LMFDB - Embedded newform 616.2.bi.c.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, degree $4$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35856 + 0.392821i) q^{2} +(1.28776 - 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(-0.995233 - 3.06301i) q^{5} +(-1.38197 + 1.77694i) q^{6} +(-2.15566 + 1.53399i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +O(q^{10})$	\(q+(-1.35856 + 0.392821i) q^{2} +(1.28776 - 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(-0.995233 - 3.06301i) q^{5} +(-1.38197 + 1.77694i) q^{6} +(-2.15566 + 1.53399i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +(2.55530 + 3.77034i) q^{10} +(-2.01928 + 2.63107i) q^{11} +(1.17947 - 2.95696i) q^{12} +(-4.03458 - 1.31092i) q^{13} +(2.32602 - 2.93081i) q^{14} +(-4.14740 - 3.01326i) q^{15} +(1.72155 - 3.61058i) q^{16} +(1.29426 + 3.98331i) q^{17} +(0.0215547 - 0.659118i) q^{18} +(-3.55010 - 4.88630i) q^{19} +(-4.95261 - 4.11847i) q^{20} +(-1.34076 + 3.99226i) q^{21} +(1.70978 - 4.36768i) q^{22} -3.89330 q^{23} +(-0.440830 + 4.48053i) q^{24} +(-4.34646 + 3.15789i) q^{25} +(5.99619 + 0.196090i) q^{26} +(1.70501 + 5.24748i) q^{27} +(-2.00876 + 4.89539i) q^{28} +(6.35670 + 4.61842i) q^{29} +(6.81818 + 2.46452i) q^{30} +(-6.00424 - 1.95090i) q^{31} +(-0.920522 + 5.58145i) q^{32} +(-0.138691 + 5.27743i) q^{33} +(-3.32306 - 4.90316i) q^{34} +(6.84400 + 5.07615i) q^{35} +(0.229632 + 0.903920i) q^{36} +(4.16827 - 5.73713i) q^{37} +(6.74248 + 5.24378i) q^{38} +(-6.42207 + 2.08666i) q^{39} +(8.34625 + 3.64970i) q^{40} +(-2.76671 + 2.01013i) q^{41} +(0.253257 - 5.95042i) q^{42} -2.51207 q^{43} +(-0.607122 + 6.60541i) q^{44} +1.50184 q^{45} +(5.28928 - 1.52937i) q^{46} +(3.34676 + 4.60642i) q^{47} +(-1.16115 - 6.26025i) q^{48} +(2.29377 - 6.61352i) q^{49} +(4.66445 - 5.99757i) q^{50} +(5.39351 + 3.91861i) q^{51} +(-8.22323 + 2.08903i) q^{52} +(-12.4561 - 4.04725i) q^{53} +(-4.37768 - 6.45926i) q^{54} +(10.0686 + 3.56656i) q^{55} +(0.806011 - 7.43978i) q^{56} +(-9.14334 - 2.97085i) q^{57} +(-10.4502 - 3.77736i) q^{58} +(1.54350 + 1.12142i) q^{59} +(-10.2310 - 0.669875i) q^{60} +(4.05980 - 1.31911i) q^{61} +(8.92349 + 0.291820i) q^{62} +(-0.369682 - 1.17707i) q^{63} +(-0.941928 - 7.94435i) q^{64} +13.6626i q^{65} +(-1.88467 - 7.22420i) q^{66} +6.26956i q^{67} +(6.44064 + 5.35588i) q^{68} +(-5.01362 + 3.64261i) q^{69} +(-11.2920 - 4.20779i) q^{70} +(-2.16619 - 6.66684i) q^{71} +(-0.667048 - 1.13783i) q^{72} +(-7.24883 - 5.26658i) q^{73} +(-3.40918 + 9.43163i) q^{74} +(-2.64263 + 8.13319i) q^{75} +(-11.2199 - 4.47542i) q^{76} +(0.316871 - 8.76924i) q^{77} +(7.90510 - 5.35758i) q^{78} +(-7.04203 - 2.28810i) q^{79} +(-12.7726 - 1.67977i) q^{80} +(5.97346 + 4.33997i) q^{81} +(2.96913 - 3.81771i) q^{82} +(-4.72307 + 1.53462i) q^{83} +(1.99339 + 8.18349i) q^{84} +(10.9128 - 7.92864i) q^{85} +(3.41280 - 0.986795i) q^{86} +12.5069 q^{87} +(-1.76993 - 9.21235i) q^{88} -8.70311i q^{89} +(-2.04034 + 0.589953i) q^{90} +(10.7081 - 3.36310i) q^{91} +(-6.58505 + 4.15549i) q^{92} +(-9.55728 + 3.10535i) q^{93} +(-6.35628 - 4.94342i) q^{94} +(-11.4336 + 15.7370i) q^{95} +(4.03666 + 8.04881i) q^{96} +(-2.25979 - 0.734250i) q^{97} +(-0.518302 + 9.88592i) q^{98} +(-0.875881 - 1.27467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.35856	+	0.392821i	−0.960649	+	0.277767i
$2$	−1.35856	+	0.392821i	−0.960649	+	0.277767i
$3$	1.28776	−	0.935610i	0.743487	−	0.540175i	−0.150314	−	0.988638i	$-0.548029\pi$
$3$	1.28776	−	0.935610i	0.743487	−	0.540175i	0.893801	+	0.448463i	$0.148029\pi$
$4$	1.69138	−	1.06734i	0.845691	−	0.533672i
$5$	−0.995233	−	3.06301i	−0.445082	−	1.36982i	−0.882394	−	0.470511i	$-0.844070\pi$
$5$	−0.995233	−	3.06301i	−0.445082	−	1.36982i	0.437313	−	0.899309i	$-0.355930\pi$
$6$	−1.38197	+	1.77694i	−0.564187	+	0.725434i
$7$	−2.15566	+	1.53399i	−0.814764	+	0.579792i
$7$	−2.15566	+	1.53399i	−0.814764	+	0.579792i
$8$	−1.87857	+	2.11447i	−0.664176	+	0.747576i
$9$	−0.144099	+	0.443493i	−0.0480332	+	0.147831i
$10$	2.55530	+	3.77034i	0.808057	+	1.19229i
$11$	−2.01928	+	2.63107i	−0.608836	+	0.793296i
$11$	−2.01928	+	2.63107i	−0.608836	+	0.793296i
$12$	1.17947	−	2.95696i	0.340484	−	0.853599i
$13$	−4.03458	−	1.31092i	−1.11899	−	0.363583i	−0.309609	−	0.950864i	$-0.600198\pi$
$13$	−4.03458	−	1.31092i	−1.11899	−	0.363583i	−0.809383	+	0.587281i	$0.800198\pi$
$14$	2.32602	−	2.93081i	0.621655	−	0.783291i
$15$	−4.14740	−	3.01326i	−1.07085	−	0.778021i
$16$	1.72155	−	3.61058i	0.430388	−	0.902644i
$17$	1.29426	+	3.98331i	0.313903	+	0.966094i	0.976204	+	0.216856i	$0.0695802\pi$
$17$	1.29426	+	3.98331i	0.313903	+	0.966094i	−0.662301	+	0.749238i	$0.730420\pi$
$18$	0.0215547	−	0.659118i	0.00508050	−	0.155356i
$19$	−3.55010	−	4.88630i	−0.814449	−	1.12099i	−0.990622	−	0.136634i	$-0.956372\pi$
$19$	−3.55010	−	4.88630i	−0.814449	−	1.12099i	0.176172	−	0.984359i	$-0.443628\pi$
$20$	−4.95261	−	4.11847i	−1.10744	−	0.920917i
$21$	−1.34076	+	3.99226i	−0.292577	+	0.871183i
$22$	1.70978	−	4.36768i	0.364526	−	0.931193i
$23$	−3.89330			−0.811808			−0.405904	−	0.913916i	$-0.633043\pi$
$23$	−3.89330			−0.811808			−0.405904	+	0.913916i	$0.633043\pi$
$24$	−0.440830	+	4.48053i	−0.0899840	+	0.914584i
$25$	−4.34646	+	3.15789i	−0.869293	+	0.631578i
$26$	5.99619	+	0.196090i	1.17595	+	0.0384564i
$27$	1.70501	+	5.24748i	0.328129	+	1.00988i
$28$	−2.00876	+	4.89539i	−0.379620	+	0.925142i
$29$	6.35670	+	4.61842i	1.18041	+	0.857618i	0.992218	−	0.124514i	$-0.0397371\pi$
$29$	6.35670	+	4.61842i	1.18041	+	0.857618i	0.188192	+	0.982132i	$0.439737\pi$
$30$	6.81818	+	2.46452i	1.24482	+	0.449957i
$31$	−6.00424	−	1.95090i	−1.07839	−	0.350391i	−0.284642	−	0.958634i	$-0.591875\pi$
$31$	−6.00424	−	1.95090i	−1.07839	−	0.350391i	−0.793751	+	0.608242i	$0.791875\pi$
$32$	−0.920522	+	5.58145i	−0.162727	+	0.986671i
$33$	−0.138691	+	5.27743i	−0.0241429	+	0.918683i
$34$	−3.32306	−	4.90316i	−0.569899	−	0.840885i
$35$	6.84400	+	5.07615i	1.15685	+	0.858026i
$36$	0.229632	+	0.903920i	0.0382720	+	0.150653i
$37$	4.16827	−	5.73713i	0.685259	−	0.943178i	−0.314723	−	0.949184i	$-0.601912\pi$
$37$	4.16827	−	5.73713i	0.685259	−	0.943178i	0.999982	+	0.00600547i	$0.00191161\pi$
$38$	6.74248	+	5.24378i	1.09377	+	0.850654i
$39$	−6.42207	+	2.08666i	−1.02835	+	0.334133i
$40$	8.34625	+	3.64970i	1.31966	+	0.577069i
$41$	−2.76671	+	2.01013i	−0.432088	+	0.313930i	−0.782483	−	0.622672i	$-0.786047\pi$
$41$	−2.76671	+	2.01013i	−0.432088	+	0.313930i	0.350395	+	0.936602i	$0.386047\pi$
$42$	0.253257	−	5.95042i	0.0390784	−	0.918169i
$43$	−2.51207			−0.383087			−0.191544	−	0.981484i	$-0.561349\pi$
$43$	−2.51207			−0.383087			−0.191544	+	0.981484i	$0.561349\pi$
$44$	−0.607122	+	6.60541i	−0.0915271	+	0.995803i
$45$	1.50184			0.223880
$46$	5.28928	−	1.52937i	0.779862	−	0.225493i
$47$	3.34676	+	4.60642i	0.488175	+	0.671915i	0.980050	−	0.198751i	$-0.0636885\pi$
$47$	3.34676	+	4.60642i	0.488175	+	0.671915i	−0.491875	+	0.870666i	$0.663688\pi$
$48$	−1.16115	−	6.26025i	−0.167598	−	0.903589i
$49$	2.29377	−	6.61352i	0.327682	−	0.944788i
$50$	4.66445	−	5.99757i	0.659653	−	0.848185i
$51$	5.39351	+	3.91861i	0.755242	+	0.548716i
$52$	−8.22323	+	2.08903i	−1.14036	+	0.289697i
$53$	−12.4561	−	4.04725i	−1.71098	−	0.555932i	−0.720486	−	0.693470i	$-0.756081\pi$
$53$	−12.4561	−	4.04725i	−1.71098	−	0.555932i	−0.990497	+	0.137538i	$0.956081\pi$
$54$	−4.37768	−	6.45926i	−0.595727	−	0.878994i
$55$	10.0686	+	3.56656i	1.35765	+	0.480914i
$56$	0.806011	−	7.43978i	0.107708	−	0.994183i
$57$	−9.14334	−	2.97085i	−1.21106	−	0.393499i
$58$	−10.4502	−	3.77736i	−1.37218	−	0.495991i
$59$	1.54350	+	1.12142i	0.200947	+	0.145996i	0.683708	−	0.729756i	$-0.260366\pi$
$59$	1.54350	+	1.12142i	0.200947	+	0.145996i	−0.482761	+	0.875752i	$0.660366\pi$
$60$	−10.2310	−	0.669875i	−1.32082	−	0.0864805i
$61$	4.05980	−	1.31911i	0.519805	−	0.168895i	−0.0373520	−	0.999302i	$-0.511892\pi$
$61$	4.05980	−	1.31911i	0.519805	−	0.168895i	0.557157	+	0.830407i	$0.311892\pi$
$62$	8.92349	+	0.291820i	1.13328	+	0.0370611i
$63$	−0.369682	−	1.17707i	−0.0465755	−	0.148297i
$64$	−0.941928	−	7.94435i	−0.117741	−	0.993044i
$65$			13.6626i			1.69464i
$66$	−1.88467	−	7.22420i	−0.231987	−	0.889238i
$67$			6.26956i			0.765948i	0.923759	+	0.382974i	$0.125100\pi$
$67$			6.26956i			0.765948i	−0.923759	+	0.382974i	$0.874900\pi$
$68$	6.44064	+	5.35588i	0.781043	+	0.649496i
$69$	−5.01362	+	3.64261i	−0.603569	+	0.438518i
$70$	−11.2920	−	4.20779i	−1.34966	−	0.502927i
$71$	−2.16619	−	6.66684i	−0.257079	−	0.791208i	−0.993413	−	0.114590i	$-0.963445\pi$
$71$	−2.16619	−	6.66684i	−0.257079	−	0.791208i	0.736334	−	0.676618i	$-0.236555\pi$
$72$	−0.667048	−	1.13783i	−0.0786124	−	0.134094i
$73$	−7.24883	−	5.26658i	−0.848411	−	0.616407i	0.0762965	−	0.997085i	$-0.475690\pi$
$73$	−7.24883	−	5.26658i	−0.848411	−	0.616407i	−0.924707	+	0.380679i	$0.875690\pi$
$74$	−3.40918	+	9.43163i	−0.396310	+	1.09640i
$75$	−2.64263	+	8.13319i	−0.305145	+	0.939140i
$76$	−11.2199	−	4.47542i	−1.28702	−	0.513365i
$77$	0.316871	−	8.76924i	0.0361108	−	0.999348i
$78$	7.90510	−	5.35758i	0.895076	−	0.606627i
$79$	−7.04203	−	2.28810i	−0.792291	−	0.257431i	−0.115211	−	0.993341i	$-0.536755\pi$
