LMFDB - Embedded newform 418.2.v.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	418.29
Dual form			418.2.v.a.173.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.898794i) q^{2} +(2.01881 - 0.815653i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(3.65522 - 1.04812i) q^{5} +(-0.151885 + 2.17205i) q^{6} +(0.300599 - 1.41421i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.25229 - 1.20932i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.898794i) q^{2} +(2.01881 - 0.815653i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(3.65522 - 1.04812i) q^{5} +(-0.151885 + 2.17205i) q^{6} +(0.300599 - 1.41421i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.25229 - 1.20932i) q^{9} +(-0.660301 + 3.74475i) q^{10} +(-1.60435 + 2.90277i) q^{11} +(-1.88565 - 1.08868i) q^{12} +(-0.562742 - 2.25704i) q^{13} +(1.13931 + 0.890123i) q^{14} +(6.52429 - 5.09734i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-1.96889 + 2.03885i) q^{17} +(0.537964 + 1.65568i) q^{18} +(-3.49195 - 2.60889i) q^{19} +(-3.07630 - 2.23506i) q^{20} +(-0.546649 - 3.10020i) q^{21} +(-1.90569 - 2.71447i) q^{22} +(-1.39140 + 0.506428i) q^{23} +(1.80511 - 1.21756i) q^{24} +(8.02182 - 5.01259i) q^{25} +(2.27530 + 0.483630i) q^{26} +(-1.11508 + 2.50452i) q^{27} +(-1.29948 + 0.633797i) q^{28} +(-3.73409 + 0.524793i) q^{29} +(1.72139 + 8.09852i) q^{30} +(1.49512 + 3.35810i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.871235 + 7.16873i) q^{33} +(-0.969398 - 2.66340i) q^{34} +(-0.383499 - 5.48429i) q^{35} +(-1.72395 - 0.242285i) q^{36} +(2.97097 - 0.965326i) q^{37} +(3.87562 - 1.99488i) q^{38} +(-2.97703 - 4.09753i) q^{39} +(3.35743 - 1.78517i) q^{40} +(3.09779 + 7.66729i) q^{41} +(3.02607 + 0.867713i) q^{42} +(-1.40366 + 3.85653i) q^{43} +(3.27515 - 0.522875i) q^{44} +(3.30988 - 5.73289i) q^{45} +(0.154775 - 1.47258i) q^{46} +(-0.903098 - 0.480185i) q^{47} +(0.303030 + 2.15617i) q^{48} +(4.48520 + 1.99694i) q^{49} +(0.988751 + 9.40734i) q^{50} +(-2.31183 + 5.72198i) q^{51} +(-1.43211 + 1.83302i) q^{52} +(2.31491 - 8.07305i) q^{53} +(-1.76222 - 2.10014i) q^{54} +(-2.82182 + 12.2918i) q^{55} -1.44580i q^{56} +(-9.17753 - 2.41864i) q^{57} +(1.16524 - 3.58623i) q^{58} +(5.62179 + 10.5731i) q^{59} +(-8.03351 - 2.00298i) q^{60} +(0.346276 + 0.233566i) q^{61} +(-3.67366 - 0.128287i) q^{62} +(-1.33379 - 2.13452i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-4.42258 - 7.66013i) q^{65} +(-6.06129 - 3.92563i) q^{66} +(-13.1148 - 2.31249i) q^{67} +(2.81880 + 0.296268i) q^{68} +(-2.39590 + 2.15728i) q^{69} +(5.09736 + 2.05947i) q^{70} +(-0.257831 - 0.899165i) q^{71} +(0.973493 - 1.44326i) q^{72} +(-0.441379 + 0.706354i) q^{73} +(-0.434757 + 3.09346i) q^{74} +(12.1060 - 16.6625i) q^{75} +(0.0940255 + 4.35788i) q^{76} +(3.62284 + 3.14145i) q^{77} +(4.98788 - 0.879497i) q^{78} +(2.06962 - 0.144722i) q^{79} +(0.132706 + 3.80020i) q^{80} +(-0.390594 + 11.1852i) q^{81} +(-8.24929 - 0.576847i) q^{82} +(13.5657 - 1.42581i) q^{83} +(-2.10644 + 2.33944i) q^{84} +(-5.05978 + 9.51605i) q^{85} +(-2.85090 - 2.95220i) q^{86} +(-7.11038 + 4.10518i) q^{87} +(-0.965774 + 3.17290i) q^{88} +(7.12034 - 8.48569i) q^{89} +(3.70173 + 5.48803i) q^{90} +(-3.36107 + 0.117371i) q^{91} +(1.25570 + 0.784649i) q^{92} +(5.75742 + 5.55987i) q^{93} +(0.827480 - 0.601199i) q^{94} +(-15.4982 - 5.87608i) q^{95} +(-2.07079 - 0.672841i) q^{96} +(-12.8026 - 6.24424i) q^{97} +(-3.76102 + 3.15587i) q^{98} +(1.50127 + 5.57529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$2$	−0.438371	+	0.898794i	−0.309975	+	0.635543i
$3$	2.01881	−	0.815653i	1.16556	−	0.470917i	0.291423	−	0.956594i	$-0.405871\pi$
$3$	2.01881	−	0.815653i	1.16556	−	0.470917i	0.874138	+	0.485677i	$0.161427\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	3.65522	−	1.04812i	1.63466	−	0.468732i	0.672250	−	0.740324i	$-0.265328\pi$
$5$	3.65522	−	1.04812i	1.63466	−	0.468732i	0.962412	+	0.271592i	$0.0875502\pi$
$6$	−0.151885	+	2.17205i	−0.0620067	+	0.886737i
$7$	0.300599	−	1.41421i	0.113616	−	0.534519i	−0.884120	−	0.467260i	$-0.845241\pi$
$7$	0.300599	−	1.41421i	0.113616	−	0.534519i	0.997736	−	0.0672594i	$-0.0214255\pi$
$8$	0.978148	−	0.207912i	0.345827	−	0.0735079i
$9$	1.25229	−	1.20932i	0.417430	−	0.403108i
$10$	−0.660301	+	3.74475i	−0.208805	+	1.18419i
$11$	−1.60435	+	2.90277i	−0.483730	+	0.875217i
$11$	−1.60435	+	2.90277i	−0.483730	+	0.875217i
$12$	−1.88565	−	1.08868i	−0.544340	−	0.314275i
$13$	−0.562742	−	2.25704i	−0.156077	−	0.625989i	−0.996465	−	0.0840050i	$-0.973229\pi$
$13$	−0.562742	−	2.25704i	−0.156077	−	0.625989i	0.840389	−	0.541984i	$-0.182327\pi$
$14$	1.13931	+	0.890123i	0.304492	+	0.237895i
$15$	6.52429	−	5.09734i	1.68457	−	1.31613i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−1.96889	+	2.03885i	−0.477526	+	0.494493i	−0.914277	−	0.405090i	$-0.867240\pi$
$17$	−1.96889	+	2.03885i	−0.477526	+	0.494493i	0.436751	+	0.899583i	$0.356129\pi$
$18$	0.537964	+	1.65568i	0.126799	+	0.390248i
$19$	−3.49195	−	2.60889i	−0.801108	−	0.598520i
$19$	−3.49195	−	2.60889i	−0.801108	−	0.598520i
$20$	−3.07630	−	2.23506i	−0.687882	−	0.499776i
$21$	−0.546649	−	3.10020i	−0.119289	−	0.676519i
$22$	−1.90569	−	2.71447i	−0.406294	−	0.578727i
$23$	−1.39140	+	0.506428i	−0.290127	+	0.105597i	−0.482984	−	0.875629i	$-0.660447\pi$
$23$	−1.39140	+	0.506428i	−0.290127	+	0.105597i	0.192857	+	0.981227i	$0.438225\pi$
$24$	1.80511	−	1.21756i	0.368467	−	0.248534i
$25$	8.02182	−	5.01259i	1.60436	−	1.00252i
$26$	2.27530	+	0.483630i	0.446223	+	0.0948476i
$27$	−1.11508	+	2.50452i	−0.214598	+	0.481995i
$28$	−1.29948	+	0.633797i	−0.245578	+	0.119776i
$29$	−3.73409	+	0.524793i	−0.693404	+	0.0974515i	−0.477067	−	0.878867i	$-0.658300\pi$
$29$	−3.73409	+	0.524793i	−0.693404	+	0.0974515i	−0.216337	+	0.976319i	$0.569411\pi$
$30$	1.72139	+	8.09852i	0.314282	+	1.47858i
$31$	1.49512	+	3.35810i	0.268532	+	0.603133i	0.996602	−	0.0823701i	$-0.0262490\pi$
$31$	1.49512	+	3.35810i	0.268532	+	0.603133i	−0.728070	+	0.685503i	$0.759582\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−0.871235	+	7.16873i	−0.151662	+	1.24792i
$34$	−0.969398	−	2.66340i	−0.166250	−	0.456769i
$35$	−0.383499	−	5.48429i	−0.0648231	−	0.927014i
$36$	−1.72395	−	0.242285i	−0.287325	−	0.0403808i
$37$	2.97097	−	0.965326i	0.488424	−	0.158699i	−0.0544435	−	0.998517i	$-0.517338\pi$
$37$	2.97097	−	0.965326i	0.488424	−	0.158699i	0.542868	+	0.839818i	$0.317338\pi$
$38$	3.87562	−	1.99488i	0.628709	−	0.323612i
$39$	−2.97703	−	4.09753i	−0.476706	−	0.656129i
$40$	3.35743	−	1.78517i	0.530856	−	0.282261i
$41$	3.09779	+	7.66729i	0.483793	+	1.19743i	0.949859	+	0.312679i	$0.101226\pi$
$41$	3.09779	+	7.66729i	0.483793	+	1.19743i	−0.466066	+	0.884750i	$0.654329\pi$
$42$	3.02607	+	0.867713i	0.466934	+	0.133891i
$43$	−1.40366	+	3.85653i	−0.214057	+	0.588115i	−0.999526	−	0.0307849i	$-0.990199\pi$
$43$	−1.40366	+	3.85653i	−0.214057	+	0.588115i	0.785470	+	0.618900i	$0.212422\pi$
$44$	3.27515	−	0.522875i	0.493747	−	0.0788264i
$45$	3.30988	−	5.73289i	0.493408	−	0.854608i
$46$	0.154775	−	1.47258i	0.0228203	−	0.217121i
$47$	−0.903098	−	0.480185i	−0.131730	−	0.0700423i	0.402298	−	0.915509i	$-0.368211\pi$
$47$	−0.903098	−	0.480185i	−0.131730	−	0.0700423i	−0.534029	+	0.845466i	$0.679323\pi$
$48$	0.303030	+	2.15617i	0.0437386	+	0.311216i
$49$	4.48520	+	1.99694i	0.640743	+	0.285277i
$50$	0.988751	+	9.40734i	0.139831	+	1.33040i
$51$	−2.31183	+	5.72198i	−0.323721	+	0.801237i
$52$	−1.43211	+	1.83302i	−0.198598	+	0.254194i
$53$	2.31491	−	8.07305i	0.317977	−	1.10892i	−0.626250	−	0.779623i	$-0.715411\pi$
$53$	2.31491	−	8.07305i	0.317977	−	1.10892i	0.944227	−	0.329296i	$-0.106811\pi$
$54$	−1.76222	−	2.10014i	−0.239808	−	0.285793i
$55$	−2.82182	+	12.2918i	−0.380494	+	1.65742i
$56$		−	1.44580i		−	0.193203i
$57$	−9.17753	−	2.41864i	−1.21559	−	0.320356i
$58$	1.16524	−	3.58623i	0.153003	−	0.470896i
$59$	5.62179	+	10.5731i	0.731895	+	1.37649i	0.919041	+	0.394162i	$0.128965\pi$
$59$	5.62179	+	10.5731i	0.731895	+	1.37649i	−0.187146	+	0.982332i	$0.559924\pi$
$60$	−8.03351	−	2.00298i	−1.03712	−	0.258584i
$61$	0.346276	+	0.233566i	0.0443361	+	0.0299051i	0.581161	−	0.813789i	$-0.302599\pi$
$61$	0.346276	+	0.233566i	0.0443361	+	0.0299051i	−0.536825	+	0.843694i	$0.680376\pi$
$62$	−3.67366	−	0.128287i	−0.466555	−	0.0162925i
$63$	−1.33379	−	2.13452i	−0.168042	−	0.268924i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−4.42258	−	7.66013i	−0.548554	−	0.950123i
$66$	−6.06129	−	3.92563i	−0.746093	−	0.483211i
$67$	−13.1148	−	2.31249i	−1.60222	−	0.282515i	−0.700117	−	0.714028i	$-0.746869\pi$
$67$	−13.1148	−	2.31249i	−1.60222	−	0.282515i	−0.902107	+	0.431513i	$0.857980\pi$
$68$	2.81880	+	0.296268i	0.341830	+	0.0359278i
$69$	−2.39590	+	2.15728i	−0.288433	+	0.259706i
$70$	5.09736	+	2.05947i	0.609251	+	0.246153i
$71$	−0.257831	−	0.899165i	−0.0305990	−	0.106711i	0.944480	−	0.328568i	$-0.106566\pi$
$71$	−0.257831	−	0.899165i	−0.0305990	−	0.106711i	−0.975079	+	0.221857i	$0.928788\pi$
$72$	0.973493	−	1.44326i	0.114727	−	0.170090i
$73$	−0.441379	+	0.706354i	−0.0516595	+	0.0826725i	−0.872870	−	0.487953i	$-0.837744\pi$
$73$	−0.441379	+	0.706354i	−0.0516595	+	0.0826725i	0.821210	+	0.570626i	$0.193299\pi$
$74$	−0.434757	+	3.09346i	−0.0505395	+	0.359607i
$75$	12.1060	−	16.6625i	1.39788	−	1.92402i
$76$	0.0940255	+	4.35788i	0.0107855	+	0.499884i
$77$	3.62284	+	3.14145i	0.412861	+	0.358002i
