LMFDB - Embedded newform 560.2.cq.a.171.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(131,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cq (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			171.5
Character	$\chi$	$=$	560.171
Dual form			560.2.cq.a.131.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39869 + 0.208965i) q^{2} +(0.308027 + 1.14957i) q^{3} +(1.91267 - 0.584555i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.671056 - 1.54353i) q^{6} +(-2.40355 - 1.10587i) q^{7} +(-2.55308 + 1.21729i) q^{8} +(1.37144 - 0.791800i) q^{9} +(-1.40511 - 0.160163i) q^{10} +(-1.19377 - 4.45522i) q^{11} +(1.26114 + 2.01869i) q^{12} +(-3.04658 - 3.04658i) q^{13} +(3.59291 + 1.04451i) q^{14} +1.19013i q^{15} +(3.31659 - 2.23612i) q^{16} +(-1.57510 - 0.909386i) q^{17} +(-1.75276 + 1.39406i) q^{18} +(-4.17703 - 1.11923i) q^{19} +(1.99879 - 0.0696019i) q^{20} +(0.530919 - 3.10370i) q^{21} +(2.60070 + 5.98202i) q^{22} +(-3.32310 - 5.75579i) q^{23} +(-2.18578 - 2.55999i) q^{24} +(0.866025 + 0.500000i) q^{25} +(4.89785 + 3.62459i) q^{26} +(3.85731 + 3.85731i) q^{27} +(-5.24363 - 0.710153i) q^{28} +(3.52167 - 3.52167i) q^{29} +(-0.248695 - 1.66462i) q^{30} +(-3.34114 + 5.78702i) q^{31} +(-4.17161 + 3.82069i) q^{32} +(4.75389 - 2.74466i) q^{33} +(2.39311 + 0.942807i) q^{34} +(-2.03543 - 1.69027i) q^{35} +(2.16025 - 2.31613i) q^{36} +(-2.41439 + 9.01063i) q^{37} +(6.07625 + 0.692604i) q^{38} +(2.56384 - 4.44070i) q^{39} +(-2.78114 + 0.515028i) q^{40} -0.385064 q^{41} +(-0.0940273 + 4.45205i) q^{42} +(2.99684 - 2.99684i) q^{43} +(-4.88761 - 7.82353i) q^{44} +(1.52964 - 0.409866i) q^{45} +(5.85075 + 7.35615i) q^{46} +(-4.73982 - 8.20960i) q^{47} +(3.59218 + 3.12388i) q^{48} +(4.55411 + 5.31602i) q^{49} +(-1.31578 - 0.518376i) q^{50} +(0.560231 - 2.09081i) q^{51} +(-7.60799 - 4.04620i) q^{52} +(4.29888 - 1.15188i) q^{53} +(-6.20123 - 4.58914i) q^{54} -4.61239i q^{55} +(7.48261 - 0.102452i) q^{56} -5.14656i q^{57} +(-4.18982 + 5.66164i) q^{58} +(1.66731 - 0.446753i) q^{59} +(0.695694 + 2.27632i) q^{60} +(1.95271 - 7.28761i) q^{61} +(3.46393 - 8.79243i) q^{62} +(-4.17194 + 0.386500i) q^{63} +(5.03640 - 6.21568i) q^{64} +(-2.15426 - 3.73128i) q^{65} +(-6.07568 + 4.83233i) q^{66} +(15.6103 - 4.18277i) q^{67} +(-3.54423 - 0.818619i) q^{68} +(5.59309 - 5.59309i) q^{69} +(3.20014 + 1.93883i) q^{70} -4.16577 q^{71} +(-2.53753 + 3.69096i) q^{72} +(2.50010 - 4.33030i) q^{73} +(1.49408 - 13.1076i) q^{74} +(-0.308027 + 1.14957i) q^{75} +(-8.64352 + 0.300985i) q^{76} +(-2.05760 + 12.0285i) q^{77} +(-2.65806 + 6.74691i) q^{78} +(0.961534 - 0.555142i) q^{79} +(3.78233 - 1.30153i) q^{80} +(-0.870708 + 1.50811i) q^{81} +(0.538585 - 0.0804649i) q^{82} +(-0.433450 + 0.433450i) q^{83} +(-0.798809 - 6.24669i) q^{84} +(-1.28607 - 1.28607i) q^{85} +(-3.56541 + 4.81788i) q^{86} +(5.13320 + 2.96365i) q^{87} +(8.47110 + 9.92135i) q^{88} +(-5.26207 - 9.11416i) q^{89} +(-2.05384 + 0.892916i) q^{90} +(3.95349 + 10.6917i) q^{91} +(-9.72056 - 9.06637i) q^{92} +(-7.68177 - 2.05832i) q^{93} +(8.34505 + 10.4922i) q^{94} +(-3.74502 - 2.16219i) q^{95} +(-5.67713 - 3.61870i) q^{96} +11.7703i q^{97} +(-7.48065 - 6.48382i) q^{98} +(-5.16483 - 5.16483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39869	+	0.208965i	−0.989023	+	0.147761i
$2$	−1.39869	+	0.208965i	−0.989023	+	0.147761i
$3$	0.308027	+	1.14957i	0.177840	+	0.663707i	0.996051	+	0.0887884i	$0.0282995\pi$
$3$	0.308027	+	1.14957i	0.177840	+	0.663707i	−0.818211	+	0.574918i	$0.805034\pi$
$4$	1.91267	−	0.584555i	0.956334	−	0.292277i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−0.671056	−	1.54353i	−0.273957	−	0.630144i
$7$	−2.40355	−	1.10587i	−0.908457	−	0.417979i
$7$	−2.40355	−	1.10587i	−0.908457	−	0.417979i
$8$	−2.55308	+	1.21729i	−0.902649	+	0.430378i
$9$	1.37144	−	0.791800i	0.457146	−	0.263933i
$10$	−1.40511	−	0.160163i	−0.444336	−	0.0506479i
$11$	−1.19377	−	4.45522i	−0.359936	−	1.34330i	−0.874158	−	0.485643i	$-0.838586\pi$
$11$	−1.19377	−	4.45522i	−0.359936	−	1.34330i	0.514221	−	0.857658i	$-0.328081\pi$
$12$	1.26114	+	2.01869i	0.364061	+	0.582747i
$13$	−3.04658	−	3.04658i	−0.844969	−	0.844969i	0.144531	−	0.989500i	$-0.453833\pi$
$13$	−3.04658	−	3.04658i	−0.844969	−	0.844969i	−0.989500	+	0.144531i	$0.953833\pi$
$14$	3.59291	+	1.04451i	0.960245	+	0.279157i
$15$			1.19013i			0.307289i
$16$	3.31659	−	2.23612i	0.829148	−	0.559029i
$17$	−1.57510	−	0.909386i	−0.382018	−	0.220558i	0.296678	−	0.954978i	$-0.404121\pi$
$17$	−1.57510	−	0.909386i	−0.382018	−	0.220558i	−0.678696	+	0.734419i	$0.737455\pi$
$18$	−1.75276	+	1.39406i	−0.413129	+	0.328584i
$19$	−4.17703	−	1.11923i	−0.958276	−	0.256769i	−0.254405	−	0.967098i	$-0.581880\pi$
$19$	−4.17703	−	1.11923i	−0.958276	−	0.256769i	−0.703870	+	0.710328i	$0.748546\pi$
$20$	1.99879	−	0.0696019i	0.446943	−	0.0155634i
$21$	0.530919	−	3.10370i	0.115856	−	0.677282i
$22$	2.60070	+	5.98202i	0.554472	+	1.27537i
$23$	−3.32310	−	5.75579i	−0.692915	−	1.20016i	−0.970878	−	0.239573i	$-0.922993\pi$
$23$	−3.32310	−	5.75579i	−0.692915	−	1.20016i	0.277963	−	0.960592i	$-0.410341\pi$
$24$	−2.18578	−	2.55999i	−0.446171	−	0.522556i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	4.89785	+	3.62459i	0.960547	+	0.710841i
$27$	3.85731	+	3.85731i	0.742340	+	0.742340i
$28$	−5.24363	−	0.710153i	−0.990953	−	0.134206i
$29$	3.52167	−	3.52167i	0.653958	−	0.653958i	−0.299985	−	0.953944i	$-0.596982\pi$
$29$	3.52167	−	3.52167i	0.653958	−	0.653958i	0.953944	+	0.299985i	$0.0969818\pi$
$30$	−0.248695	−	1.66462i	−0.0454053	−	0.303916i
$31$	−3.34114	+	5.78702i	−0.600086	+	1.03938i	0.392721	+	0.919658i	$0.371534\pi$
$31$	−3.34114	+	5.78702i	−0.600086	+	1.03938i	−0.992807	+	0.119722i	$0.961800\pi$
$32$	−4.17161	+	3.82069i	−0.737444	+	0.675408i
$33$	4.75389	−	2.74466i	0.827546	−	0.477784i
$34$	2.39311	+	0.942807i	0.410415	+	0.161690i
$35$	−2.03543	−	1.69027i	−0.344051	−	0.285708i
$36$	2.16025	−	2.31613i	0.360042	−	0.386022i
$37$	−2.41439	+	9.01063i	−0.396924	+	1.48134i	0.421556	+	0.906803i	$0.361484\pi$
$37$	−2.41439	+	9.01063i	−0.396924	+	1.48134i	−0.818479	+	0.574536i	$0.805182\pi$
$38$	6.07625	+	0.692604i	0.985697	+	0.112355i
$39$	2.56384	−	4.44070i	0.410543	−	0.711081i
$40$	−2.78114	+	0.515028i	−0.439737	+	0.0814332i
$41$	−0.385064			−0.0601369			−0.0300684	−	0.999548i	$-0.509573\pi$
$41$	−0.385064			−0.0601369			−0.0300684	+	0.999548i	$0.509573\pi$
$42$	−0.0940273	+	4.45205i	−0.0145087	+	0.686967i
$43$	2.99684	−	2.99684i	0.457014	−	0.457014i	−0.440660	−	0.897674i	$-0.645256\pi$
$43$	2.99684	−	2.99684i	0.457014	−	0.457014i	0.897674	+	0.440660i	$0.145256\pi$
$44$	−4.88761	−	7.82353i	−0.736835	−	1.17944i
$45$	1.52964	−	0.409866i	0.228025	−	0.0610992i
$46$	5.85075	+	7.35615i	0.862646	+	1.08460i
$47$	−4.73982	−	8.20960i	−0.691373	−	1.19749i	−0.971388	−	0.237498i	$-0.923673\pi$
$47$	−4.73982	−	8.20960i	−0.691373	−	1.19749i	0.280015	−	0.959996i	$-0.409661\pi$
$48$	3.59218	+	3.12388i	0.518487	+	0.450893i
$49$	4.55411	+	5.31602i	0.650587	+	0.759432i
$50$	−1.31578	−	0.518376i	−0.186080	−	0.0733094i
$51$	0.560231	−	2.09081i	0.0784481	−	0.292772i
$52$	−7.60799	−	4.04620i	−1.05504	−	0.561107i
$53$	4.29888	−	1.15188i	0.590497	−	0.158223i	0.0488167	−	0.998808i	$-0.484455\pi$
$53$	4.29888	−	1.15188i	0.590497	−	0.158223i	0.541680	+	0.840585i	$0.317788\pi$
$54$	−6.20123	−	4.58914i	−0.843880	−	0.624503i
$55$		−	4.61239i		−	0.621934i
$56$	7.48261	−	0.102452i	0.999906	−	0.0136907i
$57$		−	5.14656i		−	0.681678i
$58$	−4.18982	+	5.66164i	−0.550151	+	0.743409i
$59$	1.66731	−	0.446753i	0.217065	−	0.0581623i	−0.148648	−	0.988890i	$-0.547492\pi$
$59$	1.66731	−	0.446753i	0.217065	−	0.0581623i	0.365712	+	0.930728i	$0.380825\pi$
$60$	0.695694	+	2.27632i	0.0898137	+	0.293871i
$61$	1.95271	−	7.28761i	0.250019	−	0.933083i	−0.720775	−	0.693169i	$-0.756214\pi$
$61$	1.95271	−	7.28761i	0.250019	−	0.933083i	0.970794	−	0.239914i	$-0.0771194\pi$
$62$	3.46393	−	8.79243i	0.439920	−	1.11664i
$63$	−4.17194	+	0.386500i	−0.525616	+	0.0486944i
$64$	5.03640	−	6.21568i	0.629550	−	0.776960i
$65$	−2.15426	−	3.73128i	−0.267203	−	0.462809i
$66$	−6.07568	+	4.83233i	−0.747865	+	0.594818i
$67$	15.6103	−	4.18277i	1.90710	−	0.511007i	0.912257	−	0.409618i	$-0.134338\pi$
$67$	15.6103	−	4.18277i	1.90710	−	0.511007i	0.994847	−	0.101388i	$-0.0323285\pi$
$68$	−3.54423	−	0.818619i	−0.429801	−	0.0992721i
$69$	5.59309	−	5.59309i	0.673329	−	0.673329i
$70$	3.20014	+	1.93883i	0.382490	+	0.231735i
$71$	−4.16577			−0.494386			−0.247193	−	0.968966i	$-0.579508\pi$
$71$	−4.16577			−0.494386			−0.247193	+	0.968966i	$0.579508\pi$
$72$	−2.53753	+	3.69096i	−0.299051	+	0.434984i
$73$	2.50010	−	4.33030i	0.292615	−	0.506824i	−0.681812	−	0.731527i	$-0.738808\pi$
$73$	2.50010	−	4.33030i	0.292615	−	0.506824i	0.974427	+	0.224703i	$0.0721413\pi$
$74$	1.49408	−	13.1076i	0.173683	−	1.52373i
$75$	−0.308027	+	1.14957i	−0.0355679	+	0.132741i
$76$	−8.64352	+	0.300985i	−0.991479	+	0.0345253i
$77$	−2.05760	+	12.0285i	−0.234485	+	1.37078i
$78$	−2.65806	+	6.74691i	−0.300966	+	0.763937i
$79$	0.961534	−	0.555142i	0.108181	−	0.0624584i	−0.444933	−	0.895564i	$-0.646773\pi$
