LMFDB - Embedded newform 560.2.cq.a.411.46

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			411.46
Character	$\chi$	$=$	560.411
Dual form			560.2.cq.a.451.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.880314 + 1.10682i) q^{2} +(1.14957 + 0.308027i) q^{3} +(-0.450094 + 1.94870i) q^{4} +(0.258819 + 0.965926i) 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} +(-0.841263 + 1.13678i) q^{10} +(4.45522 + 1.19377i) q^{11} +(-1.11767 + 2.10153i) q^{12} +(3.04658 + 3.04658i) q^{13} +(-3.33988 - 1.68678i) q^{14} +1.19013i q^{15} +(-3.59483 - 1.75419i) q^{16} +(-1.57510 + 0.909386i) q^{17} +(-0.330917 - 2.21496i) q^{18} +(-1.11923 - 4.17703i) q^{19} +(-1.99879 + 0.0696019i) q^{20} +(-3.10370 + 0.530919i) q^{21} +(2.60070 + 5.98202i) q^{22} +(-3.32310 + 5.75579i) q^{23} +(-3.30991 + 0.612949i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.690064 + 6.05396i) q^{26} +(-3.85731 - 3.85731i) q^{27} +(-1.07318 - 5.18153i) q^{28} +(3.52167 - 3.52167i) q^{29} +(-1.31725 + 1.04768i) q^{30} +(3.34114 + 5.78702i) q^{31} +(-1.22301 - 5.52307i) q^{32} +(4.75389 + 2.74466i) q^{33} +(-2.39311 - 0.942807i) q^{34} +(-1.69027 - 2.03543i) q^{35} +(2.16025 - 2.31613i) q^{36} +(9.01063 - 2.41439i) q^{37} +(3.63794 - 4.91588i) q^{38} +(2.56384 + 4.44070i) q^{39} +(-1.83660 - 2.15102i) q^{40} +0.385064 q^{41} +(-3.31986 - 2.96785i) q^{42} +(2.99684 - 2.99684i) q^{43} +(-4.33157 + 8.14456i) q^{44} +(0.409866 - 1.52964i) q^{45} +(-9.29599 + 1.38883i) 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} +(-2.09081 + 0.560231i) q^{51} +(-7.30811 + 4.56561i) q^{52} +(-1.15188 + 4.29888i) q^{53} +(0.873698 - 7.66499i) q^{54} +4.61239i q^{55} +(4.79028 - 5.74919i) q^{56} -5.14656i q^{57} +(6.99803 + 0.797675i) q^{58} +(0.446753 - 1.66731i) q^{59} +(-2.31919 - 0.535669i) q^{60} +(7.28761 - 1.95271i) 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} +(1.14708 + 7.67786i) q^{66} +(-4.18277 + 15.6103i) q^{67} +(-1.06317 - 3.47870i) q^{68} +(-5.59309 + 5.59309i) q^{69} +(0.764882 - 3.66264i) q^{70} -4.16577 q^{71} +(4.46524 + 0.352086i) q^{72} +(-2.50010 - 4.33030i) q^{73} +(10.6045 + 7.84771i) q^{74} +(-1.14957 + 0.308027i) q^{75} +(8.64352 - 0.300985i) q^{76} +(-12.0285 + 2.05760i) q^{77} +(-2.65806 + 6.74691i) q^{78} +(-0.961534 - 0.555142i) q^{79} +(0.764010 - 3.92636i) q^{80} +(-0.870708 - 1.50811i) q^{81} +(0.338977 + 0.426196i) q^{82} +(0.433450 - 0.433450i) q^{83} +(0.362356 - 6.28712i) q^{84} +(-1.28607 - 1.28607i) q^{85} +(5.95512 + 0.678797i) q^{86} +(5.13320 - 2.96365i) q^{87} +(-12.8277 + 2.37551i) q^{88} +(5.26207 - 9.11416i) q^{89} +(2.05384 - 0.892916i) q^{90} +(-10.6917 - 3.95349i) q^{91} +(-9.72056 - 9.06637i) q^{92} +(2.05832 + 7.68177i) q^{93} +(13.2591 - 1.98091i) q^{94} +(3.74502 - 2.16219i) q^{95} +(0.295320 - 6.72589i) q^{96} -11.7703i q^{97} +(9.89292 + 0.360797i) 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.880314	+	1.10682i	0.622476	+	0.782639i
$2$	0.880314	+	1.10682i	0.622476	+	0.782639i
$3$	1.14957	+	0.308027i	0.663707	+	0.177840i	0.574918	−	0.818211i	$-0.305034\pi$
$3$	1.14957	+	0.308027i	0.663707	+	0.177840i	0.0887884	+	0.996051i	$0.471700\pi$
$4$	−0.450094	+	1.94870i	−0.225047	+	0.974348i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$6$	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
$10$	−0.841263	+	1.13678i	−0.266031	+	0.359483i
$11$	4.45522	+	1.19377i	1.34330	+	0.359936i	0.857658	−	0.514221i	$-0.171919\pi$
$11$	4.45522	+	1.19377i	1.34330	+	0.359936i	0.485643	+	0.874158i	$0.338586\pi$
$12$	−1.11767	+	2.10153i	−0.322643	+	0.606659i
$13$	3.04658	+	3.04658i	0.844969	+	0.844969i	0.989500	−	0.144531i	$-0.0461674\pi$
$13$	3.04658	+	3.04658i	0.844969	+	0.844969i	−0.144531	+	0.989500i	$0.546167\pi$
$14$	−3.33988	−	1.68678i	−0.892619	−	0.450811i
$15$			1.19013i			0.307289i
$16$	−3.59483	−	1.75419i	−0.898708	−	0.438548i
$17$	−1.57510	+	0.909386i	−0.382018	+	0.220558i	−0.678696	−	0.734419i	$-0.737455\pi$
$17$	−1.57510	+	0.909386i	−0.382018	+	0.220558i	0.296678	+	0.954978i	$0.404121\pi$
$18$	−0.330917	−	2.21496i	−0.0779979	−	0.522072i
$19$	−1.11923	−	4.17703i	−0.256769	−	0.958276i	−0.967098	−	0.254405i	$-0.918120\pi$
$19$	−1.11923	−	4.17703i	−0.256769	−	0.958276i	0.710328	−	0.703870i	$-0.248546\pi$
$20$	−1.99879	+	0.0696019i	−0.446943	+	0.0155634i
$21$	−3.10370	+	0.530919i	−0.677282	+	0.115856i
$22$	2.60070	+	5.98202i	0.554472	+	1.27537i
$23$	−3.32310	+	5.75579i	−0.692915	+	1.20016i	0.277963	+	0.960592i	$0.410341\pi$
$23$	−3.32310	+	5.75579i	−0.692915	+	1.20016i	−0.970878	+	0.239573i	$0.922993\pi$
$24$	−3.30991	+	0.612949i	−0.675632	+	0.125118i
$25$	−0.866025	+	0.500000i	−0.173205	+	0.100000i
$26$	−0.690064	+	6.05396i	−0.135333	+	1.18728i
$27$	−3.85731	−	3.85731i	−0.742340	−	0.742340i
$28$	−1.07318	−	5.18153i	−0.202812	−	0.979218i
$29$	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	$0.0969818\pi$
$30$	−1.31725	+	1.04768i	−0.240497	+	0.191280i
$31$	3.34114	+	5.78702i	0.600086	+	1.03938i	0.992807	+	0.119722i	$0.0382004\pi$
$31$	3.34114	+	5.78702i	0.600086	+	1.03938i	−0.392721	+	0.919658i	$0.628466\pi$
$32$	−1.22301	−	5.52307i	−0.216199	−	0.976349i
$33$	4.75389	+	2.74466i	0.827546	+	0.477784i
$34$	−2.39311	−	0.942807i	−0.410415	−	0.161690i
$35$	−1.69027	−	2.03543i	−0.285708	−	0.344051i
$36$	2.16025	−	2.31613i	0.360042	−	0.386022i
$37$	9.01063	−	2.41439i	1.48134	−	0.396924i	0.574536	−	0.818479i	$-0.305182\pi$
$37$	9.01063	−	2.41439i	1.48134	−	0.396924i	0.906803	+	0.421556i	$0.138516\pi$
$38$	3.63794	−	4.91588i	0.590151	−	0.797461i
$39$	2.56384	+	4.44070i	0.410543	+	0.711081i
$40$	−1.83660	−	2.15102i	−0.290392	−	0.340107i
$41$	0.385064			0.0601369			0.0300684	−	0.999548i	$-0.490427\pi$
$41$	0.385064			0.0601369			0.0300684	+	0.999548i	$0.490427\pi$
$42$	−3.31986	−	2.96785i	−0.512265	−	0.457950i
$43$	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	$0.145256\pi$
$44$	−4.33157	+	8.14456i	−0.653009	+	1.22784i
$45$	0.409866	−	1.52964i	0.0610992	−	0.228025i
$46$	−9.29599	+	1.38883i	−1.37062	+	0.204771i
$47$	4.73982	−	8.20960i	0.691373	−	1.19749i	−0.280015	−	0.959996i	$-0.590339\pi$
$47$	4.73982	−	8.20960i	0.691373	−	1.19749i	0.971388	−	0.237498i	$-0.0763272\pi$
$48$	−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
$51$	−2.09081	+	0.560231i	−0.292772	+	0.0784481i
$52$	−7.30811	+	4.56561i	−1.01345	+	0.633136i
$53$	−1.15188	+	4.29888i	−0.158223	+	0.590497i	0.840585	+	0.541680i	$0.182212\pi$
$53$	−1.15188	+	4.29888i	−0.158223	+	0.590497i	−0.998808	+	0.0488167i	$0.984455\pi$
$54$	0.873698	−	7.66499i	0.118895	−	1.04307i
$55$			4.61239i			0.621934i
$56$	4.79028	−	5.74919i	0.640128	−	0.768268i
$57$		−	5.14656i		−	0.681678i
$58$	6.99803	+	0.797675i	0.918887	+	0.104740i
$59$	0.446753	−	1.66731i	0.0581623	−	0.217065i	−0.930728	−	0.365712i	$-0.880825\pi$
$59$	0.446753	−	1.66731i	0.0581623	−	0.217065i	0.988890	+	0.148648i	$0.0474921\pi$
$60$	−2.31919	−	0.535669i	−0.299407	−	0.0691546i
$61$	7.28761	−	1.95271i	0.933083	−	0.250019i	0.239914	−	0.970794i	$-0.422881\pi$
$61$	7.28761	−	1.95271i	0.933083	−	0.250019i	0.693169	+	0.720775i	$0.256214\pi$
$62$	−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
$66$	1.14708	+	7.67786i	0.141195	+	0.945079i
$67$	−4.18277	+	15.6103i	−0.511007	+	1.90710i	−0.101388	+	0.994847i	$0.532329\pi$
$67$	−4.18277	+	15.6103i	−0.511007	+	1.90710i	−0.409618	+	0.912257i	$0.634338\pi$
$68$	−1.06317	−	3.47870i	−0.128928	−	0.421855i
$69$	−5.59309	+	5.59309i	−0.673329	+	0.673329i
$70$	0.764882	−	3.66264i	0.0914209	−	0.437770i
$71$	−4.16577			−0.494386			−0.247193	−	0.968966i	$-0.579508\pi$
$71$	−4.16577			−0.494386			−0.247193	+	0.968966i	$0.579508\pi$
$72$	4.46524	+	0.352086i	0.526233	+	0.0414938i
$73$	−2.50010	−	4.33030i	−0.292615	−	0.506824i	0.681812	−	0.731527i	$-0.261192\pi$
$73$	−2.50010	−	4.33030i	−0.292615	−	0.506824i	−0.974427	+	0.224703i	$0.927859\pi$
$74$	10.6045	+	7.84771i	1.23275	+	0.912278i
$75$	−1.14957	+	0.308027i	−0.132741	+	0.0355679i
$76$	8.64352	−	0.300985i	0.991479	−	0.0345253i
$77$	−12.0285	+	2.05760i	−1.37078	+	0.234485i
$78$	−2.65806	+	6.74691i	−0.300966	+	0.763937i
$79$	−0.961534	−	0.555142i	−0.108181	−	0.0624584i	0.444933	−	0.895564i	$-0.353227\pi$
$79$	−0.961534	−	0.555142i	−0.108181	−	0.0624584i	−0.553114	+	0.833105i	$0.686561\pi$
$80$	0.764010	−	3.92636i	0.0854190	−	0.438980i
