LMFDB - Embedded newform 690.2.w.b.493.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.12
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.93237 + 1.12513i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.968092 - 1.77293i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.93237 + 1.12513i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.968092 - 1.77293i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.84719 + 1.26012i) q^{10} +(0.321659 + 0.278719i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(4.67392 + 2.55215i) q^{13} +(-0.839146 - 1.83747i) q^{14} +(-0.688666 + 2.12738i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.744916 + 0.995091i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(-0.0697719 + 0.485274i) q^{19} +(1.75258 + 1.38869i) q^{20} +(1.52663 - 1.32283i) q^{21} +(0.300956 + 0.300956i) q^{22} +(-1.55878 - 4.53544i) q^{23} +1.00000i q^{24} +(2.46814 + 4.34836i) q^{25} +(4.47995 + 2.87909i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-0.705924 - 1.89266i) q^{28} +(-0.244429 + 0.0351436i) q^{29} +(-0.838677 + 2.07283i) q^{30} +(-1.06130 + 0.682055i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-0.203976 + 0.373554i) q^{33} +(-0.814007 + 0.939414i) q^{34} +(0.124066 - 4.51520i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.587159 + 1.57423i) q^{37} +(-0.104213 + 0.479060i) q^{38} +(-1.50032 + 5.10961i) q^{39} +(1.64905 + 1.51018i) q^{40} +(-0.149201 + 0.326705i) q^{41} +(1.61711 - 1.21055i) q^{42} +(-2.91534 + 0.634194i) q^{43} +(0.278719 + 0.321659i) q^{44} +(-2.22515 - 0.220721i) q^{45} +(-1.23126 - 4.63508i) q^{46} +(-0.514682 + 0.514682i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(1.57841 - 2.45606i) q^{49} +(2.15165 + 4.51336i) q^{50} +(-1.13069 - 0.516371i) q^{51} +(4.26314 + 3.19135i) q^{52} +(-11.4864 + 6.27207i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(0.307969 + 0.900499i) q^{55} +(-0.569105 - 1.93819i) q^{56} +(-0.489015 + 0.0349751i) q^{57} +(-0.246313 + 0.0176167i) q^{58} +(-2.87477 - 9.79058i) q^{59} +(-0.984414 + 2.00772i) q^{60} +(-7.18877 - 11.1859i) q^{61} +(-1.10725 + 0.604605i) q^{62} +(1.61711 + 1.21055i) q^{63} +(0.909632 + 0.415415i) q^{64} +(6.16025 + 10.1905i) q^{65} +(-0.230105 + 0.358051i) q^{66} +(0.459759 - 6.42827i) q^{67} +(-0.878950 + 0.878950i) q^{68} +(4.10045 - 2.48724i) q^{69} +(0.445861 - 4.49484i) q^{70} +(6.34548 + 7.32307i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(5.32346 - 3.98509i) q^{73} +(-0.697968 + 1.52834i) q^{74} +(-3.72435 + 3.33605i) q^{75} +(-0.138123 + 0.470405i) q^{76} +(0.182753 - 0.840104i) q^{77} +(-1.86101 + 4.98956i) q^{78} +(12.0678 - 3.54343i) q^{79} +(1.53711 + 1.62397i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.172128 + 0.315229i) q^{82} +(-8.26343 - 3.08210i) q^{83} +(1.69935 - 1.09210i) q^{84} +(-2.55907 + 1.08476i) q^{85} +(-2.95316 + 0.424600i) q^{86} +(-0.0862975 - 0.231373i) q^{87} +(0.255062 + 0.340723i) q^{88} +(12.7191 + 8.17409i) q^{89} +(-2.20373 - 0.378899i) q^{90} -10.7573i q^{91} +(-0.897457 - 4.71111i) q^{92} +(-0.892063 - 0.892063i) q^{93} +(-0.550087 + 0.476653i) q^{94} +(-0.680824 + 0.859229i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(3.50298 - 1.30655i) q^{97} +(1.74960 - 2.33720i) q^{98} +(-0.408375 - 0.119910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	1.93237	+	1.12513i	0.864184	+	0.503175i
$5$	1.93237	+	1.12513i	0.864184	+	0.503175i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−0.968092	−	1.77293i	−0.365904	−	0.670104i	0.628257	−	0.778006i	$-0.283769\pi$
$7$	−0.968092	−	1.77293i	−0.365904	−	0.670104i	−0.994162	+	0.107902i	$0.965587\pi$
$8$	0.977147	+	0.212565i	0.345474	+	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	1.84719	+	1.26012i	0.584131	+	0.398486i
$11$	0.321659	+	0.278719i	0.0969838	+	0.0840369i	0.702003	−	0.712174i	$-0.252289\pi$
$11$	0.321659	+	0.278719i	0.0969838	+	0.0840369i	−0.605019	+	0.796211i	$0.706835\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	4.67392	+	2.55215i	1.29631	+	0.707840i	0.971297	−	0.237868i	$-0.0764487\pi$
$13$	4.67392	+	2.55215i	1.29631	+	0.707840i	0.325015	+	0.945709i	$0.394630\pi$
$14$	−0.839146	−	1.83747i	−0.224271	−	0.491086i
$15$	−0.688666	+	2.12738i	−0.177813	+	0.549287i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−0.744916	+	0.995091i	−0.180669	+	0.241345i	−0.881728	−	0.471758i	$-0.843620\pi$
$17$	−0.744916	+	0.995091i	−0.180669	+	0.241345i	0.701060	+	0.713103i	$0.252711\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	−0.0697719	+	0.485274i	−0.0160068	+	0.111330i	−0.996258	−	0.0864248i	$-0.972456\pi$
$19$	−0.0697719	+	0.485274i	−0.0160068	+	0.111330i	0.980252	+	0.197754i	$0.0633649\pi$
$20$	1.75258	+	1.38869i	0.391889	+	0.310520i
$21$	1.52663	−	1.32283i	0.333138	−	0.288665i
$22$	0.300956	+	0.300956i	0.0641640	+	0.0641640i
$23$	−1.55878	−	4.53544i	−0.325029	−	0.945704i
$23$	−1.55878	−	4.53544i	−0.325029	−	0.945704i
$24$			1.00000i			0.204124i
$25$	2.46814	+	4.34836i	0.493629	+	0.869673i
$26$	4.47995	+	2.87909i	0.878590	+	0.564635i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	−0.705924	−	1.89266i	−0.133407	−	0.357679i
$29$	−0.244429	+	0.0351436i	−0.0453893	+	0.00652599i	−0.164972	−	0.986298i	$-0.552753\pi$
$29$	−0.244429	+	0.0351436i	−0.0453893	+	0.00652599i	0.119583	+	0.992824i	$0.461844\pi$
$30$	−0.838677	+	2.07283i	−0.153121	+	0.378445i
$31$	−1.06130	+	0.682055i	−0.190615	+	0.122501i	−0.632467	−	0.774587i	$-0.717958\pi$
$31$	−1.06130	+	0.682055i	−0.190615	+	0.122501i	0.441853	+	0.897088i	$0.354321\pi$
$32$	0.936950	+	0.349464i	0.165631	+	0.0617771i
$33$	−0.203976	+	0.373554i	−0.0355076	+	0.0650274i
$34$	−0.814007	+	0.939414i	−0.139601	+	0.161108i
$35$	0.124066	−	4.51520i	0.0209710	−	0.763208i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−0.587159	+	1.57423i	−0.0965284	+	0.258803i	−0.976235	−	0.216714i	$-0.930466\pi$
$37$	−0.587159	+	1.57423i	−0.0965284	+	0.258803i	0.879707	+	0.475517i	$0.157739\pi$
$38$	−0.104213	+	0.479060i	−0.0169056	+	0.0777139i
$39$	−1.50032	+	5.10961i	−0.240243	+	0.818192i
$40$	1.64905	+	1.51018i	0.260738	+	0.238780i
$41$	−0.149201	+	0.326705i	−0.0233013	+	0.0510228i	−0.920925	−	0.389740i	$-0.872565\pi$
$41$	−0.149201	+	0.326705i	−0.0233013	+	0.0510228i	0.897624	+	0.440763i	$0.145292\pi$
$42$	1.61711	−	1.21055i	0.249525	−	0.186792i
$43$	−2.91534	+	0.634194i	−0.444586	+	0.0967137i	−0.429285	−	0.903169i	$-0.641234\pi$
$43$	−2.91534	+	0.634194i	−0.444586	+	0.0967137i	−0.0153011	+	0.999883i	$0.504871\pi$
$44$	0.278719	+	0.321659i	0.0420185	+	0.0484919i
$45$	−2.22515	−	0.220721i	−0.331705	−	0.0329031i
$46$	−1.23126	−	4.63508i	−0.181539	−	0.683406i
$47$	−0.514682	+	0.514682i	−0.0750740	+	0.0750740i	−0.743647	−	0.668573i	$-0.766906\pi$
$47$	−0.514682	+	0.514682i	−0.0750740	+	0.0750740i	0.668573	+	0.743647i	$0.266906\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	1.57841	−	2.45606i	0.225487	−	0.350865i
$50$	2.15165	+	4.51336i	0.304289	+	0.638285i
$51$	−1.13069	−	0.516371i	−0.158329	−	0.0723063i
$52$	4.26314	+	3.19135i	0.591191	+	0.442560i
$53$	−11.4864	+	6.27207i	−1.57778	+	0.861536i	−0.578848	+	0.815436i	$0.696497\pi$
$53$	−11.4864	+	6.27207i	−1.57778	+	0.861536i	−0.998937	+	0.0460999i	$0.985321\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	0.307969	+	0.900499i	0.0415265	+	0.121423i
$56$	−0.569105	−	1.93819i	−0.0760499	−	0.259002i
$57$	−0.489015	+	0.0349751i	−0.0647717	+	0.00463256i
$58$	−0.246313	+	0.0176167i	−0.0323425	+	0.00231318i
$59$	−2.87477	−	9.79058i	−0.374263	−	1.27462i	−0.904390	−	0.426706i	$-0.859674\pi$
$59$	−2.87477	−	9.79058i	−0.374263	−	1.27462i	0.530127	−	0.847918i	$-0.322144\pi$
$60$	−0.984414	+	2.00772i	−0.127087	+	0.259195i
$61$	−7.18877	−	11.1859i	−0.920427	−	1.43221i	−0.901688	−	0.432388i	$-0.857671\pi$
$61$	−7.18877	−	11.1859i	−0.920427	−	1.43221i	−0.0187394	−	0.999824i	$-0.505965\pi$
$62$	−1.10725	+	0.604605i	−0.140621	+	0.0767849i
$63$	1.61711	+	1.21055i	0.203737	+	0.152515i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	6.16025	+	10.1905i	0.764085	+	1.26398i
$66$	−0.230105	+	0.358051i	−0.0283240	+	0.0440730i
$67$	0.459759	−	6.42827i	0.0561685	−	0.785338i	−0.888824	−	0.458248i	$-0.848477\pi$
$67$	0.459759	−	6.42827i	0.0561685	−	0.785338i	0.944993	−	0.327091i	$-0.106068\pi$
$68$	−0.878950	+	0.878950i	−0.106588	+	0.106588i
$69$	4.10045	−	2.48724i	0.493636	−	0.299428i
$70$	0.445861	−	4.49484i	0.0532905	−	0.537236i
$71$	6.34548	+	7.32307i	0.753070	+	0.869089i	0.994862	−	0.101239i	$-0.0322808\pi$
$71$	6.34548	+	7.32307i	0.753070	+	0.869089i	−0.241792	+	0.970328i	$0.577735\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	5.32346	−	3.98509i	0.623064	−	0.466420i	−0.240507	−	0.970647i	$-0.577314\pi$
$73$	5.32346	−	3.98509i	0.623064	−	0.466420i	0.863571	+	0.504228i	$0.168223\pi$
$74$	−0.697968	+	1.52834i	−0.0811371	+	0.177665i
$75$	−3.72435	+	3.33605i	−0.430051	+	0.385214i
$76$	−0.138123	+	0.470405i	−0.0158439	+	0.0539592i
$77$	0.182753	−	0.840104i	0.0208267	−	0.0957387i
$78$	−1.86101	+	4.98956i	−0.210718	+	0.564956i
$79$	12.0678	−	3.54343i	1.35774	−	0.398668i	0.479772	−	0.877393i	$-0.340719\pi$
$79$	12.0678	−	3.54343i	1.35774	−	0.398668i	0.877965	+	0.478726i	$0.158901\pi$
$80$	1.53711	+	1.62397i	0.171854	+	0.181566i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−0.172128	+	0.315229i	−0.0190084	+	0.0348112i
