LMFDB - Embedded newform 690.2.w.a.493.8

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			493.8
Character	$\chi$	$=$	690.493
Dual form			690.2.w.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 + 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-1.79544 - 1.33281i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35788 + 4.31814i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 + 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-1.79544 - 1.33281i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35788 + 4.31814i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-1.69579 - 1.45750i) q^{10} +(0.567261 + 0.491535i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(5.56150 + 3.03681i) q^{13} +(2.04382 + 4.47535i) q^{14} +(-0.920703 + 2.03772i) q^{15} +(0.959493 + 0.281733i) q^{16} +(0.838978 - 1.12074i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.534494 - 3.71749i) q^{19} +(-1.58749 - 1.57476i) q^{20} +(3.71825 - 3.22189i) q^{21} +(0.530750 + 0.530750i) q^{22} +(1.94164 - 4.38521i) q^{23} -1.00000i q^{24} +(1.44723 + 4.78597i) q^{25} +(5.33069 + 3.42583i) q^{26} +(0.599278 + 0.800541i) q^{27} +(1.71935 + 4.60975i) q^{28} +(-6.83863 + 0.983246i) q^{29} +(-1.06373 + 1.96685i) q^{30} +(6.38294 - 4.10207i) q^{31} +(0.936950 + 0.349464i) q^{32} +(0.359721 - 0.658781i) q^{33} +(0.916793 - 1.05804i) q^{34} +(1.52182 - 10.8956i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.34936 - 3.61778i) q^{37} +(0.798335 - 3.66989i) q^{38} +(1.78523 - 6.07993i) q^{39} +(-1.47110 - 1.68400i) q^{40} +(-0.469073 + 1.02713i) q^{41} +(3.93863 - 2.94842i) q^{42} +(-2.55221 + 0.555199i) q^{43} +(0.491535 + 0.567261i) q^{44} +(2.18686 + 0.466514i) q^{45} +(2.24953 - 4.23552i) q^{46} +(-8.63275 + 8.63275i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-9.30224 + 14.4746i) q^{49} +(1.10211 + 4.87702i) q^{50} +(-1.27347 - 0.581573i) q^{51} +(5.07271 + 3.79739i) q^{52} +(9.22729 - 5.03848i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-0.363362 - 1.63857i) q^{55} +(1.38611 + 4.72066i) q^{56} +(-3.74615 + 0.267930i) q^{57} +(-6.89135 + 0.492879i) q^{58} +(1.73187 + 5.89822i) q^{59} +(-1.20133 + 1.88595i) q^{60} +(-0.0184279 - 0.0286744i) q^{61} +(6.65932 - 3.63626i) q^{62} +(-3.93863 - 2.94842i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-5.93787 - 12.8649i) q^{65} +(0.405802 - 0.631440i) q^{66} +(0.540569 - 7.55814i) q^{67} +(0.989936 - 0.989936i) q^{68} +(-4.69772 - 0.965123i) q^{69} +(2.29523 - 10.7593i) q^{70} +(2.93682 + 3.38928i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(-7.74782 + 5.79995i) q^{73} +(1.60401 - 3.51230i) q^{74} +(4.36897 - 2.43149i) q^{75} +(1.05811 - 3.60358i) q^{76} +(-0.784980 + 3.60850i) q^{77} +(2.21442 - 5.93708i) q^{78} +(-11.4802 + 3.37088i) q^{79} +(-1.34722 - 1.78466i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.541152 + 0.991045i) q^{82} +(-0.379967 - 0.141720i) q^{83} +(4.13893 - 2.65993i) q^{84} +(-3.00007 + 0.894031i) q^{85} +(-2.58531 + 0.371712i) q^{86} +(2.41443 + 6.47334i) q^{87} +(0.449814 + 0.600882i) q^{88} +(10.9546 + 7.04011i) q^{89} +(2.14801 + 0.621334i) q^{90} +31.1758i q^{91} +(2.54596 - 4.06425i) q^{92} +(-5.36512 - 5.36512i) q^{93} +(-9.22661 + 7.99490i) q^{94} +(-5.91437 + 5.96216i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-2.96757 + 1.10685i) q^{97} +(-10.3111 + 13.7741i) q^{98} +(-0.720190 - 0.211467i) 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} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * 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
$5$	−1.79544	−	1.33281i	−0.802946	−	0.596051i
$5$	−1.79544	−	1.33281i	−0.802946	−	0.596051i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	2.35788	+	4.31814i	0.891196	+	1.63210i	0.768676	+	0.639638i	$0.220916\pi$
$7$	2.35788	+	4.31814i	0.891196	+	1.63210i	0.122520	+	0.992466i	$0.460902\pi$
$8$	0.977147	+	0.212565i	0.345474	+	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	−1.69579	−	1.45750i	−0.536255	−	0.460902i
$11$	0.567261	+	0.491535i	0.171036	+	0.148203i	0.736173	−	0.676794i	$-0.236631\pi$
$11$	0.567261	+	0.491535i	0.171036	+	0.148203i	−0.565137	+	0.824997i	$0.691177\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	5.56150	+	3.03681i	1.54248	+	0.842260i	0.999998	+	0.00219532i	$0.000698794\pi$
$13$	5.56150	+	3.03681i	1.54248	+	0.842260i	0.542486	+	0.840065i	$0.317483\pi$
$14$	2.04382	+	4.47535i	0.546235	+	1.19609i
$15$	−0.920703	+	2.03772i	−0.237725	+	0.526137i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	0.838978	−	1.12074i	0.203482	−	0.271820i	−0.687179	−	0.726488i	$-0.741151\pi$
$17$	0.838978	−	1.12074i	0.203482	−	0.271820i	0.890661	+	0.454668i	$0.150242\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	0.534494	−	3.71749i	0.122621	−	0.852851i	−0.831946	−	0.554856i	$-0.812773\pi$
$19$	0.534494	−	3.71749i	0.122621	−	0.852851i	0.954568	−	0.297994i	$-0.0963177\pi$
$20$	−1.58749	−	1.57476i	−0.354973	−	0.352128i
$21$	3.71825	−	3.22189i	0.811390	−	0.703073i
$22$	0.530750	+	0.530750i	0.113156	+	0.113156i
$23$	1.94164	−	4.38521i	0.404860	−	0.914379i
$23$	1.94164	−	4.38521i	0.404860	−	0.914379i
$24$		−	1.00000i		−	0.204124i
$25$	1.44723	+	4.78597i	0.289446	+	0.957194i
$26$	5.33069	+	3.42583i	1.04543	+	0.671860i
$27$	0.599278	+	0.800541i	0.115331	+	0.154064i
$28$	1.71935	+	4.60975i	0.324926	+	0.871161i
$29$	−6.83863	+	0.983246i	−1.26990	+	0.182584i	−0.744126	−	0.668039i	$-0.767134\pi$
$29$	−6.83863	+	0.983246i	−1.26990	+	0.182584i	−0.525775	+	0.850623i	$0.676225\pi$
$30$	−1.06373	+	1.96685i	−0.194209	+	0.359095i
$31$	6.38294	−	4.10207i	1.14641	−	0.736753i	0.177489	−	0.984123i	$-0.443202\pi$
$31$	6.38294	−	4.10207i	1.14641	−	0.736753i	0.968921	+	0.247369i	$0.0795661\pi$
$32$	0.936950	+	0.349464i	0.165631	+	0.0617771i
$33$	0.359721	−	0.658781i	0.0626195	−	0.114679i
$34$	0.916793	−	1.05804i	0.157229	−	0.181452i
$35$	1.52182	−	10.8956i	0.257235	−	1.84169i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	1.34936	−	3.61778i	0.221834	−	0.594759i	−0.777587	−	0.628775i	$-0.783557\pi$
$37$	1.34936	−	3.61778i	0.221834	−	0.594759i	0.999421	+	0.0340153i	$0.0108295\pi$
$38$	0.798335	−	3.66989i	0.129507	−	0.595334i
$39$	1.78523	−	6.07993i	0.285865	−	0.973568i
$40$	−1.47110	−	1.68400i	−0.232602	−	0.266264i
$41$	−0.469073	+	1.02713i	−0.0732568	+	0.160410i	−0.942718	−	0.333592i	$-0.891739\pi$
$41$	−0.469073	+	1.02713i	−0.0732568	+	0.160410i	0.869461	+	0.494002i	$0.164466\pi$
$42$	3.93863	−	2.94842i	0.607743	−	0.454951i
$43$	−2.55221	+	0.555199i	−0.389208	+	0.0846670i	−0.402911	−	0.915239i	$-0.632002\pi$
$43$	−2.55221	+	0.555199i	−0.389208	+	0.0846670i	0.0137032	+	0.999906i	$0.495638\pi$
$44$	0.491535	+	0.567261i	0.0741016	+	0.0855178i
$45$	2.18686	+	0.466514i	0.325998	+	0.0695438i
$46$	2.24953	−	4.23552i	0.331675	−	0.624493i
$47$	−8.63275	+	8.63275i	−1.25922	+	1.25922i	−0.307748	+	0.951468i	$0.599575\pi$
$47$	−8.63275	+	8.63275i	−1.25922	+	1.25922i	−0.951468	+	0.307748i	$0.900425\pi$
$48$	0.0713392	−	0.997452i	0.0102969	−	0.143970i
$49$	−9.30224	+	14.4746i	−1.32889	+	2.06780i
$50$	1.10211	+	4.87702i	0.155863	+	0.689715i
$51$	−1.27347	−	0.581573i	−0.178321	−	0.0814366i
$52$	5.07271	+	3.79739i	0.703459	+	0.526603i
$53$	9.22729	−	5.03848i	1.26747	−	0.692088i	0.302171	−	0.953254i	$-0.402289\pi$
$53$	9.22729	−	5.03848i	1.26747	−	0.692088i	0.965294	+	0.261165i	$0.0841068\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	−0.363362	−	1.63857i	−0.0489957	−	0.220945i
$56$	1.38611	+	4.72066i	0.185227	+	0.630825i
$57$	−3.74615	+	0.267930i	−0.496189	+	0.0354882i
$58$	−6.89135	+	0.492879i	−0.904878	+	0.0647182i
$59$	1.73187	+	5.89822i	0.225471	+	0.767883i	0.992062	+	0.125748i	$0.0401331\pi$
$59$	1.73187	+	5.89822i	0.225471	+	0.767883i	−0.766591	+	0.642135i	$0.778049\pi$
$60$	−1.20133	+	1.88595i	−0.155091	+	0.243475i
$61$	−0.0184279	−	0.0286744i	−0.00235946	−	0.00367138i	0.840072	−	0.542475i	$-0.182513\pi$
$61$	−0.0184279	−	0.0286744i	−0.00235946	−	0.00367138i	−0.842431	+	0.538804i	$0.818876\pi$
$62$	6.65932	−	3.63626i	0.845734	−	0.461806i
$63$	−3.93863	−	2.94842i	−0.496220	−	0.371466i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	−5.93787	−	12.8649i	−0.736502	−	1.59569i
$66$	0.405802	−	0.631440i	0.0499507	−	0.0777249i
$67$	0.540569	−	7.55814i	0.0660410	−	0.923374i	−0.851149	−	0.524924i	$-0.824094\pi$
$67$	0.540569	−	7.55814i	0.0660410	−	0.923374i	0.917190	−	0.398450i	$-0.130452\pi$
$68$	0.989936	−	0.989936i	0.120047	−	0.120047i
$69$	−4.69772	−	0.965123i	−0.565539	−	0.116187i
$70$	2.29523	−	10.7593i	0.274332	−	1.28598i
$71$	2.93682	+	3.38928i	0.348537	+	0.402233i	0.902767	−	0.430131i	$-0.141533\pi$
$71$	2.93682	+	3.38928i	0.348537	+	0.402233i	−0.554230	+	0.832364i	$0.686987\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	−7.74782	+	5.79995i	−0.906814	+	0.678832i	−0.947300	−	0.320348i	$-0.896200\pi$
$73$	−7.74782	+	5.79995i	−0.906814	+	0.678832i	0.0404861	+	0.999180i	$0.487109\pi$
$74$	1.60401	−	3.51230i	0.186463	−	0.408297i
$75$	4.36897	−	2.43149i	0.504485	−	0.280764i
$76$	1.05811	−	3.60358i	0.121373	−	0.413359i
$77$	−0.784980	+	3.60850i	−0.0894568	+	0.411226i
$78$	2.21442	−	5.93708i	0.250733	−	0.672242i
$79$	−11.4802	+	3.37088i	−1.29162	+	0.379254i	−0.854173	−	0.519989i	$-0.825936\pi$
$79$	−11.4802	+	3.37088i	−1.29162	+	0.379254i	−0.437448	+	0.899244i	$0.644118\pi$
