LMFDB - Embedded newform 966.2.y.a.25.5

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			25.5
Character	$\chi$	$=$	966.25
Dual form			966.2.y.a.541.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.373397 + 1.53917i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-2.64405 - 0.0947728i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.373397 + 1.53917i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-2.64405 - 0.0947728i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-1.55519 + 0.299738i) q^{10} +(-0.294704 - 6.18660i) q^{11} +(0.888835 + 0.458227i) q^{12} +(1.38644 + 1.60003i) q^{13} +(0.220475 - 2.63655i) q^{14} +(0.225400 - 1.56769i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.702235 + 0.986151i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(1.64844 - 2.31492i) q^{19} +(-0.225400 - 1.56769i) q^{20} +(2.41943 + 1.07068i) q^{21} +6.19362 q^{22} +(3.99332 + 2.65583i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.21457 - 1.14169i) q^{25} +(-1.66419 + 1.30873i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.62307 + 0.345677i) q^{28} +(-1.05300 + 2.30574i) q^{29} +(1.55519 + 0.299738i) q^{30} +(2.88109 + 2.26572i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-2.02573 + 5.85297i) q^{33} +(-1.01845 + 0.654517i) q^{34} +(-0.841412 - 4.10502i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.85738 + 2.72451i) q^{37} +(2.23386 + 1.75673i) q^{38} +(-0.692451 - 2.00070i) q^{39} +(1.57664 - 0.150551i) q^{40} +(-3.49306 - 1.02566i) q^{41} +(-1.18459 + 2.36575i) q^{42} +(-1.68095 - 11.6913i) q^{43} +(-0.294704 + 6.18660i) q^{44} +(-0.791905 + 1.37162i) q^{45} +(-2.84283 + 3.86242i) q^{46} +(3.62832 + 6.28443i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(6.98204 + 0.501169i) q^{49} +(1.03502 + 2.26639i) q^{50} +(-0.285417 - 1.17651i) q^{51} +(-1.22807 - 1.72458i) q^{52} +(2.02907 + 5.86262i) q^{53} +(0.928368 - 0.371662i) q^{54} +(9.41216 - 2.76366i) q^{55} +(-0.470096 + 2.60365i) q^{56} +(-2.39073 + 1.53643i) q^{57} +(-2.25302 - 1.16151i) q^{58} +(7.52976 - 1.45124i) q^{59} +(-0.373397 + 1.53917i) q^{60} +(7.46397 - 2.98812i) q^{61} +(-2.40024 + 2.77002i) q^{62} +(-1.84819 - 1.89320i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.94502 + 2.73140i) q^{65} +(-5.74995 - 2.30193i) q^{66} +(-1.18897 + 0.612955i) q^{67} +(-0.605316 - 1.04844i) q^{68} +(-2.72020 - 3.94975i) q^{69} +(4.14041 - 0.645134i) q^{70} +(10.8058 + 6.94447i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-0.646786 - 0.0617606i) q^{73} +(-2.85738 + 2.72451i) q^{74} +(-2.48026 + 0.236836i) q^{75} +(-1.86103 + 2.14774i) q^{76} +(0.192892 + 16.3856i) q^{77} +(2.03139 - 0.596469i) q^{78} +(3.54088 - 10.2307i) q^{79} +(0.0753607 + 1.58202i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(1.19070 - 3.44030i) q^{82} +(-7.14702 + 2.09855i) q^{83} +(-2.30670 - 1.29581i) q^{84} +(-1.25564 + 1.44908i) q^{85} +(11.7580 - 1.12275i) q^{86} +(1.83452 - 1.74922i) q^{87} +(-6.16557 - 0.588741i) q^{88} +(6.79460 - 5.34333i) q^{89} +(-1.33239 - 0.856273i) q^{90} +(-3.51417 - 4.36197i) q^{91} +(-3.72278 - 3.02339i) q^{92} +(-1.83263 - 3.17421i) q^{93} +(-6.44996 + 3.32518i) q^{94} +(4.17857 + 1.67285i) q^{95} +(0.580057 - 0.814576i) q^{96} +(12.3358 + 3.62211i) q^{97} +(-0.832820 + 6.95028i) q^{98} +(4.05596 - 4.68082i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.373397	+	1.53917i	0.166988	+	0.688336i	0.992321	+	0.123689i	$0.0394725\pi$
$5$	0.373397	+	1.53917i	0.166988	+	0.688336i	−0.825333	+	0.564647i	$0.809012\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	−2.64405	−	0.0947728i	−0.999358	−	0.0358208i
$7$	−2.64405	−	0.0947728i	−0.999358	−	0.0358208i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−1.55519	+	0.299738i	−0.491794	+	0.0947855i
$11$	−0.294704	−	6.18660i	−0.0888566	−	1.86533i	−0.402020	−	0.915631i	$-0.631692\pi$
$11$	−0.294704	−	6.18660i	−0.0888566	−	1.86533i	0.313163	−	0.949699i	$-0.398611\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	1.38644	+	1.60003i	0.384528	+	0.443769i	0.914708	−	0.404116i	$-0.132421\pi$
$13$	1.38644	+	1.60003i	0.384528	+	0.443769i	−0.530180	+	0.847885i	$0.677875\pi$
$14$	0.220475	−	2.63655i	0.0589243	−	0.704647i
$15$	0.225400	−	1.56769i	0.0581980	−	0.404776i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	0.702235	+	0.986151i	0.170317	+	0.239177i	0.890908	−	0.454183i	$-0.150069\pi$
$17$	0.702235	+	0.986151i	0.170317	+	0.239177i	−0.720591	+	0.693360i	$0.756130\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	1.64844	−	2.31492i	0.378179	−	0.531078i	−0.580990	−	0.813911i	$-0.697335\pi$
$19$	1.64844	−	2.31492i	0.378179	−	0.531078i	0.959169	+	0.282832i	$0.0912739\pi$
$20$	−0.225400	−	1.56769i	−0.0504009	−	0.350546i
$21$	2.41943	+	1.07068i	0.527963	+	0.233641i
$22$	6.19362			1.32048
$23$	3.99332	+	2.65583i	0.832664	+	0.553778i
$23$	3.99332	+	2.65583i	0.832664	+	0.553778i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.21457	−	1.14169i	0.442915	−	0.228338i
$26$	−1.66419	+	1.30873i	−0.326374	+	0.256664i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	2.62307	+	0.345677i	0.495714	+	0.0653268i
$29$	−1.05300	+	2.30574i	−0.195536	+	0.428165i	−0.981849	−	0.189664i	$-0.939260\pi$
$29$	−1.05300	+	2.30574i	−0.195536	+	0.428165i	0.786313	+	0.617829i	$0.211987\pi$
$30$	1.55519	+	0.299738i	0.283937	+	0.0547244i
$31$	2.88109	+	2.26572i	0.517460	+	0.406935i	0.842443	−	0.538785i	$-0.181116\pi$
$31$	2.88109	+	2.26572i	0.517460	+	0.406935i	−0.324984	+	0.945720i	$0.605359\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	−2.02573	+	5.85297i	−0.352635	+	1.01887i
$34$	−1.01845	+	0.654517i	−0.174662	+	0.112249i
$35$	−0.841412	−	4.10502i	−0.142225	−	0.693876i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	2.85738	+	2.72451i	0.469751	+	0.447907i	0.887604	−	0.460608i	$-0.152369\pi$
$37$	2.85738	+	2.72451i	0.469751	+	0.447907i	−0.417853	+	0.908515i	$0.637217\pi$
$38$	2.23386	+	1.75673i	0.362380	+	0.284979i
$39$	−0.692451	−	2.00070i	−0.110881	−	0.320369i
$40$	1.57664	−	0.150551i	0.249289	−	0.0238042i
$41$	−3.49306	−	1.02566i	−0.545524	−	0.160180i	−0.00265337	−	0.999996i	$-0.500845\pi$
$41$	−3.49306	−	1.02566i	−0.545524	−	0.160180i	−0.542871	+	0.839816i	$0.682663\pi$
$42$	−1.18459	+	2.36575i	−0.182786	+	0.365042i
$43$	−1.68095	−	11.6913i	−0.256343	−	1.78290i	−0.558358	−	0.829600i	$-0.688568\pi$
$43$	−1.68095	−	11.6913i	−0.256343	−	1.78290i	0.302015	−	0.953303i	$-0.402341\pi$
$44$	−0.294704	+	6.18660i	−0.0444283	+	0.932665i
$45$	−0.791905	+	1.37162i	−0.118050	+	0.204469i
$46$	−2.84283	+	3.86242i	−0.419152	+	0.569483i
$47$	3.62832	+	6.28443i	0.529245	+	0.916679i	0.999418	+	0.0341047i	$0.0108580\pi$
$47$	3.62832	+	6.28443i	0.529245	+	0.916679i	−0.470174	+	0.882574i	$0.655809\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	6.98204	+	0.501169i	0.997434	+	0.0715955i
$50$	1.03502	+	2.26639i	0.146375	+	0.320516i
$51$	−0.285417	−	1.17651i	−0.0399664	−	0.164744i
$52$	−1.22807	−	1.72458i	−0.170302	−	0.239156i
$53$	2.02907	+	5.86262i	0.278715	+	0.805293i	0.994286	+	0.106753i	$0.0340454\pi$
$53$	2.02907	+	5.86262i	0.278715	+	0.805293i	−0.715571	+	0.698540i	$0.753833\pi$
$54$	0.928368	−	0.371662i	0.126335	−	0.0505769i
$55$	9.41216	−	2.76366i	1.26914	−	0.372652i
$56$	−0.470096	+	2.60365i	−0.0628192	+	0.347928i
$57$	−2.39073	+	1.53643i	−0.316660	+	0.203505i
$58$	−2.25302	−	1.16151i	−0.295837	−	0.152514i
$59$	7.52976	−	1.45124i	0.980291	−	0.188936i	0.326158	−	0.945315i	$-0.394246\pi$
$59$	7.52976	−	1.45124i	0.980291	−	0.188936i	0.654133	+	0.756380i	$0.273034\pi$
$60$	−0.373397	+	1.53917i	−0.0482054	+	0.198705i
$61$	7.46397	−	2.98812i	0.955663	−	0.382590i	0.159180	−	0.987250i	$-0.449115\pi$
$61$	7.46397	−	2.98812i	0.955663	−	0.382590i	0.796484	+	0.604660i	$0.206691\pi$
$62$	−2.40024	+	2.77002i	−0.304831	+	0.351793i
$63$	−1.84819	−	1.89320i	−0.232850	−	0.238520i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.94502	+	2.73140i	−0.241250	+	0.338789i
$66$	−5.74995	−	2.30193i	−0.707771	−	0.283349i
$67$	−1.18897	+	0.612955i	−0.145256	+	0.0748844i	−0.529322	−	0.848421i	$-0.677554\pi$
$67$	−1.18897	+	0.612955i	−0.145256	+	0.0748844i	0.384066	+	0.923305i	$0.374523\pi$
$68$	−0.605316	−	1.04844i	−0.0734053	−	0.127142i
$69$	−2.72020	−	3.94975i	−0.327473	−	0.475494i
$70$	4.14041	−	0.645134i	0.494874	−	0.0771083i
$71$	10.8058	+	6.94447i	1.28241	+	0.824157i	0.991183	−	0.132496i	$-0.0422993\pi$
$71$	10.8058	+	6.94447i	1.28241	+	0.824157i	0.291230	+	0.956653i	$0.405936\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	−0.646786	−	0.0617606i	−0.0757006	−	0.00722853i	0.0571370	−	0.998366i	$-0.481803\pi$
$73$	−0.646786	−	0.0617606i	−0.0757006	−	0.00722853i	−0.132838	+	0.991138i	$0.542409\pi$
$74$	−2.85738	+	2.72451i	−0.332164	+	0.316718i
$75$	−2.48026	+	0.236836i	−0.286396	+	0.0273475i
$76$	−1.86103	+	2.14774i	−0.213474	+	0.246363i
$77$	0.192892	+	16.3856i	0.0219821	+	1.86732i
$78$	2.03139	−	0.596469i	0.230009	−	0.0675368i
$79$	3.54088	−	10.2307i	0.398381	−	1.15105i	−0.550343	−	0.834939i	$-0.685503\pi$
$79$	3.54088	−	10.2307i	0.398381	−	1.15105i	0.948724	−	0.316107i	$-0.102376\pi$
$80$	0.0753607	+	1.58202i	0.00842559	+	0.176875i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	1.19070	−	3.44030i	0.131491	−	0.379918i