$79$	0.961534	−	0.555142i	0.108181	−	0.0624584i	0.553114	+	0.833105i	$0.313439\pi$
$80$	3.78233	−	1.30153i	0.422877	−	0.145515i
$81$	−0.870708	+	1.50811i	−0.0967453	+	0.167568i
$82$	0.538585	−	0.0804649i	0.0594768	−	0.00888586i
$83$	−0.433450	+	0.433450i	−0.0475773	+	0.0475773i	−0.730495	−	0.682918i	$-0.760711\pi$
$83$	−0.433450	+	0.433450i	−0.0475773	+	0.0475773i	0.682918	+	0.730495i	$0.260711\pi$
$84$	−0.798809	−	6.24669i	−0.0871572	−	0.681570i
$85$	−1.28607	−	1.28607i	−0.139493	−	0.139493i
$86$	−3.56541	+	4.81788i	−0.384468	+	0.519526i
$87$	5.13320	+	2.96365i	0.550336	+	0.317737i
$88$	8.47110	+	9.92135i	0.903022	+	1.05762i
$89$	−5.26207	−	9.11416i	−0.557778	−	0.966099i	−0.997682	−	0.0680546i	$-0.978321\pi$
$89$	−5.26207	−	9.11416i	−0.557778	−	0.966099i	0.439904	−	0.898045i	$-0.355013\pi$
$90$	−2.05384	+	0.892916i	−0.216494	+	0.0941216i
$91$	3.95349	+	10.6917i	0.414438	+	1.12080i
$92$	−9.72056	−	9.06637i	−1.01344	−	0.945234i
$93$	−7.68177	−	2.05832i	−0.796563	−	0.213438i
$94$	8.34505	+	10.4922i	0.860726	+	1.08219i
$95$	−3.74502	−	2.16219i	−0.384231	−	0.221836i
$96$	−5.67713	−	3.61870i	−0.579420	−	0.369332i
$97$			11.7703i			1.19509i	0.801834	+	0.597547i	$0.203858\pi$
$97$			11.7703i			1.19509i	−0.801834	+	0.597547i	$0.796142\pi$
$98$	−7.48065	−	6.48382i	−0.755659	−	0.654965i
$99$	−5.16483	−	5.16483i	−0.519085	−	0.519085i
$100$	1.94870	+	0.450094i	0.194870	+	0.0450094i
$101$	3.30637	+	12.3396i	0.328997	+	1.22783i	0.910233	+	0.414097i	$0.135903\pi$
$101$	3.30637	+	12.3396i	0.328997	+	1.22783i	−0.581236	+	0.813735i	$0.697431\pi$
$102$	−0.346683	+	3.04147i	−0.0343268	+	0.301150i
$103$	−12.1526	+	7.01633i	−1.19743	+	0.691339i	−0.959982	−	0.280060i	$-0.909646\pi$
$103$	−12.1526	+	7.01633i	−1.19743	+	0.691339i	−0.237452	+	0.971399i	$0.576312\pi$
$104$	11.4867	+	4.06958i	1.12637	+	0.399055i
$105$	1.31612	−	2.86053i	0.128441	−	0.279159i
$106$	−5.77210	+	2.50944i	−0.560636	+	0.243739i
$107$	−7.30124	−	1.95636i	−0.705837	−	0.189129i	−0.111994	−	0.993709i	$-0.535724\pi$
$107$	−7.30124	−	1.95636i	−0.705837	−	0.189129i	−0.593844	+	0.804580i	$0.702390\pi$
$108$	9.63256	+	5.12294i	0.926894	+	0.492955i
$109$	−0.0899952	−	0.335867i	−0.00861998	−	0.0321702i	0.961482	−	0.274868i	$-0.0886342\pi$
$109$	−0.0899952	−	0.335867i	−0.00861998	−	0.0321702i	−0.970102	+	0.242698i	$0.921968\pi$
$110$	0.963828	+	6.45130i	0.0918974	+	0.615107i
$111$	−11.1021			−1.05376
$112$	−10.4444	+	1.70690i	−0.986908	+	0.161287i
$113$	14.8306			1.39515			0.697573	−	0.716514i	$-0.254263\pi$
$113$	14.8306			1.39515			0.697573	+	0.716514i	$0.254263\pi$
$114$	1.07545	+	7.19844i	0.100725	+	0.674195i
$115$	−1.72017	−	6.41974i	−0.160406	−	0.598644i
$116$	4.67718	−	8.79440i	0.434265	−	0.816540i
$117$	−6.59047	−	1.76591i	−0.609289	−	0.163259i
$118$	−2.23869	+	0.973278i	−0.206088	+	0.0895975i
$119$	2.78017	+	3.92761i	0.254858	+	0.360043i
$120$	−1.44873	−	3.03848i	−0.132250	−	0.277374i
$121$	−8.89763	+	5.13705i	−0.808876	+	0.467005i
$122$	−1.20838	+	10.6012i	−0.109402	+	0.959784i
$123$	−0.118610	−	0.442659i	−0.0106947	−	0.0399133i
$124$	−3.00766	+	13.0217i	−0.270095	+	1.16939i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	5.75449	−	1.41238i	0.512651	−	0.125825i
$127$			14.1753i			1.25786i	0.777463	+	0.628929i	$0.216506\pi$
$127$			14.1753i			1.25786i	−0.777463	+	0.628929i	$0.783494\pi$
$128$	−5.74551	+	9.74624i	−0.507836	+	0.861454i
$129$	4.36820	+	2.52198i	0.384598	+	0.222048i
$130$	3.79285	+	4.76874i	0.332655	+	0.418246i
$131$	−1.86089	−	0.498624i	−0.162587	−	0.0435650i	0.176607	−	0.984281i	$-0.443488\pi$
$131$	−1.86089	−	0.498624i	−0.162587	−	0.0435650i	−0.339194	+	0.940716i	$0.610154\pi$
$132$	7.48821	−	8.02853i	0.651765	−	0.698794i
$133$	8.80197	+	7.30938i	0.763228	+	0.633803i
$134$	−20.9599	+	9.11241i	−1.81066	+	0.787193i
$135$	2.72753	+	4.72422i	0.234749	+	0.406596i
$136$	5.12834	+	0.404373i	0.439752	+	0.0346747i
$137$	3.57730	+	2.06536i	0.305630	+	0.176455i	0.644969	−	0.764209i	$-0.276870\pi$
$137$	3.57730	+	2.06536i	0.305630	+	0.176455i	−0.339339	+	0.940664i	$0.610204\pi$
$138$	−6.65424	+	8.99176i	−0.566447	+	0.765430i
$139$	8.42160	+	8.42160i	0.714311	+	0.714311i	0.967434	−	0.253123i	$-0.0814579\pi$
$139$	8.42160	+	8.42160i	0.714311	+	0.714311i	−0.253123	+	0.967434i	$0.581458\pi$
$140$	−4.88116	−	2.04311i	−0.412533	−	0.172674i
$141$	7.97755	−	7.97755i	0.671831	−	0.671831i
$142$	5.82662	−	0.870501i	0.488959	−	0.0730508i
$143$	−9.93626	+	17.2101i	−0.830912	+	1.43918i
$144$	2.77794	−	5.69277i	0.231495	−	0.474398i
$145$	4.31315	−	2.49020i	0.358188	−	0.206800i
$146$	−2.59199	+	6.57919i	−0.214514	+	0.544497i
$147$	−4.70837	+	6.87276i	−0.388340	+	0.566856i
$148$	0.649281	+	18.6457i	0.0533705	+	1.53267i
$149$	5.86028	−	21.8709i	0.480093	−	1.79173i	−0.121114	−	0.992639i	$-0.538647\pi$
$149$	5.86028	−	21.8709i	0.480093	−	1.79173i	0.601207	−	0.799093i	$-0.294687\pi$
$150$	0.190614	−	1.67226i	0.0155636	−	0.136540i
$151$	−8.73800	+	15.1347i	−0.711088	+	1.23164i	0.253361	+	0.967372i	$0.418464\pi$
$151$	−8.73800	+	15.1347i	−0.711088	+	1.23164i	−0.964449	+	0.264269i	$0.914869\pi$
$152$	12.0267	−	2.22718i	0.975494	−	0.180648i
$153$	−2.88020			−0.232851
$154$	0.364407	−	17.2541i	0.0293647	−	1.39038i
$155$	−4.72508	+	4.72508i	−0.379528	+	0.379528i
$156$	2.30794	−	9.99228i	0.184783	−	0.800023i
$157$	2.24116	−	0.600517i	0.178864	−	0.0479265i	−0.168275	−	0.985740i	$-0.553820\pi$
$157$	2.24116	−	0.600517i	0.178864	−	0.0479265i	0.347139	+	0.937814i	$0.387153\pi$
$158$	−1.22888	+	0.977399i	−0.0977647	+	0.0777577i
$159$	2.64835	+	4.58707i	0.210028	+	0.363779i
$160$	−5.01833	+	2.61081i	−0.396734	+	0.206402i
$161$	1.62210	+	17.5092i	0.127839	+	1.37992i
$162$	0.902708	−	2.29133i	0.0709234	−	0.180024i
$163$	2.44829	−	9.13716i	0.191765	−	0.715677i	−0.801315	−	0.598242i	$-0.795866\pi$
$163$	2.44829	−	9.13716i	0.191765	−	0.715677i	0.993081	−	0.117435i	$-0.0374672\pi$
$164$	−0.736499	+	0.225091i	−0.0575109	+	0.0175767i
$165$	5.30228	−	1.42074i	0.412782	−	0.110605i
$166$	0.515686	−	0.696838i	0.0400250	−	0.0540851i
$167$		−	8.47531i		−	0.655840i	−0.944706	−	0.327920i	$-0.893652\pi$
$167$		−	8.47531i		−	0.655840i	0.944706	−	0.327920i	$-0.106348\pi$
$168$	2.42263	+	8.57026i	0.186910	+	0.661210i
$169$			5.56330i			0.427946i
$170$	2.06755	+	1.53006i	0.158574	+	0.117351i
$171$	−6.61474	+	1.77241i	−0.505842	+	0.135540i
$172$	3.98014	−	7.48377i	0.303483	−	0.570632i
$173$	5.97768	−	22.3090i	0.454475	−	1.69612i	−0.235153	−	0.971958i	$-0.575559\pi$
$173$	5.97768	−	22.3090i	0.454475	−	1.69612i	0.689628	−	0.724164i	$-0.257774\pi$
$174$	−7.79905	−	3.07257i	−0.591244	−	0.232931i
$175$	−1.52860	−	2.15949i	−0.115551	−	0.163242i
$176$	−13.9217	−	12.1067i	−1.04938	−	0.912579i
$177$	1.02715	+	1.77908i	0.0772054	+	0.133724i
$178$	9.26454	+	11.6483i	0.694407	+	0.873077i
$179$	7.72734	−	2.07053i	0.577568	−	0.154759i	0.0418030	−	0.999126i	$-0.486690\pi$
$179$	7.72734	−	2.07053i	0.577568	−	0.154759i	0.535765	+	0.844367i	$0.320023\pi$
$180$	2.68610	−	1.67809i	0.200210	−	0.125078i
$181$	−3.39799	+	3.39799i	−0.252571	+	0.252571i	−0.822024	−	0.569453i	$-0.807155\pi$
$181$	−3.39799	+	3.39799i	−0.252571	+	0.252571i	0.569453	+	0.822024i	$0.307155\pi$
$182$	−7.76390	−	14.1283i	−0.575499	−	1.04726i
$183$	8.97914			0.663757
$184$	15.4906	+	10.6498i	1.14198	+	0.785112i
$185$	−4.66425	+	8.07871i	−0.342922	+	0.593959i
$186$	11.1745	+	1.27374i	0.819357	+	0.0933948i
$187$	−2.17120	+	8.10303i	−0.158774	+	0.592552i
$188$	−13.8647	−	12.9316i	−1.01118	−	0.943130i
$189$	−5.00556	−	13.5369i	−0.364101	−	0.984666i
$190$	5.68994	+	2.24165i	0.412792	+	0.162627i
$191$	−1.72061	+	0.993396i	−0.124499	+	0.0718796i	−0.560956	−	0.827845i	$-0.689566\pi$
$191$	−1.72061	+	0.993396i	−0.124499	+	0.0718796i	0.436457	+	0.899725i	$0.356233\pi$
$192$	8.69673	+	3.87512i	0.627632	+	0.279663i
$193$	−3.57150	+	6.18602i	−0.257082	+	0.445280i	−0.965459	−	0.260555i	$-0.916094\pi$
$193$	−3.57150	+	6.18602i	−0.257082	+	0.445280i	0.708377	+	0.705835i	$0.249428\pi$
$194$	−2.45959	−	16.4630i	−0.176588	−	1.18198i
$195$	3.62582	−	3.62582i	0.259650	−	0.259650i
$196$	11.8180	+	7.50566i	0.844143	+	0.536119i
$197$	−11.8250	−	11.8250i	−0.842496	−	0.842496i	0.146687	−	0.989183i	$-0.453139\pi$
$197$	−11.8250	−	11.8250i	−0.842496	−	0.842496i	−0.989183	+	0.146687i	$0.953139\pi$
$198$	8.30326	+	6.14472i	0.590087	+	0.436687i
$199$	−20.0353	−	11.5674i	−1.42026	−	0.819989i	−0.423942	−	0.905690i	$-0.639354\pi$
$199$	−20.0353	−	11.5674i	−1.42026	−	0.819989i	−0.996321	+	0.0857006i	$0.972687\pi$
$200$	−2.81968	−	0.222333i	−0.199381	−	0.0157213i
$201$	9.61681	+	16.6568i	0.678318	+	1.17488i
$202$	−7.20313	−	16.5683i	−0.506810	−	1.16574i
$203$	−12.3590	+	4.57001i	−0.867434	+	0.320752i
$204$	−0.150658	−	4.32651i	−0.0105482	−	0.302916i
$205$	−0.371943	−	0.0996619i	−0.0259776	−	0.00696069i
$206$	15.5316	−	12.3531i	1.08214	−	0.860684i
$207$	−9.11486	−	5.26247i	−0.633526	−	0.365767i
$208$	−16.9168	−	3.29175i	−1.17297	−	0.228242i
$209$			19.9457i			1.37967i
$210$	−1.24310	+	4.27602i	−0.0857820	+	0.295073i
$211$	−17.5061	−	17.5061i	−1.20517	−	1.20517i	−0.972574	−	0.232592i	$-0.925279\pi$