$81$	−0.870708	−	1.50811i	−0.0967453	−	0.167568i
$82$	0.338977	+	0.426196i	0.0374338	+	0.0470655i
$83$	0.433450	−	0.433450i	0.0475773	−	0.0475773i	−0.682918	−	0.730495i	$-0.739289\pi$
$83$	0.433450	−	0.433450i	0.0475773	−	0.0475773i	0.730495	+	0.682918i	$0.239289\pi$
$84$	0.362356	−	6.28712i	0.0395363	−	0.685981i
$85$	−1.28607	−	1.28607i	−0.139493	−	0.139493i
$86$	5.95512	+	0.678797i	0.642157	+	0.0731966i
$87$	5.13320	−	2.96365i	0.550336	−	0.317737i
$88$	−12.8277	+	2.37551i	−1.36744	+	0.253230i
$89$	5.26207	−	9.11416i	0.557778	−	0.966099i	−0.439904	−	0.898045i	$-0.644987\pi$
$89$	5.26207	−	9.11416i	0.557778	−	0.966099i	0.997682	−	0.0680546i	$-0.0216792\pi$
$90$	2.05384	−	0.892916i	0.216494	−	0.0941216i
$91$	−10.6917	−	3.95349i	−1.12080	−	0.414438i
$92$	−9.72056	−	9.06637i	−1.01344	−	0.945234i
$93$	2.05832	+	7.68177i	0.213438	+	0.796563i
$94$	13.2591	−	1.98091i	1.36757	−	0.204315i
$95$	3.74502	−	2.16219i	0.384231	−	0.221836i
$96$	0.295320	−	6.72589i	0.0301410	−	0.686458i
$97$		−	11.7703i		−	1.19509i	−0.801834	−	0.597547i	$-0.796142\pi$
$97$		−	11.7703i		−	1.19509i	0.801834	−	0.597547i	$-0.203858\pi$
$98$	9.89292	+	0.360797i	0.999336	+	0.0364460i
$99$	−5.16483	−	5.16483i	−0.519085	−	0.519085i
$100$	−0.584555	−	1.91267i	−0.0584555	−	0.191267i
$101$	12.3396	+	3.30637i	1.22783	+	0.328997i	0.813735	−	0.581236i	$-0.197431\pi$
$101$	12.3396	+	3.30637i	1.22783	+	0.328997i	0.414097	+	0.910233i	$0.364097\pi$
$102$	−2.46065	−	1.82097i	−0.243640	−	0.180303i
$103$	−12.1526	−	7.01633i	−1.19743	−	0.691339i	−0.237452	−	0.971399i	$-0.576312\pi$
$103$	−12.1526	−	7.01633i	−1.19743	−	0.691339i	−0.959982	+	0.280060i	$0.909646\pi$
$104$	−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
$107$	1.95636	+	7.30124i	0.189129	+	0.705837i	0.993709	+	0.111994i	$0.0357236\pi$
$107$	1.95636	+	7.30124i	0.189129	+	0.705837i	−0.804580	+	0.593844i	$0.797610\pi$
$108$	9.25288	−	5.78057i	0.890359	−	0.556236i
$109$	0.335867	+	0.0899952i	0.0321702	+	0.00861998i	0.274868	−	0.961482i	$-0.411366\pi$
$109$	0.335867	+	0.0899952i	0.0321702	+	0.00861998i	−0.242698	+	0.970102i	$0.578032\pi$
$110$	−5.10507	+	4.06035i	−0.486750	+	0.387139i
$111$	11.1021			1.05376
$112$	10.5803	+	0.240880i	0.999741	+	0.0227610i
$113$	14.8306			1.39515			0.697573	−	0.716514i	$-0.254263\pi$
$113$	14.8306			1.39515			0.697573	+	0.716514i	$0.254263\pi$
$114$	5.69630	−	4.53059i	0.533508	−	0.424328i
$115$	−6.41974	−	1.72017i	−0.598644	−	0.160406i
$116$	5.27759	+	8.44776i	0.490011	+	0.784354i
$117$	−1.76591	−	6.59047i	−0.163259	−	0.609289i
$118$	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
$122$	8.57668	+	6.34707i	0.776497	+	0.574636i
$123$	0.442659	+	0.118610i	0.0399133	+	0.0106947i
$124$	−12.7810	+	3.90616i	−1.14777	+	0.350783i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	3.24484	+	4.95783i	0.289073	+	0.441678i
$127$			14.1753i			1.25786i	0.777463	+	0.628929i	$0.216506\pi$
$127$			14.1753i			1.25786i	−0.777463	+	0.628929i	$0.783494\pi$
$128$	11.3132	+	0.102635i	0.999959	+	0.00907171i
$129$	4.36820	−	2.52198i	0.384598	−	0.222048i
$130$	−6.02628	+	0.900329i	−0.528539	+	0.0789641i
$131$	−0.498624	−	1.86089i	−0.0435650	−	0.162587i	0.940716	−	0.339194i	$-0.110154\pi$
$131$	−0.498624	−	1.86089i	−0.0435650	−	0.162587i	−0.984281	+	0.176607i	$0.943488\pi$
$132$	−7.48821	+	8.02853i	−0.651765	+	0.698794i
$133$	7.30938	+	8.80197i	0.633803	+	0.763228i
$134$	−20.9599	+	9.11241i	−1.81066	+	0.787193i
$135$	2.72753	−	4.72422i	0.234749	−	0.406596i
$136$	2.91437	−	4.23909i	0.249905	−	0.363499i
$137$	−3.57730	+	2.06536i	−0.305630	+	0.176455i	−0.644969	−	0.764209i	$-0.723130\pi$
$137$	−3.57730	+	2.06536i	−0.305630	+	0.176455i	0.339339	+	0.940664i	$0.389796\pi$
$138$	−11.1142	−	1.26686i	−0.946105	−	0.107842i
$139$	−8.42160	−	8.42160i	−0.714311	−	0.714311i	0.253123	−	0.967434i	$-0.418542\pi$
$139$	−8.42160	−	8.42160i	−0.714311	−	0.714311i	−0.967434	+	0.253123i	$0.918542\pi$
$140$	4.72722	−	2.37769i	0.399523	−	0.200952i
$141$	7.97755	−	7.97755i	0.671831	−	0.671831i
$142$	−3.66719	−	4.61075i	−0.307743	−	0.386926i
$143$	9.93626	+	17.2101i	0.830912	+	1.43918i
$144$	3.54111	+	5.25215i	0.295093	+	0.437679i
$145$	4.31315	+	2.49020i	0.358188	+	0.206800i
$146$	2.59199	−	6.57919i	0.214514	−	0.544497i
$147$	6.87276	−	4.70837i	0.566856	−	0.388340i
$148$	0.649281	+	18.6457i	0.0533705	+	1.53267i
$149$	−21.8709	+	5.86028i	−1.79173	+	0.480093i	−0.992639	−	0.121114i	$-0.961353\pi$
$149$	−21.8709	+	5.86028i	−1.79173	+	0.480093i	−0.799093	+	0.601207i	$0.794687\pi$
$150$	−1.35292	−	1.00121i	−0.110465	−	0.0817483i
$151$	−8.73800	−	15.1347i	−0.711088	−	1.23164i	−0.964449	−	0.264269i	$-0.914869\pi$
$151$	−8.73800	−	15.1347i	−0.711088	−	1.23164i	0.253361	−	0.967372i	$-0.418464\pi$
$152$	7.94214	+	9.30184i	0.644193	+	0.754479i
$153$	2.88020			0.232851
$154$	−12.8663	−	11.5020i	−1.03679	−	0.926861i
$155$	−4.72508	+	4.72508i	−0.379528	+	0.379528i
$156$	−9.80754	+	2.99741i	−0.785232	+	0.239985i
$157$	0.600517	−	2.24116i	0.0479265	−	0.178864i	−0.937814	−	0.347139i	$-0.887153\pi$
$157$	0.600517	−	2.24116i	0.0479265	−	0.178864i	0.985740	+	0.168275i	$0.0538198\pi$
$158$	−0.232011	−	1.55294i	−0.0184578	−	0.123546i
$159$	−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
$163$	−9.13716	+	2.44829i	−0.715677	+	0.191765i	−0.598242	−	0.801315i	$-0.704134\pi$
$163$	−9.13716	+	2.44829i	−0.715677	+	0.191765i	−0.117435	+	0.993081i	$0.537467\pi$
$164$	−0.173315	+	0.750372i	−0.0135336	+	0.0585942i
$165$	−1.42074	+	5.30228i	−0.110605	+	0.412782i
$166$	0.861323	+	0.0981784i	0.0668516	+	0.00762012i
$167$			8.47531i			0.655840i	0.944706	+	0.327920i	$0.106348\pi$
$167$			8.47531i			0.655840i	−0.944706	+	0.327920i	$0.893652\pi$
$168$	7.27769	−	5.13358i	0.561486	−	0.396064i
$169$			5.56330i			0.427946i
$170$	0.291299	−	2.55558i	0.0223417	−	0.196004i
$171$	−1.77241	+	6.61474i	−0.135540	+	0.505842i
$172$	4.49107	+	7.18879i	0.342441	+	0.548140i
$173$	22.3090	−	5.97768i	1.69612	−	0.454475i	0.724164	−	0.689628i	$-0.242226\pi$
$173$	22.3090	−	5.97768i	1.69612	−	0.454475i	0.971958	+	0.235153i	$0.0755591\pi$
$174$	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
$178$	14.7200	−	2.19918i	1.10331	−	0.164835i
$179$	−2.07053	+	7.72734i	−0.154759	+	0.577568i	0.844367	+	0.535765i	$0.179977\pi$
$179$	−2.07053	+	7.72734i	−0.154759	+	0.577568i	−0.999126	+	0.0418030i	$0.986690\pi$
$180$	2.79632	+	1.48719i	0.208426	+	0.110848i
$181$	3.39799	−	3.39799i	0.252571	−	0.252571i	−0.569453	−	0.822024i	$-0.692845\pi$
$181$	3.39799	−	3.39799i	0.252571	−	0.252571i	0.822024	+	0.569453i	$0.192845\pi$
$182$	−5.03628	−	15.3141i	−0.373314	−	1.13516i
$183$	8.97914			0.663757
$184$	1.47767	−	18.7402i	0.108935	−	1.38154i
$185$	4.66425	+	8.07871i	0.342922	+	0.593959i
$186$	−6.69036	+	9.04056i	−0.490561	+	0.662886i
$187$	−8.10303	+	2.17120i	−0.592552	+	0.158774i
$188$	13.8647	+	12.9316i	1.01118	+	0.943130i
$189$	13.5369	+	5.00556i	0.984666	+	0.364101i
$190$	5.68994	+	2.24165i	0.412792	+	0.162627i
$191$	1.72061	+	0.993396i	0.124499	+	0.0718796i	0.560956	−	0.827845i	$-0.310434\pi$
$191$	1.72061	+	0.993396i	0.124499	+	0.0718796i	−0.436457	+	0.899725i	$0.643767\pi$
$192$	7.70432	−	5.59403i	0.556011	−	0.403714i
$193$	−3.57150	−	6.18602i	−0.257082	−	0.445280i	0.708377	−	0.705835i	$-0.249428\pi$
$193$	−3.57150	−	6.18602i	−0.257082	−	0.445280i	−0.965459	+	0.260555i	$0.916094\pi$
$194$	13.0276	−	10.3616i	0.935327	−	0.743918i
$195$	−3.62582	+	3.62582i	−0.259650	+	0.259650i
$196$	8.30954	+	11.2673i	0.593538	+	0.804806i
$197$	−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	$0.953139\pi$
$198$	1.16986	−	10.2632i	0.0831381	−	0.729374i
$199$	−20.0353	+	11.5674i	−1.42026	+	0.819989i	−0.996321	−	0.0857006i	$-0.972687\pi$
$199$	−20.0353	+	11.5674i	−1.42026	+	0.819989i	−0.423942	+	0.905690i	$0.639354\pi$
$200$	1.60238	−	2.33074i	0.113306	−	0.164808i
$201$	−9.61681	+	16.6568i	−0.678318	+	1.17488i
$202$	7.20313	+	16.5683i	0.506810	+	1.16574i
$203$	−4.57001	+	12.3590i	−0.320752	+	0.867434i
$204$	−0.150658	−	4.32651i	−0.0105482	−	0.302916i
$205$	0.0996619	+	0.371943i	0.00696069	+	0.0259776i
$206$	−2.93233	−	19.6273i	−0.204305	−	1.36750i
$207$	9.11486	−	5.26247i	0.633526	−	0.365767i
$208$	−5.60765	−	16.2962i	−0.388820	−	1.12994i
$209$		−	19.9457i		−	1.37967i
$210$	2.00748	−	3.97487i	0.138529	−	0.274292i
$211$	−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	$-0.574721\pi$
