+	0.172714i	$0.944746\pi$
$522$	−18.1260	−	5.02175i	−0.793352	−	0.219796i
$523$	3.33680	−	1.92651i	0.145908	−	0.0842402i	−0.425269	−	0.905067i	$-0.639820\pi$
$523$	3.33680	−	1.92651i	0.145908	−	0.0842402i	0.571177	+	0.820827i	$0.306487\pi$
$524$	19.3262	−	3.38083i	0.844270	−	0.147692i
$525$	−8.40793	−	6.50385i	−0.366952	−	0.283851i
$526$	11.2138	+	1.98510i	0.488944	+	0.0865545i
$527$	−1.78683	+	1.49932i	−0.0778353	+	0.0653116i
$528$	24.8369	−	15.5934i	1.08089	−	0.678617i
$529$	−21.6963	+	7.89682i	−0.943319	+	0.343340i
$530$	2.52299	−	6.91732i	0.109592	−	0.300469i
$531$	2.68427	+	33.7049i	0.116487	+	1.46267i
$532$	−6.29320	+	7.47940i	−0.272845	+	0.324273i
$533$	−21.1929	−	3.73687i	−0.917965	−	0.161862i
$534$	−6.01206	+	18.7682i	−0.260167	+	0.812178i
$535$	3.77033	+	1.37229i	0.163006	+	0.0593292i
$536$	1.57780	−	1.31849i	0.0681506	−	0.0569502i
$537$	13.0321	+	14.3338i	0.562376	+	0.618547i
$538$	−9.28484	−	0.00627080i	−0.400298	−	0.000270353i
$539$		−	19.2380i		−	0.828638i
$540$	−10.3570	+	3.11764i	−0.445692	+	0.134162i
$541$			4.51542i			0.194133i	0.995278	+	0.0970665i	$0.0309460\pi$
$541$			4.51542i			0.194133i	−0.995278	+	0.0970665i	$0.969054\pi$
$542$	−0.0103749	+	15.3616i	−0.000445642	+	0.659839i
$543$	1.95473	−	6.11640i	0.0838856	−	0.262480i
$544$	4.85901	−	2.78352i	0.208328	−	0.119342i
$545$	3.25483	+	1.18466i	0.139421	+	0.0507453i
$546$	19.1830	−	17.4173i	0.820956	−	0.745391i
$547$	12.3037	+	2.16948i	0.526069	+	0.0927602i	0.430374	−	0.902651i	$-0.358382\pi$
$547$	12.3037	+	2.16948i	0.526069	+	0.0927602i	0.0956949	+	0.995411i	$0.469493\pi$
$548$	33.8077	+	28.4460i	1.44419	+	1.21515i
$549$	−15.9685	+	4.14564i	−0.681520	+	0.176931i
$550$	22.0273	+	8.03412i	0.939245	+	0.342576i
$551$	−12.9942	+	4.72950i	−0.553572	+	0.201484i
$552$	12.5453	+	30.8017i	0.533962	+	1.31101i
$553$	10.6237	−	8.91435i	0.451766	−	0.379077i
$554$	7.81584	−	44.1514i	0.332063	−	1.87581i
$555$	−6.14756	+	2.51838i	−0.260949	+	0.106899i
$556$	−9.37920	+	1.64075i	−0.397767	+	0.0695831i
$557$	3.03004	−	1.74940i	0.128387	−	0.0741243i	−0.434431	−	0.900705i	$-0.643051\pi$
$557$	3.03004	−	1.74940i	0.128387	−	0.0741243i	0.562818	+	0.826581i	$0.309717\pi$
$558$	−8.23725	+	5.66443i	−0.348711	+	0.239794i
$559$	−36.6233	+	63.4335i	−1.54900	+	2.68295i
$560$	−5.64029	−	3.27677i	−0.238346	−	0.138469i
$561$	−6.42449	−	3.37627i	−0.271242	−	0.142546i
$562$	−9.47855	−	26.0969i	−0.399828	−	1.10083i
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.709653	−	0.704552i	$-0.751148\pi$
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.425885	+	0.904777i	$0.640037\pi$
$564$	3.09419	−	0.118831i	0.130289	−	0.00500367i
$565$	−5.59013	+	6.66206i	−0.235179	+	0.280275i
$566$	21.3775	−	17.9132i	0.898562	−	0.752949i
$567$	8.89504	+	10.9427i	0.373557	+	0.459549i
$568$	−12.3634	+	7.10466i	−0.518757	+	0.298105i
$569$	3.15771	+	2.64963i	0.132378	+	0.111078i	0.706573	−	0.707640i	$-0.250240\pi$
$569$	3.15771	+	2.64963i	0.132378	+	0.111078i	−0.574195	+	0.818719i	$0.694685\pi$
$570$	−4.86961	+	6.28648i	−0.203966	+	0.263312i
$571$	−2.91629	+	0.514220i	−0.122043	+	0.0215194i	−0.234336	−	0.972156i	$-0.575292\pi$
$571$	−2.91629	+	0.514220i	−0.122043	+	0.0215194i	0.112293	+	0.993675i	$0.464180\pi$
$572$	−28.6427	+	49.4561i	−1.19761	+	2.06787i
$573$	−14.5476	+	27.6817i	−0.607733	+	1.15642i
$574$	6.11963	−	3.52766i	0.255428	−	0.147242i
$575$	−13.2953	+	23.0281i	−0.554453	+	0.960340i
$576$	21.8700	−	9.88446i	0.911251	−	0.411853i
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	0.764414	−	0.644725i	$-0.223028\pi$
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	−0.940556	+	0.339640i	$0.889695\pi$
$578$	19.6128	+	11.3411i	0.815786	+	0.471729i
$579$	−7.11321	+	2.91396i	−0.295615	+	0.121100i
$580$	−4.60321	−	7.99793i	−0.191138	−	0.332096i
$581$	6.31802	+	7.52952i	0.262115	+	0.312377i
$582$	22.3493	−	14.0948i	0.926409	−	0.584250i
$583$	19.8980	−	7.24228i	0.824092	−	0.299945i
$584$	−34.3415	−	19.9200i	−1.42106	−	0.824294i
$585$	15.0205	−	14.7881i	0.621020	−	0.611414i
$586$	−6.50499	−	37.0379i	−0.268719	−	1.53002i
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.991079	−	0.133275i	$-0.0425493\pi$
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.885727	+	0.464206i	$0.153660\pi$
$588$	2.13689	−	15.5983i	0.0881237	−	0.643262i
$589$	−2.51375	+	6.90646i	−0.103577	+	0.284576i
$590$	−10.6717	+	12.7006i	−0.439345	+	0.522874i