$211$	−17.5061	−	17.5061i	−1.20517	−	1.20517i	−0.232592	−	0.972574i	$-0.574721\pi$
$212$	7.54899	−	4.71610i	0.518467	−	0.323903i
$213$	−1.28317	−	4.78886i	−0.0879215	−	0.328127i
$214$	10.6210	+	1.21064i	0.726035	+	0.0827575i
$215$	3.67036	−	2.11908i	0.250317	−	0.144520i
$216$	−14.5435	−	5.15254i	−0.989559	−	0.350586i
$217$	14.4303	−	10.2145i	0.979592	−	0.693408i
$218$	0.196060	+	0.450968i	0.0132789	+	0.0305434i
$219$	5.74810	+	1.54020i	0.388421	+	0.104077i
$220$	−2.69619	−	8.82196i	−0.181777	−	0.594776i
$221$	2.02816	+	7.56919i	0.136429	+	0.509159i
$222$	15.5284	−	2.31995i	1.04220	−	0.155705i
$223$	13.8892			0.930091			0.465046	−	0.885287i	$-0.346038\pi$
$223$	13.8892			0.930091			0.465046	+	0.885287i	$0.346038\pi$
$224$	14.2519	−	4.56995i	0.952242	−	0.305343i
$225$	1.58360			0.105573
$226$	−20.7434	+	3.09908i	−1.37983	+	0.206148i
$227$	4.28020	+	15.9739i	0.284087	+	1.06023i	0.949504	+	0.313755i	$0.101587\pi$
$227$	4.28020	+	15.9739i	0.284087	+	1.06023i	−0.665417	+	0.746472i	$0.731746\pi$
$228$	−3.00844	−	9.84365i	−0.199239	−	0.651911i
$229$	−14.9288	−	4.00016i	−0.986523	−	0.264338i	−0.270734	−	0.962654i	$-0.587266\pi$
$229$	−14.9288	−	4.00016i	−0.986523	−	0.264338i	−0.715789	+	0.698316i	$0.753933\pi$
$230$	3.74748	+	8.61978i	0.247102	+	0.568371i
$231$	−14.4615	+	1.33975i	−0.951494	+	0.0881488i
$232$	−4.70420	+	13.2780i	−0.308846	+	0.871744i
$233$	−5.96831	+	3.44581i	−0.390997	+	0.225742i	−0.682592	−	0.730800i	$-0.739147\pi$
$233$	−5.96831	+	3.44581i	−0.390997	+	0.225742i	0.291595	+	0.956542i	$0.405814\pi$
$234$	9.58704	+	1.09278i	0.626725	+	0.0714376i
$235$	−2.45351	−	9.15662i	−0.160049	−	0.597312i
$236$	2.92785	−	1.82912i	0.190587	−	0.119066i
$237$	0.934356	+	0.934356i	0.0606929	+	0.0606929i
$238$	−4.70934	−	4.91255i	−0.305261	−	0.318433i
$239$			8.79422i			0.568850i	0.958698	+	0.284425i	$0.0918028\pi$
$239$			8.79422i			0.568850i	−0.958698	+	0.284425i	$0.908197\pi$
$240$	2.66126	+	3.94716i	0.171784	+	0.254788i
$241$	13.0878	+	7.55627i	0.843062	+	0.486742i	0.858304	−	0.513142i	$-0.171518\pi$
$241$	13.0878	+	7.55627i	0.843062	+	0.486742i	−0.0152416	+	0.999884i	$0.504852\pi$
$242$	11.3716	−	9.04443i	0.730992	−	0.581398i
$243$	13.8057	+	3.69922i	0.885634	+	0.237305i
$244$	−0.525125	−	15.0802i	−0.0336177	−	0.965414i
$245$	3.02304	+	6.31358i	0.193135	+	0.403360i
$246$	0.258399	+	0.594358i	0.0164749	+	0.0378949i
$247$	9.31582	+	16.1355i	0.592751	+	1.02668i
$248$	1.48569	−	18.8419i	0.0943415	−	1.19646i
$249$	−0.631797	−	0.364768i	−0.0400385	−	0.0231163i
$250$	−1.13678	−	0.841263i	−0.0718965	−	0.0532061i
$251$	17.8247	+	17.8247i	1.12508	+	1.12508i	0.990965	+	0.134118i	$0.0428202\pi$
$251$	17.8247	+	17.8247i	1.12508	+	1.12508i	0.134118	+	0.990965i	$0.457180\pi$
$252$	−7.75361	+	3.17798i	−0.488432	+	0.200194i
$253$	−21.6763	+	21.6763i	−1.36278	+	1.36278i
$254$	−2.96215	−	19.8269i	−0.185862	−	1.24405i
$255$	1.08228	−	1.87457i	0.0677752	−	0.117390i
$256$	5.99956	−	14.8326i	0.374972	−	0.927036i
$257$	−9.42158	+	5.43955i	−0.587702	+	0.339310i	−0.764188	−	0.644993i	$-0.776860\pi$
$257$	−9.42158	+	5.43955i	−0.587702	+	0.339310i	0.176486	+	0.984303i	$0.443527\pi$
$258$	−6.63676	−	2.61467i	−0.413186	−	0.162782i
$259$	15.7677	−	18.9875i	0.979757	−	1.17983i
$260$	−6.30152	−	5.87742i	−0.390803	−	0.364502i
$261$	2.04129	−	7.61821i	0.126353	−	0.471556i
$262$	2.70700	+	0.308559i	0.167239	+	0.0190629i
$263$	12.3446	−	21.3815i	0.761201	−	1.31844i	−0.181031	−	0.983477i	$-0.557943\pi$
$263$	12.3446	−	21.3815i	0.761201	−	1.31844i	0.942232	−	0.334961i	$-0.108723\pi$
$264$	−8.79600	+	12.7942i	−0.541356	+	0.787429i
$265$	4.45053			0.273394
$266$	−13.8386	−	8.38424i	−0.848501	−	0.514071i
$267$	8.85654	−	8.85654i	0.542012	−	0.542012i
$268$	27.4123	−	17.1253i	1.67447	−	1.04610i
$269$	−6.19406	+	1.65969i	−0.377659	+	0.101193i	−0.442655	−	0.896692i	$-0.645963\pi$
$269$	−6.19406	+	1.65969i	−0.377659	+	0.101193i	0.0649959	+	0.997886i	$0.479297\pi$
$270$	−4.80217	−	6.03776i	−0.292251	−	0.367447i
$271$	0.129755	+	0.224743i	0.00788207	+	0.0136521i	0.869940	−	0.493158i	$-0.164158\pi$
$271$	0.129755	+	0.224743i	0.00788207	+	0.0136521i	−0.862057	+	0.506811i	$0.830824\pi$
$272$	−7.25746	+	0.506053i	−0.440048	+	0.0306840i
$273$	−11.0731	+	7.83817i	−0.670177	+	0.474388i
$274$	−5.43513	−	2.14126i	−0.328348	−	0.129358i
$275$	1.19377	−	4.45522i	0.0719872	−	0.268660i
$276$	7.42826	−	13.9672i	0.447129	−	0.840726i
$277$	10.4974	−	2.81276i	0.630725	−	0.169002i	0.0707262	−	0.997496i	$-0.477468\pi$
$277$	10.4974	−	2.81276i	0.630725	−	0.169002i	0.559999	+	0.828494i	$0.310802\pi$
$278$	−13.5390	−	10.0194i	−0.812017	−	0.600923i
$279$			10.5821i			0.633531i
$280$	7.25417	+	1.83768i	0.433519	+	0.109823i
$281$		−	7.39157i		−	0.440944i	−0.975393	−	0.220472i	$-0.929240\pi$
$281$		−	7.39157i		−	0.440944i	0.975393	−	0.220472i	$-0.0707597\pi$
$282$	−9.49109	+	12.8251i	−0.565186	+	0.763726i
$283$	24.9589	−	6.68770i	1.48365	−	0.397543i	0.576062	−	0.817406i	$-0.304589\pi$
$283$	24.9589	−	6.68770i	1.48365	−	0.397543i	0.907588	+	0.419863i	$0.137922\pi$
$284$	−7.96773	+	2.43512i	−0.472798	+	0.144498i
$285$	1.33203	−	4.97119i	0.0789024	−	0.294468i
$286$	10.3014	−	26.1479i	0.609137	−	1.54616i
$287$	0.925520	+	0.425830i	0.0546317	+	0.0251360i
$288$	−2.69589	+	8.54291i	−0.158857	+	0.503396i
$289$	−6.84604	−	11.8577i	−0.402708	−	0.697511i
$290$	−5.51240	+	4.38431i	−0.323699	+	0.257456i
$291$	−13.5308	+	3.62558i	−0.793192	+	0.212535i
$292$	2.25056	−	9.74388i	0.131704	−	0.570217i
$293$	12.5963	−	12.5963i	0.735886	−	0.735886i	−0.235893	−	0.971779i	$-0.575802\pi$
$293$	12.5963	−	12.5963i	0.735886	−	0.735886i	0.971779	+	0.235893i	$0.0758016\pi$
$294$	5.14939	−	10.5967i	0.300318	−	0.618015i
$295$	1.72612			0.100499
$296$	−4.80444	−	25.9439i	−0.279252	−	1.50796i
$297$	12.5804	−	21.7899i	0.729990	−	1.26438i
$298$	−3.62647	+	31.8152i	−0.210076	+	1.84300i
$299$	−7.41136	+	27.6596i	−0.428610	+	1.59959i
$300$	0.0828350	+	2.37881i	0.00478248	+	0.137341i
$301$	−10.5172	+	3.88894i	−0.606199	+	0.224155i
$302$	9.05914	−	22.9946i	0.521295	−	1.32319i
$303$	−13.1668	+	7.60184i	−0.756412	+	0.436714i
$304$	−16.3562	+	5.62829i	−0.938094	+	0.322805i
$305$	3.77235	−	6.53390i	0.216004	−	0.374130i
$306$	4.02851	−	0.601862i	0.230295	−	0.0344062i
$307$	2.87922	−	2.87922i	0.164326	−	0.164326i	−0.620154	−	0.784480i	$-0.712930\pi$
$307$	2.87922	−	2.87922i	0.164326	−	0.164326i	0.784480	+	0.620154i	$0.212930\pi$
$308$	3.09582	+	24.2093i	0.176401	+	1.37945i
$309$	−11.8091	−	11.8091i	−0.671798	−	0.671798i
$310$	5.62155	−	7.59631i	0.319283	−	0.431441i
$311$	−3.51155	−	2.02739i	−0.199122	−	0.114963i	0.397124	−	0.917765i	$-0.370008\pi$
$311$	−3.51155	−	2.02739i	−0.199122	−	0.114963i	−0.596246	+	0.802802i	$0.703342\pi$
$312$	−1.14005	+	14.4584i	−0.0645427	+	0.818545i
$313$	0.0514433	+	0.0891025i	0.00290775	+	0.00503637i	0.867476	−	0.497480i	$-0.165741\pi$
$313$	0.0514433	+	0.0891025i	0.00290775	+	0.00503637i	−0.864568	+	0.502516i	$0.832408\pi$
$314$	−3.00920	+	1.30826i	−0.169819	+	0.0738294i
$315$	−4.12982	−	0.706449i	−0.232689	−	0.0398039i
$316$	1.51458	−	1.62387i	0.0852020	−	0.0913499i
$317$	−26.0415	−	6.97779i	−1.46263	−	0.391912i	−0.562236	−	0.826977i	$-0.690059\pi$
$317$	−26.0415	−	6.97779i	−1.46263	−	0.391912i	−0.900399	+	0.435065i	$0.856725\pi$
$318$	−4.66276	−	5.86248i	−0.261474	−	0.328752i
$319$	−19.8939	−	11.4858i	−1.11385	−	0.643079i
$320$	6.47353	−	4.70037i	0.361881	−	0.262758i
$321$		−	8.99592i		−	0.502104i
$322$	−5.92764	−	24.1510i	−0.330334	−	1.34588i
$323$	5.56143	+	5.56143i	0.309446	+	0.309446i
$324$	−0.783801	+	3.39349i	−0.0435445	+	0.188527i
$325$	−1.11513	−	4.16171i	−0.0618560	−	0.230850i
$326$	−1.51506	+	13.2917i	−0.0839112	+	0.736157i
$327$	0.358383	−	0.206912i	0.0198186	−	0.0114423i
$328$	0.983098	−	0.468735i	0.0542825	−	0.0258816i
$329$	2.31364	+	24.9738i	0.127555	+	1.37685i
$330$	−7.11936	+	3.09517i	−0.391908	+	0.170383i
$331$	8.20812	+	2.19936i	0.451159	+	0.120888i	0.477242	−	0.878772i	$-0.341637\pi$
$331$	8.20812	+	2.19936i	0.451159	+	0.120888i	−0.0260827	+	0.999660i	$0.508303\pi$
$332$	−0.575671	+	1.08242i	−0.0315940	+	0.0594056i
$333$	3.82343	+	14.2692i	0.209523	+	0.781949i
$334$	1.77105	+	11.8543i	0.0969073	+	0.648641i
$335$	16.1610			0.882969
$336$	−5.17939	−	11.4809i	−0.282559	−	0.626334i
$337$	−26.3332			−1.43446			−0.717231	−	0.696835i	$-0.754591\pi$
$337$	−26.3332			−1.43446			−0.717231	+	0.696835i	$0.754591\pi$
$338$	−1.16254	−	7.78133i	−0.0632336	−	0.423248i
$339$	4.56823	+	17.0489i	0.248112	+	0.925968i
$340$	−3.21159	−	1.70804i	−0.174173	−	0.0926314i
$341$	29.7710	+	7.97712i	1.61219	+	0.431986i
$342$	8.88159	−	3.86131i	0.480262	−	0.208796i
$343$	−5.06719	−	17.8136i	−0.273603	−	0.961843i
$344$	−4.00313	+	11.2992i	−0.215834	+	0.609211i
$345$	6.85011	−	3.95491i	0.368798	−	0.212925i
$346$	−3.69912	+	32.4525i	−0.198866	+	1.74466i
$347$	−7.83659	−	29.2465i	−0.420690	−	1.57004i	−0.773159	−	0.634213i	$-0.781324\pi$
$347$	−7.83659	−	29.2465i	−0.420690	−	1.57004i	0.352469	−	0.935824i	$-0.385342\pi$
$348$	11.5505	+	2.66785i	0.619172	+	0.143012i
