LMFDB - Embedded newform 966.2.y.a.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.4
Character	$\chi$	$=$	966.151
Dual form			966.2.y.a.499.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.00054 + 0.0955401i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.50267 - 0.858289i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.00054 + 0.0955401i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.50267 - 0.858289i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.236960 + 0.976761i) q^{10} +(1.37041 + 3.95954i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(-2.89239 + 0.849281i) q^{13} +(-1.62963 + 2.08430i) q^{14} +(-0.845538 + 0.543394i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-7.01682 - 2.80911i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-4.72260 + 1.89064i) q^{19} +(0.845538 + 0.543394i) q^{20} +(-2.61775 + 0.383911i) q^{21} +4.18999 q^{22} +(3.91582 + 2.76882i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.91769 + 0.755072i) q^{25} +(-0.143435 + 3.01108i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.43667 + 2.22171i) q^{28} +(-1.23712 - 8.60435i) q^{29} +(0.236960 + 0.976761i) q^{30} +(-0.0777420 - 1.63201i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(3.03244 + 2.89142i) q^{33} +(-4.94959 + 5.71213i) q^{34} +(2.58602 + 0.619648i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.0483316 - 0.0678723i) q^{37} +(0.242049 + 5.08123i) q^{38} +(-2.18169 + 2.08024i) q^{39} +(0.790056 - 0.621307i) q^{40} +(-2.34256 + 5.12949i) q^{41} +(-0.493386 + 2.59934i) q^{42} +(8.12166 + 5.21947i) q^{43} +(1.37041 - 3.95954i) q^{44} +(-0.502546 + 0.870436i) q^{45} +(3.89728 - 2.79486i) q^{46} +(-3.19731 - 5.53790i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.52668 + 4.29602i) q^{49} +(-0.567806 + 3.94918i) q^{50} +(-7.52400 + 0.718455i) q^{51} +(2.79856 + 1.12037i) q^{52} +(-9.13561 + 8.71079i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-1.74945 - 3.83076i) q^{55} +(2.56940 - 0.631005i) q^{56} +(-3.33127 + 3.84449i) q^{57} +(-8.53574 - 1.64513i) q^{58} +(0.962033 - 3.96555i) q^{59} +(1.00054 + 0.0955401i) q^{60} +(12.9408 + 6.67147i) q^{61} +(-1.56767 - 0.460311i) q^{62} +(-2.15083 + 1.54076i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.81281 - 1.12608i) q^{65} +(3.72421 - 1.91996i) q^{66} +(-7.95757 + 1.53370i) q^{67} +(3.77911 + 6.54562i) q^{68} +(4.74926 + 0.666698i) q^{69} +(1.43137 - 2.24113i) q^{70} +(-3.15211 - 3.63773i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(0.674879 + 0.530731i) q^{73} +(-0.0483316 - 0.0678723i) q^{74} +(-3.13619 + 2.46632i) q^{75} +(4.88093 + 1.43317i) q^{76} +(-0.0312509 - 11.0856i) q^{77} +(1.25227 + 2.74208i) q^{78} +(-5.02217 - 4.78863i) q^{79} +(-0.328734 - 0.949813i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(4.08120 + 3.89141i) q^{82} +(-6.21133 - 13.6009i) q^{83} +(2.29501 + 1.31641i) q^{84} +(7.28900 + 2.14024i) q^{85} +(7.58874 - 5.96785i) q^{86} +(-5.04234 - 7.08097i) q^{87} +(-3.29355 - 2.59008i) q^{88} +(0.414150 - 8.69409i) q^{89} +(0.658196 + 0.759598i) q^{90} +(7.96761 + 0.357035i) q^{91} +(-1.36647 - 4.59704i) q^{92} +(-0.816928 - 1.41496i) q^{93} +(-6.27906 + 1.21019i) q^{94} +(4.54452 - 2.34286i) q^{95} +(0.928368 - 0.371662i) q^{96} +(1.55033 - 3.39474i) q^{97} +(5.86734 - 3.81763i) q^{98} +(4.02026 + 1.18046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−1.00054	+	0.0955401i	−0.447456	+	0.0427268i	−0.316352	−	0.948642i	$-0.602458\pi$
$5$	−1.00054	+	0.0955401i	−0.447456	+	0.0427268i	−0.131104	+	0.991369i	$0.541852\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−2.50267	−	0.858289i	−0.945919	−	0.324403i
$7$	−2.50267	−	0.858289i	−0.945919	−	0.324403i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	−0.236960	+	0.976761i	−0.0749332	+	0.308879i
$11$	1.37041	+	3.95954i	0.413194	+	1.19385i	0.939201	+	0.343366i	$0.111567\pi$
$11$	1.37041	+	3.95954i	0.413194	+	1.19385i	−0.526007	+	0.850480i	$0.676311\pi$
$12$	−0.981929	−	0.189251i	−0.283458	−	0.0546321i
$13$	−2.89239	+	0.849281i	−0.802204	+	0.235548i	−0.657036	−	0.753859i	$-0.728190\pi$
$13$	−2.89239	+	0.849281i	−0.802204	+	0.235548i	−0.145167	+	0.989407i	$0.546372\pi$
$14$	−1.62963	+	2.08430i	−0.435536	+	0.557053i
$15$	−0.845538	+	0.543394i	−0.218317	+	0.140304i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−7.01682	−	2.80911i	−1.70183	−	0.681309i	−0.702295	−	0.711886i	$-0.747841\pi$
$17$	−7.01682	−	2.80911i	−1.70183	−	0.681309i	−0.999532	+	0.0305766i	$0.990266\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	−4.72260	+	1.89064i	−1.08344	+	0.433743i	−0.843546	−	0.537056i	$-0.819536\pi$
$19$	−4.72260	+	1.89064i	−1.08344	+	0.433743i	−0.239892	+	0.970800i	$0.577112\pi$
$20$	0.845538	+	0.543394i	0.189068	+	0.121507i
$21$	−2.61775	+	0.383911i	−0.571240	+	0.0837762i
$22$	4.18999			0.893308
$23$	3.91582	+	2.76882i	0.816504	+	0.577340i
$23$	3.91582	+	2.76882i	0.816504	+	0.577340i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−3.91769	+	0.755072i	−0.783538	+	0.151014i
$26$	−0.143435	+	3.01108i	−0.0281300	+	0.590522i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	1.43667	+	2.22171i	0.271505	+	0.419863i
$29$	−1.23712	−	8.60435i	−0.229727	−	1.59779i	−0.699257	−	0.714871i	$-0.746486\pi$
$29$	−1.23712	−	8.60435i	−0.229727	−	1.59779i	0.469530	−	0.882917i	$-0.344424\pi$
$30$	0.236960	+	0.976761i	0.0432627	+	0.178331i
$31$	−0.0777420	−	1.63201i	−0.0139629	−	0.293117i	−0.995038	−	0.0994915i	$-0.968278\pi$
$31$	−0.0777420	−	1.63201i	−0.0139629	−	0.293117i	0.981076	−	0.193625i	$-0.0620246\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	3.03244	+	2.89142i	0.527879	+	0.503332i
$34$	−4.94959	+	5.71213i	−0.848847	+	0.979622i
$35$	2.58602	+	0.619648i	0.437118	+	0.104740i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.0483316	−	0.0678723i	0.00794567	−	0.0111581i	−0.810584	−	0.585622i	$-0.800850\pi$
$37$	0.0483316	−	0.0678723i	0.00794567	−	0.0111581i	0.818530	+	0.574464i	$0.194790\pi$
$38$	0.242049	+	5.08123i	0.0392655	+	0.824284i
$39$	−2.18169	+	2.08024i	−0.349350	+	0.333105i
$40$	0.790056	−	0.621307i	0.124919	−	0.0982373i
$41$	−2.34256	+	5.12949i	−0.365846	+	0.801092i	0.633773	+	0.773519i	$0.281505\pi$
$41$	−2.34256	+	5.12949i	−0.365846	+	0.801092i	−0.999620	+	0.0275731i	$0.991222\pi$
$42$	−0.493386	+	2.59934i	−0.0761311	+	0.401087i
$43$	8.12166	+	5.21947i	1.23854	+	0.795962i	0.985199	−	0.171415i	$-0.0548338\pi$
$43$	8.12166	+	5.21947i	1.23854	+	0.795962i	0.253342	+	0.967377i	$0.418470\pi$
$44$	1.37041	−	3.95954i	0.206597	−	0.596923i
$45$	−0.502546	+	0.870436i	−0.0749152	+	0.129757i
$46$	3.89728	−	2.79486i	0.574622	−	0.412079i
$47$	−3.19731	−	5.53790i	−0.466376	−	0.807786i	0.532887	−	0.846186i	$-0.321107\pi$
$47$	−3.19731	−	5.53790i	−0.466376	−	0.807786i	−0.999262	+	0.0384004i	$0.987774\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	5.52668	+	4.29602i	0.789526	+	0.613717i
$50$	−0.567806	+	3.94918i	−0.0802999	+	0.558498i
$51$	−7.52400	+	0.718455i	−1.05357	+	0.100604i
$52$	2.79856	+	1.12037i	0.388091	+	0.155368i
$53$	−9.13561	+	8.71079i	−1.25487	+	1.19652i	−0.283496	+	0.958973i	$0.591494\pi$
$53$	−9.13561	+	8.71079i	−1.25487	+	1.19652i	−0.971376	+	0.237546i	$0.923657\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	−1.74945	−	3.83076i	−0.235895	−	0.516539i
$56$	2.56940	−	0.631005i	0.343351	−	0.0843216i
$57$	−3.33127	+	3.84449i	−0.441237	+	0.509215i
$58$	−8.53574	−	1.64513i	−1.12080	−	0.216016i
$59$	0.962033	−	3.96555i	0.125246	−	0.516271i	−0.874278	−	0.485425i	$-0.838665\pi$
$59$	0.962033	−	3.96555i	0.125246	−	0.516271i	0.999524	−	0.0308459i	$-0.00982010\pi$
$60$	1.00054	+	0.0955401i	0.129169	+	0.0123342i
$61$	12.9408	+	6.67147i	1.65690	+	0.854194i	0.994464	+	0.105080i	$0.0335097\pi$
$61$	12.9408	+	6.67147i	1.65690	+	0.854194i	0.662441	+	0.749114i	$0.269521\pi$
$62$	−1.56767	−	0.460311i	−0.199095	−	0.0584595i
$63$	−2.15083	+	1.54076i	−0.270979	+	0.194117i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	2.81281	−	1.12608i	0.348887	−	0.139673i
$66$	3.72421	−	1.91996i	0.458418	−	0.236331i
$67$	−7.95757	+	1.53370i	−0.972172	+	0.187371i	−0.650521	−	0.759488i	$-0.725450\pi$
$67$	−7.95757	+	1.53370i	−0.972172	+	0.187371i	−0.321650	+	0.946859i	$0.604237\pi$
$68$	3.77911	+	6.54562i	0.458285	+	0.793773i
$69$	4.74926	+	0.666698i	0.571744	+	0.0802610i
$70$	1.43137	−	2.24113i	0.171082	−	0.267866i
$71$	−3.15211	−	3.63773i	−0.374087	−	0.431719i	0.537223	−	0.843440i	$-0.319473\pi$
$71$	−3.15211	−	3.63773i	−0.374087	−	0.431719i	−0.911310	+	0.411721i	$0.864928\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	0.674879	+	0.530731i	0.0789886	+	0.0621173i	0.656873	−	0.754002i	$-0.271879\pi$
$73$	0.674879	+	0.530731i	0.0789886	+	0.0621173i	−0.577884	+	0.816119i	$0.696121\pi$
$74$	−0.0483316	−	0.0678723i	−0.00561844	−	0.00788999i
$75$	−3.13619	+	2.46632i	−0.362136	+	0.284787i
$76$	4.88093	+	1.43317i	0.559881	+	0.164396i
$77$	−0.0312509	−	11.0856i	−0.00356137	−	1.26332i
$78$	1.25227	+	2.74208i	0.141791	+	0.310480i
$79$	−5.02217	−	4.78863i	−0.565039	−	0.538763i	0.352809	−	0.935695i	$-0.385226\pi$
$79$	−5.02217	−	4.78863i	−0.565039	−	0.538763i	−0.917848	+	0.396932i	$0.870075\pi$
$80$	−0.328734	−	0.949813i	−0.0367535	−	0.106192i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	4.08120	+	3.89141i	0.450693	+	0.429735i