$80$	−1.34722	−	1.78466i	−0.150624	−	0.199531i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−0.541152	+	0.991045i	−0.0597602	+	0.109443i
$83$	−0.379967	−	0.141720i	−0.0417068	−	0.0155558i	0.328524	−	0.944496i	$-0.393449\pi$
$83$	−0.379967	−	0.141720i	−0.0417068	−	0.0155558i	−0.370231	+	0.928940i	$0.620721\pi$
$84$	4.13893	−	2.65993i	0.451594	−	0.290222i
$85$	−3.00007	+	0.894031i	−0.325404	+	0.0969713i
$86$	−2.58531	+	0.371712i	−0.278781	+	0.0400827i
$87$	2.41443	+	6.47334i	0.258854	+	0.694015i
$88$	0.449814	+	0.600882i	0.0479504	+	0.0640542i
$89$	10.9546	+	7.04011i	1.16119	+	0.746250i	0.971836	−	0.235659i	$-0.0757249\pi$
$89$	10.9546	+	7.04011i	1.16119	+	0.746250i	0.189352	+	0.981909i	$0.439361\pi$
$90$	2.14801	+	0.621334i	0.226420	+	0.0654944i
$91$			31.1758i			3.26811i
$92$	2.54596	−	4.06425i	0.265434	−	0.423727i
$93$	−5.36512	−	5.36512i	−0.556337	−	0.556337i
$94$	−9.22661	+	7.99490i	−0.951652	+	0.824611i
$95$	−5.91437	+	5.96216i	−0.606801	+	0.611705i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−2.96757	+	1.10685i	−0.301311	+	0.112383i	−0.495572	−	0.868567i	$-0.665042\pi$
$97$	−2.96757	+	1.10685i	−0.301311	+	0.112383i	0.194262	+	0.980950i	$0.437769\pi$
$98$	−10.3111	+	13.7741i	−1.04158	+	1.39139i
$99$	−0.720190	−	0.211467i	−0.0723818	−	0.0212532i
$100$	0.751384	+	4.94322i	0.0751384	+	0.494322i
$101$	1.39059	+	3.04497i	0.138369	+	0.302986i	0.966113	−	0.258120i	$-0.0831031\pi$
$101$	1.39059	+	3.04497i	0.138369	+	0.302986i	−0.827744	+	0.561106i	$0.810376\pi$
$102$	−1.22873	−	0.670940i	−0.121663	−	0.0664329i
$103$	−0.903417	−	12.6314i	−0.0890163	−	1.24461i	−0.824025	−	0.566553i	$-0.808277\pi$
$103$	−0.903417	−	12.6314i	−0.0890163	−	1.24461i	0.735009	−	0.678057i	$-0.237178\pi$
$104$	4.78889	+	4.14959i	0.469589	+	0.406901i
$105$	−10.9701	+	0.828981i	−1.07057	+	0.0809002i
$106$	9.56322	−	4.36737i	0.928862	−	0.424197i
$107$	−12.7799	−	2.78010i	−1.23548	−	0.268763i	−0.453043	−	0.891489i	$-0.649661\pi$
$107$	−12.7799	−	2.78010i	−1.23548	−	0.268763i	−0.782440	+	0.622726i	$0.786025\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	0.234240	+	1.62918i	0.0224361	+	0.156047i	0.997960	−	0.0638487i	$-0.0203375\pi$
$109$	0.234240	+	1.62918i	0.0224361	+	0.156047i	−0.975523	+	0.219895i	$0.929428\pi$
$110$	−0.245542	−	1.66032i	−0.0234115	−	0.158305i
$111$	−3.82193	−	0.549511i	−0.362762	−	0.0521572i
$112$	1.04581	+	4.80752i	0.0988199	+	0.454268i
$113$	−4.95942	−	0.354705i	−0.466543	−	0.0333678i	−0.163911	−	0.986475i	$-0.552411\pi$
$113$	−4.95942	−	0.354705i	−0.466543	−	0.0333678i	−0.302632	+	0.953107i	$0.597865\pi$
$114$	−3.75572			−0.351755
$115$	−9.33075	+	5.28555i	−0.870097	+	0.492880i
$116$	−6.90895			−0.641480
$117$	−6.32046	−	0.452048i	−0.584327	−	0.0417919i
$118$	1.30669	+	6.00675i	0.120290	+	0.552966i
$119$	6.81774	+	0.980243i	0.624981	+	0.0898587i
$120$	−1.33281	+	1.79544i	−0.121668	+	0.163901i
$121$	−1.48528	−	10.3304i	−0.135026	−	0.939125i
$122$	−0.0163354	−	0.0299160i	−0.00147894	−	0.00270847i
$123$	1.10336	+	0.240022i	0.0994867	+	0.0216420i
$124$	6.90176	−	3.15193i	0.619796	−	0.283051i
$125$	3.78038	−	10.5218i	0.338127	−	0.941100i
$126$	−3.71825	−	3.22189i	−0.331248	−	0.287028i
$127$	−0.798904	−	11.1701i	−0.0708913	−	0.991190i	−0.901065	−	0.433685i	$-0.857213\pi$
$127$	−0.798904	−	11.1701i	−0.0708913	−	0.991190i	0.830173	−	0.557505i	$-0.188241\pi$
$128$	0.877679	+	0.479249i	0.0775766	+	0.0423600i
$129$	1.08502	+	2.37586i	0.0955308	+	0.209183i
$130$	−5.00497	−	13.2557i	−0.438965	−	1.16260i
$131$	−0.777663	−	0.228343i	−0.0679448	−	0.0199504i	0.247584	−	0.968867i	$-0.420364\pi$
$131$	−0.777663	−	0.228343i	−0.0679448	−	0.0199504i	−0.315528	+	0.948916i	$0.602182\pi$
$132$	0.449814	−	0.600882i	0.0391513	−	0.0523000i
$133$	17.3129	−	6.45739i	1.50122	−	0.559926i
$134$	1.07838	−	7.50032i	0.0931581	−	0.647929i
$135$	−0.00899852	−	2.23605i	−0.000774470	−	0.192449i
$136$	1.05804	−	0.916793i	0.0907258	−	0.0786143i
$137$	−5.44313	−	5.44313i	−0.465038	−	0.465038i	0.435265	−	0.900302i	$-0.356655\pi$
$137$	−5.44313	−	5.44313i	−0.465038	−	0.465038i	−0.900302	+	0.435265i	$0.856655\pi$
$138$	−4.61690	−	1.29780i	−0.393016	−	0.110476i
$139$		−	0.149384i		−	0.0126706i	−0.999980	−	0.00633530i	$-0.997983\pi$
$139$		−	0.149384i		−	0.0126706i	0.999980	−	0.00633530i	$-0.00201660\pi$
$140$	3.05694	−	10.5681i	0.258358	−	0.893168i
$141$	10.2705	+	6.60044i	0.864931	+	0.555858i
$142$	2.68755	+	3.59015i	0.225535	+	0.301279i
$143$	1.66213	+	4.45634i	0.138994	+	0.372658i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	13.5888	+	7.34924i	1.12849	+	0.610321i
$146$	−8.14184	+	5.23245i	−0.673824	+	0.433040i
$147$	16.1211	+	6.01287i	1.32965	+	0.495933i
$148$	1.85049	−	3.38892i	0.152109	−	0.278568i
$149$	8.99761	−	10.3838i	0.737113	−	0.850674i	−0.256140	−	0.966640i	$-0.582451\pi$
$149$	8.99761	−	10.3838i	0.737113	−	0.850674i	0.993253	+	0.115966i	$0.0369964\pi$
$150$	4.53130	−	2.11361i	0.369979	−	0.172576i
$151$	−18.4094	+	5.40549i	−1.49814	+	0.439892i	−0.925127	−	0.379657i	$-0.876042\pi$
$151$	−18.4094	+	5.40549i	−1.49814	+	0.439892i	−0.573008	+	0.819550i	$0.694224\pi$
$152$	1.31249	−	3.51892i	0.106457	−	0.285422i
$153$	−0.297587	+	1.36799i	−0.0240585	+	0.110595i
$154$	−1.04041	+	3.54330i	−0.0838384	+	0.285527i
$155$	−16.9275	−	1.14223i	−1.35965	−	0.0917460i
$156$	2.63232	−	5.76398i	0.210754	−	0.461488i
$157$	3.71894	−	2.78397i	0.296804	−	0.222185i	−0.440489	−	0.897758i	$-0.645195\pi$
$157$	3.71894	−	2.78397i	0.296804	−	0.222185i	0.737293	+	0.675573i	$0.236104\pi$
$158$	−11.6914	+	2.54331i	−0.930118	+	0.202335i
$159$	−6.88473	−	7.94541i	−0.545995	−	0.630112i
$160$	−1.21647	−	1.87622i	−0.0961704	−	0.148328i
$161$	23.5141	−	1.95554i	1.85317	−	0.154118i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	0.819633	−	11.4600i	0.0641986	−	0.897614i	−0.858677	−	0.512516i	$-0.828713\pi$
$163$	0.819633	−	11.4600i	0.0641986	−	0.897614i	0.922876	−	0.385097i	$-0.125832\pi$
$164$	−0.610473	+	0.949915i	−0.0476700	+	0.0741759i
$165$	−1.52389	+	0.703362i	−0.118635	+	0.0547567i
$166$	−0.368889	−	0.168466i	−0.0286313	−	0.0130755i
$167$	−12.0130	−	8.99282i	−0.929594	−	0.695886i	0.0231265	−	0.999733i	$-0.492638\pi$
$167$	−12.0130	−	8.99282i	−0.929594	−	0.695886i	−0.952721	+	0.303847i	$0.901729\pi$
$168$	4.31814	−	2.35788i	0.333152	−	0.181915i
$169$	14.6798	+	22.8422i	1.12921	+	1.75709i
$170$	−3.05621	+	0.677730i	−0.234401	+	0.0519795i
$171$	1.05811	+	3.60358i	0.0809155	+	0.275573i
$172$	−2.60524	+	0.186331i	−0.198648	+	0.0142076i
$173$	−7.34793	+	0.525534i	−0.558653	+	0.0399556i	−0.347811	−	0.937565i	$-0.613075\pi$
$173$	−7.34793	+	0.525534i	−0.558653	+	0.0399556i	−0.210842	+	0.977520i	$0.567620\pi$
$174$	1.94648	+	6.62909i	0.147562	+	0.502550i
$175$	−17.2541	+	17.5341i	−1.30429	+	1.32545i
$176$	0.405802	+	0.631440i	0.0305885	+	0.0475966i
$177$	5.39529	−	2.94605i	0.405535	−	0.221439i
$178$	10.4245	+	7.80367i	0.781348	+	0.584910i
$179$	−14.4095	−	6.58058i	−1.07701	−	0.491856i	−0.203710	−	0.979031i	$-0.565300\pi$
$179$	−14.4095	−	6.58058i	−1.07701	−	0.491856i	−0.873304	+	0.487175i	$0.838027\pi$
$180$	2.09821	+	0.772988i	0.156391	+	0.0576151i
$181$	13.4906	−	20.9918i	1.00275	−	1.56031i	0.186626	−	0.982431i	$-0.440245\pi$
$181$	13.4906	−	20.9918i	1.00275	−	1.56031i	0.816123	−	0.577878i	$-0.196119\pi$
$182$	−2.22406	+	31.0964i	−0.164858	+	2.30502i
$183$	−0.0241020	+	0.0241020i	−0.00178167	+	0.00178167i
$184$	2.82941	−	3.87227i	0.208587	−	0.285467i
$185$	−7.24452	+	4.69707i	−0.532628	+	0.345336i
$186$	−4.96870	−	5.73419i	−0.364323	−	0.420451i
$187$	1.02680	−	0.223367i	0.0750873	−	0.0163342i
$188$	−9.77345	+	7.31631i	−0.712802	+	0.533597i
$189$	−2.04382	+	4.47535i	−0.148666	+	0.325534i
$190$	−6.32463	+	5.52504i	−0.458837	+	0.400829i
$191$	4.29162	−	14.6159i	0.310530	−	1.05757i	−0.645368	−	0.763872i	$-0.723296\pi$
$191$	4.29162	−	14.6159i	0.310530	−	1.05757i	0.955898	−	0.293698i	$-0.0948859\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	−3.76392	+	10.0915i	−0.270933	+	0.726400i	0.728223	+	0.685340i	$0.240346\pi$
$193$	−3.76392	+	10.0915i	−0.270933	+	0.726400i	−0.999157	+	0.0410603i	$0.986926\pi$
$194$	−3.03897	+	0.892321i	−0.218185	+	0.0640649i
$195$	−11.3087	+	8.53679i	−0.809831	+	0.611332i
$196$	−11.2675	+	13.0034i	−0.804822	+	0.928814i
$197$	7.85260	−	14.3810i	0.559475	−	1.02460i	−0.432911	−	0.901436i	$-0.642514\pi$
$197$	7.85260	−	14.3810i	0.559475	−	1.02460i	0.992386	−	0.123165i	$-0.0393045\pi$
$198$	−0.703269	−	0.262306i	−0.0499791	−	0.0186413i
$199$	−20.5702	+	13.2196i	−1.45818	+	0.937116i	−0.459376	+	0.888242i	$0.651927\pi$
$199$	−20.5702	+	13.2196i	−1.45818	+	0.937116i	−0.998805	+	0.0488743i	$0.984437\pi$
$200$	0.396824	+	4.98423i	0.0280597	+	0.352438i
$201$	−7.50032	+	1.07838i	−0.529032	+	0.0760633i
$202$	1.16982	+	3.13642i	0.0823085	+	0.220678i
$203$	−20.3705	−	27.2118i	−1.42973	−	1.90989i
$204$	−1.17774	−	0.756887i	−0.0824582	−	0.0529927i
$205$	2.21116	−	1.21896i	0.154434	−	0.0851359i
$206$		−	12.6637i		−	0.882320i
$207$	0.0555044	+	4.79551i	0.00385782	+	0.333311i
$208$	4.48066	+	4.48066i	0.310678	+	0.310678i
$209$	2.13047	−	1.84607i	0.147368	−	0.127695i
$210$	−11.0013	+	0.0442723i	−0.759159	+	0.00305508i
$211$	−0.683538	+	4.75411i	−0.0470567	+	0.327287i	0.952672	+	0.304000i	$0.0983222\pi$
$211$	−0.683538	+	4.75411i	−0.0470567	+	0.327287i	−0.999729	+	0.0232869i	$0.992587\pi$