$349$	19.2744	+	19.2744i	1.03173	+	1.03173i	0.999480	+	0.0322540i	$0.0102686\pi$
$349$	19.2744	+	19.2744i	1.03173	+	1.03173i	0.0322540	+	0.999480i	$0.489731\pi$
$350$	2.58930	+	2.70103i	0.138404	+	0.144376i
$351$		−	23.5032i		−	1.25451i
$352$	22.0020	+	14.0244i	1.17271	+	0.747505i
$353$	3.08010	+	1.77830i	0.163937	+	0.0946492i	0.579724	−	0.814813i	$-0.303160\pi$
$353$	3.08010	+	1.77830i	0.163937	+	0.0946492i	−0.415787	+	0.909462i	$0.636494\pi$
$354$	−1.80843	−	2.27374i	−0.0961170	−	0.120848i
$355$	−4.02383	−	1.07818i	−0.213562	−	0.0572239i
$356$	−15.3923	−	14.3564i	−0.815791	−	0.760888i
$357$	−3.65871	+	4.40583i	−0.193639	+	0.233181i
$358$	−10.3755	+	4.51078i	−0.548361	+	0.238402i
$359$	11.2447	+	19.4763i	0.593471	+	1.02792i	0.993761	+	0.111533i	$0.0355762\pi$
$359$	11.2447	+	19.4763i	0.593471	+	1.02792i	−0.400290	+	0.916389i	$0.631091\pi$
$360$	−3.40636	+	2.90844i	−0.179531	+	0.153288i
$361$	−0.259601	−	0.149881i	−0.0136632	−	0.00788847i
$362$	4.04267	−	5.46279i	0.212478	−	0.287118i
$363$	−8.64613	−	8.64613i	−0.453804	−	0.453804i
$364$	13.8116	+	18.1387i	0.723925	+	0.950725i
$365$	3.53568	−	3.53568i	0.185066	−	0.185066i
$366$	−12.5590	+	1.87633i	−0.656471	+	0.0980772i
$367$	10.5951	−	18.3512i	0.553059	−	0.957926i	−0.444993	−	0.895534i	$-0.646794\pi$
$367$	10.5951	−	18.3512i	0.553059	−	0.957926i	0.998052	−	0.0623921i	$-0.0198729\pi$
$368$	−23.8920	−	11.6587i	−1.24546	−	0.607754i
$369$	−0.528091	+	0.304893i	−0.0274913	+	0.0158721i
$370$	4.83567	−	12.2743i	0.251394	−	0.638109i
$371$	−11.6064	−	1.98540i	−0.602575	−	0.103077i
$372$	−15.8959	+	0.553527i	−0.824163	+	0.0286990i
$373$	7.85854	−	29.3285i	0.406900	−	1.51857i	−0.393625	−	0.919271i	$-0.628779\pi$
$373$	7.85854	−	29.3285i	0.406900	−	1.51857i	0.800525	−	0.599300i	$-0.204554\pi$
$374$	1.34359	−	11.7873i	0.0694752	−	0.609508i
$375$	−0.595063	+	1.03068i	−0.0307289	+	0.0532241i
$376$	22.0946	+	15.1900i	1.13944	+	0.783365i
$377$	−21.4581			−1.10515
$378$	9.82997	+	17.8880i	0.505599	+	0.920058i
$379$	12.1374	−	12.1374i	0.623459	−	0.623459i	−0.322955	−	0.946414i	$-0.604676\pi$
$379$	12.1374	−	12.1374i	0.623459	−	0.623459i	0.946414	+	0.322955i	$0.104676\pi$
$380$	−8.42690	−	1.94638i	−0.432291	−	0.0998471i
$381$	−16.2956	+	4.36639i	−0.834849	+	0.223697i
$382$	2.19902	−	1.74900i	0.112512	−	0.0894867i
$383$	−7.89225	−	13.6698i	−0.403275	−	0.698493i	0.590844	−	0.806786i	$-0.298795\pi$
$383$	−7.89225	−	13.6698i	−0.403275	−	0.698493i	−0.994119	+	0.108293i	$0.965462\pi$
$384$	−12.9738	−	3.60277i	−0.662066	−	0.183853i
$385$	−5.10070	+	11.0861i	−0.259956	+	0.565000i
$386$	3.70276	−	9.39865i	0.188466	−	0.478379i
$387$	1.73708	−	6.48287i	0.0883007	−	0.329543i
$388$	6.88039	+	22.5127i	0.349299	+	1.14291i
$389$	7.35180	−	1.96991i	0.372751	−	0.0998783i	−0.0675800	−	0.997714i	$-0.521528\pi$
$389$	7.35180	−	1.96991i	0.372751	−	0.0998783i	0.440331	+	0.897836i	$0.354861\pi$
$390$	−4.31372	+	5.82906i	−0.218434	+	0.295166i
$391$			12.0879i			0.611313i
$392$	−18.0981	−	8.02855i	−0.914094	−	0.405503i
$393$		−	2.29282i		−	0.115657i
$394$	19.0105	+	14.0685i	0.957736	+	0.708760i
$395$	1.07245	−	0.287363i	0.0539609	−	0.0144588i
$396$	−12.8977	−	6.85947i	−0.648135	−	0.344701i
$397$	−4.58415	+	17.1083i	−0.230072	+	0.858640i	0.750237	+	0.661169i	$0.229939\pi$
$397$	−4.58415	+	17.1083i	−0.230072	+	0.858640i	−0.980309	+	0.197471i	$0.936727\pi$
$398$	30.4403	+	11.9925i	1.52583	+	0.601129i
$399$	−5.69142	+	12.3700i	−0.284927	+	0.619275i
$400$	3.99031	−	0.278239i	0.199516	−	0.0139119i
$401$	5.00754	+	8.67331i	0.250065	+	0.433125i	0.963543	−	0.267552i	$-0.0862148\pi$
$401$	5.00754	+	8.67331i	0.250065	+	0.433125i	−0.713479	+	0.700677i	$0.752881\pi$
$402$	−16.9316	−	21.2881i	−0.844473	−	1.06176i
$403$	27.8097	−	7.45158i	1.38530	−	0.371190i
$404$	13.5371	+	21.6687i	0.673498	+	1.07806i
$405$	−1.23137	+	1.23137i	−0.0611871	+	0.0611871i
$406$	16.3315	−	8.97463i	0.810518	−	0.445403i
$407$	43.0266			2.13275
$408$	1.11481	+	6.01997i	0.0551915	+	0.298033i
$409$	−18.0618	+	31.2840i	−0.893101	+	1.54690i	−0.0569627	+	0.998376i	$0.518142\pi$
$409$	−18.0618	+	31.2840i	−0.893101	+	1.54690i	−0.836138	+	0.548519i	$0.815192\pi$
$410$	0.541059	+	0.0616729i	0.0267210	+	0.00304581i
$411$	−1.27237	+	4.74856i	−0.0627615	+	0.234229i
$412$	−19.1425	+	20.5238i	−0.943084	+	1.01113i
$413$	−4.50150	−	0.770028i	−0.221504	−	0.0378906i
$414$	13.8485	+	5.45587i	0.680618	+	0.268141i
$415$	−0.530866	+	0.306496i	−0.0260592	+	0.0150453i
$416$	24.3492	+	1.06912i	1.19382	+	0.0524181i
$417$	−7.08717	+	12.2753i	−0.347060	+	0.601126i
$418$	−4.16795	−	27.8978i	−0.203861	−	1.36453i
$419$	−9.17610	+	9.17610i	−0.448282	+	0.448282i	−0.894783	−	0.446501i	$-0.852670\pi$
$419$	−9.17610	+	9.17610i	−0.448282	+	0.448282i	0.446501	+	0.894783i	$0.352670\pi$
$420$	0.845172	−	6.24059i	0.0412402	−	0.304509i
$421$	6.76265	+	6.76265i	0.329592	+	0.329592i	0.852431	−	0.522840i	$-0.175127\pi$
$421$	6.76265	+	6.76265i	0.329592	+	0.329592i	−0.522840	+	0.852431i	$0.675127\pi$
$422$	28.1437	+	20.8274i	1.37001	+	1.01386i
$423$	−13.0007	−	7.50597i	−0.632117	−	0.364953i
$424$	−9.57320	+	8.17384i	−0.464916	+	0.396957i
$425$	−0.909386	−	1.57510i	−0.0441117	−	0.0764037i
$426$	2.79546	+	6.42999i	0.135441	+	0.311534i
$427$	−12.7526	+	15.3567i	−0.617141	+	0.743163i
$428$	−15.1084	+	0.526106i	−0.730294	+	0.0254303i
$429$	−22.8449	−	6.12128i	−1.10296	−	0.295538i
$430$	−4.69088	+	3.73092i	−0.226215	+	0.179921i
$431$	9.02906	+	5.21293i	0.434914	+	0.251098i	0.701438	−	0.712730i	$-0.252542\pi$
$431$	9.02906	+	5.21293i	0.434914	+	0.251098i	−0.266524	+	0.963828i	$0.585875\pi$
$432$	21.4185	+	4.16772i	1.03050	+	0.200520i
$433$		−	18.4445i		−	0.886384i	−0.896427	−	0.443192i	$-0.853846\pi$
$433$		−	18.4445i		−	0.886384i	0.896427	−	0.443192i	$-0.146154\pi$
$434$	−18.0490	+	17.3024i	−0.866380	+	0.830542i
$435$	4.19124	+	4.19124i	0.200954	+	0.200954i
$436$	−0.368464	−	0.589794i	−0.0176462	−	0.0282460i
$437$	7.43864	+	27.7614i	0.355839	+	1.32801i
$438$	−8.36166	−	0.953109i	−0.399536	−	0.0455413i
$439$	13.0191	−	7.51655i	0.621365	−	0.358745i	−0.156035	−	0.987752i	$-0.549871\pi$
$439$	13.0191	−	7.51655i	0.621365	−	0.358745i	0.777400	+	0.629006i	$0.216538\pi$
$440$	5.61462	+	11.7758i	0.267666	+	0.561388i
$441$	10.4549	+	3.68465i	0.497852	+	0.175460i
$442$	−4.41846	−	10.1631i	−0.210165	−	0.483411i
$443$	26.2256	+	7.02713i	1.24602	+	0.333869i	0.820796	−	0.571221i	$-0.193530\pi$
$443$	26.2256	+	7.02713i	1.24602	+	0.333869i	0.425220	+	0.905090i	$0.360197\pi$
$444$	−21.2346	+	6.48978i	−1.00775	+	0.307991i
$445$	−2.72385	−	10.1655i	−0.129123	−	0.481892i
$446$	−19.4267	+	2.90236i	−0.919882	+	0.137431i
$447$	26.9473			1.27456
$448$	−18.9790	+	9.37009i	−0.896672	+	0.442695i
$449$	20.6152			0.972893			0.486447	−	0.873710i	$-0.338293\pi$
$449$	20.6152			0.972893			0.486447	+	0.873710i	$0.338293\pi$
$450$	−2.21496	+	0.330917i	−0.104414	+	0.0155996i
$451$	0.459679	+	1.71555i	0.0216454	+	0.0807819i
$452$	28.3660	−	8.66930i	1.33423	−	0.407770i
$453$	−20.0899	−	5.38309i	−0.943908	−	0.252919i
$454$	−9.32467	−	21.4482i	−0.437629	−	1.00661i
$455$	1.05155	+	11.3507i	0.0492976	+	0.532127i
$456$	6.26486	+	13.1396i	0.293379	+	0.615316i
$457$	−15.7723	+	9.10613i	−0.737796	+	0.425967i	−0.821267	−	0.570543i	$-0.806733\pi$
$457$	−15.7723	+	9.10613i	−0.737796	+	0.425967i	0.0834714	+	0.996510i	$0.473399\pi$
$458$	21.7167	+	2.47539i	1.01475	+	0.115667i
$459$	−2.56788	−	9.58344i	−0.119858	−	0.447317i
$460$	−7.04280	−	11.2733i	−0.328372	−	0.525621i
$461$	18.8727	+	18.8727i	0.878987	+	0.878987i	0.993430	−	0.114443i	$-0.0365082\pi$
$461$	18.8727	+	18.8727i	0.878987	+	0.878987i	−0.114443	+	0.993430i	$0.536508\pi$
$462$	19.9471	−	4.89583i	0.928024	−	0.227775i
$463$		−	18.6589i		−	0.867154i	−0.901117	−	0.433577i	$-0.857251\pi$
$463$		−	18.6589i		−	0.867154i	0.901117	−	0.433577i	$-0.142749\pi$
$464$	3.80508	−	19.5548i	0.176646	−	0.907810i
$465$	−6.88729	−	3.97638i	−0.319390	−	0.184400i
$466$	7.62777	−	6.06678i	0.353349	−	0.281038i
$467$	6.49511	+	1.74036i	0.300558	+	0.0805342i	0.405946	−	0.913897i	$-0.366942\pi$
$467$	6.49511	+	1.74036i	0.300558	+	0.0805342i	−0.105389	+	0.994431i	$0.533609\pi$
$468$	−13.6377	+	0.474891i	−0.630401	+	0.0219518i
$469$	−42.1458	−	7.20947i	−1.94611	−	0.332902i
$470$	5.34511	+	12.2946i	0.246552	+	0.567106i
$471$	1.38068	+	2.39140i	0.0636182	+	0.110190i
$472$	−3.71293	+	3.17019i	−0.170901	+	0.145920i
$473$	−16.9291	−	9.77404i	−0.778402	−	0.449411i
$474$	−1.50212	−	1.11163i	−0.0689947	−	0.0510587i
$475$	−3.05780	−	3.05780i	−0.140301	−	0.140301i
$476$	7.61345	+	5.88705i	0.348962	+	0.269832i
$477$	4.98359	−	4.98359i	0.228183	−	0.228183i
$478$	−1.83768	−	12.3004i	−0.0840537	−	0.562606i
$479$	−12.5344	+	21.7102i	−0.572711	+	0.991965i	0.423575	+	0.905861i	$0.360775\pi$
$479$	−12.5344	+	21.7102i	−0.572711	+	0.991965i	−0.996286	+	0.0861036i	$0.972558\pi$
$480$	−4.54710	−	4.96475i	−0.207546	−	0.226609i
$481$	34.8072	−	20.0960i	1.58707	−	0.916298i
$482$	−19.8848	−	7.83398i	−0.905730	−	0.356828i
$483$	−19.6285	+	7.25805i	−0.893128	+	0.330253i
$484$	−14.0153	+	15.0266i	−0.637060	+	0.683028i