$83$	−6.21133	−	13.6009i	−0.681782	−	1.49289i	−0.860744	−	0.509038i	$-0.830001\pi$
$83$	−6.21133	−	13.6009i	−0.681782	−	1.49289i	0.178963	−	0.983856i	$-0.442726\pi$
$84$	2.29501	+	1.31641i	0.250406	+	0.143632i
$85$	7.28900	+	2.14024i	0.790603	+	0.232142i
$86$	7.58874	−	5.96785i	0.818315	−	0.643530i
$87$	−5.04234	−	7.08097i	−0.540595	−	0.759160i
$88$	−3.29355	−	2.59008i	−0.351094	−	0.276103i
$89$	0.414150	−	8.69409i	0.0438998	−	0.921571i	−0.864285	−	0.503002i	$-0.832229\pi$
$89$	0.414150	−	8.69409i	0.0438998	−	0.921571i	0.908185	−	0.418569i	$-0.137468\pi$
$90$	0.658196	+	0.759598i	0.0693799	+	0.0800687i
$91$	7.96761	+	0.357035i	0.835232	+	0.0374274i
$92$	−1.36647	−	4.59704i	−0.142464	−	0.479274i
$93$	−0.816928	−	1.41496i	−0.0847115	−	0.146725i
$94$	−6.27906	+	1.21019i	−0.647636	+	0.124822i
$95$	4.54452	−	2.34286i	0.466258	−	0.240373i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	1.55033	−	3.39474i	0.157412	−	0.344684i	−0.814451	−	0.580233i	$-0.802962\pi$
$97$	1.55033	−	3.39474i	0.157412	−	0.344684i	0.971862	+	0.235549i	$0.0756888\pi$
$98$	5.86734	−	3.81763i	0.592691	−	0.385639i
$99$	4.02026	+	1.18046i	0.404052	+	0.118640i
$100$	3.54627	+	1.82823i	0.354627	+	0.182823i
$101$	−17.1635	−	1.63892i	−1.70783	−	0.163078i	−0.805060	−	0.593194i	$-0.797867\pi$
$101$	−17.1635	−	1.63892i	−1.70783	−	0.163078i	−0.902774	+	0.430116i	$0.858473\pi$
$102$	−1.78192	+	7.34517i	−0.176436	+	0.727280i
$103$	−4.45319	−	0.858282i	−0.438786	−	0.0845690i	−0.0349259	−	0.999390i	$-0.511120\pi$
$103$	−4.45319	−	0.858282i	−0.438786	−	0.0845690i	−0.403860	+	0.914821i	$0.632332\pi$
$104$	1.97407	−	2.27820i	0.193574	−	0.223396i
$105$	2.58249	−	0.634219i	0.252025	−	0.0618934i
$106$	5.24374	+	11.4822i	0.509317	+	1.11525i
$107$	−2.76404	−	1.42496i	−0.267210	−	0.137756i	0.319415	−	0.947615i	$-0.396514\pi$
$107$	−2.76404	−	1.42496i	−0.267210	−	0.137756i	−0.586625	+	0.809859i	$0.699544\pi$
$108$	−0.723734	+	0.690079i	−0.0696413	+	0.0664029i
$109$	9.05922	+	3.62676i	0.867715	+	0.347381i	0.762437	−	0.647062i	$-0.224003\pi$
$109$	9.05922	+	3.62676i	0.867715	+	0.347381i	0.105278	+	0.994443i	$0.466427\pi$
$110$	−4.19226	+	0.400312i	−0.399716	+	0.0381682i
$111$	0.0118580	−	0.0824741i	0.00112551	−	0.00782810i
$112$	0.244069	−	2.63447i	0.0230623	−	0.248934i
$113$	0.171529	+	0.197955i	0.0161360	+	0.0186220i	0.763760	−	0.645500i	$-0.223351\pi$
$113$	0.171529	+	0.197955i	0.0161360	+	0.0186220i	−0.747624	+	0.664122i	$0.768806\pi$
$114$	2.54349	+	4.40546i	0.238220	+	0.412609i
$115$	−4.18247	−	2.39621i	−0.390017	−	0.223447i
$116$	−4.34641	+	7.52821i	−0.403554	+	0.698977i
$117$	−0.985945	+	2.84870i	−0.0911506	+	0.263362i
$118$	−3.43280	−	2.20613i	−0.316015	−	0.203091i
$119$	15.1497	+	13.0527i	1.38877	+	1.19654i
$120$	0.417531	−	0.914264i	0.0381152	−	0.0834605i
$121$	−5.15336	+	4.05265i	−0.468487	+	0.368422i
$122$	10.5371	−	10.0471i	0.953982	−	0.909620i
$123$	0.268318	+	5.63270i	0.0241935	+	0.507883i
$124$	−0.947730	+	1.33090i	−0.0851087	+	0.119518i
$125$	8.66957	−	2.54561i	0.775430	−	0.227687i
$126$	0.752548	+	2.53647i	0.0670423	+	0.225967i
$127$	2.65911	−	3.06878i	0.235958	−	0.272310i	−0.625405	−	0.780301i	$-0.715066\pi$
$127$	2.65911	−	3.06878i	0.235958	−	0.272310i	0.861363	+	0.507991i	$0.169612\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	9.61052	+	0.917693i	0.846159	+	0.0807984i
$130$	−0.144166	−	3.02642i	−0.0126442	−	0.265434i
$131$	1.57479	+	6.49137i	0.137590	+	0.567153i	0.998312	+	0.0580783i	$0.0184973\pi$
$131$	1.57479	+	6.49137i	0.137590	+	0.567153i	−0.860722	+	0.509075i	$0.829988\pi$
$132$	−0.596297	−	4.14734i	−0.0519010	−	0.360980i
$133$	13.4418	−	0.678296i	1.16555	−	0.0588157i
$134$	−1.15332	+	8.02153i	−0.0996319	+	0.692955i
$135$	−0.0478242	+	1.00395i	−0.00411605	+	0.0864066i
$136$	7.42164	−	1.43040i	0.636400	−	0.122656i
$137$	−5.63027	+	9.75191i	−0.481026	+	0.833162i	−0.999763	−	0.0217721i	$-0.993069\pi$
$137$	−5.63027	+	9.75191i	−0.481026	+	0.833162i	0.518737	+	0.854934i	$0.326403\pi$
$138$	2.18336	−	4.27000i	0.185860	−	0.363487i
$139$	−5.33442			−0.452459			−0.226230	−	0.974074i	$-0.572640\pi$
$139$	−5.33442			−0.452459			−0.226230	+	0.974074i	$0.572640\pi$
$140$	−1.64971	−	2.08565i	−0.139426	−	0.176270i
$141$	−5.37950	−	3.45719i	−0.453035	−	0.291148i
$142$	−4.46861	+	1.78896i	−0.374998	+	0.150126i
$143$	−7.32652	−	10.2887i	−0.612675	−	0.860381i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	2.05985	+	8.49081i	0.171061	+	0.705124i
$146$	0.722272	−	0.464176i	0.0597757	−	0.0384155i
$147$	6.88086	+	1.28598i	0.567524	+	0.106066i
$148$	−0.0799471	+	0.0234746i	−0.00657161	+	0.00192960i
$149$	−1.07496	−	0.207181i	−0.0880640	−	0.0169729i	0.145029	−	0.989427i	$-0.453672\pi$
$149$	−1.07496	−	0.207181i	−0.0880640	−	0.0169729i	−0.233093	+	0.972454i	$0.574885\pi$
$150$	1.30493	+	3.77035i	0.106547	+	0.307848i
$151$	0.629517	−	2.59491i	0.0512294	−	0.211170i	−0.940444	−	0.339949i	$-0.889590\pi$
$151$	0.629517	−	2.59491i	0.0512294	−	0.211170i	0.991673	+	0.128778i	$0.0411055\pi$
$152$	2.95074	−	4.14374i	0.239337	−	0.336102i
$153$	−6.35839	+	4.08629i	−0.514045	+	0.330357i
$154$	−10.4861	−	3.59622i	−0.844997	−	0.289792i
$155$	0.233706	+	1.62546i	0.0187717	+	0.130560i
$156$	3.00085	−	0.286546i	0.240260	−	0.0229420i
$157$	−6.34955	−	4.99334i	−0.506749	−	0.398512i	0.331790	−	0.943353i	$-0.392347\pi$
$157$	−6.34955	−	4.99334i	−0.506749	−	0.398512i	−0.838539	+	0.544841i	$0.816590\pi$
$158$	−6.16786	+	3.17975i	−0.490688	+	0.252967i
$159$	−4.12854	+	11.9286i	−0.327415	+	0.946002i
$160$	−1.00509			−0.0794596
$161$	−7.42353	−	10.2903i	−0.585056	−	0.810993i
$162$	−1.00000			−0.0785674
$163$	3.15183	−	9.10662i	0.246871	−	0.713286i	−0.751683	−	0.659524i	$-0.770758\pi$
$163$	3.15183	−	9.10662i	0.246871	−	0.713286i	0.998554	−	0.0537613i	$-0.0171210\pi$
$164$	5.01222	−	2.58398i	0.391388	−	0.201775i
$165$	−3.31033	−	2.60327i	−0.257708	−	0.202664i
$166$	−14.8844	+	1.42129i	−1.15525	+	0.110313i
$167$	−2.95980	−	20.5859i	−0.229037	−	1.59298i	−0.702180	−	0.711999i	$-0.747790\pi$
$167$	−2.95980	−	20.5859i	−0.229037	−	1.59298i	0.473144	−	0.880985i	$-0.343119\pi$
$168$	1.99463	−	1.73823i	0.153889	−	0.134107i
$169$	−3.29167	+	2.11543i	−0.253206	+	0.162725i
$170$	4.40653	−	6.18810i	0.337965	−	0.474606i
$171$	−1.19930	+	4.94359i	−0.0917130	+	0.378046i
$172$	−3.15759	−	9.12326i	−0.240764	−	0.695642i
$173$	8.18450	+	1.57743i	0.622256	+	0.119930i	0.490628	−	0.871369i	$-0.336767\pi$
$173$	8.18450	+	1.57743i	0.622256	+	0.119930i	0.131628	+	0.991299i	$0.457980\pi$
$174$	−8.34071	+	2.44905i	−0.632307	+	0.185662i
$175$	10.4527	+	1.47281i	0.790153	+	0.111334i
$176$	−3.52484	+	2.26528i	−0.265695	+	0.170752i
$177$	−0.962033	−	3.96555i	−0.0723108	−	0.298069i
$178$	−8.08046	−	3.23493i	−0.605656	−	0.242468i
$179$	1.31661	+	1.84892i	0.0984081	+	0.138195i	0.860844	−	0.508869i	$-0.169936\pi$
$179$	1.31661	+	1.84892i	0.0984081	+	0.138195i	−0.762436	+	0.647064i	$0.775997\pi$
$180$	0.933096	−	0.373555i	0.0695489	−	0.0278432i
$181$	22.4729	+	14.4425i	1.67040	+	1.07350i	0.899940	+	0.436013i	$0.143610\pi$
$181$	22.4729	+	14.4425i	1.67040	+	1.07350i	0.770460	+	0.637488i	$0.220026\pi$
$182$	2.94335	−	7.41262i	0.218175	−	0.549460i
$183$	14.5593			1.07626
$184$	−4.79113	−	0.212233i	−0.353207	−	0.0156460i
$185$	−0.0418733	+	0.0725267i	−0.00307859	+	0.00533227i
$186$	−1.60433	+	0.309209i	−0.117635	+	0.0226723i
$187$	1.50687	−	31.6330i	0.110193	−	2.31323i
$188$	−0.910049	+	6.32953i	−0.0663722	+	0.461629i
$189$	−1.20572	+	2.35505i	−0.0877032	+	0.171304i
$190$	−0.727641	−	5.06085i	−0.0527886	−	0.367153i
$191$	−5.77746	−	23.8150i	−0.418042	−	1.72319i	−0.658542	−	0.752544i	$-0.728826\pi$
$191$	−5.77746	−	23.8150i	−0.418042	−	1.72319i	0.240499	−	0.970649i	$-0.422689\pi$
$192$	−0.0475819	−	0.998867i	−0.00343393	−	0.0720870i
$193$	−0.448178	−	0.0427958i	−0.0322606	−	0.00308051i	0.0789133	−	0.996881i	$-0.474855\pi$
$193$	−0.448178	−	0.0427958i	−0.0322606	−	0.00308051i	−0.111174	+	0.993801i	$0.535461\pi$
$194$	−2.70097	−	2.57537i	−0.193919	−	0.184901i
$195$	1.98413	−	2.28981i	0.142086	−	0.163976i
$196$	−1.68864	−	6.79327i	−0.120617	−	0.485233i
$197$	20.3733	−	5.98215i	1.45154	−	0.426211i	0.541490	−	0.840707i	$-0.317860\pi$
$197$	20.3733	−	5.98215i	1.45154	−	0.426211i	0.910051	+	0.414496i	$0.136042\pi$
$198$	2.43043	−	3.41306i	0.172723	−	0.242556i
$199$	1.15904	+	24.3313i	0.0821624	+	1.72480i	0.545066	+	0.838393i	$0.316505\pi$
$199$	1.15904	+	24.3313i	0.0821624	+	1.72480i	−0.462903	+	0.886409i	$0.653192\pi$
$200$	2.88755	−	2.75327i	0.204180	−	0.194686i
$201$	−6.37019	+	5.00957i	−0.449318	+	0.353348i
$202$	−7.16241	+	15.6835i	−0.503946	+	1.10349i
$203$	−4.28892	+	22.5956i	−0.301023	+	1.58590i
$204$	6.35839	+	4.08629i	0.445176	+	0.286097i
$205$	1.85376	−	5.35608i	0.129472	−	0.374085i
$206$	−2.26757	+	3.92755i	−0.157989	+	0.273645i
$207$	4.52681	−	1.58365i	0.314635	−	0.110072i
$208$	−1.50725	−	2.61063i	−0.104509	−	0.181015i
$209$	−13.9580	−	16.1084i	−0.965493	−	1.11424i
$210$	0.245312	−	2.64789i	0.0169281	−	0.182722i
$211$	−1.29391	+	8.99932i	−0.0890762	+	0.619538i	0.895563	+	0.444935i	$0.146773\pi$
$211$	−1.29391	+	8.99932i	−0.0890762	+	0.619538i	−0.984639	+	0.174603i	$0.944136\pi$
$212$	12.5657	−	1.19988i	0.863018	−	0.0824082i
$213$	−4.46861	−	1.78896i	−0.306184	−	0.122578i
$214$	−2.25062	+	2.14596i	−0.153849	+	0.146695i