$83$	−7.14702	+	2.09855i	−0.784487	+	0.230346i	−0.649359	−	0.760482i	$-0.724963\pi$
$83$	−7.14702	+	2.09855i	−0.784487	+	0.230346i	−0.135128	+	0.990828i	$0.543145\pi$
$84$	−2.30670	−	1.29581i	−0.251682	−	0.141385i
$85$	−1.25564	+	1.44908i	−0.136193	+	0.157175i
$86$	11.7580	−	1.12275i	1.26790	−	0.121070i
$87$	1.83452	−	1.74922i	0.196682	−	0.187536i
$88$	−6.16557	−	0.588741i	−0.657252	−	0.0627600i
$89$	6.79460	−	5.34333i	0.720226	−	0.566392i	−0.189360	−	0.981908i	$-0.560641\pi$
$89$	6.79460	−	5.34333i	0.720226	−	0.566392i	0.909586	+	0.415516i	$0.136399\pi$
$90$	−1.33239	−	0.856273i	−0.140446	−	0.0902591i
$91$	−3.51417	−	4.36197i	−0.368385	−	0.457258i
$92$	−3.72278	−	3.02339i	−0.388127	−	0.315210i
$93$	−1.83263	−	3.17421i	−0.190035	−	0.329151i
$94$	−6.44996	+	3.32518i	−0.665262	+	0.342967i
$95$	4.17857	+	1.67285i	0.428712	+	0.171630i
$96$	0.580057	−	0.814576i	0.0592018	−	0.0831373i
$97$	12.3358	+	3.62211i	1.25251	+	0.367770i	0.839701	−	0.543049i	$-0.182730\pi$
$97$	12.3358	+	3.62211i	1.25251	+	0.367770i	0.412807	+	0.910819i	$0.364548\pi$
$98$	−0.832820	+	6.95028i	−0.0841275	+	0.702084i
$99$	4.05596	−	4.68082i	0.407639	−	0.470440i
$100$	−2.31307	+	0.926013i	−0.231307	+	0.0926013i
$101$	1.72488	−	7.11007i	0.171632	−	0.707478i	−0.819328	−	0.573325i	$-0.805653\pi$
$101$	1.72488	−	7.11007i	0.171632	−	0.707478i	0.990961	−	0.134153i	$-0.0428315\pi$
$102$	1.18875	−	0.229113i	0.117704	−	0.0226856i
$103$	1.19865	+	0.617948i	0.118107	+	0.0608882i	0.516267	−	0.856427i	$-0.327321\pi$
$103$	1.19865	+	0.617948i	0.118107	+	0.0608882i	−0.398161	+	0.917316i	$0.630351\pi$
$104$	1.78106	−	1.14462i	0.174647	−	0.112239i
$105$	−0.744543	+	4.12369i	−0.0726600	+	0.402431i
$106$	−5.95253	+	1.74782i	−0.578161	+	0.169763i
$107$	−2.66522	+	1.06699i	−0.257656	+	0.103150i	−0.496895	−	0.867811i	$-0.665526\pi$
$107$	−2.66522	+	1.06699i	−0.257656	+	0.103150i	0.239239	+	0.970961i	$0.423102\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	−3.64981	−	5.12545i	−0.349589	−	0.490929i	0.601917	−	0.798558i	$-0.294404\pi$
$109$	−3.64981	−	5.12545i	−0.349589	−	0.490929i	−0.951506	+	0.307630i	$0.900464\pi$
$110$	2.31268	+	9.53300i	0.220505	+	0.908936i
$111$	−1.64011	−	3.59133i	−0.155672	−	0.340874i
$112$	−2.57834	−	0.593451i	−0.243630	−	0.0560758i
$113$	−7.74349	−	4.97644i	−0.728447	−	0.468144i	0.123119	−	0.992392i	$-0.460710\pi$
$113$	−7.74349	−	4.97644i	−0.728447	−	0.468144i	−0.851566	+	0.524248i	$0.824347\pi$
$114$	−1.42093	−	2.46113i	−0.133083	−	0.230506i
$115$	−2.59666	+	7.13805i	−0.242140	+	0.665627i
$116$	1.26740	−	2.19520i	0.117675	−	0.203820i
$117$	−0.100738	+	2.11475i	−0.00931322	+	0.195508i
$118$	1.09132	+	7.59028i	0.100464	+	0.698742i
$119$	−1.76329	−	2.67399i	−0.161640	−	0.245124i
$120$	−1.51966	−	0.446211i	−0.138725	−	0.0407333i
$121$	−27.2370	+	2.60082i	−2.47609	+	0.236438i
$122$	2.62959	+	7.59770i	0.238072	+	0.687863i
$123$	2.86165	+	2.25042i	0.258026	+	0.202914i
$124$	−2.65268	−	2.52932i	−0.238217	−	0.227140i
$125$	7.77004	+	8.96711i	0.694974	+	0.802043i
$126$	1.97899	−	1.75602i	0.176303	−	0.156438i
$127$	11.0220	−	7.08344i	0.978048	−	0.628553i	0.0491120	−	0.998793i	$-0.484361\pi$
$127$	11.0220	−	7.08344i	0.978048	−	0.628553i	0.928936	+	0.370240i	$0.120725\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−2.78467	+	11.4786i	−0.245176	+	1.01063i
$130$	−2.63576	−	2.07278i	−0.231171	−	0.181795i
$131$	19.3909	+	3.73728i	1.69419	+	0.326528i	0.942806	−	0.333342i	$-0.108176\pi$
$131$	19.3909	+	3.73728i	1.69419	+	0.326528i	0.751380	+	0.659869i	$0.229388\pi$
$132$	2.57292	−	5.63391i	0.223944	−	0.490369i
$133$	−4.57797	+	5.96454i	−0.396960	+	0.517191i
$134$	−0.555688	−	1.21679i	−0.0480041	−	0.105114i
$135$	1.24496	−	0.979047i	0.107149	−	0.0842629i
$136$	1.07605	−	0.554743i	0.0922707	−	0.0475688i
$137$	4.36811	−	7.56579i	0.373193	−	0.646389i	−0.616862	−	0.787072i	$-0.711596\pi$
$137$	4.36811	−	7.56579i	0.373193	−	0.646389i	0.990055	+	0.140682i	$0.0449296\pi$
$138$	4.07471	−	2.52918i	0.346862	−	0.215298i
$139$	−10.6043			−0.899441			−0.449721	−	0.893169i	$-0.648476\pi$
$139$	−10.6043			−0.899441			−0.449721	+	0.893169i	$0.648476\pi$
$140$	0.447395	+	4.16642i	0.0378117	+	0.352126i
$141$	−1.03273	−	7.18278i	−0.0869713	−	0.604899i
$142$	−7.45076	+	10.4631i	−0.625254	+	0.878047i
$143$	9.49017	−	9.04886i	0.793608	−	0.756704i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−3.94210	−	0.759777i	−0.327374	−	0.0630961i
$146$	0.0924659	−	0.643115i	0.00765254	−	0.0532246i
$147$	−6.29563	−	3.06023i	−0.519255	−	0.252403i
$148$	−2.58546	−	2.98378i	−0.212524	−	0.245266i
$149$	−18.8365	−	9.71088i	−1.54314	−	0.795546i	−0.544090	−	0.839027i	$-0.683125\pi$
$149$	−18.8365	−	9.71088i	−1.54314	−	0.795546i	−0.999054	+	0.0434812i	$0.986155\pi$
$150$	−0.118552	−	2.48872i	−0.00967977	−	0.203203i
$151$	−18.4059	+	3.54745i	−1.49785	+	0.288687i	−0.871322	−	0.490711i	$-0.836737\pi$
$151$	−18.4059	+	3.54745i	−1.49785	+	0.288687i	−0.626529	+	0.779398i	$0.715525\pi$
$152$	−2.05676	−	1.96111i	−0.166825	−	0.159067i
$153$	−0.172291	+	1.19831i	−0.0139289	+	0.0968775i
$154$	−16.3763	−	0.586986i	−1.31964	−	0.0473007i
$155$	−2.41152	+	5.28049i	−0.193698	+	0.424139i
$156$	0.499136	+	2.05747i	0.0399629	+	0.164729i
$157$	17.7311	+	1.69312i	1.41510	+	0.135125i	0.774414	−	0.632679i	$-0.218045\pi$
$157$	17.7311	+	1.69312i	1.41510	+	0.135125i	0.640684	+	0.767805i	$0.278651\pi$
$158$	10.0506	+	4.02367i	0.799586	+	0.320106i
$159$	0.295190	−	6.19680i	0.0234101	−	0.491438i
$160$	−1.58381			−0.125211
$161$	−10.3068	−	7.40061i	−0.812293	−	0.583250i
$162$	−1.00000			−0.0785674
$163$	0.622533	−	13.0686i	0.0487605	−	1.02361i	−0.833403	−	0.552666i	$-0.813611\pi$
$163$	0.622533	−	13.0686i	0.0487605	−	1.02361i	0.882163	−	0.470944i	$-0.156086\pi$
$164$	3.37975	+	1.35305i	0.263914	+	0.105655i
$165$	−9.76510	−	0.932454i	−0.760212	−	0.0725914i
$166$	−1.75611	−	7.23877i	−0.136300	−	0.561838i
$167$	−6.29587	+	13.7860i	−0.487189	+	1.06680i	0.493235	+	0.869896i	$0.335814\pi$
$167$	−6.29587	+	13.7860i	−0.487189	+	1.06680i	−0.980424	+	0.196899i	$0.936913\pi$
$168$	1.40410	−	2.24243i	0.108329	−	0.173007i
$169$	1.21219	−	8.43100i	0.0932457	−	0.648538i
$170$	−1.38770	−	1.32316i	−0.106431	−	0.101482i
$171$	2.79051	−	0.537827i	0.213396	−	0.0411287i
$172$	0.562014	+	11.7981i	0.0428532	+	0.899599i
$173$	−13.2835	−	6.84814i	−1.00993	−	0.520654i	−0.127869	−	0.991791i	$-0.540814\pi$
$173$	−13.2835	−	6.84814i	−1.00993	−	0.520654i	−0.882060	+	0.471137i	$0.843844\pi$
$174$	1.65994	+	1.91568i	0.125840	+	0.145227i
$175$	−5.96365	+	2.80881i	−0.450810	+	0.212326i
$176$	0.881444	−	6.13057i	0.0664413	−	0.462109i
$177$	−7.52976	−	1.45124i	−0.565971	−	0.109082i
$178$	5.01398	+	7.04115i	0.375814	+	0.527757i
$179$	−8.65888	+	8.25623i	−0.647195	+	0.617099i	−0.940855	−	0.338811i	$-0.889975\pi$
$179$	−8.65888	+	8.25623i	−0.647195	+	0.617099i	0.293659	+	0.955910i	$0.405127\pi$
$180$	0.918700	−	1.29013i	0.0684759	−	0.0961609i
$181$	−3.32927	−	23.1556i	−0.247462	−	1.72114i	−0.612778	−	0.790255i	$-0.709948\pi$
$181$	−3.32927	−	23.1556i	−0.247462	−	1.72114i	0.365316	−	0.930884i	$-0.380961\pi$
$182$	4.52424	−	3.30264i	0.335359	−	0.244808i
$183$	−8.03988			−0.594325
$184$	3.19710	−	3.57471i	0.235694	−	0.263531i
$185$	−3.12653	+	5.41531i	−0.229867	+	0.398142i
$186$	3.25782	−	1.67952i	0.238875	−	0.123149i
$187$	5.89397	−	4.63507i	0.431010	−	0.338950i
$188$	−3.01452	−	6.60087i	−0.219856	−	0.481418i
$189$	1.01217	+	2.44449i	0.0736246	+	0.177810i
$190$	−1.86977	+	4.09424i	−0.135648	+	0.297027i
$191$	−15.6864	−	3.02332i	−1.13503	−	0.218759i	−0.413074	−	0.910697i	$-0.635545\pi$
$191$	−15.6864	−	3.02332i	−1.13503	−	0.218759i	−0.721957	+	0.691938i	$0.756757\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	1.70166	−	7.01436i	0.122488	−	0.504904i	−0.877204	−	0.480117i	$-0.840594\pi$
$193$	1.70166	−	7.01436i	0.122488	−	0.504904i	0.999693	−	0.0247870i	$-0.00789076\pi$
$194$	−4.20497	+	12.1495i	−0.301899	+	0.872280i
$195$	2.82086	−	1.81285i	0.202006	−	0.129821i
$196$	−6.90278	−	1.16258i	−0.493056	−	0.0830417i
$197$	10.6575	+	12.2994i	0.759317	+	0.876298i	0.995437	−	0.0954257i	$-0.0304212\pi$
$197$	10.6575	+	12.2994i	0.759317	+	0.876298i	−0.236120	+	0.971724i	$0.575876\pi$
$198$	4.48253	+	4.27408i	0.318560	+	0.303746i
$199$	4.16651	+	3.27658i	0.295356	+	0.232270i	0.754830	−	0.655921i	$-0.227720\pi$
$199$	4.16651	+	3.27658i	0.295356	+	0.232270i	−0.459474	+	0.888191i	$0.651962\pi$
$200$	−0.814904	−	2.35451i	−0.0576224	−	0.166489i
$201$	1.33161	−	0.127154i	0.0939247	−	0.00896872i
$202$	7.01994	+	2.06124i	0.493921	+	0.145028i
$203$	3.00270	−	5.99670i	0.210748	−	0.420886i
$204$	0.172291	+	1.19831i	0.0120628	+	0.0838984i
$205$	0.274353	−	5.75938i	0.0191616	−	0.402252i
$206$	−0.674282	+	1.16789i	−0.0469795	+	0.0813708i
$207$	1.05737	+	4.67782i	0.0734921	+	0.325131i
$208$	1.05857	+	1.83350i	0.0733988	+	0.127130i
$209$	−14.8073	−	9.51606i	−1.02424	−	0.658239i
$210$	−4.08360	−	0.939913i	−0.281795	−	0.0648602i
$211$	0.103953	+	0.227625i	0.00715642	+	0.0156704i	0.913176	−	0.407564i	$-0.133622\pi$
$211$	0.103953	+	0.227625i	0.00715642	+	0.0156704i	−0.906020	+	0.423235i	$0.860895\pi$
$212$	−1.46261	−	6.02895i	−0.100452	−	0.414070i
$213$	−7.45076	−	10.4631i	−0.510518	−	0.716922i
$214$	−0.938967	−	2.71297i	−0.0641864	−	0.185455i
$215$	17.3672	−	6.95276i	1.18443	−	0.474174i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	−7.40304	−	6.26373i	−0.502551	−	0.425209i
