LMFDB - Embedded newform 966.2.be.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.157815 - 0.0813595i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.34398 - 2.27897i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.157815 - 0.0813595i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.34398 - 2.27897i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-0.164835 + 0.0659898i) q^{10} +(0.146601 + 1.53527i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-2.37877 - 0.342016i) q^{13} +(1.12126 + 2.39641i) q^{14} +(-0.0500225 + 0.170361i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.460221 - 1.32972i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(0.496881 + 1.43564i) q^{19} +(0.170361 - 0.0500225i) q^{20} +(2.57682 + 0.599990i) q^{21} -1.54226i q^{22} +(-1.32697 + 4.60860i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.88200 + 4.04720i) q^{25} +(2.33549 + 0.566584i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-0.888392 - 2.49214i) q^{28} +(3.94613 + 4.55407i) q^{29} +(0.0659898 - 0.164835i) q^{30} +(9.17017 - 2.22466i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-1.21229 - 0.953359i) q^{33} +(-0.584535 + 1.27995i) q^{34} +(-0.397517 - 0.250312i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-7.17395 + 0.341737i) q^{37} +(-0.358165 - 1.47637i) q^{38} +(1.88907 - 1.48558i) q^{39} +(-0.174344 + 0.0336021i) q^{40} +(-4.05518 + 6.30999i) q^{41} +(-2.50812 - 0.842215i) q^{42} +(-1.94977 - 6.64032i) q^{43} +(-0.146601 + 1.53527i) q^{44} +(-0.0887765 - 0.153765i) q^{45} +(1.75903 - 4.46159i) q^{46} +(8.10684 + 4.68049i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-3.38745 + 6.12578i) q^{49} +(3.25366 - 3.75492i) q^{50} +(0.644776 + 1.25069i) q^{51} +(-2.27106 - 0.786022i) q^{52} +(3.05202 + 3.88095i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(0.148045 + 0.230362i) q^{55} +(0.647476 + 2.56530i) q^{56} +(-1.38191 - 0.631098i) q^{57} +(-3.49537 - 4.90856i) q^{58} +(4.18959 + 10.4651i) q^{59} +(-0.0813595 + 0.157815i) q^{60} +(-4.90969 + 4.68138i) q^{61} +(-9.34012 + 1.34291i) q^{62} +(-2.21244 + 1.45089i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.403234 + 0.139561i) q^{65} +(1.11618 + 1.06428i) q^{66} +(-10.1458 - 7.22480i) q^{67} +(0.703556 - 1.21859i) q^{68} +(-2.41969 - 4.14067i) q^{69} +(0.371923 + 0.286965i) q^{70} +(-3.86754 - 8.46874i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(-0.842494 + 4.37127i) q^{73} +(7.17395 + 0.341737i) q^{74} +(-0.940290 - 4.87869i) q^{75} +(0.216204 + 1.50374i) q^{76} +(3.30182 - 2.39747i) q^{77} +(-2.02173 + 1.29929i) q^{78} +(-5.84214 + 7.42888i) q^{79} +(0.176749 - 0.0168775i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(4.63662 - 5.89595i) q^{82} +(-6.24348 + 4.01244i) q^{83} +(2.41671 + 1.07681i) q^{84} +(-0.0355555 - 0.247294i) q^{85} +(1.30974 + 6.79559i) q^{86} +(-6.01908 - 0.286724i) q^{87} +(0.291874 - 1.51438i) q^{88} +(-3.74886 + 15.4530i) q^{89} +(0.0737582 + 0.161508i) q^{90} +(2.41758 + 5.88083i) q^{91} +(-2.17517 + 4.27418i) q^{92} +(-4.71808 + 8.17196i) q^{93} +(-7.62522 - 5.42990i) q^{94} +(0.195219 + 0.186141i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-0.0972074 - 0.0624714i) q^{97} +(3.95440 - 5.77605i) q^{98} +(1.52656 - 0.219486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	0.157815	−	0.0813595i	0.0705772	−	0.0363851i	−0.422577	−	0.906327i	$-0.638874\pi$
$5$	0.157815	−	0.0813595i	0.0705772	−	0.0363851i	0.493154	+	0.869942i	$0.335844\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	−1.34398	−	2.27897i	−0.507976	−	0.861371i
$7$	−1.34398	−	2.27897i	−0.507976	−	0.861371i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−0.164835	+	0.0659898i	−0.0521253	+	0.0208678i
$11$	0.146601	+	1.53527i	0.0442018	+	0.462902i	0.990292	+	0.139000i	$0.0443888\pi$
$11$	0.146601	+	1.53527i	0.0442018	+	0.462902i	−0.946091	+	0.323902i	$0.895005\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	−2.37877	−	0.342016i	−0.659753	−	0.0948582i	−0.195698	−	0.980664i	$-0.562697\pi$
$13$	−2.37877	−	0.342016i	−0.659753	−	0.0948582i	−0.464056	+	0.885806i	$0.653606\pi$
$14$	1.12126	+	2.39641i	0.299670	+	0.640467i
$15$	−0.0500225	+	0.170361i	−0.0129157	+	0.0439870i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	0.460221	−	1.32972i	0.111620	−	0.322505i	−0.875331	−	0.483524i	$-0.839357\pi$
$17$	0.460221	−	1.32972i	0.111620	−	0.322505i	0.986951	+	0.161019i	$0.0514780\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	0.496881	+	1.43564i	0.113992	+	0.329359i	0.987538	−	0.157384i	$-0.0503060\pi$
$19$	0.496881	+	1.43564i	0.113992	+	0.329359i	−0.873545	+	0.486743i	$0.838185\pi$
$20$	0.170361	−	0.0500225i	0.0380939	−	0.0111854i
$21$	2.57682	+	0.599990i	0.562309	+	0.130928i
$22$		−	1.54226i		−	0.328810i
$23$	−1.32697	+	4.60860i	−0.276692	+	0.960959i
$23$	−1.32697	+	4.60860i	−0.276692	+	0.960959i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−2.88200	+	4.04720i	−0.576400	+	0.809440i
$26$	2.33549	+	0.566584i	0.458028	+	0.111116i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	−0.888392	−	2.49214i	−0.167890	−	0.470970i
$29$	3.94613	+	4.55407i	0.732777	+	0.845670i	0.992781	−	0.119937i	$-0.0382694\pi$
$29$	3.94613	+	4.55407i	0.732777	+	0.845670i	−0.260004	+	0.965608i	$0.583724\pi$
$30$	0.0659898	−	0.164835i	0.0120480	−	0.0300945i
$31$	9.17017	−	2.22466i	1.64701	−	0.399561i	0.698325	−	0.715780i	$-0.253929\pi$
$31$	9.17017	−	2.22466i	1.64701	−	0.399561i	0.948686	+	0.316220i	$0.102414\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	−1.21229	−	0.953359i	−0.211033	−	0.165958i
$34$	−0.584535	+	1.27995i	−0.100247	+	0.219510i
$35$	−0.397517	−	0.250312i	−0.0671926	−	0.0423104i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−7.17395	+	0.341737i	−1.17939	+	0.0561812i	−0.628100	−	0.778133i	$-0.716167\pi$
$37$	−7.17395	+	0.341737i	−1.17939	+	0.0561812i	−0.551290	+	0.834314i	$0.685864\pi$
$38$	−0.358165	−	1.47637i	−0.0581020	−	0.239500i
$39$	1.88907	−	1.48558i	0.302493	−	0.237884i
$40$	−0.174344	+	0.0336021i	−0.0275663	+	0.00531297i
$41$	−4.05518	+	6.30999i	−0.633313	+	0.985455i	0.365199	+	0.930929i	$0.381001\pi$
$41$	−4.05518	+	6.30999i	−0.633313	+	0.985455i	−0.998512	+	0.0545253i	$0.982635\pi$
$42$	−2.50812	−	0.842215i	−0.387012	−	0.129957i
$43$	−1.94977	−	6.64032i	−0.297338	−	1.01264i	−0.963695	−	0.267007i	$-0.913965\pi$
$43$	−1.94977	−	6.64032i	−0.297338	−	1.01264i	0.666357	−	0.745633i	$-0.267853\pi$
$44$	−0.146601	+	1.53527i	−0.0221009	+	0.231451i
$45$	−0.0887765	−	0.153765i	−0.0132340	−	0.0229220i
$46$	1.75903	−	4.46159i	0.259355	−	0.657826i
$47$	8.10684	+	4.68049i	1.18250	+	0.682719i	0.956592	−	0.291429i	$-0.0941307\pi$
$47$	8.10684	+	4.68049i	1.18250	+	0.682719i	0.225911	+	0.974148i	$0.427464\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	−3.38745	+	6.12578i	−0.483921	+	0.875112i
$50$	3.25366	−	3.75492i	0.460137	−	0.531026i
$51$	0.644776	+	1.25069i	0.0902867	+	0.175132i
$52$	−2.27106	−	0.786022i	−0.314939	−	0.109002i
$53$	3.05202	+	3.88095i	0.419227	+	0.533090i	0.949095	−	0.314990i	$-0.102001\pi$
$53$	3.05202	+	3.88095i	0.419227	+	0.533090i	−0.529868	+	0.848080i	$0.677759\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	0.148045	+	0.230362i	0.0199624	+	0.0310620i
$56$	0.647476	+	2.56530i	0.0865227	+	0.342803i
$57$	−1.38191	−	0.631098i	−0.183039	−	0.0835910i
$58$	−3.49537	−	4.90856i	−0.458964	−	0.644525i
$59$	4.18959	+	10.4651i	0.545438	+	1.36244i	0.903439	+	0.428716i	$0.141034\pi$
$59$	4.18959	+	10.4651i	0.545438	+	1.36244i	−0.358001	+	0.933721i	$0.616542\pi$
$60$	−0.0813595	+	0.157815i	−0.0105035	+	0.0203739i
$61$	−4.90969	+	4.68138i	−0.628621	+	0.599389i	−0.935915	−	0.352226i	$-0.885425\pi$
$61$	−4.90969	+	4.68138i	−0.628621	+	0.599389i	0.307294	+	0.951615i	$0.400576\pi$
$62$	−9.34012	+	1.34291i	−1.18620	+	0.170549i
$63$	−2.21244	+	1.45089i	−0.278742	+	0.182795i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−0.403234	+	0.139561i	−0.0500150	+	0.0173104i
$66$	1.11618	+	1.06428i	0.137393	+	0.131004i
$67$	−10.1458	−	7.22480i	−1.23951	−	0.882650i	−0.243326	−	0.969944i	$-0.578239\pi$
$67$	−10.1458	−	7.22480i	−1.23951	−	0.882650i	−0.996183	+	0.0872940i	$0.972178\pi$
$68$	0.703556	−	1.21859i	0.0853187	−	0.147776i
$69$	−2.41969	−	4.14067i	−0.291296	−	0.498478i
$70$	0.371923	+	0.286965i	0.0444533	+	0.0342989i
$71$	−3.86754	−	8.46874i	−0.458993	−	1.00505i	−0.987716	−	0.156260i	$-0.950056\pi$
$71$	−3.86754	−	8.46874i	−0.458993	−	1.00505i	0.528723	−	0.848794i	$-0.322671\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	−0.842494	+	4.37127i	−0.0986064	+	0.511619i	0.898719	+	0.438526i	$0.144499\pi$
$73$	−0.842494	+	4.37127i	−0.0986064	+	0.511619i	−0.997325	+	0.0730931i	$0.976713\pi$
$74$	7.17395	+	0.341737i	0.833954	+	0.0397261i
$75$	−0.940290	−	4.87869i	−0.108575	−	0.563342i
$76$	0.216204	+	1.50374i	0.0248004	+	0.172490i
$77$	3.30182	−	2.39747i	0.376277	−	0.273217i
$78$	−2.02173	+	1.29929i	−0.228916	+	0.147115i
$79$	−5.84214	+	7.42888i	−0.657292	+	0.835815i	−0.994403	−	0.105650i	$-0.966308\pi$
$79$	−5.84214	+	7.42888i	−0.657292	+	0.835815i	0.337111	+	0.941465i	$0.390550\pi$
$80$	0.176749	−	0.0168775i	0.0197612	−	0.00188696i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	4.63662	−	5.89595i	0.512029	−	0.651098i
$83$	−6.24348	+	4.01244i	−0.685311	+	0.440423i	−0.836416	−	0.548095i	$-0.815353\pi$
