LMFDB - Embedded newform 616.2.bi.c.13.9

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			13.9
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35856 + 0.392821i) q^{2} +(-1.28776 + 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(0.995233 + 3.06301i) q^{5} +(1.38197 - 1.77694i) q^{6} +(-0.792771 + 2.52419i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +O(q^{10})$	\(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} +(-0.792771 + 2.52419i) 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} +(0.0854743 - 3.74068i) 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} +(1.35330 + 5.11552i) 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} +(-8.52060 + 0.0838862i) 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} +(3.38975 + 4.89706i) 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} +(-5.74303 - 4.00220i) 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} +(-3.84803 - 6.41815i) 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} +(-1.00522 - 0.715322i) 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} +(11.5428 - 3.46104i) 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} +(-5.04047 - 7.18287i) 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} +(-6.52885 - 5.32139i) 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} +(-6.50750 + 9.14479i) 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} +(9.37441 + 3.18126i) 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	−0.893801	−	0.448463i	$-0.851971\pi$
$3$	−1.28776	+	0.935610i	−0.743487	+	0.540175i	0.150314	+	0.988638i	$0.451971\pi$
$4$	1.69138	−	1.06734i	0.845691	−	0.533672i
$5$	0.995233	+	3.06301i	0.445082	+	1.36982i	0.882394	+	0.470511i	$0.155930\pi$
$5$	0.995233	+	3.06301i	0.445082	+	1.36982i	−0.437313	+	0.899309i	$0.644070\pi$
$6$	1.38197	−	1.77694i	0.564187	−	0.725434i
$7$	−0.792771	+	2.52419i	−0.299639	+	0.954053i
$7$	−0.792771	+	2.52419i	−0.299639	+	0.954053i
$8$	−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	0.809383	−	0.587281i	$-0.199802\pi$
$13$	4.03458	+	1.31092i	1.11899	+	0.363583i	0.309609	+	0.950864i	$0.399802\pi$
$14$	0.0854743	−	3.74068i	0.0228440	−	0.999739i
$15$	−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	$-0.930420\pi$
$17$	−1.29426	−	3.98331i	−0.313903	−	0.966094i	0.662301	−	0.749238i	$-0.269580\pi$
$18$	0.0215547	−	0.659118i	0.00508050	−	0.155356i
$19$	3.55010	+	4.88630i	0.814449	+	1.12099i	0.990622	+	0.136634i	$0.0436284\pi$
$19$	3.55010	+	4.88630i	0.814449	+	1.12099i	−0.176172	+	0.984359i	$0.556372\pi$
$20$	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
$28$	1.35330	+	5.11552i	0.255749	+	0.966743i
$29$	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	0.793751	−	0.608242i	$-0.208125\pi$
$31$	6.00424	+	1.95090i	1.07839	+	0.350391i	0.284642	+	0.958634i	$0.408125\pi$
$32$	−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
$35$	−8.52060	+	0.0838862i	−1.44024	+	0.0141794i
$36$	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	−0.350395	−	0.936602i	$-0.613953\pi$
$41$	2.76671	−	2.01013i	0.432088	−	0.313930i	0.782483	+	0.622672i	$0.213953\pi$
$42$	3.38975	+	4.89706i	0.523050	+	0.755633i
$43$	−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	0.491875	−	0.870666i	$-0.336312\pi$
$47$	−3.34676	−	4.60642i	−0.488175	−	0.671915i	−0.980050	+	0.198751i	$0.936312\pi$
$48$	1.16115	+	6.26025i	0.167598	+	0.903589i
$49$	−5.74303	−	4.00220i	−0.820433	−	0.571743i
$50$	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
$56$	−3.84803	−	6.41815i	−0.514214	−	0.857662i
$57$	−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	0.482761	−	0.875752i	$-0.339634\pi$
$59$	−1.54350	−	1.12142i	−0.200947	−	0.145996i	−0.683708	+	0.729756i	$0.739634\pi$
$60$	−10.2310	−	0.669875i	−1.32082	−	0.0864805i
$61$	−4.05980	+	1.31911i	−0.519805	+	0.168895i	−0.557157	−	0.830407i	$-0.688108\pi$