$212$	−7.85876	−	4.17957i	−0.539742	−	0.287054i
$213$	−4.78886	−	1.28317i	−0.328127	−	0.0879215i
$214$	−6.35893	+	8.59272i	−0.434688	+	0.587386i
$215$	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
$219$	−1.54020	−	5.74810i	−0.104077	−	0.388421i
$220$	−8.98814	−	2.07601i	−0.605980	−	0.139964i
$221$	−7.56919	−	2.02816i	−0.509159	−	0.136429i
$222$	9.77332	+	12.2880i	0.655942	+	0.824716i
$223$	−13.8892			−0.930091			−0.465046	−	0.885287i	$-0.653962\pi$
$223$	−13.8892			−0.930091			−0.465046	+	0.885287i	$0.653962\pi$
$224$	9.04734	+	11.9225i	0.604501	+	0.796604i
$225$	1.58360			0.105573
$226$	13.0556	+	16.4148i	0.868445	+	1.09190i
$227$	15.9739	+	4.28020i	1.06023	+	0.284087i	0.746472	−	0.665417i	$-0.231746\pi$
$227$	15.9739	+	4.28020i	1.06023	+	0.284087i	0.313755	+	0.949504i	$0.398413\pi$
$228$	10.0291	+	2.31644i	0.664191	+	0.153410i
$229$	−4.00016	−	14.9288i	−0.264338	−	0.986523i	−0.962654	−	0.270734i	$-0.912734\pi$
$229$	−4.00016	−	14.9288i	−0.264338	−	0.986523i	0.698316	−	0.715789i	$-0.253933\pi$
$230$	−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	$-0.260853\pi$
$233$	5.96831	+	3.44581i	0.390997	+	0.225742i	−0.291595	+	0.956542i	$0.594186\pi$
$234$	5.73990	−	7.75623i	0.375229	−	0.507041i
$235$	9.15662	+	2.45351i	0.597312	+	0.160049i
$236$	3.04799	+	1.62103i	0.198407	+	0.105520i
$237$	−0.934356	−	0.934356i	−0.0606929	−	0.0606929i
$238$	6.79458	−	0.380382i	0.440427	−	0.0246565i
$239$			8.79422i			0.568850i	0.958698	+	0.284425i	$0.0918028\pi$
$239$			8.79422i			0.568850i	−0.958698	+	0.284425i	$0.908197\pi$
$240$	2.08771	−	4.27830i	0.134761	−	0.276163i
$241$	13.0878	−	7.55627i	0.843062	−	0.486742i	−0.0152416	−	0.999884i	$-0.504852\pi$
$241$	13.0878	−	7.55627i	0.843062	−	0.486742i	0.858304	+	0.513142i	$0.171518\pi$
$242$	2.14693	+	14.3703i	0.138010	+	0.923757i
$243$	3.69922	+	13.8057i	0.237305	+	0.885634i
$244$	0.525125	+	15.0802i	0.0336177	+	0.965414i
$245$	6.31358	+	3.02304i	0.403360	+	0.193135i
$246$	0.258399	+	0.594358i	0.0164749	+	0.0378949i
$247$	9.31582	−	16.1355i	0.592751	−	1.02668i
$248$	−15.5747	−	10.7076i	−0.988993	−	0.679932i
$249$	0.631797	−	0.364768i	0.0400385	−	0.0231163i
$250$	0.160163	−	1.40511i	0.0101296	−	0.0888673i
$251$	−17.8247	−	17.8247i	−1.12508	−	1.12508i	−0.990965	−	0.134118i	$-0.957180\pi$
$251$	−17.8247	−	17.8247i	−1.12508	−	1.12508i	−0.134118	−	0.990965i	$-0.542820\pi$
$252$	−2.63094	+	7.95589i	−0.165734	+	0.501174i
$253$	−21.6763	+	21.6763i	−1.36278	+	1.36278i
$254$	−15.6895	+	12.4787i	−0.984448	+	0.782986i
$255$	−1.08228	−	1.87457i	−0.0677752	−	0.117390i
$256$	9.84561	+	12.6121i	0.615351	+	0.788254i
$257$	−9.42158	−	5.43955i	−0.587702	−	0.339310i	0.176486	−	0.984303i	$-0.443527\pi$
$257$	−9.42158	−	5.43955i	−0.587702	−	0.339310i	−0.764188	+	0.644993i	$0.776860\pi$
$258$	6.63676	+	2.61467i	0.413186	+	0.162782i
$259$	−18.9875	+	15.7677i	−1.17983	+	0.979757i
$260$	−6.30152	−	5.87742i	−0.390803	−	0.364502i
$261$	−7.61821	+	2.04129i	−0.471556	+	0.126353i
$262$	1.62072	−	2.19005i	0.100129	−	0.135302i
$263$	12.3446	+	21.3815i	0.761201	+	1.31844i	0.942232	+	0.334961i	$0.108723\pi$
$263$	12.3446	+	21.3815i	0.761201	+	1.31844i	−0.181031	+	0.983477i	$0.557943\pi$
$264$	−15.4781	−	1.22046i	−0.952611	−	0.0751139i
$265$	−4.45053			−0.273394
$266$	−3.30764	+	15.8387i	−0.202804	+	0.971130i
$267$	8.85654	−	8.85654i	0.542012	−	0.542012i
$268$	−28.5371	−	15.1771i	−1.74318	−	0.927087i
$269$	−1.65969	+	6.19406i	−0.101193	+	0.377659i	−0.997886	−	0.0649959i	$-0.979297\pi$
$269$	−1.65969	+	6.19406i	−0.101193	+	0.377659i	0.896692	+	0.442655i	$0.145963\pi$
$270$	7.62994	−	1.13992i	0.464343	−	0.0693732i
$271$	−0.129755	+	0.224743i	−0.00788207	+	0.0136521i	−0.869940	−	0.493158i	$-0.835842\pi$
$271$	−0.129755	+	0.224743i	−0.00788207	+	0.0136521i	0.862057	+	0.506811i	$0.169176\pi$
$272$	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
$275$	−4.45522	+	1.19377i	−0.268660	+	0.0719872i
$276$	−8.38182	−	13.4167i	−0.504526	−	0.807588i
$277$	−2.81276	+	10.4974i	−0.169002	+	0.630725i	0.828494	+	0.559999i	$0.189198\pi$
$277$	−2.81276	+	10.4974i	−0.169002	+	0.630725i	−0.997496	+	0.0707262i	$0.977468\pi$
$278$	1.90753	−	16.7348i	0.114406	−	1.00369i
$279$		−	10.5821i		−	0.633531i
$280$	6.79311	+	3.13906i	0.405966	+	0.187595i
$281$		−	7.39157i		−	0.440944i	−0.975393	−	0.220472i	$-0.929240\pi$
$281$		−	7.39157i		−	0.440944i	0.975393	−	0.220472i	$-0.0707597\pi$
$282$	15.8524	+	1.80695i	0.944000	+	0.107602i
$283$	6.68770	−	24.9589i	0.397543	−	1.48365i	−0.419863	−	0.907588i	$-0.637922\pi$
$283$	6.68770	−	24.9589i	0.397543	−	1.48365i	0.817406	−	0.576062i	$-0.195411\pi$
$284$	1.87499	−	8.11782i	0.111260	−	0.481704i
$285$	4.97119	−	1.33203i	0.294468	−	0.0789024i
$286$	−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
$290$	1.04073	+	6.96603i	0.0611137	+	0.409060i
$291$	3.62558	−	13.5308i	0.212535	−	0.793192i
$292$	9.56373	−	2.92289i	0.559675	−	0.171049i
$293$	−12.5963	+	12.5963i	−0.735886	+	0.735886i	−0.971779	−	0.235893i	$-0.924198\pi$
$293$	−12.5963	+	12.5963i	−0.735886	+	0.735886i	0.235893	+	0.971779i	$0.424198\pi$
$294$	11.2615	+	3.46205i	0.656784	+	0.201911i
$295$	1.72612			0.100499
$296$	−20.0658	+	17.1327i	−1.16630	+	0.995818i
$297$	−12.5804	−	21.7899i	−0.729990	−	1.26438i
$298$	−25.7395	−	19.0482i	−1.49105	−	1.10343i
$299$	−27.6596	+	7.41136i	−1.59959	+	0.428610i
$300$	−0.0828350	−	2.37881i	−0.00478248	−	0.137341i
$301$	−3.88894	+	10.5172i	−0.224155	+	0.606199i
$302$	9.05914	−	22.9946i	0.521295	−	1.32319i
$303$	13.1668	+	7.60184i	0.756412	+	0.436714i
$304$	−3.30387	+	16.9791i	−0.189490	+	0.973816i
$305$	3.77235	+	6.53390i	0.216004	+	0.374130i
$306$	2.53548	+	3.18786i	0.144944	+	0.182238i
$307$	−2.87922	+	2.87922i	−0.164326	+	0.164326i	−0.784480	−	0.620154i	$-0.787070\pi$
$307$	−2.87922	+	2.87922i	−0.164326	+	0.164326i	0.620154	+	0.784480i	$0.287070\pi$
$308$	1.40433	−	24.3660i	0.0800189	−	1.38838i
$309$	−11.8091	−	11.8091i	−0.671798	−	0.671798i
$310$	−9.38937	−	1.07025i	−0.533280	−	0.0607863i
$311$	−3.51155	+	2.02739i	−0.199122	+	0.114963i	−0.596246	−	0.802802i	$-0.703342\pi$
$311$	−3.51155	+	2.02739i	−0.199122	+	0.114963i	0.397124	+	0.917765i	$0.370008\pi$
$312$	−11.9513	−	8.21651i	−0.676609	−	0.465168i
$313$	−0.0514433	+	0.0891025i	−0.00290775	+	0.00503637i	−0.867476	−	0.497480i	$-0.834259\pi$
$313$	−0.0514433	+	0.0891025i	−0.00290775	+	0.00503637i	0.864568	+	0.502516i	$0.167592\pi$
$314$	3.00920	−	1.30826i	0.169819	−	0.0738294i
$315$	0.706449	+	4.12982i	0.0398039	+	0.232689i
$316$	1.51458	−	1.62387i	0.0852020	−	0.0913499i
$317$	6.97779	+	26.0415i	0.391912	+	1.46263i	0.826977	+	0.562236i	$0.190059\pi$
$317$	6.97779	+	26.0415i	0.391912	+	1.46263i	−0.435065	+	0.900399i	$0.643275\pi$
$318$	−7.40843	+	1.10682i	−0.415444	+	0.0620676i
$319$	19.8939	−	11.4858i	1.11385	−	0.643079i
$320$	7.30740	+	3.25606i	0.408496	+	0.182019i
$321$			8.99592i			0.502104i
$322$	20.8075	−	13.6183i	1.15956	−	0.758916i
$323$	5.56143	+	5.56143i	0.309446	+	0.309446i
$324$	3.33075	−	1.01795i	0.185042	−	0.0565529i
$325$	−4.16171	−	1.11513i	−0.230850	−	0.0618560i
$326$	−10.7534	−	7.95791i	−0.595575	−	0.440748i
$327$	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
$331$	−2.19936	−	8.20812i	−0.120888	−	0.451159i	0.878772	−	0.477242i	$-0.158363\pi$
$331$	−2.19936	−	8.20812i	−0.120888	−	0.451159i	−0.999660	+	0.0260827i	$0.991697\pi$
$332$	0.649569	+	1.03976i	0.0356497	+	0.0570640i
$333$	−14.2692	−	3.82343i	−0.781949	−	0.209523i
$334$	−9.38064	+	7.46094i	−0.513286	+	0.408244i
$335$	−16.1610			−0.882969
$336$	12.0886	+	3.53592i	0.659487	+	0.192900i
$337$	−26.3332			−1.43446			−0.717231	−	0.696835i	$-0.754591\pi$
$337$	−26.3332			−1.43446			−0.717231	+	0.696835i	$0.754591\pi$
$338$	−6.15756	+	4.89745i	−0.334927	+	0.266386i
$339$	17.0489	+	4.56823i	0.925968	+	0.248112i
$340$	3.08500	−	1.92730i	0.167308	−	0.104522i
$341$	7.97712	+	29.7710i	0.431986	+	1.61219i
$342$	−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
$346$	26.2551	+	19.4298i	1.41149	+	1.04455i
$347$	29.2465	+	7.83659i	1.57004	+	0.420690i	0.935824	−	0.352469i	$-0.114658\pi$
$347$	29.2465	+	7.83659i	1.57004	+	0.420690i	0.634213	+	0.773159i	$0.281324\pi$
$348$	3.46483	+	11.3370i	0.185735	+	0.607725i
$349$	−19.2744	−	19.2744i	−1.03173	−	1.03173i	−0.999480	−	0.0322540i	$-0.989731\pi$
