LMFDB - Embedded newform 966.2.be.a.157.11

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			157.11
Character	$\chi$	$=$	966.157
Dual form			966.2.be.a.523.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 + 0.814576i) q^{2} +(0.971812 + 0.235759i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(-0.0853919 + 1.79260i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-2.08108 - 1.63375i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 + 0.814576i) q^{2} +(0.971812 + 0.235759i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(-0.0853919 + 1.79260i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-2.08108 - 1.63375i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.888835 + 0.458227i) q^{9} +(-1.41067 - 1.10937i) q^{10} +(3.89971 - 2.77697i) q^{11} +(-0.0950560 - 0.995472i) q^{12} +(-0.860526 - 0.123725i) q^{13} +(2.53795 - 0.747529i) q^{14} +(-0.505605 + 1.72193i) q^{15} +(-0.786053 + 0.618159i) q^{16} +(0.0247007 - 0.00476066i) q^{17} +(-0.888835 + 0.458227i) q^{18} +(5.11257 + 0.985366i) q^{19} +(1.72193 - 0.505605i) q^{20} +(-1.63724 - 2.07832i) q^{21} +4.78741i q^{22} +(4.68016 + 1.04695i) q^{23} +(0.866025 + 0.500000i) q^{24} +(1.77125 + 0.169134i) q^{25} +(0.599938 - 0.629196i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-0.863237 + 2.50096i) q^{28} +(3.22932 + 3.72683i) q^{29} +(-1.10937 - 1.41067i) q^{30} +(-2.19143 - 2.29830i) q^{31} +(-0.0475819 - 0.998867i) q^{32} +(4.44448 - 1.77930i) q^{33} +(-0.0104499 + 0.0228820i) q^{34} +(3.10635 - 3.59102i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-3.65077 + 7.08151i) q^{37} +(-3.76823 + 3.59300i) q^{38} +(-0.807100 - 0.323114i) q^{39} +(-0.586966 + 1.69593i) q^{40} +(1.20695 - 1.87805i) q^{41} +(2.64265 - 0.128113i) q^{42} +(2.56923 + 8.74999i) q^{43} +(-3.89971 - 2.77697i) q^{44} +(-0.897315 + 1.55419i) q^{45} +(-3.56758 + 3.20505i) q^{46} +(-3.07852 + 1.77738i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.66175 + 6.79990i) q^{49} +(-1.16520 + 1.34471i) q^{50} +(0.0251267 + 0.00119693i) q^{51} +(0.164530 + 0.853664i) q^{52} +(0.476667 - 1.19066i) q^{53} +(-0.971812 + 0.235759i) q^{54} +(4.64498 + 7.22773i) q^{55} +(-1.53650 - 2.15387i) q^{56} +(4.73614 + 2.16292i) q^{57} +(-4.90898 + 0.468750i) q^{58} +(6.29817 - 8.00877i) q^{59} +(1.79260 - 0.0853919i) q^{60} +(-2.19828 - 9.06143i) q^{61} +(3.14330 - 0.451938i) q^{62} +(-1.10111 - 2.40573i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.295271 - 1.53201i) q^{65} +(-1.12867 + 4.65246i) q^{66} +(0.333518 - 3.49276i) q^{67} +(-0.0125776 - 0.0217851i) q^{68} +(4.30140 + 2.12083i) q^{69} +(1.12330 + 4.61336i) q^{70} +(0.134708 + 0.294968i) q^{71} +(0.723734 + 0.690079i) q^{72} +(-3.06934 + 1.06231i) q^{73} +(-3.65077 - 7.08151i) q^{74} +(1.68145 + 0.581954i) q^{75} +(-0.740984 - 5.15366i) q^{76} +(-12.6524 - 0.592044i) q^{77} +(0.731365 - 0.470020i) q^{78} +(5.56059 + 13.8897i) q^{79} +(-1.04099 - 1.46186i) q^{80} +(0.580057 + 0.814576i) q^{81} +(0.829715 + 2.07253i) q^{82} +(8.52400 - 5.47804i) q^{83} +(-1.42853 + 2.22695i) q^{84} +(0.00642471 + 0.0446848i) q^{85} +(-8.61783 - 2.98266i) q^{86} +(2.25966 + 4.38312i) q^{87} +(4.52410 - 1.56581i) q^{88} +(-11.3606 - 10.8323i) q^{89} +(-0.745516 - 1.63245i) q^{90} +(1.58869 + 1.66336i) q^{91} +(-0.541358 - 4.76518i) q^{92} +(-1.58781 - 2.75017i) q^{93} +(0.337902 - 3.53867i) q^{94} +(-2.20294 + 9.08062i) q^{95} +(0.189251 - 0.981929i) q^{96} +(6.67740 + 4.29131i) q^{97} +(-6.50294 - 2.59070i) q^{98} +(4.73868 - 0.681319i) 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} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+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 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.580057	+	0.814576i	−0.410162	+	0.575992i
$2$	−0.580057	+	0.814576i	−0.410162	+	0.575992i
$3$	0.971812	+	0.235759i	0.561076	+	0.136115i
$3$	0.971812	+	0.235759i	0.561076	+	0.136115i
$4$	−0.327068	−	0.945001i	−0.163534	−	0.472500i
$5$	−0.0853919	+	1.79260i	−0.0381884	+	0.801674i	0.895819	+	0.444419i	$0.146590\pi$
$5$	−0.0853919	+	1.79260i	−0.0381884	+	0.801674i	−0.934007	+	0.357254i	$0.883713\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	−2.08108	−	1.63375i	−0.786573	−	0.617498i
$7$	−2.08108	−	1.63375i	−0.786573	−	0.617498i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	0.888835	+	0.458227i	0.296278	+	0.152742i
$10$	−1.41067	−	1.10937i	−0.446094	−	0.350812i
$11$	3.89971	−	2.77697i	1.17581	−	0.837288i	0.186402	−	0.982474i	$-0.440317\pi$
$11$	3.89971	−	2.77697i	1.17581	−	0.837288i	0.989404	+	0.145186i	$0.0463781\pi$
$12$	−0.0950560	−	0.995472i	−0.0274403	−	0.287368i
$13$	−0.860526	−	0.123725i	−0.238667	−	0.0343151i	0.0219433	−	0.999759i	$-0.493015\pi$
$13$	−0.860526	−	0.123725i	−0.238667	−	0.0343151i	−0.260610	+	0.965444i	$0.583924\pi$
$14$	2.53795	−	0.747529i	0.678296	−	0.199786i
$15$	−0.505605	+	1.72193i	−0.130547	+	0.444601i
$16$	−0.786053	+	0.618159i	−0.196513	+	0.154540i
$17$	0.0247007	−	0.00476066i	0.00599079	−	0.00115463i	−0.186255	−	0.982501i	$-0.559635\pi$
$17$	0.0247007	−	0.00476066i	0.00599079	−	0.00115463i	0.192246	+	0.981347i	$0.438423\pi$
$18$	−0.888835	+	0.458227i	−0.209501	+	0.108005i
$19$	5.11257	+	0.985366i	1.17290	+	0.226059i	0.738242	−	0.674536i	$-0.235656\pi$
$19$	5.11257	+	0.985366i	1.17290	+	0.226059i	0.434661	+	0.900594i	$0.356868\pi$
$20$	1.72193	−	0.505605i	0.385036	−	0.113057i
$21$	−1.63724	−	2.07832i	−0.357276	−	0.453528i
$22$			4.78741i			1.02068i
$23$	4.68016	+	1.04695i	0.975881	+	0.218305i
$23$	4.68016	+	1.04695i	0.975881	+	0.218305i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	1.77125	+	0.169134i	0.354250	+	0.0338268i
$26$	0.599938	−	0.629196i	0.117657	−	0.123396i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	−0.863237	+	2.50096i	−0.163136	+	0.472638i
$29$	3.22932	+	3.72683i	0.599669	+	0.692055i	0.971714	−	0.236159i	$-0.0758887\pi$
$29$	3.22932	+	3.72683i	0.599669	+	0.692055i	−0.372045	+	0.928215i	$0.621343\pi$
$30$	−1.10937	−	1.41067i	−0.202542	−	0.257553i
$31$	−2.19143	−	2.29830i	−0.393592	−	0.412788i	0.496884	−	0.867817i	$-0.334477\pi$
$31$	−2.19143	−	2.29830i	−0.393592	−	0.412788i	−0.890477	+	0.455029i	$0.849629\pi$
$32$	−0.0475819	−	0.998867i	−0.00841137	−	0.176576i
$33$	4.44448	−	1.77930i	0.773684	−	0.309736i
$34$	−0.0104499	+	0.0228820i	−0.00179214	+	0.00392423i
$35$	3.10635	−	3.59102i	0.525069	−	0.606993i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−3.65077	+	7.08151i	−0.600183	+	1.16419i	0.371617	+	0.928386i	$0.378803\pi$
$37$	−3.65077	+	7.08151i	−0.600183	+	1.16419i	−0.971800	+	0.235806i	$0.924227\pi$
$38$	−3.76823	+	3.59300i	−0.611288	+	0.582862i
$39$	−0.807100	−	0.323114i	−0.129239	−	0.0517397i
$40$	−0.586966	+	1.69593i	−0.0928074	+	0.268149i
$41$	1.20695	−	1.87805i	0.188494	−	0.293302i	−0.734126	−	0.679014i	$-0.762408\pi$
$41$	1.20695	−	1.87805i	0.188494	−	0.293302i	0.922619	+	0.385712i	$0.126044\pi$
$42$	2.64265	−	0.128113i	0.407769	−	0.0197682i
$43$	2.56923	+	8.74999i	0.391804	+	1.33436i	0.885465	+	0.464707i	$0.153840\pi$
$43$	2.56923	+	8.74999i	0.391804	+	1.33436i	−0.493661	+	0.869655i	$0.664341\pi$
$44$	−3.89971	−	2.77697i	−0.587903	−	0.418644i
$45$	−0.897315	+	1.55419i	−0.133764	+	0.231686i
$46$	−3.56758	+	3.20505i	−0.526011	+	0.472559i
$47$	−3.07852	+	1.77738i	−0.449048	+	0.259258i	−0.707428	−	0.706785i	$-0.750145\pi$
$47$	−3.07852	+	1.77738i	−0.449048	+	0.259258i	0.258380	+	0.966043i	$0.416811\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	1.66175	+	6.79990i	0.237393	+	0.971414i
$50$	−1.16520	+	1.34471i	−0.164784	+	0.190171i
$51$	0.0251267	+	0.00119693i	0.00351845	+	0.000167604i
$52$	0.164530	+	0.853664i	0.0228163	+	0.118382i
$53$	0.476667	−	1.19066i	0.0654752	−	0.163549i	−0.892022	−	0.451992i	$-0.850713\pi$
$53$	0.476667	−	1.19066i	0.0654752	−	0.163549i	0.957497	+	0.288443i	$0.0931376\pi$
$54$	−0.971812	+	0.235759i	−0.132247	+	0.0320827i
$55$	4.64498	+	7.22773i	0.626329	+	0.974587i
$56$	−1.53650	−	2.15387i	−0.205323	−	0.287823i
$57$	4.73614	+	2.16292i	0.627317	+	0.286486i
$58$	−4.90898	+	0.468750i	−0.644580	+	0.0615499i
$59$	6.29817	−	8.00877i	0.819952	−	1.04265i	−0.178325	−	0.983972i	$-0.557068\pi$
$59$	6.29817	−	8.00877i	0.819952	−	1.04265i	0.998277	−	0.0586819i	$-0.0186898\pi$
$60$	1.79260	−	0.0853919i	0.231423	−	0.0110240i
$61$	−2.19828	−	9.06143i	−0.281461	−	1.16020i	−0.920412	−	0.390950i	$-0.872147\pi$
$61$	−2.19828	−	9.06143i	−0.281461	−	1.16020i	0.638951	−	0.769247i	$-0.279369\pi$
$62$	3.14330	−	0.451938i	0.399199	−	0.0573962i
$63$	−1.10111	−	2.40573i	−0.138727	−	0.303094i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	0.295271	−	1.53201i	0.0366239	−	0.190023i
$66$	−1.12867	+	4.65246i	−0.138930	+	0.572678i
$67$	0.333518	−	3.49276i	0.0407457	−	0.426708i	−0.951967	−	0.306201i	$-0.900942\pi$
$67$	0.333518	−	3.49276i	0.0407457	−	0.426708i	0.992712	−	0.120507i	$-0.0384520\pi$
$68$	−0.0125776	−	0.0217851i	−0.00152526	−	0.00264183i
$69$	4.30140	+	2.12083i	0.517828	+	0.255318i
$70$	1.12330	+	4.61336i	0.134260	+	0.551402i
$71$	0.134708	+	0.294968i	0.0159868	+	0.0350063i	0.917457	−	0.397835i	$-0.130238\pi$
$71$	0.134708	+	0.294968i	0.0159868	+	0.0350063i	−0.901470	+	0.432841i	$0.857511\pi$
$72$	0.723734	+	0.690079i	0.0852929	+	0.0813266i
$73$	−3.06934	+	1.06231i	−0.359239	+	0.124334i	−0.500725	−	0.865606i	$-0.666933\pi$
$73$	−3.06934	+	1.06231i	−0.359239	+	0.124334i	0.141486	+	0.989940i	$0.454812\pi$
$74$	−3.65077	−	7.08151i	−0.424393	−	0.823208i
