LMFDB - Embedded newform 216.2.t.a.205.32

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			205.32
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39256 - 0.246516i) q^{2} +(-0.368292 - 1.69244i) q^{3} +(1.87846 - 0.686578i) q^{4} +(0.355965 - 0.978005i) q^{5} +(-0.930084 - 2.26604i) q^{6} +(-0.272085 + 1.54307i) q^{7} +(2.44662 - 1.41917i) q^{8} +(-2.72872 + 1.24663i) q^{9} +(0.254609 - 1.44968i) q^{10} +(1.44773 + 3.97760i) q^{11} +(-1.85382 - 2.92632i) q^{12} +(-4.33941 - 5.17151i) q^{13} +(0.00149657 + 2.21590i) q^{14} +(-1.78632 - 0.242259i) q^{15} +(3.05722 - 2.57942i) q^{16} +(-0.494959 - 0.857294i) q^{17} +(-3.49260 + 2.40868i) q^{18} +(2.70129 + 1.55959i) q^{19} +(-0.00281166 - 2.08154i) q^{20} +(2.71177 - 0.107812i) q^{21} +(2.99660 + 5.18217i) q^{22} +(1.17888 + 6.68573i) q^{23} +(-3.30294 - 3.61809i) 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} +(-2.54728 + 0.102996i) q^{30} +(-0.409166 - 2.32049i) q^{31} +(3.62150 - 4.34566i) q^{32} +(6.19868 - 3.91512i) q^{33} +(-0.900598 - 1.07182i) q^{34} +(1.41228 + 0.815381i) q^{35} +(-4.26989 + 4.21522i) q^{36} +(-3.19157 + 1.84266i) q^{37} +(4.14618 + 1.50592i) q^{38} +(-7.15431 + 9.24883i) q^{39} +(-0.517049 - 2.89798i) q^{40} +(-2.44191 + 2.04900i) q^{41} +(3.74973 - 0.818631i) q^{42} +(-3.71087 - 10.1955i) q^{43} +(5.45044 + 6.47779i) q^{44} +(0.247877 + 3.11246i) q^{45} +(3.28980 + 9.01969i) q^{46} +(-0.155220 + 0.880296i) q^{47} +(-5.49147 - 4.22419i) q^{48} +(4.27080 + 1.55445i) q^{49} +(4.79894 + 2.76635i) q^{50} +(-1.26863 + 1.15342i) q^{51} +(-11.7021 - 6.73512i) q^{52} -5.00251i q^{53} +(5.36285 + 5.02393i) q^{54} +4.40546 q^{55} +(1.52420 + 4.16145i) q^{56} +(1.64465 - 5.14616i) q^{57} +(-3.13112 + 5.43173i) q^{58} +(-3.85475 + 10.5908i) q^{59} +(-3.52185 + 0.771373i) q^{60} +(-5.41575 - 0.954943i) q^{61} +(-1.14183 - 3.13057i) q^{62} +(-1.18119 - 4.54981i) q^{63} +(3.97189 - 6.94436i) q^{64} +(-6.60244 + 2.40309i) q^{65} +(7.66690 - 6.98012i) q^{66} +(-0.467287 - 0.556891i) q^{67} +(-1.51836 - 1.27056i) q^{68} +(10.8810 - 4.45748i) q^{69} +(2.16769 + 0.787319i) q^{70} +(-2.52073 - 4.36603i) q^{71} +(-4.90697 + 6.92255i) q^{72} +(7.01816 - 12.1558i) q^{73} +(-3.99022 + 3.35279i) q^{74} +(3.15597 - 6.00531i) q^{75} +(6.14505 + 1.07498i) q^{76} +(-6.53164 + 1.15170i) q^{77} +(-7.68284 + 14.6432i) 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} +(5.01993 - 2.06436i) q^{84} +(-1.01463 + 0.178906i) q^{85} +(-7.68099 - 13.2831i) q^{86} +(6.79716 + 3.57211i) q^{87} +(9.18695 + 7.67710i) q^{88} +(4.02279 - 6.96768i) q^{89} +(1.11246 + 4.27319i) q^{90} +(9.16071 - 5.28894i) q^{91} +(6.80475 + 11.7495i) q^{92} +(-3.77661 + 1.54711i) q^{93} +(0.000853769 + 1.26413i) q^{94} +(2.48685 - 2.08672i) q^{95} +(-8.68854 - 4.52871i) q^{96} +(-10.1365 + 3.68937i) q^{97} +(6.33056 + 1.11184i) 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 $

$2$	1.39256	−	0.246516i	0.984690	−	0.174313i
$2$	1.39256	−	0.246516i	0.984690	−	0.174313i
$3$	−0.368292	−	1.69244i	−0.212633	−	0.977132i
$3$	−0.368292	−	1.69244i	−0.212633	−	0.977132i
$4$	1.87846	−	0.686578i	0.939230	−	0.343289i
$5$	0.355965	−	0.978005i	0.159192	−	0.437377i	−0.834295	−	0.551318i	$-0.814125\pi$
$5$	0.355965	−	0.978005i	0.159192	−	0.437377i	0.993488	+	0.113941i	$0.0363474\pi$
$6$	−0.930084	−	2.26604i	−0.379705	−	0.925108i
$7$	−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	$0.959865\pi$
$8$	2.44662	−	1.41917i	0.865011	−	0.501754i
$9$	−2.72872	+	1.24663i	−0.909574	+	0.415542i
$10$	0.254609	−	1.44968i	0.0805145	−	0.458430i
$11$	1.44773	+	3.97760i	0.436507	+	1.19929i	0.941750	+	0.336315i	$0.109181\pi$
$11$	1.44773	+	3.97760i	0.436507	+	1.19929i	−0.505243	+	0.862977i	$0.668597\pi$
$12$	−1.85382	−	2.92632i	−0.535150	−	0.844757i
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.871039	−	0.491214i	$-0.836553\pi$
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.332497	−	0.943104i	$-0.607891\pi$
$14$	0.00149657	+	2.21590i	0.000399976	+	0.592224i
$15$	−1.78632	−	0.242259i	−0.461225	−	0.0625509i
$16$	3.05722	−	2.57942i	0.764305	−	0.644855i
$17$	−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	$0.871637\pi$
$18$	−3.49260	+	2.40868i	−0.823214	+	0.567731i
$19$	2.70129	+	1.55959i	0.619719	+	0.357795i	0.776759	−	0.629797i	$-0.216862\pi$
$19$	2.70129	+	1.55959i	0.619719	+	0.357795i	−0.157041	+	0.987592i	$0.550195\pi$
$20$	−0.00281166	−	2.08154i	−0.000628707	−	0.465447i
$21$	2.71177	−	0.107812i	0.591757	−	0.0235266i
$22$	2.99660	+	5.18217i	0.638876	+	1.10484i
$23$	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	$0.694137\pi$
$24$	−3.30294	−	3.61809i	−0.674210	−	0.738540i
$25$	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	−0.962722	−	0.270491i	$-0.912814\pi$
$29$	−2.84964	+	3.39607i	−0.529166	+	0.630635i	0.433557	+	0.901126i	$0.357258\pi$
$30$	−2.54728	+	0.102996i	−0.465067	+	0.0188044i
$31$	−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	$-0.123423\pi$
$32$	3.62150	−	4.34566i	0.640197	−	0.768211i
$33$	6.19868	−	3.91512i	1.07905	−	0.681534i
$34$	−0.900598	−	1.07182i	−0.154451	−	0.183816i
$35$	1.41228	+	0.815381i	0.238719	+	0.137825i
$36$	−4.26989	+	4.21522i	−0.711648	+	0.702536i
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	−0.738852	−	0.673868i	$-0.764632\pi$
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	0.214161	+	0.976798i	$0.431298\pi$
$38$	4.14618	+	1.50592i	0.672599	+	0.244292i
$39$	−7.15431	+	9.24883i	−1.14561	+	1.48100i
$40$	−0.517049	−	2.89798i	−0.0817526	−	0.458211i
$41$	−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	$0.357852\pi$
$42$	3.74973	−	0.818631i	0.578596	−	0.126317i
$43$	−3.71087	−	10.1955i	−0.565903	−	1.55481i	−0.810841	−	0.585267i	$-0.800990\pi$
$43$	−3.71087	−	10.1955i	−0.565903	−	1.55481i	0.244938	−	0.969539i	$-0.421233\pi$
$44$	5.45044	+	6.47779i	0.821684	+	0.976563i
$45$	0.247877	+	3.11246i	0.0369513	+	0.463978i
$46$	3.28980	+	9.01969i	0.485054	+	1.32988i
$47$	−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	$0.0763217\pi$
$48$	−5.49147	−	4.22419i	−0.792625	−	0.609709i
$49$	4.27080	+	1.55445i	0.610115	+	0.222064i
$50$	4.79894	+	2.76635i	0.678673	+	0.391221i
$51$	−1.26863	+	1.15342i	−0.177644	+	0.161512i
$52$	−11.7021	−	6.73512i	−1.62278	−	0.933994i
$53$		−	5.00251i		−	0.687148i	−0.939126	−	0.343574i	$-0.888362\pi$
$53$		−	5.00251i		−	0.687148i	0.939126	−	0.343574i	$-0.111638\pi$
$54$	5.36285	+	5.02393i	0.729791	+	0.683671i
$55$	4.40546			0.594032
$56$	1.52420	+	4.16145i	0.203680	+	0.556097i
$57$	1.64465	−	5.14616i	0.217840	−	0.681626i
$58$	−3.13112	+	5.43173i	−0.411136	+	0.713221i
$59$	−3.85475	+	10.5908i	−0.501846	+	1.37881i	0.387625	+	0.921817i	$0.373296\pi$
$59$	−3.85475	+	10.5908i	−0.501846	+	1.37881i	−0.889470	+	0.456993i	$0.848927\pi$
$60$	−3.52185	+	0.771373i	−0.454669	+	0.0995839i
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.184177	−	0.982893i	$-0.558962\pi$
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.509239	+	0.860625i	$0.670073\pi$
$62$	−1.14183	−	3.13057i	−0.145012	−	0.397582i
$63$	−1.18119	−	4.54981i	−0.148816	−	0.573222i
$64$	3.97189	−	6.94436i	0.496487	−	0.868044i
$65$	−6.60244	+	2.40309i	−0.818932	+	0.298067i
$66$	7.66690	−	6.98012i	0.943731	−	0.859193i
$67$	−0.467287	−	0.556891i	−0.0570882	−	0.0680351i	0.736745	−	0.676171i	$-0.236362\pi$
$67$	−0.467287	−	0.556891i	−0.0570882	−	0.0680351i	−0.793833	+	0.608136i	$0.791918\pi$
$68$	−1.51836	−	1.27056i	−0.184128	−	0.154078i
$69$	10.8810	−	4.45748i	1.30992	−	0.536617i
$70$	2.16769	+	0.787319i	0.259089	+	0.0941026i
$71$	−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	$0.930038\pi$
$72$	−4.90697	+	6.92255i	−0.578292	+	0.815830i
$73$	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	$-0.140147\pi$
$74$	−3.99022	+	3.35279i	−0.463854	+	0.389753i
$75$	3.15597	−	6.00531i	0.364420	−	0.693433i
$76$	6.14505	+	1.07498i	0.704885	+	0.123309i
$77$	−6.53164	+	1.15170i	−0.744349	+	0.131249i
$78$	−7.68284	+	14.6432i	−0.869910	+	1.65802i