$218$	5.29331	−	3.40180i	0.358508	−	0.230399i
$219$	0.577501	+	0.297723i	0.0390239	+	0.0201182i
$220$	−9.63224	+	1.85646i	−0.649406	+	0.125163i
$221$	−0.604270	+	2.49083i	−0.0406476	+	0.167552i
$222$	3.66530	−	1.46737i	0.245999	−	0.0984831i
$223$	5.23455	−	6.04099i	0.350531	−	0.404535i	−0.552914	−	0.833238i	$-0.686484\pi$
$223$	5.23455	−	6.04099i	0.350531	−	0.404535i	0.903445	+	0.428704i	$0.141030\pi$
$224$	0.715461	−	2.54718i	0.0478037	−	0.170190i
$225$	2.39062	+	0.701949i	0.159375	+	0.0467966i
$226$	5.33926	−	7.49793i	0.355162	−	0.498755i
$227$	19.6752	+	7.87676i	1.30589	+	0.522799i	0.917147	−	0.398548i	$-0.130486\pi$
$227$	19.6752	+	7.87676i	1.30589	+	0.522799i	0.388741	+	0.921347i	$0.372910\pi$
$228$	2.52595	−	1.30222i	0.167285	−	0.0862416i
$229$	9.11562	+	15.7887i	0.602377	+	1.04335i	0.992460	+	0.122568i	$0.0391129\pi$
$229$	9.11562	+	15.7887i	0.602377	+	1.04335i	−0.390083	+	0.920780i	$0.627554\pi$
$230$	−7.00641	−	2.93337i	−0.461989	−	0.193420i
$231$	5.91085	−	15.2836i	0.388905	−	1.00559i
$232$	2.13241	+	1.37042i	0.140000	+	0.0899724i
$233$	−16.8577	+	13.2571i	−1.10439	+	0.868498i	−0.992134	−	0.125182i	$-0.960049\pi$
$233$	−16.8577	+	13.2571i	−1.10439	+	0.868498i	−0.112252	+	0.993680i	$0.535806\pi$
$234$	−2.10756	−	0.201247i	−0.137775	−	0.0131560i
$235$	−8.31798	+	7.93117i	−0.542605	+	0.517373i
$236$	−7.63361	+	0.728922i	−0.496906	+	0.0474488i
$237$	−7.08962	+	8.18185i	−0.460520	+	0.531468i
$238$	2.75486	−	1.63406i	0.178571	−	0.105920i
$239$	−2.88818	+	0.848046i	−0.186821	+	0.0548555i	−0.373805	−	0.927507i	$-0.621947\pi$
$239$	−2.88818	+	0.848046i	−0.186821	+	0.0548555i	0.186984	+	0.982363i	$0.440129\pi$
$240$	0.518014	−	1.49670i	0.0334376	−	0.0966117i
$241$	0.498274	+	10.4601i	0.0320967	+	0.673792i	0.956387	+	0.292102i	$0.0943547\pi$
$241$	0.498274	+	10.4601i	0.0320967	+	0.673792i	−0.924290	+	0.381690i	$0.875342\pi$
$242$	−1.30188	−	27.3299i	−0.0836882	−	1.75683i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	−7.71421	+	2.26510i	−0.493852	+	0.145008i
$245$	1.83569	+	10.9336i	0.117278	+	0.698525i
$246$	−2.38404	+	2.75133i	−0.152001	+	0.175418i
$247$	5.98940	−	0.571919i	0.381097	−	0.0363903i
$248$	2.65268	−	2.52932i	0.168445	−	0.160612i
$249$	7.41501	+	0.708048i	0.469907	+	0.0448707i
$250$	−9.32667	+	7.33457i	−0.589870	+	0.463879i
$251$	−5.40756	−	3.47523i	−0.341322	−	0.219354i	0.358738	−	0.933438i	$-0.383207\pi$
$251$	−5.40756	−	3.47523i	−0.341322	−	0.219354i	−0.700060	+	0.714084i	$0.746844\pi$
$252$	1.65986	+	2.06031i	0.104561	+	0.129787i
$253$	15.2537	−	25.4877i	0.958992	−	1.60240i
$254$	6.55096	+	11.3466i	0.411044	+	0.711949i
$255$	1.70426	−	0.878608i	0.106725	−	0.0550206i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−1.51729	+	2.13073i	−0.0946458	+	0.132911i	−0.859183	−	0.511668i	$-0.829028\pi$
$257$	−1.51729	+	2.13073i	−0.0946458	+	0.132911i	0.764538	+	0.644579i	$0.222967\pi$
$258$	−11.3331	−	3.32769i	−0.705565	−	0.207173i
$259$	−7.29687	−	7.47455i	−0.453405	−	0.464446i
$260$	2.19585	−	2.53415i	0.136181	−	0.157161i
$261$	−2.35323	+	0.942092i	−0.145661	+	0.0583140i
$262$	−4.65570	+	19.1911i	−0.287630	+	1.18563i
$263$	1.02577	−	0.197702i	0.0632520	−	0.0121908i	−0.157527	−	0.987515i	$-0.550352\pi$
$263$	1.02577	−	0.197702i	0.0632520	−	0.0121908i	0.220779	+	0.975324i	$0.429140\pi$
$264$	5.50511	+	2.83808i	0.338816	+	0.174672i
$265$	−8.26589	+	5.31217i	−0.507770	+	0.326324i
$266$	−5.73995	−	4.85659i	−0.351939	−	0.297776i
$267$	−8.29381	+	2.43528i	−0.507573	+	0.149037i
$268$	1.24185	−	0.497161i	0.0758580	−	0.0303690i
$269$	3.52235	+	10.1772i	0.214762	+	0.620513i	0.999999	+	0.00131847i	$0.000419683\pi$
$269$	3.52235	+	10.1772i	0.214762	+	0.620513i	−0.785237	+	0.619195i	$0.787459\pi$
$270$	0.918700	+	1.29013i	0.0559103	+	0.0785151i
$271$	−5.81811	−	23.9826i	−0.353425	−	1.45684i	−0.820004	−	0.572358i	$-0.806029\pi$
$271$	−5.81811	−	23.9826i	−0.353425	−	1.45684i	0.466579	−	0.884480i	$-0.345486\pi$
$272$	0.502914	+	1.10123i	0.0304937	+	0.0667718i
$273$	1.64126	+	5.35559i	0.0993338	+	0.324135i
$274$	7.34938	+	4.72316i	0.443992	+	0.285337i
$275$	−7.71583	−	13.3642i	−0.465282	−	0.805893i
$276$	2.33243	+	4.19044i	0.140396	+	0.252235i
$277$	10.0040	−	17.3274i	0.601081	−	1.04110i	−0.391576	−	0.920146i	$-0.628070\pi$
$277$	10.0040	−	17.3274i	0.601081	−	1.04110i	0.992658	−	0.120958i	$-0.0385966\pi$
$278$	0.504571	−	10.5922i	0.0302621	−	0.635281i
$279$	0.521622	+	3.62796i	0.0312287	+	0.217200i
$280$	−4.18299	+	0.248642i	−0.249981	+	0.0148592i
$281$	18.1400	+	5.32640i	1.08214	+	0.317746i	0.773736	−	0.633508i	$-0.218386\pi$
$281$	18.1400	+	5.32640i	1.08214	+	0.317746i	0.308408	+	0.951254i	$0.400204\pi$
$282$	7.22378	−	0.689787i	0.430170	−	0.0410762i
$283$	−2.51915	−	7.27860i	−0.149748	−	0.432668i	0.845032	−	0.534716i	$-0.179581\pi$
$283$	−2.51915	−	7.27860i	−0.149748	−	0.432668i	−0.994779	+	0.102049i	$0.967460\pi$
$284$	−10.0968	−	7.94018i	−0.599133	−	0.471163i
$285$	−3.25751	−	3.10603i	−0.192958	−	0.183985i
$286$	8.58705	+	9.90998i	0.507763	+	0.585990i
$287$	9.13863	+	3.04293i	0.539437	+	0.179619i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	5.08080	−	14.6800i	0.298870	−	0.863529i
$290$	0.946490	−	3.90148i	0.0555798	−	0.229103i
$291$	−10.1059	−	7.94739i	−0.592420	−	0.465884i
$292$	0.637987	+	0.122962i	0.0373353	+	0.00719580i
$293$	−0.893732	+	1.95700i	−0.0522124	+	0.114329i	−0.933940	−	0.357429i	$-0.883653\pi$
$293$	−0.893732	+	1.95700i	−0.0522124	+	0.114329i	0.881728	+	0.471758i	$0.156381\pi$
$294$	3.35632	−	6.14289i	0.195745	−	0.358261i
$295$	5.04530	+	11.0477i	0.293748	+	0.643219i
$296$	3.10343	−	2.44056i	0.180383	−	0.141855i
$297$	−5.50511	+	2.83808i	−0.319439	+	0.164682i
$298$	10.5962	−	18.3531i	0.613819	−	1.06316i
$299$	1.28707	+	10.0716i	0.0744329	+	0.582454i
$300$	2.49154			0.143849
$301$	3.33651	+	31.0717i	0.192313	+	1.79094i
$302$	−2.66764	−	18.5539i	−0.153505	−	1.06765i
$303$	−4.24387	+	5.95968i	−0.243804	+	0.342375i
$304$	2.05676	−	1.96111i	0.117963	−	0.112478i
$305$	7.38624	+	10.3725i	0.422935	+	0.593929i
$306$	−1.18875	−	0.229113i	−0.0679565	−	0.0130975i
$307$	3.25787	−	22.6590i	0.185937	−	1.29322i	−0.656461	−	0.754360i	$-0.727947\pi$
$307$	3.25787	−	22.6590i	0.185937	−	1.29322i	0.842397	−	0.538857i	$-0.181144\pi$
$308$	1.36554	−	16.3298i	0.0778086	−	0.930475i
$309$	−0.883122	−	1.01918i	−0.0502390	−	0.0579789i
$310$	−5.15977	−	2.66004i	−0.293055	−	0.151080i
$311$	−0.459556	−	9.64727i	−0.0260590	−	0.547047i	−0.973717	−	0.227760i	$-0.926860\pi$
$311$	−0.459556	−	9.64727i	−0.0260590	−	0.547047i	0.947658	−	0.319286i	$-0.103443\pi$
$312$	−2.07889	+	0.400672i	−0.117694	+	0.0226836i
$313$	−0.480072	−	0.457748i	−0.0271353	−	0.0258734i	0.676390	−	0.736544i	$-0.263543\pi$
$313$	−0.480072	−	0.457748i	−0.0271353	−	0.0258734i	−0.703525	+	0.710670i	$0.748392\pi$
$314$	−2.53488	+	17.6305i	−0.143052	+	0.994945i
$315$	2.22383	−	3.55159i	0.125299	−	0.200109i
$316$	−4.49734	+	9.84781i	−0.252995	+	0.553982i
$317$	3.36227	+	13.8594i	0.188844	+	0.778424i	0.984889	+	0.173187i	$0.0554065\pi$
$317$	3.36227	+	13.8594i	0.188844	+	0.778424i	−0.796045	+	0.605237i	$0.793078\pi$
$318$	6.17573	+	0.589711i	0.346318	+	0.0330694i
$319$	14.5750	+	5.83495i	0.816044	+	0.326695i
$320$	0.0753607	−	1.58202i	0.00421279	−	0.0884374i
$321$	2.87086			0.160236
$322$	7.88265	−	9.94303i	0.439283	−	0.554104i
$323$	3.44045			0.191432
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	4.89711	+	1.96051i	0.271643	+	0.108749i
$326$	13.0241	+	1.24366i	0.721341	+	0.0688797i
$327$	1.48343	+	6.11480i	0.0820341	+	0.338149i
$328$	−1.51233	+	3.31154i	−0.0835044	+	0.182849i
$329$	−8.99788	−	16.9602i	−0.496069	−	0.935048i
$330$	1.39604	−	9.70967i	0.0768494	−	0.534500i
$331$	10.2003	+	9.72596i	0.560659	+	0.534587i	0.916539	−	0.399944i	$-0.130971\pi$
$331$	10.2003	+	9.72596i	0.560659	+	0.534587i	−0.355881	+	0.934531i	$0.615819\pi$
$332$	7.31413	−	1.40968i	0.401415	−	0.0773665i
$333$	0.187859	+	3.94364i	0.0102946	+	0.216110i
$334$	−13.4708	−	6.94470i	−0.737092	−	0.379997i
$335$	−1.38740	−	1.60114i	−0.0758016	−	0.0874797i
$336$	2.17308	+	1.50921i	0.118551	+	0.0823342i
$337$	−2.23381	+	15.5365i	−0.121683	+	0.846325i	0.833966	+	0.551817i	$0.186065\pi$
$337$	−2.23381	+	15.5365i	−0.121683	+	0.846325i	−0.955649	+	0.294509i	$0.904844\pi$
$338$	8.36377	+	1.61198i	0.454929	+	0.0876804i
$339$	5.33926	+	7.49793i	0.289989	+	0.407232i
$340$	1.38770	−	1.32316i	0.0752583	−	0.0717587i
$341$	13.1680	−	18.4919i	0.713088	−	1.00139i
$342$	0.404440	+	2.81294i	0.0218696	+	0.152106i
$343$	−18.4134	−	1.98682i	−0.994229	−	0.107278i
$344$	−11.8115			−0.636834
$345$	5.06361	−	5.66166i	0.272615	−	0.304813i
$346$	7.47244	−	12.9426i	0.401721	−	0.695801i
$347$	−17.2188	+	8.87690i	−0.924353	+	0.476537i	−0.853584	−	0.520956i	$-0.825576\pi$
$347$	−17.2188	+	8.87690i	−0.924353	+	0.476537i	−0.0707691	+	0.997493i	$0.522545\pi$
$348$	−1.99249	+	1.56691i	−0.106809	+	0.0839953i
$349$	−0.149341	−	0.327010i	−0.00799402	−	0.0175045i	0.905593	−	0.424148i	$-0.139426\pi$
$349$	−0.149341	−	0.327010i	−0.00799402	−	0.0175045i	−0.913587	+	0.406644i	$0.866699\pi$
$350$	−2.52187	−	6.09054i	−0.134800	−	0.325553i
$351$	0.879494	−	1.92582i	0.0469439	−	0.102793i
$352$	6.08169	+	1.17215i	0.324155	+	0.0624758i