$83$	−6.24348	+	4.01244i	−0.685311	+	0.440423i	0.151105	+	0.988518i	$0.451717\pi$
$84$	2.41671	+	1.07681i	0.263684	+	0.117490i
$85$	−0.0355555	−	0.247294i	−0.00385654	−	0.0268228i
$86$	1.30974	+	6.79559i	0.141233	+	0.732788i
$87$	−6.01908	−	0.286724i	−0.645313	−	0.0307400i
$88$	0.291874	−	1.51438i	0.0311138	−	0.161434i
$89$	−3.74886	+	15.4530i	−0.397378	+	1.63802i	0.324420	+	0.945913i	$0.394831\pi$
$89$	−3.74886	+	15.4530i	−0.397378	+	1.63802i	−0.721799	+	0.692103i	$0.756684\pi$
$90$	0.0737582	+	0.161508i	0.00777480	+	0.0170244i
$91$	2.41758	+	5.88083i	0.253431	+	0.616478i
$92$	−2.17517	+	4.27418i	−0.226777	+	0.445614i
$93$	−4.71808	+	8.17196i	−0.489242	+	0.847392i
$94$	−7.62522	−	5.42990i	−0.786482	−	0.560051i
$95$	0.195219	+	0.186141i	0.0200290	+	0.0190976i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	−0.0972074	−	0.0624714i	−0.00986992	−	0.00634301i	0.535697	−	0.844411i	$-0.320049\pi$
$97$	−0.0972074	−	0.0624714i	−0.00986992	−	0.00634301i	−0.545566	+	0.838068i	$0.683685\pi$
$98$	3.95440	−	5.77605i	0.399455	−	0.583469i
$99$	1.52656	−	0.219486i	0.153425	−	0.0220592i
$100$	−3.59585	+	3.42864i	−0.359585	+	0.342864i
$101$	−4.18605	+	8.11980i	−0.416527	+	0.807950i	−0.999991	−	0.00418909i	$-0.998667\pi$
$101$	−4.18605	+	8.11980i	−0.416527	+	0.807950i	0.583464	+	0.812139i	$0.301697\pi$
$102$	−0.522971	−	1.30632i	−0.0517818	−	0.129345i
$103$	7.67868	+	10.7832i	0.756603	+	1.06250i	0.995802	+	0.0915295i	$0.0291756\pi$
$103$	7.67868	+	10.7832i	0.756603	+	1.06250i	−0.239200	+	0.970970i	$0.576885\pi$
$104$	2.18606	+	0.998340i	0.214361	+	0.0978953i
$105$	0.455477	−	0.114961i	0.0444500	−	0.0112191i
$106$	−2.66929	−	4.15349i	−0.259264	−	0.403423i
$107$	4.02698	+	4.22338i	0.389303	+	0.408289i	0.888997	−	0.457913i	$-0.151403\pi$
$107$	4.02698	+	4.22338i	0.389303	+	0.408289i	−0.499694	+	0.866202i	$0.666554\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	−2.63271	−	0.911190i	−0.252168	−	0.0872762i	0.198060	−	0.980190i	$-0.436536\pi$
$109$	−2.63271	−	0.911190i	−0.252168	−	0.0872762i	−0.450228	+	0.892914i	$0.648657\pi$
$110$	−0.125477	−	0.243392i	−0.0119638	−	0.0232065i
$111$	4.70326	−	5.42785i	0.446414	−	0.515189i
$112$	−0.400697	−	2.61523i	−0.0378623	−	0.247116i
$113$	17.9550	−	8.19978i	1.68906	−	0.771370i	0.690206	−	0.723613i	$-0.257520\pi$
$113$	17.9550	−	8.19978i	1.68906	−	0.771370i	0.998859	−	0.0477571i	$-0.0152074\pi$
$114$	1.31566	+	0.759599i	0.123223	+	0.0711430i
$115$	0.165537	+	0.835269i	0.0154364	+	0.0778893i
$116$	3.01295	+	5.21859i	0.279746	+	0.484533i
$117$	−0.228442	+	2.39235i	−0.0211195	+	0.221173i
$118$	−3.17585	−	10.8159i	−0.292360	−	0.995688i
$119$	−3.64893	+	0.738285i	−0.334497	+	0.0676784i
$120$	0.0959924	−	0.149367i	0.00876287	−	0.0136353i
$121$	8.46565	−	1.63162i	0.769604	−	0.148329i
$122$	5.33245	−	4.19348i	0.482777	−	0.379660i
$123$	−1.76836	−	7.28927i	−0.159447	−	0.657251i
$124$	9.42547	−	0.448991i	0.846433	−	0.0403206i
$125$	−0.251888	+	1.75192i	−0.0225295	+	0.156696i
$126$	2.34034	−	1.23402i	0.208494	−	0.109935i
$127$	−6.24667	+	13.6783i	−0.554302	+	1.21375i	0.400442	+	0.916322i	$0.368857\pi$
$127$	−6.24667	+	13.6783i	−0.554302	+	1.21375i	−0.954744	+	0.297430i	$0.903871\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	6.15133	+	3.17123i	0.541594	+	0.279211i
$130$	0.414674	−	0.100599i	0.0363693	−	0.00882310i
$131$	0.708421	−	1.76955i	0.0618950	−	0.154606i	−0.894196	−	0.447675i	$-0.852252\pi$
$131$	0.708421	−	1.76955i	0.0618950	−	0.154606i	0.956091	+	0.293069i	$0.0946764\pi$
$132$	−1.00996	−	1.16556i	−0.0879059	−	0.101449i
$133$	2.60400	−	3.06185i	0.225795	−	0.265496i
$134$	9.41312	+	8.15651i	0.813169	+	0.704615i
$135$	0.172548	+	0.0418597i	0.0148506	+	0.00360271i
$136$	−0.816205	+	1.14620i	−0.0699890	+	0.0982858i
$137$	−5.53108	+	3.19337i	−0.472552	+	0.272828i	−0.717307	−	0.696757i	$-0.754626\pi$
$137$	−5.53108	+	3.19337i	−0.472552	+	0.272828i	0.244755	+	0.969585i	$0.421292\pi$
$138$	2.01513	+	4.35192i	0.171540	+	0.370460i
$139$		−	21.1905i		−	1.79735i	−0.438613	−	0.898676i	$-0.644530\pi$
$139$		−	21.1905i		−	1.79735i	0.438613	−	0.898676i	$-0.355470\pi$
$140$	−0.342961	−	0.321019i	−0.0289855	−	0.0271311i
$141$	−8.98178	+	2.63729i	−0.756403	+	0.222100i
$142$	3.04503	+	8.79803i	0.255533	+	0.738314i
$143$	0.176358	−	3.70221i	0.0147478	−	0.309594i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	0.993277	+	0.397648i	0.0824872	+	0.0330229i
$146$	1.25419	−	4.27140i	0.103798	−	0.353503i
$147$	−2.09583	−	6.67888i	−0.172861	−	0.550865i
$148$	−7.10898	−	1.02212i	−0.584354	−	0.0840175i
$149$	−17.7917	+	12.6694i	−1.45755	+	1.03792i	−0.469646	+	0.882855i	$0.655618\pi$
$149$	−17.7917	+	12.6694i	−1.45755	+	1.03792i	−0.987905	+	0.155062i	$0.950442\pi$
$150$	0.472284	+	4.94598i	0.0385618	+	0.403837i
$151$	12.6127	−	5.04936i	1.02641	−	0.410911i	0.203492	−	0.979077i	$-0.434771\pi$
$151$	12.6127	−	5.04936i	1.02641	−	0.410911i	0.822915	+	0.568165i	$0.192347\pi$
$152$	−0.0722864	−	1.51748i	−0.00586320	−	0.123084i
$153$	−1.35011	−	0.396429i	−0.109150	−	0.0320494i
$154$	−3.51476	+	2.07276i	−0.283227	+	0.167028i
$155$	1.26620	−	1.09717i	0.101703	−	0.0881265i
$156$	2.13608	−	1.10123i	0.171023	−	0.0881687i
$157$	2.85185	+	0.549649i	0.227603	+	0.0438668i	0.301777	−	0.953378i	$-0.402420\pi$
$157$	2.85185	+	0.549649i	0.227603	+	0.0438668i	−0.0741747	+	0.997245i	$0.523632\pi$
$158$	6.52185	−	6.83992i	0.518850	−	0.544154i
$159$	−4.91491	−	0.469317i	−0.389778	−	0.0372193i
$160$	−0.177553			−0.0140368
$161$	12.2863	−	3.16973i	0.968295	−	0.249809i
$162$	1.00000			0.0785674
$163$	4.20248	+	0.401288i	0.329163	+	0.0314313i	0.258330	−	0.966057i	$-0.416828\pi$
$163$	4.20248	+	0.401288i	0.329163	+	0.0314313i	0.0708338	+	0.997488i	$0.477434\pi$
$164$	−5.17607	+	5.42851i	−0.404184	+	0.423895i
$165$	−0.268884	−	0.0518231i	−0.0209326	−	0.00403442i
$166$	6.59662	−	3.40079i	0.511997	−	0.263953i
$167$	−0.275604	+	0.238812i	−0.0213269	+	0.0184798i	−0.665459	−	0.746434i	$-0.731764\pi$
$167$	−0.275604	+	0.238812i	−0.0213269	+	0.0184798i	0.644132	+	0.764914i	$0.277219\pi$
$168$	−2.30341	−	1.30166i	−0.177712	−	0.100425i
$169$	−6.93181	−	2.03536i	−0.533217	−	0.156566i
$170$	0.0118877	+	0.249554i	0.000911747	+	0.0191399i
$171$	1.41038	−	0.564629i	0.107854	−	0.0431783i
$172$	−0.657850	−	6.88932i	−0.0501606	−	0.525306i
$173$	−14.0169	+	9.98141i	−1.06569	+	0.758873i	−0.971585	−	0.236690i	$-0.923938\pi$
$173$	−14.0169	+	9.98141i	−1.06569	+	0.758873i	−0.0941025	+	0.995563i	$0.529998\pi$
$174$	5.96457	+	0.857575i	0.452173	+	0.0650126i
$175$	13.0968	+	1.12865i	0.990026	+	0.0853180i
$176$	−0.434503	+	1.47978i	−0.0327519	+	0.111543i
$177$	−10.4651	−	4.18959i	−0.786604	−	0.314909i
$178$	5.20079	−	15.0267i	0.389816	−	1.12630i
$179$	1.08495	−	22.7760i	0.0810933	−	1.70236i	−0.482168	−	0.876079i	$-0.660151\pi$
$179$	1.08495	−	22.7760i	0.0810933	−	1.70236i	0.563261	−	0.826279i	$-0.309546\pi$
$180$	−0.0580719	−	0.167788i	−0.00432843	−	0.0125062i
$181$	−0.0515727	+	0.0151431i	−0.00383337	+	0.00112558i	−0.283649	−	0.958928i	$-0.591545\pi$
$181$	−0.0515727	+	0.0151431i	−0.00383337	+	0.00112558i	0.279815	+	0.960054i	$0.409727\pi$
$182$	−1.84762	−	6.08400i	−0.136955	−	0.450976i
$183$		−	6.78383i		−	0.501475i
$184$	2.57161	−	4.04807i	0.189581	−	0.298427i
$185$	−1.10436	+	0.637600i	−0.0811939	+	0.0468773i
$186$	5.47351	−	7.68647i	0.401337	−	0.563599i
$187$	2.10895	+	0.511626i	0.154222	+	0.0374138i
$188$	7.07455	+	6.13013i	0.515965	+	0.447086i
$189$	0.476700	−	2.60245i	0.0346748	−	0.189301i
$190$	−0.176641	−	0.203855i	−0.0128149	−	0.0147892i
$191$	3.25687	−	8.13526i	0.235659	−	0.588647i	−0.762648	−	0.646813i	$-0.776101\pi$
$191$	3.25687	−	8.13526i	0.235659	−	0.588647i	0.998307	+	0.0581668i	$0.0185255\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	−20.2732	−	10.4516i	−1.45930	−	0.752320i	−0.467971	−	0.883744i	$-0.655015\pi$
$193$	−20.2732	−	10.4516i	−1.45930	−	0.752320i	−0.991326	+	0.131424i	$0.958045\pi$
$194$	0.0908290	+	0.0714287i	0.00652114	+	0.00512828i
$195$	0.177258	−	0.388142i	0.0126937	−	0.0277954i
$196$	−4.48554	+	5.37400i	−0.320396	+	0.383857i
$197$	2.48807	−	17.3049i	0.177267	−	1.23292i	−0.685784	−	0.727805i	$-0.740540\pi$
$197$	2.48807	−	17.3049i	0.177267	−	1.23292i	0.863051	−	0.505117i	$-0.168551\pi$
$198$	−1.54051	+	0.0733835i	−0.109479	+	0.00521514i
$199$	3.31924	+	13.6821i	0.235294	+	0.969897i	0.959813	+	0.280641i	$0.0905471\pi$
$199$	3.31924	+	13.6821i	0.235294	+	0.969897i	−0.724518	+	0.689255i	$0.757938\pi$
$200$	3.90549	−	3.07131i	0.276159	−	0.217174i
$201$	12.2303	−	2.35719i	0.862656	−	0.166263i
$202$	4.93893	−	7.68512i	0.347502	−	0.540723i
$203$	5.07511	−	15.1137i	0.356203	−	1.06077i
$204$	0.396429	+	1.35011i	0.0277556	+	0.0945269i
$205$	−0.126593	+	1.32574i	−0.00884164	+	0.0925938i
$206$	−6.61890	−	11.4643i	−0.461161	−	0.798754i
$207$	4.66652	+	1.10618i	0.324345	+	0.0768848i
$208$	−2.08126	−	1.20162i	−0.144310	−	0.0833172i
$209$	−2.13126	+	0.973314i	−0.147422	+	0.0673255i
$210$	−0.464343	+	0.0711450i	−0.0320427	+	0.00490947i
$211$	8.60134	−	9.92648i	0.592141	−	0.683367i	−0.378029	−	0.925794i	$-0.623398\pi$
$211$	8.60134	−	9.92648i	0.592141	−	0.683367i	0.970170	+	0.242427i	$0.0779434\pi$
$212$	2.26239	+	4.38842i	0.155381	+	0.301398i
$213$	8.79803	+	3.04503i	0.602831	+	0.208642i
$214$	−3.60729	−	4.58704i	−0.246589	−	0.313564i
$215$	−0.847958	−	0.889313i	−0.0578303	−	0.0606506i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	−17.3945	−	17.9087i	−1.18081	−	1.21572i