$591$	8.61628	−	26.9605i	0.354426	−	1.10901i
$592$	12.7862	−	7.33611i	0.525508	−	0.301512i
$593$	22.0816			0.906784			0.453392	−	0.891311i	$-0.350214\pi$
$593$	22.0816			0.906784			0.453392	+	0.891311i	$0.350214\pi$
$594$	−26.0252	−	17.0359i	−1.06782	−	0.698992i
$595$			1.61432i			0.0661807i
$596$	−29.5356	−	35.2959i	−1.20982	−	1.44577i
$597$	1.17601	−	1.06922i	0.0481311	−	0.0437602i
$598$	−49.6230	−	41.6958i	−2.02924	−	1.70507i
$599$	−23.2555	−	8.46431i	−0.950194	−	0.345842i	−0.180010	−	0.983665i	$-0.557613\pi$
$599$	−23.2555	−	8.46431i	−0.950194	−	0.345842i	−0.770184	+	0.637822i	$0.779835\pi$
$600$	16.9674	+	8.96083i	0.692693	+	0.365824i
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	−0.887034	−	0.461705i	$-0.847238\pi$
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	0.991451	−	0.130477i	$-0.0416509\pi$
$602$	−4.15890	−	23.6798i	−0.169504	−	0.965116i
$603$	−1.96933	−	0.937069i	−0.0801974	−	0.0381604i
$604$	−37.3741	+	13.5459i	−1.52073	+	0.551175i
$605$	−2.46229	−	6.76510i	−0.100107	−	0.275040i
$606$	16.1713	−	0.631988i	0.656916	−	0.0256728i
$607$	−23.2768	+	19.5315i	−0.944775	+	0.792761i	−0.978410	−	0.206674i	$-0.933736\pi$
$607$	−23.2768	+	19.5315i	−0.944775	+	0.792761i	0.0336346	+	0.999434i	$0.489292\pi$
$608$	8.87393	−	15.2509i	0.359885	−	0.618507i
$609$	−7.36144	+	9.51660i	−0.298301	+	0.385632i
$610$	−7.00710	−	4.05187i	−0.283709	−	0.164055i
$611$	−5.22602	+	3.01724i	−0.211422	+	0.122065i
$612$	−4.83400	−	3.45111i	−0.195403	−	0.139503i
$613$	−8.97166	−	5.17979i	−0.362362	−	0.209210i	0.307754	−	0.951466i	$-0.400422\pi$
$613$	−8.97166	−	5.17979i	−0.362362	−	0.209210i	−0.670116	+	0.742256i	$0.733756\pi$
$614$	−16.3440	−	28.3529i	−0.659592	−	1.14423i
$615$	4.85841	−	3.06859i	0.195910	−	0.123738i
$616$	−3.22007	−	18.4808i	−0.129740	−	0.744614i
$617$	2.09885	+	11.9032i	0.0844965	+	0.479204i	0.997464	+	0.0711715i	$0.0226738\pi$
$617$	2.09885	+	11.9032i	0.0844965	+	0.479204i	−0.912968	+	0.408032i	$0.866215\pi$
$618$	38.5653	+	5.25672i	1.55132	+	0.211456i
$619$	1.25371	−	1.49411i	0.0503908	−	0.0600535i	−0.740260	−	0.672320i	$-0.765298\pi$
$619$	1.25371	−	1.49411i	0.0503908	−	0.0600535i	0.790651	+	0.612267i	$0.209742\pi$
$620$	−4.82905	−	0.858220i	−0.193939	−	0.0344669i
$621$	24.1345	−	25.7278i	0.968486	−	1.03242i
$622$	−22.1498	−	26.4334i	−0.888127	−	1.05988i
$623$	9.65710	+	8.10327i	0.386904	+	0.324651i
$624$	−28.7171	+	36.9179i	−1.14960	+	1.47790i
$625$	1.72350	+	9.77447i	0.0689401	+	0.390979i
$626$	12.4414	+	34.2545i	0.497259	+	1.36908i
$627$	−22.8504	+	0.908468i	−0.912557	+	0.0362807i
$628$	−3.35768	+	9.18651i	−0.133986	+	0.366582i
$629$	−3.15939	−	1.82408i	−0.125973	−	0.0727307i
$630$	−0.661359	+	6.88705i	−0.0263492	+	0.274387i
$631$	−6.64702	−	11.5130i	−0.264614	−	0.458325i	0.702849	−	0.711340i	$-0.251911\pi$
$631$	−6.64702	−	11.5130i	−0.264614	−	0.458325i	−0.967462	+	0.253015i	$0.918578\pi$
$632$	−16.1304	+	19.1446i	−0.641634	+	0.761531i
$633$	10.5250	+	1.42739i	0.418330	+	0.0567335i
$634$	−4.54006	+	25.6467i	−0.180309	+	1.01856i
$635$	2.44868	+	2.91823i	0.0971730	+	0.115806i
$636$	16.9379	−	3.66189i	0.671631	−	0.145204i
$637$	10.4939	+	28.8319i	0.415785	+	1.14236i
$638$	9.09349	−	24.9317i	0.360015	−	0.987057i
$639$	12.3212	+	8.77127i	0.487418	+	0.346986i
$640$	11.0457	+	4.07955i	0.436620	+	0.161258i
$641$	4.99251	−	28.3139i	0.197192	−	1.11833i	−0.712069	−	0.702109i	$-0.752242\pi$
$641$	4.99251	−	28.3139i	0.197192	−	1.11833i	0.909262	−	0.416225i	$-0.136647\pi$
$642$	2.00168	+	9.22850i	0.0790002	+	0.364220i
$643$	12.8078	−	35.1891i	0.505090	−	1.38772i	−0.381157	−	0.924510i	$-0.624474\pi$
$643$	12.8078	−	35.1891i	0.505090	−	1.38772i	0.886247	−	0.463213i	$-0.153303\pi$
$644$	21.2746	+	0.0287370i	0.838338	+	0.00113239i
$645$	−4.15884	−	19.1115i	−0.163754	−	0.752513i
$646$	−4.36671	−	0.00294919i	−0.171806	−	0.000116034i
$647$	−23.8383			−0.937182			−0.468591	−	0.883415i	$-0.655238\pi$
$647$	−23.8383			−0.937182			−0.468591	+	0.883415i	$0.655238\pi$
$648$	−19.2091	−	16.7036i	−0.754604	−	0.656180i
$649$	−47.7068			−1.87266
$650$	−37.3946	−	0.0252556i	−1.46674	−	0.000990605i
$651$	1.35974	+	6.24853i	0.0532925	+	0.244899i
$652$	−0.0112945	+	8.36161i	−0.000442328	+	0.327466i
$653$	16.8138	−	46.1955i	0.657974	−	1.80777i	0.0720526	−	0.997401i	$-0.477045\pi$
$653$	16.8138	−	46.1955i	0.657974	−	1.80777i	0.585921	−	0.810368i	$-0.300733\pi$