$353$	16.2786	+	12.8016i	0.866423	+	0.681363i	0.949018	−	0.315220i	$-0.102078\pi$
$353$	16.2786	+	12.8016i	0.866423	+	0.681363i	−0.0825952	+	0.996583i	$0.526321\pi$
$354$	1.80788	−	7.45218i	0.0960877	−	0.396079i
$355$	−6.65383	+	19.2250i	−0.353148	+	1.02036i
$356$	−7.27175	+	4.67327i	−0.385402	+	0.247683i
$357$	0.643157	+	3.13779i	0.0340395	+	0.166070i
$358$	−7.83487	−	9.04192i	−0.414086	−	0.477880i
$359$	0.0402231	+	0.0383526i	0.00212289	+	0.00202418i	0.691140	−	0.722721i	$-0.257109\pi$
$359$	0.0402231	+	0.0383526i	0.00212289	+	0.00202418i	−0.689017	+	0.724745i	$0.741957\pi$
$360$	1.24496	+	0.979047i	0.0656151	+	0.0516003i
$361$	3.57282	+	10.3230i	0.188043	+	0.543315i
$362$	23.2877	−	2.22371i	1.22398	−	0.116876i
$363$	26.2526	+	7.70845i	1.37790	+	0.404589i
$364$	3.08363	+	4.67626i	0.161626	+	0.245103i
$365$	−0.146449	−	1.01857i	−0.00766547	−	0.0533145i
$366$	0.382553	−	8.03078i	0.0199964	−	0.419775i
$367$	−14.3052	+	24.7774i	−0.746726	+	1.29337i	0.202658	+	0.979250i	$0.435042\pi$
$367$	−14.3052	+	24.7774i	−0.746726	+	1.29337i	−0.949384	+	0.314118i	$0.898291\pi$
$368$	3.41853	+	3.36357i	0.178203	+	0.175338i
$369$	−1.82026	−	3.15279i	−0.0947592	−	0.164128i
$370$	−5.26041	−	3.38066i	−0.273476	−	0.175752i
$371$	−4.80936	−	15.6934i	−0.249690	−	0.814760i
$372$	1.52261	+	3.33404i	0.0789435	+	0.172862i
$373$	1.66221	+	6.85172i	0.0860659	+	0.354768i	0.998518	−	0.0544141i	$-0.0173291\pi$
$373$	1.66221	+	6.85172i	0.0860659	+	0.354768i	−0.912453	+	0.409182i	$0.865814\pi$
$374$	4.34937	+	6.10784i	0.224901	+	0.315829i
$375$	−3.88072	−	11.2126i	−0.200400	−	0.579017i
$376$	6.73683	−	2.69702i	0.347425	−	0.139088i
$377$	−5.14917	+	1.51193i	−0.265196	+	0.0778685i
$378$	−2.48988	+	0.894711i	−0.128065	+	0.0460190i
$379$	7.24688	−	4.65729i	0.372247	−	0.239229i	−0.341119	−	0.940020i	$-0.610806\pi$
$379$	7.24688	−	4.65729i	0.372247	−	0.239229i	0.713366	+	0.700791i	$0.247170\pi$
$380$	−4.00063	−	2.06247i	−0.205228	−	0.105802i
$381$	−12.8652	+	2.47956i	−0.659102	+	0.127032i
$382$	3.76628	−	15.5248i	0.192700	−	0.794319i
$383$	−13.9941	+	5.60241i	−0.715067	+	0.286270i	−0.700528	−	0.713625i	$-0.747052\pi$
$383$	−13.9941	+	5.60241i	−0.715067	+	0.286270i	−0.0145387	+	0.999894i	$0.504628\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	−25.1482	+	6.41525i	−1.28167	+	0.326951i
$386$	6.92544	+	2.03349i	0.352496	+	0.103502i
$387$	6.85135	−	9.62137i	0.348273	−	0.489082i
$388$	−11.9356	−	4.77830i	−0.605939	−	0.242581i
$389$	−31.9879	+	16.4909i	−1.62185	+	0.836122i	−0.623317	+	0.781969i	$0.714215\pi$
$389$	−31.9879	+	16.4909i	−1.62185	+	0.836122i	−0.998533	+	0.0541524i	$0.982754\pi$
$390$	1.67658	+	2.90392i	0.0848969	+	0.147046i
$391$	0.185199	+	5.80303i	0.00936590	+	0.293472i
$392$	1.48971	−	6.83965i	0.0752420	−	0.345454i
$393$	−16.6128	−	10.6764i	−0.838007	−	0.538554i
$394$	−12.7926	+	10.0602i	−0.644482	+	0.506826i
$395$	17.0689	+	1.62988i	0.858831	+	0.0820084i
$396$	−4.48253	+	4.27408i	−0.225256	+	0.214781i
$397$	−13.9385	+	1.33097i	−0.699555	+	0.0667994i	−0.438773	−	0.898598i	$-0.644587\pi$
$397$	−13.9385	+	1.33097i	−0.699555	+	0.0667994i	−0.260783	+	0.965398i	$0.583981\pi$
$398$	−3.47112	+	4.00588i	−0.173991	+	0.200797i
$399$	6.46683	−	3.83583i	0.323747	−	0.192031i
$400$	2.39062	−	0.701949i	0.119531	−	0.0350975i
$401$	−2.60033	+	7.51317i	−0.129854	+	0.375190i	−0.991121	−	0.132964i	$-0.957551\pi$
$401$	−2.60033	+	7.51317i	−0.129854	+	0.375190i	0.861266	+	0.508154i	$0.169672\pi$
$402$	0.0636488	+	1.33615i	0.00317452	+	0.0666413i
$403$	0.369231	+	7.75111i	0.0183927	+	0.386110i
$404$	−2.39293	+	6.91391i	−0.119053	+	0.343980i
$405$	−1.51966	+	0.446211i	−0.0755123	+	0.0221724i
$406$	5.84704	+	3.28463i	0.290183	+	0.163014i
$407$	16.0134	−	18.4804i	0.793753	−	0.916040i
$408$	−1.20515	+	0.115078i	−0.0596638	+	0.00569720i
$409$	−17.0982	+	16.3031i	−0.845450	+	0.806135i	−0.982855	−	0.184380i	$-0.940972\pi$
$409$	−17.0982	+	16.3031i	−0.845450	+	0.806135i	0.137405	+	0.990515i	$0.456124\pi$
$410$	5.73980	+	0.548084i	0.283468	+	0.0270680i
$411$	−6.86714	+	5.40038i	−0.338731	+	0.266381i
$412$	−1.13448	−	0.729089i	−0.0558920	−	0.0359196i
$413$	−20.0466	+	3.12355i	−0.986430	+	0.153700i
$414$	−4.72283	+	0.833591i	−0.232114	+	0.0409687i
$415$	−5.89870	−	10.2168i	−0.289556	−	0.501525i
$416$	−1.88179	+	0.970132i	−0.0922626	+	0.0475647i
$417$	9.84465	+	3.94120i	0.482095	+	0.193002i
$418$	10.2098	−	14.3377i	0.499379	−	0.701280i
$419$	−23.8611	−	7.00626i	−1.16569	−	0.342278i	−0.359050	−	0.933318i	$-0.616899\pi$
$419$	−23.8611	−	7.00626i	−1.16569	−	0.342278i	−0.806642	+	0.591040i	$0.798717\pi$
$420$	1.13315	−	4.03425i	0.0552922	−	0.196851i
$421$	7.22558	−	8.33877i	0.352153	−	0.406407i	−0.551842	−	0.833949i	$-0.686075\pi$
$421$	7.22558	−	8.33877i	0.352153	−	0.406407i	0.903996	+	0.427542i	$0.140620\pi$
$422$	−0.232314	+	0.0930044i	−0.0113089	+	0.00452738i
$423$	−1.71082	+	7.05208i	−0.0831828	+	0.342884i
$424$	6.09171	−	1.17408i	0.295840	−	0.0570185i
$425$	2.68103	+	1.38217i	0.130049	+	0.0670450i
$426$	10.8058	−	6.94447i	0.523543	−	0.336461i
$427$	−20.0183	+	7.19337i	−0.968755	+	0.348112i
$428$	2.75457	−	0.808815i	0.133147	−	0.0390955i
$429$	−12.1735	+	4.87353i	−0.587742	+	0.235296i
$430$	6.11852	+	17.6783i	0.295061	+	0.852524i
$431$	−2.61355	−	3.67021i	−0.125890	−	0.176788i	0.746821	−	0.665026i	$-0.231579\pi$
$431$	−2.61355	−	3.67021i	−0.125890	−	0.176788i	−0.872711	+	0.488238i	$0.837640\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	10.5728	+	23.1512i	0.508095	+	1.11257i	0.973753	+	0.227608i	$0.0730906\pi$
$433$	10.5728	+	23.1512i	0.508095	+	1.11257i	−0.465658	+	0.884965i	$0.654182\pi$
$434$	6.60888	−	7.09661i	0.317236	−	0.340648i
$435$	3.37734	+	2.17048i	0.161931	+	0.104067i
$436$	3.14608	+	5.44917i	0.150670	+	0.260968i
$437$	12.7308	−	4.86621i	0.608996	−	0.232782i
$438$	−0.324864	+	0.562681i	−0.0155226	+	0.0268859i
$439$	−1.47967	+	31.0621i	−0.0706207	+	1.48251i	0.634223	+	0.773150i	$0.281320\pi$
$439$	−1.47967	+	31.0621i	−0.0706207	+	1.48251i	−0.704844	+	0.709362i	$0.748983\pi$
$440$	−1.39604	−	9.70967i	−0.0665536	−	0.462890i
$441$	4.70729	+	5.18087i	0.224157	+	0.246708i
$442$	−2.45926	−	0.722104i	−0.116975	−	0.0343470i
$443$	−8.20689	+	0.783663i	−0.389921	+	0.0372330i	−0.288176	−	0.957578i	$-0.593049\pi$
$443$	−8.20689	+	0.783663i	−0.389921	+	0.0372330i	−0.101745	+	0.994810i	$0.532443\pi$
$444$	1.29130	+	3.73097i	0.0612824	+	0.177064i
$445$	10.7614	+	8.46283i	0.510137	+	0.401176i
$446$	5.78508	+	5.51606i	0.273931	+	0.261193i
$447$	13.8780	+	16.0161i	0.656407	+	0.757534i
$448$	2.51025	+	0.835850i	0.118598	+	0.0394902i
$449$	19.5349	−	12.5543i	0.921910	−	0.592476i	0.00869876	−	0.999962i	$-0.497231\pi$
$449$	19.5349	−	12.5543i	0.921910	−	0.592476i	0.913211	+	0.407487i	$0.133595\pi$
$450$	−0.814904	+	2.35451i	−0.0384150	+	0.110993i
$451$	−5.31590	+	21.9124i	−0.250316	+	1.03182i
$452$	7.23539	+	5.68997i	0.340324	+	0.267634i
$453$	18.4059	+	3.54745i	0.864785	+	0.166674i
$454$	−8.80402	+	19.2781i	−0.413193	+	0.904767i
$455$	5.40161	−	7.03764i	0.253231	−	0.329929i
$456$	1.18055	+	2.58505i	0.0552845	+	0.121056i
$457$	−4.16843	+	3.27809i	−0.194991	+	0.153342i	−0.710881	−	0.703312i	$-0.751704\pi$
$457$	−4.16843	+	3.27809i	−0.194991	+	0.153342i	0.515890	+	0.856655i	$0.327461\pi$
$458$	−16.2046	+	8.35404i	−0.757190	+	0.390358i
$459$	0.605316	−	1.04844i	0.0282537	−	0.0489369i
$460$	3.26342	−	6.85890i	0.152158	−	0.319798i
$461$	22.1247			1.03045			0.515226	−	0.857055i	$-0.327708\pi$
$461$	22.1247			1.03045			0.515226	+	0.857055i	$0.327708\pi$
$462$	14.9850	+	6.63138i	0.697167	+	0.308520i
$463$	1.02152	+	7.10483i	0.0474741	+	0.330190i	0.999693	+	0.0247735i	$0.00788644\pi$
$463$	1.02152	+	7.10483i	0.0474741	+	0.330190i	−0.952219	+	0.305416i	$0.901204\pi$
$464$	−1.47033	+	2.06479i	−0.0682584	+	0.0958555i
$465$	4.20134	−	4.00597i	0.194832	−	0.185772i
$466$	−12.4399	−	17.4694i	−0.576268	−	0.809255i
$467$	35.4513	+	6.83267i	1.64049	+	0.316178i	0.924282	−	0.381709i	$-0.124664\pi$
$467$	35.4513	+	6.83267i	1.64049	+	0.316178i	0.716207	+	0.697888i	$0.245877\pi$
$468$	0.301301	−	2.09560i	0.0139277	−	0.0968690i
$469$	3.20179	−	1.50800i	0.147845	−	0.0696332i
$470$	−7.52641	−	8.68594i	−0.347167	−	0.400652i
$471$	−15.8317	−	8.16183i	−0.729488	−	0.376077i
$472$	−0.364874	−	7.65965i	−0.0167947	−	0.352564i
$473$	−71.8339	+	13.8449i	−3.30293	+	0.636587i
$474$	−7.83525	−	7.47089i	−0.359885	−	0.343150i
$475$	1.00768	−	7.00857i	0.0462355	−	0.321575i
$476$	1.50112	+	2.82949i	0.0688039	+	0.129690i
$477$	−2.57716	+	5.64320i	−0.118000	+	0.258384i
$478$	−0.709660	−	2.92526i	−0.0324591	−	0.133798i
$479$	−11.2576	−	1.07497i	−0.514372	−	0.0491165i	−0.165357	−	0.986234i	$-0.552878\pi$
$479$	−11.2576	−	1.07497i	−0.514372	−	0.0491165i	−0.349015	+	0.937117i	$0.613484\pi$
$480$	1.47036	+	0.588643i	0.0671124	+	0.0268678i
$481$	−0.397724	+	8.34926i	−0.0181347	+	0.380694i
$482$	−10.4719			−0.476983
$483$	6.81801	+	10.7012i	0.310230	+	0.486919i
$484$	27.3609			1.24368
$485$	−0.968879	+	20.3393i	−0.0439945	+	0.923559i
$486$	0.928368	+	0.371662i	0.0421116	+	0.0168590i
$487$	16.2567	+	1.55232i	0.736660	+	0.0703425i	0.456640	−	0.889652i	$-0.349053\pi$
$487$	16.2567	+	1.55232i	0.736660	+	0.0703425i	0.280020	+	0.959994i	$0.409659\pi$
$488$	−1.89547	−	7.81325i	−0.0858041	−	0.353689i
$489$	−5.43504	+	11.9011i	−0.245781	+	0.538185i