$75$	1.68145	+	0.581954i	0.194157	+	0.0671983i
$76$	−0.740984	−	5.15366i	−0.0849967	−	0.591165i
$77$	−12.6524	−	0.592044i	−1.44188	−	0.0674697i
$78$	0.731365	−	0.470020i	0.0828108	−	0.0532192i
$79$	5.56059	+	13.8897i	0.625616	+	1.56271i	0.814156	+	0.580647i	$0.197200\pi$
$79$	5.56059	+	13.8897i	0.625616	+	1.56271i	−0.188540	+	0.982065i	$0.560376\pi$
$80$	−1.04099	−	1.46186i	−0.116386	−	0.163441i
$81$	0.580057	+	0.814576i	0.0644508	+	0.0905084i
$82$	0.829715	+	2.07253i	0.0916266	+	0.228872i
$83$	8.52400	−	5.47804i	0.935631	−	0.601294i	0.0184782	−	0.999829i	$-0.494118\pi$
$83$	8.52400	−	5.47804i	0.935631	−	0.601294i	0.917153	+	0.398536i	$0.130482\pi$
$84$	−1.42853	+	2.22695i	−0.155865	+	0.242980i
$85$	0.00642471	+	0.0446848i	0.000696857	+	0.00484675i
$86$	−8.61783	−	2.98266i	−0.929285	−	0.321629i
$87$	2.25966	+	4.38312i	0.242260	+	0.469920i
$88$	4.52410	−	1.56581i	0.482271	−	0.166916i
$89$	−11.3606	−	10.8323i	−1.20422	−	1.14822i	−0.985002	−	0.172545i	$-0.944801\pi$
$89$	−11.3606	−	10.8323i	−1.20422	−	1.14822i	−0.219218	−	0.975676i	$-0.570351\pi$
$90$	−0.745516	−	1.63245i	−0.0785843	−	0.172076i
$91$	1.58869	+	1.66336i	0.166539	+	0.174368i
$92$	−0.541358	−	4.76518i	−0.0564404	−	0.496804i
$93$	−1.58781	−	2.75017i	−0.164648	−	0.285179i
$94$	0.337902	−	3.53867i	0.0348519	−	0.364986i
$95$	−2.20294	+	9.08062i	−0.226016	+	0.931652i
$96$	0.189251	−	0.981929i	0.0193154	−	0.100218i
$97$	6.67740	+	4.29131i	0.677988	+	0.435716i	0.833797	−	0.552071i	$-0.186162\pi$
$97$	6.67740	+	4.29131i	0.677988	+	0.435716i	−0.155809	+	0.987787i	$0.549799\pi$
$98$	−6.50294	−	2.59070i	−0.656896	−	0.261700i
$99$	4.73868	−	0.681319i	0.476255	−	0.0684751i
$100$	−0.419487	−	1.72915i	−0.0419487	−	0.172915i
$101$	4.77546	−	0.227483i	0.475176	−	0.0226354i	0.191372	−	0.981518i	$-0.438706\pi$
$101$	4.77546	−	0.227483i	0.475176	−	0.0226354i	0.283804	+	0.958882i	$0.408403\pi$
$102$	−0.0155499	+	0.0197734i	−0.00153967	+	0.00195785i
$103$	5.43359	−	0.518844i	0.535387	−	0.0511233i	0.176139	−	0.984365i	$-0.443639\pi$
$103$	5.43359	−	0.518844i	0.535387	−	0.0511233i	0.359248	+	0.933242i	$0.383033\pi$
$104$	−0.790811	−	0.361151i	−0.0775454	−	0.0354138i
$105$	3.86540	−	2.75745i	0.377225	−	0.269099i
$106$	0.693386	+	1.07893i	0.0673476	+	0.104795i
$107$	−0.339899	+	0.0824585i	−0.0328593	+	0.00797157i	−0.252155	−	0.967687i	$-0.581139\pi$
$107$	−0.339899	+	0.0824585i	−0.0328593	+	0.00797157i	0.219296	+	0.975658i	$0.429624\pi$
$108$	0.371662	−	0.928368i	0.0357632	−	0.0893322i
$109$	−1.33571	−	6.93032i	−0.127938	−	0.663804i	−0.988104	−	0.153790i	$-0.950852\pi$
$109$	−1.33571	−	6.93032i	−0.127938	−	0.663804i	0.860166	−	0.510014i	$-0.170360\pi$
$110$	−8.58189	−	0.408806i	−0.818251	−	0.0389781i
$111$	−5.21739	+	6.02119i	−0.495213	+	0.571506i
$112$	2.64575	−	0.00222539i	0.250000	−	0.000210279i
$113$	−4.92805	+	2.25056i	−0.463592	+	0.211715i	−0.633497	−	0.773745i	$-0.718381\pi$
$113$	−4.92805	+	2.25056i	−0.463592	+	0.211715i	0.169905	+	0.985460i	$0.445654\pi$
$114$	−4.50910	+	2.60333i	−0.422316	+	0.243824i
$115$	−2.27641	+	8.30024i	−0.212277	+	0.774001i
$116$	2.46565	−	4.27064i	0.228930	−	0.396519i
$117$	−0.708172	−	0.504287i	−0.0654705	−	0.0466214i
$118$	2.87046	+	9.77588i	0.264247	+	0.899943i
$119$	−0.0591816	−	0.0304473i	−0.00542517	−	0.00279110i
$120$	−0.970250	+	1.50974i	−0.0885713	+	0.137820i
$121$	3.89841	−	11.2637i	0.354401	−	1.02397i
$122$	8.65635	+	3.46548i	0.783709	+	0.313750i
$123$	1.61569	−	1.54056i	0.145682	−	0.138908i
$124$	−1.45515	+	2.82260i	−0.130677	+	0.253477i
$125$	−1.73145	+	12.0425i	−0.154866	+	1.07711i
$126$	2.59836	+	0.498526i	0.231480	+	0.0444123i
$127$	−2.59751	+	5.68776i	−0.230492	+	0.504707i	−0.989173	−	0.146755i	$-0.953117\pi$
$127$	−2.59751	+	5.68776i	−0.230492	+	0.504707i	0.758681	+	0.651463i	$0.225844\pi$
$128$	−0.928368	+	0.371662i	−0.0820569	+	0.0328506i
$129$	0.433918	+	9.10906i	0.0382044	+	0.802008i
$130$	1.07667	+	1.12917i	0.0944298	+	0.0990351i
$131$	−2.90805	−	3.69789i	−0.254078	−	0.323086i	0.642236	−	0.766507i	$-0.278007\pi$
$131$	−2.90805	−	3.69789i	−0.254078	−	0.323086i	−0.896313	+	0.443421i	$0.853765\pi$
$132$	−3.13509	−	3.61808i	−0.272874	−	0.314914i
$133$	−9.02980	−	10.4033i	−0.782983	−	0.902076i
$134$	2.65166	+	2.29767i	0.229068	+	0.198489i
$135$	−1.23844	+	1.29883i	−0.106588	+	0.111786i
$136$	0.0250413	+	0.00239116i	0.00214728	+	0.000205040i
$137$	17.3002	+	9.98829i	1.47806	+	0.853358i	0.999692	−	0.0248028i	$-0.00789577\pi$
$137$	17.3002	+	9.98829i	1.47806	+	0.853358i	0.478366	+	0.878160i	$0.341229\pi$
$138$	−4.22264	+	2.27362i	−0.359455	+	0.193543i
$139$		−	1.81073i		−	0.153584i	−0.997047	−	0.0767921i	$-0.975532\pi$
$139$		−	1.81073i		−	0.153584i	0.997047	−	0.0767921i	$-0.0244678\pi$
$140$	−4.40951	−	1.76100i	−0.372671	−	0.148831i
$141$	−3.41077	+	1.00149i	−0.287239	+	0.0843409i
$142$	−0.318412	−	0.0613689i	−0.0267205	−	0.00514996i
$143$	−3.69938	+	1.90716i	−0.309358	+	0.159485i
$144$	−0.981929	+	0.189251i	−0.0818274	+	0.0157709i
$145$	−6.95646	+	5.47062i	−0.577703	+	0.454311i
$146$	0.915061	−	3.11641i	0.0757310	−	0.257916i
$147$	0.0117756	+	6.99999i	0.000971238	+	0.577349i
$148$	7.88608	+	1.13385i	0.648232	+	0.0932017i
$149$	0.714166	+	7.47908i	0.0585068	+	0.612710i	0.976413	+	0.215912i	$0.0692726\pi$
$149$	0.714166	+	7.47908i	0.0585068	+	0.612710i	−0.917906	+	0.396798i	$0.870121\pi$
$150$	−1.44938	+	1.03210i	−0.118341	+	0.0842705i
$151$	−11.2447	−	8.84294i	−0.915081	−	0.719628i	0.0451067	−	0.998982i	$-0.485637\pi$
$151$	−11.2447	−	8.84294i	−0.915081	−	0.719628i	−0.960188	+	0.279354i	$0.909880\pi$
$152$	4.62786	+	2.38583i	0.375369	+	0.193516i
$153$	0.0241363	+	0.00708705i	0.00195130	+	0.000572954i
$154$	7.82140	−	9.96296i	0.630267	−	0.802838i
$155$	4.30706	−	3.73209i	0.345952	−	0.299769i
$156$	−0.0413665	+	0.868390i	−0.00331197	+	0.0695269i
$157$	−1.00869	−	2.91441i	−0.0805020	−	0.232595i	0.897566	−	0.440879i	$-0.145333\pi$
$157$	−1.00869	−	2.91441i	−0.0805020	−	0.232595i	−0.978068	+	0.208284i	$0.933212\pi$
$158$	−14.5397	−	3.52729i	−1.15671	−	0.280616i
$159$	0.743938	−	1.04472i	0.0589981	−	0.0828513i
$160$	1.79463			0.141878
$161$	−8.02931	−	9.82498i	−0.632798	−	0.774317i
$162$	−1.00000			−0.0785674
$163$	−6.97092	+	9.78929i	−0.546005	+	0.766756i	−0.991720	−	0.128418i	$-0.959010\pi$
$163$	−6.97092	+	9.78929i	−0.546005	+	0.766756i	0.445715	+	0.895175i	$0.352949\pi$
$164$	−2.16951	−	0.526318i	−0.169410	−	0.0410985i
$165$	2.81004	+	8.11909i	0.218762	+	0.632070i
$166$	−0.482124	+	10.1210i	−0.0374201	+	0.785544i
$167$	4.21752	−	3.65450i	0.326361	−	0.282794i	−0.476233	−	0.879319i	$-0.657998\pi$
$167$	4.21752	−	3.65450i	0.326361	−	0.282794i	0.802594	+	0.596526i	$0.203453\pi$
$168$	−0.985392	−	2.45540i	−0.0760246	−	0.189438i
$169$	−11.7482	−	3.44959i	−0.903709	−	0.265353i
$170$	−0.0401259	−	0.0206863i	−0.00307751	−	0.00158657i
$171$	4.09271	+	3.21854i	0.312977	+	0.246128i
$172$	7.42844	−	5.28977i	0.566413	−	0.403341i
$173$	−0.402752	−	4.21781i	−0.0306207	−	0.320674i	−0.997785	−	0.0665222i	$-0.978810\pi$
$173$	−0.402752	−	4.21781i	−0.0306207	−	0.320674i	0.967164	−	0.254152i	$-0.0817964\pi$
$174$	−4.88111	−	0.701798i	−0.370036	−	0.0532032i
$175$	−3.40978	−	3.24575i	−0.257755	−	0.245356i
$176$	−1.34877	+	4.59348i	−0.101667	+	0.346247i
$177$	8.00877	−	6.29817i	0.601976	−	0.473399i
$178$	15.4135	−	2.97071i	1.15529	−	0.222664i
$179$	0.729408	−	0.376036i	0.0545185	−	0.0281062i	−0.430752	−	0.902470i	$-0.641752\pi$
$179$	0.729408	−	0.376036i	0.0545185	−	0.0281062i	0.485270	+	0.874364i	$0.338721\pi$
$180$	1.76220	+	0.339636i	0.131346	+	0.0253150i
$181$	12.1778	−	3.57574i	0.905172	−	0.265782i	0.204165	−	0.978937i	$-0.434552\pi$
$181$	12.1778	−	3.57574i	0.905172	−	0.265782i	0.701007	+	0.713154i	$0.252734\pi$
$182$	−2.27646	+	0.329260i	−0.168743	+	0.0244064i
$183$		−	9.32426i		−	0.689269i
$184$	4.19562	+	2.32310i	0.309305	+	0.171261i
$185$	−12.3825	−	7.14906i	−0.910382	−	0.525609i
$186$	3.16124	+	0.301862i	0.231793	+	0.0221336i
$187$	0.0831051	−	0.0871581i	0.00607725	−	0.00637363i
$188$	2.68651	+	2.32788i	0.195934	+	0.169778i
$189$	−0.502897	−	2.59752i	−0.0365804	−	0.188942i
$190$	−6.11903	−	7.06174i	−0.443921	−	0.512312i
$191$	−12.8916	−	16.3931i	−0.932806	−	1.18616i	−0.982287	−	0.187385i	$-0.939999\pi$
$191$	−12.8916	−	16.3931i	−0.932806	−	1.18616i	0.0494803	−	0.998775i	$-0.484243\pi$
$192$	0.690079	+	0.723734i	0.0498022	+	0.0522310i
$193$	−0.774319	−	16.2550i	−0.0557367	−	1.17006i	−0.837484	−	0.546462i	$-0.815974\pi$
$193$	−0.774319	−	16.2550i	−0.0557367	−	1.17006i	0.781747	−	0.623596i	$-0.214329\pi$
$194$	−7.36887	+	2.95005i	−0.529054	+	0.211801i
$195$	0.648133	−	1.41921i	0.0464138	−	0.101632i
$196$	5.88240	−	3.79439i	0.420171	−	0.271028i
$197$	2.03270	−	14.1377i	0.144824	−	1.00727i	−0.779702	−	0.626151i	$-0.784629\pi$
$197$	2.03270	−	14.1377i	0.144824	−	1.00727i	0.924525	−	0.381120i	$-0.124462\pi$
$198$	−2.19372	+	4.25522i	−0.155901	+	0.302405i
$199$	−14.5138	+	13.8388i	−1.02885	+	0.981010i	−0.999828	−	0.0185688i	$-0.994089\pi$
$199$	−14.5138	+	13.8388i	−1.02885	+	0.981010i	−0.0290260	+	0.999579i	$0.509241\pi$
$200$	1.65185	+	0.661301i	0.116803	+	0.0467611i
$201$	1.14756	−	3.31567i	0.0809430	−	0.233869i
$202$	−2.58474	+	4.02193i	−0.181861	+	0.282982i
$203$	−0.631763	−	13.0317i	−0.0443411	−	0.914646i
$204$	−0.00708705	−	0.0241363i	−0.000496193	−	0.00168988i
$205$	3.26352	+	2.32394i	0.227934	+	0.162311i
$206$	−2.72915	+	4.72703i	−0.190149	+	0.329348i
$207$	3.68015	+	3.07514i	0.255788	+	0.213737i
$208$	0.752901	−	0.434688i	0.0522043	−	0.0301402i