$79$	−7.04203	−	2.28810i	−0.792291	−	0.257431i	−0.677079	+	0.735910i	$0.736755\pi$
$80$	−12.7726	−	1.67977i	−1.42802	−	0.187804i
$81$	5.97346	+	4.33997i	0.663718	+	0.482219i
$82$	2.96913	−	3.81771i	0.327885	−	0.421596i
$83$	−4.72307	+	1.53462i	−0.518425	+	0.168446i	−0.556530	−	0.830827i	$-0.687868\pi$
$83$	−4.72307	+	1.53462i	−0.518425	+	0.168446i	0.0381057	+	0.999274i	$0.487868\pi$
$84$	1.99339	+	8.18349i	0.217496	+	0.892892i
$85$	10.9128	−	7.92864i	1.18366	−	0.859981i
$86$	3.41280	−	0.986795i	0.368012	−	0.106409i
$87$	12.5069			1.34088
$88$	−1.76993	−	9.21235i	−0.188675	−	0.982040i
$89$		−	8.70311i		−	0.922528i	−0.887263	−	0.461264i	$-0.847396\pi$
$89$		−	8.70311i		−	0.922528i	0.887263	−	0.461264i	$-0.152604\pi$
$90$	−2.04034	+	0.589953i	−0.215070	+	0.0621865i
$91$	10.7081	−	3.36310i	1.12252	−	0.352549i
$92$	−6.58505	+	4.15549i	−0.686539	+	0.433240i
$93$	−9.55728	+	3.10535i	−0.991044	+	0.322010i
$94$	−6.35628	−	4.94342i	−0.655600	−	0.509875i
$95$	−11.4336	+	15.7370i	−1.17306	+	1.61458i
$96$	4.03666	+	8.04881i	0.411990	+	0.821478i
$97$	−2.25979	−	0.734250i	−0.229447	−	0.0745518i	0.192037	−	0.981388i	$-0.438491\pi$
$97$	−2.25979	−	0.734250i	−0.229447	−	0.0745518i	−0.421484	+	0.906836i	$0.638491\pi$
$98$	−0.518302	+	9.88592i	−0.0523564	+	0.998628i
$99$	−0.875881	−	1.27467i	−0.0880293	−	0.128109i
$100$	−3.98098	+	9.98037i	−0.398098	+	0.998037i
$101$	−12.2375	−	3.97621i	−1.21768	−	0.395648i	−0.371443	−	0.928456i	$-0.621137\pi$
$101$	−12.2375	−	3.97621i	−1.21768	−	0.395648i	−0.846236	+	0.532808i	$0.821137\pi$
$102$	−8.86673	−	3.20500i	−0.877938	−	0.317342i
$103$	−8.87376	+	12.2137i	−0.874357	+	1.20345i	0.103595	+	0.994620i	$0.466965\pi$
$103$	−8.87376	+	12.2137i	−0.874357	+	1.20345i	−0.977952	+	0.208830i	$0.933035\pi$
$104$	10.3511	−	6.06834i	1.01501	−	0.595050i
$105$	13.5627	+	0.133526i	1.32358	+	0.0130308i
$106$	18.5123	+	0.605396i	1.79807	+	0.0588013i
$107$	−4.66341	+	3.38817i	−0.450829	+	0.327547i	−0.789923	−	0.613206i	$-0.789880\pi$
$107$	−4.66341	+	3.38817i	−0.450829	+	0.327547i	0.339094	+	0.940753i	$0.389880\pi$
$108$	8.48469	+	7.05566i	0.816440	+	0.678931i
$109$	4.92835			0.472050			0.236025	−	0.971747i	$-0.424155\pi$
$109$	4.92835			0.472050			0.236025	+	0.971747i	$0.424155\pi$
$110$	−15.0799	−	0.890212i	−1.43781	−	0.0848784i
$111$		−	11.2879i		−	1.07140i
$112$	1.82749	+	10.4240i	0.172682	+	0.984978i
$113$	9.81753	−	7.13285i	0.923555	−	0.671002i	−0.0208510	−	0.999783i	$-0.506638\pi$
$113$	9.81753	−	7.13285i	0.923555	−	0.671002i	0.944406	+	0.328780i	$0.106638\pi$
$114$	13.5888	+	0.444387i	1.27271	+	0.0416206i
$115$	3.87473	+	11.9252i	0.361321	+	1.11203i
$116$	15.6811	+	1.02671i	1.45595	+	0.0953281i
$117$	1.16276	−	1.60041i	0.107497	−	0.147958i
$118$	−2.53746	−	0.917198i	−0.233592	−	0.0844349i
$119$	−8.90032	−	6.60130i	−0.815891	−	0.605141i
$120$	14.1626	−	3.10890i	1.29287	−	0.283803i
$121$	−2.84501	−	10.6257i	−0.258638	−	0.965974i
$122$	−4.99732	+	3.38687i	−0.452436	+	0.306633i
$123$	−1.68215	+	5.17713i	−0.151674	+	0.466806i
$124$	−12.2378	+	3.10888i	−1.09898	+	0.279186i
$125$	0.970630	+	0.705204i	0.0868158	+	0.0630753i
$126$	0.964613	+	1.45390i	0.0859345	+	0.129524i
$127$	7.63772	−	2.48164i	0.677738	−	0.220210i	0.0501331	−	0.998743i	$-0.484035\pi$
$127$	7.63772	−	2.48164i	0.677738	−	0.220210i	0.627605	+	0.778532i	$0.284035\pi$
$128$	4.40038	+	10.4229i	0.388942	+	0.921262i
$129$	−3.23494	+	2.35032i	−0.284820	+	0.206934i
$130$	−5.36698	−	18.5616i	−0.470715	−	1.62796i
$131$		−	18.0079i		−	1.57336i	−0.617363	−	0.786678i	$-0.711799\pi$
$131$		−	18.0079i		−	1.57336i	0.617363	−	0.786678i	$-0.288201\pi$
$132$	5.39826	+	9.07419i	0.469858	+	0.789807i
$133$	15.1483	+	5.08741i	1.31353	+	0.441134i
$134$	−2.46282	−	8.51758i	−0.212755	−	0.735807i
$135$	14.3762	−	10.4449i	1.23731	−	0.898956i
$136$	−10.8539	−	4.74628i	−0.930716	−	0.406990i
$137$	4.26240	+	13.1183i	0.364161	+	1.12077i	0.950505	+	0.310711i	$0.100567\pi$
$137$	4.26240	+	13.1183i	0.364161	+	1.12077i	−0.586343	+	0.810063i	$0.699433\pi$
$138$	5.38042	−	6.91816i	0.458012	−	0.588913i
$139$	0.368887	−	0.507730i	0.0312886	−	0.0430651i	−0.793086	−	0.609110i	$-0.791527\pi$
$139$	0.368887	−	0.507730i	0.0312886	−	0.0430651i	0.824375	+	0.566044i	$0.191527\pi$
$140$	16.9938	+	1.28080i	1.43624	+	0.108247i
$141$	8.61962	+	2.80068i	0.725903	+	0.235860i
$142$	5.56178	+	8.20639i	0.466734	+	0.688665i
$143$	11.5961	−	7.96815i	0.969712	−	0.666330i
$144$	1.35319	+	1.28378i	0.112766	+	0.106981i
$145$	7.81986	−	24.0671i	0.649404	−	1.99866i
$146$	11.9168	+	4.30748i	0.986242	+	0.356490i
$147$	−3.23385	−	10.6627i	−0.266724	−	0.879443i
$148$	0.926643	−	14.1527i	0.0761696	−	1.16334i
$149$	−2.77777	−	8.54911i	−0.227564	−	0.700370i	−0.998021	−	0.0628784i	$-0.979972\pi$
$149$	−2.77777	−	8.54911i	−0.227564	−	0.700370i	0.770457	−	0.637492i	$-0.220028\pi$
$150$	0.395291	−	12.0875i	0.0322754	−	0.986942i
$151$	0.890713	+	1.22596i	0.0724852	+	0.0997673i	0.843720	−	0.536783i	$-0.180361\pi$
$151$	0.890713	+	1.22596i	0.0724852	+	0.0997673i	−0.771235	+	0.636551i	$0.780361\pi$
$152$	17.0010	+	1.67270i	1.37897	+	0.135674i
$153$	−1.95307			−0.157896
$154$	3.01426	+	12.0380i	0.242896	+	0.970052i
$155$			20.3327i			1.63316i
$156$	−8.63500	+	10.3839i	−0.691353	+	0.831377i
$157$	13.6491	−	9.91665i	1.08932	−	0.791435i	0.110033	−	0.993928i	$-0.464904\pi$
$157$	13.6491	−	9.91665i	1.08932	−	0.791435i	0.979284	+	0.202493i	$0.0649044\pi$
$158$	10.4659	+	0.342259i	0.832619	+	0.0272286i
$159$	−19.8271	+	6.44222i	−1.57239	+	0.510902i
$160$	18.0122	−	2.73528i	1.42399	−	0.216243i
$161$	8.39264	−	5.97226i	0.661432	−	0.470680i
$162$	−9.82015	−	3.54962i	−0.771544	−	0.278884i
$163$	−11.5568	−	3.75504i	−0.905200	−	0.294117i	−0.180819	−	0.983516i	$-0.557875\pi$
$163$	−11.5568	−	3.75504i	−0.905200	−	0.294117i	−0.724382	+	0.689399i	$0.757875\pi$
$164$	−2.53406	+	6.35294i	−0.197877	+	0.496081i
$165$	16.3029	−	4.82746i	1.26918	−	0.375817i
$166$	5.81376	−	3.94020i	0.451235	−	0.305819i
$167$	−5.34108	+	16.4381i	−0.413305	+	1.27202i	0.500453	+	0.865764i	$0.333167\pi$
$167$	−5.34108	+	16.4381i	−0.413305	+	1.27202i	−0.913758	+	0.406258i	$0.866833\pi$
$168$	−5.92279	−	10.3347i	−0.456953	−	0.797343i
$169$	4.04215	+	2.93680i	0.310935	+	0.225907i
$170$	−11.7112	+	15.0583i	−0.898210	+	1.15492i
$171$	2.67860	−	0.870331i	0.204838	−	0.0665559i
$172$	−4.24887	+	2.68124i	−0.323973	+	0.204443i
$173$	−1.00105	−	1.37783i	−0.0761086	−	0.104755i	0.769265	−	0.638929i	$-0.220622\pi$
$173$	−1.00105	−	1.37783i	−0.0761086	−	0.104755i	−0.845374	+	0.534175i	$0.820622\pi$
$174$	−16.9914	+	4.91299i	−1.28812	+	0.372453i
$175$	4.52535	−	13.4748i	0.342084	−	1.01860i
$176$	6.02337	+	11.8203i	0.454029	+	0.890987i
$177$	3.03687			0.228265
$178$	3.41877	+	11.8237i	0.256248	+	0.886225i
$179$	13.8039	+	18.9994i	1.03175	+	1.42008i	0.903625	+	0.428324i	$0.140896\pi$
$179$	13.8039	+	18.9994i	1.03175	+	1.42008i	0.128124	+	0.991758i	$0.459104\pi$
$180$	2.54018	−	1.60298i	0.189334	−	0.119479i
$181$	1.81283	+	5.57931i	0.134747	+	0.414707i	0.995551	−	0.0942295i	$-0.0300387\pi$
$181$	1.81283	+	5.57931i	0.134747	+	0.414707i	−0.860804	+	0.508937i	$0.830039\pi$
$182$	−13.2266	+	8.77537i	−0.980419	+	0.650474i
$183$	3.99387	−	5.49709i	0.295235	−	0.406356i
$184$	7.31384	−	8.23224i	0.539183	−	0.606889i
$185$	−21.7213	−	7.05767i	−1.59698	−	0.518890i
$186$	11.7643	−	7.97312i	0.862602	−	0.584617i
$187$	−13.0938	−	4.63815i	−0.957514	−	0.339175i
$188$	10.5773	+	4.21907i	0.771427	+	0.307707i
$189$	−11.7250	−	8.69634i	−0.852867	−	0.632566i
$190$	9.35143	−	25.8711i	0.678424	−	1.87688i
$191$	4.68748	+	3.40565i	0.339174	+	0.246424i	0.744313	−	0.667831i	$-0.232777\pi$
$191$	4.68748	+	3.40565i	0.339174	+	0.246424i	−0.405139	+	0.914255i	$0.632777\pi$
$192$	−8.64579	−	9.34912i	−0.623956	−	0.674715i
$193$	0.0446086	−	0.0144942i	0.00321100	−	0.00104332i	−0.307411	−	0.951577i	$-0.599463\pi$
$193$	0.0446086	−	0.0144942i	0.00321100	−	0.00104332i	0.310622	+	0.950534i	$0.399463\pi$
$194$	3.35849	+	0.109831i	0.241126	+	0.00788539i
$195$	12.7829	+	17.5942i	0.915403	+	1.25994i
$196$	−3.17925	−	13.6342i	−0.227090	−	0.973874i
$197$	−16.0476			−1.14335			−0.571674	−	0.820481i	$-0.693706\pi$
$197$	−16.0476			−1.14335			−0.571674	+	0.820481i	$0.693706\pi$
$198$	1.69066	+	1.38766i	0.120150	+	0.0986164i
$199$			22.0257i			1.56136i	0.624931	+	0.780680i	$0.285127\pi$
$199$			22.0257i			1.56136i	−0.624931	+	0.780680i	$0.714873\pi$
$200$	1.48790	−	15.1228i	0.105210	−	1.06934i
$201$	5.86586	+	8.07366i	0.413746	+	0.569472i
$202$	18.1874	+	0.594771i	1.27966	+	0.0418479i
$203$	−20.7875	−	0.204655i	−1.45900	−	0.0143640i
$204$	13.3050	+	0.871143i	0.931536	+	0.0609922i
$205$	8.91058	+	6.47392i	0.622342	+	0.452158i
$206$	7.25776	−	20.0788i	0.505672	−	1.39896i
$207$	0.561022	−	1.72665i	0.0389937	−	0.120010i
$208$	−11.6789	+	12.3104i	−0.809786	+	0.853570i
$209$	20.0248	+	0.526251i	1.38515	+	0.0364015i
$210$	−18.4782	+	5.14632i	−1.27512	+	0.355130i
$211$	5.20304	−	16.0133i	0.358192	−	1.10240i	−0.595944	−	0.803026i	$-0.703222\pi$
$211$	5.20304	−	16.0133i	0.358192	−	1.10240i	0.954136	−	0.299375i	$-0.0967782\pi$