$490$	−11.0086	+	1.31337i	−0.497318	+	0.0593320i
$491$	0.661231	−	4.59897i	0.0298410	−	0.207548i	−0.969446	−	0.245305i	$-0.921112\pi$
$491$	0.661231	−	4.59897i	0.0298410	−	0.207548i	0.999287	+	0.0377563i	$0.0120211\pi$
$492$	−2.63477	−	2.51225i	−0.118785	−	0.113261i
$493$	−3.01326	+	0.580758i	−0.135710	+	0.0261560i
$494$	0.286284	+	6.00983i	0.0128805	+	0.270395i
$495$	8.71904	+	4.49498i	0.391892	+	0.202034i
$496$	2.40024	+	2.77002i	0.107774	+	0.124378i
$497$	−27.9130	−	19.3856i	−1.25207	−	0.869565i
$498$	−1.06007	+	7.37293i	−0.0475027	+	0.330389i
$499$	−8.01741	−	1.54523i	−0.358908	−	0.0691739i	0.00660971	−	0.999978i	$-0.497896\pi$
$499$	−8.01741	−	1.54523i	−0.358908	−	0.0691739i	−0.365518	+	0.930804i	$0.619108\pi$
$500$	−6.88248	−	9.66510i	−0.307794	−	0.432236i
$501$	10.9686	−	10.4586i	0.490042	−	0.467254i
$502$	3.72859	−	5.23608i	0.166415	−	0.233698i
$503$	3.69716	+	25.7143i	0.164848	+	1.14654i	0.889335	+	0.457256i	$0.151168\pi$
$503$	3.69716	+	25.7143i	0.164848	+	1.14654i	−0.724487	+	0.689288i	$0.757923\pi$
$504$	−2.13695	+	1.55995i	−0.0951874	+	0.0694856i
$505$	11.5876			0.515643
$506$	24.7331	+	16.4492i	1.09952	+	0.731255i
$507$	−4.25885	+	7.37654i	−0.189142	+	0.327604i
$508$	−11.6455	+	6.00365i	−0.516684	+	0.266369i
$509$	−30.4799	+	23.9697i	−1.35100	+	1.06244i	−0.359386	+	0.933189i	$0.617014\pi$
$509$	−30.4799	+	23.9697i	−1.35100	+	1.06244i	−0.991612	+	0.129248i	$0.958744\pi$
$510$	0.796521	+	1.74414i	0.0352705	+	0.0772317i
$511$	1.70428	+	0.224596i	0.0753931	+	0.00993554i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−2.79051	−	0.537827i	−0.123204	−	0.0237456i
$514$	−2.05612	−	1.61695i	−0.0906917	−	0.0713208i
$515$	−0.503550	+	2.07566i	−0.0221891	+	0.0914646i
$516$	3.86317	−	11.1619i	0.170066	−	0.491374i
$517$	37.8100	−	24.2990i	1.66288	−	1.06867i
$518$	7.81328	−	6.93295i	0.343296	−	0.304616i
$519$	9.78681	+	11.2946i	0.429593	+	0.495777i
$520$	2.42679	+	2.31394i	0.106422	+	0.101473i
$521$	18.1851	+	14.3009i	0.796702	+	0.626534i	0.931253	−	0.364373i	$-0.118717\pi$
$521$	18.1851	+	14.3009i	0.796702	+	0.626534i	−0.134551	+	0.990907i	$0.542959\pi$
$522$	−0.829053	−	2.39539i	−0.0362867	−	0.104843i
$523$	28.7452	−	2.74483i	1.25694	−	0.120023i	0.554753	−	0.832015i	$-0.312813\pi$
$523$	28.7452	−	2.74483i	1.25694	−	0.120023i	0.702188	+	0.711992i	$0.252207\pi$
$524$	−18.9478	−	5.56358i	−0.827738	−	0.243046i
$525$	6.58039	−	0.391146i	0.287192	−	0.0170710i
$526$	0.148670	+	1.03402i	0.00648230	+	0.0450854i
$527$	−0.211135	+	4.43226i	−0.00919716	+	0.193072i
$528$	−3.09681	+	5.36383i	−0.134771	+	0.233431i
$529$	8.89315	+	21.2111i	0.386659	+	0.922223i
$530$	−4.91284	−	8.50929i	−0.213400	−	0.369620i
$531$	6.45102	+	4.14582i	0.279950	+	0.179913i
$532$	5.12420	−	5.50236i	0.222162	−	0.238558i
$533$	−3.20182	−	7.01101i	−0.138686	−	0.303681i
$534$	−2.03789	−	8.40029i	−0.0881880	−	0.363516i
$535$	−2.63746	−	3.70380i	−0.114027	−	0.160129i
$536$	0.437509	+	1.26410i	0.0188975	+	0.0546007i
$537$	11.1072	−	4.44664i	0.479309	−	0.191886i
$538$	−10.3332	+	3.03412i	−0.445498	+	0.130810i
$539$	1.04290	−	43.3428i	0.0449207	−	1.86691i
$540$	−1.33239	+	0.856273i	−0.0573368	+	0.0368481i
$541$	−35.6694	−	18.3888i	−1.53355	−	0.790598i	−0.535018	−	0.844841i	$-0.679695\pi$
$541$	−35.6694	−	18.3888i	−1.53355	−	0.790598i	−0.998528	+	0.0542427i	$0.982726\pi$
$542$	24.2322	−	4.67038i	1.04086	−	0.200610i
$543$	−5.51527	+	22.7342i	−0.236683	+	0.975619i
$544$	−1.12391	+	0.449946i	−0.0481873	+	0.0192913i
$545$	6.52608	−	7.53150i	0.279546	−	0.322614i
$546$	−5.42762	+	1.38458i	−0.232281	+	0.0592544i
$547$	28.2640	+	8.29906i	1.20848	+	0.354842i	0.823090	−	0.567911i	$-0.192248\pi$
$547$	28.2640	+	8.29906i	1.20848	+	0.354842i	0.385391	+	0.922753i	$0.374067\pi$
$548$	−5.06751	+	7.11632i	−0.216473	+	0.303994i
$549$	7.46397	+	2.98812i	0.318554	+	0.127530i
$550$	13.7162	−	7.07120i	0.584861	−	0.301517i
$551$	3.60179	+	6.23848i	0.153441	+	0.265768i
$552$	−4.29667	+	2.13040i	−0.182879	+	0.0906758i
$553$	−10.3319	+	26.7150i	−0.439356	+	1.13604i
$554$	16.8318	+	10.8171i	0.715114	+	0.459576i
$555$	4.91524	−	3.86539i	0.208640	−	0.164077i
$556$	10.5562	+	1.00800i	0.447684	+	0.0427487i
$557$	25.4896	−	24.3042i	1.08003	−	1.02980i	0.0805739	−	0.996749i	$-0.474325\pi$
$557$	25.4896	−	24.3042i	1.08003	−	1.02980i	0.999454	−	0.0330555i	$-0.0105238\pi$
$558$	−3.64867	+	0.348406i	−0.154460	+	0.0147492i
$559$	16.3759	−	18.8988i	0.692626	−	0.799334i
$560$	−0.0493257	−	4.19008i	−0.00208439	−	0.177063i
$561$	−7.19446	+	2.11248i	−0.303750	+	0.0891891i
$562$	−6.18350	+	17.8661i	−0.260835	+	0.753634i
$563$	−1.41829	−	29.7735i	−0.0597737	−	1.25480i	−0.807127	−	0.590377i	$-0.798979\pi$
$563$	−1.41829	−	29.7735i	−0.0597737	−	1.25480i	0.747354	−	0.664426i	$-0.231324\pi$
$564$	0.345285	+	7.24842i	0.0145391	+	0.305213i
$565$	4.76817	−	13.7767i	0.200598	−	0.579591i
$566$	7.39022	−	2.16996i	0.310634	−	0.0912104i
$567$	−0.0311437	−	2.64557i	−0.00130791	−	0.111103i
$568$	8.41161	−	9.70752i	0.352943	−	0.407318i
$569$	−10.7056	+	1.02226i	−0.448802	+	0.0428554i	−0.317010	−	0.948422i	$-0.602679\pi$
$569$	−10.7056	+	1.02226i	−0.448802	+	0.0428554i	−0.131791	+	0.991277i	$0.542073\pi$
$570$	3.25751	−	3.10603i	0.136442	−	0.130097i
$571$	37.3774	+	3.56911i	1.56420	+	0.149363i	0.840906	−	0.541182i	$-0.182023\pi$
$571$	37.3774	+	3.56911i	1.56420	+	0.149363i	0.723290	+	0.690544i	$0.242629\pi$
$572$	−10.3073	+	8.10579i	−0.430972	+	0.338920i
$573$	13.4391	+	8.63681i	0.561428	+	0.360808i
$574$	−3.47432	+	8.98350i	−0.145015	+	0.374964i
$575$	11.8756	+	1.32239i	0.495248	+	0.0551474i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.19835	+	0.617791i	−0.0498878	+	0.0257190i	−0.482990	−	0.875626i	$-0.660449\pi$
$577$	−1.19835	+	0.617791i	−0.0498878	+	0.0257190i	0.433102	+	0.901345i	$0.357419\pi$
$578$	14.4216	+	5.77354i	0.599860	+	0.240148i
$579$	−4.18674	+	5.87946i	−0.173995	+	0.244342i
$580$	3.85203	+	1.13106i	0.159947	+	0.0469646i
$581$	19.0960	−	4.87134i	0.792235	−	0.202097i
$582$	8.41925	−	9.71633i	0.348989	−	0.402755i
$583$	35.6717	−	14.2808i	1.47737	−	0.591450i
$584$	−0.153179	+	0.631413i	−0.00633860	+	0.0261281i
$585$	−3.29256	+	0.634589i	−0.136131	+	0.0262370i
$586$	−1.91226	−	0.985837i	−0.0789946	−	0.0407246i
$587$	35.8535	−	23.0417i	1.47983	−	0.951031i	0.482666	−	0.875804i	$-0.339668\pi$
$587$	35.8535	−	23.0417i	1.47983	−	0.951031i	0.997166	−	0.0752266i	$-0.0239680\pi$
$588$	5.97623	+	3.64481i	0.246456	+	0.150309i
$589$	9.99427	−	2.93458i	0.411807	−	0.120917i
$590$	−11.2752	+	4.51391i	−0.464193	+	0.185835i
$591$	−5.32286	−	15.3794i	−0.218953	−	0.632624i
$592$	2.29013	+	3.21604i	0.0941238	+	0.132178i
$593$	−2.11112	−	8.70214i	−0.0866932	−	0.357354i	0.911898	−	0.410417i	$-0.134617\pi$
$593$	−2.11112	−	8.70214i	−0.0866932	−	0.357354i	−0.998591	+	0.0530628i	$0.983102\pi$
$594$	−2.57292	−	5.63391i	−0.105568	−	0.231162i
$595$	3.45730	−	3.71245i	0.141736	−	0.152196i
$596$	17.8281	+	11.4574i	0.730267	+	0.469314i
$597$	−2.65027	−	4.59040i	−0.108468	−	0.187873i
$598$	−10.1214	+	0.806384i	−0.413895	+	0.0329755i
$599$	−7.02290	+	12.1640i	−0.286948	+	0.497008i	−0.973080	−	0.230469i	$-0.925974\pi$
$599$	−7.02290	+	12.1640i	−0.286948	+	0.497008i	0.686132	+	0.727477i	$0.259307\pi$
$600$	−0.118552	+	2.48872i	−0.00483988	+	0.101602i
$601$	4.67536	+	32.5178i	0.190712	+	1.32643i	0.830129	+	0.557571i	$0.188267\pi$
$601$	4.67536	+	32.5178i	0.190712	+	1.32643i	−0.639417	+	0.768860i	$0.720824\pi$
$602$	−31.1952	+	1.85428i	−1.27142	+	0.0755749i
$603$	−1.28348	−	0.376865i	−0.0522675	−	0.0153471i
$604$	18.6598	−	1.78179i	0.759255	−	0.0725001i
$605$	−14.1733	−	40.9511i	−0.576227	−	1.66490i
$606$	−5.75100	−	4.52264i	−0.233618	−	0.183720i
$607$	−10.9736	−	10.4633i	−0.445405	−	0.424693i	0.433893	−	0.900964i	$-0.357139\pi$
$607$	−10.9736	−	10.4633i	−0.445405	−	0.424693i	−0.879298	+	0.476272i	$0.841988\pi$
$608$	1.86103	+	2.14774i	0.0754746	+	0.0871024i
$609$	−5.01636	+	4.45116i	−0.203273	+	0.180370i
$610$	−10.7122	+	6.88433i	−0.433726	+	0.278738i
$611$	−5.02486	+	14.5184i	−0.203284	+	0.587351i
$612$	0.285417	−	1.17651i	0.0115373	−	0.0475574i
$613$	21.5200	+	16.9235i	0.869186	+	0.683535i	0.949681	−	0.313220i	$-0.101408\pi$
$613$	21.5200	+	16.9235i	0.869186	+	0.683535i	−0.0804949	+	0.996755i	$0.525650\pi$
$614$	22.4783	+	4.33234i	0.907151	+	0.174839i
$615$	−2.39524	+	5.24485i	−0.0965856	+	0.211493i
$616$	16.2463	+	2.14099i	0.654582	+	0.0862630i
$617$	−10.8924	−	23.8511i	−0.438512	−	0.960208i	−0.991869	−	0.127263i	$-0.959381\pi$
$617$	−10.8924	−	23.8511i	−0.438512	−	0.960208i	0.553357	−	0.832944i	$-0.313347\pi$
$618$	1.06004	−	0.833627i	0.0426412	−	0.0335334i
$619$	−36.3675	+	18.7487i	−1.46173	+	0.753576i	−0.991639	−	0.129041i	$-0.958810\pi$
$619$	−36.3675	+	18.7487i	−1.46173	+	0.753576i	−0.470094	+	0.882617i	$0.655780\pi$
$620$	2.90254	−	5.02735i	0.116569	−	0.201903i
$621$	0.756943	−	4.73572i	0.0303751	−	0.190038i
$622$	9.65821			0.387259
$623$	−18.4717	+	13.4841i	−0.740053	+	0.540230i
$624$	−0.301301	−	2.09560i	−0.0120617	−	0.0838910i
$625$	−3.67436	+	5.15992i	−0.146975	+	0.206397i
$626$	0.480072	−	0.457748i	0.0191875	−	0.0182953i
$627$	10.2098	+	14.3377i	0.407742	+	0.572593i
$628$	−17.4899	−	3.37090i	−0.697923	−	0.134514i
$629$	−0.680223	+	4.73106i	−0.0271223	+	0.188640i
$630$	3.44175	+	2.39030i	0.137123	+	0.0952320i