$212$	9.85042	−	3.67402i	0.676529	−	0.252332i
$213$	2.68755	−	3.59015i	0.184148	−	0.245993i
$214$	−12.5490	−	3.68473i	−0.857835	−	0.251883i
$215$	5.32232	+	2.40478i	0.362979	+	0.164005i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	32.7635	+	17.8903i	2.22413	+	1.21447i
$218$	0.117419	+	1.64173i	0.00795263	+	0.111192i
$219$	7.31432	+	6.33789i	0.494256	+	0.428275i
$220$	−0.126470	−	1.67361i	−0.00852662	−	0.112835i
$221$	8.06946	−	3.68520i	0.542811	−	0.247893i
$222$	−3.77299	−	0.820764i	−0.253227	−	0.0550861i
$223$	5.54810	+	10.1606i	0.371528	+	0.680403i	0.994827	−	0.101580i	$-0.0323899\pi$
$223$	5.54810	+	10.1606i	0.371528	+	0.680403i	−0.623299	+	0.781984i	$0.714208\pi$
$224$	0.700183	+	4.86988i	0.0467829	+	0.325382i
$225$	−3.30461	−	3.75227i	−0.220307	−	0.250151i
$226$	−4.92148	−	0.707602i	−0.327372	−	0.0470690i
$227$	2.20080	+	10.1169i	0.146072	+	0.671482i	0.990693	+	0.136117i	$0.0434623\pi$
$227$	2.20080	+	10.1169i	0.146072	+	0.671482i	−0.844621	+	0.535365i	$0.820174\pi$
$228$	−3.74615	−	0.267930i	−0.248095	−	0.0177441i
$229$	−21.3745			−1.41247			−0.706234	−	0.707978i	$-0.749607\pi$
$229$	−21.3745			−1.41247			−0.706234	+	0.707978i	$0.749607\pi$
$230$	−9.68405	+	4.60644i	−0.638547	+	0.303739i
$231$	3.69289			0.242974
$232$	−6.89135	−	0.492879i	−0.452439	−	0.0323591i
$233$	−3.75734	−	17.2722i	−0.246152	−	1.13154i	−0.919769	−	0.392461i	$-0.871624\pi$
$233$	−3.75734	−	17.2722i	−0.246152	−	1.13154i	0.673617	−	0.739081i	$-0.264740\pi$
$234$	−6.27211	−	0.901793i	−0.410020	−	0.0589520i
$235$	27.0054	−	3.99378i	1.76164	−	0.260526i
$236$	0.874842	+	6.08466i	0.0569474	+	0.396078i
$237$	5.73414	+	10.5013i	0.372472	+	0.682132i
$238$	6.73044	+	1.46412i	0.436269	+	0.0949046i
$239$	−13.0099	+	5.94141i	−0.841539	+	0.384318i	−0.789069	−	0.614305i	$-0.789437\pi$
$239$	−13.0099	+	5.94141i	−0.841539	+	0.384318i	−0.0524698	+	0.998623i	$0.516709\pi$
$240$	−1.45750	+	1.69579i	−0.0940813	+	0.109463i
$241$	−13.1576	−	11.4011i	−0.847553	−	0.734409i	0.118444	−	0.992961i	$-0.462209\pi$
$241$	−13.1576	−	11.4011i	−0.847553	−	0.734409i	−0.965997	+	0.258551i	$0.916755\pi$
$242$	−0.744539	−	10.4100i	−0.0478608	−	0.669181i
$243$	−0.877679	−	0.479249i	−0.0563031	−	0.0307438i
$244$	−0.0141596	−	0.0310051i	−0.000906473	−	0.00198490i
$245$	35.9935	−	13.5901i	2.29954	−	0.868242i
$246$	1.08343	+	0.318123i	0.0690768	+	0.0202828i
$247$	14.2619	−	19.0517i	0.907463	−	1.21223i
$248$	7.10903	−	2.65153i	0.451424	−	0.168372i
$249$	−0.0577138	+	0.401408i	−0.00365746	+	0.0254382i
$250$	4.52137	−	10.2253i	0.285956	−	0.646706i
$251$	−11.8975	+	10.3093i	−0.750965	+	0.650715i	−0.943800	−	0.330516i	$-0.892777\pi$
$251$	−11.8975	+	10.3093i	−0.750965	+	0.650715i	0.192835	+	0.981231i	$0.438232\pi$
$252$	−3.47893	−	3.47893i	−0.219152	−	0.219152i
$253$	3.25690	−	1.53318i	0.204759	−	0.0963899i
$254$		−	11.1987i		−	0.702667i
$255$	1.51131	+	2.74147i	0.0946420	+	0.171678i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−2.85577	−	3.81487i	−0.178138	−	0.237965i	0.702581	−	0.711604i	$-0.252031\pi$
$257$	−2.85577	−	3.81487i	−0.178138	−	0.237965i	−0.880719	+	0.473639i	$0.842940\pi$
$258$	0.912764	+	2.44722i	0.0568262	+	0.152357i
$259$	18.8037	−	2.70357i	1.16841	−	0.167992i
$260$	−4.04657	−	13.5790i	−0.250958	−	0.842131i
$261$	5.81218	−	3.73526i	0.359765	−	0.231207i
$262$	−0.759392	−	0.283239i	−0.0469154	−	0.0174985i
$263$	−2.37823	+	4.35541i	−0.146648	+	0.268566i	−0.940670	−	0.339324i	$-0.889802\pi$
$263$	−2.37823	+	4.35541i	−0.146648	+	0.268566i	0.794022	+	0.607890i	$0.207984\pi$
$264$	0.491535	−	0.567261i	0.0302519	−	0.0349125i
$265$	−23.2824	−	3.25193i	−1.43023	−	0.199764i
$266$	17.7295	−	5.20584i	1.08706	−	0.319191i
$267$	4.55065	−	12.2008i	0.278495	−	0.746674i
$268$	1.61070	−	7.40428i	0.0983893	−	0.452288i
$269$	−3.22334	+	10.9777i	−0.196530	+	0.669321i	0.800973	+	0.598701i	$0.204316\pi$
$269$	−3.22334	+	10.9777i	−0.196530	+	0.669321i	−0.997503	+	0.0706205i	$0.977502\pi$
$270$	0.150542	−	2.23099i	0.00916172	−	0.135774i
$271$	0.0408956	−	0.0895489i	0.00248423	−	0.00543971i	−0.908386	−	0.418133i	$-0.862685\pi$
$271$	0.0408956	−	0.0895489i	0.00248423	−	0.00543971i	0.910870	+	0.412693i	$0.135412\pi$
$272$	1.12074	−	0.838978i	0.0679550	−	0.0508705i
$273$	30.4633	−	6.62690i	1.84373	−	0.401078i
$274$	−5.04095	−	5.81757i	−0.304535	−	0.351452i
$275$	−1.53151	+	3.42626i	−0.0923538	+	0.206611i
$276$	−4.51255	−	1.62385i	−0.271624	−	0.0977445i
$277$	1.92518	−	1.92518i	0.115673	−	0.115673i	−0.646901	−	0.762574i	$-0.723935\pi$
$277$	1.92518	−	1.92518i	0.115673	−	0.115673i	0.762574	+	0.646901i	$0.223935\pi$
$278$	0.0106569	−	0.149004i	0.000639161	−	0.00893664i
$279$	−4.10207	+	6.38294i	−0.245584	+	0.382137i
$280$	3.80307	−	10.3231i	0.227277	−	0.616923i
$281$	9.63694	+	4.40104i	0.574892	+	0.262544i	0.681574	−	0.731749i	$-0.261296\pi$
$281$	9.63694	+	4.40104i	0.574892	+	0.262544i	−0.106683	+	0.994293i	$0.534023\pi$
$282$	9.77345	+	7.31631i	0.582001	+	0.435680i
$283$	3.08610	−	1.68514i	0.183450	−	0.100171i	−0.384900	−	0.922958i	$-0.625764\pi$
$283$	3.08610	−	1.68514i	0.183450	−	0.100171i	0.568349	+	0.822787i	$0.307582\pi$
$284$	2.42459	+	3.77273i	0.143873	+	0.223870i
$285$	7.08309	+	4.51186i	0.419566	+	0.267259i
$286$	1.33998	+	4.56356i	0.0792348	+	0.269849i
$287$	−5.54129	+	0.396321i	−0.327092	+	0.0233941i
$288$	−0.997452	+	0.0713392i	−0.0587754	+	0.00420370i
$289$	4.23727	+	14.4308i	0.249251	+	0.848872i
$290$	13.0299	+	8.29993i	0.765144	+	0.487389i
$291$	1.71235	+	2.66447i	0.100380	+	0.156194i
$292$	−8.49438	+	4.63828i	−0.497096	+	0.271435i
$293$	20.2558	+	15.1633i	1.18336	+	0.885849i	0.995351	−	0.0963189i	$-0.0307068\pi$
$293$	20.2558	+	15.1633i	1.18336	+	0.885849i	0.188005	+	0.982168i	$0.439798\pi$
$294$	15.6511	+	7.14761i	0.912790	+	0.416857i
$295$	4.75173	−	12.8982i	0.276657	−	0.750961i
$296$	2.08754	−	3.24828i	0.121336	−	0.188802i
$297$	−0.0535468	+	0.748682i	−0.00310710	+	0.0434429i
$298$	9.71546	−	9.71546i	0.562801	−	0.562801i
$299$	24.1155	−	18.4920i	1.39463	−	1.06942i
$300$	4.67053	−	1.78497i	0.269653	−	0.103055i
$301$	−8.41523	−	9.71170i	−0.485046	−	0.559773i
$302$	−18.7481	+	4.07840i	−1.07883	+	0.234686i
$303$	2.67979	−	2.00607i	0.153950	−	0.115246i
$304$	1.56018	−	3.41632i	0.0894825	−	0.195939i
$305$	−0.00513129	+	0.0760442i	−0.000293817	+	0.00435428i
$306$	−0.394420	+	1.34327i	−0.0225475	+	0.0767898i
$307$	1.19711	−	5.50300i	0.0683224	−	0.314073i	−0.930285	−	0.366839i	$-0.880440\pi$
$307$	1.19711	−	5.50300i	0.0683224	−	0.314073i	0.998607	+	0.0527658i	$0.0168037\pi$
$308$	−1.29053	+	3.46005i	−0.0735349	+	0.197155i
$309$	−12.1507	+	3.56777i	−0.691230	+	0.202963i
$310$	−16.8029	−	2.34691i	−0.954339	−	0.133296i
$311$	−5.40438	+	6.23699i	−0.306454	+	0.353667i	−0.887997	−	0.459848i	$-0.847904\pi$
$311$	−5.40438	+	6.23699i	−0.306454	+	0.353667i	0.581543	+	0.813516i	$0.302449\pi$
$312$	3.03681	−	5.56150i	0.171926	−	0.314858i
$313$	−10.0631	−	3.75335i	−0.568802	−	0.212152i	0.0485754	−	0.998820i	$-0.484532\pi$
$313$	−10.0631	−	3.75335i	−0.568802	−	0.212152i	−0.617377	+	0.786668i	$0.711805\pi$
$314$	3.90807	−	2.51157i	0.220545	−	0.141736i
$315$	3.14189	+	10.5432i	0.177026	+	0.594040i
$316$	−11.8431	+	1.70277i	−0.666224	+	0.0957885i
$317$	1.92705	+	5.16661i	0.108234	+	0.290186i	0.979764	−	0.200156i	$-0.0641448\pi$
$317$	1.92705	+	5.16661i	0.108234	+	0.290186i	−0.871530	+	0.490342i	$0.836872\pi$
$318$	−6.30037	−	8.41632i	−0.353307	−	0.471964i
$319$	−4.36259	−	2.80367i	−0.244258	−	0.156975i
$320$	−1.07952	−	1.95822i	−0.0603471	−	0.109468i
$321$			13.0788i			0.729989i
$322$	23.5937	−	0.273079i	1.31483	−	0.0152181i
$323$	−3.71792	−	3.71792i	−0.206871	−	0.206871i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	−6.48532	+	31.0122i	−0.359741	+	1.72025i
$326$	1.63509	−	11.3723i	0.0905592	−	0.629853i
$327$	1.54215	−	0.575193i	0.0852812	−	0.0318082i
$328$	−0.676684	+	0.903944i	−0.0373636	+	0.0499120i
$329$	−57.6325	−	16.9224i	−3.17738	−	0.932963i
$330$	−1.57018	+	0.592857i	−0.0864358	+	0.0326357i
$331$	2.21340	+	4.84666i	0.121659	+	0.266397i	0.960657	−	0.277739i	$-0.0895850\pi$
$331$	2.21340	+	4.84666i	0.121659	+	0.266397i	−0.838997	+	0.544136i	$0.816858\pi$
$332$	−0.355931	−	0.194353i	−0.0195342	−	0.0106665i
$333$	0.275457	+	3.85139i	0.0150950	+	0.211055i
$334$	−11.3409	−	9.82691i	−0.620544	−	0.537705i
$335$	−11.0441	+	12.8497i	−0.603406	+	0.702056i
$336$	4.47535	−	2.04382i	0.244150	−	0.111500i
$337$	9.65584	+	2.10050i	0.525987	+	0.114422i	0.467715	−	0.883879i	$-0.345077\pi$
$337$	9.65584	+	2.10050i	0.525987	+	0.114422i	0.0582720	+	0.998301i	$0.481441\pi$
$338$	13.0128	+	23.8312i	0.707805	+	1.29625i
$339$	0.707602	+	4.92148i	0.0384317	+	0.267298i
$340$	−3.09677	+	0.457976i	−0.167946	+	0.0248372i
$341$	5.63710	+	0.810493i	0.305266	+	0.0438907i
$342$	0.798335	+	3.66989i	0.0431690	+	0.198445i
$343$	−50.0849	−	3.58214i	−2.70433	−	0.193418i
$344$	−2.61190			−0.140824
$345$	7.14815	+	7.99399i	0.384844	+	0.430382i
$346$	−7.36670			−0.396036
$347$	35.9704	+	2.57265i	1.93099	+	0.138107i	0.983409	−	0.181405i	$-0.0580644\pi$
$347$	35.9704	+	2.57265i	1.93099	+	0.138107i	0.947582	+	0.319512i	$0.103519\pi$
$348$	1.46860	+	6.75106i	0.0787254	+	0.361895i
$349$	22.7925	+	3.27706i	1.22005	+	0.175417i	0.722101	−	0.691787i	$-0.243176\pi$
