LMFDB - Embedded newform 560.2.cz.c.157.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(157,560)] 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([0, 9, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.157"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [360,2,-24,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.20
Character	$\chi$	$=$	560.157
Dual form			560.2.cz.c.453.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09307 + 0.897326i) q^{2} +(-0.623698 - 0.360092i) q^{3} +(0.389613 - 1.96168i) q^{4} +(2.21506 + 0.305784i) q^{5} +(1.00487 - 0.166053i) q^{6} +(0.529295 + 2.59227i) q^{7} +(1.33439 + 2.49387i) q^{8} +(-1.24067 - 2.14890i) q^{9} +(-2.69561 + 1.65339i) q^{10} +(1.03636 + 3.86774i) q^{11} +(-0.949387 + 1.08320i) q^{12} -1.30220i q^{13} +(-2.90466 - 2.35858i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(-3.69640 - 1.52860i) q^{16} +(0.797258 + 2.97541i) q^{17} +(3.28440 + 1.23562i) q^{18} +(0.832549 - 3.10711i) q^{19} +(1.46287 - 4.22611i) q^{20} +(0.603335 - 1.80739i) q^{21} +(-4.60343 - 3.29776i) q^{22} +(-0.421249 + 1.57212i) q^{23} +(0.0657649 - 2.03593i) q^{24} +(4.81299 + 1.35466i) q^{25} +(1.16850 + 1.42340i) q^{26} +3.94757i q^{27} +(5.29143 - 0.0283273i) q^{28} +(1.22355 - 1.22355i) q^{29} +(2.27662 - 0.0605462i) q^{30} +(4.67056 + 2.69655i) q^{31} +(5.41208 - 1.64601i) q^{32} +(0.746367 - 2.78548i) q^{33} +(-3.54137 - 2.53693i) q^{34} +(0.379746 + 5.90388i) q^{35} +(-4.69884 + 1.59656i) q^{36} +(0.612879 + 1.06154i) q^{37} +(1.87806 + 4.14337i) q^{38} +(-0.468911 + 0.812178i) q^{39} +(2.19318 + 5.93211i) q^{40} -5.53618 q^{41} +(0.962325 + 2.51699i) q^{42} +6.24099i q^{43} +(7.99105 - 0.526083i) q^{44} +(-2.09105 - 5.13932i) q^{45} +(-0.950251 - 2.09644i) q^{46} +(9.27457 + 2.48511i) q^{47} +(1.75500 + 2.28443i) q^{48} +(-6.43969 + 2.74415i) q^{49} +(-6.47652 + 2.83808i) q^{50} +(0.574172 - 2.14284i) q^{51} +(-2.55450 - 0.507353i) q^{52} +(4.64563 + 2.68216i) q^{53} +(-3.54226 - 4.31498i) q^{54} +(1.11290 + 8.88417i) q^{55} +(-5.75849 + 4.77910i) q^{56} +(-1.63811 + 1.63811i) q^{57} +(-0.239506 + 2.43536i) q^{58} +(2.37530 + 8.86473i) q^{59} +(-2.43418 + 2.10905i) q^{60} +(-4.72039 - 1.26482i) q^{61} +(-7.52494 + 1.24349i) q^{62} +(4.91384 - 4.35354i) q^{63} +(-4.43879 + 6.65561i) q^{64} +(0.398192 - 2.88445i) q^{65} +(1.68365 + 3.71447i) q^{66} +(7.00704 + 4.04552i) q^{67} +(6.14743 - 0.404710i) q^{68} +(0.828841 - 0.828841i) q^{69} +(-5.71279 - 6.11261i) q^{70} -14.6273i q^{71} +(3.70354 - 5.96154i) q^{72} +(-1.68877 - 6.30257i) q^{73} +(-1.62247 - 0.610385i) q^{74} +(-2.51405 - 2.57802i) q^{75} +(-5.77080 - 2.84377i) q^{76} +(-9.47766 + 4.73368i) q^{77} +(-0.216234 - 1.30853i) q^{78} +(-10.0365 + 5.79459i) q^{79} +(-7.72034 - 4.51623i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(6.05144 - 4.96775i) q^{82} +9.57150i q^{83} +(-3.31045 - 1.88773i) q^{84} +(0.856142 + 6.83450i) q^{85} +(-5.60020 - 6.82185i) q^{86} +(-1.20372 + 0.322536i) q^{87} +(-8.26273 + 7.74562i) q^{88} +(14.0247 - 8.09717i) q^{89} +(6.89732 + 3.74129i) q^{90} +(3.37564 - 0.689246i) q^{91} +(2.91988 + 1.43888i) q^{92} +(-1.94201 - 3.36366i) q^{93} +(-12.3677 + 5.60590i) q^{94} +(2.79425 - 6.62787i) q^{95} +(-3.96822 - 0.922233i) q^{96} +(0.176114 - 0.176114i) q^{97} +(4.57666 - 8.77805i) q^{98} +(7.02560 - 7.02560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.09307	+	0.897326i	−0.772919	+	0.634505i
$2$	−1.09307	+	0.897326i	−0.772919	+	0.634505i
$3$	−0.623698	−	0.360092i	−0.360092	−	0.207899i	0.309029	−	0.951053i	$-0.399996\pi$
$3$	−0.623698	−	0.360092i	−0.360092	−	0.207899i	−0.669121	+	0.743153i	$0.733329\pi$
$4$	0.389613	−	1.96168i	0.194807	−	0.980842i
$5$	2.21506	+	0.305784i	0.990605	+	0.136751i
$5$	2.21506	+	0.305784i	0.990605	+	0.136751i
$6$	1.00487	−	0.166053i	0.410235	−	0.0677910i
$7$	0.529295	+	2.59227i	0.200055	+	0.979785i
$7$	0.529295	+	2.59227i	0.200055	+	0.979785i
$8$	1.33439	+	2.49387i	0.471779	+	0.881717i
$9$	−1.24067	−	2.14890i	−0.413556	−	0.716300i
$10$	−2.69561	+	1.65339i	−0.852427	+	0.522847i
$11$	1.03636	+	3.86774i	0.312473	+	1.16617i	0.926319	+	0.376740i	$0.122955\pi$
$11$	1.03636	+	3.86774i	0.312473	+	1.16617i	−0.613846	+	0.789426i	$0.710378\pi$
$12$	−0.949387	+	1.08320i	−0.274065	+	0.312693i
$13$		−	1.30220i		−	0.361165i	−0.983560	−	0.180582i	$-0.942202\pi$
$13$		−	1.30220i		−	0.361165i	0.983560	−	0.180582i	$-0.0577982\pi$
$14$	−2.90466	−	2.35858i	−0.776304	−	0.630358i
$15$	−1.27142	−	0.988343i	−0.328279	−	0.255189i
$16$	−3.69640	−	1.52860i	−0.924101	−	0.382149i
$17$	0.797258	+	2.97541i	0.193363	+	0.721642i	0.992684	+	0.120738i	$0.0385261\pi$
$17$	0.797258	+	2.97541i	0.193363	+	0.721642i	−0.799321	+	0.600904i	$0.794807\pi$
$18$	3.28440	+	1.23562i	0.774141	+	0.291238i
$19$	0.832549	−	3.10711i	0.191000	−	0.712821i	−0.802266	−	0.596966i	$-0.796373\pi$
$19$	0.832549	−	3.10711i	0.191000	−	0.712821i	0.993266	−	0.115855i	$-0.0369607\pi$
$20$	1.46287	−	4.22611i	0.327107	−	0.944987i
$21$	0.603335	−	1.80739i	0.131658	−	0.394404i
$22$	−4.60343	−	3.29776i	−0.981455	−	0.703086i
$23$	−0.421249	+	1.57212i	−0.0878365	+	0.327810i	−0.995836	−	0.0911604i	$-0.970942\pi$
$23$	−0.421249	+	1.57212i	−0.0878365	+	0.327810i	0.908000	+	0.418971i	$0.137609\pi$
$24$	0.0657649	−	2.03593i	0.0134242	−	0.415582i
$25$	4.81299	+	1.35466i	0.962598	+	0.270932i
$26$	1.16850	+	1.42340i	0.229161	+	0.279151i
$27$			3.94757i			0.759710i
$28$	5.29143	−	0.0283273i	0.999986	−	0.00535336i
$29$	1.22355	−	1.22355i	0.227208	−	0.227208i	−0.584317	−	0.811525i	$-0.698638\pi$
$29$	1.22355	−	1.22355i	0.227208	−	0.227208i	0.811525	+	0.584317i	$0.198638\pi$
$30$	2.27662	−	0.0605462i	0.415651	−	0.0110542i
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	0.856876	−	0.515523i	$-0.172402\pi$
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	−0.0180184	+	0.999838i	$0.505736\pi$
$32$	5.41208	−	1.64601i	0.956730	−	0.290977i
$33$	0.746367	−	2.78548i	0.129926	−	0.484890i
$34$	−3.54137	−	2.53693i	−0.607340	−	0.435081i
$35$	0.379746	+	5.90388i	0.0641887	+	0.997938i
$36$	−4.69884	+	1.59656i	−0.783140	+	0.266093i
$37$	0.612879	+	1.06154i	0.100757	+	0.174516i	0.911997	−	0.410198i	$-0.134540\pi$
$37$	0.612879	+	1.06154i	0.100757	+	0.174516i	−0.811240	+	0.584713i	$0.801207\pi$
$38$	1.87806	+	4.14337i	0.304661	+	0.672143i
$39$	−0.468911	+	0.812178i	−0.0750859	+	0.130053i
$40$	2.19318	+	5.93211i	0.346772	+	0.937950i
$41$	−5.53618			−0.864606			−0.432303	−	0.901728i	$-0.642299\pi$
$41$	−5.53618			−0.864606			−0.432303	+	0.901728i	$0.642299\pi$
$42$	0.962325	+	2.51699i	0.148490	+	0.388380i
$43$			6.24099i			0.951741i	0.879515	+	0.475871i	$0.157867\pi$
$43$			6.24099i			0.951741i	−0.879515	+	0.475871i	$0.842133\pi$
$44$	7.99105	−	0.526083i	1.20470	−	0.0793100i
$45$	−2.09105	−	5.13932i	−0.311716	−	0.766125i
$46$	−0.950251	−	2.09644i	−0.140107	−	0.309104i
$47$	9.27457	+	2.48511i	1.35284	+	0.362491i	0.861181	−	0.508299i	$-0.169726\pi$
$47$	9.27457	+	2.48511i	1.35284	+	0.362491i	0.491655	+	0.870790i	$0.336392\pi$
$48$	1.75500	+	2.28443i	0.253313	+	0.329729i
$49$	−6.43969	+	2.74415i	−0.919956	+	0.392021i
$50$	−6.47652	+	2.83808i	−0.915918	+	0.401365i
$51$	0.574172	−	2.14284i	0.0804002	−	0.300058i
$52$	−2.55450	−	0.507353i	−0.354245	−	0.0703573i
$53$	4.64563	+	2.68216i	0.638127	+	0.368423i	0.783893	−	0.620896i	$-0.213231\pi$
$53$	4.64563	+	2.68216i	0.638127	+	0.368423i	−0.145766	+	0.989319i	$0.546565\pi$
$54$	−3.54226	−	4.31498i	−0.482040	−	0.587194i
$55$	1.11290	+	8.88417i	0.150063	+	1.19794i
$56$	−5.75849	+	4.77910i	−0.769511	+	0.638634i
$57$	−1.63811	+	1.63811i	−0.216972	+	0.216972i
$58$	−0.239506	+	2.43536i	−0.0314487	+	0.319778i
$59$	2.37530	+	8.86473i	0.309237	+	1.15409i	0.929236	+	0.369487i	$0.120466\pi$
$59$	2.37530	+	8.86473i	0.309237	+	1.15409i	−0.619999	+	0.784603i	$0.712867\pi$
$60$	−2.43418	+	2.10905i	−0.314251	+	0.272277i
$61$	−4.72039	−	1.26482i	−0.604384	−	0.161944i	−0.0563651	−	0.998410i	$-0.517951\pi$
$61$	−4.72039	−	1.26482i	−0.604384	−	0.161944i	−0.548019	+	0.836466i	$0.684618\pi$
$62$	−7.52494	+	1.24349i	−0.955668	+	0.157923i
$63$	4.91384	−	4.35354i	0.619086	−	0.548495i
$64$	−4.43879	+	6.65561i	−0.554848	+	0.831951i
$65$	0.398192	−	2.88445i	0.0493896	−	0.357772i
$66$	1.68365	+	3.71447i	0.207243	+	0.457219i
$67$	7.00704	+	4.04552i	0.856046	+	0.494239i	0.862686	−	0.505739i	$-0.168780\pi$
$67$	7.00704	+	4.04552i	0.856046	+	0.494239i	−0.00664007	+	0.999978i	$0.502114\pi$
$68$	6.14743	−	0.404710i	0.745485	−	0.0490783i
$69$	0.828841	−	0.828841i	0.0997808	−	0.0997808i
$70$	−5.71279	−	6.11261i	−0.682809	−	0.730597i
$71$		−	14.6273i		−	1.73594i	−0.496619	−	0.867969i	$-0.665425\pi$
$71$		−	14.6273i		−	1.73594i	0.496619	−	0.867969i	$-0.334575\pi$
$72$	3.70354	−	5.96154i	0.436466	−	0.702574i
$73$	−1.68877	−	6.30257i	−0.197655	−	0.737660i	−0.991563	−	0.129622i	$-0.958624\pi$
$73$	−1.68877	−	6.30257i	−0.197655	−	0.737660i	0.793908	−	0.608038i	$-0.208043\pi$
$74$	−1.62247	−	0.610385i	−0.188608	−	0.0709558i
$75$	−2.51405	−	2.57802i	−0.290297	−	0.297684i
$76$	−5.77080	−	2.84377i	−0.661957	−	0.326203i
$77$	−9.47766	+	4.73368i	−1.08008	+	0.539453i
$78$	−0.216234	−	1.30853i	−0.0244837	−	0.148162i