$654$	1.72800	+	7.96672i	0.0675702	+	0.311523i
$655$	1.77292	−	10.0547i	0.0692736	−	0.392870i
$656$	−9.78973	+	8.16959i	−0.382225	+	0.318969i
$657$	−3.99687	+	41.9188i	−0.155933	+	1.63541i
$658$	0.678710	−	1.86083i	0.0264589	−	0.0725426i
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	0.982039	+	0.188678i	$0.0604202\pi$
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	−0.631006	+	0.775778i	$0.717358\pi$
$660$	−3.22484	−	14.9163i	−0.125527	−	0.580618i
$661$	−0.937603	−	1.11739i	−0.0364685	−	0.0434615i	0.747502	−	0.664260i	$-0.231253\pi$
$661$	−0.937603	−	1.11739i	−0.0364685	−	0.0434615i	−0.783970	+	0.620798i	$0.786809\pi$
$662$	−3.81412	+	21.5458i	−0.148240	+	0.837402i
$663$	11.4701	+	1.55556i	0.445460	+	0.0604128i
$664$	−13.5687	−	11.4324i	−0.526566	−	0.443663i
$665$	2.54332	+	4.40516i	0.0986258	+	0.170825i
$666$	−12.7314	−	9.07627i	−0.493332	−	0.351698i
$667$	26.0646	+	15.0484i	1.00923	+	0.582677i
$668$	−11.4499	−	4.18493i	−0.443008	−	0.161920i
$669$	−37.1082	+	1.47532i	−1.43469	+	0.0570392i
$670$	−0.365285	−	1.00572i	−0.0141122	−	0.0388545i
$671$	−4.04215	−	22.9242i	−0.156046	−	0.884979i
$672$	−0.558073	−	15.3421i	−0.0215282	−	0.591833i
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	0.874783	−	0.484514i	$-0.161004\pi$
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	−0.325249	+	0.945628i	$0.605448\pi$
$674$	11.0575	+	13.1959i	0.425920	+	0.508289i
$675$	1.12540	−	20.3211i	0.0433165	−	0.782160i
$676$	11.3998	−	64.1448i	0.438455	−	2.46711i
$677$	2.04257	−	2.43424i	0.0785022	−	0.0935553i	−0.725364	−	0.688366i	$-0.758328\pi$
$677$	2.04257	−	2.43424i	0.0785022	−	0.0935553i	0.803866	+	0.594810i	$0.202773\pi$
$678$	−20.2804	−	2.76436i	−0.778865	−	0.106165i
$679$	−2.93499	−	16.6451i	−0.112634	−	0.638782i
$680$	−0.500207	−	2.87081i	−0.0191821	−	0.110091i
$681$	−27.2501	+	17.2113i	−1.04423	+	0.659538i
$682$	−7.04435	−	12.2202i	−0.269742	−	0.467937i
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	0.644459	−	0.764639i	$-0.277082\pi$
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	−0.339967	+	0.940437i	$0.610416\pi$
$684$	−18.6282	−	1.80155i	−0.712266	−	0.0688840i
$685$	19.9118	−	11.4961i	0.760792	−	0.439243i
$686$	−22.1463	−	12.8061i	−0.845550	−	0.488940i
$687$	9.41089	−	12.1660i	0.359048	−	0.464164i
$688$	14.7333	+	40.8221i	0.561701	+	1.55633i
$689$	−25.8705	+	21.7080i	−0.985589	+	0.827008i
$690$	17.2941	−	0.675865i	0.658374	−	0.0257298i
$691$	6.14708	+	16.8890i	0.233846	+	0.642487i	1.00000		0.000170287i	$-5.42042e-5\pi$
$691$	6.14708	+	16.8890i	0.233846	+	0.642487i	−0.766154	+	0.642657i	$0.777832\pi$
$692$	−0.903886	−	2.49388i	−0.0343606	−	0.0948032i
$693$	−16.3873	+	11.2852i	−0.622501	+	0.428689i
$694$	−5.76665	−	32.8339i	−0.218899	−	1.24636i
$695$	−0.860413	+	4.87964i	−0.0326373	+	0.185095i
$696$	10.1424	−	19.2048i	0.384446	−	0.727955i
$697$	2.96524	+	1.07926i	0.112316	+	0.0408799i
$698$	24.7759	+	20.8180i	0.937780	+	0.787971i
$699$	−24.0863	+	21.8989i	−0.911027	+	0.828294i
$700$	9.41329	−	7.87705i	0.355789	−	0.297724i
$701$		−	19.1567i		−	0.723538i	−0.932268	−	0.361769i	$-0.882173\pi$
$701$		−	19.1567i		−	0.723538i	0.932268	−	0.361769i	$-0.117827\pi$
$702$	48.2965	+	11.3354i	1.82284	+	0.427829i
$703$	−11.4952			−0.433548
$704$	11.4528	+	31.8675i	0.431643	+	1.20105i
$705$	0.490531	−	1.53488i	0.0184745	−	0.0578070i
$706$	−0.643607	+	0.765969i	−0.0242225	+	0.0288276i
$707$	3.54070	−	9.72798i	0.133162	−	0.365858i
$708$	−38.6810	−	5.29910i	−1.45372	−	0.199152i
$709$	9.23990	+	1.62924i	0.347012	+	0.0611875i	0.344438	−	0.938809i	$-0.388070\pi$
$709$	9.23990	+	1.62924i	0.347012	+	0.0611875i	0.00257396	+	0.999997i	$0.499181\pi$
$710$	1.28360	+	7.30852i	0.0481726	+	0.274284i
$711$	25.5936	+	7.07202i	0.959834	+	0.265222i
$712$	−19.6845	−	11.4181i	−0.737707	−	0.427911i
$713$	15.0318	−	5.47115i	0.562947	−	0.204896i
$714$	−3.21364	+	2.02672i	−0.120268	+	0.0758481i
$715$	19.1171	+	22.7829i	0.714938	+	0.852031i
$716$	−19.3875	+	11.1585i	−0.724546	+	0.417013i
$717$	−32.9192	+	13.4855i	−1.22939	+	0.503626i
$718$	−12.4363	−	7.19129i	−0.464118	−	0.268377i
$719$	10.7417	+	18.6051i	0.400596	+	0.693853i	0.993798	−	0.111201i	$-0.0354698\pi$
$719$	10.7417	+	18.6051i	0.400596	+	0.693853i	−0.593202	+	0.805054i	$0.702136\pi$
$720$	−0.957871	−	12.4525i	−0.0356978	−	0.464076i
$721$	12.4487	−	21.5618i	0.463614	−	0.803003i
$722$	11.3587	−	6.54771i	0.422726	−	0.243681i