$218$	2.53418	+	1.15732i	0.171636	+	0.0783835i
$219$	−2.58225	−	3.62626i	−0.174492	−	0.245040i
$220$	0.101773	+	0.254217i	0.00686154	+	0.0171393i
$221$	−1.54955	+	3.00570i	−0.104234	+	0.202186i
$222$	−5.19792	+	4.95620i	−0.348861	+	0.332639i
$223$	20.1331	−	2.89470i	1.34821	−	0.193844i	0.569897	−	0.821716i	$-0.306983\pi$
$223$	20.1331	−	2.89470i	1.34821	−	0.193844i	0.778316	+	0.627873i	$0.216074\pi$
$224$	0.150289	+	2.64148i	0.0100416	+	0.176491i
$225$	4.17975	+	2.68616i	0.278650	+	0.179077i
$226$	−18.6531	+	6.45592i	−1.24079	+	0.429441i
$227$	−2.57092	−	2.45137i	−0.170638	−	0.162703i	0.599948	−	0.800039i	$-0.295188\pi$
$227$	−2.57092	−	2.45137i	−0.170638	−	0.162703i	−0.770586	+	0.637336i	$0.780036\pi$
$228$	−1.23750	−	0.881222i	−0.0819556	−	0.0583603i
$229$	9.69949	−	16.8000i	0.640960	−	1.11018i	−0.344259	−	0.938875i	$-0.611870\pi$
$229$	9.69949	−	16.8000i	0.640960	−	1.11018i	0.985219	−	0.171301i	$-0.0547969\pi$
$230$	−0.0853902	−	0.847222i	−0.00563046	−	0.0558642i
$231$	−0.543383	+	4.04408i	−0.0357520	+	0.266081i
$232$	−2.50325	−	5.48135i	−0.164346	−	0.359869i
$233$	−1.25394	+	5.16880i	−0.0821482	+	0.338619i	−0.998023	−	0.0628437i	$-0.979983\pi$
$233$	−1.25394	+	5.16880i	−0.0821482	+	0.338619i	0.915875	+	0.401463i	$0.131498\pi$
$234$	0.454815	−	2.35981i	0.0297322	−	0.154265i
$235$	1.66019	+	0.0790844i	0.108299	+	0.00515890i
$236$	2.13335	+	11.0688i	0.138869	+	0.720521i
$237$	−1.34500	−	9.35467i	−0.0873671	−	0.607651i
$238$	3.70258	−	0.388089i	0.240003	−	0.0251561i
$239$	−0.386376	+	0.248309i	−0.0249926	+	0.0160617i	−0.553077	−	0.833130i	$-0.686547\pi$
$239$	−0.386376	+	0.248309i	−0.0249926	+	0.0160617i	0.528085	+	0.849192i	$0.322910\pi$
$240$	−0.109756	+	0.139566i	−0.00708472	+	0.00900896i
$241$	−1.56689	+	0.149619i	−0.100932	+	0.00963783i	−0.145400	−	0.989373i	$-0.546447\pi$
$241$	−1.56689	+	0.149619i	−0.100932	+	0.00963783i	0.0444678	+	0.999011i	$0.485841\pi$
$242$	−8.58241	+	0.819521i	−0.551698	+	0.0526808i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	−5.70692	+	3.66761i	−0.365348	+	0.234795i
$245$	−0.0362006	+	1.24234i	−0.00231277	+	0.0793705i
$246$	1.06746	+	7.42435i	0.0680588	+	0.473359i
$247$	−0.690955	−	3.58501i	−0.0439644	−	0.228109i
$248$	−9.42547	−	0.448991i	−0.598518	−	0.0285109i
$249$	1.40456	−	7.28752i	0.0890101	−	0.461828i
$250$	0.417278	−	1.72004i	0.0263910	−	0.108785i
$251$	−0.457352	−	1.00146i	−0.0288678	−	0.0632116i	0.894649	−	0.446770i	$-0.147426\pi$
$251$	−0.457352	−	1.00146i	−0.0288678	−	0.0632116i	−0.923517	+	0.383558i	$0.874698\pi$
$252$	−2.44705	+	1.00597i	−0.154149	+	0.0633699i
$253$	−7.26998	−	1.36163i	−0.457060	−	0.0856051i
$254$	7.51859	−	13.0226i	0.471758	−	0.817109i
$255$	0.203511	+	0.144920i	0.0127444	+	0.00907522i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	27.2912	−	9.44558i	1.70238	−	0.589199i	0.709116	−	0.705091i	$-0.249094\pi$
$257$	27.2912	−	9.44558i	1.70238	−	0.589199i	0.993262	+	0.115893i	$0.0369728\pi$
$258$	−5.82203	−	3.74159i	−0.362464	−	0.232941i
$259$	10.4204	+	15.8899i	0.647494	+	0.987353i
$260$	−0.422359	+	0.0607260i	−0.0261936	+	0.00376607i
$261$	4.36115	−	4.15835i	0.269948	−	0.257395i
$262$	−0.873419	+	1.69420i	−0.0539600	+	0.104668i
$263$	−3.11840	−	7.78938i	−0.192289	−	0.480313i	0.800623	−	0.599168i	$-0.204502\pi$
$263$	−3.11840	−	7.78938i	−0.192289	−	0.480313i	−0.992912	+	0.118855i	$0.962078\pi$
$264$	0.894596	+	1.25628i	0.0550586	+	0.0773189i
$265$	0.797408	+	0.364164i	0.0489844	+	0.0223704i
$266$	−2.88325	+	2.80046i	−0.176784	+	0.171707i
$267$	−8.59686	−	13.3770i	−0.526119	−	0.818658i
$268$	−8.59517	−	9.01435i	−0.525033	−	0.550639i
$269$	2.06495	+	2.62580i	0.125902	+	0.160098i	0.844918	−	0.534896i	$-0.179649\pi$
$269$	2.06495	+	2.62580i	0.125902	+	0.160098i	−0.719015	+	0.694994i	$0.755407\pi$
$270$	−0.167788	−	0.0580719i	−0.0102112	−	0.00353414i
$271$	3.12731	+	6.06613i	0.189970	+	0.368491i	0.964515	−	0.264028i	$-0.0850512\pi$
$271$	3.12731	+	6.06613i	0.189970	+	0.368491i	−0.774545	+	0.632519i	$0.782021\pi$
$272$	0.921462	−	1.06342i	0.0558718	−	0.0644795i
$273$	−5.92447	−	2.30855i	−0.358565	−	0.139720i
$274$	5.80958	−	2.65315i	0.350970	−	0.160282i
$275$	−6.63605	−	3.83133i	−0.400169	−	0.231038i
$276$	−1.59233	−	4.52377i	−0.0958471	−	0.272299i
$277$	7.67138	+	13.2872i	0.460929	+	0.798352i	0.999007	−	0.0445425i	$-0.0141830\pi$
$277$	7.67138	+	13.2872i	0.460929	+	0.798352i	−0.538079	+	0.842895i	$0.680850\pi$
$278$	−2.01428	+	21.0945i	−0.120809	+	1.26516i
$279$	−2.65847	−	9.05393i	−0.159159	−	0.542045i
$280$	0.310894	+	0.352166i	0.0185794	+	0.0210459i
$281$	−0.718042	+	1.11730i	−0.0428348	+	0.0666523i	−0.862011	−	0.506890i	$-0.830795\pi$
$281$	−0.718042	+	1.11730i	−0.0428348	+	0.0666523i	0.819176	+	0.573543i	$0.194431\pi$
$282$	9.19181	−	1.77158i	0.547364	−	0.105496i
$283$	−10.4891	+	8.24875i	−0.623515	+	0.490338i	−0.879219	−	0.476418i	$-0.841935\pi$
$283$	−10.4891	+	8.24875i	−0.623515	+	0.490338i	0.255704	+	0.966755i	$0.417693\pi$
$284$	−2.19493	−	9.04764i	−0.130245	−	0.536878i
$285$	−0.269433	+	0.0128347i	−0.0159598	+	0.000760260i
$286$	−0.527476	+	3.66868i	−0.0311903	+	0.216933i
$287$	19.8304	+	0.761172i	1.17055	+	0.0449305i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	11.8065	+	9.28477i	0.694503	+	0.546163i
$290$	−0.950981	−	0.490265i	−0.0558435	−	0.0287893i
$291$	0.112293	−	0.0272421i	0.00658276	−	0.00159696i
$292$	−1.65454	+	4.13284i	−0.0968245	+	0.241856i
$293$	−5.83035	−	6.72859i	−0.340613	−	0.393088i	0.559439	−	0.828872i	$-0.311017\pi$
$293$	−5.83035	−	6.72859i	−0.340613	−	0.393088i	−0.900051	+	0.435784i	$0.856471\pi$
$294$	1.45147	+	6.84786i	0.0846517	+	0.399375i
$295$	1.51262	+	1.31069i	0.0880679	+	0.0763113i
$296$	6.97963	+	1.69324i	0.405683	+	0.0984176i
$297$	−0.894596	+	1.25628i	−0.0519097	+	0.0728970i
$298$	18.9154	−	10.9208i	1.09574	−	0.632626i
$299$	4.73277	−	10.5090i	0.273703	−	0.607749i
$300$		−	4.96847i		−	0.286855i
$301$	−12.5127	+	13.3679i	−0.721218	+	0.770515i
$302$	−13.0356	+	3.82759i	−0.750112	+	0.220253i
$303$	−2.98787	−	8.63288i	−0.171649	−	0.495946i
$304$	−0.0722864	+	1.51748i	−0.00414591	+	0.0870333i
$305$	−0.393950	+	1.13824i	−0.0225575	+	0.0651756i
$306$	1.30632	+	0.522971i	0.0746772	+	0.0298962i
$307$	3.84107	−	13.0815i	0.219222	−	0.746601i	−0.774286	−	0.632836i	$-0.781891\pi$
$307$	3.84107	−	13.0815i	0.219222	−	0.746601i	0.993508	−	0.113765i	$-0.0362910\pi$
$308$	3.69587	−	1.72927i	0.210592	−	0.0985344i
$309$	−13.1031	−	1.88394i	−0.745407	−	0.107173i
$310$	−1.36476	+	0.971839i	−0.0775130	+	0.0551967i
$311$	0.619655	+	6.48932i	0.0351374	+	0.367976i	0.995890	+	0.0905695i	$0.0288687\pi$
$311$	0.619655	+	6.48932i	0.0351374	+	0.367976i	−0.960753	+	0.277406i	$0.910525\pi$
$312$	−2.23109	+	0.893193i	−0.126310	+	0.0505671i
$313$	1.12266	+	23.5675i	0.0634563	+	1.33211i	0.776111	+	0.630596i	$0.217190\pi$
$313$	1.12266	+	23.5675i	0.0634563	+	1.33211i	−0.712655	+	0.701515i	$0.752507\pi$
$314$	−2.78669	−	0.818246i	−0.157262	−	0.0461763i
$315$	−0.231114	+	0.408977i	−0.0130218	+	0.0230432i
$316$	−7.14249	+	6.18900i	−0.401796	+	0.348159i
$317$	−25.8706	+	13.3372i	−1.45304	+	0.749094i	−0.990501	−	0.137506i	$-0.956092\pi$
$317$	−25.8706	+	13.3372i	−1.45304	+	0.749094i	−0.462538	+	0.886599i	$0.653061\pi$
$318$	4.84804	+	0.934384i	0.271865	+	0.0523976i
$319$	−6.41324	+	6.72601i	−0.359072	+	0.376584i
$320$	0.176749	+	0.0168775i	0.00988058	+	0.000943481i
$321$	−5.83554			−0.325708
$322$	−12.5320	+	1.98749i	−0.698379	+	0.110758i
$323$	2.13768			0.118944
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	8.23983	−	8.64169i	0.457064	−	0.479355i
$326$	−4.14530	−	0.798942i	−0.229587	−	0.0442493i
$327$	2.47624	−	1.27659i	0.136936	−	0.0705955i
$328$	5.66865	−	4.91191i	0.312999	−	0.271215i
$329$	−0.228708	−	24.7657i	−0.0126091	−	1.36538i
$330$	0.262740	+	0.0771474i	0.0144634	+	0.00424683i
$331$	1.02419	+	21.5004i	0.0562947	+	1.18177i	0.833498	+	0.552522i	$0.186334\pi$
$331$	1.02419	+	21.5004i	0.0562947	+	1.18177i	−0.777204	+	0.629249i	$0.783363\pi$
$332$	−6.89002	+	2.75835i	−0.378139	+	0.151384i
$333$	0.682700	+	7.14956i	0.0374117	+	0.391793i
$334$	0.297056	−	0.211533i	0.0162542	−	0.0115746i
$335$	−2.18897	−	0.314727i	−0.119596	−	0.0171954i
$336$	2.16925	+	1.51472i	0.118342	+	0.0826347i
$337$	8.26045	−	28.1325i	0.449976	−	1.53248i	−0.352512	−	0.935807i	$-0.614672\pi$
$337$	8.26045	−	28.1325i	0.449976	−	1.53248i	0.802488	−	0.596669i	$-0.203509\pi$
$338$	6.70695	+	2.68506i	0.364810	+	0.146048i
$339$	−6.45592	+	18.6531i	−0.350637	+	1.01310i
$340$	0.0118877	−	0.249554i	0.000644702	−	0.0135340i
$341$	4.75981	+	13.7526i	0.257758	+	0.744743i
$342$	−1.45766	+	0.428008i	−0.0788212	+	0.0231440i
$343$	18.5132	−	0.513016i	0.999616	−	0.0277003i
$344$			6.92066i			0.373137i
$345$	−0.718746	−	0.456597i	−0.0386960	−	0.0245824i
$346$	14.9023	−	8.60382i	0.801150	−	0.462544i
$347$	1.79373	−	2.51894i	0.0962925	−	0.135224i	−0.763619	−	0.645667i	$-0.776579\pi$
$347$	1.79373	−	2.51894i	0.0962925	−	0.135224i	0.859911	+	0.510443i	$0.170519\pi$
$348$	−5.85604	−	1.42066i	−0.313917	−	0.0761554i
$349$	11.8481	+	10.2664i	0.634215	+	0.549550i	0.911533	−	0.411228i	$-0.134900\pi$
$349$	11.8481	+	10.2664i	0.634215	+	0.549550i	−0.277318	+	0.960778i	$0.589445\pi$
$350$	−12.9302	−	2.36847i	−0.691149	−	0.126600i
$351$	−1.57378	−	1.81624i	−0.0840024	−	0.0969440i
$352$	0.573198	−	1.43178i	0.0305516	−	0.0763141i