$349$	22.7925	+	3.27706i	1.22005	+	0.175417i	0.497952	+	0.867204i	$0.334085\pi$
$350$	−18.4610	+	16.2585i	−0.986783	+	0.869055i
$351$	0.901793	+	6.27211i	0.0481341	+	0.334780i
$352$	0.359721	+	0.658781i	0.0191732	+	0.0351131i
$353$	28.2864	+	6.15333i	1.50553	+	0.327508i	0.888297	−	0.459270i	$-0.151889\pi$
$353$	28.2864	+	6.15333i	1.50553	+	0.327508i	0.617235	+	0.786778i	$0.288253\pi$
$354$	5.59172	−	2.55365i	0.297196	−	0.135725i
$355$	−0.755636	−	9.99948i	−0.0401050	−	0.530718i
$356$	9.84121	+	8.52746i	0.521583	+	0.451954i
$357$	−0.491373	−	6.87030i	−0.0260062	−	0.363615i
$358$	−13.9033	−	7.59178i	−0.734812	−	0.401238i
$359$	−5.12912	−	11.2312i	−0.270704	−	0.592760i	0.724642	−	0.689126i	$-0.242005\pi$
$359$	−5.12912	−	11.2312i	−0.270704	−	0.592760i	−0.995346	+	0.0963661i	$0.969278\pi$
$360$	2.03772	+	0.920703i	0.107397	+	0.0485253i
$361$	4.69632	+	1.37896i	0.247175	+	0.0725771i
$362$	14.9538	−	19.9759i	0.785953	−	1.04991i
$363$	−9.77858	+	3.64722i	−0.513242	+	0.191429i
$364$	−4.43678	+	30.8585i	−0.232550	+	1.61742i
$365$	21.6410	−	0.0870898i	1.13274	−	0.00455849i
$366$	−0.0257600	+	0.0223212i	−0.00134650	+	0.00116675i
$367$	−19.4385	−	19.4385i	−1.01468	−	1.01468i	−0.999891	−	0.0147888i	$-0.995292\pi$
$367$	−19.4385	−	19.4385i	−1.01468	−	1.01468i	−0.0147888	−	0.999891i	$-0.504708\pi$
$368$	3.09844	−	3.66055i	0.161518	−	0.190819i
$369$		−	1.12917i		−	0.0587820i
$370$	−7.56115	+	4.16829i	−0.393085	+	0.216699i
$371$	43.5137	+	27.9646i	2.25912	+	1.45185i
$372$	−4.54697	−	6.07404i	−0.235749	−	0.314924i
$373$	−4.34306	−	11.6442i	−0.224875	−	0.602913i	0.774692	−	0.632339i	$-0.217905\pi$
$373$	−4.34306	−	11.6442i	−0.224875	−	0.602913i	−0.999567	+	0.0294256i	$0.990632\pi$
$374$	1.04012	−	0.149547i	0.0537834	−	0.00773289i
$375$	−11.0849	−	1.45741i	−0.572424	−	0.0752604i
$376$	−10.2705	+	6.60044i	−0.529660	+	0.340392i
$377$	−41.0190	−	15.2993i	−2.11259	−	0.787954i
$378$	−2.35788	+	4.31814i	−0.121276	+	0.222101i
$379$	22.1103	−	25.5167i	1.13573	−	1.31070i	0.191472	−	0.981498i	$-0.438674\pi$
$379$	22.1103	−	25.5167i	1.13573	−	1.31070i	0.944258	−	0.329205i	$-0.106781\pi$
$380$	−6.70267	+	5.05977i	−0.343840	+	0.259561i
$381$	−10.7450	+	3.15503i	−0.550486	+	0.161637i
$382$	5.32337	−	14.2725i	0.272367	−	0.730245i
$383$	−5.53752	+	25.4556i	−0.282954	+	1.30072i	0.587803	+	0.809004i	$0.299993\pi$
$383$	−5.53752	+	25.4556i	−0.282954	+	1.30072i	−0.870757	+	0.491714i	$0.836371\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	6.21883	−	5.43262i	0.316941	−	0.276872i
$386$	−4.47425	+	9.79725i	−0.227733	+	0.498667i
$387$	2.09093	−	1.56525i	0.106288	−	0.0795662i
$388$	−3.09488	+	0.673250i	−0.157119	+	0.0341791i
$389$	−0.632306	−	0.729720i	−0.0320592	−	0.0369983i	0.739494	−	0.673164i	$-0.235065\pi$
$389$	−0.632306	−	0.729720i	−0.0320592	−	0.0369983i	−0.771553	+	0.636165i	$0.780520\pi$
$390$	−11.8889	+	7.70829i	−0.602016	+	0.390324i
$391$	−3.28570	−	5.85517i	−0.166165	−	0.296109i
$392$	−12.1664	+	12.1664i	−0.614499	+	0.614499i
$393$	−0.0578200	+	0.808429i	−0.00291663	+	0.0407799i
$394$	8.85852	−	13.7841i	0.446286	−	0.694434i
$395$	25.1048	+	9.24868i	1.26316	+	0.465352i
$396$	−0.682764	−	0.311808i	−0.0343102	−	0.0156689i
$397$	7.89714	+	5.91172i	0.396346	+	0.296701i	0.778798	−	0.627274i	$-0.215829\pi$
$397$	7.89714	+	5.91172i	0.396346	+	0.296701i	−0.382452	+	0.923975i	$0.624920\pi$
$398$	−21.4608	+	11.7185i	−1.07573	+	0.587396i
$399$	−9.98994	−	15.5446i	−0.500123	−	0.778206i
$400$	0.0402423	+	4.99984i	0.00201211	+	0.249992i
$401$	6.46808	+	22.0282i	0.323000	+	1.10004i	0.947697	+	0.319171i	$0.103404\pi$
$401$	6.46808	+	22.0282i	0.323000	+	1.10004i	−0.624697	+	0.780867i	$0.714777\pi$
$402$	−7.55814	+	0.540569i	−0.376966	+	0.0269611i
$403$	47.9560	−	3.42988i	2.38886	−	0.170854i
$404$	0.943094	+	3.21188i	0.0469207	+	0.159797i
$405$	−2.18304	+	0.484099i	−0.108476	+	0.0240551i
$406$	−18.3773	−	28.5957i	−0.912051	−	1.41918i
$407$	2.54371	−	1.38897i	0.126087	−	0.0688486i
$408$	−1.12074	−	0.838978i	−0.0554850	−	0.0415356i
$409$	32.3656	+	14.7809i	1.60037	+	0.730867i	0.997743	−	0.0671528i	$-0.0213915\pi$
$409$	32.3656	+	14.7809i	1.60037	+	0.730867i	0.602632	+	0.798019i	$0.294119\pi$
$410$	2.29248	−	1.05811i	0.113218	−	0.0522564i
$411$	−4.16171	+	6.47575i	−0.205282	+	0.319425i
$412$	0.903417	−	12.6314i	0.0445081	−	0.622305i
$413$	−21.3858	+	21.3858i	−1.05233	+	1.05233i
$414$	−0.286745	+	4.78725i	−0.0140927	+	0.235281i
$415$	0.493322	+	0.760875i	0.0242162	+	0.0373499i
$416$	4.14959	+	4.78889i	0.203451	+	0.234794i
$417$	−0.145970	+	0.0317539i	−0.00714820	+	0.00155499i
$418$	2.25674	−	1.68938i	0.110381	−	0.0826300i
$419$	−8.32405	+	18.2271i	−0.406656	+	0.890453i	0.589896	+	0.807480i	$0.299169\pi$
$419$	−8.32405	+	18.2271i	−0.406656	+	0.890453i	−0.996552	+	0.0829734i	$0.973558\pi$
$420$	−10.9764	−	0.740662i	−0.535593	−	0.0361406i
$421$	−8.95419	+	30.4952i	−0.436401	+	1.48624i	0.388756	+	0.921341i	$0.372905\pi$
$421$	−8.95419	+	30.4952i	−0.436401	+	1.48624i	−0.825157	+	0.564904i	$0.808913\pi$
$422$	−1.02095	+	4.69324i	−0.0496991	+	0.228463i
$423$	4.26645	−	11.4388i	0.207442	−	0.556174i
$424$	10.0874	−	2.96193i	0.489888	−	0.143844i
$425$	6.57804	+	2.39335i	0.319082	+	0.116095i
$426$	2.93682	−	3.38928i	0.142290	−	0.164211i
$427$	0.0803693	−	0.147185i	0.00388934	−	0.00712280i
$428$	−12.2542	−	4.57058i	−0.592329	−	0.220927i
$429$	4.00119	−	2.57141i	0.193179	−	0.124149i
$430$	5.13720	+	2.77834i	0.247738	+	0.133984i
$431$	2.41040	−	0.346563i	0.116105	−	0.0166934i	−0.0840174	−	0.996464i	$-0.526775\pi$
$431$	2.41040	−	0.346563i	0.116105	−	0.0166934i	0.200122	+	0.979771i	$0.435866\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	14.8669	+	19.8599i	0.714459	+	0.954406i	0.999992	−	0.00396308i	$-0.00126149\pi$
$433$	14.8669	+	19.8599i	0.714459	+	0.954406i	−0.285533	+	0.958369i	$0.592171\pi$
$434$	31.4038	+	20.1820i	1.50743	+	0.968767i
$435$	4.29277	−	14.8405i	0.205822	−	0.711547i
$436$			1.64593i			0.0788257i
$437$	−15.2642	−	9.56189i	−0.730184	−	0.457407i
$438$	6.84354	+	6.84354i	0.326997	+	0.326997i
$439$	3.49731	−	3.03044i	0.166918	−	0.144635i	−0.567397	−	0.823445i	$-0.692049\pi$
$439$	3.49731	−	3.03044i	0.166918	−	0.144635i	0.734314	+	0.678810i	$0.237504\pi$
$440$	−0.00675424	−	1.67837i	−0.000321996	−	0.0800130i
$441$	2.44866	−	17.0308i	0.116603	−	0.810992i
$442$	8.31180	−	3.10014i	0.395352	−	0.147459i
$443$	7.09989	−	9.48434i	0.337326	−	0.450615i	−0.599519	−	0.800361i	$-0.704641\pi$
$443$	7.09989	−	9.48434i	0.337326	−	0.450615i	0.936844	+	0.349746i	$0.113732\pi$
$444$	−3.70483	−	1.08783i	−0.175823	−	0.0516264i
$445$	−10.2853	−	27.2406i	−0.487568	−	1.29133i
$446$	4.80912	+	10.5305i	0.227718	+	0.498633i
$447$	−12.0591	−	6.58475i	−0.570375	−	0.311448i
$448$	0.350986	+	4.90742i	0.0165825	+	0.231854i
$449$	3.55513	+	3.08054i	0.167777	+	0.145380i	0.734702	−	0.678389i	$-0.237322\pi$
$449$	3.55513	+	3.08054i	0.167777	+	0.145380i	−0.566925	+	0.823769i	$0.691867\pi$
$450$	−3.02851	−	3.97846i	−0.142765	−	0.187546i
$451$	−0.770955	+	0.352083i	−0.0363028	+	0.0165789i
$452$	−4.85846	−	1.05689i	−0.228523	−	0.0497121i
$453$	9.19515	+	16.8397i	0.432026	+	0.791197i
$454$	1.47346	+	10.2481i	0.0691528	+	0.480968i
$455$	41.5515	−	55.9744i	1.94796	−	2.62412i
$456$	−3.71749	−	0.534494i	−0.174087	−	0.0250300i
$457$	−3.88867	−	17.8759i	−0.181904	−	0.836201i	−0.974133	−	0.225976i	$-0.927443\pi$
$457$	−3.88867	−	17.8759i	−0.181904	−	0.836201i	0.792229	−	0.610224i	$-0.208921\pi$
$458$	−21.3201	−	1.52484i	−0.996221	−	0.0712512i
$459$	1.39998			0.0653455
$460$	−9.98799	+	3.90385i	−0.465693	+	0.182018i
$461$	−27.8588			−1.29751			−0.648756	−	0.760996i	$-0.724711\pi$
$461$	−27.8588			−1.29751			−0.648756	+	0.760996i	$0.724711\pi$
$462$	3.68348	+	0.263448i	0.171371	+	0.0122567i
$463$	−6.28766	−	28.9039i	−0.292212	−	1.34328i	−0.855836	−	0.517247i	$-0.826957\pi$
$463$	−6.28766	−	28.9039i	−0.292212	−	1.34328i	0.563624	−	0.826032i	$-0.309407\pi$
$464$	−6.83863	−	0.983246i	−0.317475	−	0.0456461i
$465$	2.48207	+	16.7834i	0.115103	+	0.778314i
$466$	−2.51558	−	17.4963i	−0.116532	−	0.810499i
$467$	−8.25213	−	15.1126i	−0.381863	−	0.699330i	0.614087	−	0.789238i	$-0.289524\pi$
$467$	−8.25213	−	15.1126i	−0.381863	−	0.699330i	−0.995950	+	0.0899086i	$0.971343\pi$
$468$	−6.19179	−	1.34694i	−0.286216	−	0.0622624i
$469$	33.9117	−	15.4870i	1.56590	−	0.715122i
$470$	27.2215	−	2.05706i	1.25564	−	0.0948852i
$471$	−3.51086	−	3.04218i	−0.161772	−	0.140176i
$472$	0.438538	+	6.13157i	0.0201854	+	0.282228i
$473$	−1.72067	−	0.939555i	−0.0791164	−	0.0432008i
$474$	4.97037	+	10.8836i	0.228297	+	0.499900i
$475$	18.5653	−	2.82199i	0.851836	−	0.129482i
$476$	6.60884	+	1.94053i	0.302916	+	0.0889441i
$477$	−6.30037	+	8.41632i	−0.288474	+	0.385357i
$478$	−13.4006	+	4.99816i	−0.612928	+	0.228610i
$479$	−3.77808	+	26.2771i	−0.172625	+	1.20063i	0.700686	+	0.713469i	$0.252877\pi$
$479$	−3.77808	+	26.2771i	−0.172625	+	1.20063i	−0.873311	+	0.487163i	$0.838032\pi$
$480$	−1.57476	+	1.58749i	−0.0718778	+	0.0724586i
$481$	18.4910	−	16.0225i	0.843117	−	0.730565i
$482$	−12.3107	−	12.3107i	−0.560737	−	0.560737i
$483$	−6.90913	−	22.5610i	−0.314376	−	1.02656i
$484$		−	10.4366i		−	0.474391i
$485$	6.80331	+	1.96793i	0.308922	+	0.0893590i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	6.50751	+	8.69302i	0.294884	+	0.393918i	0.923376	−	0.383898i	$-0.125418\pi$