$79$	−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	−0.940512	−	0.339760i	$-0.889654\pi$
$83$	−4.03223	+	4.80543i	−0.442595	+	0.527464i	0.497917	+	0.867225i	$0.334098\pi$
$84$	5.01993	−	2.06436i	0.547719	−	0.225241i
$85$	−1.01463	+	0.178906i	−0.110052	+	0.0194051i
$86$	−7.68099	−	13.2831i	−0.828262	−	1.43236i
$87$	6.79716	+	3.57211i	0.728732	+	0.382971i
$88$	9.18695	+	7.67710i	0.979332	+	0.818382i
$89$	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	$0.0264430\pi$
$90$	1.11246	+	4.27319i	0.117263	+	0.450434i
$91$	9.16071	−	5.28894i	0.960303	−	0.554431i
$92$	6.80475	+	11.7495i	0.709444	+	1.22497i
$93$	−3.77661	+	1.54711i	−0.391616	+	0.160428i
$94$	0.000853769		1.26413i	8.80595e−5		0.130385i
$95$	2.48685	−	2.08672i	0.255146	−	0.214093i
$96$	−8.68854	−	4.52871i	−0.886771	−	0.462210i
$97$	−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	$0.573358\pi$
$98$	6.33056	+	1.11184i	0.639483	+	0.112313i
$99$	−8.90903	−	9.04900i	−0.895391	−	0.909458i
$100$	7.36478	+	2.66930i	0.736478	+	0.266930i
$101$	6.50659	+	1.14729i	0.647430	+	0.114159i	0.487714	−	0.873004i	$-0.337831\pi$
$101$	6.50659	+	1.14729i	0.647430	+	0.114159i	0.159716	+	0.987163i	$0.448942\pi$
$102$	−1.48231	+	1.91895i	−0.146771	+	0.190005i
$103$	−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	$0.897338\pi$
$104$	−17.9562	−	6.49433i	−1.76075	−	0.636822i
$105$	0.859854	−	2.69050i	0.0839131	−	0.262566i
$106$	−1.23320	−	6.96631i	−0.119779	−	0.676628i
$107$			3.85513i			0.372689i	0.982484	+	0.186345i	$0.0596641\pi$
$107$			3.85513i			0.372689i	−0.982484	+	0.186345i	$0.940336\pi$
$108$	8.70658	+	5.67411i	0.837791	+	0.545992i
$109$			3.32803i			0.318767i	0.987217	+	0.159384i	$0.0509507\pi$
$109$			3.32803i			0.318767i	−0.987217	+	0.159384i	$0.949049\pi$
$110$	6.13487	−	1.08602i	0.584937	−	0.103548i
$111$	4.29402	+	4.72292i	0.407570	+	0.448279i
$112$	3.14841	+	5.41934i	0.297497	+	0.512079i
$113$	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	$0.482537\pi$
$114$	1.02167	−	7.57179i	0.0956883	−	0.709163i
$115$	6.95832	+	1.22694i	0.648867	+	0.114413i
$116$	−3.02127	+	8.33589i	−0.280518	+	0.773968i
$117$	18.2880	+	8.70199i	1.69072	+	0.804499i
$118$	−2.75717	+	15.6987i	−0.253818	+	1.44518i
$119$	1.45754	−	0.530501i	0.133612	−	0.0486309i
$120$	−4.71424	+	1.94238i	−0.430350	+	0.177314i
$121$	−5.29891	+	4.44632i	−0.481719	+	0.404211i
$122$	−7.77718	+	0.00525255i	−0.704112	+	0.000475544i
$123$	4.36715	+	3.37815i	0.393773	+	0.304598i
$124$	−2.36180	−	4.07803i	−0.212096	−	0.366218i
$125$	8.03702	−	4.64017i	0.718853	−	0.415030i
$126$	−2.76648	−	6.04471i	−0.246458	−	0.538505i
$127$	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	$0.114744\pi$
$128$	3.81921	−	10.6496i	0.337574	−	0.941299i
$129$	−15.8887	+	10.0354i	−1.39892	+	0.883566i
$130$	−8.60191	+	4.97406i	−0.754437	+	0.436254i
$131$	9.66082	−	1.70346i	0.844070	−	0.148832i	0.265140	−	0.964210i	$-0.414582\pi$
$131$	9.66082	−	1.70346i	0.844070	−	0.148832i	0.578930	+	0.815378i	$0.303471\pi$
$132$	8.95593	−	11.6103i	0.779514	−	1.01054i
$133$	−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	$-0.670460\pi$
$138$	14.0537	−	8.88967i	1.19633	−	0.756739i
$139$	−4.68849	+	0.826707i	−0.397672	+	0.0701203i	−0.368908	−	0.929466i	$-0.620268\pi$
$139$	−4.68849	+	0.826707i	−0.397672	+	0.0701203i	−0.0287641	+	0.999586i	$0.509157\pi$
$140$	3.21274	+	0.562019i	0.271526	+	0.0474992i
$141$	1.54702	−	0.0615050i	0.130282	−	0.00517966i
$142$	−4.58657	−	5.45856i	−0.384896	−	0.458073i
$143$	14.2879	−	24.7474i	1.19482	−	2.06948i
$144$	−5.12674	+	10.8497i	−0.427228	+	0.904144i
$145$	2.30701	+	3.99585i	0.191586	+	0.331837i
$146$	6.77662	−	18.6578i	0.560837	−	1.54413i
$147$	1.05791	−	7.80058i	0.0872547	−	0.643381i
$148$	−4.73011	+	5.65262i	−0.388813	+	0.464642i
$149$	−14.7916	−	17.6280i	−1.21178	−	1.44414i	−0.861700	−	0.507418i	$-0.830600\pi$
$149$	−14.7916	−	17.6280i	−1.21178	−	1.44414i	−0.350076	−	0.936721i	$-0.613844\pi$
$150$	2.91448	−	9.14076i	0.237966	−	0.746340i
$151$	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	$0.0890245\pi$
$152$	8.82236	−	0.0178754i	0.715588	−	0.00144988i
$153$	2.41933	+	1.72229i	0.195591	+	0.139239i
$154$	−8.81180	+	3.21397i	−0.710075	+	0.258989i
$155$	−2.41510	−	0.425848i	−0.193986	−	0.0342049i
$156$	−7.08904	+	22.2855i	−0.567577	+	1.78427i
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	−0.988371	−	0.152063i	$-0.951408\pi$
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	0.854880	+	0.518825i	$0.173631\pi$
$158$	−10.8443	−	6.25120i	−0.862727	−	0.497319i
$159$	−8.46647	+	1.84239i	−0.671435	+	0.146111i
$160$	−2.96095	−	5.08875i	−0.234083	−	0.402301i
$161$	−10.6373			−0.838339
$162$	6.52762	−	10.9266i	0.512859	−	0.858473i
$163$			4.18081i			0.327466i	0.986505	+	0.163733i	$0.0523536\pi$
$163$			4.18081i			0.327466i	−0.986505	+	0.163733i	$0.947646\pi$
$164$	−3.18022	+	5.52553i	−0.248334	+	0.431471i
$165$	−1.62249	−	7.45598i	−0.126311	−	0.580447i
$166$	−4.43052	+	7.68587i	−0.343875	+	0.596539i
$167$	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	$0.535328\pi$
$168$	6.48166	−	4.11225i	0.500071	−	0.317267i
$169$	−5.65659	+	32.0801i	−0.435122	+	2.46770i
$170$	−1.36883	+	0.499259i	−0.104984	+	0.0382914i
$171$	−9.31530	−	0.888193i	−0.712359	−	0.0679218i
$172$	−13.9708	−	16.6041i	−1.06526	−	1.26605i
$173$	−0.453627	−	1.24633i	−0.0344886	−	0.0947567i	0.921253	−	0.388964i	$-0.127167\pi$
$173$	−0.453627	−	1.24633i	−0.0344886	−	0.0947567i	−0.955742	+	0.294207i	$0.904945\pi$
$174$	10.3461	+	3.29878i	0.784332	+	0.250080i
$175$	−4.70132	+	3.94488i	−0.355386	+	0.298205i
$176$	14.6859	+	8.42611i	1.10699	+	0.635142i
$177$	19.3441	+	2.62342i	1.45399	+	0.197189i
$178$	3.88434	−	10.6946i	0.291144	−	0.801595i
$179$	−9.68622	+	5.59234i	−0.723982	+	0.417991i	−0.816217	−	0.577746i	$-0.803932\pi$
$179$	−9.68622	+	5.59234i	−0.723982	+	0.417991i	0.0922343	+	0.995737i	$0.470599\pi$
$180$	2.60257	+	5.67644i	0.193984	+	0.423097i
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	0.614552	−	0.788876i	$-0.289337\pi$
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	−0.375911	+	0.926656i	$0.622670\pi$
$182$	11.4530	−	9.62344i	0.848956	−	0.713337i
$183$	0.378391	+	9.51754i	0.0279714	+	0.703557i
$184$	12.3725	+	14.6844i	0.912111	+	1.08255i
$185$	0.666039	+	3.77730i	0.0489682	+	0.277712i
$186$	−4.87778	+	3.08544i	−0.357656	+	0.226235i
$187$	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	$0.495651\pi$
$192$	−13.2157	−	4.16465i	−0.953764	−	0.300558i
$193$	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	$0.893382\pi$
$194$	−13.2062	+	7.63648i	−0.948148	+	0.548268i
$195$	6.49872	+	10.2892i	0.465383	+	0.736826i
$196$	9.08978	−	0.0122781i	0.649270	−	0.000877008i
$197$	14.1519	+	8.17063i	1.00828	+	0.582133i	0.910689	−	0.413093i	$-0.135551\pi$
$197$	14.1519	+	8.17063i	1.00828	+	0.582133i	0.0975957	+	0.995226i	$0.468885\pi$
$198$	−14.6371	−	10.4051i	−1.04021	−	0.739456i
$199$	−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	$0.843688\pi$
$200$	10.9139	+	1.90163i	0.771732	+	0.134465i
$201$	−0.770408	+	0.995955i	−0.0543404	+	0.0702493i
$202$	9.34365	−	0.00631052i	0.657417	−	0.000444006i
$203$	−4.46504	−	5.32123i	−0.313385	−	0.373477i
$204$	−1.59116	+	3.03767i	−0.111403	+	0.212680i
$205$	1.13470	+	3.11757i	0.0792511	+	0.217741i
$206$	−22.1328	−	3.88720i	−1.54207	−	0.270834i
$207$	−11.5514	−	16.7739i	−0.802880	−	1.16587i
$208$	−26.6060	−	4.61728i	−1.84480	−	0.320151i
$209$	−2.29270	+	13.0025i	−0.158589	+	0.899403i
$210$	0.534147	−	3.95866i	0.0368597	−	0.273174i
$211$	−2.09734	+	5.76240i	−0.144387	+	0.396700i	−0.990714	−	0.135964i	$-0.956587\pi$
$211$	−2.09734	+	5.76240i	−0.144387	+	0.396700i	0.846327	+	0.532664i	$0.178809\pi$
$212$	−3.43462	−	9.39702i	−0.235891	−	0.645390i
$213$	−6.46089	+	5.87416i	−0.442693	+	0.402491i
$214$	0.950351	+	5.36850i	0.0649647	+	0.366983i
$215$	−11.2922			−0.770124
$216$	13.5232	+	5.75524i	0.920138	+	0.391594i
$217$	3.69202			0.250631
$218$	0.820412	+	4.63448i	0.0555653	+	0.313887i
