LMFDB - Embedded newform 560.2.ch.c.117.64

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(117,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.117"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 3, 10])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [360,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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			117.64
Character	$\chi$	$=$	560.117
Dual form			560.2.ch.c.493.64

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.897326 - 1.09307i) q^{2} +(0.360092 + 0.623698i) q^{3} +(-0.389613 - 1.96168i) q^{4} +(-2.07119 + 0.842714i) q^{5} +(1.00487 + 0.166053i) q^{6} +(2.59227 + 0.529295i) q^{7} +(-2.49387 - 1.33439i) q^{8} +(1.24067 - 2.14890i) q^{9} +(-0.937387 + 3.02015i) q^{10} +(1.03636 - 3.86774i) q^{11} +(1.08320 - 0.949387i) q^{12} +1.30220 q^{13} +(2.90466 - 2.35858i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(-3.69640 + 1.52860i) q^{16} +(2.97541 + 0.797258i) q^{17} +(-1.23562 - 3.28440i) q^{18} +(-0.832549 - 3.10711i) q^{19} +(2.46010 + 3.73469i) q^{20} +(0.603335 + 1.80739i) q^{21} +(-3.29776 - 4.60343i) q^{22} +(-1.57212 + 0.421249i) q^{23} +(-0.0657649 - 2.03593i) q^{24} +(3.57967 - 3.49084i) q^{25} +(1.16850 - 1.42340i) q^{26} +3.94757 q^{27} +(0.0283273 - 5.29143i) q^{28} +(-1.22355 - 1.22355i) q^{29} +(-2.22121 + 0.502886i) q^{30} +(4.67056 - 2.69655i) q^{31} +(-1.64601 + 5.41208i) q^{32} +(2.78548 - 0.746367i) q^{33} +(3.54137 - 2.53693i) q^{34} +(-5.81512 + 1.08827i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(1.06154 + 0.612879i) q^{37} +(-4.14337 - 1.87806i) q^{38} +(0.468911 + 0.812178i) q^{39} +(6.28980 + 0.662165i) q^{40} -5.53618 q^{41} +(2.51699 + 0.962325i) q^{42} -6.24099 q^{43} +(-7.99105 - 0.526083i) q^{44} +(-0.758753 + 5.49631i) q^{45} +(-0.950251 + 2.09644i) q^{46} +(2.48511 + 9.27457i) q^{47} +(-2.28443 - 1.75500i) q^{48} +(6.43969 + 2.74415i) q^{49} +(-0.603615 - 7.04526i) q^{50} +(0.574172 + 2.14284i) q^{51} +(-0.507353 - 2.55450i) q^{52} +(-2.68216 - 4.64563i) 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} +(-2.43536 + 0.239506i) q^{58} +(-2.37530 + 8.86473i) q^{59} +(-1.44345 + 2.87919i) q^{60} +(-4.72039 + 1.26482i) q^{61} +(1.24349 - 7.52494i) q^{62} +(4.35354 - 4.91384i) q^{63} +(4.43879 + 6.65561i) q^{64} +(-2.69710 + 1.09738i) q^{65} +(1.68365 - 3.71447i) q^{66} +(4.04552 + 7.00704i) q^{67} +(0.404710 - 6.14743i) q^{68} +(-0.828841 - 0.828841i) q^{69} +(-4.02851 + 7.33288i) q^{70} +14.6273i q^{71} +(-5.96154 + 3.70354i) q^{72} +(6.30257 + 1.68877i) q^{73} +(1.62247 - 0.610385i) q^{74} +(3.46624 + 0.975606i) q^{75} +(-5.77080 + 2.84377i) q^{76} +(4.73368 - 9.47766i) q^{77} +(1.30853 + 0.216234i) q^{78} +(10.0365 + 5.79459i) q^{79} +(6.36779 - 6.28102i) q^{80} +(-2.30051 - 3.98461i) q^{81} +(-4.96775 + 6.05144i) q^{82} -9.57150 q^{83} +(3.31045 - 1.88773i) q^{84} +(-6.83450 + 0.856142i) q^{85} +(-5.60020 + 6.82185i) q^{86} +(0.322536 - 1.20372i) q^{87} +(-7.74562 + 8.26273i) q^{88} +(-14.0247 - 8.09717i) q^{89} +(5.32701 + 5.76135i) q^{90} +(3.37564 + 0.689246i) q^{91} +(1.43888 + 2.91988i) q^{92} +(3.36366 + 1.94201i) q^{93} +(12.3677 + 5.60590i) q^{94} +(4.34278 + 5.73383i) q^{95} +(-3.96822 + 0.922233i) q^{96} +(-0.176114 + 0.176114i) q^{97} +(8.77805 - 4.57666i) q^{98} +(-7.02560 - 7.02560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	0.897326	−	1.09307i	0.634505	−	0.772919i
$2$	0.897326	−	1.09307i	0.634505	−	0.772919i
$3$	0.360092	+	0.623698i	0.207899	+	0.360092i	0.951053	−	0.309029i	$-0.100004\pi$
$3$	0.360092	+	0.623698i	0.207899	+	0.360092i	−0.743153	+	0.669121i	$0.766671\pi$
$4$	−0.389613	−	1.96168i	−0.194807	−	0.980842i
$5$	−2.07119	+	0.842714i	−0.926265	+	0.376873i
$5$	−2.07119	+	0.842714i	−0.926265	+	0.376873i
$6$	1.00487	+	0.166053i	0.410235	+	0.0677910i