$487$	6.50751	+	8.69302i	0.294884	+	0.393918i	−0.628492	+	0.777816i	$0.716328\pi$
$488$	−0.0119116	−	0.0319363i	−0.000539213	−	0.00144569i
$489$	−11.3723	+	1.63509i	−0.514273	+	0.0739413i
$490$	36.8713	−	10.9878i	1.66568	−	0.496376i
$491$	5.29304	−	3.40163i	0.238871	−	0.153513i	−0.415729	−	0.909489i	$-0.636473\pi$
$491$	5.29304	−	3.40163i	0.238871	−	0.153513i	0.654600	+	0.755975i	$0.272837\pi$
$492$	1.05797	+	0.394603i	0.0476971	+	0.0177901i
$493$	−4.63549	+	8.48927i	−0.208772	+	0.382337i
$494$	15.5847	−	17.9857i	0.701189	−	0.809215i
$495$	1.01121	+	1.33955i	0.0454507	+	0.0602084i
$496$	7.28008	−	2.13762i	0.326885	−	0.0959821i
$497$	−7.71068	+	20.6731i	−0.345871	+	0.927317i
$498$	−0.0862029	+	0.396268i	−0.00386284	+	0.0177572i
$499$	−8.03873	+	27.3774i	−0.359863	+	1.22558i	0.558387	+	0.829580i	$0.311420\pi$
$499$	−8.03873	+	27.3774i	−0.359863	+	1.22558i	−0.918250	+	0.396000i	$0.870398\pi$
$500$	5.23931	−	9.87672i	0.234309	−	0.441700i
$501$	−6.23376	+	13.6500i	−0.278504	+	0.609839i
$502$	−12.6027	+	9.43424i	−0.562485	+	0.421071i
$503$	41.4530	−	9.01756i	1.84830	−	0.402073i	0.855097	−	0.518469i	$-0.173498\pi$
$503$	41.4530	−	9.01756i	1.84830	−	0.402073i	0.993203	+	0.116396i	$0.0371342\pi$
$504$	−3.22189	−	3.71825i	−0.143514	−	0.165624i
$505$	1.56164	−	7.32047i	0.0694923	−	0.325757i
$506$	3.35797	−	1.29692i	0.149280	−	0.0576553i
$507$	19.1998	−	19.1998i	0.852691	−	0.852691i
$508$	0.798904	−	11.1701i	0.0354456	−	0.495595i
$509$	20.6803	−	32.1791i	0.916637	−	1.42632i	0.0120972	−	0.999927i	$-0.496149\pi$
$509$	20.6803	−	32.1791i	0.916637	−	1.42632i	0.904540	−	0.426389i	$-0.140214\pi$
$510$	1.31189	+	2.84230i	0.0580913	+	0.125859i
$511$	−43.3134	−	19.7806i	−1.91607	−	0.875042i
$512$	0.800541	+	0.599278i	0.0353793	+	0.0264846i
$513$	3.29631	−	1.79992i	0.145536	−	0.0794686i
$514$	−2.57635	−	4.00888i	−0.113638	−	0.176824i
$515$	−15.2133	+	23.8831i	−0.670376	+	1.05241i
$516$	0.735856	+	2.50610i	0.0323943	+	0.110325i
$517$	−9.14032	+	0.653729i	−0.401991	+	0.0287510i
$518$	18.9487	−	1.35524i	0.832558	−	0.0595457i
$519$	2.07544	+	7.06830i	0.0911017	+	0.310264i
$520$	−3.06755	−	13.8330i	−0.134521	−	0.606619i
$521$	−6.92156	−	10.7702i	−0.303239	−	0.471849i	0.655875	−	0.754870i	$-0.272300\pi$
$521$	−6.92156	−	10.7702i	−0.303239	−	0.471849i	−0.959114	+	0.283021i	$0.908664\pi$
$522$	6.06384	−	3.31111i	0.265407	−	0.144923i
$523$	8.79048	+	6.58047i	0.384381	+	0.287744i	0.773942	−	0.633257i	$-0.218282\pi$
$523$	8.79048	+	6.58047i	0.384381	+	0.287744i	−0.389561	+	0.921001i	$0.627373\pi$
$524$	−0.737251	−	0.336691i	−0.0322070	−	0.0147084i
$525$	20.8010	+	13.1327i	0.907831	+	0.573156i
$526$	−2.68289	+	4.17465i	−0.116979	+	0.182023i
$527$	0.757782	−	10.5952i	0.0330095	−	0.461533i
$528$	0.530750	−	0.530750i	0.0230979	−	0.0230979i
$529$	−15.4601	−	17.0290i	−0.672177	−	0.740390i
$530$	−22.9911	−	4.90459i	−0.998669	−	0.213042i
$531$	−4.02558	−	4.64577i	−0.174695	−	0.201609i
$532$	18.0557	−	3.92777i	0.782813	−	0.170291i
$533$	−5.72794	+	4.28788i	−0.248104	+	0.185729i
$534$	5.40945	−	11.8450i	0.234090	−	0.512585i
$535$	19.2403	+	22.0248i	0.831830	+	0.952213i
$536$	2.13481	−	7.27051i	0.0922099	−	0.314038i
$537$	−3.36724	+	15.4790i	−0.145307	+	0.667967i
$538$	−3.99826	+	10.7198i	−0.172377	+	0.462162i
$539$	−12.3916	+	3.63849i	−0.533742	+	0.156721i
$540$	0.309316	−	2.21457i	0.0133108	−	0.0953000i
$541$	−1.04569	+	1.20679i	−0.0449578	+	0.0518840i	−0.777783	−	0.628533i	$-0.783656\pi$
$541$	−1.04569	+	1.20679i	−0.0449578	+	0.0518840i	0.732825	+	0.680417i	$0.238201\pi$
$542$	0.0471797	−	0.0864032i	0.00202654	−	0.00371134i
$543$	−23.3797	−	8.72018i	−1.00332	−	0.374219i
$544$	1.17774	−	0.756887i	0.0504952	−	0.0324513i
$545$	1.75082	−	3.23729i	0.0749968	−	0.138670i
$546$	30.8585	−	4.43678i	1.32062	−	0.189877i
$547$	−5.80148	−	15.5544i	−0.248054	−	0.665057i	−0.999983	−	0.00581380i	$-0.998149\pi$
$547$	−5.80148	−	15.5544i	−0.248054	−	0.665057i	0.751930	−	0.659243i	$-0.229123\pi$
$548$	−4.61309	−	6.16236i	−0.197061	−	0.263243i
$549$	0.0286744	+	0.0184279i	0.00122379	+	0.000786485i
$550$	−1.77204	+	3.30827i	−0.0755600	+	0.141065i
$551$			25.9481i			1.10542i
$552$	−4.38521	−	1.94164i	−0.186647	−	0.0826416i
$553$	−41.6249	−	41.6249i	−1.77007	−	1.77007i
$554$	2.05761	−	1.78293i	0.0874195	−	0.0757494i
$555$	6.12966	+	6.08053i	0.260190	+	0.258104i
$556$	0.0212596	−	0.147864i	0.000901607	−	0.00627082i
$557$	−37.4216	+	13.9575i	−1.58560	+	0.591400i	−0.979046	−	0.203639i	$-0.934723\pi$
$557$	−37.4216	+	13.9575i	−1.58560	+	0.591400i	−0.606558	+	0.795039i	$0.707450\pi$
$558$	−4.54697	+	6.07404i	−0.192489	+	0.257135i
$559$	−15.8801	−	4.66283i	−0.671659	−	0.197217i
$560$	4.52982	−	10.0255i	0.191420	−	0.423654i
$561$	−0.436526	−	0.955858i	−0.0184301	−	0.0403563i
$562$	9.29842	+	5.07732i	0.392230	+	0.214174i
$563$	0.445899	+	6.23449i	0.0187924	+	0.262752i	0.998159	+	0.0606584i	$0.0193200\pi$
$563$	0.445899	+	6.23449i	0.0187924	+	0.262752i	−0.979366	+	0.202094i	$0.935225\pi$
$564$	9.22661	+	7.99490i	0.388510	+	0.336646i
$565$	8.43160	+	7.24683i	0.354720	+	0.304876i
$566$	3.19845	−	1.46068i	0.134441	−	0.0613971i
$567$	4.80752	+	1.04581i	0.201897	+	0.0439200i
$568$	2.14927	+	3.93609i	0.0901812	+	0.165155i
$569$	2.54810	+	17.7224i	0.106822	+	0.742963i	0.970879	+	0.239569i	$0.0770063\pi$
$569$	2.54810	+	17.7224i	0.106822	+	0.742963i	−0.864057	+	0.503394i	$0.832085\pi$
$570$	6.74318	+	5.00566i	0.282441	+	0.209664i
$571$	−6.19033	−	0.890035i	−0.259057	−	0.0372468i	0.0115625	−	0.999933i	$-0.496319\pi$
$571$	−6.19033	−	0.890035i	−0.259057	−	0.0372468i	−0.270620	+	0.962686i	$0.587229\pi$
$572$	1.01101	+	4.64752i	0.0422723	+	0.194323i
$573$	−15.1941	−	1.08671i	−0.634744	−	0.0453978i
$574$	−5.55545			−0.231880
$575$	23.7975	+	2.94623i	0.992423	+	0.122866i
$576$	−1.00000			−0.0416667
$577$	−8.60566	−	0.615489i	−0.358258	−	0.0256231i	−0.108950	−	0.994047i	$-0.534749\pi$
$577$	−8.60566	−	0.615489i	−0.358258	−	0.0256231i	−0.249309	+	0.968424i	$0.580203\pi$
$578$	3.19699	+	14.6963i	0.132977	+	0.611287i
$579$	10.6609	+	1.53281i	0.443053	+	0.0637014i
$580$	12.4046	+	9.20833i	0.515074	+	0.382355i
$581$	−0.283949	−	1.97491i	−0.0117802	−	0.0819331i
$582$	1.51791	+	2.77984i	0.0629193	+	0.115228i
$583$	7.71087	+	1.67740i	0.319352	+	0.0694707i
$584$	−8.80363	+	4.02048i	−0.364297	+	0.166369i
$585$	10.7455	+	9.23561i	0.444273	+	0.381845i
$586$	19.1224	+	16.5697i	0.789941	+	0.684488i
$587$	0.985348	+	13.7770i	0.0406697	+	0.568636i	0.976407	+	0.215939i	$0.0692811\pi$
$587$	0.985348	+	13.7770i	0.0406697	+	0.568636i	−0.935737	+	0.352698i	$0.885264\pi$
$588$	15.1013	+	8.24594i	0.622767	+	0.340057i
$589$	−11.8378	−	25.9211i	−0.487766	−	1.06806i
$590$	5.65977	−	12.5263i	0.233009	−	0.515701i
$591$	−15.7215	−	4.61625i	−0.646697	−	0.189887i
$592$	2.31395	−	3.09108i	0.0951028	−	0.127042i
$593$	15.3866	−	5.73890i	0.631851	−	0.235668i	−0.0130734	−	0.999915i	$-0.504162\pi$
$593$	15.3866	−	5.73890i	0.631851	−	0.235668i	0.644925	+	0.764246i	$0.276889\pi$
$594$	−0.106821	+	0.742954i	−0.00438291	+	0.0304838i
$595$	−10.9344	−	10.8467i	−0.448266	−	0.444672i
$596$	10.3838	−	8.99761i	0.425337	−	0.368556i
$597$	17.2900	+	17.2900i	0.707634	+	0.707634i
$598$	25.3732	−	16.7245i	1.03759	−	0.683914i
$599$			30.9444i			1.26435i	0.774824	+	0.632177i	$0.217839\pi$
$599$			30.9444i			1.26435i	−0.774824	+	0.632177i	$0.782161\pi$
$600$	4.78597	−	1.44723i	0.195386	−	0.0590829i
$601$	19.4352	+	12.4902i	0.792778	+	0.509487i	0.873252	−	0.487269i	$-0.162007\pi$
$601$	19.4352	+	12.4902i	0.792778	+	0.509487i	−0.0804740	+	0.996757i	$0.525643\pi$
$602$	−7.70097	−	10.2873i	−0.313868	−	0.419279i
$603$	2.64805	+	7.09969i	0.107837	+	0.289122i
$604$	−18.9913	+	2.73054i	−0.772745	+	0.111104i
$605$	−11.1017	+	20.5272i	−0.451348	+	0.834550i
$606$	2.81608	−	1.80978i	0.114395	−	0.0735174i
$607$	−8.03428	−	2.99663i	−0.326101	−	0.121630i	0.181081	−	0.983468i	$-0.442040\pi$
$607$	−8.03428	−	2.99663i	−0.326101	−	0.121630i	−0.507183	+	0.861839i	$0.669313\pi$
$608$	1.79992	−	3.29631i	0.0729965	−	0.133683i
$609$	−22.2599	+	25.6892i	−0.902015	+	1.04098i
$610$	−0.0105432	+	0.0754844i	−0.000426880	+	0.00305628i
$611$	−74.2271	+	21.7950i	−3.00291	+	0.881733i
$612$	−0.489243	+	1.31171i	−0.0197765	+	0.0530228i
$613$	1.26685	−	5.82362i	0.0511676	−	0.235214i	−0.944460	−	0.328627i	$-0.893414\pi$
$613$	1.26685	−	5.82362i	0.0511676	−	0.235214i	0.995627	+	0.0934132i	$0.0297777\pi$
$614$	1.58664	−	5.40358i	0.0640314	−	0.218071i
$615$	−1.66112	−	1.90152i	−0.0669828	−	0.0766766i
$616$	−1.53408	+	3.35917i	−0.0618099	+	0.135345i
$617$	12.6855	−	9.49624i	0.510699	−	0.382304i	−0.312625	−	0.949877i	$-0.601208\pi$
$617$	12.6855	−	9.49624i	0.510699	−	0.382304i	0.823323	+	0.567572i	$0.192117\pi$
$618$	−12.3743	+	2.69186i	−0.497766	+	0.108282i
$619$	−29.7685	−	34.3547i	−1.19650	−	1.38083i	−0.905631	−	0.424066i	$-0.860602\pi$
$619$	−29.7685	−	34.3547i	−1.19650	−	1.38083i	−0.290865	−	0.956764i	$-0.593943\pi$
$620$	−16.5926	−	3.53964i	−0.666376	−	0.142155i
$621$	4.67412	−	1.07359i	0.187566	−	0.0430819i
$622$	−5.83555	+	5.83555i	−0.233984	+	0.233984i
$623$	−4.57046	+	63.9034i	−0.183112	+	2.56023i
$624$	3.42583	−	5.33069i	0.137143	−	0.213398i
$625$	−20.8111	+	13.8528i	−0.832442	+	0.554112i
$626$	−9.76973	−	4.46168i	−0.390477	−	0.178325i
$627$	−2.25674	−	1.68938i	−0.0901256	−	0.0674671i
$628$	4.07729	−	2.22637i	0.162702	−	0.0888418i