$79$	−10.0365	+	5.79459i	−1.12920	+	0.651942i	−0.943733	−	0.330709i	$-0.892712\pi$
$79$	−10.0365	+	5.79459i	−1.12920	+	0.651942i	−0.185464	+	0.982651i	$0.559379\pi$
$80$	−7.72034	−	4.51623i	−0.863160	−	0.504930i
$81$	−2.30051	+	3.98461i	−0.255613	+	0.442734i
$82$	6.05144	−	4.96775i	0.668270	−	0.548597i
$83$			9.57150i			1.05061i	0.850914	+	0.525305i	$0.176049\pi$
$83$			9.57150i			1.05061i	−0.850914	+	0.525305i	$0.823951\pi$
$84$	−3.31045	−	1.88773i	−0.361200	−	0.205969i
$85$	0.856142	+	6.83450i	0.0928617	+	0.741305i
$86$	−5.60020	−	6.82185i	−0.603885	−	0.735619i
$87$	−1.20372	+	0.322536i	−0.129052	+	0.0345794i
$88$	−8.26273	+	7.74562i	−0.880810	+	0.825686i
$89$	14.0247	−	8.09717i	1.48662	−	0.858298i	0.486732	−	0.873551i	$-0.338189\pi$
$89$	14.0247	−	8.09717i	1.48662	−	0.858298i	0.999884	+	0.0152534i	$0.00485550\pi$
$90$	6.89732	+	3.74129i	0.727041	+	0.394367i
$91$	3.37564	−	0.689246i	0.353864	−	0.0722526i
$92$	2.91988	+	1.43888i	0.304419	+	0.150013i
$93$	−1.94201	−	3.36366i	−0.201377	−	0.348796i
$94$	−12.3677	+	5.60590i	−1.27563	+	0.578205i
$95$	2.79425	−	6.62787i	0.286684	−	0.680005i
$96$	−3.96822	−	0.922233i	−0.405005	−	0.0941251i
$97$	0.176114	−	0.176114i	0.0178817	−	0.0178817i	−0.698109	−	0.715991i	$-0.745975\pi$
$97$	0.176114	−	0.176114i	0.0178817	−	0.0178817i	0.715991	+	0.698109i	$0.245975\pi$
$98$	4.57666	−	8.77805i	0.462312	−	0.886717i
$99$	7.02560	−	7.02560i	0.706099	−	0.706099i
$100$	4.53262	−	8.91377i	0.453262	−	0.891377i
$101$	11.8660	−	3.17949i	1.18071	−	0.316371i	0.385503	−	0.922706i	$-0.374028\pi$
$101$	11.8660	−	3.17949i	1.18071	−	0.316371i	0.795209	+	0.606335i	$0.207361\pi$
$102$	1.29521	+	2.85750i	0.128245	+	0.282935i
$103$	−11.8809	−	3.18347i	−1.17066	−	0.313676i	−0.379441	−	0.925216i	$-0.623884\pi$
$103$	−11.8809	−	3.18347i	−1.17066	−	0.313676i	−0.791214	+	0.611540i	$0.790550\pi$
$104$	3.24751	−	1.73764i	0.318445	−	0.170390i
$105$	1.88909	−	3.81898i	0.184357	−	0.372694i
$106$	−7.48478	+	1.23685i	−0.726986	+	0.120134i
$107$	−2.02564	−	3.50852i	−0.195826	−	0.339181i	0.751345	−	0.659910i	$-0.229406\pi$
$107$	−2.02564	−	3.50852i	−0.195826	−	0.339181i	−0.947171	+	0.320729i	$0.896072\pi$
$108$	7.74388	+	1.53803i	0.745155	+	0.147997i
$109$	0.313558	+	1.17022i	0.0300334	+	0.112086i	0.979315	−	0.202340i	$-0.0648546\pi$
$109$	0.313558	+	1.17022i	0.0300334	+	0.112086i	−0.949282	+	0.314426i	$0.898188\pi$
$110$	−9.18848	−	8.71241i	−0.876087	−	0.830695i
$111$		−	0.882771i		−	0.0837889i
$112$	2.00604	−	10.3911i	0.189553	−	0.981870i
$113$	12.8737	−	12.8737i	1.21106	−	1.21106i	0.240378	−	0.970679i	$-0.422729\pi$
$113$	12.8737	−	12.8737i	1.21106	−	1.21106i	0.970679	−	0.240378i	$-0.0772714\pi$
$114$	0.320653	−	3.26048i	0.0300319	−	0.305372i
$115$	−1.41382	+	3.35354i	−0.131840	+	0.312719i
$116$	−1.92351	−	2.87694i	−0.178594	−	0.267117i
$117$	−2.79829	+	1.61559i	−0.258702	+	0.149362i
$118$	−10.5509	−	7.55837i	−0.971291	−	0.695805i
$119$	−7.29106	+	3.64157i	−0.668371	+	0.333822i
$120$	0.768227	−	4.48959i	0.0701293	−	0.409842i
$121$	−4.35906	+	2.51671i	−0.396278	+	0.228791i
$122$	6.29468	−	2.85318i	0.569894	−	0.258315i
$123$	3.45290	+	1.99353i	0.311338	+	0.179751i
$124$	7.10949	−	8.11155i	0.638451	−	0.728438i
$125$	10.2468	+	4.47240i	0.916505	+	0.400023i
$126$	−1.46464	+	9.16805i	−0.130480	+	0.816755i
$127$	−13.9513	−	13.9513i	−1.23798	−	1.23798i	−0.960825	−	0.277154i	$-0.910609\pi$
$127$	−13.9513	−	13.9513i	−1.23798	−	1.23798i	−0.277154	−	0.960825i	$-0.589391\pi$
$128$	−1.12034	−	11.2581i	−0.0990248	−	0.995085i
$129$	2.24733	−	3.89249i	0.197866	−	0.342715i
$130$	2.15304	+	3.51022i	0.188834	+	0.307866i
$131$	1.36844	+	0.366673i	0.119561	+	0.0320364i	0.318104	−	0.948056i	$-0.396954\pi$
$131$	1.36844	+	0.366673i	0.119561	+	0.0320364i	−0.198542	+	0.980092i	$0.563621\pi$
$132$	−5.17344	−	2.54940i	−0.450290	−	0.221897i
$133$	8.49513	+	0.513610i	0.736622	+	0.0445356i
$134$	−11.2893	+	1.86556i	−0.975251	+	0.161160i
$135$	−1.20710	+	8.74411i	−0.103891	+	0.752573i
$136$	−6.35643	+	5.95862i	−0.545059	+	0.510948i
$137$	−1.73301	−	6.46769i	−0.148061	−	0.552572i	−0.999600	−	0.0282805i	$-0.990997\pi$
$137$	−1.73301	−	6.46769i	−0.148061	−	0.552572i	0.851539	−	0.524292i	$-0.175670\pi$
$138$	−0.162243	+	1.64972i	−0.0138110	+	0.140434i
$139$	4.62212	−	4.62212i	0.392043	−	0.392043i	−0.483372	−	0.875415i	$-0.660588\pi$
$139$	4.62212	−	4.62212i	0.392043	−	0.392043i	0.875415	+	0.483372i	$0.160588\pi$
$140$	11.7295	+	1.55529i	0.991323	+	0.131446i
$141$	−4.88966	−	4.88966i	−0.411784	−	0.411784i
$142$	13.1254	+	15.9887i	1.10146	+	1.34174i
$143$	5.03656	−	1.34954i	0.421178	−	0.112854i
$144$	1.30121	+	9.83968i	0.108434	+	0.819973i
$145$	3.08439	−	2.33610i	0.256144	−	0.194003i
$146$	7.50141	+	5.37379i	0.620821	+	0.444738i
$147$	5.00457	+	0.607365i	0.412770	+	0.0500946i
$148$	2.32119	−	0.788685i	0.190800	−	0.0648295i
$149$	1.69653	−	6.33152i	0.138985	−	0.518699i	−0.860965	−	0.508665i	$-0.830139\pi$
$149$	1.69653	−	6.33152i	0.138985	−	0.518699i	0.999950	−	0.0100340i	$-0.00319399\pi$
$150$	5.06136	+	0.562040i	0.413258	+	0.0458904i
$151$	−7.43917	−	4.29501i	−0.605391	−	0.349523i	0.165768	−	0.986165i	$-0.446990\pi$
$151$	−7.43917	−	4.29501i	−0.605391	−	0.349523i	−0.771159	+	0.636642i	$0.780323\pi$
$152$	8.85969	−	2.06984i	0.718616	−	0.167887i
$153$	5.40472	−	5.40472i	0.436946	−	0.436946i
$154$	6.11211	−	13.6788i	0.492528	−	1.10227i
$155$	9.52101	+	7.40120i	0.764746	+	0.594479i
$156$	1.41054	+	1.23629i	0.112934	+	0.0989824i
$157$	−11.3243	+	19.6143i	−0.903780	+	1.56539i	−0.0812343	+	0.996695i	$0.525886\pi$
$157$	−11.3243	+	19.6143i	−0.903780	+	1.56539i	−0.822546	+	0.568698i	$0.807447\pi$
$158$	5.77101	−	15.3399i	0.459117	−	1.22038i
$159$	−1.93165	−	3.34571i	−0.153190	−	0.265332i
$160$	12.4914	−	1.99109i	0.987533	−	0.157409i
$161$	−4.29833	−	0.259874i	−0.338756	−	0.0204809i
$162$	−1.06086	−	6.41977i	−0.0833492	−	0.504385i
$163$	−10.6154	−	18.3864i	−0.831463	−	1.44014i	−0.896878	−	0.442278i	$-0.854170\pi$
$163$	−10.6154	−	18.3864i	−0.831463	−	1.44014i	0.0654148	−	0.997858i	$-0.479163\pi$
$164$	−2.15697	+	10.8602i	−0.168431	+	0.848041i
$165$	2.50501	−	5.94178i	0.195014	−	0.462567i
$166$	−8.58876	−	10.4623i	−0.666617	−	0.812035i
$167$	5.40470	+	5.40470i	0.418228	+	0.418228i	0.884593	−	0.466365i	$-0.154437\pi$
$167$	5.40470	+	5.40470i	0.418228	+	0.418228i	−0.466365	+	0.884593i	$0.654437\pi$
$168$	5.31247	−	0.907125i	0.409866	−	0.0699862i
$169$	11.3043			0.869560
$170$	−7.06860	−	6.70236i	−0.542137	−	0.514048i
$171$	−7.70979	+	2.06583i	−0.589583	+	0.157978i
$172$	12.2428	+	2.43157i	0.933508	+	0.185405i
$173$	−22.3986	+	12.9318i	−1.70293	+	0.983187i	−0.760165	+	0.649730i	$0.774882\pi$
$173$	−22.3986	+	12.9318i	−1.70293	+	0.983187i	−0.942765	+	0.333457i	$0.891785\pi$
$174$	1.02633	−	1.43268i	0.0778060	−	0.108611i
$175$	−0.964154	+	13.1936i	−0.0728832	+	0.997340i
$176$	2.08141	−	15.8809i	0.156892	−	1.19707i
$177$	1.71065	−	6.38424i	0.128580	−	0.479869i
$178$	−8.06422	+	21.4355i	−0.604439	+	1.60666i
$179$	1.05776	+	3.94762i	0.0790608	+	0.295059i	0.994123	−	0.108253i	$-0.0345256\pi$
$179$	1.05776	+	3.94762i	0.0790608	+	0.295059i	−0.915063	+	0.403312i	$0.867859\pi$
$180$	−10.8964	+	2.09964i	−0.812171	+	0.156498i
$181$	−9.97127	−	9.97127i	−0.741159	−	0.741159i	0.231642	−	0.972801i	$-0.425590\pi$
$181$	−9.97127	−	9.97127i	−0.741159	−	0.741159i	−0.972801	+	0.231642i	$0.925590\pi$
$182$	−3.07134	+	3.78245i	−0.227663	+	0.280374i
$183$	2.48864	+	2.48864i	0.183966	+	0.183966i
$184$	−4.48279	+	1.04729i	−0.330475	+	0.0772073i
$185$	1.03296	+	2.53878i	0.0759449	+	0.186655i
$186$	5.14106	+	1.93411i	0.376961	+	0.141816i
$187$	−10.6818	+	6.16717i	−0.781134	+	0.450988i
$188$	8.48850	−	17.2255i	0.619088	−	1.25630i
$189$	−10.2332	+	2.08943i	−0.744352	+	0.151984i
$190$	2.89304	+	9.75209i	0.209883	+	0.707491i
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	−0.986003	−	0.166725i	$-0.946681\pi$
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	0.348614	−	0.937266i	$-0.386653\pi$
$192$	5.16509	−	2.55272i	0.372759	−	0.184227i
$193$	−6.62260	−	24.7159i	−0.476705	−	1.77909i	−0.614815	−	0.788672i	$-0.710769\pi$
$193$	−6.62260	−	24.7159i	−0.476705	−	1.77909i	0.138109	−	0.990417i	$-0.455898\pi$
$194$	−0.0344737	+	0.350537i	−0.00247507	+	0.0251671i
$195$	−1.28702	+	1.65564i	−0.0921653	+	0.118563i
$196$	2.87416	+	13.7018i	0.205297	+	0.978700i
$197$	−18.7829			−1.33822			−0.669112	−	0.743161i	$-0.733326\pi$
$197$	−18.7829			−1.33822			−0.669112	+	0.743161i	$0.733326\pi$
$198$	−1.37524	+	13.9837i	−0.0977337	+	0.993781i
$199$	−7.71789	−	4.45592i	−0.547106	−	0.315872i	0.200848	−	0.979622i	$-0.435630\pi$
$199$	−7.71789	−	4.45592i	−0.547106	−	0.315872i	−0.747954	+	0.663750i	$0.768964\pi$
$200$	3.04407	+	13.8106i	0.215249	+	0.976559i
$201$	−2.91352	−	5.04636i	−0.205504	−	0.355943i
$202$	−10.1174	+	14.1231i	−0.711856	+	0.993697i
$203$	3.81940	+	2.52416i	0.268069	+	0.177161i
$204$	−3.97987	−	1.96122i	−0.278647	−	0.137313i
$205$	−12.2630	−	1.69288i	−0.856483	−	0.118236i
$206$	15.8432	−	7.18124i	1.10385	−	0.500341i
$207$	3.90097	−	1.04526i	0.271136	−	0.0726506i
$208$	−1.99053	+	4.81345i	−0.138019	+	0.333753i
$209$	12.8803			0.890950
$210$	1.36195	+	5.86955i	0.0939837	+	0.405038i
$211$	−6.90757	−	6.90757i	−0.475537	−	0.475537i	0.428164	−	0.903701i	$-0.359161\pi$