$219$	−23.1577	−	7.40094i	−1.56485	−	0.500109i
$220$	8.27547	−	3.02469i	0.557932	−	0.203925i
$221$	−2.28567	+	6.27983i	−0.153751	+	0.422427i
$222$	7.14396	+	5.51841i	0.479471	+	0.370372i
$223$	−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	$0.800654\pi$
$224$	5.72031	+	6.77063i	0.382204	+	0.452382i
$225$	−11.3260	−	3.12959i	−0.755063	−	0.208639i
$226$	11.6390	+	2.04417i	0.774217	+	0.135976i
$227$	−6.36438	−	17.4860i	−0.422419	−	1.16059i	−0.950319	−	0.311279i	$-0.899243\pi$
$227$	−6.36438	−	17.4860i	−0.422419	−	1.16059i	0.527900	−	0.849307i	$-0.322980\pi$
$228$	−0.443827	−	10.7960i	−0.0293932	−	0.714985i
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	0.920930	−	0.389729i	$-0.127431\pi$
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	−0.543726	+	0.839263i	$0.682987\pi$
$230$	9.99235	−	0.00674864i	0.658876	−	0.000444992i
$231$	4.35474	+	10.6303i	0.286521	+	0.699420i
$232$	−2.15238	+	12.3530i	−0.141310	+	0.811017i
$233$	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	$0.622232\pi$
$234$	27.6123	+	7.60978i	1.80507	+	0.497467i
$235$	0.805681	+	0.465160i	0.0525568	+	0.0303437i
$236$	0.0304476	+	22.5411i	0.00198197	+	1.46730i
$237$	−7.13163	+	13.5704i	−0.463249	+	0.881489i
$238$	1.89894	−	1.09806i	0.123090	−	0.0711768i
$239$	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	$0.713185\pi$
$240$	−6.08605	+	3.86702i	−0.392853	+	0.249615i
$241$	−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
$246$	6.91430	+	3.62772i	0.440840	+	0.231295i
$247$	−3.65657	−	20.7374i	−0.232662	−	1.31949i
$248$	−4.29426	−	5.09669i	−0.272686	−	0.323640i
$249$	9.61795	+	5.05452i	0.609513	+	0.320317i
$250$	10.0482	−	8.44298i	0.635502	−	0.533981i
$251$	−0.419101	−	0.241968i	−0.0264534	−	0.0152729i	0.486715	−	0.873561i	$-0.338195\pi$
$251$	−0.419101	−	0.241968i	−0.0264534	−	0.0152729i	−0.513168	+	0.858288i	$0.671528\pi$
$252$	−5.34261	−	7.73565i	−0.336553	−	0.487300i
$253$	−24.8865	+	14.3682i	−1.56460	+	0.903323i
$254$	1.76713	−	4.86538i	0.110880	−	0.305281i
$255$	0.676466	+	1.65131i	0.0423620	+	0.103409i
$256$	2.69320	−	15.7717i	0.168325	−	0.985732i
$257$	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	$0.0911486\pi$
$258$	−19.6521	+	17.8917i	−1.22349	+	1.11389i
$259$	−1.97497	−	5.42619i	−0.122719	−	0.337167i
$260$	−10.7525	+	9.04720i	−0.666842	+	0.561084i
$261$	3.54226	−	12.8194i	0.219260	−	0.793500i
$262$	13.0334	−	4.75373i	0.805204	−	0.293686i
$263$	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	$-0.0243074\pi$
$264$	9.60957	−	18.3758i	0.591428	−	1.13095i
$265$	−4.89249	−	1.78072i	−0.300543	−	0.109389i
$266$	−3.45185	+	5.98812i	−0.211647	+	0.367155i
$267$	−13.2740	−	4.24220i	−0.812353	−	0.259619i
$268$	−1.26013	−	0.725268i	−0.0769747	−	0.0443028i
$269$		−	6.56538i		−	0.400298i	−0.979765	−	0.200149i	$-0.935857\pi$
$269$		−	6.56538i		−	0.400298i	0.979765	−	0.200149i	$-0.0641426\pi$
$270$	6.82242	−	3.45655i	0.415199	−	0.210359i
$271$	10.8623			0.659839			0.329919	−	0.944009i	$-0.392978\pi$
$271$	10.8623			0.659839			0.329919	+	0.944009i	$0.392978\pi$
$272$	−3.72452	−	1.34423i	−0.225832	−	0.0815059i
$273$	−12.3250	−	13.5561i	−0.745945	−	0.820452i
$274$	−27.0670	−	15.6028i	−1.63518	−	0.942597i
$275$	−5.67046	+	15.5795i	−0.341941	+	0.939476i
$276$	17.3792	−	15.8439i	1.04610	−	0.953690i
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.990907	−	0.134546i	$-0.0429575\pi$
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.885131	+	0.465342i	$0.154069\pi$
$278$	−6.32521	+	2.30703i	−0.379361	+	0.138366i
$279$	4.00929	+	5.82191i	0.240030	+	0.348549i
$280$	4.61248	−	0.00934555i	0.275649	−	0.000558503i
$281$	−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	$0.588029\pi$
$282$	2.13915	−	0.467014i	0.127385	−	0.0278103i
$283$	12.6768	+	15.1076i	0.753556	+	0.898053i	0.997422	−	0.0717558i	$-0.0228602\pi$
$283$	12.6768	+	15.1076i	0.753556	+	0.898053i	−0.243866	+	0.969809i	$0.578416\pi$
$284$	−7.73270	−	6.47073i	−0.458851	−	0.383967i
$285$	−4.44754	−	3.44033i	−0.263449	−	0.203788i
$286$	13.7962	−	37.9845i	0.815785	−	2.24607i
$287$	−2.49735	−	4.32554i	−0.147414	−	0.255329i
$288$	−4.46467	+	16.3727i	−0.263083	+	0.964773i
$289$	8.01003	−	13.8738i	0.471178	−	0.816105i
$290$	4.19769	+	4.99576i	0.246497	+	0.293361i
$291$	9.97723	+	15.7966i	0.584875	+	0.926014i
$292$	4.83741	−	27.6527i	0.283088	−	1.61825i
$293$	26.1866	−	4.61741i	1.52984	−	0.269752i	0.655549	−	0.755153i	$-0.272437\pi$
$293$	26.1866	−	4.61741i	1.52984	−	0.269752i	0.874292	+	0.485401i	$0.161326\pi$
$294$	−0.449767	−	11.1236i	−0.0262309	−	0.648740i
$295$	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
$300$	1.80525	−	13.4475i	0.104226	−	0.776394i
$301$	16.7421	−	2.95209i	0.965001	−	0.170156i
$302$	24.3342	−	14.0713i	1.40028	−	0.809712i
$303$	−0.454606	−	11.4346i	−0.0261164	−	0.656898i
$304$	12.2813	−	2.19975i	0.704380	−	0.126164i
$305$	−2.86175	+	4.95671i	−0.163864	+	0.283820i
$306$	3.79364	+	1.80199i	0.216868	+	0.103013i
$307$	20.0407	−	11.5705i	1.14379	−	0.660365i	0.196420	−	0.980520i	$-0.437068\pi$
$307$	20.0407	−	11.5705i	1.14379	−	0.660365i	0.947365	+	0.320155i	$0.103735\pi$
$308$	−11.4787	+	6.64791i	−0.654059	+	0.378800i
$309$	−3.69864	+	27.2723i	−0.210409	+	1.55147i
$310$	−3.46816	+	0.00234233i	−0.196978	+	0.000133035i
$311$	−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	$0.520782\pi$
$312$	−4.37818	+	32.7816i	−0.247866	+	1.85589i
$313$	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	$0.129202\pi$
$314$	−1.19637	+	6.81188i	−0.0675153	+	0.384417i
$315$	−4.87020	−	0.464362i	−0.274405	−	0.0261639i
$316$	−16.6424	−	6.03189i	−0.936208	−	0.339320i
$317$	−18.1371	−	3.19806i	−1.01868	−	0.179621i	−0.360721	−	0.932674i	$-0.617469\pi$
$317$	−18.1371	−	3.19806i	−1.01868	−	0.179621i	−0.657960	+	0.753053i	$0.728580\pi$
$318$	−11.3359	+	4.65276i	−0.635686	+	0.260914i
$319$	−17.6337	−	6.41816i	−0.987300	−	0.359348i
$320$	−5.37776	−	6.35648i	−0.300626	−	0.355338i
$321$	6.52458	−	1.41981i	0.364167	−	0.0792462i
$322$	−14.8131	+	2.62227i	−0.825504	+	0.146134i
$323$		−	3.08773i		−	0.171806i
$324$	6.39654	−	16.8251i	0.355364	−	0.934728i
$325$		−	26.4420i		−	1.46674i
$326$	1.03064	+	5.82204i	0.0570817	+	0.322453i
$327$	5.63249	−	1.22568i	0.311478	−	0.0677805i
$328$	−3.06652	+	8.47862i	−0.169320	+	0.468153i
$329$	−1.31613	−	0.479031i	−0.0725605	−	0.0264099i
$330$	−4.09744	−	9.98295i	−0.225557	−	0.549543i
$331$	−15.2370	−	2.68670i	−0.837502	−	0.147674i	−0.261583	−	0.965181i	$-0.584245\pi$
$331$	−15.2370	−	2.68670i	−0.837502	−	0.147674i	−0.575919	+	0.817507i	$0.695356\pi$
$332$	−4.27508	+	11.7952i	−0.234626	+	0.647348i
$333$	6.41181	−	9.00679i	0.351365	−	0.493569i
$334$	8.49017	+	1.49113i	0.464561	+	0.0815912i
$335$	−0.710980	+	0.258776i	−0.0388450	+	0.0141384i
$336$	8.01239	−	7.32440i	0.437111	−	0.399579i
$337$	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	$0.170198\pi$
$338$	0.0311134	+	46.0680i	0.00169235	+	2.50577i
$339$	1.94501	−	14.3417i	0.105639	−	0.778937i
$340$	−1.78310	+	1.03269i	−0.0967022	+	0.0560053i
$341$	8.63764	−	4.98695i	0.467755	−	0.270058i
$342$	−13.1911	+	1.05951i	−0.713292	+	0.0572916i
$343$	−9.04472	+	15.6659i	−0.488369	+	0.845880i
$344$	−23.5483	−	19.6782i	−1.26964	−	1.06098i
$345$	−0.486168	−	12.2284i	−0.0261744	−	0.658356i
$346$	−0.938945	−	1.62377i	−0.0504780	−	0.0872942i
$347$	23.2143	−	4.09332i	1.24621	−	0.219741i	0.488636	−	0.872488i	$-0.337495\pi$
$347$	23.2143	−	4.09332i	1.24621	−	0.219741i	0.757576	+	0.652747i	$0.226384\pi$
$348$	15.2207	+	2.04329i	0.815916	+	0.109532i
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	−0.999240	−	0.0389784i	$-0.987590\pi$
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	0.211902	+	0.977291i	$0.432034\pi$
$350$	−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	$0.716229\pi$
$354$	27.5845	−	1.11534i	1.46610	−	0.0592798i
$355$	−5.16729	+	0.911132i	−0.274251	+	0.0483579i
$356$	2.77279	−	15.8505i	0.146958	−	0.840073i
$357$	−1.43464	−	2.27142i	−0.0759293	−	0.120216i
$358$	−12.1101	+	10.1755i	−0.640037	+	0.537792i