$78$	4.98788	−	0.879497i	0.564766	−	0.0995834i
$79$	2.06962	−	0.144722i	0.232851	−	0.0162825i	0.0471456	−	0.998888i	$-0.484988\pi$
$79$	2.06962	−	0.144722i	0.232851	−	0.0162825i	0.185705	+	0.982606i	$0.440543\pi$
$80$	0.132706	+	3.80020i	0.0148370	+	0.424876i
$81$	−0.390594	+	11.1852i	−0.0433994	+	1.24279i
$82$	−8.24929	−	0.576847i	−0.910982	−	0.0637021i
$83$	13.5657	−	1.42581i	1.48903	−	0.156503i	0.675211	−	0.737624i	$-0.264052\pi$
$83$	13.5657	−	1.42581i	1.48903	−	0.156503i	0.813817	+	0.581121i	$0.197386\pi$
$84$	−2.10644	+	2.33944i	−0.229831	+	0.255254i
$85$	−5.05978	+	9.51605i	−0.548810	+	1.03216i
$86$	−2.85090	−	2.95220i	−0.307421	−	0.318343i
$87$	−7.11038	+	4.10518i	−0.762313	+	0.440122i
$88$	−0.965774	+	3.17290i	−0.102952	+	0.338232i
$89$	7.12034	−	8.48569i	0.754755	−	0.899482i	−0.242749	−	0.970089i	$-0.578049\pi$
$89$	7.12034	−	8.48569i	0.754755	−	0.899482i	0.997504	+	0.0706074i	$0.0224937\pi$
$90$	3.70173	+	5.48803i	0.390196	+	0.578490i
$91$	−3.36107	+	0.117371i	−0.352336	+	0.0123038i
$92$	1.25570	+	0.784649i	0.130916	+	0.0818053i
$93$	5.75742	+	5.55987i	0.597016	+	0.576532i
$94$	0.827480	−	0.601199i	0.0853480	−	0.0620090i
$95$	−15.4982	−	5.87608i	−1.59009	−	0.602874i
$96$	−2.07079	−	0.672841i	−0.211349	−	0.0686715i
$97$	−12.8026	−	6.24424i	−1.29991	−	0.634007i	−0.347170	−	0.937802i	$-0.612857\pi$
$97$	−12.8026	−	6.24424i	−1.29991	−	0.634007i	−0.952737	+	0.303795i	$0.901746\pi$
$98$	−3.76102	+	3.15587i	−0.379920	+	0.318791i
$99$	1.50127	+	5.57529i	0.150883	+	0.560338i
$100$	−8.88870	−	3.23522i	−0.888870	−	0.323522i
$101$	9.38428	−	2.33976i	0.933771	−	0.232815i	0.254811	−	0.966991i	$-0.417987\pi$
$101$	9.38428	−	2.33976i	0.933771	−	0.232815i	0.678960	+	0.734176i	$0.262431\pi$
$102$	−4.12944	−	4.58621i	−0.408876	−	0.454102i
$103$	−13.2538	−	11.9338i	−1.30593	−	1.17587i	−0.972450	−	0.233112i	$-0.925109\pi$
$103$	−13.2538	−	11.9338i	−1.30593	−	1.17587i	−0.333484	−	0.942756i	$-0.608224\pi$
$104$	−1.01971	−	2.09071i	−0.0999907	−	0.205011i
$105$	−5.24749	−	10.7589i	−0.512102	−	1.04997i
$106$	6.24122	+	5.61962i	0.606201	+	0.545826i
$107$	−2.18566	−	2.42742i	−0.211296	−	0.234668i	0.628176	−	0.778072i	$-0.283802\pi$
$107$	−2.18566	−	2.42742i	−0.211296	−	0.234668i	−0.839471	+	0.543404i	$0.817135\pi$
$108$	2.66010	−	0.663237i	0.255968	−	0.0638201i
$109$	−15.5957	−	5.67636i	−1.49380	−	0.543697i	−0.539350	−	0.842082i	$-0.681330\pi$
$109$	−15.5957	−	5.67636i	−1.49380	−	0.543697i	−0.954446	+	0.298385i	$0.903552\pi$
$110$	−9.81078	−	7.92460i	−0.935421	−	0.755581i
$111$	5.21045	−	4.37209i	0.494554	−	0.414980i
$112$	1.29948	+	0.633797i	0.122789	+	0.0598882i
$113$	−10.0724	−	3.27271i	−0.947529	−	0.307871i	−0.205818	−	0.978590i	$-0.565985\pi$
$113$	−10.0724	−	3.27271i	−0.947529	−	0.307871i	−0.741711	+	0.670720i	$0.765985\pi$
$114$	6.19702	−	7.18845i	0.580404	−	0.673260i
$115$	−4.55507	+	3.30945i	−0.424762	+	0.308608i
$116$	2.71248	+	2.61941i	0.251847	+	0.243206i
$117$	−3.43420	−	2.14593i	−0.317492	−	0.198391i
$118$	−11.9674	+	0.417912i	−1.10169	+	0.0384719i
$119$	2.29150	+	3.39729i	0.210062	+	0.311429i
$120$	5.32193	−	6.34242i	0.485823	−	0.578982i
$121$	−5.85211	−	9.31412i	−0.532010	−	0.846738i
$122$	−0.361725	+	0.208842i	−0.0327491	+	0.0189077i
$123$	12.5077	+	12.9521i	1.12778	+	1.16785i
$124$	1.72573	−	3.24563i	0.154975	−	0.291466i
$125$	11.3458	−	12.6008i	1.01480	−	1.12705i
$126$	2.50319	−	0.263096i	0.223002	−	0.0234384i
$127$	17.9323	+	1.25395i	1.59124	+	0.111270i	0.837698	−	0.546133i	$-0.183901\pi$
$127$	17.9323	+	1.25395i	1.59124	+	0.111270i	0.753539	+	0.657404i	$0.228345\pi$
$128$	−0.0348995	+	0.999391i	−0.00308471	+	0.0883345i
$129$	0.311860	+	8.93051i	0.0274578	+	0.786288i
$130$	8.82362	−	0.617007i	0.773882	−	0.0541151i
$131$	−20.3528	+	3.58875i	−1.77823	+	0.313550i	−0.963783	−	0.266687i	$-0.914071\pi$
$131$	−20.3528	+	3.58875i	−1.77823	+	0.313550i	−0.814448	+	0.580237i	$0.802960\pi$
$132$	6.18542	−	3.72697i	0.538372	−	0.324391i
$133$	−4.73918	+	4.15410i	−0.410939	+	0.360206i
$134$	7.82759	−	10.7737i	0.676201	−	0.930710i
$135$	−1.45084	+	10.3233i	−0.124869	+	0.888487i
$136$	−1.50197	+	2.40365i	−0.128793	+	0.206111i
$137$	5.01646	−	7.43721i	0.428585	−	0.635403i	−0.551455	−	0.834205i	$-0.685927\pi$
$137$	5.01646	−	7.43721i	0.428585	−	0.635403i	0.980040	+	0.198801i	$0.0637049\pi$
$138$	−0.888656	−	3.09911i	−0.0756474	−	0.263814i
$139$	−6.08186	−	2.45723i	−0.515857	−	0.208420i	0.101892	−	0.994796i	$-0.467511\pi$
$139$	−6.08186	−	2.45723i	−0.515857	−	0.208420i	−0.617748	+	0.786376i	$0.711955\pi$
$140$	−4.08557	+	3.67867i	−0.345294	+	0.310904i
$141$	−2.21485	−	0.232790i	−0.186524	−	0.0196044i
$142$	0.921190	+	0.162431i	0.0773045	+	0.0136309i
$143$	7.45448	+	1.98757i	0.623375	+	0.166209i
$144$	0.870445	+	1.50765i	0.0725371	+	0.125638i
$145$	−13.0989	+	5.83200i	−1.08780	+	0.484321i
$146$	−0.441379	−	0.706354i	−0.0365288	−	0.0584583i
$147$	10.6836	+	0.373079i	0.881167	+	0.0307710i
$148$	−2.58980	−	1.74684i	−0.212880	−	0.143589i
$149$	11.2339	+	2.80092i	0.920315	+	0.229460i	0.673144	−	0.739511i	$-0.264943\pi$
$149$	11.2339	+	2.80092i	0.920315	+	0.229460i	0.247171	+	0.968972i	$0.420499\pi$
$150$	9.66922	+	18.1852i	0.789489	+	1.48481i
$151$	−1.30665	+	4.02146i	−0.106334	+	0.327261i	−0.990041	−	0.140778i	$-0.955040\pi$
$151$	−1.30665	+	4.02146i	−0.106334	+	0.327261i	0.883707	+	0.468040i	$0.155040\pi$
$152$	−3.95806	−	1.82586i	−0.321041	−	0.148097i
$153$			4.93425i			0.398911i
$154$	−4.41167	+	1.87907i	−0.355502	+	0.151420i
$155$	8.98468	+	10.7075i	0.721667	+	0.860049i
$156$	−1.39605	+	4.86862i	−0.111774	+	0.389802i
$157$	−9.93446	+	12.7155i	−0.792856	+	1.01481i	0.206482	+	0.978450i	$0.433798\pi$
$157$	−9.93446	+	12.7155i	−0.792856	+	1.01481i	−0.999339	+	0.0363597i	$0.988424\pi$
$158$	−0.777188	+	1.92361i	−0.0618297	+	0.153034i
$159$	−1.91144	−	18.1861i	−0.151587	−	1.44225i
$160$	−3.47377	−	1.54662i	−0.274626	−	0.122271i
$161$	0.297940	+	2.11995i	0.0234810	+	0.167076i
$162$	−9.88193	−	5.25431i	−0.776397	−	0.412818i
$163$	−1.85611	+	17.6597i	−0.145381	+	1.38321i	0.641981	+	0.766721i	$0.278113\pi$
$163$	−1.85611	+	17.6597i	−0.145381	+	1.38321i	−0.787362	+	0.616491i	$0.788554\pi$
$164$	4.13472	−	7.16154i	0.322867	−	0.559223i
$165$	4.32912	+	27.1164i	0.337021	+	2.11101i
$166$	−4.66530	+	12.8178i	−0.362097	+	0.994854i
$167$	−12.7879	−	3.66688i	−0.989560	−	0.283752i	−0.258460	−	0.966022i	$-0.583215\pi$
$167$	−12.7879	−	3.66688i	−0.989560	−	0.283752i	−0.731100	+	0.682270i	$0.760993\pi$
$168$	−1.17927	−	2.91880i	−0.0909827	−	0.225190i
$169$	6.70079	−	3.56287i	0.515445	−	0.274067i
$170$	−6.33491	−	8.71926i	−0.485866	−	0.668737i
$171$	−7.52792	+	0.955806i	−0.575675	+	0.0730923i
$172$	3.90317	−	1.26822i	0.297614	−	0.0967006i
$173$	12.4128	+	1.74450i	0.943724	+	0.132632i	0.594220	−	0.804303i	$-0.297461\pi$
$173$	12.4128	+	1.74450i	0.943724	+	0.132632i	0.349505	+	0.936935i	$0.386350\pi$
$174$	−0.572726	−	8.19036i	−0.0434182	−	0.620910i
$175$	−4.67748	−	12.8513i	−0.353584	−	0.971465i
$176$	−2.42841	−	2.25894i	−0.183049	−	0.170274i
$177$	19.9733	+	16.7596i	1.50128	+	1.25973i
$178$	4.50554	+	10.1196i	0.337704	+	0.758496i
$179$	−3.39914	−	15.9917i	−0.254063	−	1.19527i	−0.901372	−	0.433046i	$-0.857439\pi$
$179$	−3.39914	−	15.9917i	−0.254063	−	1.19527i	0.647308	−	0.762228i	$-0.275895\pi$
$180$	−6.55534	+	0.921293i	−0.488606	+	0.0686691i
$181$	6.00320	−	2.92795i	0.446214	−	0.217633i	−0.201544	−	0.979480i	$-0.564596\pi$
$181$	6.00320	−	2.92795i	0.446214	−	0.217633i	0.647758	+	0.761846i	$0.275707\pi$
$182$	1.36790	−	3.07236i	0.101396	−	0.227739i
$183$	0.889575	+	0.189085i	0.0657593	+	0.0139776i
$184$	−1.25570	+	0.784649i	−0.0925715	+	0.0578451i
$185$	9.84776	−	6.64240i	0.724022	−	0.488359i
$186$	−7.52107	+	2.73744i	−0.551471	+	0.200719i
$187$	−2.75950	−	8.98626i	−0.201795	−	0.657140i
$188$	0.177611	+	1.00728i	0.0129536	+	0.0734636i
$189$	3.20671	+	2.32981i	0.233254	+	0.169469i
$190$	12.0754	−	11.3538i	0.876040	−	0.823693i
$191$	−3.40482	−	10.4790i	−0.246364	−	0.758230i	−0.995409	−	0.0957114i	$-0.969487\pi$
$191$	−3.40482	−	10.4790i	−0.246364	−	0.758230i	0.749045	−	0.662519i	$-0.230513\pi$
$192$	1.51252	−	1.56626i	0.109157	−	0.113035i
$193$	3.61319	−	14.4917i	0.260083	−	1.04314i	−0.688152	−	0.725566i	$-0.741578\pi$
$193$	3.61319	−	14.4917i	0.260083	−	1.04314i	0.948235	−	0.317569i	$-0.102866\pi$
$194$	11.2246	−	8.76960i	0.805878	−	0.629621i
$195$	−15.1764	−	11.8571i	−1.08680	−	0.849103i
$196$	−1.18776	−	4.76383i	−0.0848396	−	0.340273i
$197$	21.0265	+	12.1397i	1.49808	+	0.864915i	0.999998	−	0.00221583i	$-0.000705322\pi$
$197$	21.0265	+	12.1397i	1.49808	+	0.864915i	0.498080	+	0.867131i	$0.334039\pi$
$198$	−5.66915	−	1.09472i	−0.402889	−	0.0777980i
$199$	−2.89568	+	16.4222i	−0.205270	+	1.16414i	0.691745	+	0.722141i	$0.256842\pi$
$199$	−2.89568	+	16.4222i	−0.205270	+	1.16414i	−0.897015	+	0.442000i	$0.854269\pi$
$200$	6.80435	−	6.57088i	0.481140	−	0.464632i
$201$	−28.3624	+	6.02862i	−2.00053	+	0.425226i
$202$	−2.01083	+	9.46022i	−0.141482	+	0.665619i
$203$	−0.380299	+	5.43853i	−0.0266917	+	0.381710i
$204$	5.93228	−	1.70106i	0.415343	−	0.119098i
$205$	19.3593	+	24.7788i	1.35211	+	1.73062i
$206$	16.5361	−	6.68100i	1.15212	−	0.465488i
$207$	−1.13000	+	2.31684i	−0.0785405	+	0.161032i
$208$	2.32613			0.161288
$209$	13.1753	−	5.95073i	0.911355	−	0.411621i
$210$	11.9704			0.826038
$211$	−1.83765	+	3.76774i	−0.126509	+	0.259382i	−0.952642	−	0.304093i	$-0.901647\pi$