$629$	−2.92252	−	4.54753i	−0.116528	−	0.181322i
$630$	2.38175	+	10.7404i	0.0948911	+	0.427909i
$631$	−13.3158	−	45.3496i	−0.530095	−	1.80534i	−0.590341	−	0.807154i	$-0.701007\pi$
$631$	−13.3158	−	45.3496i	−0.530095	−	1.80534i	0.0602459	−	0.998184i	$-0.480812\pi$
$632$	−11.9344	+	0.853562i	−0.474723	+	0.0339529i
$633$	4.79076	−	0.342642i	0.190416	−	0.0136188i
$634$	1.55356	+	5.29092i	0.0616996	+	0.210129i
$635$	−13.4533	+	21.1201i	−0.533878	+	0.838127i
$636$	−5.68391	−	8.84433i	−0.225382	−	0.350701i
$637$	−95.6910	+	52.2513i	−3.79142	+	2.07027i
$638$	−4.15146	−	3.10775i	−0.164358	−	0.123037i
$639$	−4.07939	−	1.86299i	−0.161378	−	0.0736989i
$640$	−0.937074	−	2.03024i	−0.0370411	−	0.0802525i
$641$	1.54625	−	2.40601i	0.0610731	−	0.0950316i	−0.809374	−	0.587294i	$-0.800193\pi$
$641$	1.54625	−	2.40601i	0.0610731	−	0.0950316i	0.870447	+	0.492262i	$0.163830\pi$
$642$	−0.933033	+	13.0455i	−0.0368239	+	0.514865i
$643$	2.03772	−	2.03772i	0.0803597	−	0.0803597i	−0.665784	−	0.746144i	$-0.731903\pi$
$643$	2.03772	−	2.03772i	0.0803597	−	0.0803597i	0.746144	+	0.665784i	$0.231903\pi$
$644$	23.5531	+	1.41077i	0.928121	+	0.0555922i
$645$	1.21849	−	5.71186i	0.0479778	−	0.224904i
$646$	−3.44321	−	3.97368i	−0.135471	−	0.156342i
$647$	−20.3423	+	4.42519i	−0.799737	+	0.173972i	−0.593820	−	0.804598i	$-0.702381\pi$
$647$	−20.3423	+	4.42519i	−0.799737	+	0.173972i	−0.205916	+	0.978570i	$0.566017\pi$
$648$	0.800541	−	0.599278i	0.0314482	−	0.0235419i
$649$	−1.91676	+	4.19711i	−0.0752392	+	0.164751i
$650$	−8.68118	+	30.4705i	−0.340504	+	1.19515i
$651$	10.5170	−	35.8176i	0.412194	−	1.40380i
$652$	2.44221	−	11.2267i	0.0956445	−	0.439670i
$653$	1.10983	−	2.97558i	0.0434312	−	0.116443i	−0.913423	−	0.407011i	$-0.866571\pi$
$653$	1.10983	−	2.97558i	0.0434312	−	0.116443i	0.956855	+	0.290567i	$0.0938439\pi$
$654$	1.57926	−	0.463712i	0.0617538	−	0.0181326i
$655$	1.09191	+	1.44645i	0.0426646	+	0.0565177i
$656$	−0.739447	+	0.853367i	−0.0288705	+	0.0333184i
$657$	4.63828	−	8.49438i	0.180957	−	0.331397i
$658$	−56.2784	−	20.9908i	−2.19396	−	0.818305i
$659$	39.7931	−	25.5735i	1.55012	−	0.996202i	0.564852	−	0.825193i	$-0.308933\pi$
$659$	39.7931	−	25.5735i	1.55012	−	0.996202i	0.985269	−	0.171010i	$-0.0547030\pi$
$660$	−1.60848	+	0.479331i	−0.0626099	+	0.0186579i
$661$	−27.9161	+	4.01373i	−1.08581	+	0.156116i	−0.661903	−	0.749589i	$-0.730251\pi$
$661$	−27.9161	+	4.01373i	−1.08581	+	0.156116i	−0.423908	+	0.905705i	$0.639342\pi$
$662$	1.86200	+	4.99222i	0.0723687	+	0.194028i
$663$	−5.31627	−	7.10170i	−0.206467	−	0.275807i
$664$	−0.341159	−	0.219249i	−0.0132395	−	0.00850853i
$665$	−39.6908	−	11.4810i	−1.53914	−	0.445214i
$666$			3.86123i			0.149620i
$667$	−8.96641	+	31.8979i	−0.347181	+	1.23509i
$668$	−10.6109	−	10.6109i	−0.410549	−	0.410549i
$669$	8.74905	−	7.58110i	0.338258	−	0.293102i
$670$	−11.9327	+	12.0291i	−0.461000	+	0.464725i
$671$	0.00364102	−	0.0253239i	0.000140560	−	0.000977617i
$672$	4.60975	−	1.71935i	0.177825	−	0.0663253i
$673$	−6.28919	+	8.40137i	−0.242430	+	0.323849i	−0.905209	−	0.424966i	$-0.860286\pi$
$673$	−6.28919	+	8.40137i	−0.242430	+	0.323849i	0.662779	+	0.748815i	$0.269377\pi$
$674$	9.48139	+	2.78399i	0.365210	+	0.107235i
$675$	−2.96408	+	4.02669i	−0.114087	+	0.154987i
$676$	11.2796	+	24.6988i	0.433830	+	0.949955i
$677$	15.9536	+	8.71135i	0.613148	+	0.334804i	0.755635	−	0.654992i	$-0.227328\pi$
$677$	15.9536	+	8.71135i	0.613148	+	0.334804i	−0.142487	+	0.989797i	$0.545510\pi$
$678$	0.354705	+	4.95942i	0.0136224	+	0.190465i
$679$	−11.7767	−	10.2046i	−0.451948	−	0.391615i
$680$	−3.12155	+	0.235888i	−0.119706	+	0.00904589i
$681$	9.41788	−	4.30100i	0.360894	−	0.164815i
$682$	5.56492	+	1.21057i	0.213092	+	0.0463553i
$683$	−8.35695	−	15.3046i	−0.319770	−	0.585614i	0.667511	−	0.744600i	$-0.267360\pi$
$683$	−8.35695	−	15.3046i	−0.319770	−	0.585614i	−0.987281	+	0.158985i	$0.949178\pi$
$684$	0.534494	+	3.71749i	0.0204369	+	0.142142i
$685$	2.51816	+	17.0275i	0.0962141	+	0.650587i
$686$	−49.7018	−	7.14603i	−1.89762	−	0.272837i
$687$	4.54348	+	20.8861i	0.173345	+	0.796853i
$688$	−2.60524	−	0.186331i	−0.0993239	−	0.00710379i
$689$	66.6185			2.53796
$690$	6.55966	+	8.48357i	0.249722	+	0.322964i
$691$	−28.9191			−1.10013			−0.550067	−	0.835121i	$-0.685398\pi$
$691$	−28.9191			−1.10013			−0.550067	+	0.835121i	$0.685398\pi$
$692$	−7.34793	−	0.525534i	−0.279326	−	0.0199778i
$693$	−0.784980	−	3.60850i	−0.0298189	−	0.137075i
$694$	35.6952	+	5.13219i	1.35497	+	0.194815i
$695$	−0.199101	+	0.268211i	−0.00755233	+	0.0101738i
$696$	0.983246	+	6.83863i	0.0372699	+	0.259218i
$697$	0.757602	+	1.38745i	0.0286962	+	0.0525532i
$698$	22.5006	+	4.89471i	0.851661	+	0.185268i
$699$	−16.0788	+	7.34295i	−0.608157	+	0.277736i
$700$	−19.5738	+	14.9001i	−0.739822	+	0.563172i
$701$	−16.8924	−	14.6373i	−0.638016	−	0.552844i	0.274653	−	0.961543i	$-0.411437\pi$
$701$	−16.8924	−	14.6373i	−0.638016	−	0.552844i	−0.912669	+	0.408700i	$0.865982\pi$
$702$	0.452048	+	6.32046i	0.0170615	+	0.238550i
$703$	−12.7278	−	6.94992i	−0.480039	−	0.262121i
$704$	0.311808	+	0.682764i	0.0117517	+	0.0257327i
$705$	−9.64293	−	25.5393i	−0.363174	−	0.961867i
$706$	27.7753	+	8.15558i	1.04534	+	0.306939i
$707$	−9.86977	+	13.1845i	−0.371191	+	0.495853i
$708$	5.75964	−	2.14824i	0.216461	−	0.0807357i
$709$	6.31291	−	43.9073i	0.237086	−	1.64897i	−0.429151	−	0.903233i	$-0.641187\pi$
$709$	6.31291	−	43.9073i	0.237086	−	1.64897i	0.666237	−	0.745740i	$-0.267904\pi$
$710$	−0.0403553	−	10.0279i	−0.00151451	−	0.376341i
$711$	9.04242	−	7.83530i	0.339117	−	0.293847i
$712$	9.20779	+	9.20779i	0.345077	+	0.345077i
$713$	−5.59505	−	35.9553i	−0.209536	−	1.34654i
$714$		−	6.88785i		−	0.257771i
$715$	2.95520	−	10.2164i	0.110518	−	0.382072i
$716$	−13.3263	−	8.56428i	−0.498027	−	0.320062i
$717$	8.57108	+	11.4496i	0.320093	+	0.427594i
$718$	−4.31482	−	11.5685i	−0.161028	−	0.431732i
$719$	1.41070	−	0.202828i	0.0526103	−	0.00756422i	−0.115959	−	0.993254i	$-0.536994\pi$
$719$	1.41070	−	0.202828i	0.0526103	−	0.00756422i	0.168570	+	0.985690i	$0.446085\pi$
$720$	1.96685	+	1.06373i	0.0733000	+	0.0396428i
$721$	52.4141	−	33.6845i	1.95200	−	1.25448i
$722$	4.58598	+	1.71048i	0.170673	+	0.0636576i
$723$	−8.34370	+	15.2804i	−0.310306	+	0.568282i
$724$	16.3407	−	18.8582i	0.607299	−	0.700860i
$725$	−14.6029	−	31.3065i	−0.542336	−	1.16269i
$726$	−10.0139	+	2.94033i	−0.371649	+	0.109126i
$727$	−5.48977	+	14.7186i	−0.203604	+	0.545884i	−0.998115	−	0.0613656i	$-0.980454\pi$
$727$	−5.48977	+	14.7186i	−0.203604	+	0.545884i	0.794511	+	0.607250i	$0.207727\pi$
$728$	−6.62690	+	30.4633i	−0.245609	+	1.12905i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	21.5921	+	1.45698i	0.799159	+	0.0539254i
$731$	−1.51901	+	3.32617i	−0.0561826	+	0.123023i
$732$	−0.0272867	+	0.0204266i	−0.00100855	+	0.000754989i
$733$	21.6440	−	4.70837i	0.799441	−	0.173908i	0.205754	−	0.978604i	$-0.434035\pi$
$733$	21.6440	−	4.70837i	0.799441	−	0.173908i	0.593687	+	0.804696i	$0.297672\pi$
$734$	−18.0022	−	20.7757i	−0.664474	−	0.766844i
$735$	−20.9305	−	32.2822i	−0.772034	−	1.19075i
$736$	3.35169	−	3.43019i	0.123545	−	0.126438i
$737$	4.02173	−	4.02173i	0.148142	−	0.148142i
$738$	0.0805538	−	1.12629i	0.00296523	−	0.0414593i
$739$	−26.9555	+	41.9435i	−0.991573	+	1.54292i	−0.160290	+	0.987070i	$0.551243\pi$
$739$	−26.9555	+	41.9435i	−0.991573	+	1.54292i	−0.831284	+	0.555848i	$0.812394\pi$
$740$	−7.83925	+	3.61826i	−0.288176	+	0.133010i
$741$	−21.6479	−	9.88625i	−0.795255	−	0.363181i
$742$	41.4079	+	30.9976i	1.52013	+	1.13796i
$743$	−24.9166	+	13.6055i	−0.914101	+	0.499137i	−0.866190	−	0.499715i	$-0.833438\pi$
$743$	−24.9166	+	13.6055i	−0.914101	+	0.499137i	−0.0479107	+	0.998852i	$0.515256\pi$
$744$	−4.10207	−	6.38294i	−0.150389	−	0.234010i
$745$	−29.9943	+	6.65140i	−1.09891	+	0.243688i
$746$	−3.50130	−	11.9243i	−0.128192	−	0.436581i
$747$	0.404503	−	0.0289306i	0.0148000	−	0.00105852i
$748$	1.04814	−	0.0749645i	0.0383238	−	0.00274097i
$749$	−18.1287	−	61.7407i	−0.662409	−	2.25596i
$750$	−10.9527	−	2.24449i	−0.399937	−	0.0819571i
$751$	−2.28387	−	3.55377i	−0.0833395	−	0.129679i	0.797081	−	0.603872i	$-0.206376\pi$
$751$	−2.28387	−	3.55377i	−0.0833395	−	0.129679i	−0.880421	+	0.474193i	$0.842740\pi$
$752$	−10.7152	+	5.85094i	−0.390743	+	0.213362i
$753$	12.6027	+	9.43424i	0.459267	+	0.343803i
$754$	−39.8230	−	18.1866i	−1.45027	−	0.662316i
$755$	40.2575	+	14.8310i	1.46512	+	0.539756i
$756$	−2.65993	+	4.13893i	−0.0967407	+	0.150531i
$757$	−1.19537	+	16.7135i	−0.0434466	+	0.607462i	0.928360	+	0.371682i	$0.121219\pi$
$757$	−1.19537	+	16.7135i	−0.0434466	+	0.607462i	−0.971806	+	0.235780i	$0.924236\pi$
$758$	23.8743	−	23.8743i	0.867154	−	0.867154i
$759$	−2.19044	−	2.85657i	−0.0795080	−	0.103687i
$760$	−7.04655	+	4.56872i	−0.255605	+	0.165725i
$761$	24.1779	+	27.9027i	0.876447	+	1.01147i	0.999817	+	0.0191130i	$0.00608422\pi$
$761$	24.1779	+	27.9027i	0.876447	+	1.01147i	−0.123370	+	0.992361i	$0.539370\pi$
$762$	−10.9427	+	2.38045i	−0.396414	+	0.0862346i
$763$	−6.48270	+	4.85289i	−0.234689	+	0.175686i
$764$	6.32799	−	13.8564i	0.228939	−	0.501306i
$765$	2.35757	−	2.05952i	0.0852381	−	0.0744619i
$766$	−7.33939	+	24.9957i	−0.265183	+	0.903130i
$767$	−8.27996	+	38.0624i	−0.298972	+	1.37435i
$768$	0.349464	−	0.936950i	0.0126102	−	0.0338093i
$769$	10.0901	−	2.96273i	0.363860	−	0.106839i	−0.0946919	−	0.995507i	$-0.530187\pi$