$359$	−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	$0.253050\pi$
$360$	5.02358	+	7.26322i	0.264766	+	0.382805i
$361$	−4.63535	−	8.02867i	−0.243966	−	0.422561i
$362$	4.92789	+	1.78984i	0.259004	+	0.0940717i
$363$	9.47668	+	7.33056i	0.497397	+	0.384755i
$364$	13.5767	−	16.2246i	0.711615	−	0.850400i
$365$	−9.39023	−	11.1908i	−0.491507	−	0.585755i
$366$	2.87316	+	13.1605i	0.150182	+	0.687910i
$367$	−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	$0.404763\pi$
$368$	20.8494	+	17.3989i	1.08685	+	0.906983i
$369$	4.10894	−	8.63530i	0.213903	−	0.449536i
$370$	1.85867	+	5.09593i	0.0966274	+	0.264925i
$371$	7.71925	+	1.36111i	0.400763	+	0.0706654i
$372$	−6.03200	+	5.49912i	−0.312745	+	0.285116i
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	−0.111899	−	0.993720i	$-0.535693\pi$
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	0.724470	−	0.689306i	$-0.242084\pi$
$374$	2.95945	−	5.13392i	0.153030	−	0.265469i
$375$	−10.8132	−	11.8932i	−0.558391	−	0.614165i
$376$	0.869528	+	2.37403i	0.0448425	+	0.122431i
$377$	29.9286			1.54140
$378$	−9.21145	+	6.90833i	−0.473786	+	0.355326i
$379$			27.1937i			1.39685i	0.715685	+	0.698423i	$0.246114\pi$
$379$			27.1937i			1.39685i	−0.715685	+	0.698423i	$0.753886\pi$
$380$	3.23876	−	5.62723i	0.166145	−	0.288671i
$381$	−6.03883	−	1.92994i	−0.309378	−	0.0988738i
$382$	22.1209	+	12.7516i	1.13180	+	0.652429i
$383$	−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	$0.660446\pi$
$384$	−19.4304	−	2.54164i	−0.991553	−	0.129703i
$385$	−1.19866	+	6.79794i	−0.0610894	+	0.346455i
$386$	2.15062	+	5.89639i	0.109464	+	0.300118i
$387$	22.8360	+	23.1947i	1.16082	+	1.17905i
$388$	−16.5079	+	13.8898i	−0.838062	+	0.705148i
$389$	3.99747	+	10.9830i	0.202680	+	0.556858i	0.998836	−	0.0482330i	$-0.0153590\pi$
$389$	3.99747	+	10.9830i	0.202680	+	0.556858i	−0.796156	+	0.605091i	$0.793137\pi$
$390$	11.5863	+	12.7263i	0.586696	+	0.644423i
$391$	5.14814	−	4.31980i	0.260353	−	0.218462i
$392$	12.6551	−	2.25788i	0.639177	−	0.114040i
$393$	−6.44102	−	15.7230i	−0.324906	−	0.793121i
$394$	21.7217	+	7.88943i	1.09432	+	0.397464i
$395$	−7.97761	+	4.60588i	−0.401397	+	0.231747i
$396$	−22.9481	−	10.8814i	−1.15319	−	0.546812i
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	0.440826	−	0.897593i	$-0.354686\pi$
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	−0.556925	+	0.830563i	$0.688019\pi$
$398$	−0.834849	−	0.993571i	−0.0418472	−	0.0498032i
$399$	7.49342	+	3.93802i	0.375140	+	0.197148i
$400$	15.6671	−	0.0423251i	0.783356	−	0.00211626i
$401$	−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	$-0.155973\pi$
$402$	−0.827322	+	1.57685i	−0.0412631	+	0.0786460i
$403$	−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
$408$	−1.46695	+	4.62240i	−0.0726248	+	0.228843i
$409$	−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	$0.985118\pi$
$410$	2.34868	+	4.06169i	0.115993	+	0.200592i
$411$	−17.8003	+	33.8711i	−0.878023	+	1.67074i
$412$	−31.7796	+	0.0429266i	−1.56567	+	0.00211484i
$413$	−15.2936	−	8.82978i	−0.752550	−	0.434485i
$414$	−20.2211	−	20.5111i	−0.993814	−	1.00806i
$415$	3.26440	+	5.65411i	0.160243	+	0.277549i
$416$	−38.1888	+	0.128960i	−1.87236	+	0.00632279i
$417$	3.12588	+	7.63052i	0.153075	+	0.373668i
$418$	0.0126107	+	18.6720i	0.000616810	+	0.913278i
$419$	1.84481	+	2.19856i	0.0901248	+	0.107407i	0.809222	−	0.587503i	$-0.199889\pi$
$419$	1.84481	+	2.19856i	0.0901248	+	0.107407i	−0.719097	+	0.694909i	$0.755444\pi$
$420$	−0.232040	−	5.64436i	−0.0113224	−	0.275416i
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	0.999897	−	0.0143594i	$-0.00457089\pi$
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	−0.775195	+	0.631721i	$0.782349\pi$
$422$	−1.50016	+	8.54154i	−0.0730264	+	0.415795i
$423$	−0.673847	−	2.59558i	−0.0327636	−	0.126202i
$424$	−7.09944	−	12.2392i	−0.344779	−	0.594390i
$425$	0.673287	−	3.81840i	0.0326592	−	0.185220i
$426$	−7.54911	+	9.77284i	−0.365756	+	0.473496i
$427$	2.94709	−	8.09707i	0.142620	−	0.391845i
$428$	2.64685	+	7.24170i	0.127940	+	0.350041i
$429$	−47.1457	−	15.0672i	−2.27621	−	0.727452i
$430$	−15.7251	+	2.78372i	−0.758334	+	0.134243i
$431$	25.2153			1.21458			0.607290	−	0.794480i	$-0.292257\pi$
$431$	25.2153			1.21458			0.607290	+	0.794480i	$0.292257\pi$
$432$	20.2507	+	4.68084i	0.974311	+	0.225207i
$433$	−15.5658			−0.748046			−0.374023	−	0.927419i	$-0.622022\pi$
$433$	−15.5658			−0.748046			−0.374023	+	0.927419i	$0.622022\pi$
$434$	5.14137	−	0.910143i	0.246794	−	0.0436883i
$435$	5.91309	−	5.37611i	0.283511	−	0.257765i
$436$	2.28495	+	6.25156i	0.109429	+	0.299396i
$437$	−7.24252	+	19.8987i	−0.346457	+	0.951882i
$438$	−34.0730	−	4.59752i	−1.62807	−	0.219678i
$439$	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	$-0.219423\pi$
$440$	10.7785	−	6.25211i	0.513844	−	0.298058i
$441$	−13.5916	+	1.08244i	−0.647221	+	0.0515449i
$442$	−1.63486	+	9.30851i	−0.0777624	+	0.442761i
$443$	2.16330	+	5.94362i	0.102782	+	0.282390i	0.980415	−	0.196942i	$-0.0631011\pi$
$443$	2.16330	+	5.94362i	0.102782	+	0.282390i	−0.877634	+	0.479332i	$0.840879\pi$
$444$	11.3088	+	5.92363i	0.536691	+	0.281123i
$445$	−5.38246	−	6.41456i	−0.255153	−	0.304079i
$446$	0.0204793	+	30.3227i	0.000969725	+	1.43582i
$447$	−24.3867	+	31.5262i	−1.15345	+	1.49114i
$448$	9.63496	+	8.01838i	0.455209	+	0.378833i
$449$	−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	$0.896563\pi$
$450$	−16.5436	−	1.56612i	−0.779872	−	0.0738276i
$451$	−11.6853	−	6.74653i	−0.550241	−	0.317682i
$452$	16.7120	−	0.0225739i	0.786067	−	0.00106179i
$453$	−18.3845	−	29.1075i	−0.863777	−	1.36759i
$454$	−13.1734	−	22.7814i	−0.618257	−	1.06918i
$455$	−1.91172	−	10.8419i	−0.0896228	−	0.508276i
$456$	−3.27946	−	14.9248i	−0.153575	−	0.698916i
$457$	−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	−0.999044	−	0.0437126i	$-0.986081\pi$
$461$	−16.8013	+	20.0230i	−0.782513	+	0.932563i	0.216531	+	0.976276i	$0.430526\pi$
$462$	8.68478	+	13.7298i	0.404053	+	0.638767i
$463$	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	$0.772358\pi$
$464$	0.0479061	+	17.7330i	0.00222399	+	0.823233i
$465$	0.168740	+	4.24426i	0.00782513	+	0.196823i
$466$	17.0988	+	20.3496i	0.792086	+	0.942678i
$467$	−19.1663	−	11.0657i	−0.886910	−	0.512058i	−0.0139792	−	0.999902i	$-0.504450\pi$
$467$	−19.1663	−	11.0657i	−0.886910	−	0.512058i	−0.872930	+	0.487845i	$0.837783\pi$
$468$	40.3278	+	3.79021i	1.86415	+	0.175202i
$469$	0.986466	−	0.569536i	0.0455508	−	0.0262987i
$470$	1.23663	+	0.449151i	0.0570415	+	0.0207178i
$471$	8.39367	+	1.13834i	0.386760	+	0.0524520i
$472$	5.59913	+	31.3823i	0.257721	+	1.44449i
$473$	35.1815	−	29.5208i	1.61765	−	1.35737i
$474$	−6.58593	+	20.6556i	−0.302502	+	0.948744i
$475$	4.17853	+	11.4804i	0.191724	+	0.526757i
$476$	2.37370	−	1.99724i	0.108798	−	0.0915433i
$477$	6.23626	+	13.6505i	0.285539	+	0.625012i
$478$	9.95285	+	27.2879i	0.455233	+	1.24812i
$479$	−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	$0.967983\pi$
$480$	−7.52192	+	6.88538i	−0.343327	+	0.314273i
$481$	23.3788	+	8.50920i	1.06598	+	0.387986i
$482$	−16.8785	−	9.72963i	−0.768796	−	0.443172i
$483$	3.91764	+	18.0031i	0.178259	+	0.819168i
$484$	−6.90105	+	11.9903i	−0.313684	+	0.545016i
$485$			11.2268i			0.509783i
$486$	−20.8967	−	7.02346i	−0.947892	−	0.318590i
$487$	22.1183			1.00228			0.501138	−	0.865367i	$-0.332915\pi$
$487$	22.1183			1.00228			0.501138	+	0.865367i	$0.332915\pi$
$488$	−14.6055	+	5.34951i	−0.661160	+	0.242161i
$489$	7.07578	−	1.53976i	0.319978	−	0.0696303i
$490$	3.34084	−	5.79554i	0.150924	−	0.261816i
$491$	2.55319	−	7.01484i	0.115224	−	0.316575i	−0.868653	−	0.495421i	$-0.835014\pi$
$491$	2.55319	−	7.01484i	0.115224	−	0.316575i	0.983877	+	0.178845i	$0.0572362\pi$
$492$	10.5229	+	3.34733i	0.474408	+	0.150909i
$493$	4.32189	+	0.762066i	0.194648	+	0.0343217i
$494$	−10.2041	−	27.9768i	−0.459105	−	1.25874i
$495$	−12.0213	+	5.49195i	−0.540316	+	0.246845i
$496$	−7.23644	−	6.03885i	−0.324926	−	0.271153i
$497$	7.42295	−	2.70173i	0.332965	−	0.121189i