$61$	−4.05980	+	1.31911i	−0.519805	+	0.168895i	0.0373520	+	0.999302i	$0.488108\pi$
$62$	−8.92349	−	0.291820i	−1.13328	−	0.0370611i
$63$	−1.00522	−	0.715322i	−0.126646	−	0.0901221i
$64$	−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
$70$	11.5428	−	3.46104i	1.37963	−	0.413673i
$71$	−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	0.924707	−	0.380679i	$-0.124310\pi$
$73$	7.24883	+	5.26658i	0.848411	+	0.616407i	−0.0762965	+	0.997085i	$0.524310\pi$
$74$	−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
$77$	−5.04047	−	7.18287i	−0.574415	−	0.818564i
$78$	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	−0.0381057	−	0.999274i	$-0.512132\pi$
$83$	4.72307	−	1.53462i	0.518425	−	0.168446i	0.556530	+	0.830827i	$0.312132\pi$
$84$	−6.52885	−	5.32139i	−0.712356	−	0.580612i
$85$	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	$0.152604\pi$
$89$			8.70311i			0.922528i	−0.887263	+	0.461264i	$0.847396\pi$
$90$	2.04034	−	0.589953i	0.215070	−	0.0621865i
$91$	−6.50750	+	9.14479i	−0.682171	+	0.958634i
$92$	−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	0.421484	−	0.906836i	$-0.361509\pi$
$97$	2.25979	+	0.734250i	0.229447	+	0.0745518i	−0.192037	+	0.981388i	$0.561509\pi$
$98$	9.37441	+	3.18126i	0.946959	+	0.321355i
$99$	−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	0.846236	−	0.532808i	$-0.178863\pi$
$101$	12.2375	+	3.97621i	1.21768	+	0.395648i	0.371443	+	0.928456i	$0.378863\pi$
$102$	−8.86673	−	3.20500i	−0.877938	−	0.317342i
$103$	8.87376	−	12.2137i	0.874357	−	1.20345i	−0.103595	−	0.994620i	$-0.533035\pi$
$103$	8.87376	−	12.2137i	0.874357	−	1.20345i	0.977952	−	0.208830i	$-0.0669654\pi$
$104$	−10.3511	+	6.06834i	−1.01501	+	0.595050i
$105$	10.8940	−	8.07999i	1.06314	−	0.788526i
$106$	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
$112$	7.74897	+	7.20787i	0.732209	+	0.681080i
$113$	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
$119$	11.0807	−	0.109090i	1.01576	−	0.0100003i
$120$	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
$126$	1.64665	+	0.576937i	0.146695	+	0.0513977i
$127$	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	$0.288201\pi$
$131$			18.0079i			1.57336i	−0.617363	+	0.786678i	$0.711799\pi$
$132$	−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	−0.824375	−	0.566044i	$-0.808473\pi$
$139$	−0.368887	+	0.507730i	−0.0312886	+	0.0430651i	0.793086	+	0.609110i	$0.208473\pi$
$140$	−14.3221	+	9.23630i	−1.21044	+	0.780610i
$141$	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
$147$	11.1401	−	0.219373i	0.918822	−	0.0180936i
$148$	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
$154$	9.66938	+	7.77837i	0.779181	+	0.626799i
$155$			20.3327i			1.63316i
$156$	−8.63500	+	10.3839i	−0.691353	+	0.831377i
$157$	−13.6491	+	9.91665i	−1.08932	+	0.791435i	−0.979284	−	0.202493i	$-0.935096\pi$
$157$	−13.6491	+	9.91665i	−1.08932	+	0.791435i	−0.110033	+	0.993928i	$0.535096\pi$
$158$	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
$161$	3.08649	−	9.82740i	0.243250	−	0.774508i
$162$	−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	$-0.666833\pi$
$167$	5.34108	−	16.4381i	0.413305	−	1.27202i	0.913758	−	0.406258i	$-0.133167\pi$
$168$	10.9602	+	4.66477i	0.845599	+	0.359895i
$169$	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	0.845374	−	0.534175i	$-0.179378\pi$
$173$	1.00105	+	1.37783i	0.0761086	+	0.104755i	−0.769265	+	0.638929i	$0.779378\pi$
$174$	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	0.860804	−	0.508937i	$-0.169961\pi$
$181$	−1.81283	−	5.57931i	−0.134747	−	0.414707i	−0.995551	+	0.0942295i	$0.969961\pi$
$182$	5.24857	−	14.9800i	0.389050	−	1.11039i
$183$	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
$189$	14.5973	−	0.143712i	1.06180	−	0.0104535i
$190$	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