$215$	−8.62472	−	4.44635i	−0.588201	−	0.303239i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−1.20617	+	4.15109i	−0.0818802	+	0.281794i
$218$	6.39027	−	7.37477i	0.432804	−	0.499482i
$219$	0.843051	+	0.162485i	0.0569681	+	0.0109797i
$220$	−0.992858	+	4.09261i	−0.0669384	+	0.275924i
$221$	22.6811	+	2.16578i	1.52569	+	0.145686i
$222$	−0.0740598	−	0.0381805i	−0.00497057	−	0.00256250i
$223$	−20.0937	−	5.90004i	−1.34557	−	0.395096i	−0.471918	−	0.881643i	$-0.656438\pi$
$223$	−20.0937	−	5.90004i	−1.34557	−	0.395096i	−0.873655	+	0.486547i	$0.838256\pi$
$224$	−2.40975	−	1.09230i	−0.161008	−	0.0729821i
$225$	−1.65742	+	3.62924i	−0.110495	+	0.241949i
$226$	0.243169	−	0.0973501i	0.0161753	−	0.00647563i
$227$	−22.5029	+	11.6010i	−1.49357	+	0.769988i	−0.995282	−	0.0970240i	$-0.969068\pi$
$227$	−22.5029	+	11.6010i	−1.49357	+	0.769988i	−0.498287	+	0.867012i	$0.666037\pi$
$228$	4.99506	−	0.962719i	0.330806	−	0.0637576i
$229$	−8.13465	−	14.0896i	−0.537553	−	0.931069i	−0.999035	−	0.0439194i	$-0.986016\pi$
$229$	−8.13465	−	14.0896i	−0.537553	−	0.931069i	0.461482	−	0.887149i	$-0.347318\pi$
$230$	−3.63237	+	3.16872i	−0.239511	+	0.208939i
$231$	−5.10750	−	9.83897i	−0.336049	−	0.647357i
$232$	5.69259	+	6.56960i	0.373737	+	0.431316i
$233$	0.836076	−	17.5514i	0.0547732	−	1.14983i	−0.789442	−	0.613826i	$-0.789630\pi$
$233$	0.836076	−	17.5514i	0.0547732	−	1.14983i	0.844215	−	0.536005i	$-0.180067\pi$
$234$	2.36955	+	1.86344i	0.154903	+	0.121817i
$235$	3.72813	+	5.23543i	0.243197	+	0.341522i
$236$	−3.20755	+	2.52245i	−0.208794	+	0.164197i
$237$	−6.65817	−	1.95501i	−0.432494	−	0.126992i
$238$	17.2898	−	10.0474i	1.12073	−	0.651275i
$239$	0.950777	+	2.08191i	0.0615007	+	0.134668i	0.937887	−	0.346941i	$-0.112780\pi$
$239$	0.950777	+	2.08191i	0.0615007	+	0.134668i	−0.876386	+	0.481609i	$0.840052\pi$
$240$	−0.727420	−	0.693593i	−0.0469547	−	0.0447713i
$241$	−0.359263	−	1.03802i	−0.0231422	−	0.0668649i	0.932838	−	0.360296i	$-0.117324\pi$
$241$	−0.359263	−	1.03802i	−0.0231422	−	0.0668649i	−0.955980	+	0.293431i	$0.905203\pi$
$242$	2.14426	+	6.19542i	0.137838	+	0.398257i
$243$	−0.723734	−	0.690079i	−0.0464276	−	0.0442686i
$244$	−6.04816	−	13.2436i	−0.387194	−	0.847836i
$245$	−5.94012	−	3.77033i	−0.379500	−	0.240877i
$246$	5.41066	+	1.58871i	0.344971	+	0.101293i
$247$	12.0539	−	9.47928i	0.766971	−	0.603152i
$248$	0.947730	+	1.33090i	0.0601809	+	0.0845123i
$249$	−11.7531	−	9.24277i	−0.744825	−	0.585737i
$250$	0.429930	−	9.02534i	0.0271911	−	0.570812i
$251$	17.5753	+	20.2830i	1.10934	+	1.28025i	0.956414	+	0.292015i	$0.0943257\pi$
$251$	17.5753	+	20.2830i	1.10934	+	1.28025i	0.152931	+	0.988237i	$0.451129\pi$
$252$	2.64310	+	0.118439i	0.166500	+	0.00746098i
$253$	−5.59700	+	19.2993i	−0.351880	+	1.21333i
$254$	−2.03029	−	3.51656i	−0.127391	−	0.220649i
$255$	7.45944	−	1.43769i	0.467128	−	0.0900315i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−4.75965	+	1.90547i	−0.296899	+	0.118860i	−0.515329	−	0.856992i	$-0.672330\pi$
$257$	−4.75965	+	1.90547i	−0.296899	+	0.118860i	0.218431	+	0.975852i	$0.429906\pi$
$258$	4.01051	−	8.78180i	0.249684	−	0.546731i
$259$	−0.179212	+	0.128379i	−0.0111357	+	0.00797710i
$260$	−2.90712	−	0.853607i	−0.180292	−	0.0529384i
$261$	−7.72649	−	3.98328i	−0.478258	−	0.246559i
$262$	6.64941	+	0.634942i	0.410802	+	0.0392268i
$263$	3.68526	−	15.1909i	0.227243	−	0.936708i	−0.737884	−	0.674927i	$-0.764175\pi$
$263$	3.68526	−	15.1909i	0.227243	−	0.936708i	0.965127	−	0.261781i	$-0.0843098\pi$
$264$	−4.11427	−	0.792960i	−0.253216	−	0.0488033i
$265$	8.30833	−	9.58832i	0.510377	−	0.589006i
$266$	3.75539	−	12.9244i	0.230258	−	0.792444i
$267$	−3.61575	−	7.91739i	−0.221280	−	0.484536i
$268$	7.20314	+	3.71348i	0.440002	+	0.226837i
$269$	7.75076	−	7.39034i	0.472572	−	0.450597i	−0.415979	−	0.909374i	$-0.636561\pi$
$269$	7.75076	−	7.39034i	0.472572	−	0.450597i	0.888551	+	0.458778i	$0.151713\pi$
$270$	0.933096	+	0.373555i	0.0567864	+	0.0227338i
$271$	2.05645	−	0.196367i	0.124920	−	0.0119285i	−0.0324085	−	0.999475i	$-0.510318\pi$
$271$	2.05645	−	0.196367i	0.124920	−	0.0119285i	0.157329	+	0.987546i	$0.449712\pi$
$272$	1.07565	−	7.48130i	0.0652207	−	0.453620i
$273$	7.24550	−	3.33362i	0.438517	−	0.201760i
$274$	7.37408	+	8.51015i	0.445485	+	0.514117i
$275$	−8.35858	−	14.4775i	−0.504041	−	0.873025i
$276$	−3.32105	−	3.45986i	−0.199904	−	0.208259i
$277$	−12.9397	+	22.4122i	−0.777471	+	1.34662i	0.155923	+	0.987769i	$0.450165\pi$
$277$	−12.9397	+	22.4122i	−0.777471	+	1.34662i	−0.933395	+	0.358851i	$0.883169\pi$
$278$	−1.74472	+	5.04103i	−0.104641	+	0.302341i
$279$	−1.37449	−	0.883330i	−0.0822884	−	0.0528836i
$280$	−2.51051	+	0.876828i	−0.150032	+	0.0524005i
$281$	−8.09138	+	17.7176i	−0.482691	+	1.05695i	0.499024	+	0.866588i	$0.333692\pi$
$281$	−8.09138	+	17.7176i	−0.482691	+	1.05695i	−0.981715	+	0.190358i	$0.939035\pi$
$282$	−5.02651	+	3.95289i	−0.299324	+	0.235391i
$283$	−6.12708	+	5.84216i	−0.364217	+	0.347280i	−0.849984	−	0.526808i	$-0.823389\pi$
$283$	−6.12708	+	5.84216i	−0.364217	+	0.347280i	0.485767	+	0.874088i	$0.338540\pi$
$284$	0.229031	+	4.80796i	0.0135905	+	0.285300i
$285$	2.96577	−	4.16484i	0.175677	−	0.246704i
$286$	−12.1191	+	3.55848i	−0.716615	+	0.210417i
$287$	10.2652	−	10.8268i	0.605937	−	0.639086i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	29.0411	+	27.6907i	1.70830	+	1.62886i
$290$	8.69754	+	0.830514i	0.510737	+	0.0487695i
$291$	−0.177576	−	3.72777i	−0.0104097	−	0.218526i
$292$	−0.202415	−	0.834365i	−0.0118454	−	0.0488275i
$293$	−0.201985	−	1.40484i	−0.0118001	−	0.0820716i	0.983070	−	0.183228i	$-0.0586547\pi$
$293$	−0.201985	−	1.40484i	−0.0118001	−	0.0820716i	−0.994871	+	0.101157i	$0.967746\pi$
$294$	3.46577	−	6.08181i	0.202128	−	0.354699i
$295$	−0.583685	+	4.05961i	−0.0339834	+	0.236360i
$296$	−0.00396463	+	0.0832279i	−0.000230440	+	0.00483752i
$297$	4.11427	−	0.792960i	0.238734	−	0.0460122i
$298$	−0.547371	+	0.948074i	−0.0317083	+	0.0549204i
$299$	−13.6776	−	4.68288i	−0.790994	−	0.270818i
$300$	3.98979			0.230351
$301$	−15.8460	−	20.0333i	−0.913347	−	1.15470i
$302$	−2.24629	−	1.44361i	−0.129260	−	0.0830701i
$303$	−16.0065	+	6.40805i	−0.919551	+	0.368133i
$304$	−2.95074	−	4.14374i	−0.169237	−	0.237660i
$305$	−13.5852	−	5.43871i	−0.777889	−	0.311420i
$306$	1.78192	+	7.34517i	0.101866	+	0.419896i
$307$	−0.639101	+	0.410725i	−0.0364754	+	0.0234413i	−0.558751	−	0.829335i	$-0.688719\pi$
$307$	−0.639101	+	0.410725i	−0.0364754	+	0.0234413i	0.522276	+	0.852776i	$0.325083\pi$
$308$	−6.82811	+	8.73320i	−0.389068	+	0.497620i
$309$	−4.35144	+	1.27770i	−0.247545	+	0.0726857i
$310$	1.61250	+	0.310784i	0.0915839	+	0.0176514i
$311$	0.0758009	+	0.219012i	0.00429827	+	0.0124190i	0.947130	−	0.320851i	$-0.103969\pi$
$311$	0.0758009	+	0.219012i	0.00429827	+	0.0124190i	−0.942831	+	0.333270i	$0.891848\pi$
$312$	0.710694	−	2.92952i	0.0402351	−	0.165851i
$313$	−14.1191	+	19.8276i	−0.798061	+	1.12072i	0.192181	+	0.981359i	$0.438444\pi$
$313$	−14.1191	+	19.8276i	−0.798061	+	1.12072i	−0.990242	+	0.139360i	$0.955495\pi$
$314$	−6.79544	+	4.36717i	−0.383489	+	0.246453i
$315$	2.00479	−	1.74708i	0.112957	−	0.0984368i
$316$	0.987559	+	6.86862i	0.0555545	+	0.386390i
$317$	23.2689	−	2.22192i	1.30691	−	0.124795i	0.581748	−	0.813369i	$-0.302369\pi$
$317$	23.2689	−	2.22192i	1.30691	−	0.124795i	0.725166	+	0.688574i	$0.241763\pi$
$318$	9.92226	+	7.80295i	0.556413	+	0.437568i
$319$	32.3739	−	16.6899i	1.81259	−	0.934456i
$320$	−0.328734	+	0.949813i	−0.0183768	+	0.0530962i
$321$	−3.10973			−0.173568
$322$	−12.1524	+	3.64960i	−0.677226	+	0.203384i
$323$	38.4486			2.13934
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	10.6902	−	5.51118i	0.592986	−	0.305705i
$326$	−7.57490	−	5.95697i	−0.419535	−	0.329926i
$327$	9.71403	−	0.927577i	0.537187	−	0.0512951i
$328$	−0.802525	−	5.58169i	−0.0443120	−	0.308197i
$329$	3.24868	+	16.6037i	0.179106	+	0.915394i
$330$	−3.54279	+	2.27681i	−0.195024	+	0.125335i
$331$	1.00844	−	1.41616i	0.0554290	−	0.0778391i	−0.785931	−	0.618314i	$-0.787816\pi$
$331$	1.00844	−	1.41616i	0.0554290	−	0.0778391i	0.841360	+	0.540475i	$0.181755\pi$
$332$	−3.52509	+	14.5306i	−0.193464	+	0.797472i
$333$	−0.0272520	−	0.0787396i	−0.00149340	−	0.00431490i
$334$	−20.4217	−	3.93597i	−1.11743	−	0.215367i
$335$	7.81535	−	2.29479i	0.426998	−	0.125378i
$336$	−0.990247	−	2.45345i	−0.0540224	−	0.133847i
$337$	−26.3772	+	16.9516i	−1.43686	+	0.923412i	−0.437145	+	0.899391i	$0.644010\pi$
$337$	−26.3772	+	16.9516i	−1.43686	+	0.923412i	−0.999711	+	0.0240209i	$0.992353\pi$
$338$	0.922482	+	3.80252i	0.0501764	+	0.206830i
$339$	0.243169	+	0.0973501i	0.0132071	+	0.00528733i
$340$	−4.40653	−	6.18810i	−0.238978	−	0.335597i
$341$	6.35546	−	2.54434i	0.344167	−	0.137784i
$342$	4.27945	+	2.75023i	0.231406	+	0.148716i
$343$	−10.1442	−	15.4950i	−0.547736	−	0.836651i
$344$	−9.65423			−0.520521
$345$	−4.81553	−	0.213314i	−0.259260	−	0.0114844i
$346$	4.16756	−	7.21843i	0.224049	−	0.388065i
$347$	−29.8427	+	5.75171i	−1.60204	+	0.308768i	−0.910481	−	0.413552i	$-0.864288\pi$
$347$	−29.8427	+	5.75171i	−1.60204	+	0.308768i	−0.691559	+	0.722320i	$0.743076\pi$
$348$	−0.413621	+	8.68298i	−0.0221724	+	0.465457i
$349$	3.55810	−	24.7471i	0.190461	−	1.32468i	−0.640330	−	0.768100i	$-0.721202\pi$
$349$	3.55810	−	24.7471i	0.190461	−	1.32468i	0.830791	−	0.556585i	$-0.187888\pi$
$350$	4.81057	−	9.39614i	0.257136	−	0.502245i