$209$	22.6738	−	10.3548i	1.56838	−	0.716256i
$210$	0.00399374	+	4.74814i	0.000275595	+	0.327653i
$211$	1.76738	−	2.03966i	0.121671	−	0.140416i	−0.691646	−	0.722237i	$-0.743114\pi$
$211$	1.76738	−	2.03966i	0.121671	−	0.140416i	0.813317	+	0.581821i	$0.197659\pi$
$212$	−1.28107	−	0.0610251i	−0.0879845	−	0.00419122i
$213$	0.0613689	+	0.318412i	0.00420493	+	0.0218172i
$214$	0.129992	−	0.324704i	0.00888606	−	0.0221963i
$215$	−15.9046	+	3.85841i	−1.08468	+	0.263142i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	0.805686	+	8.36318i	0.0546935	+	0.567730i
$218$	6.42006	+	2.93194i	0.434821	+	0.198576i
$219$	−3.23327	+	0.308740i	−0.218484	+	0.0208627i
$220$	5.31099	−	6.75347i	0.358067	−	0.455319i
$221$	−0.0218446	+	0.00104059i	−0.00146942	+	6.99973e-5i
$222$	−1.87833	−	7.74259i	−0.126065	−	0.519649i
$223$	−21.7178	+	3.12255i	−1.45433	+	0.209101i	−0.823720	−	0.566997i	$-0.808105\pi$
$223$	−21.7178	+	3.12255i	−1.45433	+	0.209101i	−0.630612	+	0.776099i	$0.717196\pi$
$224$	−1.53287	+	2.15646i	−0.102419	+	0.144084i
$225$	1.49685	+	0.961965i	0.0997898	+	0.0641310i
$226$	1.02529	−	5.31973i	0.0682015	−	0.353863i
$227$	0.676182	−	2.78726i	0.0448798	−	0.184997i	−0.944960	−	0.327187i	$-0.893899\pi$
$227$	0.676182	−	2.78726i	0.0448798	−	0.184997i	0.989839	+	0.142190i	$0.0454144\pi$
$228$	0.494924	−	5.18308i	0.0327772	−	0.343258i
$229$	−11.0249	−	19.0957i	−0.728548	−	1.26188i	−0.957497	−	0.288444i	$-0.906862\pi$
$229$	−11.0249	−	19.0957i	−0.728548	−	1.26188i	0.228949	−	0.973438i	$-0.426471\pi$
$230$	−5.44072	−	6.66892i	−0.358751	−	0.439736i
$231$	−12.1562	−	3.55828i	−0.799820	−	0.234118i
$232$	2.04854	+	4.48567i	0.134493	+	0.294499i
$233$	−2.54720	−	2.42875i	−0.166873	−	0.159113i	0.602041	−	0.798465i	$-0.294354\pi$
$233$	−2.54720	−	2.42875i	−0.166873	−	0.159113i	−0.768914	+	0.639352i	$0.779203\pi$
$234$	0.821560	−	0.284345i	0.0537071	−	0.0185882i
$235$	−2.92325	−	5.67031i	−0.190692	−	0.369890i
$236$	−9.62823	−	3.33236i	−0.626744	−	0.216918i
$237$	2.12923	+	14.8091i	0.138308	+	0.961956i
$238$	0.0591303	−	0.0305468i	0.00383285	−	0.00198005i
$239$	21.6113	−	13.8887i	1.39792	−	0.898388i	0.398098	−	0.917343i	$-0.369670\pi$
$239$	21.6113	−	13.8887i	1.39792	−	0.898388i	0.999820	+	0.0189549i	$0.00603390\pi$
$240$	−0.666996	−	1.66608i	−0.0430544	−	0.107545i
$241$	7.46653	+	10.4853i	0.480962	+	0.675416i	0.981755	−	0.190151i	$-0.0608977\pi$
$241$	7.46653	+	10.4853i	0.480962	+	0.675416i	−0.500793	+	0.865567i	$0.666958\pi$
$242$	6.91385	+	9.70915i	0.444439	+	0.624128i
$243$	0.371662	+	0.928368i	0.0238422	+	0.0595548i
$244$	−7.84407	+	5.04108i	−0.502165	+	0.322722i
$245$	−12.3314	+	2.39820i	−0.787822	+	0.153215i
$246$	0.317709	+	2.20972i	0.0202564	+	0.140886i
$247$	−4.27758	−	1.48049i	−0.272176	−	0.0942010i
$248$	−1.45515	−	2.82260i	−0.0924023	−	0.179236i
$249$	9.57522	−	3.31402i	0.606805	−	0.210017i
$250$	−8.80519	−	8.39574i	−0.556889	−	0.530993i
$251$	0.671561	+	1.47051i	0.0423885	+	0.0928179i	0.929642	−	0.368465i	$-0.120117\pi$
$251$	0.671561	+	1.47051i	0.0423885	+	0.0928179i	−0.887253	+	0.461283i	$0.847389\pi$
$252$	−1.91328	+	1.82739i	−0.120526	+	0.115115i
$253$	21.1586	−	8.91384i	1.33023	−	0.560408i
$254$	−3.12641	−	5.41510i	−0.196168	−	0.339773i
$255$	−0.00429124	+	0.0449399i	−0.000268728	+	0.00281425i
$256$	0.235759	−	0.971812i	0.0147349	−	0.0607382i
$257$	3.13072	−	16.2437i	0.195289	−	1.01325i	−0.743493	−	0.668743i	$-0.766832\pi$
$257$	3.13072	−	16.2437i	0.195289	−	1.01325i	0.938782	−	0.344511i	$-0.111955\pi$
$258$	−7.67172	−	4.93032i	−0.477621	−	0.306948i
$259$	19.1669	−	8.77273i	1.19097	−	0.545111i
$260$	−1.54433	+	0.222040i	−0.0957750	+	0.0137704i
$261$	1.16260	+	4.79230i	0.0719631	+	0.296636i
$262$	4.69904	−	0.223843i	0.290308	−	0.0138291i
$263$	−12.0371	+	15.3065i	−0.742242	+	0.943838i	−0.999748	−	0.0224389i	$-0.992857\pi$
$263$	−12.0371	+	15.3065i	−0.742242	+	0.943838i	0.257506	+	0.966277i	$0.417099\pi$
$264$	4.76573	−	0.455072i	0.293310	−	0.0280077i
$265$	2.09366	+	0.956144i	0.128613	+	0.0587354i
$266$	13.7120	−	1.32098i	0.840739	−	0.0809945i
$267$	−8.48654	−	13.2053i	−0.519368	−	0.808152i
$268$	−3.40974	+	0.827194i	−0.208283	+	0.0505289i
$269$	6.96619	−	17.4007i	0.424736	−	1.06094i	−0.549517	−	0.835483i	$-0.685188\pi$
$269$	6.96619	−	17.4007i	0.424736	−	1.06094i	0.974253	−	0.225457i	$-0.0723875\pi$
$270$	−0.339636	−	1.76220i	−0.0206696	−	0.107244i
$271$	13.0924	+	0.623670i	0.795309	+	0.0378853i	0.441303	−	0.897358i	$-0.354516\pi$
$271$	13.0924	+	0.623670i	0.795309	+	0.0378853i	0.354006	+	0.935243i	$0.384819\pi$
$272$	−0.0164732	+	0.0190111i	−0.000998833	+	0.00115271i
$273$	1.15175	+	1.99102i	0.0697071	+	0.120502i
$274$	−18.1713	+	8.29858i	−1.09777	+	0.501335i
$275$	7.37703	−	4.25913i	0.444852	−	0.256835i
$276$	0.597336	−	4.75849i	0.0359554	−	0.286427i
$277$	−0.396002	+	0.685896i	−0.0237935	+	0.0412115i	−0.877677	−	0.479253i	$-0.840908\pi$
$277$	−0.396002	+	0.685896i	−0.0237935	+	0.0412115i	0.853883	+	0.520464i	$0.174241\pi$
$278$	1.47498	+	1.05033i	0.0884632	+	0.0629944i
$279$	−0.894676	−	3.04699i	−0.0535628	−	0.182418i
$280$	3.99223	−	2.57040i	0.238581	−	0.153611i
$281$	1.05610	−	1.64333i	0.0630018	−	0.0980327i	−0.808323	−	0.588739i	$-0.799625\pi$
$281$	1.05610	−	1.64333i	0.0630018	−	0.0980327i	0.871325	+	0.490706i	$0.163261\pi$
$282$	1.16265	−	3.35926i	0.0692348	−	0.200041i
$283$	−28.8506	−	11.5501i	−1.71499	−	0.686579i	−0.715070	−	0.699053i	$-0.753605\pi$
$283$	−28.8506	−	11.5501i	−1.71499	−	0.686579i	−0.999922	+	0.0124732i	$0.996030\pi$
$284$	0.234687	−	0.223773i	0.0139261	−	0.0132785i
$285$	−4.28168	+	8.30529i	−0.253625	+	0.491963i
$286$	0.592322	−	4.11969i	0.0350247	−	0.243602i
$287$	−5.58001	+	1.93652i	−0.329377	+	0.114309i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−15.7817	+	6.31803i	−0.928333	+	0.371649i
$290$	−0.421094	−	8.83984i	−0.0247275	−	0.519093i
$291$	5.47746	+	5.74460i	0.321095	+	0.336754i
$292$	2.00777	+	2.55308i	0.117496	+	0.149408i
$293$	−7.13606	−	8.23546i	−0.416893	−	0.481121i	0.507995	−	0.861360i	$-0.330387\pi$
$293$	−7.13606	−	8.23546i	−0.416893	−	0.481121i	−0.924888	+	0.380240i	$0.875841\pi$
$294$	−5.70885	−	4.05080i	−0.332947	−	0.236247i
$295$	13.8187	+	11.9740i	0.804555	+	0.697151i
$296$	−5.49798	+	5.76612i	−0.319564	+	0.335149i
$297$	4.76573	+	0.455072i	0.276536	+	0.0264060i
$298$	−6.50654	−	3.75655i	−0.376914	−	0.217611i
$299$	−3.89786	−	1.47998i	−0.225419	−	0.0855897i
$300$		−	1.77931i		−	0.102728i
$301$	8.94850	−	22.4069i	0.515783	−	1.29151i
$302$	13.7258	−	4.03026i	0.789832	−	0.231916i
$303$	4.69448	+	0.904787i	0.269691	+	0.0519787i
$304$	−4.62786	+	2.38583i	−0.265426	+	0.136837i
$305$	16.4312	−	3.16685i	0.940848	−	0.181334i
$306$	−0.0197734	+	0.0155499i	−0.00113037	+	0.000888931i
$307$	−5.18129	+	17.6458i	−0.295712	+	1.00710i	0.668884	+	0.743367i	$0.266772\pi$
$307$	−5.18129	+	17.6458i	−0.295712	+	1.00710i	−0.964595	+	0.263734i	$0.915046\pi$
$308$	3.57873	+	12.1502i	0.203917	+	0.692322i
$309$	5.40274	+	0.776797i	0.307351	+	0.0441904i
$310$	0.541730	+	5.67325i	0.0307682	+	0.322219i
$311$	5.91554	−	4.21244i	0.335440	−	0.238865i	−0.399908	−	0.916555i	$-0.630958\pi$
$311$	5.91554	−	4.21244i	0.335440	−	0.238865i	0.735348	+	0.677690i	$0.237019\pi$
$312$	−0.683375	−	0.537412i	−0.0386885	−	0.0304250i
$313$	−18.7256	−	9.65373i	−1.05844	−	0.545661i	−0.161067	−	0.986943i	$-0.551493\pi$
$313$	−18.7256	−	9.65373i	−1.05844	−	0.545661i	−0.897368	+	0.441282i	$0.854524\pi$
$314$	2.95910	+	0.868871i	0.166992	+	0.0490332i
$315$	4.40654	−	1.76841i	0.248280	−	0.0996388i
$316$	11.3071	−	9.79764i	0.636073	−	0.551160i
$317$	−1.56324	+	32.8165i	−0.0878005	+	1.84316i	0.341361	+	0.939932i	$0.389112\pi$
$317$	−1.56324	+	32.8165i	−0.0878005	+	1.84316i	−0.429161	+	0.903228i	$0.641191\pi$
$318$	0.419473	+	1.21199i	0.0235229	+	0.0679649i
$319$	22.9427	+	5.56584i	1.28454	+	0.311627i
$320$	−1.04099	+	1.46186i	−0.0581929	+	0.0817206i
$321$	−0.349758			−0.0195216
$322$	12.6606	−	0.841437i	0.705550	−	0.0468914i
$323$	0.130975			0.00728763
$324$	0.580057	−	0.814576i	0.0322254	−	0.0452542i
$325$	−1.50328	−	0.364692i	−0.0833870	−	0.0202295i
$326$	−3.93059	−	11.3567i	−0.217695	−	0.628989i
$327$	0.335827	−	7.04987i	0.0185713	−	0.389859i
$328$	1.68717	−	1.46194i	0.0931582	−	0.0807220i
$329$	9.31042	+	1.33064i	0.513300	+	0.0733608i
$330$	−8.24360	−	2.42054i	−0.453795	−	0.133246i
$331$	−12.4135	−	6.39960i	−0.682307	−	0.351754i	0.0819761	−	0.996634i	$-0.473877\pi$
$331$	−12.4135	−	6.39960i	−0.682307	−	0.351754i	−0.764284	+	0.644880i	$0.776907\pi$
$332$	−7.96469	−	6.26350i	−0.437119	−	0.343754i
$333$	−6.48987	+	4.62141i	−0.355643	+	0.253252i
$334$	0.530467	+	5.55531i	0.0290259	+	0.303973i
$335$	6.23262	+	0.896116i	0.340525	+	0.0489600i
$336$	2.57170	+	0.621597i	0.140297	+	0.0339109i
$337$	3.76726	−	12.8301i	0.205216	−	0.698901i	−0.790986	−	0.611834i	$-0.790432\pi$
$337$	3.76726	−	12.8301i	0.205216	−	0.698901i	0.996202	−	0.0870677i	$-0.0277496\pi$
$338$	9.62458	−	7.56885i	0.523508	−	0.411691i
$339$	−5.31973	+	1.02529i	−0.288928	+	0.0556863i
$340$	0.0401259	−	0.0206863i	0.00217613	−	0.00112187i
$341$	−14.9282	−	2.87718i	−0.808410	−	0.155808i
$342$	−4.99575	+	1.46688i	−0.270139	+	0.0793200i
$343$	7.65106	−	16.8660i	0.413118	−	0.910677i
$344$			9.11939i			0.491685i
$345$	−4.16910	+	7.52958i	−0.224457	+	0.405379i
$346$	3.66935	+	2.11850i	0.197265	+	0.113891i
$347$	19.5702	+	1.86872i	1.05058	+	0.100318i	0.606036	−	0.795438i	$-0.292759\pi$
$347$	19.5702	+	1.86872i	1.05058	+	0.100318i	0.444546	+	0.895756i	$0.353365\pi$