$349$	−19.2744	−	19.2744i	−1.03173	−	1.03173i	−0.0322540	−	0.999480i	$-0.510269\pi$
$350$	3.73581	−	0.209142i	0.199687	−	0.0111791i
$351$		−	23.5032i		−	1.25451i
$352$	1.14453	−	26.0665i	0.0610035	−	1.38935i
$353$	3.08010	−	1.77830i	0.163937	−	0.0946492i	−0.415787	−	0.909462i	$-0.636494\pi$
$353$	3.08010	−	1.77830i	0.163937	−	0.0946492i	0.579724	+	0.814813i	$0.303160\pi$
$354$	2.87333	−	0.429278i	0.152716	−	0.0228158i
$355$	−1.07818	−	4.02383i	−0.0572239	−	0.213562i
$356$	15.3923	+	14.3564i	0.815791	+	0.760888i
$357$	4.40583	−	3.65871i	0.233181	−	0.193639i
$358$	−10.3755	+	4.51078i	−0.548361	+	0.238402i
$359$	11.2447	−	19.4763i	0.593471	−	1.02792i	−0.400290	−	0.916389i	$-0.631091\pi$
$359$	11.2447	−	19.4763i	0.593471	−	1.02792i	0.993761	−	0.111533i	$-0.0355762\pi$
$360$	0.815599	+	4.40421i	0.0429858	+	0.232122i
$361$	0.259601	−	0.149881i	0.0136632	−	0.00788847i
$362$	6.75225	+	0.769659i	0.354891	+	0.0404524i
$363$	8.64613	+	8.64613i	0.453804	+	0.453804i
$364$	12.5164	−	19.0555i	0.656039	−	0.998779i
$365$	3.53568	−	3.53568i	0.185066	−	0.185066i
$366$	7.90446	+	9.93828i	0.413173	+	0.519482i
$367$	−10.5951	−	18.3512i	−0.553059	−	0.957926i	−0.998052	−	0.0623921i	$-0.980127\pi$
$367$	−10.5951	−	18.3512i	−0.553059	−	0.957926i	0.444993	−	0.895534i	$-0.353206\pi$
$368$	22.0428	−	14.8617i	1.14906	−	0.774720i
$369$	−0.528091	−	0.304893i	−0.0274913	−	0.0158721i
$370$	−4.83567	+	12.2743i	−0.251394	+	0.638109i
$371$	−1.98540	−	11.6064i	−0.103077	−	0.602575i
$372$	−15.8959	+	0.553527i	−0.824163	+	0.0286990i
$373$	−29.3285	+	7.85854i	−1.51857	+	0.406900i	−0.919271	−	0.393625i	$-0.871221\pi$
$373$	−29.3285	+	7.85854i	−1.51857	+	0.406900i	−0.599300	+	0.800525i	$0.704554\pi$
$374$	−9.53634	−	7.05724i	−0.493112	−	0.364921i
$375$	−0.595063	−	1.03068i	−0.0307289	−	0.0532241i
$376$	−2.10763	+	26.7295i	−0.108693	+	1.37847i
$377$	21.4581			1.10515
$378$	6.37650	+	19.3894i	0.327972	+	0.997282i
$379$	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	$0.104676\pi$
$380$	2.52784	+	8.27109i	0.129675	+	0.424298i
$381$	−4.36639	+	16.2956i	−0.223697	+	0.834849i
$382$	0.415170	+	2.77891i	0.0212420	+	0.142181i
$383$	7.89225	−	13.6698i	0.403275	−	0.698493i	−0.590844	−	0.806786i	$-0.701205\pi$
$383$	7.89225	−	13.6698i	0.403275	−	0.698493i	0.994119	+	0.108293i	$0.0345385\pi$
$384$	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
$387$	−6.48287	+	1.73708i	−0.329543	+	0.0883007i
$388$	22.9368	+	5.29775i	1.16444	+	0.268953i
$389$	−1.96991	+	7.35180i	−0.0998783	+	0.372751i	−0.997714	−	0.0675800i	$-0.978472\pi$
$389$	−1.96991	+	7.35180i	−0.0998783	+	0.372751i	0.897836	+	0.440331i	$0.145139\pi$
$390$	−7.20498	−	0.821263i	−0.364838	−	0.0415863i
$391$		−	12.0879i		−	0.611313i
$392$	−5.15583	+	19.1159i	−0.260409	+	0.965498i
$393$		−	2.29282i		−	0.115657i
$394$	2.67841	−	23.4978i	0.134937	−	1.18380i
$395$	0.287363	−	1.07245i	0.0144588	−	0.0539609i
$396$	12.3893	−	7.74002i	0.622588	−	0.388951i
$397$	−17.1083	+	4.58415i	−0.858640	+	0.230072i	−0.661169	−	0.750237i	$-0.729939\pi$
$397$	−17.1083	+	4.58415i	−0.858640	+	0.230072i	−0.197471	+	0.980309i	$0.563273\pi$
$398$	−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	−0.713479	−	0.700677i	$-0.752881\pi$
$401$	5.00754	−	8.67331i	0.250065	−	0.433125i	0.963543	+	0.267552i	$0.0862148\pi$
$402$	−26.9019	+	4.01916i	−1.34174	+	0.200457i
$403$	−7.45158	+	27.8097i	−0.371190	+	1.38530i
$404$	−11.9971	+	22.5579i	−0.596877	+	1.12230i
$405$	1.23137	−	1.23137i	0.0611871	−	0.0611871i
$406$	−17.7022	+	5.82166i	−0.878548	+	0.288924i
$407$	43.0266			2.13275
$408$	4.65604	−	3.97544i	0.230508	−	0.196814i
$409$	18.0618	+	31.2840i	0.893101	+	1.54690i	0.836138	+	0.548519i	$0.184808\pi$
$409$	18.0618	+	31.2840i	0.893101	+	1.54690i	0.0569627	+	0.998376i	$0.481858\pi$
$410$	−0.323940	+	0.437734i	−0.0159982	+	0.0216182i
$411$	−4.74856	+	1.27237i	−0.234229	+	0.0627615i
$412$	19.1425	−	20.5238i	0.943084	−	1.01113i
$413$	0.770028	+	4.50150i	0.0378906	+	0.221504i
$414$	13.8485	+	5.45587i	0.680618	+	0.268141i
$415$	0.530866	+	0.306496i	0.0260592	+	0.0150453i
$416$	13.1005	−	20.5524i	0.642304	−	1.00767i
$417$	−7.08717	−	12.2753i	−0.347060	−	0.601126i
$418$	22.0763	−	17.5585i	1.07979	−	0.858813i
$419$	9.17610	−	9.17610i	0.448282	−	0.448282i	−0.446501	−	0.894783i	$-0.647330\pi$
$419$	9.17610	−	9.17610i	0.448282	−	0.448282i	0.894783	+	0.446501i	$0.147330\pi$
$420$	6.16668	−	1.27722i	0.300903	−	0.0623219i
$421$	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	$0.675127\pi$
$422$	3.96520	−	34.7868i	0.193023	−	1.69340i
$423$	−13.0007	+	7.50597i	−0.632117	+	0.364953i
$424$	−2.29215	−	12.3776i	−0.111317	−	0.601107i
$425$	0.909386	−	1.57510i	0.0441117	−	0.0764037i
$426$	−2.79546	−	6.42999i	−0.135441	−	0.311534i
$427$	−15.3567	+	12.7526i	−0.743163	+	0.617141i
$428$	−15.1084	+	0.526106i	−0.730294	+	0.0254303i
$429$	6.12128	+	22.8449i	0.295538	+	1.10296i
$430$	0.885630	+	5.92789i	0.0427089	+	0.285868i
$431$	−9.02906	+	5.21293i	−0.434914	+	0.251098i	−0.701438	−	0.712730i	$-0.747458\pi$
$431$	−9.02906	+	5.21293i	−0.434914	+	0.251098i	0.266524	+	0.963828i	$0.414125\pi$
$432$	7.09991	+	20.6329i	0.341595	+	0.992699i
$433$			18.4445i			0.886384i	0.896427	+	0.443192i	$0.146154\pi$
$433$			18.4445i			0.886384i	−0.896427	+	0.443192i	$0.853846\pi$
$434$	−1.39755	−	24.9637i	−0.0670844	−	1.19830i
$435$	4.19124	+	4.19124i	0.200954	+	0.200954i
$436$	−0.326545	+	0.613996i	−0.0156387	+	0.0294051i
$437$	27.7614	+	7.43864i	1.32801	+	0.355839i
$438$	5.00625	−	6.76486i	0.239208	−	0.323237i
$439$	13.0191	+	7.51655i	0.621365	+	0.358745i	0.777400	−	0.629006i	$-0.216538\pi$
$439$	13.0191	+	7.51655i	0.621365	+	0.358745i	−0.156035	+	0.987752i	$0.549871\pi$
$440$	−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
$443$	−7.02713	−	26.2256i	−0.333869	−	1.24602i	−0.905090	−	0.425220i	$-0.860197\pi$
$443$	−7.02713	−	26.2256i	−0.333869	−	1.24602i	0.571221	−	0.820796i	$-0.306470\pi$
$444$	−4.99699	+	21.6346i	−0.237146	+	1.02673i
$445$	10.1655	+	2.72385i	0.481892	+	0.129123i
$446$	−12.2269	−	15.3728i	−0.578959	−	0.727925i
$447$	−26.9473			−1.27456
$448$	−5.23152	+	20.5093i	−0.247166	+	0.968973i
$449$	20.6152			0.972893			0.486447	−	0.873710i	$-0.338293\pi$
$449$	20.6152			0.972893			0.486447	+	0.873710i	$0.338293\pi$
$450$	1.39406	+	1.75276i	0.0657168	+	0.0826258i
$451$	1.71555	+	0.459679i	0.0807819	+	0.0216454i
$452$	−6.67517	+	28.9003i	−0.313974	+	1.35936i
$453$	−5.38309	−	20.0899i	−0.252919	−	0.943908i
$454$	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	$-0.193267\pi$
$457$	15.7723	+	9.10613i	0.737796	+	0.425967i	−0.0834714	+	0.996510i	$0.526601\pi$
$458$	13.0021	−	17.5695i	0.607547	−	0.820968i
$459$	9.58344	+	2.56788i	0.447317	+	0.119858i
$460$	6.24157	−	11.7359i	0.291015	−	0.547189i
$461$	−18.8727	−	18.8727i	−0.878987	−	0.878987i	0.114443	−	0.993430i	$-0.463492\pi$
$461$	−18.8727	−	18.8727i	−0.878987	−	0.878987i	−0.993430	+	0.114443i	$0.963492\pi$
$462$	−11.2478	−	17.1856i	−0.523293	−	0.799547i
$463$		−	18.6589i		−	0.867154i	−0.901117	−	0.433577i	$-0.857251\pi$
$463$		−	18.6589i		−	0.867154i	0.901117	−	0.433577i	$-0.142749\pi$
$464$	−18.8375	+	6.48212i	−0.874510	+	0.300925i
$465$	−6.88729	+	3.97638i	−0.319390	+	0.184400i
$466$	1.44011	+	9.63923i	0.0667117	+	0.446529i
$467$	1.74036	+	6.49511i	0.0805342	+	0.300558i	0.994431	−	0.105389i	$-0.0336087\pi$
$467$	1.74036	+	6.49511i	0.0805342	+	0.300558i	−0.913897	+	0.405946i	$0.866942\pi$
$468$	13.6377	−	0.474891i	0.630401	−	0.0219518i
$469$	−7.20947	−	42.1458i	−0.332902	−	1.94611i
$470$	5.34511	+	12.2946i	0.246552	+	0.567106i
$471$	1.38068	−	2.39140i	0.0636182	−	0.110190i
$472$	0.889002	+	4.80059i	0.0409196	+	0.220965i
$473$	16.9291	−	9.77404i	0.778402	−	0.449411i
$474$	0.211636	−	1.85669i	0.00972075	−	0.0852805i
$475$	3.05780	+	3.05780i	0.140301	+	0.140301i
$476$	6.40238	+	7.18551i	0.293453	+	0.329347i
$477$	4.98359	−	4.98359i	0.228183	−	0.228183i
$478$	−9.73360	+	7.74167i	−0.445204	+	0.354096i
$479$	12.5344	+	21.7102i	0.572711	+	0.991965i	0.996286	+	0.0861036i	$0.0274416\pi$
$479$	12.5344	+	21.7102i	0.572711	+	0.991965i	−0.423575	+	0.905861i	$0.639225\pi$
$480$	6.57315	−	1.45553i	0.300022	−	0.0664356i
$481$	34.8072	+	20.0960i	1.58707	+	0.916298i
$482$	19.8848	+	7.83398i	0.905730	+	0.356828i
$483$	7.25805	−	19.6285i	0.330253	−	0.893128i