$211$	−6.90757	−	6.90757i	−0.475537	−	0.475537i	−0.903701	+	0.428164i	$0.859161\pi$
$212$	7.07154	−	8.06826i	0.485676	−	0.554130i
$213$	−5.26716	+	9.12299i	−0.360900	+	0.625097i
$214$	5.36245	+	2.01740i	0.366570	+	0.137907i
$215$	−1.90840	+	13.8242i	−0.130151	+	0.942800i
$216$	−9.84473	+	5.26761i	−0.669849	+	0.358416i
$217$	−4.51807	+	13.5346i	−0.306707	+	0.918789i
$218$	−1.39281	−	0.997766i	−0.0943327	−	0.0675772i
$219$	−1.21622	+	4.53901i	−0.0821848	+	0.306718i
$220$	17.8615	+	1.27823i	1.20422	+	0.0861784i
$221$	3.87457	−	1.03819i	0.260632	−	0.0698361i
$222$	0.792133	+	0.964932i	0.0531645	+	0.0647620i
$223$	4.16871	+	4.16871i	0.279157	+	0.279157i	0.832773	−	0.553615i	$-0.186752\pi$
$223$	4.16871	+	4.16871i	0.279157	+	0.279157i	−0.553615	+	0.832773i	$0.686752\pi$
$224$	7.13149	+	13.1583i	0.476493	+	0.879178i
$225$	−3.06029	−	12.0233i	−0.204019	−	0.801555i
$226$	−2.51998	+	25.6238i	−0.167627	+	1.70447i
$227$	−7.18744	+	12.4490i	−0.477047	+	0.826270i	−0.999654	−	0.0263039i	$-0.991626\pi$
$227$	−7.18744	+	12.4490i	−0.477047	+	0.826270i	0.522607	+	0.852574i	$0.324960\pi$
$228$	2.57522	+	3.85167i	0.170548	+	0.255083i
$229$	−3.84511	−	1.03029i	−0.254092	−	0.0680838i	0.129524	−	0.991576i	$-0.458655\pi$
$229$	−3.84511	−	1.03029i	−0.254092	−	0.0680838i	−0.383617	+	0.923492i	$0.625322\pi$
$230$	−1.46381	−	4.93432i	−0.0965205	−	0.325359i
$231$	7.61576	+	0.460443i	0.501080	+	0.0302949i
$232$	4.68408	+	1.41868i	0.307525	+	0.0931410i
$233$	−0.145597	+	0.543375i	−0.00953837	+	0.0355977i	−0.970531	−	0.240976i	$-0.922532\pi$
$233$	−0.145597	+	0.543375i	−0.00953837	+	0.0355977i	0.960993	+	0.276574i	$0.0891991\pi$
$234$	1.60902	−	4.27694i	0.105185	−	0.279592i
$235$	19.7838	+	8.34070i	1.29056	+	0.544087i
$236$	18.3152	−	1.20577i	1.19222	−	0.0784887i
$237$	8.34634			0.542153
$238$	4.70198	−	10.5230i	0.304784	−	0.682102i
$239$		−	16.8638i		−	1.09083i	−0.838167	−	0.545414i	$-0.816372\pi$
$239$		−	16.8638i		−	1.09083i	0.838167	−	0.545414i	$-0.183628\pi$
$240$	3.18890	+	5.59680i	0.205842	+	0.361272i
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	0.657248	−	0.753675i	$-0.271720\pi$
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	−0.324077	+	0.946031i	$0.605054\pi$
$242$	2.50646	−	6.66244i	0.161122	−	0.428278i
$243$	13.1257	−	7.57815i	0.842017	−	0.486138i
$244$	−4.32031	+	8.76712i	−0.276580	+	0.561257i
$245$	−15.1034	+	4.10929i	−0.964923	+	0.262533i
$246$	−5.56312	+	0.919301i	−0.354692	+	0.0586125i
$247$	−4.04608	−	1.08414i	−0.257446	−	0.0689824i
$248$	−0.492480	+	15.2460i	−0.0312725	+	0.968124i
$249$	3.44662	−	5.96973i	0.218421	−	0.378316i
$250$	−15.2137	+	4.30610i	−0.962201	+	0.272342i
$251$	−0.424636	−	0.424636i	−0.0268028	−	0.0268028i	0.693578	−	0.720381i	$-0.256033\pi$
$251$	−0.424636	−	0.424636i	−0.0268028	−	0.0268028i	−0.720381	+	0.693578i	$0.756033\pi$
$252$	−6.62577	−	11.3356i	−0.417385	−	0.714076i
$253$	−6.51712			−0.409728
$254$	27.7687	+	2.73092i	1.74236	+	0.171353i
$255$	1.92707	−	4.57095i	0.120678	−	0.286244i
$256$	11.3268	+	11.3006i	0.707925	+	0.706288i
$257$	−10.0026	−	2.68019i	−0.623945	−	0.167185i	−0.0670243	−	0.997751i	$-0.521350\pi$
$257$	−10.0026	−	2.68019i	−0.623945	−	0.167185i	−0.556920	+	0.830566i	$0.688017\pi$
$258$	1.03634	+	6.27136i	0.0645195	+	0.390438i
$259$	−2.42739	+	2.15061i	−0.150831	+	0.133632i
$260$	−5.50323	−	1.90494i	−0.341296	−	0.118140i
$261$	−4.14731	−	1.11127i	−0.256712	−	0.0687859i
$262$	−1.82483	+	0.827139i	−0.112738	+	0.0511008i
$263$	−20.1291	+	5.39358i	−1.24121	+	0.332582i	−0.818937	−	0.573884i	$-0.805436\pi$
$263$	−20.1291	+	5.39358i	−1.24121	+	0.332582i	−0.422278	+	0.906466i	$0.638769\pi$
$264$	7.94258	−	1.85558i	0.488832	−	0.114203i
$265$	9.47020	+	7.36170i	0.581750	+	0.452226i
$266$	−9.74667	+	7.06149i	−0.597607	+	0.432968i
$267$	−11.6629			−0.713758
$268$	10.6661	−	12.1694i	0.651533	−	0.743365i
$269$	28.7671	−	7.70811i	1.75396	−	0.469972i	0.768495	−	0.639856i	$-0.221006\pi$
$269$	28.7671	−	7.70811i	1.75396	−	0.469972i	0.985464	+	0.169884i	$0.0543394\pi$
$270$	−6.52686	−	10.6411i	−0.397212	−	0.647597i
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	−0.611742	−	0.791058i	$-0.709531\pi$
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	0.379205	+	0.925313i	$0.376197\pi$
$272$	1.60121	−	12.2170i	0.0970874	−	0.740764i
$273$	−2.35357	−	0.785661i	−0.142445	−	0.0475504i
$274$	7.69793	+	5.51457i	0.465049	+	0.333148i
$275$	−0.251498	+	20.0193i	−0.0151659	+	1.20721i
$276$	−1.30300	−	1.94885i	−0.0784312	−	0.117307i
$277$	4.24736	−	7.35664i	0.255199	−	0.442018i	−0.709751	−	0.704453i	$-0.751192\pi$
$277$	4.24736	−	7.35664i	0.255199	−	0.442018i	0.964950	+	0.262435i	$0.0845257\pi$
$278$	−0.904763	+	9.19985i	−0.0542640	+	0.551770i
$279$		−	13.3821i		−	0.801164i
$280$	−14.2168	+	8.82514i	−0.849615	+	0.527403i
$281$			1.51577i			0.0904234i	0.998977	+	0.0452117i	$0.0143962\pi$
$281$			1.51577i			0.0904234i	−0.998977	+	0.0452117i	$0.985604\pi$
$282$	9.73237	+	0.957133i	0.579554	+	0.0569964i
$283$	−6.13216	+	10.6212i	−0.364519	+	0.631365i	−0.988699	−	0.149915i	$-0.952100\pi$
$283$	−6.13216	+	10.6212i	−0.364519	+	0.631365i	0.624180	+	0.781281i	$0.285433\pi$
$284$	−28.6941	−	5.69898i	−1.70268	−	0.338172i
$285$	−4.12941	+	3.12760i	−0.244605	+	0.185263i
$286$	−4.29434	+	5.99458i	−0.253930	+	0.354467i
$287$	−2.93027	−	14.3512i	−0.172968	−	0.847128i
$288$	−10.2517	−	9.58787i	−0.604088	−	0.564970i
$289$	6.50500	−	3.75567i	0.382647	−	0.220922i
$290$	−1.27521	+	5.32123i	−0.0748832	+	0.312473i
$291$	−0.173259	+	0.0464247i	−0.0101566	+	0.00272146i
$292$	−13.0216	+	0.857265i	−0.762032	+	0.0501677i
$293$	0.845374			0.0493873			0.0246936	−	0.999695i	$-0.492139\pi$
$293$	0.845374			0.0493873			0.0246936	+	0.999695i	$0.492139\pi$
$294$	−6.01536	+	3.82683i	−0.350823	+	0.223185i
$295$	2.55073	+	20.3622i	0.148509	+	1.18554i
$296$	−1.82952	+	2.94495i	−0.106338	+	0.171172i
$297$	−15.2682	+	4.09109i	−0.885948	+	0.237389i
$298$	3.82701	+	8.44315i	0.221693	+	0.489098i
$299$	2.04722	+	0.548550i	0.118394	+	0.0317235i
$300$	−6.03676	+	3.92734i	−0.348533	+	0.226745i
$301$	−16.1783	+	3.30332i	−0.932502	+	0.190400i
$302$	11.9856	−	1.98061i	0.689692	−	0.113971i
$303$	−8.54571	−	2.28982i	−0.490938	−	0.131547i
$304$	−7.82696	+	10.2125i	−0.448907	+	0.585728i
$305$	−10.0692	−	4.24508i	−0.576560	−	0.243073i
$306$	−1.05795	+	10.7575i	−0.0604792	+	0.614968i
$307$	16.2854			0.929459			0.464730	−	0.885453i	$-0.346152\pi$
$307$	16.2854			0.929459			0.464730	+	0.885453i	$0.346152\pi$
$308$	5.59337	+	20.4365i	0.318712	+	1.16448i
$309$	6.26372	+	6.26372i	0.356331	+	0.356331i
$310$	−17.0484	+	0.453400i	−0.968286	+	0.0257514i
$311$	1.90495	−	3.29948i	0.108020	−	0.187096i	−0.806948	−	0.590622i	$-0.798882\pi$
$311$	1.90495	−	3.29948i	0.108020	−	0.187096i	0.914968	+	0.403526i	$0.132216\pi$
$312$	−2.65118	−	0.0856389i	−0.150093	−	0.00484835i
$313$	22.7040	+	6.08353i	1.28331	+	0.343861i	0.835115	−	0.550075i	$-0.185401\pi$
$313$	22.7040	+	6.08353i	1.28331	+	0.343861i	0.448193	+	0.893937i	$0.352068\pi$
$314$	−5.22212	−	31.6015i	−0.294701	−	1.78338i
$315$	12.2157	−	8.14079i	0.688277	−	0.458681i
$316$	7.45678	+	21.9461i	0.419477	+	1.23457i
$317$	−0.0246702	+	0.0142434i	−0.00138562	+	0.000799987i	−0.500693	−	0.865625i	$-0.666921\pi$
$317$	−0.0246702	+	0.0142434i	−0.00138562	+	0.000799987i	0.499307	+	0.866425i	$0.333588\pi$
$318$	5.11362	+	1.92379i	0.286758	+	0.107881i
$319$	6.00042	+	3.46434i	0.335959	+	0.193966i
$320$	−11.8674	+	13.3853i	−0.663406	+	0.748260i
$321$			2.91767i			0.162849i
$322$	4.93157	−	3.57294i	0.274826	−	0.199112i
$323$	9.90869			0.551334
$324$	6.92023	+	6.06533i	0.384457	+	0.336963i
$325$	1.76404	−	6.26747i	0.0978512	−	0.347657i
$326$	28.1020	+	10.5722i	1.55643	+	0.585541i
$327$	0.225820	−	0.842770i	0.0124879	−	0.0466053i
$328$	−7.38744	−	13.8065i	−0.407903	−	0.762337i
$329$	−1.53310	+	25.3575i	−0.0845224	+	1.39801i
$330$	2.59356	+	8.74260i	0.142771	+	0.481265i
$331$	−1.27889	−	0.342677i	−0.0702941	−	0.0188352i	0.223501	−	0.974704i	$-0.428252\pi$
$331$	−1.27889	−	0.342677i	−0.0702941	−	0.0188352i	−0.293795	+	0.955869i	$0.594918\pi$
$332$	18.7763	+	3.72918i	1.03048	+	0.204666i
$333$	1.52076	−	2.63403i	0.0833370	−	0.144344i
$334$	−10.7575	−	1.05795i	−0.588624	−	0.0578884i
$335$	14.2840	+	11.1037i	0.780416	+	0.606660i
$336$	−4.99293	+	5.75857i	−0.272387	+	0.314156i
$337$	9.95073	+	9.95073i	0.542051	+	0.542051i	0.924130	−	0.382079i	$-0.124792\pi$
$337$	9.95073	+	9.95073i	0.542051	+	0.542051i	−0.382079	+	0.924130i	$0.624792\pi$
$338$	−12.3564	+	10.1436i	−0.672099	+	0.551740i
$339$	−12.6650	+	3.39358i	−0.687870	+	0.184314i
$340$	13.7407	+	0.983330i	0.745193	+	0.0533286i
$341$	−5.58917	+	20.8591i	−0.302671	+	1.12958i
$342$	6.57363	−	9.17630i	0.355461	−	0.496197i
$343$	−10.5221	−	15.2409i	−0.568138	−	0.822934i
$344$	−15.5642	+	8.32793i	−0.839166	+	0.449012i
$345$	2.08938	−	1.58249i	0.112488	−	0.0851983i
$346$	12.8792	−	34.2342i	0.692389	−	1.84044i
$347$	4.25411	−	7.36834i	0.228373	−	0.395553i	−0.728953	−	0.684563i	$-0.759993\pi$
$347$	4.25411	−	7.36834i	0.228373	−	0.395553i	0.957326	+	0.289010i	$0.0933262\pi$
$348$	0.163728	+	2.48698i	0.00877673	+	0.133316i
$349$	21.0228	+	21.0228i	1.12532	+	1.12532i	0.990928	+	0.134397i	$0.0429099\pi$