$7$	2.59227	+	0.529295i	0.979785	+	0.200055i
$7$	2.59227	+	0.529295i	0.979785	+	0.200055i
$8$	−2.49387	−	1.33439i	−0.881717	−	0.471779i
$9$	1.24067	−	2.14890i	0.413556	−	0.716300i
$10$	−0.937387	+	3.02015i	−0.296428	+	0.955055i
$11$	1.03636	−	3.86774i	0.312473	−	1.16617i	−0.613846	−	0.789426i	$-0.710378\pi$
$11$	1.03636	−	3.86774i	0.312473	−	1.16617i	0.926319	−	0.376740i	$-0.122955\pi$
$12$	1.08320	−	0.949387i	0.312693	−	0.274065i
$13$	1.30220			0.361165			0.180582	−	0.983560i	$-0.442202\pi$
$13$	1.30220			0.361165			0.180582	+	0.983560i	$0.442202\pi$
$14$	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
$17$	2.97541	+	0.797258i	0.721642	+	0.193363i	0.600904	−	0.799321i	$-0.294807\pi$
$17$	2.97541	+	0.797258i	0.721642	+	0.193363i	0.120738	+	0.992684i	$0.461474\pi$
$18$	−1.23562	−	3.28440i	−0.291238	−	0.774141i
$19$	−0.832549	−	3.10711i	−0.191000	−	0.712821i	−0.993266	−	0.115855i	$-0.963039\pi$
$19$	−0.832549	−	3.10711i	−0.191000	−	0.712821i	0.802266	−	0.596966i	$-0.203627\pi$
$20$	2.46010	+	3.73469i	0.550095	+	0.835102i
$21$	0.603335	+	1.80739i	0.131658	+	0.394404i
$22$	−3.29776	−	4.60343i	−0.703086	−	0.981455i
$23$	−1.57212	+	0.421249i	−0.327810	+	0.0878365i	−0.418971	−	0.908000i	$-0.637609\pi$
$23$	−1.57212	+	0.421249i	−0.327810	+	0.0878365i	0.0911604	+	0.995836i	$0.470942\pi$
$24$	−0.0657649	−	2.03593i	−0.0134242	−	0.415582i
$25$	3.57967	−	3.49084i	0.715934	−	0.698168i
$26$	1.16850	−	1.42340i	0.229161	−	0.279151i
$27$	3.94757			0.759710
$28$	0.0283273	−	5.29143i	0.00535336	−	0.999986i
$29$	−1.22355	−	1.22355i	−0.227208	−	0.227208i	0.584317	−	0.811525i	$-0.301362\pi$
$29$	−1.22355	−	1.22355i	−0.227208	−	0.227208i	−0.811525	+	0.584317i	$0.801362\pi$
$30$	−2.22121	+	0.502886i	−0.405535	+	0.0918140i
$31$	4.67056	−	2.69655i	0.838857	−	0.484314i	−0.0180184	−	0.999838i	$-0.505736\pi$
$31$	4.67056	−	2.69655i	0.838857	−	0.484314i	0.856876	+	0.515523i	$0.172402\pi$
$32$	−1.64601	+	5.41208i	−0.290977	+	0.956730i
$33$	2.78548	−	0.746367i	0.484890	−	0.129926i
$34$	3.54137	−	2.53693i	0.607340	−	0.435081i
$35$	−5.81512	+	1.08827i	−0.982935	+	0.183951i
$36$	−4.69884	−	1.59656i	−0.783140	−	0.266093i
$37$	1.06154	+	0.612879i	0.174516	+	0.100757i	0.584713	−	0.811240i	$-0.301207\pi$
$37$	1.06154	+	0.612879i	0.174516	+	0.100757i	−0.410198	+	0.911997i	$0.634540\pi$
$38$	−4.14337	−	1.87806i	−0.672143	−	0.304661i
$39$	0.468911	+	0.812178i	0.0750859	+	0.130053i
$40$	6.28980	+	0.662165i	0.994504	+	0.104698i
$41$	−5.53618			−0.864606			−0.432303	−	0.901728i	$-0.642299\pi$
$41$	−5.53618			−0.864606			−0.432303	+	0.901728i	$0.642299\pi$
$42$	2.51699	+	0.962325i	0.388380	+	0.148490i
$43$	−6.24099			−0.951741			−0.475871	−	0.879515i	$-0.657867\pi$
$43$	−6.24099			−0.951741			−0.475871	+	0.879515i	$0.657867\pi$
$44$	−7.99105	−	0.526083i	−1.20470	−	0.0793100i
$45$	−0.758753	+	5.49631i	−0.113108	+	0.819341i
$46$	−0.950251	+	2.09644i	−0.140107	+	0.309104i
$47$	2.48511	+	9.27457i	0.362491	+	1.35284i	0.870790	+	0.491655i	$0.163608\pi$
$47$	2.48511	+	9.27457i	0.362491	+	1.35284i	−0.508299	+	0.861181i	$0.669726\pi$
$48$	−2.28443	−	1.75500i	−0.329729	−	0.253313i
$49$	6.43969	+	2.74415i	0.919956	+	0.392021i
$50$	−0.603615	−	7.04526i	−0.0853640	−	0.996350i
$51$	0.574172	+	2.14284i	0.0804002	+	0.300058i
$52$	−0.507353	−	2.55450i	−0.0703573	−	0.354245i
$53$	−2.68216	−	4.64563i	−0.368423	−	0.638127i	0.620896	−	0.783893i	$-0.286769\pi$
$53$	−2.68216	−	4.64563i	−0.368423	−	0.638127i	−0.989319	+	0.145766i	$0.953435\pi$
$54$	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
$58$	−2.43536	+	0.239506i	−0.319778	+	0.0314487i
$59$	−2.37530	+	8.86473i	−0.309237	+	1.15409i	0.619999	+	0.784603i	$0.287133\pi$
$59$	−2.37530	+	8.86473i	−0.309237	+	1.15409i	−0.929236	+	0.369487i	$0.879534\pi$
$60$	−1.44345	+	2.87919i	−0.186349	+	0.371702i