$212$	−25.3879	+	6.44955i	−1.74365	+	0.442957i
$213$	−9.02708	−	6.55856i	−0.618526	−	0.449385i
$214$	5.00459	−	6.43493i	0.342107	−	0.439882i
$215$	2.50009	+	7.69450i	0.170505	+	0.524760i
$216$	−14.2986	−	6.25259i	−0.972896	−	0.425435i
$217$	15.9358	−	5.00495i	1.08179	−	0.339758i
$218$	−6.69547	+	1.93596i	−0.453475	+	0.131120i
$219$	−14.2622			−0.963750
$220$	20.8367	−	4.71429i	1.40481	−	0.317838i
$221$		−	17.7677i		−	1.19518i
$222$	4.43413	+	15.3353i	0.297599	+	1.02924i
$223$	−14.2595	−	19.6265i	−0.954887	−	1.31429i	−0.949322	−	0.314305i	$-0.898229\pi$
$223$	−14.2595	−	19.6265i	−0.954887	−	1.31429i	−0.00556523	−	0.999985i	$-0.501771\pi$
$224$	−6.57754	−	13.4438i	−0.439480	−	0.898252i
$225$	−0.774178	−	2.38267i	−0.0516119	−	0.158845i
$226$	−10.5358	+	13.5470i	−0.700830	+	0.901130i
$227$	−2.09501	+	2.88354i	−0.139051	+	0.191387i	−0.872863	−	0.487965i	$-0.837739\pi$
$227$	−2.09501	+	2.88354i	−0.139051	+	0.191387i	0.733812	+	0.679353i	$0.237739\pi$
$228$	−18.6358	+	4.73425i	−1.23419	+	0.313533i
$229$	−6.07252	+	18.6893i	−0.401283	+	1.23502i	0.522675	+	0.852532i	$0.324934\pi$
$229$	−6.07252	+	18.6893i	−0.401283	+	1.23502i	−0.923959	+	0.382492i	$0.875066\pi$
$230$	−9.94854	−	14.6791i	−0.655988	−	0.967908i
$231$	−7.79654	−	11.5891i	−0.512975	−	0.762508i
$232$	−21.7070	+	4.76500i	−1.42514	+	0.312838i
$233$	13.1344	+	4.26763i	0.860465	+	0.279582i	0.705823	−	0.708389i	$-0.250578\pi$
$233$	13.1344	+	4.26763i	0.860465	+	0.279582i	0.154642	+	0.987971i	$0.450578\pi$
$234$	−0.951012	+	2.63101i	−0.0621696	+	0.171994i
$235$	10.7787	−	14.8356i	0.703125	−	0.967768i
$236$	3.80759	+	0.249302i	0.247853	+	0.0162281i
$237$	−11.2092	+	3.64209i	−0.728115	+	0.236579i
$238$	14.6848	+	5.47205i	0.951872	+	0.354700i
$239$	3.35531	+	4.61819i	0.217037	+	0.298726i	0.903628	−	0.428318i	$-0.140894\pi$
$239$	3.35531	+	4.61819i	0.217037	+	0.298726i	−0.686591	+	0.727044i	$0.740894\pi$
$240$	−18.0196	+	9.78702i	−1.16316	+	0.631750i
$241$	15.8866			1.02335			0.511673	−	0.859180i	$-0.329026\pi$
$241$	15.8866			1.02335			0.511673	+	0.859180i	$0.329026\pi$
$242$	8.03914	+	13.3181i	0.516775	+	0.856121i
$243$	−4.79969			−0.307900
$244$	5.45874	−	6.56433i	0.349460	−	0.420238i
$245$	−22.5401	−	0.443863i	−1.44003	−	0.0283573i
$246$	0.251620	−	7.69423i	0.0160427	−	0.490566i
$247$	7.91766	+	24.3681i	0.503789	+	1.55050i
$248$	15.4045	−	9.03086i	0.978187	−	0.573460i
$249$	−4.64636	+	6.39517i	−0.294451	+	0.405277i
$250$	−1.59568	−	0.576779i	−0.100920	−	0.0364787i
$251$	0.736953	−	2.26811i	0.0465161	−	0.143162i	−0.925101	−	0.379721i	$-0.876020\pi$
$251$	0.736953	−	2.26811i	0.0465161	−	0.143162i	0.971617	+	0.236560i	$0.0760199\pi$
$252$	−1.88161	−	1.59629i	−0.118530	−	0.100557i
$253$	7.86165	−	10.2435i	0.494258	−	0.644004i
$254$	−9.40147	+	6.37173i	−0.589901	+	0.399798i
$255$	6.63496	−	20.4203i	0.415497	−	1.27877i
$256$	−10.0725	−	12.4316i	−0.629533	−	0.776974i
$257$	9.07259	−	12.4873i	0.565933	−	0.778939i	−0.426133	−	0.904661i	$-0.640124\pi$
$257$	9.07259	−	12.4873i	0.565933	−	0.778939i	0.992066	+	0.125721i	$0.0401245\pi$
$258$	3.47161	−	4.46381i	0.216133	−	0.277904i
$259$	−0.184708	+	18.7614i	−0.0114772	+	1.16578i
$260$	14.5827	+	23.1088i	0.904384	+	1.43314i
$261$	−2.96423	+	2.15364i	−0.183481	+	0.133307i
$262$	7.07388	+	24.4648i	0.437026	+	1.51144i
$263$			17.8587i			1.10122i	0.834764	+	0.550608i	$0.185604\pi$
$263$			17.8587i			1.10122i	−0.834764	+	0.550608i	$0.814396\pi$
$264$	−10.8984	−	10.2073i	−0.670751	−	0.628216i
$265$			42.1812i			2.59117i
$266$	−22.5784	−	0.960964i	−1.38437	−	0.0589205i
$267$	−8.14272	−	11.2075i	−0.498326	−	0.685887i
$268$	6.69178	+	10.6042i	0.408765	+	0.647756i
$269$	−0.794762	−	2.44603i	−0.0484575	−	0.149137i	0.923900	−	0.382634i	$-0.124983\pi$
$269$	−0.794762	−	2.44603i	−0.0484575	−	0.149137i	−0.972357	+	0.233497i	$0.924983\pi$
$270$	−15.4280	+	19.8374i	−0.938917	+	1.20726i
$271$	−6.27529	−	4.55926i	−0.381197	−	0.276956i	0.380642	−	0.924723i	$-0.375703\pi$
$271$	−6.27529	−	4.55926i	−0.381197	−	0.276956i	−0.761839	+	0.647767i	$0.775703\pi$
$272$	16.6102	+	2.18446i	1.00714	+	0.132452i
$273$	10.6429	−	14.3495i	0.644139	−	0.868471i
$274$	−10.9439	−	16.1477i	−0.661145	−	0.975517i
$275$	0.468111	−	17.8125i	0.0282282	−	1.07413i
$276$	−4.59203	+	11.5123i	−0.276408	+	0.692959i
$277$	−2.09157	+	6.43718i	−0.125670	+	0.386773i	−0.994023	−	0.109175i	$-0.965179\pi$
$277$	−2.09157	+	6.43718i	−0.125670	+	0.386773i	0.868352	+	0.495948i	$0.165179\pi$
$278$	−0.301709	+	0.834689i	−0.0180953	+	0.0500613i
$279$	1.73042	−	2.38171i	0.103597	−	0.142589i
$280$	−23.5903	+	4.93549i	−1.40979	+	0.294952i
$281$	5.38301	−	1.74905i	0.321123	−	0.104339i	−0.144020	−	0.989575i	$-0.546003\pi$
$281$	5.38301	−	1.74905i	0.321123	−	0.104339i	0.465143	+	0.885236i	$0.346003\pi$
$282$	−12.8105	−	0.418933i	−0.762852	−	0.0249471i
$283$	−1.88682	−	2.59698i	−0.112160	−	0.154374i	0.749247	−	0.662291i	$-0.230416\pi$
$283$	−1.88682	−	2.59698i	−0.112160	−	0.154374i	−0.861406	+	0.507917i	$0.830416\pi$
$284$	−10.7797	−	8.96411i	−0.639655	−	0.531922i
$285$			30.9628i			1.83408i
$286$	−12.6239	+	15.3804i	−0.746468	+	0.909463i
$287$	2.88058	−	8.57727i	0.170035	−	0.506300i
$288$	−2.34269	−	1.21253i	−0.138044	−	0.0714490i
$289$	−0.438360	+	0.318487i	−0.0257859	+	0.0187345i
$290$	−1.16971	+	35.7684i	−0.0686879	+	2.10039i
$291$	−3.59703	+	1.16875i	−0.210862	+	0.0685131i
$292$	−17.8818	−	1.17081i	−1.04645	−	0.0685163i
$293$	−0.839761	+	1.15583i	−0.0490594	+	0.0675245i	−0.832842	−	0.553511i	$-0.813288\pi$
$293$	−0.839761	+	1.15583i	−0.0490594	+	0.0675245i	0.783783	+	0.621035i	$0.213288\pi$
$294$	8.58192	+	13.2156i	0.500508	+	0.770749i
$295$	1.89878	−	5.84384i	0.110551	−	0.340241i
$296$	4.30056	+	19.5913i	0.249965	+	1.13872i
$297$	−17.2494	−	6.11014i	−1.00091	−	0.354546i
$298$	7.13205	+	10.5233i	0.413149	+	0.609600i
$299$	15.7078	+	5.10378i	0.908407	+	0.295159i
$300$	4.21121	+	16.5769i	0.243134	+	0.957070i
$301$	5.41518	−	3.85348i	0.312126	−	0.222111i
$302$	−1.69167	−	1.31565i	−0.0973449	−	0.0757074i
$303$	−19.4791	+	6.32916i	−1.11905	+	0.363601i
$304$	−23.7540	+	4.40591i	−1.36239	+	0.252696i
$305$	−8.08090	−	11.1224i	−0.462711	−	0.636867i
$306$	2.65337	−	0.767207i	0.151683	−	0.0438583i
$307$		−	29.6323i		−	1.69121i	−0.533813	−	0.845603i	$-0.679241\pi$
$307$		−	29.6323i		−	1.69121i	0.533813	−	0.845603i	$-0.320759\pi$
$308$	−8.82385	−	15.1704i	−0.502786	−	0.864411i
$309$			24.0306i			1.36705i
$310$	−7.98710	−	27.6232i	−0.453637	−	1.56889i
$311$	−0.395282	−	0.544060i	−0.0224144	−	0.0308508i	0.797663	−	0.603104i	$-0.206070\pi$
$311$	−0.395282	−	0.544060i	−0.0224144	−	0.0308508i	−0.820077	+	0.572253i	$0.806070\pi$
$312$	7.65216	−	17.4992i	0.433218	−	0.990696i
$313$	3.43697	−	1.11674i	0.194269	−	0.0631219i	−0.210266	−	0.977644i	$-0.567433\pi$
$313$	3.43697	−	1.11674i	0.194269	−	0.0631219i	0.404536	+	0.914522i	$0.367433\pi$
$314$	−14.6477	+	18.8340i	−0.826616	+	1.06287i
$315$	−3.23745	+	2.30379i	−0.182410	+	0.129804i
$316$	−14.3530	+	3.64623i	−0.807417	+	0.205117i
$317$	−8.14632	−	2.64690i	−0.457543	−	0.148665i	0.0711722	−	0.997464i	$-0.477326\pi$
$317$	−8.14632	−	2.64690i	−0.457543	−	0.148665i	−0.528715	+	0.848799i	$0.677326\pi$
$318$	24.4057	−	16.5407i	1.36861	−	0.927555i
$319$	−24.9873	+	7.39903i	−1.39902	+	0.414266i
$320$	−23.3962	+	10.7916i	−1.30789	+	0.603270i
$321$	−2.83534	+	8.72627i	−0.158253	+	0.487053i
$322$	−9.05589	+	11.4105i	−0.504665	+	0.635882i
$323$	14.8689	−	20.4653i	0.827327	−	1.13872i
$324$	14.7357	+	0.964814i	0.818647	+	0.0536008i
$325$	21.6759	−	7.04293i	1.20236	−	0.390671i
$326$	17.1757	+	0.561688i	0.951276	+	0.0311090i
$327$	6.34652	−	4.61102i	0.350963	−	0.254990i
$328$	0.947111	−	9.62630i	0.0522955	−	0.531523i
$329$	−14.2807	−	4.79600i	−0.787318	−	0.264412i
$330$	−20.2521	+	12.9625i	−1.11484	+	0.713563i
$331$		−	2.30950i		−	0.126941i	−0.997984	−	0.0634707i	$-0.979783\pi$
$331$		−	2.30950i		−	0.126941i	0.997984	−	0.0634707i	$-0.0202169\pi$
$332$	−6.35055	+	7.63677i	−0.348532	+	0.419122i
$333$	1.94373	+	2.67531i	0.106516	+	0.146606i
$334$	0.798931	−	24.4303i	0.0437155	−	1.33677i
$335$	19.2037	−	6.23967i	1.04921	−	0.340909i
$336$	12.1062	+	11.7138i	0.660447	+	0.639040i
$337$	−21.3643	+	29.4054i	−1.16378	+	1.60181i	−0.467623	+	0.883928i	$0.654889\pi$
$337$	−21.3643	+	29.4054i	−1.16378	+	1.60181i	−0.696162	+	0.717884i	$0.745111\pi$
$338$	−6.64515	−	2.40198i	−0.361449	−	0.130650i
$339$	5.96902	−	18.3708i	0.324193	−	0.997763i
$340$	9.99519	−	25.0581i	0.542065	−	1.35897i
$341$	17.2572	−	11.8581i	0.934529	−	0.642155i
$342$	−3.29717	+	2.23461i	−0.178290	+	0.120834i
$343$	5.20044	+	17.7751i	0.280797	+	0.959767i
$344$	4.71911	−	5.31168i	0.254437	−	0.286387i
$345$	16.1471	+	11.7315i	0.869328	+	0.631604i
$346$	1.90123	+	1.47863i	0.102211	+	0.0794918i
$347$	−5.02487	−	15.4649i	−0.269749	−	0.830202i	−0.990561	−	0.137072i	$-0.956231\pi$
$347$	−5.02487	−	15.4649i	−0.269749	−	0.830202i	0.720812	−	0.693130i	$-0.243769\pi$
$348$	21.1540	−	13.3492i	1.13397	−	0.715592i
$349$	−18.2089	−	25.0624i	−0.974699	−	1.34156i	−0.939637	−	0.342173i	$-0.888837\pi$
$349$	−18.2089	−	25.0624i	−0.974699	−	1.34156i	−0.0350626	−	0.999385i	$-0.511163\pi$