$485$	−3.04638	+	11.3693i	−0.138329	+	0.516251i
$486$	−20.0829	−	2.28916i	−0.910977	−	0.103838i
$487$	2.25854	−	3.91190i	0.102344	−	0.177265i	−0.810306	−	0.586007i	$-0.800699\pi$
$487$	2.25854	−	3.91190i	0.102344	−	0.177265i	0.912650	+	0.408742i	$0.134032\pi$
$488$	3.88573	+	20.9829i	0.175899	+	0.949849i
$489$	11.2580			0.509103
$490$	−5.54761	−	8.19902i	−0.250616	−	0.370394i
$491$	2.78757	−	2.78757i	0.125801	−	0.125801i	−0.641403	−	0.767204i	$-0.721647\pi$
$491$	2.78757	−	2.78757i	0.125801	−	0.125801i	0.767204	+	0.641403i	$0.221647\pi$
$492$	−0.485621	−	0.777326i	−0.0218935	−	0.0350446i
$493$	−8.74955	+	2.34444i	−0.394060	+	0.105588i
$494$	−16.4017	−	20.6218i	−0.737947	−	0.927821i
$495$	−3.65208	−	6.32560i	−0.164149	−	0.284314i
$496$	1.85927	+	26.6644i	0.0834836	+	1.19727i
$497$	10.0126	+	4.60680i	0.449128	+	0.206643i
$498$	0.959913	+	0.378174i	0.0430147	+	0.0169464i
$499$	−0.521268	+	1.94540i	−0.0233351	+	0.0870880i	−0.976611	−	0.215012i	$-0.931021\pi$
$499$	−0.521268	+	1.94540i	−0.0233351	+	0.0870880i	0.953276	+	0.302100i	$0.0976876\pi$
$500$	1.76580	+	0.939117i	0.0789691	+	0.0419986i
$501$	9.74300	−	2.61063i	0.435285	−	0.116634i
$502$	−28.6559	−	21.2065i	−1.27898	−	0.946491i
$503$			8.87468i			0.395702i	0.980232	+	0.197851i	$0.0633963\pi$
$503$			8.87468i			0.395702i	−0.980232	+	0.197851i	$0.936604\pi$
$504$	10.1808	−	6.06524i	0.453489	−	0.270167i
$505$			12.7749i			0.568473i
$506$	25.7888	−	34.8480i	1.14645	−	1.54918i
$507$	−6.39542	+	1.71365i	−0.284031	+	0.0761058i
$508$	8.28626	+	27.1127i	0.367643	+	1.20293i
$509$	−0.847140	+	3.16157i	−0.0375488	+	0.140134i	−0.982156	−	0.188070i	$-0.939777\pi$
$509$	−0.847140	+	3.16157i	−0.0375488	+	0.140134i	0.944607	+	0.328204i	$0.106443\pi$
$510$	−1.12206	+	2.84810i	−0.0496856	+	0.126116i
$511$	−10.7979	+	7.64332i	−0.477670	+	0.338120i
$512$	−5.29203	+	21.9999i	−0.233877	+	0.972266i
$513$	−11.7949	−	20.4293i	−0.520756	−	0.901977i
$514$	12.0412	−	9.57703i	0.531114	−	0.422424i
$515$	−13.5545	+	3.63192i	−0.597283	+	0.160041i
$516$	9.82914	+	2.27026i	0.432704	+	0.0999425i
$517$	−30.9173	+	30.9173i	−1.35974	+	1.35974i
$518$	−18.0864	+	29.8525i	−0.794670	+	1.31164i
$519$	27.4871			1.20655
$520$	10.0420	+	6.90389i	0.440373	+	0.302756i
$521$	16.8766	−	29.2312i	0.739378	−	1.28064i	−0.213398	−	0.976965i	$-0.568453\pi$
$521$	16.8766	−	29.2312i	0.739378	−	1.28064i	0.952776	−	0.303675i	$-0.0982137\pi$
$522$	−1.26320	+	11.0821i	−0.0552886	+	0.485049i
$523$	0.632789	−	2.36160i	0.0276699	−	0.103266i	−0.950710	−	0.310082i	$-0.899644\pi$
$523$	0.632789	−	2.36160i	0.0276699	−	0.103266i	0.978380	+	0.206816i	$0.0663102\pi$
$524$	−3.85074	+	0.134090i	−0.168220	+	0.00585777i
$525$	2.01164	−	2.42242i	0.0877951	−	0.105723i
$526$	−12.7983	+	32.4857i	−0.558032	+	1.41644i
$527$	10.5253	−	6.07677i	0.458488	−	0.264708i
$528$	9.62933	−	19.7332i	0.419063	−	0.858776i
$529$	−10.5860	+	18.3356i	−0.460263	+	0.797199i
$530$	−6.22491	+	0.930006i	−0.270393	+	0.0403969i
$531$	1.93287	−	1.93287i	0.0838792	−	0.0838792i
$532$	21.1080	+	8.83517i	0.915147	+	0.383053i
$533$	1.17313	+	1.17313i	0.0508138	+	0.0508138i
$534$	−10.5369	+	14.2383i	−0.455974	+	0.616150i
$535$	−6.54611	−	3.77940i	−0.283013	−	0.163398i
$536$	−34.7627	+	29.6812i	−1.50152	+	1.28203i
$537$	4.76046	+	8.24537i	0.205429	+	0.355814i
$538$	8.31676	−	3.61574i	0.358561	−	0.155886i
$539$	18.2475	−	26.6357i	0.785976	−	1.14728i
$540$	7.97843	+	7.44147i	0.343337	+	0.320230i
$541$	−1.26012	−	0.337649i	−0.0541769	−	0.0145166i	0.231629	−	0.972804i	$-0.425595\pi$
$541$	−1.26012	−	0.337649i	−0.0541769	−	0.0145166i	−0.285806	+	0.958288i	$0.592261\pi$
$542$	−0.228451	−	0.287231i	−0.00981280	−	0.0123376i
$543$	−4.95291	−	2.85957i	−0.212550	−	0.122716i
$544$	10.0452	−	2.22437i	0.430684	−	0.0953690i
$545$		−	0.347715i		−	0.0148945i
$546$	13.8500	−	13.2771i	0.592725	−	0.568206i
$547$	3.61700	+	3.61700i	0.154652	+	0.154652i	0.780192	−	0.625540i	$-0.215121\pi$
$547$	3.61700	+	3.61700i	0.154652	+	0.154652i	−0.625540	+	0.780192i	$0.715121\pi$
$548$	8.04951	+	1.85921i	0.343858	+	0.0794216i
$549$	−3.09231	−	11.5407i	−0.131977	−	0.492543i
$550$	−0.738733	+	6.48093i	−0.0314997	+	0.276348i
$551$	−18.6517	+	10.7686i	−0.794589	+	0.458756i
$552$	−7.47117	+	21.0880i	−0.317994	+	0.897566i
$553$	−2.92501	+	0.270980i	−0.124384	+	0.0115233i
$554$	−14.0948	+	6.12775i	−0.598829	+	0.260343i
$555$	−10.7238	−	2.87343i	−0.455200	−	0.121970i
$556$	21.0306	+	11.1848i	0.891896	+	0.474342i
$557$	−0.903655	−	3.37249i	−0.0382891	−	0.142897i	0.944135	−	0.329558i	$-0.106900\pi$
$557$	−0.903655	−	3.37249i	−0.0382891	−	0.142897i	−0.982424	+	0.186662i	$0.940233\pi$
$558$	−2.21128	−	14.8010i	−0.0936109	−	0.626577i
$559$	−18.2602			−0.772325
$560$	−10.5303	−	1.05448i	−0.444988	−	0.0445599i
$561$	−9.98382			−0.421517
$562$	1.54458	+	10.3385i	0.0651541	+	0.436104i
$563$	−0.334926	−	1.24996i	−0.0141154	−	0.0526796i	0.958509	−	0.285063i	$-0.0920144\pi$
$563$	−0.334926	−	1.24996i	−0.0141154	−	0.0526796i	−0.972624	+	0.232383i	$0.925348\pi$
$564$	10.5951	−	19.9217i	0.446133	−	0.838855i
$565$	14.3253	+	3.83844i	0.602668	+	0.161485i
$566$	−33.5122	+	14.5696i	−1.40862	+	0.612404i
$567$	3.76056	−	2.66193i	0.157929	−	0.111791i
$568$	10.6355	−	5.07096i	0.446257	−	0.212773i
$569$	−29.2221	+	16.8714i	−1.22505	+	0.707285i	−0.965991	−	0.258576i	$-0.916747\pi$
$569$	−29.2221	+	16.8714i	−1.22505	+	0.707285i	−0.259062	+	0.965861i	$0.583413\pi$
$570$	−0.824287	+	7.23150i	−0.0345256	+	0.302894i
$571$	−6.16942	−	23.0246i	−0.258182	−	0.963548i	−0.966293	−	0.257447i	$-0.917119\pi$
$571$	−6.16942	−	23.0246i	−0.258182	−	0.963548i	0.708111	−	0.706102i	$-0.249548\pi$
$572$	−8.94451	+	38.7255i	−0.373989	+	1.61920i
$573$	−1.67198	−	1.67198i	−0.0698479	−	0.0698479i
$574$	−1.38350	−	0.402203i	−0.0577462	−	0.0167876i
$575$		−	6.64621i		−	0.277166i
$576$	1.98554	−	12.5122i	0.0827308	−	0.521343i
$577$	−38.6718	−	22.3272i	−1.60993	−	0.929493i	−0.989384	−	0.145322i	$-0.953578\pi$
$577$	−38.6718	−	22.3272i	−1.60993	−	0.929493i	−0.620545	−	0.784171i	$-0.713089\pi$
$578$	12.0533	+	15.1546i	0.501352	+	0.630350i
$579$	−8.21141	−	2.20024i	−0.341255	−	0.0914389i
$580$	6.79397	−	7.28420i	0.282104	−	0.302460i
$581$	1.52116	−	0.562480i	0.0631083	−	0.0233356i
$582$	18.1678	−	7.89854i	0.753081	−	0.327405i
$583$	−10.2638	−	17.7774i	−0.425082	−	0.736264i
$584$	−1.11171	+	14.0990i	−0.0460029	+	0.583419i
$585$	−5.90886	−	3.41148i	−0.244301	−	0.141047i
$586$	−14.9862	+	20.2506i	−0.619073	+	0.836543i
$587$	−12.9617	−	12.9617i	−0.534985	−	0.534985i	0.387067	−	0.922052i	$-0.373488\pi$
$587$	−12.9617	−	12.9617i	−0.534985	−	0.534985i	−0.922052	+	0.387067i	$0.873488\pi$
$588$	−4.98805	+	15.8976i	−0.205704	+	0.655606i
$589$	20.4330	−	20.4330i	0.841929	−	0.841929i
$590$	−2.41431	+	0.360699i	−0.0993955	+	0.0148497i
$591$	9.95128	−	17.2361i	0.409341	−	0.708999i
$592$	12.1413	+	35.2835i	0.499004	+	1.45014i
$593$	−5.33980	+	3.08294i	−0.219279	+	0.126601i	−0.605617	−	0.795757i	$-0.707073\pi$
$593$	−5.33980	+	3.08294i	−0.219279	+	0.126601i	0.386337	+	0.922358i	$0.373740\pi$
$594$	−13.0428	+	33.1062i	−0.535152	+	1.35837i
$595$	1.66890	+	4.51334i	0.0684183	+	0.185029i
$596$	−1.57595	−	45.2574i	−0.0645535	−	1.85381i
$597$	7.12613	−	26.5951i	0.291653	−	1.08846i
$598$	4.58631	−	40.2359i	0.187548	−	1.64537i
$599$	7.49718	−	12.9855i	0.306327	−	0.530573i	−0.671229	−	0.741250i	$-0.734233\pi$
$599$	7.49718	−	12.9855i	0.306327	−	0.530573i	0.977556	+	0.210677i	$0.0675667\pi$
$600$	−0.612949	−	3.30991i	−0.0250235	−	0.135126i
$601$	−21.3544			−0.871066			−0.435533	−	0.900173i	$-0.643440\pi$
$601$	−21.3544			−0.871066			−0.435533	+	0.900173i	$0.643440\pi$
$602$	13.8976	−	7.63714i	0.566424	−	0.311267i
$603$	18.0967	−	18.0967i	0.736953	−	0.736953i
$604$	−7.86585	+	34.0554i	−0.320057	+	1.38569i
$605$	−9.92402	+	2.65913i	−0.403469	+	0.108109i
$606$	16.8277	−	13.3840i	0.683579	−	0.543689i
$607$	17.4214	+	30.1747i	0.707113	+	1.22476i	0.965924	+	0.258827i	$0.0833360\pi$
$607$	17.4214	+	30.1747i	0.707113	+	1.22476i	−0.258811	+	0.965928i	$0.583331\pi$
$608$	21.7012	−	11.2901i	0.880099	−	0.457875i
$609$	−9.06048	−	12.7999i	−0.367149	−	0.518679i
$610$	−3.91099	+	9.92718i	−0.158351	+	0.401940i
$611$	−10.5710	+	39.4514i	−0.427656	+	1.59603i
$612$	−5.50887	+	1.68364i	−0.222683	+	0.0680570i
$613$	−25.2610	+	6.76867i	−1.02028	+	0.273384i	−0.729920	−	0.683533i	$-0.760443\pi$
$613$	−25.2610	+	6.76867i	−1.02028	+	0.273384i	−0.290363	+	0.956917i	$0.593776\pi$
$614$	−3.42548	+	4.62879i	−0.138241	+	0.186803i
$615$		−	0.458275i		−	0.0184794i
$616$	−9.38899	−	33.2144i	−0.378293	−	1.33825i
$617$		−	28.9800i		−	1.16669i	−0.812224	−	0.583346i	$-0.801743\pi$
$617$		−	28.9800i		−	1.16669i	0.812224	−	0.583346i	$-0.198257\pi$
$618$	18.9850	+	14.0496i	0.763689	+	0.565158i
$619$	31.6003	−	8.46728i	1.27012	−	0.340329i	0.440045	−	0.897975i	$-0.354962\pi$
$619$	31.6003	−	8.46728i	1.27012	−	0.340329i	0.830078	+	0.557647i	$0.188296\pi$
$620$	−6.27544	+	11.7996i	−0.252028	+	0.473883i
$621$	9.38361	−	35.0201i	0.376551	−	1.40531i
$622$	5.33522	+	2.10190i	0.213923	+	0.0842786i
$623$	2.56856	+	27.7255i	0.102907	+	1.11080i