$196$	−13.9854	−	0.639464i	−0.998956	−	0.0456760i
$197$	−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	$-0.714873\pi$
$199$		−	22.0257i		−	1.56136i	0.624931	−	0.780680i	$-0.285127\pi$
$200$	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
$203$	−16.6971	+	12.3842i	−1.17191	+	0.869197i
$204$	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
$210$	−11.6262	+	15.2566i	−0.802281	+	1.05280i
$211$	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
$217$	−9.68441	+	13.6092i	−0.657421	+	0.923853i
$218$	−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	$0.101771\pi$
$223$	14.2595	+	19.6265i	0.954887	+	1.31429i	0.00556523	+	0.999985i	$0.498229\pi$
$224$	−13.3589	−	6.74838i	−0.892577	−	0.450895i
$225$	−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	−0.733812	−	0.679353i	$-0.762261\pi$
$227$	2.09501	−	2.88354i	0.139051	−	0.191387i	0.872863	+	0.487965i	$0.162261\pi$
$228$	−18.6358	+	4.73425i	−1.23419	+	0.313533i
$229$	6.07252	−	18.6893i	0.401283	−	1.23502i	−0.522675	−	0.852532i	$-0.675066\pi$
$229$	6.07252	−	18.6893i	0.401283	−	1.23502i	0.923959	−	0.382492i	$-0.124934\pi$
$230$	9.94854	+	14.6791i	0.655988	+	0.967908i
$231$	13.2113	+	4.53388i	0.869238	+	0.298307i
$232$	−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
$238$	−15.0109	+	4.50093i	−0.973013	+	0.291752i
$239$	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	$-0.670974\pi$
$241$	−15.8866			−1.02335			−0.511673	+	0.859180i	$0.670974\pi$
$242$	8.03914	+	13.3181i	0.516775	+	0.856121i
$243$	4.79969			0.307900
$244$	−5.45874	+	6.56433i	−0.349460	+	0.420238i
$245$	6.54314	−	21.5741i	0.418026	−	1.37832i
$246$	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	−0.971617	−	0.236560i	$-0.923980\pi$
$251$	−0.736953	+	2.26811i	−0.0465161	+	0.143162i	0.925101	+	0.379721i	$0.123980\pi$
$252$	−2.46371	−	0.136967i	−0.155199	−	0.00862811i
$253$	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	−0.992066	−	0.125721i	$-0.959876\pi$
$257$	−9.07259	+	12.4873i	−0.565933	+	0.778939i	0.426133	+	0.904661i	$0.359876\pi$
$258$	−3.47161	+	4.46381i	−0.216133	+	0.277904i
$259$	11.1771	+	15.0697i	0.694511	+	0.936386i
$260$	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
$266$	18.5815	−	12.8621i	1.13931	−	0.788629i
$267$	−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	0.972357	−	0.233497i	$-0.0750170\pi$
$269$	0.794762	+	2.44603i	0.0484575	+	0.149137i	−0.923900	+	0.382634i	$0.875017\pi$
$270$	−15.4280	+	19.8374i	−0.938917	+	1.20726i
$271$	6.27529	+	4.55926i	0.381197	+	0.276956i	0.761839	−	0.647767i	$-0.224297\pi$
$271$	6.27529	+	4.55926i	0.381197	+	0.276956i	−0.380642	+	0.924723i	$0.624297\pi$
$272$	−16.6102	−	2.18446i	−1.00714	−	0.132452i
$273$	−0.175880	−	17.8647i	−0.0106448	−	1.08122i
$274$	−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
$280$	15.8292	−	18.1741i	0.945975	−	1.08611i
$281$	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	0.861406	−	0.507917i	$-0.169584\pi$
$283$	1.88682	+	2.59698i	0.112160	+	0.154374i	−0.749247	+	0.662291i	$0.769584\pi$
$284$	−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	−0.783783	−	0.621035i	$-0.786712\pi$
$293$	0.839761	−	1.15583i	0.0490594	−	0.0675245i	0.832842	+	0.553511i	$0.186712\pi$
$294$	−15.0484	+	4.67411i	−0.877639	+	0.272600i
$295$	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
$301$	1.99150	−	6.34093i	0.114788	−	0.365485i
$302$	−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	$0.320759\pi$
$307$			29.6323i			1.69121i	−0.533813	+	0.845603i	$0.679241\pi$
$308$	−16.1920	−	6.76906i	−0.922623	−	0.385703i
$309$			24.0306i			1.36705i
$310$	−7.98710	−	27.6232i	−0.453637	−	1.56889i
$311$	0.395282	+	0.544060i	0.0224144	+	0.0308508i	0.820077	−	0.572253i	$-0.193930\pi$
$311$	0.395282	+	0.544060i	0.0224144	+	0.0308508i	−0.797663	+	0.603104i	$0.793930\pi$