$350$	−0.854798	+	20.0840i	−0.0456909	+	1.07353i
$351$		−	23.4065i		−	1.24935i
$352$	−12.8264	−	13.6925i	−0.683648	−	0.729811i
$353$			21.8530i			1.16312i	0.813504	+	0.581560i	$0.197557\pi$
$353$			21.8530i			1.16312i	−0.813504	+	0.581560i	$0.802443\pi$
$354$	−4.12577	+	1.19295i	−0.219282	+	0.0634044i
$355$	−18.2647	+	13.2701i	−0.969392	+	0.704304i
$356$	−9.28922	−	14.7203i	−0.492328	−	0.780174i
$357$	−17.6377	−	0.173645i	−0.933486	−	0.00919027i
$358$	−26.2168	−	20.3894i	−1.38560	−	1.07761i
$359$	6.79149	−	9.34768i	0.358441	−	0.493352i	−0.591273	−	0.806472i	$-0.701374\pi$
$359$	6.79149	−	9.34768i	0.358441	−	0.493352i	0.949714	+	0.313120i	$0.101374\pi$
$360$	−2.82131	+	3.17558i	−0.148696	+	0.167368i
$361$	−5.40135	+	16.6236i	−0.284281	+	0.874928i
$362$	−4.65452	−	6.86773i	−0.244636	−	0.360960i
$363$	−13.6052	−	11.0215i	−0.714089	−	0.578480i
$364$	14.5220	−	17.1176i	0.761158	−	0.897204i
$365$	−8.91732	+	27.4447i	−0.466754	+	1.43652i
$366$	−3.26654	+	9.03701i	−0.170745	+	0.472372i
$367$	−5.11814	+	7.04451i	−0.267165	+	0.367720i	−0.921430	−	0.388545i	$-0.872978\pi$
$367$	−5.11814	+	7.04451i	−0.267165	+	0.367720i	0.654265	+	0.756265i	$0.272978\pi$
$368$	−6.70251	+	14.0570i	−0.349392	+	0.732774i
$369$	−0.492798	−	1.51668i	−0.0256540	−	0.0789550i
$370$	32.2821	+	1.05570i	1.67827	+	0.0548834i
$371$	33.0597	−	10.3830i	1.71637	−	0.539061i
$372$	−12.8505	+	15.4532i	−0.666270	+	0.801214i
$373$	−3.20017			−0.165699			−0.0828494	−	0.996562i	$-0.526402\pi$
$373$	−3.20017			−0.165699			−0.0828494	+	0.996562i	$0.526402\pi$
$374$	19.6107	+	1.15768i	1.01405	+	0.0598623i
$375$	1.90973			0.0986181
$376$	−16.0272	−	1.57689i	−0.826541	−	0.0813217i
$377$	−19.5923	−	26.9665i	−1.00906	−	1.38885i
$378$	19.3452	+	7.20869i	0.995011	+	0.370775i
$379$	−17.2039	+	5.58987i	−0.883703	+	0.287133i	−0.715494	−	0.698619i	$-0.753798\pi$
$379$	−17.2039	+	5.58987i	−0.883703	+	0.287133i	−0.168209	+	0.985751i	$0.553798\pi$
$380$	−2.54179	+	38.8209i	−0.130391	+	1.99147i
$381$	7.51367	−	10.3417i	0.384937	−	0.529820i
$382$	−7.70604	−	2.78545i	−0.394275	−	0.142516i
$383$	33.1542	+	10.7725i	1.69410	+	0.550447i	0.987562	−	0.157227i	$-0.0502555\pi$
$383$	33.1542	+	10.7725i	1.69410	+	0.550447i	0.706539	+	0.707674i	$0.250255\pi$
$384$	15.4184	+	9.30511i	0.786816	+	0.474849i
$385$	−27.1756	+	7.75685i	−1.38500	+	0.395326i
$386$	−0.0549099	+	0.0372145i	−0.00279484	+	0.00189417i
$387$	0.361988	−	1.11408i	0.0184009	−	0.0566321i
$388$	−4.60586	+	1.17008i	−0.233827	+	0.0594016i
$389$	3.58544	−	4.93494i	0.181789	−	0.250211i	−0.708391	−	0.705820i	$-0.750579\pi$
$389$	3.58544	−	4.93494i	0.181789	−	0.250211i	0.890180	+	0.455609i	$0.150579\pi$
$390$	−24.2777	−	18.8814i	−1.22935	−	0.956095i
$391$	−5.03892	−	15.5082i	−0.254829	−	0.784283i
$392$	9.67503	+	17.2741i	0.488663	+	0.872473i
$393$	−16.8484	−	23.1898i	−0.849887	−	1.16977i
$394$	21.8017	−	6.30386i	1.09836	−	0.317584i
$395$			23.8470i			1.19987i
$396$	−2.84196	−	1.22109i	−0.142814	−	0.0613621i
$397$	17.5352			0.880066			0.440033	−	0.897982i	$-0.354967\pi$
$397$	17.5352			0.880066			0.440033	+	0.897982i	$0.354967\pi$
$398$	−8.65216	−	29.9233i	−0.433694	−	1.49992i
$399$	24.2672	−	7.62160i	1.21488	−	0.381557i
$400$	3.91915	+	21.1297i	0.195957	+	1.05649i
$401$	−10.0116	−	30.8125i	−0.499955	−	1.53870i	−0.809089	−	0.587686i	$-0.800039\pi$
$401$	−10.0116	−	30.8125i	−0.499955	−	1.53870i	0.309134	−	0.951019i	$-0.399961\pi$
$402$	−11.1406	−	8.66434i	−0.555645	−	0.432138i
$403$	21.6672	+	15.7421i	1.07932	+	0.784171i
$404$	−24.9423	+	6.33636i	−1.24093	+	0.315246i
$405$	7.34840	−	22.6161i	0.365145	−	1.12380i
$406$	28.3215	−	7.88774i	1.40557	−	0.391462i
$407$	6.67786	+	22.5519i	0.331009	+	1.11785i
$408$	−18.4179	+	4.04299i	−0.911821	+	0.200158i
$409$	11.1713	−	34.3818i	0.552386	−	1.70007i	−0.150361	−	0.988631i	$-0.548044\pi$
$409$	11.1713	−	34.3818i	0.552386	−	1.70007i	0.702748	−	0.711439i	$-0.251956\pi$
$410$	−14.6487	−	5.29495i	−0.723446	−	0.261499i
$411$	17.7626	+	12.9053i	0.876163	+	0.636569i
$412$	−1.97271	+	30.1294i	−0.0971887	+	1.48437i
$413$	−5.04751	−	0.0496933i	−0.248372	−	0.00244525i
$414$	−0.0839189	+	2.56614i	−0.00412439	+	0.126119i
$415$	9.40111	+	12.9395i	0.461482	+	0.635176i
$416$	11.0307	−	21.3121i	0.540827	−	1.04491i
$417$		−	0.998967i		−	0.0489196i
$418$	−27.4117	+	7.15123i	−1.34075	+	0.349778i
$419$	−8.04077			−0.392817			−0.196409	−	0.980522i	$-0.562928\pi$
$419$	−8.04077			−0.392817			−0.196409	+	0.980522i	$0.562928\pi$
$420$	23.0822	−	14.2502i	1.12630	−	0.695341i
$421$	13.4215	+	18.4731i	0.654123	+	0.900323i	0.999269	−	0.0382259i	$-0.0121707\pi$
$421$	13.4215	+	18.4731i	0.654123	+	0.900323i	−0.345146	+	0.938549i	$0.612171\pi$
$422$	−0.778282	+	23.7989i	−0.0378862	+	1.15851i
$423$	−2.52518	+	0.820480i	−0.122778	+	0.0398931i
$424$	31.9575	−	18.7350i	1.55199	−	0.909854i
$425$	−18.2043	−	13.2262i	−0.883037	−	0.641564i
$426$	14.8402	+	5.36418i	0.719010	+	0.259895i
$427$	−6.72808	+	9.07124i	−0.325594	+	0.438988i
$428$	−4.27127	+	10.7082i	−0.206460	+	0.517598i
$429$	7.47783	−	21.1104i	0.361033	−	1.01922i
$430$	−6.41910	−	9.47136i	−0.309556	−	0.456750i
$431$	18.7005	+	6.07617i	0.900773	+	0.292679i	0.722556	−	0.691312i	$-0.242967\pi$
$431$	18.7005	+	6.07617i	0.900773	+	0.292679i	0.178217	+	0.983991i	$0.442967\pi$
$432$	21.8817	+	2.87774i	1.05278	+	0.138455i
$433$	6.81144	−	9.37515i	0.327337	−	0.450541i	−0.613353	−	0.789809i	$-0.710180\pi$
$433$	6.81144	−	9.37515i	0.327337	−	0.450541i	0.940690	+	0.339268i	$0.110180\pi$
$434$	−19.6837	+	13.0594i	−0.944847	+	0.626874i
$435$	−12.4473	−	38.3089i	−0.596802	−	1.83677i
$436$	8.33573	−	5.26025i	0.399209	−	0.251920i
$437$	13.8216	+	19.0238i	0.661177	+	0.910032i
$438$	19.3761	−	5.60249i	0.925825	−	0.267698i
$439$	17.0358			0.813075			0.406537	−	0.913634i	$-0.366736\pi$
$439$	17.0358			0.813075			0.406537	+	0.913634i	$0.366736\pi$
$440$	−26.4560	+	14.5897i	−1.26124	+	0.695539i
$441$	2.60251	+	1.97028i	0.123929	+	0.0938227i
$442$	6.97952	+	24.1385i	0.331982	+	1.14815i
$443$	6.47507	+	8.91218i	0.307640	+	0.423430i	0.934643	−	0.355586i	$-0.115719\pi$
$443$	6.47507	+	8.91218i	0.307640	+	0.423430i	−0.627003	+	0.779017i	$0.715719\pi$
$444$	−12.0481	−	19.0922i	−0.571777	−	0.906074i
$445$	−26.6577	+	8.66162i	−1.26370	+	0.410600i
$446$	27.0821	+	21.0624i	1.28238	+	0.997335i
$447$	−11.5757	−	8.41026i	−0.547513	−	0.397792i
$448$	14.2170	+	15.6805i	0.671691	+	0.740832i
$449$	−7.52843	+	23.1701i	−0.355289	+	1.09347i	0.600553	+	0.799585i	$0.294947\pi$
$449$	−7.52843	+	23.1701i	−0.355289	+	1.09347i	−0.955842	+	0.293882i	$0.905053\pi$
$450$	1.98773	+	2.93290i	0.0937027	+	0.138258i
$451$	0.297973	−	11.3384i	0.0140310	−	0.533905i
$452$	8.99199	−	22.5431i	0.422947	−	1.06034i
$453$	2.29404	+	0.745380i	0.107784	+	0.0350210i
$454$	1.71349	−	4.74044i	0.0804181	−	0.222480i
$455$	−20.9583	−	29.4521i	−0.982541	−	1.38073i
$456$	23.4582	−	13.7523i	1.09853	−	0.644011i
$457$	−22.5320	+	7.32109i	−1.05400	+	0.342466i	−0.784238	−	0.620460i	$-0.786946\pi$
$457$	−22.5320	+	7.32109i	−1.05400	+	0.342466i	−0.269764	+	0.962926i	$0.586946\pi$
$458$	0.908342	−	27.7760i	0.0424440	−	1.29789i
$459$	−18.6956	+	13.5832i	−0.872636	+	0.634007i
$460$	19.2820	+	16.0344i	0.899026	+	0.747608i
$461$			22.7253i			1.05842i	0.848490	+	0.529211i	$0.177512\pi$
$461$			22.7253i			1.05842i	−0.848490	+	0.529211i	$0.822488\pi$
$462$	15.1445	+	12.6819i	0.704588	+	0.590015i
$463$	30.3617			1.41103			0.705514	−	0.708695i	$-0.250716\pi$
$463$	30.3617			1.41103			0.705514	+	0.708695i	$0.250716\pi$
$464$	27.6185	−	15.0005i	1.28216	−	0.696382i
$465$	19.0234	+	26.1835i	0.882191	+	1.21423i
$466$	−19.5204	−	0.638363i	−0.904263	−	0.0295716i
$467$	9.02600	+	27.7792i	0.417674	+	1.28547i	0.909838	+	0.414965i	$0.136206\pi$
$467$	9.02600	+	27.7792i	0.417674	+	1.28547i	−0.492164	+	0.870502i	$0.663794\pi$
$468$	0.258493	−	3.94797i	0.0119488	−	0.182495i
$469$	−9.61741	−	13.5151i	−0.444091	−	0.624067i
$470$	−8.81579	+	24.3892i	−0.406642	+	1.12499i
$471$	8.29860	−	25.5405i	0.382379	−	1.17684i
$472$	−5.27078	+	1.15701i	−0.242607	+	0.0532558i
$473$	5.07257	−	6.60942i	0.233237	−	0.303901i
$474$	13.7977	−	9.35121i	0.633749	−	0.429515i
$475$	30.8608	+	10.0273i	1.41599	+	0.460083i
$476$	−22.0997	−	1.66562i	−1.01294	−	0.0763437i
$477$	3.58985	−	4.94100i	0.164368	−	0.226233i
$478$	−6.37252	−	4.95606i	−0.291472	−	0.226685i
$479$	0.315495	+	0.970994i	0.0144153	+	0.0443659i	0.958005	−	0.286750i	$-0.0925749\pi$
$479$	0.315495	+	0.970994i	0.0144153	+	0.0443659i	−0.943590	+	0.331116i	$0.892575\pi$
$480$	20.6362	−	20.3748i	0.941908	−	0.929976i
$481$	−24.3381	+	17.6827i	−1.10972	+	0.806261i
$482$	−21.5829	+	6.24060i	−0.983076	+	0.284251i
$483$	5.21997	−	15.5431i	0.237517	−	0.707233i
$484$	−16.1533	−	14.9355i	−0.734241	−	0.678889i
$485$			7.65250i			0.347482i
$486$	6.52068	−	1.88542i	0.295784	−	0.0855244i
$487$	−26.1215	+	18.9784i	−1.18368	+	0.859994i	−0.992582	−	0.121578i	$-0.961205\pi$
$487$	−26.1215	+	18.9784i	−1.18368	+	0.859994i	−0.191098	+	0.981571i	$0.561205\pi$
$488$	−4.83742	+	11.0624i	−0.218980	+	0.500770i
$489$	−18.3956	+	5.97710i	−0.831879	+	0.270294i