$61$	−4.72039	+	1.26482i	−0.604384	+	0.161944i	−0.548019	−	0.836466i	$-0.684618\pi$
$61$	−4.72039	+	1.26482i	−0.604384	+	0.161944i	−0.0563651	+	0.998410i	$0.517951\pi$
$62$	1.24349	−	7.52494i	0.157923	−	0.955668i
$63$	4.35354	−	4.91384i	0.548495	−	0.619086i
$64$	4.43879	+	6.65561i	0.554848	+	0.831951i
$65$	−2.69710	+	1.09738i	−0.334534	+	0.136113i
$66$	1.68365	−	3.71447i	0.207243	−	0.457219i
$67$	4.04552	+	7.00704i	0.494239	+	0.856046i	0.999978	−	0.00664007i	$-0.00211362\pi$
$67$	4.04552	+	7.00704i	0.494239	+	0.856046i	−0.505739	+	0.862686i	$0.668780\pi$
$68$	0.404710	−	6.14743i	0.0490783	−	0.745485i
$69$	−0.828841	−	0.828841i	−0.0997808	−	0.0997808i
$70$	−4.02851	+	7.33288i	−0.481498	+	0.876447i
$71$			14.6273i			1.73594i	0.496619	+	0.867969i	$0.334575\pi$
$71$			14.6273i			1.73594i	−0.496619	+	0.867969i	$0.665425\pi$
$72$	−5.96154	+	3.70354i	−0.702574	+	0.436466i
$73$	6.30257	+	1.68877i	0.737660	+	0.197655i	0.608038	−	0.793908i	$-0.291957\pi$
$73$	6.30257	+	1.68877i	0.737660	+	0.197655i	0.129622	+	0.991563i	$0.458624\pi$
$74$	1.62247	−	0.610385i	0.188608	−	0.0709558i
$75$	3.46624	+	0.975606i	0.400247	+	0.112653i
$76$	−5.77080	+	2.84377i	−0.661957	+	0.326203i
$77$	4.73368	−	9.47766i	0.539453	−	1.08008i
$78$	1.30853	+	0.216234i	0.148162	+	0.0244837i
$79$	10.0365	+	5.79459i	1.12920	+	0.651942i	0.943733	−	0.330709i	$-0.107288\pi$
$79$	10.0365	+	5.79459i	1.12920	+	0.651942i	0.185464	+	0.982651i	$0.440621\pi$
$80$	6.36779	−	6.28102i	0.711941	−	0.702240i
$81$	−2.30051	−	3.98461i	−0.255613	−	0.442734i
$82$	−4.96775	+	6.05144i	−0.548597	+	0.668270i
$83$	−9.57150			−1.05061			−0.525305	−	0.850914i	$-0.676049\pi$
$83$	−9.57150			−1.05061			−0.525305	+	0.850914i	$0.676049\pi$
$84$	3.31045	−	1.88773i	0.361200	−	0.205969i
$85$	−6.83450	+	0.856142i	−0.741305	+	0.0928617i
$86$	−5.60020	+	6.82185i	−0.603885	+	0.735619i
$87$	0.322536	−	1.20372i	0.0345794	−	0.129052i
$88$	−7.74562	+	8.26273i	−0.825686	+	0.880810i
$89$	−14.0247	−	8.09717i	−1.48662	−	0.858298i	−0.486732	−	0.873551i	$-0.661811\pi$
$89$	−14.0247	−	8.09717i	−1.48662	−	0.858298i	−0.999884	+	0.0152534i	$0.995145\pi$
$90$	5.32701	+	5.76135i	0.561516	+	0.607300i
$91$	3.37564	+	0.689246i	0.353864	+	0.0722526i
$92$	1.43888	+	2.91988i	0.150013	+	0.304419i
$93$	3.36366	+	1.94201i	0.348796	+	0.201377i
$94$	12.3677	+	5.60590i	1.27563	+	0.578205i
$95$	4.34278	+	5.73383i	0.445559	+	0.588278i
$96$	−3.96822	+	0.922233i	−0.405005	+	0.0941251i
$97$	−0.176114	+	0.176114i	−0.0178817	+	0.0178817i	−0.715991	−	0.698109i	$-0.754025\pi$
$97$	−0.176114	+	0.176114i	−0.0178817	+	0.0178817i	0.698109	+	0.715991i	$0.254025\pi$
$98$	8.77805	−	4.57666i	0.886717	−	0.462312i
$99$	−7.02560	−	7.02560i	−0.706099	−	0.706099i
$100$	−8.24261	−	5.66210i	−0.824261	−	0.566210i
$101$	11.8660	+	3.17949i	1.18071	+	0.316371i	0.795209	−	0.606335i	$-0.207361\pi$
$101$	11.8660	+	3.17949i	1.18071	+	0.316371i	0.385503	+	0.922706i	$0.374028\pi$
$102$	2.85750	+	1.29521i	0.282935	+	0.128245i
$103$	3.18347	+	11.8809i	0.313676	+	1.17066i	0.925216	+	0.379441i	$0.123884\pi$
$103$	3.18347	+	11.8809i	0.313676	+	1.17066i	−0.611540	+	0.791214i	$0.709450\pi$
$104$	−3.24751	−	1.73764i	−0.318445	−	0.170390i
$105$	−2.77273	−	3.23500i	−0.270591	−	0.315704i
$106$	−7.48478	−	1.23685i	−0.726986	−	0.120134i
$107$	−3.50852	−	2.02564i	−0.339181	−	0.195826i	0.320729	−	0.947171i	$-0.396072\pi$
$107$	−3.50852	−	2.02564i	−0.339181	−	0.195826i	−0.659910	+	0.751345i	$0.729406\pi$
$108$	−1.53803	−	7.74388i	−0.147997	−	0.745155i
$109$	−0.313558	+	1.17022i	−0.0300334	+	0.112086i	−0.979315	−	0.202340i	$-0.935145\pi$
$109$	−0.313558	+	1.17022i	−0.0300334	+	0.112086i	0.949282	+	0.314426i	$0.101812\pi$
$110$	10.7097	+	6.75552i	1.02113	+	0.644113i
$111$			0.882771i			0.0837889i
$112$	−10.3911	+	2.00604i	−0.981870	+	0.189553i