$631$	−22.1646	−	25.5793i	−0.882357	−	1.01829i	−0.999682	−	0.0252010i	$-0.991977\pi$
$631$	−22.1646	−	25.5793i	−0.882357	−	1.01829i	0.117325	−	0.993094i	$-0.462568\pi$
$632$	−9.62266	−	4.96083i	−0.382769	−	0.197331i
$633$	−0.0119068	−	0.249955i	−0.000473255	−	0.00993484i
$634$	−14.0037	+	2.69900i	−0.556159	+	0.107191i
$635$	15.0182	+	14.3198i	0.595978	+	0.568264i
$636$	−0.882896	+	6.14068i	−0.0350091	+	0.243494i
$637$	8.87826	+	11.8663i	0.351769	+	0.470161i
$638$	−6.52185	+	14.2809i	−0.258203	+	0.565385i
$639$	3.02830	+	12.4828i	0.119798	+	0.493812i
$640$	1.57664	+	0.150551i	0.0623221	+	0.00595104i
$641$	21.4562	+	8.58978i	0.847471	+	0.339276i	0.754425	−	0.656386i	$-0.227916\pi$
$641$	21.4562	+	8.58978i	0.847471	+	0.339276i	0.0930453	+	0.995662i	$0.470340\pi$
$642$	−0.136601	+	2.86761i	−0.00539121	+	0.113176i
$643$	9.76940			0.385267			0.192634	−	0.981271i	$-0.438297\pi$
$643$	9.76940			0.385267			0.192634	+	0.981271i	$0.438297\pi$
$644$	9.55670	+	8.34683i	0.376587	+	0.328911i
$645$	−18.7072			−0.736595
$646$	−0.163703	+	3.43656i	−0.00644082	+	0.135210i
$647$	−44.6419	−	17.8719i	−1.75505	−	0.702617i	−0.998833	−	0.0482988i	$-0.984620\pi$
$647$	−44.6419	−	17.8719i	−1.75505	−	0.702617i	−0.756219	−	0.654318i	$-0.772956\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−11.1973	−	46.1559i	−0.439533	−	1.81178i
$650$	−2.19130	+	4.79827i	−0.0859498	+	0.188204i
$651$	4.54475	+	8.56647i	0.178123	+	0.335747i
$652$	−1.86196	+	12.9502i	−0.0729200	+	0.507170i
$653$	14.1012	+	13.4454i	0.551822	+	0.526161i	0.913875	−	0.405997i	$-0.133076\pi$
$653$	14.1012	+	13.4454i	0.551822	+	0.526161i	−0.362053	+	0.932158i	$0.617924\pi$
$654$	−6.17846	+	1.19080i	−0.241597	+	0.0465640i
$655$	1.48820	+	31.2412i	0.0581489	+	1.22070i
$656$	−3.23583	−	1.66819i	−0.126338	−	0.0651317i
$657$	−0.425481	−	0.491032i	−0.0165996	−	0.0191570i
$658$	17.3692	−	8.18068i	0.677121	−	0.318916i
$659$	4.07854	−	28.3669i	0.158878	−	1.10502i	−0.741829	−	0.670589i	$-0.766041\pi$
$659$	4.07854	−	28.3669i	0.158878	−	1.10502i	0.900706	−	0.434428i	$-0.143050\pi$
$660$	9.63224	+	1.85646i	0.374935	+	0.0722627i
$661$	−23.2874	−	32.7026i	−0.905776	−	1.27198i	−0.961856	−	0.273557i	$-0.911800\pi$
$661$	−23.2874	−	32.7026i	−0.905776	−	1.27198i	0.0560801	−	0.998426i	$-0.482140\pi$
$662$	−10.2003	+	9.72596i	−0.396446	+	0.378010i
$663$	1.48673	−	2.08783i	0.0577400	−	0.0810844i
$664$	1.06007	+	7.37293i	0.0411386	+	0.286125i
$665$	−10.8898	−	4.81911i	−0.422289	−	0.186877i
$666$	−3.94811			−0.152986
$667$	−10.3286	+	6.41097i	−0.399925	+	0.248234i
$668$	7.57781	−	13.1251i	0.293194	−	0.507827i
$669$	−7.10480	+	3.66278i	−0.274687	+	0.141611i
$670$	1.66534	−	1.30964i	0.0643378	−	0.0505958i
$671$	−20.6860	−	45.2960i	−0.798574	−	1.74863i
$672$	−1.61090	+	2.09881i	−0.0621419	+	0.0809633i
$673$	7.00543	−	15.3397i	0.270039	−	0.591304i	−0.725225	−	0.688512i	$-0.758264\pi$
$673$	7.00543	−	15.3397i	0.270039	−	0.591304i	0.995264	+	0.0972086i	$0.0309914\pi$
$674$	−15.4126	−	2.97053i	−0.593671	−	0.114421i
$675$	−1.95849	−	1.54017i	−0.0753822	−	0.0592812i
$676$	−2.00812	+	8.27759i	−0.0772355	+	0.318369i
$677$	−10.9917	+	31.7585i	−0.422446	+	1.22058i	0.510285	+	0.860006i	$0.329540\pi$
$677$	−10.9917	+	31.7585i	−0.422446	+	1.22058i	−0.932731	+	0.360573i	$0.882581\pi$
$678$	−7.74349	+	4.97644i	−0.297387	+	0.191119i
$679$	−32.2732	−	10.7461i	−1.23853	−	0.412399i
$680$	1.25564	+	1.44908i	0.0481515	+	0.0555698i
$681$	−15.3383	−	14.6251i	−0.587766	−	0.560434i
$682$	17.8444	+	14.0330i	0.683297	+	0.537351i
$683$	−6.22280	−	17.9796i	−0.238109	−	0.687970i	−0.999225	−	0.0393551i	$-0.987470\pi$
$683$	−6.22280	−	17.9796i	−0.238109	−	0.687970i	0.761116	−	0.648615i	$-0.224652\pi$
$684$	−2.82900	+	0.270137i	−0.108169	+	0.0103289i
$685$	13.2760	+	3.89820i	0.507252	+	0.148943i
$686$	2.86072	−	18.2980i	0.109223	−	0.698620i
$687$	−2.59458	−	18.0457i	−0.0989892	−	0.688485i
$688$	0.562014	−	11.7981i	0.0214266	−	0.449799i
$689$	−6.56720	+	11.3747i	−0.250190	+	0.433343i
$690$	5.41431	+	5.32726i	0.206119	+	0.202805i
$691$	−2.72561	−	4.72090i	−0.103687	−	0.179592i	0.809514	−	0.587101i	$-0.199731\pi$
$691$	−2.72561	−	4.72090i	−0.103687	−	0.179592i	−0.913201	+	0.407509i	$0.866397\pi$
$692$	12.5724	+	8.07981i	0.477932	+	0.307148i
$693$	−11.1678	+	11.9920i	−0.424229	+	0.455537i
$694$	−8.04754	−	17.6217i	−0.305481	−	0.668909i
$695$	−3.95960	−	16.3217i	−0.150196	−	0.619117i
$696$	−1.47033	−	2.06479i	−0.0557327	−	0.0782657i
$697$	−1.44150	−	4.16494i	−0.0546006	−	0.157758i
$698$	0.333746	−	0.133612i	0.0126325	−	0.00505727i
$699$	20.5773	−	6.04204i	0.778305	−	0.228531i
$700$	6.20364	−	2.22921i	0.234476	−	0.0842563i
$701$	−16.6071	+	10.6727i	−0.627240	+	0.403103i	−0.815287	−	0.579057i	$-0.803421\pi$
$701$	−16.6071	+	10.6727i	−0.627240	+	0.403103i	0.188047	+	0.982160i	$0.439784\pi$
$702$	1.88179	+	0.970132i	0.0710237	+	0.0366153i
$703$	11.0173	−	2.12340i	0.415524	−	0.0800856i
$704$	−1.46020	+	6.01903i	−0.0550334	+	0.226851i
$705$	10.6699	−	4.27157i	0.401850	−	0.160877i
$706$	−13.5617	+	15.6510i	−0.510402	+	0.589035i
$707$	−5.23452	+	18.6359i	−0.196865	+	0.700876i
$708$	7.35772	+	2.16042i	0.276520	+	0.0811936i
$709$	16.4247	−	23.0653i	0.616843	−	0.866235i	−0.381465	−	0.924383i	$-0.624580\pi$
$709$	16.4247	−	23.0653i	0.616843	−	0.866235i	0.998308	+	0.0581482i	$0.0185196\pi$
$710$	−18.8866	−	7.56105i	−0.708801	−	0.283761i
$711$	9.62266	−	4.96083i	0.360878	−	0.186046i
$712$	−4.32197	−	7.48588i	−0.161973	−	0.280545i
$713$	5.48776	+	16.6994i	0.205518	+	0.625398i
$714$	−3.16484	+	0.493127i	−0.118441	+	0.0184548i
$715$	17.4713	+	11.2281i	0.653390	+	0.419908i
$716$	9.40448	−	7.39576i	0.351462	−	0.276393i
$717$	2.99648	+	0.286129i	0.111906	+	0.0106857i
$718$	−0.0402231	+	0.0383526i	−0.00150111	+	0.00143131i
$719$	−11.9556	+	1.14162i	−0.445868	+	0.0425752i	−0.315576	−	0.948900i	$-0.602198\pi$
$719$	−11.9556	+	1.14162i	−0.445868	+	0.0425752i	−0.130292	+	0.991476i	$0.541592\pi$
$720$	−1.03718	+	1.19696i	−0.0386532	+	0.0446082i
$721$	−3.11073	−	1.74749i	−0.115850	−	0.0650798i
$722$	−10.4813	+	3.07759i	−0.390074	+	0.114536i
$723$	3.42503	−	9.89598i	0.127378	−	0.368035i
$724$	1.11312	+	23.3672i	0.0413686	+	0.868434i
$725$	0.300507	+	6.30842i	0.0111606	+	0.234289i
$726$	−8.94887	+	25.8561i	−0.332124	+	0.959608i
$727$	−36.7986	+	10.8050i	−1.36478	+	0.400737i	−0.880447	−	0.474145i	$-0.842757\pi$
$727$	−36.7986	+	10.8050i	−1.36478	+	0.400737i	−0.484337	+	0.874882i	$0.660939\pi$
$728$	−4.81769	+	2.85763i	−0.178555	+	0.105911i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	1.02439	−	0.0978170i	0.0379142	−	0.00362037i
$731$	10.3489	−	9.86770i	0.382770	−	0.364970i
$732$	8.00348	+	0.764240i	0.295817	+	0.0282471i
$733$	−17.5952	+	13.8370i	−0.649892	+	0.511081i	−0.887813	−	0.460204i	$-0.847776\pi$
$733$	−17.5952	+	13.8370i	−0.649892	+	0.511081i	0.237921	+	0.971284i	$0.423534\pi$
$734$	−24.0686	−	15.4680i	−0.888389	−	0.570933i
$735$	2.35943	−	10.8327i	0.0870287	−	0.399570i
$736$	−3.52242	+	3.25462i	−0.129838	+	0.119967i
$737$	4.14250	+	7.17503i	0.152591	+	0.264296i
$738$	3.23583	−	1.66819i	0.119113	−	0.0614068i
$739$	−3.49789	−	1.40034i	−0.128672	−	0.0515125i	0.306433	−	0.951892i	$-0.400864\pi$
$739$	−3.49789	−	1.40034i	−0.128672	−	0.0515125i	−0.435105	+	0.900380i	$0.643289\pi$
$740$	3.62713	−	5.09359i	0.133336	−	0.187244i
$741$	−5.77293	−	1.69509i	−0.212074	−	0.0622705i
$742$	15.9044	−	4.05719i	0.583871	−	0.148944i
$743$	8.90800	−	10.2804i	0.326803	−	0.377150i	−0.568443	−	0.822722i	$-0.692454\pi$
$743$	8.90800	−	10.2804i	0.326803	−	0.377150i	0.895246	+	0.445572i	$0.147000\pi$
$744$	−3.40272	+	1.36224i	−0.124750	+	0.0499422i
$745$	7.91315	−	32.6185i	0.289915	−	1.19505i
$746$	−6.92305	+	1.33431i	−0.253471	+	0.0488525i
$747$	−6.62071	−	3.41321i	−0.242239	−	0.124883i
$748$	−6.30787	+	4.05382i	−0.230639	+	0.148223i
$749$	7.14809	−	2.56859i	0.261186	−	0.0938543i
$750$	11.3846	−	3.34281i	0.415705	−	0.122062i
$751$	9.24461	−	3.70098i	0.337341	−	0.135051i	−0.196806	−	0.980442i	$-0.563057\pi$
$751$	9.24461	−	3.70098i	0.337341	−	0.135051i	0.534147	+	0.845392i	$0.320633\pi$
$752$	2.37341	+	6.85753i	0.0865495	+	0.250068i
$753$	3.72859	+	5.23608i	0.135877	+	0.190813i
$754$	−1.26521	−	5.21528i	−0.0460763	−	0.189929i
$755$	−12.3328	−	27.0051i	−0.448838	−	0.982817i
$756$	−0.775225	−	2.52963i	−0.0281947	−	0.0920017i
$757$	−10.4881	−	6.74028i	−0.381196	−	0.244980i	0.335984	−	0.941868i	$-0.390931\pi$
$757$	−10.4881	−	6.74028i	−0.381196	−	0.244980i	−0.717180	+	0.696888i	$0.754568\pi$
$758$	4.30719	+	7.46027i	0.156444	+	0.270969i
$759$	−23.6339	+	17.9928i	−0.857856	+	0.653096i
$760$	2.25049	−	3.89796i	0.0816338	−	0.141394i
$761$	1.74959	−	36.7283i	0.0634225	−	1.33140i	−0.712989	−	0.701175i	$-0.752659\pi$
$761$	1.74959	−	36.7283i	0.0634225	−	1.33140i	0.776412	−	0.630226i	$-0.217038\pi$
$762$	−1.86460	−	12.9686i	−0.0675473	−	0.469802i
$763$	9.16455	+	13.8979i	0.331779	+	0.503136i
$764$	15.3280	+	4.50072i	0.554549	+	0.162830i
$765$	−1.90873	+	0.182261i	−0.0690102	+	0.00658968i
$766$	−4.93019	−	14.2449i	−0.178135	−	0.514688i
$767$	12.7616	+	10.0358i	0.460793	+	0.362372i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	0.846221	+	0.976591i	0.0305155	+	0.0352168i	0.770802	−	0.637075i	$-0.219856\pi$
$769$	0.846221	+	0.976591i	0.0305155	+	0.0352168i	−0.740287	+	0.672291i	$0.765310\pi$