$490$	30.7965	−	8.25122i	1.39124	−	0.372752i
$491$	−2.06392	−	1.49952i	−0.0931434	−	0.0676726i	0.540239	−	0.841512i	$-0.318334\pi$
$491$	−2.06392	−	1.49952i	−0.0931434	−	0.0676726i	−0.633382	+	0.773839i	$0.718334\pi$
$492$	2.68062	+	10.5519i	0.120852	+	0.475718i
$493$	−10.1694	+	31.2981i	−0.458006	+	1.40960i
$494$	−20.3289	−	29.9953i	−0.914642	−	1.34955i
$495$	−3.03263	+	3.95143i	−0.136306	+	0.177603i
$496$	−17.3805	+	18.3202i	−0.780406	+	0.822602i
$497$	14.8964	+	11.0486i	0.668195	+	0.495596i
$498$	3.80021	−	10.5134i	0.170292	−	0.471118i
$499$	15.3474	−	21.1239i	0.687043	−	0.945634i	−0.312948	−	0.949770i	$-0.601317\pi$
$499$	15.3474	−	21.1239i	0.687043	−	0.945634i	0.999991	+	0.00413609i	$0.00131656\pi$
$500$	2.39440	+	0.156773i	0.107081	+	0.00701110i
$501$	8.50169	+	26.1655i	0.379827	+	1.16899i
$502$	−0.110235	+	3.37086i	−0.00492003	+	0.150449i
$503$	−16.2871	+	11.8333i	−0.726206	+	0.527619i	−0.888361	−	0.459146i	$-0.848156\pi$
$503$	−16.2871	+	11.8333i	−0.726206	+	0.527619i	0.162155	+	0.986765i	$0.448156\pi$
$504$	3.18334	+	1.42953i	0.141797	+	0.0636763i
$505$			41.4409i			1.84410i
$506$	−6.65668	+	17.0047i	−0.295925	+	0.755950i
$507$	7.95300			0.353205
$508$	10.2695	−	12.3495i	0.455637	−	0.547920i
$509$	33.2358	−	24.1472i	1.47315	−	1.07031i	0.493466	−	0.869765i	$-0.335730\pi$
$509$	33.2358	−	24.1472i	1.47315	−	1.07031i	0.979685	−	0.200541i	$-0.0642701\pi$
$510$	−0.992473	+	30.3486i	−0.0439474	+	1.34386i
$511$	23.7049	+	0.233377i	1.04864	+	0.0103240i
$512$	18.5675	+	12.9324i	0.820577	+	0.571536i
$513$	19.5878	−	26.9603i	0.864822	−	1.19032i
$514$	−7.42038	+	20.5287i	−0.327299	+	0.905484i
$515$	46.2421	+	15.0250i	2.03767	+	0.662079i
$516$	−2.96291	+	7.42808i	−0.130435	+	0.327003i
$517$	−18.8778	−	0.496108i	−0.830246	−	0.0218188i
$518$	−7.11894	−	25.5611i	−0.312788	−	1.12309i
$519$	−2.57822	−	0.837716i	−0.113171	−	0.0367716i
$520$	−28.8892	−	25.6663i	−1.26687	−	1.12554i
$521$	−5.14983	+	7.08814i	−0.225618	+	0.310537i	−0.906787	−	0.421590i	$-0.861472\pi$
$521$	−5.14983	+	7.08814i	−0.225618	+	0.310537i	0.681168	+	0.732127i	$0.261472\pi$
$522$	3.18110	−	4.09027i	0.139233	−	0.179026i
$523$	−22.0452	+	7.16291i	−0.963969	+	0.313212i	−0.748379	−	0.663272i	$-0.769167\pi$
$523$	−22.0452	+	7.16291i	−0.963969	+	0.313212i	−0.215590	+	0.976484i	$0.569167\pi$
$524$	−19.2206	−	30.4582i	−0.839657	−	1.33057i
$525$	−6.77957	−	21.5862i	−0.295885	−	0.942098i
$526$	−7.01529	−	24.2622i	−0.305881	−	1.05788i
$527$		−	26.4417i		−	1.15182i
$528$	18.8158	+	9.58612i	0.818853	+	0.417182i
$529$	−7.84225			−0.340968
$530$	−16.5697	−	57.3058i	−0.719742	−	2.48921i
$531$	−0.719759	+	0.522936i	−0.0312349	+	0.0226935i
$532$	31.0517	−	7.56375i	1.34626	−	0.327930i
$533$	13.7976	−	4.48313i	0.597642	−	0.194186i
$534$	15.4649	+	12.0274i	0.669233	+	0.520478i
$535$	15.0192	+	10.9121i	0.649336	+	0.471770i
$536$	−13.2568	−	11.7778i	−0.572605	−	0.508724i
$537$	35.5521	+	11.5516i	1.53418	+	0.498487i
$538$	2.04059	+	3.01088i	0.0879759	+	0.129808i
$539$	12.7688	+	19.3896i	0.549992	+	0.835170i
$540$	13.1673	−	33.0107i	0.566632	−	1.42056i
$541$	−10.4057	+	32.0256i	−0.447378	+	1.37689i	0.432477	+	0.901645i	$0.357640\pi$
$541$	−10.4057	+	32.0256i	−0.447378	+	1.37689i	−0.879855	+	0.475243i	$0.842360\pi$
$542$	10.3163	+	3.72898i	0.443125	+	0.160173i
$543$	7.55455	+	5.48870i	0.324197	+	0.235543i
$544$	−23.4240	+	3.55710i	−1.00430	+	0.152510i
$545$	−4.90486	−	15.0956i	−0.210101	−	0.646624i
$546$	−8.82228	+	23.6755i	−0.377559	+	1.01322i
$547$	−5.15875	+	3.74805i	−0.220572	+	0.160255i	−0.692584	−	0.721337i	$-0.743528\pi$
$547$	−5.15875	+	3.74805i	−0.220572	+	0.160255i	0.472012	+	0.881592i	$0.343528\pi$
$548$	21.2111	+	17.6386i	0.906094	+	0.753485i
$549$			1.99058i			0.0849557i
$550$	6.36117	+	24.3833i	0.271241	+	1.03971i
$551$		−	47.4566i		−	2.02172i
$552$	1.71628	−	17.4440i	0.0730498	−	0.742467i
$553$	18.6902	−	5.87002i	0.794787	−	0.249619i
$554$	0.312861	−	9.56693i	0.0132922	−	0.406460i
$555$	−34.5750	+	11.2341i	−1.46763	+	0.476860i
$556$	0.0820069	−	1.25250i	0.00347787	−	0.0531176i
$557$	0.218211	+	0.158539i	0.00924588	+	0.00671753i	0.592399	−	0.805645i	$-0.298181\pi$
$557$	0.218211	+	0.158539i	0.00924588	+	0.00671753i	−0.583153	+	0.812363i	$0.698181\pi$
$558$	−1.41529	+	3.91545i	−0.0599140	+	0.165754i
$559$	10.1352	+	3.29311i	0.428672	+	0.139284i
$560$	30.1101	−	15.9719i	1.27238	−	0.674938i
$561$	−21.2011	+	6.27790i	−0.895113	+	0.265053i
$562$	−6.62609	+	4.49075i	−0.279505	+	0.189431i
$563$	−14.9128	−	4.84546i	−0.628500	−	0.204212i	−0.0225894	−	0.999745i	$-0.507191\pi$
$563$	−14.9128	−	4.84546i	−0.628500	−	0.204212i	−0.605910	+	0.795533i	$0.707191\pi$
$564$	17.5684	−	4.46308i	0.739762	−	0.187929i
$565$	−31.6187	−	22.9724i	−1.33021	−	0.966454i
$566$	3.58351	+	2.78698i	0.150626	+	0.117145i
$567$	−19.5342	−	0.192317i	−0.820361	−	0.00807654i
$568$	18.1661	+	7.94381i	0.762234	+	0.333315i
$569$	−11.3221	−	15.5835i	−0.474646	−	0.653294i	0.502819	−	0.864392i	$-0.332296\pi$
$569$	−11.3221	−	15.5835i	−0.474646	−	0.653294i	−0.977465	+	0.211098i	$0.932296\pi$
$570$	−12.1629	−	42.0649i	−0.509446	−	1.76191i
$571$	−2.77691			−0.116210			−0.0581050	−	0.998310i	$-0.518506\pi$
$571$	−2.77691			−0.116210			−0.0581050	+	0.998310i	$0.518506\pi$
$572$	11.1086	−	25.8542i	0.464475	−	1.08102i
$573$	9.22269			0.385283
$574$	−0.544116	+	12.7843i	−0.0227110	+	0.533607i
$575$	16.9221	−	12.2946i	0.705699	−	0.512720i
$576$	3.65899	+	0.727039i	0.152458	+	0.0302933i
$577$	25.0553	−	8.14096i	1.04307	−	0.338912i	0.263122	−	0.964763i	$-0.415248\pi$
$577$	25.0553	−	8.14096i	1.04307	−	0.338912i	0.779943	+	0.625850i	$0.215248\pi$
$578$	0.470431	−	0.604882i	0.0195673	−	0.0251598i
$579$	0.0438841	−	0.0604013i	0.00182376	−	0.00251019i
$580$	−12.4615	−	49.0531i	−0.517434	−	2.03682i
$581$	7.82727	−	10.5533i	0.324730	−	0.437823i
$582$	4.42768	−	3.00080i	0.183533	−	0.124387i
$583$	35.8010	−	24.6004i	1.48273	−	1.01884i
$584$	24.7534	−	5.43374i	1.02431	−	0.224850i
$585$	−6.05928	−	1.96878i	−0.250520	−	0.0813990i
$586$	0.686832	−	1.90015i	0.0283728	−	0.0784943i
$587$	−22.7811	−	16.5515i	−0.940278	−	0.683152i	0.00820940	−	0.999966i	$-0.497387\pi$
$587$	−22.7811	−	16.5515i	−0.940278	−	0.683152i	−0.948488	+	0.316814i	$0.897387\pi$
$588$	−16.8504	−	14.5830i	−0.694900	−	0.601394i
$589$	11.7830	+	36.2644i	0.485511	+	1.49425i
$590$	−0.284023	+	8.68510i	−0.0116931	+	0.357560i
$591$	−20.6655	+	15.0143i	−0.850064	+	0.617608i
$592$	−13.5385	−	24.9266i	−0.556427	−	1.02448i
$593$	−34.2001			−1.40443			−0.702214	−	0.711966i	$-0.747805\pi$
$593$	−34.2001			−1.40443			−0.702214	+	0.711966i	$0.747805\pi$
$594$	25.8345	+	1.52509i	1.06000	+	0.0625752i
$595$	−11.3620	+	33.8316i	−0.465796	+	1.38696i
$596$	−13.8231	−	11.4950i	−0.566217	−	0.470852i
$597$	20.6075	+	28.3637i	0.843407	+	1.16085i
$598$	−23.3449	−	0.763436i	−0.954645	−	0.0312192i
$599$	5.72413	+	17.6171i	0.233882	+	0.719814i	0.997268	+	0.0738712i	$0.0235354\pi$
$599$	5.72413	+	17.6171i	0.233882	+	0.719814i	−0.763386	+	0.645942i	$0.776465\pi$
$600$	−12.2330	−	20.8665i	−0.499409	−	0.851873i
$601$	11.7209	+	8.51570i	0.478104	+	0.347363i	0.800591	−	0.599211i	$-0.204519\pi$
$601$	11.7209	+	8.51570i	0.478104	+	0.347363i	−0.322487	+	0.946574i	$0.604519\pi$
$602$	−5.84313	+	7.36239i	−0.238148	+	0.300069i
$603$	−2.78050	−	0.903440i	−0.113231	−	0.0367909i
$604$	2.81506	+	1.12287i	0.114543	+	0.0456890i
$605$	−29.7152	+	19.2894i	−1.20810	+	0.784224i
$606$	23.9774	−	16.2504i	0.974015	−	0.660126i
$607$	−7.86628	+	24.2099i	−0.319283	+	0.982651i	0.654673	+	0.755912i	$0.272806\pi$
$607$	−7.86628	+	24.2099i	−0.319283	+	0.982651i	−0.973956	+	0.226739i	$0.927194\pi$
$608$	30.5406	−	15.3168i	1.23858	−	0.621178i
$609$	−26.9607	+	19.1855i	−1.09250	+	0.777434i
$610$	15.3475	+	11.9361i	0.621403	+	0.483280i
$611$	−7.46415	−	22.9723i	−0.301967	−	0.929359i
$612$	−3.30339	+	2.08460i	−0.133532	+	0.0842649i
$613$	10.1723	−	7.39060i	0.410855	−	0.298504i	−0.363093	−	0.931753i	$-0.618279\pi$
$613$	10.1723	−	7.39060i	0.410855	−	0.298504i	0.773948	+	0.633249i	$0.218279\pi$
$614$	11.6402	+	40.2573i	0.469760	+	1.62465i
$615$	17.5317			0.706947
$616$	17.9470	+	17.1437i	0.723105	+	0.690738i
$617$	−23.7543			−0.956310			−0.478155	−	0.878275i	$-0.658694\pi$
$617$	−23.7543			−0.956310			−0.478155	+	0.878275i	$0.658694\pi$
$618$	−9.43974	−	32.6471i	−0.379722	−	1.31326i
$619$	−19.3728	+	14.0751i	−0.778657	+	0.565727i	−0.904576	−	0.426313i	$-0.859812\pi$
$619$	−19.3728	+	14.0751i	−0.778657	+	0.565727i	0.125919	+	0.992041i	$0.459812\pi$
$620$	21.7020	+	34.3903i	0.871571	+	1.38115i
$621$	−6.63810	−	20.4300i	−0.266378	−	0.819827i
$622$	0.750734	+	0.583863i	0.0301017	+	0.0234108i
$623$	13.3505	+	18.7610i	0.534875	+	0.751643i
$624$	−3.52189	+	26.7797i	−0.140988	+	1.07204i
$625$	−7.10696	+	21.8730i	−0.284278	+	0.874919i
$626$	−4.23066	+	2.86728i	−0.169091	+	0.114599i
$627$	26.2795	−	18.0577i	1.04950	−	0.721157i
$628$	12.5014	−	31.3411i	0.498859	−	1.25065i
$629$	28.2476	+	9.17819i	1.12630	+	0.365958i
$630$	3.49330	−	4.40159i	0.139176	−	0.175363i
$631$	−3.76418	−	2.73484i	−0.149850	−	0.108872i	0.510334	−	0.859976i	$-0.329522\pi$