$498$	14.6396	+	4.66776i	0.656017	+	0.209167i
$499$	−6.65452	−	7.93054i	−0.297897	−	0.355020i	0.596246	−	0.802802i	$-0.296658\pi$
$499$	−6.65452	−	7.93054i	−0.297897	−	0.355020i	−0.894143	+	0.447782i	$0.852214\pi$
$500$	11.9114	−	14.2344i	0.532692	−	0.636582i
$501$	1.41880	−	10.4617i	0.0633874	−	0.467393i
$502$	−0.643273	−	0.233640i	−0.0287107	−	0.0104279i
$503$	−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	$-0.439261\pi$
$504$	−9.34689	−	9.45534i	−0.416343	−	0.421174i
$505$	3.43817	−	5.95508i	0.152997	−	0.264998i
$506$	−31.1140	+	26.1436i	−1.38319	+	1.16222i
$507$	56.3770	−	2.24139i	2.50379	−	0.0995436i
$508$	1.26145	−	7.21098i	0.0559678	−	0.319935i
$509$	16.7517	−	2.95378i	0.742508	−	0.130924i	0.210417	−	0.977612i	$-0.432518\pi$
$509$	16.7517	−	2.95378i	0.742508	−	0.130924i	0.532090	+	0.846688i	$0.321407\pi$
$510$	1.34910	+	2.13279i	0.0597389	+	0.0944414i
$511$	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
$516$	−22.9562	+	29.7599i	−1.01059	+	1.31011i
$517$	−3.72618	+	0.657026i	−0.163877	+	0.0288960i
$518$	−4.08791	−	7.06945i	−0.179613	−	0.310614i
$519$	−1.94227	+	1.22675i	−0.0852564	+	0.0538484i
$520$	−12.7433	+	15.2495i	−0.558829	+	0.668733i
$521$	−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	$0.944746\pi$
$522$	1.77263	−	18.7250i	0.0775858	−	0.819571i
$523$	−3.33680	+	1.92651i	−0.145908	+	0.0842402i	−0.571177	−	0.820827i	$-0.693513\pi$
$523$	−3.33680	+	1.92651i	−0.145908	+	0.0842402i	0.425269	+	0.905067i	$0.360180\pi$
$524$	16.9779	−	9.83280i	0.741683	−	0.429548i
$525$	8.40793	+	6.50385i	0.366952	+	0.283851i
$526$	−0.00769131	−	11.3881i	−0.000335357	−	0.496546i
$527$	−1.78683	+	1.49932i	−0.0778353	+	0.0653116i
$528$	8.85200	−	27.9584i	0.385234	−	1.21673i
$529$	−21.6963	+	7.89682i	−0.943319	+	0.343340i
$530$	−7.25207	−	1.27369i	−0.315010	−	0.0553254i
$531$	−2.68427	−	33.7049i	−0.116487	−	1.46267i
$532$	−3.33075	+	9.18977i	−0.144406	+	0.398427i
$533$	21.1929	+	3.73687i	0.917965	+	0.161862i
$534$	−19.5306	−	2.63529i	−0.845171	−	0.114040i
$535$	3.77033	+	1.37229i	0.163006	+	0.0593292i
$536$	−1.93360	−	0.699339i	−0.0835188	−	0.0302068i
$537$	13.0321	+	14.3338i	0.562376	+	0.618547i
$538$	−1.61847	−	9.14269i	−0.0697773	−	0.394170i
$539$			19.2380i			0.828638i
$540$	8.64854	−	6.49529i	0.372174	−	0.279513i
$541$		−	4.51542i		−	0.194133i	−0.995278	−	0.0970665i	$-0.969054\pi$
$541$		−	4.51542i		−	0.194133i	0.995278	−	0.0970665i	$-0.0309460\pi$
$542$	15.1265	−	2.67774i	0.649737	−	0.115019i
$543$	1.95473	−	6.11640i	0.0838856	−	0.262480i
$544$	−5.51800	−	0.953770i	−0.236582	−	0.0408926i
$545$	3.25483	+	1.18466i	0.139421	+	0.0507453i
$546$	−20.5052	−	15.8394i	−0.877541	−	0.677863i
$547$	−12.3037	−	2.16948i	−0.526069	−	0.0927602i	−0.0956949	−	0.995411i	$-0.530507\pi$
$547$	−12.3037	−	2.16948i	−0.526069	−	0.0927602i	−0.430374	+	0.902651i	$0.641618\pi$
$548$	−41.5388	−	15.0554i	−1.77445	−	0.643134i
$549$	15.9685	−	4.14564i	0.681520	−	0.176931i
$550$	−4.05588	+	23.0932i	−0.172943	+	0.984698i
$551$	−12.9942	+	4.72950i	−0.553572	+	0.201484i
$552$	20.2958	−	26.3478i	0.863848	−	1.12144i
$553$	10.6237	−	8.91435i	0.451766	−	0.379077i
$554$	44.8379	−	0.0302826i	1.90498	−	0.00128658i
$555$	6.14756	−	2.51838i	0.260949	−	0.106899i
$556$	−8.23953	+	4.77195i	−0.349434	+	0.202376i
$557$	−3.03004	+	1.74940i	−0.128387	+	0.0741243i	−0.562818	−	0.826581i	$-0.690283\pi$
$557$	−3.03004	+	1.74940i	−0.128387	+	0.0741243i	0.434431	+	0.900705i	$0.356949\pi$
$558$	7.01838	+	7.11902i	0.297112	+	0.301372i
$559$	−36.6233	+	63.4335i	−1.54900	+	2.68295i
$560$	6.42086	−	1.15007i	0.271331	−	0.0485991i
$561$	−6.42449	−	3.37627i	−0.271242	−	0.142546i
$562$	−24.0358	+	13.8987i	−1.01389	+	0.586282i
$563$	26.9436	−	4.75088i	1.13554	−	0.200226i	0.425885	−	0.904777i	$-0.359963\pi$
$563$	26.9436	−	4.75088i	1.13554	−	0.200226i	0.709653	+	0.704552i	$0.248852\pi$
$564$	2.86378	−	1.17768i	0.120587	−	0.0495894i
$565$	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	$0.694685\pi$
$570$	−7.04157	−	3.69449i	−0.294939	−	0.154745i
$571$	2.91629	−	0.514220i	0.122043	−	0.0215194i	−0.112293	−	0.993675i	$-0.535820\pi$
$571$	2.91629	−	0.514220i	0.122043	−	0.0215194i	0.234336	+	0.972156i	$0.424708\pi$
$572$	9.84825	−	56.2967i	0.411776	−	2.35389i
$573$	14.5476	−	27.6817i	0.607733	−	1.15642i
$574$	−4.54404	−	5.40795i	−0.189664	−	0.225724i
$575$	−13.2953	+	23.0281i	−0.554453	+	0.960340i
$576$	−2.18118	+	23.9007i	−0.0908825	+	0.995862i
$577$	−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	$0.889695\pi$
$578$	7.73436	−	21.2947i	0.321707	−	0.885743i
$579$	7.11321	−	2.91396i	0.295615	−	0.121100i
$580$	7.07708	+	5.92210i	0.293860	+	0.245902i
$581$	−6.31802	−	7.52952i	−0.262115	−	0.312377i
$582$	17.7880	+	19.5382i	0.737338	+	0.809886i
$583$	19.8980	−	7.24228i	0.824092	−	0.299945i
$584$	−0.0804391	−	39.7006i	−0.00332859	−	1.64282i
$585$	15.0205	−	14.7881i	0.621020	−	0.611414i
$586$	35.3283	−	12.8855i	1.45940	−	0.532294i
$587$	−45.4714	−	8.01784i	−1.87681	−	0.330932i	−0.885727	−	0.464206i	$-0.846340\pi$
$587$	−45.4714	−	8.01784i	−1.87681	−	0.330932i	−0.991079	+	0.133275i	$0.957451\pi$
$588$	−3.36847	−	15.3794i	−0.138913	−	0.634236i
$589$	2.51375	−	6.90646i	0.103577	−	0.284576i
$590$	14.3719	+	8.28470i	0.591683	+	0.341076i
$591$	8.61628	−	26.9605i	0.354426	−	1.10901i
$592$	−5.00436	+	13.8658i	−0.205678	+	0.569881i
$593$	22.0816			0.906784			0.453392	−	0.891311i	$-0.350214\pi$
$593$	22.0816			0.906784			0.453392	+	0.891311i	$0.350214\pi$
$594$	−12.2193	+	28.6046i	−0.501362	+	1.17366i
$595$		−	1.61432i		−	0.0661807i
$596$	−39.8884	−	22.9578i	−1.63389	−	0.940389i
$597$	−1.17601	+	1.06922i	−0.0481311	+	0.0437602i
$598$	32.3696	−	56.1533i	1.32369	−	2.29628i
$599$	−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	$0.779835\pi$
$600$	−0.801117	−	19.1716i	−0.0327054	−	0.782676i
$601$	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	$-0.0416509\pi$
$602$	22.5867	−	8.23818i	0.920567	−	0.335763i
$603$	1.96933	+	0.937069i	0.0801974	+	0.0381604i
$604$	30.4181	−	25.5939i	1.23770	−	1.04140i
$605$	2.46229	+	6.76510i	0.100107	+	0.275040i
$606$	−3.45187	−	15.8113i	−0.140223	−	0.642289i
$607$	−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	$0.489292\pi$
$608$	16.5602	−	6.09082i	0.671604	−	0.247015i
$609$	−7.36144	+	9.51660i	−0.298301	+	0.385632i
$610$	−2.76326	+	7.60799i	−0.111881	+	0.308038i
$611$	5.22602	−	3.01724i	0.211422	−	0.122065i
$612$	5.72710	+	1.57419i	0.231504	+	0.0636329i
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	0.670116	−	0.742256i	$-0.266244\pi$
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	−0.307754	+	0.951466i	$0.599578\pi$
$614$	25.0556	−	21.0530i	1.01116	−	0.849631i
$615$	4.85841	−	3.06859i	0.195910	−	0.123738i
$616$	−14.3460	+	12.0873i	−0.578015	+	0.487012i
$617$	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	$0.866215\pi$
$618$	1.57247	+	38.8902i	0.0632541	+	1.56439i
$619$	−1.25371	+	1.49411i	−0.0503908	+	0.0600535i	−0.790651	−	0.612267i	$-0.790258\pi$
$619$	−1.25371	+	1.49411i	−0.0503908	+	0.0600535i	0.740260	+	0.672320i	$0.234702\pi$
$620$	−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
$624$	1.98429	+	46.7297i	0.0794354	+	1.87068i
$625$	1.72350	+	9.77447i	0.0689401	+	0.390979i
$626$	31.5490	−	18.2433i	1.26095	−	0.729147i
$627$	22.8504	−	0.908468i	0.912557	−	0.0362807i
$628$	0.0132116	+	9.78089i	0.000527202	+	0.390300i
$629$	3.15939	+	1.82408i	0.125973	+	0.0727307i
$630$	−6.89653	+	0.553929i	−0.274764	+	0.0220691i
$631$	−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	$0.918578\pi$
$632$	−24.6625	−	4.29716i	−0.981023	−	0.170932i
$633$	10.5250	+	1.42739i	0.418330	+	0.0567335i
$634$	−26.0454	+	0.0175906i	−1.03440	+	0.000698610i
$635$	−2.44868	−	2.91823i	−0.0971730	−	0.115806i
$636$	−14.6390	+	9.27374i	−0.580473	+	0.367728i
$637$	−10.4939	−	28.8319i	−0.415785	−	1.14236i
$638$	−26.1383	−	4.59068i	−1.03482	−	0.181747i
$639$	12.3212	+	8.77127i	0.487418	+	0.346986i
$640$	−9.05584	−	7.52609i	−0.357964	−	0.297495i