$312$	7.65216	−	17.4992i	0.433218	−	0.990696i
$313$	−3.43697	+	1.11674i	−0.194269	+	0.0631219i	−0.404536	−	0.914522i	$-0.632567\pi$
$313$	−3.43697	+	1.11674i	−0.194269	+	0.0631219i	0.210266	+	0.977644i	$0.432567\pi$
$314$	14.6477	−	18.8340i	0.826616	−	1.06287i
$315$	1.19061	−	3.79091i	0.0670833	−	0.213594i
$316$	−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
$322$	−0.332777	+	14.5636i	−0.0185449	+	0.811596i
$323$	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
$336$	−16.7226	−	2.03197i	−0.912290	−	0.110853i
$337$	−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
$343$	14.6552	−	11.3236i	0.791307	−	0.611419i
$344$	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	$0.111163\pi$
$349$	18.2089	+	25.0624i	0.974699	+	1.34156i	0.0350626	+	0.999385i	$0.488837\pi$
$350$	11.4411	+	16.5286i	0.611555	+	0.883493i
$351$		−	23.4065i		−	1.24935i
$352$	−12.8264	−	13.6925i	−0.683648	−	0.729811i
$353$		−	21.8530i		−	1.16312i	−0.813504	−	0.581560i	$-0.802443\pi$
$353$		−	21.8530i		−	1.16312i	0.813504	−	0.581560i	$-0.197557\pi$
$354$	−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
$357$	−14.1671	+	10.5077i	−0.749804	+	0.556124i
$358$	−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
$364$	−1.24603	+	22.4131i	−0.0653097	+	1.17476i
$365$	−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	−0.654265	−	0.756265i	$-0.727022\pi$
$367$	5.11814	−	7.04451i	0.267165	−	0.367720i	0.921430	+	0.388545i	$0.127022\pi$
$368$	−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
$371$	20.0909	−	28.2331i	1.04307	−	1.46579i
$372$	−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
$378$	−19.7749	+	5.92937i	−1.01711	+	0.304974i
$379$	−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	−0.706539	−	0.707674i	$-0.749745\pi$
$383$	−33.1542	−	10.7725i	−1.69410	−	0.550447i	−0.987562	+	0.157227i	$0.949745\pi$
$384$	−15.4184	−	9.30511i	−0.786816	−	0.474849i
$385$	16.9848	−	22.5876i	0.865624	−	1.15117i
$386$	−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
$392$	19.2512	−	4.62501i	0.972333	−	0.233598i
$393$	−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	$-0.645033\pi$
$397$	−17.5352			−0.880066			−0.440033	+	0.897982i	$0.645033\pi$
$398$	8.65216	+	29.9233i	0.433694	+	1.49992i
$399$	14.7476	−	20.7243i	0.738301	−	1.03751i
$400$	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
$406$	17.8194	−	23.3836i	0.884360	−	1.16051i
$407$	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	$0.451956\pi$
$409$	−11.1713	+	34.3818i	−0.552386	+	1.70007i	−0.702748	+	0.711439i	$0.748044\pi$
$410$	−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
$413$	4.05431	−	3.00706i	0.199500	−	0.147968i
$414$	−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	$-0.437072\pi$
$419$	8.04077			0.392817			0.196409	+	0.980522i	$0.437072\pi$
$420$	9.80176	−	25.2940i	0.478277	−	1.23422i
$421$	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
$427$	−0.111185	−	11.2935i	−0.00538063	−	0.546528i
$428$	−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	−0.940690	−	0.339268i	$-0.889820\pi$
$433$	−6.81144	+	9.37515i	−0.327337	+	0.450541i	0.613353	+	0.789809i	$0.289820\pi$
$434$	7.81089	−	22.2932i	0.374935	−	1.07011i
$435$	−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	$-0.633264\pi$
$439$	−17.0358			−0.813075			−0.406537	+	0.913634i	$0.633264\pi$
$440$	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
$448$	20.7998	+	3.92045i	0.982696	+	0.185224i
$449$	−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
$455$	−34.4871	−	10.8313i	−1.61678	−	0.507781i
$456$	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	$-0.822488\pi$
$461$		−	22.7253i		−	1.05842i	0.848490	−	0.529211i	$-0.177512\pi$
$462$	−19.7293	−	0.969882i	−0.917892	−	0.0451230i
$463$	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	$-0.863794\pi$