$723$	11.1000	−	21.1215i	0.412812	−	0.785516i
$724$	6.41615	+	3.71593i	0.238454	+	0.138102i
$725$	17.1004	−	3.01526i	0.635092	−	0.111984i
$726$	10.3760	−	13.3950i	0.385091	−	0.497137i
$727$	−22.5451	−	18.9176i	−0.836151	−	0.701614i	0.120543	−	0.992708i	$-0.461536\pi$
$727$	−22.5451	−	18.9176i	−0.836151	−	0.701614i	−0.956694	+	0.291094i	$0.905981\pi$
$728$	14.9068	+	25.9406i	0.552484	+	0.961424i
$729$	−7.59595	+	25.9095i	−0.281331	+	0.959611i
$730$	−15.8352	+	13.2691i	−0.586087	+	0.491111i
$731$	6.90385	−	8.22768i	0.255348	−	0.304312i
$732$	−0.731069	−	19.0361i	−0.0270211	−	0.703594i
$733$	−43.1488	+	7.60829i	−1.59374	+	0.281019i	−0.898901	−	0.438151i	$-0.855634\pi$
$733$	−43.1488	+	7.60829i	−1.59374	+	0.281019i	−0.694835	+	0.719170i	$0.744522\pi$
$734$	−0.922114	−	2.53882i	−0.0340358	−	0.0937096i
$735$	−7.25243	−	3.81137i	−0.267510	−	0.140584i
$736$	−37.8425	+	6.54097i	−1.39489	+	0.241103i
$737$	1.53859	−	2.66491i	0.0566746	−	0.0981632i
$738$	12.2082	+	5.81917i	0.449391	+	0.214207i
$739$	−21.9574	+	12.6771i	−0.807716	+	0.466335i	−0.846162	−	0.532926i	$-0.821093\pi$
$739$	−21.9574	+	12.6771i	−0.807716	+	0.466335i	0.0384462	+	0.999261i	$0.487759\pi$
$740$	−1.32187	−	7.55638i	−0.0485930	−	0.277778i
$741$	33.7503	−	13.8260i	1.23985	−	0.507910i
$742$	1.93227	−	10.9154i	0.0709360	−	0.400716i
$743$	−3.44991	+	2.89482i	−0.126565	+	0.106201i	−0.703873	−	0.710326i	$-0.748548\pi$
$743$	−3.44991	+	2.89482i	−0.126565	+	0.106201i	0.577308	+	0.816526i	$0.304103\pi$
$744$	−4.35423	−	10.6907i	−0.159634	−	0.391941i
$745$	−22.5055	+	8.19135i	−0.824539	+	0.300108i
$746$	−45.9572	−	16.7622i	−1.68261	−	0.613708i
$747$	−5.01228	+	18.1394i	−0.183390	+	0.663685i
$748$	5.39548	−	6.41247i	0.197278	−	0.234463i
$749$	5.94874	+	1.04892i	0.217362	+	0.0383268i
$750$	16.8299	−	15.2808i	0.614542	−	0.557976i
$751$	36.9941	+	13.4647i	1.34993	+	0.491335i	0.912927	−	0.408124i	$-0.133817\pi$
$751$	36.9941	+	13.4647i	1.34993	+	0.491335i	0.437006	+	0.899459i	$0.356039\pi$
$752$	−0.630390	+	3.51949i	−0.0229879	+	0.128343i
$753$	−0.255166	+	0.798419i	−0.00929875	+	0.0290960i
$754$	−0.0285857	+	42.3254i	−0.00104103	+	1.54140i
$755$			20.6870i			0.752876i
$756$	−14.5404	+	7.32987i	−0.528831	+	0.266585i
$757$			33.7213i			1.22562i	0.790229	+	0.612811i	$0.209961\pi$
$757$			33.7213i			1.22562i	−0.790229	+	0.612811i	$0.790039\pi$
$758$	38.4577	+	0.0259735i	1.39685	+	0.000943402i
$759$	33.4829	+	36.8273i	1.21535	+	1.33674i
$760$	−5.88786	−	7.04583i	−0.213575	−	0.255579i
$761$	−34.7776	−	12.6580i	−1.26069	−	0.458852i	−0.376687	−	0.926341i	$-0.622937\pi$
$761$	−34.7776	−	12.6580i	−1.26069	−	0.458852i	−0.883999	+	0.467489i	$0.845159\pi$
$762$	−2.73511	+	8.53834i	−0.0990827	+	0.309312i
$763$	5.13539	+	0.905508i	0.185914	+	0.0327816i
$764$	−27.6299	−	23.2479i	−0.999615	−	0.841080i
$765$	−2.54560	+	1.75304i	−0.0920365	+	0.0633814i
$766$	2.92794	−	8.02758i	0.105791	−	0.290048i
$767$	71.4980	−	26.0231i	2.58164	−	0.939641i
$768$	5.74627	+	27.1105i	0.207351	+	0.978267i
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	−0.719372	−	0.694625i	$-0.755570\pi$
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	0.559154	+	0.829064i	$0.311126\pi$
$770$	−9.61260	−	1.70166i	−0.346414	−	0.0613234i
$771$	24.3039	+	18.7999i	0.875283	+	0.677064i
$772$	−1.52951	−	8.74333i	−0.0550483	−	0.314679i
$773$	36.8149	−	21.2551i	1.32414	−	0.764492i	0.339753	−	0.940515i	$-0.389656\pi$
$773$	36.8149	−	21.2551i	1.32414	−	0.764492i	0.984386	+	0.176022i	$0.0563231\pi$
$774$	32.8241	−	32.2728i	1.17984	−	1.16002i
$775$	4.61456	−	7.99264i	0.165760	−	0.287104i
$776$	10.3770	+	28.6913i	0.372513	+	1.02996i
$777$	−8.45615	+	5.34095i	−0.303363	+	0.191605i
$778$	15.5361	−	5.64278i	0.556995	−	0.202304i
$779$	9.79190	−	1.72658i	0.350831	−	0.0618610i
$780$	12.9696	+	20.5960i	0.464387	+	0.737454i
$781$	−13.7170	+	16.3473i	−0.490833	+	0.584951i
$782$	6.10421	+	7.28470i	0.218286	+	0.260500i
$783$	−23.0006	−	1.27379i	−0.821976	−	0.0455216i
$784$	17.0664	+	6.26391i	0.609513	+	0.223711i
$785$	3.89904	+	3.27169i	0.139163	+	0.116771i
$786$	22.2418	−	9.09395i	0.793340	−	0.324371i
$787$	16.8983	−	2.97963i	0.602359	−	0.106212i	0.135851	−	0.990729i	$-0.456623\pi$
$787$	16.8983	−	2.97963i	0.602359	−	0.106212i	0.466508	+	0.884517i	$0.345512\pi$
$788$	28.2818	+	16.3795i	1.00750	+	0.583495i
$789$	13.9365	−	0.554078i	0.496154	−	0.0197257i