$351$	0.429007	+	2.98381i	0.0228987	+	0.159264i
$352$	0.987827	+	4.07188i	0.0526514	+	0.217032i
$353$	0.486438	+	10.2116i	0.0258905	+	0.543508i	0.974135	+	0.225967i	$0.0725542\pi$
$353$	0.486438	+	10.2116i	0.0258905	+	0.543508i	−0.948244	+	0.317541i	$0.897143\pi$
$354$	−4.06210	−	0.387884i	−0.215898	−	0.0206158i
$355$	3.50137	+	3.33855i	0.185833	+	0.177192i
$356$	−5.69987	+	6.57800i	−0.302093	+	0.348633i
$357$	19.4467	+	4.65971i	1.02923	+	0.246618i
$358$	2.17785	−	0.639475i	0.115103	−	0.0337973i
$359$	10.1642	−	14.2737i	0.536448	−	0.753336i	−0.454033	−	0.890985i	$-0.650015\pi$
$359$	10.1642	−	14.2737i	0.536448	−	0.753336i	0.990481	+	0.137649i	$0.0439547\pi$
$360$	−0.0478242	−	1.00395i	−0.00252056	−	0.0529130i
$361$	4.97745	−	4.74598i	0.261971	−	0.249789i
$362$	20.9983	−	16.5133i	1.10365	−	0.867918i
$363$	−2.72346	+	5.96354i	−0.142944	+	0.313005i
$364$	−6.04226	−	5.20590i	−0.316700	−	0.272863i
$365$	−0.725951	−	0.466540i	−0.0379980	−	0.0244198i
$366$	4.76189	−	13.7586i	0.248908	−	0.719172i
$367$	−2.14617	+	3.71728i	−0.112029	+	0.194041i	−0.916588	−	0.399832i	$-0.869068\pi$
$367$	−2.14617	+	3.71728i	−0.112029	+	0.194041i	0.804559	+	0.593873i	$0.202402\pi$
$368$	−1.76759	+	4.45821i	−0.0921418	+	0.232400i
$369$	2.81954	+	4.88359i	0.146779	+	0.254230i
$370$	0.0548423	+	0.0632914i	0.00285112	+	0.00329037i
$371$	30.3398	−	13.9592i	1.57516	−	0.724726i
$372$	−0.232522	+	1.61723i	−0.0120557	+	0.0838493i
$373$	−23.7211	+	2.26509i	−1.22823	+	0.117282i	−0.688928	−	0.724830i	$-0.741918\pi$
$373$	−23.7211	+	2.26509i	−1.22823	+	0.117282i	−0.539303	+	0.842112i	$0.681312\pi$
$374$	−29.4004	−	11.7701i	−1.52026	−	0.608619i
$375$	6.53935	−	6.23526i	0.337691	−	0.321987i
$376$	5.68376	+	2.93018i	0.293118	+	0.151113i
$377$	10.8857	+	23.8364i	0.560644	+	1.22764i
$378$	1.83117	+	1.90967i	0.0941851	+	0.0982226i
$379$	0.961110	−	1.10918i	0.0493689	−	0.0569748i	−0.730528	−	0.682883i	$-0.760726\pi$
$379$	0.961110	−	1.10918i	0.0493689	−	0.0569748i	0.779897	+	0.625908i	$0.215271\pi$
$380$	−5.02050	−	0.967622i	−0.257546	−	0.0496379i
$381$	0.957316	−	3.94611i	0.0490448	−	0.202165i
$382$	−24.3948	−	2.32942i	−1.24815	−	0.119184i
$383$	−0.196434	−	0.101269i	−0.0100373	−	0.00517459i	0.453201	−	0.891409i	$-0.350282\pi$
$383$	−0.196434	−	0.101269i	−0.0100373	−	0.00517459i	−0.463238	+	0.886234i	$0.653312\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	1.09039	+	11.0886i	0.0555714	+	0.565129i
$386$	−0.187027	+	0.409532i	−0.00951941	+	0.0208446i
$387$	8.96268	−	3.58812i	0.455599	−	0.182394i
$388$	−3.31713	+	1.71010i	−0.168402	+	0.0868172i
$389$	6.43641	−	1.24052i	0.326339	−	0.0628967i	−0.0234505	−	0.999725i	$-0.507465\pi$
$389$	6.43641	−	1.24052i	0.326339	−	0.0628967i	0.349790	+	0.936828i	$0.386253\pi$
$390$	−1.51492	−	2.62392i	−0.0767111	−	0.132868i
$391$	−19.6986	−	30.4283i	−0.996203	−	1.53882i
$392$	−6.97194	−	0.626094i	−0.352136	−	0.0316225i
$393$	4.37425	+	5.04815i	0.220651	+	0.254645i
$394$	1.01033	−	21.2094i	0.0508996	−	1.06851i
$395$	5.48240	+	4.31141i	0.275850	+	0.216930i
$396$	−2.43043	−	3.41306i	−0.122134	−	0.171513i
$397$	5.37022	−	4.22319i	0.269524	−	0.211956i	−0.474245	−	0.880393i	$-0.657279\pi$
$397$	5.37022	−	4.22319i	0.269524	−	0.211956i	0.743769	+	0.668437i	$0.233036\pi$
$398$	23.3722	+	6.86270i	1.17154	+	0.343996i
$399$	11.6367	−	6.76228i	0.582566	−	0.338538i
$400$	−1.65742	−	3.62924i	−0.0828709	−	0.181462i
$401$	9.06455	+	8.64303i	0.452662	+	0.431612i	0.881798	−	0.471628i	$-0.156333\pi$
$401$	9.06455	+	8.64303i	0.452662	+	0.431612i	−0.429136	+	0.903240i	$0.641182\pi$
$402$	2.65056	+	7.65830i	0.132198	+	0.381961i
$403$	1.61089	+	4.65437i	0.0802443	+	0.231851i
$404$	12.4783	+	11.8981i	0.620820	+	0.591950i
$405$	0.417531	+	0.914264i	0.0207473	+	0.0454302i
$406$	19.9501	+	11.4433i	0.990107	+	0.567923i
$407$	0.334977	+	0.0983582i	0.0166042	+	0.00487544i
$408$	5.94117	−	4.67219i	0.294132	−	0.231308i
$409$	−11.5671	−	16.2437i	−0.571956	−	0.803199i	0.422719	−	0.906261i	$-0.361076\pi$
$409$	−11.5671	−	16.2437i	−0.571956	−	0.803199i	−0.994675	+	0.103061i	$0.967136\pi$
$410$	−4.45519	−	3.50360i	−0.220026	−	0.173031i
$411$	−0.535798	+	11.2478i	−0.0264290	+	0.554812i
$412$	2.96989	+	3.42743i	0.146316	+	0.168858i
$413$	−5.81124	+	9.09876i	−0.285952	+	0.447721i
$414$	−0.0159790	−	4.79580i	−0.000785325	−	0.235701i
$415$	7.51412	+	13.0148i	0.368854	+	0.638873i
$416$	−2.96002	+	0.570497i	−0.145127	+	0.0279709i
$417$	−4.74142	+	2.44437i	−0.232188	+	0.119701i
$418$	−19.7876	+	7.92177i	−0.967844	+	0.387466i
$419$	−13.3420	+	29.2149i	−0.651800	+	1.42724i	0.238169	+	0.971224i	$0.423453\pi$
$419$	−13.3420	+	29.2149i	−0.651800	+	1.42724i	−0.889970	+	0.456020i	$0.849275\pi$
$420$	−2.42202	−	1.09786i	−0.118183	−	0.0535700i
$421$	37.6777	+	11.0632i	1.83630	+	0.539186i	0.999959	−	0.00902845i	$-0.00287388\pi$
$421$	37.6777	+	11.0632i	1.83630	+	0.539186i	0.836338	+	0.548214i	$0.184692\pi$
$422$	8.08117	+	4.16613i	0.393385	+	0.202804i
$423$	−6.36566	−	0.607847i	−0.309509	−	0.0295545i
$424$	2.97596	−	12.2671i	0.144525	−	0.595741i
$425$	29.6108	+	5.70701i	1.43633	+	0.276831i
$426$	−3.15211	+	3.63773i	−0.152720	+	0.176249i
$427$	−26.6606	−	27.8034i	−1.29020	−	1.34550i
$428$	1.29183	+	2.82871i	0.0624429	+	0.136731i
$429$	−11.2266	−	5.78772i	−0.542026	−	0.279434i
$430$	−7.02268	+	6.69611i	−0.338664	+	0.322915i
$431$	14.6117	+	5.84965i	0.703821	+	0.281768i	0.695836	−	0.718201i	$-0.255034\pi$
$431$	14.6117	+	5.84965i	0.703821	+	0.281768i	0.00798525	+	0.999968i	$0.497458\pi$
$432$	0.995472	−	0.0950560i	0.0478947	−	0.00457339i
$433$	−2.52771	+	17.5806i	−0.121474	+	0.844871i	0.834414	+	0.551139i	$0.185806\pi$
$433$	−2.52771	+	17.5806i	−0.121474	+	0.844871i	−0.955888	+	0.293732i	$0.905103\pi$
$434$	3.52829	+	2.49752i	0.169363	+	0.119885i
$435$	5.72158	+	6.60306i	0.274329	+	0.316592i
$436$	−4.87911	−	8.45086i	−0.233667	−	0.404723i
$437$	−23.7277	−	5.67263i	−1.13505	−	0.271359i
$438$	0.429283	−	0.743541i	0.0205120	−	0.0355277i
$439$	−2.07128	+	5.98458i	−0.0988570	+	0.285629i	−0.983576	−	0.180497i	$-0.942229\pi$
$439$	−2.07128	+	5.98458i	−0.0988570	+	0.285629i	0.884718	+	0.466126i	$0.154351\pi$
$440$	3.54279	+	2.27681i	0.168896	+	0.108543i
$441$	6.70523	−	2.00996i	0.319296	−	0.0957126i
$442$	9.46492	−	20.7253i	0.450200	−	0.985801i
$443$	−23.7553	+	18.6814i	−1.12865	+	0.887578i	−0.994640	−	0.103402i	$-0.967027\pi$
$443$	−23.7553	+	18.6814i	−1.12865	+	0.887578i	−0.134008	+	0.990980i	$0.542785\pi$
$444$	−0.0603031	+	0.0574989i	−0.00286186	+	0.00272878i
$445$	0.416259	+	8.73836i	0.0197326	+	0.414238i
$446$	−12.1475	+	17.0588i	−0.575203	+	0.807759i
$447$	−1.05040	+	0.308424i	−0.0496821	+	0.0145880i
$448$	−1.82037	+	1.91996i	−0.0860045	+	0.0907096i
$449$	−13.6672	+	15.7728i	−0.644994	+	0.744363i	−0.980250	−	0.197764i	$-0.936632\pi$
$449$	−13.6672	+	15.7728i	−0.644994	+	0.744363i	0.335255	+	0.942127i	$0.391177\pi$
$450$	2.88755	+	2.75327i	0.136120	+	0.129790i
$451$	−23.5207	−	2.24595i	−1.10755	−	0.105758i
$452$	−0.0124632	−	0.261635i	−0.000586219	−	0.0123063i
$453$	−0.629517	−	2.59491i	−0.0295773	−	0.121919i
$454$	3.60302	+	25.0596i	0.169098	+	1.17610i
$455$	−8.00604	+	0.403998i	−0.375329	+	0.0189397i
$456$	0.723954	−	5.03521i	0.0339022	−	0.235795i
$457$	−1.26819	+	26.6225i	−0.0593232	+	1.24535i	0.751372	+	0.659879i	$0.229393\pi$
$457$	−1.26819	+	26.6225i	−0.0593232	+	1.24535i	−0.810695	+	0.585469i	$0.800910\pi$
$458$	−15.9753	+	3.07899i	−0.746476	+	0.143872i
$459$	−3.77911	+	6.54562i	−0.176394	+	0.305523i
$460$	1.80641	+	4.46898i	0.0842242	+	0.208367i
$461$	−29.7277			−1.38456			−0.692279	−	0.721630i	$-0.743393\pi$
$461$	−29.7277			−1.38456			−0.692279	+	0.721630i	$0.743393\pi$
$462$	−10.9683	+	1.60858i	−0.510293	+	0.0748380i
$463$	18.7874	+	12.0740i	0.873127	+	0.561124i	0.898708	−	0.438548i	$-0.144507\pi$
$463$	18.7874	+	12.0740i	0.873127	+	0.561124i	−0.0255809	+	0.999673i	$0.508144\pi$
$464$	8.07014	−	3.23080i	0.374647	−	0.149986i
$465$	0.952556	+	1.33768i	0.0441737	+	0.0620333i
$466$	−16.3126	−	6.53059i	−0.755668	−	0.302524i
$467$	−5.21000	−	21.4759i	−0.241090	−	0.993787i	−0.955718	−	0.294283i	$-0.904919\pi$
$467$	−5.21000	−	21.4759i	−0.241090	−	0.993787i	0.714628	−	0.699504i	$-0.246596\pi$
$468$	2.53595	−	1.62976i	0.117225	−	0.0753356i
$469$	21.2315	+	2.99156i	0.980379	+	0.138138i
$470$	6.16684	−	1.81075i	0.284455	−	0.0835235i
$471$	−7.93178	−	1.52873i	−0.365477	−	0.0704400i
$472$	1.33463	+	3.85615i	0.0614312	+	0.177494i
$473$	−9.53671	+	39.3109i	−0.438498	+	1.80752i
$474$	−4.02516	+	5.65255i	−0.184882	+	0.259630i
$475$	17.0741	−	10.9729i	0.783413	−	0.503469i
$476$	−3.83983	−	19.6251i	−0.175998	−	0.899513i
$477$	1.79642	+	12.4944i	0.0822526	+	0.572079i
$478$	2.27838	−	0.217559i	0.104211	−	0.00995090i
$479$	−21.2201	−	16.6877i	−0.969571	−	0.762479i	0.00181155	−	0.999998i	$-0.499423\pi$
$479$	−21.2201	−	16.6877i	−0.969571	−	0.762479i	−0.971383	+	0.237519i	$0.923666\pi$
$480$	−0.893362	+	0.460560i	−0.0407762	+	0.0210216i
$481$	−0.0821511	+	0.237360i	−0.00374577	+	0.0108227i
$482$	−1.09844			−0.0500324
$483$	−11.3136	−	5.74476i	−0.514787	−	0.261396i
$484$	6.55599			0.298000
$485$	−1.22683	+	3.54470i	−0.0557076	+	0.160957i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	31.5775	+	24.8329i	1.43092	+	1.12528i	0.971494	+	0.237066i	$0.0761858\pi$
$487$	31.5775	+	24.8329i	1.43092	+	1.12528i	0.459422	+	0.888218i	$0.348057\pi$