$211$	−1.83765	+	3.76774i	−0.126509	+	0.259382i	0.826134	+	0.563474i	$0.190536\pi$
$212$	−7.78685	+	3.14609i	−0.534803	+	0.216074i
$213$	−1.25392	−	1.60494i	−0.0859171	−	0.109969i
$214$	3.13988	−	0.900347i	0.214638	−	0.0615465i
$215$	−1.08860	+	15.5677i	−0.0742417	+	1.06171i
$216$	−0.569997	+	2.68163i	−0.0387834	+	0.182462i
$217$	5.19848	−	1.10497i	0.352896	−	0.0750103i
$218$	11.9386	−	11.5290i	0.808583	−	0.780839i
$219$	−0.314921	+	1.78601i	−0.0212804	+	0.120687i
$220$	11.4233	−	5.34396i	0.770162	−	0.360290i
$221$	5.70973	+	3.29651i	0.384078	+	0.221747i
$222$	1.64550	+	6.59972i	0.110438	+	0.442944i
$223$	12.3973	+	9.68582i	0.830184	+	0.648611i	0.938413	−	0.345515i	$-0.112296\pi$
$223$	12.3973	+	9.68582i	0.830184	+	0.648611i	−0.108229	+	0.994126i	$0.534518\pi$
$224$	−1.13931	+	0.890123i	−0.0761231	+	0.0594739i
$225$	3.98381	−	15.9782i	0.265587	−	1.06521i
$226$	7.35693	−	7.61832i	0.489376	−	0.506763i
$227$	−4.37576	−	13.4672i	−0.290430	−	0.893851i	−0.984718	−	0.174154i	$-0.944281\pi$
$227$	−4.37576	−	13.4672i	−0.290430	−	0.893851i	0.694289	−	0.719697i	$-0.255719\pi$
$228$	3.74434	+	8.72106i	0.247975	+	0.577566i
$229$	18.3959	+	13.3654i	1.21563	+	0.883210i	0.995730	−	0.0923114i	$-0.0294255\pi$
$229$	18.3959	+	13.3654i	1.21563	+	0.883210i	0.219904	+	0.975521i	$0.429426\pi$
$230$	−0.977704	−	5.54483i	−0.0644679	−	0.365616i
$231$	9.87617	+	3.38702i	0.649804	+	0.222849i
$232$	−3.54338	+	1.28969i	−0.232635	+	0.0846721i
$233$	18.1030	−	12.2106i	1.18597	−	0.799945i	0.202192	−	0.979346i	$-0.435194\pi$
$233$	18.1030	−	12.2106i	1.18597	−	0.799945i	0.983776	+	0.179401i	$0.0574158\pi$
$234$	3.43420	−	2.14593i	0.224501	−	0.140284i
$235$	−3.80431	−	0.808630i	−0.248166	−	0.0527492i
$236$	4.87056	−	10.9395i	0.317046	−	0.712098i
$237$	4.06014	−	1.98026i	0.263734	−	0.128632i
$238$	−4.05799	+	0.570314i	−0.263041	+	0.0369680i
$239$	1.83425	+	8.62947i	0.118648	+	0.558194i	0.996809	+	0.0798286i	$0.0254373\pi$
$239$	1.83425	+	8.62947i	0.118648	+	0.558194i	−0.878161	+	0.478366i	$0.841229\pi$
$240$	3.36755	+	7.56365i	0.217375	+	0.488232i
$241$	−18.2658	−	15.3268i	−1.17660	−	0.987286i	−0.999995	−	0.00300456i	$-0.999044\pi$
$241$	−18.2658	−	15.3268i	−1.17660	−	0.987286i	−0.176606	−	0.984282i	$-0.556512\pi$
$242$	10.9369	−	1.17680i	0.703049	−	0.0756475i
$243$	5.52169	+	15.1707i	0.354216	+	0.973201i
$244$	−0.0291362	−	0.416667i	−0.00186525	−	0.0266744i
$245$	18.4874	+	2.59824i	1.18112	+	0.165995i
$246$	−17.1243	+	5.56401i	−1.09180	+	0.354749i
$247$	−3.92329	+	9.34958i	−0.249633	+	0.594900i
$248$	2.16064	+	2.97387i	0.137201	+	0.188841i
$249$	26.2236	−	13.9433i	1.66185	−	0.883623i
$250$	6.35184	+	15.7214i	0.401726	+	0.994306i
$251$	−21.9456	−	6.29279i	−1.38519	−	0.397197i	−0.501456	−	0.865183i	$-0.667202\pi$
$251$	−21.9456	−	6.29279i	−1.38519	−	0.397197i	−0.883736	+	0.467986i	$0.844980\pi$
$252$	−0.860857	+	2.36518i	−0.0542289	+	0.148993i
$253$	0.762252	−	4.85139i	0.0479223	−	0.305004i
$254$	−8.98806	+	15.5678i	−0.563961	+	0.976809i
$255$	−2.45294	+	23.3381i	−0.153609	+	1.46149i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	2.13839	+	15.2155i	0.133389	+	0.949115i	0.935847	+	0.352406i	$0.114636\pi$
$257$	2.13839	+	15.2155i	0.133389	+	0.949115i	−0.802458	+	0.596709i	$0.796475\pi$
$258$	−8.16340	−	3.63458i	−0.508231	−	0.226279i
$259$	−0.472100	−	4.49174i	−0.0293349	−	0.279103i
$260$	−3.31346	+	8.20109i	−0.205492	+	0.508610i
$261$	−4.04153	+	5.17292i	−0.250164	+	0.320196i
$262$	5.69653	−	19.8662i	0.351933	−	1.22734i
$263$	−9.03390	−	10.7662i	−0.557054	−	0.663871i	0.411866	−	0.911244i	$-0.364877\pi$
$263$	−9.03390	−	10.7662i	−0.557054	−	0.663871i	−0.968920	+	0.247373i	$0.920433\pi$
$264$	0.638267	+	7.19322i	0.0392826	+	0.442712i
$265$		−	31.9350i		−	1.96175i
$266$	−1.65616	−	6.08059i	−0.101546	−	0.372825i
$267$	7.45325	−	22.9387i	0.456131	−	1.40383i
$268$	6.25199	+	11.7583i	0.381901	+	0.718252i
$269$	−6.16371	−	1.53679i	−0.375808	−	0.0936995i	0.0494381	−	0.998777i	$-0.484257\pi$
$269$	−6.16371	−	1.53679i	−0.375808	−	0.0936995i	−0.425246	+	0.905078i	$0.639813\pi$
$270$	−8.64250	−	5.82944i	−0.525966	−	0.354769i
$271$	−26.9394	−	0.940744i	−1.63645	−	0.0571461i	−0.798186	−	0.602411i	$-0.794207\pi$
$271$	−26.9394	−	0.940744i	−1.63645	−	0.0571461i	−0.838264	+	0.545265i	$0.816429\pi$
$272$	−1.50197	−	2.40365i	−0.0910701	−	0.145743i
$273$	−6.68964	+	2.97842i	−0.404875	+	0.180262i
$274$	4.48545	+	7.76902i	0.270976	+	0.469344i
$275$	1.68055	+	31.3274i	0.101341	+	1.88911i
$276$	3.17502	+	0.559842i	0.191114	+	0.0336986i
$277$	11.0427	+	1.16063i	0.663490	+	0.0697356i	0.430286	−	0.902692i	$-0.358413\pi$
$277$	11.0427	+	1.16063i	0.663490	+	0.0697356i	0.233203	+	0.972428i	$0.425079\pi$
$278$	4.87466	−	4.38916i	0.292363	−	0.263244i
$279$	5.93336	+	2.39723i	0.355221	+	0.143519i
$280$	−1.51537	−	5.28471i	−0.0905605	−	0.315822i
$281$	9.08892	−	13.4749i	0.542199	−	0.803844i	−0.453995	−	0.891004i	$-0.650002\pi$
$281$	9.08892	−	13.4749i	0.542199	−	0.803844i	0.996194	+	0.0871606i	$0.0277793\pi$
$282$	1.18016	−	1.88864i	0.0702773	−	0.112467i
$283$	2.31710	−	16.4870i	0.137737	−	0.980053i	−0.791657	−	0.610966i	$-0.790781\pi$
$283$	2.31710	−	16.4870i	0.137737	−	0.980053i	0.929395	−	0.369087i	$-0.120330\pi$
$284$	−0.549815	+	0.756755i	−0.0326255	+	0.0449052i
$285$	−36.0809	+	0.778479i	−2.13725	+	0.0461131i
$286$	−5.05425	+	5.82875i	−0.298864	+	0.344661i
$287$	11.7743	−	2.07613i	0.695016	−	0.122550i
$288$	−1.73665	+	0.121438i	−0.102333	+	0.00715582i
$289$	0.312929	+	8.96111i	0.0184076	+	0.527124i
$290$	0.500407	−	14.3298i	0.0293849	−	0.841473i
$291$	−30.9392	−	2.16348i	−1.81369	−	0.126825i
$292$	0.828355	−	0.0870636i	0.0484758	−	0.00509501i
$293$	−6.58330	+	7.31150i	−0.384601	+	0.427142i	−0.904095	−	0.427332i	$-0.859454\pi$
$293$	−6.58330	+	7.31150i	−0.384601	+	0.427142i	0.519494	+	0.854474i	$0.326120\pi$
$294$	−5.01870	+	9.43879i	−0.292696	+	0.550482i
$295$	31.6307	+	32.7545i	1.84161	+	1.90704i
$296$	2.70534	−	1.56193i	0.157245	−	0.0907854i
$297$	−5.48104	−	7.25495i	−0.318042	−	0.420975i
$298$	−7.44206	+	8.86910i	−0.431107	+	0.513773i
$299$	1.92602	+	2.85545i	0.111385	+	0.165135i
$300$	−20.5834	+	0.718789i	−1.18838	+	0.0414993i
$301$	5.03199	+	3.14434i	0.290039	+	0.181236i
$302$	−3.04166	−	2.93730i	−0.175028	−	0.169023i
$303$	17.0367	−	12.3779i	0.978731	−	0.711089i
$304$	3.37617	−	2.75707i	0.193637	−	0.158129i
$305$	1.51052	+	0.490797i	0.0864920	+	0.0281030i
$306$	−4.43488	−	2.16304i	−0.253525	−	0.123652i
$307$	20.3309	−	17.0597i	1.16035	−	0.973646i	0.160436	−	0.987046i	$-0.448710\pi$
$307$	20.3309	−	17.0597i	1.16035	−	0.973646i	0.999910	+	0.0133997i	$0.00426540\pi$
$308$	0.245053	−	4.78891i	0.0139632	−	0.272873i
$309$	−36.4907	−	13.2815i	−2.07588	−	0.755559i
$310$	−13.5625	+	3.38151i	−0.770297	+	0.192057i
$311$	2.01579	+	2.23876i	0.114305	+	0.126948i	0.797582	−	0.603211i	$-0.206112\pi$
$311$	2.01579	+	2.23876i	0.114305	+	0.126948i	−0.683277	+	0.730160i	$0.739446\pi$
$312$	−3.76390	−	3.38903i	−0.213089	−	0.191866i
$313$	−2.37100	−	4.86128i	−0.134017	−	0.274776i	0.821223	−	0.570607i	$-0.193292\pi$
$313$	−2.37100	−	4.86128i	−0.134017	−	0.274776i	−0.955240	+	0.295832i	$0.904403\pi$
$314$	−7.07366	−	14.5032i	−0.399190	−	0.818461i
$315$	−7.11253	−	6.40415i	−0.400746	−	0.360833i
$316$	−1.38823	−	1.54179i	−0.0780940	−	0.0867322i
$317$	−24.5331	+	6.11680i	−1.37792	+	0.343553i	−0.859308	−	0.511458i	$-0.829106\pi$
$317$	−24.5331	+	6.11680i	−1.37792	+	0.343553i	−0.518609	+	0.855011i	$0.673550\pi$
$318$	17.1835	+	6.25428i	0.963603	+	0.350723i
$319$	4.46745	−	11.6812i	0.250129	−	0.654019i
$320$	2.91290	−	2.44421i	0.162836	−	0.136636i
$321$	−6.39237	−	3.11777i	−0.356787	−	0.174017i
$322$	−2.03601	−	0.661540i	−0.113462	−	0.0368662i
$323$	12.1944	−	1.98293i	0.678514	−	0.110333i
$324$	9.05450	−	6.57848i	0.503028	−	0.365471i
$325$	−15.8278	−	15.2847i	−0.877969	−	0.847845i
$326$	−15.0587	−	9.40974i	−0.834026	−	0.521158i
$327$	−36.1147	+	1.26115i	−1.99715	+	0.0697419i
$328$	4.62421	+	6.85567i	0.255329	+	0.378541i
$329$	−0.950551	+	1.13282i	−0.0524056	+	0.0624545i
$330$	−26.2698	−	7.99608i	−1.44611	−	0.440169i
$331$	−18.2753	+	10.5513i	−1.00450	+	0.579950i	−0.909577	−	0.415535i	$-0.863595\pi$
$331$	−18.2753	+	10.5513i	−1.00450	+	0.579950i	−0.0949251	+	0.995484i	$0.530261\pi$
$332$	−9.47543	−	9.81209i	−0.520032	−	0.538509i
$333$	2.55313	−	4.80173i	0.139910	−	0.263133i
$334$	8.90163	−	9.88626i	0.487076	−	0.540952i
$335$	−50.3611	+	5.29316i	−2.75152	+	0.289196i
$336$	3.14036	+	0.219595i	0.171320	+	0.0119799i
$337$	−0.0389076	+	1.11417i	−0.00211943	+	0.0606926i	−0.999990	−	0.00453712i	$-0.998556\pi$
$337$	−0.0389076	+	1.11417i	−0.00211943	+	0.0606926i	0.997870	+	0.0652297i	$0.0207780\pi$
$338$	0.264856	+	7.58449i	0.0144063	+	0.412542i
$339$	−23.0036	+	1.60857i	−1.24938	+	0.0873655i
$340$	10.6139	−	1.87151i	0.575617	−	0.101497i
$341$	−12.1465	−	1.04758i	−0.657769	−	0.0567298i
$342$	2.44095	−	7.18505i	0.131992	−	0.388523i
$343$	10.1211	−	13.9305i	0.546486	−	0.752174i
$344$	−0.571171	+	4.06409i	−0.0307955	+	0.219121i
$345$	−6.49646	+	10.3965i	−0.349758	+	0.559729i
$346$	−7.00934	+	10.3918i	−0.376824	+	0.558665i
$347$	5.05922	+	17.6436i	0.271593	+	0.947159i	0.972305	+	0.233714i	$0.0750880\pi$
$347$	5.05922	+	17.6436i	0.271593	+	0.947159i	−0.700712	+	0.713444i	$0.747134\pi$
$348$	7.61251	+	3.07566i	0.408074	+	0.164872i