$484$	−14.0153	+	15.0266i	−0.637060	+	0.683028i
$485$	11.3693	−	3.04638i	0.516251	−	0.138329i
$486$	−12.0239	+	16.2477i	−0.545415	+	0.737010i
$487$	2.25854	+	3.91190i	0.102344	+	0.177265i	0.912650	−	0.408742i	$-0.134032\pi$
$487$	2.25854	+	3.91190i	0.102344	+	0.177265i	−0.810306	+	0.586007i	$0.800699\pi$
$488$	−16.2288	+	13.8566i	−0.734644	+	0.627257i
$489$	−11.2580			−0.509103
$490$	2.21197	+	9.64921i	0.0999267	+	0.435907i
$491$	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	$0.221647\pi$
$492$	−0.430374	+	0.809223i	−0.0194027	+	0.0364826i
$493$	−2.34444	+	8.74955i	−0.105588	+	0.394060i
$494$	26.0599	−	3.89336i	1.17249	−	0.175171i
$495$	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
$499$	1.94540	−	0.521268i	0.0870880	−	0.0233351i	−0.215012	−	0.976611i	$-0.568979\pi$
$499$	1.94540	−	0.521268i	0.0870880	−	0.0233351i	0.302100	+	0.953276i	$0.402312\pi$
$500$	1.69620	−	1.05967i	0.0758564	−	0.0473899i
$501$	−2.61063	+	9.74300i	−0.116634	+	0.435285i
$502$	4.03737	−	35.4200i	0.180197	−	1.58087i
$503$		−	8.87468i		−	0.395702i	−0.980232	−	0.197851i	$-0.936604\pi$
$503$		−	8.87468i		−	0.395702i	0.980232	−	0.197851i	$-0.0633963\pi$
$504$	−11.1218	+	4.09171i	−0.495403	+	0.182259i
$505$			12.7749i			0.568473i
$506$	−43.0736	−	4.90977i	−1.91486	−	0.218266i
$507$	−1.71365	+	6.39542i	−0.0761058	+	0.284031i
$508$	−27.6234	−	6.38024i	−1.22559	−	0.283077i
$509$	−3.16157	+	0.847140i	−0.140134	+	0.0375488i	−0.328204	−	0.944607i	$-0.606443\pi$
$509$	−3.16157	+	0.847140i	−0.140134	+	0.0375488i	0.188070	+	0.982156i	$0.439777\pi$
$510$	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
$514$	−2.27335	−	15.2165i	−0.100273	−	0.671171i
$515$	3.63192	−	13.5545i	0.160041	−	0.597283i
$516$	2.94847	+	9.64741i	0.129799	+	0.424704i
$517$	30.9173	−	30.9173i	1.35974	−	1.35974i
$518$	−34.1669	−	7.13520i	−1.50121	−	0.313503i
$519$	27.4871			1.20655
$520$	0.957925	−	12.1486i	0.0420078	−	0.532752i
$521$	−16.8766	−	29.2312i	−0.739378	−	1.28064i	−0.952776	−	0.303675i	$-0.901786\pi$
$521$	−16.8766	−	29.2312i	−0.739378	−	1.28064i	0.213398	−	0.976965i	$-0.431547\pi$
$522$	−8.96576	−	6.63500i	−0.392421	−	0.290406i
$523$	2.36160	−	0.632789i	0.103266	−	0.0276699i	−0.206816	−	0.978380i	$-0.566310\pi$
$523$	2.36160	−	0.632789i	0.103266	−	0.0276699i	0.310082	+	0.950710i	$0.399644\pi$
$524$	3.85074	−	0.134090i	0.168220	−	0.00585777i
$525$	2.42242	−	2.01164i	0.105723	−	0.0877951i
$526$	−12.7983	+	32.4857i	−0.558032	+	1.41644i
$527$	−10.5253	−	6.07677i	−0.458488	−	0.264708i
$528$	−12.2748	−	18.2058i	−0.534191	−	0.792307i
$529$	−10.5860	−	18.3356i	−0.460263	−	0.797199i
$530$	−3.91787	−	4.92593i	−0.170181	−	0.213969i
$531$	−1.93287	+	1.93287i	−0.0838792	+	0.0838792i
$532$	−20.4423	+	10.2820i	−0.886285	+	0.445783i
$533$	1.17313	+	1.17313i	0.0508138	+	0.0508138i
$534$	17.5991	+	2.00605i	0.761589	+	0.0868101i
$535$	−6.54611	+	3.77940i	−0.283013	+	0.163398i
$536$	−8.32337	−	44.9460i	−0.359515	−	1.94137i
$537$	−4.76046	+	8.24537i	−0.205429	+	0.355814i
$538$	−8.31676	+	3.61574i	−0.358561	+	0.155886i
$539$	26.6357	−	18.2475i	1.14728	−	0.785976i
$540$	7.97843	+	7.44147i	0.343337	+	0.320230i
$541$	0.337649	+	1.26012i	0.0145166	+	0.0541769i	0.972804	−	0.231629i	$-0.0744055\pi$
$541$	0.337649	+	1.26012i	0.0145166	+	0.0541769i	−0.958288	+	0.285806i	$0.907739\pi$
$542$	−0.362975	+	0.0542286i	−0.0155911	+	0.00232932i
$543$	4.95291	−	2.85957i	0.212550	−	0.122716i
$544$	6.94896	+	7.58721i	0.297934	+	0.325299i
$545$			0.347715i			0.0148945i
$546$	−1.07241	−	19.1560i	−0.0458951	−	0.819802i
$547$	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	$0.715121\pi$
$548$	−2.41463	−	7.90068i	−0.103148	−	0.337500i
$549$	−11.5407	−	3.09231i	−0.492543	−	0.131977i
$550$	−5.24329	−	3.88023i	−0.223574	−	0.165453i
$551$	−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
$555$	2.87343	+	10.7238i	0.121970	+	0.455200i
$556$	20.2016	−	12.6206i	0.856741	−	0.535233i
$557$	3.37249	+	0.903655i	0.142897	+	0.0382891i	0.329558	−	0.944135i	$-0.393100\pi$
$557$	3.37249	+	0.903655i	0.142897	+	0.0382891i	−0.186662	+	0.982424i	$0.559767\pi$
$558$	11.7124	−	9.31553i	0.495826	−	0.394358i
$559$	18.2602			0.772325
$560$	2.50570	+	10.2821i	0.105885	+	0.434498i
$561$	−9.98382			−0.421517
$562$	8.18112	−	6.50690i	0.345100	−	0.274477i
$563$	−1.24996	−	0.334926i	−0.0526796	−	0.0141154i	0.232383	−	0.972624i	$-0.425348\pi$
$563$	−1.24996	−	0.334926i	−0.0526796	−	0.0141154i	−0.285063	+	0.958509i	$0.592014\pi$
$564$	11.9552	+	19.1365i	0.503403	+	0.805791i
$565$	3.83844	+	14.3253i	0.161485	+	0.602668i
$566$	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	$-0.0832533\pi$
$569$	29.2221	+	16.8714i	1.22505	+	0.707285i	0.259062	+	0.965861i	$0.416587\pi$
$570$	5.85052	+	4.32960i	0.245051	+	0.181347i
$571$	23.0246	+	6.16942i	0.963548	+	0.258182i	0.706102	−	0.708111i	$-0.250452\pi$
$571$	23.0246	+	6.16942i	0.963548	+	0.258182i	0.257447	+	0.966293i	$0.417119\pi$
$572$	−38.0095	+	11.6166i	−1.58926	+	0.485714i
$573$	1.67198	+	1.67198i	0.0698479	+	0.0698479i
$574$	−1.28607	−	0.649519i	−0.0536793	−	0.0271104i
$575$		−	6.64621i		−	0.277166i
$576$	−11.8287	+	4.53659i	−0.492862	+	0.189025i
$577$	−38.6718	+	22.3272i	−1.60993	+	0.929493i	−0.620545	+	0.784171i	$0.713089\pi$
$577$	−38.6718	+	22.3272i	−1.60993	+	0.929493i	−0.989384	+	0.145322i	$0.953578\pi$
$578$	−19.1510	+	2.86117i	−0.796575	+	0.119009i
$579$	−2.20024	−	8.21141i	−0.0914389	−	0.341255i
$580$	−6.79397	+	7.28420i	−0.282104	+	0.302460i
$581$	−0.562480	+	1.52116i	−0.0233356	+	0.0631083i
$582$	18.1678	−	7.89854i	0.753081	−	0.327405i
$583$	−10.2638	+	17.7774i	−0.425082	+	0.736264i
$584$	11.6542	+	8.01225i	0.482254	+	0.331549i
$585$	5.90886	−	3.41148i	0.244301	−	0.141047i
$586$	−25.0306	−	2.85312i	−1.03400	−	0.117862i
$587$	12.9617	+	12.9617i	0.534985	+	0.534985i	0.922052	−	0.387067i	$-0.126512\pi$
$587$	12.9617	+	12.9617i	0.534985	+	0.534985i	−0.387067	+	0.922052i	$0.626512\pi$
$588$	6.08180	+	15.5121i	0.250809	+	0.639710i
$589$	20.4330	−	20.4330i	0.841929	−	0.841929i
$590$	1.51953	+	1.91050i	0.0625580	+	0.0786542i
$591$	−9.95128	−	17.2361i	−0.409341	−	0.708999i
$592$	−36.6270	−	7.12707i	−1.50536	−	0.292921i
$593$	−5.33980	−	3.08294i	−0.219279	−	0.126601i	0.386337	−	0.922358i	$-0.373740\pi$
$593$	−5.33980	−	3.08294i	−0.219279	−	0.126601i	−0.605617	+	0.795757i	$0.707073\pi$
$594$	13.0428	−	33.1062i	0.535152	−	1.35837i
$595$	4.51334	+	1.66890i	0.185029	+	0.0684183i
$596$	−1.57595	−	45.2574i	−0.0645535	−	1.85381i
$597$	−26.5951	+	7.12613i	−1.08846	+	0.291653i
$598$	−32.5521	−	24.0898i	−1.33116	−	0.985105i
$599$	7.49718	+	12.9855i	0.306327	+	0.530573i	0.977556	−	0.210677i	$-0.0675667\pi$
$599$	7.49718	+	12.9855i	0.306327	+	0.530573i	−0.671229	+	0.741250i	$0.734233\pi$
$600$	2.55999	−	2.18578i	0.104511	−	0.0892343i
$601$	21.3544			0.871066			0.435533	−	0.900173i	$-0.356560\pi$
$601$	21.3544			0.871066			0.435533	+	0.900173i	$0.356560\pi$
$602$	−15.0641	+	4.95406i	−0.613966	+	0.201912i
$603$	18.0967	−	18.0967i	0.736953	−	0.736953i
$604$	33.4258	−	10.2157i	1.36008	−	0.415670i
$605$	−2.65913	+	9.92402i	−0.108109	+	0.403469i
$606$	3.17704	+	21.2652i	0.129058	+	0.863841i
$607$	−17.4214	+	30.1747i	−0.707113	+	1.22476i	0.258811	+	0.965928i	$0.416669\pi$
$607$	−17.4214	+	30.1747i	−0.707113	+	1.22476i	−0.965924	+	0.258827i	$0.916664\pi$
$608$	−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
$611$	39.4514	−	10.5710i	1.59603	−	0.427656i
$612$	−1.29636	+	5.61264i	−0.0524024	+	0.226878i
$613$	6.76867	−	25.2610i	0.273384	−	1.02028i	−0.683533	−	0.729920i	$-0.739557\pi$
$613$	6.76867	−	25.2610i	0.273384	−	1.02028i	0.956917	−	0.290363i	$-0.0937761\pi$
$614$	−5.72139	−	0.652155i	−0.230896	−	0.0263188i
$615$			0.458275i			0.0184794i
$616$	28.2050	−	19.8954i	1.13641	−	0.801609i
$617$		−	28.9800i		−	1.16669i	−0.812224	−	0.583346i	$-0.801743\pi$
$617$		−	28.9800i		−	1.16669i	0.812224	−	0.583346i	$-0.198257\pi$
$618$	2.67482	−	23.4663i	0.107597	−	0.943953i
$619$	8.46728	−	31.6003i	0.340329	−	1.27012i	−0.557647	−	0.830078i	$-0.688296\pi$
$619$	8.46728	−	31.6003i	0.340329	−	1.27012i	0.897975	−	0.440045i	$-0.145038\pi$
$620$	−7.08102	−	11.3345i	−0.284381	−	0.455204i
$621$	35.0201	−	9.38361i	1.40531	−	0.376551i
$622$	−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
$626$	−0.143907	+	0.0214997i	−0.00575166	+	0.000859302i
$627$	6.14382	−	22.9290i	0.245361	−	0.915698i