$790$	6.50607	+	11.2864i	0.231476	+	0.401554i
$791$	−6.54642	+	11.3387i	−0.232764	+	0.403159i
$792$	25.6454	−	25.1466i	0.911271	−	0.893547i
$793$	18.5627	+	32.1515i	0.659179	+	1.14173i
$794$	−1.89098	+	3.27017i	−0.0671084	+	0.116054i
$795$	1.21190	−	8.93607i	0.0429817	−	0.316930i
$796$	0.915501	+	1.59065i	0.0324491	+	0.0563791i
$797$	4.53298	+	5.40220i	0.160567	+	0.191356i	0.840329	−	0.542076i	$-0.182362\pi$
$797$	4.53298	+	5.40220i	0.160567	+	0.191356i	−0.679763	+	0.733432i	$0.737917\pi$
$798$	−5.57636	+	10.5935i	−0.197401	+	0.375007i
$799$	0.831499	−	0.302641i	0.0294163	−	0.0107067i
$800$	−14.2993	+	16.9249i	−0.505557	+	0.598384i
$801$	−2.29100	+	24.0278i	−0.0809483	+	0.848980i
$802$	17.3081	−	3.03984i	0.611171	−	0.107340i
$803$	−58.5114	−	10.3171i	−2.06482	−	0.364084i
$804$	1.54351	−	1.98983i	0.0544352	−	0.0701758i
$805$	3.78652	−	10.4034i	0.133457	−	0.366670i
$806$	17.2232	+	14.4719i	0.606663	+	0.509749i
$807$	−11.1115	+	2.41797i	−0.391144	+	0.0851167i
$808$	−3.28230	+	18.3968i	−0.115471	+	0.647197i
$809$	−34.2649			−1.20469			−0.602345	−	0.798236i	$-0.705767\pi$
$809$	−34.2649			−1.20469			−0.602345	+	0.798236i	$0.705767\pi$
$810$	−11.5783	+	6.43599i	−0.406820	+	0.226138i
$811$			5.06146i			0.177732i	0.996044	+	0.0888659i	$0.0283243\pi$
$811$			5.06146i			0.177732i	−0.996044	+	0.0888659i	$0.971676\pi$
$812$	−8.91571	−	10.6545i	−0.312880	−	0.373900i
$813$	4.00050	+	18.3839i	0.140304	+	0.644750i
$814$	14.1919	−	16.8901i	0.497427	−	0.591998i
$815$	4.08885	+	1.48822i	0.143226	+	0.0521301i
$816$	5.08697	−	4.59997i	0.178080	−	0.161031i
$817$	5.87673	−	33.3286i	0.205601	−	1.16602i
$818$	7.17937	−	1.26092i	0.251021	−	0.0440869i
$819$	18.4037	−	25.8520i	0.643077	−	0.903342i
$820$	2.26098	+	6.23820i	0.0789569	+	0.217847i
$821$	−5.19050	−	14.2608i	−0.181150	−	0.497705i	0.815568	−	0.578661i	$-0.196425\pi$
$821$	−5.19050	−	14.2608i	−0.181150	−	0.497705i	−0.996718	+	0.0809566i	$0.974202\pi$
$822$	47.8840	+	25.2057i	1.67014	+	0.879151i
$823$	22.8496	−	19.1731i	0.796487	−	0.668332i	−0.150855	−	0.988556i	$-0.548203\pi$
$823$	22.8496	−	19.1731i	0.796487	−	0.668332i	0.947342	+	0.320224i	$0.103758\pi$
$824$	−15.4570	+	42.2015i	−0.538471	+	1.47016i
$825$	28.4557	+	3.85914i	0.990701	+	0.134358i
$826$	−12.5018	+	21.6200i	−0.434993	+	0.752256i
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	−0.368706	−	0.929546i	$-0.620199\pi$
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	0.620658	+	0.784082i	$0.286866\pi$
$828$	23.0575	+	33.5790i	0.801304	+	1.16695i
$829$	−26.4946	−	15.2967i	−0.920196	−	0.531276i	−0.0364987	−	0.999334i	$-0.511620\pi$
$829$	−26.4946	−	15.2967i	−0.920196	−	0.531276i	−0.883698	+	0.468058i	$0.844954\pi$
$830$	−7.99923	+	4.61116i	−0.277657	+	0.160056i
$831$	−2.18154	−	54.8716i	−0.0756768	−	1.90348i
$832$	−34.5473	−	41.5124i	−1.19771	−	1.43918i
$833$	−0.781255	−	4.43072i	−0.0270689	−	0.153515i
$834$	−10.7942	+	4.41338i	−0.373772	+	0.152823i
$835$	−4.07776	+	4.85968i	−0.141117	+	0.168176i
$836$	4.62051	−	25.9988i	0.159804	−	0.899188i
$837$	−8.37666	+	8.92965i	−0.289540	+	0.308654i
$838$	3.11099	−	2.60685i	0.107467	−	0.0900522i
$839$	5.60536	+	4.70346i	0.193519	+	0.162381i	0.734399	−	0.678718i	$-0.237464\pi$
$839$	5.60536	+	4.70346i	0.193519	+	0.162381i	−0.540880	+	0.841100i	$0.681909\pi$
$840$	−7.60495	−	2.44745i	−0.262396	−	0.0844449i
$841$	1.62295	+	9.20422i	0.0559639	+	0.317387i
$842$	17.9185	−	6.50811i	0.617514	−	0.224284i
$843$	−18.1590	−	28.7505i	−0.625428	−	0.990219i
$844$	−4.21025	+	11.5191i	−0.144923	+	0.396505i
$845$	−29.3610	−	16.9516i	−1.01005	−	0.583151i
$846$	3.67135	−	0.950484i	0.126224	−	0.0326783i
$847$	−5.41924	−	9.38639i	−0.186207	−	0.322520i
$848$	−0.0540575	+	20.0100i	−0.00185634	+	0.687146i
$849$	20.9000	−	27.0187i	0.717285	−	0.927280i
$850$	5.39939	+	0.955818i	0.185197	+	0.0327843i
$851$	16.0820	+	19.1657i	0.551283	+	0.656993i
$852$	−12.9376	+	11.7308i	−0.443236	+	0.401892i
$853$	−15.5473	−	42.7160i	−0.532331	−	1.46257i	−0.856290	−	0.516496i	$-0.827236\pi$
$853$	−15.5473	−	42.7160i	−0.532331	−	1.46257i	0.323959	−	0.946071i	$-0.394986\pi$
$854$	−11.4482	−	4.17555i	−0.391748	−	0.142884i
$855$	−4.18458	+	8.79424i	−0.143109	+	0.300757i
$856$	−10.9039	−	0.0220929i	−0.372688	−	0.000755120i
$857$	−3.84017	+	21.7787i	−0.131178	+	0.743946i	0.846268	+	0.532758i	$0.178844\pi$
$857$	−3.84017	+	21.7787i	−0.131178	+	0.743946i	−0.977445	+	0.211188i	$0.932267\pi$
