LMFDB - Embedded newform 280.2.bf.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(109,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 4]))

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

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

chi := DirichletCharacter("280.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	280.109
Dual form			280.2.bf.a.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14463 + 0.830552i) q^{2} +(-0.755963 + 1.30937i) q^{3} +(0.620368 - 1.90135i) q^{4} +(1.54124 + 1.62006i) q^{5} +(-0.222196 - 2.12661i) q^{6} +(0.727432 - 2.54379i) q^{7} +(0.869078 + 2.69160i) q^{8} +(0.357040 + 0.618411i) q^{9} +O(q^{10})$	\(q+(-1.14463 + 0.830552i) q^{2} +(-0.755963 + 1.30937i) q^{3} +(0.620368 - 1.90135i) q^{4} +(1.54124 + 1.62006i) q^{5} +(-0.222196 - 2.12661i) q^{6} +(0.727432 - 2.54379i) q^{7} +(0.869078 + 2.69160i) q^{8} +(0.357040 + 0.618411i) q^{9} +(-3.10969 - 0.574295i) q^{10} +(2.74300 + 1.58367i) q^{11} +(2.02059 + 2.24964i) q^{12} +2.70350 q^{13} +(1.28010 + 3.51587i) q^{14} +(-3.28637 + 0.793340i) q^{15} +(-3.23029 - 2.35908i) q^{16} +(-1.04534 - 0.603526i) q^{17} +(-0.922301 - 0.411313i) q^{18} +(-1.40659 + 0.812094i) q^{19} +(4.03644 - 1.92540i) q^{20} +(2.78084 + 2.87548i) q^{21} +(-4.45505 + 0.465481i) q^{22} +(-4.43276 + 2.55925i) q^{23} +(-4.18128 - 0.896807i) q^{24} +(-0.249177 + 4.99379i) q^{25} +(-3.09452 + 2.24540i) q^{26} -5.61541 q^{27} +(-4.38536 - 2.96119i) q^{28} +7.61892i q^{29} +(3.10277 - 3.63758i) q^{30} +(3.28998 - 5.69841i) q^{31} +(5.65683 + 0.0173567i) q^{32} +(-4.14721 + 2.39439i) q^{33} +(1.69779 - 0.177391i) q^{34} +(5.24222 - 2.74209i) q^{35} +(1.39731 - 0.295216i) q^{36} +(3.37235 + 5.84109i) q^{37} +(0.935541 - 2.09779i) q^{38} +(-2.04375 + 3.53987i) q^{39} +(-3.02109 + 5.55635i) q^{40} +1.50265 q^{41} +(-5.57127 - 0.981744i) q^{42} -10.2537 q^{43} +(4.71279 - 4.23295i) q^{44} +(-0.451579 + 1.53154i) q^{45} +(2.94829 - 6.61104i) q^{46} +(9.29346 - 5.36558i) q^{47} +(5.53087 - 2.44625i) q^{48} +(-5.94169 - 3.70086i) q^{49} +(-3.86238 - 5.92301i) q^{50} +(1.58047 - 0.912487i) q^{51} +(1.67717 - 5.14031i) q^{52} +(6.00716 - 10.4047i) q^{53} +(6.42759 - 4.66389i) q^{54} +(1.66197 + 6.88463i) q^{55} +(7.47904 - 0.252794i) q^{56} -2.45565i q^{57} +(-6.32791 - 8.72087i) q^{58} +(-3.70520 - 2.13920i) q^{59} +(-0.530338 + 6.74071i) q^{60} +(1.49532 - 0.863325i) q^{61} +(0.967007 + 9.25509i) q^{62} +(1.83283 - 0.458380i) q^{63} +(-6.48941 + 4.67842i) q^{64} +(4.16674 + 4.37983i) q^{65} +(2.75837 - 6.18518i) q^{66} +(3.51118 - 6.08154i) q^{67} +(-1.79601 + 1.61315i) q^{68} -7.73880i q^{69} +(-3.72297 + 7.49263i) q^{70} +3.59648 q^{71} +(-1.35422 + 1.49845i) q^{72} +(6.79792 + 3.92478i) q^{73} +(-8.71143 - 3.88499i) q^{74} +(-6.35033 - 4.10138i) q^{75} +(0.671475 + 3.17822i) q^{76} +(6.02387 - 5.82559i) q^{77} +(-0.600708 - 5.74929i) q^{78} +(6.05565 + 10.4887i) q^{79} +(-1.15680 - 8.86915i) q^{80} +(3.17393 - 5.49740i) q^{81} +(-1.71998 + 1.24803i) q^{82} -5.03944 q^{83} +(7.19245 - 3.50349i) q^{84} +(-0.633366 - 2.62368i) q^{85} +(11.7367 - 8.51622i) q^{86} +(-9.97596 - 5.75962i) q^{87} +(-1.87873 + 8.75939i) q^{88} +(-4.65527 - 8.06316i) q^{89} +(-0.755133 - 2.12811i) q^{90} +(1.96661 - 6.87713i) q^{91} +(2.11610 + 10.0159i) q^{92} +(4.97421 + 8.61558i) q^{93} +(-6.18120 + 13.8603i) q^{94} +(-3.48353 - 1.02713i) q^{95} +(-4.29908 + 7.39374i) q^{96} -15.2877i q^{97} +(9.87480 - 0.698751i) q^{98} +2.26173i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) $ 88 * q - 2 * q^4 - 40 * q^9	$ 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) $ 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.14463	+	0.830552i	−0.809378	+	0.587289i
$2$	−1.14463	+	0.830552i	−0.809378	+	0.587289i
$3$	−0.755963	+	1.30937i	−0.436455	+	0.755963i	−0.997413	−	0.0718814i	$-0.977100\pi$
$3$	−0.755963	+	1.30937i	−0.436455	+	0.755963i	0.560958	+	0.827844i	$0.310433\pi$
$4$	0.620368	−	1.90135i	0.310184	−	0.950677i
$5$	1.54124	+	1.62006i	0.689262	+	0.724512i
$5$	1.54124	+	1.62006i	0.689262	+	0.724512i
$6$	−0.222196	−	2.12661i	−0.0907113	−	0.868185i
$7$	0.727432	−	2.54379i	0.274943	−	0.961460i
$7$	0.727432	−	2.54379i	0.274943	−	0.961460i
$8$	0.869078	+	2.69160i	0.307266	+	0.951624i
$9$	0.357040	+	0.618411i	0.119013	+	0.206137i
$10$	−3.10969	−	0.574295i	−0.983371	−	0.181608i
$11$	2.74300	+	1.58367i	0.827045	+	0.477495i	0.852840	−	0.522172i	$-0.174878\pi$
$11$	2.74300	+	1.58367i	0.827045	+	0.477495i	−0.0257945	+	0.999667i	$0.508212\pi$
$12$	2.02059	+	2.24964i	0.583295	+	0.649416i
$13$	2.70350			0.749816			0.374908	−	0.927062i	$-0.377674\pi$
$13$	2.70350			0.749816			0.374908	+	0.927062i	$0.377674\pi$
$14$	1.28010	+	3.51587i	0.342122	+	0.939656i
$15$	−3.28637	+	0.793340i	−0.848537	+	0.204839i
$16$	−3.23029	−	2.35908i	−0.807572	−	0.589769i
$17$	−1.04534	−	0.603526i	−0.253532	−	0.146377i	0.367849	−	0.929886i	$-0.380094\pi$
$17$	−1.04534	−	0.603526i	−0.253532	−	0.146377i	−0.621380	+	0.783509i	$0.713428\pi$
$18$	−0.922301	−	0.411313i	−0.217389	−	0.0969475i
$19$	−1.40659	+	0.812094i	−0.322693	+	0.186307i	−0.652593	−	0.757709i	$-0.726319\pi$
$19$	−1.40659	+	0.812094i	−0.322693	+	0.186307i	0.329899	+	0.944016i	$0.392985\pi$
$20$	4.03644	−	1.92540i	0.902575	−	0.430533i
$21$	2.78084	+	2.87548i	0.606828	+	0.627482i
$22$	−4.45505	+	0.465481i	−0.949819	+	0.0992408i
$23$	−4.43276	+	2.55925i	−0.924294	+	0.533641i	−0.885002	−	0.465587i	$-0.845843\pi$
$23$	−4.43276	+	2.55925i	−0.924294	+	0.533641i	−0.0392914	+	0.999228i	$0.512510\pi$
$24$	−4.18128	−	0.896807i	−0.853500	−	0.183060i
$25$	−0.249177	+	4.99379i	−0.0498354	+	0.998757i
$26$	−3.09452	+	2.24540i	−0.606885	+	0.440359i
$27$	−5.61541			−1.08069
$28$	−4.38536	−	2.96119i	−0.828755	−	0.559612i
$29$			7.61892i			1.41480i	0.706814	+	0.707399i	$0.250132\pi$
$29$			7.61892i			1.41480i	−0.706814	+	0.707399i	$0.749868\pi$
$30$	3.10277	−	3.63758i	0.566487	−	0.664128i
$31$	3.28998	−	5.69841i	0.590898	−	1.02347i	−0.403214	−	0.915106i	$-0.632107\pi$
$31$	3.28998	−	5.69841i	0.590898	−	1.02347i	0.994112	−	0.108359i	$-0.0345597\pi$
$32$	5.65683	+	0.0173567i	0.999995	+	0.00306826i
$33$	−4.14721	+	2.39439i	−0.721937	+	0.416811i
$34$	1.69779	−	0.177391i	0.291168	−	0.0304224i
$35$	5.24222	−	2.74209i	0.886098	−	0.463498i
$36$	1.39731	−	0.295216i	0.232886	−	0.0492027i
$37$	3.37235	+	5.84109i	0.554411	+	0.960269i	0.997949	+	0.0640130i	$0.0203899\pi$
$37$	3.37235	+	5.84109i	0.554411	+	0.960269i	−0.443538	+	0.896256i	$0.646277\pi$
$38$	0.935541	−	2.09779i	0.151765	−	0.340307i
$39$	−2.04375	+	3.53987i	−0.327261	+	0.566833i
$40$	−3.02109	+	5.55635i	−0.477676	+	0.878536i
$41$	1.50265			0.234675			0.117337	−	0.993092i	$-0.462564\pi$
$41$	1.50265			0.234675			0.117337	+	0.993092i	$0.462564\pi$
$42$	−5.57127	−	0.981744i	−0.859666	−	0.151486i
$43$	−10.2537			−1.56367			−0.781837	−	0.623483i	$-0.785717\pi$
$43$	−10.2537			−1.56367			−0.781837	+	0.623483i	$0.785717\pi$
$44$	4.71279	−	4.23295i	0.710479	−	0.638141i
$45$	−0.451579	+	1.53154i	−0.0673174	+	0.228309i
$46$	2.94829	−	6.61104i	0.434701	−	0.974744i
$47$	9.29346	−	5.36558i	1.35559	−	0.782650i	0.366564	−	0.930393i	$-0.380534\pi$
$47$	9.29346	−	5.36558i	1.35559	−	0.782650i	0.989026	+	0.147743i	$0.0472007\pi$
$48$	5.53087	−	2.44625i	0.798313	−	0.353086i
$49$	−5.94169	−	3.70086i	−0.848812	−	0.528694i
$50$	−3.86238	−	5.92301i	−0.546223	−	0.837640i
$51$	1.58047	−	0.912487i	0.221311	−	0.127774i
$52$	1.67717	−	5.14031i	0.232581	−	0.712833i
$53$	6.00716	−	10.4047i	0.825147	−	1.42920i	−0.0766604	−	0.997057i	$-0.524426\pi$
$53$	6.00716	−	10.4047i	0.825147	−	1.42920i	0.901807	−	0.432139i	$-0.142241\pi$
$54$	6.42759	−	4.66389i	0.874684	−	0.634675i
$55$	1.66197	+	6.88463i	0.224100	+	0.928324i
$56$	7.47904	−	0.252794i	0.999429	−	0.0337811i
$57$		−	2.45565i		−	0.325259i
$58$	−6.32791	−	8.72087i	−0.830895	−	1.14511i
$59$	−3.70520	−	2.13920i	−0.482376	−	0.278500i	0.239030	−	0.971012i	$-0.423170\pi$
$59$	−3.70520	−	2.13920i	−0.482376	−	0.278500i	−0.721406	+	0.692512i	$0.756504\pi$
$60$	−0.530338	+	6.74071i	−0.0684664	+	0.870222i
$61$	1.49532	−	0.863325i	0.191456	−	0.110537i	−0.401208	−	0.915987i	$-0.631409\pi$
$61$	1.49532	−	0.863325i	0.191456	−	0.110537i	0.592664	+	0.805450i	$0.298076\pi$
$62$	0.967007	+	9.25509i	0.122810	+	1.17540i
$63$	1.83283	−	0.458380i	0.230914	−	0.0577505i
$64$	−6.48941	+	4.67842i	−0.811176	+	0.584803i
$65$	4.16674	+	4.37983i	0.516820	+	0.543251i
$66$	2.75837	−	6.18518i	0.339532	−	0.761343i
$67$	3.51118	−	6.08154i	0.428958	−	0.742978i	−0.567823	−	0.823151i	$-0.692214\pi$
$67$	3.51118	−	6.08154i	0.428958	−	0.742978i	0.996781	+	0.0801732i	$0.0255473\pi$
$68$	−1.79601	+	1.61315i	−0.217798	+	0.195623i
$69$		−	7.73880i		−	0.931643i
$70$	−3.72297	+	7.49263i	−0.444980	+	0.895540i
$71$	3.59648			0.426823			0.213412	−	0.976962i	$-0.431542\pi$
$71$	3.59648			0.426823			0.213412	+	0.976962i	$0.431542\pi$
$72$	−1.35422	+	1.49845i	−0.159596	+	0.176595i
$73$	6.79792	+	3.92478i	0.795636	+	0.459361i	0.841943	−	0.539567i	$-0.181412\pi$
$73$	6.79792	+	3.92478i	0.795636	+	0.459361i	−0.0463069	+	0.998927i	$0.514745\pi$
$74$	−8.71143	−	3.88499i	−1.01268	−	0.451620i
$75$	−6.35033	−	4.10138i	−0.733273	−	0.473587i
$76$	0.671475	+	3.17822i	0.0770235	+	0.364567i