$348$	3.40299	−	3.56895i	0.182419	−	0.191316i
$349$	−16.7873	−	14.5463i	−0.898605	−	0.778646i	0.0772618	−	0.997011i	$-0.475382\pi$
$349$	−16.7873	−	14.5463i	−0.898605	−	0.778646i	−0.975867	+	0.218365i	$0.929928\pi$
$350$	4.62178	−	0.894807i	0.247044	−	0.0478295i
$351$	−0.569320	−	0.657030i	−0.0303880	−	0.0350697i
$352$	−2.95938	−	3.76316i	−0.157735	−	0.200577i
$353$	−18.7380	−	19.6518i	−0.997322	−	1.04596i	−0.998943	−	0.0459628i	$-0.985364\pi$
$353$	−18.7380	−	19.6518i	−0.997322	−	1.04596i	0.00162092	−	0.999999i	$-0.499484\pi$
$354$	0.484793	+	10.1771i	0.0257664	+	0.540904i
$355$	−0.540262	+	0.216288i	−0.0286741	+	0.0114794i
$356$	−6.52085	+	14.2787i	−0.345604	+	0.756768i
$357$	−0.0503352	−	0.0435416i	−0.00266402	−	0.00230447i
$358$	−0.116788	+	0.812280i	−0.00617245	+	0.0429303i
$359$	−15.1621	+	29.4103i	−0.800223	+	1.55222i	0.0331142	+	0.999452i	$0.489458\pi$
$359$	−15.1621	+	29.4103i	−0.800223	+	1.55222i	−0.833337	+	0.552765i	$0.813573\pi$
$360$	−1.29883	+	1.23844i	−0.0684546	+	0.0652713i
$361$	7.52839	+	3.01391i	0.396231	+	0.158627i
$362$	−4.15113	+	11.9939i	−0.218179	+	0.630386i
$363$	6.44404	−	10.0271i	0.338225	−	0.526288i
$364$	1.05227	−	2.04534i	0.0551539	−	0.107205i
$365$	−1.64220	−	5.59280i	−0.0859564	−	0.292741i
$366$	7.59532	+	5.40860i	0.397014	+	0.282712i
$367$	−15.5448	+	26.9243i	−0.811431	+	1.40544i	0.100432	+	0.994944i	$0.467977\pi$
$367$	−15.5448	+	26.9243i	−0.811431	+	1.40544i	−0.911863	+	0.410495i	$0.865356\pi$
$368$	−4.32604	+	2.07012i	−0.225510	+	0.107913i
$369$	1.93335	−	1.11622i	0.100646	−	0.0581081i
$370$	13.0060	−	5.93966i	0.676151	−	0.308788i
$371$	−2.93721	+	1.69909i	−0.152492	+	0.0882126i
$372$	−2.07959	+	2.39997i	−0.107822	+	0.124433i
$373$	−21.4104	−	1.01991i	−1.10859	−	0.0528087i	−0.514712	−	0.857363i	$-0.672101\pi$
$373$	−21.4104	−	1.01991i	−1.10859	−	0.0528087i	−0.593879	+	0.804554i	$0.702404\pi$
$374$	0.0227912	+	0.118252i	0.00117851	+	0.00611467i
$375$	−4.52177	+	11.2948i	−0.233503	+	0.583263i
$376$	−3.45456	+	0.838068i	−0.178155	+	0.0432200i
$377$	−2.31781	−	3.60658i	−0.119373	−	0.185749i
$378$	2.40758	+	1.09706i	0.123833	+	0.0564267i
$379$	22.8620	+	10.4407i	1.17434	+	0.536305i	0.904448	−	0.426584i	$-0.140283\pi$
$379$	22.8620	+	10.4407i	1.17434	+	0.536305i	0.269897	+	0.962889i	$0.413011\pi$
$380$	9.30171	−	0.888205i	0.477168	−	0.0455640i
$381$	−3.86523	+	4.91505i	−0.198022	+	0.251805i
$382$	20.8313	−	0.992316i	1.06582	−	0.0507713i
$383$	3.53215	+	14.5597i	0.180484	+	0.743966i	0.988043	+	0.154179i	$0.0492732\pi$
$383$	3.53215	+	14.5597i	0.180484	+	0.743966i	−0.807559	+	0.589787i	$0.799212\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	2.14171	−	22.6302i	0.109152	−	1.15334i
$386$	13.6900	+	8.79806i	0.696805	+	0.447809i
$387$	−1.72586	+	8.95459i	−0.0877302	+	0.455188i
$388$	1.87132	−	7.71370i	0.0950021	−	0.391604i
$389$	−2.89065	+	30.2723i	−0.146562	+	1.53487i	0.560763	+	0.827976i	$0.310508\pi$
$389$	−2.89065	+	30.2723i	−0.146562	+	1.53487i	−0.707325	+	0.706889i	$0.750098\pi$
$390$	0.780103	+	1.35118i	0.0395021	+	0.0684196i
$391$	0.120587	+	0.00357980i	0.00609836	+	0.000181038i
$392$	−0.321311	+	6.99262i	−0.0162286	+	0.353181i
$393$	−1.95427	−	4.27925i	−0.0985797	−	0.215860i
$394$	10.3372	+	9.85647i	0.520779	+	0.496562i
$395$	−25.3734	+	8.78183i	−1.27668	+	0.441862i
$396$	−2.19372	−	4.25522i	−0.110238	−	0.213833i
$397$	−33.3687	−	11.5490i	−1.67473	−	0.579629i	−0.685768	−	0.727820i	$-0.740534\pi$
$397$	−33.3687	−	11.5490i	−1.67473	−	0.579629i	−0.988959	+	0.148191i	$0.952655\pi$
$398$	−2.85398	−	19.8499i	−0.143057	−	0.994985i
$399$	−6.32260	−	12.2389i	−0.316526	−	0.612709i
$400$	−1.49685	+	0.961965i	−0.0748424	+	0.0480983i
$401$	6.53537	+	16.3246i	0.326361	+	0.815209i	0.997282	+	0.0736808i	$0.0234746\pi$
$401$	6.53537	+	16.3246i	0.326361	+	0.815209i	−0.670921	+	0.741529i	$0.734101\pi$
$402$	2.03521	+	2.85806i	0.101507	+	0.142547i
$403$	1.60142	+	2.24889i	0.0797726	+	0.112025i
$404$	−1.77687	−	4.43841i	−0.0884027	−	0.220819i
$405$	−1.50974	+	0.970250i	−0.0750195	+	0.0482121i
$406$	10.9818	+	7.04451i	0.545016	+	0.349613i
$407$	5.42819	+	37.7539i	0.269065	+	1.87139i
$408$	0.0237717	+	0.00822747i	0.00117688	+	0.000407321i
$409$	7.07423	+	13.7221i	0.349798	+	0.678514i	0.996442	−	0.0842780i	$-0.0268584\pi$
$409$	7.07423	+	13.7221i	0.349798	+	0.678514i	−0.646644	+	0.762792i	$0.723828\pi$
$410$	−3.78606	+	1.31037i	−0.186980	+	0.0647144i
$411$	14.4577	+	13.7854i	0.713148	+	0.679985i
$412$	−2.26746	−	4.96504i	−0.111710	−	0.244610i
$413$	−26.1913	+	6.37726i	−1.28879	+	0.313805i
$414$	−4.63963	+	1.21400i	−0.228026	+	0.0596650i
$415$	9.09204	+	15.7479i	0.446311	+	0.773033i
$416$	−0.0826394	+	0.865439i	−0.00405173	+	0.0424316i
$417$	0.426896	−	1.75969i	0.0209052	−	0.0861723i
$418$	−4.71735	+	24.4759i	−0.230733	+	1.19716i
$419$	−5.53631	−	3.55797i	−0.270467	−	0.173818i	0.398376	−	0.917222i	$-0.369574\pi$
$419$	−5.53631	−	3.55797i	−0.270467	−	0.173818i	−0.668843	+	0.743404i	$0.733210\pi$
$420$	−3.87004	−	2.75094i	−0.188839	−	0.134232i
$421$	−29.1100	+	4.18539i	−1.41874	+	0.203983i	−0.808621	−	0.588330i	$-0.799786\pi$
$421$	−29.1100	+	4.18539i	−1.41874	+	0.203983i	−0.610115	+	0.792313i	$0.708877\pi$
$422$	0.636281	+	2.62279i	0.0309737	+	0.127675i
$423$	−3.55074	+	0.169143i	−0.172643	+	0.00822399i
$424$	0.792805	−	1.00813i	0.0385020	−	0.0489593i
$425$	0.0445562	−	0.00425460i	0.00216129	−	0.000206378i
$426$	−0.294968	−	0.134708i	−0.0142913	−	0.00652660i
$427$	−10.2293	+	22.4489i	−0.495029	+	1.08638i
$428$	0.189093	+	0.294235i	0.00914017	+	0.0142224i
$429$	−4.04473	+	0.981241i	−0.195281	+	0.0473748i
$430$	6.08260	−	15.1936i	0.293329	−	0.732701i
$431$	−2.33345	−	12.1071i	−0.112398	−	0.583177i	−0.993834	−	0.110874i	$-0.964635\pi$
$431$	−2.33345	−	12.1071i	−0.112398	−	0.583177i	0.881436	−	0.472303i	$-0.156577\pi$
$432$	−0.998867	−	0.0475819i	−0.0480580	−	0.00228929i
$433$	−19.9807	+	23.0590i	−0.960213	+	1.10814i	0.0338599	+	0.999427i	$0.489220\pi$
$433$	−19.9807	+	23.0590i	−0.960213	+	1.10814i	−0.994073	+	0.108718i	$0.965325\pi$
$434$	−7.27979	−	4.19483i	−0.349441	−	0.201358i
$435$	−8.05012	+	3.67637i	−0.385974	+	0.176268i
$436$	−6.11229	+	3.52893i	−0.292726	+	0.169005i
$437$	22.8960	+	9.96429i	1.09526	+	0.476657i
$438$	1.62399	−	2.81283i	0.0775972	−	0.134402i
$439$	1.59509	+	1.13586i	0.0761296	+	0.0542117i	0.617488	−	0.786580i	$-0.288150\pi$
$439$	1.59509	+	1.13586i	0.0761296	+	0.0542117i	−0.541358	+	0.840792i	$0.682090\pi$
$440$	2.42054	+	8.24360i	0.115395	+	0.392998i
$441$	−1.63887	+	6.80545i	−0.0780413	+	0.324069i
$442$	0.0118235	−	0.0183977i	0.000562385	−	0.000875087i
$443$	6.24574	−	18.0459i	0.296744	−	0.857385i	−0.693797	−	0.720170i	$-0.744064\pi$
$443$	6.24574	−	18.0459i	0.296744	−	0.857385i	0.990541	−	0.137215i	$-0.0438151\pi$
$444$	7.39647	+	2.96110i	0.351021	+	0.140528i
$445$	20.3880	−	19.4400i	0.966486	−	0.921542i
$446$	10.0540	−	19.5020i	0.476071	−	0.923449i
$447$	−1.06923	+	7.43663i	−0.0505727	+	0.351741i
$448$	−0.867443	−	2.49951i	−0.0409828	−	0.118091i
$449$	−10.7391	+	23.5154i	−0.506811	+	1.10976i	0.467384	+	0.884054i	$0.345196\pi$
$449$	−10.7391	+	23.5154i	−0.506811	+	1.10976i	−0.974195	+	0.225707i	$0.927531\pi$
$450$	−1.65185	+	0.661301i	−0.0778690	+	0.0311740i
$451$	−0.508537	−	10.6755i	−0.0239461	−	0.502690i
$452$	3.73859	+	3.92092i	0.175849	+	0.184425i
$453$	−8.84294	−	11.2447i	−0.415477	−	0.528322i
$454$	1.87821	+	2.16757i	0.0881488	+	0.101729i
$455$	−3.11740	+	2.70583i	−0.146146	+	0.126851i
$456$	3.93493	+	3.40963i	0.184270	+	0.159671i
$457$	24.5668	−	25.7649i	1.14919	−	1.20523i	0.173789	−	0.984783i	$-0.444399\pi$
$457$	24.5668	−	25.7649i	1.14919	−	1.20523i	0.975398	−	0.220450i	$-0.0707526\pi$
$458$	21.9500	+	2.09597i	1.02566	+	0.0979384i
$459$	0.0217851	+	0.0125776i	0.00101684	+	0.000587073i
$460$	8.58827	−	0.563528i	0.400430	−	0.0262746i
$461$		−	32.7567i		−	1.52563i	−0.646616	−	0.762816i	$-0.723816\pi$
$461$		−	32.7567i		−	1.52563i	0.646616	−	0.762816i	$-0.276184\pi$
$462$	9.94979	−	7.83815i	0.462906	−	0.364664i
$463$	−2.33689	+	0.686173i	−0.108605	+	0.0318892i	−0.335583	−	0.942011i	$-0.608933\pi$
$463$	−2.33689	+	0.686173i	−0.108605	+	0.0318892i	0.226979	+	0.973900i	$0.427115\pi$
$464$	−4.84219	−	0.933256i	−0.224793	−	0.0433253i
$465$	5.06553	−	2.61146i	0.234908	−	0.121104i
$466$	3.45593	−	0.666075i	0.160093	−	0.0308553i
$467$	−17.1063	+	13.4525i	−0.791583	+	0.622508i	−0.929872	−	0.367884i	$-0.880082\pi$
$467$	−17.1063	+	13.4525i	−0.791583	+	0.622508i	0.138288	+	0.990392i	$0.455840\pi$
$468$	−0.244931	+	0.834159i	−0.0113220	+	0.0385590i
$469$	−6.40035	+	6.72381i	−0.295541	+	0.310477i
$470$	6.31455	+	0.907895i	0.291269	+	0.0418781i
$471$	−0.293156	−	3.07006i	−0.0135079	−	0.141461i
$472$	8.29938	−	5.90996i	0.382010	−	0.272028i
$473$	34.3177	+	26.9877i	1.57793	+	1.24090i
$474$	−13.2982	−	6.85571i	−0.610808	−	0.314893i
$475$	8.88897	+	2.61004i	0.407854	+	0.119757i
$476$	−0.00941628	+	0.0658850i	−0.000431595	+	0.00301984i
$477$	0.969269	−	0.839876i	0.0443798	−	0.0384553i
$478$	−1.22235	+	25.6603i	−0.0559090	+	1.17367i
$479$	11.0571	+	31.9475i	0.505214	+	1.45972i	0.852883	+	0.522102i	$0.174852\pi$
$479$	11.0571	+	31.9475i	0.505214	+	1.45972i	−0.347669	+	0.937617i	$0.613027\pi$
$480$	1.74404	+	0.423100i	0.0796042	+	0.0193118i
$481$	4.01774	−	5.64213i	0.183193	−	0.257259i
$482$	−12.8721			−0.586307
$483$	−5.48665	−	11.4410i	−0.249651	−	0.520584i
$484$	−11.9193			−0.541785
$485$	−8.26278	+	11.6034i	−0.375193	+	0.526885i
$486$	−0.971812	−	0.235759i	−0.0440823	−	0.0106942i