$349$	21.0228	+	21.0228i	1.12532	+	1.12532i	0.134397	+	0.990928i	$0.457090\pi$
$350$	−10.7850	−	15.2867i	−0.576485	−	0.817108i
$351$	5.14052			0.274381
$352$	11.9752	+	19.2266i	0.638280	+	1.02478i
$353$	−13.5031	+	3.61815i	−0.718698	+	0.192574i	−0.599591	−	0.800307i	$-0.704670\pi$
$353$	−13.5031	+	3.61815i	−0.718698	+	0.192574i	−0.119107	+	0.992881i	$0.538003\pi$
$354$	3.85888	+	8.51344i	0.205097	+	0.452484i
$355$	4.47279	−	32.4003i	0.237391	−	1.71963i
$356$	−10.4199	−	30.6668i	−0.552252	−	1.62534i
$357$	5.85872	+	0.354214i	0.310076	+	0.0187470i
$358$	−4.69851	−	3.36588i	−0.248324	−	0.177892i
$359$	−11.6770	−	20.2251i	−0.616287	−	1.06744i	−0.990157	−	0.139959i	$-0.955303\pi$
$359$	−11.6770	−	20.2251i	−0.616287	−	1.06744i	0.373870	−	0.927481i	$-0.378030\pi$
$360$	10.0265	−	12.0727i	0.528444	−	0.636287i
$361$	7.49346	+	4.32635i	0.394393	+	0.227703i
$362$	19.8468	+	1.95184i	1.04312	+	0.102586i
$363$	3.62498			0.190262
$364$	−0.0368878	−	6.89048i	−0.00193345	−	0.361160i
$365$	−1.81350	−	14.4770i	−0.0949229	−	0.757760i
$366$	−4.95339	−	0.487143i	−0.258918	−	0.0254634i
$367$	1.82038	+	6.79376i	0.0950232	+	0.354631i	0.997023	−	0.0771051i	$-0.0245677\pi$
$367$	1.82038	+	6.79376i	0.0950232	+	0.354631i	−0.902000	+	0.431736i	$0.857901\pi$
$368$	3.96025	−	5.16728i	0.206442	−	0.269363i
$369$	6.86856	+	11.8967i	0.357563	+	0.619317i
$370$	−3.40721	−	1.84816i	−0.177133	−	0.0960815i
$371$	−4.49396	+	13.4624i	−0.233315	+	0.698932i
$372$	−7.35507	+	2.49908i	−0.381343	+	0.129571i
$373$	24.8817	−	14.3654i	1.28832	−	0.743814i	0.309969	−	0.950747i	$-0.399681\pi$
$373$	24.8817	−	14.3654i	1.28832	−	0.743814i	0.978355	+	0.206932i	$0.0663480\pi$
$374$	6.14207	−	16.3262i	0.317599	−	0.844210i
$375$	−4.78045	−	6.47923i	−0.246862	−	0.334586i
$376$	6.17838	+	26.4457i	0.318625	+	1.36383i
$377$	−1.59331	−	1.59331i	−0.0820595	−	0.0820595i
$378$	9.31068	−	11.4664i	0.478890	−	0.589766i
$379$	12.2721	+	12.2721i	0.630375	+	0.630375i	0.948162	−	0.317787i	$-0.102940\pi$
$379$	12.2721	+	12.2721i	0.630375	+	0.630375i	−0.317787	+	0.948162i	$0.602940\pi$
$380$	−11.9131	−	8.06375i	−0.611129	−	0.413661i
$381$	3.67765	+	13.7252i	0.188412	+	0.703162i
$382$	23.3197	+	8.77306i	1.19314	+	0.448869i
$383$	3.88593	−	14.5025i	0.198562	−	0.741042i	−0.792754	−	0.609541i	$-0.791354\pi$
$383$	3.88593	−	14.5025i	0.198562	−	0.741042i	0.991316	−	0.131501i	$-0.0419796\pi$
$384$	−3.35520	+	7.42508i	−0.171219	+	0.378909i
$385$	−22.4411	+	7.58728i	−1.14370	+	0.386684i
$386$	29.4172	+	21.0736i	1.49730	+	1.07262i
$387$	13.4112	−	7.74299i	0.681732	−	0.393598i
$388$	−0.276864	−	0.414096i	−0.0140556	−	0.0210226i
$389$	−24.4030	+	6.53876i	−1.23728	+	0.331528i	−0.817410	−	0.576056i	$-0.804591\pi$
$389$	−24.4030	+	6.53876i	−1.23728	+	0.331528i	−0.419870	+	0.907584i	$0.637924\pi$
$390$	−0.0788431	−	2.96461i	−0.00399237	−	0.150119i
$391$	−5.01355			−0.253546
$392$	−15.4366	−	12.3980i	−0.779668	−	0.626193i
$393$	−0.721458	−	0.721458i	−0.0363928	−	0.0363928i
$394$	20.5310	−	16.8544i	1.03434	−	0.849110i
$395$	−24.0034	+	9.76635i	−1.20774	+	0.491399i
$396$	−11.0447	−	16.5193i	−0.555019	−	0.830124i
$397$	−6.09474	−	10.5564i	−0.305886	−	0.529811i	0.671572	−	0.740939i	$-0.265619\pi$
$397$	−6.09474	−	10.5564i	−0.305886	−	0.529811i	−0.977458	+	0.211129i	$0.932286\pi$
$398$	12.4346	−	2.05481i	0.623291	−	0.102998i
$399$	−5.11345	−	3.37937i	−0.255993	−	0.169180i
$400$	−15.7200	−	12.3645i	−0.786001	−	0.618225i
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.837851	+	0.545899i	$0.183812\pi$
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.0538373	+	0.998550i	$0.482855\pi$
$402$	7.71291	+	2.90166i	0.384685	+	0.144722i
$403$	3.51144	−	6.08199i	0.174917	−	0.302966i
$404$	−1.61400	−	24.5161i	−0.0802993	−	1.21972i
$405$	−6.31421	+	8.12269i	−0.313756	+	0.403620i
$406$	−6.43986	+	0.668158i	−0.319605	+	0.0331601i
$407$	−3.47058	+	3.47058i	−0.172030	+	0.172030i
$408$	6.11014	−	1.42748i	0.302497	−	0.0706708i
$409$	−13.5323	−	7.81290i	−0.669131	−	0.386323i	0.126616	−	0.991952i	$-0.459588\pi$
$409$	−13.5323	−	7.81290i	−0.669131	−	0.386323i	−0.795747	+	0.605629i	$0.792922\pi$
$410$	14.9234	−	9.15344i	0.737013	−	0.452056i
$411$	−1.24809	+	4.65793i	−0.0615636	+	0.229759i
$412$	−10.8739	+	22.0662i	−0.535718	+	1.08712i
$413$	−21.7225	+	10.8495i	−1.06889	+	0.533867i
$414$	−3.32610	+	4.64298i	−0.163469	+	0.228190i
$415$	−2.92682	+	21.2015i	−0.143672	+	1.04074i
$416$	−2.14343	−	7.04760i	−0.105091	−	0.345537i
$417$	−4.54719	+	1.21842i	−0.222677	+	0.0596661i
$418$	−14.0791	+	11.5578i	−0.688632	+	0.565312i
$419$	3.05027	+	3.05027i	0.149016	+	0.149016i	0.777678	−	0.628663i	$-0.216397\pi$
$419$	3.05027	+	3.05027i	0.149016	+	0.149016i	−0.628663	+	0.777678i	$0.716397\pi$
$420$	−6.75561	−	5.19373i	−0.329640	−	0.253428i
$421$	21.6422	−	21.6422i	1.05478	−	1.05478i	0.0563674	−	0.998410i	$-0.482048\pi$
$421$	21.6422	−	21.6422i	1.05478	−	1.05478i	0.998410	−	0.0563674i	$-0.0179518\pi$
$422$	13.7488	+	1.35213i	0.669282	+	0.0658208i
$423$	−6.16640	−	23.0133i	−0.299821	−	1.11895i
$424$	−0.489852	+	15.1647i	−0.0237893	+	0.736461i
$425$	−0.193474	+	15.4006i	−0.00938489	+	0.747040i
$426$	−2.42891	−	14.6984i	−0.117681	−	0.712142i
$427$	0.780286	−	12.9060i	0.0377607	−	0.624564i
$428$	−7.67181	+	2.60671i	−0.370831	+	0.126000i
$429$	−3.62725	−	0.971918i	−0.175125	−	0.0469246i
$430$	−10.3188	−	16.8233i	−0.497615	−	0.811290i
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	−0.797624	−	0.603155i	$-0.793910\pi$
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	0.921160	+	0.389185i	$0.127243\pi$
$432$	6.03424	−	14.5918i	0.290322	−	0.702049i
$433$	−29.1874	−	29.1874i	−1.40266	−	1.40266i	−0.791540	−	0.611117i	$-0.790720\pi$
$433$	−29.1874	−	29.1874i	−1.40266	−	1.40266i	−0.611117	−	0.791540i	$-0.709280\pi$
$434$	−7.20637	−	18.8485i	−0.345917	−	0.904756i
$435$	−2.76494	+	0.346358i	−0.132569	+	0.0166066i
$436$	2.41776	−	0.159171i	0.115790	−	0.00762290i
$437$	4.53406	+	2.61774i	0.216893	+	0.125223i
$438$	−2.74355	−	6.05282i	−0.131092	−	0.289215i
$439$	27.2269	−	15.7195i	1.29947	−	0.750250i	0.319158	−	0.947701i	$-0.396600\pi$
$439$	27.2269	−	15.7195i	1.29947	−	0.750250i	0.980313	+	0.197452i	$0.0632666\pi$
$440$	−20.6709	+	14.6304i	−0.985448	+	0.697478i
$441$	13.8864	+	10.4337i	0.661258	+	0.496842i
$442$	−3.30359	+	4.61156i	−0.157136	+	0.219350i
$443$	12.4689	−	7.19894i	0.592417	−	0.342032i	−0.173636	−	0.984810i	$-0.555552\pi$
$443$	12.4689	−	7.19894i	0.592417	−	0.342032i	0.766053	+	0.642778i	$0.222218\pi$
$444$	−1.73172	−	0.343939i	−0.0821837	−	0.0163226i
$445$	33.5416	−	13.6472i	1.59002	−	0.646939i
$446$	−8.29739	−	0.816009i	−0.392893	−	0.0386392i
$447$	−3.33805	+	3.33805i	−0.157884	+	0.157884i
$448$	−19.6025	−	7.98374i	−0.926133	−	0.377196i
$449$		−	24.3063i		−	1.14709i	−0.819175	−	0.573544i	$-0.805568\pi$
$449$		−	24.3063i		−	1.14709i	0.819175	−	0.573544i	$-0.194432\pi$
$450$	14.1340	+	10.3963i	0.666281	+	0.490085i
$451$	−5.73745	−	21.4125i	−0.270166	−	1.00827i
$452$	−20.2384	−	30.2699i	−0.951934	−	1.42378i
$453$	3.09319	+	5.35757i	0.145331	+	0.251721i
$454$	−3.31443	−	20.0571i	−0.155554	−	0.941328i
$455$	7.68802	−	0.494504i	0.360420	−	0.0231827i
$456$	−6.27110	−	1.89935i	−0.293671	−	0.0889451i
$457$	−10.4424	−	2.79803i	−0.488474	−	0.130886i	0.00617169	−	0.999981i	$-0.498035\pi$
$457$	−10.4424	−	2.79803i	−0.488474	−	0.130886i	−0.494646	+	0.869095i	$0.664702\pi$
$458$	5.12750	−	2.32413i	0.239592	−	0.108600i
$459$	−11.7456	+	3.14723i	−0.548239	+	0.146900i
$460$	6.02774	+	4.08006i	0.281045	+	0.190234i
$461$	9.72905	−	9.72905i	0.453127	−	0.453127i	−0.443264	−	0.896391i	$-0.646180\pi$
$461$	9.72905	−	9.72905i	0.453127	−	0.453127i	0.896391	+	0.443264i	$0.146180\pi$
$462$	−8.73774	+	6.33052i	−0.406517	+	0.294522i
$463$	−17.8524	+	17.8524i	−0.829671	+	0.829671i	−0.987471	−	0.157800i	$-0.949560\pi$
$463$	−17.8524	+	17.8524i	−0.829671	+	0.829671i	0.157800	+	0.987471i	$0.449560\pi$
$464$	−6.39306	+	2.65243i	−0.296790	+	0.123136i
$465$	−3.27312	−	8.04455i	−0.151787	−	0.373057i
$466$	−0.328436	−	0.724596i	−0.0152145	−	0.0335662i
$467$	−0.164592	−	0.285082i	−0.00761641	−	0.0131920i	0.862192	−	0.506582i	$-0.169091\pi$
$467$	−0.164592	−	0.285082i	−0.00761641	−	0.0131920i	−0.869808	+	0.493389i	$0.835758\pi$
$468$	2.07903	+	6.11882i	0.0961034	+	0.282843i
$469$	−6.77827	+	20.3054i	−0.312991	+	0.937616i
$470$	−29.1095	+	8.63556i	−1.34272	+	0.398329i
$471$	14.1259	−	8.15561i	0.650888	−	0.375790i
$472$	−18.9379	+	17.7527i	−0.871688	+	0.817135i
$473$	−24.1385	+	6.46789i	−1.10989	+	0.297394i
$474$	−9.12315	+	7.48938i	−0.419040	+	0.343999i
$475$	8.21614	−	13.8267i	0.376982	−	0.634412i
$476$	4.30292	+	15.7216i	0.197224	+	0.720597i
$477$		−	13.3107i		−	0.609453i
$478$	15.1323	+	18.4333i	0.692136	+	0.843122i
$479$	−8.80324	+	15.2477i	−0.402230	+	0.696683i	−0.993995	−	0.109428i	$-0.965098\pi$
$479$	−8.80324	+	15.2477i	−0.402230	+	0.696683i	0.591764	+	0.806111i	$0.298432\pi$
$480$	−8.50785	−	3.25622i	−0.388328	−	0.148626i
$481$	1.38233	−	0.798089i	0.0630289	−	0.0363897i
$482$	−8.33315	+	1.37705i	−0.379565	+	0.0627228i
$483$	2.58728	+	1.70988i	0.117725	+	0.0778021i
$484$	3.23863	+	9.53164i	0.147211	+	0.433256i
$485$	0.443956	−	0.336251i	0.0201590	−	0.0152684i