$77$	6.02387	−	5.82559i	0.686483	−	0.663887i
$78$	−0.600708	−	5.74929i	−0.0680168	−	0.650979i
$79$	6.05565	+	10.4887i	0.681313	+	1.18007i	0.974580	+	0.224039i	$0.0719243\pi$
$79$	6.05565	+	10.4887i	0.681313	+	1.18007i	−0.293267	+	0.956031i	$0.594742\pi$
$80$	−1.15680	−	8.86915i	−0.129334	−	0.991601i
$81$	3.17393	−	5.49740i	0.352659	−	0.610822i
$82$	−1.71998	+	1.24803i	−0.189940	+	0.137822i
$83$	−5.03944			−0.553151			−0.276575	−	0.960992i	$-0.589200\pi$
$83$	−5.03944			−0.553151			−0.276575	+	0.960992i	$0.589200\pi$
$84$	7.19245	−	3.50349i	0.784761	−	0.382262i
$85$	−0.633366	−	2.62368i	−0.0686982	−	0.284579i
$86$	11.7367	−	8.51622i	1.26560	−	0.918328i
$87$	−9.97596	−	5.75962i	−1.06954	−	0.617496i
$88$	−1.87873	+	8.75939i	−0.200273	+	0.933754i
$89$	−4.65527	−	8.06316i	−0.493457	−	0.854693i	0.506514	−	0.862232i	$-0.330934\pi$
$89$	−4.65527	−	8.06316i	−0.493457	−	0.854693i	−0.999972	+	0.00753847i	$0.997600\pi$
$90$	−0.755133	−	2.12811i	−0.0795980	−	0.224323i
$91$	1.96661	−	6.87713i	0.206157	−	0.720919i
$92$	2.11610	+	10.0159i	0.220619	+	1.04423i
$93$	4.97421	+	8.61558i	0.515801	+	0.893394i
$94$	−6.18120	+	13.8603i	−0.637542	+	1.42958i
$95$	−3.48353	−	1.02713i	−0.357402	−	0.105381i
$96$	−4.29908	+	7.39374i	−0.438773	+	0.754620i
$97$		−	15.2877i		−	1.55224i	−0.630588	−	0.776118i	$-0.717186\pi$
$97$		−	15.2877i		−	1.55224i	0.630588	−	0.776118i	$-0.282814\pi$
$98$	9.87480	−	0.698751i	0.997506	−	0.0705845i
$99$			2.26173i			0.227313i
$100$	9.34037	+	3.57176i	0.934037	+	0.357176i
$101$	−5.94317	−	3.43129i	−0.591368	−	0.341426i	0.174270	−	0.984698i	$-0.444243\pi$
$101$	−5.94317	−	3.43129i	−0.591368	−	0.341426i	−0.765638	+	0.643272i	$0.777577\pi$
$102$	−1.05119	+	2.35713i	−0.104084	+	0.233390i
$103$	−0.446355	+	0.257703i	−0.0439806	+	0.0253922i	−0.521829	−	0.853050i	$-0.674750\pi$
$103$	−0.446355	+	0.257703i	−0.0439806	+	0.0253922i	0.477848	+	0.878442i	$0.341417\pi$
$104$	2.34955	+	7.27674i	0.230393	+	0.713543i
$105$	−0.372523	+	8.93692i	−0.0363545	+	0.872154i
$106$	1.76565	+	16.8988i	0.171495	+	1.64136i
$107$	4.14689	+	7.18262i	0.400895	+	0.694370i	0.993834	−	0.110877i	$-0.0353660\pi$
$107$	4.14689	+	7.18262i	0.400895	+	0.694370i	−0.592940	+	0.805247i	$0.702033\pi$
$108$	−3.48362	+	10.6769i	−0.335212	+	1.02738i
$109$	−11.3268	−	6.53951i	−1.08491	−	0.626372i	−0.152691	−	0.988274i	$-0.548794\pi$
$109$	−11.3268	−	6.53951i	−1.08491	−	0.626372i	−0.932216	+	0.361902i	$0.882127\pi$
$110$	−7.62039	−	6.50002i	−0.726576	−	0.619753i
$111$	−10.1975			−0.967904
$112$	−8.35080	+	6.50109i	−0.789076	+	0.614295i
$113$		−	0.0149801i		−	0.00140921i	−1.00000		0.000704606i	$-0.999776\pi$
$113$		−	0.0149801i		−	0.00140921i	1.00000		0.000704606i	$-0.000224283\pi$
$114$	2.03955	+	2.81082i	0.191021	+	0.263257i
$115$	−10.9781	−	3.23691i	−1.02371	−	0.301843i
$116$	14.4863	+	4.72654i	1.34502	+	0.438848i
$117$	0.965257	+	1.67187i	0.0892380	+	0.154565i
$118$	6.01780	−	0.628763i	0.553984	−	0.0578823i
$119$	−2.29565	+	2.22009i	−0.210442	+	0.203515i
$120$	−4.99146	−	8.15611i	−0.455656	−	0.744547i
$121$	−0.483970	−	0.838260i	−0.0439972	−	0.0762054i
$122$	−0.994559	+	2.23013i	−0.0900431	+	0.201907i
$123$	−1.13595	+	1.96752i	−0.102425	+	0.177405i
$124$	−8.79370	−	9.79053i	−0.789697	−	0.879215i
$125$	−8.47427	+	7.29293i	−0.757961	+	0.652299i
$126$	−1.71720	+	2.04693i	−0.152981	+	0.182355i
$127$		−	4.21851i		−	0.374332i	−0.982328	−	0.187166i	$-0.940070\pi$
$127$		−	4.21851i		−	0.374332i	0.982328	−	0.187166i	$-0.0599302\pi$
$128$	3.54232	−	10.7449i	0.313099	−	0.949720i
$129$	7.75141	−	13.4258i	0.682474	−	1.18208i
$130$	−8.40706	−	1.55261i	−0.737348	−	0.136173i
$131$	−11.6736	+	6.73978i	−1.01993	+	0.588858i	−0.914084	−	0.405525i	$-0.867089\pi$
$131$	−11.6736	+	6.73978i	−1.01993	+	0.588858i	−0.105847	+	0.994382i	$0.533755\pi$
$132$	1.97979	+	9.37072i	0.172319	+	0.815617i
$133$	1.04260	+	4.16880i	0.0904045	+	0.361481i
$134$	1.03202	+	9.87734i	0.0891531	+	0.853272i
$135$	−8.65468	−	9.09730i	−0.744877	−	0.782971i
$136$	0.715969	−	3.33814i	0.0613939	−	0.286243i
$137$	7.07465	+	4.08455i	0.604428	+	0.348967i	0.770782	−	0.637100i	$-0.219866\pi$
$137$	7.07465	+	4.08455i	0.604428	+	0.348967i	−0.166354	+	0.986066i	$0.553199\pi$
$138$	6.42748	+	8.85809i	0.547143	+	0.754051i
$139$		−	7.58198i		−	0.643095i	−0.946893	−	0.321548i	$-0.895797\pi$
$139$		−	7.58198i		−	0.643095i	0.946893	−	0.321548i	$-0.104203\pi$
$140$	−1.96158	−	11.6684i	−0.165784	−	0.986162i
$141$			16.2247i			1.36637i
$142$	−4.11665	+	2.98706i	−0.345461	+	0.250669i
$143$	7.41570	+	4.28146i	0.620132	+	0.358033i
$144$	0.305538	−	2.83993i	0.0254615	−	0.236661i
$145$	−12.3431	+	11.7426i	−1.02504	+	0.975167i
$146$	−11.0409	+	1.15359i	−0.913747	+	0.0954718i
$147$	9.33748	−	4.98213i	0.770142	−	0.410919i
$148$	13.1981	−	2.78841i	1.08487	−	0.229206i
$149$	6.99868	−	4.04069i	0.573354	−	0.331026i	−0.185134	−	0.982713i	$-0.559272\pi$
$149$	6.99868	−	4.04069i	0.573354	−	0.331026i	0.758488	+	0.651687i	$0.225939\pi$
$150$	10.6752	−	0.579700i	0.871627	−	0.0473323i
$151$	5.86473	−	10.1580i	0.477265	−	0.826647i	−0.522396	−	0.852703i	$-0.674962\pi$
$151$	5.86473	−	10.1580i	0.477265	−	0.826647i	0.999660	+	0.0260563i	$0.00829492\pi$
$152$	−3.40827	−	3.08020i	−0.276447	−	0.249837i
$153$		−	0.861931i		−	0.0696830i
$154$	−2.05666	+	11.6713i	−0.165730	+	0.940499i
$155$	14.3024	−	3.45265i	1.14880	−	0.277323i
$156$	5.46267	+	6.08191i	0.437364	+	0.486942i
$157$	−2.69276	+	4.66399i	−0.214905	+	0.372227i	−0.953243	−	0.302204i	$-0.902278\pi$
$157$	−2.69276	+	4.66399i	−0.214905	+	0.372227i	0.738338	+	0.674431i	$0.235611\pi$
$158$	−15.6429	−	6.97617i	−1.24448	−	0.554994i
$159$	9.08238	+	15.7311i	0.720280	+	1.24756i
$160$	8.69039	+	9.19114i	0.687036	+	0.726623i
$161$	3.28566	+	13.1377i	0.258946	+	1.03539i
$162$	0.932896	+	8.92862i	0.0732952	+	0.701498i
$163$	6.78320	+	11.7488i	0.531301	+	0.920240i	0.999333	+	0.0365284i	$0.0116299\pi$
$163$	6.78320	+	11.7488i	0.531301	+	0.920240i	−0.468032	+	0.883712i	$0.655037\pi$
$164$	0.932197	−	2.85707i	0.0727923	−	0.223100i
$165$	−10.2709	−	3.02840i	−0.799588	−	0.235760i
$166$	5.76831	−	4.18552i	0.447708	−	0.324859i
$167$			2.64012i			0.204299i	0.994769	+	0.102149i	$0.0325719\pi$
$167$			2.64012i			0.204299i	−0.994769	+	0.102149i	$0.967428\pi$
$168$	−5.32288	+	9.98391i	−0.410669	+	0.770276i
$169$	−5.69108			−0.437775
$170$	2.90408	+	2.47711i	0.222733	+	0.189986i
$171$	−1.00442	−	0.579900i	−0.0768096	−	0.0443460i
$172$	−6.36106	+	19.4959i	−0.485026	+	1.48655i
$173$	−9.88500	−	17.1213i	−0.751542	−	1.30171i	−0.947075	−	0.321012i	$-0.895977\pi$
$173$	−9.88500	−	17.1213i	−0.751542	−	1.30171i	0.195533	−	0.980697i	$-0.437356\pi$
$174$	16.2025	−	1.69290i	1.22831	−	0.128338i
$175$	12.5219	+	4.26649i	0.946564	+	0.322516i
$176$	−5.12467	−	11.5867i	−0.386287	−	0.873377i
$177$	5.60198	−	3.23431i	0.421071	−	0.243105i
$178$	12.0254	+	5.36292i	0.901345	+	0.401968i
$179$	10.1585	+	5.86504i	0.759285	+	0.438374i	0.829039	−	0.559191i	$-0.188888\pi$
$179$	10.1585	+	5.86504i	0.759285	+	0.438374i	−0.0697537	+	0.997564i	$0.522221\pi$
$180$	2.63186	+	1.80873i	0.196167	+	0.134815i
$181$		−	25.0507i		−	1.86200i	−0.365017	−	0.931001i	$-0.618937\pi$
$181$		−	25.0507i		−	1.86200i	0.365017	−	0.931001i	$-0.381063\pi$
$182$	3.46076	+	9.50516i	0.256529	+	0.704569i
$183$			2.61057i			0.192979i
$184$	−10.7409	−	9.70701i	−0.791829	−	0.715610i
$185$	−4.26531	+	14.4659i	−0.313591	+	1.06355i
$186$	−12.8493	−	5.73034i	−0.942158	−	0.420169i
$187$	−1.91157	−	3.31094i	−0.139788	−	0.242120i
$188$	−4.43650	−	20.9988i	−0.323565	−	1.53149i
$189$	−4.08483	+	14.2844i	−0.297128	+	1.03904i
$190$	4.84044	−	1.71757i	0.351162	−	0.124605i
$191$	−7.84336	−	13.5851i	−0.567525	−	0.982983i	−0.996810	−	0.0798133i	$-0.974568\pi$
$191$	−7.84336	−	13.5851i	−0.567525	−	0.982983i	0.429285	−	0.903169i	$-0.358766\pi$
$192$	−1.22002	−	12.0337i	−0.0880471	−	0.868459i
$193$	−0.118285	−	0.0682916i	−0.00851431	−	0.00491574i	0.495737	−	0.868473i	$-0.334898\pi$
$193$	−0.118285	−	0.0682916i	−0.00851431	−	0.00491574i	−0.504251	+	0.863557i	$0.668231\pi$
$194$	12.6973	+	17.4989i	0.911610	+	1.25634i
$195$	−8.88470	+	2.14480i	−0.636247	+	0.153592i
$196$	−10.7227	+	9.00135i	−0.765905	+	0.642953i
$197$	−7.82223			−0.557311			−0.278655	−	0.960391i	$-0.589889\pi$
$197$	−7.82223			−0.557311			−0.278655	+	0.960391i	$0.589889\pi$
$198$	−1.87849	−	2.58885i	−0.133498	−	0.183982i
$199$	−0.796260	+	1.37916i	−0.0564454	+	0.0977663i	−0.892867	−	0.450320i	$-0.851310\pi$
$199$	−0.796260	+	1.37916i	−0.0564454	+	0.0977663i	0.836422	+	0.548086i	$0.184643\pi$
$200$	−13.6578	+	3.66931i	−0.965754	+	0.259459i
$201$	5.30864	+	9.19483i	0.374443	+	0.648553i
$202$	9.65261	−	1.00854i	0.679155	−	0.0709608i
$203$	19.3809	+	5.54225i	1.36027	+	0.388989i
$204$	−0.754484	−	3.57112i	−0.0528245	−	0.250028i
$205$	2.31594	+	2.43438i	0.161752	+	0.170025i
$206$	0.296876	−	0.665696i	0.0206844	−	0.0463812i
$207$	−3.16534	−	1.82751i	−0.220006	−	0.127021i
$208$	−8.73309	−	6.37777i	−0.605531	−	0.442219i
$209$	−5.14436			−0.355843
$210$	−6.99617	−	10.5389i	−0.482781	−	0.727252i
$211$		−	13.7155i		−	0.944217i	−0.881541	−	0.472108i	$-0.843493\pi$
$211$		−	13.7155i		−	0.944217i	0.881541	−	0.472108i	$-0.156507\pi$
$212$	−16.0564	−	17.8765i	−1.10276	−	1.22776i