$488$	−14.4934	+	1.38395i	−0.656085	+	0.0626485i
$489$	−1.37144	−	9.53854i	−0.0620184	−	0.431348i
$490$	−5.50578	+	4.38026i	−0.248726	+	0.197880i
$491$	4.70253	−	3.02213i	0.212222	−	0.136387i	−0.430212	−	0.902728i	$-0.641561\pi$
$491$	4.70253	−	3.02213i	0.212222	−	0.136387i	0.642434	+	0.766341i	$0.277925\pi$
$492$	3.27099	−	4.59346i	0.147468	−	0.207089i
$493$	−15.4899	+	63.8503i	−0.697631	+	2.87567i
$494$	−5.01549	−	14.4913i	−0.225658	−	0.651995i
$495$	−4.13522	−	0.796999i	−0.185864	−	0.0358224i
$496$	1.56767	−	0.460311i	0.0703906	−	0.0206686i
$497$	4.76646	+	11.8095i	0.213805	+	0.529726i
$498$	−12.5785	+	8.08372i	−0.563656	+	0.362240i
$499$	4.41566	+	18.2016i	0.197672	+	0.814816i	0.981127	+	0.193366i	$0.0619406\pi$
$499$	4.41566	+	18.2016i	0.197672	+	0.814816i	−0.783455	+	0.621449i	$0.786544\pi$
$500$	−8.38833	−	3.35818i	−0.375138	−	0.150182i
$501$	−12.0638	−	16.9412i	−0.538970	−	0.756878i
$502$	24.9158	−	9.97477i	1.11205	−	0.445196i
$503$	29.1399	+	18.7271i	1.29928	+	0.834999i	0.993134	−	0.116984i	$-0.0373227\pi$
$503$	29.1399	+	18.7271i	1.29928	+	0.834999i	0.306150	+	0.951983i	$0.400959\pi$
$504$	0.976398	−	2.45899i	0.0434922	−	0.109532i
$505$	17.3294			0.771148
$506$	16.4072	+	11.6013i	0.729390	+	0.515742i
$507$	−1.95641	+	3.38860i	−0.0868872	+	0.150493i
$508$	−3.98719	+	0.768468i	−0.176903	+	0.0340953i
$509$	−1.30743	+	27.4463i	−0.0579508	+	1.21654i	0.763329	+	0.646010i	$0.223564\pi$
$509$	−1.30743	+	27.4463i	−0.0579508	+	1.21654i	−0.821279	+	0.570526i	$0.806739\pi$
$510$	1.08113	−	7.51940i	0.0478731	−	0.332964i
$511$	−1.23348	−	1.90748i	−0.0545658	−	0.0843821i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	1.19930	+	4.94359i	0.0529505	+	0.218265i
$514$	0.243948	+	5.12109i	0.0107601	+	0.225882i
$515$	4.53760	+	0.433288i	0.199951	+	0.0190930i
$516$	−6.98710	−	6.66218i	−0.307590	−	0.293286i
$517$	17.5459	−	20.2491i	0.771669	−	0.890554i
$518$	0.0627040	+	0.211344i	0.00275505	+	0.00928593i
$519$	7.99749	−	2.34828i	0.351051	−	0.103078i
$520$	−1.75748	+	2.46804i	−0.0770708	+	0.108231i
$521$	1.28877	+	27.0546i	0.0564621	+	1.18528i	0.832290	+	0.554340i	$0.187029\pi$
$521$	1.28877	+	27.0546i	0.0564621	+	1.18528i	−0.775828	+	0.630944i	$0.782668\pi$
$522$	−6.29130	+	5.99874i	−0.275363	+	0.262558i
$523$	9.16897	−	7.21056i	0.400931	−	0.315296i	−0.397253	−	0.917709i	$-0.630037\pi$
$523$	9.16897	−	7.21056i	0.400931	−	0.315296i	0.798184	+	0.602413i	$0.205794\pi$
$524$	2.77483	−	6.07603i	0.121219	−	0.265433i
$525$	9.96565	−	3.48063i	0.434936	−	0.151907i
$526$	−13.1500	−	8.45102i	−0.573369	−	0.368482i
$527$	−4.03898	+	11.6699i	−0.175941	+	0.508348i
$528$	−2.09499	+	3.62864i	−0.0911729	+	0.157916i
$529$	7.66723	+	21.6844i	0.333358	+	0.942800i
$530$	−6.34359	−	10.9874i	−0.275548	−	0.477263i
$531$	−2.67221	−	3.08390i	−0.115964	−	0.133830i
$532$	−10.9853	−	7.77599i	−0.476272	−	0.337132i
$533$	2.41921	−	16.8260i	0.104788	−	0.728813i
$534$	−8.66453	+	0.827362i	−0.374951	+	0.0358035i
$535$	2.90168	+	1.16166i	0.125451	+	0.0502228i
$536$	5.86515	−	5.59241i	0.253336	−	0.241555i
$537$	2.01747	+	1.04008i	0.0870604	+	0.0448828i
$538$	−4.44885	−	9.74162i	−0.191803	−	0.419991i
$539$	−9.43645	+	27.7704i	−0.406457	+	1.19616i
$540$	0.658196	−	0.759598i	0.0283242	−	0.0326879i
$541$	−8.03209	−	1.54806i	−0.345327	−	0.0665563i	0.0136391	−	0.999907i	$-0.495658\pi$
$541$	−8.03209	−	1.54806i	−0.345327	−	0.0665563i	−0.358966	+	0.933351i	$0.616871\pi$
$542$	0.487032	−	2.00757i	0.0209198	−	0.0862326i
$543$	26.5927	+	2.53929i	1.14120	+	0.108971i
$544$	−6.71802	−	3.46338i	−0.288033	−	0.148491i
$545$	−9.41062	−	2.76321i	−0.403107	−	0.118363i
$546$	−0.780508	−	7.93732i	−0.0334027	−	0.339686i
$547$	10.1990	−	22.3326i	0.436076	−	0.954874i	−0.556226	−	0.831031i	$-0.687751\pi$
$547$	10.1990	−	22.3326i	0.436076	−	0.954874i	0.992302	−	0.123843i	$-0.0395218\pi$
$548$	10.4539	−	4.18512i	0.446569	−	0.178779i
$549$	12.9408	−	6.67147i	0.552302	−	0.284731i
$550$	−16.4151	+	3.16374i	−0.699941	+	0.134902i
$551$	22.1102	+	38.2959i	0.941925	+	1.63146i
$552$	−4.35578	+	2.00678i	−0.185394	+	0.0854144i
$553$	8.45880	+	16.2948i	0.359705	+	0.692927i
$554$	16.9474	+	19.5584i	0.720026	+	0.830955i
$555$	−0.00398482	+	0.0836517i	−0.000169146	+	0.00355082i
$556$	4.19313	+	3.29752i	0.177829	+	0.139846i
$557$	−23.0951	−	32.4326i	−0.978572	−	1.37421i	−0.926801	−	0.375553i	$-0.877453\pi$
$557$	−23.0951	−	32.4326i	−0.978572	−	1.37421i	−0.0517715	−	0.998659i	$-0.516487\pi$
$558$	−1.28430	+	1.00998i	−0.0543687	+	0.0427560i
$559$	−27.9238	−	8.19916i	−1.18105	−	0.346788i
$560$	0.00749645	+	2.65921i	0.000316783	+	0.112372i
$561$	−13.1557	−	28.8070i	−0.555435	−	1.21623i
$562$	14.0968	+	13.4412i	0.594636	+	0.566984i
$563$	−9.15178	−	26.4423i	−0.385702	−	1.11441i	−0.956099	−	0.293043i	$-0.905332\pi$
$563$	−9.15178	−	26.4423i	−0.385702	−	1.11441i	0.570398	−	0.821369i	$-0.306789\pi$
$564$	2.09148	+	6.04292i	0.0880670	+	0.254453i
$565$	−0.190534	−	0.181674i	−0.00801583	−	0.00764308i
$566$	3.51687	+	7.70088i	0.147825	+	0.323692i
$567$	0.00745847	+	2.64574i	0.000313226	+	0.111111i
$568$	4.61843	+	1.35609i	0.193785	+	0.0569004i
$569$	−13.5119	+	10.6259i	−0.566447	+	0.445459i	−0.859862	−	0.510526i	$-0.829451\pi$
$569$	−13.5119	+	10.6259i	−0.566447	+	0.445459i	0.293415	+	0.955985i	$0.405208\pi$
$570$	−2.96577	−	4.16484i	−0.124222	−	0.174446i
$571$	−30.0211	−	23.6089i	−1.25635	−	0.988001i	−0.999769	−	0.0214773i	$-0.993163\pi$
$571$	−30.0211	−	23.6089i	−1.25635	−	0.988001i	−0.256576	−	0.966524i	$-0.582595\pi$
$572$	−0.600993	+	12.6164i	−0.0251288	+	0.527518i
$573$	−16.0479	−	18.5202i	−0.670410	−	0.773694i
$574$	−6.87392	−	13.2418i	−0.286912	−	0.552700i
$575$	−17.4316	−	7.89066i	−0.726948	−	0.329063i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.7585	+	2.26626i	−0.489511	+	0.0943455i	−0.428033	−	0.903763i	$-0.640793\pi$
$577$	−11.7585	+	2.26626i	−0.489511	+	0.0943455i	−0.0614777	+	0.998108i	$0.519581\pi$
$578$	35.6661	−	18.3872i	1.48351	−	0.764805i
$579$	−0.417967	+	0.167329i	−0.0173701	+	0.00695394i
$580$	3.62952	−	7.94755i	0.150708	−	0.330004i
$581$	3.87137	+	39.3696i	0.160612	+	1.63333i
$582$	−3.58082	−	1.05142i	−0.148430	−	0.0435830i
$583$	−47.0103	−	24.2355i	−1.94697	−	1.00373i
$584$	−0.854679	−	0.0816120i	−0.0353669	−	0.00337713i
$585$	0.714314	−	2.94444i	0.0295332	−	0.121738i
$586$	−1.39364	−	0.268601i	−0.0575706	−	0.0110958i
$587$	2.26920	−	2.61879i	0.0936598	−	0.108089i	−0.706985	−	0.707229i	$-0.749945\pi$
$587$	2.26920	−	2.61879i	0.0936598	−	0.108089i	0.800645	+	0.599140i	$0.204491\pi$
$588$	−4.61378	−	5.26432i	−0.190269	−	0.217097i
$589$	3.45268	+	7.56032i	0.142265	+	0.311518i
$590$	3.64543	+	1.87935i	0.150080	+	0.0773717i
$591$	15.3674	−	14.6528i	0.632129	−	0.602734i
$592$	0.0773537	+	0.0309678i	0.00317922	+	0.00127277i
$593$	−21.8398	+	2.08544i	−0.896851	+	0.0856389i	−0.533291	−	0.845932i	$-0.679045\pi$
$593$	−21.8398	+	2.08544i	−0.896851	+	0.0856389i	−0.363560	+	0.931571i	$0.618439\pi$
$594$	0.596297	−	4.14734i	0.0244664	−	0.170167i
$595$	−16.4050	−	11.6124i	−0.672539	−	0.476061i
$596$	0.716903	+	0.827350i	0.0293655	+	0.0338896i
$597$	12.1795	+	21.0954i	0.498472	+	0.863379i
$598$	−8.89882	+	11.3937i	−0.363900	+	0.465923i
$599$	3.64074	−	6.30595i	0.148757	−	0.257654i	−0.782011	−	0.623264i	$-0.785806\pi$
$599$	3.64074	−	6.30595i	0.148757	−	0.257654i	0.930768	+	0.365610i	$0.119140\pi$
$600$	1.30493	−	3.77035i	0.0532736	−	0.153924i
$601$	16.4766	+	10.5889i	0.672095	+	0.431929i	0.831680	−	0.555255i	$-0.187379\pi$
$601$	16.4766	+	10.5889i	0.672095	+	0.431929i	−0.159585	+	0.987184i	$0.551016\pi$
$602$	−24.1142	+	8.42221i	−0.982822	+	0.343264i
$603$	−3.36653	+	7.37167i	−0.137096	+	0.300198i
$604$	−2.09890	+	1.65059i	−0.0854030	+	0.0671616i
$605$	4.76896	−	4.54719i	0.193886	−	0.184870i
$606$	0.820388	+	17.2221i	0.0333260	+	0.699598i
$607$	7.49964	−	10.5318i	0.304401	−	0.427471i	−0.633835	−	0.773469i	$-0.718520\pi$
$607$	7.49964	−	10.5318i	0.304401	−	0.427471i	0.938235	+	0.345997i	$0.112459\pi$
$608$	−4.88093	+	1.43317i	−0.197948	+	0.0581227i
$609$	6.54177	+	22.0491i	0.265086	+	0.893474i
$610$	−9.58288	+	11.0592i	−0.388000	+	0.447775i
$611$	13.9511	+	13.3023i	0.564401	+	0.538155i
$612$	7.52400	+	0.718455i	0.304140	+	0.0290418i
$613$	0.443893	+	9.31846i	0.0179287	+	0.376369i	0.989945	+	0.141455i	$0.0451779\pi$
$613$	0.443893	+	9.31846i	0.0179287	+	0.376369i	−0.972016	+	0.234914i	$0.924519\pi$
$614$	0.179106	+	0.738286i	0.00722814	+	0.0297948i
$615$	−0.806612	−	5.61011i	−0.0325257	−	0.226222i
$616$	6.01963	+	9.30892i	0.242538	+	0.375067i
$617$	−3.42685	+	23.8342i	−0.137960	+	0.959530i	0.796798	+	0.604245i	$0.206525\pi$
$617$	−3.42685	+	23.8342i	−0.137960	+	0.959530i	−0.934758	+	0.355285i	$0.884384\pi$
$618$	−0.215791	+	4.53001i	−0.00868038	+	0.182224i
$619$	10.2840	−	1.98209i	0.413350	−	0.0796667i	0.0216634	−	0.999765i	$-0.493104\pi$
$619$	10.2840	−	1.98209i	0.413350	−	0.0796667i	0.391687	+	0.920099i	$0.371892\pi$
$620$	0.821089	−	1.42217i	0.0329757	−	0.0571156i
$621$	3.29792	−	3.48191i	0.132341	−	0.139724i
$622$	0.231759			0.00929268
$623$	−8.49852	+	21.4029i	−0.340486	+	0.857491i
$624$	−2.53595	−	1.62976i	−0.101519	−	0.0652426i
$625$	10.0889	−	4.03899i	0.403556	−	0.161560i
$626$	14.1191	+	19.8276i	0.564314	+	0.792468i
$627$	−19.7876	−	7.92177i	−0.790241	−	0.316365i