$486$	−7.54731	+	20.0615i	−0.342353	+	0.910009i
$487$	−4.22342	−	15.7620i	−0.191381	−	0.714245i	−0.993174	−	0.116643i	$-0.962787\pi$
$487$	−4.22342	−	15.7620i	−0.191381	−	0.714245i	0.801793	−	0.597603i	$-0.203880\pi$
$488$	−3.14455	−	13.4598i	−0.142347	−	0.609297i
$489$			15.2901i			0.691442i
$490$	12.8218	−	18.0445i	0.579228	−	0.815165i
$491$	26.7226	−	26.7226i	1.20597	−	1.20597i	0.233652	−	0.972320i	$-0.424932\pi$
$491$	26.7226	−	26.7226i	1.20597	−	1.20597i	0.972320	−	0.233652i	$-0.0750676\pi$
$492$	5.25598	−	5.99679i	0.236958	−	0.270356i
$493$	4.61606	+	2.66508i	0.207897	+	0.120029i
$494$	5.39548	−	2.44560i	0.242754	−	0.110033i
$495$	17.7104	−	13.4138i	0.796025	−	0.602906i
$496$	−13.1423	−	17.1069i	−0.590108	−	0.768124i
$497$	37.9178	−	7.74213i	1.70084	−	0.347282i
$498$	1.58938	+	9.61808i	0.0712219	+	0.430997i
$499$	−38.6769	−	10.3634i	−1.73142	−	0.463931i	−0.750907	−	0.660408i	$-0.770383\pi$
$499$	−38.6769	−	10.3634i	−1.73142	−	0.463931i	−0.980509	+	0.196476i	$0.937050\pi$
$500$	12.7657	−	18.3585i	0.570901	−	0.821019i
$501$	−1.42471	−	5.31709i	−0.0636513	−	0.237550i
$502$	0.845195	+	0.0831210i	0.0377229	+	0.00370987i
$503$	−16.4835	+	16.4835i	−0.734965	+	0.734965i	−0.971599	−	0.236634i	$-0.923956\pi$
$503$	−16.4835	+	16.4835i	−0.734965	+	0.734965i	0.236634	+	0.971599i	$0.423956\pi$
$504$	17.4142	+	6.44515i	0.775689	+	0.287090i
$505$	27.2562	−	3.41432i	1.21288	−	0.151935i
$506$	7.12368	−	5.84798i	0.316686	−	0.259974i
$507$	−7.05045	−	4.07058i	−0.313122	−	0.180781i
$508$	−32.8037	+	21.9325i	−1.45543	+	0.973095i
$509$	−7.73911	+	28.8827i	−0.343030	+	1.28020i	0.551867	+	0.833932i	$0.313916\pi$
$509$	−7.73911	+	28.8827i	−0.343030	+	1.28020i	−0.894897	+	0.446273i	$0.852751\pi$
$510$	1.99520	+	6.72559i	0.0883490	+	0.297814i
$511$	15.4441	−	7.71366i	0.683206	−	0.341232i
$512$	−22.5213	−	2.18856i	−0.995311	−	0.0967215i
$513$	12.2656	+	3.28654i	0.541537	+	0.145105i
$514$	13.3386	−	6.04595i	0.588339	−	0.266675i
$515$	−25.3434	−	10.6845i	−1.11676	−	0.470817i
$516$	−6.76024	−	5.92511i	−0.297603	−	0.260839i
$517$			38.4471i			1.69090i
$518$	0.723518	−	4.52894i	0.0317896	−	0.198990i
$519$	18.6266			0.817616
$520$	7.72479	−	2.85595i	0.338754	−	0.125242i
$521$	15.0914	−	26.1390i	0.661165	−	1.14517i	−0.319145	−	0.947706i	$-0.603396\pi$
$521$	15.0914	−	26.1390i	0.661165	−	1.14517i	0.980310	−	0.197465i	$-0.0632708\pi$
$522$	5.53048	−	2.50679i	0.242063	−	0.109719i
$523$	−4.48449	−	7.76736i	−0.196093	−	0.339643i	0.751165	−	0.660114i	$-0.229492\pi$
$523$	−4.48449	−	7.76736i	−0.196093	−	0.339643i	−0.947258	+	0.320471i	$0.896159\pi$
$524$	1.25246	−	2.54159i	0.0547139	−	0.111030i
$525$	5.35224	−	7.88162i	0.233591	−	0.343982i
$526$	17.1628	−	23.9580i	0.748333	−	1.04462i
$527$	−4.29969	+	16.0467i	−0.187297	+	0.699003i
$528$	−7.01675	+	9.15537i	−0.305365	+	0.398436i
$529$	17.6245	+	10.1755i	0.766281	+	0.442413i
$530$	−16.9575	+	0.450980i	−0.736585	+	0.0195893i
$531$	16.1025	−	16.1025i	0.698787	−	0.698787i
$532$	4.31735	−	16.4647i	0.187181	−	0.713833i
$533$			7.20920i			0.312265i
$534$	12.7484	−	10.4654i	0.551677	−	0.452883i
$535$	−3.41407	−	8.39099i	−0.147603	−	0.362774i
$536$	−0.738847	+	22.8730i	−0.0319133	+	0.987962i
$537$	0.761783	−	2.84301i	0.0328734	−	0.122685i
$538$	−24.5278	+	34.2389i	−1.05747	+	1.47615i
$539$	−17.2874	−	22.0631i	−0.744623	−	0.950326i
$540$	16.6829	+	5.77478i	0.717916	+	0.248507i
$541$	−0.690427	+	2.57671i	−0.0296838	+	0.110781i	−0.979178	−	0.203003i	$-0.934930\pi$
$541$	−0.690427	+	2.57671i	−0.0296838	+	0.110781i	0.949494	+	0.313784i	$0.101597\pi$
$542$	2.20112	−	5.85081i	0.0945464	−	0.251314i
$543$	2.62848	+	9.80963i	0.112799	+	0.420972i
$544$	9.21238	+	14.7909i	0.394978	+	0.634153i
$545$	0.336717	+	2.68798i	0.0144234	+	0.115140i
$546$	3.27762	−	1.25314i	0.140269	−	0.0536293i
$547$		−	9.41386i		−	0.402508i	−0.979539	−	0.201254i	$-0.935498\pi$
$547$		−	9.41386i		−	0.402508i	0.979539	−	0.201254i	$-0.0645016\pi$
$548$	−13.3628	+	0.879724i	−0.570829	+	0.0375800i
$549$	3.13845	+	11.7129i	0.133946	+	0.499893i
$550$	−17.6889	−	22.1082i	−0.754258	−	0.942697i
$551$	−2.78305	−	4.82039i	−0.118562	−	0.205355i
$552$	3.17302	+	0.961023i	0.135053	+	0.0409039i
$553$	−20.3334	−	22.9503i	−0.864664	−	0.975945i
$554$	1.95863	+	11.8526i	0.0832144	+	0.503569i
$555$	0.269938	−	1.95539i	0.0114582	−	0.0830018i
$556$	−7.26629	−	10.8680i	−0.308159	−	0.460904i
$557$	−20.6283	−	11.9097i	−0.874048	−	0.504632i	−0.00535649	−	0.999986i	$-0.501705\pi$
$557$	−20.6283	−	11.9097i	−0.874048	−	0.504632i	−0.868691	+	0.495354i	$0.835038\pi$
$558$	12.0081	+	14.6276i	0.508343	+	0.619235i
$559$	8.12700			0.343735
$560$	7.62095	−	22.4036i	0.322044	−	0.946725i
$561$	8.88299			0.375040
$562$	−1.36014	−	1.65685i	−0.0573741	−	0.0698899i
$563$	23.6088	+	13.6305i	0.994992	+	0.574459i	0.906763	−	0.421641i	$-0.138546\pi$
$563$	23.6088	+	13.6305i	0.994992	+	0.574459i	0.0882292	+	0.996100i	$0.471879\pi$
$564$	−11.4970	+	7.68689i	−0.484113	+	0.323676i
$565$	32.4526	−	24.5795i	1.36529	−	1.03407i
$566$	−2.82779	−	17.1123i	−0.118861	−	0.719283i
$567$	−11.5468	−	3.85451i	−0.484921	−	0.161874i
$568$	36.4785	−	19.5185i	1.53060	−	0.818979i
$569$	18.6660	+	32.3304i	0.782519	+	1.35536i	0.930470	+	0.366368i	$0.119399\pi$
$569$	18.6660	+	32.3304i	0.782519	+	1.35536i	−0.147951	+	0.988995i	$0.547268\pi$
$570$	1.70727	−	7.12412i	0.0715097	−	0.298396i
$571$	5.89295	+	21.9928i	0.246612	+	0.920369i	0.972566	+	0.232626i	$0.0747317\pi$
$571$	5.89295	+	21.9928i	0.246612	+	0.920369i	−0.725954	+	0.687743i	$0.758602\pi$
$572$	−0.685064	−	10.4059i	−0.0286440	−	0.435094i
$573$			12.6881i			0.530051i
$574$	16.0807	+	13.0575i	0.671197	+	0.545011i
$575$	−4.15716	+	6.99597i	−0.173366	+	0.291752i
$576$	19.8093	+	1.28110i	0.825387	+	0.0533793i
$577$	0.792593	+	2.95800i	0.0329961	+	0.123143i	0.980459	−	0.196721i	$-0.0630294\pi$
$577$	0.792593	+	2.95800i	0.0329961	+	0.123143i	−0.947463	+	0.319864i	$0.896363\pi$
$578$	−3.74038	+	9.94232i	−0.155579	+	0.413546i
$579$	−4.76949	+	17.8000i	−0.198213	+	0.739742i
$580$	−3.38097	−	6.96077i	−0.140387	−	0.289030i
$581$	−24.8119	+	5.06615i	−1.02937	+	0.210179i
$582$	0.147727	−	0.206215i	0.00612347	−	0.00854791i
$583$	−5.55934	+	20.7478i	−0.230244	+	0.859284i
$584$	13.4643	−	12.6217i	0.557157	−	0.522289i
$585$	−6.69241	+	2.72297i	−0.276697	+	0.112581i
$586$	−0.924054	+	0.758576i	−0.0381723	+	0.0313365i
$587$			16.5240i			0.682019i	0.940060	+	0.341010i	$0.110769\pi$
$587$			16.5240i			0.682019i	−0.940060	+	0.341010i	$0.889231\pi$
$588$	3.14130	−	9.58074i	0.129545	−	0.395103i
$589$	12.2670	−	12.2670i	0.505451	−	0.505451i
$590$	−21.0597	−	19.9686i	−0.867014	−	0.822093i
$591$	11.7148	+	6.76357i	0.481884	+	0.278216i
$592$	−0.642786	−	4.86071i	−0.0264184	−	0.199774i
$593$	−9.26597	+	34.5811i	−0.380508	+	1.42007i	0.464620	+	0.885510i	$0.346191\pi$
$593$	−9.26597	+	34.5811i	−0.380508	+	1.42007i	−0.845128	+	0.534564i	$0.820476\pi$
$594$	13.0182	−	18.1724i	0.534141	−	0.745621i
$595$	−17.2637	+	5.83681i	−0.707742	+	0.239286i
$596$	−11.7595	−	5.79489i	−0.481686	−	0.237368i
$597$	3.20909	+	5.55830i	0.131339	+	0.227486i
$598$	−2.72998	+	1.23741i	−0.111637	+	0.0506017i
$599$	15.7308	−	27.2465i	0.642742	−	1.11326i	−0.342077	−	0.939672i	$-0.611130\pi$
$599$	15.7308	−	27.2465i	0.642742	−	1.11326i	0.984818	−	0.173589i	$-0.0555364\pi$
$600$	3.07452	−	9.70981i	0.125517	−	0.396401i
$601$	−42.9833			−1.75333			−0.876663	−	0.481104i	$-0.840236\pi$
$601$	−42.9833			−1.75333			−0.876663	+	0.481104i	$0.840236\pi$
$602$	14.7199	−	18.1280i	0.599938	−	0.738841i
$603$		−	20.0766i		−	0.817581i
$604$	−11.3238	+	12.9199i	−0.460761	+	0.525703i
$605$	−10.4252	+	4.24172i	−0.423843	+	0.172451i
$606$	11.3958	−	5.16535i	0.462922	−	0.209828i
$607$	−12.6219	−	3.38204i	−0.512308	−	0.137273i	−0.00660186	−	0.999978i	$-0.502101\pi$
$607$	−12.6219	−	3.38204i	−0.512308	−	0.137273i	−0.505706	+	0.862706i	$0.668768\pi$
$608$	−0.608527	−	18.1863i	−0.0246790	−	0.737554i
$609$	−1.47322	−	2.94964i	−0.0596979	−	0.119526i
$610$	14.8156	−	4.39516i	0.599865	−	0.177955i
$611$	3.23611	−	12.0773i	0.130919	−	0.488596i
$612$	−8.49660	−	12.7081i	−0.343455	−	0.513694i
$613$	−32.2284	−	18.6071i	−1.30169	−	0.751534i	−0.321000	−	0.947079i	$-0.604019\pi$
$613$	−32.2284	−	18.6071i	−1.30169	−	0.751534i	−0.980695	+	0.195546i	$0.937352\pi$
$614$	−17.8012	+	14.6133i	−0.718396	+	0.589747i
$615$	7.03880	+	5.47164i	0.283832	+	0.220638i
$616$	−24.4521	−	17.3195i	−0.985205	−	0.697821i
$617$	0.636726	−	0.636726i	0.0256336	−	0.0256336i	−0.694174	−	0.719807i	$-0.744230\pi$
$617$	0.636726	−	0.636726i	0.0256336	−	0.0256336i	0.719807	+	0.694174i	$0.244230\pi$
$618$	−12.4673	−	1.22610i	−0.501508	−	0.0493210i
$619$	1.47025	+	5.48706i	0.0590945	+	0.220544i	0.989158	−	0.146855i	$-0.0469151\pi$
$619$	1.47025	+	5.48706i	0.0590945	+	0.220544i	−0.930064	+	0.367399i	$0.880248\pi$
$620$	18.2283	−	15.7936i	0.732067	−	0.634286i
$621$	−6.20607	−	1.66291i	−0.249041	−	0.0667303i
$622$	0.878454	+	5.31593i	0.0352228	+	0.213149i
$623$	28.4132	+	32.0700i	1.13835	+	1.28486i
$624$	2.97478	−	2.28536i	0.119086	−	0.0914877i
$625$	21.3298	+	13.0400i	0.853191	+	0.521598i
$626$	−30.2761	+	13.7232i	−1.21007	+	0.548489i
$627$	−8.03342	−	4.63810i	−0.320824	−	0.185228i