$353$	−8.54966	+	2.07412i	−0.455052	+	0.110394i	−0.456732	−	0.889604i	$-0.650980\pi$
$353$	−8.54966	+	2.07412i	−0.455052	+	0.110394i	0.00168017	+	0.999999i	$0.499465\pi$
$354$	10.0194	+	5.16539i	0.532528	+	0.274537i
$355$	−1.29937	−	1.02184i	−0.0689635	−	0.0542335i
$356$	−6.60562	+	14.4643i	−0.350097	+	0.766605i
$357$	1.98373	−	3.15033i	0.104990	−	0.166733i
$358$	−3.24504	+	22.5697i	−0.171506	+	1.19285i
$359$	−5.43702	+	0.258997i	−0.286955	+	0.0136693i	−0.190566	−	0.981674i	$-0.561032\pi$
$359$	−5.43702	+	0.258997i	−0.286955	+	0.0136693i	−0.0963889	+	0.995344i	$0.530729\pi$
$360$	0.0418597	+	0.172548i	0.00220620	+	0.00909409i
$361$	13.1208	−	10.3183i	0.690570	−	0.543070i
$362$	0.0527786	−	0.0101722i	0.00277398	−	0.000534641i
$363$	−4.66111	+	7.25282i	−0.244645	+	0.380675i
$364$	1.26093	+	6.23208i	0.0660908	+	0.326650i
$365$	0.222686	+	0.758399i	0.0116559	+	0.0396964i
$366$	−0.644844	+	6.75311i	−0.0337065	+	0.352991i
$367$	−11.7458	−	20.3443i	−0.613126	−	1.06197i	−0.990710	−	0.135990i	$-0.956578\pi$
$367$	−11.7458	−	20.3443i	−0.613126	−	1.06197i	0.377584	−	0.925975i	$-0.376755\pi$
$368$	−2.94476	+	3.78529i	−0.153506	+	0.197322i
$369$	6.49580	+	3.75035i	0.338158	+	0.195235i
$370$	1.15996	−	0.529737i	0.0603036	−	0.0275397i
$371$	4.74275	−	12.1714i	0.246231	−	0.631907i
$372$	−6.17937	+	7.13138i	−0.320386	+	0.369745i
$373$	6.78071	+	13.1527i	0.351092	+	0.681024i	0.996570	−	0.0827554i	$-0.0263720\pi$
$373$	6.78071	+	13.1527i	0.351092	+	0.681024i	−0.645478	+	0.763779i	$0.723342\pi$
$374$	−2.05077	−	0.709778i	−0.106043	−	0.0367018i
$375$	−1.09410	−	1.39126i	−0.0564991	−	0.0718444i
$376$	−6.45981	−	6.77485i	−0.333139	−	0.349386i
$377$	−7.82938	−	12.1828i	−0.403234	−	0.627444i
$378$	−0.721920	+	2.54535i	−0.0371316	+	0.130919i
$379$	−16.4516	−	7.51319i	−0.845061	−	0.385926i	−0.0546516	−	0.998505i	$-0.517405\pi$
$379$	−16.4516	−	7.51319i	−0.845061	−	0.385926i	−0.790409	+	0.612579i	$0.790132\pi$
$380$	0.156464	+	0.219722i	0.00802641	+	0.0112715i
$381$	−5.58875	−	13.9600i	−0.286320	−	0.715194i
$382$	−4.01542	+	7.78883i	−0.205447	+	0.398511i
$383$	12.5088	−	11.9271i	0.639169	−	0.609446i	−0.299571	−	0.954074i	$-0.596843\pi$
$383$	12.5088	−	11.9271i	0.639169	−	0.609446i	0.938739	+	0.344628i	$0.111995\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	0.326021	−	0.646992i	0.0166155	−	0.0329738i
$386$	19.1879	+	12.3313i	0.976640	+	0.627648i
$387$	−6.54003	+	2.26353i	−0.332448	+	0.115061i
$388$	−0.0836280	−	0.0797391i	−0.00424557	−	0.00404814i
$389$	−12.2883	−	8.75043i	−0.623040	−	0.443665i	0.224443	−	0.974487i	$-0.427944\pi$
$389$	−12.2883	−	8.75043i	−0.623040	−	0.443665i	−0.847483	+	0.530823i	$0.821883\pi$
$390$	−0.213351	+	0.369535i	−0.0108034	+	0.0187121i
$391$	5.51745	+	3.88547i	0.279029	+	0.196497i
$392$	4.97606	−	4.92329i	0.251329	−	0.248664i
$393$	0.791817	+	1.73384i	0.0399419	+	0.0874605i
$394$	−4.12173	+	16.9900i	−0.207650	+	0.855945i
$395$	−0.317569	+	1.64771i	−0.0159787	+	0.0829051i
$396$	1.54051	+	0.0733835i	0.0774135	+	0.00368766i
$397$	0.0363849	+	0.188783i	0.00182611	+	0.00947474i	0.982830	−	0.184512i	$-0.0590704\pi$
$397$	0.0363849	+	0.188783i	0.00182611	+	0.00947474i	−0.981004	+	0.193986i	$0.937858\pi$
$398$	−2.00364	−	13.9356i	−0.100433	−	0.698530i
$399$	0.419003	+	3.99752i	0.0209764	+	0.200126i
$400$	−4.17975	+	2.68616i	−0.208987	+	0.134308i
$401$	10.0328	−	12.7578i	0.501015	−	0.637092i	−0.468108	−	0.883671i	$-0.655064\pi$
$401$	10.0328	−	12.7578i	0.501015	−	0.637092i	0.969123	+	0.246579i	$0.0793066\pi$
$402$	−12.3989	+	1.18396i	−0.618403	+	0.0590503i
$403$	−22.5746	+	2.15562i	−1.12452	+	0.107379i
$404$	−5.64708	+	7.18085i	−0.280953	+	0.357260i
$405$	−0.149367	+	0.0959924i	−0.00742211	+	0.00476990i
$406$	−6.48878	+	14.5628i	−0.322032	+	0.722742i
$407$	−1.57636	−	10.9639i	−0.0781375	−	0.543458i
$408$	−0.266298	−	1.38168i	−0.0131837	−	0.0684035i
$409$	−0.269884	−	0.0128562i	−0.0133449	−	0.000635697i	0.0409084	−	0.999163i	$-0.486975\pi$
$409$	−0.269884	−	0.0128562i	−0.0133449	−	0.000635697i	−0.0542533	+	0.998527i	$0.517278\pi$
$410$	0.252040	−	1.30771i	0.0124473	−	0.0645830i
$411$	1.50573	−	6.20671i	0.0742722	−	0.306154i
$412$	5.49918	+	12.0415i	0.270925	+	0.593244i
$413$	18.2189	−	23.6128i	0.896495	−	1.16191i
$414$	−4.54024	−	1.54475i	−0.223140	−	0.0759204i
$415$	−0.658868	+	1.14119i	−0.0323425	+	0.0560189i
$416$	1.95762	+	1.39401i	0.0959801	+	0.0683471i
$417$	15.3363	+	14.6231i	0.751020	+	0.716096i
$418$	2.21413	−	0.766318i	0.108297	−	0.0374818i
$419$	30.5603	+	19.6399i	1.49297	+	0.959472i	0.995775	+	0.0918313i	$0.0292721\pi$
$419$	30.5603	+	19.6399i	1.49297	+	0.959472i	0.497192	+	0.867640i	$0.334364\pi$
$420$	0.469003	−	0.0266843i	0.0228850	−	0.00130206i
$421$	−9.10754	+	1.30947i	−0.443874	+	0.0638195i	−0.360629	−	0.932710i	$-0.617438\pi$
$421$	−9.10754	+	1.30947i	−0.443874	+	0.0638195i	−0.0832459	+	0.996529i	$0.526529\pi$
$422$	−9.50597	+	9.06392i	−0.462743	+	0.441225i
$423$	4.28944	−	8.32036i	0.208560	−	0.404550i
$424$	−1.83500	−	4.58360i	−0.0891153	−	0.222599i
$425$	4.05529	+	5.69486i	0.196711	+	0.276241i
$426$	−8.46874	−	3.86754i	−0.410312	−	0.187383i
$427$	17.2672	+	4.89738i	0.835621	+	0.237001i
$428$	3.15493	+	4.90917i	0.152499	+	0.237294i
$429$	2.55771	+	2.68245i	0.123487	+	0.129510i
$430$	0.759584	+	0.965889i	0.0366304	+	0.0465793i
$431$	0.959298	+	0.332016i	0.0462078	+	0.0159927i	0.350074	−	0.936722i	$-0.386156\pi$
$431$	0.959298	+	0.332016i	0.0462078	+	0.0159927i	−0.303866	+	0.952715i	$0.598278\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	−12.0484	+	13.9046i	−0.579008	+	0.668211i	−0.967391	−	0.253287i	$-0.918488\pi$
$433$	−12.0484	+	13.9046i	−0.579008	+	0.668211i	0.388383	+	0.921498i	$0.373034\pi$
$434$	15.6134	+	19.4810i	0.749465	+	0.935120i
$435$	−0.973231	+	0.444460i	−0.0466629	+	0.0213102i
$436$	−2.41269	−	1.39297i	−0.115547	−	0.0667110i
$437$	−7.27565	+	0.384871i	−0.348041	+	0.0184109i
$438$	2.22586	+	3.85530i	0.106356	+	0.184214i
$439$	−3.02501	+	31.6794i	−0.144376	+	1.51197i	0.575460	+	0.817830i	$0.304823\pi$
$439$	−3.02501	+	31.6794i	−0.144376	+	1.51197i	−0.719836	+	0.694144i	$0.755783\pi$
$440$	−0.0771474	−	0.262740i	−0.00367786	−	0.0125256i
$441$	6.28003	+	3.09213i	0.299049	+	0.147244i
$442$	1.82824	−	2.84480i	0.0869606	−	0.135313i
$443$	−11.8040	+	2.27504i	−0.560827	+	0.108091i	−0.461784	−	0.886993i	$-0.652790\pi$
$443$	−11.8040	+	2.27504i	−0.560827	+	0.108091i	−0.0990434	+	0.995083i	$0.531578\pi$
$444$	5.64550	−	4.43967i	0.267923	−	0.210697i
$445$	0.665622	+	2.74373i	0.0315535	+	0.130065i
$446$	−20.3171	+	0.967823i	−0.962043	+	0.0458278i
$447$	3.10839	−	21.6193i	0.147022	−	1.02256i
$448$	0.101480	−	2.64380i	0.00479448	−	0.124908i
$449$	−15.2429	+	33.3774i	−0.719358	+	1.57517i	0.0954436	+	0.995435i	$0.469573\pi$
$449$	−15.2429	+	33.3774i	−0.719358	+	1.57517i	−0.814802	+	0.579740i	$0.803154\pi$
$450$	−3.90549	−	3.07131i	−0.184106	−	0.144783i
$451$	−10.2820	−	5.30076i	−0.484162	−	0.249603i
$452$	19.1824	−	4.65359i	0.902262	−	0.218886i
$453$	−5.04936	+	12.6127i	−0.237240	+	0.592596i
$454$	2.32626	+	2.68465i	0.109177	+	0.125997i
$455$	0.859992	+	0.731393i	0.0403171	+	0.0342882i
$456$	1.14813	+	0.994863i	0.0537663	+	0.0465887i
$457$	−30.4365	−	7.38381i	−1.42376	−	0.345400i	−0.551390	−	0.834248i	$-0.685902\pi$
$457$	−30.4365	−	7.38381i	−1.42376	−	0.345400i	−0.872369	+	0.488848i	$0.837417\pi$
$458$	−11.2525	+	15.8019i	−0.525795	+	0.738376i
$459$	1.21859	−	0.703556i	0.0568791	−	0.0328392i
$460$	0.00446994	+	0.851503i	0.000208412	+	0.0397015i
$461$			30.1030i			1.40204i	0.713144	+	0.701018i	$0.247271\pi$
$461$			30.1030i			1.40204i	−0.713144	+	0.701018i	$0.752729\pi$
$462$	0.925337	−	3.97412i	0.0430506	−	0.184893i
$463$	16.3666	−	4.80565i	0.760618	−	0.223338i	0.121652	−	0.992573i	$-0.461181\pi$
$463$	16.3666	−	4.80565i	0.760618	−	0.223338i	0.638966	+	0.769235i	$0.279363\pi$
$464$	1.97088	+	5.69448i	0.0914958	+	0.264360i
$465$	−0.0797197	+	1.67352i	−0.00369691	+	0.0776077i
$466$	1.73958	−	5.02620i	0.0805847	−	0.232834i
$467$	−32.3707	−	12.9593i	−1.49794	−	0.599683i	−0.529359	−	0.848398i	$-0.677568\pi$
$467$	−32.3707	−	12.9593i	−1.49794	−	0.599683i	−0.968577	+	0.248715i	$0.919992\pi$
$468$	−0.677070	+	2.30589i	−0.0312976	+	0.106590i
$469$	−2.82939	+	32.8320i	−0.130649	+	1.51604i
$470$	−1.64515	−	0.236537i	−0.0758852	−	0.0109106i
$471$	−2.36580	+	1.68468i	−0.109010	+	0.0776260i
$472$	−1.07152	−	11.2215i	−0.0493209	−	0.516512i
$473$	9.90886	−	3.96691i	0.455610	−	0.182399i
$474$	0.449690	+	9.44016i	0.0206550	+	0.433601i
$475$	−7.24235	−	2.12655i	−0.332302	−	0.0975726i
$476$	−3.72271	+	0.0343787i	−0.170630	+	0.00157575i
$477$	3.73134	−	3.23322i	0.170846	−	0.148039i
$478$	0.408229	−	0.210457i	0.0186720	−	0.00962607i
$479$	−4.79558	−	0.924272i	−0.219116	−	0.0422311i	0.0785118	−	0.996913i	$-0.474983\pi$
$479$	−4.79558	−	0.924272i	−0.219116	−	0.0422311i	−0.297627	+	0.954682i	$0.596195\pi$
$480$	0.122526	−	0.128501i	0.00559251	−	0.00586525i
$481$	17.1821	+	1.64069i	0.783435	+	0.0748090i
$482$	1.57401			0.0716943
$483$	−6.18447	+	11.0794i	−0.281403	+	0.504129i
$484$	8.62145			0.391884
$485$	−0.0204235	−	0.00195021i	−0.000927382	−	8.85543e-5i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	−10.6758	−	2.05760i	−0.483768	−	0.0932386i	−0.0584645	−	0.998289i	$-0.518620\pi$
$487$	−10.6758	−	2.05760i	−0.483768	−	0.0932386i	−0.425303	+	0.905051i	$0.639833\pi$
$488$	6.02971	−	3.10853i	0.272952	−	0.140717i