$628$	1.90440	+	7.85006i	0.0759940	+	0.313251i
$629$	−0.529795	+	0.340479i	−0.0211243	+	0.0135758i
$630$	−0.995290	−	2.46594i	−0.0396533	−	0.0982455i
$631$	35.3106	−	10.3681i	1.40569	−	0.412749i	0.511059	−	0.859546i	$-0.329254\pi$
$631$	35.3106	−	10.3681i	1.40569	−	0.412749i	0.894635	+	0.446797i	$0.147435\pi$
$632$	6.81385	+	1.31326i	0.271041	+	0.0522388i
$633$	2.97366	+	8.59181i	0.118192	+	0.341494i
$634$	5.51082	−	22.7159i	0.218862	−	0.902163i
$635$	−2.36736	+	3.32449i	−0.0939457	+	0.131928i
$636$	10.6190	−	6.82445i	0.421073	−	0.270607i
$637$	−19.6338	−	7.73205i	−0.777921	−	0.306355i
$638$	−5.18351	−	36.0521i	−0.205217	−	1.42732i
$639$	−4.79161	+	0.457544i	−0.189553	+	0.0181001i
$640$	0.790056	+	0.621307i	0.0312297	+	0.0245593i
$641$	34.8060	−	17.9437i	1.37475	−	0.708735i	0.396868	−	0.917876i	$-0.370097\pi$
$641$	34.8060	−	17.9437i	1.37475	−	0.708735i	0.977886	+	0.209141i	$0.0670666\pi$
$642$	−1.01709	+	2.93870i	−0.0401415	+	0.115981i
$643$	16.9562			0.668688			0.334344	−	0.942451i	$-0.391485\pi$
$643$	16.9562			0.668688			0.334344	+	0.942451i	$0.391485\pi$
$644$	−0.525778	+	12.6777i	−0.0207186	+	0.499571i
$645$	−9.70340			−0.382071
$646$	12.5753	−	36.3340i	0.494769	−	1.42954i
$647$	−23.1604	+	11.9400i	−0.910528	+	0.469410i	−0.848818	−	0.528684i	$-0.822686\pi$
$647$	−23.1604	+	11.9400i	−0.910528	+	0.469410i	−0.0617094	+	0.998094i	$0.519655\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	17.0202	−	1.62523i	0.668100	−	0.0637958i
$650$	−1.71165	−	11.9048i	−0.0671364	−	0.466944i
$651$	0.830054	+	4.24234i	0.0325324	+	0.166270i
$652$	−8.10685	+	5.20995i	−0.317489	+	0.204038i
$653$	6.52375	−	9.16132i	0.255294	−	0.358510i	−0.666961	−	0.745093i	$-0.732405\pi$
$653$	6.52375	−	9.16132i	0.255294	−	0.358510i	0.922255	+	0.386583i	$0.126345\pi$
$654$	2.30059	−	9.48315i	0.0899601	−	0.370820i
$655$	−2.19583	−	6.34443i	−0.0857981	−	0.247897i
$656$	−5.53718	−	1.06720i	−0.216190	−	0.0416673i
$657$	0.823789	−	0.241886i	0.0321391	−	0.00943688i
$658$	16.7531	+	2.36055i	0.653103	+	0.0920237i
$659$	−21.2686	+	13.6685i	−0.828506	+	0.532448i	−0.884803	−	0.465966i	$-0.845707\pi$
$659$	−21.2686	+	13.6685i	−0.828506	+	0.532448i	0.0562968	+	0.998414i	$0.482071\pi$
$660$	0.992858	+	4.09261i	0.0386469	+	0.159305i
$661$	10.4442	+	4.18125i	0.406234	+	0.162632i	0.565775	−	0.824560i	$-0.308577\pi$
$661$	10.4442	+	4.18125i	0.406234	+	0.162632i	−0.159541	+	0.987191i	$0.551001\pi$
$662$	−1.00844	−	1.41616i	−0.0391942	−	0.0550405i
$663$	21.1522	−	8.46805i	0.821482	−	0.328872i
$664$	12.5785	+	8.08372i	0.488141	+	0.313709i
$665$	−13.3843	+	1.96290i	−0.519020	+	0.0761178i
$666$	−0.0833222			−0.00322867
$667$	18.9796	−	37.1184i	0.734893	−	1.43723i
$668$	−10.3988	+	18.0112i	−0.402341	+	0.696876i
$669$	−20.5635	+	3.96330i	−0.795032	+	0.153230i
$670$	0.387568	−	8.13606i	0.0149731	−	0.314324i
$671$	−8.68168	+	60.3824i	−0.335153	+	2.33104i
$672$	−2.64239	+	0.133339i	−0.101932	+	0.00514368i
$673$	−3.34406	−	23.2585i	−0.128904	−	0.896548i	−0.946947	−	0.321391i	$-0.895850\pi$
$673$	−3.34406	−	23.2585i	−0.128904	−	0.896548i	0.818043	−	0.575158i	$-0.195059\pi$
$674$	7.39213	+	30.4708i	0.284734	+	1.17369i
$675$	0.189842	+	3.98527i	0.00730701	+	0.153393i
$676$	3.89510	+	0.371937i	0.149812	+	0.0143053i
$677$	6.12497	+	5.84015i	0.235402	+	0.224455i	0.798593	−	0.601872i	$-0.205578\pi$
$677$	6.12497	+	5.84015i	0.235402	+	0.224455i	−0.563191	+	0.826327i	$0.690427\pi$
$678$	0.171529	−	0.197955i	0.00658751	−	0.00760240i
$679$	−6.79362	+	7.16528i	−0.260715	+	0.274978i
$680$	−7.28900	+	2.14024i	−0.279520	+	0.0820746i
$681$	−14.6855	+	20.6228i	−0.562748	+	0.790269i
$682$	−0.325738	−	6.83808i	−0.0124732	−	0.261844i
$683$	33.8385	−	32.2650i	1.29479	−	1.23458i	0.338918	−	0.940816i	$-0.389939\pi$
$683$	33.8385	−	32.2650i	1.29479	−	1.23458i	0.955877	−	0.293768i	$-0.0949094\pi$
$684$	3.99864	−	3.14457i	0.152892	−	0.120236i
$685$	4.70162	−	10.2951i	0.179640	−	0.393356i
$686$	−17.9606	+	4.51837i	−0.685740	+	0.172512i
$687$	−13.6866	−	8.79585i	−0.522177	−	0.335583i
$688$	−3.15759	+	9.12326i	−0.120382	+	0.347821i
$689$	19.0258	−	32.9537i	0.724826	−	1.25544i
$690$	−1.77659	+	4.48091i	−0.0676335	+	0.170586i
$691$	−21.7579	−	37.6858i	−0.827709	−	1.43363i	−0.899831	−	0.436238i	$-0.856311\pi$
$691$	−21.7579	−	37.6858i	−0.827709	−	1.43363i	0.0721224	−	0.997396i	$-0.477023\pi$
$692$	−5.45834	−	6.29927i	−0.207495	−	0.239462i
$693$	−9.04821	−	6.40483i	−0.343713	−	0.243300i
$694$	−4.32522	+	30.0826i	−0.164183	+	1.14192i
$695$	5.33731	−	0.509651i	0.202456	−	0.0193322i
$696$	8.07014	+	3.23080i	0.305898	+	0.122463i
$697$	30.8466	−	29.4122i	1.16840	−	1.11407i
$698$	−22.2223	−	11.4564i	−0.841128	−	0.433631i
$699$	−7.29938	−	15.9834i	−0.276088	−	0.604549i
$700$	−7.30597	−	7.61916i	−0.276140	−	0.287977i
$701$	16.3616	−	18.8823i	0.617971	−	0.713176i	−0.357350	−	0.933971i	$-0.616320\pi$
$701$	16.3616	−	18.8823i	0.617971	−	0.713176i	0.975320	+	0.220794i	$0.0708650\pi$
$702$	2.96002	+	0.570497i	0.111719	+	0.0215320i
$703$	−0.0999286	+	0.411911i	−0.00376888	+	0.0155355i
$704$	4.17101	+	0.398284i	0.157201	+	0.0150109i
$705$	5.71271	+	2.94511i	0.215153	+	0.110919i
$706$	9.80906	+	2.88020i	0.369169	+	0.108398i
$707$	41.5479	+	18.8329i	1.56257	+	0.708285i
$708$	−1.69513	+	3.71183i	−0.0637070	+	0.139499i
$709$	−31.3798	+	12.5626i	−1.17849	+	0.471797i	−0.876448	−	0.481497i	$-0.840093\pi$
$709$	−31.3798	+	12.5626i	−1.17849	+	0.471797i	−0.302044	+	0.953294i	$0.597669\pi$
$710$	4.30012	−	2.21686i	0.161380	−	0.0831974i
$711$	−6.81385	+	1.31326i	−0.255539	+	0.0492512i
$712$	4.35197	+	7.53784i	0.163097	+	0.282492i
$713$	4.21431	−	6.60589i	0.157827	−	0.247393i
$714$	10.7638	−	16.8531i	0.402826	−	0.630712i
$715$	8.31347	+	9.59426i	0.310906	+	0.358805i
$716$	0.108001	−	2.26722i	0.00403619	−	0.0847301i
$717$	1.79907	+	1.41481i	0.0671876	+	0.0528369i
$718$	−10.1642	−	14.2737i	−0.379326	−	0.532689i
$719$	0.506867	−	0.398605i	0.0189030	−	0.0148655i	−0.608663	−	0.793429i	$-0.708294\pi$
$719$	0.506867	−	0.398605i	0.0189030	−	0.0148655i	0.627566	+	0.778564i	$0.284051\pi$
$720$	−0.964379	−	0.283167i	−0.0359403	−	0.0105530i
$721$	10.4082	+	5.97011i	0.387621	+	0.222339i
$722$	−2.85700	−	6.25595i	−0.106326	−	0.232822i
$723$	−0.794975	−	0.758007i	−0.0295654	−	0.0281906i
$724$	−8.73717	−	25.2444i	−0.324715	−	0.938201i
$725$	11.3436	+	32.7750i	0.421289	+	1.21723i
$726$	4.74480	+	4.52415i	0.176096	+	0.167907i
$727$	−2.22707	−	4.87659i	−0.0825973	−	0.180863i	0.863827	−	0.503788i	$-0.168061\pi$
$727$	−2.22707	−	4.87659i	−0.0825973	−	0.180863i	−0.946424	+	0.322926i	$0.895334\pi$
$728$	−6.89581	+	4.00726i	−0.255576	+	0.148519i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.678316	+	0.533434i	−0.0251056	+	0.0197433i
$731$	−42.3261	−	59.4387i	−1.56549	−	2.19842i
$732$	−11.4444	−	8.99997i	−0.422997	−	0.332649i
$733$	−1.52281	+	31.9676i	−0.0562461	+	1.18075i	0.777602	+	0.628757i	$0.216436\pi$
$733$	−1.52281	+	31.9676i	−0.0562461	+	1.18075i	−0.833848	+	0.551994i	$0.813867\pi$
$734$	2.81089	+	3.24394i	0.103752	+	0.119736i
$735$	−7.00745	−	0.629283i	−0.258474	−	0.0232114i
$736$	3.63489	+	3.12851i	0.133984	+	0.115318i
$737$	−16.9779	−	29.4065i	−0.625388	−	1.08320i
$738$	5.53718	−	1.06720i	0.203826	−	0.0392843i
$739$	5.06451	−	2.61093i	0.186301	−	0.0960448i	−0.362553	−	0.931963i	$-0.618095\pi$
$739$	5.06451	−	2.61093i	0.186301	−	0.0960448i	0.548854	+	0.835918i	$0.315064\pi$
$740$	0.0777476	−	0.0311255i	0.00285806	−	0.00114419i
$741$	6.37027	−	13.9489i	0.234018	−	0.512427i
$742$	−3.26830	−	33.2367i	−0.119983	−	1.22016i
$743$	−33.5646	−	9.85545i	−1.23136	−	0.361561i	−0.399600	−	0.916690i	$-0.630851\pi$
$743$	−33.5646	−	9.85545i	−1.23136	−	0.361561i	−0.831765	+	0.555128i	$0.812669\pi$
$744$	1.45223	+	0.748676i	0.0532413	+	0.0274478i
$745$	1.09533	+	0.104592i	0.0401299	+	0.00383194i
$746$	−5.61789	+	23.1573i	−0.205686	+	0.847848i
$747$	−14.6819	−	2.82970i	−0.537182	−	0.103533i
$748$	−20.7387	+	23.9337i	−0.758282	+	0.875104i
$749$	5.69444	+	5.93855i	0.208070	+	0.216990i
$750$	−3.75351	−	8.21904i	−0.137059	−	0.300117i
$751$	−6.11884	−	3.15448i	−0.223280	−	0.115109i	0.342958	−	0.939351i	$-0.388571\pi$
$751$	−6.11884	−	3.15448i	−0.223280	−	0.115109i	−0.566237	+	0.824242i	$0.691601\pi$
$752$	4.62800	−	4.41279i	0.168766	−	0.160918i
$753$	24.9158	+	9.97477i	0.907982	+	0.363501i
$754$	26.0858	−	2.49090i	0.949990	−	0.0907131i
$755$	−0.381941	+	2.65646i	−0.0139002	+	0.0966783i
$756$	2.40355	−	1.10586i	0.0874163	−	0.0402199i
$757$	−19.7384	−	22.7793i	−0.717405	−	0.827930i	0.273587	−	0.961847i	$-0.411790\pi$
$757$	−19.7384	−	22.7793i	−0.717405	−	0.827930i	−0.990992	+	0.133918i	$0.957244\pi$
$758$	−0.733828	−	1.27103i	−0.0266538	−	0.0461658i
$759$	3.86862	+	19.7186i	0.140422	+	0.715738i
$760$	−2.55645	+	4.42790i	−0.0927321	+	0.160617i
$761$	−4.72662	+	13.6567i	−0.171340	+	0.495054i	−0.997677	−	0.0681217i	$-0.978299\pi$
$761$	−4.72662	+	13.6567i	−0.171340	+	0.495054i	0.826337	+	0.563176i	$0.190421\pi$
$762$	−3.41597	−	2.19531i	−0.123748	−	0.0795277i
$763$	−19.5594	−	16.8520i	−0.708097	−	0.610083i
$764$	−10.1801	+	22.2912i	−0.368302	+	0.806469i
$765$	5.97142	−	4.69598i	0.215897	−	0.169784i
$766$	−0.159946	+	0.152508i	−0.00577909	+	0.00551035i
$767$	0.585300	+	12.2870i	0.0211340	+	0.443656i
$768$	−0.580057	+	0.814576i	−0.0209310	+	0.0293935i