$628$	34.0650	+	29.8568i	1.35934	+	1.19141i
$629$	−2.66988	+	2.66988i	−0.106455	+	0.106455i
$630$	−6.04771	+	19.8599i	−0.240946	+	0.791239i
$631$			32.0044i			1.27408i	0.770832	+	0.637038i	$0.219841\pi$
$631$			32.0044i			1.27408i	−0.770832	+	0.637038i	$0.780159\pi$
$632$	−27.8436	−	17.2975i	−1.10756	−	0.688058i
$633$	1.82087	+	6.79560i	0.0723733	+	0.270101i
$634$	0.0141854	−	0.0377063i	0.000563374	−	0.00149751i
$635$	−26.6369	−	35.1691i	−1.05705	−	1.39564i
$636$	−7.31582	+	2.48575i	−0.290091	+	0.0985663i
$637$	3.57342	+	8.38576i	0.141584	+	0.332256i
$638$	−9.66753	+	1.59755i	−0.382741	+	0.0632477i
$639$	−31.4325	+	18.1476i	−1.24345	+	0.717907i
$640$	0.960934	−	25.2800i	0.0379843	−	0.999278i
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	0.323231	+	0.946320i	$0.395231\pi$
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	−0.981153	+	0.193233i	$0.938103\pi$
$642$	−2.61810	−	3.18922i	−0.103328	−	0.125869i
$643$			5.26026i			0.207444i	0.994606	+	0.103722i	$0.0330753\pi$
$643$			5.26026i			0.207444i	−0.994606	+	0.103722i	$0.966925\pi$
$644$	−2.18448	+	8.33071i	−0.0860804	+	0.328276i
$645$	6.16823	−	7.93490i	0.242874	−	0.312436i
$646$	−10.8309	+	8.89132i	−0.426136	+	0.349824i
$647$	41.4921	−	11.1178i	1.63122	−	0.437085i	0.676952	−	0.736027i	$-0.263301\pi$
$647$	41.4921	−	11.1178i	1.63122	−	0.437085i	0.954271	+	0.298942i	$0.0966339\pi$
$648$	−13.0069	−	0.420151i	−0.510959	−	0.0165051i
$649$	−31.8248	+	18.3740i	−1.24923	+	0.721244i
$650$	3.69574	+	8.43371i	0.144959	+	0.330797i
$651$	7.69161	−	6.81458i	0.301458	−	0.267084i
$652$	−40.2043	+	13.6605i	−1.57452	+	0.534986i
$653$	9.98010	+	17.2860i	0.390552	+	0.676455i	0.992522	−	0.122063i	$-0.0389510\pi$
$653$	9.98010	+	17.2860i	0.390552	+	0.676455i	−0.601971	+	0.798518i	$0.705618\pi$
$654$	0.509402	+	1.12384i	0.0199192	+	0.0439457i
$655$	2.91906	+	1.23065i	0.114057	+	0.0480855i
$656$	20.4639	+	8.46257i	0.798983	+	0.330408i
$657$	−11.4484	+	11.4484i	−0.446644	+	0.446644i
$658$	−21.0782	−	29.0933i	−0.821713	−	1.13417i
$659$	−29.6719	+	29.6719i	−1.15585	+	1.15585i	−0.170494	+	0.985359i	$0.554536\pi$
$659$	−29.6719	+	29.6719i	−1.15585	+	1.15585i	−0.985359	+	0.170494i	$0.945464\pi$
$660$	−10.6799	−	7.22903i	−0.415715	−	0.281389i
$661$	11.8427	−	3.17323i	0.460626	−	0.123424i	−0.0210412	−	0.999779i	$-0.506698\pi$
$661$	11.8427	−	3.17323i	0.460626	−	0.123424i	0.481667	+	0.876354i	$0.340031\pi$
$662$	1.70541	−	0.773009i	0.0662827	−	0.0300438i
$663$	−2.79040	−	0.747686i	−0.108370	−	0.0290377i
$664$	−23.8701	+	12.7722i	−0.926339	+	0.495656i
$665$	18.6602	+	3.73535i	0.723611	+	0.144851i
$666$	0.701285	+	4.24380i	0.0271742	+	0.164444i
$667$	1.40816	+	2.43900i	0.0545240	+	0.0944384i
$668$	12.7080	−	8.49656i	0.491689	−	0.328742i
$669$	−1.09889	−	4.10113i	−0.0424857	−	0.158559i
$670$	−25.5770	+	0.680216i	−0.988128	+	0.0262791i
$671$		−	19.5680i		−	0.755415i
$672$	0.290318	−	10.7748i	0.0111992	−	0.415648i
$673$	20.2676	−	20.2676i	0.781258	−	0.781258i	−0.198785	−	0.980043i	$-0.563700\pi$
$673$	20.2676	−	20.2676i	0.781258	−	0.781258i	0.980043	+	0.198785i	$0.0636996\pi$
$674$	−19.8059	−	1.94782i	−0.762895	−	0.0750272i
$675$	−5.34762	+	18.9996i	−0.205830	+	0.731296i
$676$	4.40430	−	22.1754i	0.169396	−	0.852901i
$677$	−6.08766	+	3.51471i	−0.233968	+	0.135081i	−0.612401	−	0.790547i	$-0.709796\pi$
$677$	−6.08766	+	3.51471i	−0.233968	+	0.135081i	0.378433	+	0.925629i	$0.376463\pi$
$678$	10.7986	−	15.0741i	0.414719	−	0.578917i
$679$	0.549751	+	0.363318i	0.0210975	+	0.0139429i
$680$	−15.9019	+	11.2550i	−0.609811	+	0.431610i
$681$	8.96558	−	5.17628i	0.343562	−	0.198355i
$682$	−12.6080	−	27.8158i	−0.482786	−	1.06512i
$683$	41.2356	+	23.8074i	1.57784	+	0.910965i	0.995161	+	0.0982608i	$0.0313279\pi$
$683$	41.2356	+	23.8074i	1.57784	+	0.910965i	0.582677	+	0.812704i	$0.302005\pi$
$684$	1.04867	+	15.9290i	0.0400970	+	0.609062i
$685$	−1.86101	−	14.8563i	−0.0711055	−	0.567628i
$686$	25.1775	+	7.21774i	0.961280	+	0.275575i
$687$	2.02719	+	2.02719i	0.0773420	+	0.0773420i
$688$	9.53994	−	23.0692i	0.363707	−	0.879505i
$689$	3.49270	−	6.04953i	0.133061	−	0.230469i
$690$	−0.863837	+	3.60463i	−0.0328857	+	0.137226i
$691$	−22.1174	−	5.92635i	−0.841387	−	0.225449i	−0.187712	−	0.982224i	$-0.560107\pi$
$691$	−22.1174	−	5.92635i	−0.841387	−	0.225449i	−0.653675	+	0.756775i	$0.726774\pi$
$692$	16.6413	+	48.9773i	0.632609	+	1.86184i
$693$	21.9308	+	14.4936i	0.833084	+	0.550567i
$694$	1.96175	+	11.8715i	0.0744670	+	0.450634i
$695$	11.6516	−	8.82490i	0.441972	−	0.334748i
$696$	−2.41060	−	2.57153i	−0.0913734	−	0.0974736i
$697$	−4.41376	−	16.4724i	−0.167183	−	0.623936i
$698$	−41.8437	−	4.11514i	−1.58381	−	0.155760i
$699$	0.286473	−	0.286473i	0.0108354	−	0.0108354i
$700$	25.5060	+	7.03175i	0.964035	+	0.265775i
$701$	18.7237	+	18.7237i	0.707185	+	0.707185i	0.965942	−	0.258757i	$-0.0833130\pi$
$701$	18.7237	+	18.7237i	0.707185	+	0.707185i	−0.258757	+	0.965942i	$0.583313\pi$
$702$	−5.61896	+	4.61272i	−0.212074	+	0.174096i
$703$	3.80857	−	1.02050i	0.143643	−	0.0384890i
$704$	−30.3423	−	10.2705i	−1.14357	−	0.387083i
$705$	−9.33571	−	12.3261i	−0.351603	−	0.464227i
$706$	11.5132	−	16.0716i	0.433305	−	0.604862i
$707$	14.5227	+	29.0770i	0.546182	+	1.09355i
$708$	−11.8574	−	5.84314i	−0.445627	−	0.219599i
$709$	4.93857	−	18.4310i	0.185472	−	0.692190i	−0.809057	−	0.587730i	$-0.800022\pi$
$709$	4.93857	−	18.4310i	0.185472	−	0.692190i	0.994529	−	0.104460i	$-0.0333115\pi$
$710$	24.1845	+	39.4294i	0.907629	+	1.47976i
$711$	24.9040	+	14.3783i	0.933971	+	0.539229i
$712$	38.9078	+	24.1710i	1.45813	+	0.905846i
$713$	−6.20678	+	6.20678i	−0.232446	+	0.232446i
$714$	−6.72185	+	4.87000i	−0.251559	+	0.182255i
$715$	11.5689	−	1.44922i	0.432654	−	0.0541976i
$716$	8.15610	−	0.536949i	0.304808	−	0.0200667i
$717$	−6.07252	+	10.5179i	−0.226782	+	0.392799i
$718$	30.9123	+	11.6295i	1.15364	+	0.434007i
$719$	−7.09781	−	12.2938i	−0.264704	−	0.458480i	0.702782	−	0.711405i	$-0.251941\pi$
$719$	−7.09781	−	12.2938i	−0.264704	−	0.458480i	−0.967486	+	0.252925i	$0.918607\pi$
$720$	−0.126558	+	22.1934i	−0.00471653	+	0.827098i
$721$	1.96392	−	32.4833i	0.0731401	−	1.20974i
$722$	−12.0730	+	1.99506i	−0.449312	+	0.0742485i
$723$	−2.15059	−	3.72493i	−0.0799814	−	0.138532i
$724$	−23.4454	+	15.6755i	−0.871342	+	0.582577i
$725$	7.54645	−	4.23145i	0.280268	−	0.157152i
$726$	−3.96237	+	3.25279i	−0.147057	+	0.120722i
$727$	−5.68905	−	5.68905i	−0.210995	−	0.210995i	0.593695	−	0.804690i	$-0.297669\pi$
$727$	−5.68905	−	5.68905i	−0.210995	−	0.210995i	−0.804690	+	0.593695i	$0.797669\pi$
$728$	6.22333	+	7.49870i	0.230652	+	0.277920i
$729$	2.88776			0.106954
$730$	14.9729	+	14.1971i	0.554170	+	0.525458i
$731$	−18.5695	+	4.97568i	−0.686817	+	0.184032i
$732$	5.85154	−	3.91232i	0.216279	−	0.144604i
$733$	11.0423	−	6.37528i	0.407857	−	0.235476i	−0.282012	−	0.959411i	$-0.591002\pi$
$733$	11.0423	−	6.37528i	0.407857	−	0.235476i	0.689869	+	0.723935i	$0.257668\pi$
$734$	−8.08602	−	5.79259i	−0.298461	−	0.213808i
$735$	10.8997	+	2.87567i	0.402042	+	0.106071i
$736$	0.307900	+	9.20184i	0.0113493	+	0.339185i
$737$	−8.38520	+	31.2940i	−0.308873	+	1.15273i
$738$	−18.1830	−	6.84061i	−0.669327	−	0.251806i
$739$	−2.78670	−	10.4001i	−0.102510	−	0.382574i	0.895540	−	0.444980i	$-0.146789\pi$
$739$	−2.78670	−	10.4001i	−0.102510	−	0.382574i	−0.998051	+	0.0624060i	$0.980123\pi$
$740$	5.38274	−	1.03720i	0.197873	−	0.0381284i
$741$	2.13314	+	2.13314i	0.0783628	+	0.0783628i
$742$	−7.16791	−	18.7479i	−0.263142	−	0.688257i
$743$	12.8147	+	12.8147i	0.470126	+	0.470126i	0.901955	−	0.431829i	$-0.142132\pi$
$743$	12.8147	+	12.8147i	0.470126	+	0.470126i	−0.431829	+	0.901955i	$0.642132\pi$
$744$	5.79713	−	9.33158i	0.212533	−	0.342112i
$745$	5.69399	−	13.5059i	0.208612	−	0.494819i
$746$	−14.3070	+	38.0294i	−0.523816	+	1.39236i
$747$	20.5682	−	11.8751i	0.752551	−	0.434485i
$748$	7.93624	+	23.3572i	0.290178	+	0.854024i
$749$	8.02285	−	7.10804i	0.293148	−	0.259722i
$750$	11.0394	+	2.79264i	0.403100	+	0.101973i
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.787142	−	0.616772i	$-0.788440\pi$
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.140569	−	0.990071i	$-0.544893\pi$
$752$	−30.4838	−	23.3631i	−1.11163	−	0.851963i
$753$	0.111937	+	0.417753i	0.00407919	+	0.0152238i
$754$	3.17132	+	0.311884i	0.115493	+	0.0113582i
$755$	−15.1649	−	11.7885i	−0.551906	−	0.429027i
$756$	0.111824	+	20.8883i	0.00406701	+	0.759699i
$757$	−16.7501			−0.608791			−0.304396	−	0.952546i	$-0.598454\pi$
$757$	−16.7501			−0.608791			−0.304396	+	0.952546i	$0.598454\pi$
$758$	−24.4264	−	2.40222i	−0.887205	−	0.0872525i
$759$	4.06471	+	2.34676i	0.147540	+	0.0851821i
$760$	20.2577	−	1.87568i	0.734823	−	0.0680380i
$761$	3.95436	+	6.84916i	0.143346	+	0.248282i	0.928754	−	0.370695i	$-0.120881\pi$
$761$	3.95436	+	6.84916i	0.143346	+	0.248282i	−0.785409	+	0.618977i	$0.787547\pi$
$762$	−16.3359	−	11.7025i	−0.591786	−	0.423939i
$763$	−2.86755	+	1.43222i	−0.103812	+	0.0518497i
$764$	−33.3624	+	11.3358i	−1.20701	+	0.410114i
$765$	13.6245	−	10.3191i	0.492593	−	0.373088i
$766$	8.76585	+	19.3392i	0.316723	+	0.698754i
$767$	11.5436	−	3.09311i	0.416816	−	0.111686i
$768$	−2.99524	−	11.1269i	−0.108081	−	0.401506i
$769$	32.4594			1.17052			0.585258	−	0.810847i	$-0.300993\pi$