$349$	21.8037	−	19.6322i	1.16713	−	1.05089i	0.169263	−	0.985571i	$-0.445861\pi$
$349$	21.8037	−	19.6322i	1.16713	−	1.05089i	0.997865	−	0.0653157i	$-0.0208055\pi$
$350$	13.6011	+	1.42954i	0.727011	+	0.0764119i
$351$	6.28029	+	1.10738i	0.335217	+	0.0591078i
$352$	3.09487	−	1.19239i	0.164957	−	0.0635546i
$353$	−9.47277	−	16.4073i	−0.504185	−	0.873274i	−0.999988	−	0.00483888i	$-0.998460\pi$
$353$	−9.47277	−	16.4073i	−0.504185	−	0.873274i	0.495804	−	0.868435i	$-0.334874\pi$
$354$	−23.8191	+	10.6050i	−1.26597	+	0.563647i
$355$	−1.88486	−	3.01641i	−0.100038	−	0.160094i
$356$	−11.0705	−	0.386592i	−0.586737	−	0.0204893i
$357$	7.39712	+	4.98942i	0.391497	+	0.264068i
$358$	15.8633	+	3.95517i	0.838402	+	0.209037i
$359$	10.8393	+	20.3857i	0.572075	+	1.07592i	0.986178	+	0.165687i	$0.0529843\pi$
$359$	10.8393	+	20.3857i	0.572075	+	1.07592i	−0.414103	+	0.910230i	$0.635905\pi$
$360$	2.04562	−	6.29577i	0.107814	−	0.331816i
$361$	5.38740	+	18.2202i	0.283547	+	0.958958i
$362$			6.67917i			0.351049i
$363$	−19.4114	−	14.0302i	−1.01883	−	0.736393i
$364$	2.16177	+	2.57630i	0.113308	+	0.135035i
$365$	−0.872995	+	3.04449i	−0.0456946	+	0.159356i
$366$	−0.559912	+	0.716655i	−0.0292671	+	0.0374602i
$367$	0.730963	−	1.80920i	0.0381559	−	0.0944393i	−0.906903	−	0.421340i	$-0.861560\pi$
$367$	0.730963	−	1.80920i	0.0381559	−	0.0944393i	0.945059	+	0.326901i	$0.106004\pi$
$368$	−0.154775	−	1.47258i	−0.00806819	−	0.0767637i
$369$	13.1516	+	5.85545i	0.684643	+	0.304823i
$370$	1.65317	+	11.7629i	0.0859444	+	0.611526i
$371$	−10.7211	−	5.70050i	−0.556611	−	0.295955i
$372$	0.836620	−	7.95991i	0.0433767	−	0.412702i
$373$	−13.1660	+	22.8042i	−0.681710	+	1.18076i	0.292748	+	0.956190i	$0.405430\pi$
$373$	−13.1660	+	22.8042i	−0.681710	+	1.18076i	−0.974459	+	0.224567i	$0.927903\pi$
$374$	9.28648	+	1.45909i	0.480193	+	0.0754479i
$375$	12.6272	−	34.6928i	0.652064	−	1.79153i
$376$	−0.983199	−	0.281928i	−0.0507046	−	0.0145393i
$377$	3.28581	+	8.13266i	0.169228	+	0.418853i
$378$	−3.49975	+	1.86085i	−0.180008	+	0.0957118i
$379$	−16.9470	−	23.3256i	−0.870511	−	1.19816i	−0.978960	−	0.204054i	$-0.934588\pi$
$379$	−16.9470	−	23.3256i	−0.870511	−	1.19816i	0.108449	−	0.994102i	$-0.465412\pi$
$380$	4.91125	+	15.8305i	0.251942	+	0.812086i
$381$	37.2248	−	12.0951i	1.90708	−	0.619649i
$382$	10.9110	+	1.53344i	0.558255	+	0.0784576i
$383$	0.651698	+	9.31971i	0.0333002	+	0.476215i	0.985381	+	0.170367i	$0.0544954\pi$
$383$	0.651698	+	9.31971i	0.0333002	+	0.476215i	−0.952080	+	0.305848i	$0.901060\pi$
$384$	0.744700	+	2.04605i	0.0380028	+	0.104412i
$385$	16.5349	+	7.68552i	0.842696	+	0.391691i
$386$	11.4411	+	9.60025i	0.582338	+	0.488640i
$387$	2.90600	+	6.52698i	0.147720	+	0.331785i
$388$	2.96153	+	13.9329i	0.150349	+	0.707337i
$389$	20.7275	−	2.91307i	1.05093	−	0.147698i	0.407500	−	0.913205i	$-0.366401\pi$
$389$	20.7275	−	2.91307i	1.05093	−	0.147698i	0.643428	+	0.765507i	$0.277512\pi$
$390$	17.3100	−	8.44263i	0.876523	−	0.427509i
$391$	1.70698	−	3.83395i	0.0863259	−	0.193891i
$392$	4.80238	+	1.02078i	0.242557	+	0.0515570i
$393$	−38.1613	+	23.8458i	−1.92498	+	1.20286i
$394$	−20.1285	+	13.5768i	−1.01406	+	0.683991i
$395$	7.41324	−	2.69820i	0.373000	−	0.135761i
$396$	3.46911	−	4.61551i	0.174330	−	0.231938i
$397$	−5.71744	−	32.4252i	−0.286950	−	1.62737i	−0.698236	−	0.715868i	$-0.746031\pi$
$397$	−5.71744	−	32.4252i	−0.286950	−	1.62737i	0.411285	−	0.911507i	$-0.365080\pi$
$398$	−13.4908	−	9.80166i	−0.676234	−	0.491313i
$399$	−6.17920	+	12.2519i	−0.309347	+	0.613361i
$400$	2.92304	+	8.99619i	0.146152	+	0.449810i
$401$	18.3363	−	18.9878i	0.915669	−	0.948203i	−0.0831623	−	0.996536i	$-0.526502\pi$
$401$	18.3363	−	18.9878i	0.915669	−	0.948203i	0.998831	+	0.0483330i	$0.0153909\pi$
$402$	7.01478	−	28.1348i	0.349866	−	1.40323i
$403$	6.73799	−	5.26429i	0.335643	−	0.262233i
$404$	−7.62130	−	5.95441i	−0.379174	−	0.296243i
$405$	10.2956	+	41.2935i	0.511594	+	2.05189i
$406$	−4.72140	−	2.72590i	−0.234319	−	0.135284i
$407$	−1.96436	+	10.1728i	−0.0973698	+	0.504245i
$408$	−1.07164	+	6.07760i	−0.0530543	+	0.300886i
$409$	−9.69157	+	9.35904i	−0.479217	+	0.462775i	−0.894597	−	0.446873i	$-0.852538\pi$
$409$	−9.69157	+	9.35904i	−0.479217	+	0.462775i	0.415380	+	0.909648i	$0.363649\pi$
$410$	−30.7576	+	6.53772i	−1.51901	+	0.322875i
$411$	4.06111	−	19.1060i	0.200320	−	0.942430i
$412$	−1.24409	+	17.7913i	−0.0612918	+	0.876513i
$413$	16.6424	−	4.77212i	0.818918	−	0.234821i
$414$	−1.58701	−	2.03128i	−0.0779971	−	0.0998318i
$415$	48.0911	−	19.4301i	2.36070	−	0.953785i
$416$	−1.01971	+	2.09071i	−0.0499953	+	0.102506i
$417$	−14.2824			−0.699411
$418$	−0.427191	+	14.4505i	−0.0208946	+	0.706798i
$419$	16.3680			0.799628			0.399814	−	0.916596i	$-0.369075\pi$
$419$	16.3680			0.799628			0.399814	+	0.916596i	$0.369075\pi$
$420$	−5.24749	+	10.7589i	−0.256051	+	0.524983i
$421$	3.61473	−	1.46045i	0.176171	−	0.0711778i	−0.284827	−	0.958579i	$-0.591936\pi$
$421$	3.61473	−	1.46045i	0.176171	−	0.0711778i	0.460998	+	0.887401i	$0.347492\pi$
$422$	−2.58085	−	3.30333i	−0.125634	−	0.160804i
$423$	−1.71164	+	0.490805i	−0.0832228	+	0.0238638i
$424$	0.585842	−	8.37793i	0.0284510	−	0.406868i
$425$	−5.57419	+	26.2245i	−0.270388	+	1.27208i
$426$	1.99220	−	0.423454i	0.0965222	−	0.0205164i
$427$	0.434401	−	0.419496i	0.0210221	−	0.0203008i
$428$	−0.567208	+	3.21679i	−0.0274170	+	0.155490i
$429$	16.6704	−	2.06774i	0.804853	−	0.0998315i
$430$	−13.5149	−	7.80284i	−0.651747	−	0.376286i
$431$	−0.624743	−	2.50571i	−0.0300928	−	0.120696i	0.953371	−	0.301801i	$-0.0975880\pi$
$431$	−0.624743	−	2.50571i	−0.0300928	−	0.120696i	−0.983464	+	0.181106i	$0.942032\pi$
$432$	−2.16036	−	1.68786i	−0.103940	−	0.0812071i
$433$	18.9607	−	14.8137i	0.911194	−	0.711903i	−0.0467351	−	0.998907i	$-0.514882\pi$
$433$	18.9607	−	14.8137i	0.911194	−	0.711903i	0.957929	+	0.287004i	$0.0926594\pi$
$434$	−1.28572	+	5.15675i	−0.0617166	+	0.247532i
$435$	−21.6873	+	22.4578i	−1.03983	+	1.07677i
$436$	5.12862	+	15.7843i	0.245617	+	0.755930i
$437$	6.17990	+	1.86158i	0.295625	+	0.0890517i
$438$	−1.46720	−	1.06598i	−0.0701056	−	0.0509347i
$439$	−4.12204	−	23.3772i	−0.196734	−	1.11573i	−0.909928	−	0.414767i	$-0.863863\pi$
$439$	−4.12204	−	23.3772i	−0.196734	−	1.11573i	0.713194	−	0.700967i	$-0.247248\pi$
$440$	−0.204546	+	12.6099i	−0.00975137	+	0.601152i
$441$	8.03172	−	2.92331i	0.382463	−	0.139205i
$442$	−5.46587	+	3.68677i	−0.259985	+	0.175362i
$443$	23.4404	−	14.6472i	1.11369	−	0.695910i	0.157167	−	0.987572i	$-0.449764\pi$
$443$	23.4404	−	14.6472i	1.11369	−	0.695910i	0.956521	+	0.291662i	$0.0942084\pi$
$444$	−6.65313	−	1.41417i	−0.315744	−	0.0671134i
$445$	17.1324	−	38.4800i	0.812153	−	1.82413i
$446$	−14.1402	+	6.89662i	−0.669557	+	0.326565i
$447$	24.9637	−	3.50841i	1.18074	−	0.165942i
$448$	−0.300599	−	1.41421i	−0.0142020	−	0.0668149i
$449$	−5.96581	−	13.3994i	−0.281544	−	0.632359i	0.716314	−	0.697778i	$-0.245828\pi$
$449$	−5.96581	−	13.3994i	−0.281544	−	0.632359i	−0.997858	+	0.0654199i	$0.979161\pi$
$450$	12.6147	+	10.5850i	0.594663	+	0.498982i
$451$	−27.2263	−	3.30888i	−1.28204	−	0.155809i
$452$	3.62224	+	9.95202i	0.170376	+	0.468104i
$453$	0.642231	+	9.18433i	0.0301746	+	0.431518i
$454$	14.0225	+	1.97073i	0.658107	+	0.0924909i
$455$	−12.1624	+	3.95181i	−0.570183	+	0.185264i
$456$	−9.47984	−	0.457668i	−0.443934	−	0.0214323i
$457$	2.51865	+	3.46662i	0.117817	+	0.162162i	0.863852	−	0.503745i	$-0.168045\pi$
$457$	2.51865	+	3.46662i	0.117817	+	0.162162i	−0.746035	+	0.665907i	$0.768045\pi$
$458$	−20.0770	+	10.6751i	−0.938135	+	0.498815i
$459$	−2.91085	−	7.20460i	−0.135867	−	0.336282i
$460$	5.41226	+	1.55194i	0.252348	+	0.0723596i
$461$	−12.2651	+	33.6980i	−0.571242	+	1.56947i	0.231303	+	0.972882i	$0.425701\pi$
$461$	−12.2651	+	33.6980i	−0.571242	+	1.56947i	−0.802545	+	0.596592i	$0.796521\pi$
$462$	−7.37366	+	7.39187i	−0.343054	+	0.343901i
$463$	8.31779	−	14.4068i	0.386561	−	0.669543i	−0.605424	−	0.795903i	$-0.706996\pi$
$463$	8.31779	−	14.4068i	0.386561	−	0.669543i	0.991984	+	0.126361i	$0.0403297\pi$
$464$	0.394155	−	3.75013i	0.0182982	−	0.174096i
$465$	26.8720	+	14.2881i	1.24616	+	0.662595i
$466$	3.03901	+	21.6237i	0.140779	+	1.00170i
$467$	24.7399	+	11.0149i	1.14483	+	0.509710i	0.889405	−	0.457119i	$-0.151119\pi$
$467$	24.7399	+	11.0149i	1.14483	+	0.509710i	0.255422	+	0.966830i	$0.417785\pi$
$468$	0.423292	+	4.02735i	0.0195667	+	0.186164i
$469$	−7.21262	+	17.8518i	−0.333048	+	0.824322i
$470$	2.39449	−	3.06481i	0.110450	−	0.141369i
$471$	−9.68435	+	33.7733i	−0.446231	+	1.55619i
$472$	7.69720	+	9.17317i	0.354293	+	0.422229i
$473$	−8.94264	−	10.2617i	−0.411183	−	0.471835i
$474$			4.51732i			0.207487i
$475$	−41.0891	−	3.42433i	−1.88530	−	0.157119i
$476$	1.26631	−	3.89731i	0.0580413	−	0.178633i
$477$	−6.86398	−	12.9093i	−0.314280	−	0.591075i
$478$	−8.56020	−	2.13430i	−0.391535	−	0.0976205i
$479$	13.6866	+	9.23170i	0.625355	+	0.421807i	0.830574	−	0.556909i	$-0.188013\pi$
$479$	13.6866	+	9.23170i	0.625355	+	0.421807i	−0.205219	+	0.978716i	$0.565791\pi$
$480$	−8.27440	−	0.288949i	−0.377673	−	0.0131886i
$481$	−3.85067	−	6.16235i	−0.175575	−	0.280979i
$482$	21.7828	−	9.69834i	0.992181	−	0.441747i
$483$	2.33063	+	4.03677i	0.106047	+	0.183680i
$484$	−3.73671	+	10.3459i	−0.169850	+	0.470267i
$485$	−53.3410	−	9.40545i	−2.42209	−	0.427080i
$486$	−16.0559	−	1.68754i	−0.728310	−	0.0765485i
$487$	10.0686	−	9.06584i	0.456253	−	0.410812i	−0.408697	−	0.912670i	$-0.634017\pi$