$624$	−1.42672	−	20.4610i	−0.0571145	−	0.819097i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−0.0905726	−	0.113877i	−0.00362001	−	0.00455144i
$627$	−22.9290	+	6.14382i	−0.915698	+	0.245361i
$628$	3.93556	−	2.45867i	0.157046	−	0.0981116i
$629$	11.9971	−	11.9971i	0.478354	−	0.478354i
$630$	5.92396	+	0.125114i	0.236016	+	0.00498466i
$631$	15.3927			0.612775			0.306387	−	0.951907i	$-0.400880\pi$
$631$	15.3927			0.612775			0.306387	+	0.951907i	$0.400880\pi$
$632$	−1.77910	+	2.58779i	−0.0707688	+	0.102937i
$633$	14.7322	−	25.5168i	0.585551	−	1.01420i
$634$	37.8821	+	4.31801i	1.50449	+	0.171490i
$635$	−3.66885	+	13.6923i	−0.145594	+	0.543363i
$636$	7.74680	+	7.22544i	0.307181	+	0.286507i
$637$	2.32125	−	30.0701i	0.0919712	−	1.19142i
$638$	30.2255	+	11.9079i	1.19664	+	0.471438i
$639$	−5.71309	+	3.29846i	−0.226006	+	0.130485i
$640$	−8.07224	+	7.92710i	−0.319083	+	0.313346i
$641$	−4.79261	+	8.30104i	−0.189297	+	0.327872i	−0.945016	−	0.327024i	$-0.893954\pi$
$641$	−4.79261	+	8.30104i	−0.189297	+	0.327872i	0.755719	+	0.654896i	$0.227287\pi$
$642$	1.87983	+	12.5825i	0.0741911	+	0.496592i
$643$	12.4069	−	12.4069i	0.489281	−	0.489281i	−0.418798	−	0.908079i	$-0.637549\pi$
$643$	12.4069	−	12.4069i	0.489281	−	0.489281i	0.908079	+	0.418798i	$0.137549\pi$
$644$	13.3376	+	32.5411i	0.525577	+	1.28230i
$645$	3.56662	+	3.56662i	0.140435	+	0.140435i
$646$	−8.94086	−	6.61657i	−0.351774	−	0.260326i
$647$	40.3903	+	23.3193i	1.58791	+	0.916778i	0.993652	+	0.112500i	$0.0358858\pi$
$647$	40.3903	+	23.3193i	1.58791	+	0.916778i	0.594254	+	0.804278i	$0.297447\pi$
$648$	0.387174	−	4.91023i	0.0152096	−	0.192892i
$649$	−3.98077	−	6.89489i	−0.156259	−	0.270648i
$650$	2.42937	+	5.58791i	0.0952876	+	0.219176i
$651$	16.1873	+	13.4423i	0.634430	+	0.526846i
$652$	−0.658397	−	18.9075i	−0.0257848	−	0.740475i
$653$	20.6894	+	5.54370i	0.809637	+	0.216942i	0.639811	−	0.768532i	$-0.279013\pi$
$653$	20.6894	+	5.54370i	0.809637	+	0.216942i	0.169826	+	0.985474i	$0.445679\pi$
$654$	−0.458029	+	0.364296i	−0.0179103	+	0.0142451i
$655$	−1.66843	−	0.963268i	−0.0651909	−	0.0376380i
$656$	−1.27710	+	0.861048i	−0.0498624	+	0.0336183i
$657$		−	7.91832i		−	0.308923i
$658$	−8.45471	−	34.4471i	−0.329599	−	1.34289i
$659$	−12.6779	−	12.6779i	−0.493860	−	0.493860i	0.415660	−	0.909520i	$-0.363551\pi$
$659$	−12.6779	−	12.6779i	−0.493860	−	0.493860i	−0.909520	+	0.415660i	$0.863551\pi$
$660$	9.31099	−	5.81688i	0.362430	−	0.226422i
$661$	−9.24479	−	34.5020i	−0.359581	−	1.34197i	−0.874621	−	0.484807i	$-0.838890\pi$
$661$	−9.24479	−	34.5020i	−0.359581	−	1.34197i	0.515040	−	0.857166i	$-0.327777\pi$
$662$	−11.9402	−	1.36101i	−0.464069	−	0.0528972i
$663$	−8.07661	+	4.66304i	−0.313670	+	0.181097i
$664$	0.578996	−	1.63427i	0.0224694	−	0.0634219i
$665$	6.61025	+	9.33843i	0.256334	+	0.362129i
$666$	−8.32956	−	19.1593i	−0.322764	−	0.742407i
$667$	−31.9729	−	8.56711i	−1.23800	−	0.331720i
$668$	−4.95429	−	16.2105i	−0.191687	−	0.627201i
$669$	4.27826	+	15.9667i	0.165407	+	0.617308i
$670$	−22.6042	+	3.37708i	−0.873277	+	0.130468i
$671$	−34.7990			−1.34340
$672$	9.64346	+	14.9759i	0.372005	+	0.577708i
$673$	22.1001			0.851895			0.425947	−	0.904748i	$-0.359941\pi$
$673$	22.1001			0.851895			0.425947	+	0.904748i	$0.359941\pi$
$674$	36.8320	−	5.50273i	1.41872	−	0.211957i
$675$	1.41187	+	5.26919i	0.0543431	+	0.202811i
$676$	3.25205	+	10.6407i	0.125079	+	0.409259i
$677$	6.70740	+	1.79724i	0.257786	+	0.0690736i	0.385397	−	0.922751i	$-0.374064\pi$
$677$	6.70740	+	1.79724i	0.257786	+	0.0690736i	−0.127611	+	0.991824i	$0.540731\pi$
$678$	−9.95216	−	22.8915i	−0.382210	−	0.879142i
$679$	13.0164	−	28.2905i	0.499525	−	1.08569i
$680$	4.84894	+	1.71791i	0.185948	+	0.0658787i
$681$	−17.0448	+	9.84082i	−0.653158	+	0.377101i
$682$	−43.3074	−	4.93642i	−1.65833	−	0.189025i
$683$	−0.625115	−	2.33296i	−0.0239194	−	0.0892683i	0.952934	−	0.303177i	$-0.0980472\pi$
$683$	−0.625115	−	2.33296i	−0.0239194	−	0.0892683i	−0.976854	+	0.213908i	$0.931381\pi$
$684$	−11.6157	+	7.25671i	−0.444138	+	0.277467i
$685$	2.92086	+	2.92086i	0.111600	+	0.111600i
$686$	10.8098	+	23.8568i	0.412722	+	0.910857i
$687$		−	18.3939i		−	0.701772i
$688$	3.23801	−	16.6406i	0.123448	−	0.634416i
$689$	−16.6062	−	9.58759i	−0.632646	−	0.365258i
$690$	−8.75474	+	6.96313i	−0.333287	+	0.265082i
$691$	−0.385301	−	0.103241i	−0.0146575	−	0.00392747i	0.251483	−	0.967862i	$-0.419082\pi$
$691$	−0.385301	−	0.103241i	−0.0146575	−	0.00392747i	−0.266140	+	0.963934i	$0.585748\pi$
$692$	−1.60752	−	46.1640i	−0.0611089	−	1.75489i
$693$	6.70230	+	18.1255i	0.254599	+	0.688533i
$694$	17.0725	+	39.2693i	0.648062	+	1.49064i
$695$	5.95497	+	10.3143i	0.225885	+	0.391244i
$696$	−16.7131	−	1.31784i	−0.633507	−	0.0499524i
$697$	0.606515	+	0.350172i	0.0229734	+	0.0132637i
$698$	−30.9865	−	22.9312i	−1.17286	−	0.867959i
$699$	−5.79961	−	5.79961i	−0.219362	−	0.219362i
$700$	−4.18604	−	3.23683i	−0.158218	−	0.122341i
$701$	−15.5299	+	15.5299i	−0.586558	+	0.586558i	−0.936697	−	0.350140i	$-0.886134\pi$
$701$	−15.5299	+	15.5299i	−0.586558	+	0.586558i	0.350140	+	0.936697i	$0.386134\pi$
$702$	4.91135	+	32.8737i	0.185367	+	1.24074i
$703$	20.1700	−	34.9354i	0.760725	−	1.31761i
$704$	−33.7045	−	15.0182i	−1.27029	−	0.566019i
$705$	9.77046	−	5.64098i	0.367977	−	0.212452i
$706$	−4.67971	−	1.84365i	−0.176123	−	0.0693868i
$707$	5.69890	−	33.3152i	0.214329	−	1.25295i
$708$	3.00457	+	2.80236i	0.112919	+	0.105319i
$709$	−2.19082	+	8.17625i	−0.0822779	+	0.307065i	−0.994785	−	0.101996i	$-0.967477\pi$
$709$	−2.19082	+	8.17625i	−0.0822779	+	0.307065i	0.912507	+	0.409061i	$0.134144\pi$
$710$	5.85339	+	0.667202i	0.219674	+	0.0250396i
$711$	0.879123	−	1.52268i	0.0329697	−	0.0571051i
$712$	24.5291	+	16.8637i	0.919265	+	0.631994i
$713$	44.4118			1.66324
$714$	4.19673	−	6.92693i	0.157059	−	0.259234i
$715$	−14.0520	+	14.0520i	−0.525515	+	0.525515i
$716$	13.5695	−	8.47730i	0.507116	−	0.316811i
$717$	−10.1096	+	2.70886i	−0.377550	+	0.101164i
$718$	−19.7977	−	24.8916i	−0.738843	−	0.928947i
$719$	5.64697	+	9.78084i	0.210597	+	0.364764i	0.951901	−	0.306405i	$-0.0991260\pi$
$719$	5.64697	+	9.78084i	0.210597	+	0.364764i	−0.741305	+	0.671168i	$0.765793\pi$
$720$	4.15668	−	4.77981i	0.154910	−	0.178133i
$721$	36.9686	−	3.42487i	1.37678	−	0.127549i
$722$	0.394422	+	0.155389i	0.0146789	+	0.00578299i
$723$	−4.65508	+	17.3730i	−0.173124	+	0.646108i
$724$	−4.51291	+	8.48553i	−0.167721	+	0.315362i
$725$	4.81070	−	1.28902i	0.178665	−	0.0478731i
$726$	13.9000	+	10.2865i	0.515877	+	0.381768i
$727$			23.3848i			0.867296i	0.901082	+	0.433648i	$0.142774\pi$
$727$			23.3848i			0.867296i	−0.901082	+	0.433648i	$0.857226\pi$
$728$	−23.1085	−	22.4843i	−0.856458	−	0.833322i
$729$			22.2343i			0.823494i
$730$	−4.20649	+	5.68415i	−0.155689	+	0.210380i
$731$	−7.44561	+	1.99504i	−0.275386	+	0.0737894i
$732$	17.1741	−	5.24880i	0.634773	−	0.194001i
$733$	12.0316	−	44.9027i	0.444399	−	1.65852i	−0.273121	−	0.961980i	$-0.588056\pi$
$733$	12.0316	−	44.9027i	0.444399	−	1.65852i	0.717519	−	0.696539i	$-0.245278\pi$
$734$	−10.9845	+	27.8817i	−0.405444	+	1.02913i
$735$	−6.32674	+	5.41996i	−0.233365	+	0.199918i
$736$	35.8538	+	11.3144i	1.32159	+	0.417053i
$737$	−37.2704	−	64.5542i	−1.37287	−	2.37788i
$738$	0.674923	−	0.536804i	0.0248443	−	0.0197600i
$739$	33.8157	−	9.06090i	1.24393	−	0.333311i	0.423943	−	0.905689i	$-0.360646\pi$
$739$	33.8157	−	9.06090i	1.24393	−	0.333311i	0.819990	+	0.572378i	$0.193979\pi$
$740$	−4.19870	+	18.1784i	−0.154347	+	0.668251i
$741$	−15.6794	+	15.6794i	−0.575997	+	0.575997i
$742$	16.6487	+	0.351619i	0.611191	+	0.0129083i
$743$	35.4732			1.30138			0.650692	−	0.759341i	$-0.274479\pi$
$743$	35.4732			1.30138			0.650692	+	0.759341i	$0.274479\pi$
$744$	22.1177	−	4.09590i	0.810876	−	0.150163i
$745$	11.3212	−	19.6089i	0.414777	−	0.718414i
$746$	−4.86304	+	42.6636i	−0.178048	+	1.56203i
$747$	−0.251244	+	0.937655i	−0.00919254	+	0.0343070i
$748$	0.583881	+	16.7676i	0.0213488	+	0.613084i
$749$	15.3854	+	12.7764i	0.562171	+	0.466840i
$750$	0.616933	−	1.56595i	0.0225272	−	0.0571804i
$751$	46.2437	−	26.6988i	1.68746	−	0.974253i	0.730998	−	0.682379i	$-0.239055\pi$
$751$	46.2437	−	26.6988i	1.68746	−	0.974253i	0.956457	−	0.291873i	$-0.0942786\pi$
$752$	−34.0777	−	16.6291i	−1.24268	−	0.606401i
$753$	−15.0003	+	25.9813i	−0.546641	+	0.946810i
$754$	30.0133	−	4.48400i	1.09302	−	0.163298i
$755$	−12.3574	+	12.3574i	−0.449732	+	0.449732i
$756$	−17.4870	−	22.9656i	−0.635998	−	0.835251i
$757$	14.8367	+	14.8367i	0.539247	+	0.539247i	0.923308	−	0.384061i	$-0.125475\pi$
$757$	14.8367	+	14.8367i	0.539247	+	0.539247i	−0.384061	+	0.923308i	$0.625475\pi$
$758$	−14.4402	+	19.5128i	−0.524492	+	0.708738i
$759$	−31.5954	−	18.2416i	−1.14684	−	0.662128i
$760$	12.1933	+	0.961452i	0.442299	+	0.0348755i
$761$	2.60139	+	4.50575i	0.0943005	+	0.163333i	0.909316	−	0.416105i	$-0.136605\pi$
$761$	2.60139	+	4.50575i	0.0943005	+	0.163333i	−0.815016	+	0.579439i	$0.803272\pi$
$762$	21.8801	−	9.51244i	0.792631	−	0.344599i
$763$	−0.155117	+	0.906796i	−0.00561560	+	0.0328282i
$764$	−2.71026	+	2.90583i	−0.0980539	+	0.105129i
$765$	−2.78206	−	0.745452i	−0.100586	−	0.0269519i