$213$	−2.71880	+	4.70911i	−0.186289	+	0.322663i
$214$	−10.7122	−	4.77725i	−0.732270	−	0.326566i
$215$	−15.8034	−	16.6116i	−1.07778	−	1.13290i
$216$	−4.88023	−	15.1144i	−0.332058	−	1.02841i
$217$	−12.1023	−	12.5142i	−0.821558	−	0.849520i
$218$	18.3964	−	1.92213i	1.24596	−	0.130183i
$219$	−10.2779	+	5.93398i	−0.694519	+	0.400981i
$220$	14.1211	+	1.11101i	0.952048	+	0.0749042i
$221$	−2.82607	−	1.63163i	−0.190102	−	0.109756i
$222$	11.6724	−	8.46955i	0.783399	−	0.568439i
$223$		−	5.92472i		−	0.396749i	−0.980126	−	0.198374i	$-0.936434\pi$
$223$		−	5.92472i		−	0.396749i	0.980126	−	0.198374i	$-0.0635662\pi$
$224$	4.15911	−	14.3771i	0.277892	−	0.960612i
$225$	−3.17718	+	1.62889i	−0.211812	+	0.108592i
$226$	0.0124418	+	0.0171467i	0.000827614	+	0.00114058i
$227$	−2.98908	+	5.17724i	−0.198392	+	0.343626i	−0.948007	−	0.318248i	$-0.896905\pi$
$227$	−2.98908	+	5.17724i	−0.198392	+	0.343626i	0.749615	+	0.661874i	$0.230239\pi$
$228$	−4.66906	−	1.52341i	−0.309216	−	0.100890i
$229$	25.5815	−	14.7695i	1.69047	−	0.975996i	0.736343	−	0.676609i	$-0.236551\pi$
$229$	25.5815	−	14.7695i	1.69047	−	0.975996i	0.954132	−	0.299387i	$-0.0967821\pi$
$230$	15.2543	−	5.41278i	1.00584	−	0.356908i
$231$	3.07401	+	12.2914i	0.202255	+	0.808713i
$232$	−20.5071	+	6.62144i	−1.34636	+	0.434719i
$233$	−12.2773	+	7.08832i	−0.804315	+	0.464371i	−0.844978	−	0.534802i	$-0.820386\pi$
$233$	−12.2773	+	7.08832i	−0.804315	+	0.464371i	0.0406629	+	0.999173i	$0.487053\pi$
$234$	−2.49344	−	1.11199i	−0.163001	−	0.0726928i
$235$	23.0160	+	6.78631i	1.50140	+	0.442690i
$236$	−6.36595	+	5.71780i	−0.414388	+	0.372197i
$237$	−18.3114			−1.18945
$238$	0.783779	−	4.44785i	0.0508049	−	0.288311i
$239$	9.49569			0.614225			0.307113	−	0.951673i	$-0.400637\pi$
$239$	9.49569			0.614225			0.307113	+	0.951673i	$0.400637\pi$
$240$	12.4875	+	5.19008i	0.806062	+	0.335018i
$241$	−5.97700	+	10.3525i	−0.385012	+	0.666861i	−0.991771	−	0.128025i	$-0.959136\pi$
$241$	−5.97700	+	10.3525i	−0.385012	+	0.666861i	0.606759	+	0.794886i	$0.292469\pi$
$242$	1.25019	+	0.557538i	0.0803650	+	0.0358399i
$243$	−3.62438	−	6.27761i	−0.232504	−	0.402709i
$244$	−0.713835	−	3.37871i	−0.0456986	−	0.216300i
$245$	−3.16194	−	15.3298i	−0.202009	−	0.979384i
$246$	−0.333884	−	3.19555i	−0.0212876	−	0.203741i
$247$	−3.80271	+	2.19550i	−0.241961	+	0.139696i
$248$	18.1971	+	3.90294i	1.15552	+	0.247837i
$249$	3.80963	−	6.59848i	0.241426	−	0.418162i
$250$	3.64277	−	15.3860i	0.230389	−	0.973099i
$251$			23.0141i			1.45264i	0.687358	+	0.726318i	$0.258770\pi$
$251$			23.0141i			1.45264i	−0.687358	+	0.726318i	$0.741230\pi$
$252$	0.265484	−	3.76921i	0.0167239	−	0.237438i
$253$	−16.2121			−1.01924
$254$	3.50369	+	4.82864i	0.219841	+	0.302976i
$255$	3.91417	+	1.15410i	0.245115	+	0.0722726i
$256$	4.86951	+	15.2410i	0.304344	+	0.952562i
$257$	19.8038	−	11.4337i	1.23533	−	0.713217i	0.267193	−	0.963643i	$-0.413904\pi$
$257$	19.8038	−	11.4337i	1.23533	−	0.713217i	0.968136	+	0.250426i	$0.0805705\pi$
$258$	2.27833	+	21.8056i	0.141843	+	1.35756i
$259$	17.3116	−	4.32955i	1.07569	−	0.269025i
$260$	10.9125	−	5.20533i	0.676765	−	0.322821i
$261$	−4.71162	+	2.72026i	−0.291642	+	0.168380i
$262$	7.76430	−	17.4101i	0.479680	−	1.07560i
$263$	0.469868	+	0.271278i	0.0289733	+	0.0167277i	0.514417	−	0.857540i	$-0.328008\pi$
$263$	0.469868	+	0.271278i	0.0289733	+	0.0167277i	−0.485443	+	0.874268i	$0.661342\pi$
$264$	−10.0490	−	9.08171i	−0.618473	−	0.558941i
$265$	26.1147	−	6.30417i	1.60421	−	0.387262i
$266$	−4.65579	−	3.90582i	−0.285465	−	0.239481i
$267$	14.0768			0.861489
$268$	−9.38492	−	10.4488i	−0.573276	−	0.638261i
$269$	19.5158	+	11.2675i	1.18990	+	0.686989i	0.958284	−	0.285819i	$-0.0922655\pi$
$269$	19.5158	+	11.2675i	1.18990	+	0.686989i	0.231616	+	0.972807i	$0.425599\pi$
$270$	17.4622	+	3.22490i	1.06272	+	0.196261i
$271$	−1.46148	−	2.53136i	−0.0887785	−	0.153769i	0.818217	−	0.574910i	$-0.194963\pi$
$271$	−1.46148	−	2.53136i	−0.0887785	−	0.153769i	−0.906995	+	0.421141i	$0.861630\pi$
$272$	1.95298	+	4.41560i	0.118417	+	0.267735i
$273$	7.51799	+	7.77387i	0.455010	+	0.470496i
$274$	−11.4903	+	1.20055i	−0.694155	+	0.0725279i
$275$	−8.59201	+	13.3033i	−0.518118	+	0.802222i
$276$	−14.7142	−	4.80091i	−0.885691	−	0.288981i
$277$	4.70275	−	8.14541i	0.282561	−	0.489410i	−0.689454	−	0.724330i	$-0.742149\pi$
$277$	4.70275	−	8.14541i	0.282561	−	0.489410i	0.972015	+	0.234920i	$0.0754827\pi$
$278$	6.29722	+	8.67858i	0.377682	+	0.520507i
$279$	4.69861			0.281299
$280$	11.9365	+	11.7269i	0.713344	+	0.700815i
$281$	−1.11325			−0.0664107			−0.0332054	−	0.999449i	$-0.510572\pi$
$281$	−1.11325			−0.0664107			−0.0332054	+	0.999449i	$0.510572\pi$
$282$	−13.4755	−	18.5713i	−0.802452	−	1.10591i
$283$	10.2186	−	17.6991i	0.607431	−	1.05210i	−0.384231	−	0.923237i	$-0.625533\pi$
$283$	10.2186	−	17.6991i	0.607431	−	1.05210i	0.991662	−	0.128865i	$-0.0411333\pi$
$284$	2.23114	−	6.83817i	0.132394	−	0.405771i
$285$	3.97830	−	3.78474i	0.235654	−	0.224189i
$286$	−12.0442	+	1.25843i	−0.712190	+	0.0744124i
$287$	1.09308	−	3.82242i	0.0645223	−	0.225630i
$288$	2.00898	+	3.50444i	0.118380	+	0.206501i
$289$	−7.77151	−	13.4607i	−0.457148	−	0.791803i
$290$	4.37551	−	23.6925i	0.256939	−	1.39127i
$291$	20.0173	+	11.5570i	1.17343	+	0.677482i
$292$	11.6796	−	10.4904i	0.683497	−	0.613906i
$293$	−14.4186			−0.842341			−0.421171	−	0.906981i	$-0.638381\pi$
$293$	−14.4186			−0.842341			−0.421171	+	0.906981i	$0.638381\pi$
$294$	−6.55007	+	13.4580i	−0.382008	+	0.784885i
$295$	−2.24496	−	9.29964i	−0.130707	−	0.541446i
$296$	−12.7910	+	14.1534i	−0.743463	+	0.822649i
$297$	−15.4031	−	8.89297i	−0.893777	−	0.516022i
$298$	−4.65491	+	10.4379i	−0.269652	+	0.604649i
$299$	−11.9840	+	6.91894i	−0.693051	+	0.400133i
$300$	−11.7377	+	9.52985i	−0.677677	+	0.550206i
$301$	−7.45886	+	26.0832i	−0.429922	+	1.50341i
$302$	1.72379	+	16.4981i	0.0991930	+	0.949362i
$303$	8.98564	−	5.18786i	0.516211	−	0.298035i
$304$	6.45948	+	0.694953i	0.370476	+	0.0398583i
$305$	3.70328	+	1.09192i	0.212049	+	0.0625232i
$306$	0.715878	+	0.986594i	0.0409240	+	0.0563998i
$307$	2.89856			0.165430			0.0827149	−	0.996573i	$-0.473641\pi$
$307$	2.89856			0.165430			0.0827149	+	0.996573i	$0.473641\pi$
$308$	−7.33949	−	15.0675i	−0.418206	−	0.858551i
$309$		−	0.779256i		−	0.0443303i
$310$	−13.5034	+	15.8309i	−0.766941	+	0.899134i
$311$	−12.8947	+	22.3342i	−0.731189	+	1.26646i	0.225186	+	0.974316i	$0.427701\pi$
$311$	−12.8947	+	22.3342i	−0.731189	+	1.26646i	−0.956375	+	0.292141i	$0.905632\pi$
$312$	−11.3041	−	2.42452i	−0.639968	−	0.137261i
$313$	16.1061	−	9.29884i	0.910369	−	0.525602i	0.0298191	−	0.999555i	$-0.490507\pi$
$313$	16.1061	−	9.29884i	0.910369	−	0.525602i	0.880550	+	0.473954i	$0.157174\pi$
$314$	−0.791468	−	7.57503i	−0.0446651	−	0.427484i
$315$	3.56742	+	2.26281i	0.201001	+	0.127495i
$316$	23.6994	−	5.00708i	1.33320	−	0.281670i
$317$	−5.64192	−	9.77210i	−0.316882	−	0.548856i	0.662954	−	0.748660i	$-0.269303\pi$
$317$	−5.64192	−	9.77210i	−0.316882	−	0.548856i	−0.979836	+	0.199805i	$0.935969\pi$
$318$	−23.4615	−	10.4630i	−1.31566	−	0.586736i
$319$	−12.0659	+	20.8987i	−0.675559	+	1.17010i
$320$	−17.5810	−	3.30266i	−0.982809	−	0.184624i
$321$	−12.5396			−0.699890
$322$	−14.6724	−	12.3089i	−0.817660	−	0.685947i
$323$	1.96048			0.109084
$324$	−8.48350	−	9.44517i	−0.471306	−	0.524732i
$325$	−0.673650	+	13.5007i	−0.0373674	+	0.748885i
$326$	−17.5223	−	7.81431i	−0.970470	−	0.432795i
$327$	17.1252	−	9.88726i	0.947028	−	0.546767i
$328$	1.30592	+	4.04453i	0.0721075	+	0.223322i
$329$	−6.88852	−	27.5436i	−0.379777	−	1.51853i
$330$	14.2716	−	5.06411i	0.785628	−	0.278770i
$331$	8.44678	−	4.87675i	0.464277	−	0.268051i	−0.249564	−	0.968358i	$-0.580287\pi$
$331$	8.44678	−	4.87675i	0.464277	−	0.268051i	0.713841	+	0.700308i	$0.246954\pi$
$332$	−3.12631	+	9.58176i	−0.171579	+	0.525868i
$333$	−2.40813	+	4.17100i	−0.131965	+	0.228569i
$334$	−2.19276	−	3.02197i	−0.119982	−	0.165355i
$335$	15.2640	−	3.68478i	0.833961	−	0.201321i
$336$	−2.19941	−	15.8488i	−0.119988	−	0.864625i
$337$			29.9279i			1.63028i	0.579265	+	0.815139i	$0.303340\pi$
$337$			29.9279i			1.63028i	−0.579265	+	0.815139i	$0.696660\pi$
$338$	6.51420	−	4.72674i	0.354326	−	0.257101i
$339$	0.0196145	+	0.0113244i	0.00106531	+	0.000615058i
$340$	−5.38147	−	0.423398i	−0.291851	−	0.0229620i
$341$	18.0488	−	10.4205i	0.977399	−	0.564301i
$342$	1.63132	−	0.170447i	0.0882119	−	0.00921671i
$343$	−13.7364	+	12.4222i	−0.741694	+	0.670738i
$344$	−8.91126	−	27.5988i	−0.480463	−	1.48803i
$345$	12.5373	−	11.9273i	0.674986	−	0.642146i
$346$	25.5348	+	11.3876i	1.37276	+	0.612202i
$347$	−12.2549	+	21.2261i	−0.657876	+	1.13947i	0.323289	+	0.946300i	$0.395212\pi$
$347$	−12.2549	+	21.2261i	−0.657876	+	1.13947i	−0.981165	+	0.193174i	$0.938122\pi$
$348$	−17.1398	+	15.3947i	−0.918792	+	0.825245i
$349$			9.66747i			0.517488i	0.965946	+	0.258744i	$0.0833086\pi$
$349$			9.66747i			0.517488i	−0.965946	+	0.258744i	$0.916691\pi$
$350$	−17.8765	+	5.51649i	−0.955538	+	0.294869i
$351$	−15.1813			−0.810317
$352$	15.4892	+	9.00617i	0.825576	+	0.480030i
$353$	−19.4519	−	11.2306i	−1.03532	−	0.597743i	−0.116817	−	0.993153i	$-0.537269\pi$
$353$	−19.4519	−	11.2306i	−1.03532	−	0.597743i	−0.918505	+	0.395410i	$0.870602\pi$
$354$	−3.72596	+	8.35483i	−0.198032	+	0.444054i