$489$	−3.19047	+	2.76456i	−0.144278	+	0.125018i
$490$	0.154129	−	1.23328i	0.00696284	−	0.0557138i
$491$	22.5860	+	6.63186i	1.01929	+	0.299292i	0.748350	−	0.663304i	$-0.230846\pi$
$491$	22.5860	+	6.63186i	1.01929	+	0.299292i	0.270943	+	0.962595i	$0.412664\pi$
$492$	−0.356898	−	7.49220i	−0.0160902	−	0.337775i
$493$	7.87174	−	3.15137i	0.354525	−	0.141931i
$494$	0.347049	+	3.63446i	0.0156145	+	0.163522i
$495$	0.223057	−	0.158838i	0.0100257	−	0.00713925i
$496$	9.34012	+	1.34291i	0.419384	+	0.0602983i
$497$	−14.1021	+	20.1958i	−0.632568	+	0.905907i
$498$	−2.09092	+	7.12101i	−0.0936963	+	0.319100i
$499$	16.8706	+	6.75396i	0.755231	+	0.302349i	0.717144	−	0.696926i	$-0.245449\pi$
$499$	16.8706	+	6.75396i	0.755231	+	0.302349i	0.0380875	+	0.999274i	$0.487873\pi$
$500$	−0.578889	+	1.67259i	−0.0258887	+	0.0748004i
$501$	0.0173520	−	0.364263i	0.000775230	−	0.0162741i
$502$	0.360086	+	1.04040i	0.0160714	+	0.0464353i
$503$	10.8570	−	3.18789i	0.484088	−	0.142141i	−0.0305772	−	0.999532i	$-0.509735\pi$
$503$	10.8570	−	3.18789i	0.484088	−	0.142141i	0.514665	+	0.857391i	$0.327916\pi$
$504$	2.53159	−	0.768805i	0.112766	−	0.0342453i
$505$			1.62200i			0.0721782i
$506$	7.10763	+	2.04652i	0.315973	+	0.0909790i
$507$	6.25656	−	3.61223i	0.277864	−	0.160425i
$508$	−8.72242	+	12.2489i	−0.386995	+	0.543458i
$509$	−19.8272	−	4.81002i	−0.878825	−	0.213201i	−0.229130	−	0.973396i	$-0.573588\pi$
$509$	−19.8272	−	4.81002i	−0.878825	−	0.213201i	−0.649695	+	0.760195i	$0.725103\pi$
$510$	−0.188814	−	0.163608i	−0.00836083	−	0.00724470i
$511$	11.0943	−	3.95487i	0.490783	−	0.174953i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.564629	+	1.41038i	−0.0249290	+	0.0622696i
$514$	−28.0655	+	6.80861i	−1.23792	+	0.300315i
$515$	2.08913	+	1.07702i	0.0920581	+	0.0474592i
$516$	5.44000	+	4.27807i	0.239483	+	0.188331i
$517$	−5.99735	+	13.1324i	−0.263763	+	0.577561i
$518$	−8.86282	−	16.8085i	−0.389410	−	0.738524i
$519$	2.44890	−	17.0325i	0.107495	−	0.747644i
$520$	0.426219	−	0.0203033i	0.0186909	−	0.000890359i
$521$	2.03150	+	8.37395i	0.0890016	+	0.366869i	0.998843	−	0.0480863i	$-0.0153122\pi$
$521$	2.03150	+	8.37395i	0.0890016	+	0.366869i	−0.909842	+	0.414956i	$0.863797\pi$
$522$	−4.73668	+	3.72497i	−0.207319	+	0.163037i
$523$	18.7454	−	3.61288i	0.819678	−	0.157980i	0.237861	−	0.971299i	$-0.423554\pi$
$523$	18.7454	−	3.61288i	0.819678	−	0.157980i	0.581818	+	0.813319i	$0.302342\pi$
$524$	1.03051	−	1.60350i	0.0450180	−	0.0700493i
$525$	−9.85467	+	8.69975i	−0.430093	+	0.379688i
$526$	2.36385	+	8.05053i	0.103069	+	0.351020i
$527$	1.26213	−	13.2176i	0.0549792	−	0.575768i
$528$	−0.771128	−	1.33563i	−0.0335590	−	0.0581259i
$529$	−19.4783	−	12.2309i	−0.846883	−	0.531779i
$530$	−0.759181	−	0.438313i	−0.0329767	−	0.0190391i
$531$	10.2539	−	4.68279i	0.444980	−	0.203216i
$532$	3.13640	−	2.51371i	0.135980	−	0.108983i
$533$	11.8045	−	13.6231i	0.511309	−	0.590082i
$534$	7.28637	+	14.1336i	0.315312	+	0.611620i
$535$	0.979132	+	0.338881i	0.0423316	+	0.0146511i
$536$	7.69938	+	9.79056i	0.332563	+	0.422888i
$537$	15.7351	+	16.5025i	0.679018	+	0.712133i
$538$	−1.80600	−	2.81019i	−0.0778622	−	0.121156i
$539$	−9.90134	−	4.30261i	−0.426481	−	0.185326i
$540$	0.161508	+	0.0737582i	0.00695020	+	0.00317405i
$541$	6.63957	+	9.32398i	0.285458	+	0.400869i	0.932260	−	0.361788i	$-0.117834\pi$
$541$	6.63957	+	9.32398i	0.285458	+	0.400869i	−0.646803	+	0.762657i	$0.723894\pi$
$542$	−2.53652	−	6.33593i	−0.108953	−	0.272152i
$543$	0.0246297	−	0.0477749i	0.00105696	−	0.00205022i
$544$	−1.01837	+	0.971018i	−0.0436624	+	0.0416321i
$545$	−0.489616	+	0.0703962i	−0.0209729	+	0.00301544i
$546$	5.67820	+	2.86126i	0.243005	+	0.122451i
$547$	−15.7893	−	10.1472i	−0.675101	−	0.433861i	0.157660	−	0.987493i	$-0.449605\pi$
$547$	−15.7893	−	10.1472i	−0.675101	−	0.433861i	−0.832761	+	0.553632i	$0.813241\pi$
$548$	−6.03547	+	2.08890i	−0.257823	+	0.0892333i
$549$	4.90969	+	4.68138i	0.209540	+	0.199796i
$550$	6.24182	+	4.44478i	0.266152	+	0.189526i
$551$	−4.57727	+	7.92807i	−0.194998	+	0.337747i
$552$	1.15511	+	4.65465i	0.0491648	+	0.198115i
$553$	24.7819	+	3.32983i	1.05384	+	0.141599i
$554$	−6.37362	−	13.9563i	−0.270789	−	0.592945i
$555$	0.300640	−	1.23925i	0.0127615	−	0.0526034i
$556$	4.01032	−	20.8075i	0.170076	−	0.882436i
$557$	24.0223	+	1.14432i	1.01786	+	0.0484865i	0.549871	−	0.835250i	$-0.314677\pi$
$557$	24.0223	+	1.14432i	1.01786	+	0.0484865i	0.467985	+	0.883736i	$0.344980\pi$
$558$	1.78581	+	9.26564i	0.0755992	+	0.392246i
$559$	2.36698	+	16.4627i	0.100112	+	0.696297i
$560$	−0.276010	−	0.380124i	−0.0116636	−	0.0160632i
$561$	−1.82563	+	1.17326i	−0.0770780	+	0.0495350i
$562$	0.820997	−	1.04398i	0.0346317	−	0.0440377i
$563$	−39.2521	+	3.74812i	−1.65428	+	0.157965i	−0.880031	−	0.474917i	$-0.842478\pi$
$563$	−39.2521	+	3.74812i	−1.65428	+	0.157965i	−0.774249	+	0.632881i	$0.781872\pi$
$564$	−9.31858	+	0.889817i	−0.392383	+	0.0374680i
$565$	2.16645	−	2.75486i	0.0911431	−	0.115898i
$566$	11.2257	−	7.21435i	0.471853	−	0.303242i
$567$	1.55452	+	2.14090i	0.0652838	+	0.0899094i
$568$	1.32496	+	9.21531i	0.0555942	+	0.386666i
$569$	−0.700967	−	3.63696i	−0.0293861	−	0.152469i	0.964272	−	0.264915i	$-0.0853438\pi$
$569$	−0.700967	−	3.63696i	−0.0293861	−	0.152469i	−0.993658	+	0.112445i	$0.964132\pi$
$570$	0.269433	+	0.0128347i	0.0112853	+	0.000537585i
$571$	−6.89643	+	35.7821i	−0.288606	+	1.49743i	0.490998	+	0.871161i	$0.336632\pi$
$571$	−6.89643	+	35.7821i	−0.288606	+	1.49743i	−0.779605	+	0.626272i	$0.784580\pi$
$572$	0.873818	−	3.60193i	0.0365362	−	0.150604i
$573$	3.64027	+	7.97107i	0.152074	+	0.332996i
$574$	−19.6682	−	2.64272i	−0.820936	−	0.110305i
$575$	−14.8276	−	18.6525i	−0.618353	−	0.777862i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	21.2473	+	15.1301i	0.884537	+	0.629876i	0.929383	−	0.369118i	$-0.120340\pi$
$577$	21.2473	+	15.1301i	0.884537	+	0.629876i	−0.0448455	+	0.998994i	$0.514280\pi$
$578$	−10.8705	−	10.3650i	−0.452154	−	0.431128i
$579$	21.5543	−	7.46001i	0.895765	−	0.310027i
$580$	0.900072	+	0.578441i	0.0373735	+	0.0240185i
$581$	17.5354	+	8.83610i	0.727489	+	0.366583i
$582$	−0.114375	+	0.0164446i	−0.00474098	+	0.000681650i
$583$	−5.51089	+	5.25462i	−0.228238	+	0.217624i
$584$	2.03990	−	3.95685i	0.0844115	−	0.163736i
$585$	0.158589	+	0.396136i	0.00655685	+	0.0163782i
$586$	5.16436	+	7.25233i	0.213338	+	0.299591i
$587$	−26.8234	−	12.2498i	−1.10712	−	0.505604i	−0.223922	−	0.974607i	$-0.571886\pi$
$587$	−26.8234	−	12.2498i	−1.10712	−	0.505604i	−0.883197	+	0.469003i	$0.844614\pi$
$588$	−0.793971	−	6.95483i	−0.0327428	−	0.286812i
$589$	7.75030	+	12.0597i	0.319346	+	0.496912i
$590$	−1.38118	−	1.44854i	−0.0568622	−	0.0596353i
$591$	10.8072	+	13.7424i	0.444548	+	0.565288i
$592$	−6.78707	−	2.34903i	−0.278947	−	0.0965445i
$593$	−18.7217	−	36.3151i	−0.768810	−	1.49128i	−0.868189	−	0.496233i	$-0.834716\pi$
$593$	−18.7217	−	36.3151i	−0.768810	−	1.49128i	0.0993796	−	0.995050i	$-0.468314\pi$
$594$	1.00996	−	1.16556i	0.0414393	−	0.0478235i
$595$	−0.515791	+	0.413388i	−0.0211454	+	0.0169472i
$596$	−19.8679	+	9.07334i	−0.813819	+	0.371659i
$597$	−12.1927	−	7.03947i	−0.499015	−	0.288106i
$598$	−5.71028	+	10.0115i	−0.233511	+	0.409401i
$599$	−7.87317	−	13.6367i	−0.321689	−	0.557182i	0.659148	−	0.752014i	$-0.270917\pi$
$599$	−7.87317	−	13.6367i	−0.321689	−	0.557182i	−0.980837	+	0.194832i	$0.937584\pi$
$600$	−0.472284	+	4.94598i	−0.0192809	+	0.201919i
$601$	−7.80018	−	26.5650i	−0.318176	−	1.08361i	−0.950969	−	0.309287i	$-0.899910\pi$
$601$	−7.80018	−	26.5650i	−0.318176	−	1.08361i	0.632793	−	0.774321i	$-0.281908\pi$
$602$	13.7267	−	12.1180i	0.559459	−	0.493893i
$603$	−6.73386	+	10.4781i	−0.274224	+	0.426701i
$604$	13.3404	−	2.57115i	0.542812	−	0.104618i
$605$	1.20326	−	0.946256i	0.0489196	−	0.0384708i
$606$	2.15373	+	8.87781i	0.0874894	+	0.360636i
$607$	9.12449	−	0.434653i	0.370352	−	0.0176420i	0.138419	−	0.990374i	$-0.455798\pi$
$607$	9.12449	−	0.434653i	0.370352	−	0.0176420i	0.231933	+	0.972732i	$0.425495\pi$
$608$	0.216204	−	1.50374i	0.00876825	−	0.0609845i
$609$	7.43607	+	14.1027i	0.301325	+	0.571469i
$610$	0.500363	−	1.09564i	0.0202591	−	0.0443613i
$611$	−17.6835	−	13.9065i	−0.715399	−	0.562596i
$612$	−1.25069	−	0.644776i	−0.0505562	−	0.0260635i
$613$	−34.3297	+	8.32830i	−1.38656	+	0.336377i	−0.858494	−	0.512824i	$-0.828599\pi$
$613$	−34.3297	+	8.32830i	−1.38656	+	0.336377i	−0.528070	+	0.849201i	$0.677084\pi$
$614$	−5.06716	+	12.6571i	−0.204494	+	0.510801i
$615$	−0.872125	−	1.00649i	−0.0351675	−	0.0405854i
$616$	−3.84352	+	1.37013i	−0.154860	+	0.0552040i
$617$	3.57415	+	3.09702i	0.143890	+	0.124681i	0.723832	−	0.689977i	$-0.242379\pi$
$617$	3.57415	+	3.09702i	0.143890	+	0.124681i	−0.579942	+	0.814658i	$0.696925\pi$
$618$	12.8647	+	3.12093i	0.517492	+	0.125542i
$619$	20.1769	−	28.3344i	0.810977	−	1.13886i	−0.176993	−	0.984212i	$-0.556637\pi$
$619$	20.1769	−	28.3344i	0.810977	−	1.13886i	0.987970	−	0.154645i	$-0.0494235\pi$
$620$	1.45096	−	0.837710i	0.0582718	−	0.0336432i
$621$	−4.02084	+	2.61397i	−0.161351	+	0.104895i
$622$		−	6.51884i		−	0.261382i
$623$	40.2554	−	12.2250i	1.61280	−	0.489782i
$624$	2.30589	−	0.677070i	0.0923094	−	0.0271045i
$625$	−8.02236	−	23.1791i	−0.320894	−	0.927164i
$626$	1.12266	−	23.5675i	0.0448704	−	0.941945i
$627$	0.766318	−	2.21413i	0.0306038	−	0.0884238i
$628$	2.69629	+	1.07943i	0.107594	+	0.0430741i
$629$	−2.84719	+	9.69662i	−0.113525	+	0.386630i