$487$	1.39272	+	4.02400i	0.0631102	+	0.182345i	0.972148	−	0.234370i	$-0.0753026\pi$
$487$	1.39272	+	4.02400i	0.0631102	+	0.182345i	−0.909037	+	0.416715i	$0.863181\pi$
$488$	0.443666	−	9.31370i	0.0200838	−	0.421611i
$489$	−9.08234	+	7.86989i	−0.410717	+	0.355889i
$490$	5.19938	−	11.4359i	0.234884	−	0.516623i
$491$	6.91875	+	2.03153i	0.312239	+	0.0916816i	0.434098	−	0.900866i	$-0.357067\pi$
$491$	6.91875	+	2.03153i	0.312239	+	0.0916816i	−0.121859	+	0.992547i	$0.538885\pi$
$492$	−1.98427	−	1.02296i	−0.0894579	−	0.0461188i
$493$	0.0975085	+	0.0766815i	0.00439156	+	0.00345356i
$494$	3.68721	−	2.62565i	0.165895	−	0.118134i
$495$	0.816686	+	8.55272i	0.0367073	+	0.384416i
$496$	3.14330	+	0.451938i	0.141138	+	0.0202926i
$497$	0.201566	−	0.833929i	0.00904149	−	0.0374068i
$498$	−2.85466	+	9.72207i	−0.127920	+	0.435656i
$499$	−2.58276	+	2.03110i	−0.115620	+	0.0909246i	−0.674295	−	0.738462i	$-0.735552\pi$
$499$	−2.58276	+	2.03110i	−0.115620	+	0.0909246i	0.558675	+	0.829387i	$0.311310\pi$
$500$	11.9465	−	2.30250i	0.534263	−	0.102971i
$501$	4.96021	−	2.55717i	0.221606	−	0.114246i
$502$	−1.58739	−	0.305944i	−0.0708486	−	0.0136549i
$503$	37.9112	−	11.1317i	1.69038	−	0.496340i	0.711829	−	0.702353i	$-0.247867\pi$
$503$	37.9112	−	11.1317i	1.69038	−	0.496340i	0.978549	+	0.206013i	$0.0660489\pi$
$504$	−0.378732	−	2.61850i	−0.0168701	−	0.116637i
$505$			8.57990i			0.381801i
$506$	−5.01220	+	22.4058i	−0.222819	+	0.996061i
$507$	−10.6038	−	6.12209i	−0.470930	−	0.271892i
$508$	6.22450	+	0.594368i	0.276168	+	0.0263708i
$509$	20.0175	−	20.9938i	0.887261	−	0.930532i	−0.110733	−	0.993850i	$-0.535320\pi$
$509$	20.0175	−	20.9938i	0.887261	−	0.930532i	0.997993	+	0.0633181i	$0.0201683\pi$
$510$	−0.0341178	−	0.0295632i	−0.00151076	−	0.00130908i
$511$	8.12308	+	2.80378i	0.359344	+	0.124032i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	3.21854	+	4.09271i	0.142102	+	0.180697i
$514$	11.4157	+	11.9725i	0.503527	+	0.528084i
$515$	0.466095	+	9.78453i	0.0205386	+	0.431158i
$516$	8.46615	−	3.38934i	0.372702	−	0.149207i
$517$	−7.06958	+	15.4802i	−0.310920	+	0.680819i
$518$	−3.97185	+	20.7016i	−0.174513	+	0.909575i
$519$	0.602988	−	4.19387i	0.0264682	−	0.184090i
$520$	0.714928	−	1.38677i	0.0313517	−	0.0608137i
$521$	−18.2505	+	17.4018i	−0.799567	+	0.762385i	−0.975024	−	0.222102i	$-0.928708\pi$
$521$	−18.2505	+	17.4018i	−0.799567	+	0.762385i	0.175457	+	0.984487i	$0.443860\pi$
$522$	−4.57807	−	1.83278i	−0.200377	−	0.0802187i
$523$	−13.1668	+	38.0431i	−0.575746	+	1.66351i	0.160694	+	0.987004i	$0.448627\pi$
$523$	−13.1668	+	38.0431i	−0.575746	+	1.66351i	−0.736439	+	0.676504i	$0.763494\pi$
$524$	−2.54338	+	3.95757i	−0.111108	+	0.172887i
$525$	−2.54845	−	3.95814i	−0.111224	−	0.172748i
$526$	−5.48606	−	18.6838i	−0.239203	−	0.814652i
$527$	−0.0650712	−	0.0463370i	−0.00283454	−	0.00201847i
$528$	−2.39370	+	4.14602i	−0.104173	+	0.180432i
$529$	20.8078	+	9.79982i	0.904686	+	0.426079i
$530$	−1.99330	+	1.15083i	−0.0865832	+	0.0499888i
$531$	9.26787	−	4.23249i	0.402191	−	0.183675i
$532$	−6.87772	+	11.9357i	−0.298187	+	0.517480i
$533$	−1.27097	+	1.46678i	−0.0550519	+	0.0635333i
$534$	15.6794	+	0.746902i	0.678514	+	0.0323216i
$535$	−0.118790	−	0.616343i	−0.00513575	−	0.0266468i
$536$	1.30403	−	3.25731i	0.0563256	−	0.140694i
$537$	0.797500	−	0.193472i	0.0344147	−	0.00834891i
$538$	10.1334	+	15.7679i	0.436882	+	0.679802i
$539$	25.3634	+	21.9030i	1.09248	+	0.943427i
$540$	1.63245	+	0.745516i	0.0702496	+	0.0320819i
$541$	39.3916	−	3.76144i	1.69358	−	0.161717i	0.796812	−	0.604228i	$-0.206518\pi$
$541$	39.3916	−	3.76144i	1.69358	−	0.161717i	0.896763	+	0.442511i	$0.145912\pi$
$542$	−8.10239	+	10.3030i	−0.348027	+	0.442553i
$543$	12.6776	−	0.603908i	0.544047	−	0.0259162i
$544$	−0.00593057	−	0.0244462i	−0.000254271	−	0.00104812i
$545$	12.5373	−	1.80260i	0.537040	−	0.0772147i
$546$	−2.28992	−	0.216717i	−0.0979995	−	0.00927464i
$547$	−19.8943	−	12.7853i	−0.850620	−	0.546661i	0.0411478	−	0.999153i	$-0.486899\pi$
$547$	−19.8943	−	12.7853i	−0.850620	−	0.546661i	−0.891768	+	0.452493i	$0.850535\pi$
$548$	3.78059	−	19.6156i	0.161499	−	0.837936i
$549$	2.19828	−	9.06143i	0.0938202	−	0.386732i
$550$	−0.809712	+	8.47969i	−0.0345263	+	0.361575i
$551$	12.8378	+	22.2357i	0.546909	+	0.947274i
$552$	3.52966	+	3.24677i	0.150232	+	0.138192i
$553$	11.1202	−	37.9901i	0.472879	−	1.61550i
$554$	−0.329010	−	0.720432i	−0.0139783	−	0.0306082i
$555$	−10.3480	−	9.86684i	−0.439250	−	0.418824i
$556$	−1.71114	+	0.592232i	−0.0725686	+	0.0251162i
$557$	−0.291364	−	0.565167i	−0.0123455	−	0.0239469i	0.882582	−	0.470158i	$-0.155803\pi$
$557$	−0.291364	−	0.565167i	−0.0123455	−	0.0239469i	−0.894928	+	0.446212i	$0.852773\pi$
$558$	3.00096	+	1.03864i	0.127041	+	0.0439693i
$559$	−1.12830	−	7.84748i	−0.0477219	−	0.331913i
$560$	−0.221936	+	4.74295i	−0.00937853	+	0.200426i
$561$	0.101311	−	0.0651085i	0.00427735	−	0.00274888i
$562$	0.726016	+	1.81350i	0.0306251	+	0.0764979i
$563$	15.7929	+	22.1780i	0.665589	+	0.934690i	0.999970	−	0.00774855i	$-0.00246646\pi$
$563$	15.7929	+	22.1780i	0.665589	+	0.934690i	−0.334381	+	0.942438i	$0.608527\pi$
$564$	2.06197	+	2.89563i	0.0868244	+	0.121928i
$565$	−3.61354	−	9.02618i	−0.152023	−	0.379734i
$566$	26.1434	−	16.8013i	1.09889	−	0.706213i
$567$	0.123667	−	2.64286i	0.00519353	−	0.110990i
$568$	0.0461487	+	0.320971i	0.00193636	+	0.0134677i
$569$	−29.3621	−	10.1623i	−1.23092	−	0.426027i	−0.367272	−	0.930114i	$-0.619708\pi$
$569$	−29.3621	−	10.1623i	−1.23092	−	0.426027i	−0.863653	+	0.504086i	$0.831829\pi$
$570$	−4.28168	−	8.30529i	−0.179340	−	0.347870i
$571$	17.5852	−	6.08630i	0.735918	−	0.254704i	0.0667032	−	0.997773i	$-0.478752\pi$
$571$	17.5852	−	6.08630i	0.735918	−	0.254704i	0.669215	+	0.743069i	$0.266631\pi$
$572$	3.01222	+	2.87215i	0.125947	+	0.120090i
$573$	−8.66344	−	18.9703i	−0.361920	−	0.792495i
$574$	1.65928	−	5.66863i	0.0692571	−	0.236604i
$575$	8.11265	+	2.64599i	0.338321	+	0.110345i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−0.173048	+	1.81225i	−0.00720410	+	0.0754448i	−0.998359	−	0.0572654i	$-0.981762\pi$
$577$	−0.173048	+	1.81225i	−0.00720410	+	0.0754448i	0.991155	+	0.132710i	$0.0423679\pi$
$578$	4.00775	−	16.5202i	0.166701	−	0.687149i
$579$	3.07976	−	15.9793i	0.127990	−	0.664077i
$580$	7.44498	+	4.78460i	0.309136	+	0.198670i
$581$	−26.6888	−	2.52582i	−1.10724	−	0.104789i
$582$	−7.85665	+	1.12962i	−0.325669	+	0.0468241i
$583$	−1.44755	−	5.96690i	−0.0599516	−	0.247124i
$584$	−3.24430	+	0.154545i	−0.134250	+	0.00639512i
$585$	0.964455	−	1.22640i	0.0398753	−	0.0507056i
$586$	10.8477	−	1.03583i	0.448116	−	0.0427898i
$587$	−2.66424	−	1.21672i	−0.109965	−	0.0502194i	0.359673	−	0.933078i	$-0.382888\pi$
$587$	−2.66424	−	1.21672i	−0.109965	−	0.0502194i	−0.469638	+	0.882859i	$0.655616\pi$
$588$	6.61114	−	2.30060i	0.272639	−	0.0948752i
$589$	−8.93915	−	13.9096i	−0.368331	−	0.573135i
$590$	−17.7693	+	4.31079i	−0.731552	+	0.177472i
$591$	5.30850	−	13.2600i	0.218362	−	0.545443i
$592$	−1.50780	−	7.82320i	−0.0619701	−	0.321531i
$593$	25.6993	+	1.22421i	1.05534	+	0.0502722i	0.568072	−	0.822979i	$-0.307689\pi$
$593$	25.6993	+	1.22421i	1.05534	+	0.0502722i	0.487271	+	0.873251i	$0.337992\pi$
$594$	−3.13509	+	3.61808i	−0.128634	+	0.148452i
$595$	0.0596333	−	0.103489i	0.00244473	−	0.00424263i
$596$	6.83416	−	3.12106i	0.279938	−	0.127843i
$597$	−17.3673	+	10.0270i	−0.710795	+	0.410378i
$598$	3.46654	−	2.31663i	0.141757	−	0.0947341i
$599$	3.90791	−	6.76869i	0.159673	−	0.276561i	−0.775078	−	0.631866i	$-0.782289\pi$
$599$	3.90791	−	6.76869i	0.159673	−	0.276561i	0.934751	+	0.355304i	$0.115623\pi$
$600$	1.44938	+	1.03210i	0.0591707	+	0.0421353i
$601$	7.42334	+	25.2816i	0.302804	+	1.03126i	0.960571	+	0.278035i	$0.0896831\pi$
$601$	7.42334	+	25.2816i	0.302804	+	1.03126i	−0.657767	+	0.753222i	$0.728499\pi$
$602$	13.0615	+	20.2865i	0.532345	+	0.826816i
$603$	1.89692	−	2.95166i	0.0772484	−	0.120201i
$604$	−4.67880	+	13.5185i	−0.190378	+	0.550060i
$605$	19.8584	+	7.95011i	0.807359	+	0.323218i
$606$	−3.46008	+	3.29918i	−0.140556	+	0.134020i
$607$	6.96210	−	13.5046i	0.282583	−	0.548135i	−0.704235	−	0.709967i	$-0.748710\pi$
$607$	6.96210	−	13.5046i	0.282583	−	0.548135i	0.986818	+	0.161832i	$0.0517403\pi$
$608$	0.740984	−	5.15366i	0.0300509	−	0.209009i
$609$	2.45839	−	12.8133i	0.0996188	−	0.519221i
$610$	−6.95139	+	15.2214i	−0.281453	+	0.616297i
$611$	2.86905	−	1.14859i	0.116069	−	0.0464672i
$612$	−0.00119693	−	0.0251267i	−4.83832e−5	−	0.00101569i
$613$	3.63224	+	3.80938i	0.146705	+	0.153859i	0.792986	−	0.609240i	$-0.208525\pi$
$613$	3.63224	+	3.80938i	0.146705	+	0.153859i	−0.646281	+	0.763099i	$0.723677\pi$
$614$	−11.3684	−	14.4561i	−0.458793	−	0.583403i
$615$	2.62364	+	3.02784i	0.105795	+	0.122094i
$616$	−11.9731	−	4.13267i	−0.482411	−	0.166510i
$617$	15.1505	+	13.1280i	0.609935	+	0.528512i	0.904143	−	0.427230i	$-0.140510\pi$
$617$	15.1505	+	13.1280i	0.609935	+	0.528512i	−0.294208	+	0.955741i	$0.595056\pi$
$618$	−3.76666	+	3.95036i	−0.151517	+	0.158907i
$619$	−4.09384	−	0.390914i	−0.164545	−	0.0157122i	0.0124583	−	0.999922i	$-0.496034\pi$
$619$	−4.09384	−	0.390914i	−0.164545	−	0.0157122i	−0.177003	+	0.984210i	$0.556640\pi$
$620$	−4.93553	−	2.84953i	−0.198216	−	0.114440i
$621$	2.85142	+	3.85609i	0.114424	+	0.154739i
$622$			7.26211i			0.291184i
$623$	5.94503	+	41.1031i	0.238183	+	1.64676i
$624$	0.834159	−	0.244931i	0.0333931	−	0.00980510i
$625$	−12.7037	−	2.44845i	−0.508150	−	0.0979378i
$626$	18.7256	−	9.65373i	0.748427	−	0.385841i
$627$	24.4759	−	4.71735i	0.977475	−	0.188393i