$487$	10.0686	−	9.06584i	0.456253	−	0.410812i	0.864950	+	0.501858i	$0.167350\pi$
$488$	0.387270	+	0.156467i	0.0175309	+	0.00708294i
$489$	10.6570	+	37.1655i	0.481927	+	1.68068i
$490$	−10.4396	+	15.4774i	−0.471614	+	0.699197i
$491$	−4.71271	+	7.54191i	−0.212682	+	0.340362i	−0.937138	−	0.348959i	$-0.886535\pi$
$491$	−4.71271	+	7.54191i	−0.212682	+	0.340362i	0.724456	+	0.689321i	$0.242091\pi$
$492$	2.50589	−	17.8303i	0.112974	−	0.803852i
$493$	6.28205	−	8.64650i	0.282929	−	0.389419i
$494$	−6.68349	−	7.62482i	−0.300705	−	0.343057i
$495$	11.3310	+	18.8054i	0.509291	+	0.845239i
$496$	−3.62006	+	0.638313i	−0.162545	+	0.0286611i
$497$	−1.34911	+	0.0943388i	−0.0605158	+	0.00423167i
$498$	1.03652	+	29.6820i	0.0464475	+	1.33008i
$499$	0.0858945	−	2.45970i	0.00384517	−	0.110111i	−0.995951	−	0.0899021i	$-0.971345\pi$
$499$	0.0858945	−	2.45970i	0.00384517	−	0.110111i	0.999796	−	0.0202091i	$-0.00643319\pi$
$500$	−16.9147	−	1.18279i	−0.756449	−	0.0528961i
$501$	−28.8073	+	3.02777i	−1.28702	+	0.135271i
$502$	15.2762	−	16.9660i	0.681811	−	0.757228i
$503$	16.2707	−	30.6007i	0.725473	−	1.36442i	−0.197789	−	0.980245i	$-0.563376\pi$
$503$	16.2707	−	30.6007i	0.725473	−	1.36442i	0.923262	−	0.384172i	$-0.125513\pi$
$504$	−1.74844	−	1.81056i	−0.0778817	−	0.0806488i
$505$	31.8492	−	18.3882i	1.41727	−	0.818263i
$506$	4.02625	+	2.81182i	0.178989	+	0.125001i
$507$	10.6216	−	12.6583i	0.471720	−	0.562174i
$508$	−10.0521	−	14.9029i	−0.445991	−	0.661208i
$509$	−19.3340	+	0.675158i	−0.856964	+	0.0299258i	−0.460011	−	0.887913i	$-0.652155\pi$
$509$	−19.3340	+	0.675158i	−0.856964	+	0.0299258i	−0.396953	+	0.917839i	$0.629932\pi$
$510$	−19.9009	−	12.4355i	−0.881226	−	0.550651i
$511$	0.866252	+	0.836530i	0.0383207	+	0.0370059i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	10.4278	−	5.83652i	0.460399	−	0.257688i
$514$	−14.6130	−	4.74804i	−0.644551	−	0.209427i
$515$	−60.9534	−	29.7290i	−2.68593	−	1.31001i
$516$	6.84534	−	5.74392i	0.301349	−	0.252862i
$517$	2.84275	−	1.85109i	0.125024	−	0.0814111i
$518$	4.24410	+	1.54473i	0.186475	+	0.0678714i
$519$	26.4819	−	6.60268i	1.16243	−	0.289826i
$520$	−5.91857	−	6.57324i	−0.259546	−	0.288255i
$521$	6.07167	+	5.46695i	0.266005	+	0.239512i	0.791329	−	0.611390i	$-0.209389\pi$
$521$	6.07167	+	5.46695i	0.266005	+	0.239512i	−0.525325	+	0.850902i	$0.676056\pi$
$522$	−2.87770	−	5.90016i	−0.125953	−	0.258243i
$523$	1.63169	+	3.34546i	0.0713488	+	0.146287i	0.931487	−	0.363774i	$-0.118512\pi$
$523$	1.63169	+	3.34546i	0.0713488	+	0.146287i	−0.860139	+	0.510060i	$0.829623\pi$
$524$	15.3584	+	13.8288i	0.670935	+	0.604112i
$525$	−19.9251	−	22.1291i	−0.869604	−	0.965793i
$526$	13.6368	−	3.40003i	0.594592	−	0.148248i
$527$	−9.79039	−	3.56341i	−0.426476	−	0.155225i
$528$	−6.74502	−	2.57963i	−0.293539	−	0.112264i
$529$	−15.9395	+	13.3748i	−0.693022	+	0.581514i
$530$	28.7030	+	13.9994i	1.24678	+	0.608095i
$531$	19.8264	+	6.44197i	0.860391	+	0.279558i
$532$	6.19121	+	1.17700i	0.268423	+	0.0510295i
$533$	15.5621	−	11.3065i	0.674069	−	0.489740i
$534$	17.3499	+	16.7546i	0.750804	+	0.725043i
$535$	−10.5333	−	6.58193i	−0.455394	−	0.284561i
$536$	−13.3090	+	0.464760i	−0.574860	+	0.0200746i
$537$	−19.9059	−	29.5117i	−0.859002	−	1.27352i
$538$	4.08325	−	4.86623i	0.176041	−	0.209798i
$539$	−12.9925	+	9.81570i	−0.559626	+	0.422792i
$540$	9.02809	−	5.21237i	0.388507	−	0.224305i
$541$	−2.22447	−	2.30351i	−0.0956376	−	0.0990356i	0.669815	−	0.742528i	$-0.266374\pi$
$541$	−2.22447	−	2.30351i	−0.0956376	−	0.0990356i	−0.765452	+	0.643493i	$0.777485\pi$
$542$	12.6550	−	23.8005i	0.543578	−	1.02232i
$543$	9.73113	−	10.8075i	0.417603	−	0.463795i
$544$	2.81880	−	0.296268i	0.120855	−	0.0127024i
$545$	−62.9551	−	4.40225i	−2.69670	−	0.188572i
$546$	0.255559	−	7.31826i	0.0109369	−	0.313193i
$547$	1.09292	+	31.2972i	0.0467299	+	1.33817i	0.765731	+	0.643161i	$0.222377\pi$
$547$	1.09292	+	31.2972i	0.0467299	+	1.33817i	−0.719001	+	0.695009i	$0.755400\pi$
$548$	−8.94904	+	0.625778i	−0.382284	+	0.0267319i
$549$	0.716095	−	0.126267i	0.0305622	−	0.00538894i
$550$	−28.8936	−	12.2226i	−1.23203	−	0.521172i
$551$	14.4084	+	7.90929i	0.613818	+	0.336947i
$552$	−1.89502	+	2.60827i	−0.0806575	+	0.111016i
$553$	0.417459	−	2.97038i	0.0177522	−	0.126313i
$554$	−5.88396	+	9.41630i	−0.249985	+	0.400060i
$555$	14.4629	−	21.4421i	0.613915	−	0.910166i
$556$	1.80804	+	6.30540i	0.0766781	+	0.267408i
$557$	−7.52250	−	3.03929i	−0.318738	−	0.128779i	0.209662	−	0.977774i	$-0.432764\pi$
$557$	−7.52250	−	3.03929i	−0.318738	−	0.128779i	−0.528400	+	0.848995i	$0.677208\pi$
$558$	−4.75563	+	4.28199i	−0.201322	+	0.181271i
$559$	9.49423	+	0.997883i	0.401563	+	0.0422060i
$560$	5.41416	+	0.954662i	0.228790	+	0.0403419i
$561$	−12.9006	−	15.8908i	−0.544663	−	0.670909i
$562$	8.12682	+	14.0761i	0.342809	+	0.593763i
$563$	25.8724	−	11.5191i	1.09039	−	0.485474i	0.218832	−	0.975763i	$-0.429775\pi$
$563$	25.8724	−	11.5191i	1.09039	−	0.485474i	0.871560	+	0.490289i	$0.163109\pi$
$564$	1.18016	+	1.88864i	0.0496935	+	0.0795263i
$565$	−40.2469	−	1.40545i	−1.69320	−	0.0591278i
$566$	13.8027	+	9.31004i	0.580171	+	0.391330i
$567$	15.7007	+	3.91462i	0.659367	+	0.164399i
$568$	−0.439144	−	0.825910i	−0.0184261	−	0.0346544i
$569$	−5.71777	+	17.5975i	−0.239701	+	0.737725i	0.756762	+	0.653691i	$0.226780\pi$
$569$	−5.71777	+	17.5975i	−0.239701	+	0.737725i	−0.996463	+	0.0840339i	$0.973220\pi$
$570$	15.1171	−	32.7705i	0.633187	−	1.37261i
$571$		−	13.3332i		−	0.557978i	−0.960294	−	0.278989i	$-0.910001\pi$
$571$		−	13.3332i		−	0.557978i	0.960294	−	0.278989i	$-0.0899992\pi$
$572$	−3.02321	−	7.09788i	−0.126407	−	0.296777i
$573$	−15.4209	−	18.3779i	−0.644216	−	0.767747i
$574$	−3.29551	+	11.4928i	−0.137552	+	0.479700i
$575$	−8.62303	+	11.0370i	−0.359605	+	0.460274i
$576$	0.652149	−	1.61412i	0.0271729	−	0.0672552i
$577$	3.04996	+	29.0184i	0.126971	+	1.20805i	0.853566	+	0.520985i	$0.174435\pi$
$577$	3.04996	+	29.0184i	0.126971	+	1.20805i	−0.726594	+	0.687067i	$0.758898\pi$
$578$	−8.19137	−	3.64703i	−0.340716	−	0.151697i
$579$	−4.52585	−	32.2031i	−0.188088	−	1.33832i
$580$	12.6601	+	6.73152i	0.525684	+	0.279511i
$581$	2.06144	−	19.6133i	0.0855229	−	0.813696i
$582$	15.5074	−	26.8595i	0.642801	−	1.11336i
$583$	19.7202	+	19.6717i	0.816729	+	0.814717i
$584$	−0.284875	+	0.782687i	−0.0117882	+	0.0323878i
$585$	−14.8019	−	4.24439i	−0.611985	−	0.175484i
$586$	−3.68560	−	9.12219i	−0.152251	−	0.376834i
$587$	15.6995	−	8.34758i	0.647989	−	0.344542i	−0.112728	−	0.993626i	$-0.535959\pi$
$587$	15.6995	−	8.34758i	0.647989	−	0.344542i	0.760717	+	0.649084i	$0.224848\pi$
$588$	−6.28348	−	8.64847i	−0.259126	−	0.356657i
$589$	3.54002	−	15.6269i	0.145864	−	0.643896i
$590$	−43.3055	+	14.0708i	−1.78286	+	0.579286i
$591$	52.3503	+	7.35736i	2.15340	+	0.302641i
$592$	0.217910	+	3.11625i	0.00895603	+	0.128077i
$593$	8.27979	+	22.7485i	0.340010	+	0.934170i	0.985391	+	0.170309i	$0.0544766\pi$
$593$	8.27979	+	22.7485i	0.340010	+	0.934170i	−0.645381	+	0.763861i	$0.723301\pi$
$594$	8.92344	−	1.74597i	0.366133	−	0.0716379i
$595$	11.9367	+	10.0161i	0.489357	+	0.410619i
$596$	−4.70911	−	10.5768i	−0.192893	−	0.433244i
$597$	7.54900	+	35.5153i	0.308960	+	1.45354i
$598$	−3.41077	+	0.479353i	−0.139477	+	0.0196022i
$599$	−12.2419	+	5.97076i	−0.500189	+	0.243959i	−0.671153	−	0.741319i	$-0.734201\pi$
$599$	−12.2419	+	5.97076i	−0.500189	+	0.243959i	0.170964	+	0.985277i	$0.445312\pi$
$600$	8.37714	−	18.8154i	0.341995	−	0.768134i
$601$	−2.02619	−	0.430680i	−0.0826500	−	0.0175678i	0.166401	−	0.986058i	$-0.446785\pi$
$601$	−2.02619	−	0.430680i	−0.0826500	−	0.0175678i	−0.249051	+	0.968490i	$0.580119\pi$
$602$	−5.03199	+	3.14434i	−0.205089	+	0.128154i
$603$	−19.2201	+	12.9641i	−0.782701	+	0.527939i
$604$	3.97340	−	1.44620i	0.161676	−	0.0588451i
$605$	−31.1530	−	27.9114i	−1.26655	−	1.13476i
$606$	3.65677	+	20.7385i	0.148546	+	0.842446i
$607$	27.9428	+	20.3016i	1.13416	+	0.824017i	0.986295	−	0.164990i	$-0.0527593\pi$
$607$	27.9428	+	20.3016i	1.13416	+	0.824017i	0.147867	+	0.989007i	$0.452759\pi$
$608$	0.998026	+	4.24311i	0.0404753	+	0.172081i
$609$	3.66820	+	11.2896i	0.148643	+	0.457476i
$610$	−1.10329	+	1.14249i	−0.0446710	+	0.0462582i
$611$	−0.575585	+	2.30854i	−0.0232857	+	0.0933937i
$612$	3.88825	−	3.03783i	0.157173	−	0.122797i
$613$	15.8369	+	12.3731i	0.639645	+	0.499746i	0.882497	−	0.470318i	$-0.155861\pi$
$613$	15.8369	+	12.3731i	0.639645	+	0.499746i	−0.242852	+	0.970063i	$0.578083\pi$
$614$	6.42064	+	25.7518i	0.259116	+	1.03926i
$615$	59.2936	+	34.2332i	2.39095	+	1.38042i
$616$	4.19682	+	2.31957i	0.169095	+	0.0934582i
$617$	−3.91775	+	22.2187i	−0.157723	+	0.894490i	0.798531	+	0.601953i	$0.205611\pi$
$617$	−3.91775	+	22.2187i	−0.157723	+	0.894490i	−0.956254	+	0.292537i	$0.905500\pi$
$618$	27.9338	−	26.9754i	1.12366	−	1.08511i
$619$	2.38272	−	0.506462i	0.0957694	−	0.0203564i	−0.159778	−	0.987153i	$-0.551078\pi$
$619$	2.38272	−	0.506462i	0.0957694	−	0.0203564i	0.255547	+	0.966797i	$0.417744\pi$
$620$	2.90612	−	13.6722i	0.116713	−	0.549090i
$621$	0.283168	−	4.04949i	0.0113631	−	0.162500i
$622$	−2.89585	+	0.830370i	−0.116113	+	0.0332948i
$623$	−9.86015	−	12.6204i	−0.395039	−	0.505626i
$624$	4.69602	−	1.89732i	0.187991	−	0.0759534i
$625$	7.53115	−	15.4411i	0.301246	−	0.617646i
$626$	5.40867			0.216174
$627$	21.7447	−	22.7599i	0.868401	−	0.908942i
$628$	16.1362			0.643906
$629$	−3.88136	+	7.95797i	−0.154760	+	0.317305i