$83$	−8.26343	−	3.08210i	−0.907030	−	0.338305i	−0.147716	−	0.989030i	$-0.547192\pi$
$83$	−8.26343	−	3.08210i	−0.907030	−	0.338305i	−0.759313	+	0.650725i	$0.774465\pi$
$84$	1.69935	−	1.09210i	0.185414	−	0.119158i
$85$	−2.55907	+	1.08476i	−0.277570	+	0.117659i
$86$	−2.95316	+	0.424600i	−0.318447	+	0.0457858i
$87$	−0.0862975	−	0.231373i	−0.00925206	−	0.0248057i
$88$	0.255062	+	0.340723i	0.0271897	+	0.0363212i
$89$	12.7191	+	8.17409i	1.34823	+	0.866452i	0.997544	−	0.0700423i	$-0.0223134\pi$
$89$	12.7191	+	8.17409i	1.34823	+	0.866452i	0.350682	+	0.936495i	$0.385950\pi$
$90$	−2.20373	−	0.378899i	−0.232294	−	0.0399394i
$91$		−	10.7573i		−	1.12767i
$92$	−0.897457	−	4.71111i	−0.0935664	−	0.491167i
$93$	−0.892063	−	0.892063i	−0.0925026	−	0.0925026i
$94$	−0.550087	+	0.476653i	−0.0567372	+	0.0491630i
$95$	−0.680824	+	0.859229i	−0.0698511	+	0.0881550i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	3.50298	−	1.30655i	0.355674	−	0.132660i	−0.165274	−	0.986248i	$-0.552851\pi$
$97$	3.50298	−	1.30655i	0.355674	−	0.132660i	0.520949	+	0.853588i	$0.325578\pi$
$98$	1.74960	−	2.33720i	0.176737	−	0.236093i
$99$	−0.408375	−	0.119910i	−0.0410433	−	0.0120514i
$100$	1.82419	+	4.65536i	0.182419	+	0.465536i
$101$	−1.24216	−	2.71995i	−0.123600	−	0.270645i	0.837710	−	0.546115i	$-0.183894\pi$
$101$	−1.24216	−	2.71995i	−0.123600	−	0.270645i	−0.961310	+	0.275470i	$0.911167\pi$
$102$	−1.09098	−	0.595718i	−0.108023	−	0.0589848i
$103$	−0.711413	−	9.94685i	−0.0700976	−	0.980092i	−0.903821	−	0.427910i	$-0.859250\pi$
$103$	−0.711413	−	9.94685i	−0.0700976	−	0.980092i	0.833724	−	0.552182i	$-0.186205\pi$
$104$	4.02461	+	3.48734i	0.394645	+	0.341962i
$105$	4.43838	−	0.838543i	0.433142	−	0.0818334i
$106$	−11.9046	+	5.43666i	−1.15628	+	0.528055i
$107$	−5.60980	−	1.22034i	−0.542320	−	0.117974i	−0.0669430	−	0.997757i	$-0.521325\pi$
$107$	−5.60980	−	1.22034i	−0.542320	−	0.117974i	−0.475377	+	0.879782i	$0.657688\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	0.454044	+	3.15794i	0.0434895	+	0.302476i	0.999944	+	0.0105943i	$0.00337234\pi$
$109$	0.454044	+	3.15794i	0.0434895	+	0.302476i	−0.956454	+	0.291882i	$0.905719\pi$
$110$	0.242944	+	0.920175i	0.0231638	+	0.0877352i
$111$	−1.66307	−	0.239113i	−0.157851	−	0.0226956i
$112$	−0.429386	−	1.97386i	−0.0405732	−	0.186512i
$113$	−11.0438	−	0.789865i	−1.03891	−	0.0743043i	−0.458553	−	0.888667i	$-0.651632\pi$
$113$	−11.0438	−	0.789865i	−1.03891	−	0.0743043i	−0.580356	+	0.814363i	$0.697087\pi$
$114$	−0.490265			−0.0459175
$115$	2.09082	−	10.5180i	0.194970	−	0.980809i
$116$	−0.246942			−0.0229280
$117$	−5.31175	−	0.379904i	−0.491072	−	0.0351221i
$118$	−2.16900	−	9.97071i	−0.199672	−	0.917879i
$119$	2.48537	+	0.357343i	0.227834	+	0.0327576i
$120$	−1.12513	+	1.93237i	−0.102710	+	0.176401i
$121$	−1.53968	−	10.7087i	−0.139971	−	0.973521i
$122$	−6.37245	−	11.6703i	−0.576935	−	1.05658i
$123$	−0.350954	−	0.0763454i	−0.0316445	−	0.00688384i
$124$	−1.14756	+	0.524074i	−0.103054	+	0.0470632i
$125$	−0.123114	+	11.1797i	−0.0110116	+	0.999939i
$126$	1.52663	+	1.32283i	0.136003	+	0.117847i
$127$	0.00850050	+	0.118852i	0.000754297	+	0.0105465i	0.997815	−	0.0660650i	$-0.0210445\pi$
$127$	0.00850050	+	0.118852i	0.000754297	+	0.0105465i	−0.997061	+	0.0766114i	$0.975590\pi$
$128$	0.877679	+	0.479249i	0.0775766	+	0.0423600i
$129$	−1.23940	−	2.71391i	−0.109123	−	0.238947i
$130$	5.41757	+	10.6040i	0.475153	+	0.930034i
$131$	−6.95705	−	2.04277i	−0.607840	−	0.178478i	−0.0366944	−	0.999327i	$-0.511683\pi$
$131$	−6.95705	−	2.04277i	−0.607840	−	0.178478i	−0.571146	+	0.820848i	$0.693501\pi$
$132$	−0.255062	+	0.340723i	−0.0222003	+	0.0296561i
$133$	0.927903	−	0.346090i	0.0804594	−	0.0300098i
$134$	0.917175	−	6.37909i	0.0792319	−	0.551070i
$135$	−0.257312	−	2.22121i	−0.0221459	−	0.191172i
$136$	−0.939414	+	0.814007i	−0.0805541	+	0.0698005i
$137$	−14.6440	−	14.6440i	−1.25112	−	1.25112i	−0.955217	−	0.295905i	$-0.904379\pi$
$137$	−14.6440	−	14.6440i	−1.25112	−	1.25112i	−0.295905	−	0.955217i	$-0.595621\pi$
$138$	4.26744	−	2.18838i	0.363268	−	0.186287i
$139$		−	2.99155i		−	0.253740i	−0.991919	−	0.126870i	$-0.959507\pi$
$139$		−	2.99155i		−	0.253740i	0.991919	−	0.126870i	$-0.0404932\pi$
$140$	0.765383	−	4.45158i	0.0646867	−	0.376227i
$141$	−0.612323	−	0.393516i	−0.0515669	−	0.0331400i
$142$	5.80689	+	7.75709i	0.487303	+	0.650961i
$143$	0.792075	+	2.12363i	0.0662366	+	0.177587i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−0.511869	−	0.207105i	−0.0425084	−	0.0171991i
$146$	5.59419	−	3.59517i	0.462978	−	0.297538i
$147$	2.73544	+	1.02027i	0.225616	+	0.0841503i
$148$	−0.805220	+	1.47465i	−0.0661886	+	0.121215i
$149$	−3.00356	+	3.46629i	−0.246061	+	0.283970i	−0.865323	−	0.501215i	$-0.832887\pi$
$149$	−3.00356	+	3.46629i	−0.246061	+	0.283970i	0.619262	+	0.785185i	$0.287432\pi$
$150$	−3.95285	+	3.06186i	−0.322749	+	0.250000i
$151$	−15.3577	+	4.50943i	−1.24979	+	0.366972i	−0.838686	−	0.544615i	$-0.816676\pi$
$151$	−15.3577	+	4.50943i	−1.24979	+	0.366972i	−0.411106	+	0.911587i	$0.634857\pi$
$152$	−0.171330	+	0.459353i	−0.0138967	+	0.0372585i
$153$	0.264224	−	1.21462i	0.0213612	−	0.0981959i
$154$	0.242220	−	0.824926i	0.0195187	−	0.0664744i
$155$	−2.81823	+	0.123882i	−0.226366	+	0.00995048i
$156$	−2.21222	+	4.84408i	−0.177119	+	0.387837i
$157$	−7.06033	+	5.28529i	−0.563475	+	0.421812i	−0.842676	−	0.538420i	$-0.819021\pi$
$157$	−7.06033	+	5.28529i	−0.563475	+	0.421812i	0.279201	+	0.960233i	$0.409930\pi$
$158$	12.2899	−	2.67350i	0.977729	−	0.212692i
$159$	−8.57036	−	9.89072i	−0.679673	−	0.784385i
$160$	1.41734	+	1.72949i	0.112051	+	0.136728i
$161$	−6.53196	+	7.15433i	−0.514791	+	0.563840i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−0.0367262	+	0.513499i	−0.00287662	+	0.0402204i	−0.998688	−	0.0512145i	$-0.983691\pi$
$163$	−0.0367262	+	0.513499i	−0.00287662	+	0.0402204i	0.995811	+	0.0914349i	$0.0291453\pi$
$164$	−0.194178	+	0.302147i	−0.0151627	+	0.0235937i
$165$	−0.814456	+	0.492346i	−0.0634053	+	0.0383291i
$166$	−8.02250	−	3.66376i	−0.622667	−	0.284363i
$167$	−10.5262	−	7.87983i	−0.814544	−	0.609760i	0.108656	−	0.994079i	$-0.465345\pi$
$167$	−10.5262	−	7.87983i	−0.814544	−	0.609760i	−0.923200	+	0.384320i	$0.874436\pi$
$168$	1.77293	−	0.968092i	0.136784	−	0.0746899i
$169$	8.30373	+	12.9209i	0.638748	+	0.993912i
$170$	−2.62993	+	0.899433i	−0.201707	+	0.0689834i
$171$	−0.138123	−	0.470405i	−0.0105626	−	0.0359728i
$172$	−2.97593	+	0.212842i	−0.226912	+	0.0162291i
$173$	−5.22546	+	0.373732i	−0.397284	+	0.0284143i	−0.268552	−	0.963265i	$-0.586545\pi$
$173$	−5.22546	+	0.373732i	−0.397284	+	0.0284143i	−0.128732	+	0.991679i	$0.541091\pi$
$174$	−0.0695717	−	0.236939i	−0.00527422	−	0.0179623i
$175$	5.31995	−	8.58546i	0.402150	−	0.649000i
$176$	0.230105	+	0.358051i	0.0173448	+	0.0269891i
$177$	8.95575	−	4.89021i	0.673156	−	0.367571i
$178$	12.1036	+	9.06064i	0.907203	+	0.679124i
$179$	20.2096	+	9.22942i	1.51054	+	0.689839i	0.986785	−	0.162032i	$-0.0518049\pi$
$179$	20.2096	+	9.22942i	1.51054	+	0.689839i	0.523751	+	0.851871i	$0.324532\pi$
$180$	−2.17109	−	0.535146i	−0.161823	−	0.0398874i
$181$	9.41541	−	14.6507i	0.699842	−	1.08897i	−0.291360	−	0.956613i	$-0.594108\pi$
$181$	9.41541	−	14.6507i	0.699842	−	1.08897i	0.991202	−	0.132361i	$-0.0422559\pi$
$182$	0.767414	−	10.7298i	0.0568845	−	0.795349i
$183$	9.40222	−	9.40222i	0.695032	−	0.695032i
$184$	−0.559083	−	4.76313i	−0.0412162	−	0.351143i
$185$	−2.90584	+	2.38138i	−0.213641	+	0.175082i
$186$	−0.826151	−	0.953429i	−0.0605763	−	0.0699088i
$187$	−0.516960	+	0.112458i	−0.0378038	+	0.00822372i
$188$	−0.582690	+	0.436196i	−0.0424970	+	0.0318129i
$189$	−0.839146	+	1.83747i	−0.0610389	+	0.133657i
$190$	−0.740387	+	0.808470i	−0.0537133	+	0.0586526i
$191$	0.628879	−	2.14177i	0.0455041	−	0.154973i	−0.933607	−	0.358299i	$-0.883357\pi$
$191$	0.628879	−	2.14177i	0.0455041	−	0.154973i	0.979111	+	0.203326i	$0.0651751\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	−4.34530	+	11.6502i	−0.312781	+	0.838599i	0.681501	+	0.731817i	$0.261327\pi$
$193$	−4.34530	+	11.6502i	−0.312781	+	0.838599i	−0.994282	+	0.106782i	$0.965945\pi$
$194$	3.58727	−	1.05332i	0.257551	−	0.0756237i
$195$	−8.64817	+	8.18562i	−0.619308	+	0.586184i
$196$	1.91188	−	2.20643i	0.136563	−	0.157602i
$197$	−6.73334	+	12.3312i	−0.479730	+	0.878561i	0.519972	+	0.854183i	$0.325942\pi$
$197$	−6.73334	+	12.3312i	−0.479730	+	0.878561i	−0.999703	+	0.0243776i	$0.992240\pi$
$198$	−0.398780	−	0.148737i	−0.0283401	−	0.0105703i
$199$	11.0213	−	7.08299i	0.781282	−	0.502100i	−0.0881767	−	0.996105i	$-0.528104\pi$
$199$	11.0213	−	7.08299i	0.781282	−	0.502100i	0.869459	+	0.494005i	$0.164468\pi$
$200$	1.48743	+	4.77363i	0.105177	+	0.337547i
$201$	6.37909	−	0.917175i	0.449947	−	0.0646926i
$202$	−1.04496	−	2.80164i	−0.0735229	−	0.197122i
$203$	0.298937	+	0.399333i	0.0209812	+	0.0280277i
$204$	−1.04570	−	0.672029i	−0.0732135	−	0.0470515i
$205$	−0.655901	+	0.463446i	−0.0458101	+	0.0323685i
$206$		−	9.97226i		−	0.694800i
$207$	3.30201	+	3.47804i	0.229505	+	0.241740i
$208$	3.76557	+	3.76557i	0.261095	+	0.261095i
$209$	−0.157698	+	0.136646i	−0.0109082	+	0.00945200i
$210$	4.48690	−	0.519776i	0.309625	−	0.0358680i
$211$	2.44962	−	17.0375i	0.168639	−	1.17291i	−0.713063	−	0.701100i	$-0.752693\pi$
$211$	2.44962	−	17.0375i	0.168639	−	1.17291i	0.881702	−	0.471808i	$-0.156398\pi$
$212$	−12.2621	+	4.57354i	−0.842167	+	0.314112i
$213$	−5.80689	+	7.75709i	−0.397881	+	0.531507i