$630$	0.268943	−	0.385156i	0.0107149	−	0.0153450i
$631$	−38.7480	−	5.57112i	−1.54253	−	0.221783i	−0.682067	−	0.731290i	$-0.738919\pi$
$631$	−38.7480	−	5.57112i	−1.54253	−	0.221783i	−0.860467	+	0.509507i	$0.829828\pi$
$632$	7.69845	−	5.48204i	0.306228	−	0.218064i
$633$	1.24852	+	13.0751i	0.0496244	+	0.519690i
$634$	27.0213	−	10.8177i	1.07315	−	0.429625i
$635$	0.127039	+	2.66687i	0.00504138	+	0.105832i
$636$	−4.73727	−	1.39099i	−0.187845	−	0.0551563i
$637$	10.1531	−	13.4133i	0.402280	−	0.531454i
$638$	7.02354	−	6.08594i	0.278065	−	0.240944i
$639$	−8.27512	+	4.26612i	−0.327359	+	0.168765i
$640$	−0.174344	−	0.0336021i	−0.00689157	−	0.00132824i
$641$	−21.2028	+	22.2369i	−0.837460	+	0.878303i	−0.994001	−	0.109368i	$-0.965117\pi$
$641$	−21.2028	+	22.2369i	−0.837460	+	0.878303i	0.156541	+	0.987671i	$0.449966\pi$
$642$	5.80911	+	0.554703i	0.229267	+	0.0218924i
$643$	23.2015			0.914977			0.457488	−	0.889216i	$-0.348749\pi$
$643$	23.2015			0.914977			0.457488	+	0.889216i	$0.348749\pi$
$644$	12.6641	−	0.787251i	0.499037	−	0.0310220i
$645$	1.22878			0.0483833
$646$	−2.12800	−	0.203200i	−0.0837251	−	0.00799478i
$647$	−16.5033	+	17.3082i	−0.648813	+	0.680455i	−0.963183	−	0.268845i	$-0.913358\pi$
$647$	−16.5033	+	17.3082i	−0.648813	+	0.680455i	0.314371	+	0.949300i	$0.398207\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	−15.4525	+	7.96634i	−0.606566	+	0.312706i
$650$	−9.02397	+	7.81931i	−0.353949	+	0.306699i
$651$	24.9647	−	0.230545i	0.978443	−	0.00903579i
$652$	4.05059	+	1.18936i	0.158633	+	0.0465789i
$653$	0.639115	+	13.4167i	0.0250105	+	0.525035i	0.976259	+	0.216608i	$0.0694995\pi$
$653$	0.639115	+	13.4167i	0.0250105	+	0.525035i	−0.951248	+	0.308427i	$0.900197\pi$
$654$	−2.58637	+	1.03543i	−0.101135	+	0.0404884i
$655$	−0.0321700	−	0.336899i	−0.00125698	−	0.0131637i
$656$	−6.10989	+	4.35083i	−0.238551	+	0.169871i
$657$	4.40641	+	0.633546i	0.171910	+	0.0247170i
$658$	−2.12646	+	24.6753i	−0.0828981	+	0.961945i
$659$	−2.13861	+	7.28345i	−0.0833085	+	0.283723i	−0.990602	−	0.136775i	$-0.956326\pi$
$659$	−2.13861	+	7.28345i	−0.0833085	+	0.283723i	0.907294	+	0.420498i	$0.138145\pi$
$660$	−0.254217	−	0.101773i	−0.00989538	−	0.00396151i
$661$	4.13523	−	11.9480i	0.160842	−	0.464722i	−0.835568	−	0.549388i	$-0.814861\pi$
$661$	4.13523	−	11.9480i	0.160842	−	0.464722i	0.996409	+	0.0846658i	$0.0269822\pi$
$662$	1.02419	−	21.5004i	0.0398064	−	0.835638i
$663$	−1.10602	−	3.19563i	−0.0429543	−	0.124108i
$664$	7.12101	−	2.09092i	0.276349	−	0.0811434i
$665$	0.161840	−	0.695068i	0.00627589	−	0.0269536i
$666$		−	7.18208i		−	0.278300i
$667$	−26.2243	+	12.1430i	−1.01541	+	0.470179i
$668$	−0.315819	+	0.182338i	−0.0122194	+	0.00705487i
$669$	−11.7984	+	16.5686i	−0.456154	+	0.640579i
$670$	2.14915	+	0.521377i	0.0830287	+	0.0201426i
$671$	−7.90695	−	6.85141i	−0.305244	−	0.264496i
$672$	−2.01544	−	1.71406i	−0.0777473	−	0.0661213i
$673$	8.87397	+	10.2411i	0.342067	+	0.394766i	0.900552	−	0.434749i	$-0.143163\pi$
$673$	8.87397	+	10.2411i	0.342067	+	0.394766i	−0.558485	+	0.829514i	$0.688617\pi$
$674$	−10.8972	+	27.2199i	−0.419745	+	1.04847i
$675$	−4.82842	+	1.17136i	−0.185846	+	0.0450858i
$676$	−6.42135	−	3.31044i	−0.246975	−	0.127325i
$677$	−27.6973	−	21.7814i	−1.06449	−	0.837127i	−0.0773568	−	0.997003i	$-0.524648\pi$
$677$	−27.6973	−	21.7814i	−1.06449	−	0.837127i	−0.987137	+	0.159876i	$0.948890\pi$
$678$	8.19978	−	17.9550i	0.314911	−	0.689558i
$679$	−0.0117261	+	0.305493i	−0.000450006	+	0.0117238i
$680$	−0.0355555	+	0.247294i	−0.00136349	+	0.00948329i
$681$	3.54828	−	0.169025i	0.135970	−	0.00647706i
$682$	−3.43099	−	14.1427i	−0.131380	−	0.541554i
$683$	−0.460026	+	0.361769i	−0.0176024	+	0.0138427i	−0.626921	−	0.779082i	$-0.715685\pi$
$683$	−0.460026	+	0.361769i	−0.0176024	+	0.0138427i	0.609319	+	0.792925i	$0.291443\pi$
$684$	1.49174	−	0.287510i	0.0570383	−	0.0109932i
$685$	−0.613079	+	0.953969i	−0.0234245	+	0.0364493i
$686$	−18.4781	−	1.24909i	−0.705497	−	0.0476906i
$687$	5.46532	+	18.6132i	0.208515	+	0.710137i
$688$	0.657850	−	6.88932i	0.0250803	−	0.262653i
$689$	−5.93271	−	10.2758i	−0.226018	−	0.391475i
$690$	0.672090	+	0.522851i	0.0255860	+	0.0199046i
$691$	32.5612	+	18.7992i	1.23869	+	0.715156i	0.968826	−	0.247743i	$-0.0796889\pi$
$691$	32.5612	+	18.7992i	1.23869	+	0.715156i	0.269861	+	0.962899i	$0.413022\pi$
$692$	−15.6526	+	7.14831i	−0.595024	+	0.271738i
$693$	−2.55186	−	3.18400i	−0.0969372	−	0.120950i
$694$	−2.02505	+	2.33703i	−0.0768698	+	0.0887125i
$695$	−1.72405	−	3.34418i	−0.0653968	−	0.126852i
$696$	5.69448	+	1.97088i	0.215849	+	0.0747060i
$697$	6.52425	+	8.29625i	0.247123	+	0.314243i
$698$	−10.8186	−	11.3462i	−0.409489	−	0.429460i
$699$	−2.87552	−	4.47440i	−0.108762	−	0.169237i
$700$	12.6465	+	3.58684i	0.477994	+	0.135570i
$701$	9.26865	+	4.23285i	0.350072	+	0.159873i	0.582688	−	0.812696i	$-0.302001\pi$
$701$	9.26865	+	4.23285i	0.350072	+	0.159873i	−0.232616	+	0.972569i	$0.574728\pi$
$702$	1.39401	+	1.95762i	0.0526137	+	0.0738855i
$703$	−4.05521	−	10.1294i	−0.152945	−	0.382039i
$704$	−0.706702	+	1.37081i	−0.0266348	+	0.0516644i
$705$	−1.20290	+	1.14696i	−0.0453037	+	0.0431970i
$706$	8.70810	−	1.25204i	0.327734	−	0.0471210i
$707$	24.1308	−	1.37294i	0.907530	−	0.0516346i
$708$	−9.48308	−	6.09440i	−0.356396	−	0.229042i
$709$	13.0977	−	4.53315i	0.491893	−	0.170246i	−0.0698500	−	0.997558i	$-0.522252\pi$
$709$	13.0977	−	4.53315i	0.491893	−	0.170246i	0.561743	+	0.827312i	$0.310131\pi$
$710$	1.19636	+	1.14072i	0.0448984	+	0.0428106i
$711$	7.69845	+	5.48204i	0.288714	+	0.205593i
$712$	7.95062	−	13.7709i	0.297962	−	0.516086i
$713$	−1.91597	+	45.2137i	−0.0717535	+	1.69327i
$714$	−2.27420	+	2.94750i	−0.0851099	+	0.110307i
$715$	−0.273378	−	0.598614i	−0.0102237	−	0.0223869i
$716$	5.37573	−	22.1591i	0.200901	−	0.828123i
$717$	0.0869204	−	0.450986i	0.00324610	−	0.0168424i
$718$	5.43702	+	0.258997i	0.202908	+	0.00966568i
$719$	−2.63484	−	13.6708i	−0.0982628	−	0.509836i	−0.997393	−	0.0721554i	$-0.977012\pi$
$719$	−2.63484	−	13.6708i	−0.0982628	−	0.509836i	0.899131	−	0.437680i	$-0.144200\pi$
$720$	−0.0252684	−	0.175746i	−0.000941699	−	0.00654966i
$721$	14.2546	−	31.9919i	0.530871	−	1.19144i
$722$	−14.0422	+	9.02440i	−0.522598	+	0.335853i
$723$	0.972990	−	1.23726i	0.0361859	−	0.0460141i
$724$	−0.0535066	+	0.00510926i	−0.00198856	+	0.000189884i
$725$	−29.8040	+	2.84593i	−1.10689	+	0.105695i
$726$	5.32943	−	6.77692i	0.197794	−	0.251515i
$727$	−0.825227	+	0.530341i	−0.0306060	+	0.0196693i	−0.555854	−	0.831280i	$-0.687609\pi$
$727$	−0.825227	+	0.530341i	−0.0306060	+	0.0196693i	0.525248	+	0.850949i	$0.323972\pi$
$728$	−0.662826	−	6.32372i	−0.0245659	−	0.234373i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−0.149587	−	0.776133i	−0.00553648	−	0.0287260i
$731$	−9.72711	−	0.463359i	−0.359770	−	0.0171380i
$732$	1.28385	−	6.66123i	0.0474524	−	0.246206i
$733$	5.95030	−	24.5275i	0.219779	−	0.905943i	−0.749898	−	0.661554i	$-0.769897\pi$
$733$	5.95030	−	24.5275i	0.219779	−	0.905943i	0.969677	−	0.244389i	$-0.0785874\pi$
$734$	9.75877	+	21.3687i	0.360203	+	0.788734i
$735$	−0.874146	−	0.883515i	−0.0322433	−	0.0325890i
$736$	3.29124	−	3.48823i	0.121317	−	0.128578i
$737$	9.60465	−	16.6358i	0.353792	−	0.612786i
$738$	−6.10989	−	4.35083i	−0.224908	−	0.160156i
$739$	−15.3303	−	14.6174i	−0.563935	−	0.537711i	0.353584	−	0.935403i	$-0.384963\pi$
$739$	−15.3303	−	14.6174i	−0.563935	−	0.537711i	−0.917519	+	0.397692i	$0.869811\pi$
$740$	−1.20507	+	0.417077i	−0.0442991	+	0.0153321i
$741$	3.07141	+	1.97388i	0.112831	+	0.0725121i
$742$	−5.87824	+	11.6654i	−0.215797	+	0.428252i
$743$	9.82156	−	1.41213i	0.360318	−	0.0518059i	0.0402214	−	0.999191i	$-0.487194\pi$
$743$	9.82156	−	1.41213i	0.360318	−	0.0518059i	0.320097	+	0.947385i	$0.396285\pi$
$744$	6.82927	−	6.51170i	0.250373	−	0.238730i
$745$	−1.77703	+	3.44695i	−0.0651052	+	0.126286i
$746$	−5.49976	−	13.7377i	−0.201361	−	0.502974i
$747$	4.30498	+	6.04549i	0.157511	+	0.221193i
$748$	1.97402	+	0.901502i	0.0721771	+	0.0329622i
$749$	4.21279	−	14.8535i	0.153932	−	0.542736i
$750$	0.956898	+	1.48896i	0.0349410	+	0.0543692i
$751$	−32.9736	−	34.5817i	−1.20322	−	1.26191i	−0.956140	−	0.292912i	$-0.905376\pi$
$751$	−32.9736	−	34.5817i	−1.20322	−	1.26191i	−0.247085	−	0.968994i	$-0.579473\pi$
$752$	5.78657	+	7.35822i	0.211014	+	0.268327i
$753$	1.04040	+	0.360086i	0.0379143	+	0.0131223i
$754$	6.63588	+	12.8718i	0.241665	+	0.468764i
$755$	1.57967	−	1.82303i	0.0574899	−	0.0663469i
$756$	0.960603	−	2.46521i	0.0349368	−	0.0896587i
$757$	−23.0389	+	10.5215i	−0.837362	+	0.382411i	−0.787477	−	0.616344i	$-0.788613\pi$
$757$	−23.0389	+	10.5215i	−0.837362	+	0.382411i	−0.0498856	+	0.998755i	$0.515886\pi$
$758$	15.6629	+	9.04299i	0.568903	+	0.328456i
$759$	6.00232	−	4.32190i	0.217870	−	0.156875i
$760$	−0.134869	−	0.233600i	−0.00489222	−	0.00847357i
$761$	3.07188	−	32.1702i	0.111356	−	1.16617i	−0.751153	−	0.660128i	$-0.770502\pi$
$761$	3.07188	−	32.1702i	0.111356	−	1.16617i	0.862509	−	0.506041i	$-0.168892\pi$
$762$	4.23646	+	14.4281i	0.153471	+	0.522674i
$763$	1.46173	+	7.22450i	0.0529181	+	0.261544i
$764$	4.73762	−	7.37188i	0.171401	−	0.266705i
$765$	−0.245322	+	0.0472820i	−0.00886964	+	0.00170948i
$766$	−13.5859	+	10.6841i	−0.490878	+	0.386031i
$767$	−6.38686	−	26.3270i	−0.230616	−	0.950612i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	5.67968	−	39.5031i	0.204815	−	1.42452i	−0.584931	−	0.811083i	$-0.698879\pi$