$467$	−9.02600	−	27.7792i	−0.417674	−	1.28547i	0.492164	−	0.870502i	$-0.336206\pi$
$468$	−0.258493	+	3.94797i	−0.0119488	+	0.182495i
$469$	−15.8255	−	4.97032i	−0.730755	−	0.229508i
$470$	−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
$476$	18.6252	−	12.0114i	0.853685	−	0.550541i
$477$	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	0.943590	−	0.331116i	$-0.107425\pi$
$479$	−0.315495	−	0.970994i	−0.0144153	−	0.0443659i	−0.958005	+	0.286750i	$0.907425\pi$
$480$	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
$490$	−0.414501	+	31.8800i	−0.0187253	+	1.44019i
$491$	−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
$497$	18.5456	−	0.182584i	0.831885	−	0.00819000i
$498$	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	−0.162155	−	0.986765i	$-0.551844\pi$
$503$	16.2871	−	11.8333i	0.726206	−	0.527619i	0.888361	+	0.459146i	$0.151844\pi$
$504$	3.40090	−	0.781718i	0.151488	−	0.0348205i
$505$			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	$0.664270\pi$
$509$	−33.2358	+	24.1472i	−1.47315	+	1.07031i	−0.979685	+	0.200541i	$0.935730\pi$
$510$	0.992473	−	30.3486i	0.0439474	−	1.34386i
$511$	−19.0405	+	14.1222i	−0.842301	+	0.624729i
$512$	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
$518$	−21.1045	−	16.0825i	−0.927278	−	0.706626i
$519$	−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	−0.681168	−	0.732127i	$-0.738528\pi$
$521$	5.14983	−	7.08814i	0.225618	−	0.310537i	0.906787	+	0.421590i	$0.138528\pi$
$522$	3.18110	−	4.09027i	0.139233	−	0.179026i
$523$	22.0452	−	7.16291i	0.963969	−	0.313212i	0.215590	−	0.976484i	$-0.430833\pi$
$523$	22.0452	−	7.16291i	0.963969	−	0.313212i	0.748379	+	0.663272i	$0.230833\pi$
$524$	19.2206	+	30.4582i	0.839657	+	1.33057i
$525$	18.4347	+	13.1183i	0.804555	+	0.572528i
$526$	−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
$532$	−20.1916	+	24.7732i	−0.875418	+	1.07406i
$533$	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
$539$	22.1268	−	7.02872i	0.953071	−	0.302748i
$540$	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
$546$	7.25660	+	24.2013i	0.310554	+	1.03572i
$547$	−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
$553$	11.3583	−	15.9615i	0.483004	−	0.678751i
$554$	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
$560$	−14.3658	+	30.9087i	−0.607065	+	1.30613i
$561$	−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	0.605910	−	0.795533i	$-0.292809\pi$
$563$	14.9128	+	4.84546i	0.628500	+	0.204212i	0.0225894	+	0.999745i	$0.492809\pi$
$564$	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
$567$	−15.6905	+	11.6375i	−0.658938	+	0.488730i
$568$	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
$574$	−7.28279	−	10.5212i	−0.303978	−	0.439146i
$575$	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	−0.779943	−	0.625850i	$-0.784752\pi$
$577$	−25.0553	+	8.14096i	−1.04307	+	0.338912i	−0.263122	+	0.964763i	$0.584752\pi$
$578$	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
$581$	0.129350	+	13.1385i	0.00536634	+	0.545077i
$582$	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	0.948488	−	0.316814i	$-0.102613\pi$
$587$	22.7811	+	16.5515i	0.940278	+	0.683152i	−0.00820940	+	0.999966i	$0.502613\pi$
$588$	18.6081	−	12.2614i	0.767384	−	0.505651i
$589$	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	$-0.252195\pi$
$593$	34.2001			1.40443			0.702214	+	0.711966i	$0.252195\pi$
$594$	−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	0.322487	−	0.946574i	$-0.395481\pi$
$601$	−11.7209	−	8.51570i	−0.478104	−	0.347363i	−0.800591	+	0.599211i	$0.795481\pi$
$602$	−0.214718	+	9.39685i	−0.00875123	+	0.382987i
$603$	−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	$-0.727194\pi$
$607$	7.86628	−	24.2099i	0.319283	−	0.982651i	0.973956	−	0.226739i	$-0.0728063\pi$
$608$	−30.5406	+	15.3168i	−1.23858	+	0.621178i
$609$	9.91513	−	31.5698i	0.401781	−	1.27927i