$769$	32.4594			1.17052			0.585258	+	0.810847i	$0.300993\pi$
$770$	17.7215	−	28.4304i	0.638637	−	1.02456i
$771$	5.27348	+	5.27348i	0.189920	+	0.189920i
$772$	−51.0650	+	3.36181i	−1.83787	+	0.120994i
$773$	−0.911466	+	1.57871i	−0.0327832	+	0.0567821i	−0.881951	−	0.471340i	$-0.843770\pi$
$773$	−0.911466	+	1.57871i	−0.0327832	+	0.0567821i	0.849168	+	0.528122i	$0.177104\pi$
$774$	−7.71148	+	20.4979i	−0.277183	+	0.736782i
$775$	18.8265	+	19.3055i	0.676266	+	0.693474i
$776$	0.674211	+	0.204200i	0.0242028	+	0.00733037i
$777$	2.28838	−	0.467246i	0.0820951	−	0.0167624i
$778$	20.8068	−	29.0448i	0.745961	−	1.04131i
$779$	−4.60914	+	17.2015i	−0.165140	+	0.616309i
$780$	2.74640	+	3.16978i	0.0983368	+	0.113496i
$781$	56.5744	−	15.1591i	2.02439	−	0.542434i
$782$	5.48017	−	4.49879i	0.195971	−	0.160876i
$783$	4.83006	+	4.83006i	0.172612	+	0.172612i
$784$	27.9984	−	0.299784i	0.999943	−	0.0107066i
$785$	−31.0818	+	39.9841i	−1.10936	+	1.42709i
$786$	1.43599	+	0.141223i	0.0512200	+	0.00503725i
$787$	16.5605	−	28.6835i	0.590316	−	1.02246i	−0.403873	−	0.914815i	$-0.632336\pi$
$787$	16.5605	−	28.6835i	0.590316	−	1.02246i	0.994190	−	0.107643i	$-0.0343304\pi$
$788$	−7.31806	+	36.8461i	−0.260695	+	1.31259i
$789$	14.4967	+	3.88437i	0.516095	+	0.138287i
$790$	17.4738	−	32.2142i	0.621691	−	1.14613i
$791$	40.1861	+	26.5581i	1.42885	+	0.944298i
$792$	26.8959	+	8.14602i	0.955703	+	0.289456i
$793$	−1.64705	+	6.14688i	−0.0584885	+	0.218282i
$794$	16.1345	+	6.06994i	0.572593	+	0.215414i
$795$	−3.25565	−	8.00162i	−0.115466	−	0.283788i
$796$	−11.7481	+	13.4040i	−0.416400	+	0.475091i
$797$	−37.6739			−1.33448			−0.667238	−	0.744844i	$-0.732524\pi$
$797$	−37.6739			−1.33448			−0.667238	+	0.744844i	$0.732524\pi$
$798$	8.62176	−	0.894537i	0.305207	−	0.0316663i
$799$			29.5769i			1.04636i
$800$	28.2781	−	0.590705i	0.999782	−	0.0208846i
$801$	−34.8000	−	20.0918i	−1.22960	−	0.709908i
$802$	−47.2700	−	17.7834i	−1.66916	−	0.627953i
$803$	22.6265	−	13.0634i	0.798472	−	0.460998i
$804$	−11.0345	+	3.74927i	−0.389157	+	0.132227i
$805$	−9.44160	−	1.89000i	−0.332773	−	0.0666137i
$806$	1.61927	+	9.79896i	0.0570364	+	0.345154i
$807$	−20.7176	−	5.55126i	−0.729293	−	0.195414i
$808$	23.7632	+	25.3496i	0.835985	+	0.891796i
$809$	−0.337958	+	0.585360i	−0.0118820	+	0.0205802i	−0.871905	−	0.489675i	$-0.837116\pi$
$809$	−0.337958	+	0.585360i	−0.0118820	+	0.0205802i	0.860023	+	0.510255i	$0.170449\pi$
$810$	−0.386810	−	14.5446i	−0.0135911	−	0.511045i
$811$	8.03712	+	8.03712i	0.282222	+	0.282222i	0.833994	−	0.551773i	$-0.186048\pi$
$811$	8.03712	+	8.03712i	0.282222	+	0.282222i	−0.551773	+	0.833994i	$0.686048\pi$
$812$	6.43968	−	6.50900i	0.225989	−	0.228421i
$813$	3.18338			0.111646
$814$	0.679354	−	6.90784i	0.0238114	−	0.242120i
$815$	−17.8915	−	43.9731i	−0.626712	−	1.54031i
$816$	−5.39791	+	7.04313i	−0.188965	+	0.246559i
$817$	19.3915	+	5.19593i	0.678421	+	0.181782i
$818$	21.8025	−	3.60285i	0.762308	−	0.125971i
$819$	−5.66917	−	6.39879i	−0.198097	−	0.223592i
$820$	−8.09870	+	23.3965i	−0.282819	+	0.817041i
$821$	−24.7397	−	6.62898i	−0.863421	−	0.231353i	−0.200180	−	0.979759i	$-0.564153\pi$
$821$	−24.7397	−	6.62898i	−0.863421	−	0.231353i	−0.663241	+	0.748406i	$0.730819\pi$
$822$	−2.81543	−	6.21139i	−0.0981993	−	0.216647i
$823$	−7.86830	+	2.10830i	−0.274272	+	0.0734909i	−0.393333	−	0.919396i	$-0.628678\pi$
$823$	−7.86830	+	2.10830i	−0.274272	+	0.0734909i	0.119062	+	0.992887i	$0.462011\pi$
$824$	−7.91458	−	33.8773i	−0.275718	−	1.18017i
$825$	7.36565	−	12.3954i	0.256439	−	0.431553i
$826$	14.0088	−	31.3514i	0.487428	−	1.09086i
$827$	24.7546			0.860801			0.430400	−	0.902638i	$-0.358372\pi$
$827$	24.7546			0.860801			0.430400	+	0.902638i	$0.358372\pi$
$828$	−0.530603	−	8.05971i	−0.0184397	−	0.280094i
$829$	22.3099	−	5.97792i	0.774854	−	0.207622i	0.150339	−	0.988634i	$-0.451963\pi$
$829$	22.3099	−	5.97792i	0.774854	−	0.207622i	0.624515	+	0.781013i	$0.285297\pi$
$830$	−15.8254	−	25.8010i	−0.549308	−	0.895567i
$831$	−5.29813	+	3.05888i	−0.183790	+	0.106111i
$832$	8.66692	+	5.78018i	0.300472	+	0.200392i
$833$	−13.2990	−	16.9729i	−0.460785	−	0.588077i
$834$	3.87709	−	5.41213i	0.134253	−	0.187407i
$835$	10.3191	+	13.6244i	0.357106	+	0.471492i
$836$	5.01834	−	25.2671i	0.173563	−	0.873881i
$837$	−10.6448	+	18.4374i	−0.367939	+	0.637288i
$838$	−6.07126	−	0.597080i	−0.209728	−	0.0206258i
$839$		−	9.36329i		−	0.323257i	−0.986852	−	0.161628i	$-0.948325\pi$
$839$		−	9.36329i		−	0.323257i	0.986852	−	0.161628i	$-0.0516746\pi$
$840$	12.0448	−	0.384866i	0.415586	−	0.0132791i
$841$			26.0058i			0.896753i
$842$	−4.23639	+	43.0766i	−0.145996	+	1.48452i
$843$	0.545817	−	0.945384i	0.0187990	−	0.0325607i
$844$	−16.2417	+	10.8592i	−0.559064	+	0.373789i
$845$	25.0397	+	3.45667i	0.861391	+	0.118913i
$846$	27.3908	+	19.6219i	0.941714	+	0.674616i
$847$	−8.83120	−	9.96777i	−0.303444	−	0.342497i
$848$	−13.0722	−	17.0156i	−0.448901	−	0.584319i
$849$	7.64923	−	4.41628i	0.262521	−	0.151566i
$850$	−13.6079	−	17.0076i	−0.466747	−	0.583356i
$851$	−1.92704	+	0.516349i	−0.0660582	+	0.0177002i
$852$	15.8443	+	13.8869i	0.542816	+	0.475759i
$853$	14.6246			0.500735			0.250368	−	0.968151i	$-0.419449\pi$
$853$	14.6246			0.500735			0.250368	+	0.968151i	$0.419449\pi$
$854$	10.7280	+	14.8073i	0.367103	+	0.506696i
$855$	−17.7094	+	2.21841i	−0.605647	+	0.0758681i
$856$	6.04678	−	9.73343i	0.206675	−	0.332682i
$857$	37.9291	−	10.1631i	1.29563	−	0.347164i	0.455836	−	0.890064i	$-0.349340\pi$
$857$	37.9291	−	10.1631i	1.29563	−	0.347164i	0.839798	+	0.542900i	$0.182674\pi$
$858$	4.83697	−	2.19245i	0.165131	−	0.0748489i
$859$	−28.7522	−	7.70414i	−0.981013	−	0.262862i	−0.267542	−	0.963546i	$-0.586211\pi$
$859$	−28.7522	−	7.70414i	−0.981013	−	0.262862i	−0.713471	+	0.700684i	$0.752878\pi$
$860$	26.3751	+	9.12974i	0.899383	+	0.311322i
$861$	−3.34017	+	10.0060i	−0.113833	+	0.341004i
$862$	1.18268	+	7.15692i	0.0402821	+	0.243766i
$863$	−9.74854	−	2.61211i	−0.331844	−	0.0889174i	0.0890498	−	0.996027i	$-0.471617\pi$
$863$	−9.74854	−	2.61211i	−0.331844	−	0.0889174i	−0.420894	+	0.907110i	$0.638284\pi$
$864$	6.49775	+	21.3646i	0.221058	+	0.726838i
$865$	−53.5685	+	21.7956i	−1.82138	+	0.741073i
$866$	58.0946	+	5.71333i	1.97413	+	0.194147i
$867$	−5.40954			−0.183718
$868$	24.7903	+	14.1363i	0.841438	+	0.479817i
$869$	−32.8133	−	32.8133i	−1.11312	−	1.11312i
$870$	2.71148	−	2.85964i	0.0919278	−	0.0969510i
$871$	5.26806	−	9.12455i	0.178501	−	0.309174i
$872$	−2.49996	+	2.34350i	−0.0846592	+	0.0793610i
$873$	−0.596950	−	0.159952i	−0.0202037	−	0.00541357i
$874$	−7.30502	+	1.20715i	−0.247096	+	0.0408324i
$875$	−6.17005	+	28.9298i	−0.208586	+	0.978004i
$876$	8.43025	+	4.15431i	0.284832	+	0.140361i
$877$	21.4403	−	12.3785i	0.723986	−	0.417994i	−0.0922319	−	0.995738i	$-0.529400\pi$
$877$	21.4403	−	12.3785i	0.723986	−	0.417994i	0.816218	+	0.577744i	$0.196067\pi$
$878$	−15.6555	+	41.6140i	−0.528348	+	1.40440i
$879$	−0.527258	−	0.304412i	−0.0177840	−	0.0102676i
$880$	9.46657	−	34.5407i	0.319118	−	1.16437i
$881$			32.4793i			1.09426i	0.837049	+	0.547128i	$0.184279\pi$
$881$			32.4793i			1.09426i	−0.837049	+	0.547128i	$0.815721\pi$
$882$	−24.5413	+	1.05587i	−0.826347	+	0.0355530i
$883$	−5.96843			−0.200854			−0.100427	−	0.994944i	$-0.532021\pi$
$883$	−5.96843			−0.200854			−0.100427	+	0.994944i	$0.532021\pi$
$884$	−0.527012	−	8.00517i	−0.0177253	−	0.269243i
$885$	5.74140	−	13.6184i	0.192995	−	0.457777i
$886$	−7.16965	+	19.0577i	−0.240869	+	0.640255i
$887$	6.40678	−	23.9104i	0.215118	−	0.802833i	−0.771006	−	0.636827i	$-0.780246\pi$
$887$	6.40678	−	23.9104i	0.215118	−	0.802833i	0.986125	−	0.166006i	$-0.0530870\pi$
$888$	2.20152	−	1.17796i	0.0738781	−	0.0395299i
$889$	28.7812	−	43.5499i	0.965290	−	1.46062i
$890$	−24.4174	+	45.0151i	−0.818472	+	1.50891i
$891$	−17.7956	−	4.76831i	−0.596174	−	0.159744i
$892$	9.80187	−	6.55350i	0.328191	−	0.219427i
$893$	15.4431	−	26.7482i	0.516783	−	0.895094i
$894$	0.653411	−	6.64405i	0.0218533	−	0.222210i
$895$	1.13589	+	9.06767i	0.0379685	+	0.303099i
$896$	28.5910	−	8.86307i	0.955159	−	0.296094i
$897$	−1.07932	−	1.07932i	−0.0360373	−	0.0360373i
$898$	21.8107	+	26.5686i	0.727833	+	0.886605i
$899$	9.01405	−	2.41531i	0.300635	−	0.0805550i
$900$	−24.7783	+	1.31888i	−0.825942	+	0.0439626i
$901$	−4.27674	+	15.9610i	−0.142479	+	0.531739i
$902$	25.4854	+	18.2570i	0.848571	+	0.607892i
$903$	11.2799	+	3.76540i	0.375371	+	0.125305i
$904$	49.2840	+	14.9268i	1.63916	+	0.496457i
$905$	−19.0379	−	25.1360i	−0.632842	−	0.835550i
$906$	−8.18857	−	3.08061i	−0.272047	−	0.102346i
$907$	−25.2867	+	43.7978i	−0.839630	+	1.45428i	0.0505746	+	0.998720i	$0.483895\pi$
$907$	−25.2867	+	43.7978i	−0.839630	+	1.45428i	−0.890204	+	0.455561i	$0.849439\pi$
$908$	21.6207	+	18.9498i	0.717508	+	0.628871i
$909$	−21.5542	−	21.5542i	−0.714907	−	0.714907i
$910$	−7.95983	+	7.43919i	−0.263866	+	0.246607i
$911$	−29.4944			−0.977193			−0.488597	−	0.872510i	$-0.662491\pi$
$911$	−29.4944			−0.977193			−0.488597	+	0.872510i	$0.662491\pi$
$912$	8.55910	−	3.55110i	0.283420	−	0.117589i
$913$	−37.0200	+	9.91949i	−1.22518	+	0.328287i
$914$	13.9250	−	6.31177i	0.460599	−	0.208775i
$915$	4.75151	+	6.27348i	0.157080	+	0.207395i
$916$	−3.51922	+	7.14148i	−0.116278	+	0.235961i