$214$	−5.50845	−	1.61743i	−0.376550	−	0.110565i
$215$	−6.34709	−	2.05465i	−0.432868	−	0.140126i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	2.23667	+	1.22131i	0.151835	+	0.0829082i
$218$	0.227602	+	3.18229i	0.0154151	+	0.215532i
$219$	5.02560	+	4.35471i	0.339599	+	0.294264i
$220$	0.176680	+	0.935162i	0.0119118	+	0.0630486i
$221$	−6.02131	+	2.74984i	−0.405037	+	0.184974i
$222$	−1.64177	−	0.357146i	−0.110189	−	0.0239701i
$223$	9.34418	+	17.1126i	0.625732	+	1.14594i	0.977715	+	0.209937i	$0.0673258\pi$
$223$	9.34418	+	17.1126i	0.625732	+	1.14594i	−0.351983	+	0.936007i	$0.614492\pi$
$224$	−0.287479	−	1.99946i	−0.0192080	−	0.133594i
$225$	−4.05148	−	2.93011i	−0.270099	−	0.195340i
$226$	−10.9593	−	1.57571i	−0.729000	−	0.104814i
$227$	1.06268	+	4.88507i	0.0705327	+	0.324234i	0.998871	−	0.0475026i	$-0.0151262\pi$
$227$	1.06268	+	4.88507i	0.0705327	+	0.324234i	−0.928338	+	0.371736i	$0.878763\pi$
$228$	−0.489015	−	0.0349751i	−0.0323858	−	0.00231628i
$229$	6.18889			0.408973			0.204487	−	0.978869i	$-0.434447\pi$
$229$	6.18889			0.408973			0.204487	+	0.978869i	$0.434447\pi$
$230$	2.83584	−	10.3420i	0.186990	−	0.681935i
$231$	0.859752			0.0565675
$232$	−0.246313	−	0.0176167i	−0.0161712	−	0.00115659i
$233$	3.56179	+	16.3733i	0.233341	+	1.07265i	0.933476	+	0.358640i	$0.116759\pi$
$233$	3.56179	+	16.3733i	0.233341	+	1.07265i	−0.700135	+	0.714010i	$0.746877\pi$
$234$	−5.27112	−	0.757872i	−0.344584	−	0.0495437i
$235$	−1.57364	+	0.415472i	−0.102653	+	0.0271024i
$236$	−1.45217	−	10.1000i	−0.0945280	−	0.657457i
$237$	6.02766	+	11.0388i	0.391538	+	0.717049i
$238$	2.45355	+	0.533737i	0.159040	+	0.0345970i
$239$	20.1973	−	9.22378i	1.30645	−	0.596637i	0.364131	−	0.931348i	$-0.381366\pi$
$239$	20.1973	−	9.22378i	1.30645	−	0.596637i	0.942321	+	0.334711i	$0.108639\pi$
$240$	−1.26012	+	1.84719i	−0.0813405	+	0.119235i
$241$	5.42682	+	4.70237i	0.349572	+	0.302906i	0.811893	−	0.583807i	$-0.198437\pi$
$241$	5.42682	+	4.70237i	0.349572	+	0.302906i	−0.462320	+	0.886713i	$0.652983\pi$
$242$	−0.771808	−	10.7913i	−0.0496137	−	0.693690i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	−5.52367	−	12.0951i	−0.353617	−	0.774313i
$245$	5.81348	−	2.97010i	0.371410	−	0.189753i
$246$	−0.344614	−	0.101188i	−0.0219718	−	0.00645149i
$247$	−1.56460	+	2.09007i	−0.0995534	+	0.132988i
$248$	−1.18203	+	0.440873i	−0.0750587	+	0.0279954i
$249$	1.25515	−	8.72974i	0.0795417	−	0.553225i
$250$	−0.920348	+	11.1424i	−0.0582079	+	0.704707i
$251$	−19.9335	+	17.2725i	−1.25819	+	1.09023i	−0.266201	+	0.963918i	$0.585768\pi$
$251$	−19.9335	+	17.2725i	−1.25819	+	1.09023i	−0.991991	+	0.126311i	$0.959686\pi$
$252$	1.42837	+	1.42837i	0.0899788	+	0.0899788i
$253$	0.762716	−	1.89333i	0.0479516	−	0.119032i
$254$			0.119156i			0.00747652i
$255$	−1.60394	−	2.27000i	−0.100442	−	0.142153i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	16.0808	+	21.4815i	1.00310	+	1.33998i	0.939704	+	0.341990i	$0.111101\pi$
$257$	16.0808	+	21.4815i	1.00310	+	1.33998i	0.0633920	+	0.997989i	$0.479808\pi$
$258$	−1.04264	−	2.79542i	−0.0649117	−	0.174035i
$259$	3.35943	−	0.483013i	0.208745	−	0.0300130i
$260$	4.64729	+	10.9635i	0.288213	+	0.679926i
$261$	0.207741	−	0.133507i	0.0128589	−	0.00826388i
$262$	−6.79360	−	2.53388i	−0.419710	−	0.156544i
$263$	−9.98394	+	18.2842i	−0.615636	+	1.12745i	0.364888	+	0.931052i	$0.381107\pi$
$263$	−9.98394	+	18.2842i	−0.615636	+	1.12745i	−0.980524	+	0.196401i	$0.937074\pi$
$264$	−0.278719	+	0.321659i	−0.0171540	+	0.0197967i
$265$	−29.2530	−	0.803800i	−1.79700	−	0.0493770i
$266$	0.950228	−	0.279012i	0.0582622	−	0.0171073i
$267$	−5.28364	+	14.1660i	−0.323354	+	0.866945i
$268$	1.36992	−	6.29741i	0.0836810	−	0.384676i
$269$	−4.04189	+	13.7654i	−0.246438	+	0.839291i	0.739639	+	0.673004i	$0.234996\pi$
$269$	−4.04189	+	13.7654i	−0.246438	+	0.839291i	−0.986077	+	0.166288i	$0.946822\pi$
$270$	−0.0981972	−	2.23391i	−0.00597609	−	0.135951i
$271$	4.92305	−	10.7800i	0.299054	−	0.654836i	−0.699135	−	0.714989i	$-0.746432\pi$
$271$	4.92305	−	10.7800i	0.299054	−	0.654836i	0.998189	+	0.0601529i	$0.0191588\pi$
$272$	−0.995091	+	0.744916i	−0.0603363	+	0.0451672i
$273$	10.5114	−	2.28662i	0.636180	−	0.138392i
$274$	−13.5620	−	15.6514i	−0.819311	−	0.945535i
$275$	−0.418071	+	2.08661i	−0.0252106	+	0.125827i
$276$	4.41268	−	1.87837i	0.265612	−	0.113064i
$277$	17.9030	−	17.9030i	1.07569	−	1.07569i	0.0787992	−	0.996891i	$-0.474891\pi$
$277$	17.9030	−	17.9030i	1.07569	−	1.07569i	0.996891	−	0.0787992i	$-0.0251086\pi$
$278$	0.213415	−	2.98393i	0.0127998	−	0.178964i
$279$	0.682055	−	1.06130i	0.0408335	−	0.0635382i
$280$	1.08101	−	4.38564i	0.0646024	−	0.262092i
$281$	15.0582	+	6.87683i	0.898295	+	0.410238i	0.810390	−	0.585891i	$-0.199255\pi$
$281$	15.0582	+	6.87683i	0.898295	+	0.410238i	0.0879053	+	0.996129i	$0.471983\pi$
$282$	−0.582690	−	0.436196i	−0.0346987	−	0.0259751i
$283$	−17.1865	+	9.38456i	−1.02163	+	0.557854i	−0.900534	−	0.434786i	$-0.856824\pi$
$283$	−17.1865	+	9.38456i	−1.02163	+	0.557854i	−0.121100	+	0.992640i	$0.538642\pi$
$284$	5.23871	+	8.15159i	0.310860	+	0.483708i
$285$	−0.984313	−	0.482623i	−0.0583057	−	0.0285881i
$286$	0.638558	+	2.17473i	0.0377587	+	0.128594i
$287$	0.723666	−	0.0517576i	0.0427167	−	0.00305516i
$288$	−0.997452	+	0.0713392i	−0.0587754	+	0.00420370i
$289$	4.35415	+	14.8289i	0.256126	+	0.872286i
$290$	−0.495790	−	0.243093i	−0.0291138	−	0.0142749i
$291$	2.02130	+	3.14520i	0.118491	+	0.184375i
$292$	5.83641	−	3.18692i	0.341550	−	0.186501i
$293$	1.64811	+	1.23376i	0.0962839	+	0.0720772i	0.646335	−	0.763054i	$-0.276301\pi$
$293$	1.64811	+	1.23376i	0.0962839	+	0.0720772i	−0.550051	+	0.835131i	$0.685392\pi$
$294$	2.65569	+	1.21281i	0.154883	+	0.0707327i
$295$	5.46058	−	22.1536i	0.317927	−	1.28983i
$296$	−0.908368	+	1.41345i	−0.0527978	+	0.0821550i
$297$	0.0303631	−	0.424531i	0.00176184	−	0.0246338i
$298$	−3.24319	+	3.24319i	−0.187873	+	0.187873i
$299$	4.28951	−	25.1765i	0.248069	−	1.45600i
$300$	−4.16121	+	2.77206i	−0.240247	+	0.160045i
$301$	3.94670	+	4.55474i	0.227484	+	0.262531i
$302$	−15.6403	+	3.40233i	−0.899997	+	0.195782i
$303$	2.39375	−	1.79194i	0.137517	−	0.102944i
$304$	−0.203663	+	0.445960i	−0.0116809	+	0.0255776i
$305$	−1.30570	−	29.7038i	−0.0747644	−	1.70083i
$306$	0.350200	−	1.19267i	0.0200196	−	0.0681805i
$307$	−4.37707	+	20.1211i	−0.249813	+	1.14837i	0.665744	+	0.746180i	$0.268114\pi$
$307$	−4.37707	+	20.1211i	−0.249813	+	1.14837i	−0.915556	+	0.402190i	$0.868249\pi$
$308$	0.300452	−	0.805544i	0.0171199	−	0.0459001i
$309$	9.56831	−	2.80951i	0.544322	−	0.159827i
$310$	−2.81989	−	0.0774833i	−0.160159	−	0.00440076i
$311$	−9.64472	+	11.1306i	−0.546902	+	0.631158i	−0.960158	−	0.279456i	$-0.909846\pi$
$311$	−9.64472	+	11.1306i	−0.546902	+	0.631158i	0.413257	+	0.910615i	$0.364391\pi$
$312$	−2.55215	+	4.67392i	−0.144487	+	0.264609i
$313$	−6.65571	−	2.48245i	−0.376203	−	0.140316i	0.154248	−	0.988032i	$-0.450705\pi$
$313$	−6.65571	−	2.48245i	−0.376203	−	0.140316i	−0.530451	+	0.847716i	$0.677977\pi$
$314$	−7.41939	+	4.76815i	−0.418700	+	0.269082i
$315$	1.76283	+	4.15871i	0.0993240	+	0.234317i
$316$	12.4493	−	1.78994i	0.700327	−	0.100692i
$317$	−8.11970	−	21.7698i	−0.456048	−	1.22271i	−0.938037	−	0.346535i	$-0.887358\pi$
$317$	−8.11970	−	21.7698i	−0.456048	−	1.22271i	0.481989	−	0.876177i	$-0.339914\pi$
$318$	−7.84292	−	10.4769i	−0.439809	−	0.587517i
$319$	−0.0884179	−	0.0568227i	−0.00495045	−	0.00318146i
$320$	1.29035	+	1.82620i	0.0721329	+	0.102087i
$321$		−	5.74100i		−	0.320431i
$322$	−7.02570	+	6.67012i	−0.391527	+	0.371711i
$323$	−0.430918	−	0.430918i	−0.0239769	−	0.0239769i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	0.438220	+	26.6230i	0.0243081	+	1.47678i
$326$	−0.0732652	+	0.509571i	−0.00405778	+	0.0282225i
$327$	−2.98926	+	1.11494i	−0.165307	+	0.0616562i
$328$	−0.215238	+	0.287524i	−0.0118845	+	0.0158759i
$329$	1.41075	+	0.414234i	0.0777773	+	0.0228375i
$330$	−0.847505	+	0.432989i	−0.0466536	+	0.0238352i
$331$	6.36854	+	13.9451i	0.350046	+	0.766495i	0.999979	+	0.00650270i	$0.00206989\pi$
$331$	6.36854	+	13.9451i	0.350046	+	0.766495i	−0.649932	+	0.759992i	$0.725203\pi$
$332$	−7.74069	−	4.22674i	−0.424826	−	0.231972i
$333$	−0.119862	−	1.67589i	−0.00656839	−	0.0918381i
$334$	−9.93726	−	8.61069i	−0.543743	−	0.471156i
$335$	8.12110	−	11.9045i	0.443703	−	0.650414i
$336$	1.83747	−	0.839146i	0.100242	−	0.0457792i
$337$	19.8139	+	4.31024i	1.07933	+	0.234794i	0.716871	−	0.697206i	$-0.245574\pi$
$337$	19.8139	+	4.31024i	1.07933	+	0.234794i	0.362459	+	0.932000i	$0.381937\pi$
$338$	7.36081	+	13.4803i	0.400375	+	0.733232i
$339$	−1.57571	−	10.9593i	−0.0855806	−	0.595226i
$340$	−2.68740	+	0.709524i	−0.145745	+	0.0384793i
$341$	−0.531477	−	0.0764149i	−0.0287811	−	0.00413810i
$342$	−0.104213	−	0.479060i	−0.00563521	−	0.0259046i
$343$	−19.9866	−	1.42947i	−1.07917	−	0.0771840i
$344$	−2.98353			−0.160861
$345$	10.7221	−	0.192721i	0.577257	−	0.0103757i
$346$	−5.23880			−0.281640
$347$	−9.05710	−	0.647777i	−0.486211	−	0.0347745i	−0.173917	−	0.984760i	$-0.555643\pi$
$347$	−9.05710	−	0.647777i	−0.486211	−	0.0347745i	−0.312293	+	0.949986i	$0.601097\pi$
$348$	−0.0524914	−	0.241299i	−0.00281383	−	0.0129350i
$349$	−22.4242	−	3.22412i	−1.20034	−	0.172583i	−0.487001	−	0.873401i	$-0.661909\pi$
$349$	−22.4242	−	3.22412i	−1.20034	−	0.172583i	−0.713340	+	0.700818i	$0.752818\pi$
$350$	5.91887	−	8.18407i	0.316377	−	0.437457i