$355$	5.54302	+	5.82650i	0.294193	+	0.309239i
$356$	−18.2189	+	3.84918i	−0.965599	+	0.204006i
$357$	−1.17148	−	4.68416i	−0.0620015	−	0.247912i
$358$	−16.4990	+	1.72388i	−0.872000	+	0.0911100i
$359$	15.3058	+	26.5104i	0.807810	+	1.39917i	0.914378	+	0.404862i	$0.132680\pi$
$359$	15.3058	+	26.5104i	0.807810	+	1.39917i	−0.106568	+	0.994305i	$0.533986\pi$
$360$	−4.51476	+	0.115562i	−0.237948	+	0.00609065i
$361$	−8.18101	+	14.1699i	−0.430579	+	0.745785i
$362$	20.8059	+	28.6738i	1.09353	+	1.50706i
$363$	1.46345			0.0768113
$364$	−11.8558	−	8.00557i	−0.621414	−	0.419606i
$365$	4.11883	+	17.0620i	0.215589	+	0.893068i
$366$	−2.16821	−	2.98814i	−0.113334	−	0.156193i
$367$	−3.56786	−	2.05990i	−0.186241	−	0.107526i	0.403981	−	0.914767i	$-0.367626\pi$
$367$	−3.56786	−	2.05990i	−0.186241	−	0.107526i	−0.590221	+	0.807241i	$0.700960\pi$
$368$	20.3566	+	2.19009i	1.06116	+	0.114166i
$369$	0.536506	+	0.929256i	0.0279294	+	0.0483751i
$370$	−7.13248	−	20.1007i	−0.370800	−	1.04499i
$371$	−22.0975	−	22.8496i	−1.14725	−	1.18629i
$372$	19.4671	−	4.11289i	1.00932	−	0.213244i
$373$	9.31127	+	16.1276i	0.482119	+	0.835055i	0.999789	−	0.0205252i	$-0.00653383\pi$
$373$	9.31127	+	16.1276i	0.482119	+	0.835055i	−0.517670	+	0.855580i	$0.673200\pi$
$374$	4.93796	+	2.20215i	0.255336	+	0.113871i
$375$	−3.14288	−	16.6091i	−0.162298	−	0.857690i
$376$	22.5187	+	20.3511i	1.16131	+	1.04953i
$377$			20.5978i			1.06084i
$378$	−7.18831	−	19.7431i	−0.369727	−	1.01547i
$379$		−	21.9946i		−	1.12979i	−0.825164	−	0.564894i	$-0.808917\pi$
$379$		−	21.9946i		−	1.12979i	0.825164	−	0.564894i	$-0.191083\pi$
$380$	−4.11400	+	5.98622i	−0.211044	+	0.307086i
$381$	5.52357	+	3.18904i	0.282981	+	0.163379i
$382$	20.2609	+	9.03563i	1.03664	+	0.462303i
$383$	−31.3796	+	18.1170i	−1.60342	+	0.925736i	−0.612625	+	0.790374i	$0.709886\pi$
$383$	−31.3796	+	18.1170i	−1.60342	+	0.925736i	−0.990796	+	0.135362i	$0.956780\pi$
$384$	11.3911	+	12.7609i	0.581300	+	0.651202i
$385$	18.7220	+	0.780400i	0.954161	+	0.0397728i
$386$	0.192112	−	0.0200726i	0.00977825	−	0.00102167i
$387$	−3.66097	−	6.34099i	−0.186098	−	0.322331i
$388$	−29.0674	−	9.48403i	−1.47567	−	0.481479i
$389$	−24.7891	−	14.3120i	−1.25686	−	0.725647i	−0.284395	−	0.958707i	$-0.591793\pi$
$389$	−24.7891	−	14.3120i	−1.25686	−	0.725647i	−0.972462	+	0.233060i	$0.925126\pi$
$390$	8.38836	−	9.83421i	0.424761	−	0.497974i
$391$	6.17830			0.312450
$392$	4.79744	−	19.2090i	0.242307	−	0.970200i
$393$		−	20.3801i		−	1.02804i
$394$	8.95358	−	6.49676i	0.451075	−	0.327302i
$395$	−7.65910	+	25.9761i	−0.385371	+	1.30700i
$396$	4.30035	+	1.40311i	0.216101	+	0.0705088i
$397$	11.7892	+	20.4195i	0.591684	+	1.02483i	0.994006	+	0.109328i	$0.0348699\pi$
$397$	11.7892	+	20.4195i	0.591684	+	1.02483i	−0.402322	+	0.915498i	$0.631797\pi$
$398$	−0.234041	−	2.23997i	−0.0117314	−	0.112280i
$399$	−6.24665	−	1.78632i	−0.312724	−	0.0894279i
$400$	12.5856	−	15.5435i	0.629282	−	0.777177i
$401$	−3.25503	−	5.63788i	−0.162549	−	0.281543i	0.773233	−	0.634122i	$-0.218638\pi$
$401$	−3.25503	−	5.63788i	−0.162549	−	0.281543i	−0.935782	+	0.352579i	$0.885305\pi$
$402$	−13.7132	−	6.11561i	−0.683953	−	0.305019i
$403$	8.89447	−	15.4057i	0.443065	−	0.767411i
$404$	−10.2110	+	9.17140i	−0.508019	+	0.456294i
$405$	13.7979	−	3.33085i	0.685622	−	0.165511i
$406$	−26.7871	+	9.75300i	−1.32942	+	0.484033i
$407$			21.3628i			1.05891i
$408$	3.82960	+	3.46098i	0.189594	+	0.171344i
$409$	8.49966	−	14.7218i	0.420281	−	0.727948i	−0.575686	−	0.817671i	$-0.695265\pi$
$409$	8.49966	−	14.7218i	0.420281	−	0.727948i	0.995967	+	0.0897227i	$0.0285981\pi$
$410$	−4.67278	−	0.862965i	−0.230772	−	0.0426188i
$411$	−10.6963	+	6.17554i	−0.527612	+	0.304617i
$412$	0.213080	+	1.00855i	0.0104977	+	0.0496876i
$413$	−8.13693	+	7.86911i	−0.400392	+	0.387213i
$414$	5.14099	−	0.537151i	0.252666	−	0.0263995i
$415$	−7.76698	−	8.16419i	−0.381266	−	0.400764i
$416$	15.2932	+	0.0469238i	0.749813	+	0.00230063i
$417$	9.92759	+	5.73170i	0.486156	+	0.280682i
$418$	5.88840	−	4.27266i	0.288011	−	0.208982i
$419$			28.6447i			1.39938i	0.714445	+	0.699692i	$0.246679\pi$
$419$			28.6447i			1.39938i	−0.714445	+	0.699692i	$0.753321\pi$
$420$	16.7611	+	6.25247i	0.817859	+	0.305089i
$421$		−	23.4495i		−	1.14286i	−0.820651	−	0.571430i	$-0.806389\pi$
$421$		−	23.4495i		−	1.14286i	0.820651	−	0.571430i	$-0.193611\pi$
$422$	11.3915	+	15.6993i	0.554528	+	0.764228i
$423$	6.63626	+	3.83145i	0.322666	+	0.186291i
$424$	33.2260	+	7.12636i	1.61360	+	0.346086i
$425$	3.27435	−	5.06981i	0.158830	−	0.245922i
$426$	−0.799124	−	7.64830i	−0.0387177	−	0.370562i
$427$	−1.10837	−	4.43179i	−0.0536377	−	0.214469i
$428$	16.2293	−	3.42883i	0.784472	−	0.165739i
$429$	−11.2120	+	6.47325i	−0.541320	+	0.312531i
$430$	31.8858	+	5.88864i	1.53767	+	0.283975i
$431$	1.46391	−	2.53556i	0.0705140	−	0.122134i	−0.828613	−	0.559822i	$-0.810869\pi$
$431$	1.46391	−	2.53556i	0.0705140	−	0.122134i	0.899127	+	0.437688i	$0.144203\pi$
$432$	18.1394	+	13.2472i	0.872732	+	0.637356i
$433$			35.4962i			1.70584i	0.522043	+	0.852919i	$0.325170\pi$
$433$			35.4962i			1.70584i	−0.522043	+	0.852919i	$0.674830\pi$
$434$	24.2464	+	4.27259i	1.16386	+	0.205091i
$435$	−6.04439	−	25.0386i	−0.289807	−	1.20051i
$436$	−19.4607	+	17.4793i	−0.931998	+	0.837106i
$437$	4.15671	−	7.19963i	0.198842	−	0.344405i
$438$	6.83600	−	15.3286i	0.326637	−	0.732428i
$439$	−4.07704	−	7.06165i	−0.194587	−	0.337034i	0.752178	−	0.658960i	$-0.229003\pi$
$439$	−4.07704	−	7.06165i	−0.194587	−	0.337034i	−0.946765	+	0.321926i	$0.895670\pi$
$440$	−17.0863	+	10.4566i	−0.814556	+	0.498501i
$441$	0.167235	−	4.99576i	0.00796356	−	0.237893i
$442$	4.58997	−	0.479578i	0.218323	−	0.0228112i
$443$	1.58322	+	2.74221i	0.0752210	+	0.130287i	0.901182	−	0.433440i	$-0.142700\pi$
$443$	1.58322	+	2.74221i	0.0752210	+	0.130287i	−0.825961	+	0.563727i	$0.809367\pi$
$444$	−6.32620	+	19.3890i	−0.300228	+	0.920163i
$445$	5.88792	−	19.9690i	0.279114	−	0.946623i
$446$	4.92079	+	6.78163i	0.233006	+	0.321119i
$447$			12.2184i			0.577912i
$448$	7.18030	+	19.9109i	0.339237	+	0.940701i
$449$	7.31370			0.345155			0.172578	−	0.984996i	$-0.444790\pi$
$449$	7.31370			0.345155			0.172578	+	0.984996i	$0.444790\pi$
$450$	2.28383	−	4.50329i	0.107661	−	0.212287i
$451$	4.12177	+	2.37971i	0.194087	+	0.112056i
$452$	−0.0284825	−	0.00929319i	−0.00133970	−	0.000437115i
$453$	8.86704	+	15.3582i	0.416610	+	0.721589i
$454$	−0.878566	−	8.40863i	−0.0412332	−	0.394637i
$455$	14.1724	−	7.41325i	0.664411	−	0.347539i
$456$	6.60963	−	2.13415i	0.309524	−	0.0999409i
$457$	−29.4543	+	17.0054i	−1.37781	+	0.795481i	−0.991896	−	0.127052i	$-0.959449\pi$
$457$	−29.4543	+	17.0054i	−1.37781	+	0.795481i	−0.385918	+	0.922533i	$0.626115\pi$
$458$	−17.0146	+	38.1524i	−0.795041	+	1.78275i
$459$	5.87000	+	3.38905i	0.273988	+	0.158187i
$460$	−12.9649	+	18.8651i	−0.604494	+	0.879590i
$461$		−	7.03412i		−	0.327612i	−0.986493	−	0.163806i	$-0.947623\pi$
$461$		−	7.03412i		−	0.327612i	0.986493	−	0.163806i	$-0.0523770\pi$
$462$	−13.7272	−	11.5160i	−0.638649	−	0.535772i
$463$		−	19.4227i		−	0.902648i	−0.892360	−	0.451324i	$-0.850952\pi$
$463$		−	19.4227i		−	0.902648i	0.892360	−	0.451324i	$-0.149048\pi$
$464$	17.9736	−	24.6113i	0.834405	−	1.14255i
$465$	−6.29131	+	21.3372i	−0.291752	+	0.989487i
$466$	8.16582	−	18.3105i	0.378274	−	0.848217i
$467$	6.29531	+	10.9038i	0.291312	+	0.504567i	0.974120	−	0.226030i	$-0.0725749\pi$
$467$	6.29531	+	10.9038i	0.291312	+	0.504567i	−0.682808	+	0.730598i	$0.739242\pi$
$468$	3.77764	−	0.798117i	0.174621	−	0.0368930i
$469$	−12.9160	−	13.3556i	−0.596404	−	0.616703i
$470$	−31.9812	+	11.3481i	−1.47518	+	0.523450i
$471$	−4.07125	−	7.05161i	−0.187593	−	0.324921i
$472$	2.53775	−	11.8320i	0.116809	−	0.544613i
$473$	−28.1259	−	16.2385i	−1.29323	−	0.746646i
$474$	20.9598	−	15.2085i	0.962716	−	0.698552i
$475$	−3.70494	−	7.22656i	−0.169994	−	0.331577i
$476$	2.79703	+	5.74212i	0.128202	+	0.263190i
$477$	8.57918			0.392813
$478$	−10.8691	+	7.88666i	−0.497140	+	0.360728i
$479$	14.0130	−	24.2712i	0.640268	−	1.10898i	−0.345104	−	0.938564i	$-0.612156\pi$
$479$	14.0130	−	24.2712i	0.640268	−	1.10898i	0.985373	−	0.170413i	$-0.0545102\pi$
$480$	−18.6042	+	4.43075i	−0.849161	+	0.202235i
$481$	9.11716	+	15.7914i	0.415707	+	0.720025i
$482$	−1.75679	−	16.8140i	−0.0800195	−	0.765856i
$483$	−19.6859	−	5.62945i	−0.895737	−	0.256149i
$484$	−1.89407	+	0.400167i	−0.0860940	+	0.0181894i
$485$	24.7670	−	23.5620i	1.12461	−	1.06990i
$486$	9.36246	+	4.17532i	0.424690	+	0.189396i
$487$	16.5442	+	9.55182i	0.749691	+	0.432834i	0.825582	−	0.564282i	$-0.190847\pi$
$487$	16.5442	+	9.55182i	0.749691	+	0.432834i	−0.0758911	+	0.997116i	$0.524180\pi$
$488$	3.62328	+	3.27451i	0.164018	+	0.148230i
$489$	−20.5114			−0.927557
$490$	16.3514	+	14.9208i	0.738682	+	0.674054i
$491$		−	9.80405i		−	0.442450i	−0.975223	−	0.221225i	$-0.928994\pi$
$491$		−	9.80405i		−	0.442450i	0.975223	−	0.221225i	$-0.0710056\pi$
$492$	3.03625	+	3.38043i	0.136885	+	0.152401i
$493$	4.59822	−	7.96435i	0.207093	−	0.358696i
$494$	2.52924	−	5.67139i	0.113796	−	0.255168i
$495$	−3.66414	+	3.48587i	−0.164691	+	0.156678i
$496$	−24.0706	+	10.6462i	−1.08080	+	0.478028i
$497$	2.61619	−	9.14867i	0.117352	−	0.410374i
$498$	1.11975	+	10.7169i	0.0501770	+	0.480237i
$499$	−21.8842	+	12.6348i	−0.979670	+	0.565613i	−0.902171	−	0.431379i	$-0.858027\pi$