$770$	−5.21138	−	25.4249i	−0.187805	−	0.916251i
$771$	2.20051	−	1.41418i	0.0792496	−	0.0509306i
$772$	−2.36072	+	6.82084i	−0.0849640	+	0.245487i
$773$	−3.09949	+	12.7763i	−0.111481	+	0.459530i	0.888519	+	0.458840i	$0.151735\pi$
$773$	−3.09949	+	12.7763i	−0.111481	+	0.459530i	−1.00000		0.000690236i	$0.999780\pi$
$774$	9.28447	+	7.30139i	0.333723	+	0.262443i
$775$	8.96714	+	1.72827i	0.322109	+	0.0620815i
$776$	5.34081	−	11.6947i	0.191724	−	0.419816i
$777$	3.99617	+	9.65111i	0.143362	+	0.346231i
$778$	−14.9502	−	32.7363i	−0.535990	−	1.17365i
$779$	−8.13242	+	6.39541i	−0.291374	+	0.229139i
$780$	−2.98041	+	1.53651i	−0.106716	+	0.0550157i
$781$	39.7781	−	68.8978i	1.42337	−	2.46536i
$782$	−5.80527	−	0.0911303i	−0.207596	−	0.00325881i
$783$	2.53480			0.0905865
$784$	6.76101	+	1.81347i	0.241465	+	0.0647668i
$785$	4.01477	+	27.9233i	0.143293	+	0.996627i
$786$	11.4548	−	16.0860i	0.408579	−	0.573769i
$787$	23.3936	−	22.3058i	0.833893	−	0.795115i	−0.147108	−	0.989120i	$-0.546996\pi$
$787$	23.3936	−	22.3058i	0.833893	−	0.795115i	0.981000	+	0.194005i	$0.0621479\pi$
$788$	−9.44013	−	13.2568i	−0.336291	−	0.472254i
$789$	−1.02577	−	0.197702i	−0.0365185	−	0.00703837i
$790$	−2.44021	+	16.9720i	−0.0868188	+	0.603838i
$791$	20.0026	+	13.8918i	0.711210	+	0.493937i
$792$	−4.05596	−	4.68082i	−0.144122	−	0.166326i
$793$	15.1294	+	7.79975i	0.537261	+	0.276977i
$794$	−0.666239	−	13.9861i	−0.0236439	−	0.496347i
$795$	9.64812	−	1.85952i	0.342184	−	0.0659505i
$796$	−3.83618	−	3.65779i	−0.135970	−	0.129647i
$797$	4.19819	−	29.1990i	0.148707	−	1.03428i	−0.769632	−	0.638488i	$-0.779560\pi$
$797$	4.19819	−	29.1990i	0.148707	−	1.03428i	0.918339	−	0.395795i	$-0.129531\pi$
$798$	3.52378	+	6.64202i	0.124740	+	0.235125i
$799$	−3.64947	+	7.99122i	−0.129109	+	0.282709i
$800$	0.587404	+	2.42131i	0.0207679	+	0.0856063i
$801$	8.60481	+	0.821659i	0.304036	+	0.0290319i
$802$	−7.38093	−	2.95488i	−0.260630	−	0.104340i
$803$	−0.191478	+	4.01961i	−0.00675710	+	0.141849i
$804$	−1.33767			−0.0471759
$805$	7.54221	−	18.6273i	0.265828	−	0.656526i
$806$	−7.75990			−0.273331
$807$	0.512433	−	10.7573i	0.0180385	−	0.378675i
$808$	−6.79222	−	2.71919i	−0.238949	−	0.0956609i
$809$	−24.0135	−	2.29301i	−0.844269	−	0.0806179i	−0.336048	−	0.941845i	$-0.609090\pi$
$809$	−24.0135	−	2.29301i	−0.844269	−	0.0806179i	−0.508220	+	0.861227i	$0.669697\pi$
$810$	−0.373397	−	1.53917i	−0.0131199	−	0.0540808i
$811$	−20.4266	+	44.7279i	−0.717274	+	1.57061i	0.100412	+	0.994946i	$0.467984\pi$
$811$	−20.4266	+	44.7279i	−0.717274	+	1.57061i	−0.817686	+	0.575664i	$0.804743\pi$
$812$	−3.55912	+	5.68412i	−0.124901	+	0.199474i
$813$	−3.51208	+	24.4270i	−0.123174	+	0.856693i
$814$	17.6975	+	16.8746i	0.620298	+	0.591453i
$815$	20.3471	−	3.92159i	0.712729	−	0.137367i
$816$	−0.0576041	−	1.20926i	−0.00201655	−	0.0423326i
$817$	−29.8353	−	15.3812i	−1.04381	−	0.538119i
$818$	−15.4710	−	17.8545i	−0.540933	−	0.624269i
$819$	0.466777	−	5.58196i	0.0163105	−	0.195049i
$820$	−0.820574	+	5.70722i	−0.0286557	+	0.199305i
$821$	39.6023	+	7.63271i	1.38213	+	0.266383i	0.825511	−	0.564385i	$-0.190887\pi$
$821$	39.6023	+	7.63271i	1.38213	+	0.266383i	0.556617	+	0.830769i	$0.312099\pi$
$822$	−5.06751	−	7.11632i	−0.176750	−	0.248210i
$823$	−4.34286	+	4.14090i	−0.151382	+	0.144343i	−0.761986	−	0.647594i	$-0.775775\pi$
$823$	−4.34286	+	4.14090i	−0.151382	+	0.144343i	0.610603	+	0.791937i	$0.290927\pi$
$824$	0.782244	−	1.09851i	0.0272508	−	0.0382683i
$825$	2.19616	+	15.2746i	0.0764603	+	0.531793i
$826$	−2.16615	−	20.1725i	−0.0753700	−	0.701893i
$827$	22.1803			0.771284			0.385642	−	0.922648i	$-0.373980\pi$
$827$	22.1803			0.771284			0.385642	+	0.922648i	$0.373980\pi$
$828$	−0.607925	−	4.75714i	−0.0211269	−	0.165322i
$829$	−0.248449	+	0.430327i	−0.00862900	+	0.0149459i	−0.870308	−	0.492508i	$-0.836080\pi$
$829$	−0.248449	+	0.430327i	−0.00862900	+	0.0149459i	0.861679	+	0.507454i	$0.169413\pi$
$830$	10.4859	−	5.40588i	0.363972	−	0.187641i
$831$	−15.7273	+	12.3681i	−0.545575	+	0.429045i
$832$	−0.879494	−	1.92582i	−0.0304910	−	0.0667659i
$833$	4.40880	+	7.23728i	0.152756	+	0.250757i
$834$	−4.40517	+	9.64597i	−0.152538	+	0.334013i
$835$	−23.5698	−	4.54272i	−0.815668	−	0.157207i
$836$	13.8357	+	10.8805i	0.478516	+	0.376310i
$837$	0.864119	−	3.56195i	0.0298683	−	0.123119i
$838$	8.13368	−	23.5007i	0.280973	−	0.811819i
$839$	−6.90765	+	4.43928i	−0.238479	+	0.153261i	−0.654422	−	0.756130i	$-0.727088\pi$
$839$	−6.90765	+	4.43928i	−0.238479	+	0.153261i	0.415943	+	0.909391i	$0.363452\pi$
$840$	3.97576	+	1.32383i	0.137177	+	0.0456764i
$841$	14.7833	+	17.0609i	0.509770	+	0.588306i
$842$	7.98552	+	7.61418i	0.275199	+	0.262402i
$843$	−14.8610	−	11.6868i	−0.511841	−	0.402516i
$844$	−0.0818451	−	0.236476i	−0.00281723	−	0.00813984i
$845$	13.4293	−	1.28235i	0.461983	−	0.0441140i
$846$	−6.96269	−	2.04443i	−0.239382	−	0.0702890i
$847$	72.2625	−	4.29537i	2.48297	−	0.147591i
$848$	0.882896	+	6.14068i	0.0303188	+	0.210872i
$849$	−0.366486	+	7.69349i	−0.0125778	+	0.264040i
$850$	−1.50817	+	2.61223i	−0.0517298	+	0.0895987i
$851$	4.17461	+	18.4686i	0.143104	+	0.633094i
$852$	6.42244	+	11.1240i	0.220029	+	0.381102i
$853$	9.76436	+	6.27517i	0.334325	+	0.214858i	0.697023	−	0.717049i	$-0.254508\pi$
$853$	9.76436	+	6.27517i	0.334325	+	0.214858i	−0.362697	+	0.931907i	$0.618144\pi$
$854$	−6.23272	−	20.3379i	−0.213279	−	0.695950i
$855$	1.86977	+	4.09424i	0.0639449	+	0.140020i
$856$	0.676831	+	2.78994i	0.0231336	+	0.0953580i
$857$	1.96926	+	2.76544i	0.0672687	+	0.0944656i	0.846840	−	0.531848i	$-0.178502\pi$
$857$	1.96926	+	2.76544i	0.0672687	+	0.0944656i	−0.779571	+	0.626314i	$0.784563\pi$
$858$	−4.28877	−	12.3916i	−0.146416	−	0.423042i
$859$	8.53829	−	3.41822i	0.291323	−	0.116628i	−0.221398	−	0.975184i	$-0.571062\pi$
$859$	8.53829	−	3.41822i	0.291323	−	0.116628i	0.512721	+	0.858556i	$0.328638\pi$
$860$	−17.9494	+	5.27042i	−0.612070	+	0.179720i
$861$	−7.35307	−	6.22145i	−0.250592	−	0.212026i
$862$	3.79042	−	2.43595i	0.129102	−	0.0829688i
$863$	−23.2995	−	12.0118i	−0.793126	−	0.408885i	0.0135284	−	0.999908i	$-0.495694\pi$
$863$	−23.2995	−	12.0118i	−0.793126	−	0.408885i	−0.806654	+	0.591024i	$0.798724\pi$
$864$	0.981929	−	0.189251i	0.0334059	−	0.00643846i
$865$	5.58038	−	23.0026i	0.189739	−	0.782113i
$866$	−23.6280	+	9.45923i	−0.802912	+	0.321438i
$867$	−10.1729	+	11.7401i	−0.345488	+	0.398715i
$868$	6.77411	+	6.93907i	0.229928	+	0.235527i
$869$	−64.3369	−	18.8910i	−2.18248	−	0.640834i
$870$	−2.32873	+	3.27024i	−0.0789512	+	0.110871i
$871$	−2.62918	−	1.05256i	−0.0890862	−	0.0356647i
$872$	−5.59270	+	2.88324i	−0.189393	+	0.0976387i
$873$	6.42828	+	11.1341i	0.217564	+	0.376832i
$874$	4.25494	+	12.9479i	0.143926	+	0.437970i
$875$	−19.6946	−	24.4459i	−0.665798	−	0.826422i
$876$	−0.546586	−	0.351269i	−0.0184674	−	0.0118683i
$877$	−28.7700	+	22.6250i	−0.971496	+	0.763993i	−0.971751	−	0.236007i	$-0.924161\pi$
$877$	−28.7700	+	22.6250i	−0.971496	+	0.763993i	0.000255700		1.00000i	$0.499919\pi$
$878$	−30.9565	−	2.95599i	−1.04473	−	0.0997597i
$879$	1.55705	−	1.48465i	0.0525182	−	0.0500760i
$880$	9.76510	−	0.932454i	0.329181	−	0.0314330i
$881$	−14.5567	+	16.7993i	−0.490427	+	0.565983i	−0.945980	−	0.324226i	$-0.894896\pi$
$881$	−14.5567	+	16.7993i	−0.490427	+	0.565983i	0.455553	+	0.890209i	$0.349442\pi$
$882$	−5.39898	+	4.45544i	−0.181793	+	0.150023i
$883$	−51.7047	+	15.1819i	−1.74000	+	0.510911i	−0.988811	−	0.149175i	$-0.952338\pi$
$883$	−51.7047	+	15.1819i	−1.74000	+	0.510911i	−0.751191	+	0.660085i	$0.770520\pi$
$884$	0.838302	−	2.42212i	0.0281952	−	0.0814645i
$885$	−0.577892	−	12.1314i	−0.0194256	−	0.407794i
$886$	−0.392276	−	8.23488i	−0.0131788	−	0.276656i
$887$	−15.0561	+	43.5019i	−0.505536	+	1.46065i	0.346942	+	0.937886i	$0.387220\pi$
$887$	−15.0561	+	43.5019i	−0.505536	+	1.46065i	−0.852478	+	0.522763i	$0.824901\pi$
$888$	−3.78819	+	1.11231i	−0.127123	+	0.0373267i
$889$	−29.8142	+	17.6844i	−0.999936	+	0.593116i
$890$	−8.96529	+	10.3465i	−0.300517	+	0.346815i
$891$	6.16557	−	0.588741i	0.206554	−	0.0197236i
$892$	−5.78508	+	5.51606i	−0.193699	+	0.184691i
$893$	20.5290	+	1.96028i	0.686978	+	0.0655984i
$894$	−16.6583	+	13.1002i	−0.557136	+	0.438137i
$895$	−15.9409	−	10.2446i	−0.532846	−	0.342439i
$896$	−0.954346	+	2.46764i	−0.0318824	+	0.0824379i
$897$	2.54835	−	9.82848i	0.0850870	−	0.328163i
$898$	11.6106	+	20.1102i	0.387451	+	0.671085i
$899$	−8.25793	+	4.25726i	−0.275417	+	0.141988i
$900$	−2.31307	−	0.926013i	−0.0771023	−	0.0308671i
$901$	−4.35654	+	6.11791i	−0.145137	+	0.203817i
$902$	−21.6347	−	6.35251i	−0.720356	−	0.211516i
$903$	8.45067	−	30.0860i	0.281221	−	1.00120i
$904$	−6.02780	+	6.95646i	−0.200482	+	0.231368i
$905$	34.3971	−	13.7705i	1.14340	−	0.457747i
$906$	−4.41922	+	18.2163i	−0.146819	+	0.605195i
$907$	37.8653	−	7.29794i	1.25730	−	0.242324i	0.483266	−	0.875473i	$-0.339450\pi$
$907$	37.8653	−	7.29794i	1.25730	−	0.242324i	0.774030	+	0.633149i	$0.218238\pi$
$908$	−18.8374	−	9.71134i	−0.625140	−	0.322282i
$909$	6.15486	−	3.95549i	0.204144	−	0.131195i
$910$	6.77265	+	5.73035i	0.224511	+	0.189959i
$911$	−18.5593	+	5.44951i	−0.614898	+	0.180550i	−0.574326	−	0.818626i	$-0.694736\pi$
$911$	−18.5593	+	5.44951i	−0.614898	+	0.180550i	−0.0405713	+	0.999177i	$0.512918\pi$
$912$	−2.63830	+	1.05622i	−0.0873628	+	0.0349748i
$913$	15.0892	+	43.5973i	0.499379	+	1.44286i