$641$	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	$-0.136647\pi$
$642$	8.73588	−	3.58559i	0.344778	−	0.141512i
$643$	−12.8078	+	35.1891i	−0.505090	+	1.38772i	0.381157	+	0.924510i	$0.375526\pi$
$643$	−12.8078	+	35.1891i	−0.505090	+	1.38772i	−0.886247	+	0.463213i	$0.846697\pi$
$644$	−19.9818	+	7.30336i	−0.787393	+	0.287793i
$645$	4.15884	+	19.1115i	0.163754	+	0.752513i
$646$	−0.761176	−	4.29986i	−0.0299481	−	0.169176i
$647$	−23.8383			−0.937182			−0.468591	−	0.883415i	$-0.655238\pi$
$647$	−23.8383			−0.937182			−0.468591	+	0.883415i	$0.655238\pi$
$648$	4.75992	−	25.0069i	0.186987	−	0.982362i
$649$	−47.7068			−1.87266
$650$	−6.51838	−	36.8221i	−0.255672	−	1.44428i
$651$	−1.35974	−	6.24853i	−0.0532925	−	0.244899i
$652$	2.87045	+	7.85348i	0.112416	+	0.307566i
$653$	−16.8138	+	46.1955i	−0.657974	+	1.80777i	−0.0720526	+	0.997401i	$0.522955\pi$
$653$	−16.8138	+	46.1955i	−0.657974	+	1.80777i	−0.585921	+	0.810368i	$0.699267\pi$
$654$	7.54145	−	3.09534i	0.294894	−	0.121038i
$655$	1.77292	−	10.0547i	0.0692736	−	0.392870i
$656$	−2.18021	+	12.5630i	−0.0851229	+	0.490501i
$657$	−3.99687	+	41.9188i	−0.155933	+	1.63541i
$658$	−1.95088	−	0.342634i	−0.0760532	−	0.0133573i
$659$	−9.01137	−	24.7585i	−0.351033	−	0.964456i	−0.982039	−	0.188678i	$-0.939580\pi$
$659$	−9.01137	−	24.7585i	−0.351033	−	0.964456i	0.631006	−	0.775778i	$-0.282642\pi$
$660$	−8.16690	−	12.8918i	−0.317896	−	0.501812i
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	0.783970	−	0.620798i	$-0.213191\pi$
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	−0.747502	+	0.664260i	$0.768747\pi$
$662$	−21.8808	+	0.0147779i	−0.850422	+	0.000574358i
$663$	11.4701	+	1.55556i	0.445460	+	0.0604128i
$664$	−3.04560	+	17.4795i	−0.118192	+	0.678336i
$665$	2.54332	+	4.40516i	0.0986258	+	0.170825i
$666$	6.70853	−	14.1231i	0.259950	−	0.547260i
$667$	−26.0646	−	15.0484i	−1.00923	−	0.582677i
$668$	12.1907	−	0.0164667i	0.471672	−	0.000637115i
$669$	37.1082	−	1.47532i	1.43469	−	0.0570392i
$670$	−0.926292	+	0.535629i	−0.0357858	+	0.0206932i
$671$	−4.04215	−	22.9242i	−0.156046	−	0.884979i
$672$	9.35216	−	12.1749i	0.360768	−	0.469655i
$673$	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	−0.803866	−	0.594810i	$-0.797227\pi$
$677$	−2.04257	+	2.43424i	−0.0785022	+	0.0935553i	0.725364	+	0.688366i	$0.241672\pi$
$678$	−0.826919	−	20.4513i	−0.0317576	−	0.785426i
$679$	−2.93499	−	16.6451i	−0.112634	−	0.638782i
$680$	−2.22850	+	1.87764i	−0.0854593	+	0.0720044i
$681$	−27.2501	+	17.2113i	−1.04423	+	0.659538i
$682$	10.7991	−	9.07395i	0.413519	−	0.347460i
$683$	−7.95770	−	4.59438i	−0.304493	−	0.175799i	0.339967	−	0.940437i	$-0.389584\pi$
$683$	−7.95770	−	4.59438i	−0.304493	−	0.175799i	−0.644459	+	0.764639i	$0.722918\pi$
$684$	−18.1082	+	4.72725i	−0.692385	+	0.180751i
$685$	−19.9118	+	11.4961i	−0.760792	+	0.439243i
$686$	−8.73343	+	24.0454i	−0.333444	+	0.918059i
$687$	9.41089	−	12.1660i	0.359048	−	0.464164i
$688$	−37.6435	−	21.5981i	−1.43515	−	0.823421i
$689$	−25.8705	+	21.7080i	−0.985589	+	0.827008i
$690$	−3.69152	−	16.9090i	−0.140534	−	0.643715i
$691$	−6.14708	−	16.8890i	−0.233846	−	0.642487i	0.766154	−	0.642657i	$-0.222168\pi$
$691$	−6.14708	−	16.8890i	−0.233846	−	0.642487i	−1.00000		0.000170287i	$0.999946\pi$
$692$	−1.70782	−	2.02973i	−0.0649217	−	0.0771588i
$693$	16.3873	−	11.2852i	0.622501	−	0.428689i
$694$	31.3184	−	11.4229i	1.18883	−	0.433608i
$695$	−0.860413	+	4.87964i	−0.0326373	+	0.185095i
$696$	21.6995	−	0.906751i	0.822518	−	0.0343703i
$697$	2.96524	+	1.07926i	0.112316	+	0.0408799i
$698$	−16.1615	+	28.0363i	−0.611723	+	1.06119i
$699$	24.0863	−	21.8989i	0.911027	−	0.828294i
$700$	−6.12277	+	10.6381i	−0.231419	+	0.402083i
$701$			19.1567i			0.723538i	0.932268	+	0.361769i	$0.117827\pi$
$701$			19.1567i			0.723538i	−0.932268	+	0.361769i	$0.882173\pi$
$702$	2.70972	−	49.5349i	0.102272	−	1.86957i
$703$	−11.4952			−0.433548
$704$	33.3721	+	5.74506i	1.25776	+	0.216525i
$705$	0.490531	−	1.53488i	0.0184745	−	0.0578070i
$706$	0.866769	+	0.499649i	0.0326213	+	0.0188045i
$707$	−3.54070	+	9.72798i	−0.133162	+	0.365858i
$708$	38.1382	−	8.35322i	1.43332	−	0.313933i
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.00257396	−	0.999997i	$-0.500819\pi$
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.344438	+	0.938809i	$0.611930\pi$
$710$	−6.97116	+	2.54263i	−0.261623	+	0.0954231i
$711$	25.5936	+	7.07202i	0.959834	+	0.265222i
$712$	−0.0461075	−	22.7563i	−0.00172795	−	0.852828i
$713$	15.0318	−	5.47115i	0.562947	−	0.204896i
$714$	−2.55777	−	2.80943i	−0.0957221	−	0.105140i
$715$	−19.1171	−	22.7829i	−0.714938	−	0.852031i
$716$	−14.3556	+	17.1553i	−0.536494	+	0.641125i
$717$	32.9192	−	13.4855i	1.22939	−	0.503626i
$718$	−4.90427	+	13.5027i	−0.183026	+	0.503918i
$719$	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	$0.702136\pi$
$720$	8.78615	+	8.87610i	0.327441	+	0.330793i
$721$	12.4487	−	21.5618i	0.463614	−	0.803003i
$722$	−8.43421	−	10.0377i	−0.313889	−	0.373566i
$723$	−11.1000	+	21.1215i	−0.412812	+	0.785516i
$724$	7.30361	+	1.27765i	0.271437	+	0.0474836i
$725$	−17.1004	+	3.01526i	−0.635092	+	0.111984i
$726$	15.0040	+	7.87211i	0.556850	+	0.292161i
$727$	−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
$732$	7.24533	+	17.6185i	0.267795	+	0.651199i
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.694835	−	0.719170i	$-0.255478\pi$
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.898901	+	0.438151i	$0.144366\pi$
$734$	−2.33830	+	1.35213i	−0.0863083	+	0.0499079i
$735$	−7.25243	−	3.81137i	−0.267510	−	0.140584i
$736$	33.3232	+	19.0894i	1.22831	+	0.703645i
$737$	1.53859	−	2.66491i	0.0566746	−	0.0981632i
$738$	3.59322	−	13.0381i	0.132268	−	0.479940i
$739$	21.9574	−	12.6771i	0.807716	−	0.466335i	−0.0384462	−	0.999261i	$-0.512241\pi$
$739$	21.9574	−	12.6771i	0.807716	−	0.466335i	0.846162	+	0.532926i	$0.178907\pi$
$740$	3.84454	+	6.63821i	0.141328	+	0.244025i
$741$	−33.7503	+	13.8260i	−1.23985	+	0.507910i
$742$	11.0851	−	0.00748664i	0.406946	−	0.000274843i
$743$	−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	$0.304103\pi$
$744$	−7.04431	+	9.14485i	−0.258257	+	0.335267i
$745$	−22.5055	+	8.19135i	−0.824539	+	0.300108i
$746$	8.46209	−	48.1812i	0.309819	−	1.76404i
$747$	5.01228	−	18.1394i	0.183390	−	0.663685i
$748$	2.85562	−	7.87886i	0.104412	−	0.288080i
$749$	−5.94874	−	1.04892i	−0.217362	−	0.0383268i
$750$	−17.9899	−	13.8965i	−0.656899	−	0.507427i
$751$	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	$0.356039\pi$
$752$	1.79611	+	3.09163i	0.0654974	+	0.112740i
$753$	−0.255166	+	0.798419i	−0.00929875	+	0.0290960i
$754$	41.6774	−	7.37788i	1.51780	−	0.268687i
$755$		−	20.6870i		−	0.752876i
$756$	−11.1245	+	11.8910i	−0.404594	+	0.432473i
$757$		−	33.7213i		−	1.22562i	−0.790229	−	0.612811i	$-0.790039\pi$
$757$		−	33.7213i		−	1.22562i	0.790229	−	0.612811i	$-0.209961\pi$
$758$	6.70368	+	37.8689i	0.243489	+	1.37546i
$759$	33.4829	+	36.8273i	1.21535	+	1.33674i
$760$	3.12297	−	8.63468i	0.113282	−	0.313213i
$761$	−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	$0.845159\pi$
$762$	−8.88520	−	1.19889i	−0.321877	−	0.0434313i
$763$	−5.13539	−	0.905508i	−0.185914	−	0.0327816i
$764$	33.9482	+	12.3042i	1.22820	+	0.445152i
$765$	2.54560	−	1.75304i	0.0920365	−	0.0633814i
$766$	−8.41606	−	1.47812i	−0.304085	−	0.0534066i
$767$	71.4980	−	26.0231i	2.58164	−	0.939641i
$768$	−27.6846	+	1.25051i	−0.998981	+	0.0451240i
$769$	−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	$0.311126\pi$
$770$	0.00659309	+	9.76205i	0.000237599	+	0.351800i
$771$	−24.3039	−	18.7999i	−0.875283	−	0.677064i
$772$	4.44843	+	7.68093i	0.160103	+	0.276443i
$773$	−36.8149	+	21.2551i	−1.32414	+	0.764492i	−0.984386	−	0.176022i	$-0.943677\pi$
$773$	−36.8149	+	21.2551i	−1.32414	+	0.764492i	−0.339753	+	0.940515i	$0.610344\pi$
$774$	37.5184	+	26.6707i	1.34857	+	0.958658i
$775$	4.61456	−	7.99264i	0.165760	−	0.287104i
$776$	−19.5642	+	23.4119i	−0.702314	+	0.840438i
$777$	−8.45615	+	5.34095i	−0.303363	+	0.191605i
$778$	8.27420	+	14.3090i	0.296644	+	0.513003i