$499$	−21.8842	+	12.6348i	−0.979670	+	0.565613i	−0.0774997	+	0.996992i	$0.524694\pi$
$500$	8.60927	+	20.6369i	0.385018	+	0.922909i
$501$	−3.45688	−	1.99583i	−0.154442	−	0.0891672i
$502$	−19.1144	−	26.3427i	−0.853117	−	1.17573i
$503$		−	38.1363i		−	1.70041i	−0.526450	−	0.850206i	$-0.676477\pi$
$503$		−	38.1363i		−	1.70041i	0.526450	−	0.850206i	$-0.323523\pi$
$504$	2.82665	+	4.53486i	0.125909	+	0.201999i
$505$	−3.60094	−	14.9167i	−0.160240	−	0.663785i
$506$	18.5569	−	13.4650i	0.824953	−	0.598590i
$507$	4.30225	−	7.45171i	0.191070	−	0.330942i
$508$	−8.02087	−	2.61703i	−0.355869	−	0.116112i
$509$	−15.4278	+	8.90725i	−0.683826	+	0.394807i	−0.801295	−	0.598270i	$-0.795855\pi$
$509$	−15.4278	+	8.90725i	−0.683826	+	0.394807i	0.117469	+	0.993077i	$0.462522\pi$
$510$	−5.43882	+	1.92990i	−0.240835	+	0.0854572i
$511$	14.9288	−	14.4374i	0.660412	−	0.638674i
$512$	−18.2322	−	13.4010i	−0.805758	−	0.592244i
$513$	7.89857	−	4.56024i	0.348731	−	0.201340i
$514$	−13.1718	+	29.5355i	−0.580983	+	1.30276i
$515$	−1.10543	−	0.325939i	−0.0487111	−	0.0143626i
$516$	−20.7185	−	23.0671i	−0.912083	−	1.01547i
$517$	33.9893			1.49485
$518$	−16.2195	+	19.3339i	−0.712646	+	0.849485i
$519$	29.8908			1.31206
$520$	−8.16752	+	15.0216i	−0.358170	+	0.658741i
$521$	0.0385673	−	0.0668005i	0.00168966	−	0.00292658i	−0.865179	−	0.501463i	$-0.832795\pi$
$521$	0.0385673	−	0.0668005i	0.00168966	−	0.00292658i	0.866869	+	0.498536i	$0.166129\pi$
$522$	3.13376	−	7.02694i	0.137161	−	0.307561i
$523$	−12.8904	−	22.3268i	−0.563657	−	0.976283i	−0.997173	−	0.0751372i	$-0.976061\pi$
$523$	−12.8904	−	22.3268i	−0.563657	−	0.976283i	0.433516	−	0.901146i	$-0.357273\pi$
$524$	5.57275	+	26.3769i	0.243447	+	1.15228i
$525$	−15.0525	+	13.1704i	−0.656944	+	0.574803i
$526$	−0.763137	+	0.0797355i	−0.0332743	+	0.00347663i
$527$	−6.87828	+	3.97118i	−0.299623	+	0.172987i
$528$	19.0452	+	2.04901i	0.828838	+	0.0891719i
$529$	1.59956	−	2.77051i	0.0695459	−	0.120457i
$530$	−24.6558	+	28.9055i	−1.07098	+	1.25558i
$531$		−	3.05511i		−	0.132581i
$532$	8.57316	+	0.603848i	0.371693	+	0.0261801i
$533$	4.06242			0.175963
$534$	−16.1128	+	11.6915i	−0.697269	+	0.505942i
$535$	−5.24492	+	17.7883i	−0.226758	+	0.769056i
$536$	19.4205	+	4.16535i	0.838840	+	0.179916i
$537$	−15.3590	+	8.86751i	−0.662789	+	0.382661i
$538$	−31.6966	+	3.31178i	−1.36654	+	0.142781i
$539$	−10.4371	−	19.5611i	−0.449557	−	0.842558i
$540$	−22.6663	+	10.8119i	−0.975401	+	0.465272i
$541$	−32.8506	+	18.9663i	−1.41236	+	0.815425i	−0.995610	−	0.0935970i	$-0.970163\pi$
$541$	−32.8506	+	18.9663i	−1.41236	+	0.815425i	−0.416748	+	0.909022i	$0.636830\pi$
$542$	3.77528	+	1.68364i	0.162162	+	0.0723185i
$543$	32.8005	+	18.9374i	1.40760	+	0.812681i
$544$	−5.90282	−	3.43219i	−0.253081	−	0.147154i
$545$	−6.86284	−	28.4290i	−0.293972	−	1.21776i
$546$	−15.0619	−	2.65415i	−0.644592	−	0.113587i
$547$	−32.7592			−1.40068			−0.700341	−	0.713808i	$-0.746969\pi$
$547$	−32.7592			−1.40068			−0.700341	+	0.713808i	$0.746969\pi$
$548$	12.1551	−	10.9175i	0.519238	−	0.466372i
$549$	1.06778	+	0.616482i	0.0455717	+	0.0263108i
$550$	−1.21442	−	22.3635i	−0.0517829	−	0.953585i
$551$	−6.18728	−	10.7167i	−0.263587	−	0.456546i
$552$	20.8298	−	6.72563i	0.886573	−	0.286262i
$553$	31.0860	−	7.77446i	1.32191	−	0.330604i
$554$	1.38226	+	13.2294i	0.0587264	+	0.562062i
$555$	−15.7168	−	16.5205i	−0.667139	−	0.701258i
$556$	−14.4160	−	4.70362i	−0.611375	−	0.199478i
$557$	0.890646	−	1.54264i	0.0377379	−	0.0653639i	−0.846540	−	0.532326i	$-0.821318\pi$
$557$	0.890646	−	1.54264i	0.0377379	−	0.0653639i	0.884277	+	0.466962i	$0.154651\pi$
$558$	−5.37819	+	3.90244i	−0.227677	+	0.165204i
$559$	−27.7209			−1.17247
$560$	−23.4027	−	3.50906i	−0.988945	−	0.148285i
$561$	5.78032			0.244045
$562$	1.27426	−	0.924609i	0.0537513	−	0.0390023i
$563$	−4.79715	+	8.30892i	−0.202176	+	0.350179i	−0.949229	−	0.314585i	$-0.898135\pi$
$563$	−4.79715	+	8.30892i	−0.202176	+	0.350179i	0.747053	+	0.664764i	$0.231468\pi$
$564$	30.8489	+	10.0653i	1.29897	+	0.423825i
$565$	0.0242687	−	0.0230879i	0.00102099	−	0.000971316i
$566$	3.00349	+	28.7460i	0.126246	+	1.20829i
$567$	−11.6754	−	12.0728i	−0.490320	−	0.507009i
$568$	3.12562	+	9.68027i	0.131148	+	0.406175i
$569$	22.5992	+	39.1430i	0.947407	+	1.64096i	0.750858	+	0.660464i	$0.229640\pi$
$569$	22.5992	+	39.1430i	0.947407	+	1.64096i	0.196550	+	0.980494i	$0.437026\pi$
$570$	−1.41027	+	7.63632i	−0.0590696	+	0.319850i
$571$	−13.9077	−	8.02961i	−0.582018	−	0.336029i	0.179917	−	0.983682i	$-0.442417\pi$
$571$	−13.9077	−	8.02961i	−0.582018	−	0.336029i	−0.761935	+	0.647653i	$0.775751\pi$
$572$	12.7410	−	11.4438i	0.532729	−	0.478489i
$573$	23.7171			0.990798
$574$	1.92355	+	5.28313i	0.0802873	+	0.220513i
$575$	−11.6758	−	22.7740i	−0.486916	−	0.949739i
$576$	−5.21016	−	2.34274i	−0.217090	−	0.0976140i
$577$	15.9985	+	9.23672i	0.666025	+	0.384530i	0.794569	−	0.607174i	$-0.207697\pi$
$577$	15.9985	+	9.23672i	0.666025	+	0.384530i	−0.128544	+	0.991704i	$0.541030\pi$
$578$	20.0753	+	8.95286i	0.835022	+	0.372390i
$579$	0.178837	−	0.103252i	0.00743223	−	0.00429100i
$580$	14.6695	+	30.7533i	0.609118	+	1.27696i
$581$	−3.66585	+	12.8193i	−0.152085	+	0.531833i
$582$	−32.5111	+	3.39688i	−1.34763	+	0.140805i
$583$	32.9553	−	19.0267i	1.36487	−	0.788007i
$584$	−4.65601	+	21.7082i	−0.192667	+	0.898292i
$585$	−1.22084	+	4.14053i	−0.0504757	+	0.171190i
$586$	16.5040	−	11.9754i	0.681772	−	0.494698i
$587$	−24.4386			−1.00869			−0.504344	−	0.863503i	$-0.668266\pi$
$587$	−24.4386			−1.00869			−0.504344	+	0.863503i	$0.668266\pi$
$588$	−3.68012	−	20.8446i	−0.151765	−	0.859617i
$589$			10.6871i			0.440354i
$590$	10.2935	+	8.78012i	0.423776	+	0.361472i
$591$	5.91332	−	10.2422i	0.243241	−	0.421306i
$592$	2.88591	−	26.8240i	0.118610	−	1.10246i
$593$	5.45737	−	3.15081i	0.224107	−	0.129388i	−0.383743	−	0.923440i	$-0.625365\pi$
$593$	5.45737	−	3.15081i	0.224107	−	0.129388i	0.607851	+	0.794051i	$0.292032\pi$
$594$	25.0169	−	2.61387i	1.02646	−	0.107248i
$595$	−7.13482	−	0.297405i	−0.292499	−	0.0121924i
$596$	−3.34102	−	15.8137i	−0.136853	−	0.647753i
$597$	−1.20389	−	2.08519i	−0.0492718	−	0.0853413i
$598$	7.97070	−	17.8730i	0.325946	−	0.730879i
$599$	−5.74165	+	9.94483i	−0.234598	+	0.406335i	−0.959156	−	0.282879i	$-0.908711\pi$
$599$	−5.74165	+	9.94483i	−0.234598	+	0.406335i	0.724558	+	0.689214i	$0.242044\pi$
$600$	5.52034	−	20.6570i	0.225367	−	0.843317i
$601$	29.7620			1.21402			0.607009	−	0.794695i	$-0.292369\pi$
$601$	29.7620			1.21402			0.607009	+	0.794695i	$0.292369\pi$
$602$	−13.1258	−	36.0506i	−0.534967	−	1.46931i
$603$	5.01452			0.204207
$604$	−15.6757	−	17.4526i	−0.637834	−	0.710137i
$605$	0.612118	−	2.07602i	0.0248861	−	0.0844021i
$606$	−5.97647	+	13.4012i	−0.242777	+	0.544388i
$607$	−16.9430	+	9.78207i	−0.687697	+	0.397042i	−0.802749	−	0.596318i	$-0.796630\pi$
$607$	−16.9430	+	9.78207i	−0.687697	+	0.397042i	0.115052	+	0.993359i	$0.463297\pi$
$608$	−7.97092	+	4.56946i	−0.323264	+	0.185316i
$609$	−21.9081	+	21.1870i	−0.887760	+	0.858539i
$610$	−5.14580	+	1.82592i	−0.208347	+	0.0739293i
$611$	25.1249	−	14.5059i	1.01644	−	0.586844i
$612$	−1.63883	−	0.534714i	−0.0662460	−	0.0216145i
$613$	4.25022	−	7.36160i	0.171665	−	0.297332i	−0.767337	−	0.641244i	$-0.778419\pi$
$613$	4.25022	−	7.36160i	0.171665	−	0.297332i	0.939002	+	0.343912i	$0.111752\pi$
$614$	−3.31779	+	2.40741i	−0.133895	+	0.0971550i
$615$	−4.93827	+	1.19211i	−0.199130	+	0.0480706i
$616$	20.9154	+	11.1509i	0.842704	+	0.449284i
$617$			20.3924i			0.820969i	0.911868	+	0.410484i	$0.134640\pi$
$617$			20.3924i			0.820969i	−0.911868	+	0.410484i	$0.865360\pi$
$618$	0.647212	+	0.891961i	0.0260347	+	0.0358799i
$619$	−16.3560	−	9.44314i	−0.657403	−	0.379552i	0.133884	−	0.990997i	$-0.457255\pi$
$619$	−16.3560	−	9.44314i	−0.657403	−	0.379552i	−0.791287	+	0.611445i	$0.790588\pi$
$620$	2.30805	−	29.3358i	0.0926936	−	1.17816i
$621$	24.8918	−	14.3713i	0.998872	−	0.576699i
$622$	−3.79006	−	36.2741i	−0.151968	−	1.45446i
$623$	−23.8973	+	5.97660i	−0.957426	+	0.239447i
$624$	14.9527	−	6.61345i	0.598588	−	0.264750i
$625$	−24.8758	−	2.48867i	−0.995033	−	0.0995469i
$626$	−10.7124	+	24.0207i	−0.428152	+	0.960060i
$627$	3.88895	−	6.73585i	0.155310	−	0.269004i
$628$	7.19739	+	8.01327i	0.287207	+	0.319764i
$629$		−	8.14121i		−	0.324611i
$630$	−5.96277	+	0.372840i	−0.237562	+	0.0148543i
$631$	18.6953			0.744247			0.372124	−	0.928183i	$-0.378630\pi$
$631$	18.6953			0.744247			0.372124	+	0.928183i	$0.378630\pi$
$632$	−22.9685	+	25.4149i	−0.913638	+	1.01095i
$633$	17.9587	+	10.3684i	0.713793	+	0.412109i
$634$	14.5742	+	6.49955i	0.578814	+	0.258130i
$635$	6.83423	−	6.50172i	0.271208	−	0.258013i
$636$	35.5449	−	7.50971i	1.40945	−	0.297780i
$637$	−16.0634	−	10.0053i	−0.636453	−	0.396424i
$638$	−3.54646	−	33.9427i	−0.140406	−	1.34380i
$639$	1.28408	+	2.22410i	0.0507976	+	0.0879840i
$640$	22.8668	−	10.8216i	0.903891	−	0.427762i
$641$	18.3482	−	31.7801i	0.724712	−	1.25524i	−0.234381	−	0.972145i	$-0.575306\pi$
$641$	18.3482	−	31.7801i	0.724712	−	1.25524i	0.959093	−	0.283092i	$-0.0913603\pi$
$642$	14.3532	−	10.4148i	0.566476	−	0.411038i
$643$	22.8237			0.900079			0.450039	−	0.893009i	$-0.351410\pi$
$643$	22.8237			0.900079			0.450039	+	0.893009i	$0.351410\pi$