$113$	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
$115$	2.90118	−	2.19734i	0.270536	−	0.204903i
$116$	−1.92351	+	2.87694i	−0.178594	+	0.267117i
$117$	1.61559	−	2.79829i	0.149362	−	0.258702i
$118$	7.55837	+	10.5509i	0.695805	+	0.971291i
$119$	7.29106	+	3.64157i	0.668371	+	0.333822i
$120$	1.85191	+	4.16137i	0.169056	+	0.379880i
$121$	−4.35906	−	2.51671i	−0.396278	−	0.228791i
$122$	−2.85318	+	6.29468i	−0.258315	+	0.569894i
$123$	−1.99353	−	3.45290i	−0.179751	−	0.311338i
$124$	−7.10949	−	8.11155i	−0.638451	−	0.728438i
$125$	−4.47240	+	10.2468i	−0.400023	+	0.916505i
$126$	−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	$-0.589391\pi$
$128$	11.2581	+	1.12034i	0.995085	+	0.0990248i
$129$	−2.24733	−	3.89249i	−0.197866	−	0.342715i
$130$	−1.22066	+	3.93283i	−0.107059	+	0.344932i
$131$	1.36844	−	0.366673i	0.119561	−	0.0320364i	−0.198542	−	0.980092i	$-0.563621\pi$
$131$	1.36844	−	0.366673i	0.119561	−	0.0320364i	0.318104	+	0.948056i	$0.396954\pi$
$132$	−2.54940	−	5.17344i	−0.221897	−	0.450290i
$133$	−0.513610	−	8.49513i	−0.0445356	−	0.736622i
$134$	11.2893	+	1.86556i	0.975251	+	0.161160i
$135$	−8.17617	+	3.32667i	−0.703693	+	0.286314i
$136$	−6.35643	−	5.95862i	−0.545059	−	0.510948i
$137$	−6.46769	−	1.73301i	−0.552572	−	0.148061i	−0.0282805	−	0.999600i	$-0.509003\pi$
$137$	−6.46769	−	1.73301i	−0.552572	−	0.148061i	−0.524292	+	0.851539i	$0.675670\pi$
$138$	−1.64972	+	0.162243i	−0.140434	+	0.0138110i
$139$	−4.62212	−	4.62212i	−0.392043	−	0.392043i	0.483372	−	0.875415i	$-0.339412\pi$
$139$	−4.62212	−	4.62212i	−0.392043	−	0.392043i	−0.875415	+	0.483372i	$0.839412\pi$
$140$	4.40049	+	10.9834i	0.371909	+	0.928269i
$141$	−4.88966	+	4.88966i	−0.411784	+	0.411784i
$142$	15.9887	+	13.1254i	1.34174	+	1.10146i
$143$	1.34954	−	5.03656i	0.112854	−	0.421178i
$144$	−1.30121	+	9.83968i	−0.108434	+	0.819973i
$145$	3.56532	+	1.50311i	0.296083	+	0.124826i
$146$	7.50141	−	5.37379i	0.620821	−	0.444738i
$147$	0.607365	+	5.00457i	0.0500946	+	0.412770i
$148$	0.788685	−	2.32119i	0.0648295	−	0.190800i
$149$	−1.69653	−	6.33152i	−0.138985	−	0.518699i	−0.999950	−	0.0100340i	$-0.996806\pi$
$149$	−1.69653	−	6.33152i	−0.138985	−	0.518699i	0.860965	−	0.508665i	$-0.169861\pi$
$150$	4.17675	−	2.91341i	0.341031	−	0.237879i
$151$	−7.43917	+	4.29501i	−0.605391	+	0.349523i	−0.771159	−	0.636642i	$-0.780323\pi$
$151$	−7.43917	+	4.29501i	−0.605391	+	0.349523i	0.165768	+	0.986165i	$0.446990\pi$
$152$	−2.06984	+	8.85969i	−0.167887	+	0.718616i
$153$	5.40472	−	5.40472i	0.436946	−	0.436946i
$154$	−6.11211	−	13.6788i	−0.492528	−	1.10227i
$155$	−7.40120	+	9.52101i	−0.594479	+	0.764746i
$156$	1.41054	−	1.23629i	0.112934	−	0.0989824i
$157$	19.6143	−	11.3243i	1.56539	−	0.903780i	0.568698	−	0.822546i	$-0.307447\pi$
$157$	19.6143	−	11.3243i	1.56539	−	0.903780i	0.996695	−	0.0812343i	$-0.0258862\pi$
$158$	15.3399	−	5.77101i	1.22038	−	0.459117i
$159$	1.93165	−	3.34571i	0.153190	−	0.265332i
$160$	−1.15163	−	12.5966i	−0.0910442	−	0.995847i
$161$	−4.29833	+	0.259874i	−0.338756	+	0.0204809i
$162$	−6.41977	−	1.06086i	−0.504385	−	0.0833492i
$163$	18.3864	+	10.6154i	1.44014	+	0.831463i	0.997858	−	0.0654148i	$-0.0208371\pi$
$163$	18.3864	+	10.6154i	1.44014	+	0.831463i	0.442278	+	0.896878i	$0.354170\pi$
$164$	2.15697	+	10.8602i	0.168431	+	0.848041i
$165$	−5.14029	+	3.89323i	−0.400171	+	0.303088i
$166$	−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	$0.654437\pi$
$168$	0.907125	−	5.31247i	0.0699862	−	0.409866i
$169$	−11.3043			−0.869560
$170$	−5.19695	+	8.23884i	−0.398588	+	0.631890i
$171$	−7.70979	−	2.06583i	−0.589583	−	0.157978i
$172$	2.43157	+	12.2428i	0.185405	+	0.933508i
$173$	−12.9318	+	22.3986i	−0.983187	+	1.70293i	−0.333457	+	0.942765i	$0.608215\pi$
$173$	−12.9318	+	22.3986i	−0.983187	+	1.70293i	−0.649730	+	0.760165i	$0.725118\pi$
$174$	−1.02633	−	1.43268i	−0.0778060	−	0.108611i