$628$	4.09705	+	2.17896i	0.163490	+	0.0869499i
$629$	−11.9971	+	11.9971i	−0.478354	+	0.478354i
$630$	−3.94907	+	4.41745i	−0.157335	+	0.175995i
$631$	15.3927			0.612775			0.306387	−	0.951907i	$-0.400880\pi$
$631$	15.3927			0.612775			0.306387	+	0.951907i	$0.400880\pi$
$632$	3.13064	+	0.246853i	0.124530	+	0.00981928i
$633$	−14.7322	−	25.5168i	−0.585551	−	1.01420i
$634$	−22.6805	+	30.6478i	−0.900759	+	1.21718i
$635$	−13.6923	+	3.66885i	−0.543363	+	0.145594i
$636$	−7.74680	−	7.22544i	−0.307181	−	0.286507i
$637$	30.0701	−	2.32125i	1.19142	−	0.0919712i
$638$	30.2255	+	11.9079i	1.19664	+	0.471438i
$639$	5.71309	+	3.29846i	0.226006	+	0.130485i
$640$	2.82895	+	10.9543i	0.111824	+	0.433007i
$641$	−4.79261	−	8.30104i	−0.189297	−	0.327872i	0.755719	−	0.654896i	$-0.227287\pi$
$641$	−4.79261	−	8.30104i	−0.189297	−	0.327872i	−0.945016	+	0.327024i	$0.893954\pi$
$642$	−9.95686	+	7.91924i	−0.392966	+	0.312547i
$643$	−12.4069	+	12.4069i	−0.489281	+	0.489281i	−0.908079	−	0.418798i	$-0.862451\pi$
$643$	−12.4069	+	12.4069i	−0.489281	+	0.489281i	0.418798	+	0.908079i	$0.362451\pi$
$644$	33.3901	+	11.0418i	1.31575	+	0.435107i
$645$	3.56662	+	3.56662i	0.140435	+	0.140435i
$646$	−1.25969	+	11.0513i	−0.0495618	+	0.434808i
$647$	40.3903	−	23.3193i	1.58791	−	0.916778i	0.594254	−	0.804278i	$-0.297447\pi$
$647$	40.3903	−	23.3193i	1.58791	−	0.916778i	0.993652	−	0.112500i	$-0.0358858\pi$
$648$	4.05879	+	2.79042i	0.159445	+	0.109618i
$649$	3.98077	−	6.89489i	0.156259	−	0.270648i
$650$	−2.42937	−	5.58791i	−0.0952876	−	0.219176i
$651$	−13.4423	−	16.1873i	−0.526846	−	0.634430i
$652$	−0.658397	−	18.9075i	−0.0257848	−	0.740475i
$653$	−5.54370	−	20.6894i	−0.216942	−	0.809637i	−0.985474	−	0.169826i	$-0.945679\pi$
$653$	−5.54370	−	20.6894i	−0.216942	−	0.809637i	0.768532	−	0.639811i	$-0.220987\pi$
$654$	0.0864749	+	0.578812i	0.00338144	+	0.0226334i
$655$	1.66843	−	0.963268i	0.0651909	−	0.0376380i
$656$	−1.38424	−	0.675477i	−0.0540455	−	0.0263729i
$657$			7.91832i			0.308923i
$658$	−29.6782	+	19.4240i	−1.15698	+	0.757227i
$659$	−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	$0.863551\pi$
$660$	−9.69306	−	5.15512i	−0.377302	−	0.200663i
$661$	−34.5020	−	9.24479i	−1.34197	−	0.359581i	−0.484807	−	0.874621i	$-0.661110\pi$
$661$	−34.5020	−	9.24479i	−1.34197	−	0.359581i	−0.857166	+	0.515040i	$0.827777\pi$
$662$	7.14877	−	9.66001i	0.277845	−	0.375447i
$663$	−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
$667$	8.56711	+	31.9729i	0.331720	+	1.23800i
$668$	−16.5158	−	3.81469i	−0.639016	−	0.147595i
$669$	−15.9667	−	4.27826i	−0.617308	−	0.165407i
$670$	−14.2267	−	17.8873i	−0.549627	−	0.691046i
$671$	34.7990			1.34340
$672$	6.72814	+	16.4926i	0.259544	+	0.636216i
$673$	22.1001			0.851895			0.425947	−	0.904748i	$-0.359941\pi$
$673$	22.1001			0.851895			0.425947	+	0.904748i	$0.359941\pi$
$674$	−23.1815	−	29.1461i	−0.892919	−	1.12267i
$675$	5.26919	+	1.41187i	0.202811	+	0.0543431i
$676$	−10.8412	−	2.50401i	−0.416968	−	0.0963080i
$677$	1.79724	+	6.70740i	0.0690736	+	0.257786i	0.991824	−	0.127611i	$-0.0407310\pi$
$677$	1.79724	+	6.70740i	0.0690736	+	0.257786i	−0.922751	+	0.385397i	$0.874064\pi$
$678$	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
$682$	−25.9288	+	35.0371i	−0.992863	+	1.34164i
$683$	2.33296	+	0.625115i	0.0892683	+	0.0239194i	0.303177	−	0.952934i	$-0.401953\pi$
$683$	2.33296	+	0.625115i	0.0892683	+	0.0239194i	−0.213908	+	0.976854i	$0.568619\pi$
$684$	−12.0924	−	6.43115i	−0.462363	−	0.245901i
$685$	−2.92086	−	2.92086i	−0.111600	−	0.111600i
$686$	−24.1771	+	10.0731i	−0.923087	+	0.384592i
$687$		−	18.3939i		−	0.701772i
$688$	−16.0302	+	5.51609i	−0.611144	+	0.210299i
$689$	−16.6062	+	9.58759i	−0.632646	+	0.365258i
$690$	−1.65288	−	11.0634i	−0.0629240	−	0.421176i
$691$	−0.103241	−	0.385301i	−0.00392747	−	0.0146575i	0.963934	−	0.266140i	$-0.0857485\pi$
$691$	−0.103241	−	0.385301i	−0.00392747	−	0.0146575i	−0.967862	+	0.251483i	$0.919082\pi$
$692$	1.60752	+	46.1640i	0.0611089	+	1.75489i
$693$	18.1255	+	6.70230i	0.688533	+	0.254599i
$694$	17.0725	+	39.2693i	0.648062	+	1.49064i
$695$	5.95497	−	10.3143i	0.225885	−	0.391244i
$696$	−9.49781	+	13.8150i	−0.360014	+	0.523657i
$697$	−0.606515	+	0.350172i	−0.0229734	+	0.0132637i
$698$	4.36573	−	38.3007i	0.165245	−	1.44970i
$699$	5.79961	+	5.79961i	0.219362	+	0.219362i
$700$	3.52017	+	3.95075i	0.133050	+	0.149324i
$701$	−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	$0.386134\pi$
$702$	26.0138	−	20.6902i	0.981827	−	0.780902i
$703$	−20.1700	−	34.9354i	−0.760725	−	1.31761i
$704$	29.8584	−	21.6799i	1.12533	−	0.817092i
$705$	9.77046	+	5.64098i	0.367977	+	0.212452i
$706$	4.67971	+	1.84365i	0.176123	+	0.0693868i
$707$	−33.3152	+	5.69890i	−1.25295	+	0.214329i
$708$	3.00457	+	2.80236i	0.112919	+	0.105319i
$709$	8.17625	−	2.19082i	0.307065	−	0.0822779i	−0.101996	−	0.994785i	$-0.532523\pi$
$709$	8.17625	−	2.19082i	0.307065	−	0.0822779i	0.409061	+	0.912507i	$0.365856\pi$
$710$	3.50451	−	4.73558i	0.131522	−	0.177723i
$711$	0.879123	+	1.52268i	0.0329697	+	0.0571051i
$712$	−2.33986	+	29.6746i	−0.0876900	+	1.11210i
$713$	−44.4118			−1.66324
$714$	7.92804	+	1.65564i	0.296699	+	0.0619607i
$715$	−14.0520	+	14.0520i	−0.525515	+	0.525515i
$716$	−14.1263	−	7.51287i	−0.527925	−	0.280769i
$717$	−2.70886	+	10.1096i	−0.101164	+	0.377550i
$718$	31.4556	−	4.69949i	1.17391	−	0.175383i
$719$	−5.64697	+	9.78084i	−0.210597	+	0.364764i	−0.951901	−	0.306405i	$-0.900874\pi$
$719$	−5.64697	+	9.78084i	−0.210597	+	0.364764i	0.741305	+	0.671168i	$0.234207\pi$
$720$	−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
$723$	17.3730	−	4.65508i	0.646108	−	0.173124i
$724$	5.09223	+	8.15106i	0.189251	+	0.302932i
$725$	−1.28902	+	4.81070i	−0.0478731	+	0.178665i
$726$	−1.95839	+	17.1810i	−0.0726826	+	0.637647i
$727$		−	23.3848i		−	0.867296i	−0.901082	−	0.433648i	$-0.857226\pi$
$727$		−	23.3848i		−	0.867296i	0.901082	−	0.433648i	$-0.142774\pi$
$728$	32.1093	−	2.92139i	1.19005	−	0.108274i
$729$			22.2343i			0.823494i
$730$	7.02586	+	0.800847i	0.260039	+	0.0296407i
$731$	−1.99504	+	7.44561i	−0.0737894	+	0.275386i
$732$	−4.04146	+	17.4976i	−0.149377	+	0.646730i
$733$	44.9027	−	12.0316i	1.65852	−	0.444399i	0.696539	−	0.717519i	$-0.254722\pi$
$733$	44.9027	−	12.0316i	1.65852	−	0.444399i	0.961980	+	0.273121i	$0.0880558\pi$
$734$	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
$738$	−0.127424	−	0.852903i	−0.00469055	−	0.0313958i
$739$	−9.06090	+	33.8157i	−0.333311	+	1.24393i	0.572378	+	0.819990i	$0.306021\pi$
$739$	−9.06090	+	33.8157i	−0.333311	+	1.24393i	−0.905689	+	0.423943i	$0.860646\pi$
$740$	−17.8423	+	5.45302i	−0.655896	+	0.200457i
$741$	15.6794	−	15.6794i	0.575997	−	0.575997i
$742$	11.0984	−	12.4148i	0.407436	−	0.455760i
$743$	35.4732			1.30138			0.650692	−	0.759341i	$-0.274479\pi$
$743$	35.4732			1.30138			0.650692	+	0.759341i	$0.274479\pi$
$744$	−14.6060	−	17.1066i	−0.535483	−	0.627157i
$745$	−11.3212	−	19.6089i	−0.414777	−	0.718414i
$746$	−34.5163	−	25.5433i	−1.26373	−	0.935207i
$747$	−0.937655	+	0.251244i	−0.0343070	+	0.00919254i
$748$	−0.583881	−	16.7676i	−0.0213488	−	0.613084i
$749$	−12.7764	−	15.3854i	−0.466840	−	0.562171i
$750$	0.616933	−	1.56595i	0.0225272	−	0.0571804i
$751$	−46.2437	−	26.6988i	−1.68746	−	0.974253i	−0.956457	−	0.291873i	$-0.905721\pi$
$751$	−46.2437	−	26.6988i	−1.68746	−	0.974253i	−0.730998	−	0.682379i	$-0.760945\pi$
$752$	−31.4401	+	21.1976i	−1.14650	+	0.772996i
$753$	−15.0003	−	25.9813i	−0.546641	−	0.946810i
$754$	18.8899	+	23.7502i	0.687929	+	0.864933i
$755$	12.3574	−	12.3574i	0.449732	−	0.449732i
$756$	−15.8472	+	24.1264i	−0.576357	+	0.877468i
$757$	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	$0.625475\pi$
$758$	24.1187	+	2.74919i	0.876031	+	0.0998549i
$759$	−31.5954	+	18.2416i	−1.14684	+	0.662128i
$760$	−6.92931	+	10.0790i	−0.251353	+	0.365604i
$761$	−2.60139	+	4.50575i	−0.0943005	+	0.163333i	−0.909316	−	0.416105i	$-0.863395\pi$
$761$	−2.60139	+	4.50575i	−0.0943005	+	0.163333i	0.815016	+	0.579439i	$0.196728\pi$
$762$	−21.8801	+	9.51244i	−0.792631	+	0.344599i
$763$	−0.906796	+	0.155117i	−0.0328282	+	0.00561560i
$764$	−2.71026	+	2.90583i	−0.0980539	+	0.105129i
$765$	0.745452	+	2.78206i	0.0269519	+	0.100586i
$766$	22.0776	−	3.29841i	0.797697	−	0.119176i
$767$	6.44065	−	3.71851i	0.232558	−	0.134268i
$768$	7.43340	+	17.5312i	0.268230	+	0.632603i