$630$	8.87394	−	3.58531i	0.353546	−	0.142842i
$631$	24.3692	+	31.1912i	0.970123	+	1.24170i	0.970351	+	0.241701i	$0.0777054\pi$
$631$	24.3692	+	31.1912i	0.970123	+	1.24170i	−0.000227495		1.00000i	$0.500072\pi$
$632$	1.99431	−	0.571859i	0.0793293	−	0.0227473i
$633$	−0.636700	+	9.10523i	−0.0253066	+	0.361901i
$634$	5.25688	−	24.7317i	0.208777	−	0.982219i
$635$	66.8608	−	14.2117i	2.65329	−	0.563974i
$636$	−13.1541	+	12.7027i	−0.521592	+	0.503696i
$637$	1.98315	−	11.2470i	0.0785754	−	0.445623i
$638$	8.54055	+	9.13600i	0.338124	+	0.361698i
$639$	−1.41026	−	0.814215i	−0.0557891	−	0.0322098i
$640$	0.919913	+	3.68957i	0.0363627	+	0.145843i
$641$	30.9872	+	24.2099i	1.22392	+	0.956233i	0.999832	−	0.0183356i	$-0.00583674\pi$
$641$	30.9872	+	24.2099i	1.22392	+	0.956233i	0.224090	+	0.974568i	$0.428059\pi$
$642$	5.60446	−	4.37869i	0.221190	−	0.172813i
$643$	−2.74818	+	11.0223i	−0.108377	+	0.434678i	−0.999830	−	0.0184357i	$-0.994131\pi$
$643$	−2.74818	+	11.0223i	−0.108377	+	0.434678i	0.891453	+	0.453114i	$0.149687\pi$
$644$	1.48712	−	1.53995i	0.0586006	−	0.0606827i
$645$	10.5001	+	32.3161i	0.413442	+	1.27244i
$646$	−3.56342	+	11.8295i	−0.140201	+	0.465426i
$647$	11.9510	+	8.68292i	0.469843	+	0.341361i	0.797380	−	0.603477i	$-0.206219\pi$
$647$	11.9510	+	8.68292i	0.469843	+	0.341361i	−0.327537	+	0.944838i	$0.606219\pi$
$648$	1.94347	+	11.0219i	0.0763465	+	0.432983i
$649$	−39.7104	−	0.644149i	−1.55877	−	0.0252850i
$650$	20.6763	−	7.52555i	0.810991	−	0.295176i
$651$	9.59348	−	6.47088i	0.375998	−	0.253614i
$652$	15.0587	−	9.40974i	0.589746	−	0.368514i
$653$	−25.3100	−	5.37981i	−0.990457	−	0.210528i	−0.315934	−	0.948781i	$-0.602318\pi$
$653$	−25.3100	−	5.37981i	−0.990457	−	0.210528i	−0.674524	+	0.738253i	$0.735651\pi$
$654$	14.6981	−	33.0125i	0.574742	−	1.29089i
$655$	−70.6324	+	34.4497i	−2.75984	+	1.34606i
$656$	−8.18896	+	1.15088i	−0.319725	+	0.0449344i
$657$	0.301476	+	1.41833i	0.0117617	+	0.0553344i
$658$	−0.601480	−	1.35095i	−0.0234481	−	0.0526654i
$659$	2.31305	+	1.94088i	0.0901037	+	0.0756060i	0.686727	−	0.726916i	$-0.259047\pi$
$659$	2.31305	+	1.94088i	0.0901037	+	0.0756060i	−0.596623	+	0.802522i	$0.703491\pi$
$660$	18.7028	−	20.1059i	0.728004	−	0.782622i
$661$	−5.27401	−	14.4902i	−0.205135	−	0.563605i	0.793875	−	0.608081i	$-0.208060\pi$
$661$	−5.27401	−	14.4902i	−0.205135	−	0.563605i	−0.999010	+	0.0444761i	$0.985838\pi$
$662$	−1.47204	−	21.0511i	−0.0572124	−	0.818175i
$663$	14.2157	+	1.99788i	0.552091	+	0.0775913i
$664$	12.9728	−	4.21512i	0.503443	−	0.163578i
$665$	−12.9687	+	20.1514i	−0.502906	+	0.781436i
$666$	3.19655	+	4.39967i	0.123864	+	0.170484i
$667$	4.92984	−	2.62124i	0.190884	−	0.101495i
$668$	4.98350	+	12.3346i	0.192817	+	0.477240i
$669$	32.9281	+	9.44197i	1.27307	+	0.365048i
$670$	17.3194	−	47.5846i	0.669106	−	1.83835i
$671$	−1.23354	+	0.630436i	−0.0476201	+	0.0243377i
$672$	−1.57401	+	2.72627i	−0.0607188	+	0.105168i
$673$	1.13426	−	10.7917i	0.0437224	−	0.415991i	−0.950667	−	0.310212i	$-0.899600\pi$
$673$	1.13426	−	10.7917i	0.0437224	−	0.415991i	0.994390	−	0.105779i	$-0.0337335\pi$
$674$	−0.984351	−	0.523389i	−0.0379158	−	0.0201602i
$675$	3.60912	+	25.6802i	0.138915	+	0.988433i
$676$	−6.93300	−	3.08677i	−0.266654	−	0.118722i
$677$	−0.714849	−	6.80133i	−0.0274739	−	0.261396i	−0.999633	−	0.0270763i	$-0.991380\pi$
$677$	−0.714849	−	6.80133i	−0.0274739	−	0.261396i	0.972159	−	0.234320i	$-0.0752864\pi$
$678$	8.63835	−	21.3807i	0.331754	−	0.821119i
$679$	−12.6791	+	16.2285i	−0.486579	+	0.622792i
$680$	−2.97071	+	10.3601i	−0.113921	+	0.397291i
$681$	−19.8184	−	23.6187i	−0.759443	−	0.905069i
$682$	6.26623	−	10.4580i	0.239946	−	0.400456i
$683$		−	16.8597i		−	0.645120i	−0.946549	−	0.322560i	$-0.895457\pi$
$683$		−	16.8597i		−	0.645120i	0.946549	−	0.322560i	$-0.104543\pi$
$684$	5.38784	+	5.34363i	0.206009	+	0.204319i
$685$	10.5412	−	32.4424i	0.402758	−	1.23956i
$686$	8.08383	+	15.2035i	0.308642	+	0.580471i
$687$	48.0393	+	11.9776i	1.83282	+	0.456972i
$688$	−3.40240	−	2.29495i	−0.129715	−	0.0874940i
$689$	−19.5239	−	0.681788i	−0.743800	−	0.0259741i
$690$	−6.49646	−	10.3965i	−0.247316	−	0.395788i
$691$	−25.5009	+	11.3537i	−0.970100	+	0.431916i	−0.829719	−	0.558181i	$-0.811499\pi$
$691$	−25.5009	+	11.3537i	−0.970100	+	0.431916i	−0.140381	+	0.990098i	$0.544833\pi$
$692$	−6.26737	−	10.8554i	−0.238250	−	0.412660i
$693$	8.33588	−	0.447177i	0.316654	−	0.0169868i
$694$	−18.0758	−	3.18725i	−0.686148	−	0.120986i
$695$	−24.8060	−	2.60721i	−0.940945	−	0.0988973i
$696$	−6.10149	+	5.49380i	−0.231276	+	0.208242i
$697$	−21.7316	−	8.78015i	−0.823144	−	0.332572i
$698$	8.08715	+	28.2033i	0.306103	+	1.06751i
$699$	26.5869	−	39.4167i	1.00561	−	1.49088i
$700$	−7.24720	+	11.5979i	−0.273918	+	0.438361i
$701$	0.884034	−	6.29023i	0.0333895	−	0.237579i	−0.966423	−	0.256958i	$-0.917280\pi$
$701$	0.884034	−	6.29023i	0.0333895	−	0.237579i	0.999812	+	0.0193788i	$0.00616884\pi$
$702$	−3.74841	+	5.15924i	−0.141475	+	0.194723i
$703$	−12.8929	−	4.38006i	−0.486265	−	0.165197i
$704$	−0.284987	+	3.30436i	−0.0107408	+	0.124538i
$705$	−8.33974	+	1.47052i	−0.314093	+	0.0553830i
$706$	18.8994	−	1.32157i	0.711288	−	0.0497381i
$707$	−0.488005	−	13.9746i	−0.0183533	−	0.525570i
$708$	0.909944	−	26.0574i	0.0341978	−	0.979296i
$709$	−32.3272	−	2.26054i	−1.21407	−	0.0848964i	−0.551683	−	0.834054i	$-0.686014\pi$
$709$	−32.3272	−	2.26054i	−1.21407	−	0.0848964i	−0.662392	+	0.749158i	$0.730459\pi$
$710$	3.53739	−	0.371795i	0.132756	−	0.0139532i
$711$	2.41675	−	2.68408i	0.0906354	−	0.100661i
$712$	5.20047	−	9.78066i	0.194896	−	0.366546i
$713$	−3.78095	−	3.91529i	−0.141598	−	0.146629i
$714$	−7.72715	+	4.46127i	−0.289181	+	0.166959i
$715$	29.3310	−	0.548168i	1.09692	−	0.0205003i
$716$	−10.5089	+	12.5240i	−0.392736	+	0.468045i
$717$	10.7417	+	15.9252i	0.401155	+	0.594736i
$718$	−23.0742	+	0.805769i	−0.861121	+	0.0300710i
$719$	−6.87388	−	4.29528i	−0.256352	−	0.160187i	0.395655	−	0.918399i	$-0.370517\pi$
$719$	−6.87388	−	4.29528i	−0.256352	−	0.160187i	−0.652008	+	0.758212i	$0.726073\pi$
$720$	4.76186	+	4.59848i	0.177464	+	0.171375i
$721$	−20.8609	+	15.1563i	−0.776899	+	0.564450i
$722$	−18.7379	−	3.14505i	−0.697352	−	0.117047i
$723$	−49.3765	−	16.0434i	−1.83633	−	0.596660i
$724$	−6.00320	−	2.92795i	−0.223107	−	0.108817i
$725$	−27.3237	+	22.9273i	−1.01477	+	0.851497i
$726$	21.1196	−	11.2964i	0.783823	−	0.419250i
$727$	40.2280	+	14.6418i	1.49198	+	0.543035i	0.953969	−	0.299906i	$-0.0969553\pi$
$727$	40.2280	+	14.6418i	1.49198	+	0.543035i	0.538007	+	0.842941i	$0.319177\pi$
$728$	−3.26322	+	0.813613i	−0.120943	+	0.0301545i
$729$	1.05460	+	1.17125i	0.0390591	+	0.0433796i
$730$	−2.35368	−	2.11926i	−0.0871135	−	0.0784374i
$731$	−5.09922	−	10.4549i	−0.188601	−	0.386690i
$732$	−0.398676	−	0.817407i	−0.0147355	−	0.0302122i
$733$	−18.5081	−	16.6648i	−0.683614	−	0.615528i	0.252346	−	0.967637i	$-0.418798\pi$
$733$	−18.5081	−	16.6648i	−0.683614	−	0.615528i	−0.935959	+	0.352109i	$0.885465\pi$
$734$	1.30566	+	1.45008i	0.0481929	+	0.0535236i
$735$	39.4418	−	9.83396i	1.45483	−	0.362731i
$736$	1.39140	+	0.506428i	0.0512876	+	0.0186672i
$737$	27.7533	−	34.3591i	1.02231	−	1.26563i
$738$	−11.0281	+	9.25368i	−0.405950	+	0.340633i
$739$	−6.87827	−	3.35476i	−0.253021	−	0.123407i	0.307496	−	0.951549i	$-0.400509\pi$
$739$	−6.87827	−	3.35476i	−0.253021	−	0.123407i	−0.560517	+	0.828143i	$0.689398\pi$
$740$	−11.2972	−	3.67067i	−0.415292	−	0.134937i
$741$	−0.294366	+	22.0751i	−0.0108138	+	0.810949i
$742$	9.82340	−	7.13712i	0.360628	−	0.262012i
$743$	36.3019	+	35.0563i	1.33179	+	1.28609i	0.928653	+	0.370950i	$0.120968\pi$
$743$	36.3019	+	35.0563i	1.33179	+	1.28609i	0.403134	+	0.915141i	$0.367921\pi$
$744$	6.78757	+	4.24134i	0.248844	+	0.155495i
$745$	43.9979	−	1.53644i	1.61196	−	0.0562909i
$746$	−14.7247	−	21.8302i	−0.539109	−	0.799262i
$747$	15.2639	−	18.1908i	0.558478	−	0.665568i
$748$	−5.38235	+	7.70701i	−0.196798	+	0.281796i
$749$	−4.08988	+	2.36129i	−0.149441	+	0.0862798i
$750$	25.6463	+	26.5576i	0.936472	+	0.969745i
$751$	−15.2062	+	28.5987i	−0.554881	+	1.04358i	0.434831	+	0.900512i	$0.356808\pi$
$751$	−15.2062	+	28.5987i	−0.554881	+	1.04358i	−0.989713	+	0.143068i	$0.954303\pi$
$752$	0.684401	−	0.760104i	0.0249575	−	0.0277182i
$753$	−49.4367	+	5.19600i	−1.80157	+	0.189353i
$754$	−8.74999	−	0.611859i	−0.318656	−	0.0222826i
$755$	−0.561135	+	16.0688i	−0.0204218	+	0.584804i
$756$	−0.138332	−	3.96130i	−0.00503107	−	0.144071i
$757$	−3.73697	+	0.261314i	−0.135823	+	0.00949764i	−0.137506	−	0.990501i	$-0.543909\pi$
$757$	−3.73697	+	0.261314i	−0.135823	+	0.00949764i	0.00168338	+	0.999999i	$0.499464\pi$
$758$	28.3940	−	5.00663i	1.03132	−	0.181849i
$759$	−2.41821	−	10.4158i	−0.0877754	−	0.378069i
$760$	−16.3813	−	2.52541i	−0.594211	−	0.0916063i
$761$	15.1869	−	20.9030i	0.550526	−	0.757733i	−0.439558	−	0.898214i	$-0.644865\pi$
$761$	15.1869	−	20.9030i	0.550526	−	0.757733i	0.990083	+	0.140481i	$0.0448649\pi$
$762$	−5.44730	+	38.7595i	−0.197335	+	1.40411i
$763$	−12.7156	+	20.3492i	−0.460335	+	0.736690i
$764$	−6.16131	+	9.13452i	−0.222908	+	0.330475i
$765$	5.17167	+	18.0358i	0.186982	+	0.652085i
$766$	−8.66219	−	3.49975i	−0.312978	−	0.126451i
$767$	20.7001	−	18.6385i	0.747439	−	0.672997i
$768$	−2.16543	−	0.227596i	−0.0781382	−	0.00821266i
$769$	5.01978	+	0.885122i	0.181018	+	0.0319183i	0.263422	−	0.964681i	$-0.415149\pi$
$769$	5.01978	+	0.885122i	0.181018	+	0.0319183i	−0.0824044	+	0.996599i	$0.526260\pi$