$769$	26.4081	−	7.75413i	0.952301	−	0.279621i	0.231557	−	0.972821i	$-0.425618\pi$
$769$	26.4081	−	7.75413i	0.952301	−	0.279621i	0.720745	+	0.693201i	$0.243800\pi$
$770$	10.8354	+	2.59632i	0.390481	+	0.0935649i
$771$	−3.35740	+	3.87465i	−0.120914	+	0.139542i
$772$	0.325837	+	0.310685i	0.0117271	+	0.0111818i
$773$	8.23620	+	0.786462i	0.296236	+	0.0282871i	0.242116	−	0.970247i	$-0.422159\pi$
$773$	8.23620	+	0.786462i	0.296236	+	0.0282871i	0.0541199	+	0.998534i	$0.482765\pi$
$774$	−0.459367	−	9.64330i	−0.0165116	−	0.346621i
$775$	1.53685	+	6.33499i	0.0552053	+	0.227560i
$776$	0.531118	+	3.69401i	0.0190660	+	0.132607i
$777$	−0.100463	+	0.196228i	−0.00360410	+	0.00703963i
$778$	0.932855	−	6.48815i	0.0334445	−	0.232611i
$779$	1.36493	−	28.6535i	0.0489038	−	1.02662i
$780$	−2.97509	+	0.573402i	−0.106525	+	0.0205311i
$781$	10.0841	−	17.4661i	0.360836	−	0.624986i
$782$	−35.1975	+	8.66311i	−1.25866	+	0.309792i
$783$	−8.69283			−0.310656
$784$	−2.87196	+	6.38372i	−0.102570	+	0.227990i
$785$	6.83005	+	4.38941i	0.243775	+	0.156665i
$786$	6.20118	−	2.48258i	0.221189	−	0.0885506i
$787$	−10.5720	−	14.8463i	−0.376852	−	0.529214i	0.581975	−	0.813207i	$-0.302280\pi$
$787$	−10.5720	−	14.8463i	−0.376852	−	0.529214i	−0.958826	+	0.283993i	$0.908341\pi$
$788$	−19.7125	−	7.89168i	−0.702227	−	0.281129i
$789$	−3.68526	−	15.1909i	−0.131199	−	0.540809i
$790$	5.86740	−	3.77075i	0.208753	−	0.134157i
$791$	−0.259377	−	0.642635i	−0.00922237	−	0.0228495i
$792$	−4.02026	+	1.18046i	−0.142854	+	0.0419457i
$793$	−43.0959	−	8.30605i	−1.53038	−	0.294956i
$794$	−2.23449	−	6.45613i	−0.0792991	−	0.229120i
$795$	2.99111	−	12.3295i	0.106084	−	0.437284i
$796$	14.1296	−	19.8422i	0.500809	−	0.703288i
$797$	8.85659	−	5.69178i	0.313716	−	0.201613i	−0.374301	−	0.927307i	$-0.622117\pi$
$797$	8.85659	−	5.69178i	0.313716	−	0.201613i	0.688018	+	0.725694i	$0.258481\pi$
$798$	−2.58436	−	13.2085i	−0.0914854	−	0.467574i
$799$	6.87836	+	47.8400i	0.243339	+	1.69246i
$800$	−3.97172	+	0.379254i	−0.140422	+	0.0134086i
$801$	−6.84176	−	5.38042i	−0.241742	−	0.190108i
$802$	11.1324	−	5.73915i	0.393098	−	0.202656i
$803$	−1.17659	+	3.39953i	−0.0415209	+	0.119967i
$804$	8.10402			0.285807
$805$	8.41069	+	9.58667i	0.296438	+	0.337886i
$806$	4.92525			0.173485
$807$	3.50270	−	10.1204i	0.123301	−	0.356255i
$808$	15.3249	−	7.90055i	0.539129	−	0.277940i
$809$	−18.2212	−	14.3293i	−0.640624	−	0.503792i	0.244196	−	0.969726i	$-0.421476\pi$
$809$	−18.2212	−	14.3293i	−0.640624	−	0.503792i	−0.884819	+	0.465934i	$0.845718\pi$
$810$	1.00054	−	0.0955401i	0.0351554	−	0.00335694i
$811$	−5.06310	−	35.2146i	−0.177789	−	1.23655i	−0.861864	−	0.507140i	$-0.830703\pi$
$811$	−5.06310	−	35.2146i	−0.177789	−	1.23655i	0.684074	−	0.729412i	$-0.260206\pi$
$812$	17.3390	−	15.1101i	0.608480	−	0.530261i
$813$	1.73787	−	1.11686i	0.0609496	−	0.0391699i
$814$	0.202509	−	0.284384i	0.00709794	−	0.00996766i
$815$	−2.28349	+	9.41268i	−0.0799872	+	0.329712i
$816$	−2.47205	−	7.14253i	−0.0865392	−	0.250039i
$817$	−48.2235	−	9.29431i	−1.68713	−	0.325167i
$818$	−19.1335	+	5.61811i	−0.668988	+	0.196433i
$819$	4.91250	−	6.28312i	0.171657	−	0.219550i
$820$	−4.76806	+	3.06424i	−0.166508	+	0.107008i
$821$	−0.704274	−	2.90306i	−0.0245793	−	0.101317i	0.958201	−	0.286097i	$-0.0923580\pi$
$821$	−0.704274	−	2.90306i	−0.0245793	−	0.101317i	−0.982780	+	0.184780i	$0.940843\pi$
$822$	10.4539	+	4.18512i	0.364622	+	0.145973i
$823$	22.2254	+	31.2112i	0.774729	+	1.08795i	0.993683	+	0.112220i	$0.0357960\pi$
$823$	22.2254	+	31.2112i	0.774729	+	1.08795i	−0.218954	+	0.975735i	$0.570265\pi$
$824$	4.21028	−	1.68554i	0.146672	−	0.0587187i
$825$	−14.0634	−	9.03798i	−0.489624	−	0.314662i
$826$	6.69766	+	8.46754i	0.233042	+	0.294623i
$827$	22.3225			0.776229			0.388115	−	0.921611i	$-0.373126\pi$
$827$	22.3225			0.776229			0.388115	+	0.921611i	$0.373126\pi$
$828$	−4.53727	−	1.55345i	−0.157681	−	0.0539863i
$829$	−14.8631	+	25.7437i	−0.516218	+	0.894116i	0.483605	+	0.875287i	$0.339327\pi$
$829$	−14.8631	+	25.7437i	−0.516218	+	0.894116i	−0.999823	+	0.0188293i	$0.994006\pi$
$830$	14.7567	−	2.84411i	0.512211	−	0.0987206i
$831$	−1.23139	+	25.8501i	−0.0427165	+	0.896730i
$832$	−0.429007	+	2.98381i	−0.0148732	+	0.103445i
$833$	−26.7117	−	45.6694i	−0.925506	−	1.58235i
$834$	0.759167	+	5.28012i	0.0262878	+	0.182836i
$835$	4.92819	+	20.3143i	0.170547	+	0.703004i
$836$	1.01418	+	21.2903i	0.0350762	+	0.736340i
$837$	−1.62646	−	0.155308i	−0.0562186	−	0.00536823i
$838$	23.2444	+	22.1635i	0.802964	+	0.765625i
$839$	−3.67168	+	4.23734i	−0.126760	+	0.146289i	−0.815582	−	0.578642i	$-0.803583\pi$
$839$	−3.67168	+	4.23734i	−0.126760	+	0.146289i	0.688821	+	0.724931i	$0.258128\pi$
$840$	−1.82964	+	1.92974i	−0.0631287	+	0.0665823i
$841$	−44.6791	+	13.1190i	−1.54066	+	0.452378i
$842$	22.7779	−	31.9870i	0.784977	−	1.10235i
$843$	0.926792	+	19.4558i	0.0319204	+	0.670092i
$844$	6.58009	−	6.27410i	0.226496	−	0.215963i
$845$	3.09135	−	2.43106i	0.106346	−	0.0836311i
$846$	−2.65642	+	5.81675i	−0.0913296	+	0.199984i
$847$	16.3755	−	5.71935i	0.562668	−	0.196519i
$848$	−10.6190	−	6.82445i	−0.364660	−	0.234352i
$849$	−2.76893	+	8.00031i	−0.0950295	+	0.274570i
$850$	15.0779	−	26.1156i	0.517166	−	0.895759i
$851$	0.377184	−	0.131954i	0.0129297	−	0.00452331i
$852$	2.40670	+	4.16853i	0.0824523	+	0.142812i
$853$	−11.5999	−	13.3870i	−0.397172	−	0.458361i	0.521576	−	0.853205i	$-0.325344\pi$
$853$	−11.5999	−	13.3870i	−0.397172	−	0.458361i	−0.918748	+	0.394844i	$0.870799\pi$
$854$	−34.9941	+	16.1006i	−1.19747	+	0.550953i
$855$	0.727641	−	5.06085i	0.0248848	−	0.173078i
$856$	3.09565	−	0.295599i	0.105807	−	0.0101034i
$857$	12.5399	+	5.02020i	0.428353	+	0.171487i	0.575813	−	0.817581i	$-0.304686\pi$
$857$	12.5399	+	5.02020i	0.428353	+	0.171487i	−0.147460	+	0.989068i	$0.547110\pi$
$858$	−9.14127	+	8.71618i	−0.312078	+	0.297565i
$859$	21.7344	+	11.2049i	0.741569	+	0.382305i	0.787236	−	0.616651i	$-0.211511\pi$
$859$	21.7344	+	11.2049i	0.741569	+	0.382305i	−0.0456673	+	0.998957i	$0.514541\pi$
$860$	4.03094	+	8.82652i	0.137454	+	0.300982i
$861$	4.16297	−	14.3271i	0.141874	−	0.488265i
$862$	10.3069	−	11.8948i	0.351056	−	0.405140i
$863$	−10.8272	−	2.08677i	−0.368563	−	0.0710346i	0.00160729	−	0.999999i	$-0.499488\pi$
$863$	−10.8272	−	2.08677i	−0.368563	−	0.0710346i	−0.370170	+	0.928964i	$0.620701\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	−8.33964	−	0.796339i	−0.283556	−	0.0270763i
$866$	15.7870	+	8.13875i	0.536463	+	0.276566i
$867$	38.5014	+	11.3050i	1.30758	+	0.383939i
$868$	3.51415	−	2.51737i	0.119278	−	0.0854452i
$869$	12.0784	−	26.4479i	0.409730	−	0.897184i
$870$	8.11124	−	3.24725i	0.274997	−	0.110092i
$871$	21.7138	−	11.1943i	0.735745	−	0.379303i
$872$	−9.58187	+	1.84675i	−0.324483	+	0.0625390i
$873$	−1.86600	−	3.23200i	−0.0631545	−	0.109387i
$874$	−13.1212	+	20.5673i	−0.443831	+	0.695701i
$875$	−23.8819	−	1.07017i	−0.807356	−	0.0361783i
$876$	−0.562242	−	0.648862i	−0.0189964	−	0.0219230i
$877$	1.25887	−	26.4268i	0.0425089	−	0.892371i	−0.872420	−	0.488756i	$-0.837451\pi$
$877$	1.25887	−	26.4268i	0.0425089	−	0.892371i	0.914929	−	0.403614i	$-0.132246\pi$
$878$	4.97799	+	3.91473i	0.167999	+	0.132116i
$879$	−0.823266	−	1.15612i	−0.0277681	−	0.0389948i
$880$	3.31033	−	2.60327i	0.111591	−	0.0877562i
$881$	−16.9798	−	4.98573i	−0.572065	−	0.167974i	−0.0171099	−	0.999854i	$-0.505447\pi$
$881$	−16.9798	−	4.98573i	−0.572065	−	0.167974i	−0.554955	+	0.831880i	$0.687265\pi$
$882$	0.293646	−	6.99384i	0.00988759	−	0.235495i
$883$	1.50078	+	3.28626i	0.0505054	+	0.110591i	0.933202	−	0.359351i	$-0.117002\pi$
$883$	1.50078	+	3.28626i	0.0505054	+	0.110591i	−0.882697	+	0.469942i	$0.844275\pi$
$884$	−16.4897	−	15.7229i	−0.554610	−	0.528819i
$885$	1.34142	+	3.87579i	0.0450915	+	0.130283i
$886$	9.88431	+	28.5588i	0.332070	+	0.959453i
$887$	11.9533	+	11.3975i	0.401354	+	0.382690i	0.863697	−	0.504011i	$-0.168143\pi$
$887$	11.9533	+	11.3975i	0.401354	+	0.382690i	−0.462344	+	0.886701i	$0.652991\pi$
$888$	0.0346133	+	0.0757926i	0.00116155	+	0.00254343i
$889$	−9.28876	+	5.39784i	−0.311535	+	0.181038i
$890$	8.39390	+	2.46467i	0.281364	+	0.0826160i
$891$	3.29355	−	2.59008i	0.110338	−	0.0867709i
$892$	12.1475	+	17.0588i	0.406730	+	0.571172i
$893$	25.5698	+	20.1083i	0.855661	+	0.672899i
$894$	−0.0520899	+	1.09350i	−0.00174215	+	0.0365722i
$895$	−1.49397	−	1.72413i	−0.0499379	−	0.0576314i
$896$	1.21898	+	2.34821i	0.0407232	+	0.0784482i
$897$	−14.3029	+	2.10511i	−0.477561	+	0.0702877i
$898$	10.4352	+	18.0743i	0.348226	+	0.603146i
$899$	−13.9462	+	2.68790i	−0.465131	+	0.0896466i
$900$	3.54627	−	1.82823i	0.118209	−	0.0609409i
$901$	88.5725	−	35.4591i	2.95078	−	1.18131i
$902$	−9.81530	+	21.4925i	−0.326814	+	0.715622i
$903$	−23.2643	−	10.5453i	−0.774187	−	0.350925i
$904$	−0.251321	−	0.0737946i	−0.00835882	−	0.00245437i
$905$	−23.8649	−	12.3032i	−0.793298	−	0.408973i
$906$	−2.65808	−	0.253816i	−0.0883089	−	0.00843248i
$907$	3.11022	−	12.8205i	0.103273	−	0.425698i	−0.896579	−	0.442884i	$-0.853955\pi$
$907$	3.11022	−	12.8205i	0.103273	−	0.425698i	0.999852	+	0.0171856i	$0.00547063\pi$
$908$	24.8597	+	4.79132i	0.825000	+	0.159006i
$909$	−11.2908	+	13.0303i	−0.374493	+	0.432188i
$910$	−2.23674	+	7.69784i	−0.0741472	+	0.255181i
$911$	−6.55613	−	14.3559i	−0.217214	−	0.475633i	0.769387	−	0.638783i	$-0.220562\pi$
$911$	−6.55613	−	14.3559i	−0.217214	−	0.475633i	−0.986601	+	0.163150i	$0.947835\pi$