$858$	−21.3533	+	66.6596i	−0.728989	+	2.27572i
$859$	10.5655	−	29.0285i	0.360491	−	0.990441i	−0.618365	−	0.785891i	$-0.712205\pi$
$859$	10.5655	−	29.0285i	0.360491	−	0.990441i	0.978856	−	0.204550i	$-0.0655730\pi$
$860$	22.5845	+	0.0305062i	0.770123	+	0.00104025i
$861$	6.40098	−	5.81969i	0.218145	−	0.198335i
$862$	−0.0240840	+	35.6599i	−0.000820303	+	1.21458i
$863$	−27.4661			−0.934956			−0.467478	−	0.884005i	$-0.654837\pi$
$863$	−27.4661			−0.934956			−0.467478	+	0.884005i	$0.654837\pi$
$864$	23.5867	−	17.5405i	0.802436	−	0.596739i
$865$	−1.38039			−0.0469348
$866$	0.0148674	−	22.0134i	0.000505215	−	0.748046i
$867$	26.4306	+	8.44692i	0.897630	+	0.286872i
$868$	−7.38404	−	0.00997407i	−0.250631	−	0.000338542i
$869$	−12.8137	+	35.2053i	−0.434675	+	1.19426i
$870$	−7.59732	−	8.36751i	−0.257573	−	0.283685i
$871$	−0.852216	+	4.83316i	−0.0288762	+	0.163765i
$872$	−9.41306	−	0.0190722i	−0.318766	−	0.000645866i
$873$	23.0603	−	22.7036i	0.780474	−	0.768402i
$874$	28.1340	+	10.2615i	0.951648	+	0.347100i
$875$	−4.97337	−	13.6642i	−0.168131	−	0.461935i
$876$	−46.2954	−	14.8644i	−1.56418	−	0.502223i
$877$	7.68788	+	9.16206i	0.259601	+	0.309381i	0.880064	−	0.474855i	$-0.157500\pi$
$877$	7.68788	+	9.16206i	0.259601	+	0.309381i	−0.620463	+	0.784236i	$0.713055\pi$
$878$	44.3708	+	7.85468i	1.49744	+	0.265083i
$879$	−17.4590	−	42.6188i	−0.588879	−	1.43750i
$880$	17.6218	+	0.0476057i	0.594030	+	0.00160479i
$881$	18.8243	+	32.6046i	0.634205	+	1.09848i	0.986683	+	0.162655i	$0.0520059\pi$
$881$	18.8243	+	32.6046i	0.634205	+	1.09848i	−0.352478	+	0.935820i	$0.614661\pi$
$882$	−1.51782	−	19.2225i	−0.0511077	−	0.647256i
$883$	19.8345	+	11.4515i	0.667485	+	0.385373i	0.795123	−	0.606448i	$-0.207406\pi$
$883$	19.8345	+	11.4515i	0.667485	+	0.385373i	−0.127638	+	0.991821i	$0.540739\pi$
$884$	−4.58831	+	12.5535i	−0.154321	+	0.422219i
$885$	−9.45153	+	17.9847i	−0.317710	+	0.604551i
$886$	8.40762	−	3.05369i	0.282459	−	0.102591i
$887$	0.995710	+	5.64695i	0.0334327	+	0.189606i	0.996950	−	0.0780387i	$-0.0248658\pi$
$887$	0.995710	+	5.64695i	0.0334327	+	0.189606i	−0.963518	+	0.267645i	$0.913755\pi$
$888$	13.3830	−	12.1182i	0.449104	−	0.406661i
$889$	4.39338	+	3.68648i	0.147349	+	0.123641i
$890$	−9.07670	+	7.60581i	−0.304252	+	0.254947i
$891$	−35.5910	−	13.5860i	−1.19234	−	0.455147i
$892$	7.50355	−	42.2212i	0.251237	−	1.41367i
$893$	1.79219	−	2.13585i	0.0599735	−	0.0714737i
$894$	−44.5615	−	34.5181i	−1.49036	−	1.15446i
$895$	2.02139	+	11.4639i	0.0675675	+	0.383194i
$896$	17.4431	+	3.16080i	0.582734	+	0.105595i
$897$	−70.2692	−	36.9286i	−2.34622	−	1.23301i
$898$	10.2465	−	5.90660i	0.341931	−	0.197106i
$899$	−9.04655	−	5.22303i	−0.301719	−	0.174198i
$900$	22.6434	+	6.28977i	0.754781	+	0.209659i
$901$	4.28862	−	2.47604i	0.142875	−	0.0824888i
$902$	−9.55219	+	16.5191i	−0.318053	+	0.550026i
$903$	−11.1622	−	27.2479i	−0.371456	−	0.906753i
$904$	8.12841	−	22.1926i	0.270347	−	0.738116i
$905$	2.95572	−	2.48014i	0.0982513	−	0.0824426i
$906$	−41.1818	+	25.9717i	−1.36817	+	0.862853i
$907$	8.42248	+	23.1406i	0.279664	+	0.768370i	0.997401	+	0.0720557i	$0.0229559\pi$
$907$	8.42248	+	23.1406i	0.279664	+	0.768370i	−0.717737	+	0.696315i	$0.754822\pi$
$908$	−12.6815	−	34.9891i	−0.420851	−	1.16116i
$909$	19.1849	−	4.98065i	0.636323	−	0.165198i
$910$	15.3346	−	2.69322i	0.508336	−	0.0892795i
$911$	6.32793	−	35.8875i	0.209654	−	1.18901i	−0.680293	−	0.732940i	$-0.738147\pi$
$911$	6.32793	−	35.8875i	0.209654	−	1.18901i	0.889947	−	0.456065i	$-0.150741\pi$
$912$	6.63420	−	20.5668i	0.219680	−	0.681035i
$913$	−24.9517	−	9.08166i	−0.825780	−	0.300559i
$914$	25.6218	−	30.4930i	0.847494	−	1.00862i
$915$	−9.44290	−	3.01784i	−0.312173	−	0.0997668i
$916$	11.3979	+	13.6208i	0.376596	+	0.450043i
$917$		−	15.3708i		−	0.507590i
$918$	−6.68571	−	2.86668i	−0.220661	−	0.0946145i
$919$	27.8245			0.917845			0.458923	−	0.888476i	$-0.348236\pi$
$919$	27.8245			0.917845			0.458923	+	0.888476i	$0.348236\pi$
$920$	−3.51018	+	19.6740i	−0.115727	+	0.648634i
$921$	−26.9633	−	29.6565i	−0.888470	−	0.977213i
$922$	28.3007	+	23.7797i	0.932034	+	0.783143i
$923$	11.6405	−	31.9819i	0.383151	−	1.05270i
$924$	−8.68076	−	21.2723i	−0.285576	−	0.699806i
$925$	14.2153	+	2.50654i	0.467397	+	0.0824146i
$926$	−30.8511	+	5.41840i	−1.01383	+	0.178060i
$927$	47.5190	−	3.78443i	1.56073	−	0.124297i
$928$	19.1565	+	16.1848i	0.628845	+	0.531292i