$769$		−	6.99371i		−	0.252200i	−0.992018	−	0.126100i	$-0.959754\pi$
$769$		−	6.99371i		−	0.252200i	0.992018	−	0.126100i	$-0.0402460\pi$
$770$	7.78009	−	15.4048i	0.280375	−	0.555150i
$771$	−9.15527	−	9.15527i	−0.329719	−	0.329719i
$772$	13.6622	−	4.17548i	0.491713	−	0.150279i
$773$	19.4448	+	5.21023i	0.699382	+	0.187399i	0.590954	−	0.806705i	$-0.298752\pi$
$773$	19.4448	+	5.21023i	0.699382	+	0.187399i	0.108428	+	0.994104i	$0.465418\pi$
$774$	−7.62960	−	5.64619i	−0.274240	−	0.202948i
$775$	−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
$779$	−0.430976	−	1.60842i	−0.0154413	−	0.0576277i
$780$	−5.43365	−	8.69757i	−0.194556	−	0.311423i
$781$	−18.5594	−	4.97299i	−0.664109	−	0.177947i
$782$	13.3791	−	10.6412i	0.478437	−	0.380528i
$783$	−27.1684			−0.970919
$784$	−25.6966	+	11.1214i	−0.917735	+	0.397194i
$785$	2.32022			0.0828122
$786$	2.53774	−	2.01840i	0.0905181	−	0.0719940i
$787$	44.2342	+	11.8525i	1.57678	+	0.422497i	0.937927	−	0.346832i	$-0.112743\pi$
$787$	44.2342	+	11.8525i	1.57678	+	0.422497i	0.638852	+	0.769329i	$0.279409\pi$
$788$	28.3657	−	17.7210i	1.01049	−	0.631283i
$789$	7.60495	+	28.3821i	0.270743	+	1.01043i
$790$	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
$794$	−20.1345	−	14.9003i	−0.714546	−	0.528791i
$795$	−5.11621	−	1.37089i	−0.181453	−	0.0486203i
$796$	−13.5235	−	44.2490i	−0.479328	−	1.56837i
$797$	−29.4099	−	29.4099i	−1.04175	−	1.04175i	−0.999090	−	0.0426629i	$-0.986416\pi$
$797$	−29.4099	−	29.4099i	−1.04175	−	1.04175i	−0.0426629	−	0.999090i	$-0.513584\pi$
$798$	−8.68111	+	17.1889i	−0.307308	+	0.608479i
$799$			17.2413i			0.609953i
$800$	3.82069	+	4.17161i	0.135082	+	0.147489i
$801$	−14.4332	+	8.33300i	−0.509971	+	0.294432i
$802$	14.0080	−	2.09280i	0.494639	−	0.0738994i
$803$	−5.96911	−	22.2770i	−0.210645	−	0.786139i
$804$	−28.1306	−	26.2374i	−0.992089	−	0.925321i
$805$	17.3325	−	2.96490i	0.610889	−	0.104499i
$806$	−37.3400	+	16.2337i	−1.31525	+	0.571808i
$807$	−3.81588	+	6.60930i	−0.134325	+	0.232658i
$808$	−35.5287	+	6.57941i	−1.24989	+	0.231463i
$809$	36.3755	−	21.0014i	1.27889	−	0.738370i	0.302249	−	0.953229i	$-0.402263\pi$
$809$	36.3755	−	21.0014i	1.27889	−	0.738370i	0.976645	+	0.214859i	$0.0689293\pi$
$810$	2.44689	+	0.278910i	0.0859749	+	0.00979990i
$811$	25.6966	+	25.6966i	0.902328	+	0.902328i	0.995637	−	0.0933091i	$-0.0297445\pi$
$811$	25.6966	+	25.6966i	0.902328	+	0.902328i	−0.0933091	+	0.995637i	$0.529744\pi$
$812$	−22.0271	−	14.4683i	−0.772998	−	0.507737i
$813$	−0.218390	+	0.218390i	−0.00765928	+	0.00765928i
$814$	37.8769	+	47.6226i	1.32759	+	1.66917i
$815$	−4.72974	−	8.19215i	−0.165676	−	0.286959i
$816$	8.49887	+	1.65375i	0.297520	+	0.0578929i
$817$	−15.8720	−	9.16372i	−0.555292	−	0.320598i
$818$	−18.7256	+	47.5310i	−0.654727	+	1.66188i
$819$	11.5327	+	13.8877i	0.402984	+	0.485274i
$820$	−0.769661	+	0.0268012i	−0.0268777	+	0.000935937i
$821$	35.6178	−	9.54376i	1.24307	−	0.333080i	0.423414	−	0.905936i	$-0.360831\pi$
$821$	35.6178	−	9.54376i	1.24307	−	0.333080i	0.819656	+	0.572856i	$0.194165\pi$
$822$	−5.58851	−	4.13571i	−0.194922	−	0.144249i
$823$	−28.0736	−	48.6249i	−0.978585	−	1.69496i	−0.667559	−	0.744557i	$-0.732661\pi$
$823$	−28.0736	−	48.6249i	−0.978585	−	1.69496i	−0.311026	−	0.950402i	$-0.600672\pi$
$824$	39.5675	+	3.11992i	1.37840	+	0.108688i
$825$	−5.48932			−0.191114
$826$	−4.30448	+	4.81502i	−0.149772	+	0.167536i
$827$	−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	$0.963472\pi$
$828$	6.15240	+	20.1307i	0.213811	+	0.699590i
$829$	−4.12158	+	15.3819i	−0.143148	+	0.534237i	0.856683	+	0.515844i	$0.172522\pi$
$829$	−4.12158	+	15.3819i	−0.143148	+	0.534237i	−0.999831	+	0.0183927i	$0.994145\pi$
$830$	0.128094	+	0.857384i	0.00444620	+	0.0297602i
$831$	−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
$835$	−8.18653	+	2.19357i	−0.283306	+	0.0759117i
$836$	38.8681	+	8.97744i	1.34428	+	0.310491i
$837$	9.43454	−	35.2102i	0.326105	−	1.21704i
$838$	18.2341	+	2.07843i	0.629887	+	0.0717981i
$839$			53.7004i			1.85394i	0.375131	+	0.926972i	$0.377598\pi$
$839$			53.7004i			1.85394i	−0.375131	+	0.926972i	$0.622402\pi$
$840$	6.84226	+	5.70104i	0.236081	+	0.196705i
$841$			4.19563i			0.144677i
$842$	−1.53177	+	13.4383i	−0.0527883	+	0.463114i
$843$	2.27680	−	8.49715i	0.0784173	−	0.292657i
$844$	41.9933	−	26.2346i	1.44547	−	0.903032i
$845$	−5.37373	+	1.43989i	−0.184862	+	0.0495336i
$846$	−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
$850$	2.54390	−	0.380060i	0.0872549	−	0.0130359i
$851$	−16.0466	+	59.8865i	−0.550069	+	2.05288i
$852$	4.65595	−	8.75449i	0.159510	−	0.299924i
$853$	−11.8429	+	11.8429i	−0.405495	+	0.405495i	−0.880164	−	0.474669i	$-0.842568\pi$
$853$	−11.8429	+	11.8429i	−0.405495	+	0.405495i	0.474669	+	0.880164i	$0.342568\pi$
$854$	−27.6335	−	5.77080i	−0.945600	−	0.197473i
$855$	−6.84808			−0.234199
$856$	−13.8825	−	16.2592i	−0.474493	−	0.555727i
$857$	−26.6655	−	46.1860i	−0.910875	−	1.57768i	−0.812830	−	0.582500i	$-0.802074\pi$
$857$	−26.6655	−	46.1860i	−0.910875	−	1.57768i	−0.0980448	−	0.995182i	$-0.531259\pi$
$858$	−19.8965	+	26.8859i	−0.679257	+	0.917868i
$859$	−4.27535	+	1.14558i	−0.145873	+	0.0390866i	−0.331017	−	0.943625i	$-0.607392\pi$
$859$	−4.27535	+	1.14558i	−0.145873	+	0.0390866i	0.185144	+	0.982711i	$0.440725\pi$
$860$	−5.78146	+	6.19863i	−0.197146	+	0.211372i
$861$	−1.19512	+	0.204438i	−0.0407296	+	0.00696722i
$862$	−13.7182	−	5.40451i	−0.467243	−	0.184078i
$863$	25.6631	+	14.8166i	0.873584	+	0.504364i	0.868538	−	0.495623i	$-0.165060\pi$
$863$	25.6631	+	14.8166i	0.873584	+	0.504364i	0.00504627	+	0.999987i	$0.498394\pi$
$864$	−16.5867	+	26.0217i	−0.564290	+	0.885276i
$865$	11.5480	+	20.0017i	0.392644	+	0.680079i
$866$	−20.4147	+	16.2369i	−0.693719	+	0.551753i
$867$	−11.5225	+	11.5225i	−0.391325	+	0.391325i
$868$	26.4000	−	23.5227i	0.896075	−	0.798414i
$869$	−3.62114	−	3.62114i	−0.122839	−	0.122839i
$870$	−0.949334	+	8.32854i	−0.0321854	+	0.282364i
$871$	−60.3012	+	34.8149i	−2.04323	+	1.17966i
$872$	−0.967044	+	0.179083i	−0.0327483	+	0.00606452i
$873$	−9.31973	+	16.1422i	−0.315425	+	0.546332i
$874$	16.2055	+	37.2752i	0.548160	+	1.26085i
$875$	2.48153	+	0.917599i	0.0838912	+	0.0310205i
$876$	11.8945	−	0.414192i	0.401879	−	0.0139943i
$877$	−8.93439	−	33.3436i	−0.301693	−	1.12593i	−0.935755	−	0.352651i	$-0.885280\pi$
$877$	−8.93439	−	33.3436i	−0.301693	−	1.12593i	0.634062	−	0.773282i	$-0.281386\pi$
$878$	3.14139	+	21.0267i	0.106017	+	0.709615i
$879$	−18.3604	+	10.6004i	−0.619282	+	0.357543i
$880$	8.09102	−	16.5807i	0.272748	−	0.558937i
$881$			36.3956i			1.22620i	0.790006	+	0.613099i	$0.210077\pi$
$881$			36.3956i			1.22620i	−0.790006	+	0.613099i	$0.789923\pi$
$882$	−13.2818	−	8.32802i	−0.447223	−	0.280419i
$883$	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	$0.651990\pi$
$884$	7.35911	−	13.8372i	0.247514	−	0.465395i
$885$	1.98430	+	0.531693i	0.0667016	+	0.0178727i
$886$	22.8409	−	30.8645i	0.767355	−	1.03691i
$887$	−24.8000	−	14.3183i	−0.832702	−	0.480761i	0.0220749	−	0.999756i	$-0.492973\pi$
$887$	−24.8000	−	14.3183i	−0.832702	−	0.480761i	−0.854777	+	0.518996i	$0.826306\pi$
$888$	−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
$891$	−2.07886	−	7.75840i	−0.0696443	−	0.259916i
$892$	6.25146	−	27.0659i	0.209314	−	0.906232i
$893$	−39.5967	−	10.6099i	−1.32505	−	0.355047i
$894$	−23.7221	−	29.8258i	−0.793385	−	0.997523i
$895$	−7.99993			−0.267408
$896$	−27.3054	+	12.2643i	−0.912211	+	0.409721i
$897$	−34.0796			−1.13789
$898$	18.1479	+	22.8173i	0.605603	+	0.761424i
$899$	32.1464	+	8.61360i	1.07214	+	0.287280i
$900$	−0.712769	+	3.08595i	−0.0237590	+	0.102865i
$901$	−2.09501	−	7.81869i	−0.0697949	−	0.260478i
$902$	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
$906$	17.4971	−	23.6436i	0.581303	−	0.785505i
$907$	−33.1507	−	8.88271i	−1.10075	−	0.294946i	−0.337681	−	0.941261i	$-0.609643\pi$
$907$	−33.1507	−	8.88271i	−1.10075	−	0.294946i	−0.763071	+	0.646315i	$0.776309\pi$
$908$	−15.5306	+	29.2018i	−0.515401	+	0.969097i
$909$	−14.3049	−	14.3049i	−0.474465	−	0.474465i
$910$	13.4888	−	8.82826i	0.447150	−	0.292654i
$911$		−	9.35688i		−	0.310007i	−0.987914	−	0.155004i	$-0.950461\pi$
$911$		−	9.35688i		−	0.310007i	0.987914	−	0.155004i	$-0.0495389\pi$
$912$	−9.02806	+	18.5010i	−0.298949	+	0.612629i
$913$	2.44856	−	1.41368i	0.0810354	−	0.0467858i