$766$	13.8953	+	17.4706i	0.502058	+	0.631237i
$767$	−6.44065	−	3.71851i	−0.232558	−	0.134268i
$768$	18.8992	+	2.32809i	0.681965	+	0.0840079i
$769$			6.99371i			0.252200i	0.992018	+	0.126100i	$0.0402460\pi$
$769$			6.99371i			0.252200i	−0.992018	+	0.126100i	$0.959754\pi$
$770$	4.81768	−	16.5719i	0.173617	−	0.597209i
$771$	−9.15527	−	9.15527i	−0.329719	−	0.329719i
$772$	−3.21503	+	13.9195i	−0.115711	+	0.500975i
$773$	5.21023	+	19.4448i	0.187399	+	0.699382i	0.994104	+	0.108428i	$0.0345818\pi$
$773$	5.21023	+	19.4448i	0.187399	+	0.699382i	−0.806705	+	0.590954i	$0.798752\pi$
$774$	−1.07494	+	9.43052i	−0.0386380	+	0.338973i
$775$	−5.78702	+	3.34114i	−0.207876	+	0.120017i
$776$	−14.3279	−	30.0505i	−0.514342	−	1.07875i
$777$	26.6844	+	12.2775i	0.957298	+	0.440451i
$778$	−9.87124	+	4.29156i	−0.353901	+	0.153860i
$779$	1.60842	+	0.430976i	0.0576277	+	0.0154413i
$780$	4.81549	−	9.05446i	0.172422	−	0.324202i
$781$	4.97299	+	18.5594i	0.177947	+	0.664109i
$782$	−2.52596	−	16.9073i	−0.0903280	−	0.604603i
$783$	27.1684			0.970919
$784$	26.9914	+	7.44757i	0.963977	+	0.265985i
$785$	2.32022			0.0828122
$786$	0.479119	+	3.20695i	0.0170896	+	0.114388i
$787$	11.8525	+	44.2342i	0.422497	+	1.57678i	0.769329	+	0.638852i	$0.220591\pi$
$787$	11.8525	+	44.2342i	0.422497	+	1.57678i	−0.346832	+	0.937927i	$0.612743\pi$
$788$	−29.5296	−	15.7049i	−1.05195	−	0.559465i
$789$	28.3821	+	7.60495i	1.01043	+	0.270743i
$790$	−1.43998	+	0.626036i	−0.0512322	+	0.0222734i
$791$	−35.6461	−	16.4007i	−1.26743	−	0.583142i
$792$	19.4733	+	6.89910i	0.691954	+	0.245149i
$793$	−28.1514	+	16.2532i	−0.999685	+	0.577168i
$794$	2.83677	−	24.8871i	0.100673	−	0.883210i
$795$	1.37089	+	5.11621i	0.0486203	+	0.181453i
$796$	−45.0826	−	10.4128i	−1.59791	−	0.369072i
$797$	29.4099	+	29.4099i	1.04175	+	1.04175i	0.999090	+	0.0426629i	$0.0135841\pi$
$797$	29.4099	+	29.4099i	1.04175	+	1.04175i	0.0426629	+	0.999090i	$0.486416\pi$
$798$	5.37563	−	18.4911i	0.190295	−	0.654578i
$799$			17.2413i			0.609953i
$800$	−5.52307	+	1.22301i	−0.195270	+	0.0432398i
$801$	−14.4332	−	8.33300i	−0.509971	−	0.294432i
$802$	−8.81641	−	11.0849i	−0.311318	−	0.391421i
$803$	−22.2770	−	5.96911i	−0.786139	−	0.210645i
$804$	28.1306	+	26.2374i	0.992089	+	0.925321i
$805$	−2.96490	+	17.3325i	−0.104499	+	0.610889i
$806$	−37.3400	+	16.2337i	−1.31525	+	0.571808i
$807$	−3.81588	−	6.60930i	−0.134325	−	0.232658i
$808$	−23.4623	−	27.4790i	−0.825400	−	0.966708i
$809$	−36.3755	−	21.0014i	−1.27889	−	0.738370i	−0.302249	−	0.953229i	$-0.597737\pi$
$809$	−36.3755	−	21.0014i	−1.27889	−	0.738370i	−0.976645	+	0.214859i	$0.931071\pi$
$810$	1.46499	−	1.97961i	0.0514744	−	0.0695565i
$811$	−25.6966	−	25.6966i	−0.902328	−	0.902328i	0.0933091	−	0.995637i	$-0.470256\pi$
$811$	−25.6966	−	25.6966i	−0.902328	−	0.902328i	−0.995637	+	0.0933091i	$0.970256\pi$
$812$	−20.9673	+	15.9654i	−0.735808	+	0.560277i
$813$	−0.218390	+	0.218390i	−0.00765928	+	0.00765928i
$814$	−60.1809	+	8.99106i	−2.10934	+	0.315136i
$815$	4.72974	−	8.19215i	0.165676	−	0.286959i
$816$	−2.81724	−	8.18711i	−0.0986232	−	0.286606i
$817$	−15.8720	+	9.16372i	−0.555292	+	0.320598i
$818$	18.7256	−	47.5310i	0.654727	−	1.66188i
$819$	13.8877	+	11.5327i	0.485274	+	0.402984i
$820$	−0.769661	+	0.0268012i	−0.0268777	+	0.000935937i
$821$	−9.54376	+	35.6178i	−0.333080	+	1.24307i	0.572856	+	0.819656i	$0.305835\pi$
$821$	−9.54376	+	35.6178i	−0.333080	+	1.24307i	−0.905936	+	0.423414i	$0.860831\pi$
$822$	0.787372	−	6.90765i	0.0274628	−	0.240932i
$823$	−28.0736	+	48.6249i	−0.978585	+	1.69496i	−0.311026	+	0.950402i	$0.600672\pi$
$823$	−28.0736	+	48.6249i	−0.978585	+	1.69496i	−0.667559	+	0.744557i	$0.732661\pi$
$824$	22.4857	−	32.7065i	0.783326	−	1.13939i
$825$	5.48932			0.191114
$826$	6.45711	+	0.136374i	0.224672	+	0.00474506i
$827$	−31.8614	+	31.8614i	−1.10793	+	1.10793i	−0.114506	+	0.993423i	$0.536528\pi$
$827$	−31.8614	+	31.8614i	−1.10793	+	1.10793i	−0.993423	+	0.114506i	$0.963472\pi$
$828$	−20.5099	−	4.73721i	−0.712768	−	0.164629i
$829$	−15.3819	+	4.12158i	−0.534237	+	0.143148i	−0.515844	−	0.856683i	$-0.672522\pi$
$829$	−15.3819	+	4.12158i	−0.534237	+	0.143148i	−0.0183927	+	0.999831i	$0.505855\pi$
$830$	0.678470	−	0.539625i	0.0235500	−	0.0187306i
$831$	6.46694	+	11.2011i	0.224336	+	0.388561i
$832$	−34.2804	+	3.59276i	−1.18846	+	0.124556i
$833$	−2.33886	−	12.5147i	−0.0810369	−	0.433609i
$834$	7.34763	−	18.6504i	0.254428	−	0.645809i
$835$	2.19357	−	8.18653i	0.0759117	−	0.283306i
$836$	11.6594	+	38.1495i	0.403247	+	1.31943i
$837$	−35.2102	+	9.43454i	−1.21704	+	0.326105i
$838$	10.9170	−	14.7520i	0.377123	−	0.509600i
$839$		−	53.7004i		−	1.85394i	−0.375131	−	0.926972i	$-0.622402\pi$
$839$		−	53.7004i		−	1.85394i	0.375131	−	0.926972i	$-0.377598\pi$
$840$	0.121931	+	8.90526i	0.00420700	+	0.307261i
$841$			4.19563i			0.144677i
$842$	−10.8720	−	8.04570i	−0.374674	−	0.277273i
$843$	8.49715	−	2.27680i	0.292657	−	0.0784173i
$844$	−43.7165	−	23.2500i	−1.50478	−	0.800298i
$845$	−1.43989	+	5.37373i	−0.0495336	+	0.184862i
$846$	19.7525	+	7.78183i	0.679104	+	0.267545i
$847$	27.0668	−	2.50754i	0.930027	−	0.0861600i
$848$	11.6819	−	13.4331i	0.401158	−	0.461296i
$849$	15.3760	+	26.6320i	0.527704	+	0.914010i
$850$	1.60109	+	2.01305i	0.0549169	+	0.0690470i
$851$	59.8865	−	16.0466i	2.05288	−	0.550069i
$852$	−5.25363	−	8.40941i	−0.179986	−	0.288102i
$853$	11.8429	−	11.8429i	0.405495	−	0.405495i	−0.474669	−	0.880164i	$-0.657432\pi$
$853$	11.8429	−	11.8429i	0.405495	−	0.405495i	0.880164	+	0.474669i	$0.157432\pi$
$854$	14.6279	−	24.1441i	0.500556	−	0.826194i
$855$	−6.84808			−0.234199
$856$	21.0221	−	3.89300i	0.718520	−	0.133060i
$857$	26.6655	−	46.1860i	0.910875	−	1.57768i	0.0980448	−	0.995182i	$-0.468741\pi$
$857$	26.6655	−	46.1860i	0.910875	−	1.57768i	0.812830	−	0.582500i	$-0.197926\pi$
$858$	33.2321	+	3.78798i	1.13453	+	0.129320i
$859$	−1.14558	+	4.27535i	−0.0390866	+	0.145873i	−0.982711	−	0.185144i	$-0.940725\pi$
$859$	−1.14558	+	4.27535i	−0.0390866	+	0.145873i	0.943625	+	0.331017i	$0.107392\pi$
$860$	5.78146	−	6.19863i	0.197146	−	0.211372i
$861$	−0.204438	+	1.19512i	−0.00696722	+	0.0407296i
$862$	−13.7182	−	5.40451i	−0.467243	−	0.184078i
$863$	−25.6631	+	14.8166i	−0.873584	+	0.504364i	−0.868538	−	0.495623i	$-0.834940\pi$
$863$	−25.6631	+	14.8166i	−0.873584	+	0.504364i	−0.00504627	+	0.999987i	$0.501606\pi$
$864$	−30.8288	−	1.35363i	−1.04882	−	0.0460514i
$865$	11.5480	−	20.0017i	0.392644	−	0.680079i
$866$	3.85425	+	25.7981i	0.130973	+	0.876654i
$867$	11.5225	−	11.5225i	0.391325	−	0.391325i
$868$	21.6294	−	27.9723i	0.734149	−	0.949442i
$869$	−3.62114	−	3.62114i	−0.122839	−	0.122839i
$870$	−6.73806	−	4.98642i	−0.228442	−	0.169055i
$871$	−60.3012	−	34.8149i	−2.04323	−	1.17966i
$872$	0.638613	+	0.747943i	0.0216262	+	0.0253286i
$873$	9.31973	+	16.1422i	0.315425	+	0.546332i
$874$	−16.2055	−	37.2752i	−0.548160	−	1.26085i
$875$	−0.917599	−	2.48153i	−0.0310205	−	0.0838912i
$876$	11.8945	−	0.414192i	0.401879	−	0.0139943i
$877$	33.3436	+	8.93439i	1.12593	+	0.301693i	0.773282	−	0.634062i	$-0.218614\pi$
$877$	33.3436	+	8.93439i	1.12593	+	0.301693i	0.352651	+	0.935755i	$0.385280\pi$
$878$	−16.6389	+	13.2339i	−0.561536	+	0.446621i
$879$	18.3604	+	10.6004i	0.619282	+	0.357543i
$880$	−10.3138	−	15.2974i	−0.347679	−	0.515675i
$881$		−	36.3956i		−	1.22620i	−0.790006	−	0.613099i	$-0.789923\pi$
$881$		−	36.3956i		−	1.22620i	0.790006	−	0.613099i	$-0.210077\pi$
$882$	−15.3931	−	2.96898i	−0.518313	−	0.0999708i
$883$	12.7360	+	12.7360i	0.428600	+	0.428600i	0.888151	−	0.459552i	$-0.151990\pi$
$883$	12.7360	+	12.7360i	0.428600	+	0.428600i	−0.459552	+	0.888151i	$0.651990\pi$
$884$	8.30380	+	13.2918i	0.279287	+	0.447051i
$885$	0.531693	+	1.98430i	0.0178727	+	0.0667016i
$886$	−38.1499	−	4.34854i	−1.28167	−	0.146092i
$887$	−24.8000	+	14.3183i	−0.832702	+	0.480761i	−0.854777	−	0.518996i	$-0.826306\pi$
$887$	−24.8000	+	14.3183i	−0.832702	+	0.480761i	0.0220749	+	0.999756i	$0.492973\pi$
$888$	28.3445	−	13.5145i	0.951178	−	0.453516i
$889$	15.6761	−	34.0711i	0.525759	−	1.14271i
$890$	5.93406	+	13.6492i	0.198910	+	0.457523i
$891$	7.75840	+	2.07886i	0.259916	+	0.0696443i
$892$	26.5655	−	8.11901i	0.889477	−	0.271845i
$893$	10.6099	+	39.5967i	0.355047	+	1.32505i
$894$	−37.6909	+	5.63105i	−1.26057	+	0.188330i
$895$	7.99993			0.267408
$896$	24.5877	−	17.0718i	0.821417	−	0.570329i
$897$	−34.0796			−1.13789
$898$	−28.8343	+	4.30786i	−0.962214	+	0.143755i
$899$	8.61360	+	32.1464i	0.287280	+	1.07214i
$900$	3.02890	−	0.925700i	0.100963	−	0.0308567i
$901$	−7.81869	−	2.09501i	−0.260478	−	0.0697949i
$902$	−1.00144	−	2.30346i	−0.0333442	−	0.0766968i
$903$	−7.71020	−	10.8924i	−0.256579	−	0.362475i
$904$	−37.8637	+	18.0532i	−1.25933	+	0.600440i
$905$	−4.16167	+	2.40274i	−0.138339	+	0.0798698i
$906$	29.2245	+	3.33117i	0.970918	+	0.110671i
$907$	8.88271	+	33.1507i	0.294946	+	1.10075i	0.941261	+	0.337681i	$0.109643\pi$
$907$	8.88271	+	33.1507i	0.294946	+	1.10075i	−0.646315	+	0.763071i	$0.723691\pi$
$908$	17.5242	+	28.0508i	0.581563	+	0.930899i
$909$	14.3049	+	14.3049i	0.474465	+	0.474465i
$910$	−3.84269	−	15.6563i	−0.127384	−	0.519001i