$644$	27.0177	+	1.90298i	1.06464	+	0.0749880i
$645$	33.6974	−	8.13466i	1.32683	−	0.320302i
$646$	−2.24403	+	1.62828i	−0.0882902	+	0.0640638i
$647$	0.582307	+	0.336195i	0.0228929	+	0.0132172i	0.511403	−	0.859341i	$-0.329126\pi$
$647$	0.582307	+	0.336195i	0.0228929	+	0.0132172i	−0.488510	+	0.872558i	$0.662459\pi$
$648$	17.5552	+	3.76526i	0.689633	+	0.147913i
$649$	−6.77557	−	11.7356i	−0.265964	−	0.460664i
$650$	−10.4420	−	16.0129i	−0.409567	−	0.628076i
$651$	25.5346	−	6.38607i	1.00078	−	0.250290i
$652$	26.5468	−	5.60865i	1.03965	−	0.219652i
$653$	−11.5768	−	20.0515i	−0.453034	−	0.784677i	0.545539	−	0.838085i	$-0.316325\pi$
$653$	−11.5768	−	20.0515i	−0.453034	−	0.784677i	−0.998573	+	0.0534082i	$0.982992\pi$
$654$	−11.3902	+	25.5407i	−0.445393	+	0.998719i
$655$	−28.9107	−	8.52438i	−1.12963	−	0.333075i
$656$	−4.85400	−	3.54487i	−0.189517	−	0.138404i
$657$			5.60521i			0.218680i
$658$	30.7613	+	25.8061i	1.19920	+	1.00603i
$659$		−	23.5733i		−	0.918287i	−0.888362	−	0.459143i	$-0.848156\pi$
$659$		−	23.5733i		−	0.918287i	0.888362	−	0.459143i	$-0.151844\pi$
$660$	−12.1298	+	17.6499i	−0.472151	+	0.687021i
$661$	10.6874	+	6.17038i	0.415692	+	0.240000i	0.693232	−	0.720714i	$-0.256186\pi$
$661$	10.6874	+	6.17038i	0.415692	+	0.240000i	−0.277541	+	0.960714i	$0.589519\pi$
$662$	−5.61807	+	12.5976i	−0.218352	+	0.489619i
$663$	4.27281	−	2.46691i	0.165942	−	0.0958068i
$664$	−4.37967	−	13.5642i	−0.169964	−	0.526391i
$665$	−5.14681	+	8.11418i	−0.199585	+	0.314654i
$666$	−0.707809	−	6.77434i	−0.0274270	−	0.262500i
$667$	−19.4988	−	33.7728i	−0.754995	−	1.30769i
$668$	5.01980	+	1.63785i	0.194222	+	0.0633702i
$669$	7.75763	+	4.47887i	0.299927	+	0.173163i
$670$	−14.4113	+	16.8953i	−0.556756	+	0.652721i
$671$	5.46889			0.211124
$672$	15.6808	+	16.3144i	0.604900	+	0.629341i
$673$		−	33.0667i		−	1.27463i	−0.770605	−	0.637313i	$-0.780046\pi$
$673$		−	33.0667i		−	1.27463i	0.770605	−	0.637313i	$-0.219954\pi$
$674$	−24.8567	−	34.2565i	−0.957444	−	1.31951i
$675$	1.39923	−	28.0422i	0.0538564	−	1.07934i
$676$	−3.53056	+	10.8208i	−0.135791	+	0.416183i
$677$	−3.98063	−	6.89466i	−0.152988	−	0.264983i	0.779336	−	0.626606i	$-0.215556\pi$
$677$	−3.98063	−	6.89466i	−0.152988	−	0.264983i	−0.932325	+	0.361622i	$0.882223\pi$
$678$	−0.0318569	+	0.00332853i	−0.00122346	+	0.000127831i
$679$	−38.8887	−	11.1208i	−1.49241	−	0.426777i
$680$	6.51146	−	3.98495i	0.249703	−	0.152816i
$681$	−4.51927	−	7.82761i	−0.173179	−	0.299955i
$682$	−12.0045	+	26.9181i	−0.459677	+	1.03075i
$683$	−18.6736	+	32.3436i	−0.714524	+	1.23759i	0.248618	+	0.968602i	$0.420024\pi$
$683$	−18.6736	+	32.3436i	−0.714524	+	1.23759i	−0.963143	+	0.268991i	$0.913310\pi$
$684$	−1.72570	+	1.55000i	−0.0659838	+	0.0592656i
$685$	4.28650	+	17.7566i	0.163779	+	0.678445i
$686$	5.40578	−	25.6277i	0.206393	−	0.978469i
$687$			44.6608i			1.70391i
$688$	33.1224	+	24.1892i	1.26278	+	0.922206i
$689$	16.2404	−	28.1291i	0.618708	−	1.07163i
$690$	−4.44435	+	24.0653i	−0.169194	+	0.916150i
$691$	−24.5639	+	14.1820i	−0.934454	+	0.539508i	−0.888218	−	0.459423i	$-0.848056\pi$
$691$	−24.5639	+	14.1820i	−0.934454	+	0.539508i	−0.0462368	+	0.998931i	$0.514723\pi$
$692$	−38.6860	+	8.17335i	−1.47062	+	0.310704i
$693$	5.75336	+	1.64526i	0.218552	+	0.0624982i
$694$	−3.60201	−	34.4743i	−0.136730	−	1.30863i
$695$	12.2832	−	11.6856i	0.465930	−	0.443261i
$696$	6.83270	−	31.8568i	0.258993	−	1.20753i
$697$	−1.57078	−	0.906889i	−0.0594975	−	0.0343509i
$698$	−8.02933	−	11.0657i	−0.303915	−	0.418843i
$699$		−	21.4340i		−	0.810710i
$700$	15.8803	−	21.1617i	0.600218	−	0.799837i
$701$			20.9697i			0.792013i	0.918248	+	0.396007i	$0.129604\pi$
$701$			20.9697i			0.792013i	−0.918248	+	0.396007i	$0.870396\pi$
$702$	17.3770	−	12.6088i	0.655852	−	0.475890i
$703$	−9.48702	−	5.47734i	−0.357810	−	0.206582i
$704$	−25.2095	+	2.55582i	−0.950119	+	0.0963260i
$705$	−26.2850	+	25.0061i	−0.989950	+	0.941786i
$706$	31.5929	−	3.30095i	1.18901	−	0.124233i
$707$	−13.0517	+	12.6221i	−0.490860	+	0.474704i
$708$	−2.67427	−	12.6578i	−0.100505	−	0.475710i
$709$	11.6206	−	6.70915i	0.436420	−	0.251967i	−0.265658	−	0.964067i	$-0.585589\pi$
$709$	11.6206	−	6.70915i	0.436420	−	0.251967i	0.702078	+	0.712100i	$0.252256\pi$
$710$	−11.1839	−	2.06544i	−0.419726	−	0.0775145i
$711$	−4.32421	+	7.48975i	−0.162171	+	0.280888i
$712$	17.6570	−	19.5376i	0.661724	−	0.732203i
$713$			33.6796i			1.26131i
$714$	5.23135	+	4.38866i	0.195778	+	0.164242i
$715$	4.49314	+	18.6126i	0.168034	+	0.696072i
$716$	17.4535	−	15.6765i	0.652270	−	0.585858i
$717$	−7.17839	+	12.4333i	−0.268082	+	0.464332i
$718$	−39.5378	−	17.6325i	−1.47554	−	0.658037i
$719$	10.8084	+	18.7207i	0.403084	+	0.698163i	0.994096	−	0.108500i	$-0.0346048\pi$
$719$	10.8084	+	18.7207i	0.403084	+	0.698163i	−0.591012	+	0.806663i	$0.701271\pi$
$720$	5.07176	−	3.88201i	0.189013	−	0.144674i
$721$	0.330848	+	1.32289i	0.0123214	+	0.0492670i
$722$	−2.40460	−	23.0141i	−0.0894900	−	0.856496i
$723$	−9.03678	−	15.6522i	−0.336081	−	0.582110i
$724$	−47.6302	−	15.5406i	−1.77016	−	0.577563i
$725$	−38.0473	−	1.89846i	−1.41304	−	0.0705070i
$726$	−1.67512	+	1.21547i	−0.0621694	+	0.0451104i
$727$			14.6601i			0.543714i	0.962338	+	0.271857i	$0.0876377\pi$
$727$			14.6601i			0.543714i	−0.962338	+	0.271857i	$0.912362\pi$
$728$	20.2196	−	0.683430i	0.749388	−	0.0253296i
$729$	30.0031			1.11123
$730$	−18.8855	−	16.1089i	−0.698982	−	0.596216i
$731$	10.7186	+	6.18837i	0.396441	+	0.228885i
$732$	4.96361	+	1.61951i	0.183460	+	0.0598589i
$733$	21.7313	+	37.6398i	0.802665	+	1.39026i	0.917856	+	0.396913i	$0.129919\pi$
$733$	21.7313	+	37.6398i	0.802665	+	1.39026i	−0.115191	+	0.993343i	$0.536748\pi$
$734$	5.79474	−	0.605457i	0.213888	−	0.0223478i
$735$	22.4626	+	7.44861i	0.828546	+	0.274746i
$736$	−25.1198	+	14.4003i	−0.925927	+	0.530803i
$737$	19.2623	−	11.1211i	0.709536	−	0.409651i
$738$	−1.38590	−	0.618061i	−0.0510156	−	0.0227511i
$739$	45.6524	+	26.3574i	1.67935	+	0.969574i	0.962075	+	0.272784i	$0.0879443\pi$
$739$	45.6524	+	26.3574i	1.67935	+	0.969574i	0.717275	+	0.696790i	$0.245389\pi$
$740$	24.8587	+	17.0840i	0.913825	+	0.628022i
$741$		−	6.63886i		−	0.243885i
$742$	44.2714	+	7.80130i	1.62525	+	0.286395i
$743$			28.0138i			1.02773i	0.857872	+	0.513863i	$0.171786\pi$
$743$			28.0138i			1.02773i	−0.857872	+	0.513863i	$0.828214\pi$
$744$	−18.8667	+	20.8762i	−0.691687	+	0.765358i
$745$	17.3328	+	5.11060i	0.635023	+	0.187238i
$746$	−24.0528	−	10.7267i	−0.880635	−	0.392732i
$747$	−1.79928	−	3.11645i	−0.0658323	−	0.114025i
$748$	−7.48115	+	1.58057i	−0.273538	+	0.0577915i
$749$	21.2876	−	5.32392i	0.777832	−	0.194532i
$750$	17.3922	+	16.4010i	0.635072	+	0.598880i
$751$	6.67963	+	11.5695i	0.243743	+	0.422176i	0.961778	−	0.273832i	$-0.0882913\pi$
$751$	6.67963	+	11.5695i	0.243743	+	0.422176i	−0.718034	+	0.696008i	$0.754958\pi$
$752$	−42.6783	−	4.59162i	−1.55632	−	0.167439i
$753$	−30.1339	−	17.3978i	−1.09814	−	0.634011i
$754$	−17.1075	−	23.5769i	−0.623019	−	0.858619i
$755$	25.4955	−	6.15470i	0.927876	−	0.223992i
$756$	24.6256	+	16.6283i	0.895624	+	0.604765i
$757$	−12.0202			−0.436880			−0.218440	−	0.975850i	$-0.570097\pi$
$757$	−12.0202			−0.436880			−0.218440	+	0.975850i	$0.570097\pi$
$758$	18.2677	+	25.1758i	0.663512	+	0.914425i
$759$	12.2557	−	21.2275i	0.444855	−	0.770511i
$760$	−0.262848	−	10.2689i	−0.00953450	−	0.372492i
$761$	−14.7805	−	25.6006i	−0.535793	−	0.928021i	−0.999124	−	0.0418359i	$-0.986679\pi$
$761$	−14.7805	−	25.6006i	−0.535793	−	0.928021i	0.463331	−	0.886185i	$-0.346654\pi$
$762$	−8.97112	+	0.937337i	−0.324989	+	0.0339561i
$763$	−24.8746	+	24.0558i	−0.900520	+	0.870879i
$764$	−30.6958	+	6.48523i	−1.11054	+	0.234627i
$765$	1.39638	−	1.32844i	0.0504862	−	0.0480298i
$766$	20.8710	−	46.7997i	0.754099	−	1.69094i
$767$	−10.0170	−	5.78332i	−0.361693	−	0.208824i
$768$	−23.6372	−	5.14566i	−0.852935	−	0.185678i
$769$	−41.6325			−1.50131			−0.750653	−	0.660697i	$-0.770261\pi$
$769$	−41.6325			−1.50131			−0.750653	+	0.660697i	$0.770261\pi$
$770$	−22.0780	+	14.6563i	−0.795635	+	0.528177i
$771$			34.5740i			1.24515i
$772$	−0.203226	+	0.182535i	−0.00731428	+	0.00656957i
$773$	12.5350	−	21.7113i	0.450853	−	0.780900i	−0.547586	−	0.836749i	$-0.684453\pi$
$773$	12.5350	−	21.7113i	0.450853	−	0.780900i	0.998439	+	0.0558490i	$0.0177866\pi$
$774$	9.45699	+	4.21748i	0.339925	+	0.151594i
$775$	27.6369	+	17.8494i	0.992746	+	0.641168i
$776$	41.1485	−	13.2862i	1.47714	−	0.476949i
$777$	−7.41798	+	25.9402i	−0.266119	+	0.930601i
$778$	40.2613	−	4.20665i	1.44344	−	0.150816i
$779$	−2.11361	+	1.22029i	−0.0757280	+	0.0437216i
$780$	−1.43377	+	18.2235i	−0.0513372	+	0.652507i
$781$	9.86514	+	5.69564i	0.353002	+	0.203806i
$782$	−7.07189	+	5.13140i	−0.252890	+	0.183499i
$783$		−	42.7834i		−	1.52895i
$784$	10.4627	+	25.9717i	0.373669	+	0.927562i
$785$	−11.7061	+	2.82589i	−0.417809	+	0.100860i
$786$	16.9267	+	23.3277i	0.603756	+	0.832073i
$787$	−0.509964	+	0.883283i	−0.0181782	+	0.0314856i	−0.874971	−	0.484175i	$-0.839120\pi$
$787$	−0.509964	+	0.883283i	−0.0181782	+	0.0314856i	0.856793	+	0.515660i	$0.172453\pi$
$788$	−4.85266	+	14.8728i	−0.172869	+	0.529822i
$789$	−0.710406	+	0.410153i	−0.0252911	+	0.0146018i
$790$	−12.8076	−	36.0943i	−0.455674	−	1.28418i
$791$	−0.0381062	−	0.0108970i	−0.00135490	−	0.000387453i
$792$	−6.08768	+	1.96562i	−0.216316	+	0.0698454i