$914$	−3.07603	−	4.31968i	−0.101746	−	0.142882i
$915$	−3.00207	−	12.3747i	−0.0992455	−	0.409095i
$916$	−7.57353	−	16.5837i	−0.250236	−	0.547941i
$917$	−50.9163	−	11.7193i	−1.68140	−	0.387005i
$918$	1.01845	+	0.654517i	0.0336138	+	0.0216023i
$919$	2.89752	+	5.01866i	0.0955805	+	0.165550i	0.909851	−	0.414936i	$-0.136196\pi$
$919$	2.89752	+	5.01866i	0.0955805	+	0.165550i	−0.814270	+	0.580486i	$0.802863\pi$
$920$	6.69586	+	3.58609i	0.220756	+	0.118230i
$921$	−11.4460	+	19.8251i	−0.377158	+	0.653258i
$922$	−1.05274	+	22.0997i	−0.0346700	+	0.727814i
$923$	3.87018	+	26.9177i	0.127389	+	0.886007i
$924$	−7.33688	+	14.6525i	−0.241366	+	0.482033i
$925$	9.43843	+	2.77137i	0.310334	+	0.0911222i
$926$	−7.14539	+	0.682302i	−0.234812	+	0.0224218i
$927$	0.441072	+	1.27439i	0.0144867	+	0.0418566i
$928$	−1.99249	−	1.56691i	−0.0654067	−	0.0514364i
$929$	−2.58413	−	2.46397i	−0.0847827	−	0.0808401i	0.646503	−	0.762912i	$-0.276231\pi$
$929$	−2.58413	−	2.46397i	−0.0847827	−	0.0808401i	−0.731286	+	0.682071i	$0.761079\pi$
$930$	3.80152	+	4.38719i	0.124657	+	0.143862i
$931$	12.6697	−	15.3367i	0.415232	−	0.502640i
$932$	18.0415	−	11.5946i	0.590970	−	0.379794i
$933$	−3.15889	+	9.12702i	−0.103417	+	0.298805i
$934$	−8.51178	+	35.0860i	−0.278514	+	1.14805i
$935$	9.33493	+	7.34107i	0.305285	+	0.240079i
$936$	2.07889	+	0.400672i	0.0679505	+	0.0130964i
$937$	−6.21824	+	13.6160i	−0.203141	+	0.444817i	−0.983594	−	0.180398i	$-0.942261\pi$
$937$	−6.21824	+	13.6160i	−0.203141	+	0.444817i	0.780453	+	0.625215i	$0.214989\pi$
$938$	1.35395	+	3.26991i	0.0442080	+	0.106766i
$939$	0.275556	+	0.603383i	0.00899242	+	0.0196907i
$940$	9.03422	−	7.10459i	0.294664	−	0.231726i
$941$	49.4146	−	25.4750i	1.61087	−	0.830461i	0.611643	−	0.791134i	$-0.290509\pi$
$941$	49.4146	−	25.4750i	1.61087	−	0.830461i	0.999226	−	0.0393269i	$-0.0125214\pi$
$942$	8.90589	−	15.4254i	0.290169	−	0.502588i
$943$	−11.2249	−	13.3727i	−0.365534	−	0.435476i
$944$	7.66834			0.249583
$945$	−3.38453	+	2.47066i	−0.110099	+	0.0803707i
$946$	−10.4112	−	72.4113i	−0.338496	−	2.35429i
$947$	−20.9172	+	29.3741i	−0.679718	+	0.954530i	0.320256	+	0.947331i	$0.396231\pi$
$947$	−20.9172	+	29.3741i	−0.679718	+	0.954530i	−0.999974	+	0.00719913i	$0.997708\pi$
$948$	7.83525	−	7.47089i	0.254477	−	0.242643i
$949$	−0.797908	−	1.12051i	−0.0259012	−	0.0363731i
$950$	6.95268	+	1.34002i	0.225575	+	0.0434760i
$951$	2.02962	−	14.1163i	0.0658148	−	0.457752i
$952$	−2.89771	+	1.36479i	−0.0939154	+	0.0442331i
$953$	−25.6926	−	29.6509i	−0.832266	−	0.960486i	0.167411	−	0.985887i	$-0.446459\pi$
$953$	−25.6926	−	29.6509i	−0.832266	−	0.960486i	−0.999677	+	0.0254007i	$0.991914\pi$
$954$	−5.51418	−	2.84276i	−0.178528	−	0.0920377i
$955$	−1.20390	−	25.2729i	−0.0389572	−	0.817813i
$956$	2.95571	−	0.569667i	0.0955946	−	0.0184243i
$957$	−11.3623	−	10.8340i	−0.367292	−	0.350212i
$958$	1.60941	−	11.1937i	0.0519976	−	0.361651i
$959$	−12.2666	+	19.5904i	−0.396108	+	0.632606i
$960$	−0.657939	+	1.44068i	−0.0212349	+	0.0464979i
$961$	−4.14130	−	17.0707i	−0.133590	−	0.550667i
$962$	−8.32088	−	0.794548i	−0.268276	−	0.0256173i
$963$	−2.66522	−	1.06699i	−0.0858854	−	0.0343833i
$964$	0.498274	−	10.4601i	0.0160483	−	0.336896i
$965$	11.4317			0.367998
$966$	−11.0134	+	6.30111i	−0.354352	+	0.202735i
$967$	−5.08643			−0.163569			−0.0817843	−	0.996650i	$-0.526062\pi$
$967$	−5.08643			−0.163569			−0.0817843	+	0.996650i	$0.526062\pi$
$968$	−1.30188	+	27.3299i	−0.0418441	+	0.878416i
$969$	−3.19401	−	1.27869i	−0.102606	−	0.0410774i
$970$	−20.2701	−	1.93556i	−0.650835	−	0.0621472i
$971$	−9.24967	−	38.1277i	−0.296836	−	1.22358i	−0.903490	−	0.428609i	$-0.859004\pi$
$971$	−9.24967	−	38.1277i	−0.296836	−	1.22358i	0.606654	−	0.794966i	$-0.292511\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	28.0382	+	1.00499i	0.898864	+	0.0322187i
$974$	−2.32409	+	16.1644i	−0.0744686	+	0.517941i
$975$	−3.81767	−	3.64014i	−0.122263	−	0.116578i
$976$	7.89459	−	1.52156i	0.252700	−	0.0487039i
$977$	2.71945	+	57.0883i	0.0870030	+	1.82642i	0.448206	+	0.893930i	$0.352063\pi$
$977$	2.71945	+	57.0883i	0.0870030	+	1.82642i	−0.361203	+	0.932487i	$0.617634\pi$
$978$	−11.6290	−	5.99516i	−0.371854	−	0.191704i
$979$	−35.0595	−	40.4608i	−1.12051	−	1.29313i
$980$	−0.788072	−	11.0586i	−0.0251740	−	0.353255i
$981$	0.895468	−	6.22812i	0.0285901	−	0.198849i
$982$	4.56229	+	0.879310i	0.145589	+	0.0280599i
$983$	−0.189536	−	0.266166i	−0.00604525	−	0.00848937i	0.811542	−	0.584294i	$-0.198628\pi$
$983$	−0.189536	−	0.266166i	−0.00604525	−	0.00848937i	−0.817588	+	0.575804i	$0.804689\pi$
$984$	2.63477	−	2.51225i	0.0839935	−	0.0800877i
$985$	−14.9514	+	20.9963i	−0.476390	+	0.668997i
$986$	−0.436723	−	3.03748i	−0.0139081	−	0.0967330i
$987$	2.04985	+	19.0895i	0.0652476	+	0.607626i
$988$	−6.01665			−0.191415
$989$	24.3375	−	51.1513i	0.773886	−	1.62652i
$990$	−4.90476	+	8.49529i	−0.155883	+	0.269998i
$991$	−34.7018	+	17.8900i	−1.10234	+	0.568296i	−0.910658	−	0.413161i	$-0.864425\pi$
$991$	−34.7018	+	17.8900i	−1.10234	+	0.568296i	−0.191682	+	0.981457i	$0.561394\pi$
$992$	−2.88109	+	2.26572i	−0.0914748	+	0.0719366i
$993$	−5.85485	−	12.8203i	−0.185798	−	0.406841i
$994$	20.6918	−	26.9590i	0.656305	−	0.855086i
$995$	−3.48743	+	7.63641i	−0.110559	+	0.242090i
$996$	−7.31413	−	1.40968i	−0.231757	−	0.0446675i
$997$	5.45751	+	4.29183i	0.172841	+	0.135924i	0.700832	−	0.713326i	$-0.252812\pi$
$997$	5.45751	+	4.29183i	0.172841	+	0.135924i	−0.527991	+	0.849250i	$0.677055\pi$
$998$	1.92496	−	7.93480i	0.0609336	−	0.251172i
$999$	1.29130	−	3.73097i	0.0408550	−	0.118043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.25.5	✓	160
7.2	even	3	inner	966.2.y.a.163.5	yes	160
23.12	even	11	inner	966.2.y.a.403.5	yes	160
161.58	even	33	inner	966.2.y.a.541.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.25.5	✓	160	1.1	even	1	trivial
966.2.y.a.163.5	yes	160	7.2	even	3	inner
966.2.y.a.403.5	yes	160	23.12	even	11	inner
966.2.y.a.541.5	yes	160	161.58	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)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.373397 + 1.53917i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-2.64405 - 0.0947728i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.373397 + 1.53917i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-2.64405 - 0.0947728i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-1.55519 + 0.299738i) q^{10} +(-0.294704 - 6.18660i) q^{11} +(0.888835 + 0.458227i) q^{12} +(1.38644 + 1.60003i) q^{13} +(0.220475 - 2.63655i) q^{14} +(0.225400 - 1.56769i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.702235 + 0.986151i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(1.64844 - 2.31492i) q^{19} +(-0.225400 - 1.56769i) q^{20} +(2.41943 + 1.07068i) q^{21} +6.19362 q^{22} +(3.99332 + 2.65583i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.21457 - 1.14169i) q^{25} +(-1.66419 + 1.30873i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.62307 + 0.345677i) q^{28} +(-1.05300 + 2.30574i) q^{29} +(1.55519 + 0.299738i) q^{30} +(2.88109 + 2.26572i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-2.02573 + 5.85297i) q^{33} +(-1.01845 + 0.654517i) q^{34} +(-0.841412 - 4.10502i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.85738 + 2.72451i) q^{37} +(2.23386 + 1.75673i) q^{38} +(-0.692451 - 2.00070i) q^{39} +(1.57664 - 0.150551i) q^{40} +(-3.49306 - 1.02566i) q^{41} +(-1.18459 + 2.36575i) q^{42} +(-1.68095 - 11.6913i) q^{43} +(-0.294704 + 6.18660i) q^{44} +(-0.791905 + 1.37162i) q^{45} +(-2.84283 + 3.86242i) q^{46} +(3.62832 + 6.28443i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(6.98204 + 0.501169i) q^{49} +(1.03502 + 2.26639i) q^{50} +(-0.285417 - 1.17651i) q^{51} +(-1.22807 - 1.72458i) q^{52} +(2.02907 + 5.86262i) q^{53} +(0.928368 - 0.371662i) q^{54} +(9.41216 - 2.76366i) q^{55} +(-0.470096 + 2.60365i) q^{56} +(-2.39073 + 1.53643i) q^{57} +(-2.25302 - 1.16151i) q^{58} +(7.52976 - 1.45124i) q^{59} +(-0.373397 + 1.53917i) q^{60} +(7.46397 - 2.98812i) q^{61} +(-2.40024 + 2.77002i) q^{62} +(-1.84819 - 1.89320i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.94502 + 2.73140i) q^{65} +(-5.74995 - 2.30193i) q^{66} +(-1.18897 + 0.612955i) q^{67} +(-0.605316 - 1.04844i) q^{68} +(-2.72020 - 3.94975i) q^{69} +(4.14041 - 0.645134i) q^{70} +(10.8058 + 6.94447i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-0.646786 - 0.0617606i) q^{73} +(-2.85738 + 2.72451i) q^{74} +(-2.48026 + 0.236836i) q^{75} +(-1.86103 + 2.14774i) q^{76} +(0.192892 + 16.3856i) q^{77} +(2.03139 - 0.596469i) q^{78} +(3.54088 - 10.2307i) q^{79} +(0.0753607 + 1.58202i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(1.19070 - 3.44030i) q^{82} +(-7.14702 + 2.09855i) q^{83} +(-2.30670 - 1.29581i) q^{84} +(-1.25564 + 1.44908i) q^{85} +(11.7580 - 1.12275i) q^{86} +(1.83452 - 1.74922i) q^{87} +(-6.16557 - 0.588741i) q^{88} +(6.79460 - 5.34333i) q^{89} +(-1.33239 - 0.856273i) q^{90} +(-3.51417 - 4.36197i) q^{91} +(-3.72278 - 3.02339i) q^{92} +(-1.83263 - 3.17421i) q^{93} +(-6.44996 + 3.32518i) q^{94} +(4.17857 + 1.67285i) q^{95} +(0.580057 - 0.814576i) q^{96} +(12.3358 + 3.62211i) q^{97} +(-0.832820 + 6.95028i) q^{98} +(4.05596 - 4.68082i) 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

Fields

Representations

Groups

Database

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