$770$	−14.1561	+	11.4923i	−0.510151	+	0.414155i
$771$	16.7276	+	28.9730i	0.602428	+	1.04344i
$772$	−13.6441	+	6.07475i	−0.491062	+	0.218635i
$773$	−14.8728	−	23.8014i	−0.534937	−	0.856079i	0.464630	−	0.885505i	$-0.346187\pi$
$773$	−14.8728	−	23.8014i	−0.534937	−	0.856079i	−0.999567	+	0.0294265i	$0.990632\pi$
$774$	−7.14032	−	0.249345i	−0.256653	−	0.00896253i
$775$	28.8264	+	19.4436i	1.03547	+	0.698436i
$776$	−13.8211	−	3.44598i	−0.496148	−	0.123704i
$777$	−4.61678	−	8.68290i	−0.165626	−	0.311497i
$778$	−6.46811	+	19.9068i	−0.231893	+	0.713693i
$779$	9.18580	−	34.8555i	0.329115	−	1.24883i
$780$			19.2591i			0.689586i
$781$	3.02372	+	0.694153i	0.108197	+	0.0248387i
$782$	2.69764	+	3.21492i	0.0964673	+	0.114965i
$783$	2.84947	−	9.93729i	0.101832	−	0.355130i
$784$	−3.02269	+	3.86887i	−0.107953	+	0.138174i
$785$	−22.9853	+	56.8905i	−0.820379	+	2.03051i
$786$	−4.70367	−	44.7524i	−0.167774	−	1.59627i
$787$	−43.4166	−	19.3303i	−1.54764	−	0.689052i	−0.557631	−	0.830089i	$-0.688290\pi$
$787$	−43.4166	−	19.3303i	−1.54764	−	0.689052i	−0.990004	+	0.141037i	$0.954956\pi$
$788$	−3.37903	−	24.0430i	−0.120373	−	0.856498i
$789$	−27.0192	−	14.3664i	−0.961910	−	0.511456i
$790$	−0.824625	+	7.84578i	−0.0293388	+	0.279140i
$791$	−7.65603	+	13.2606i	−0.272217	+	0.471494i
$792$	2.62763	+	5.14132i	0.0933687	+	0.182689i
$793$	0.332303	−	0.912995i	0.0118004	−	0.0324214i
$794$	31.6499	+	9.07548i	1.12321	+	0.322077i
$795$	−26.0479	−	64.4708i	−0.923824	−	2.28654i
$796$	14.7237	−	7.82871i	0.521866	−	0.277481i
$797$	26.0647	+	35.8749i	0.923257	+	1.27075i	0.962432	+	0.271522i	$0.0875271\pi$
$797$	26.0647	+	35.8749i	0.923257	+	1.27075i	−0.0391749	+	0.999232i	$0.512473\pi$
$798$	−8.30313	−	10.9247i	−0.293928	−	0.386730i
$799$	2.75713	−	0.895844i	0.0975401	−	0.0316927i
$800$	−9.36710	−	1.31646i	−0.331177	−	0.0465439i
$801$	−1.34521	−	19.2374i	−0.0475305	−	0.679718i
$802$	9.02799	+	24.8042i	0.318789	+	0.875867i
$803$	−1.34225	−	2.41446i	−0.0473671	−	0.0852045i
$804$	22.2123	+	18.6383i	0.783367	+	0.657323i
$805$	3.31100	+	7.43662i	0.116697	+	0.262106i
$806$	1.77778	+	8.36378i	0.0626195	+	0.294601i
$807$	−13.6969	+	1.92497i	−0.482152	+	0.0677621i
$808$	8.69275	−	4.23974i	0.305810	−	0.149153i
$809$	−14.3443	+	32.2178i	−0.504318	+	1.13272i	0.464642	+	0.885499i	$0.346183\pi$
$809$	−14.3443	+	32.2178i	−0.504318	+	1.13272i	−0.968960	+	0.247218i	$0.920484\pi$
$810$	−41.6277	−	8.84824i	−1.46265	−	0.310896i
$811$	1.70903	−	1.06792i	0.0600123	−	0.0374998i	−0.499581	−	0.866267i	$-0.666513\pi$
$811$	1.70903	−	1.06792i	0.0600123	−	0.0374998i	0.559594	+	0.828767i	$0.310957\pi$
$812$	4.51975	−	3.04861i	0.158612	−	0.106985i
$813$	−55.1528	+	20.0740i	−1.93429	+	0.704025i
$814$	−8.28209	−	6.22500i	−0.290287	−	0.218186i
$815$	11.7249	+	66.4953i	0.410706	+	2.32923i
$816$	−4.99273	−	3.62743i	−0.174780	−	0.126985i
$817$	14.9628	−	9.80481i	0.523481	−	0.343027i
$818$	−4.16335	−	12.8135i	−0.145568	−	0.448012i
$819$	−4.06710	+	4.21161i	−0.142116	+	0.147165i
$820$	7.60716	−	30.5107i	0.265654	−	1.06548i
$821$	−2.07660	+	1.62242i	−0.0724739	+	0.0566228i	−0.651247	−	0.758866i	$-0.725754\pi$
$821$	−2.07660	+	1.62242i	−0.0724739	+	0.0566228i	0.578773	+	0.815489i	$0.303532\pi$
$822$	15.3921	+	12.0256i	0.536861	+	0.419442i
$823$	−5.15871	−	20.6904i	−0.179821	−	0.721224i	−0.990706	−	0.136018i	$-0.956569\pi$
$823$	−5.15871	−	20.6904i	−0.179821	−	0.721224i	0.810885	−	0.585205i	$-0.198986\pi$
$824$	−15.4453	−	8.91736i	−0.538063	−	0.310651i
$825$	28.9450	+	61.8734i	1.00774	+	2.15416i
$826$	−3.00638	+	17.0500i	−0.104605	+	0.593246i
$827$	−7.32550	+	7.07416i	−0.254733	+	0.245993i	−0.811049	−	0.584978i	$-0.801103\pi$
$827$	−7.32550	+	7.07416i	−0.254733	+	0.245993i	0.556316	+	0.830971i	$0.312214\pi$
$828$	2.52140	−	0.535939i	0.0876246	−	0.0186252i
$829$	6.87621	−	32.3500i	0.238821	−	1.12356i	−0.681324	−	0.731982i	$-0.738595\pi$
$829$	6.87621	−	32.3500i	0.238821	−	1.12356i	0.920144	−	0.391580i	$-0.128071\pi$
$830$	−3.61813	+	51.7416i	−0.125587	+	1.79598i
$831$	23.2397	−	6.66389i	0.806178	−	0.231168i
$832$	−1.43211	−	1.83302i	−0.0496495	−	0.0635484i
$833$	−12.9023	+	5.21288i	−0.447039	+	0.180616i
$834$	6.26098	−	12.8369i	0.216800	−	0.444506i
$835$	−50.5860			−1.75060
$836$	−12.8008	−	6.71865i	−0.442724	−	0.232369i
$837$	−10.0776			−0.348333
$838$	−7.17524	+	14.7114i	−0.247865	+	0.508198i
$839$	−0.417608	+	0.168724i	−0.0144174	+	0.00582501i	−0.381804	−	0.924243i	$-0.624697\pi$
$839$	−0.417608	+	0.168724i	−0.0144174	+	0.00582501i	0.367387	+	0.930068i	$0.380253\pi$
$840$	−7.36973	−	9.43282i	−0.254280	−	0.325463i
$841$	−14.2085	+	4.07423i	−0.489950	+	0.140491i
$842$	−0.271953	+	3.88911i	−0.00937213	+	0.134028i
$843$	7.35799	−	34.6166i	0.253423	−	1.19226i
$844$	4.10039	−	0.871564i	0.141141	−	0.0300005i
$845$	20.7585	−	20.0463i	0.714115	−	0.689613i
$846$	0.309201	−	1.75357i	0.0106306	−	0.0602889i
$847$	−14.9312	+	5.47627i	−0.513043	+	0.188167i
$848$	7.27322	+	4.19919i	0.249763	+	0.144201i
$849$	−8.76991	−	35.1742i	−0.300982	−	1.20717i
$850$	−21.1269	−	16.5061i	−0.724645	−	0.566155i
$851$	−3.64493	+	2.84773i	−0.124947	+	0.0976190i
$852$	−0.492723	+	1.97620i	−0.0168804	+	0.0677036i
$853$	−7.62388	+	7.89476i	−0.261037	+	0.270311i	−0.837047	−	0.547131i	$-0.815720\pi$
$853$	−7.62388	+	7.89476i	−0.261037	+	0.270311i	0.576010	+	0.817442i	$0.304609\pi$
$854$	0.186612	+	0.574332i	0.00638572	+	0.0196532i
$855$	−26.5144	+	11.3838i	−0.906773	+	0.389318i
$856$	−2.64259	−	1.91995i	−0.0903218	−	0.0656226i
$857$	6.05755	+	34.3541i	0.206922	+	1.17351i	0.894387	+	0.447295i	$0.147612\pi$
$857$	6.05755	+	34.3541i	0.206922	+	1.17351i	−0.687465	+	0.726218i	$0.741276\pi$
$858$	−5.44933	+	15.8897i	−0.186037	+	0.542464i
$859$	−27.2955	+	9.93474i	−0.931309	+	0.338969i	−0.762728	−	0.646719i	$-0.776141\pi$
$859$	−27.2955	+	9.93474i	−0.931309	+	0.338969i	−0.168581	+	0.985688i	$0.553918\pi$
$860$	12.9377	−	8.72658i	0.441171	−	0.297574i
$861$	22.0767	−	13.7951i	0.752372	−	0.470134i
$862$	2.52599	+	0.536915i	0.0860354	+	0.0182874i
$863$	16.8748	−	37.9014i	0.574425	−	1.29018i	−0.359645	−	0.933089i	$-0.617102\pi$
$863$	16.8748	−	37.9014i	0.574425	−	1.29018i	0.934070	−	0.357090i	$-0.116231\pi$
$864$	2.46408	−	1.20181i	0.0838296	−	0.0408864i
$865$	47.1997	−	6.63349i	1.60484	−	0.225545i
$866$	5.00267	+	23.5357i	0.169998	+	0.799776i
$867$	7.94090	+	17.8356i	0.269687	+	0.605727i
$868$	−4.07123	−	3.41617i	−0.138187	−	0.115952i
$869$	−2.90031	+	6.23982i	−0.0983863	+	0.211671i
$870$	−10.6779	−	29.3373i	−0.362014	−	0.994626i
$871$	2.16087	+	30.9018i	0.0732182	+	1.04707i
$872$	−16.4351	−	2.30980i	−0.556561	−	0.0782196i
$873$	−23.5839	+	7.66287i	−0.798194	+	0.259349i
$874$	−4.38227	+	4.73840i	−0.148233	+	0.160279i
$875$	−14.4096	−	19.8331i	−0.487132	−	0.670480i
$876$	1.60128	−	0.851415i	0.0541022	−	0.0287666i
$877$	−2.94652	−	7.29289i	−0.0994968	−	0.246263i	0.869223	−	0.494420i	$-0.164620\pi$
$877$	−2.94652	−	7.29289i	−0.0994968	−	0.246263i	−0.968720	+	0.248157i	$0.920175\pi$
$878$	22.8183	+	6.54304i	0.770080	+	0.220817i
$879$	−7.32680	+	20.1302i	−0.247127	+	0.678976i
$880$	−11.2440	−	5.71165i	−0.379036	−	0.192540i
$881$	−14.9570	+	25.9063i	−0.503915	+	0.872806i	0.496075	+	0.868280i	$0.334774\pi$
$881$	−14.9570	+	25.9063i	−0.503915	+	0.872806i	−0.999990	+	0.00452600i	$0.998559\pi$
$882$	−0.893424	+	8.50036i	−0.0300831	+	0.286222i
$883$	12.4744	+	6.63274i	0.419796	+	0.223210i	0.665911	−	0.746031i	$-0.268043\pi$
$883$	12.4744	+	6.63274i	0.419796	+	0.223210i	−0.246115	+	0.969241i	$0.579154\pi$
$884$	−0.917572	−	6.52886i	−0.0308613	−	0.219589i
$885$	90.5726	+	40.3255i	3.04457	+	1.35553i
$886$	2.88921	+	27.4890i	0.0970650	+	0.923512i
$887$	0.312983	−	0.774660i	0.0105089	−	0.0260105i	−0.921838	−	0.387575i	$-0.873313\pi$
$887$	0.312983	−	0.774660i	0.0105089	−	0.0260105i	0.932347	+	0.361564i	$0.117757\pi$
$888$	4.18758	−	5.35986i	0.140526	−	0.179865i
$889$	7.16378	−	24.9831i	0.240265	−	0.837905i
$890$	27.0752	+	32.2670i	0.907564	+	1.08159i
$891$	−31.8412	−	19.0787i	−1.06672	−	0.639161i
$892$		−	15.7324i		−	0.526759i
$893$	1.90082	+	4.03286i	0.0636085	+	0.134955i
$894$	−7.79001	+	23.9752i	−0.260537	+	0.801850i
$895$	−29.1857	−	54.8904i	−0.975571	−	1.83478i
$896$	1.40285	+	0.349771i	0.0468660	+	0.0116850i
$897$	6.21733	+	4.19364i	0.207591	+	0.140022i
$898$	14.6586	+	0.511889i	0.489163	+	0.0170819i
$899$	−7.34524	−	11.7548i	−0.244977	−	0.392046i
$900$	−15.0437	+	6.69787i	−0.501456	+	0.223262i
$901$	11.9019	+	20.6147i	0.396510	+	0.686775i
$902$	14.9092	−	23.0203i	0.496423	−	0.766492i
$903$	12.7233	+	2.24346i	0.423406	+	0.0746578i
$904$	−10.5327	−	1.10703i	−0.350312	−	0.0368193i
$905$	18.8741	−	16.9944i	0.627398	−	0.564911i
$906$	−8.53636	−	3.44891i	−0.283602	−	0.114582i
$907$	12.6839	+	44.2340i	0.421161	+	1.46876i	0.830828	+	0.556529i	$0.187867\pi$
$907$	12.6839	+	44.2340i	0.421161	+	1.46876i	−0.409667	+	0.912235i	$0.634355\pi$
$908$	−7.91832	+	11.7394i	−0.262779	+	0.389586i
$909$	8.92232	−	14.2787i	0.295935	−	0.473594i
$910$	1.77979	−	12.6639i	0.0589995	−	0.419803i
$911$	−15.2972	+	21.0547i	−0.506818	+	0.697575i	−0.983379	−	0.181567i	$-0.941883\pi$
$911$	−15.2972	+	21.0547i	−0.506818	+	0.697575i	0.476561	+	0.879141i	$0.341883\pi$
$912$	4.56704	−	8.31980i	0.151230	−	0.275496i
$913$	−17.6253	+	41.6655i	−0.583314	+	1.37893i
$914$	−4.21988	+	0.744079i	−0.139581	+	0.0246119i
$915$	3.44977	−	0.241232i	0.114046	−	0.00797487i