$793$	4.04261	−	2.33400i	0.143557	−	0.0828828i
$794$	−30.4538	−	13.5813i	−1.08076	−	0.481982i
$795$	−11.4873	+	38.9594i	−0.407411	+	1.38175i
$796$	2.12830	+	2.36956i	0.0754357	+	0.0839868i
$797$	11.8904			0.421178			0.210589	−	0.977575i	$-0.432462\pi$
$797$	11.8904			0.421178			0.210589	+	0.977575i	$0.432462\pi$
$798$	8.63375	−	3.14349i	0.305632	−	0.111278i
$799$	−12.9531			−0.458247
$800$	−1.49623	+	28.2447i	−0.0528996	+	0.998600i
$801$	3.32423	−	5.75773i	0.117456	−	0.203440i
$802$	8.40837	+	3.74983i	0.296910	+	0.132411i
$803$	12.4311	+	21.5313i	0.438685	+	0.759824i
$804$	20.7759	−	4.38942i	0.732711	−	0.154803i
$805$	−16.2198	+	25.5712i	−0.571673	+	0.901267i
$806$	2.61431	+	25.0211i	0.0920850	+	0.881332i
$807$	−29.5064	+	17.0356i	−1.03868	+	0.599680i
$808$	4.07058	−	18.9787i	0.143202	−	0.667668i
$809$	−24.0241	+	41.6109i	−0.844641	+	1.46296i	0.0412909	+	0.999147i	$0.486853\pi$
$809$	−24.0241	+	41.6109i	−0.844641	+	1.46296i	−0.885932	+	0.463815i	$0.846480\pi$
$810$	−13.0271	+	15.2725i	−0.457724	+	0.536620i
$811$			41.9077i			1.47158i	0.677211	+	0.735789i	$0.263188\pi$
$811$			41.9077i			1.47158i	−0.677211	+	0.735789i	$0.736812\pi$
$812$	22.5611	−	33.4117i	0.791738	−	1.17252i
$813$	4.41930			0.154991
$814$	−17.7429	−	24.4526i	−0.621889	−	0.857062i
$815$	−8.57929	+	29.0969i	−0.300519	+	1.01922i
$816$	−7.25801	−	0.780865i	−0.254081	−	0.0273357i
$817$	14.4227	−	8.32696i	0.504587	−	0.291324i
$818$	2.49826	+	23.9105i	0.0873497	+	0.836012i
$819$	4.95505	−	1.23923i	0.173143	−	0.0433023i
$820$	6.06536	−	2.89321i	0.211811	−	0.101035i
$821$	13.3722	−	7.72043i	0.466692	−	0.269445i	−0.248162	−	0.968719i	$-0.579827\pi$
$821$	13.3722	−	7.72043i	0.466692	−	0.269445i	0.714854	+	0.699274i	$0.246493\pi$
$822$	7.11428	−	15.9526i	0.248139	−	0.556410i
$823$	26.0571	+	15.0441i	0.908292	+	0.524403i	0.879881	−	0.475194i	$-0.157622\pi$
$823$	26.0571	+	15.0441i	0.908292	+	0.524403i	0.0284109	+	0.999596i	$0.490955\pi$
$824$	−1.08155	−	0.977443i	−0.0376776	−	0.0340508i
$825$	−10.9237	−	21.3069i	−0.380315	−	0.741812i
$826$	2.77810	−	15.7654i	0.0966626	−	0.548548i
$827$	26.3773			0.917227			0.458614	−	0.888636i	$-0.348346\pi$
$827$	26.3773			0.917227			0.458614	+	0.888636i	$0.348346\pi$
$828$	−5.43842	+	4.88470i	−0.188998	+	0.169755i
$829$	3.18446	+	1.83855i	0.110601	+	0.0638554i	0.554280	−	0.832330i	$-0.312994\pi$
$829$	3.18446	+	1.83855i	0.110601	+	0.0638554i	−0.443679	+	0.896186i	$0.646327\pi$
$830$	15.6711	+	2.89413i	0.543952	+	0.100457i
$831$	7.11021	+	12.3153i	0.246651	+	0.427211i
$832$	−17.5441	+	12.6481i	−0.608233	+	0.438495i
$833$	3.97750	+	7.45461i	0.137812	+	0.258287i
$834$	−16.1239	+	1.68469i	−0.558325	+	0.0583360i
$835$	−4.27715	+	4.06905i	−0.148017	+	0.140815i
$836$	−3.19140	+	9.78125i	−0.110377	+	0.338291i
$837$	−18.4746	+	31.9989i	−0.638576	+	1.10605i
$838$	−23.7909	−	32.7876i	−0.821842	−	1.13263i
$839$	−20.9969			−0.724892			−0.362446	−	0.932005i	$-0.618058\pi$
$839$	−20.9969			−0.724892			−0.362446	+	0.932005i	$0.618058\pi$
$840$	−24.3783	+	6.76420i	−0.841133	+	0.233387i
$841$	−29.0480			−1.00165
$842$	19.4760	+	26.8411i	0.671189	+	0.925006i
$843$	0.841573	−	1.45765i	0.0289853	−	0.0502041i
$844$	−26.0781	−	8.50868i	−0.897645	−	0.292881i
$845$	−8.77130	−	9.21988i	−0.301742	−	0.317174i
$846$	−10.7783	+	1.12616i	−0.370566	+	0.0387181i
$847$	−2.48441	+	0.621338i	−0.0853653	+	0.0213494i
$848$	−43.9503	+	19.4388i	−1.50926	+	0.667532i
$849$	15.4497	+	26.7597i	0.530233	+	0.918391i
$850$	0.462805	+	8.52259i	0.0158741	+	0.292322i
$851$	−29.8976	−	17.2614i	−1.02488	−	0.591714i
$852$	7.26702	+	8.09079i	0.248964	+	0.277186i
$853$	−1.70587			−0.0584080			−0.0292040	−	0.999573i	$-0.509297\pi$
$853$	−1.70587			−0.0584080			−0.0292040	+	0.999573i	$0.509297\pi$
$854$	4.94950	+	4.15221i	0.169369	+	0.142086i
$855$	−0.608571	−	2.52097i	−0.0208127	−	0.0862155i
$856$	−15.7288	+	17.4040i	−0.537598	+	0.594857i
$857$	−21.9640	−	12.6809i	−0.750276	−	0.433172i	0.0755175	−	0.997144i	$-0.475939\pi$
$857$	−21.9640	−	12.6809i	−0.750276	−	0.433172i	−0.825794	+	0.563972i	$0.809272\pi$
$858$	7.45725	−	16.7216i	0.254586	−	0.570867i
$859$	−10.5811	+	6.10903i	−0.361024	+	0.208437i	−0.669530	−	0.742785i	$-0.733504\pi$
$859$	−10.5811	+	6.10903i	−0.361024	+	0.208437i	0.308506	+	0.951222i	$0.400171\pi$
$860$	−41.3884	+	19.7425i	−1.41133	+	0.673213i
$861$	4.17863	+	4.32085i	0.142407	+	0.147254i
$862$	0.430279	+	4.11814i	0.0146554	+	0.140264i
$863$	−6.03122	+	3.48212i	−0.205305	+	0.118533i	−0.599128	−	0.800654i	$-0.704486\pi$
$863$	−6.03122	+	3.48212i	−0.205305	+	0.118533i	0.393823	+	0.919186i	$0.371152\pi$
$864$	−31.7654	−	0.0974649i	−1.08068	−	0.00331582i
$865$	12.5024	−	42.4023i	0.425095	−	1.44172i
$866$	−29.4814	−	40.6301i	−1.00182	−	1.38067i
$867$	23.4999			0.798099
$868$	−31.3018	+	15.2473i	−1.06245	+	0.517528i
$869$			38.3606i			1.30129i
$870$	27.7144	+	23.6398i	0.939608	+	0.801464i
$871$	9.49247	−	16.4414i	0.321640	−	0.557097i
$872$	7.75789	−	36.1705i	0.262715	−	1.22489i
$873$	9.45411	−	5.45833i	0.319973	−	0.184737i
$874$	1.22176	+	11.6933i	0.0413267	+	0.395532i
$875$	12.3872	+	26.8618i	0.418764	+	0.908095i
$876$	4.90647	+	23.2233i	0.165774	+	0.784641i
$877$	−2.30237	−	3.98782i	−0.0777454	−	0.134659i	0.824531	−	0.565816i	$-0.191439\pi$
$877$	−2.30237	−	3.98782i	−0.0777454	−	0.134659i	−0.902277	+	0.431157i	$0.858105\pi$
$878$	10.5318	+	4.69680i	0.355430	+	0.158509i
$879$	10.8999	−	18.8792i	0.367644	−	0.636779i
$880$	10.8727	−	26.1601i	0.366520	−	0.881855i
$881$	3.20640			0.108026			0.0540132	−	0.998540i	$-0.482799\pi$
$881$	3.20640			0.108026			0.0540132	+	0.998540i	$0.482799\pi$
$882$	3.95781	+	5.85720i	0.133266	+	0.197222i
$883$	9.44205			0.317750			0.158875	−	0.987299i	$-0.449213\pi$
$883$	9.44205			0.317750			0.158875	+	0.987299i	$0.449213\pi$
$884$	−4.85552	+	4.36115i	−0.163309	+	0.146681i
$885$	13.8738	+	4.09071i	0.466361	+	0.137508i
$886$	−4.08975	−	1.82388i	−0.137398	−	0.0612746i
$887$	25.7906	−	14.8902i	0.865964	−	0.499965i	−4.06316e−5	−	1.00000i	$-0.500013\pi$
$887$	25.7906	−	14.8902i	0.865964	−	0.499965i	0.866005	+	0.500035i	$0.166680\pi$
$888$	−8.86243	−	27.4476i	−0.297404	−	0.921080i
$889$	−10.7310	−	3.06868i	−0.359905	−	0.102920i
$890$	9.84582	+	27.7474i	0.330033	+	0.930096i
$891$	17.4122	−	10.0529i	0.583329	−	0.336785i
$892$	−11.2650	−	3.67551i	−0.377180	−	0.123065i
$893$	−8.71471	+	15.0943i	−0.291627	+	0.505112i
$894$	−10.1480	−	13.9856i	−0.339401	−	0.467749i
$895$	6.15502	+	25.4969i	0.205740	+	0.852266i
$896$	−24.7558	−	16.8270i	−0.827034	−	0.562152i
$897$		−	20.9219i		−	0.698561i
$898$	−8.37151	+	6.07441i	−0.279361	+	0.202706i
$899$	43.4158	+	25.0661i	1.44800	+	0.836001i
$900$	1.12607	+	7.05145i	0.0375356	+	0.235048i
$901$	−12.5590	+	7.25095i	−0.418402	+	0.241564i
$902$	−6.69438	+	0.699455i	−0.222899	+	0.0232893i
$903$	−28.5138	−	29.4843i	−0.948881	−	0.981176i
$904$	0.0403205	−	0.0130189i	0.00134104	−	0.000433002i
$905$	40.5835	−	38.6090i	1.34904	−	1.28341i
$906$	−22.9052	−	10.2149i	−0.760976	−	0.339368i
$907$	−7.20438	+	12.4784i	−0.239218	+	0.414337i	−0.960490	−	0.278314i	$-0.910224\pi$
$907$	−7.20438	+	12.4784i	−0.239218	+	0.414337i	0.721272	+	0.692652i	$0.243558\pi$
$908$	7.98944	+	8.89510i	0.265139	+	0.295194i
$909$		−	4.90043i		−	0.162537i
$910$	−10.0651	+	20.2563i	−0.333653	+	0.671491i
$911$	−21.7395			−0.720261			−0.360130	−	0.932902i	$-0.617268\pi$
$911$	−21.7395			−0.720261			−0.360130	+	0.932902i	$0.617268\pi$
$912$	−5.79307	+	7.93246i	−0.191828	+	0.262670i
$913$	−13.8232	−	7.98082i	−0.457481	−	0.264127i
$914$	19.5905	−	43.9283i	0.647995	−	1.45302i
$915$	−4.22927	+	4.02350i	−0.139815	+	0.133013i
$916$	−12.2121	−	57.8020i	−0.403498	−	1.90983i
$917$	8.65278	+	34.5980i	0.285740	+	1.14253i
$918$	−9.53378	+	0.996126i	−0.314662	+	0.0328771i
$919$	3.72612	+	6.45382i	0.122913	+	0.212892i	0.920915	−	0.389763i	$-0.127443\pi$
$919$	3.72612	+	6.45382i	0.122913	+	0.212892i	−0.798002	+	0.602655i	$0.794110\pi$
$920$	−0.828346	−	32.3617i	−0.0273098	−	1.06693i
$921$	−2.19121	+	3.79528i	−0.0722027	+	0.125059i
$922$	5.84220	+	8.05148i	0.192403	+	0.265161i
$923$	9.72308			0.320039
$924$	25.2773	+	1.78040i	0.831561	+	0.0585708i
$925$	−30.0095	+	15.3854i	−0.986705	+	0.505867i
$926$	16.1315	+	22.2318i	0.530115	+	0.730583i
$927$	−0.318733	−	0.184020i	−0.0104685	−	0.00604402i
$928$	−0.132239	+	43.0989i	−0.00434096	+	1.41479i
$929$	28.8679	+	50.0006i	0.947124	+	1.64047i	0.751442	+	0.659799i	$0.229359\pi$
$929$	28.8679	+	50.0006i	0.947124	+	1.64047i	0.195682	+	0.980667i	$0.437308\pi$
$930$	−10.5204	−	29.6485i	−0.344977	−	0.972211i
$931$	11.3630	+	0.380379i	0.372406	+	0.0124664i
$932$	5.86094	+	27.7409i	0.191981	+	0.908684i
$933$	−19.4958	−	33.7677i	−0.638263	−	1.10550i
$934$	−16.2620	−	7.25226i	−0.532108	−	0.237301i
$935$	2.41773	−	8.19981i	0.0790683	−	0.268162i
$936$	−3.66113	+	4.05107i	−0.119668	+	0.132414i
$937$		−	8.50064i		−	0.277704i	−0.990313	−	0.138852i	$-0.955659\pi$
$937$		−	8.50064i		−	0.277704i	0.990313	−	0.138852i	$-0.0443412\pi$
$938$	25.8765	+	4.55985i	0.844899	+	0.148884i
$939$			28.1183i			0.917607i
$940$	27.1815	−	39.5515i	0.886564	−	1.29003i
$941$	−22.6504	−	13.0772i	−0.738382	−	0.426305i	0.0830988	−	0.996541i	$-0.473518\pi$