$769$	10.0901	−	2.96273i	0.363860	−	0.106839i	0.458552	+	0.888668i	$0.348368\pi$
$770$	6.59054	−	4.97513i	0.237507	−	0.179291i
$771$	−3.12065	+	3.60142i	−0.112387	+	0.129702i
$772$	−5.16178	+	9.45309i	−0.185777	+	0.340224i
$773$	2.65025	+	0.988494i	0.0953230	+	0.0355537i	0.396673	−	0.917960i	$-0.370165\pi$
$773$	2.65025	+	0.988494i	0.0953230	+	0.0355537i	−0.301350	+	0.953514i	$0.597437\pi$
$774$	2.19727	−	1.41210i	0.0789791	−	0.0507568i
$775$	28.8700	+	24.6120i	1.03704	+	0.884088i
$776$	−3.13503	+	0.450749i	−0.112541	+	0.0161809i
$777$	−6.63880	−	17.7993i	−0.238166	−	0.638547i
$778$	−0.578637	−	0.772969i	−0.0207451	−	0.0277123i
$779$	3.56761	+	2.29277i	0.127823	+	0.0821468i
$780$	−12.4085	+	6.84051i	−0.444295	+	0.244929i
$781$			3.36616i			0.120451i
$782$	−2.85962	−	6.07465i	−0.102260	−	0.217229i
$783$	−4.88537	−	4.88537i	−0.174589	−	0.174589i
$784$	−13.0034	+	11.2675i	−0.464407	+	0.402411i
$785$	−10.3877	+	0.0418030i	−0.370751	+	0.00149201i
$786$	−0.115345	+	0.802245i	−0.00411423	+	0.0286151i
$787$	14.8002	−	5.52019i	0.527571	−	0.196774i	−0.0715432	−	0.997438i	$-0.522792\pi$
$787$	14.8002	−	5.52019i	0.527571	−	0.196774i	0.599114	+	0.800664i	$0.295520\pi$
$788$	9.81930	−	13.1171i	0.349798	−	0.467276i
$789$	4.76141	+	1.39807i	0.169511	+	0.0497728i
$790$	24.3810	+	11.0161i	0.867437	+	0.391934i
$791$	−10.1621	−	22.2518i	−0.361322	−	0.791184i
$792$	−0.658781	−	0.359721i	−0.0234088	−	0.0127821i
$793$	−0.0154082	−	0.215435i	−0.000547162	−	0.00765033i
$794$	7.45528	+	6.46004i	0.264578	+	0.229258i
$795$	1.77142	+	23.4416i	0.0628258	+	0.831387i
$796$	−22.2422	+	10.1577i	−0.788352	+	0.360028i
$797$	−11.0532	−	2.40448i	−0.391526	−	0.0851712i	0.0124929	−	0.999922i	$-0.496023\pi$
$797$	−11.0532	−	2.40448i	−0.391526	−	0.0851712i	−0.404019	+	0.914751i	$0.632387\pi$
$798$	−8.85554	−	16.2177i	−0.313483	−	0.574101i
$799$	2.43241	+	16.9178i	0.0860525	+	0.598508i
$800$	−0.316545	+	4.98997i	−0.0111915	+	0.176422i
$801$	−12.8892	−	1.85319i	−0.455419	−	0.0654794i
$802$	4.88012	+	22.4335i	0.172323	+	0.792156i
$803$	−7.24591	−	0.518238i	−0.255703	−	0.0182882i
$804$	−7.57745			−0.267236
$805$	−44.8246	−	27.8288i	−1.57986	−	0.980836i
$806$	48.0785			1.69349
$807$	11.4120	+	0.816201i	0.401721	+	0.0287316i
$808$	0.711558	+	3.27098i	0.0250325	+	0.115073i
$809$	−54.6947	−	7.86391i	−1.92296	−	0.276481i	−0.927672	−	0.373397i	$-0.878193\pi$
$809$	−54.6947	−	7.86391i	−1.92296	−	0.276481i	−0.995293	+	0.0969162i	$0.969102\pi$
$810$	−2.21201	+	0.327130i	−0.0777221	+	0.0114942i
$811$	−4.39299	−	30.5539i	−0.154259	−	1.07289i	−0.908978	−	0.416845i	$-0.863136\pi$
$811$	−4.39299	−	30.5539i	−0.154259	−	1.07289i	0.754719	−	0.656049i	$-0.227773\pi$
$812$	−16.2905	−	29.8338i	−0.571685	−	1.04696i
$813$	−0.0961954	−	0.0209260i	−0.00337372	−	0.000733908i
$814$	2.63631	−	1.20396i	0.0924027	−	0.0421989i
$815$	−16.7456	+	19.4833i	−0.586572	+	0.682470i
$816$	−1.05804	−	0.916793i	−0.0370386	−	0.0320942i
$817$	0.699805	+	9.78455i	0.0244831	+	0.342318i
$818$	31.2287	+	17.0521i	1.09188	+	0.596214i
$819$	−12.9509	−	28.3585i	−0.452541	−	0.990927i
$820$	2.36213	−	0.891872i	0.0824891	−	0.0311455i
$821$	−1.99355	−	0.585358i	−0.0695753	−	0.0204291i	0.246760	−	0.969077i	$-0.420634\pi$
$821$	−1.99355	−	0.585358i	−0.0695753	−	0.0204291i	−0.316335	+	0.948648i	$0.602452\pi$
$822$	−4.61309	+	6.16236i	−0.160900	+	0.214937i
$823$	50.5275	−	18.8458i	1.76128	−	0.656922i	0.761313	−	0.648384i	$-0.224555\pi$
$823$	50.5275	−	18.8458i	1.76128	−	0.656922i	0.999964	−	0.00853804i	$-0.00271777\pi$
$824$	1.80223	−	12.5348i	0.0627836	−	0.436670i
$825$	3.67351	+	0.768210i	0.127895	+	0.0267456i
$826$	−22.8570	+	19.8057i	−0.795295	+	0.689127i
$827$	−4.92833	−	4.92833i	−0.171375	−	0.171375i	0.616208	−	0.787583i	$-0.288668\pi$
$827$	−4.92833	−	4.92833i	−0.171375	−	0.171375i	−0.787583	+	0.616208i	$0.788668\pi$
$828$	−0.627533	+	4.75460i	−0.0218083	+	0.165234i
$829$			2.87645i			0.0999034i	0.998752	+	0.0499517i	$0.0159067\pi$
$829$			2.87645i			0.0999034i	−0.998752	+	0.0499517i	$0.984093\pi$
$830$	0.437785	+	0.794129i	0.0151957	+	0.0275646i
$831$	−2.29040	−	1.47195i	−0.0794532	−	0.0510615i
$832$	3.79739	+	5.07271i	0.131651	+	0.175865i
$833$	8.41790	+	22.5693i	0.291663	+	0.781979i
$834$	−0.147864	+	0.0212596i	−0.00512010	+	0.000736159i
$835$	9.58293	+	32.1572i	0.331631	+	1.11284i
$836$	2.37151	−	1.52408i	0.0820204	−	0.0527113i
$837$	7.10903	+	2.65153i	0.245724	+	0.0916503i
$838$	−9.60314	+	17.5868i	−0.331735	+	0.607528i
$839$	1.38206	−	1.59498i	0.0477139	−	0.0550648i	−0.731391	−	0.681958i	$-0.761128\pi$
$839$	1.38206	−	1.59498i	0.0477139	−	0.0550648i	0.779105	+	0.626894i	$0.215674\pi$
$840$	−10.8956	−	1.52182i	−0.375934	−	0.0525078i
$841$	17.9748	−	5.27787i	0.619820	−	0.181995i
$842$	−11.1069	+	29.7787i	−0.382768	+	1.02624i
$843$	2.25199	−	10.3522i	0.0775626	−	0.356549i
$844$	−1.35316	+	4.60845i	−0.0465777	+	0.158629i
$845$	4.08761	−	60.5772i	0.140618	−	2.08392i
$846$	5.07162	−	11.1053i	0.174366	−	0.381808i
$847$	41.1059	−	30.7715i	1.41242	−	1.05732i
$848$	10.2730	−	2.23476i	0.352777	−	0.0767419i
$849$	−2.30262	−	2.65737i	−0.0790259	−	0.0912007i
$850$	6.39054	+	2.85653i	0.219194	+	0.0979780i
$851$	−13.2447	−	12.9417i	−0.454024	−	0.443634i
$852$	3.17113	−	3.17113i	0.108641	−	0.108641i
$853$	−2.98399	+	41.7217i	−0.102170	+	1.42852i	0.645149	+	0.764057i	$0.276795\pi$
$853$	−2.98399	+	41.7217i	−0.102170	+	1.42852i	−0.747319	+	0.664466i	$0.768659\pi$
$854$	0.0906646	−	0.141077i	0.00310248	−	0.00482755i
$855$	2.90313	−	7.88029i	0.0992848	−	0.269500i
$856$	−11.8969	−	5.43314i	−0.406628	−	0.185701i
$857$	−14.9398	−	11.1838i	−0.510333	−	0.382031i	0.312853	−	0.949801i	$-0.398715\pi$
$857$	−14.9398	−	11.1838i	−0.510333	−	0.382031i	−0.823187	+	0.567771i	$0.807806\pi$
$858$	4.17443	−	2.27941i	0.142513	−	0.0778179i
$859$	10.1155	+	15.7401i	0.345138	+	0.537045i	0.969816	−	0.243837i	$-0.0784063\pi$
$859$	10.1155	+	15.7401i	0.345138	+	0.537045i	−0.624678	+	0.780882i	$0.714770\pi$
$860$	4.92591	+	3.13775i	0.167972	+	0.106996i
$861$	1.56515	+	5.33041i	0.0533402	+	0.181660i
$862$	2.42898	−	0.173724i	0.0827314	−	0.00591707i
$863$	−15.5695	+	1.11355i	−0.529992	+	0.0379058i	−0.333772	−	0.942654i	$-0.608321\pi$
$863$	−15.5695	+	1.11355i	−0.529992	+	0.0379058i	−0.196221	+	0.980560i	$0.562867\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	13.8932	+	8.84983i	0.472384	+	0.300903i
$866$	13.4123	+	20.8699i	0.455767	+	0.709188i
$867$	13.2003	−	7.20793i	0.448307	−	0.244794i
$868$	29.8840	+	22.3709i	1.01433	+	0.759318i
$869$	−8.16917	−	3.73073i	−0.277120	−	0.126556i
$870$	5.34054	−	14.4964i	0.181061	−	0.491475i
$871$	25.9590	−	40.3930i	0.879588	−	1.36867i
$872$	−0.117419	+	1.64173i	−0.00397632	+	0.0555962i
$873$	2.23959	−	2.23959i	0.0757988	−	0.0757988i
$874$	−14.5431	−	10.6265i	−0.491929	−	0.359445i
$875$	54.3484	−	8.48502i	1.83731	−	0.286846i
$876$	6.33789	+	7.31432i	0.214138	+	0.247128i
$877$	44.7561	−	9.73609i	1.51131	−	0.328764i	0.620884	−	0.783902i	$-0.286774\pi$
$877$	44.7561	−	9.73609i	1.51131	−	0.328764i	0.890421	+	0.455138i	$0.150410\pi$
$878$	3.70459	−	2.77322i	0.125024	−	0.0935917i
$879$	10.5111	−	23.0161i	0.354530	−	0.776313i
$880$	0.112996	−	1.67457i	0.00380910	−	0.0564498i
$881$	−6.43699	+	21.9224i	−0.216868	+	0.738584i	0.777145	+	0.629321i	$0.216667\pi$
$881$	−6.43699	+	21.9224i	−0.216868	+	0.738584i	−0.994013	+	0.109263i	$0.965151\pi$
$882$	3.65739	−	16.8127i	0.123151	−	0.566115i
$883$	−14.2235	+	38.1346i	−0.478657	+	1.28333i	0.443416	+	0.896316i	$0.353766\pi$
$883$	−14.2235	+	38.1346i	−0.478657	+	1.28333i	−0.922074	+	0.387015i	$0.873506\pi$
$884$	8.51179	−	2.49929i	0.286282	−	0.0840601i
$885$	−13.6135	−	1.90144i	−0.457612	−	0.0639161i
$886$	7.75840	−	8.95367i	0.260649	−	0.300805i
$887$	4.10397	−	7.51586i	0.137798	−	0.252358i	−0.799663	−	0.600449i	$-0.794988\pi$
$887$	4.10397	−	7.51586i	0.137798	−	0.252358i	0.937461	+	0.348092i	$0.113170\pi$
$888$	−3.61778	−	1.34936i	−0.121405	−	0.0452816i
$889$	46.3505	−	29.7877i	1.55455	−	0.999046i
$890$	−8.31574	−	27.9049i	−0.278744	−	0.935374i
$891$	0.742954	−	0.106821i	0.0248899	−	0.00357863i
$892$	4.04563	+	10.8467i	0.135458	+	0.363176i
$893$	27.4780	+	36.7063i	0.919516	+	1.22833i
$894$	−11.5586	−	7.42826i	−0.386577	−	0.248438i
$895$	17.1007	+	31.0202i	0.571613	+	1.03689i
$896$			4.91996i			0.164364i
$897$	−23.1955	−	19.6336i	−0.774474	−	0.655547i
$898$	3.32631	+	3.32631i	0.111000	+	0.111000i
$899$	−39.6172	+	34.3285i	−1.32131	+	1.14492i
$900$	−2.73697	−	4.18437i	−0.0912324	−	0.139479i
$901$	2.09465	−	14.5686i	0.0697828	−	0.485350i
$902$	−0.794108	+	0.296187i	−0.0264409	+	0.00986194i
$903$	−7.70097	+	10.2873i	−0.256272	+	0.342339i
$904$	−4.77069	−	1.40080i	−0.158671	−	0.0465899i
$905$	−52.1997	+	19.7091i	−1.73518	+	0.655154i
$906$	7.97040	+	17.4527i	0.264799	+	0.579828i
$907$	−4.82858	−	2.63660i	−0.160330	−	0.0875469i	0.397081	−	0.917784i	$-0.370023\pi$
$907$	−4.82858	−	2.63660i	−0.160330	−	0.0875469i	−0.557411	+	0.830237i	$0.688205\pi$
$908$	0.738611	+	10.3271i	0.0245117	+	0.342718i
$909$	−2.52986	−	2.19213i	−0.0839100	−	0.0727084i
$910$	45.4388	−	52.8675i	1.50628	−	1.75254i
$911$	9.02431	−	4.12126i	0.298989	−	0.136544i	−0.260272	−	0.965535i	$-0.583812\pi$
$911$	9.02431	−	4.12126i	0.298989	−	0.136544i	0.559261	+	0.828992i	$0.311085\pi$
$912$	−3.66989	−	0.798335i	−0.121522	−	0.0264355i