$175$	11.1271	−	7.15450i	0.841133	−	0.540829i
$176$	2.08141	+	15.8809i	0.156892	+	1.19707i
$177$	−6.38424	+	1.71065i	−0.479869	+	0.128580i
$178$	−21.4355	+	8.06422i	−1.60666	+	0.604439i
$179$	−1.05776	+	3.94762i	−0.0790608	+	0.295059i	−0.994123	−	0.108253i	$-0.965474\pi$
$179$	−1.05776	+	3.94762i	−0.0790608	+	0.295059i	0.915063	+	0.403312i	$0.132141\pi$
$180$	11.0776	−	0.653000i	0.825678	−	0.0486718i
$181$	−9.97127	+	9.97127i	−0.741159	+	0.741159i	−0.972801	−	0.231642i	$-0.925590\pi$
$181$	−9.97127	+	9.97127i	−0.741159	+	0.741159i	0.231642	+	0.972801i	$0.425590\pi$
$182$	3.78245	−	3.07134i	0.280374	−	0.227663i
$183$	−2.48864	−	2.48864i	−0.183966	−	0.183966i
$184$	4.48279	+	1.04729i	0.330475	+	0.0772073i
$185$	−2.71513	−	0.374817i	−0.199620	−	0.0275571i
$186$	5.14106	−	1.93411i	0.376961	−	0.141816i
$187$	6.16717	−	10.6818i	0.450988	−	0.781134i
$188$	17.2255	−	8.48850i	1.25630	−	0.619088i
$189$	10.2332	+	2.08943i	0.744352	+	0.151984i
$190$	10.1644	+	0.398145i	0.737401	+	0.0288845i
$191$	−8.80890	+	15.2575i	−0.637390	+	1.10399i	0.348614	+	0.937266i	$0.386653\pi$
$191$	−8.80890	+	15.2575i	−0.637390	+	1.10399i	−0.986003	+	0.166725i	$0.946681\pi$
$192$	−2.55272	+	5.16509i	−0.184227	+	0.372759i
$193$	24.7159	+	6.62260i	1.77909	+	0.476705i	0.990417	−	0.138109i	$-0.0441025\pi$
$193$	24.7159	+	6.62260i	1.77909	+	0.476705i	0.788672	+	0.614815i	$0.210769\pi$
$194$	0.0344737	+	0.350537i	0.00247507	+	0.0251671i
$195$	−1.65564	−	1.28702i	−0.118563	−	0.0921653i
$196$	2.87416	−	13.7018i	0.205297	−	0.978700i
$197$		−	18.7829i		−	1.33822i	−0.743161	−	0.669112i	$-0.766674\pi$
$197$		−	18.7829i		−	1.33822i	0.743161	−	0.669112i	$-0.233326\pi$
$198$	−13.9837	+	1.37524i	−0.993781	+	0.0977337i
$199$	7.71789	−	4.45592i	0.547106	−	0.315872i	−0.200848	−	0.979622i	$-0.564370\pi$
$199$	7.71789	−	4.45592i	0.547106	−	0.315872i	0.747954	+	0.663750i	$0.231036\pi$
$200$	−13.5854	+	3.92903i	−0.960632	+	0.277824i
$201$	−2.91352	+	5.04636i	−0.205504	+	0.355943i
$202$	14.1231	−	10.1174i	0.993697	−	0.711856i
$203$	−2.52416	−	3.81940i	−0.177161	−	0.268069i
$204$	3.97987	−	1.96122i	0.278647	−	0.137313i
$205$	11.4665	−	4.66541i	0.800854	−	0.325847i
$206$	15.8432	+	7.18124i	1.10385	+	0.500341i
$207$	−1.04526	+	3.90097i	−0.0726506	+	0.271136i
$208$	−4.81345	+	1.99053i	−0.333753	+	0.138019i
$209$	−12.8803			−0.890950
$210$	−6.02413	+	0.127943i	−0.415705	+	0.00882887i
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	−0.903701	−	0.428164i	$-0.859161\pi$
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	0.428164	+	0.903701i	$0.359161\pi$
$212$	−8.06826	+	7.07154i	−0.554130	+	0.485676i
$213$	−9.12299	+	5.26716i	−0.625097	+	0.360900i
$214$	−5.36245	+	2.01740i	−0.366570	+	0.137907i
$215$	12.9263	−	5.25936i	0.881565	−	0.358686i
$216$	−9.84473	−	5.26761i	−0.669849	−	0.358416i
$217$	13.5346	−	4.51807i	0.918789	−	0.306707i
$218$	0.997766	+	1.39281i	0.0675772	+	0.0943327i
$219$	1.21622	+	4.53901i	0.0821848	+	0.306718i
$220$	16.9943	−	5.64455i	1.14576	−	0.380555i
$221$	3.87457	+	1.03819i	0.260632	+	0.0698361i
$222$	0.964932	+	0.792133i	0.0647620	+	0.0531645i
$223$	−4.16871	−	4.16871i	−0.279157	−	0.279157i	0.553615	−	0.832773i	$-0.313248\pi$
$223$	−4.16871	−	4.16871i	−0.279157	−	0.279157i	−0.832773	+	0.553615i	$0.813248\pi$
$224$	−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
$227$	12.4490	−	7.18744i	0.826270	−	0.477047i	−0.0263039	−	0.999654i	$-0.508374\pi$
$227$	12.4490	−	7.18744i	0.826270	−	0.477047i	0.852574	+	0.522607i	$0.175040\pi$
$228$	−3.85167	−	2.57522i	−0.255083	−	0.170548i
$229$	3.84511	−	1.03029i	0.254092	−	0.0680838i	−0.129524	−	0.991576i	$-0.541345\pi$
$229$	3.84511	−	1.03029i	0.254092	−	0.0680838i	0.383617	+	0.923492i	$0.374678\pi$
$230$	0.201452	−	5.14292i	0.0132833	−	0.339114i
$231$	7.61576	−	0.460443i	0.501080	−	0.0302949i