$351$	−0.757872	−	5.27112i	−0.0404522	−	0.281351i
$352$	0.203976	+	0.373554i	0.0108719	+	0.0199105i
$353$	9.33679	+	2.03109i	0.496947	+	0.108104i	0.454052	−	0.890975i	$-0.349978\pi$
$353$	9.33679	+	2.03109i	0.496947	+	0.108104i	0.0428955	+	0.999080i	$0.486342\pi$
$354$	9.28180	−	4.23886i	0.493322	−	0.225293i
$355$	4.02240	+	21.2904i	0.213487	+	1.12998i
$356$	11.4264	+	9.90102i	0.605597	+	0.524753i
$357$	0.179128	+	2.50453i	0.00948045	+	0.132554i
$358$	19.4997	+	10.6476i	1.03059	+	0.562745i
$359$	−3.18130	−	6.96608i	−0.167903	−	0.367655i	0.806912	−	0.590671i	$-0.201137\pi$
$359$	−3.18130	−	6.96608i	−0.167903	−	0.367655i	−0.974815	+	0.223016i	$0.928410\pi$
$360$	−2.12738	−	0.688666i	−0.112123	−	0.0362959i
$361$	17.9997	+	5.28520i	0.947355	+	0.278169i
$362$	10.4366	−	13.9416i	0.548535	−	0.732756i
$363$	10.1367	−	3.78080i	0.532040	−	0.198441i
$364$	1.53092	−	10.6478i	0.0802418	−	0.558094i
$365$	14.7707	−	1.71108i	0.773133	−	0.0895622i
$366$	10.0490	−	8.70752i	0.525270	−	0.455149i
$367$	−5.48234	−	5.48234i	−0.286176	−	0.286176i	0.549390	−	0.835566i	$-0.314860\pi$
$367$	−5.48234	−	5.48234i	−0.286176	−	0.286176i	−0.835566	+	0.549390i	$0.814860\pi$
$368$	−0.217861	−	4.79088i	−0.0113568	−	0.249742i
$369$		−	0.359162i		−	0.0186972i
$370$	−3.06832	+	2.16801i	−0.159514	+	0.112709i
$371$	22.2399	+	14.2927i	1.15464	+	0.742040i
$372$	−0.756029	−	1.00994i	−0.0391983	−	0.0523628i
$373$	6.69643	+	17.9538i	0.346728	+	0.929614i	0.986893	+	0.161377i	$0.0515933\pi$
$373$	6.69643	+	17.9538i	0.346728	+	0.929614i	−0.640165	+	0.768238i	$0.721134\pi$
$374$	−0.523665	+	0.0752917i	−0.0270781	+	0.00389324i
$375$	−10.9503	+	2.25611i	−0.565473	+	0.116505i
$376$	−0.612323	+	0.393516i	−0.0315781	+	0.0202940i
$377$	−1.23213	−	0.459562i	−0.0634581	−	0.0236686i
$378$	−0.968092	+	1.77293i	−0.0497933	+	0.0911896i
$379$	8.74731	−	10.0949i	0.449319	−	0.518542i	−0.485225	−	0.874389i	$-0.661262\pi$
$379$	8.74731	−	10.0949i	0.449319	−	0.518542i	0.934544	+	0.355848i	$0.115808\pi$
$380$	−0.796176	+	0.753592i	−0.0408430	+	0.0386585i
$381$	−0.114329	+	0.0335701i	−0.00585727	+	0.00171985i
$382$	0.780069	−	2.09145i	0.0399118	−	0.107008i
$383$	−0.187283	+	0.860928i	−0.00956974	+	0.0439914i	−0.981684	−	0.190516i	$-0.938984\pi$
$383$	−0.187283	+	0.860928i	−0.00956974	+	0.0439914i	0.972114	+	0.234507i	$0.0753476\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	1.29838	−	1.41777i	0.0661715	−	0.0722564i
$386$	−5.16534	+	11.3105i	−0.262909	+	0.575690i
$387$	2.38844	−	1.78796i	0.121411	−	0.0908872i
$388$	3.65327	−	0.794720i	0.185467	−	0.0403458i
$389$	−6.45123	−	7.44512i	−0.327090	−	0.377483i	0.568257	−	0.822851i	$-0.307618\pi$
$389$	−6.45123	−	7.44512i	−0.327090	−	0.377483i	−0.895347	+	0.445369i	$0.853073\pi$
$390$	−9.21009	+	7.54781i	−0.466371	+	0.382198i
$391$	5.67434	+	1.82739i	0.286964	+	0.0924150i
$392$	2.06441	−	2.06441i	0.104269	−	0.104269i
$393$	0.517263	−	7.23228i	0.0260925	−	0.364820i
$394$	−7.59588	+	11.8194i	−0.382675	+	0.595454i
$395$	27.3064	+	6.73069i	1.37393	+	0.338658i
$396$	−0.387154	−	0.176807i	−0.0194552	−	0.00888489i
$397$	17.5490	+	13.1370i	0.880760	+	0.659329i	0.940835	−	0.338865i	$-0.110043\pi$
$397$	17.5490	+	13.1370i	0.880760	+	0.659329i	−0.0600749	+	0.998194i	$0.519134\pi$
$398$	11.4986	−	6.27869i	0.576371	−	0.314722i
$399$	0.535420	+	0.833130i	0.0268045	+	0.0417087i
$400$	1.14309	+	4.86758i	0.0571546	+	0.243379i
$401$	3.95538	+	13.4708i	0.197522	+	0.672700i	0.997369	+	0.0724948i	$0.0230961\pi$
$401$	3.95538	+	13.4708i	0.197522	+	0.672700i	−0.799846	+	0.600205i	$0.795086\pi$
$402$	6.42827	−	0.459759i	0.320613	−	0.0229307i
$403$	−6.70113	+	0.479274i	−0.333807	+	0.0238744i
$404$	−0.842427	−	2.86904i	−0.0419123	−	0.142740i
$405$	2.11576	−	0.723585i	0.105133	−	0.0359552i
$406$	0.269687	+	0.419641i	0.0133843	+	0.0208264i
$407$	−0.627634	+	0.342714i	−0.0311107	+	0.0169877i
$408$	−0.995091	−	0.744916i	−0.0492644	−	0.0368788i
$409$	15.1472	+	6.91749i	0.748980	+	0.342048i	0.753067	−	0.657944i	$-0.228574\pi$
$409$	15.1472	+	6.91749i	0.748980	+	0.342048i	−0.00408695	+	0.999992i	$0.501301\pi$
$410$	−0.687291	+	0.415474i	−0.0339429	+	0.0205188i
$411$	11.1965	−	17.4222i	0.552285	−	0.859372i
$412$	0.711413	−	9.94685i	0.0350488	−	0.490046i
$413$	−14.5749	+	14.5749i	−0.717186	+	0.717186i
$414$	3.04547	+	3.70474i	0.149677	+	0.182078i
$415$	−12.5003	−	15.2532i	−0.613614	−	0.748753i
$416$	3.48734	+	4.02461i	0.170981	+	0.197323i
$417$	2.92319	−	0.635901i	0.143149	−	0.0311402i
$418$	−0.167044	+	0.125048i	−0.00817041	+	0.00611629i
$419$	7.41032	−	16.2263i	0.362018	−	0.792709i	−0.637730	−	0.770260i	$-0.720126\pi$
$419$	7.41032	−	16.2263i	0.362018	−	0.792709i	0.999748	−	0.0224487i	$-0.00714625\pi$
$420$	4.51254	−	0.198360i	0.220190	−	0.00967899i
$421$	3.09041	−	10.5250i	0.150617	−	0.512956i	−0.849270	−	0.527959i	$-0.822958\pi$
$421$	3.09041	−	10.5250i	0.150617	−	0.512956i	0.999887	+	0.0150030i	$0.00477579\pi$
$422$	3.65882	−	16.8193i	0.178108	−	0.818751i
$423$	0.254364	−	0.681977i	0.0123676	−	0.0331589i
$424$	−12.5572	+	3.68712i	−0.609830	+	0.179062i
$425$	−6.16558	−	0.783137i	−0.299075	−	0.0379877i
$426$	−6.34548	+	7.32307i	−0.307439	+	0.354804i
$427$	−12.8725	+	23.5742i	−0.622943	+	1.14083i
$428$	−5.37903	−	2.00627i	−0.260005	−	0.0969769i
$429$	−1.90673	+	1.22538i	−0.0920580	+	0.0591621i
$430$	−6.18434	−	2.50222i	−0.298236	−	0.120668i
$431$	−8.33097	+	1.19781i	−0.401289	+	0.0576966i	−0.340005	−	0.940424i	$-0.610429\pi$
$431$	−8.33097	+	1.19781i	−0.401289	+	0.0576966i	−0.0612840	+	0.998120i	$0.519520\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	−8.84854	−	11.8203i	−0.425234	−	0.568046i	0.535846	−	0.844316i	$-0.319993\pi$
$433$	−8.84854	−	11.8203i	−0.425234	−	0.568046i	−0.961080	+	0.276270i	$0.910902\pi$
$434$	2.14384	+	1.37776i	0.102908	+	0.0661348i
$435$	0.0935661	−	0.544195i	0.00448615	−	0.0260921i
$436$			3.19042i			0.152793i
$437$	2.30969	−	0.439991i	0.110488	−	0.0210476i
$438$	4.70214	+	4.70214i	0.224677	+	0.224677i
$439$	−30.5157	+	26.4420i	−1.45644	+	1.26201i	−0.553073	+	0.833133i	$0.686545\pi$
$439$	−30.5157	+	26.4420i	−1.45644	+	1.26201i	−0.903363	+	0.428876i	$0.858910\pi$
$440$	0.109516	+	0.945383i	0.00522098	+	0.0450694i
$441$	−0.415491	+	2.88980i	−0.0197853	+	0.137610i
$442$	−6.20214	+	2.31328i	−0.295006	+	0.110031i
$443$	−9.90121	+	13.2265i	−0.470421	+	0.628409i	−0.971513	−	0.236985i	$-0.923841\pi$
$443$	−9.90121	+	13.2265i	−0.470421	+	0.628409i	0.501092	+	0.865394i	$0.332932\pi$
$444$	−1.61211	−	0.473358i	−0.0765074	−	0.0224646i
$445$	15.3812	+	30.1062i	0.729138	+	1.42717i
$446$	8.09957	+	17.7356i	0.383526	+	0.839804i
$447$	−4.02553	−	2.19811i	−0.190401	−	0.103967i
$448$	−0.144107	−	2.01487i	−0.00680839	−	0.0951938i
$449$	14.8752	+	12.8895i	0.702005	+	0.608291i	0.930949	−	0.365149i	$-0.118982\pi$
$449$	14.8752	+	12.8895i	0.702005	+	0.608291i	−0.228944	+	0.973440i	$0.573527\pi$
$450$	−3.83212	−	3.21167i	−0.180648	−	0.151400i
$451$	−0.139051	+	0.0635024i	−0.00654765	+	0.00299021i
$452$	−10.8189	−	2.35352i	−0.508880	−	0.110700i
$453$	−7.67089	−	14.0482i	−0.360410	−	0.660041i
$454$	0.711478	+	4.94844i	0.0333913	+	0.232242i
$455$	12.1034	−	20.7870i	0.567414	−	0.974512i
$456$	−0.485274	−	0.0697719i	−0.0227251	−	0.00326737i
$457$	2.01070	+	9.24302i	0.0940564	+	0.432370i	0.999961	+	0.00888741i	$0.00282899\pi$
$457$	2.01070	+	9.24302i	0.0940564	+	0.432370i	−0.905904	+	0.423483i	$0.860807\pi$
$458$	6.17312	+	0.441510i	0.288451	+	0.0206304i
$459$	1.24302			0.0580194
$460$	3.56641	−	10.1134i	0.166285	−	0.471539i
$461$	10.4710			0.487682			0.243841	−	0.969815i	$-0.421592\pi$
$461$	10.4710			0.487682			0.243841	+	0.969815i	$0.421592\pi$
$462$	0.857561	+	0.0613340i	0.0398974	+	0.00285352i
$463$	8.26699	+	38.0027i	0.384200	+	1.76614i	0.610437	+	0.792065i	$0.290994\pi$
$463$	8.26699	+	38.0027i	0.384200	+	1.76614i	−0.226238	+	0.974072i	$0.572643\pi$
$464$	−0.244429	−	0.0351436i	−0.0113473	−	0.00163150i
$465$	−0.720109	−	2.72749i	−0.0333942	−	0.126484i
$466$	2.38466	+	16.5857i	0.110467	+	0.768316i
$467$	15.0346	+	27.5338i	0.695719	+	1.27411i	0.951580	+	0.307400i	$0.0994590\pi$
$467$	15.0346	+	27.5338i	0.695719	+	1.27411i	−0.255862	+	0.966713i	$0.582359\pi$
$468$	−5.20362	−	1.13198i	−0.240537	−	0.0523257i
$469$	−11.8420	+	5.40804i	−0.546811	+	0.249720i
$470$	−1.59927	+	0.302151i	−0.0737690	+	0.0139372i
$471$	−6.66529	−	5.77551i	−0.307120	−	0.266121i
$472$	−0.727938	−	10.1779i	−0.0335061	−	0.468476i
$473$	−1.11451	−	0.608568i	−0.0512451	−	0.0279820i
$474$	5.22480	+	11.4407i	0.239983	+	0.525489i
$475$	−2.28236	+	0.894334i	−0.104722	+	0.0410348i
$476$	2.40922	+	0.707411i	0.110426	+	0.0324241i
$477$	7.84292	−	10.4769i	0.359103	−	0.479705i
$478$	20.8038	−	7.75942i	0.951545	−	0.354908i
$479$	3.20483	−	22.2901i	0.146432	−	1.01846i	−0.775566	−	0.631266i	$-0.782535\pi$
$479$	3.20483	−	22.2901i	0.146432	−	1.01846i	0.921998	−	0.387194i	$-0.126555\pi$
$480$	−1.38869	+	1.75258i	−0.0633846	+	0.0799941i
$481$	−6.76203	+	5.85933i	−0.308322	+	0.267162i
$482$	5.07753	+	5.07753i	0.231275	+	0.231275i
$483$	−8.37930	−	4.86192i	−0.381271	−	0.221225i
$484$		−	10.8189i		−	0.491766i
$485$	8.23912	+	1.41659i	0.374119	+	0.0643242i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−14.9638	−	19.9893i	−0.678076	−	0.905803i	0.321073	−	0.947054i	$-0.395956\pi$
$487$	−14.9638	−	19.9893i	−0.678076	−	0.905803i	−0.999149	+	0.0412514i	$0.986866\pi$