$610$	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
$616$	24.6568	+	2.83564i	0.993452	+	0.114251i
$617$	−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	−0.125919	−	0.992041i	$-0.540188\pi$
$619$	19.3728	−	14.0751i	0.778657	−	0.565727i	0.904576	+	0.426313i	$0.140188\pi$
$620$	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
$623$	−21.9683	−	6.89957i	−0.880140	−	0.276426i
$624$	−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
$630$	−0.128368	+	5.61789i	−0.00511432	+	0.223822i
$631$	−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	0.960588	−	0.277978i	$-0.0896641\pi$
$643$	0.508791	+	1.56590i	0.0200647	+	0.0617529i	−0.940523	+	0.339731i	$0.889664\pi$
$644$	−5.26879	−	19.9162i	−0.207619	−	0.784810i
$645$	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	0.821291	−	0.570510i	$-0.193254\pi$
$647$	29.2616	+	9.50766i	1.15039	+	0.373785i	0.329101	+	0.944295i	$0.393254\pi$
$648$	−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
$651$	−0.261744	−	26.5862i	−0.0102586	−	1.04199i
$652$	−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
$658$	−17.5172	+	12.1254i	−0.682891	+	0.472698i
$659$	−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	$-0.438151\pi$
$661$	9.92841			0.386170			0.193085	+	0.981182i	$0.438151\pi$
$662$	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
$665$	−30.6589	−	41.3364i	−1.18890	−	1.60296i
$666$	−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
$672$	23.5168	−	3.80841i	0.907181	−	0.146913i
$673$	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	−0.429986	−	0.902836i	$-0.641481\pi$
$677$	−6.43137	+	2.08968i	−0.247178	+	0.0803129i	0.182808	+	0.983149i	$0.441481\pi$
$678$	0.892860	−	27.3026i	0.0342901	−	1.04855i
$679$	−3.64488	+	5.12203i	−0.139878	+	0.196566i
$680$	−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
$686$	−15.4618	+	21.1408i	−0.590336	+	0.807158i
$687$	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	$0.367134\pi$
$691$	−12.0892	+	37.2068i	−0.459895	+	1.41541i	−0.865290	+	0.501271i	$0.832866\pi$
$692$	3.16378	+	1.26197i	0.120269	+	0.0479729i
$693$	3.91188	−	1.20036i	0.148600	−	0.0455981i
$694$	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
$700$	−22.0363	−	17.9609i	−0.832895	−	0.678857i
$701$	−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
$707$	−19.7383	+	27.7376i	−0.742333	+	1.04318i
$708$	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
$714$	15.1193	−	19.8405i	0.565825	−	0.742511i
$715$	−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	−0.360383	−	0.932804i	$-0.617354\pi$
$719$	17.1110	−	23.5512i	0.638131	−	0.878312i	0.998514	+	0.0544925i	$0.0173541\pi$
$720$	−2.58549	+	5.42249i	−0.0963554	+	0.202084i
$721$	23.7947	+	32.0817i	0.886162	+	1.19478i
$722$	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	$-0.935089\pi$
$727$		−	10.9207i		−	0.405028i	0.979279	−	0.202514i	$-0.0649111\pi$
$728$	−7.11153	−	30.9390i	−0.263571	−	1.14668i
$729$	−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	$-0.593009\pi$
$733$	19.2686	−	26.5210i	0.711704	−	0.979576i	0.999759	−	0.0219624i	$-0.00699141\pi$
$734$	−4.18607	+	11.5809i	−0.154511	+	0.427459i
$735$	11.7590	+	33.9040i	0.433736	+	1.25057i
$736$	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
$742$	−16.2041	+	46.2485i	−0.594872	+	1.69784i
$743$	−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
$756$	24.5362	−	15.8234i	0.892374	−	0.575492i
$757$	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	$-0.590268\pi$
$761$	14.0930	−	43.3739i	0.510872	−	1.57230i	0.790670	−	0.612242i	$-0.209732\pi$
$762$	6.14536	−	17.0013i	0.222623	−	0.615894i
$763$	−3.90705	+	12.4401i	−0.141445	+	0.450361i
$764$	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	$-0.612635\pi$
$769$	−19.2183			−0.693030			−0.346515	+	0.938044i	$0.612635\pi$