$779$	−9.79190	+	1.72658i	−0.350831	+	0.0618610i
$780$	19.2719	+	14.8660i	0.690046	+	0.532288i
$781$	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
$786$	−12.8455	−	20.3075i	−0.458184	−	0.724343i
$787$	−16.8983	+	2.97963i	−0.602359	+	0.106212i	−0.466508	−	0.884517i	$-0.654488\pi$
$787$	−16.8983	+	2.97963i	−0.602359	+	0.106212i	−0.135851	+	0.990729i	$0.543377\pi$
$788$	32.1936	+	5.63178i	1.14685	+	0.200624i
$789$	−13.9365	+	0.554078i	−0.496154	+	0.0197257i
$790$	−9.97390	+	8.38058i	−0.354855	+	0.298168i
$791$	−6.54642	+	11.3387i	−0.232764	+	0.403159i
$792$	−34.6391	−	9.49599i	−1.23085	−	0.337425i
$793$	18.5627	+	32.1515i	0.659179	+	1.14173i
$794$	−3.55060	−	1.28960i	−0.126006	−	0.0457662i
$795$	−1.21190	+	8.93607i	−0.0429817	+	0.316930i
$796$	−1.40751	−	1.17781i	−0.0498879	−	0.0417462i
$797$	−4.53298	−	5.40220i	−0.160567	−	0.191356i	0.679763	−	0.733432i	$-0.262083\pi$
$797$	−4.53298	−	5.40220i	−0.160567	−	0.191356i	−0.840329	+	0.542076i	$0.817638\pi$
$798$	11.4058	+	3.63669i	0.403762	+	0.128737i
$799$	0.831499	−	0.302641i	0.0294163	−	0.0107067i
$800$	21.8070	−	3.92114i	0.770994	−	0.138633i
$801$	−2.29100	+	24.0278i	−0.0809483	+	0.848980i
$802$	−6.02149	−	16.5092i	−0.212626	−	0.582960i
$803$	58.5114	+	10.3171i	2.06482	+	0.364084i
$804$	−0.763379	+	2.39981i	−0.0269223	+	0.0846347i
$805$	−3.78652	+	10.4034i	−0.133457	+	0.366670i
$806$	−11.2349	+	19.4898i	−0.395732	+	0.686499i
$807$	−11.1115	+	2.41797i	−0.391144	+	0.0851167i
$808$	17.5473	−	6.42700i	0.617313	−	0.226101i
$809$	−34.2649			−1.20469			−0.602345	−	0.798236i	$-0.705767\pi$
$809$	−34.2649			−1.20469			−0.602345	+	0.798236i	$0.705767\pi$
$810$	−8.36265	−	10.2735i	−0.293834	−	0.360975i
$811$		−	5.06146i		−	0.177732i	−0.996044	−	0.0888659i	$-0.971676\pi$
$811$		−	5.06146i		−	0.177732i	0.996044	−	0.0888659i	$-0.0283243\pi$
$812$	−12.0408	−	6.93012i	−0.422551	−	0.243199i
$813$	−4.00050	−	18.3839i	−0.140304	−	0.644750i
$814$	−19.1128	−	11.0176i	−0.669904	−	0.386166i
$815$	4.08885	+	1.48822i	0.143226	+	0.0521301i
$816$	−0.903322	+	6.79860i	−0.0316226	+	0.237999i
$817$	5.87673	−	33.3286i	0.205601	−	1.16602i
$818$	−2.49770	−	6.84797i	−0.0873300	−	0.239434i
$819$	−18.4037	+	25.8520i	−0.643077	+	0.903342i
$820$	4.27195	+	5.07717i	0.149183	+	0.177302i
$821$	5.19050	+	14.2608i	0.181150	+	0.497705i	0.996718	−	0.0809566i	$-0.0257975\pi$
$821$	5.19050	+	14.2608i	0.181150	+	0.497705i	−0.815568	+	0.578661i	$0.803575\pi$
$822$	−16.4382	+	51.5557i	−0.573349	+	1.79821i
$823$	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	$0.103758\pi$
$824$	−44.2445	+	7.89396i	−1.54133	+	0.274999i
$825$	28.4557	+	3.85914i	0.990701	+	0.134358i
$826$	−23.4740	−	8.52589i	−0.816765	−	0.296654i
$827$	−7.24554	+	4.18322i	−0.251952	+	0.145465i	−0.620658	−	0.784082i	$-0.713134\pi$
$827$	−7.24554	+	4.18322i	−0.251952	+	0.145465i	0.368706	+	0.929546i	$0.379801\pi$
$828$	−33.2155	−	23.5781i	−1.15432	−	0.819396i
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.883698	−	0.468058i	$-0.155046\pi$
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.0364987	+	0.999334i	$0.488380\pi$
$830$	5.93971	+	7.06897i	0.206170	+	0.245368i
$831$	−2.18154	−	54.8716i	−0.0756768	−	1.90348i
$832$	−53.1485	+	9.59374i	−1.84259	+	0.332603i
$833$	−0.781255	−	4.43072i	−0.0270689	−	0.153515i
$834$	6.23404	+	9.85540i	0.215867	+	0.341264i
$835$	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	$0.681909\pi$
$840$	−1.71456	−	7.80292i	−0.0591578	−	0.269226i
$841$	1.62295	+	9.20422i	0.0559639	+	0.317387i
$842$	9.54306	+	16.5033i	0.328876	+	0.568742i
$843$	18.1590	+	28.7505i	0.625428	+	0.990219i
$844$	0.0165663	+	12.2644i	0.000570236	+	0.422159i
$845$	29.3610	+	16.9516i	1.01005	+	0.583151i
$846$	−1.57823	−	3.44840i	−0.0542606	−	0.118558i
$847$	−5.41924	−	9.38639i	−0.186207	−	0.322520i
$848$	−12.9036	−	15.2938i	−0.443111	−	0.525191i
$849$	20.9000	−	27.0187i	0.717285	−	0.927280i
$850$	−0.00370334	−	5.48333i	−0.000127023	−	0.188077i
$851$	−16.0820	−	19.1657i	−0.551283	−	0.656993i
$852$	−8.10344	+	15.4703i	−0.277619	+	0.530003i
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	0.856290	+	0.516496i	$0.172764\pi$
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	−0.323959	+	0.946071i	$0.605014\pi$
$854$	2.10795	−	12.0022i	0.0721326	−	0.410706i
$855$	−4.18458	+	8.79424i	−0.143109	+	0.300757i
$856$	5.47109	+	9.43203i	0.186998	+	0.322380i
$857$	−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	$0.932267\pi$
$858$	−69.3676	−	9.35986i	−2.36817	−	0.319540i
$859$	−10.5655	+	29.0285i	−0.360491	+	0.990441i	0.618365	+	0.785891i	$0.287795\pi$
$859$	−10.5655	+	29.0285i	−0.360491	+	0.990441i	−0.978856	+	0.204550i	$0.934427\pi$
$860$	−21.2120	+	7.75300i	−0.723324	+	0.264375i
$861$	−6.40098	+	5.81969i	−0.218145	+	0.198335i
$862$	35.1139	−	6.21599i	1.19598	−	0.211717i
$863$	−27.4661			−0.934956			−0.467478	−	0.884005i	$-0.654837\pi$
$863$	−27.4661			−0.934956			−0.467478	+	0.884005i	$0.654837\pi$
$864$	29.3542	+	1.52624i	0.998651	+	0.0519239i
$865$	−1.38039			−0.0469348
$866$	−21.6764	+	3.83723i	−0.736594	+	0.130394i
$867$	−26.4306	−	8.44692i	−0.897630	−	0.286872i
$868$	6.93531	−	2.53486i	0.235400	−	0.0860388i
$869$	12.8137	−	35.2053i	0.434675	−	1.19426i
$870$	6.90905	−	8.94424i	0.234239	−	0.303238i
$871$	−0.852216	+	4.83316i	−0.0288762	+	0.163765i
$872$	4.72305	+	8.14241i	0.159943	+	0.275737i
$873$	23.0603	−	22.7036i	0.780474	−	0.768402i
$874$	−5.18032	+	29.4955i	−0.175227	+	0.997701i
$875$	4.97337	+	13.6642i	0.168131	+	0.461935i
$876$	−48.5822	+	1.99722i	−1.64144	+	0.0674799i
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	0.620463	−	0.784236i	$-0.286945\pi$
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	−0.880064	+	0.474855i	$0.842500\pi$
$878$	−0.0304331	−	45.0607i	−0.00102707	−	1.52072i
$879$	−17.4590	−	42.6188i	−0.588879	−	1.43750i
$880$	13.4685	−	11.3635i	0.454021	−	0.383064i
$881$	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	$0.614661\pi$
$882$	−18.6604	+	4.85793i	−0.628327	+	0.163575i
$883$	−19.8345	−	11.4515i	−0.667485	−	0.385373i	0.127638	−	0.991821i	$-0.459261\pi$
$883$	−19.8345	−	11.4515i	−0.667485	−	0.385373i	−0.795123	+	0.606448i	$0.792594\pi$
$884$	0.0180539	+	13.3657i	0.000607217	+	0.449537i
$885$	9.45153	−	17.9847i	0.317710	−	0.604551i
$886$	4.47773	+	7.74358i	0.150432	+	0.260151i
$887$	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	$0.913755\pi$
$888$	17.2085	+	5.46122i	0.577478	+	0.183267i
$889$	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
$894$	−26.1883	+	49.9139i	−0.875866	+	1.66937i
$895$	2.02139	+	11.4639i	0.0675675	+	0.383194i
$896$	15.3939	+	8.79092i	0.514275	+	0.293684i
$897$	−70.2692	−	36.9286i	−2.34622	−	1.23301i
$898$	−7.60840	−	9.05491i	−0.253895	−	0.302166i
$899$	9.04655	+	5.22303i	0.301719	+	0.174198i
$900$	−23.4241	+	1.89734i	−0.780802	+	0.0632447i
$901$	−4.28862	+	2.47604i	−0.142875	+	0.0824888i
$902$	−17.9357	−	6.51434i	−0.597193	−	0.216904i
$903$	−11.1622	−	27.2479i	−0.371456	−	0.906753i
$904$	23.2669	−	4.15122i	0.773847	−	0.138067i
$905$	2.95572	−	2.48014i	0.0982513	−	0.0824426i
$906$	−32.7770	−	36.0020i	−1.08894	−	1.19608i
$907$	−8.42248	−	23.1406i	−0.279664	−	0.768370i	−0.997401	−	0.0720557i	$-0.977044\pi$
$907$	−8.42248	−	23.1406i	−0.279664	−	0.768370i	0.717737	−	0.696315i	$-0.245178\pi$
$908$	−23.9607	−	28.4771i	−0.795165	−	0.945045i
$909$	−19.1849	+	4.98065i	−0.636323	+	0.165198i
$910$	−5.33489	−	14.6267i	−0.176850	−	0.484872i
$911$	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	$-0.150741\pi$
$912$	−8.24604	−	19.9752i	−0.273054	−	0.661445i
$913$	−24.9517	−	9.08166i	−0.825780	−	0.300559i
$914$	−34.5058	−	19.8909i	−1.14135	−	0.657932i
$915$	9.44290	+	3.01784i	0.312173	+	0.0997668i
$916$	15.3931	+	8.85948i	0.508601	+	0.292726i
$917$			15.3708i			0.507590i
$918$	1.65260	−	7.08417i	0.0545439	−	0.233813i
$919$	27.8245			0.917845			0.458923	−	0.888476i	$-0.348236\pi$
$919$	27.8245			0.917845			0.458923	+	0.888476i	$0.348236\pi$