$232$	1.41868	+	4.68408i	0.0931410	+	0.307525i
$233$	−0.543375	+	0.145597i	−0.0355977	+	0.00953837i	−0.276574	−	0.960993i	$-0.589199\pi$
$233$	−0.543375	+	0.145597i	−0.0355977	+	0.00953837i	0.240976	+	0.970531i	$0.422532\pi$
$234$	−1.60902	−	4.27694i	−0.105185	−	0.279592i
$235$	−12.9630	−	17.1152i	−0.845610	−	1.11647i
$236$	18.3152	+	1.20577i	1.19222	+	0.0784887i
$237$			8.34634i			0.542153i
$238$	10.5230	−	4.70198i	0.682102	−	0.304784i
$239$		−	16.8638i		−	1.09083i	−0.838167	−	0.545414i	$-0.816372\pi$
$239$		−	16.8638i		−	1.09083i	0.838167	−	0.545414i	$-0.183628\pi$
$240$	6.21045	+	1.70983i	0.400883	+	0.110369i
$241$	5.17220	−	2.98617i	0.333170	−	0.192356i	−0.324077	−	0.946031i	$-0.605054\pi$
$241$	5.17220	−	2.98617i	0.333170	−	0.192356i	0.657248	+	0.753675i	$0.271720\pi$
$242$	−6.66244	+	2.50646i	−0.428278	+	0.161122i
$243$	7.57815	−	13.1257i	0.486138	−	0.842017i
$244$	4.32031	+	8.76712i	0.276580	+	0.561257i
$245$	−15.6504	−	0.256833i	−0.999865	−	0.0164085i
$246$	−5.56312	−	0.919301i	−0.354692	−	0.0586125i
$247$	−1.08414	−	4.04608i	−0.0689824	−	0.257446i
$248$	−15.2460	+	0.492480i	−0.968124	+	0.0312725i
$249$	−3.44662	−	5.96973i	−0.218421	−	0.378316i
$250$	7.18734	+	14.0834i	0.454567	+	0.890713i
$251$	−0.424636	+	0.424636i	−0.0268028	+	0.0268028i	−0.720381	−	0.693578i	$-0.756033\pi$
$251$	−0.424636	+	0.424636i	−0.0268028	+	0.0268028i	0.693578	+	0.720381i	$0.256033\pi$
$252$	−11.3356	−	6.62577i	−0.714076	−	0.417385i
$253$			6.51712i			0.409728i
$254$	−27.7687	+	2.73092i	−1.74236	+	0.171353i
$255$	−2.99502	−	3.95437i	−0.187556	−	0.247632i
$256$	11.3268	−	11.3006i	0.707925	−	0.706288i
$257$	−2.68019	−	10.0026i	−0.167185	−	0.623945i	−0.997751	−	0.0670243i	$-0.978650\pi$
$257$	−2.68019	−	10.0026i	−0.167185	−	0.623945i	0.830566	−	0.556920i	$-0.188017\pi$
$258$	−6.27136	−	1.03634i	−0.390438	−	0.0645195i
$259$	2.42739	+	2.15061i	0.150831	+	0.133632i
$260$	3.20354	+	4.86330i	0.198675	+	0.301609i
$261$	−4.14731	+	1.11127i	−0.256712	+	0.0687859i
$262$	0.827139	−	1.82483i	0.0511008	−	0.112738i
$263$	−5.39358	+	20.1291i	−0.332582	+	1.24121i	0.573884	+	0.818937i	$0.305436\pi$
$263$	−5.39358	+	20.1291i	−0.332582	+	1.24121i	−0.906466	+	0.422278i	$0.861231\pi$
$264$	−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
$267$		−	11.6629i		−	0.713758i
$268$	12.1694	−	10.6661i	0.743365	−	0.651533i
$269$	−28.7671	−	7.70811i	−1.75396	−	0.469972i	−0.768495	−	0.639856i	$-0.778994\pi$
$269$	−28.7671	−	7.70811i	−1.75396	−	0.469972i	−0.985464	+	0.169884i	$0.945661\pi$
$270$	−3.70040	+	11.9223i	−0.225199	+	0.725565i
$271$	−3.82804	−	2.21012i	−0.232537	−	0.134255i	0.379205	−	0.925313i	$-0.376197\pi$
$271$	−3.82804	−	2.21012i	−0.232537	−	0.134255i	−0.611742	+	0.791058i	$0.709531\pi$
$272$	−12.2170	+	1.60121i	−0.740764	+	0.0970874i
$273$	0.785661	+	2.35357i	0.0475504	+	0.142445i
$274$	−7.69793	+	5.51457i	−0.465049	+	0.333148i
$275$	−9.79184	−	17.4630i	−0.590470	−	1.05306i
$276$	−1.30300	+	1.94885i	−0.0784312	+	0.117307i
$277$	−7.35664	+	4.24736i	−0.442018	+	0.255199i	−0.704453	−	0.709751i	$-0.748808\pi$
$277$	−7.35664	+	4.24736i	−0.442018	+	0.255199i	0.262435	+	0.964950i	$0.415474\pi$
$278$	−9.19985	+	0.904763i	−0.551770	+	0.0542640i
$279$		−	13.3821i		−	0.801164i
$280$	15.9543	+	5.04567i	0.953455	+	0.301536i
$281$		−	1.51577i		−	0.0904234i	−0.998977	−	0.0452117i	$-0.985604\pi$
$281$		−	1.51577i		−	0.0904234i	0.998977	−	0.0452117i	$-0.0143962\pi$
$282$	0.957133	+	9.73237i	0.0569964	+	0.579554i
$283$	−10.6212	+	6.13216i	−0.631365	+	0.364519i	−0.781281	−	0.624180i	$-0.785433\pi$
$283$	−10.6212	+	6.13216i	−0.631365	+	0.364519i	0.149915	+	0.988699i	$0.452100\pi$
$284$	28.6941	−	5.69898i	1.70268	−	0.338172i
$285$	−2.01238	+	4.77329i	−0.119203	+	0.282745i
$286$	−4.29434	−	5.99458i	−0.253930	−	0.354467i
$287$	−14.3512	−	2.93027i	−0.847128	−	0.172968i