$488$	−4.64674	−	12.4584i	−0.210348	−	0.563965i
$489$	−0.509571	+	0.0732652i	−0.0230436	+	0.00331317i
$490$	6.01055	−	2.54780i	0.271529	−	0.115098i
$491$	2.89265	−	1.85900i	0.130544	−	0.0838953i	−0.473739	−	0.880665i	$-0.657096\pi$
$491$	2.89265	−	1.85900i	0.130544	−	0.0838953i	0.604283	+	0.796770i	$0.293460\pi$
$492$	−0.336517	−	0.125514i	−0.0151714	−	0.00565862i
$493$	0.147108	−	0.269408i	0.00662541	−	0.0121335i
$494$	−1.70972	+	1.97312i	−0.0769240	+	0.0887750i
$495$	−0.654219	−	0.691188i	−0.0294050	−	0.0310666i
$496$	−1.21046	+	0.355425i	−0.0543515	+	0.0159590i
$497$	6.84028	−	18.3395i	0.306828	−	0.822638i
$498$	1.87472	−	8.61795i	0.0840082	−	0.386180i
$499$	−7.65659	+	26.0759i	−0.342756	+	1.16732i	0.590178	+	0.807273i	$0.299057\pi$
$499$	−7.65659	+	26.0759i	−0.342756	+	1.16732i	−0.932934	+	0.360047i	$0.882761\pi$
$500$	−1.71289	+	11.0483i	−0.0766029	+	0.494097i
$501$	5.46224	−	11.9606i	0.244035	−	0.534362i
$502$	−21.1149	+	15.8064i	−0.942405	+	0.705475i
$503$	−1.65481	+	0.359981i	−0.0737842	+	0.0160508i	−0.249306	−	0.968425i	$-0.580202\pi$
$503$	−1.65481	+	0.359981i	−0.0737842	+	0.0160508i	0.175522	+	0.984476i	$0.443839\pi$
$504$	1.32283	+	1.52663i	0.0589236	+	0.0680015i
$505$	0.659992	−	6.65356i	0.0293693	−	0.296080i
$506$	0.895841	−	1.83409i	0.0398250	−	0.0815353i
$507$	−10.8605	+	10.8605i	−0.482331	+	0.482331i
$508$	−0.00850050	+	0.118852i	−0.000377149	+	0.00527323i
$509$	−13.3412	+	20.7593i	−0.591339	+	0.920141i	0.408633	+	0.912699i	$0.366005\pi$
$509$	−13.3412	+	20.7593i	−0.591339	+	0.920141i	−0.999972	+	0.00744261i	$0.997631\pi$
$510$	−1.43791	−	2.37864i	−0.0636718	−	0.105328i
$511$	−12.2189	−	5.58018i	−0.540532	−	0.246853i
$512$	0.800541	+	0.599278i	0.0353793	+	0.0264846i
$513$	0.430295	−	0.234959i	0.0189980	−	0.0103737i
$514$	14.5074	+	22.5740i	0.639894	+	0.995694i
$515$	9.81683	−	20.0215i	0.432581	−	0.882252i
$516$	−0.840557	−	2.86267i	−0.0370035	−	0.126022i
$517$	−0.309003	+	0.0221004i	−0.0135900	+	0.000971973i
$518$	3.38533	−	0.242123i	0.148743	−	0.0106383i
$519$	−1.47594	−	5.02659i	−0.0647866	−	0.220643i
$520$	3.85332	+	11.2671i	0.168979	+	0.494094i
$521$	−23.4331	−	36.4627i	−1.02662	−	1.59746i	−0.777394	−	0.629014i	$-0.783459\pi$
$521$	−23.4331	−	36.4627i	−1.02662	−	1.59746i	−0.249231	−	0.968444i	$-0.580178\pi$
$522$	0.216736	−	0.118347i	0.00948628	−	0.00517990i
$523$	−16.8304	−	12.5991i	−0.735942	−	0.550919i	0.164247	−	0.986419i	$-0.447481\pi$
$523$	−16.8304	−	12.5991i	−0.735942	−	0.550919i	−0.900189	+	0.435500i	$0.856571\pi$
$524$	−6.59552	−	3.01207i	−0.288127	−	0.131583i
$525$	9.52009	+	3.37340i	0.415491	+	0.147227i
$526$	−11.2629	+	17.5254i	−0.491085	+	0.764143i
$527$	0.111871	−	1.56416i	0.00487318	−	0.0681360i
$528$	−0.300956	+	0.300956i	−0.0130974	+	0.0130974i
$529$	−18.1404	+	14.1395i	−0.788713	+	0.614762i
$530$	−29.1212	−	2.88864i	−1.26494	−	0.125475i
$531$	6.68214	+	7.71160i	0.289980	+	0.334655i
$532$	0.967712	−	0.210513i	0.0419556	−	0.00912689i
$533$	−1.53116	+	1.14621i	−0.0663218	+	0.0496479i
$534$	−6.28077	+	13.7530i	−0.271796	+	0.595149i
$535$	−9.46719	−	8.66992i	−0.409302	−	0.374834i
$536$	1.81568	−	6.18364i	0.0784254	−	0.267092i
$537$	−4.72264	+	21.7096i	−0.203797	+	0.936839i
$538$	−5.01360	+	13.4420i	−0.216152	+	0.579525i
$539$	1.19226	−	0.350079i	0.0513543	−	0.0150790i
$540$	0.0614183	−	2.23522i	0.00264302	−	0.0961887i
$541$	14.7021	−	16.9671i	0.632091	−	0.729471i	−0.345865	−	0.938284i	$-0.612415\pi$
$541$	14.7021	−	16.9671i	0.632091	−	0.729471i	0.977956	+	0.208813i	$0.0669600\pi$
$542$	5.67954	−	10.4013i	0.243957	−	0.446774i
$543$	16.3172	+	6.08601i	0.700239	+	0.261176i
$544$	−1.04570	+	0.672029i	−0.0448339	+	0.0288130i
$545$	−2.67573	+	6.61319i	−0.114616	+	0.283278i
$546$	10.6478	−	1.53092i	0.455682	−	0.0655172i
$547$	9.01780	+	24.1777i	0.385573	+	1.03376i	0.974265	+	0.225405i	$0.0723704\pi$
$547$	9.01780	+	24.1777i	0.385573	+	1.03376i	−0.588692	+	0.808357i	$0.700357\pi$
$548$	−12.4109	−	16.5790i	−0.530167	−	0.708221i
$549$	11.1859	+	7.18877i	0.477404	+	0.306809i
$550$	−0.565863	+	2.05147i	−0.0241285	+	0.0874748i
$551$		−	0.121067i		−	0.00515763i
$552$	4.53544	−	1.55878i	0.193041	−	0.0663462i
$553$	−17.9650	−	17.9650i	−0.763951	−	0.763951i
$554$	19.1346	−	16.5802i	0.812952	−	0.704427i
$555$	−2.94464	−	2.33323i	−0.124993	−	0.0990402i
$556$	0.425743	−	2.96110i	0.0180555	−	0.125579i
$557$	−26.3469	+	9.82690i	−1.11636	+	0.416379i	−0.838860	−	0.544348i	$-0.816777\pi$
$557$	−26.3469	+	9.82690i	−1.11636	+	0.416379i	−0.277496	+	0.960727i	$0.589505\pi$
$558$	0.756029	−	1.00994i	0.0320053	−	0.0427540i
$559$	−15.2447	−	4.47624i	−0.644780	−	0.189325i
$560$	1.39112	−	4.29735i	0.0587855	−	0.181596i
$561$	−0.219775	−	0.481241i	−0.00927892	−	0.0203180i
$562$	14.5292	+	7.93355i	0.612878	+	0.334657i
$563$	−2.98414	−	41.7238i	−0.125767	−	1.75845i	−0.533921	−	0.845534i	$-0.679282\pi$
$563$	−2.98414	−	41.7238i	−0.125767	−	1.75845i	0.408155	−	0.912913i	$-0.366172\pi$
$564$	−0.550087	−	0.476653i	−0.0231628	−	0.0200707i
$565$	−20.4520	−	13.9520i	−0.860421	−	0.586966i
$566$	−17.8122	+	8.13458i	−0.748704	+	0.341922i
$567$	−1.97386	−	0.429386i	−0.0828941	−	0.0180325i
$568$	4.64383	+	8.50454i	0.194851	+	0.356843i
$569$	3.59387	+	24.9959i	0.150663	+	1.04788i	0.915112	+	0.403199i	$0.132102\pi$
$569$	3.59387	+	24.9959i	0.150663	+	1.04788i	−0.764449	+	0.644684i	$0.776989\pi$
$570$	−0.947375	−	0.551614i	−0.0396812	−	0.0231046i
$571$	29.0804	+	4.18113i	1.21698	+	0.174975i	0.720736	−	0.693210i	$-0.243804\pi$
$571$	29.0804	+	4.18113i	1.21698	+	0.174975i	0.496241	+	0.868185i	$0.334713\pi$
$572$	0.481788	+	2.21474i	0.0201446	+	0.0926030i
$573$	2.22650	+	0.159242i	0.0930133	+	0.00665244i
$574$	0.725515			0.0302824
$575$	15.8744	−	17.9723i	0.662009	−	0.749496i
$576$	−1.00000			−0.0416667
$577$	20.5040	+	1.46647i	0.853591	+	0.0610500i	0.491274	−	0.871005i	$-0.336531\pi$
$577$	20.5040	+	1.46647i	0.853591	+	0.0610500i	0.362317	+	0.932055i	$0.381986\pi$
$578$	3.28517	+	15.1017i	0.136645	+	0.628148i
$579$	−12.3076	−	1.76957i	−0.511487	−	0.0735407i
$580$	−0.477185	−	0.277843i	−0.0198140	−	0.0115368i
$581$	2.53542	+	17.6342i	0.105187	+	0.731591i
$582$	1.79177	+	3.28139i	0.0742714	+	0.136018i
$583$	−5.44286	−	1.18402i	−0.225420	−	0.0490372i
$584$	6.04889	−	2.76244i	0.250305	−	0.114310i
$585$	−9.83685	−	6.71055i	−0.406704	−	0.277447i
$586$	1.55590	+	1.34819i	0.0642736	+	0.0556934i
$587$	−1.91063	−	26.7141i	−0.0788602	−	1.10261i	−0.870678	−	0.491853i	$-0.836320\pi$
$587$	−1.91063	−	26.7141i	−0.0788602	−	1.10261i	0.791818	−	0.610757i	$-0.209135\pi$
$588$	2.56240	+	1.39918i	0.105672	+	0.0577011i
$589$	−0.256935	−	0.562609i	−0.0105868	−	0.0231819i
$590$	7.02708	−	21.7076i	0.289300	−	0.893686i
$591$	−13.4807	−	3.95828i	−0.554520	−	0.162822i
$592$	−1.00689	+	1.34505i	−0.0413828	+	0.0552810i
$593$	27.5274	−	10.2672i	1.13042	−	0.421623i	0.286490	−	0.958083i	$-0.407512\pi$
$593$	27.5274	−	10.2672i	1.13042	−	0.421623i	0.843926	+	0.536460i	$0.180239\pi$
$594$	0.0605714	−	0.421283i	0.00248528	−	0.0172855i
$595$	4.40061	+	3.48690i	0.180408	+	0.142949i
$596$	−3.46629	+	3.00356i	−0.141985	+	0.123031i
$597$	9.26387	+	9.26387i	0.379145	+	0.379145i
$598$	6.07465	−	24.8064i	0.248411	−	1.01441i
$599$		−	17.5421i		−	0.716750i	−0.933578	−	0.358375i	$-0.883331\pi$
$599$		−	17.5421i		−	0.716750i	0.933578	−	0.358375i	$-0.116669\pi$
$600$	−4.34836	+	2.46814i	−0.177521	+	0.100762i
$601$	19.7350	+	12.6829i	0.805009	+	0.517348i	0.877247	−	0.480040i	$-0.159378\pi$
$601$	19.7350	+	12.6829i	0.805009	+	0.517348i	−0.0722380	+	0.997387i	$0.523014\pi$
$602$	3.61172	+	4.82469i	0.147203	+	0.196640i
$603$	2.25219	+	6.03835i	0.0917162	+	0.245901i
$604$	−15.8431	+	2.27790i	−0.644648	+	0.0926864i
$605$	9.07352	−	22.4256i	0.368891	−	0.911732i
$606$	2.51549	−	1.61661i	0.102185	−	0.0656701i
$607$	−23.4469	−	8.74523i	−0.951679	−	0.354958i	−0.174797	−	0.984604i	$-0.555927\pi$
$607$	−23.4469	−	8.74523i	−0.951679	−	0.354958i	−0.776882	+	0.629646i	$0.783200\pi$
$608$	−0.234959	+	0.430295i	−0.00952884	+	0.0174508i
$609$	−0.326663	+	0.376989i	−0.0132371	+	0.0152764i
$610$	0.816664	−	29.7212i	0.0330658	−	1.20338i
$611$	−3.71913	+	1.09203i	−0.150460	+	0.0441790i
$612$	0.434392	−	1.16465i	0.0175593	−	0.0470782i
$613$	2.68987	−	12.3651i	0.108643	−	0.499422i	−0.890380	−	0.455218i	$-0.849561\pi$
$613$	2.68987	−	12.3651i	0.108643	−	0.499422i	0.999023	−	0.0442041i	$-0.0140752\pi$
$614$	−5.80134	+	19.7575i	−0.234123	+	0.797350i
$615$	−0.592276	−	0.542399i	−0.0238829	−	0.0218716i
$616$	0.357154	−	0.782058i	0.0143901	−	0.0315100i
$617$	25.7437	−	19.2715i	1.03640	−	0.775842i	0.0614183	−	0.998112i	$-0.480438\pi$
$617$	25.7437	−	19.2715i	1.03640	−	0.775842i	0.974985	+	0.222270i	$0.0713467\pi$
$618$	9.74436	−	2.11976i	0.391976	−	0.0852691i
$619$	11.3318	+	13.0775i	0.455462	+	0.525631i	0.936311	−	0.351173i	$-0.114217\pi$
$619$	11.3318	+	13.0775i	0.455462	+	0.525631i	−0.480849	+	0.876803i	$0.659671\pi$
$620$	−2.80717	−	0.278454i	−0.112739	−	0.0111830i
$621$	−2.69666	+	3.96586i	−0.108213	+	0.159144i
$622$	−10.4142	+	10.4142i	−0.417571	+	0.417571i
$623$	2.17879	−	30.4634i	0.0872912	−	1.22049i
$624$	−2.87909	+	4.47995i	−0.115256	+	0.179341i
$625$	−12.8165	+	21.4648i	−0.512661	+	0.858591i
$626$	−6.46166	−	2.95094i	−0.258260	−	0.117943i
$627$	−0.167044	−	0.125048i	−0.00667111	−	0.00499393i
$628$	−7.74064	+	4.22671i	−0.308885	+	0.168664i