$929$	14.0864	−	5.12703i	0.462160	−	0.168212i	−0.100438	−	0.994943i	$-0.532024\pi$
$929$	14.0864	−	5.12703i	0.462160	−	0.168212i	0.562598	+	0.826731i	$0.309802\pi$
$930$	−6.00245	+	0.234580i	−0.196828	+	0.00769219i
$931$	−9.11238	−	10.8597i	−0.298646	−	0.355913i
$932$	−18.7506	−	32.5786i	−0.614197	−	1.06715i
$933$	−33.4088	−	25.8429i	−1.09375	−	0.846060i
$934$	−15.6675	+	27.0946i	−0.512656	+	0.886564i
$935$	−2.18052	−	3.77677i	−0.0713106	−	0.123514i
$936$	−24.7177	+	51.6762i	−0.807923	+	1.68909i
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	−0.978952	−	0.204090i	$-0.934577\pi$
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	0.666223	+	0.745753i	$0.267910\pi$
$938$	−0.804504	−	1.39562i	−0.0262680	−	0.0455685i
$939$	23.8352	+	37.7375i	0.777833	+	1.23152i
$940$	1.61010	+	0.932496i	0.0525158	+	0.0304147i
$941$	−36.4053	+	6.41923i	−1.18678	+	0.209261i	−0.731975	−	0.681331i	$-0.761401\pi$
$941$	−36.4053	+	6.41923i	−1.18678	+	0.209261i	−0.454803	+	0.890592i	$0.650290\pi$
$942$	−1.61787	+	11.8693i	−0.0527132	+	0.386724i
$943$	−16.5778	−	13.9104i	−0.539847	−	0.452985i
$944$	15.5334	−	42.3216i	0.505569	−	1.37745i
$945$	1.00775	+	8.41355i	0.0327820	+	0.273693i
$946$	41.7151	+	49.7823i	1.35627	+	1.61856i
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	−0.439627	−	0.898180i	$-0.644890\pi$
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	0.960875	+	0.276981i	$0.0893340\pi$
$948$	−14.2999	+	27.1214i	−0.464439	+	0.880863i
$949$	93.3185	−	16.4546i	3.02925	−	0.534138i
$950$	16.2397	−	5.89836i	0.526887	−	0.191368i
$951$	1.26721	+	31.8738i	0.0410922	+	1.03358i
$952$	−1.49213	−	4.12557i	−0.0483601	−	0.133711i
$953$	−7.31014	+	12.6615i	−0.236799	+	0.410147i	−0.959794	−	0.280706i	$-0.909432\pi$
$953$	−7.31014	+	12.6615i	−0.236799	+	0.410147i	0.722995	+	0.690853i	$0.242765\pi$
$954$	19.3106	−	8.80637i	0.625205	−	0.285117i
$955$	−16.2733	+	9.39537i	−0.526590	+	0.304027i
$956$	−7.07841	−	40.4632i	−0.228932	−	1.30867i
$957$	4.36800	−	32.2079i	0.141197	−	1.04113i
$958$	−16.5592	−	2.93137i	−0.535004	−	0.0947083i
$959$	26.5164	−	22.2499i	0.856258	−	0.718486i
$960$	14.2826	+	1.99596i	0.460968	+	0.0644194i
$961$	23.9132	−	8.70369i	0.771393	−	0.280764i
$962$	−12.0562	+	33.0545i	−0.388706	+	1.06572i
$963$	4.80590	+	10.5196i	0.154868	+	0.338988i
$964$	21.0819	+	17.7384i	0.679004	+	0.571316i
$965$	−4.54883	−	0.802081i	−0.146432	−	0.0258199i
$966$	25.4639	−	5.52319i	0.819288	−	0.177706i
$967$	48.8192	+	17.7687i	1.56992	+	0.571404i	0.972981	−	0.230884i	$-0.0741619\pi$
$967$	48.8192	+	17.7687i	1.56992	+	0.571404i	0.596937	+	0.802288i	$0.296384\pi$
$968$	12.5457	+	15.0130i	0.403234	+	0.482537i
$969$	−5.22581	+	1.13719i	−0.167877	+	0.0365317i
$970$	15.8771	+	0.0107231i	0.509783	+	0.000344297i
$971$			20.4952i			0.657724i	0.944378	+	0.328862i	$0.106665\pi$
$971$			20.4952i			0.657724i	−0.944378	+	0.328862i	$0.893335\pi$
$972$	−27.3483	−	14.9689i	−0.877198	−	0.480128i
$973$			7.45961i			0.239144i
$974$	−0.0211259	+	31.2800i	−0.000676918	+	1.00228i
$975$	−44.7515	+	9.73837i	−1.43320	+	0.311877i
$976$	21.6526	+	3.87828i	0.693083	+	0.124141i
$977$	−7.72505	−	2.81169i	−0.247146	−	0.0899539i	0.215477	−	0.976509i	$-0.430869\pi$
$977$	−7.72505	−	2.81169i	−0.247146	−	0.0899539i	−0.462623	+	0.886555i	$0.653092\pi$
$978$	2.17079	+	10.0081i	0.0694142	+	0.320025i
$979$	−33.5386	−	5.91376i	−1.07190	−	0.189004i
$980$	6.09081	−	7.23886i	0.194564	−	0.231237i
$981$	4.14880	+	9.08126i	0.132461	+	0.289942i
$982$	−9.91804	−	3.61746i	−0.316497	−	0.115438i
$983$	−22.5289	+	8.19984i	−0.718559	+	0.261534i	−0.675314	−	0.737530i	$-0.735992\pi$
$983$	−22.5289	+	8.19984i	−0.718559	+	0.261534i	−0.0432453	+	0.999064i	$0.513770\pi$
$984$	−9.57987	+	12.3328i	−0.305395	+	0.393155i
$985$	13.0285	−	10.9322i	0.415123	−	0.348330i
$986$	1.08185	−	6.11135i	0.0344532	−	0.194625i
$987$	0.326014	−	2.40389i	0.0103771	−	0.0765168i
$988$	7.25711	+	41.4847i	0.230880	+	1.31981i
$989$	−63.7900	+	36.8292i	−2.02840	+	1.17110i
$990$	−7.75531	−	17.0059i	−0.246480	−	0.540482i
$991$	8.43544	−	14.6106i	0.267960	−	0.464121i	−0.700375	−	0.713776i	$-0.746984\pi$
$991$	8.43544	−	14.6106i	0.267960	−	0.464121i	0.968335	+	0.249654i	$0.0803170\pi$
$992$	13.1344	−	2.27025i	0.417019	−	0.0720805i
$993$	1.06459	+	26.7773i	0.0337837	+	0.849751i
$994$	3.81374	+	10.5002i	0.120964	+	0.333047i
$995$	0.940553	−	0.165845i	0.0298175	−	0.00525763i