$769$	5.67968	−	39.5031i	0.204815	−	1.42452i	0.789746	−	0.613434i	$-0.210212\pi$
$770$	−0.386045	+	0.613072i	−0.0139121	+	0.0220936i
$771$	−11.9970	+	26.2698i	−0.432061	+	0.946082i
$772$	−17.9289	−	14.0994i	−0.645274	−	0.507449i
$773$	35.2510	+	18.1731i	1.26789	+	0.653643i	0.955129	−	0.296189i	$-0.0957159\pi$
$773$	35.2510	+	18.1731i	1.26789	+	0.653643i	0.312761	+	0.949832i	$0.398746\pi$
$774$	6.72557	−	1.63161i	0.241746	−	0.0586469i
$775$	−17.4248	+	43.5250i	−0.625916	+	1.56346i
$776$	0.0756696	+	0.0873274i	0.00271638	+	0.00313487i
$777$	−18.6910	−	3.42370i	−0.670537	−	0.122824i
$778$	11.4008	+	9.87888i	0.408740	+	0.354175i
$779$	−11.0738	−	2.68648i	−0.396762	−	0.0962533i
$780$	0.247511	−	0.347581i	0.00886233	−	0.0124454i
$781$	12.4348	−	7.17925i	0.444953	−	0.256894i
$782$	−5.12313	−	4.39234i	−0.183203	−	0.157070i
$783$			6.02590i			0.215348i
$784$	−5.42152	+	4.42799i	−0.193626	+	0.158143i
$785$	0.494786	−	0.145282i	0.0176597	−	0.00518534i
$786$	−0.623420	−	1.80125i	−0.0222367	−	0.0642486i
$787$	0.971836	−	20.4014i	0.0346422	−	0.727230i	−0.913012	−	0.407932i	$-0.866250\pi$
$787$	0.971836	−	20.4014i	0.0346422	−	0.727230i	0.947654	−	0.319298i	$-0.103447\pi$
$788$	5.71808	−	16.5213i	0.203698	−	0.588547i
$789$	7.78938	+	3.11840i	0.277309	+	0.111018i
$790$	0.472756	−	1.61006i	0.0168199	−	0.0572833i
$791$	−42.8182	−	29.8987i	−1.52244	−	1.06307i
$792$	−1.52656	−	0.219486i	−0.0542438	−	0.00779909i
$793$	13.2801	−	9.45675i	0.471592	−	0.335819i
$794$	−0.0182752	−	0.191387i	−0.000648563	−	0.00679206i
$795$	−0.813832	+	0.325809i	−0.0288637	+	0.0115553i
$796$	0.669903	+	14.0630i	0.0237441	+	0.498450i
$797$	19.7497	+	5.79904i	0.699571	+	0.205412i	0.612130	−	0.790757i	$-0.290313\pi$
$797$	19.7497	+	5.79904i	0.699571	+	0.205412i	0.0874407	+	0.996170i	$0.472131\pi$
$798$	−0.0371172	−	4.01925i	−0.00131394	−	0.142280i
$799$	9.95468	−	8.62578i	0.352171	−	0.305158i
$800$	4.41616	−	2.27669i	0.156135	−	0.0804930i
$801$	15.6139	+	3.00933i	0.551690	+	0.106329i
$802$	−11.2001	+	11.7463i	−0.395489	+	0.414777i
$803$	−6.83460	−	0.652625i	−0.241188	−	0.0230306i
$804$	12.4553			0.439266
$805$	1.68108	−	1.49984i	0.0592502	−	0.0528624i
$806$	22.6773			0.798775
$807$	−3.32536	−	0.317533i	−0.117058	−	0.0111777i
$808$	6.30409	−	6.61154i	0.221777	−	0.232593i
$809$	−9.63661	−	1.85730i	−0.338805	−	0.0652994i	0.0170110	−	0.999855i	$-0.494585\pi$
$809$	−9.63661	−	1.85730i	−0.338805	−	0.0652994i	−0.355816	+	0.934556i	$0.615797\pi$
$810$	0.157815	−	0.0813595i	0.00554507	−	0.00285868i
$811$	−7.32095	+	6.34364i	−0.257073	+	0.222755i	−0.773856	−	0.633361i	$-0.781675\pi$
$811$	−7.32095	+	6.34364i	−0.257073	+	0.222755i	0.516783	+	0.856116i	$0.327129\pi$
$812$	7.84368	−	13.8801i	0.275259	−	0.487096i
$813$	−6.54836	−	1.92277i	−0.229661	−	0.0674345i
$814$	0.527046	+	11.0641i	0.0184729	+	0.387795i
$815$	0.695865	−	0.278582i	0.0243751	−	0.00975831i
$816$	0.133754	+	1.40074i	0.00468234	+	0.0490357i
$817$	8.56433	−	6.09863i	0.299628	−	0.213364i
$818$	0.267440	+	0.0384521i	0.00935083	+	0.00134445i
$819$	5.75913	−	2.69466i	0.201240	−	0.0941590i
$820$	−0.375204	+	1.27783i	−0.0131027	+	0.0446236i
$821$	−20.7753	−	8.31717i	−0.725062	−	0.290271i	−0.0203782	−	0.999792i	$-0.506487\pi$
$821$	−20.7753	−	8.31717i	−0.725062	−	0.290271i	−0.704684	+	0.709521i	$0.748911\pi$
$822$	−2.08890	+	6.03547i	−0.0728587	+	0.210511i
$823$	−2.47006	+	51.8530i	−0.0861010	+	1.80748i	0.382377	+	0.924007i	$0.375106\pi$
$823$	−2.47006	+	51.8530i	−0.0861010	+	1.80748i	−0.468478	+	0.883475i	$0.655197\pi$
$824$	−4.32966	−	12.5097i	−0.150831	−	0.435797i
$825$	7.35226	−	2.15882i	0.255973	−	0.0751605i
$826$	−20.3810	+	21.7741i	−0.709145	+	0.757616i
$827$		−	24.9021i		−	0.865931i	−0.901410	−	0.432966i	$-0.857467\pi$
$827$		−	24.9021i		−	0.865931i	0.901410	−	0.432966i	$-0.142533\pi$
$828$	4.37284	+	1.96933i	0.151967	+	0.0684390i
$829$	−27.3089	+	15.7668i	−0.948477	+	0.547604i	−0.892608	−	0.450835i	$-0.851126\pi$
$829$	−27.3089	+	15.7668i	−0.948477	+	0.547604i	−0.0558696	+	0.998438i	$0.517793\pi$
$830$	0.764362	−	1.07340i	0.0265314	−	0.0372581i
$831$	−14.9103	−	3.61719i	−0.517232	−	0.125479i
$832$	−1.81624	−	1.57378i	−0.0629670	−	0.0545612i
$833$	6.58661	+	7.32357i	0.228213	+	0.253747i
$834$	−13.8768	−	16.0147i	−0.480514	−	0.554543i
$835$	−0.0240649	+	0.0601112i	−0.000832801	+	0.00208024i
$836$	−2.27695	+	0.552381i	−0.0787498	+	0.0191045i
$837$	8.38720	+	4.32390i	0.289904	+	0.149456i
$838$	−28.5550	−	22.4559i	−0.986416	−	0.775726i
$839$	20.0721	−	43.9517i	0.692965	−	1.51738i	−0.155332	−	0.987862i	$-0.549645\pi$
$839$	20.0721	−	43.9517i	0.692965	−	1.51738i	0.848298	−	0.529520i	$-0.177628\pi$
$840$	−0.469416	−	0.0180181i	−0.0161964	−	0.000621684i
$841$	−1.04054	+	7.23709i	−0.0358806	+	0.249555i
$842$	9.19078	−	0.437811i	0.316735	−	0.0150880i
$843$	−0.313119	−	1.29069i	−0.0107844	−	0.0444539i
$844$	10.3245	−	8.11928i	0.355384	−	0.279477i
$845$	−1.25954	+	0.242757i	−0.0433296	+	0.00835110i
$846$	−5.06092	+	7.87495i	−0.173998	+	0.270746i
$847$	−15.0961	−	17.1001i	−0.518707	−	0.587567i
$848$	1.39099	+	4.73727i	0.0477667	+	0.162679i
$849$	1.26843	−	13.2836i	0.0435325	−	0.455893i
$850$	−3.49560	−	6.05456i	−0.119898	−	0.207670i
$851$	7.94467	−	33.5153i	0.272340	−	1.14889i
$852$	8.06276	+	4.65504i	0.276226	+	0.159479i
$853$	−5.49580	+	2.50985i	−0.188173	+	0.0859355i	−0.507273	−	0.861785i	$-0.669346\pi$
$853$	−5.49580	+	2.50985i	−0.188173	+	0.0859355i	0.319101	+	0.947721i	$0.396619\pi$
$854$	−16.7235	−	6.51656i	−0.572268	−	0.222992i
$855$	0.176641	−	0.203855i	0.00604100	−	0.00697168i
$856$	−2.67400	−	5.18683i	−0.0913954	−	0.177282i
$857$	47.3494	+	16.3878i	1.61743	+	0.559797i	0.977918	−	0.208988i	$-0.0670170\pi$
$857$	47.3494	+	16.3878i	1.61743	+	0.559797i	0.639508	+	0.768785i	$0.279138\pi$
$858$	−2.29115	−	2.91343i	−0.0782185	−	0.0994629i
$859$	14.0055	+	14.6886i	0.477862	+	0.501167i	0.917900	−	0.396812i	$-0.129883\pi$
$859$	14.0055	+	14.6886i	0.477862	+	0.501167i	−0.440038	+	0.897979i	$0.645035\pi$
$860$	−0.664331	−	1.03372i	−0.0226535	−	0.0352495i
$861$	−14.2354	+	13.8267i	−0.485142	+	0.471211i
$862$	−0.923394	−	0.421700i	−0.0314509	−	0.0143632i
$863$	19.1333	+	26.8690i	0.651305	+	0.914631i	0.999742	−	0.0227017i	$-0.00722680\pi$
$863$	19.1333	+	26.8690i	0.651305	+	0.914631i	−0.348437	+	0.937332i	$0.613287\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	−1.40001	+	2.71563i	−0.0476016	+	0.0923343i
$866$	13.3155	−	12.6963i	0.452480	−	0.431439i
$867$	−14.8672	+	2.13757i	−0.504915	+	0.0725958i
$868$	−13.6909	−	20.8770i	−0.464698	−	0.708611i
$869$	−12.2618	−	7.88019i	−0.415954	−	0.267317i
$870$	1.01107	−	0.349936i	0.0342786	−	0.0118639i
$871$	21.6636	+	20.6562i	0.734044	+	0.699909i
$872$	2.26936	+	1.61600i	0.0768501	+	0.0547247i
$873$	−0.0577753	+	0.100070i	−0.00195540	+	0.00338685i
$874$	7.27929	+	0.308466i	0.246226	+	0.0104340i
$875$	4.33111	−	1.78049i	0.146418	−	0.0601917i
$876$	−1.84931	−	4.04943i	−0.0624825	−	0.136817i
$877$	5.63553	−	23.2300i	0.190298	−	0.784420i	−0.794002	−	0.607916i	$-0.792006\pi$
$877$	5.63553	−	23.2300i	0.190298	−	0.784420i	0.984300	−	0.176504i	$-0.0564790\pi$
$878$	6.02263	−	31.2484i	0.203254	−	1.05458i
$879$	8.89311	+	0.423631i	0.299957	+	0.0142887i
$880$	0.0518231	+	0.268884i	0.00174696	+	0.00906407i
$881$	−0.585772	−	4.07413i	−0.0197352	−	0.137261i	0.977572	−	0.210603i	$-0.0675427\pi$
$881$	−0.585772	−	4.07413i	−0.0197352	−	0.137261i	−0.997307	+	0.0733418i	$0.976634\pi$
$882$	−5.95766	−	3.67509i	−0.200605	−	0.123747i
$883$	−10.3376	+	6.64360i	−0.347890	+	0.223575i	−0.702902	−	0.711286i	$-0.748113\pi$
$883$	−10.3376	+	6.64360i	−0.347890	+	0.223575i	0.355013	+	0.934861i	$0.384477\pi$
$884$	−2.09038	+	2.65813i	−0.0703071	+	0.0894027i
$885$	−1.99241	+	0.190253i	−0.0669743	+	0.00639527i
$886$	11.9669	−	1.14270i	0.402034	−	0.0383896i
$887$	−0.582549	+	0.740771i	−0.0195601	+	0.0248727i	−0.795735	−	0.605645i	$-0.792915\pi$
$887$	−0.582549	+	0.740771i	−0.0195601	+	0.0248727i	0.776175	+	0.630518i	$0.217157\pi$
$888$	−6.04195	+	3.88293i	−0.202755	+	0.130302i
$889$	39.5679	−	4.14733i	1.32706	−	0.139097i
$890$	−0.401800	−	2.79458i	−0.0134684	−	0.0936745i
$891$	−0.291874	−	1.51438i	−0.00977814	−	0.0507338i
$892$	20.3171	+	0.967823i	0.680267	+	0.0324051i
$893$	−2.69137	+	13.9642i	−0.0900634	+	0.467293i
$894$	−5.14936	+	21.2260i	−0.172220	+	0.709902i
$895$	−1.68182	−	3.68268i	−0.0562171	−	0.123098i
$896$	−0.352330	+	2.62219i	−0.0117705	+	0.0876011i
$897$	4.33971	+	10.6773i	0.144899	+	0.356504i
$898$	18.3466	−	31.7773i	0.612235	−	1.06042i
$899$	46.3179	+	32.9828i	1.54479	+	1.10004i
$900$	3.59585	+	3.42864i	0.119862	+	0.114288i
$901$	6.56519	−	2.27223i	0.218718	−	0.0756991i
$902$	9.73161	+	6.25413i	0.324027	+	0.208240i
$903$	−1.04010	−	18.2808i	−0.0346123	−	0.608346i
$904$	−19.5378	+	2.80912i	−0.649819	+	0.0934299i
$905$	−0.00690693	+	0.00658575i	−0.000229594	+	0.000218918i
$906$	6.22541	−	12.0756i	0.206825	−	0.401185i
$907$	−11.8577	−	29.6191i	−0.393728	−	0.983486i	−0.984300	−	0.176501i	$-0.943522\pi$
$907$	−11.8577	−	29.6191i	−0.393728	−	0.983486i	0.590572	−	0.806985i	$-0.298902\pi$
$908$	−2.06054	−	2.89362i	−0.0683813	−	0.0960281i
$909$	8.30978	+	3.79495i	0.275618	+	0.125870i
$910$	−0.786575	−	0.809829i	−0.0260747	−	0.0268456i
$911$	20.0261	+	31.1613i	0.663495	+	1.03242i	0.996003	+	0.0893180i	$0.0284688\pi$
$911$	20.0261	+	31.1613i	0.663495	+	1.03242i	−0.332508	+	0.943100i	$0.607895\pi$