$628$	−2.42421	+	1.90642i	−0.0967365	+	0.0760745i
$629$	−0.0564638	+	0.192298i	−0.00225136	+	0.00766742i
$630$	−1.11554	+	4.61524i	−0.0444440	+	0.183876i
$631$	−10.4912	−	1.50840i	−0.417646	−	0.0600485i	−0.0697115	−	0.997567i	$-0.522208\pi$
$631$	−10.4912	−	1.50840i	−0.417646	−	0.0600485i	−0.347935	+	0.937519i	$0.613117\pi$
$632$	1.42217	+	14.8937i	0.0565710	+	0.592438i
$633$	2.19843	−	1.56549i	0.0873797	−	0.0622228i
$634$	−25.8248	−	20.3088i	−1.02563	−	0.806567i
$635$	−9.97405	−	5.14198i	−0.395808	−	0.204053i
$636$	−1.23058	−	0.361329i	−0.0487955	−	0.0143276i
$637$	−0.588666	−	6.05709i	−0.0233238	−	0.239991i
$638$	−17.8419	+	15.4601i	−0.706366	+	0.612070i
$639$	−0.0154295	+	0.323905i	−0.000610381	+	0.0128135i
$640$	−0.586966	−	1.69593i	−0.0232019	−	0.0670374i
$641$	−19.7291	−	4.78623i	−0.779252	−	0.189045i	−0.173645	−	0.984808i	$-0.555555\pi$
$641$	−19.7291	−	4.78623i	−0.779252	−	0.189045i	−0.605607	+	0.795764i	$0.707070\pi$
$642$	0.202879	−	0.284904i	0.00800701	−	0.0112443i
$643$	−15.0682			−0.594231			−0.297115	−	0.954842i	$-0.596025\pi$
$643$	−15.0682			−0.594231			−0.297115	+	0.954842i	$0.596025\pi$
$644$	−6.65848	+	10.8011i	−0.262381	+	0.425625i
$645$	−16.3659			−0.644408
$646$	−0.0759728	+	0.106689i	−0.00298911	+	0.00419762i
$647$	−3.77471	−	0.915734i	−0.148399	−	0.0360012i	0.160871	−	0.986975i	$-0.448570\pi$
$647$	−3.77471	−	0.915734i	−0.148399	−	0.0360012i	−0.309270	+	0.950974i	$0.600085\pi$
$648$	0.327068	+	0.945001i	0.0128484	+	0.0371231i
$649$	2.32090	−	48.7217i	0.0911033	−	1.91249i
$650$	1.16906	−	1.01299i	0.0458542	−	0.0397329i
$651$	−1.18872	+	8.31738i	−0.0465896	+	0.325984i
$652$	11.5309	+	3.38576i	0.451583	+	0.132597i
$653$	13.9286	+	7.18067i	0.545066	+	0.281001i	0.708688	−	0.705522i	$-0.249287\pi$
$653$	13.9286	+	7.18067i	0.545066	+	0.281001i	−0.163622	+	0.986523i	$0.552318\pi$
$654$	5.54786	+	4.36288i	0.216938	+	0.170602i
$655$	6.87714	−	4.89719i	0.268712	−	0.191349i
$656$	0.212207	+	2.22233i	0.00828529	+	0.0867675i
$657$	−3.21492	−	0.462235i	−0.125426	−	0.0180335i
$658$	−6.48448	+	6.81219i	−0.252791	+	0.265567i
$659$	−8.63387	+	29.4043i	−0.336328	+	1.14543i	0.601658	+	0.798754i	$0.294507\pi$
$659$	−8.63387	+	29.4043i	−0.336328	+	1.14543i	−0.937986	+	0.346673i	$0.887311\pi$
$660$	6.75347	−	5.31099i	0.262878	−	0.206730i
$661$	−15.2675	+	2.94258i	−0.593838	+	0.114453i	−0.477311	−	0.878734i	$-0.658388\pi$
$661$	−15.2675	+	2.94258i	−0.593838	+	0.114453i	−0.116528	+	0.993187i	$0.537176\pi$
$662$	12.4135	−	6.39960i	0.482464	−	0.248728i
$663$	−0.0214741	−	0.00413880i	−0.000833986	−	0.000160738i
$664$	9.72207	−	2.85466i	0.377289	−	0.110782i
$665$	19.4199	−	15.2984i	0.753072	−	0.593248i
$666$		−	7.96717i		−	0.308722i
$667$	11.2119	+	20.8231i	0.434127	+	0.806274i
$668$	−4.83292	−	2.79029i	−0.186991	−	0.107959i
$669$	−21.8418	−	2.08564i	−0.844452	−	0.0806354i
$670$	−4.34523	+	4.55715i	−0.167871	+	0.176058i
$671$	−33.7359	−	29.2324i	−1.30236	−	1.12850i
$672$	−1.99807	+	1.73428i	−0.0770771	+	0.0669013i
$673$	−24.8092	−	28.6314i	−0.956326	−	1.10366i	−0.994537	−	0.104389i	$-0.966711\pi$
$673$	−24.8092	−	28.6314i	−0.956326	−	1.10366i	0.0382106	−	0.999270i	$-0.487834\pi$
$674$	8.26588	+	10.5109i	0.318390	+	0.404866i
$675$	1.22786	+	1.28774i	0.0472604	+	0.0495653i
$676$	0.582602	+	12.2303i	0.0224078	+	0.470397i
$677$	−38.2732	+	15.3223i	−1.47096	+	0.588884i	−0.962277	−	0.272070i	$-0.912292\pi$
$677$	−38.2732	+	15.3223i	−1.47096	+	0.588884i	−0.508683	+	0.860954i	$0.669867\pi$
$678$	2.25056	−	4.92805i	0.0864324	−	0.189261i
$679$	−6.88528	−	19.8397i	−0.264233	−	0.761378i
$680$	−0.00642471	+	0.0446848i	−0.000246376	+	0.00171358i
$681$	1.31424	−	2.54928i	0.0503619	−	0.0976885i
$682$	11.0029	−	10.4913i	0.421324	−	0.401731i
$683$	−42.2481	−	16.9136i	−1.61658	−	0.647180i	−0.625471	−	0.780247i	$-0.715093\pi$
$683$	−42.2481	−	16.9136i	−1.61658	−	0.647180i	−0.991107	+	0.133067i	$0.957517\pi$
$684$	1.70293	−	4.92029i	0.0651132	−	0.188132i
$685$	−19.3823	+	30.1594i	−0.740559	+	1.15233i
$686$	9.30057	+	16.0156i	0.355097	+	0.611478i
$687$	−6.21216	−	21.1567i	−0.237009	−	0.807178i
$688$	−7.42844	−	5.28977i	−0.283207	−	0.201670i
$689$	−0.557498	+	0.965615i	−0.0212390	+	0.0367870i
$690$	−3.71510	−	7.76363i	−0.141431	−	0.295556i
$691$	12.7988	−	7.38937i	0.486888	−	0.281105i	−0.236395	−	0.971657i	$-0.575966\pi$
$691$	12.7988	−	7.38937i	0.486888	−	0.281105i	0.723283	+	0.690552i	$0.242632\pi$
$692$	−3.85411	+	1.76011i	−0.146511	+	0.0669094i
$693$	−10.9747	−	6.32392i	−0.416893	−	0.240226i
$694$	−12.8740	+	14.8574i	−0.488692	+	0.563980i
$695$	3.24591	+	0.154622i	0.123124	+	0.00586513i
$696$	0.933256	+	4.84219i	0.0353750	+	0.183543i
$697$	0.0208717	−	0.0521349i	0.000790571	−	0.00197475i
$698$	21.5867	−	5.23687i	0.817068	−	0.198219i
$699$	−1.90280	−	2.96082i	−0.0719706	−	0.111988i
$700$	−1.95201	+	4.28383i	−0.0737789	+	0.161913i
$701$	15.4753	+	7.06733i	0.584494	+	0.266929i	0.685638	−	0.727942i	$-0.259523\pi$
$701$	15.4753	+	7.06733i	0.584494	+	0.266929i	−0.101145	+	0.994872i	$0.532250\pi$
$702$	0.865439	−	0.0826394i	0.0326639	−	0.00311902i
$703$	−25.6427	+	32.6073i	−0.967132	+	1.22981i
$704$	4.78198	−	0.227794i	0.180228	−	0.00858531i
$705$	−1.50402	−	6.19966i	−0.0566447	−	0.233493i
$706$	26.8770	−	3.86433i	1.01153	−	0.145436i
$707$	−10.3097	−	7.32848i	−0.387738	−	0.275616i
$708$	−8.57119	−	5.50837i	−0.322125	−	0.207017i
$709$	0.685683	−	3.55766i	0.0257514	−	0.133611i	−0.966778	−	0.255618i	$-0.917721\pi$
$709$	0.685683	−	3.55766i	0.0257514	−	0.133611i	0.992529	+	0.122007i	$0.0389331\pi$
$710$	0.137199	−	0.565544i	0.00514901	−	0.0212245i
$711$	−1.42217	+	14.8937i	−0.0533356	+	0.558556i
$712$	−7.84859	−	13.5942i	−0.294138	−	0.509463i
$713$	−7.85002	−	13.0508i	−0.293985	−	0.488755i
$714$	0.0646652	−	0.0157452i	0.00242004	−	0.000589250i
$715$	−3.10288	−	6.79435i	−0.116041	−	0.254094i
$716$	−0.593920	−	0.566301i	−0.0221958	−	0.0211637i
$717$	24.2765	−	8.40218i	0.906623	−	0.313785i
$718$	−15.1621	−	29.4103i	−0.565843	−	1.09758i
$719$	−23.6104	−	8.17162i	−0.880518	−	0.304750i	−0.150854	−	0.988556i	$-0.548202\pi$
$719$	−23.6104	−	8.17162i	−0.880518	−	0.304750i	−0.729664	+	0.683806i	$0.760323\pi$
$720$	−0.255402	−	1.77636i	−0.00951828	−	0.0662011i
$721$	−12.1554	−	7.79734i	−0.452689	−	0.290388i
$722$	−6.82195	+	4.38420i	−0.253887	+	0.163163i
$723$	4.78407	+	11.9500i	0.177921	+	0.444426i
$724$	−7.36206	−	10.3386i	−0.273609	−	0.384230i
$725$	5.08959	+	7.14734i	0.189023	+	0.265445i
$726$	4.42994	+	11.0655i	0.164411	+	0.410678i
$727$	35.5320	−	22.8350i	1.31781	−	0.846905i	0.322779	−	0.946474i	$-0.395383\pi$
$727$	35.5320	−	22.8350i	1.31781	−	0.846905i	0.995031	+	0.0995692i	$0.0317465\pi$
$728$	1.05571	+	2.04357i	0.0391272	+	0.0757397i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	5.50833	+	1.90645i	0.203872	+	0.0705609i
$731$	0.105117	+	0.203899i	0.00388791	+	0.00754149i
$732$	−8.81144	+	3.04967i	−0.325680	+	0.112719i
$733$	13.7206	+	13.0825i	0.506780	+	0.483214i	0.899792	−	0.436320i	$-0.143718\pi$
$733$	13.7206	+	13.0825i	0.506780	+	0.483214i	−0.393012	+	0.919534i	$0.628567\pi$
$734$	−12.9151	−	28.2800i	−0.476704	−	1.04384i
$735$	−12.5492	−	0.576633i	−0.462883	−	0.0212694i
$736$	0.823077	−	4.72467i	0.0303390	−	0.174154i
$737$	−8.39865	−	14.5469i	−0.309368	−	0.535842i
$738$	−0.212207	+	2.22233i	−0.00781145	+	0.0818052i
$739$	−9.93469	+	40.9514i	−0.365453	+	1.50642i	0.431352	+	0.902184i	$0.358037\pi$
$739$	−9.93469	+	40.9514i	−0.365453	+	1.50642i	−0.796805	+	0.604236i	$0.793478\pi$
$740$	−2.70594	+	14.0397i	−0.0994723	+	0.516111i
$741$	−3.80797	−	2.44723i	−0.139889	−	0.0899013i
$742$	0.319707	−	3.37815i	0.0117368	−	0.124016i
$743$	38.0384	−	5.46909i	1.39549	−	0.200641i	0.596804	−	0.802387i	$-0.296437\pi$
$743$	38.0384	−	5.46909i	1.39549	−	0.200641i	0.798688	+	0.601746i	$0.205528\pi$
$744$	−0.748681	−	3.08610i	−0.0274480	−	0.113142i
$745$	−13.4680	+	0.641558i	−0.493428	+	0.0235049i
$746$	13.2501	−	16.8488i	0.485120	−	0.616880i
$747$	10.0866	−	0.963156i	0.369050	−	0.0352400i
$748$	−0.109546	−	0.0500278i	−0.00400538	−	0.00182920i
$749$	0.842071	+	0.383705i	0.0307686	+	0.0140203i
$750$	−6.57762	−	10.2350i	−0.240181	−	0.373729i
$751$	28.7773	−	6.98131i	1.05010	−	0.254752i	0.326662	−	0.945141i	$-0.394076\pi$
$751$	28.7773	−	6.98131i	1.05010	−	0.254752i	0.723438	+	0.690390i	$0.242561\pi$
$752$	1.32117	−	3.30013i	0.0481782	−	0.120343i
$753$	0.305944	+	1.58739i	0.0111492	+	0.0578476i
$754$	4.28230	+	0.203991i	0.155952	+	0.00742892i
$755$	16.8120	−	19.4021i	0.611852	−	0.706115i
$756$	−2.29017	+	1.32480i	−0.0832928	+	0.0481826i
$757$	−34.6520	+	15.8251i	−1.25945	+	0.575172i	−0.929498	−	0.368826i	$-0.879760\pi$
$757$	−34.6520	+	15.8251i	−1.25945	+	0.575172i	−0.329952	+	0.943998i	$0.607032\pi$
$758$	−21.7661	+	12.5666i	−0.790579	+	0.456441i
$759$	22.6637	−	3.67424i	0.822640	−	0.133367i
$760$	−4.67201	+	8.09216i	−0.169472	+	0.293533i
$761$	−36.8696	−	26.2547i	−1.33652	−	0.951733i	−0.999949	−	0.0100755i	$-0.996793\pi$
$761$	−36.8696	−	26.2547i	−1.33652	−	0.951733i	−0.336573	−	0.941657i	$-0.609268\pi$
$762$	−1.76162	−	5.99953i	−0.0638168	−	0.217340i
$763$	−8.54266	+	16.6047i	−0.309265	+	0.601132i
$764$	−11.2750	+	17.5443i	−0.407915	+	0.634729i
$765$	−0.0147653	+	0.0426614i	−0.000533839	+	0.00154243i
$766$	−13.9088	−	5.56826i	−0.502547	−	0.201189i
$767$	−6.41063	+	6.11252i	−0.231474	+	0.220710i
$768$	0.458227	−	0.888835i	0.0165348	−	0.0320731i
$769$	6.62458	−	46.0750i	0.238888	−	1.66151i	−0.418697	−	0.908126i	$-0.637513\pi$