$941$	−22.6504	−	13.0772i	−0.738382	−	0.426305i	−0.821481	+	0.570236i	$0.806852\pi$
$942$	10.5168	+	4.69012i	0.342656	+	0.152812i
$943$	−6.66089	+	3.84567i	−0.216908	+	0.125232i
$944$	6.92232	+	15.6511i	0.225302	+	0.509399i
$945$	−29.4373	+	15.3980i	−0.957594	+	0.500897i
$946$	45.6807	−	4.77289i	1.48521	−	0.155180i
$947$	3.93964	+	6.82365i	0.128021	+	0.221739i	0.922910	−	0.385016i	$-0.125804\pi$
$947$	3.93964	+	6.82365i	0.128021	+	0.221739i	−0.794889	+	0.606755i	$0.792471\pi$
$948$	−11.3598	+	34.8164i	−0.368949	+	1.13078i
$949$	18.3782	+	10.6106i	0.596581	+	0.344436i
$950$	10.2428	+	5.19461i	0.332321	+	0.168536i
$951$	17.0603			0.553220
$952$	−7.97070	−	4.24954i	−0.258332	−	0.137728i
$953$			10.1906i			0.330107i	0.986285	+	0.165054i	$0.0527798\pi$
$953$			10.1906i			0.330107i	−0.986285	+	0.165054i	$0.947220\pi$
$954$	−9.82000	+	7.12545i	−0.317934	+	0.230695i
$955$	9.92017	−	33.6445i	0.321009	−	1.08871i
$956$	5.89082	−	18.0547i	0.190523	−	0.583930i
$957$	−18.2427	−	31.5973i	−0.589703	−	1.02140i
$958$	4.11876	+	39.4200i	0.133071	+	1.27360i
$959$	15.5365	−	15.0252i	0.501701	−	0.485187i
$960$	17.6150	−	20.5233i	0.568522	−	0.662387i
$961$	−6.14794	−	10.6485i	−0.198321	−	0.343502i
$962$	−23.5514	−	10.5031i	−0.759326	−	0.338632i
$963$	−2.96120	+	5.12896i	−0.0954235	+	0.165278i
$964$	15.9758	+	17.7867i	0.514544	+	0.572872i
$965$	−0.0716681	−	0.296881i	−0.00230708	−	0.00955695i
$966$	27.2086	−	9.90646i	0.875423	−	0.318735i
$967$		−	23.0461i		−	0.741113i	−0.928810	−	0.370557i	$-0.879167\pi$
$967$		−	23.0461i		−	0.741113i	0.928810	−	0.370557i	$-0.120833\pi$
$968$	1.83565	−	2.03117i	0.0590001	−	0.0652841i
$969$	−1.48205	+	2.56699i	−0.0476103	+	0.0824635i
$970$	−8.77967	+	47.5402i	−0.281898	+	1.52642i
$971$	36.7491	−	21.2171i	1.17933	−	0.680888i	0.223473	−	0.974710i	$-0.428261\pi$
$971$	36.7491	−	21.2171i	1.17933	−	0.680888i	0.955860	+	0.293822i	$0.0949272\pi$
$972$	−14.1844	+	2.99680i	−0.454965	+	0.0961223i
$973$	−19.2869	−	5.51537i	−0.618310	−	0.176815i
$974$	−26.8704	+	2.80752i	−0.860982	+	0.0899587i
$975$	−17.1681	−	11.0881i	−0.549820	−	0.355103i
$976$	−6.86697	−	0.738794i	−0.219806	−	0.0236482i
$977$	32.0699	+	18.5155i	1.02601	+	0.592365i	0.915838	−	0.401548i	$-0.131528\pi$
$977$	32.0699	+	18.5155i	1.02601	+	0.592365i	0.110168	+	0.993913i	$0.464861\pi$
$978$	23.4780	−	17.0358i	0.750744	−	0.544744i
$979$		−	29.4897i		−	0.942493i
$980$	−31.1089	−	3.49815i	−0.993737	−	0.111744i
$981$		−	9.33946i		−	0.298186i
$982$	8.14277	+	11.2220i	0.259846	+	0.358109i
$983$	4.40244	+	2.54175i	0.140416	+	0.0810692i	0.568562	−	0.822640i	$-0.307500\pi$
$983$	4.40244	+	2.54175i	0.140416	+	0.0810692i	−0.428146	+	0.903709i	$0.640833\pi$
$984$	−6.28301	−	1.34759i	−0.200295	−	0.0429595i
$985$	−12.0559	−	12.6725i	−0.384133	−	0.403778i
$986$	1.35153	+	12.9353i	0.0430415	+	0.411944i
$987$	41.2722	+	11.8024i	1.31371	+	0.375674i
$988$	1.81533	+	8.59232i	0.0577535	+	0.273358i
$989$	45.4521	−	26.2418i	1.44529	−	0.834440i
$990$	1.29890	−	7.03330i	0.0412818	−	0.223533i
$991$	−5.44141	+	9.42480i	−0.172852	+	0.299388i	−0.939416	−	0.342780i	$-0.888632\pi$
$991$	−5.44141	+	9.42480i	−0.172852	+	0.299388i	0.766564	+	0.642168i	$0.221965\pi$
$992$	18.7098	−	32.1778i	0.594035	−	1.02165i
$993$			14.7466i			0.467969i
$994$	4.60386	+	12.6447i	0.146026	+	0.401067i
$995$	−3.46155	+	0.835629i	−0.109739	+	0.0264912i
$996$	−10.1827	−	11.3369i	−0.322650	−	0.359225i
$997$	10.4885	−	18.1667i	0.332175	−	0.575344i	−0.650763	−	0.759281i	$-0.725551\pi$
$997$	10.4885	−	18.1667i	0.332175	−	0.575344i	0.982938	+	0.183937i	$0.0588842\pi$
$998$	14.5555	−	32.6382i	0.460745	−	1.03314i
$999$	−18.9372	−	32.8001i	−0.599145	−	1.03775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bf.a.109.9	yes	88
4.3	odd	2		1120.2.bv.a.529.31		88
5.4	even	2	inner	280.2.bf.a.109.36	yes	88
7.2	even	3	inner	280.2.bf.a.149.38	yes	88
8.3	odd	2		1120.2.bv.a.529.14		88
8.5	even	2	inner	280.2.bf.a.109.7	✓	88
20.19	odd	2		1120.2.bv.a.529.13		88
28.23	odd	6		1120.2.bv.a.849.32		88
35.9	even	6	inner	280.2.bf.a.149.7	yes	88
40.19	odd	2		1120.2.bv.a.529.32		88
40.29	even	2	inner	280.2.bf.a.109.38	yes	88
56.37	even	6	inner	280.2.bf.a.149.36	yes	88
56.51	odd	6		1120.2.bv.a.849.13		88
140.79	odd	6		1120.2.bv.a.849.14		88
280.149	even	6	inner	280.2.bf.a.149.9	yes	88
280.219	odd	6		1120.2.bv.a.849.31		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bf.a.109.7	✓	88	8.5	even	2	inner
280.2.bf.a.109.9	yes	88	1.1	even	1	trivial
280.2.bf.a.109.36	yes	88	5.4	even	2	inner
280.2.bf.a.109.38	yes	88	40.29	even	2	inner
280.2.bf.a.149.7	yes	88	35.9	even	6	inner
280.2.bf.a.149.9	yes	88	280.149	even	6	inner
280.2.bf.a.149.36	yes	88	56.37	even	6	inner
280.2.bf.a.149.38	yes	88	7.2	even	3	inner
1120.2.bv.a.529.13		88	20.19	odd	2
1120.2.bv.a.529.14		88	8.3	odd	2
1120.2.bv.a.529.31		88	4.3	odd	2
1120.2.bv.a.529.32		88	40.19	odd	2
1120.2.bv.a.849.13		88	56.51	odd	6
1120.2.bv.a.849.14		88	140.79	odd	6
1120.2.bv.a.849.31		88	280.219	odd	6
1120.2.bv.a.849.32		88	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14463 + 0.830552i) q^{2} +(-0.755963 + 1.30937i) q^{3} +(0.620368 - 1.90135i) q^{4} +(1.54124 + 1.62006i) q^{5} +(-0.222196 - 2.12661i) q^{6} +(0.727432 - 2.54379i) q^{7} +(0.869078 + 2.69160i) q^{8} +(0.357040 + 0.618411i) q^{9} +O(q^{10})\)	\(q+(-1.14463 + 0.830552i) q^{2} +(-0.755963 + 1.30937i) q^{3} +(0.620368 - 1.90135i) q^{4} +(1.54124 + 1.62006i) q^{5} +(-0.222196 - 2.12661i) q^{6} +(0.727432 - 2.54379i) q^{7} +(0.869078 + 2.69160i) q^{8} +(0.357040 + 0.618411i) q^{9} +(-3.10969 - 0.574295i) q^{10} +(2.74300 + 1.58367i) q^{11} +(2.02059 + 2.24964i) q^{12} +2.70350 q^{13} +(1.28010 + 3.51587i) q^{14} +(-3.28637 + 0.793340i) q^{15} +(-3.23029 - 2.35908i) q^{16} +(-1.04534 - 0.603526i) q^{17} +(-0.922301 - 0.411313i) q^{18} +(-1.40659 + 0.812094i) q^{19} +(4.03644 - 1.92540i) q^{20} +(2.78084 + 2.87548i) q^{21} +(-4.45505 + 0.465481i) q^{22} +(-4.43276 + 2.55925i) q^{23} +(-4.18128 - 0.896807i) q^{24} +(-0.249177 + 4.99379i) q^{25} +(-3.09452 + 2.24540i) q^{26} -5.61541 q^{27} +(-4.38536 - 2.96119i) q^{28} +7.61892i q^{29} +(3.10277 - 3.63758i) q^{30} +(3.28998 - 5.69841i) q^{31} +(5.65683 + 0.0173567i) q^{32} +(-4.14721 + 2.39439i) q^{33} +(1.69779 - 0.177391i) q^{34} +(5.24222 - 2.74209i) q^{35} +(1.39731 - 0.295216i) q^{36} +(3.37235 + 5.84109i) q^{37} +(0.935541 - 2.09779i) q^{38} +(-2.04375 + 3.53987i) q^{39} +(-3.02109 + 5.55635i) q^{40} +1.50265 q^{41} +(-5.57127 - 0.981744i) q^{42} -10.2537 q^{43} +(4.71279 - 4.23295i) q^{44} +(-0.451579 + 1.53154i) q^{45} +(2.94829 - 6.61104i) q^{46} +(9.29346 - 5.36558i) q^{47} +(5.53087 - 2.44625i) q^{48} +(-5.94169 - 3.70086i) q^{49} +(-3.86238 - 5.92301i) q^{50} +(1.58047 - 0.912487i) q^{51} +(1.67717 - 5.14031i) q^{52} +(6.00716 - 10.4047i) q^{53} +(6.42759 - 4.66389i) q^{54} +(1.66197 + 6.88463i) q^{55} +(7.47904 - 0.252794i) q^{56} -2.45565i q^{57} +(-6.32791 - 8.72087i) q^{58} +(-3.70520 - 2.13920i) q^{59} +(-0.530338 + 6.74071i) q^{60} +(1.49532 - 0.863325i) q^{61} +(0.967007 + 9.25509i) q^{62} +(1.83283 - 0.458380i) q^{63} +(-6.48941 + 4.67842i) q^{64} +(4.16674 + 4.37983i) q^{65} +(2.75837 - 6.18518i) q^{66} +(3.51118 - 6.08154i) q^{67} +(-1.79601 + 1.61315i) q^{68} -7.73880i q^{69} +(-3.72297 + 7.49263i) q^{70} +3.59648 q^{71} +(-1.35422 + 1.49845i) q^{72} +(6.79792 + 3.92478i) q^{73} +(-8.71143 - 3.88499i) q^{74} +(-6.35033 - 4.10138i) q^{75} +(0.671475 + 3.17822i) q^{76} +(6.02387 - 5.82559i) q^{77} +(-0.600708 - 5.74929i) q^{78} +(6.05565 + 10.4887i) q^{79} +(-1.15680 - 8.86915i) q^{80} +(3.17393 - 5.49740i) q^{81} +(-1.71998 + 1.24803i) q^{82} -5.03944 q^{83} +(7.19245 - 3.50349i) q^{84} +(-0.633366 - 2.62368i) q^{85} +(11.7367 - 8.51622i) q^{86} +(-9.97596 - 5.75962i) q^{87} +(-1.87873 + 8.75939i) q^{88} +(-4.65527 - 8.06316i) q^{89} +(-0.755133 - 2.12811i) q^{90} +(1.96661 - 6.87713i) q^{91} +(2.11610 + 10.0159i) q^{92} +(4.97421 + 8.61558i) q^{93} +(-6.18120 + 13.8603i) q^{94} +(-3.48353 - 1.02713i) q^{95} +(-4.29908 + 7.39374i) q^{96} -15.2877i q^{97} +(9.87480 - 0.698751i) q^{98} +2.26173i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} - 40 q^{9}+O(q^{10}) \) 88 * q - 2 * q^4 - 40 * q^9	\( 88 q - 2 q^{4} - 40 q^{9} + 6 q^{10} - 6 q^{14} + 4 q^{15} + 2 q^{16} - 24 q^{20} - 8 q^{24} - 2 q^{25} - 14 q^{26} + 14 q^{30} - 28 q^{31} + 24 q^{34} + 60 q^{36} - 16 q^{39} - 32 q^{40} - 16 q^{41} - 2 q^{44} - 42 q^{46} - 8 q^{49} - 12 q^{50} + 8 q^{54} - 28 q^{55} + 36 q^{56} + 10 q^{60} + 52 q^{64} - 12 q^{65} - 44 q^{66} - 48 q^{70} + 16 q^{71} - 42 q^{74} - 36 q^{76} - 4 q^{79} - 40 q^{80} - 20 q^{81} + 12 q^{84} - 24 q^{86} + 4 q^{89} - 96 q^{90} - 22 q^{94} - 34 q^{95} + 80 q^{96}+O(q^{100}) \) 88 * q - 2 * q^4 - 40 * q^9 + 6 * q^10 - 6 * q^14 + 4 * q^15 + 2 * q^16 - 24 * q^20 - 8 * q^24 - 2 * q^25 - 14 * q^26 + 14 * q^30 - 28 * q^31 + 24 * q^34 + 60 * q^36 - 16 * q^39 - 32 * q^40 - 16 * q^41 - 2 * q^44 - 42 * q^46 - 8 * q^49 - 12 * q^50 + 8 * q^54 - 28 * q^55 + 36 * q^56 + 10 * q^60 + 52 * q^64 - 12 * q^65 - 44 * q^66 - 48 * q^70 + 16 * q^71 - 42 * q^74 - 36 * q^76 - 4 * q^79 - 40 * q^80 - 20 * q^81 + 12 * q^84 - 24 * q^86 + 4 * q^89 - 96 * q^90 - 22 * q^94 - 34 * q^95 + 80 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more