$631$	−3.76418	−	2.73484i	−0.149850	−	0.108872i	−0.660184	+	0.751104i	$0.729522\pi$
$632$	18.0671	−	10.5918i	0.718670	−	0.421318i
$633$	−8.28196	−	25.4893i	−0.329178	−	1.01311i
$634$	12.1070	+	0.395929i	0.480832	+	0.0157244i
$635$	−15.2026	−	20.9246i	−0.603297	−	0.830367i
$636$	−26.6592	+	32.0586i	−1.05711	+	1.27121i
$637$	−17.9242	+	23.6759i	−0.710182	+	0.938071i
$638$	31.0403	−	19.8676i	1.22890	−	0.786566i
$639$	3.26884			0.129313
$640$	27.5460	−	23.8516i	1.08885	−	0.942818i
$641$	−5.56411	+	4.04256i	−0.219769	+	0.159671i	−0.692223	−	0.721684i	$-0.743368\pi$
$641$	−5.56411	+	4.04256i	−0.219769	+	0.159671i	0.472454	+	0.881355i	$0.343368\pi$
$642$	0.424116	−	12.9690i	0.0167385	−	0.511844i
$643$	−0.508791	−	1.56590i	−0.0200647	−	0.0617529i	0.940523	−	0.339731i	$-0.110336\pi$
$643$	−0.508791	−	1.56590i	−0.0200647	−	0.0617529i	−0.960588	+	0.277978i	$0.910336\pi$
$644$	7.82070	−	19.0592i	0.308179	−	0.751038i
$645$	10.4186	+	7.56953i	0.410231	+	0.298050i
$646$	−12.1611	+	33.6442i	−0.478473	+	1.32371i
$647$	−29.2616	−	9.50766i	−1.15039	−	0.373785i	−0.329101	−	0.944295i	$-0.606746\pi$
$647$	−29.2616	−	9.50766i	−1.15039	−	0.373785i	−0.821291	+	0.570510i	$0.806746\pi$
$648$	−20.3983	+	4.47772i	−0.801321	+	0.175901i
$649$	−6.06729	+	1.79659i	−0.238162	+	0.0705225i
$650$	−26.6814	+	18.0830i	−1.04653	+	0.709274i
$651$	15.8387	−	21.3548i	0.620769	−	0.836962i
$652$	−23.5549	+	5.98391i	−0.922483	+	0.234348i
$653$	−12.8424	+	17.6760i	−0.502562	+	0.691717i	−0.982643	−	0.185507i	$-0.940607\pi$
$653$	−12.8424	+	17.6760i	−0.502562	+	0.691717i	0.480081	+	0.877224i	$0.340607\pi$
$654$	−6.81084	+	8.75740i	−0.266325	+	0.342441i
$655$	−55.1583	+	17.9220i	−2.15522	+	0.700272i
$656$	2.49471	+	13.4500i	0.0974019	+	0.525133i
$657$	3.38024	−	2.45589i	0.131876	−	0.0958134i
$658$	21.2851	+	0.905921i	0.829781	+	0.0353165i
$659$	−45.9668			−1.79061			−0.895306	−	0.445452i	$-0.853043\pi$
$659$	−45.9668			−1.79061			−0.895306	+	0.445452i	$0.853043\pi$
$660$	22.4218	−	25.5659i	0.872768	−	0.995150i
$661$	−9.92841			−0.386170			−0.193085	−	0.981182i	$-0.561849\pi$
$661$	−9.92841			−0.386170			−0.193085	+	0.981182i	$0.561849\pi$
$662$	0.907219	+	3.13759i	0.0352601	+	0.121946i
$663$	−16.6236	−	22.8804i	−0.645607	−	0.888602i
$664$	5.62774	−	12.8697i	0.218399	−	0.499440i
$665$	0.506656	−	51.4627i	0.0196473	−	1.99564i
$666$	−3.69160	−	2.87104i	−0.143046	−	0.111251i
$667$	−24.7485	−	17.9809i	−0.958267	−	0.696222i
$668$	8.51136	+	33.5040i	0.329314	+	1.29631i
$669$	−36.7256	−	11.9329i	−1.41989	−	0.461351i
$670$	−23.6384	+	16.0206i	−0.913230	+	0.618930i
$671$	−4.72722	+	13.3453i	−0.182492	+	0.515188i
$672$	−21.0484	−	11.1583i	−0.811961	−	0.430443i
$673$	15.9915	+	5.19596i	0.616427	+	0.200289i	0.600553	−	0.799585i	$-0.294947\pi$
$673$	15.9915	+	5.19596i	0.616427	+	0.200289i	0.0158739	+	0.999874i	$0.494947\pi$
$674$	17.4736	−	48.3414i	0.673058	−	1.86204i
$675$	−23.9817	−	17.4237i	−0.923057	−	0.670640i
$676$	9.97140	+	0.652876i	0.383515	+	0.0251106i
$677$	6.43137	−	2.08968i	0.247178	−	0.0803129i	−0.182808	−	0.983149i	$-0.558519\pi$
$677$	6.43137	−	2.08968i	0.247178	−	0.0803129i	0.429986	+	0.902836i	$0.358519\pi$
$678$	−0.892860	+	27.3026i	−0.0342901	+	1.04855i
$679$	5.99767	−	1.88369i	0.230170	−	0.0722893i
$680$	−3.73572	+	37.9693i	−0.143258	+	1.45606i
$681$			5.67342i			0.217406i
$682$	−18.7868	+	22.8890i	−0.719385	+	0.876466i
$683$			7.36710i			0.281894i	0.990017	+	0.140947i	$0.0450148\pi$
$683$			7.36710i			0.281894i	−0.990017	+	0.140947i	$0.954985\pi$
$684$	3.60160	−	4.33106i	0.137711	−	0.165602i
$685$	35.9395	−	26.1115i	1.37318	−	0.997671i
$686$	−14.0476	−	22.1058i	−0.536339	−	0.844003i
$687$	9.66597	+	29.7488i	0.368780	+	1.13499i
$688$	−4.32466	+	9.07002i	−0.164876	+	0.345791i
$689$	44.9498	+	32.6579i	1.71245	+	1.24417i
$690$	−26.5452	−	9.59510i	−1.01056	−	0.365279i
$691$	12.0892	−	37.2068i	0.459895	−	1.41541i	−0.405395	−	0.914142i	$-0.632866\pi$
$691$	12.0892	−	37.2068i	0.459895	−	1.41541i	0.865290	−	0.501271i	$-0.167134\pi$
$692$	−3.16378	−	1.26197i	−0.120269	−	0.0479729i
$693$	3.84343	+	1.40417i	0.146000	+	0.0533401i
$694$	12.9016	+	19.0362i	0.489736	+	0.722605i
$695$	−1.92231	−	0.624597i	−0.0729174	−	0.0236923i
$696$	−23.4952	+	26.4455i	−0.890582	+	1.00241i
$697$	−11.5878	−	8.41904i	−0.438920	−	0.318894i
$698$	34.5829	+	26.8960i	1.30898	+	1.01803i
$699$	20.9068	−	6.79303i	0.790767	−	0.256936i
$700$	−6.72811	−	27.6211i	−0.254299	−	1.04398i
$701$	−23.0733	+	16.7637i	−0.871466	+	0.633157i	−0.930980	−	0.365070i	$-0.881045\pi$
$701$	−23.0733	+	16.7637i	−0.871466	+	0.633157i	0.0595139	+	0.998227i	$0.481045\pi$
$702$	9.19458	+	31.7992i	0.347027	+	1.20018i
$703$	−42.8311			−1.61541
$704$	22.8041	+	13.5636i	0.859463	+	0.511198i
$705$		−	29.1893i		−	1.09933i
$706$	−8.58434	−	29.6887i	−0.323076	−	1.11735i
$707$	32.4794	−	10.2008i	1.22152	−	0.383641i
$708$	5.13650	−	3.24138i	0.193042	−	0.121819i
$709$	10.2013	−	3.31459i	0.383116	−	0.124482i	−0.111126	−	0.993806i	$-0.535446\pi$
$709$	10.2013	−	3.31459i	0.383116	−	0.124482i	0.494242	+	0.869324i	$0.335446\pi$
$710$	19.6010	−	25.2030i	0.735612	−	0.945854i
$711$	2.02951	−	2.79338i	0.0761125	−	0.104760i
$712$	18.4024	+	16.3494i	0.689660	+	0.612721i
$713$	23.3763	+	7.59542i	0.875449	+	0.284451i
$714$	24.0301	−	6.69256i	0.899305	−	0.250463i
$715$	−35.9473	−	27.5887i	−1.34435	−	1.03176i
$716$	43.6265	+	17.4018i	1.63040	+	0.650335i
$717$	8.64165	+	2.80784i	0.322728	+	0.104861i
$718$	−5.55469	+	15.3672i	−0.207299	+	0.573500i
$719$	−17.1110	+	23.5512i	−0.638131	+	0.878312i	−0.998514	−	0.0544925i	$-0.982646\pi$
$719$	−17.1110	+	23.5512i	−0.638131	+	0.878312i	0.360383	+	0.932804i	$0.382646\pi$
$720$	2.58549	−	5.42249i	0.0963554	−	0.202084i
$721$	0.393221	−	39.9408i	0.0146443	−	1.48747i
$722$	0.807946	−	24.7060i	0.0300686	−	0.919463i
$723$	20.4581	−	14.8637i	0.760844	−	0.552786i
$724$	9.02124	+	7.50184i	0.335272	+	0.278804i
$725$	−42.2136			−1.56777
$726$	22.8130	+	9.62900i	0.846671	+	0.357366i
$727$			10.9207i			0.405028i	0.979279	+	0.202514i	$0.0649111\pi$
$727$			10.9207i			0.405028i	−0.979279	+	0.202514i	$0.935089\pi$
$728$	−13.0048	+	28.9598i	−0.481992	+	1.07332i
$729$	−24.1012	+	17.5106i	−0.892638	+	0.648539i
$730$	1.33387	−	40.7883i	0.0493689	−	1.50964i
$731$	−3.25126	−	10.0063i	−0.120252	−	0.370098i
$732$	0.887872	−	13.5605i	0.0328167	−	0.501211i
$733$	−19.2686	+	26.5210i	−0.711704	+	0.979576i	0.288055	+	0.957614i	$0.406991\pi$
$733$	−19.2686	+	26.5210i	−0.711704	+	0.979576i	−0.999759	+	0.0219624i	$0.993009\pi$
$734$	4.18607	−	11.5809i	0.154511	−	0.427459i
$735$	−29.4415	+	20.5172i	−1.08596	+	0.756787i
$736$	3.58387	−	21.7303i	0.132103	−	0.800988i
$737$	−16.4956	−	12.6600i	−0.607624	−	0.466337i
$738$	1.26528	+	1.86692i	0.0465756	+	0.0687221i
$739$	6.59660	−	20.3023i	0.242660	−	0.746831i	−0.753353	−	0.657617i	$-0.771565\pi$
$739$	6.59660	−	20.3023i	0.242660	−	0.746831i	0.996013	−	0.0892137i	$-0.0284354\pi$
$740$	−44.2720	+	11.2469i	−1.62747	+	0.413443i
$741$	32.9950	+	23.9723i	1.21210	+	0.880644i
$742$	−40.8349	+	27.0926i	−1.49910	+	0.994599i
$743$	−23.4483	+	7.61883i	−0.860236	+	0.279508i	−0.705727	−	0.708484i	$-0.749380\pi$
$743$	−23.4483	+	7.61883i	−0.860236	+	0.279508i	−0.154509	+	0.987991i	$0.549380\pi$
$744$	11.3879	−	26.0422i	0.417501	−	0.954752i
$745$	−23.4215	+	17.0167i	−0.858097	+	0.623444i
$746$	4.34763	−	1.25710i	0.159178	−	0.0460256i
$747$		−	2.31579i		−	0.0847302i
$748$	−27.0971	+	6.13073i	−0.990770	+	0.224162i
$749$	4.85535	−	14.4574i	0.177411	−	0.528261i
$750$	−2.59449	+	0.750183i	−0.0947373	+	0.0273928i
$751$	−0.388808	+	0.282486i	−0.0141878	+	0.0103080i	−0.594857	−	0.803832i	$-0.702791\pi$
$751$	−0.388808	+	0.282486i	−0.0141878	+	0.0103080i	0.580669	+	0.814140i	$0.302791\pi$
$752$	22.3934	−	4.15354i	0.816604	−	0.151464i
$753$	−1.17305	−	3.61027i	−0.0427483	−	0.131566i
$754$	37.2104	+	28.9394i	1.35512	+	1.05391i
$755$	2.86867	−	3.94838i	0.104401	−	0.143696i
$756$	−29.1134	−	2.19424i	−1.05885	−	0.0798036i
$757$	24.6450	+	8.00765i	0.895738	+	0.291043i	0.720477	−	0.693479i	$-0.243923\pi$
$757$	24.6450	+	8.00765i	0.895738	+	0.291043i	0.175261	+	0.984522i	$0.443923\pi$
$758$	21.1767	−	14.3522i	0.769172	−	0.521297i
$759$	0.539963	−	20.5466i	0.0195994	−	0.745794i
$760$	−11.7965	−	53.7391i	−0.427904	−	1.94932i
$761$	−14.0930	+	43.3739i	−0.510872	+	1.57230i	0.279799	+	0.960059i	$0.409732\pi$
$761$	−14.0930	+	43.3739i	−0.510872	+	1.57230i	−0.790670	+	0.612242i	$0.790268\pi$
$762$	−6.14536	+	17.0013i	−0.222623	+	0.615894i
$763$	−10.6239	+	7.56002i	−0.384610	+	0.273691i
$764$	11.5633	+	0.757106i	0.418346	+	0.0273911i
$765$	1.94376	+	5.98227i	0.0702767	+	0.216290i
$766$	−49.2737	−	1.61137i	−1.78033	−	0.0582211i
$767$	−4.75730	−	6.54786i	−0.171776	−	0.236430i
$768$	−24.6021	−	6.58490i	−0.887751	−	0.237612i
$769$	19.2183			0.693030			0.346515	−	0.938044i	$-0.387365\pi$
$769$	19.2183			0.693030			0.346515	+	0.938044i	$0.387365\pi$
$770$	33.8727	−	21.2133i	1.22069	−	0.764476i
$771$		−	24.5691i		−	0.884834i
$772$	0.0599799	−	0.0721280i	0.00215872	−	0.00259594i
$773$	−27.2835	+	19.8226i	−0.981318	+	0.712969i	−0.958003	−	0.286759i	$-0.907422\pi$