$629$	−1.12912	−	1.75695i	−0.0450211	−	0.0700542i
$630$	1.46166	+	4.27387i	0.0582338	+	0.170275i
$631$	−8.05579	−	27.4355i	−0.320696	−	1.09219i	−0.949276	−	0.314445i	$-0.898182\pi$
$631$	−8.05579	−	27.4355i	−0.320696	−	1.09219i	0.628580	−	0.777745i	$-0.283636\pi$
$632$	12.5453	−	0.897254i	0.499023	−	0.0356909i
$633$	17.1688	−	1.22794i	0.682399	−	0.0488061i
$634$	−6.54598	−	22.2935i	−0.259974	−	0.885390i
$635$	−0.117299	+	0.239232i	−0.00465486	+	0.00949362i
$636$	−7.07553	−	11.0097i	−0.280563	−	0.436564i
$637$	13.6456	−	7.45107i	0.540659	−	0.295222i
$638$	−0.0841389	−	0.0629856i	−0.00333109	−	0.00249362i
$639$	−8.81416	−	4.02529i	−0.348683	−	0.159238i
$640$	1.15679	+	1.91360i	0.0457259	+	0.0756415i
$641$	11.4862	−	17.8728i	0.453676	−	0.705933i	−0.536786	−	0.843718i	$-0.680362\pi$
$641$	11.4862	−	17.8728i	0.453676	−	0.705933i	0.990462	+	0.137785i	$0.0439982\pi$
$642$	0.409558	−	5.72637i	0.0161640	−	0.226002i
$643$	−25.3187	+	25.3187i	−0.998471	+	0.998471i	−0.999999	−	0.00152801i	$-0.999514\pi$
$643$	−25.3187	+	25.3187i	−0.998471	+	0.998471i	0.00152801	+	0.999999i	$0.499514\pi$
$644$	−7.48364	+	6.15192i	−0.294897	+	0.242420i
$645$	0.658527	−	6.63879i	0.0259295	−	0.261402i
$646$	−0.399079	−	0.460562i	−0.0157015	−	0.0181206i
$647$	−28.0497	+	6.10184i	−1.10275	+	0.239888i	−0.726866	−	0.686779i	$-0.759024\pi$
$647$	−28.0497	+	6.10184i	−1.10275	+	0.239888i	−0.375882	+	0.926668i	$0.622660\pi$
$648$	0.800541	−	0.599278i	0.0314482	−	0.0235419i
$649$	1.80412	−	3.95048i	0.0708180	−	0.155070i
$650$	−1.46216	+	26.5864i	−0.0573506	+	1.04281i
$651$	−0.717965	+	2.44516i	−0.0281392	+	0.0958335i
$652$	−0.109431	+	0.503046i	−0.00428564	+	0.0197008i
$653$	−4.57552	+	12.2674i	−0.179054	+	0.480062i	−0.995209	−	0.0977710i	$-0.968829\pi$
$653$	−4.57552	+	12.2674i	−0.179054	+	0.480062i	0.816155	+	0.577833i	$0.196101\pi$
$654$	−3.06118	+	0.898845i	−0.119702	+	0.0351476i
$655$	−11.1452	−	11.7750i	−0.435480	−	0.460088i
$656$	−0.235201	+	0.271437i	−0.00918307	+	0.0105978i
$657$	−3.18692	+	5.83641i	−0.124334	+	0.227700i
$658$	1.37761	+	0.513821i	0.0537047	+	0.0200308i
$659$	29.5561	−	18.9946i	1.15134	−	0.739924i	0.181438	−	0.983402i	$-0.441925\pi$
$659$	29.5561	−	18.9946i	1.15134	−	0.739924i	0.969906	+	0.243479i	$0.0782886\pi$
$660$	−0.876234	+	0.371425i	−0.0341074	+	0.0144577i
$661$	−38.6464	+	5.55651i	−1.50317	+	0.216123i	−0.844193	−	0.536040i	$-0.819920\pi$
$661$	−38.6464	+	5.55651i	−1.50317	+	0.216123i	−0.658977	+	0.752163i	$0.729011\pi$
$662$	5.35747	+	14.3639i	0.208224	+	0.558271i
$663$	−3.96692	−	5.29918i	−0.154062	−	0.205803i
$664$	−7.41944	−	4.76818i	−0.287930	−	0.185041i
$665$	2.18245	+	0.375240i	0.0846319	+	0.0145512i
$666$		−	1.68017i		−	0.0651053i
$667$	0.540403	+	1.05381i	0.0209245	+	0.0408037i
$668$	−9.29766	−	9.29766i	−0.359737	−	0.359737i
$669$	−14.7353	+	12.7682i	−0.569698	+	0.493646i
$670$	8.94967	−	11.2949i	0.345756	−	0.436358i
$671$	0.805403	−	5.60170i	0.0310922	−	0.216251i
$672$	1.89266	−	0.705924i	0.0730108	−	0.0272316i
$673$	12.8567	−	17.1745i	0.495587	−	0.662027i	−0.481107	−	0.876662i	$-0.659765\pi$
$673$	12.8567	−	17.1745i	0.495587	−	0.662027i	0.976694	+	0.214635i	$0.0688561\pi$
$674$	19.4559	+	5.71276i	0.749413	+	0.220047i
$675$	2.00194	−	4.58173i	0.0770547	−	0.176351i
$676$	6.38038	+	13.9711i	0.245399	+	0.537349i
$677$	−19.5366	−	10.6678i	−0.750853	−	0.409997i	0.0577652	−	0.998330i	$-0.481603\pi$
$677$	−19.5366	−	10.6678i	−0.750853	−	0.409997i	−0.808619	+	0.588333i	$0.799784\pi$
$678$	−0.789865	−	11.0438i	−0.0303346	−	0.424133i
$679$	−5.70763	−	4.94569i	−0.219039	−	0.189798i
$680$	−2.73117	+	0.515999i	−0.104736	+	0.0197877i
$681$	−4.54754	+	2.07679i	−0.174262	+	0.0795829i
$682$	−0.524672	−	0.114135i	−0.0200907	−	0.00437047i
$683$	1.58032	+	2.89414i	0.0604693	+	0.110741i	0.906165	−	0.422924i	$-0.138996\pi$
$683$	1.58032	+	2.89414i	0.0604693	+	0.110741i	−0.845696	+	0.533665i	$0.820814\pi$
$684$	−0.0697719	−	0.485274i	−0.00266780	−	0.0185549i
$685$	−11.8212	−	44.7742i	−0.451666	−	1.71073i
$686$	−19.8337	−	2.85165i	−0.757253	−	0.108877i
$687$	1.31554	+	6.04746i	0.0501911	+	0.230725i
$688$	−2.97593	−	0.212842i	−0.113456	−	0.00811454i
$689$	−69.6941			−2.65513
$690$	10.7085	+	0.572674i	0.407666	+	0.0218013i
$691$	−6.70888			−0.255218			−0.127609	−	0.991825i	$-0.540730\pi$
$691$	−6.70888			−0.255218			−0.127609	+	0.991825i	$0.540730\pi$
$692$	−5.22546	−	0.373732i	−0.198642	−	0.0142072i
$693$	0.182753	+	0.840104i	0.00694223	+	0.0319129i
$694$	−8.98781	−	1.29225i	−0.341173	−	0.0490532i
$695$	3.36590	−	5.78080i	0.127676	−	0.219278i
$696$	−0.0351436	−	0.244429i	−0.00133211	−	0.00926505i
$697$	−0.213959	−	0.391837i	−0.00810429	−	0.0148419i
$698$	−22.1371	−	4.81563i	−0.837901	−	0.182274i
$699$	−15.2420	+	6.96078i	−0.576505	+	0.263281i
$700$	6.48764	−	7.74097i	0.245210	−	0.292581i
$701$	14.8858	+	12.8986i	0.562228	+	0.487173i	0.888986	−	0.457935i	$-0.151411\pi$
$701$	14.8858	+	12.8986i	0.562228	+	0.487173i	−0.326758	+	0.945108i	$0.605956\pi$
$702$	−0.379904	−	5.31175i	−0.0143386	−	0.200479i
$703$	−0.722968	−	0.394771i	−0.0272673	−	0.0148891i
$704$	0.176807	+	0.387154i	0.00666367	+	0.0145914i
$705$	−0.740479	−	1.44937i	−0.0278880	−	0.0545863i
$706$	9.16810	+	2.69200i	0.345046	+	0.101315i
$707$	−3.61975	+	4.83543i	−0.136135	+	0.181855i
$708$	9.56055	−	3.56590i	0.359307	−	0.134015i
$709$	5.02263	−	34.9331i	0.188629	−	1.31194i	−0.646934	−	0.762546i	$-0.723949\pi$
$709$	5.02263	−	34.9331i	0.188629	−	1.31194i	0.835563	−	0.549395i	$-0.185142\pi$
$710$	2.49331	+	21.5231i	0.0935722	+	0.807749i
$711$	−9.50529	+	8.23638i	−0.356476	+	0.308888i
$712$	10.6909	+	10.6909i	0.400660	+	0.400660i
$713$	4.74775	+	3.75027i	0.177805	+	0.140449i
$714$			2.51093i			0.0939692i
$715$	−0.858789	+	4.99485i	−0.0321169	+	0.186797i
$716$	18.6904	+	12.0116i	0.698494	+	0.448895i
$717$	13.3062	+	17.7750i	0.496930	+	0.663821i
$718$	−2.67624	−	7.17528i	−0.0998764	−	0.267779i
$719$	3.78306	−	0.543922i	0.141084	−	0.0202849i	−0.0714108	−	0.997447i	$-0.522750\pi$
$719$	3.78306	−	0.543922i	0.141084	−	0.0202849i	0.212495	+	0.977162i	$0.431841\pi$
$720$	−2.07283	−	0.838677i	−0.0772498	−	0.0312556i
$721$	−16.9463	+	10.8908i	−0.631115	+	0.405593i
$722$	17.5768	+	6.55582i	0.654142	+	0.243982i
$723$	−3.44135	+	6.30236i	−0.127985	+	0.234387i
$724$	11.4046	−	13.1616i	0.423848	−	0.489146i
$725$	−0.756103	−	0.976126i	−0.0280809	−	0.0362524i
$726$	10.3806	−	3.04802i	0.385261	−	0.113123i
$727$	7.31117	−	19.6020i	0.271156	−	0.726998i	−0.727986	−	0.685592i	$-0.759544\pi$
$727$	7.31117	−	19.6020i	0.271156	−	0.726998i	0.999142	−	0.0414060i	$-0.0131837\pi$
$728$	2.28662	−	10.5114i	0.0847477	−	0.389579i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	14.8551	−	0.652995i	0.549813	−	0.0241684i
$731$	1.54061	−	3.37346i	0.0569814	−	0.124772i
$732$	10.6446	−	7.96844i	0.393436	−	0.294522i
$733$	47.8187	−	10.4023i	1.76622	−	0.384219i	0.792129	−	0.610354i	$-0.208973\pi$
$733$	47.8187	−	10.4023i	1.76622	−	0.384219i	0.974096	+	0.226135i	$0.0726091\pi$
$734$	−5.07726	−	5.85947i	−0.187405	−	0.216277i
$735$	4.13797	+	5.04928i	0.152631	+	0.186246i
$736$	0.124472	−	4.79422i	0.00458808	−	0.176717i
$737$	1.93957	−	1.93957i	0.0714449	−	0.0714449i
$738$	0.0256223	−	0.358247i	0.000943171	−	0.0131873i
$739$	−19.3799	+	30.1557i	−0.712900	+	1.10929i	0.276064	+	0.961139i	$0.410970\pi$
$739$	−19.3799	+	30.1557i	−0.712900	+	1.10929i	−0.988964	+	0.148155i	$0.952666\pi$
$740$	−3.21517	+	1.94360i	−0.118192	+	0.0714480i
$741$	−2.37488	−	1.08457i	−0.0872435	−	0.0398428i
$742$	21.1636	+	15.8429i	0.776940	+	0.581610i
$743$	16.7269	−	9.13357i	0.613650	−	0.335078i	−0.142186	−	0.989840i	$-0.545413\pi$
$743$	16.7269	−	9.13357i	0.613650	−	0.335078i	0.755835	+	0.654762i	$0.227231\pi$
$744$	−0.682055	−	1.06130i	−0.0250053	−	0.0389091i
$745$	−9.70405	+	3.31877i	−0.355529	+	0.121590i
$746$	5.39856	+	18.3858i	0.197655	+	0.673152i
$747$	8.79703	−	0.629176i	0.321867	−	0.0230204i
$748$	−0.527702	+	0.0377420i	−0.0192947	+	0.00137998i
$749$	3.26723	+	11.1272i	0.119382	+	0.406578i
$750$	−11.0834	+	1.46917i	−0.404708	+	0.0536465i
$751$	10.2355	+	15.9267i	0.373497	+	0.581173i	0.976221	−	0.216777i	$-0.0695543\pi$
$751$	10.2355	+	15.9267i	0.373497	+	0.581173i	−0.602724	+	0.797950i	$0.705918\pi$
$752$	−0.638836	+	0.348831i	−0.0232959	+	0.0127205i
$753$	−21.1149	−	15.8064i	−0.769470	−	0.576018i
$754$	−1.19621	−	0.546290i	−0.0435634	−	0.0198947i
$755$	−34.7506	−	8.56558i	−1.26470	−	0.311733i
$756$	−1.09210	+	1.69935i	−0.0397195	+	0.0618047i
$757$	1.81556	−	25.3848i	0.0659876	−	0.922627i	−0.851371	−	0.524564i	$-0.824228\pi$
$757$	1.81556	−	25.3848i	0.0659876	−	0.922627i	0.917358	−	0.398062i	$-0.130317\pi$
$758$	9.44518	−	9.44518i	0.343064	−	0.343064i
$759$	2.01218	+	0.342830i	0.0730377	+	0.0124440i
$760$	−0.847908	+	0.694873i	−0.0307568	+	0.0252057i
$761$	−6.37380	−	7.35576i	−0.231050	−	0.266646i	0.628372	−	0.777913i	$-0.283722\pi$
$761$	−6.37380	−	7.35576i	−0.231050	−	0.266646i	−0.859422	+	0.511267i	$0.829176\pi$
$762$	−0.116433	+	0.0253284i	−0.00421792	+	0.000917553i
$763$	5.15925	−	3.86217i	0.186778	−	0.139820i
$764$	0.927283	−	2.03047i	0.0335479	−	0.0734597i
$765$	1.87719	−	2.04981i	0.0678698	−	0.0741109i
$766$	−0.248224	+	0.845374i	−0.00896871	+	0.0305446i
$767$	11.5506	−	53.0973i	0.417068	−	1.91723i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	−26.1823	+	7.68781i	−0.944157	+	0.277229i	−0.717352	−	0.696711i	$-0.754646\pi$