$920$	18.7656	−	6.87321i	0.618684	−	0.226603i
$921$	−26.9633	−	29.6565i	−0.888470	−	0.977213i
$922$	−18.4608	+	32.0250i	−0.607975	+	1.05469i
$923$	−11.6405	+	31.9819i	−0.383151	+	1.05270i
$924$	15.4787	+	16.9786i	0.509212	+	0.558556i
$925$	−14.2153	−	2.50654i	−0.467397	−	0.0824146i
$926$	10.7331	+	29.4270i	0.352711	+	0.967032i
$927$	47.5190	−	3.78443i	1.56073	−	0.124297i
$928$	4.43818	+	24.6825i	0.145690	+	0.810241i
$929$	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	$0.309802\pi$
$930$	1.28126	+	5.86880i	0.0420142	+	0.192446i
$931$	9.11238	+	10.8597i	0.298646	+	0.355913i
$932$	28.8276	+	24.1230i	0.944281	+	0.790174i
$933$	33.4088	+	25.8429i	1.09375	+	0.846060i
$934$	−29.4181	−	10.6848i	−0.962590	−	0.349618i
$935$	−2.18052	−	3.77677i	−0.0713106	−	0.123514i
$936$	57.0934	−	4.66336i	1.86615	−	0.152427i
$937$	−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	$0.267910\pi$
$938$	1.23332	−	1.03629i	0.0402692	−	0.0338362i
$939$	−23.8352	−	37.7375i	−0.777833	−	1.23152i
$940$	1.83281	+	0.320621i	0.0597796	+	0.0104575i
$941$	36.4053	−	6.41923i	1.18678	−	0.209261i	0.454803	−	0.890592i	$-0.349710\pi$
$941$	36.4053	−	6.41923i	1.18678	−	0.209261i	0.731975	+	0.681331i	$0.238599\pi$
$942$	11.9693	−	0.483964i	0.389982	−	0.0157684i
$943$	−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	−0.960875	−	0.276981i	$-0.910666\pi$
$947$	−16.0406	+	19.1164i	−0.521248	+	0.621199i	0.439627	+	0.898180i	$0.355110\pi$
$948$	−4.07937	+	30.3878i	−0.132492	+	0.986949i
$949$	−93.3185	+	16.4546i	−3.02925	+	0.534138i
$950$	8.64896	+	14.9571i	0.280609	+	0.485273i
$951$	1.26721	+	31.8738i	0.0410922	+	1.03358i
$952$	2.81317	−	3.36643i	0.0911753	−	0.109107i
$953$	−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	$0.242765\pi$
$954$	12.0494	+	17.4718i	0.390115	+	0.565670i
$955$	16.2733	−	9.39537i	0.526590	−	0.304027i
$956$	20.5869	+	35.5465i	0.665827	+	1.14966i
$957$	−4.36800	+	32.2079i	−0.141197	+	1.04113i
$958$	0.0113577	+	16.8167i	0.000366949	+	0.543322i
$959$	26.5164	−	22.2499i	0.856258	−	0.718486i
$960$	−8.77739	+	11.4426i	−0.283289	+	0.369308i
$961$	23.9132	−	8.70369i	0.771393	−	0.280764i
$962$	34.6542	+	6.08633i	1.11729	+	0.196231i
$963$	−4.80590	−	10.5196i	−0.154868	−	0.338988i
$964$	−25.9029	−	9.38828i	−0.834276	−	0.302376i
$965$	4.54883	+	0.802081i	0.146432	+	0.0258199i
$966$	9.89361	+	24.1046i	0.318322	+	0.775554i
$967$	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	$0.296384\pi$
$968$	−6.65433	+	18.3985i	−0.213878	+	0.591351i
$969$	−5.22581	+	1.13719i	−0.167877	+	0.0365317i
$970$	2.76759	+	15.6340i	0.0888619	+	0.501978i
$971$		−	20.4952i		−	0.657724i	−0.944378	−	0.328862i	$-0.893335\pi$
$971$		−	20.4952i		−	0.657724i	0.944378	−	0.328862i	$-0.106665\pi$
$972$	−30.8313	−	4.62923i	−0.988915	−	0.148483i
$973$		−	7.45961i		−	0.239144i
$974$	30.8011	−	5.45252i	0.986932	−	0.174710i
$975$	−44.7515	+	9.73837i	−1.43320	+	0.311877i
$976$	−19.0203	+	11.0500i	−0.608826	+	0.353702i
$977$	−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	$0.653092\pi$
$978$	9.47389	−	3.88850i	0.302942	−	0.124341i
$979$	33.5386	+	5.91376i	1.07190	+	0.189004i
$980$	3.22363	−	8.89422i	0.102975	−	0.284116i
$981$	−4.14880	−	9.08126i	−0.132461	−	0.289942i
$982$	1.82621	−	10.3980i	0.0582767	−	0.331814i
$983$	−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	$0.513770\pi$
$984$	15.4789	+	2.06731i	0.493451	+	0.0659034i
$985$	13.0285	−	10.9322i	0.415123	−	0.348330i
$986$	6.20636	−	0.00419165i	0.197651	−	0.000133489i
$987$	−0.326014	+	2.40389i	−0.0103771	+	0.0765168i
$988$	−21.1066	−	36.4439i	−0.671491	−	1.15944i
$989$	63.7900	−	36.8292i	2.02840	−	1.17110i
$990$	−15.3865	+	10.6113i	−0.489015	+	0.337250i
$991$	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	$0.0803170\pi$
$992$	−11.5659	−	6.62558i	−0.367217	−	0.210362i
$993$	1.06459	+	26.7773i	0.0337837	+	0.849751i
$994$	9.67090	−	5.59221i	0.306742	−	0.177374i
$995$	−0.940553	+	0.165845i	−0.0298175	+	0.00525763i
$996$	21.5373	+	2.89124i	0.682434	+	0.0916125i
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	−0.314180	−	0.949363i	$-0.601730\pi$
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	0.989497	+	0.144552i	$0.0461740\pi$
$998$	−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.205.32	yes	204
3.2	odd	2		648.2.t.a.613.3		204
4.3	odd	2		864.2.bf.a.529.20		204
8.3	odd	2		864.2.bf.a.529.15		204
8.5	even	2	inner	216.2.t.a.205.18	yes	204
24.5	odd	2		648.2.t.a.613.17		204
27.5	odd	18		648.2.t.a.37.17		204
27.22	even	9	inner	216.2.t.a.157.18	✓	204
108.103	odd	18		864.2.bf.a.49.15		204
216.5	odd	18		648.2.t.a.37.3		204
216.157	even	18	inner	216.2.t.a.157.32	yes	204
216.211	odd	18		864.2.bf.a.49.20		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.18	✓	204	27.22	even	9	inner
216.2.t.a.157.32	yes	204	216.157	even	18	inner
216.2.t.a.205.18	yes	204	8.5	even	2	inner
216.2.t.a.205.32	yes	204	1.1	even	1	trivial
648.2.t.a.37.3		204	216.5	odd	18
648.2.t.a.37.17		204	27.5	odd	18
648.2.t.a.613.3		204	3.2	odd	2
648.2.t.a.613.17		204	24.5	odd	2
864.2.bf.a.49.15		204	108.103	odd	18
864.2.bf.a.49.20		204	216.211	odd	18
864.2.bf.a.529.15		204	8.3	odd	2
864.2.bf.a.529.20		204	4.3	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+(1.39256 - 0.246516i) q^{2} +(-0.368292 - 1.69244i) q^{3} +(1.87846 - 0.686578i) q^{4} +(0.355965 - 0.978005i) q^{5} +(-0.930084 - 2.26604i) q^{6} +(-0.272085 + 1.54307i) q^{7} +(2.44662 - 1.41917i) q^{8} +(-2.72872 + 1.24663i) q^{9} +(0.254609 - 1.44968i) q^{10} +(1.44773 + 3.97760i) q^{11} +(-1.85382 - 2.92632i) q^{12} +(-4.33941 - 5.17151i) q^{13} +(0.00149657 + 2.21590i) q^{14} +(-1.78632 - 0.242259i) q^{15} +(3.05722 - 2.57942i) q^{16} +(-0.494959 - 0.857294i) q^{17} +(-3.49260 + 2.40868i) q^{18} +(2.70129 + 1.55959i) q^{19} +(-0.00281166 - 2.08154i) q^{20} +(2.71177 - 0.107812i) q^{21} +(2.99660 + 5.18217i) q^{22} +(1.17888 + 6.68573i) q^{23} +(-3.30294 - 3.61809i) 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} +(-2.54728 + 0.102996i) q^{30} +(-0.409166 - 2.32049i) q^{31} +(3.62150 - 4.34566i) q^{32} +(6.19868 - 3.91512i) q^{33} +(-0.900598 - 1.07182i) q^{34} +(1.41228 + 0.815381i) q^{35} +(-4.26989 + 4.21522i) q^{36} +(-3.19157 + 1.84266i) q^{37} +(4.14618 + 1.50592i) q^{38} +(-7.15431 + 9.24883i) q^{39} +(-0.517049 - 2.89798i) q^{40} +(-2.44191 + 2.04900i) q^{41} +(3.74973 - 0.818631i) q^{42} +(-3.71087 - 10.1955i) q^{43} +(5.45044 + 6.47779i) q^{44} +(0.247877 + 3.11246i) q^{45} +(3.28980 + 9.01969i) q^{46} +(-0.155220 + 0.880296i) q^{47} +(-5.49147 - 4.22419i) q^{48} +(4.27080 + 1.55445i) q^{49} +(4.79894 + 2.76635i) q^{50} +(-1.26863 + 1.15342i) q^{51} +(-11.7021 - 6.73512i) q^{52} -5.00251i q^{53} +(5.36285 + 5.02393i) q^{54} +4.40546 q^{55} +(1.52420 + 4.16145i) q^{56} +(1.64465 - 5.14616i) q^{57} +(-3.13112 + 5.43173i) q^{58} +(-3.85475 + 10.5908i) q^{59} +(-3.52185 + 0.771373i) q^{60} +(-5.41575 - 0.954943i) q^{61} +(-1.14183 - 3.13057i) q^{62} +(-1.18119 - 4.54981i) q^{63} +(3.97189 - 6.94436i) q^{64} +(-6.60244 + 2.40309i) q^{65} +(7.66690 - 6.98012i) q^{66} +(-0.467287 - 0.556891i) q^{67} +(-1.51836 - 1.27056i) q^{68} +(10.8810 - 4.45748i) q^{69} +(2.16769 + 0.787319i) q^{70} +(-2.52073 - 4.36603i) q^{71} +(-4.90697 + 6.92255i) q^{72} +(7.01816 - 12.1558i) q^{73} +(-3.99022 + 3.35279i) q^{74} +(3.15597 - 6.00531i) q^{75} +(6.14505 + 1.07498i) q^{76} +(-6.53164 + 1.15170i) q^{77} +(-7.68284 + 14.6432i) 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} +(5.01993 - 2.06436i) q^{84} +(-1.01463 + 0.178906i) q^{85} +(-7.68099 - 13.2831i) q^{86} +(6.79716 + 3.57211i) q^{87} +(9.18695 + 7.67710i) q^{88} +(4.02279 - 6.96768i) q^{89} +(1.11246 + 4.27319i) q^{90} +(9.16071 - 5.28894i) q^{91} +(6.80475 + 11.7495i) q^{92} +(-3.77661 + 1.54711i) q^{93} +(0.000853769 + 1.26413i) q^{94} +(2.48685 - 2.08672i) q^{95} +(-8.68854 - 4.52871i) q^{96} +(-10.1365 + 3.68937i) q^{97} +(6.33056 + 1.11184i) 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

Related objects

Downloads

Learn more