$769$	6.62458	−	46.0750i	0.238888	−	1.66151i	0.657586	−	0.753380i	$-0.271578\pi$
$770$	17.1917	+	14.8714i	0.619545	+	0.535927i
$771$	6.87207	−	15.0477i	0.247491	−	0.541931i
$772$	−15.1077	+	6.04821i	−0.543738	+	0.217680i
$773$	−1.50991	−	31.6969i	−0.0543077	−	1.14006i	−0.847399	−	0.530957i	$-0.821833\pi$
$773$	−1.50991	−	31.6969i	−0.0543077	−	1.14006i	0.793091	−	0.609103i	$-0.208470\pi$
$774$	−6.29310	−	6.60002i	−0.226201	−	0.237233i
$775$	−3.49285	−	4.44151i	−0.125467	−	0.159544i
$776$	5.19792	+	5.99872i	0.186595	+	0.215342i
$777$	20.6949	−	4.00667i	0.742424	−	0.143738i
$778$	−22.9823	−	19.9143i	−0.823956	−	0.713962i
$779$	8.02117	−	8.41236i	0.287388	−	0.301404i
$780$	−1.55314	−	0.148307i	−0.0556114	−	0.00531024i
$781$	1.34444	+	0.776211i	0.0481078	+	0.0277750i
$782$	−0.0728634	+	0.0961509i	−0.00260559	+	0.00343835i
$783$			4.93131i			0.176230i
$784$	−5.50964	−	4.31785i	−0.196773	−	0.154209i
$785$	5.31049	−	1.55930i	0.189540	−	0.0556539i
$786$	4.61936	+	0.890308i	0.164767	+	0.0317562i
$787$	−11.1633	+	5.75507i	−0.397928	+	0.205146i	−0.645563	−	0.763707i	$-0.723377\pi$
$787$	−11.1633	+	5.75507i	−0.397928	+	0.205146i	0.247635	+	0.968853i	$0.420347\pi$
$788$	−14.0250	+	2.70310i	−0.499620	+	0.0962938i
$789$	−15.3065	+	12.0371i	−0.544925	+	0.428534i
$790$	7.56457	−	25.7626i	0.269135	−	0.916591i
$791$	13.9325	+	3.36758i	0.495382	+	0.119737i
$792$	4.73868	+	0.681319i	0.168382	+	0.0242096i
$793$	0.770551	+	8.06958i	0.0273631	+	0.286559i
$794$	28.7633	−	20.4823i	1.02077	−	0.726888i
$795$	1.80923	+	1.42279i	0.0641666	+	0.0504612i
$796$	17.8247	+	9.18928i	0.631780	+	0.325705i
$797$	−6.39070	−	1.87648i	−0.226370	−	0.0664683i	0.166580	−	0.986028i	$-0.446727\pi$
$797$	−6.39070	−	1.87648i	−0.226370	−	0.0664683i	−0.392951	+	0.919560i	$0.628546\pi$
$798$	13.6369	+	1.94899i	0.482743	+	0.0689935i
$799$	−0.0675799	+	0.0585583i	−0.00239080	+	0.00207164i
$800$	0.0846628	−	1.77729i	0.00299328	−	0.0628367i
$801$	−5.13405	−	14.8339i	−0.181403	−	0.524128i
$802$	−17.0885	−	4.14562i	−0.603415	−	0.146387i
$803$	−9.01953	+	12.6662i	−0.318292	+	0.446979i
$804$	−3.50864			−0.123740
$805$	18.2979	−	13.5543i	0.644915	−	0.477728i
$806$	−2.76081			−0.0972452
$807$	10.8722	−	15.2679i	0.382719	−	0.537454i
$808$	4.64611	+	1.12713i	0.163450	+	0.0396525i
$809$	−9.86283	−	28.4968i	−0.346758	−	1.00189i	−0.974678	−	0.223614i	$-0.928214\pi$
$809$	−9.86283	−	28.4968i	−0.346758	−	1.00189i	0.627919	−	0.778279i	$-0.283907\pi$
$810$	0.0853919	−	1.79260i	0.00300037	−	0.0629854i
$811$	16.5634	−	14.3522i	0.581618	−	0.503975i	−0.313629	−	0.949546i	$-0.601545\pi$
$811$	16.5634	−	14.3522i	0.581618	−	0.503975i	0.895247	+	0.445571i	$0.146999\pi$
$812$	−12.1083	+	4.85927i	−0.424920	+	0.170527i
$813$	12.5764	+	3.69275i	0.441072	+	0.129510i
$814$	−33.9021	−	17.4777i	−1.18827	−	0.612594i
$815$	−16.9530	−	13.3320i	−0.593837	−	0.466999i
$816$	−0.0204909	+	0.0145915i	−0.000717323	+	0.000510804i
$817$	4.51341	+	47.2666i	0.157904	+	1.65365i
$818$	−15.2811	−	2.19710i	−0.534293	−	0.0768197i
$819$	0.649883	+	2.20643i	0.0227088	+	0.0770990i
$820$	1.12873	−	3.84412i	0.0394171	−	0.134242i
$821$	17.8151	−	14.0099i	0.621750	−	0.488949i	−0.256886	−	0.966442i	$-0.582697\pi$
$821$	17.8151	−	14.0099i	0.621750	−	0.488949i	0.878636	+	0.477492i	$0.158454\pi$
$822$	−19.6156	+	3.78059i	−0.684172	+	0.131863i
$823$	−11.3547	+	5.85375i	−0.395799	+	0.204049i	−0.644624	−	0.764500i	$-0.722986\pi$
$823$	−11.3547	+	5.85375i	−0.395799	+	0.204049i	0.248825	+	0.968549i	$0.419956\pi$
$824$	5.35966	+	1.03299i	0.186713	+	0.0359859i
$825$	8.17321	−	2.39987i	0.284555	−	0.0835528i
$826$	9.99766	−	25.0340i	0.347863	−	0.871043i
$827$			16.1650i			0.562113i	0.959691	+	0.281057i	$0.0906849\pi$
$827$			16.1650i			0.562113i	−0.959691	+	0.281057i	$0.909315\pi$
$828$	1.70235	−	4.48352i	0.0591609	−	0.155813i
$829$	−17.3154	−	9.99704i	−0.601388	−	0.347211i	0.168199	−	0.985753i	$-0.446205\pi$
$829$	−17.3154	−	9.99704i	−0.601388	−	0.347211i	−0.769587	+	0.638541i	$0.779538\pi$
$830$	−18.1017	−	1.72851i	−0.628321	−	0.0599974i
$831$	−0.546545	+	0.573200i	−0.0189595	+	0.0198841i
$832$	−0.657030	−	0.569320i	−0.0227784	−	0.0197376i
$833$	0.0734184	+	0.160051i	0.00254380	+	0.00554543i
$834$	1.18578	+	1.36846i	0.0410601	+	0.0473858i
$835$	6.19090	+	7.87237i	0.214245	+	0.272435i
$836$	−17.2012	−	18.0401i	−0.594915	−	0.623929i
$837$	−0.151102	−	3.17202i	−0.00522285	−	0.109641i
$838$	6.10961	−	2.44592i	0.211053	−	0.0844929i
$839$	0.214048	−	0.468701i	0.00738977	−	0.0161813i	−0.905901	−	0.423489i	$-0.860805\pi$
$839$	0.214048	−	0.468701i	0.00738977	−	0.0161813i	0.913291	+	0.407308i	$0.133532\pi$
$840$	4.48569	−	1.55674i	0.154771	−	0.0537126i
$841$	0.666350	−	4.63456i	0.0229776	−	0.159813i
$842$	13.4762	−	26.1401i	0.464419	−	0.900847i
$843$	1.41376	−	1.34802i	0.0486926	−	0.0464283i
$844$	−2.50554	−	1.00307i	−0.0862442	−	0.0345270i
$845$	7.18692	−	20.7652i	0.247237	−	0.714346i
$846$	1.92185	−	2.99046i	0.0660746	−	0.102814i
$847$	−26.5149	+	17.0716i	−0.911064	+	0.586589i
$848$	0.361329	+	1.23058i	0.0124081	+	0.0422581i
$849$	−25.3144	−	18.0263i	−0.868786	−	0.618660i
$850$	−0.0223794	+	0.0387623i	−0.000767608	+	0.00132954i
$851$	−24.5002	+	29.3204i	−0.839856	+	1.00509i
$852$	0.280828	−	0.162136i	0.00962100	−	0.00555469i
$853$	−22.8530	+	10.4366i	−0.782472	+	0.357343i	−0.766264	−	0.642526i	$-0.777887\pi$
$853$	−22.8530	+	10.4366i	−0.782472	+	0.357343i	−0.0162079	+	0.999869i	$0.505159\pi$
$854$	−12.3528	−	21.3542i	−0.422704	−	0.730725i
$855$	−6.11903	+	7.06174i	−0.209266	+	0.241506i
$856$	−0.349362	−	0.0166421i	−0.0119409	−	0.000568817i
$857$	0.268110	+	1.39109i	0.00915847	+	0.0475186i	0.986220	−	0.165437i	$-0.0529033\pi$
$857$	0.268110	+	1.39109i	0.00915847	+	0.0475186i	−0.977062	+	0.212955i	$0.931691\pi$
$858$	1.54688	−	3.86392i	0.0528096	−	0.131912i
$859$	1.10663	−	0.268465i	0.0377576	−	0.00915990i	−0.216836	−	0.976208i	$-0.569574\pi$
$859$	1.10663	−	0.268465i	0.0377576	−	0.00915990i	0.254593	+	0.967048i	$0.418058\pi$
$860$	8.84809	+	13.7679i	0.301717	+	0.469481i
$861$	−5.87926	+	0.566392i	−0.200365	+	0.0193026i
$862$	11.2157	+	5.12202i	0.382007	+	0.174457i
$863$	43.9825	−	4.19982i	1.49718	−	0.142964i	0.685934	−	0.727664i	$-0.259394\pi$
$863$	43.9825	−	4.19982i	1.49718	−	0.142964i	0.811249	+	0.584700i	$0.198788\pi$
$864$	0.618159	−	0.786053i	0.0210302	−	0.0267421i
$865$	7.59523	−	0.361805i	0.258245	−	0.0123017i
$866$	−7.19334	−	29.6514i	−0.244440	−	1.00759i
$867$	−16.8263	+	2.41926i	−0.571452	+	0.0821625i
$868$	7.63970	−	3.49670i	0.259308	−	0.118686i
$869$	60.2559	+	38.7241i	2.04404	+	1.31363i
$870$	1.67485	−	8.68994i	0.0567827	−	0.294616i
$871$	−0.719142	+	2.96434i	−0.0243672	+	0.100443i
$872$	0.670893	−	7.02590i	0.0227193	−	0.237927i
$873$	3.96872	+	6.87403i	0.134321	+	0.232651i
$874$	−21.3976	+	12.8707i	−0.723786	+	0.435357i
$875$	23.2777	−	22.2326i	0.786929	−	0.751600i
$876$	1.34926	+	2.95446i	0.0455872	+	0.0998221i
$877$	36.2661	+	34.5797i	1.22462	+	1.16767i	0.980201	+	0.198003i	$0.0634455\pi$
$877$	36.2661	+	34.5797i	1.22462	+	1.16767i	0.244418	+	0.969670i	$0.421403\pi$
$878$	−1.85049	+	0.640461i	−0.0624510	+	0.0216145i
$879$	−4.99333	−	9.68570i	−0.168421	−	0.326691i
$880$	−8.11909	−	2.81004i	−0.273694	−	0.0947266i
$881$	4.46358	+	31.0449i	0.150382	+	1.04593i	0.915580	+	0.402135i	$0.131732\pi$
$881$	4.46358	+	31.0449i	0.150382	+	1.04593i	−0.765199	+	0.643794i	$0.777359\pi$
$882$	−4.59292	−	5.28253i	−0.154652	−	0.177872i
$883$	33.8858	−	21.7771i	1.14035	−	0.732858i	0.172654	−	0.984982i	$-0.444766\pi$
$883$	33.8858	−	21.7771i	1.14035	−	0.732858i	0.967695	+	0.252124i	$0.0811292\pi$
$884$	0.00812801	+	0.0203028i	0.000273375	+	0.000682857i
$885$	10.6062	+	14.8943i	0.356523	+	0.500667i
$886$	11.0768	+	15.5553i	0.372134	+	0.522589i
$887$	13.1248	+	32.7841i	0.440687	+	1.10078i	0.967964	+	0.251089i	$0.0807886\pi$
$887$	13.1248	+	32.7841i	0.440687	+	1.10078i	−0.527277	+	0.849693i	$0.676787\pi$
$888$	−6.70241	+	4.30738i	−0.224918	+	0.144546i
$889$	14.6980	−	7.59299i	0.492954	−	0.254661i
$890$	4.00910	+	27.8839i	0.134385	+	0.934670i
$891$	4.52410	+	1.56581i	0.151563	+	0.0524565i
$892$	10.0540	+	19.5020i	0.336633	+	0.652977i
$893$	−17.4905	+	6.05352i	−0.585297	+	0.202573i
$894$	−5.43749	−	5.18464i	−0.181857	−	0.173400i
$895$	0.611795	+	1.33964i	0.0204500	+	0.0447794i
$896$	2.53921	+	0.743259i	0.0848289	+	0.0248305i
$897$	−3.43907	−	2.35722i	−0.114827	−	0.0787053i
$898$	−12.9258	−	22.3881i	−0.431339	−	0.747101i
$899$	1.48857	−	15.5890i	0.0496467	−	0.519924i
$900$	0.419487	−	1.72915i	0.0139829	−	0.0576383i
$901$	0.00610567	−	0.0316792i	0.000203409	−	0.00105539i
$902$	8.99099	+	5.77816i	0.299367	+	0.192392i
$903$	13.9789	−	19.6656i	0.465188	−	0.654429i
$904$	−5.36249	+	0.771009i	−0.178354	+	0.0256434i
$905$	5.36997	+	22.1353i	0.178504	+	0.735802i
$906$	14.2891	−	0.680673i	0.474723	−	0.0226138i
$907$	−7.53570	+	9.58242i	−0.250219	+	0.318179i	−0.894895	−	0.446277i	$-0.852750\pi$
$907$	−7.53570	+	9.58242i	−0.250219	+	0.318179i	0.644676	+	0.764456i	$0.276992\pi$
$908$	−2.85512	+	0.272631i	−0.0947505	+	0.00904758i
$909$	4.34884	+	1.98605i	0.144242	+	0.0658731i
$910$	−0.395840	−	4.10889i	−0.0131220	−	0.136209i
$911$	−19.7511	−	30.7333i	−0.654383	−	1.01824i	−0.996896	−	0.0787265i	$-0.974915\pi$
$911$	−19.7511	−	30.7333i	−0.654383	−	1.01824i	0.342514	−	0.939513i	$-0.388722\pi$
$912$	−5.05989	+	1.22752i	−0.167550	+	0.0406471i
$913$	18.0288	−	45.0337i	0.596665	−	1.49040i
$914$	6.73735	+	34.9567i	0.222852	+	1.15626i
$915$	16.7146	+	0.796217i	0.552569	+	0.0263221i