$288$	9.58787	+	10.2517i	0.564970	+	0.604088i
$289$	−6.50500	−	3.75567i	−0.382647	−	0.220922i
$290$	4.84226	−	2.54837i	0.284347	−	0.149646i
$291$	−0.173259	−	0.0464247i	−0.0101566	−	0.00272146i
$292$	0.857265	−	13.0216i	0.0501677	−	0.762032i
$293$		−	0.845374i		−	0.0493873i	−0.999695	−	0.0246936i	$-0.992139\pi$
$293$		−	0.845374i		−	0.0493873i	0.999695	−	0.0246936i	$-0.00786103\pi$
$294$	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
$297$	4.09109	−	15.2682i	0.237389	−	0.885948i
$298$	−8.44315	−	3.82701i	−0.489098	−	0.221693i
$299$	−2.04722	+	0.548550i	−0.118394	+	0.0317235i
$300$	0.563337	−	7.17977i	0.0325243	−	0.414524i
$301$	−16.1783	−	3.30332i	−0.932502	−	0.190400i
$302$	−1.98061	+	11.9856i	−0.113971	+	0.689692i
$303$	2.28982	+	8.54571i	0.131547	+	0.490938i
$304$	7.82696	+	10.2125i	0.448907	+	0.585728i
$305$	8.71094	−	6.59763i	0.498787	−	0.377779i
$306$	−1.05795	−	10.7575i	−0.0604792	−	0.614968i
$307$			16.2854i			0.929459i	0.885453	+	0.464730i	$0.153848\pi$
$307$			16.2854i			0.929459i	−0.885453	+	0.464730i	$0.846152\pi$
$308$	−20.4365	−	5.59337i	−1.16448	−	0.318712i
$309$	−6.26372	+	6.26372i	−0.356331	+	0.356331i
$310$	3.76586	+	16.6335i	0.213887	+	0.944719i
$311$	1.90495	+	3.29948i	0.108020	+	0.187096i	0.914968	−	0.403526i	$-0.132216\pi$
$311$	1.90495	+	3.29948i	0.108020	+	0.187096i	−0.806948	+	0.590622i	$0.798882\pi$
$312$	−0.0856389	−	2.65118i	−0.00484835	−	0.150093i
$313$	−6.08353	−	22.7040i	−0.343861	−	1.28331i	−0.893937	−	0.448193i	$-0.852068\pi$
$313$	−6.08353	−	22.7040i	−0.343861	−	1.28331i	0.550075	−	0.835115i	$-0.314599\pi$
$314$	5.22212	−	31.6015i	0.294701	−	1.78338i
$315$	−4.87606	+	13.8463i	−0.274735	+	0.780150i
$316$	7.45678	−	21.9461i	0.419477	−	1.23457i
$317$	0.0142434	−	0.0246702i	0.000799987	−	0.00138562i	−0.865625	−	0.500693i	$-0.833079\pi$
$317$	0.0142434	−	0.0246702i	0.000799987	−	0.00138562i	0.866425	+	0.499307i	$0.166412\pi$
$318$	−1.92379	−	5.11362i	−0.107881	−	0.286758i
$319$	−6.00042	+	3.46434i	−0.335959	+	0.193966i
$320$	−14.8024	−	10.0444i	−0.827477	−	0.561500i
$321$		−	2.91767i		−	0.162849i
$322$	−3.57294	+	4.93157i	−0.199112	+	0.274826i
$323$		−	9.90869i		−	0.551334i
$324$	−6.92023	+	6.06533i	−0.384457	+	0.336963i
$325$	4.66144	−	4.54577i	0.258570	−	0.252154i
$326$	28.1020	−	10.5722i	1.55643	−	0.585541i
$327$	−0.842770	+	0.225820i	−0.0466053	+	0.0124879i
$328$	13.8065	+	7.38744i	0.762337	+	0.407903i
$329$	1.53310	+	25.3575i	0.0845224	+	1.39801i
$330$	−0.356931	+	9.11221i	−0.0196484	+	0.501610i
$331$	−1.27889	+	0.342677i	−0.0702941	+	0.0188352i	−0.293795	−	0.955869i	$-0.594918\pi$
$331$	−1.27889	+	0.342677i	−0.0702941	+	0.0188352i	0.223501	+	0.974704i	$0.428252\pi$
$332$	3.72918	+	18.7763i	0.204666	+	1.03048i
$333$	2.63403	−	1.52076i	0.144344	−	0.0833370i
$334$	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	$0.624792\pi$
$338$	−10.1436	+	12.3564i	−0.551740	+	0.672099i
$339$	12.6650	+	3.39358i	0.687870	+	0.184314i
$340$	4.34229	+	13.0736i	0.235494	+	0.709013i
$341$	−5.58917	−	20.8591i	−0.302671	−	1.12958i
$342$	−9.17630	+	6.57363i	−0.496197	+	0.355461i
$343$	15.2409	+	10.5221i	0.822934	+	0.568138i
$344$	15.5642	+	8.32793i	0.839166	+	0.449012i
$345$	2.41516	+	1.01821i	0.130028	+	0.0548188i
$346$	12.8792	+	34.2342i	0.692389	+	1.84044i
$347$	−7.36834	+	4.25411i	−0.395553	+	0.228373i	−0.684563	−	0.728953i	$-0.740007\pi$
$347$	−7.36834	+	4.25411i	−0.395553	+	0.228373i	0.289010	+	0.957326i	$0.406674\pi$
$348$	−2.48698	−	0.163728i	−0.133316	−	0.00877673i
$349$	−21.0228	+	21.0228i	−1.12532	+	1.12532i	−0.134397	+	0.990928i	$0.542910\pi$
$349$	−21.0228	+	21.0228i	−1.12532	+	1.12532i	−0.990928	+	0.134397i	$0.957090\pi$
$350$	2.16429	−	18.5827i	0.115686	−	0.993286i
$351$	5.14052			0.274381
$352$	19.2266	+	11.9752i	1.02478	+	0.638280i
$353$	−3.61815	+	13.5031i	−0.192574	+	0.718698i	0.800307	+	0.599591i	$0.204670\pi$