$912$	−1.04837	−	1.09950i	−0.0347149	−	0.0364079i
$913$	−7.07549	−	8.99722i	−0.234165	−	0.297764i
$914$	29.5968	+	10.2436i	0.978975	+	0.338827i
$915$	−0.551929	−	1.07059i	−0.0182462	−	0.0353927i
$916$	12.7036	−	14.6608i	0.419740	−	0.484405i
$917$	−4.98486	+	0.763763i	−0.164615	+	0.0252217i
$918$	−1.27995	+	0.584535i	−0.0422448	+	0.0192925i
$919$	27.6107	+	15.9410i	0.910791	+	0.525846i	0.880686	−	0.473701i	$-0.157082\pi$
$919$	27.6107	+	15.9410i	0.910791	+	0.525846i	0.0301057	+	0.999547i	$0.490416\pi$
$920$	0.0764908	−	0.848072i	0.00252183	−	0.0279601i
$921$	6.81688	+	11.8072i	0.224624	+	0.389060i
$922$	2.86147	−	29.9667i	0.0942375	−	0.986899i
$923$	6.30357	+	21.4680i	0.207485	+	0.706627i
$924$	−1.29891	+	3.86816i	−0.0427310	+	0.127253i
$925$	19.2922	−	30.0193i	0.634324	−	0.987028i
$926$	−16.7493	+	3.22815i	−0.550415	+	0.106084i
$927$	10.4056	−	8.18307i	0.341765	−	0.268767i
$928$	−1.42066	−	5.85604i	−0.0466355	−	0.192234i
$929$	3.97873	−	0.189530i	0.130538	−	0.00621829i	0.0177888	−	0.999842i	$-0.494337\pi$
$929$	3.97873	−	0.189530i	0.130538	−	0.00621829i	0.112749	+	0.993623i	$0.464034\pi$
$930$	0.238437	−	1.65837i	0.00781866	−	0.0543800i
$931$	−10.4776	−	1.81938i	−0.343389	−	0.0596278i
$932$	−2.20948	+	4.83808i	−0.0723739	+	0.158477i
$933$	−5.12415	−	4.02968i	−0.167757	−	0.131926i
$934$	30.9922	+	15.9776i	1.01410	+	0.522803i
$935$	0.374451	−	0.0908408i	0.0122459	−	0.00297081i
$936$	0.893193	−	2.23109i	0.0291949	−	0.0729254i
$937$	−8.75891	−	10.1083i	−0.286141	−	0.330225i	0.594422	−	0.804153i	$-0.297381\pi$
$937$	−8.75891	−	10.1083i	−0.286141	−	0.330225i	−0.880563	+	0.473929i	$0.842835\pi$
$938$	5.93746	−	32.4144i	0.193865	−	1.05837i
$939$	−17.8313	−	15.4509i	−0.581902	−	0.504221i
$940$	1.61522	+	0.391848i	0.0526826	+	0.0127807i
$941$	0.374380	−	0.525743i	0.0122044	−	0.0171387i	−0.808429	−	0.588594i	$-0.799682\pi$
$941$	0.374380	−	0.525743i	0.0122044	−	0.0171387i	0.820633	+	0.571455i	$0.193621\pi$
$942$	2.51523	−	1.45217i	0.0819506	−	0.0473142i
$943$	−23.6991	−	27.0619i	−0.771749	−	0.881255i
$944$			11.2726i			0.366891i
$945$	−0.136504	−	0.449491i	−0.00444047	−	0.0146220i
$946$	−10.2411	+	3.00705i	−0.332966	+	0.0977676i
$947$	7.72649	+	22.3242i	0.251077	+	0.725440i	0.998156	+	0.0607041i	$0.0193346\pi$
$947$	7.72649	+	22.3242i	0.251077	+	0.725440i	−0.747079	+	0.664736i	$0.768544\pi$
$948$	0.449690	−	9.44016i	0.0146053	−	0.306602i
$949$	3.49915	−	10.1101i	0.113587	−	0.328189i
$950$	7.00741	+	2.80535i	0.227351	+	0.0910174i
$951$	8.20017	−	27.9272i	0.265909	−	0.905602i
$952$	3.70912	+	0.319643i	0.120213	+	0.0103597i
$953$	6.82163	+	0.980802i	0.220974	+	0.0317713i	0.251913	−	0.967750i	$-0.418940\pi$
$953$	6.82163	+	0.980802i	0.220974	+	0.0317713i	−0.0309383	+	0.999521i	$0.509850\pi$
$954$	−4.02178	+	2.86390i	−0.130210	+	0.0927220i
$955$	−0.147897	−	1.54885i	−0.00478583	−	0.0501195i
$956$	−0.426386	+	0.170699i	−0.0137903	+	0.00552081i
$957$	−0.442202	−	9.28295i	−0.0142943	−	0.300075i
$958$	4.68601	+	1.37594i	0.151398	+	0.0444545i
$959$	14.7113	+	8.31337i	0.475051	+	0.268453i
$960$	−0.134186	+	0.116273i	−0.00433082	+	0.00375268i
$961$	51.5890	−	26.5960i	1.66416	−	0.857935i
$962$	−16.9483	−	3.26652i	−0.546436	−	0.105317i
$963$	4.02698	−	4.22338i	0.129768	−	0.136096i
$964$	−1.56689	−	0.149619i	−0.0504660	−	0.00481892i
$965$	−4.04976			−0.130366
$966$	7.20963	−	10.4413i	0.231966	−	0.335944i
$967$	−2.20096			−0.0707780			−0.0353890	−	0.999374i	$-0.511267\pi$
$967$	−2.20096			−0.0707780			−0.0353890	+	0.999374i	$0.511267\pi$
$968$	−8.58241	−	0.819521i	−0.275849	−	0.0263404i
$969$	−1.47517	+	1.54711i	−0.0473893	+	0.0497004i
$970$	0.0201456	+	0.00388275i	0.000646837	+	0.000124668i
$971$	−19.0002	+	9.79526i	−0.609744	+	0.314345i	−0.735300	−	0.677742i	$-0.762959\pi$
$971$	−19.0002	+	9.79526i	−0.609744	+	0.314345i	0.125556	+	0.992087i	$0.459928\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−48.2925	+	28.4795i	−1.54819	+	0.913011i
$974$	10.4319	+	3.06308i	0.334260	+	0.0981474i
$975$	0.568148	+	11.9269i	0.0181953	+	0.381966i
$976$	−6.29789	+	2.52129i	−0.201590	+	0.0807047i
$977$	−0.181142	−	1.89700i	−0.00579524	−	0.0606904i	0.992112	−	0.125357i	$-0.0400077\pi$
$977$	−0.181142	−	1.89700i	−0.00579524	−	0.0606904i	−0.997907	+	0.0646666i	$0.979402\pi$
$978$	3.43881	−	2.44876i	0.109961	−	0.0783029i
$979$	−24.2742	−	3.49010i	−0.775806	−	0.111544i
$980$	−0.270662	+	1.21304i	−0.00864597	+	0.0387492i
$981$	−0.784889	+	2.67308i	−0.0250596	+	0.0853450i
$982$	−21.8534	−	8.74877i	−0.697369	−	0.279184i
$983$	−6.74116	+	19.4773i	−0.215010	+	0.621230i	0.784989	+	0.619510i	$0.212669\pi$
$983$	−6.74116	+	19.4773i	−0.215010	+	0.621230i	−0.999999	+	0.00171989i	$0.999453\pi$
$984$	−0.356898	+	7.49220i	−0.0113775	+	0.238843i
$985$	−1.01526	−	2.93341i	−0.0323489	−	0.0934661i
$986$	−8.13565	+	2.38884i	−0.259092	+	0.0760763i
$987$	18.0816	+	16.9248i	0.575545	+	0.538722i
$988$		−	3.65099i		−	0.116154i
$989$	33.1898	−	0.174229i	1.05538	−	0.00554016i
$990$	−0.237146	+	0.136916i	−0.00753698	+	0.00435148i
$991$	−14.5684	+	20.4584i	−0.462780	+	0.649883i	−0.978348	−	0.206965i	$-0.933641\pi$
$991$	−14.5684	+	20.4584i	−0.462780	+	0.649883i	0.515569	+	0.856848i	$0.327581\pi$
$992$	−9.17017	−	2.22466i	−0.291153	−	0.0706330i
$993$	−16.2674	−	14.0958i	−0.516229	−	0.447315i
$994$	15.9580	−	18.7639i	0.506158	−	0.595155i
$995$	1.63699	+	1.88919i	0.0518962	+	0.0598914i
$996$	2.75835	−	6.89002i	0.0874015	−	0.218318i
$997$	−14.7683	+	3.58276i	−0.467718	+	0.113467i	−0.462690	−	0.886520i	$-0.653116\pi$
$997$	−14.7683	+	3.58276i	−0.467718	+	0.113467i	−0.00502803	+	0.999987i	$0.501600\pi$
$998$	−16.1522	−	8.32703i	−0.511289	−	0.263588i
$999$	−5.64550	−	4.43967i	−0.178616	−	0.140465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.5	✓	320
7.3	odd	6	inner	966.2.be.b.157.5	yes	320
23.17	odd	22	inner	966.2.be.b.523.5	yes	320
161.17	even	66	inner	966.2.be.b.661.5	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.5	✓	320	1.1	even	1	trivial
966.2.be.b.157.5	yes	320	7.3	odd	6	inner
966.2.be.b.523.5	yes	320	23.17	odd	22	inner
966.2.be.b.661.5	yes	320	161.17	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.157815 - 0.0813595i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.34398 - 2.27897i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(0.157815 - 0.0813595i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.34398 - 2.27897i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-0.164835 + 0.0659898i) q^{10} +(0.146601 + 1.53527i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-2.37877 - 0.342016i) q^{13} +(1.12126 + 2.39641i) q^{14} +(-0.0500225 + 0.170361i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.460221 - 1.32972i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(0.496881 + 1.43564i) q^{19} +(0.170361 - 0.0500225i) q^{20} +(2.57682 + 0.599990i) q^{21} -1.54226i q^{22} +(-1.32697 + 4.60860i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.88200 + 4.04720i) q^{25} +(2.33549 + 0.566584i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-0.888392 - 2.49214i) q^{28} +(3.94613 + 4.55407i) q^{29} +(0.0659898 - 0.164835i) q^{30} +(9.17017 - 2.22466i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-1.21229 - 0.953359i) q^{33} +(-0.584535 + 1.27995i) q^{34} +(-0.397517 - 0.250312i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-7.17395 + 0.341737i) q^{37} +(-0.358165 - 1.47637i) q^{38} +(1.88907 - 1.48558i) q^{39} +(-0.174344 + 0.0336021i) q^{40} +(-4.05518 + 6.30999i) q^{41} +(-2.50812 - 0.842215i) q^{42} +(-1.94977 - 6.64032i) q^{43} +(-0.146601 + 1.53527i) q^{44} +(-0.0887765 - 0.153765i) q^{45} +(1.75903 - 4.46159i) q^{46} +(8.10684 + 4.68049i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-3.38745 + 6.12578i) q^{49} +(3.25366 - 3.75492i) q^{50} +(0.644776 + 1.25069i) q^{51} +(-2.27106 - 0.786022i) q^{52} +(3.05202 + 3.88095i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(0.148045 + 0.230362i) q^{55} +(0.647476 + 2.56530i) q^{56} +(-1.38191 - 0.631098i) q^{57} +(-3.49537 - 4.90856i) q^{58} +(4.18959 + 10.4651i) q^{59} +(-0.0813595 + 0.157815i) q^{60} +(-4.90969 + 4.68138i) q^{61} +(-9.34012 + 1.34291i) q^{62} +(-2.21244 + 1.45089i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-0.403234 + 0.139561i) q^{65} +(1.11618 + 1.06428i) q^{66} +(-10.1458 - 7.22480i) q^{67} +(0.703556 - 1.21859i) q^{68} +(-2.41969 - 4.14067i) q^{69} +(0.371923 + 0.286965i) q^{70} +(-3.86754 - 8.46874i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(-0.842494 + 4.37127i) q^{73} +(7.17395 + 0.341737i) q^{74} +(-0.940290 - 4.87869i) q^{75} +(0.216204 + 1.50374i) q^{76} +(3.30182 - 2.39747i) q^{77} +(-2.02173 + 1.29929i) q^{78} +(-5.84214 + 7.42888i) q^{79} +(0.176749 - 0.0168775i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(4.63662 - 5.89595i) q^{82} +(-6.24348 + 4.01244i) q^{83} +(2.41671 + 1.07681i) q^{84} +(-0.0355555 - 0.247294i) q^{85} +(1.30974 + 6.79559i) q^{86} +(-6.01908 - 0.286724i) q^{87} +(0.291874 - 1.51438i) q^{88} +(-3.74886 + 15.4530i) q^{89} +(0.0737582 + 0.161508i) q^{90} +(2.41758 + 5.88083i) q^{91} +(-2.17517 + 4.27418i) q^{92} +(-4.71808 + 8.17196i) q^{93} +(-7.62522 - 5.42990i) q^{94} +(0.195219 + 0.186141i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-0.0972074 - 0.0624714i) q^{97} +(3.95440 - 5.77605i) q^{98} +(1.52656 - 0.219486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more