$916$	−14.4396	+	16.6642i	−0.477097	+	0.550600i
$917$	0.0104691	+	12.4466i	0.000345718	+	0.411023i
$918$	−0.0228820	+	0.0104499i	−0.000755219	+	0.000344897i
$919$	18.7422	−	10.8208i	0.618247	−	0.356945i	−0.157939	−	0.987449i	$-0.550485\pi$
$919$	18.7422	−	10.8208i	0.618247	−	0.356945i	0.776186	+	0.630504i	$0.217152\pi$
$920$	−4.52265	+	7.32268i	−0.149107	+	0.241422i
$921$	−9.19540	+	15.9269i	−0.302999	+	0.524809i
$922$	26.6828	+	19.0008i	0.878752	+	0.625756i
$923$	−0.0794244	−	0.270495i	−0.00261429	−	0.00890344i
$924$	0.613328	+	12.6514i	0.0201770	+	0.416202i
$925$	−7.66415	+	11.9256i	−0.251996	+	0.392113i
$926$	0.796590	−	2.30159i	0.0261776	−	0.0756351i
$927$	5.06731	+	2.02865i	0.166432	+	0.0666295i
$928$	3.56895	−	3.40299i	0.117157	−	0.111709i
$929$	2.39791	−	4.65130i	0.0786729	−	0.152604i	−0.846218	−	0.532837i	$-0.821126\pi$
$929$	2.39791	−	4.65130i	0.0786729	−	0.152604i	0.924891	+	0.380233i	$0.124156\pi$
$930$	−0.811061	+	5.64105i	−0.0265957	+	0.184977i
$931$	1.79544	+	36.4023i	0.0588431	+	1.19304i
$932$	−1.46207	+	3.20148i	−0.0478915	+	0.104868i
$933$	6.74191	−	2.69905i	0.220720	−	0.0883631i
$934$	−1.03549	−	21.7376i	−0.0338822	−	0.711275i
$935$	0.149143	+	0.156417i	0.00487749	+	0.00511537i
$936$	−0.537412	−	0.683375i	−0.0175659	−	0.0223368i
$937$	36.4082	+	42.0173i	1.18940	+	1.37264i	0.911118	+	0.412146i	$0.135221\pi$
$937$	36.4082	+	42.0173i	1.18940	+	1.37264i	0.278286	+	0.960498i	$0.410234\pi$
$938$	−1.76449	−	9.11376i	−0.0576125	−	0.297575i
$939$	−15.9218	−	13.7963i	−0.519589	−	0.450227i
$940$	−4.40235	+	4.61705i	−0.143589	+	0.150592i
$941$	7.65189	+	0.730667i	0.249445	+	0.0238191i	0.219029	−	0.975718i	$-0.429711\pi$
$941$	7.65189	+	0.730667i	0.249445	+	0.0238191i	0.0304153	+	0.999537i	$0.490317\pi$
$942$	2.67085	+	1.54201i	0.0870209	+	0.0502415i
$943$	7.61494	−	7.52595i	0.247977	−	0.245079i
$944$			10.1886i			0.331610i
$945$	4.69924	−	0.679684i	0.152866	−	0.0221101i
$946$	−41.8898	+	12.3000i	−1.36195	+	0.399906i
$947$	−3.23119	−	0.622761i	−0.105000	−	0.0202370i	0.136481	−	0.990643i	$-0.456421\pi$
$947$	−3.23119	−	0.622761i	−0.105000	−	0.0202370i	−0.241480	+	0.970406i	$0.577633\pi$
$948$	13.2982	−	6.85571i	0.431906	−	0.222663i
$949$	2.77268	−	0.534391i	0.0900051	−	0.0173471i
$950$	−7.28218	+	5.72677i	−0.236265	+	0.185801i
$951$	−9.25597	+	31.5229i	−0.300145	+	1.02220i
$952$	−0.0482064	−	0.0458873i	−0.00156238	−	0.00148722i
$953$	5.48394	+	0.788472i	0.177642	+	0.0255411i	0.230562	−	0.973058i	$-0.425944\pi$
$953$	5.48394	+	0.788472i	0.177642	+	0.0255411i	−0.0529195	+	0.998599i	$0.516853\pi$
$954$	0.121912	+	1.27672i	0.00394704	+	0.0413353i
$955$	30.4870	−	21.7097i	0.986535	−	0.702509i
$956$	−20.1932	−	15.8801i	−0.653096	−	0.513600i
$957$	20.9838	+	10.8179i	0.678309	+	0.349693i
$958$	−32.4375	−	9.52450i	−1.04801	−	0.307723i
$959$	−19.6848	−	49.0506i	−0.635654	−	1.58393i
$960$	−1.35629	+	1.17523i	−0.0437741	+	0.0379305i
$961$	0.995197	−	20.8917i	0.0321031	−	0.673927i
$962$	2.26542	+	6.54551i	0.0730402	+	0.211036i
$963$	−0.339899	−	0.0824585i	−0.0109531	−	0.00265719i
$964$	7.46653	−	10.4853i	0.240481	−	0.337708i
$965$	29.2047			0.940133
$966$	12.5021	+	2.16714i	0.402250	+	0.0697267i
$967$	−15.4124			−0.495629			−0.247815	−	0.968807i	$-0.579712\pi$
$967$	−15.4124			−0.495629			−0.247815	+	0.968807i	$0.579712\pi$
$968$	6.91385	−	9.70915i	0.222220	−	0.312064i
$969$	0.127283	+	0.0308785i	0.00408891	+	0.000991959i
$970$	−4.65901	−	13.4613i	−0.149592	−	0.432217i
$971$	2.16121	−	45.3694i	0.0693566	−	1.45597i	−0.649259	−	0.760567i	$-0.724921\pi$
$971$	2.16121	−	45.3694i	0.0693566	−	1.45597i	0.718616	−	0.695407i	$-0.244776\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−2.95827	+	3.76827i	−0.0948378	+	0.120805i
$974$	−4.08571	−	1.19967i	−0.130915	−	0.0384400i
$975$	−1.37493	−	0.708823i	−0.0440329	−	0.0227005i
$976$	7.32937	+	5.76388i	0.234607	+	0.184497i
$977$	−25.6122	+	18.2383i	−0.819406	+	0.583496i	−0.911050	−	0.412295i	$-0.864727\pi$
$977$	−25.6122	+	18.2383i	−0.819406	+	0.583496i	0.0916441	+	0.995792i	$0.470788\pi$
$978$	−1.14235	−	11.9632i	−0.0365283	−	0.382542i
$979$	−74.3839	−	10.6948i	−2.37732	−	0.341807i
$980$	6.29949	+	10.8688i	0.201230	+	0.347190i
$981$	1.98843	−	6.77197i	0.0634857	−	0.216212i
$982$	−5.66810	+	4.45744i	−0.180876	+	0.142243i
$983$	24.9884	−	4.81612i	0.797006	−	0.153610i	0.225538	−	0.974234i	$-0.427586\pi$
$983$	24.9884	−	4.81612i	0.797006	−	0.153610i	0.571468	+	0.820624i	$0.306374\pi$
$984$	1.98427	−	1.02296i	0.0632563	−	0.0326109i
$985$	25.1697	+	4.85106i	0.801972	+	0.154567i
$986$	−0.119023	+	0.0349484i	−0.00379048	+	0.00111298i
$987$	8.73426	+	3.48815i	0.278015	+	0.111029i
$988$			4.52654i			0.144008i
$989$	2.86356	+	43.6412i	0.0910560	+	1.38771i
$990$	−7.44056	−	4.29581i	−0.236477	−	0.136530i
$991$	−45.3955	−	4.33474i	−1.44204	−	0.137698i	−0.655478	−	0.755215i	$-0.727533\pi$
$991$	−45.3955	−	4.33474i	−1.44204	−	0.137698i	−0.786558	+	0.617517i	$0.788139\pi$
$992$	−2.19143	+	2.29830i	−0.0695779	+	0.0729712i
$993$	−10.5548	−	9.14580i	−0.334947	−	0.290233i
$994$	0.562379	+	0.647918i	0.0178376	+	0.0205507i
$995$	−23.5681	−	27.1991i	−0.747159	−	0.862268i
$996$	−6.26350	−	7.96469i	−0.198467	−	0.252371i
$997$	−21.6051	−	22.6588i	−0.684240	−	0.717610i	0.286410	−	0.958107i	$-0.407538\pi$
$997$	−21.6051	−	22.6588i	−0.684240	−	0.717610i	−0.970650	+	0.240497i	$0.922690\pi$
$998$	−0.156341	−	3.28201i	−0.00494890	−	0.103890i
$999$	−7.39647	+	2.96110i	−0.234014	+	0.0936850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.157.11	yes	320
7.5	odd	6	inner	966.2.be.a.19.11	✓	320
23.17	odd	22	inner	966.2.be.a.661.11	yes	320
161.40	even	66	inner	966.2.be.a.523.11	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.11	✓	320	7.5	odd	6	inner
966.2.be.a.157.11	yes	320	1.1	even	1	trivial
966.2.be.a.523.11	yes	320	161.40	even	66	inner
966.2.be.a.661.11	yes	320	23.17	odd	22	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 + 0.814576i) q^{2} +(0.971812 + 0.235759i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(-0.0853919 + 1.79260i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-2.08108 - 1.63375i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 + 0.814576i) q^{2} +(0.971812 + 0.235759i) q^{3} +(-0.327068 - 0.945001i) q^{4} +(-0.0853919 + 1.79260i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-2.08108 - 1.63375i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.888835 + 0.458227i) q^{9} +(-1.41067 - 1.10937i) q^{10} +(3.89971 - 2.77697i) q^{11} +(-0.0950560 - 0.995472i) q^{12} +(-0.860526 - 0.123725i) q^{13} +(2.53795 - 0.747529i) q^{14} +(-0.505605 + 1.72193i) q^{15} +(-0.786053 + 0.618159i) q^{16} +(0.0247007 - 0.00476066i) q^{17} +(-0.888835 + 0.458227i) q^{18} +(5.11257 + 0.985366i) q^{19} +(1.72193 - 0.505605i) q^{20} +(-1.63724 - 2.07832i) q^{21} +4.78741i q^{22} +(4.68016 + 1.04695i) q^{23} +(0.866025 + 0.500000i) q^{24} +(1.77125 + 0.169134i) q^{25} +(0.599938 - 0.629196i) q^{26} +(0.755750 + 0.654861i) q^{27} +(-0.863237 + 2.50096i) q^{28} +(3.22932 + 3.72683i) q^{29} +(-1.10937 - 1.41067i) q^{30} +(-2.19143 - 2.29830i) q^{31} +(-0.0475819 - 0.998867i) q^{32} +(4.44448 - 1.77930i) q^{33} +(-0.0104499 + 0.0228820i) q^{34} +(3.10635 - 3.59102i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-3.65077 + 7.08151i) q^{37} +(-3.76823 + 3.59300i) q^{38} +(-0.807100 - 0.323114i) q^{39} +(-0.586966 + 1.69593i) q^{40} +(1.20695 - 1.87805i) q^{41} +(2.64265 - 0.128113i) q^{42} +(2.56923 + 8.74999i) q^{43} +(-3.89971 - 2.77697i) q^{44} +(-0.897315 + 1.55419i) q^{45} +(-3.56758 + 3.20505i) q^{46} +(-3.07852 + 1.77738i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(1.66175 + 6.79990i) q^{49} +(-1.16520 + 1.34471i) q^{50} +(0.0251267 + 0.00119693i) q^{51} +(0.164530 + 0.853664i) q^{52} +(0.476667 - 1.19066i) q^{53} +(-0.971812 + 0.235759i) q^{54} +(4.64498 + 7.22773i) q^{55} +(-1.53650 - 2.15387i) q^{56} +(4.73614 + 2.16292i) q^{57} +(-4.90898 + 0.468750i) q^{58} +(6.29817 - 8.00877i) q^{59} +(1.79260 - 0.0853919i) q^{60} +(-2.19828 - 9.06143i) q^{61} +(3.14330 - 0.451938i) q^{62} +(-1.10111 - 2.40573i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.295271 - 1.53201i) q^{65} +(-1.12867 + 4.65246i) q^{66} +(0.333518 - 3.49276i) q^{67} +(-0.0125776 - 0.0217851i) q^{68} +(4.30140 + 2.12083i) q^{69} +(1.12330 + 4.61336i) q^{70} +(0.134708 + 0.294968i) q^{71} +(0.723734 + 0.690079i) q^{72} +(-3.06934 + 1.06231i) q^{73} +(-3.65077 - 7.08151i) q^{74} +(1.68145 + 0.581954i) q^{75} +(-0.740984 - 5.15366i) q^{76} +(-12.6524 - 0.592044i) q^{77} +(0.731365 - 0.470020i) q^{78} +(5.56059 + 13.8897i) q^{79} +(-1.04099 - 1.46186i) q^{80} +(0.580057 + 0.814576i) q^{81} +(0.829715 + 2.07253i) q^{82} +(8.52400 - 5.47804i) q^{83} +(-1.42853 + 2.22695i) q^{84} +(0.00642471 + 0.0446848i) q^{85} +(-8.61783 - 2.98266i) q^{86} +(2.25966 + 4.38312i) q^{87} +(4.52410 - 1.56581i) q^{88} +(-11.3606 - 10.8323i) q^{89} +(-0.745516 - 1.63245i) q^{90} +(1.58869 + 1.66336i) q^{91} +(-0.541358 - 4.76518i) q^{92} +(-1.58781 - 2.75017i) q^{93} +(0.337902 - 3.53867i) q^{94} +(-2.20294 + 9.08062i) q^{95} +(0.189251 - 0.981929i) q^{96} +(6.67740 + 4.29131i) q^{97} +(-6.50294 - 2.59070i) q^{98} +(4.73868 - 0.681319i) 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	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 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 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

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