$996$	−19.2222	−	10.1350i	−0.609079	−	0.321140i
$997$	−21.3234	+	25.4122i	−0.675317	+	0.804812i	−0.989497	−	0.144552i	$-0.953826\pi$
$997$	−21.3234	+	25.4122i	−0.675317	+	0.804812i	0.314180	+	0.949363i	$0.398270\pi$
$998$	−11.2218	+	9.40333i	−0.355221	+	0.297657i
$999$	−17.6049	−	7.53450i	−0.556994	−	0.238381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.205.18	yes	204
3.2	odd	2		648.2.t.a.613.17		204
4.3	odd	2		864.2.bf.a.529.15		204
8.3	odd	2		864.2.bf.a.529.20		204
8.5	even	2	inner	216.2.t.a.205.32	yes	204
24.5	odd	2		648.2.t.a.613.3		204
27.5	odd	18		648.2.t.a.37.3		204
27.22	even	9	inner	216.2.t.a.157.32	yes	204
108.103	odd	18		864.2.bf.a.49.20		204
216.5	odd	18		648.2.t.a.37.17		204
216.157	even	18	inner	216.2.t.a.157.18	✓	204
216.211	odd	18		864.2.bf.a.49.15		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.18	✓	204	216.157	even	18	inner
216.2.t.a.157.32	yes	204	27.22	even	9	inner
216.2.t.a.205.18	yes	204	1.1	even	1	trivial
216.2.t.a.205.32	yes	204	8.5	even	2	inner
648.2.t.a.37.3		204	27.5	odd	18
648.2.t.a.37.17		204	216.5	odd	18
648.2.t.a.613.3		204	24.5	odd	2
648.2.t.a.613.17		204	3.2	odd	2
864.2.bf.a.49.15		204	216.211	odd	18
864.2.bf.a.49.20		204	108.103	odd	18
864.2.bf.a.529.15		204	4.3	odd	2
864.2.bf.a.529.20		204	8.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.000955132 + 1.41421i) q^{2} +(0.368292 + 1.69244i) q^{3} +(-2.00000 - 0.00270152i) q^{4} +(-0.355965 + 0.978005i) q^{5} +(-2.39383 + 0.519227i) q^{6} +(-0.272085 + 1.54307i) q^{7} +(0.00573079 - 2.82842i) q^{8} +(-2.72872 + 1.24663i) q^{9} +(-1.38277 - 0.504344i) q^{10} +(-1.44773 - 3.97760i) q^{11} +(-0.732011 - 3.38588i) q^{12} +(4.33941 + 5.17151i) q^{13} +(-2.18198 - 0.386261i) q^{14} +(-1.78632 - 0.242259i) q^{15} +(3.99999 + 0.0108061i) q^{16} +(-0.494959 - 0.857294i) q^{17} +(-1.76039 - 3.86019i) q^{18} +(-2.70129 - 1.55959i) q^{19} +(0.714571 - 1.95505i) q^{20} +(-2.71177 + 0.107812i) q^{21} +(5.62656 - 2.04360i) q^{22} +(1.17888 + 6.68573i) q^{23} +(4.78905 - 1.03199i) q^{24} +(3.00044 + 2.51767i) q^{25} +(-7.31776 + 6.13191i) q^{26} +(-3.11481 - 4.15908i) q^{27} +(0.548339 - 3.08541i) q^{28} +(2.84964 - 3.39607i) q^{29} +(0.344311 - 2.52600i) q^{30} +(-0.409166 - 2.32049i) q^{31} +(-0.0191026 + 5.65682i) q^{32} +(6.19868 - 3.91512i) q^{33} +(1.21287 - 0.699158i) q^{34} +(-1.41228 - 0.815381i) q^{35} +(5.46081 - 2.48588i) q^{36} +(3.19157 - 1.84266i) q^{37} +(2.20817 - 3.81871i) q^{38} +(-7.15431 + 9.24883i) q^{39} +(2.76417 + 1.01242i) q^{40} +(-2.44191 + 2.04900i) q^{41} +(-0.149880 - 3.83512i) q^{42} +(3.71087 + 10.1955i) q^{43} +(2.88471 + 7.95911i) q^{44} +(-0.247877 - 3.11246i) q^{45} +(-9.45618 + 1.66079i) q^{46} +(-0.155220 + 0.880296i) q^{47} +(1.45487 + 6.77372i) q^{48} +(4.27080 + 1.55445i) q^{49} +(-3.56338 + 4.24086i) q^{50} +(1.26863 - 1.15342i) q^{51} +(-8.66484 - 10.3547i) q^{52} +5.00251i q^{53} +(5.88481 - 4.40103i) q^{54} +4.40546 q^{55} +(4.36290 + 0.778415i) q^{56} +(1.64465 - 5.14616i) q^{57} +(4.80005 + 4.03325i) q^{58} +(3.85475 - 10.5908i) q^{59} +(3.57198 + 0.489342i) q^{60} +(5.41575 + 0.954943i) q^{61} +(3.28206 - 0.576431i) q^{62} +(-1.18119 - 4.54981i) q^{63} +(-7.99993 - 0.0324182i) q^{64} +(-6.60244 + 2.40309i) q^{65} +(5.53089 + 8.76999i) q^{66} +(0.467287 + 0.556891i) q^{67} +(0.987601 + 1.71592i) q^{68} +(-10.8810 + 4.45748i) q^{69} +(1.15447 - 1.99649i) q^{70} +(-2.52073 - 4.36603i) q^{71} +(3.51034 + 7.72512i) q^{72} +(7.01816 - 12.1558i) q^{73} +(2.60286 + 4.51532i) q^{74} +(-3.15597 + 6.00531i) q^{75} +(5.39836 + 3.12648i) q^{76} +(6.53164 - 1.15170i) q^{77} +(-13.0730 - 10.1266i) q^{78} +(-6.78017 - 5.68924i) q^{79} +(-1.43442 + 3.90816i) q^{80} +(5.89185 - 6.80339i) q^{81} +(-2.89539 - 3.45533i) q^{82} +(4.03223 - 4.80543i) q^{83} +(5.42383 - 0.208299i) q^{84} +(1.01463 - 0.178906i) q^{85} +(-14.4222 + 5.23823i) q^{86} +(6.79716 + 3.57211i) q^{87} +(-11.2586 + 4.07199i) q^{88} +(4.02279 - 6.96768i) q^{89} +(4.40192 - 0.347578i) q^{90} +(-9.16071 + 5.28894i) q^{91} +(-2.33969 - 13.3746i) q^{92} +(3.77661 - 1.54711i) q^{93} +(-1.24478 - 0.220355i) q^{94} +(2.48685 - 2.08672i) q^{95} +(-9.58088 + 2.05103i) q^{96} +(-10.1365 + 3.68937i) q^{97} +(-2.20240 + 6.03834i) q^{98} +(8.90903 + 9.04900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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