$769$	−26.1823	+	7.68781i	−0.944157	+	0.277229i	−0.226805	+	0.973940i	$0.572828\pi$
$770$	1.39621	−	1.32154i	0.0503160	−	0.0476248i
$771$	−17.5723	+	20.2796i	−0.632853	+	0.730351i
$772$	−5.95906	+	10.9132i	−0.214471	+	0.392775i
$773$	−40.1788	−	14.9859i	−1.44513	−	0.539006i	−0.500094	−	0.865971i	$-0.666701\pi$
$773$	−40.1788	−	14.9859i	−1.44513	−	0.539006i	−0.945036	+	0.326965i	$0.893974\pi$
$774$	2.50990	−	1.61302i	0.0902166	−	0.0579787i
$775$	−5.58526	−	2.93150i	−0.200628	−	0.105303i
$776$	3.70066	−	0.532074i	0.132846	−	0.0191003i
$777$	1.18607	+	3.17998i	0.0425501	+	0.114081i
$778$	−5.90367	−	7.88638i	−0.211657	−	0.282740i
$779$	−0.148132	−	0.0951985i	−0.00530737	−	0.00341084i
$780$	−9.72508	+	6.87154i	−0.348214	+	0.246041i
$781$			4.12414i			0.147573i
$782$	5.52952	+	2.22754i	0.197735	+	0.0796565i
$783$	0.174615	+	0.174615i	0.00624022	+	0.00624022i
$784$	2.20643	−	1.91188i	0.0788010	−	0.0682814i
$785$	−19.5899	+	2.26935i	−0.699192	+	0.0809966i
$786$	1.03189	−	7.17696i	0.0368063	−	0.255994i
$787$	−16.5711	+	6.18070i	−0.590696	+	0.220318i	−0.626995	−	0.779023i	$-0.715716\pi$
$787$	−16.5711	+	6.18070i	−0.590696	+	0.220318i	0.0362999	+	0.999341i	$0.488443\pi$
$788$	−8.41971	+	11.2474i	−0.299940	+	0.400673i
$789$	−19.9886	−	5.86918i	−0.711613	−	0.208948i
$790$	26.7567	+	8.66156i	0.951960	+	0.308164i
$791$	9.29100	+	20.3445i	0.330350	+	0.723366i
$792$	−0.373554	−	0.203976i	−0.0132737	−	0.00724797i
$793$	−5.05149	−	70.6290i	−0.179384	−	2.50811i
$794$	16.5671	+	14.3555i	0.587945	+	0.509457i
$795$	−5.43275	−	28.7554i	−0.192680	−	1.01985i
$796$	11.9172	−	5.44239i	0.422393	−	0.192900i
$797$	−2.30820	−	0.502118i	−0.0817606	−	0.0177859i	0.171499	−	0.985184i	$-0.445139\pi$
$797$	−2.30820	−	0.502118i	−0.0817606	−	0.0177859i	−0.253259	+	0.967398i	$0.581503\pi$
$798$	0.474621	+	0.869204i	0.0168014	+	0.0307695i
$799$	−0.128761	−	0.895550i	−0.00455522	−	0.0316823i
$800$	0.792930	+	4.93673i	0.0280343	+	0.174540i
$801$	−14.9654	−	2.15170i	−0.528776	−	0.0760265i
$802$	2.98431	+	13.7187i	0.105380	+	0.484422i
$803$	2.82306	+	0.201909i	0.0996236	+	0.00712522i
$804$	6.44469			0.227287
$805$	−20.6718	+	6.47552i	−0.728585	+	0.228232i
$806$	−6.71825			−0.236640
$807$	−14.3100	−	1.02347i	−0.503735	−	0.0360278i
$808$	−0.635606	−	2.92183i	−0.0223605	−	0.102790i
$809$	−10.6325	−	1.52872i	−0.373819	−	0.0537470i	−0.0471547	−	0.998888i	$-0.515015\pi$
$809$	−10.6325	−	1.52872i	−0.373819	−	0.0537470i	−0.326664	+	0.945141i	$0.605924\pi$
$810$	2.16199	−	0.570805i	0.0759644	−	0.0200560i
$811$	−2.27097	−	15.7950i	−0.0797447	−	0.554637i	−0.990052	−	0.140703i	$-0.955064\pi$
$811$	−2.27097	−	15.7950i	−0.0797447	−	0.554637i	0.910307	−	0.413934i	$-0.135845\pi$
$812$	0.239063	+	0.437811i	0.00838946	+	0.0153642i
$813$	11.5801	+	2.51909i	0.406131	+	0.0883484i
$814$	−0.650484	+	0.297066i	−0.0227994	+	0.0104122i
$815$	−0.648724	+	0.950951i	−0.0227238	+	0.0333104i
$816$	−0.939414	−	0.814007i	−0.0328861	−	0.0284960i
$817$	−0.104349	−	1.45899i	−0.00365071	−	0.0510436i
$818$	14.6151	+	7.98045i	0.511005	+	0.279030i
$819$	4.46872	+	9.78514i	0.156150	+	0.341921i
$820$	−0.715180	+	0.365384i	−0.0249752	+	0.0127598i
$821$	−40.0880	−	11.7709i	−1.39908	−	0.410807i	−0.506712	−	0.862116i	$-0.669139\pi$
$821$	−40.0880	−	11.7709i	−1.39908	−	0.410807i	−0.892368	+	0.451309i	$0.850957\pi$
$822$	12.4109	−	16.5790i	0.432880	−	0.578260i
$823$	44.8556	−	16.7303i	1.56357	−	0.583181i	0.589170	−	0.808009i	$-0.299455\pi$
$823$	44.8556	−	16.7303i	1.56357	−	0.583181i	0.974398	+	0.224828i	$0.0721820\pi$
$824$	1.41920	−	9.87076i	0.0494402	−	0.343864i
$825$	−2.12779	+	0.0350238i	−0.0740801	+	0.00121937i
$826$	−15.5776	+	13.4980i	−0.542013	+	0.469657i
$827$	25.4131	+	25.4131i	0.883701	+	0.883701i	0.993909	−	0.110208i	$-0.0351517\pi$
$827$	25.4131	+	25.4131i	0.883701	+	0.883701i	−0.110208	+	0.993909i	$0.535152\pi$
$828$	2.77342	+	3.91256i	0.0963831	+	0.135971i
$829$			11.5411i			0.400839i	0.979710	+	0.200419i	$0.0642304\pi$
$829$			11.5411i			0.400839i	−0.979710	+	0.200419i	$0.935770\pi$
$830$	−11.3803	−	16.1061i	−0.395015	−	0.559052i
$831$	21.2995	+	13.6883i	0.738870	+	0.474843i
$832$	3.19135	+	4.26314i	0.110640	+	0.147798i
$833$	1.26822	+	3.40022i	0.0439411	+	0.117811i
$834$	2.96110	−	0.425743i	0.102535	−	0.0147423i
$835$	−11.4747	−	27.0702i	−0.397100	−	0.936803i
$836$	−0.175540	+	0.112812i	−0.00607116	+	0.00390170i
$837$	1.18203	+	0.440873i	0.0408568	+	0.0152388i
$838$	8.54901	−	15.6564i	0.295321	−	0.540840i
$839$	−30.4908	+	35.1882i	−1.05266	+	1.21483i	−0.0766600	+	0.997057i	$0.524426\pi$
$839$	−30.4908	+	35.1882i	−1.05266	+	1.21483i	−0.975999	+	0.217776i	$0.930120\pi$
$840$	4.51520	+	0.124066i	0.155789	+	0.00428069i
$841$	−27.7668	+	8.15306i	−0.957475	+	0.281140i
$842$	3.83338	−	10.2777i	0.132107	−	0.354192i
$843$	−3.51883	+	16.1758i	−0.121195	+	0.557125i
$844$	4.84937	−	16.5154i	0.166922	−	0.568485i
$845$	1.50822	+	34.3107i	0.0518842	+	1.18033i
$846$	0.302368	−	0.662094i	0.0103956	−	0.0227632i
$847$	−17.4953	+	13.0968i	−0.601144	+	0.450011i
$848$	−12.7882	+	2.78190i	−0.439149	+	0.0955310i
$849$	−12.8234	−	14.7989i	−0.440097	−	0.507899i
$850$	−6.09400	−	1.22099i	−0.209023	−	0.0418796i
$851$	8.05510	+	0.209133i	0.276125	+	0.00716900i
$852$	−6.85173	+	6.85173i	−0.234736	+	0.234736i
$853$	2.08914	−	29.2100i	0.0715308	−	1.00013i	−0.827279	−	0.561792i	$-0.810112\pi$
$853$	2.08914	−	29.2100i	0.0715308	−	1.00013i	0.898810	−	0.438339i	$-0.144433\pi$
$854$	−14.5214	+	22.5958i	−0.496914	+	0.773213i
$855$	0.262363	−	1.06441i	0.00897263	−	0.0364020i
$856$	−5.22219	−	2.38490i	−0.178491	−	0.0815141i
$857$	−34.1977	−	25.6001i	−1.16817	−	0.874482i	−0.174263	−	0.984699i	$-0.555754\pi$
$857$	−34.1977	−	25.6001i	−1.16817	−	0.874482i	−0.993907	+	0.110217i	$0.964845\pi$
$858$	−1.98929	+	1.08624i	−0.0679134	+	0.0370835i
$859$	7.27609	+	11.3218i	0.248257	+	0.386295i	0.942909	−	0.333051i	$-0.108078\pi$
$859$	7.27609	+	11.3218i	0.248257	+	0.386295i	−0.694652	+	0.719346i	$0.744442\pi$
$860$	−5.99008	−	2.93703i	−0.204260	−	0.100152i
$861$	0.204401	+	0.696126i	0.00696597	+	0.0237239i
$862$	−8.39519	+	0.600436i	−0.285941	+	0.0204509i
$863$	4.77417	−	0.341455i	0.162515	−	0.0116233i	0.0101553	−	0.999948i	$-0.496767\pi$
$863$	4.77417	−	0.341455i	0.162515	−	0.0116233i	0.152359	+	0.988325i	$0.451313\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−10.5180	−	5.15715i	−0.357624	−	0.175348i
$866$	−7.98275	−	12.4214i	−0.271265	−	0.422096i
$867$	−13.5644	+	7.40674i	−0.460672	+	0.251546i
$868$	2.04009	+	1.52719i	0.0692452	+	0.0518363i
$869$	4.86935	+	2.22376i	0.165181	+	0.0754358i
$870$	0.132150	−	0.536133i	0.00448031	−	0.0181766i
$871$	18.5548	−	28.8719i	0.628706	−	0.978286i
$872$	−0.227602	+	3.18229i	−0.00770757	+	0.107766i
$873$	−2.64367	+	2.64367i	−0.0894746	+	0.0894746i
$874$	2.33519	−	0.274099i	0.0789891	−	0.00927153i
$875$	19.9399	−	10.6047i	0.674093	−	0.358503i
$876$	4.35471	+	5.02560i	0.147132	+	0.169799i
$877$	43.6631	−	9.49833i	1.47440	−	0.320736i	0.597678	−	0.801736i	$-0.296090\pi$
$877$	43.6631	−	9.49833i	1.47440	−	0.320736i	0.876720	+	0.481000i	$0.159726\pi$
$878$	−32.3243	+	24.1977i	−1.09089	+	0.816632i
$879$	−0.855236	+	1.87270i	−0.0288464	+	0.0631648i
$880$	0.0417943	+	0.950787i	0.00140888	+	0.0320510i
$881$	−7.60495	+	25.9001i	−0.256217	+	0.872596i	0.726450	+	0.687219i	$0.241169\pi$
$881$	−7.60495	+	25.9001i	−0.256217	+	0.872596i	−0.982667	+	0.185377i	$0.940649\pi$
$882$	−0.620589	+	2.85280i	−0.0208963	+	0.0960588i
$883$	−2.29862	+	6.16283i	−0.0773546	+	0.207396i	−0.969871	−	0.243619i	$-0.921665\pi$
$883$	−2.29862	+	6.16283i	−0.0773546	+	0.207396i	0.892516	+	0.451015i	$0.148938\pi$
$884$	−6.35136	+	1.86493i	−0.213619	+	0.0627243i
$885$	22.8080	+	0.626707i	0.766683	+	0.0210665i
$886$	−10.8196	+	12.4864i	−0.363490	+	0.419490i
$887$	−0.118490	+	0.216998i	−0.00397850	+	0.00728608i	−0.879661	−	0.475602i	$-0.842230\pi$
$887$	−0.118490	+	0.216998i	−0.00397850	+	0.00728608i	0.875682	+	0.482888i	$0.160412\pi$
$888$	−1.57423	−	0.587159i	−0.0528279	−	0.0197038i
$889$	0.202488	−	0.130131i	0.00679122	−	0.00436445i
$890$	13.1942	+	31.1267i	0.442272	+	1.04337i
$891$	0.421283	−	0.0605714i	0.0141135	−	0.00202922i
$892$	6.81369	+	18.2682i	0.228139	+	0.611665i
$893$	−0.213851	−	0.285672i	−0.00715627	−	0.00955965i
$894$	−3.85846	−	2.47968i	−0.129046	−	0.0829330i
$895$	28.6682	+	40.5732i	0.958272	+	1.35621i
$896$		−	2.02002i		−	0.0674841i
$897$	25.5130	−	1.16018i	0.851854	−	0.0387373i
$898$	13.9178	+	13.9178i	0.464443	+	0.464443i
$899$	0.235442	−	0.204012i	0.00785243	−	0.00680417i
$900$	−3.59324	−	3.47687i	−0.119775	−	0.115896i
$901$	2.31515	−	16.1022i	0.0771289	−	0.536443i
$902$	−0.143227	+	0.0534209i	−0.00476893	+	0.00177872i
$903$	−3.61172	+	4.82469i	−0.120190	+	0.160556i
$904$	−10.6235	−	3.11933i	−0.353331	−	0.103747i
$905$	34.6781	−	17.7170i	1.15274	−	0.588932i
$906$	−6.64916	−	14.5596i	−0.220903	−	0.483711i
$907$	46.8244	+	25.5680i	1.55478	+	0.848972i	0.999854	+	0.0170706i	$0.00543400\pi$
$907$	46.8244	+	25.5680i	1.55478	+	0.848972i	0.554923	+	0.831902i	$0.312748\pi$
$908$	0.356647	+	4.98658i	0.0118358	+	0.165486i
$909$	2.25982	+	1.95814i	0.0749534	+	0.0649475i
$910$	13.5554	−	19.8706i	0.449359	−	0.658705i
$911$	35.8286	−	16.3624i	1.18706	−	0.542110i	0.278728	−	0.960370i	$-0.410087\pi$
$911$	35.8286	−	16.3624i	1.18706	−	0.542110i	0.908327	+	0.418260i	$0.137360\pi$