$773$	−27.2835	+	19.8226i	−0.981318	+	0.712969i	−0.0233150	+	0.999728i	$0.507422\pi$
$774$	−0.0541470	+	1.65575i	−0.00194627	+	0.0595147i
$775$	32.2579	−	10.4812i	1.15874	−	0.376497i
$776$	5.79772	−	3.39890i	0.208126	−	0.122013i
$777$	17.3155	+	24.3329i	0.621190	+	0.872939i
$778$	−2.93250	+	8.11286i	−0.105135	+	0.290860i
$779$	19.6442	+	6.38279i	0.703827	+	0.228687i
$780$	40.3998	+	16.1147i	1.44655	+	0.576999i
$781$	21.9150	+	7.76284i	0.784181	+	0.277776i
$782$	12.9376	+	19.0895i	0.462649	+	0.682637i
$783$	−13.3968	+	41.2311i	−0.478763	+	1.47348i
$784$	−19.9298	−	19.6673i	−0.711777	−	0.702405i
$785$	−43.9588	−	31.9380i	−1.56896	−	1.13991i
$786$	31.9990	+	24.8864i	1.14137	+	0.887667i
$787$	−18.6190	+	6.04967i	−0.663694	+	0.215647i	−0.621443	−	0.783460i	$-0.713453\pi$
$787$	−18.6190	+	6.04967i	−0.663694	+	0.215647i	−0.0422516	+	0.999107i	$0.513453\pi$
$788$	−27.1427	+	17.1284i	−0.966919	+	0.610173i
$789$	16.7088	+	22.9977i	0.594850	+	0.818740i
$790$	−9.36762	−	32.3976i	−0.333285	−	1.15266i
$791$	−10.2216	+	30.4360i	−0.363438	+	1.08218i
$792$	4.34065	+	0.542543i	0.154238	+	0.0192784i
$793$	−18.1089			−0.643065
$794$	−23.8226	+	6.88820i	−0.845434	+	0.244453i
$795$	39.4652	+	54.3192i	1.39969	+	1.92650i
$796$	23.5090	+	37.2539i	0.833254	+	1.32043i
$797$	8.00217	+	24.6281i	0.283451	+	0.872374i	0.986859	+	0.161587i	$0.0516611\pi$
$797$	8.00217	+	24.6281i	0.283451	+	0.872374i	−0.703407	+	0.710787i	$0.748339\pi$
$798$	−29.9746	+	19.8871i	−1.06109	+	0.703996i
$799$	−14.0172	+	19.2930i	−0.495893	+	0.682539i
$800$	−13.6246	−	27.1665i	−0.481703	−	0.960481i
$801$	3.85977	+	1.25411i	0.136378	+	0.0443119i
$802$	25.7052	+	37.9280i	0.907682	+	1.33928i
$803$	28.4941	−	8.43743i	1.00554	−	0.297751i
$804$	18.5388	+	7.39476i	0.653813	+	0.260793i
$805$	−26.6457	−	19.7629i	−0.939138	−	0.696552i
$806$	−35.6200	−	12.8753i	−1.25466	−	0.453514i
$807$	−3.31199	−	2.40630i	−0.116588	−	0.0847058i
$808$	31.3966	−	18.4062i	1.10453	−	0.647528i
$809$	49.6693	−	16.1385i	1.74628	−	0.567400i	0.750641	−	0.660710i	$-0.229745\pi$
$809$	49.6693	−	16.1385i	1.74628	−	0.567400i	0.995637	+	0.0933102i	$0.0297448\pi$
$810$	−1.09919	+	33.6119i	−0.0386216	+	1.18100i
$811$	24.1234	+	33.2030i	0.847086	+	1.16591i	0.984497	+	0.175400i	$0.0561218\pi$
$811$	24.1234	+	33.2030i	0.847086	+	1.16591i	−0.137411	+	0.990514i	$0.543878\pi$
$812$	−35.3781	+	21.8413i	−1.24153	+	0.766479i
$813$	−12.3467			−0.433019
$814$	−17.9311	−	28.0149i	−0.628486	−	0.981922i
$815$			39.1358i			1.37087i
$816$	23.4337	−	12.7276i	0.820342	−	0.445555i
$817$	8.91811	+	12.2747i	0.312005	+	0.429438i
$818$	−1.67103	+	51.0981i	−0.0584263	+	1.78660i
$819$	−0.0515254	+	5.23360i	−0.00180044	+	0.182877i
$820$	21.9811	+	1.43921i	0.767613	+	0.0502594i
$821$	−15.9453	−	11.5849i	−0.556493	−	0.404316i	0.273681	−	0.961821i	$-0.411759\pi$
$821$	−15.9453	−	11.5849i	−0.556493	−	0.404316i	−0.830174	+	0.557505i	$0.811759\pi$
$822$	−29.2010	−	10.5551i	−1.01850	−	0.368151i
$823$	16.0738	−	49.4702i	0.560298	−	1.72442i	−0.121225	−	0.992625i	$-0.538682\pi$
$823$	16.0738	−	49.4702i	0.560298	−	1.72442i	0.681523	−	0.731796i	$-0.261318\pi$
$824$	−9.15540	−	41.7075i	−0.318943	−	1.45295i
$825$	−16.0627	−	23.3761i	−0.559233	−	0.813852i
$826$	6.87688	−	1.91526i	0.239277	−	0.0666404i
$827$	−6.35042	+	19.5446i	−0.220826	+	0.679632i	0.777863	+	0.628434i	$0.216304\pi$
$827$	−6.35042	+	19.5446i	−0.220826	+	0.679632i	−0.998689	+	0.0511979i	$0.983696\pi$
$828$	−0.894025	−	3.51923i	−0.0310695	−	0.122302i
$829$	22.1764	+	16.1121i	0.770218	+	0.559596i	0.902027	−	0.431679i	$-0.142079\pi$
$829$	22.1764	+	16.1121i	0.770218	+	0.559596i	−0.131809	+	0.991275i	$0.542079\pi$
$830$	−17.8549	−	13.8862i	−0.619753	−	0.481996i
$831$	3.32926	+	10.2464i	0.115491	+	0.355444i
$832$	−6.61409	+	33.2870i	−0.229302	+	1.15402i
$833$	29.3124	+	0.577223i	1.01561	+	0.0199996i
$834$	0.392416	+	1.35716i	0.0135882	+	0.0469946i
$835$	55.6658			1.92640
$836$	34.4313	−	20.4833i	1.19083	−	0.708430i
$837$		−	34.8334i		−	1.20402i
$838$	10.9239	−	3.15859i	0.377359	−	0.109112i
$839$	−12.6069	−	17.3519i	−0.435238	−	0.599054i	0.533907	−	0.845543i	$-0.320723\pi$
$839$	−12.6069	−	17.3519i	−0.435238	−	0.599054i	−0.969146	+	0.246489i	$0.920723\pi$
$840$	−25.7609	+	28.4270i	−0.888835	+	0.980826i
$841$	10.1164	+	31.1352i	0.348842	+	1.07363i
$842$	−25.4905	−	19.8246i	−0.878462	−	0.683200i
$843$	5.29558	−	7.28874i	0.182390	−	0.251038i
$844$	−8.29139	−	32.6381i	−0.285401	−	1.12345i
$845$	4.97255	−	15.3039i	0.171061	−	0.526472i
$846$	3.10831	−	2.10662i	0.106866	−	0.0724270i
$847$	22.4326	+	18.5413i	0.770793	+	0.637085i
$848$	−36.0568	+	38.0063i	−1.23819	+	1.30514i
$849$	−4.85952	−	1.57895i	−0.166778	−	0.0541896i
$850$	29.9272	+	10.8176i	1.02649	+	0.371039i
$851$	−16.2283	+	22.3363i	−0.556299	+	0.765680i
$852$	−22.2685	−	1.45803i	−0.762906	−	0.0499512i
$853$	2.29556	−	0.745871i	0.0785984	−	0.0255382i	−0.269454	−	0.963013i	$-0.586843\pi$
$853$	2.29556	−	0.745871i	0.0785984	−	0.0255382i	0.348052	+	0.937475i	$0.386843\pi$
$854$	5.57713	−	14.9668i	0.190846	−	0.512153i
$855$	−5.33167	−	7.33841i	−0.182339	−	0.250968i
$856$	1.59640	−	16.2255i	0.0545637	−	0.554578i
$857$	21.5578			0.736401			0.368201	−	0.929746i	$-0.379974\pi$
$857$	21.5578			0.736401			0.368201	+	0.929746i	$0.379974\pi$
$858$	−1.86647	+	31.6173i	−0.0637201	+	1.07940i
$859$	21.3871			0.729719			0.364860	−	0.931063i	$-0.381117\pi$
$859$	21.3871			0.729719			0.364860	+	0.931063i	$0.381117\pi$
$860$	12.4413	+	10.3459i	0.424245	+	0.352792i
$861$	−4.31549	−	13.7405i	−0.147072	−	0.468276i
$862$	−27.7927	−	0.908888i	−0.946623	−	0.0309568i
$863$	−4.45632	−	13.7151i	−0.151695	−	0.466869i	0.846116	−	0.532998i	$-0.178935\pi$
$863$	−4.45632	−	13.7151i	−0.151695	−	0.466869i	−0.997811	+	0.0661298i	$0.978935\pi$
$864$	−30.8581	+	4.68601i	−1.04981	+	0.159421i
$865$	−3.22403	+	4.43750i	−0.109620	+	0.150879i
$866$	−5.57101	+	15.4124i	−0.189311	+	0.523735i
$867$	−0.266521	+	0.820268i	−0.00905154	+	0.0278578i
$868$	21.6115	−	25.4742i	0.733542	−	0.864652i
$869$	20.2400	−	13.9077i	0.686594	−	0.471788i
$870$	31.9590	+	47.1554i	1.08351	+	1.59872i
$871$	8.21886	−	25.2951i	0.278486	−	0.857090i
$872$	−9.25827	+	10.4208i	−0.313524	+	0.352894i
$873$	0.651269	−	0.896394i	0.0220421	−	0.0303384i
$874$	−26.2505	−	20.4156i	−0.887935	−	0.690568i
$875$	−3.17412	−	0.0312496i	−0.107305	−	0.00105643i
$876$	−24.1228	+	15.2227i	−0.815035	+	0.514326i
$877$	26.3586	−	19.1507i	0.890067	−	0.646672i	−0.0458281	−	0.998949i	$-0.514593\pi$
$877$	26.3586	−	19.1507i	0.890067	−	0.646672i	0.935896	+	0.352277i	$0.114593\pi$
$878$	−23.1442	+	6.69203i	−0.781079	+	0.225845i
$879$			2.27412i			0.0767042i
$880$	30.2110	−	30.2136i	1.01841	−	1.01850i
$881$		−	40.4945i		−	1.36429i	−0.731215	−	0.682147i	$-0.761047\pi$
$881$		−	40.4945i		−	1.36429i	0.731215	−	0.682147i	$-0.238953\pi$
$882$	−4.30964	−	1.65442i	−0.145113	−	0.0557072i
$883$	2.61992	+	3.60601i	0.0881673	+	0.121352i	0.850822	−	0.525454i	$-0.176104\pi$
$883$	2.61992	+	3.60601i	0.0881673	+	0.121352i	−0.762655	+	0.646806i	$0.776104\pi$
$884$	−18.9642	−	30.0519i	−0.637835	−	1.01075i
$885$	−3.02239	−	9.30196i	−0.101596	−	0.312682i
$886$	−12.2977	−	9.56420i	−0.413149	−	0.321316i
$887$	−8.31457	−	6.04089i	−0.279176	−	0.202833i	0.439382	−	0.898300i	$-0.355197\pi$
$887$	−8.31457	−	6.04089i	−0.279176	−	0.202833i	−0.718558	+	0.695467i	$0.755197\pi$
$888$	23.8679	+	21.2051i	0.800953	+	0.711598i
$889$	−12.6575	+	17.0657i	−0.424520	+	0.572367i
$890$	32.8137	−	22.2391i	1.09992	−	0.745455i
$891$	−23.4808	+	6.95294i	−0.786638	+	0.232932i
$892$	−45.0666	−	17.9762i	−1.50894	−	0.601886i
$893$	10.6270	−	32.7065i	0.355618	−	1.09448i
$894$	19.0301	+	6.87867i	0.636461	+	0.230057i
$895$	44.4573	−	61.1902i	1.48604	−	2.04536i
$896$	−25.4743	−	15.7181i	−0.851037	−	0.525106i
$897$	25.0030	−	8.12397i	0.834826	−	0.271252i
$898$	1.12612	−	34.4354i	0.0375791	−	1.14912i
$899$	−29.1571	−	40.1314i	−0.972445	−	1.33846i
$900$	−3.85257	−	3.20370i	−0.128419	−	0.106790i
$901$		−	54.8548i		−	1.82748i
$902$	4.04916	+	15.5210i	0.134822	+	0.516793i
$903$	3.36808	−	10.0288i	0.112083	−	0.333739i
$904$	−3.36077	+	34.1584i	−0.111778	+	1.13609i
$905$	15.2853	−	11.1054i	0.508101	−	0.369157i
$906$	−3.40940	−	0.111496i	−0.113270	−	0.00370420i
$907$	−30.9702	+	10.0628i	−1.02835	+	0.334130i	−0.774137	−	0.633019i	$-0.781816\pi$
$907$	−30.9702	+	10.0628i	−1.02835	+	0.334130i	−0.254211	+	0.967149i	$0.581816\pi$
$908$	−0.465740	+	7.11327i	−0.0154561	+	0.236062i
$909$	3.52684	−	4.85428i	0.116978	−	0.161006i
$910$	40.0426	+	31.7796i	1.32740	+	1.05348i
$911$	7.50457	−	23.0967i	0.248637	−	0.765227i	−0.746379	−	0.665521i	$-0.768210\pi$
$911$	7.50457	−	23.0967i	0.248637	−	0.765227i	0.995017	−	0.0997066i	$-0.0317904\pi$
$912$	−26.4672	+	27.8983i	−0.876417	+	0.923803i
$913$	5.49952	−	15.5255i	0.182008	−	0.513820i
$914$	27.7352	−	18.7972i	0.917400	−	0.621756i
$915$	−20.8125	−	6.76238i	−0.688039	−	0.223557i
$916$	9.67696	+	38.0922i	0.319736	+	1.25860i
$917$	27.6238	+	38.8189i	0.912220	+	1.28191i
$918$	20.0634	−	25.7976i	0.662191	−	0.851448i
$919$	−2.22036	+	0.721440i	−0.0732431	+	0.0237981i	−0.345409	−	0.938452i	$-0.612260\pi$