$916$	−0.793565	−	22.7247i	−0.0262201	−	0.750846i
$917$	−1.04280	+	29.8618i	−0.0344362	+	0.986123i
$918$	7.75149	+	0.542037i	0.255837	+	0.0178899i
$919$	26.9160	−	2.82899i	0.887878	−	0.0933197i	0.350402	−	0.936599i	$-0.386045\pi$
$919$	26.9160	−	2.82899i	0.887878	−	0.0933197i	0.537475	+	0.843280i	$0.319378\pi$
$920$	−3.76745	+	4.18418i	−0.124209	+	0.137948i
$921$	27.1295	−	51.0232i	0.893948	−	1.68127i
$922$	−24.9109	−	25.7960i	−0.820398	−	0.849547i
$923$	−1.88435	+	1.08793i	−0.0620243	+	0.0358097i
$924$	−3.41137	−	9.86778i	−0.112226	−	0.324626i
$925$	18.9938	−	22.6359i	0.624512	−	0.744264i
$926$	9.30250	+	13.7915i	0.305699	+	0.453218i
$927$	−31.0294	+	1.08357i	−1.01914	+	0.0355891i
$928$	3.19781	+	1.99821i	0.104973	+	0.0655946i
$929$	−29.7419	−	28.7214i	−0.975800	−	0.942319i	0.0225499	−	0.999746i	$-0.492822\pi$
$929$	−29.7419	−	28.7214i	−0.975800	−	0.942319i	−0.998350	+	0.0574268i	$0.981710\pi$
$930$	−24.6220	+	17.8889i	−0.807386	+	0.586600i
$931$	−10.4523	−	18.6746i	−0.342560	−	0.612035i
$932$	−20.7674	−	6.74775i	−0.680260	−	0.221030i
$933$	5.89554	+	2.87545i	0.193011	+	0.0941380i
$934$	−20.7454	+	17.4075i	−0.678811	+	0.569590i
$935$	−19.5052	−	29.9544i	−0.637889	−	0.979615i
$936$	−3.80532	−	1.38502i	−0.124381	−	0.0452709i
$937$	2.08652	−	0.520228i	0.0681637	−	0.0169951i	−0.207691	−	0.978195i	$-0.566595\pi$
$937$	2.08652	−	0.520228i	0.0681637	−	0.0169951i	0.275854	+	0.961199i	$0.411039\pi$
$938$	−12.8833	−	14.3084i	−0.420656	−	0.467186i
$939$	−8.75173	−	7.88009i	−0.285602	−	0.257157i
$940$	1.70496	+	3.49568i	0.0556095	+	0.114016i
$941$	−2.02483	−	4.15151i	−0.0660075	−	0.135335i	0.863239	−	0.504795i	$-0.168432\pi$
$941$	−2.02483	−	4.15151i	−0.0660075	−	0.135335i	−0.929247	+	0.369459i	$0.879543\pi$
$942$	−26.1099	−	23.5095i	−0.850708	−	0.765981i
$943$	−8.19318	−	9.09945i	−0.266807	−	0.296319i
$944$	−11.6190	+	2.89695i	−0.378167	+	0.0942876i
$945$	14.1631	+	5.15496i	0.460727	+	0.167691i
$946$	13.1434	−	3.53914i	0.427328	−	0.115067i
$947$	6.72571	−	5.64354i	0.218556	−	0.183390i	−0.526936	−	0.849905i	$-0.676659\pi$
$947$	6.72571	−	5.64354i	0.218556	−	0.183390i	0.745492	+	0.666515i	$0.232215\pi$
$948$	−4.06014	−	1.98026i	−0.131867	−	0.0643159i
$949$	1.84265	+	0.598713i	0.0598149	+	0.0194350i
$950$	21.0900	−	35.4295i	0.684251	−	1.14948i
$951$	−44.5386	+	32.3592i	−1.44426	+	1.04932i
$952$	2.94776	+	2.84662i	0.0955376	+	0.0922596i
$953$	−9.04780	−	5.65369i	−0.293087	−	0.183141i	0.375404	−	0.926861i	$-0.377504\pi$
$953$	−9.04780	−	5.65369i	−0.293087	−	0.183141i	−0.668491	+	0.743720i	$0.733060\pi$
$954$	14.6118	−	0.510254i	0.473073	−	0.0165201i
$955$	−23.4285	−	34.7342i	−0.758129	−	1.12397i
$956$	5.67084	−	6.75824i	0.183408	−	0.218577i
$957$	−0.508827	−	27.2259i	−0.0164480	−	0.880089i
$958$	−14.2972	+	8.25449i	−0.461921	+	0.266690i
$959$	−9.00980	−	9.32992i	−0.290942	−	0.301279i
$960$	3.88697	−	7.31032i	0.125451	−	0.235940i
$961$	11.7016	−	12.9959i	0.377471	−	0.419224i
$962$	7.22671	−	0.759557i	0.232998	−	0.0244891i
$963$	−5.67262	−	0.396668i	−0.182798	−	0.0127825i
$964$	−0.832153	+	23.8297i	−0.0268018	+	0.767504i
$965$	−1.98201	−	56.7573i	−0.0638031	−	1.82708i
$966$	−4.64991	+	0.325153i	−0.149608	+	0.0104616i
$967$	30.7616	−	5.42411i	0.989227	−	0.174427i	0.344456	−	0.938803i	$-0.388064\pi$
$967$	30.7616	−	5.42411i	0.989227	−	0.174427i	0.644772	+	0.764375i	$0.276952\pi$
$968$	−7.66074	−	7.89386i	−0.246226	−	0.253718i
$969$	23.0008	−	13.9495i	0.738892	−	0.448124i
$970$	31.8367	−	43.8195i	1.02221	−	1.40696i
$971$	−1.04355	+	7.42526i	−0.0334892	+	0.238288i	−0.999819	−	0.0190181i	$-0.993946\pi$
$971$	−1.04355	+	7.42526i	−0.0334892	+	0.238288i	0.966330	+	0.257306i	$0.0828349\pi$
$972$	8.55519	−	13.6912i	0.274408	−	0.439144i
$973$	−5.30323	+	7.86236i	−0.170014	+	0.252056i
$974$	3.73452	+	13.0238i	0.119662	+	0.417311i
$975$	−44.4204	−	17.9470i	−1.42259	−	0.574764i
$976$	−0.310400	+	0.279485i	−0.00993566	+	0.00894611i
$977$	−20.3105	−	2.13472i	−0.649792	−	0.0682959i	−0.226103	−	0.974104i	$-0.572598\pi$
$977$	−20.3105	−	2.13472i	−0.649792	−	0.0682959i	−0.423689	+	0.905808i	$0.639265\pi$
$978$	−38.0758	−	6.71380i	−1.21753	−	0.214684i
$979$	13.2085	+	34.2827i	0.422144	+	1.09568i
$980$	−9.33455	−	16.1679i	−0.298181	−	0.516465i
$981$	−26.3949	+	11.7518i	−0.842724	+	0.375205i
$982$	−4.71271	−	7.54191i	−0.150389	−	0.240672i
$983$	−4.78947	−	0.167252i	−0.152760	−	0.00533451i	−0.0415828	−	0.999135i	$-0.513240\pi$
$983$	−4.78947	−	0.167252i	−0.152760	−	0.00533451i	−0.111178	+	0.993801i	$0.535462\pi$
$984$	14.9273	+	10.0686i	0.475864	+	0.320974i
$985$	89.5803	+	22.3349i	2.85426	+	0.711648i
$986$	5.01755	+	9.43665i	0.159791	+	0.300524i
$987$	−0.994993	+	3.06227i	−0.0316710	+	0.0974733i
$988$	9.78299	−	2.66458i	0.311238	−	0.0847717i
$989$		−	6.07682i		−	0.193232i
$990$	−21.8694	+	1.94051i	−0.695054	+	0.0616734i
$991$	−11.8790	−	14.1569i	−0.377350	−	0.449708i	0.543626	−	0.839328i	$-0.317051\pi$
$991$	−11.8790	−	14.1569i	−0.377350	−	0.449708i	−0.920976	+	0.389619i	$0.872607\pi$
$992$	1.01322	−	3.53350i	0.0321696	−	0.112189i
$993$	−28.2883	+	36.2073i	−0.897701	+	1.14900i
$994$	0.506619	−	1.25393i	0.0160690	−	0.0397721i
$995$	6.62807	+	63.0618i	0.210124	+	1.99920i
$996$	−27.1324	−	12.0801i	−0.859722	−	0.382773i
$997$	−6.55779	−	46.6611i	−0.207687	−	1.47777i	−0.763145	−	0.646227i	$-0.776346\pi$
$997$	−6.55779	−	46.6611i	−0.207687	−	1.47777i	0.555458	−	0.831545i	$-0.312543\pi$
$998$	2.17311	+	1.15546i	0.0687885	+	0.0365755i
$999$	−0.895200	+	8.51726i	−0.0283229	+	0.269474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.29.8	✓	240
11.8	odd	10		418.2.v.b.371.3	yes	240
19.2	odd	18		418.2.v.b.249.3	yes	240
209.173	even	90	inner	418.2.v.a.173.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.29.8	✓	240	1.1	even	1	trivial
418.2.v.a.173.8	yes	240	209.173	even	90	inner
418.2.v.b.249.3	yes	240	19.2	odd	18
418.2.v.b.371.3	yes	240	11.8	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.898794i) q^{2} +(2.01881 - 0.815653i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(3.65522 - 1.04812i) q^{5} +(-0.151885 + 2.17205i) q^{6} +(0.300599 - 1.41421i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.25229 - 1.20932i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.898794i) q^{2} +(2.01881 - 0.815653i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(3.65522 - 1.04812i) q^{5} +(-0.151885 + 2.17205i) q^{6} +(0.300599 - 1.41421i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.25229 - 1.20932i) q^{9} +(-0.660301 + 3.74475i) q^{10} +(-1.60435 + 2.90277i) q^{11} +(-1.88565 - 1.08868i) q^{12} +(-0.562742 - 2.25704i) q^{13} +(1.13931 + 0.890123i) q^{14} +(6.52429 - 5.09734i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-1.96889 + 2.03885i) q^{17} +(0.537964 + 1.65568i) q^{18} +(-3.49195 - 2.60889i) q^{19} +(-3.07630 - 2.23506i) q^{20} +(-0.546649 - 3.10020i) q^{21} +(-1.90569 - 2.71447i) q^{22} +(-1.39140 + 0.506428i) q^{23} +(1.80511 - 1.21756i) q^{24} +(8.02182 - 5.01259i) q^{25} +(2.27530 + 0.483630i) q^{26} +(-1.11508 + 2.50452i) q^{27} +(-1.29948 + 0.633797i) q^{28} +(-3.73409 + 0.524793i) q^{29} +(1.72139 + 8.09852i) q^{30} +(1.49512 + 3.35810i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-0.871235 + 7.16873i) q^{33} +(-0.969398 - 2.66340i) q^{34} +(-0.383499 - 5.48429i) q^{35} +(-1.72395 - 0.242285i) q^{36} +(2.97097 - 0.965326i) q^{37} +(3.87562 - 1.99488i) q^{38} +(-2.97703 - 4.09753i) q^{39} +(3.35743 - 1.78517i) q^{40} +(3.09779 + 7.66729i) q^{41} +(3.02607 + 0.867713i) q^{42} +(-1.40366 + 3.85653i) q^{43} +(3.27515 - 0.522875i) q^{44} +(3.30988 - 5.73289i) q^{45} +(0.154775 - 1.47258i) q^{46} +(-0.903098 - 0.480185i) q^{47} +(0.303030 + 2.15617i) q^{48} +(4.48520 + 1.99694i) q^{49} +(0.988751 + 9.40734i) q^{50} +(-2.31183 + 5.72198i) q^{51} +(-1.43211 + 1.83302i) q^{52} +(2.31491 - 8.07305i) q^{53} +(-1.76222 - 2.10014i) q^{54} +(-2.82182 + 12.2918i) q^{55} -1.44580i q^{56} +(-9.17753 - 2.41864i) q^{57} +(1.16524 - 3.58623i) q^{58} +(5.62179 + 10.5731i) q^{59} +(-8.03351 - 2.00298i) q^{60} +(0.346276 + 0.233566i) q^{61} +(-3.67366 - 0.128287i) q^{62} +(-1.33379 - 2.13452i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-4.42258 - 7.66013i) q^{65} +(-6.06129 - 3.92563i) q^{66} +(-13.1148 - 2.31249i) q^{67} +(2.81880 + 0.296268i) q^{68} +(-2.39590 + 2.15728i) q^{69} +(5.09736 + 2.05947i) q^{70} +(-0.257831 - 0.899165i) q^{71} +(0.973493 - 1.44326i) q^{72} +(-0.441379 + 0.706354i) q^{73} +(-0.434757 + 3.09346i) q^{74} +(12.1060 - 16.6625i) q^{75} +(0.0940255 + 4.35788i) q^{76} +(3.62284 + 3.14145i) q^{77} +(4.98788 - 0.879497i) q^{78} +(2.06962 - 0.144722i) q^{79} +(0.132706 + 3.80020i) q^{80} +(-0.390594 + 11.1852i) q^{81} +(-8.24929 - 0.576847i) q^{82} +(13.5657 - 1.42581i) q^{83} +(-2.10644 + 2.33944i) q^{84} +(-5.05978 + 9.51605i) q^{85} +(-2.85090 - 2.95220i) q^{86} +(-7.11038 + 4.10518i) q^{87} +(-0.965774 + 3.17290i) q^{88} +(7.12034 - 8.48569i) q^{89} +(3.70173 + 5.48803i) q^{90} +(-3.36107 + 0.117371i) q^{91} +(1.25570 + 0.784649i) q^{92} +(5.75742 + 5.55987i) q^{93} +(0.827480 - 0.601199i) q^{94} +(-15.4982 - 5.87608i) q^{95} +(-2.07079 - 0.672841i) q^{96} +(-12.8026 - 6.24424i) q^{97} +(-3.76102 + 3.15587i) q^{98} +(1.50127 + 5.57529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

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