$914$	3.80573	+	25.4733i	0.125882	+	0.842582i
$915$	2.32397	+	8.67318i	0.0768281	+	0.286727i
$916$	30.8922	−	1.07573i	1.02071	−	0.0355430i
$917$	3.25637	+	3.92133i	0.107535	+	0.129494i
$918$	5.59427	+	12.8677i	0.184638	+	0.424696i
$919$	10.2064	−	17.6780i	0.336679	−	0.583145i	−0.647127	−	0.762382i	$-0.724030\pi$
$919$	10.2064	−	17.6780i	0.336679	−	0.583145i	0.983806	+	0.179238i	$0.0573631\pi$
$920$	18.4840	−	3.42299i	0.609401	−	0.112853i
$921$	−4.19675	+	2.42299i	−0.138288	+	0.0798404i
$922$	4.27474	−	37.5025i	0.140781	−	1.23508i
$923$	−12.6914	−	12.6914i	−0.417741	−	0.417741i
$924$	9.11978	−	27.5780i	0.300019	−	0.907248i
$925$	−6.59624	+	6.59624i	−0.216883	+	0.216883i
$926$	20.6520	−	16.4257i	0.678668	−	0.539783i
$927$	11.1110	+	19.2449i	0.364935	+	0.632085i
$928$	−23.7575	−	15.1434i	−0.779877	−	0.497107i
$929$	20.8897	+	12.0607i	0.685368	+	0.395697i	0.801874	−	0.597493i	$-0.203836\pi$
$929$	20.8897	+	12.0607i	0.685368	+	0.395697i	−0.116507	+	0.993190i	$0.537170\pi$
$930$	−10.4641	−	4.12252i	−0.343132	−	0.135183i
$931$	−27.3023	−	13.0728i	−0.894796	−	0.428443i
$932$	−9.40113	+	10.0795i	−0.307944	+	0.330165i
$933$	−4.66128	+	1.24898i	−0.152603	+	0.0408899i
$934$	−5.65684	+	7.64399i	−0.185097	+	0.250119i
$935$	−4.19444	−	7.26498i	−0.137173	−	0.237590i
$936$	12.5310	+	14.6764i	0.409590	+	0.479712i
$937$	−18.9747			−0.619878			−0.309939	−	0.950756i	$-0.600309\pi$
$937$	−18.9747			−0.619878			−0.309939	+	0.950756i	$0.600309\pi$
$938$	40.3011	−	45.0811i	1.31588	−	1.47195i
$939$	−0.0865839	+	0.0865839i	−0.00282556	+	0.00282556i
$940$	−8.90249	+	16.7392i	−0.290367	+	0.545971i
$941$	−2.72869	+	10.1836i	−0.0889526	+	0.331976i	−0.996033	−	0.0889811i	$-0.971639\pi$
$941$	−2.72869	+	10.1836i	−0.0889526	+	0.331976i	0.907081	+	0.420957i	$0.138306\pi$
$942$	3.86228	−	0.577027i	0.125840	−	0.0188005i
$943$	−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
$947$	−3.23796	+	0.867608i	−0.105219	+	0.0281935i	−0.311045	−	0.950395i	$-0.600679\pi$
$947$	−3.23796	+	0.867608i	−0.105219	+	0.0281935i	0.205825	+	0.978589i	$0.434012\pi$
$948$	2.24132	−	1.40023i	0.0727948	−	0.0454773i
$949$	5.57586	−	20.8094i	0.181000	−	0.675501i
$950$	−0.692604	+	6.07625i	−0.0224711	+	0.197139i
$951$			32.0859i			1.04046i
$952$	−2.31695	+	13.4118i	−0.0750929	+	0.434678i
$953$			49.2651i			1.59585i	0.602755	+	0.797927i	$0.294070\pi$
$953$			49.2651i			1.59585i	−0.602755	+	0.797927i	$0.705930\pi$
$954$	9.90305	+	1.12880i	0.320623	+	0.0365464i
$955$	−0.514220	+	1.91909i	−0.0166398	+	0.0621004i
$956$	−17.1372	−	3.95823i	−0.554258	−	0.128018i
$957$	26.4075	−	7.07586i	0.853632	−	0.228730i
$958$	−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
$962$	8.39871	+	56.2161i	0.270785	+	1.81248i
$963$	3.09809	−	11.5622i	0.0998346	−	0.372588i
$964$	8.83411	+	28.9053i	0.284528	+	0.930976i
$965$	5.05087	−	5.05087i	0.162593	−	0.162593i
$966$	28.1146	−	9.24591i	0.904571	−	0.297482i
$967$	27.3624			0.879916			0.439958	−	0.898018i	$-0.354993\pi$
$967$	27.3624			0.879916			0.439958	+	0.898018i	$0.354993\pi$
$968$	−28.9696	−	2.28427i	−0.931119	−	0.0734193i
$969$	4.68020	+	8.10635i	0.150350	+	0.260413i
$970$	13.3803	+	9.90193i	0.429616	+	0.317932i
$971$	11.5141	−	3.08520i	0.369506	−	0.0990089i	−0.0692874	−	0.997597i	$-0.522073\pi$
$971$	11.5141	−	3.08520i	0.369506	−	0.0990089i	0.438794	+	0.898588i	$0.355406\pi$
$972$	−28.5680	+	0.994797i	−0.916321	+	0.0319081i
$973$	29.5549	+	10.9285i	0.947487	+	0.350353i
$974$	−2.34154	+	5.94349i	−0.0750279	+	0.190442i
$975$	−4.44070	−	2.56384i	−0.142216	−	0.0821085i
$976$	−29.6232	−	5.76422i	−0.948214	−	0.184508i
$977$	15.8798	+	27.5046i	0.508040	+	0.879951i	0.999957	+	0.00930873i	$0.00296310\pi$
$977$	15.8798	+	27.5046i	0.508040	+	0.879951i	−0.491917	+	0.870642i	$0.663704\pi$
$978$	−9.91056	−	12.4605i	−0.316905	−	0.398444i
$979$	34.3239	−	34.3239i	1.09700	−	1.09700i
$980$	−8.73269	+	10.9426i	−0.278956	+	0.349548i
$981$	−0.389362	−	0.389362i	−0.0124314	−	0.0124314i
$982$	5.53927	+	0.631397i	0.176765	+	0.0201487i
$983$	−25.3848	+	14.6559i	−0.809648	+	0.467450i	−0.846834	−	0.531858i	$-0.821494\pi$
$983$	−25.3848	+	14.6559i	−0.809648	+	0.467450i	0.0371857	+	0.999308i	$0.488161\pi$
$984$	−1.27453	+	0.236025i	−0.0406304	+	0.00752419i
$985$	8.36153	−	14.4826i	0.266421	−	0.461454i
$986$	−11.7480	+	5.10749i	−0.374133	+	0.162656i
$987$	−10.3523	+	27.9966i	−0.329518	+	0.891141i
$988$	27.2501	+	25.4162i	0.866942	+	0.808597i
$989$	7.29035	+	27.2080i	0.231820	+	0.865163i
$990$	10.2163	−	1.52632i	0.324694	−	0.0485095i
$991$	−5.89119	+	3.40128i	−0.187140	+	0.108045i	−0.590643	−	0.806933i	$-0.701126\pi$
$991$	−5.89119	+	3.40128i	−0.187140	+	0.108045i	0.403503	+	0.914978i	$0.367792\pi$
$992$	27.8759	−	25.5309i	0.885060	−	0.810607i
$993$		−	10.1133i		−	0.320936i
$994$	13.9132	+	7.02674i	0.441299	+	0.222875i
$995$	−16.3587	−	16.3587i	−0.518607	−	0.518607i
$996$	0.426454	+	1.39536i	0.0135127	+	0.0442137i
$997$	50.8342	+	13.6210i	1.60994	+	0.431381i	0.948023	−	0.318201i	$-0.103079\pi$
$997$	50.8342	+	13.6210i	1.60994	+	0.431381i	0.661912	+	0.749581i	$0.269745\pi$
$998$	2.28951	+	1.69432i	0.0724732	+	0.0536328i
$999$	−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.411.46	yes	256
7.3	odd	6	inner	560.2.cq.a.171.5	yes	256
16.3	odd	4	inner	560.2.cq.a.131.5	✓	256
112.3	even	12	inner	560.2.cq.a.451.46	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.5	✓	256	16.3	odd	4	inner
560.2.cq.a.171.5	yes	256	7.3	odd	6	inner
560.2.cq.a.411.46	yes	256	1.1	even	1	trivial
560.2.cq.a.451.46	yes	256	112.3	even	12	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+(0.880314 + 1.10682i) q^{2} +(1.14957 + 0.308027i) q^{3} +(-0.450094 + 1.94870i) q^{4} +(0.258819 + 0.965926i) 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} +(-0.841263 + 1.13678i) q^{10} +(4.45522 + 1.19377i) q^{11} +(-1.11767 + 2.10153i) q^{12} +(3.04658 + 3.04658i) q^{13} +(-3.33988 - 1.68678i) q^{14} +1.19013i q^{15} +(-3.59483 - 1.75419i) q^{16} +(-1.57510 + 0.909386i) q^{17} +(-0.330917 - 2.21496i) q^{18} +(-1.11923 - 4.17703i) q^{19} +(-1.99879 + 0.0696019i) q^{20} +(-3.10370 + 0.530919i) q^{21} +(2.60070 + 5.98202i) q^{22} +(-3.32310 + 5.75579i) q^{23} +(-3.30991 + 0.612949i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(-0.690064 + 6.05396i) q^{26} +(-3.85731 - 3.85731i) q^{27} +(-1.07318 - 5.18153i) q^{28} +(3.52167 - 3.52167i) q^{29} +(-1.31725 + 1.04768i) q^{30} +(3.34114 + 5.78702i) q^{31} +(-1.22301 - 5.52307i) q^{32} +(4.75389 + 2.74466i) q^{33} +(-2.39311 - 0.942807i) q^{34} +(-1.69027 - 2.03543i) q^{35} +(2.16025 - 2.31613i) q^{36} +(9.01063 - 2.41439i) q^{37} +(3.63794 - 4.91588i) q^{38} +(2.56384 + 4.44070i) q^{39} +(-1.83660 - 2.15102i) q^{40} +0.385064 q^{41} +(-3.31986 - 2.96785i) q^{42} +(2.99684 - 2.99684i) q^{43} +(-4.33157 + 8.14456i) q^{44} +(0.409866 - 1.52964i) q^{45} +(-9.29599 + 1.38883i) 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} +(-2.09081 + 0.560231i) q^{51} +(-7.30811 + 4.56561i) q^{52} +(-1.15188 + 4.29888i) q^{53} +(0.873698 - 7.66499i) q^{54} +4.61239i q^{55} +(4.79028 - 5.74919i) q^{56} -5.14656i q^{57} +(6.99803 + 0.797675i) q^{58} +(0.446753 - 1.66731i) q^{59} +(-2.31919 - 0.535669i) q^{60} +(7.28761 - 1.95271i) 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} +(1.14708 + 7.67786i) q^{66} +(-4.18277 + 15.6103i) q^{67} +(-1.06317 - 3.47870i) q^{68} +(-5.59309 + 5.59309i) q^{69} +(0.764882 - 3.66264i) q^{70} -4.16577 q^{71} +(4.46524 + 0.352086i) q^{72} +(-2.50010 - 4.33030i) q^{73} +(10.6045 + 7.84771i) q^{74} +(-1.14957 + 0.308027i) q^{75} +(8.64352 - 0.300985i) q^{76} +(-12.0285 + 2.05760i) q^{77} +(-2.65806 + 6.74691i) q^{78} +(-0.961534 - 0.555142i) q^{79} +(0.764010 - 3.92636i) q^{80} +(-0.870708 - 1.50811i) q^{81} +(0.338977 + 0.426196i) q^{82} +(0.433450 - 0.433450i) q^{83} +(0.362356 - 6.28712i) q^{84} +(-1.28607 - 1.28607i) q^{85} +(5.95512 + 0.678797i) q^{86} +(5.13320 - 2.96365i) q^{87} +(-12.8277 + 2.37551i) q^{88} +(5.26207 - 9.11416i) q^{89} +(2.05384 - 0.892916i) q^{90} +(-10.6917 - 3.95349i) q^{91} +(-9.72056 - 9.06637i) q^{92} +(2.05832 + 7.68177i) q^{93} +(13.2591 - 1.98091i) q^{94} +(3.74502 - 2.16219i) q^{95} +(0.295320 - 6.72589i) q^{96} -11.7703i q^{97} +(9.89292 + 0.360797i) 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

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