$912$	−4.52150	−	2.33099i	−0.149722	−	0.0771869i
$913$	45.3413	−	43.2328i	1.50058	−	1.43080i
$914$	24.7435	+	9.90581i	0.818442	+	0.327655i
$915$	−14.5672	+	1.39100i	−0.481577	+	0.0459850i
$916$	−2.31536	+	16.1037i	−0.0765017	+	0.532081i
$917$	1.63030	−	17.5974i	0.0538371	−	0.581116i
$918$	4.94959	+	5.71213i	0.163361	+	0.188528i
$919$	6.76006	+	11.7088i	0.222994	+	0.386237i	0.955716	−	0.294292i	$-0.0950837\pi$
$919$	6.76006	+	11.7088i	0.222994	+	0.386237i	−0.732722	+	0.680528i	$0.761750\pi$
$920$	4.81400	−	0.245398i	0.158713	−	0.00809053i
$921$	−0.379851	+	0.657921i	−0.0125165	+	0.0216792i
$922$	−9.72298	+	28.0927i	−0.320209	+	0.925184i
$923$	12.2066	+	7.84470i	0.401785	+	0.258211i
$924$	−2.06728	+	10.8912i	−0.0680086	+	0.358294i
$925$	−0.138100	+	0.302396i	−0.00454069	+	0.00994273i
$926$	17.5547	−	13.8051i	0.576882	−	0.453665i
$927$	−3.28224	+	3.12961i	−0.107803	+	0.102790i
$928$	−0.413621	−	8.68298i	−0.0135778	−	0.285033i
$929$	4.09704	−	5.75349i	0.134420	−	0.188766i	−0.741880	−	0.670533i	$-0.766065\pi$
$929$	4.09704	−	5.75349i	0.134420	−	0.188766i	0.876299	+	0.481767i	$0.160005\pi$
$930$	1.57566	−	0.462655i	0.0516678	−	0.0151710i
$931$	−34.2225	−	9.83940i	−1.12160	−	0.322473i
$932$	−11.5068	+	13.2795i	−0.376916	+	0.434985i
$933$	0.167732	+	0.159932i	0.00549129	+	0.00523594i
$934$	−21.9988	−	2.10063i	−0.719822	−	0.0687347i
$935$	1.51454	+	31.7941i	0.0495307	+	1.03978i
$936$	−0.710694	−	2.92952i	−0.0232298	−	0.0957544i
$937$	0.625293	+	4.34901i	0.0204274	+	0.142076i	0.997483	−	0.0709099i	$-0.0225903\pi$
$937$	0.625293	+	4.34901i	0.0204274	+	0.142076i	−0.977055	+	0.212986i	$0.931681\pi$
$938$	9.77117	−	19.0853i	0.319040	−	0.623158i
$939$	−3.46408	+	24.0932i	−0.113046	+	0.786252i
$940$	0.305818	−	6.41991i	0.00997468	−	0.209394i
$941$	3.02385	−	0.582800i	0.0985747	−	0.0189987i	−0.139725	−	0.990190i	$-0.544622\pi$
$941$	3.02385	−	0.582800i	0.0985747	−	0.0189987i	0.238300	+	0.971192i	$0.423410\pi$
$942$	−4.03888	+	6.99554i	−0.131594	+	0.227927i
$943$	−23.3757	+	13.6000i	−0.761217	+	0.442877i
$944$	4.08058			0.132812
$945$	0.981371	−	2.47152i	0.0319240	−	0.0803984i
$946$	34.0296	+	21.8695i	1.10640	+	0.711039i
$947$	31.3591	−	12.5543i	1.01903	−	0.407960i	0.198832	−	0.980034i	$-0.436285\pi$
$947$	31.3591	−	12.5543i	1.01903	−	0.407960i	0.820202	+	0.572074i	$0.193861\pi$
$948$	4.02516	+	5.65255i	0.130731	+	0.183586i
$949$	−2.40275	−	0.961917i	−0.0779966	−	0.0312251i
$950$	−4.78497	−	19.7239i	−0.155245	−	0.639928i
$951$	19.6641	−	12.6374i	0.637653	−	0.409795i
$952$	−19.8016	−	2.79009i	−0.641773	−	0.0904272i
$953$	−32.1973	+	9.45397i	−1.04297	+	0.306244i	−0.757975	−	0.652284i	$-0.773811\pi$
$953$	−32.1973	+	9.45397i	−1.04297	+	0.306244i	−0.284998	+	0.958528i	$0.591993\pi$
$954$	12.3948	+	2.38890i	0.401296	+	0.0773434i
$955$	8.05588	+	23.2759i	0.260682	+	0.753191i
$956$	0.539591	−	2.22422i	0.0174516	−	0.0719366i
$957$	21.1273	−	29.6692i	0.682949	−	0.959068i
$958$	−22.7103	+	14.5950i	−0.733736	+	0.471543i
$959$	22.4606	−	19.5734i	0.725292	−	0.632058i
$960$	0.143040	+	0.994862i	0.00461658	+	0.0321090i
$961$	28.2022	−	2.69299i	0.909749	−	0.0868705i
$962$	0.197437	+	0.155266i	0.00636561	+	0.00500597i
$963$	−2.76404	+	1.42496i	−0.0890700	+	0.0459188i
$964$	−0.359263	+	1.03802i	−0.0115711	+	0.0334325i
$965$	0.452510			0.0145668
$966$	−9.12912	+	8.81244i	−0.293725	+	0.283536i
$967$	−36.7533			−1.18191			−0.590953	−	0.806706i	$-0.701248\pi$
$967$	−36.7533			−1.18191			−0.590953	+	0.806706i	$0.701248\pi$
$968$	2.14426	−	6.19542i	0.0689190	−	0.199128i
$969$	34.1745	−	17.6182i	1.09784	−	0.565977i
$970$	2.94849	+	2.31872i	0.0946702	+	0.0744495i
$971$	19.2016	−	1.83353i	0.616208	−	0.0588407i	0.217715	−	0.976012i	$-0.430140\pi$
$971$	19.2016	−	1.83353i	0.616208	−	0.0588407i	0.398493	+	0.917172i	$0.369533\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	13.3503	+	4.57847i	0.427990	+	0.146779i
$974$	33.7951	−	21.7188i	1.08286	−	0.695914i
$975$	6.97646	−	9.79707i	0.223426	−	0.313757i
$976$	−3.43249	+	14.1489i	−0.109871	+	0.452896i
$977$	−8.12306	−	23.4700i	−0.259880	−	0.750873i	−0.997162	−	0.0752879i	$-0.976012\pi$
$977$	−8.12306	−	23.4700i	−0.259880	−	0.750873i	0.737282	−	0.675585i	$-0.236109\pi$
$978$	−9.46248	−	1.82374i	−0.302577	−	0.0583169i
$979$	34.9921	−	10.2746i	1.11835	−	0.328378i
$980$	2.33858	+	6.63561i	0.0747033	+	0.211967i
$981$	8.20913	−	5.27569i	0.262097	−	0.168440i
$982$	−1.31787	−	5.43234i	−0.0420549	−	0.173353i
$983$	−19.8383	−	7.94205i	−0.632743	−	0.253312i	0.0330442	−	0.999454i	$-0.489480\pi$
$983$	−19.8383	−	7.94205i	−0.632743	−	0.253312i	−0.665787	+	0.746142i	$0.731904\pi$
$984$	−3.27099	−	4.59346i	−0.104275	−	0.146434i
$985$	−19.8128	+	7.93187i	−0.631290	+	0.252730i
$986$	55.2724	+	35.5214i	1.76023	+	1.13123i
$987$	10.4958	+	13.2694i	0.334085	+	0.422368i
$988$	−15.3347			−0.487862
$989$	17.3511	+	42.9259i	0.551733	+	1.36497i
$990$	−2.10566	+	3.64711i	−0.0669224	+	0.115913i
$991$	−35.6022	+	6.86176i	−1.13094	+	0.217971i	−0.720190	−	0.693776i	$-0.755946\pi$
$991$	−35.6022	+	6.86176i	−1.13094	+	0.217971i	−0.410751	+	0.911748i	$0.634733\pi$
$992$	0.0777420	−	1.63201i	0.00246831	−	0.0518162i
$993$	0.247417	−	1.72083i	0.00785155	−	0.0546088i
$994$	12.7189	−	0.641817i	0.403419	−	0.0203572i
$995$	−3.48429	−	24.2338i	−0.110459	−	0.768262i
$996$	3.52509	+	14.5306i	0.111697	+	0.460420i
$997$	−2.58652	−	54.2977i	−0.0819158	−	1.71962i	−0.549346	−	0.835595i	$-0.685123\pi$
$997$	−2.58652	−	54.2977i	−0.0819158	−	1.71962i	0.467431	−	0.884030i	$-0.345180\pi$
$998$	18.6447	+	1.78036i	0.590189	+	0.0563562i
$999$	−0.0603031	−	0.0574989i	−0.00190791	−	0.00181919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.151.4	✓	160
7.2	even	3	inner	966.2.y.a.289.5	yes	160
23.16	even	11	inner	966.2.y.a.361.5	yes	160
161.16	even	33	inner	966.2.y.a.499.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.151.4	✓	160	1.1	even	1	trivial
966.2.y.a.289.5	yes	160	7.2	even	3	inner
966.2.y.a.361.5	yes	160	23.16	even	11	inner
966.2.y.a.499.4	yes	160	161.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.00054 + 0.0955401i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.50267 - 0.858289i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.00054 + 0.0955401i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.50267 - 0.858289i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.236960 + 0.976761i) q^{10} +(1.37041 + 3.95954i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(-2.89239 + 0.849281i) q^{13} +(-1.62963 + 2.08430i) q^{14} +(-0.845538 + 0.543394i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-7.01682 - 2.80911i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-4.72260 + 1.89064i) q^{19} +(0.845538 + 0.543394i) q^{20} +(-2.61775 + 0.383911i) q^{21} +4.18999 q^{22} +(3.91582 + 2.76882i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.91769 + 0.755072i) q^{25} +(-0.143435 + 3.01108i) q^{26} +(0.142315 - 0.989821i) q^{27} +(1.43667 + 2.22171i) q^{28} +(-1.23712 - 8.60435i) q^{29} +(0.236960 + 0.976761i) q^{30} +(-0.0777420 - 1.63201i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(3.03244 + 2.89142i) q^{33} +(-4.94959 + 5.71213i) q^{34} +(2.58602 + 0.619648i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.0483316 - 0.0678723i) q^{37} +(0.242049 + 5.08123i) q^{38} +(-2.18169 + 2.08024i) q^{39} +(0.790056 - 0.621307i) q^{40} +(-2.34256 + 5.12949i) q^{41} +(-0.493386 + 2.59934i) q^{42} +(8.12166 + 5.21947i) q^{43} +(1.37041 - 3.95954i) q^{44} +(-0.502546 + 0.870436i) q^{45} +(3.89728 - 2.79486i) q^{46} +(-3.19731 - 5.53790i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.52668 + 4.29602i) q^{49} +(-0.567806 + 3.94918i) q^{50} +(-7.52400 + 0.718455i) q^{51} +(2.79856 + 1.12037i) q^{52} +(-9.13561 + 8.71079i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-1.74945 - 3.83076i) q^{55} +(2.56940 - 0.631005i) q^{56} +(-3.33127 + 3.84449i) q^{57} +(-8.53574 - 1.64513i) q^{58} +(0.962033 - 3.96555i) q^{59} +(1.00054 + 0.0955401i) q^{60} +(12.9408 + 6.67147i) q^{61} +(-1.56767 - 0.460311i) q^{62} +(-2.15083 + 1.54076i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.81281 - 1.12608i) q^{65} +(3.72421 - 1.91996i) q^{66} +(-7.95757 + 1.53370i) q^{67} +(3.77911 + 6.54562i) q^{68} +(4.74926 + 0.666698i) q^{69} +(1.43137 - 2.24113i) q^{70} +(-3.15211 - 3.63773i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(0.674879 + 0.530731i) q^{73} +(-0.0483316 - 0.0678723i) q^{74} +(-3.13619 + 2.46632i) q^{75} +(4.88093 + 1.43317i) q^{76} +(-0.0312509 - 11.0856i) q^{77} +(1.25227 + 2.74208i) q^{78} +(-5.02217 - 4.78863i) q^{79} +(-0.328734 - 0.949813i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(4.08120 + 3.89141i) q^{82} +(-6.21133 - 13.6009i) q^{83} +(2.29501 + 1.31641i) q^{84} +(7.28900 + 2.14024i) q^{85} +(7.58874 - 5.96785i) q^{86} +(-5.04234 - 7.08097i) q^{87} +(-3.29355 - 2.59008i) q^{88} +(0.414150 - 8.69409i) q^{89} +(0.658196 + 0.759598i) q^{90} +(7.96761 + 0.357035i) q^{91} +(-1.36647 - 4.59704i) q^{92} +(-0.816928 - 1.41496i) q^{93} +(-6.27906 + 1.21019i) q^{94} +(4.54452 - 2.34286i) q^{95} +(0.928368 - 0.371662i) q^{96} +(1.55033 - 3.39474i) q^{97} +(5.86734 - 3.81763i) q^{98} +(4.02026 + 1.18046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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