$770$	−14.2020	+	37.3587i	−0.511803	+	1.34631i
$771$		−	24.5691i		−	0.884834i
$772$	0.0599799	−	0.0721280i	0.00215872	−	0.00259594i
$773$	27.2835	−	19.8226i	0.981318	−	0.712969i	0.0233150	−	0.999728i	$-0.492578\pi$
$773$	27.2835	−	19.8226i	0.981318	−	0.712969i	0.958003	+	0.286759i	$0.0925779\pi$
$774$	−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
$777$	−28.4928	−	8.94872i	−1.02217	−	0.321033i
$778$	−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
$784$	−24.3372	+	13.8456i	−0.869185	+	0.494487i
$785$	−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	0.0422516	−	0.999107i	$-0.486547\pi$
$787$	18.6190	−	6.04967i	0.663694	−	0.215647i	0.621443	+	0.783460i	$0.286547\pi$
$788$	−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	$-0.948339\pi$
$797$	−8.00217	−	24.6281i	−0.283451	−	0.872374i	0.703407	−	0.710787i	$-0.251661\pi$
$798$	−11.8945	+	33.9484i	−0.421062	+	1.20176i
$799$	−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
$805$	33.1732	−	0.326594i	1.16920	−	0.0115109i
$806$	−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	$-0.943878\pi$
$811$	−24.1234	−	33.2030i	−0.847086	−	1.16591i	0.137411	−	0.990514i	$-0.456122\pi$
$812$	−15.0231	+	38.7680i	−0.527208	+	1.36049i
$813$	−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
$819$	−3.11792	−	4.20379i	−0.108949	−	0.146892i
$820$	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
$826$	−4.32680	+	5.67789i	−0.150549	+	0.197559i
$827$	−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	0.131809	−	0.991275i	$-0.457921\pi$
$829$	−22.1764	−	16.1121i	−0.770218	−	0.559596i	−0.902027	+	0.431679i	$0.857921\pi$
$830$	−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
$833$	−8.50906	+	28.0561i	−0.294821	+	0.972087i
$834$	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	0.969146	−	0.246489i	$-0.0792769\pi$
$839$	12.6069	+	17.3519i	0.435238	+	0.599054i	−0.533907	+	0.845543i	$0.679277\pi$
$840$	−3.38028	+	38.2138i	−0.116631	+	1.31850i
$841$	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
$847$	29.0767	+	1.24242i	0.999088	+	0.0426900i
$848$	−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	−0.348052	−	0.937475i	$-0.613157\pi$
$853$	−2.29556	+	0.745871i	−0.0785984	+	0.0255382i	0.269454	+	0.963013i	$0.413157\pi$
$854$	4.58736	+	15.2992i	0.156976	+	0.523527i
$855$	−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	$-0.620026\pi$
$857$	−21.5578			−0.736401			−0.368201	+	0.929746i	$0.620026\pi$
$858$	−1.86647	+	31.6173i	−0.0637201	+	1.07940i
$859$	−21.3871			−0.729719			−0.364860	−	0.931063i	$-0.618883\pi$
$859$	−21.3871			−0.729719			−0.364860	+	0.931063i	$0.618883\pi$
$860$	−12.4413	−	10.3459i	−0.424245	−	0.352792i
$861$	−11.7345	−	8.35034i	−0.399910	−	0.284579i
$862$	−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
$868$	−1.85433	+	33.3550i	−0.0629402	+	1.13214i
$869$	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
$875$	2.54955	−	1.89099i	0.0861906	−	0.0639270i
$876$	−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	$0.238953\pi$
$881$			40.4945i			1.36429i	−0.731215	+	0.682147i	$0.761047\pi$
$882$	−2.76171	+	3.69907i	−0.0929917	+	0.124554i
$883$	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	0.718558	−	0.695467i	$-0.244803\pi$
$887$	8.31457	+	6.04089i	0.279176	+	0.202833i	−0.439382	+	0.898300i	$0.644803\pi$
$888$	−23.8679	−	21.2051i	−0.800953	−	0.711598i
$889$	0.209173	+	21.2464i	0.00701544	+	0.712581i
$890$	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
$896$	−29.7978	+	2.84441i	−0.995475	+	0.0950252i
$897$	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
$910$	51.1076	+	1.16781i	1.69420	+	0.0387124i
$911$	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
$917$	−45.4552	−	14.2761i	−1.50106	−	0.471439i
$918$	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