$912$	−0.479060	−	0.104213i	−0.0158633	−	0.00345084i
$913$	−1.79897	−	3.29456i	−0.0595371	−	0.109034i
$914$	1.34618	+	9.36291i	0.0445278	+	0.309698i
$915$	28.7474	−	7.58985i	0.950359	−	0.250913i
$916$	6.12590	+	0.880771i	0.202405	+	0.0291015i
$917$	3.11337	+	14.3120i	0.102813	+	0.472622i
$918$	1.23986	+	0.0886763i	0.0409214	+	0.00292675i
$919$	4.91956			0.162281			0.0811406	−	0.996703i	$-0.474144\pi$
$919$	4.91956			0.162281			0.0811406	+	0.996703i	$0.474144\pi$
$920$	4.27881	−	9.83320i	0.141068	−	0.324191i
$921$	−20.5917			−0.678518
$922$	10.4443	+	0.746991i	0.343965	+	0.0246008i
$923$	10.9687	+	50.4221i	0.361038	+	1.65966i
$924$	0.851001	+	0.122355i	0.0279959	+	0.00402520i
$925$	−8.29454	+	1.33226i	−0.272723	+	0.0438043i
$926$	5.53484	+	38.4957i	0.181886	+	1.26505i
$927$	4.77920	+	8.75244i	0.156969	+	0.287468i
$928$	−0.241299	−	0.0524914i	−0.00792102	−	0.00172311i
$929$	9.58777	−	4.37859i	0.314565	−	0.143657i	−0.251876	−	0.967760i	$-0.581047\pi$
$929$	9.58777	−	4.37859i	0.314565	−	0.143657i	0.566440	+	0.824103i	$0.308320\pi$
$930$	−0.523697	−	2.77191i	−0.0171727	−	0.0908946i
$931$	1.08173	+	0.937327i	0.0354524	+	0.0307196i
$932$	1.19537	+	16.7135i	0.0391558	+	0.547470i
$933$	−12.9264	−	7.05833i	−0.423190	−	0.231079i
$934$	13.0321	+	28.5362i	0.426422	+	0.933734i
$935$	−1.12549	−	0.364339i	−0.0368075	−	0.0119152i
$936$	−5.10961	−	1.50032i	−0.167013	−	0.0490394i
$937$	10.8564	−	14.5025i	0.354664	−	0.473776i	−0.587357	−	0.809328i	$-0.699832\pi$
$937$	10.8564	−	14.5025i	0.354664	−	0.473776i	0.942022	+	0.335551i	$0.108923\pi$
$938$	−12.1976	+	4.54947i	−0.398265	+	0.148545i
$939$	1.01095	−	7.03129i	0.0329910	−	0.229458i
$940$	−1.61675	+	0.187290i	−0.0527327	+	0.00610872i
$941$	−26.5556	+	23.0106i	−0.865688	+	0.750123i	−0.969660	−	0.244457i	$-0.921390\pi$
$941$	−26.5556	+	23.0106i	−0.865688	+	0.750123i	0.103972	+	0.994580i	$0.466845\pi$
$942$	−6.23629	−	6.23629i	−0.203189	−	0.203189i
$943$	1.71432	+	0.167431i	0.0558261	+	0.00545229i
$944$		−	10.2039i		−	0.332109i
$945$	−3.68895	+	2.60654i	−0.120002	+	0.0847906i
$946$	−1.06825	−	0.686525i	−0.0347319	−	0.0223209i
$947$	12.7685	+	17.0568i	0.414922	+	0.554270i	0.958502	−	0.285087i	$-0.0920225\pi$
$947$	12.7685	+	17.0568i	0.414922	+	0.554270i	−0.543580	+	0.839357i	$0.682932\pi$
$948$	4.39532	+	11.7843i	0.142753	+	0.382736i
$949$	35.0520	−	5.03972i	1.13784	−	0.163596i
$950$	−2.34034	+	0.729233i	−0.0759307	+	0.0236595i
$951$	19.5463	−	12.5616i	0.633832	−	0.407339i
$952$	2.35262	+	0.877481i	0.0762487	+	0.0284393i
$953$	−15.2997	+	28.0194i	−0.495607	+	0.907637i	0.503441	+	0.864029i	$0.332067\pi$
$953$	−15.2997	+	28.0194i	−0.495607	+	0.907637i	−0.999049	+	0.0436078i	$0.986115\pi$
$954$	8.57036	−	9.89072i	0.277476	−	0.320224i
$955$	3.62500	−	3.43112i	0.117302	−	0.111028i
$956$	21.3044	−	6.25553i	0.689032	−	0.202318i
$957$	0.0367296	−	0.0984758i	0.00118730	−	0.00318327i
$958$	4.78682	−	22.0047i	0.154655	−	0.710938i
$959$	−11.7860	+	40.1395i	−0.380591	+	1.29617i
$960$	−1.51018	+	1.64905i	−0.0487408	+	0.0532228i
$961$	−12.2167	+	26.7509i	−0.394087	+	0.862931i
$962$	−7.16280	+	5.36200i	−0.230938	+	0.172878i
$963$	5.60980	−	1.22034i	0.180773	−	0.0393248i
$964$	4.70237	+	5.42682i	0.151453	+	0.174786i
$965$	−21.5048	+	17.6235i	−0.692263	+	0.567320i
$966$	−8.01111	−	5.44731i	−0.257753	−	0.175264i
$967$	0.0786012	−	0.0786012i	0.00252764	−	0.00252764i	−0.705842	−	0.708369i	$-0.749431\pi$
$967$	0.0786012	−	0.0786012i	0.00252764	−	0.00252764i	0.708369	+	0.705842i	$0.249431\pi$
$968$	0.771808	−	10.7913i	0.0248068	−	0.346845i
$969$	0.329472	−	0.512669i	0.0105842	−	0.0164693i
$970$	8.11707	+	2.00076i	0.260623	+	0.0642404i
$971$	16.6711	+	7.61342i	0.535000	+	0.244326i	0.664546	−	0.747247i	$-0.268625\pi$
$971$	16.6711	+	7.61342i	0.535000	+	0.244326i	−0.129546	+	0.991573i	$0.541352\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	−5.30381	+	2.89610i	−0.170032	+	0.0928447i
$974$	−13.4997	−	21.0059i	−0.432558	−	0.673073i
$975$	−25.9214	+	6.08733i	−0.830150	+	0.194951i
$976$	−3.74613	−	12.7581i	−0.119911	−	0.408378i
$977$	−6.39941	+	0.457695i	−0.204735	+	0.0146430i	−0.173330	−	0.984864i	$-0.555453\pi$
$977$	−6.39941	+	0.457695i	−0.204735	+	0.0146430i	−0.0314052	+	0.999507i	$0.509998\pi$
$978$	−0.513499	+	0.0367262i	−0.0164199	+	0.00117437i
$979$	1.81295	+	6.17434i	0.0579421	+	0.197333i
$980$	6.17700	−	2.11252i	0.197317	−	0.0674820i
$981$	−1.72487	−	2.68395i	−0.0550709	−	0.0856919i
$982$	3.01790	−	1.64790i	0.0963052	−	0.0525866i
$983$	38.1565	+	28.5636i	1.21700	+	0.911037i	0.997907	−	0.0646657i	$-0.0205981\pi$
$983$	38.1565	+	28.5636i	1.21700	+	0.911037i	0.219097	+	0.975703i	$0.429689\pi$
$984$	−0.326705	−	0.149201i	−0.0104150	−	0.00475637i
$985$	−26.8856	+	16.2526i	−0.856646	+	0.517850i
$986$	0.165952	−	0.258227i	0.00528500	−	0.00822362i
$987$	−0.104891	+	1.46656i	−0.00333871	+	0.0466813i
$988$	−1.84613	+	1.84613i	−0.0587331	+	0.0587331i
$989$	7.42074	+	12.2338i	0.235966	+	0.389012i
$990$	−0.603244	−	0.736098i	−0.0191723	−	0.0233947i
$991$	31.0506	+	35.8344i	0.986356	+	1.13832i	0.990387	+	0.138324i	$0.0441715\pi$
$991$	31.0506	+	35.8344i	0.986356	+	1.13832i	−0.00403073	+	0.999992i	$0.501283\pi$
$992$	−1.23274	+	0.268165i	−0.0391394	+	0.00851426i
$993$	−12.2727	+	9.18725i	−0.389463	+	0.291549i
$994$	8.13117	−	17.8048i	0.257905	−	0.564733i
$995$	29.2667	−	1.28649i	0.927816	−	0.0407845i
$996$	2.48474	−	8.46225i	0.0787321	−	0.268137i
$997$	13.0536	−	60.0066i	0.413413	−	1.90043i	−0.0211262	−	0.999777i	$-0.506725\pi$
$997$	13.0536	−	60.0066i	0.413413	−	1.90043i	0.434539	−	0.900653i	$-0.356911\pi$
$998$	−9.49732	+	25.4633i	−0.300632	+	0.806027i
$999$	1.61211	−	0.473358i	0.0510049	−	0.0149764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.12	yes	240
5.2	odd	4	inner	690.2.w.b.217.5	yes	240
23.7	odd	22	inner	690.2.w.b.283.5	yes	240
115.7	even	44	inner	690.2.w.b.7.12	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.12	✓	240	115.7	even	44	inner
690.2.w.b.217.5	yes	240	5.2	odd	4	inner
690.2.w.b.283.5	yes	240	23.7	odd	22	inner
690.2.w.b.493.12	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.93237 + 1.12513i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.968092 - 1.77293i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.93237 + 1.12513i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.968092 - 1.77293i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.84719 + 1.26012i) q^{10} +(0.321659 + 0.278719i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(4.67392 + 2.55215i) q^{13} +(-0.839146 - 1.83747i) q^{14} +(-0.688666 + 2.12738i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.744916 + 0.995091i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(-0.0697719 + 0.485274i) q^{19} +(1.75258 + 1.38869i) q^{20} +(1.52663 - 1.32283i) q^{21} +(0.300956 + 0.300956i) q^{22} +(-1.55878 - 4.53544i) q^{23} +1.00000i q^{24} +(2.46814 + 4.34836i) q^{25} +(4.47995 + 2.87909i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-0.705924 - 1.89266i) q^{28} +(-0.244429 + 0.0351436i) q^{29} +(-0.838677 + 2.07283i) q^{30} +(-1.06130 + 0.682055i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-0.203976 + 0.373554i) q^{33} +(-0.814007 + 0.939414i) q^{34} +(0.124066 - 4.51520i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-0.587159 + 1.57423i) q^{37} +(-0.104213 + 0.479060i) q^{38} +(-1.50032 + 5.10961i) q^{39} +(1.64905 + 1.51018i) q^{40} +(-0.149201 + 0.326705i) q^{41} +(1.61711 - 1.21055i) q^{42} +(-2.91534 + 0.634194i) q^{43} +(0.278719 + 0.321659i) q^{44} +(-2.22515 - 0.220721i) q^{45} +(-1.23126 - 4.63508i) q^{46} +(-0.514682 + 0.514682i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(1.57841 - 2.45606i) q^{49} +(2.15165 + 4.51336i) q^{50} +(-1.13069 - 0.516371i) q^{51} +(4.26314 + 3.19135i) q^{52} +(-11.4864 + 6.27207i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(0.307969 + 0.900499i) q^{55} +(-0.569105 - 1.93819i) q^{56} +(-0.489015 + 0.0349751i) q^{57} +(-0.246313 + 0.0176167i) q^{58} +(-2.87477 - 9.79058i) q^{59} +(-0.984414 + 2.00772i) q^{60} +(-7.18877 - 11.1859i) q^{61} +(-1.10725 + 0.604605i) q^{62} +(1.61711 + 1.21055i) q^{63} +(0.909632 + 0.415415i) q^{64} +(6.16025 + 10.1905i) q^{65} +(-0.230105 + 0.358051i) q^{66} +(0.459759 - 6.42827i) q^{67} +(-0.878950 + 0.878950i) q^{68} +(4.10045 - 2.48724i) q^{69} +(0.445861 - 4.49484i) q^{70} +(6.34548 + 7.32307i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(5.32346 - 3.98509i) q^{73} +(-0.697968 + 1.52834i) q^{74} +(-3.72435 + 3.33605i) q^{75} +(-0.138123 + 0.470405i) q^{76} +(0.182753 - 0.840104i) q^{77} +(-1.86101 + 4.98956i) q^{78} +(12.0678 - 3.54343i) q^{79} +(1.53711 + 1.62397i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.172128 + 0.315229i) q^{82} +(-8.26343 - 3.08210i) q^{83} +(1.69935 - 1.09210i) q^{84} +(-2.55907 + 1.08476i) q^{85} +(-2.95316 + 0.424600i) q^{86} +(-0.0862975 - 0.231373i) q^{87} +(0.255062 + 0.340723i) q^{88} +(12.7191 + 8.17409i) q^{89} +(-2.20373 - 0.378899i) q^{90} -10.7573i q^{91} +(-0.897457 - 4.71111i) q^{92} +(-0.892063 - 0.892063i) q^{93} +(-0.550087 + 0.476653i) q^{94} +(-0.680824 + 0.859229i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(3.50298 - 1.30655i) q^{97} +(1.74960 - 2.33720i) q^{98} +(-0.408375 - 0.119910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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