$913$	−0.145880	−	0.267159i	−0.00482792	−	0.00884168i
$914$	−2.60351	−	18.1078i	−0.0861164	−	0.598953i
$915$	0.0753971	−	0.0111503i	0.00249255	−	0.000368619i
$916$	−21.1570	−	3.04191i	−0.699046	−	0.100508i
$917$	−0.847624	−	3.89647i	−0.0279910	−	0.128673i
$918$	1.39641	+	0.0998735i	0.0460885	+	0.00329632i
$919$	26.3662			0.869740			0.434870	−	0.900493i	$-0.356794\pi$
$919$	26.3662			0.869740			0.434870	+	0.900493i	$0.356794\pi$
$920$	−10.2410	+	3.18137i	−0.337637	+	0.104887i
$921$	−5.63171			−0.185571
$922$	−27.7878	−	1.98742i	−0.915142	−	0.0654523i
$923$	6.04057	+	27.7681i	0.198828	+	0.913997i
$924$	3.65530	+	0.525553i	0.120251	+	0.0172894i
$925$	19.2674	+	1.22225i	0.633509	+	0.0401874i
$926$	−4.20966	−	29.2788i	−0.138338	−	0.962162i
$927$	6.06906	+	11.1146i	0.199334	+	0.365053i
$928$	−6.75106	−	1.46860i	−0.221614	−	0.0482093i
$929$	54.6018	−	24.9358i	1.79143	−	0.818117i	0.823320	−	0.567577i	$-0.192119\pi$
$929$	54.6018	−	24.9358i	1.79143	−	0.818117i	0.968106	−	0.250540i	$-0.0806080\pi$
$930$	1.27843	+	16.9178i	0.0419214	+	0.554755i
$931$	48.8371	+	42.3176i	1.60057	+	1.38690i
$932$	−1.26100	−	17.6312i	−0.0413056	−	0.577528i
$933$	7.24324	+	3.95511i	0.237133	+	0.129484i
$934$	−7.15298	−	15.6628i	−0.234053	−	0.512504i
$935$	−2.14127	−	0.967491i	−0.0700271	−	0.0316404i
$936$	−6.07993	−	1.78523i	−0.198729	−	0.0583520i
$937$	−28.2579	+	37.7481i	−0.923145	+	1.23318i	0.0489998	+	0.998799i	$0.484397\pi$
$937$	−28.2579	+	37.7481i	−0.923145	+	1.23318i	−0.972145	+	0.234379i	$0.924694\pi$
$938$	34.9301	−	13.0283i	1.14051	−	0.425388i
$939$	−1.52850	+	10.6310i	−0.0498809	+	0.346929i
$940$	27.2989	−	0.109859i	0.890393	−	0.00358320i
$941$	6.71997	−	5.82289i	0.219065	−	0.189821i	−0.538414	−	0.842680i	$-0.680976\pi$
$941$	6.71997	−	5.82289i	0.219065	−	0.189821i	0.757479	+	0.652860i	$0.226431\pi$
$942$	−3.28489	−	3.28489i	−0.107028	−	0.107028i
$943$	3.59339	+	4.05129i	0.117017	+	0.131928i
$944$			6.14723i			0.200075i
$945$	9.63436	−	5.31120i	0.313406	−	0.172773i
$946$	−1.64926	−	1.05991i	−0.0536219	−	0.0344607i
$947$	−17.2539	−	23.0485i	−0.560676	−	0.748976i	0.427211	−	0.904152i	$-0.359496\pi$
$947$	−17.2539	−	23.0485i	−0.560676	−	0.748976i	−0.987887	+	0.155176i	$0.950405\pi$
$948$	4.18128	+	11.2105i	0.135802	+	0.364099i
$949$	−60.7029	+	8.72776i	−1.97050	+	0.283315i
$950$	18.7194	−	1.49036i	0.607336	−	0.0483536i
$951$	4.63892	−	2.98125i	0.150427	−	0.0966737i
$952$	6.45357	+	2.40706i	0.209161	+	0.0780131i
$953$	0.200916	−	0.367949i	0.00650829	−	0.0119191i	−0.874405	−	0.485197i	$-0.838748\pi$
$953$	0.200916	−	0.367949i	0.00650829	−	0.0119191i	0.880913	+	0.473278i	$0.156930\pi$
$954$	−6.88473	+	7.94541i	−0.222902	+	0.257242i
$955$	−27.1856	+	20.5221i	−0.879705	+	0.664080i
$956$	−13.7230	+	4.02944i	−0.443834	+	0.130321i
$957$	−1.81226	+	4.85885i	−0.0585820	+	0.157064i
$958$	−5.64304	+	25.9406i	−0.182318	+	0.838104i
$959$	10.6699	−	36.3384i	0.344550	−	1.17343i
$960$	−1.68400	+	1.47110i	−0.0543509	+	0.0474796i
$961$	11.0371	−	24.1680i	0.356037	−	0.779611i
$962$	19.5869	−	14.6626i	0.631508	−	0.472741i
$963$	12.7799	−	2.78010i	0.411828	−	0.0895876i
$964$	−11.4011	−	13.1576i	−0.367205	−	0.423777i
$965$	20.2079	−	13.1021i	0.650517	−	0.421770i
$966$	−5.28204	−	22.9965i	−0.169947	−	0.739899i
$967$	27.0511	−	27.0511i	0.869905	−	0.869905i	−0.122557	−	0.992462i	$-0.539109\pi$
$967$	27.0511	−	27.0511i	0.869905	−	0.869905i	0.992462	+	0.122557i	$0.0391093\pi$
$968$	0.744539	−	10.4100i	0.0239304	−	0.334591i
$969$	−2.84265	+	4.42326i	−0.0913192	+	0.142095i
$970$	6.64559	+	2.44826i	0.213377	+	0.0786088i
$971$	27.4344	+	12.5289i	0.880411	+	0.402070i	0.803736	−	0.594986i	$-0.202842\pi$
$971$	27.4344	+	12.5289i	0.880411	+	0.402070i	0.0766748	+	0.997056i	$0.475570\pi$
$972$	−0.800541	−	0.599278i	−0.0256774	−	0.0192218i
$973$	0.645062	−	0.352230i	0.0206797	−	0.0112920i
$974$	5.87078	+	9.13511i	0.188112	+	0.292708i
$975$	31.6820	−	0.255000i	1.01464	−	0.00816652i
$976$	−0.00960295	−	0.0327047i	−0.000307383	−	0.00104685i
$977$	8.63485	−	0.617577i	0.276253	−	0.0197580i	0.0674749	−	0.997721i	$-0.478506\pi$
$977$	8.63485	−	0.617577i	0.276253	−	0.0197580i	0.208779	+	0.977963i	$0.433051\pi$
$978$	−11.4600	+	0.819633i	−0.366449	+	0.0262090i
$979$	2.75368	+	9.37816i	0.0880079	+	0.299727i
$980$	37.5612	−	8.32940i	1.19985	−	0.266073i
$981$	−0.889856	−	1.38464i	−0.0284109	−	0.0442083i
$982$	5.52222	−	3.01536i	0.176221	−	0.0962240i
$983$	−35.9572	−	26.9172i	−1.14686	−	0.858526i	−0.155258	−	0.987874i	$-0.549621\pi$
$983$	−35.9572	−	26.9172i	−1.14686	−	0.858526i	−0.991599	+	0.129348i	$0.958712\pi$
$984$	1.02713	+	0.469073i	0.0327436	+	0.0149535i
$985$	−33.2660	+	15.3542i	−1.05994	+	0.489225i
$986$	−5.22930	+	8.13694i	−0.166535	+	0.259133i
$987$	−4.28503	+	59.9125i	−0.136394	+	1.90704i
$988$	16.8281	−	16.8281i	0.535372	−	0.535372i
$989$	−2.52080	+	12.2699i	−0.0801568	+	0.390162i
$990$	0.913075	+	1.40828i	0.0290194	+	0.0447581i
$991$	−19.9533	−	23.0274i	−0.633838	−	0.731488i	0.344435	−	0.938810i	$-0.388071\pi$
$991$	−19.9533	−	23.0274i	−0.633838	−	0.731488i	−0.978273	+	0.207322i	$0.933525\pi$
$992$	7.41402	−	1.61282i	0.235395	−	0.0512072i
$993$	4.26541	−	3.19305i	0.135359	−	0.101328i
$994$	−9.16584	+	20.0704i	−0.290723	+	0.636594i
$995$	54.5519	+	3.68103i	1.72941	+	0.116697i
$996$	−0.114253	+	0.389109i	−0.00362024	+	0.0123294i
$997$	−5.62442	+	25.8551i	−0.178127	+	0.818838i	0.798175	+	0.602426i	$0.205799\pi$
$997$	−5.62442	+	25.8551i	−0.178127	+	0.818838i	−0.976302	+	0.216412i	$0.930565\pi$
$998$	−9.97133	+	26.7342i	−0.315637	+	0.846255i
$999$	3.70483	−	1.08783i	0.117215	−	0.0344176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.493.8	yes	240
5.2	odd	4	inner	690.2.w.a.217.1	yes	240
23.7	odd	22	inner	690.2.w.a.283.1	yes	240
115.7	even	44	inner	690.2.w.a.7.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.8	✓	240	115.7	even	44	inner
690.2.w.a.217.1	yes	240	5.2	odd	4	inner
690.2.w.a.283.1	yes	240	23.7	odd	22	inner
690.2.w.a.493.8	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)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-1.79544 - 1.33281i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35788 + 4.31814i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 + 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-1.79544 - 1.33281i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.35788 + 4.31814i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-1.69579 - 1.45750i) q^{10} +(0.567261 + 0.491535i) q^{11} +(-0.0713392 - 0.997452i) q^{12} +(5.56150 + 3.03681i) q^{13} +(2.04382 + 4.47535i) q^{14} +(-0.920703 + 2.03772i) q^{15} +(0.959493 + 0.281733i) q^{16} +(0.838978 - 1.12074i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.534494 - 3.71749i) q^{19} +(-1.58749 - 1.57476i) q^{20} +(3.71825 - 3.22189i) q^{21} +(0.530750 + 0.530750i) q^{22} +(1.94164 - 4.38521i) q^{23} -1.00000i q^{24} +(1.44723 + 4.78597i) q^{25} +(5.33069 + 3.42583i) q^{26} +(0.599278 + 0.800541i) q^{27} +(1.71935 + 4.60975i) q^{28} +(-6.83863 + 0.983246i) q^{29} +(-1.06373 + 1.96685i) q^{30} +(6.38294 - 4.10207i) q^{31} +(0.936950 + 0.349464i) q^{32} +(0.359721 - 0.658781i) q^{33} +(0.916793 - 1.05804i) q^{34} +(1.52182 - 10.8956i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.34936 - 3.61778i) q^{37} +(0.798335 - 3.66989i) q^{38} +(1.78523 - 6.07993i) q^{39} +(-1.47110 - 1.68400i) q^{40} +(-0.469073 + 1.02713i) q^{41} +(3.93863 - 2.94842i) q^{42} +(-2.55221 + 0.555199i) q^{43} +(0.491535 + 0.567261i) q^{44} +(2.18686 + 0.466514i) q^{45} +(2.24953 - 4.23552i) q^{46} +(-8.63275 + 8.63275i) q^{47} +(0.0713392 - 0.997452i) q^{48} +(-9.30224 + 14.4746i) q^{49} +(1.10211 + 4.87702i) q^{50} +(-1.27347 - 0.581573i) q^{51} +(5.07271 + 3.79739i) q^{52} +(9.22729 - 5.03848i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-0.363362 - 1.63857i) q^{55} +(1.38611 + 4.72066i) q^{56} +(-3.74615 + 0.267930i) q^{57} +(-6.89135 + 0.492879i) q^{58} +(1.73187 + 5.89822i) q^{59} +(-1.20133 + 1.88595i) q^{60} +(-0.0184279 - 0.0286744i) q^{61} +(6.65932 - 3.63626i) q^{62} +(-3.93863 - 2.94842i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-5.93787 - 12.8649i) q^{65} +(0.405802 - 0.631440i) q^{66} +(0.540569 - 7.55814i) q^{67} +(0.989936 - 0.989936i) q^{68} +(-4.69772 - 0.965123i) q^{69} +(2.29523 - 10.7593i) q^{70} +(2.93682 + 3.38928i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(-7.74782 + 5.79995i) q^{73} +(1.60401 - 3.51230i) q^{74} +(4.36897 - 2.43149i) q^{75} +(1.05811 - 3.60358i) q^{76} +(-0.784980 + 3.60850i) q^{77} +(2.21442 - 5.93708i) q^{78} +(-11.4802 + 3.37088i) q^{79} +(-1.34722 - 1.78466i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.541152 + 0.991045i) q^{82} +(-0.379967 - 0.141720i) q^{83} +(4.13893 - 2.65993i) q^{84} +(-3.00007 + 0.894031i) q^{85} +(-2.58531 + 0.371712i) q^{86} +(2.41443 + 6.47334i) q^{87} +(0.449814 + 0.600882i) q^{88} +(10.9546 + 7.04011i) q^{89} +(2.14801 + 0.621334i) q^{90} +31.1758i q^{91} +(2.54596 - 4.06425i) q^{92} +(-5.36512 - 5.36512i) q^{93} +(-9.22661 + 7.99490i) q^{94} +(-5.91437 + 5.96216i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-2.96757 + 1.10685i) q^{97} +(-10.3111 + 13.7741i) q^{98} +(-0.720190 - 0.211467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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