$924$	27.1845	−	6.43246i	0.894305	−	0.211612i
$925$			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	−0.114587	−	0.993413i	$-0.536554\pi$
$929$	11.4793	−	3.72985i	0.376624	−	0.122372i	0.491211	+	0.871041i	$0.336554\pi$
$930$	36.1300	+	28.0991i	1.18475	+	0.921407i
$931$	−0.832393	−	42.2704i	−0.0272806	−	1.38536i
$932$	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	$-0.771052\pi$
$937$	7.45594	−	22.9470i	0.243575	−	0.749646i	0.995868	−	0.0908172i	$-0.0289479\pi$
$938$	23.4524	+	0.535886i	0.765748	+	0.0174973i
$939$	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	0.0999726	−	0.994990i	$-0.468124\pi$
$941$	23.4882	−	7.63177i	0.765693	−	0.248789i	0.665720	+	0.746202i	$0.268124\pi$
$942$	−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
$952$	−20.5852	+	23.6346i	−0.667169	+	0.766002i
$953$	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
$959$	−36.4922	+	0.359269i	−1.17839	+	0.0116014i
$960$	−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
$966$	−13.1973	−	19.0657i	−0.424616	−	0.613429i
$967$			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	−0.619112	−	0.785302i	$-0.712507\pi$
$971$	−1.98064	+	1.43902i	−0.0635617	+	0.0461803i	0.555551	+	0.831483i	$0.312507\pi$
$972$	8.11811	−	5.12292i	0.260389	−	0.164318i
$973$	−0.989161	−	1.33365i	−0.0317111	−	0.0427550i
$974$	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
$980$	−11.9600	−	43.4738i	−0.382049	−	1.38872i
$981$	−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	−0.966322	−	0.257335i	$-0.917156\pi$
$983$	−13.2614	+	18.2527i	−0.422972	+	0.582172i	0.543350	+	0.839506i	$0.317156\pi$
$984$	−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
$987$	−13.9028	+	19.5372i	−0.442532	+	0.621877i
$988$	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
$994$	−25.1237	+	7.53317i	−0.796874	+	0.238938i
$995$	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	$0.475471\pi$
$997$	−28.2612	+	38.8982i	−0.895041	+	1.23192i	−0.972023	+	0.234885i	$0.924529\pi$
$998$	−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.13.9	✓	352
7.6	odd	2	inner	616.2.bi.c.13.10	yes	352
8.5	even	2	inner	616.2.bi.c.13.26	yes	352
11.6	odd	10	inner	616.2.bi.c.237.25	yes	352
56.13	odd	2	inner	616.2.bi.c.13.25	yes	352
77.6	even	10	inner	616.2.bi.c.237.26	yes	352
88.61	odd	10	inner	616.2.bi.c.237.10	yes	352
616.237	even	10	inner	616.2.bi.c.237.9	yes	352

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

\(f(q)\)	\(=\)	\(q+(-1.35856 + 0.392821i) q^{2} +(-1.28776 + 0.935610i) q^{3} +(1.69138 - 1.06734i) q^{4} +(0.995233 + 3.06301i) q^{5} +(1.38197 - 1.77694i) q^{6} +(-0.792771 + 2.52419i) q^{7} +(-1.87857 + 2.11447i) q^{8} +(-0.144099 + 0.443493i) q^{9} +O(q^{10})\)	\(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} +(-0.792771 + 2.52419i) 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} +(0.0854743 - 3.74068i) 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} +(1.35330 + 5.11552i) 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} +(-8.52060 + 0.0838862i) 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} +(3.38975 + 4.89706i) 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} +(-5.74303 - 4.00220i) 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} +(-3.84803 - 6.41815i) 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} +(-1.00522 - 0.715322i) 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} +(11.5428 - 3.46104i) 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} +(-5.04047 - 7.18287i) 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} +(-6.52885 - 5.32139i) 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} +(-6.50750 + 9.14479i) 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} +(9.37441 + 3.18126i) 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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