$917$	−0.226205	+	3.74145i	−0.00746995	+	0.123553i
$918$	10.0147	−	13.9798i	0.330535	−	0.461402i
$919$	−6.17836	−	10.7012i	−0.203805	−	0.353001i	0.745946	−	0.666006i	$-0.231998\pi$
$919$	−6.17836	−	10.7012i	−0.203805	−	0.353001i	−0.949751	+	0.313005i	$0.898664\pi$
$920$	−10.2499	+	0.949047i	−0.337929	+	0.0312891i
$921$	−10.1572	−	5.86426i	−0.334691	−	0.193234i
$922$	−1.90443	+	19.3647i	−0.0627190	+	0.637742i
$923$	−19.0476			−0.626959
$924$	3.87044	−	14.7603i	0.127328	−	0.485579i
$925$	1.51176	+	5.93941i	0.0497063	+	0.195287i
$926$	3.49454	−	35.5334i	0.114838	−	1.16770i
$927$	7.89924	+	29.4804i	0.259445	+	0.968263i
$928$	4.60799	−	8.63595i	0.151265	−	0.283489i
$929$	29.2360	+	50.6382i	0.959201	+	1.66138i	0.724448	+	0.689330i	$0.242095\pi$
$929$	29.2360	+	50.6382i	0.959201	+	1.66138i	0.234753	+	0.972055i	$0.424572\pi$
$930$	10.7963	+	5.85622i	0.354026	+	0.192033i
$931$	3.16502	+	22.2935i	0.103729	+	0.730640i
$932$	1.00920	+	0.497321i	0.0330575	+	0.0162903i
$933$	−2.37623	+	1.37192i	−0.0777943	+	0.0449146i
$934$	0.435722	+	0.163922i	0.0142573	+	0.00536370i
$935$	−25.5468	+	10.3943i	−0.835468	+	0.339930i
$936$	−7.76311	−	4.82274i	−0.253745	−	0.157636i
$937$	3.44627	+	3.44627i	0.112585	+	0.112585i	0.761155	−	0.648570i	$-0.224633\pi$
$937$	3.44627	+	3.44627i	0.112585	+	0.112585i	−0.648570	+	0.761155i	$0.724633\pi$
$938$	−10.8114	−	28.2776i	−0.353005	−	0.923295i
$939$	−11.9698	−	11.9698i	−0.390621	−	0.390621i
$940$	24.0699	−	35.5600i	0.785072	−	1.15984i
$941$	9.99642	+	37.3071i	0.325874	+	1.21618i	0.913430	+	0.406995i	$0.133423\pi$
$941$	9.99642	+	37.3071i	0.325874	+	1.21618i	−0.587557	+	0.809183i	$0.699910\pi$
$942$	−8.12242	+	21.5902i	−0.264643	+	0.703447i
$943$	2.33211	−	8.70356i	0.0759440	−	0.283427i
$944$	4.77053	−	36.3985i	0.155267	−	1.18467i
$945$	−23.3060	+	1.49907i	−0.758144	+	0.0487648i
$946$	20.5813	−	28.7299i	0.669156	−	0.934091i
$947$	2.23642	−	1.29120i	0.0726737	−	0.0419582i	−0.463223	−	0.886242i	$-0.653307\pi$
$947$	2.23642	−	1.29120i	0.0726737	−	0.0419582i	0.535897	+	0.844284i	$0.319974\pi$
$948$	3.25184	−	16.3729i	0.105615	−	0.531766i
$949$	−8.20719	+	2.19911i	−0.266417	+	0.0713862i
$950$	3.42622	+	22.4861i	0.111161	+	0.729546i
$951$	0.0205157			0.000665267
$952$	−18.8108	−	13.3237i	−0.609660	−	0.431823i
$953$	−19.3433	−	19.3433i	−0.626592	−	0.626592i	0.320617	−	0.947209i	$-0.396110\pi$
$953$	−19.3433	−	19.3433i	−0.626592	−	0.626592i	−0.947209	+	0.320617i	$0.896110\pi$
$954$	11.9440	+	14.5495i	0.386701	+	0.471058i
$955$	−14.8468	−	36.4898i	−0.480430	−	1.18078i
$956$	−33.0814	−	6.57036i	−1.06993	−	0.212501i
$957$	−2.49496	−	4.32140i	−0.0806507	−	0.139691i
$958$	−4.05954	−	24.5662i	−0.131158	−	0.793697i
$959$	15.8487	−	7.91574i	0.511781	−	0.255613i
$960$	12.2216	−	4.07502i	0.394450	−	0.131521i
$961$	−0.957251	−	1.65801i	−0.0308791	−	0.0534841i
$962$	−0.794842	+	2.11277i	−0.0256267	+	0.0681185i
$963$	−5.02630	+	8.70580i	−0.161970	+	0.280541i
$964$	7.87307	−	8.98276i	0.253575	−	0.289315i
$965$	−7.11174	−	56.7723i	−0.228935	−	1.82756i
$966$	−4.36240	+	0.452614i	−0.140358	+	0.0145626i
$967$	−17.8010	+	17.8010i	−0.572442	+	0.572442i	−0.932810	−	0.360368i	$-0.882651\pi$
$967$	−17.8010	+	17.8010i	−0.572442	+	0.572442i	0.360368	+	0.932810i	$0.382651\pi$
$968$	−12.0930	−	7.51266i	−0.388685	−	0.241466i
$969$	−6.18003	−	3.56804i	−0.198531	−	0.114622i
$970$	−0.183550	+	0.765920i	−0.00589344	+	0.0245922i
$971$	12.0452	−	44.9534i	0.386550	−	1.44262i	−0.449160	−	0.893451i	$-0.648277\pi$
$971$	12.0452	−	44.9534i	0.386550	−	1.44262i	0.835710	−	0.549171i	$-0.185057\pi$
$972$	−9.75197	−	28.7011i	−0.312795	−	0.920588i
$973$	14.4282	+	9.53530i	0.462548	+	0.305688i
$974$	18.7602	+	13.4392i	0.601114	+	0.430621i
$975$	−3.35709	+	3.27379i	−0.107513	+	0.104845i
$976$	15.5151	+	11.8909i	0.496625	+	0.380617i
$977$	28.8578	−	7.73241i	0.923241	−	0.247382i	0.234271	−	0.972171i	$-0.424730\pi$
$977$	28.8578	−	7.73241i	0.923241	−	0.247382i	0.688970	+	0.724790i	$0.258063\pi$
$978$	−13.7202	−	16.7132i	−0.438724	−	0.534429i
$979$	45.8523	+	45.8523i	1.46545	+	1.46545i
$980$	2.17664	+	31.2292i	0.0695301	+	0.997580i
$981$	2.12565	−	2.12565i	0.0678669	−	0.0678669i
$982$	−5.23084	+	53.1885i	−0.166923	+	1.69731i
$983$	−1.76711	−	6.59494i	−0.0563620	−	0.210346i	0.932002	−	0.362453i	$-0.118061\pi$
$983$	−1.76711	−	6.59494i	−0.0563620	−	0.210346i	−0.988364	+	0.152107i	$0.951394\pi$
$984$	−0.364086	+	11.2712i	−0.0116066	+	0.359314i
$985$	−41.6052	−	5.74351i	−1.32565	−	0.183003i
$986$	−7.43713	+	1.22898i	−0.236846	+	0.0391387i
$987$	10.0872	−	15.2634i	0.321080	−	0.485839i
$988$	−3.70315	+	7.51473i	−0.117813	+	0.239075i
$989$	−9.81160	−	2.62901i	−0.311991	−	0.0835977i
$990$	−7.32224	+	30.5543i	−0.232716	+	0.971080i
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	0.253236	+	0.967405i	$0.418505\pi$
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	−0.964415	+	0.264394i	$0.914828\pi$
$992$	29.7160	+	6.90614i	0.943484	+	0.219270i
$993$	0.674245	+	0.674245i	0.0213965	+	0.0213965i
$994$	−34.4996	+	42.4873i	−1.09426	+	1.34762i
$995$	−15.7330	−	12.2302i	−0.498771	−	0.387722i
$996$	−10.3679	−	9.08707i	−0.328518	−	0.287935i
$997$	−29.8147	−	17.2135i	−0.944242	−	0.545159i	−0.0529547	−	0.998597i	$-0.516864\pi$
$997$	−29.8147	−	17.2135i	−0.944242	−	0.545159i	−0.891288	+	0.453438i	$0.850197\pi$
$998$	51.5760	−	23.3778i	1.63261	−	0.740011i
$999$	−4.19049	+	2.41938i	−0.132581	+	0.0765459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cz.c.157.20	yes	360
5.3	odd	4		560.2.ch.c.493.64	yes	360
7.5	odd	6	inner	560.2.cz.c.397.79	yes	360
16.5	even	4		560.2.ch.c.437.56	yes	360
35.33	even	12		560.2.ch.c.173.56	yes	360
80.53	odd	4	inner	560.2.cz.c.213.79	yes	360
112.5	odd	12		560.2.ch.c.117.64	✓	360
560.453	even	12	inner	560.2.cz.c.453.20	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.64	✓	360	112.5	odd	12
560.2.ch.c.173.56	yes	360	35.33	even	12
560.2.ch.c.437.56	yes	360	16.5	even	4
560.2.ch.c.493.64	yes	360	5.3	odd	4
560.2.cz.c.157.20	yes	360	1.1	even	1	trivial
560.2.cz.c.213.79	yes	360	80.53	odd	4	inner
560.2.cz.c.397.79	yes	360	7.5	odd	6	inner
560.2.cz.c.453.20	yes	360	560.453	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.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09307 + 0.897326i) q^{2} +(-0.623698 - 0.360092i) q^{3} +(0.389613 - 1.96168i) q^{4} +(2.21506 + 0.305784i) q^{5} +(1.00487 - 0.166053i) q^{6} +(0.529295 + 2.59227i) q^{7} +(1.33439 + 2.49387i) q^{8} +(-1.24067 - 2.14890i) q^{9} +(-2.69561 + 1.65339i) q^{10} +(1.03636 + 3.86774i) q^{11} +(-0.949387 + 1.08320i) q^{12} -1.30220i q^{13} +(-2.90466 - 2.35858i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(-3.69640 - 1.52860i) q^{16} +(0.797258 + 2.97541i) q^{17} +(3.28440 + 1.23562i) q^{18} +(0.832549 - 3.10711i) q^{19} +(1.46287 - 4.22611i) q^{20} +(0.603335 - 1.80739i) q^{21} +(-4.60343 - 3.29776i) q^{22} +(-0.421249 + 1.57212i) q^{23} +(0.0657649 - 2.03593i) q^{24} +(4.81299 + 1.35466i) q^{25} +(1.16850 + 1.42340i) q^{26} +3.94757i q^{27} +(5.29143 - 0.0283273i) q^{28} +(1.22355 - 1.22355i) q^{29} +(2.27662 - 0.0605462i) q^{30} +(4.67056 + 2.69655i) q^{31} +(5.41208 - 1.64601i) q^{32} +(0.746367 - 2.78548i) q^{33} +(-3.54137 - 2.53693i) q^{34} +(0.379746 + 5.90388i) q^{35} +(-4.69884 + 1.59656i) q^{36} +(0.612879 + 1.06154i) q^{37} +(1.87806 + 4.14337i) q^{38} +(-0.468911 + 0.812178i) q^{39} +(2.19318 + 5.93211i) q^{40} -5.53618 q^{41} +(0.962325 + 2.51699i) q^{42} +6.24099i q^{43} +(7.99105 - 0.526083i) q^{44} +(-2.09105 - 5.13932i) q^{45} +(-0.950251 - 2.09644i) q^{46} +(9.27457 + 2.48511i) q^{47} +(1.75500 + 2.28443i) q^{48} +(-6.43969 + 2.74415i) q^{49} +(-6.47652 + 2.83808i) q^{50} +(0.574172 - 2.14284i) q^{51} +(-2.55450 - 0.507353i) q^{52} +(4.64563 + 2.68216i) q^{53} +(-3.54226 - 4.31498i) q^{54} +(1.11290 + 8.88417i) q^{55} +(-5.75849 + 4.77910i) q^{56} +(-1.63811 + 1.63811i) q^{57} +(-0.239506 + 2.43536i) q^{58} +(2.37530 + 8.86473i) q^{59} +(-2.43418 + 2.10905i) q^{60} +(-4.72039 - 1.26482i) q^{61} +(-7.52494 + 1.24349i) q^{62} +(4.91384 - 4.35354i) q^{63} +(-4.43879 + 6.65561i) q^{64} +(0.398192 - 2.88445i) q^{65} +(1.68365 + 3.71447i) q^{66} +(7.00704 + 4.04552i) q^{67} +(6.14743 - 0.404710i) q^{68} +(0.828841 - 0.828841i) q^{69} +(-5.71279 - 6.11261i) q^{70} -14.6273i q^{71} +(3.70354 - 5.96154i) q^{72} +(-1.68877 - 6.30257i) q^{73} +(-1.62247 - 0.610385i) q^{74} +(-2.51405 - 2.57802i) q^{75} +(-5.77080 - 2.84377i) q^{76} +(-9.47766 + 4.73368i) q^{77} +(-0.216234 - 1.30853i) q^{78} +(-10.0365 + 5.79459i) q^{79} +(-7.72034 - 4.51623i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(6.05144 - 4.96775i) q^{82} +9.57150i q^{83} +(-3.31045 - 1.88773i) q^{84} +(0.856142 + 6.83450i) q^{85} +(-5.60020 - 6.82185i) q^{86} +(-1.20372 + 0.322536i) q^{87} +(-8.26273 + 7.74562i) q^{88} +(14.0247 - 8.09717i) q^{89} +(6.89732 + 3.74129i) q^{90} +(3.37564 - 0.689246i) q^{91} +(2.91988 + 1.43888i) q^{92} +(-1.94201 - 3.36366i) q^{93} +(-12.3677 + 5.60590i) q^{94} +(2.79425 - 6.62787i) q^{95} +(-3.96822 - 0.922233i) q^{96} +(0.176114 - 0.176114i) q^{97} +(4.57666 - 8.77805i) q^{98} +(7.02560 - 7.02560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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