$919$	−2.22036	+	0.721440i	−0.0732431	+	0.0237981i	0.272166	+	0.962250i	$0.412260\pi$
$920$	−32.4944	−	14.2094i	−1.07131	−	0.468469i
$921$	−27.7243	−	38.1592i	−0.913547	−	1.25739i
$922$	−8.92697	−	30.8737i	−0.293994	−	1.01677i
$923$			29.7376i			0.978825i
$924$	−25.5565	−	11.2800i	−0.840748	−	0.371086i
$925$			38.0991i			1.25269i
$926$	−41.2483	+	11.9267i	−1.35550	+	0.391937i
$927$	−4.13797	−	5.69543i	−0.135909	−	0.187062i
$928$	−31.6290	+	31.2283i	−1.03827	+	1.02512i
$929$	−11.4793	+	3.72985i	−0.376624	+	0.122372i	−0.491211	−	0.871041i	$-0.663446\pi$
$929$	−11.4793	+	3.72985i	−0.376624	+	0.122372i	0.114587	+	0.993413i	$0.463446\pi$
$930$	−36.1300	−	28.0991i	−1.18475	−	0.921407i
$931$	−40.4587	+	12.2706i	−1.32598	+	0.402153i
$932$	26.7704	−	6.80076i	0.876893	−	0.222766i
$933$	−1.01806	−	0.330786i	−0.0333296	−	0.0108295i
$934$	−23.1746	−	34.1941i	−0.758297	−	1.11887i
$935$	−1.17530	+	44.7225i	−0.0384366	+	1.46258i
$936$	1.19967	+	5.46510i	0.0392124	+	0.178632i
$937$	−7.45594	+	22.9470i	−0.243575	+	0.749646i	0.752293	+	0.658829i	$0.228948\pi$
$937$	−7.45594	+	22.9470i	−0.243575	+	0.749646i	−0.995868	+	0.0908172i	$0.971052\pi$
$938$	18.3749	+	14.5831i	0.599960	+	0.476156i
$939$	3.38115	−	4.65376i	0.110340	−	0.151870i
$940$	2.39620	−	36.5973i	0.0781554	−	1.19367i
$941$	−23.4882	+	7.63177i	−0.765693	+	0.248789i	−0.665720	−	0.746202i	$-0.731876\pi$
$941$	−23.4882	+	7.63177i	−0.765693	+	0.248789i	−0.0999726	+	0.994990i	$0.531876\pi$
$942$	−1.24132	+	37.9582i	−0.0404445	+	1.23674i
$943$	10.7716	−	7.82604i	0.350772	−	0.254851i
$944$	6.70619	−	3.64235i	0.218268	−	0.118548i
$945$	−14.9679	+	44.5686i	−0.486906	+	1.44982i
$946$	−4.29508	+	10.9719i	−0.139645	+	0.356728i
$947$			3.73099i			0.121241i	0.998161	+	0.0606204i	$0.0193079\pi$
$947$			3.73099i			0.121241i	−0.998161	+	0.0606204i	$0.980692\pi$
$948$	−15.0717	+	18.1242i	−0.489505	+	0.588648i
$949$	22.3420	+	30.7511i	0.725251	+	0.998222i
$950$	−45.8652	−	1.49990i	−1.48806	−	0.0486633i
$951$	−12.9669	+	4.21322i	−0.420482	+	0.136623i
$952$	30.6781	−	6.41839i	0.994284	−	0.208021i
$953$	14.7750	−	20.3361i	0.478610	−	0.658750i	−0.499627	−	0.866241i	$-0.666530\pi$
$953$	14.7750	−	20.3361i	0.478610	−	0.658750i	0.978237	+	0.207490i	$0.0665296\pi$
$954$	−2.93610	+	8.12282i	−0.0950597	+	0.262986i
$955$	5.76642	−	17.7472i	0.186597	−	0.574286i
$956$	10.6043	+	4.22985i	0.342968	+	0.136803i
$957$	−25.2550	+	32.9065i	−0.816378	+	1.06372i
$958$	−0.810047	−	1.19522i	−0.0261714	−	0.0386159i
$959$	−29.3116	−	21.7402i	−0.946521	−	0.702028i
$960$	−20.0319	+	35.7867i	−0.646526	+	1.15501i
$961$	7.16540	+	5.20597i	0.231142	+	0.167934i
$962$	26.1187	−	33.5836i	0.842101	−	1.08278i
$963$	−0.830632	−	2.55642i	−0.0267667	−	0.0823796i
$964$	26.8703	−	16.9565i	0.865435	−	0.546131i
$965$	−0.0887918	−	0.122211i	−0.00285831	−	0.00393413i
$966$	−0.986004	+	23.1667i	−0.0317242	+	0.745377i
$967$			20.3329i			0.653863i	0.945048	+	0.326932i	$0.106015\pi$
$967$			20.3329i			0.653863i	−0.945048	+	0.326932i	$0.893985\pi$
$968$	27.8123	+	13.9455i	0.893921	+	0.448226i
$969$		−	40.2658i		−	1.29352i
$970$	−3.00607	−	10.3964i	−0.0965190	−	0.333808i
$971$	1.98064	−	1.43902i	0.0635617	−	0.0461803i	−0.555551	−	0.831483i	$-0.687493\pi$
$971$	1.98064	−	1.43902i	0.0635617	−	0.0461803i	0.619112	+	0.785302i	$0.287493\pi$
$972$	−8.11811	+	5.12292i	−0.260389	+	0.164318i
$973$	−0.0163464	+	1.66036i	−0.000524043	+	0.0532288i
$974$	28.0326	−	36.0444i	0.898223	−	1.15494i
$975$	21.3239	−	29.3498i	0.682910	−	0.939945i
$976$	2.22641	−	16.9291i	0.0712657	−	0.541889i
$977$	−9.26805	+	28.5241i	−0.296511	+	0.912568i	0.686198	+	0.727414i	$0.259278\pi$
$977$	−9.26805	+	28.5241i	−0.296511	+	0.912568i	−0.982710	+	0.185153i	$0.940722\pi$
$978$	22.6437	−	15.3465i	0.724065	−	0.490726i
$979$	22.8985	+	17.5740i	0.731838	+	0.561668i
$980$	−38.5977	+	23.3073i	−1.23296	+	0.744525i
$981$	−0.710173	+	2.18569i	−0.0226741	+	0.0697836i
$982$	3.39301	+	1.22645i	0.108275	+	0.0391375i
$983$	13.2614	−	18.2527i	0.422972	−	0.582172i	−0.543350	−	0.839506i	$-0.682844\pi$
$983$	13.2614	−	18.2527i	0.422972	−	0.582172i	0.966322	+	0.257335i	$0.0828443\pi$
$984$	−7.78681	−	13.2825i	−0.248235	−	0.423429i
$985$	15.9711	+	49.1541i	0.508883	+	1.56618i
$986$	1.52116	−	46.5152i	0.0484436	−	1.48135i
$987$	−22.8772	+	7.18504i	−0.728190	+	0.228702i
$988$	39.4009	+	32.7648i	1.25351	+	1.04239i
$989$	9.78023			0.310993
$990$	2.56781	−	6.55954i	0.0816103	−	0.208476i
$991$	28.9029			0.918130			0.459065	−	0.888403i	$-0.348184\pi$
$991$	28.9029			0.918130			0.459065	+	0.888403i	$0.348184\pi$
$992$	16.4159	−	31.7166i	0.521205	−	1.00700i
$993$	−2.16079	−	2.97407i	−0.0685705	−	0.0943792i
$994$	−24.5778	−	9.15853i	−0.779561	−	0.290491i
$995$	67.4649	−	21.9207i	2.13878	−	0.694932i
$996$	−1.03293	+	15.7760i	−0.0327296	+	0.499880i
$997$	28.2612	−	38.8982i	0.895041	−	1.23192i	−0.0769825	−	0.997032i	$-0.524529\pi$
$997$	28.2612	−	38.8982i	0.895041	−	1.23192i	0.972023	−	0.234885i	$-0.0754714\pi$
$998$	−12.5525	+	34.7269i	−0.397342	+	1.09926i
$999$	37.2124	+	12.0910i	1.17735	+	0.382544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.c.13.10	yes	352
7.6	odd	2	inner	616.2.bi.c.13.9	✓	352
8.5	even	2	inner	616.2.bi.c.13.25	yes	352
11.6	odd	10	inner	616.2.bi.c.237.26	yes	352
56.13	odd	2	inner	616.2.bi.c.13.26	yes	352
77.6	even	10	inner	616.2.bi.c.237.25	yes	352
88.61	odd	10	inner	616.2.bi.c.237.9	yes	352
616.237	even	10	inner	616.2.bi.c.237.10	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.9	✓	352	7.6	odd	2	inner
616.2.bi.c.13.10	yes	352	1.1	even	1	trivial
616.2.bi.c.13.25	yes	352	8.5	even	2	inner
616.2.bi.c.13.26	yes	352	56.13	odd	2	inner
616.2.bi.c.237.9	yes	352	88.61	odd	10	inner
616.2.bi.c.237.10	yes	352	616.237	even	10	inner
616.2.bi.c.237.25	yes	352	77.6	even	10	inner
616.2.bi.c.237.26	yes	352	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35856 + 0.392821i) q^{2} +(1.28776 - 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(-0.995233 - 3.06301i) q^{5} +(-1.38197 + 1.77694i) q^{6} +(-2.15566 + 1.53399i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +O(q^{10})\)	\(q+(-1.35856 + 0.392821i) q^{2} +(1.28776 - 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(-0.995233 - 3.06301i) q^{5} +(-1.38197 + 1.77694i) q^{6} +(-2.15566 + 1.53399i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +(2.55530 + 3.77034i) q^{10} +(-2.01928 + 2.63107i) q^{11} +(1.17947 - 2.95696i) q^{12} +(-4.03458 - 1.31092i) q^{13} +(2.32602 - 2.93081i) q^{14} +(-4.14740 - 3.01326i) q^{15} +(1.72155 - 3.61058i) q^{16} +(1.29426 + 3.98331i) q^{17} +(0.0215547 - 0.659118i) q^{18} +(-3.55010 - 4.88630i) q^{19} +(-4.95261 - 4.11847i) q^{20} +(-1.34076 + 3.99226i) q^{21} +(1.70978 - 4.36768i) q^{22} -3.89330 q^{23} +(-0.440830 + 4.48053i) q^{24} +(-4.34646 + 3.15789i) q^{25} +(5.99619 + 0.196090i) q^{26} +(1.70501 + 5.24748i) q^{27} +(-2.00876 + 4.89539i) q^{28} +(6.35670 + 4.61842i) q^{29} +(6.81818 + 2.46452i) q^{30} +(-6.00424 - 1.95090i) q^{31} +(-0.920522 + 5.58145i) q^{32} +(-0.138691 + 5.27743i) q^{33} +(-3.32306 - 4.90316i) q^{34} +(6.84400 + 5.07615i) q^{35} +(0.229632 + 0.903920i) q^{36} +(4.16827 - 5.73713i) q^{37} +(6.74248 + 5.24378i) q^{38} +(-6.42207 + 2.08666i) q^{39} +(8.34625 + 3.64970i) q^{40} +(-2.76671 + 2.01013i) q^{41} +(0.253257 - 5.95042i) q^{42} -2.51207 q^{43} +(-0.607122 + 6.60541i) q^{44} +1.50184 q^{45} +(5.28928 - 1.52937i) q^{46} +(3.34676 + 4.60642i) q^{47} +(-1.16115 - 6.26025i) q^{48} +(2.29377 - 6.61352i) q^{49} +(4.66445 - 5.99757i) q^{50} +(5.39351 + 3.91861i) q^{51} +(-8.22323 + 2.08903i) q^{52} +(-12.4561 - 4.04725i) q^{53} +(-4.37768 - 6.45926i) q^{54} +(10.0686 + 3.56656i) q^{55} +(0.806011 - 7.43978i) q^{56} +(-9.14334 - 2.97085i) q^{57} +(-10.4502 - 3.77736i) q^{58} +(1.54350 + 1.12142i) q^{59} +(-10.2310 - 0.669875i) q^{60} +(4.05980 - 1.31911i) q^{61} +(8.92349 + 0.291820i) q^{62} +(-0.369682 - 1.17707i) q^{63} +(-0.941928 - 7.94435i) q^{64} +13.6626i q^{65} +(-1.88467 - 7.22420i) q^{66} +6.26956i q^{67} +(6.44064 + 5.35588i) q^{68} +(-5.01362 + 3.64261i) q^{69} +(-11.2920 - 4.20779i) q^{70} +(-2.16619 - 6.66684i) q^{71} +(-0.667048 - 1.13783i) q^{72} +(-7.24883 - 5.26658i) q^{73} +(-3.40918 + 9.43163i) q^{74} +(-2.64263 + 8.13319i) q^{75} +(-11.2199 - 4.47542i) q^{76} +(0.316871 - 8.76924i) q^{77} +(7.90510 - 5.35758i) q^{78} +(-7.04203 - 2.28810i) q^{79} +(-12.7726 - 1.67977i) q^{80} +(5.97346 + 4.33997i) q^{81} +(2.96913 - 3.81771i) q^{82} +(-4.72307 + 1.53462i) q^{83} +(1.99339 + 8.18349i) q^{84} +(10.9128 - 7.92864i) q^{85} +(3.41280 - 0.986795i) q^{86} +12.5069 q^{87} +(-1.76993 - 9.21235i) q^{88} -8.70311i q^{89} +(-2.04034 + 0.589953i) q^{90} +(10.7081 - 3.36310i) q^{91} +(-6.58505 + 4.15549i) q^{92} +(-9.55728 + 3.10535i) q^{93} +(-6.35628 - 4.94342i) q^{94} +(-11.4336 + 15.7370i) q^{95} +(4.03666 + 8.04881i) q^{96} +(-2.25979 - 0.734250i) q^{97} +(-0.518302 + 9.88592i) q^{98} +(-0.875881 - 1.27467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Introduction

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