$911$		−	9.35688i		−	0.310007i	−0.987914	−	0.155004i	$-0.950461\pi$
$911$		−	9.35688i		−	0.310007i	0.987914	−	0.155004i	$-0.0495389\pi$
$912$	−11.5083	−	17.0690i	−0.381078	−	0.565212i
$913$	2.44856	+	1.41368i	0.0810354	+	0.0467858i
$914$	20.1577	−	16.0325i	0.666756	−	0.530308i
$915$	8.67318	+	2.32397i	0.286727	+	0.0768281i
$916$	−30.8922	+	1.07573i	−1.02071	+	0.0355430i
$917$	3.92133	+	3.25637i	0.129494	+	0.107535i
$918$	5.59427	+	12.8677i	0.184638	+	0.424696i
$919$	10.2064	+	17.6780i	0.336679	+	0.583145i	0.983806	−	0.179238i	$-0.0573631\pi$
$919$	10.2064	+	17.6780i	0.336679	+	0.583145i	−0.647127	+	0.762382i	$0.724030\pi$
$920$	12.2064	+	14.2962i	0.402434	+	0.471330i
$921$	4.19675	+	2.42299i	0.138288	+	0.0798404i
$922$	−30.3407	−	22.4533i	−0.999218	−	0.739459i
$923$	12.6914	+	12.6914i	0.417741	+	0.417741i
$924$	−26.8768	+	11.0160i	−0.884182	+	0.362400i
$925$	−6.59624	+	6.59624i	−0.216883	+	0.216883i
$926$	3.89906	+	26.0981i	0.128131	+	0.857635i
$927$	−11.1110	+	19.2449i	−0.364935	+	0.632085i
$928$	−1.23585	+	28.1463i	−0.0405686	+	0.923947i
$929$	20.8897	−	12.0607i	0.685368	−	0.395697i	−0.116507	−	0.993190i	$-0.537170\pi$
$929$	20.8897	−	12.0607i	0.685368	−	0.395697i	0.801874	+	0.597493i	$0.203836\pi$
$930$	10.4641	+	4.12252i	0.343132	+	0.135183i
$931$	−13.0728	−	27.3023i	−0.428443	−	0.894796i
$932$	−9.40113	+	10.0795i	−0.307944	+	0.330165i
$933$	1.24898	−	4.66128i	0.0408899	−	0.152603i
$934$	−9.44831	−	1.07697i	−0.309158	−	0.0352396i
$935$	−4.19444	+	7.26498i	−0.137173	+	0.237590i
$936$	18.9756	−	3.51402i	0.620237	−	0.114859i
$937$	18.9747			0.619878			0.309939	−	0.950756i	$-0.399691\pi$
$937$	18.9747			0.619878			0.309939	+	0.950756i	$0.399691\pi$
$938$	60.4554	+	1.27682i	1.97394	+	0.0416896i
$939$	−0.0865839	+	0.0865839i	−0.00282556	+	0.00282556i
$940$	−10.0453	−	16.0794i	−0.327641	−	0.524451i
$941$	−10.1836	+	2.72869i	−0.331976	+	0.0889526i	−0.420957	−	0.907081i	$-0.638306\pi$
$941$	−10.1836	+	2.72869i	−0.331976	+	0.0889526i	0.0889811	+	0.996033i	$0.471639\pi$
$942$	−2.43086	−	3.05632i	−0.0792016	−	0.0995802i
$943$	1.27961	+	2.21635i	0.0416698	+	0.0721741i
$944$	4.53078	−	5.20999i	0.147464	−	0.169571i
$945$	−1.33138	−	14.3712i	−0.0433099	−	0.467495i
$946$	25.7210	+	10.1332i	0.836263	+	0.329460i
$947$	0.867608	−	3.23796i	0.0281935	−	0.105219i	−0.950395	−	0.311045i	$-0.899321\pi$
$947$	0.867608	−	3.23796i	0.0281935	−	0.105219i	0.978589	+	0.205825i	$0.0659878\pi$
$948$	2.33329	+	1.24093i	0.0757819	+	0.0403035i
$949$	−20.8094	+	5.57586i	−0.675501	+	0.181000i
$950$	4.91588	+	3.63794i	0.159492	+	0.118030i
$951$		−	32.0859i		−	1.04046i
$952$	−11.8790	−	6.64321i	−0.385002	−	0.215308i
$953$			49.2651i			1.59585i	0.602755	+	0.797927i	$0.294070\pi$
$953$			49.2651i			1.59585i	−0.602755	+	0.797927i	$0.705930\pi$
$954$	−5.92910	+	8.01189i	−0.191962	+	0.259395i
$955$	−1.91909	+	0.514220i	−0.0621004	+	0.0166398i
$956$	5.14070	+	16.8204i	0.166262	+	0.544011i
$957$	7.07586	−	26.4075i	0.228730	−	0.853632i
$958$	12.9951	−	32.9851i	0.419851	−	1.06570i
$959$	−6.31421	−	8.92022i	−0.203897	−	0.288049i
$960$	7.39744	+	5.99396i	0.238751	+	0.193454i
$961$	−6.82642	−	11.8237i	−0.220207	−	0.381410i
$962$	−44.4852	+	35.3815i	−1.43426	+	1.14075i
$963$	−11.5622	+	3.09809i	−0.372588	+	0.0998346i
$964$	29.4498	+	6.80207i	0.948513	+	0.219080i
$965$	−5.05087	+	5.05087i	−0.162593	+	0.162593i
$966$	25.9375	−	14.2534i	0.834526	−	0.458597i
$967$	27.3624			0.879916			0.439958	−	0.898018i	$-0.354993\pi$
$967$	27.3624			0.879916			0.439958	+	0.898018i	$0.354993\pi$
$968$	16.4630	−	23.9463i	0.529142	−	0.769663i
$969$	−4.68020	+	8.10635i	−0.150350	+	0.260413i
$970$	1.88517	−	16.5386i	0.0605291	−	0.531024i
$971$	3.08520	−	11.5141i	0.0990089	−	0.369506i	−0.898588	−	0.438794i	$-0.855406\pi$
$971$	3.08520	−	11.5141i	0.0990089	−	0.369506i	0.997597	+	0.0692874i	$0.0220725\pi$
$972$	28.5680	−	0.994797i	0.916321	−	0.0319081i
$973$	−10.9285	−	29.5549i	−0.350353	−	0.947487i
$974$	−2.34154	+	5.94349i	−0.0750279	+	0.190442i
$975$	4.44070	−	2.56384i	0.142216	−	0.0821085i
$976$	−9.81962	−	28.5365i	−0.314318	−	0.913432i
$977$	15.8798	−	27.5046i	0.508040	−	0.879951i	−0.491917	−	0.870642i	$-0.663704\pi$
$977$	15.8798	−	27.5046i	0.508040	−	0.879951i	0.999957	−	0.00930873i	$-0.00296310\pi$
$978$	−15.7464	+	2.35252i	−0.503515	+	0.0752254i
$979$	−34.3239	+	34.3239i	−1.09700	+	1.09700i
$980$	9.47270	+	10.3086i	0.302594	+	0.329297i
$981$	−0.389362	−	0.389362i	−0.0124314	−	0.0124314i
$982$	−3.31644	+	4.48145i	−0.105832	+	0.143009i
$983$	−25.3848	−	14.6559i	−0.809648	−	0.467450i	0.0371857	−	0.999308i	$-0.488161\pi$
$983$	−25.3848	−	14.6559i	−0.809648	−	0.467450i	−0.846834	+	0.531858i	$0.821494\pi$
$984$	0.841667	+	0.985760i	0.0268314	+	0.0314249i
$985$	−8.36153	−	14.4826i	−0.266421	−	0.461454i
$986$	11.7480	−	5.10749i	0.374133	−	0.162656i
$987$	−27.9966	+	10.3523i	−0.891141	+	0.329518i
$988$	27.2501	+	25.4162i	0.866942	+	0.808597i
$989$	−27.2080	−	7.29035i	−0.865163	−	0.231820i
$990$	6.42996	+	8.08439i	0.204358	+	0.256939i
$991$	5.89119	+	3.40128i	0.187140	+	0.108045i	0.590643	−	0.806933i	$-0.298874\pi$
$991$	5.89119	+	3.40128i	0.187140	+	0.108045i	−0.403503	+	0.914978i	$0.632208\pi$
$992$	−8.17246	−	36.9067i	−0.259476	−	1.17179i
$993$			10.1133i			0.320936i
$994$	−14.9672	−	4.35119i	−0.474732	−	0.138011i
$995$	−16.3587	−	16.3587i	−0.518607	−	0.518607i
$996$	−1.42165	−	0.328360i	−0.0450466	−	0.0104045i
$997$	13.6210	+	50.8342i	0.431381	+	1.60994i	0.749581	+	0.661912i	$0.230255\pi$
$997$	13.6210	+	50.8342i	0.431381	+	1.60994i	−0.318201	+	0.948023i	$0.603079\pi$
$998$	0.322572	−	2.82993i	0.0102108	−	0.0895800i
$999$	−44.0699	+	25.4438i	−1.39431	+	0.805005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cq.a.171.5	yes	256
7.5	odd	6	inner	560.2.cq.a.411.46	yes	256
16.3	odd	4	inner	560.2.cq.a.451.46	yes	256
112.19	even	12	inner	560.2.cq.a.131.5	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.5	✓	256	112.19	even	12	inner
560.2.cq.a.171.5	yes	256	1.1	even	1	trivial
560.2.cq.a.411.46	yes	256	7.5	odd	6	inner
560.2.cq.a.451.46	yes	256	16.3	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39869 + 0.208965i) q^{2} +(0.308027 + 1.14957i) q^{3} +(1.91267 - 0.584555i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.671056 - 1.54353i) q^{6} +(-2.40355 - 1.10587i) q^{7} +(-2.55308 + 1.21729i) q^{8} +(1.37144 - 0.791800i) q^{9} +(-1.40511 - 0.160163i) q^{10} +(-1.19377 - 4.45522i) q^{11} +(1.26114 + 2.01869i) q^{12} +(-3.04658 - 3.04658i) q^{13} +(3.59291 + 1.04451i) q^{14} +1.19013i q^{15} +(3.31659 - 2.23612i) q^{16} +(-1.57510 - 0.909386i) q^{17} +(-1.75276 + 1.39406i) q^{18} +(-4.17703 - 1.11923i) q^{19} +(1.99879 - 0.0696019i) q^{20} +(0.530919 - 3.10370i) q^{21} +(2.60070 + 5.98202i) q^{22} +(-3.32310 - 5.75579i) q^{23} +(-2.18578 - 2.55999i) q^{24} +(0.866025 + 0.500000i) q^{25} +(4.89785 + 3.62459i) q^{26} +(3.85731 + 3.85731i) q^{27} +(-5.24363 - 0.710153i) q^{28} +(3.52167 - 3.52167i) q^{29} +(-0.248695 - 1.66462i) q^{30} +(-3.34114 + 5.78702i) q^{31} +(-4.17161 + 3.82069i) q^{32} +(4.75389 - 2.74466i) q^{33} +(2.39311 + 0.942807i) q^{34} +(-2.03543 - 1.69027i) q^{35} +(2.16025 - 2.31613i) q^{36} +(-2.41439 + 9.01063i) q^{37} +(6.07625 + 0.692604i) q^{38} +(2.56384 - 4.44070i) q^{39} +(-2.78114 + 0.515028i) q^{40} -0.385064 q^{41} +(-0.0940273 + 4.45205i) q^{42} +(2.99684 - 2.99684i) q^{43} +(-4.88761 - 7.82353i) q^{44} +(1.52964 - 0.409866i) q^{45} +(5.85075 + 7.35615i) q^{46} +(-4.73982 - 8.20960i) q^{47} +(3.59218 + 3.12388i) q^{48} +(4.55411 + 5.31602i) q^{49} +(-1.31578 - 0.518376i) q^{50} +(0.560231 - 2.09081i) q^{51} +(-7.60799 - 4.04620i) q^{52} +(4.29888 - 1.15188i) q^{53} +(-6.20123 - 4.58914i) q^{54} -4.61239i q^{55} +(7.48261 - 0.102452i) q^{56} -5.14656i q^{57} +(-4.18982 + 5.66164i) q^{58} +(1.66731 - 0.446753i) q^{59} +(0.695694 + 2.27632i) q^{60} +(1.95271 - 7.28761i) q^{61} +(3.46393 - 8.79243i) q^{62} +(-4.17194 + 0.386500i) q^{63} +(5.03640 - 6.21568i) q^{64} +(-2.15426 - 3.73128i) q^{65} +(-6.07568 + 4.83233i) q^{66} +(15.6103 - 4.18277i) q^{67} +(-3.54423 - 0.818619i) q^{68} +(5.59309 - 5.59309i) q^{69} +(3.20014 + 1.93883i) q^{70} -4.16577 q^{71} +(-2.53753 + 3.69096i) q^{72} +(2.50010 - 4.33030i) q^{73} +(1.49408 - 13.1076i) q^{74} +(-0.308027 + 1.14957i) q^{75} +(-8.64352 + 0.300985i) q^{76} +(-2.05760 + 12.0285i) q^{77} +(-2.65806 + 6.74691i) q^{78} +(0.961534 - 0.555142i) q^{79} +(3.78233 - 1.30153i) q^{80} +(-0.870708 + 1.50811i) q^{81} +(0.538585 - 0.0804649i) q^{82} +(-0.433450 + 0.433450i) q^{83} +(-0.798809 - 6.24669i) q^{84} +(-1.28607 - 1.28607i) q^{85} +(-3.56541 + 4.81788i) q^{86} +(5.13320 + 2.96365i) q^{87} +(8.47110 + 9.92135i) q^{88} +(-5.26207 - 9.11416i) q^{89} +(-2.05384 + 0.892916i) q^{90} +(3.95349 + 10.6917i) q^{91} +(-9.72056 - 9.06637i) q^{92} +(-7.68177 - 2.05832i) q^{93} +(8.34505 + 10.4922i) q^{94} +(-3.74502 - 2.16219i) q^{95} +(-5.67713 - 3.61870i) q^{96} +11.7703i q^{97} +(-7.48065 - 6.48382i) q^{98} +(-5.16483 - 5.16483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more