$353$	−3.61815	+	13.5031i	−0.192574	+	0.718698i	−0.992881	+	0.119107i	$0.961997\pi$
$354$	−3.85888	+	8.51344i	−0.205097	+	0.452484i
$355$	−12.3266	−	30.2959i	−0.654228	−	1.60794i
$356$	−10.4199	+	30.6668i	−0.552252	+	1.62534i
$357$	0.354214	+	5.85872i	0.0187470	+	0.310076i
$358$	3.36588	+	4.69851i	0.177892	+	0.248324i
$359$	11.6770	−	20.2251i	0.616287	−	1.06744i	−0.373870	−	0.927481i	$-0.621970\pi$
$359$	11.6770	−	20.2251i	0.616287	−	1.06744i	0.990157	−	0.139959i	$-0.0446972\pi$
$360$	9.22647	−	12.6946i	0.486278	−	0.669065i
$361$	7.49346	−	4.32635i	0.394393	−	0.227703i
$362$	1.95184	+	19.8468i	0.102586	+	1.04312i
$363$		−	3.62498i		−	0.190262i
$364$	0.0368878	−	6.89048i	0.00193345	−	0.361160i
$365$	−14.4770	+	1.81350i	−0.757760	+	0.0949229i
$366$	−4.95339	+	0.487143i	−0.258918	+	0.0254634i
$367$	6.79376	+	1.82038i	0.354631	+	0.0950232i	0.431736	−	0.902000i	$-0.357901\pi$
$367$	6.79376	+	1.82038i	0.354631	+	0.0950232i	−0.0771051	+	0.997023i	$0.524568\pi$
$368$	5.16728	−	3.96025i	0.269363	−	0.206442i
$369$	−6.86856	+	11.8967i	−0.357563	+	0.619317i
$370$	−2.84606	+	2.63150i	−0.147959	+	0.136805i
$371$	−4.49396	−	13.4624i	−0.233315	−	0.698932i
$372$	2.49908	−	7.35507i	0.129571	−	0.381343i
$373$	14.3654	−	24.8817i	0.743814	−	1.28832i	−0.206932	−	0.978355i	$-0.566348\pi$
$373$	14.3654	−	24.8817i	0.743814	−	1.28832i	0.950747	−	0.309969i	$-0.100319\pi$
$374$	−6.14207	−	16.3262i	−0.317599	−	0.844210i
$375$	−8.00140	+	0.900381i	−0.413191	+	0.0464955i
$376$	6.17838	−	26.4457i	0.318625	−	1.36383i
$377$	−1.59331	−	1.59331i	−0.0820595	−	0.0820595i
$378$	11.4664	−	9.31068i	0.589766	−	0.478890i
$379$	−12.2721	+	12.2721i	−0.630375	+	0.630375i	−0.948162	−	0.317787i	$-0.897060\pi$
$379$	−12.2721	+	12.2721i	−0.630375	+	0.630375i	0.317787	+	0.948162i	$0.397060\pi$
$380$	9.55595	−	10.7531i	0.490210	−	0.551624i
$381$	3.67765	−	13.7252i	0.188412	−	0.703162i
$382$	8.77306	+	23.3197i	0.448869	+	1.19314i
$383$	14.5025	−	3.88593i	0.741042	−	0.198562i	0.131501	−	0.991316i	$-0.458020\pi$
$383$	14.5025	−	3.88593i	0.741042	−	0.198562i	0.609541	+	0.792754i	$0.291354\pi$
$384$	3.35520	+	7.42508i	0.171219	+	0.378909i
$385$	−1.81741	+	23.6192i	−0.0926238	+	1.20375i
$386$	29.4172	−	21.0736i	1.49730	−	1.07262i
$387$	−7.74299	+	13.4112i	−0.393598	+	0.681732i
$388$	0.414096	+	0.276864i	0.0210226	+	0.0140556i
$389$	24.4030	+	6.53876i	1.23728	+	0.331528i	0.817410	−	0.576056i	$-0.195409\pi$
$389$	24.4030	+	6.53876i	1.23728	+	0.331528i	0.419870	+	0.907584i	$0.362076\pi$
$390$	−2.89245	+	0.654857i	−0.146465	+	0.0331600i
$391$	−5.01355			−0.253546
$392$	−12.3980	−	15.4366i	−0.626193	−	0.779668i
$393$	0.721458	+	0.721458i	0.0363928	+	0.0363928i
$394$	−20.5310	−	16.8544i	−1.03434	−	0.849110i
$395$	−25.6707	−	3.54379i	−1.29163	−	0.178307i
$396$	−11.0447	+	16.5193i	−0.555019	+	0.830124i
$397$	−10.5564	−	6.09474i	−0.529811	−	0.305886i	0.211129	−	0.977458i	$-0.432286\pi$
$397$	−10.5564	−	6.09474i	−0.529811	−	0.305886i	−0.740939	+	0.671572i	$0.765619\pi$
$398$	2.05481	−	12.4346i	0.102998	−	0.623291i
$399$	5.11345	−	3.37937i	0.255993	−	0.169180i
$400$	−7.89581	+	18.3754i	−0.394790	+	0.918771i
$401$	17.8560	−	30.9276i	0.891688	−	1.54445i	0.0538373	−	0.998550i	$-0.482855\pi$
$401$	17.8560	−	30.9276i	0.891688	−	1.54445i	0.837851	−	0.545899i	$-0.183812\pi$
$402$	2.90166	+	7.71291i	0.144722	+	0.384685i
$403$	6.08199	−	3.51144i	0.302966	−	0.174917i
$404$	1.61400	−	24.5161i	0.0802993	−	1.21972i
$405$	8.12269	+	6.31421i	0.403620	+	0.313756i
$406$	−6.43986	−	0.668158i	−0.319605	−	0.0331601i
$407$	3.47058	−	3.47058i	0.172030	−	0.172030i
$408$	1.42748	−	6.11014i	0.0706708	−	0.302497i
$409$	13.5323	−	7.81290i	0.669131	−	0.386323i	−0.126616	−	0.991952i	$-0.540412\pi$
$409$	13.5323	−	7.81290i	0.669131	−	0.386323i	0.795747	+	0.605629i	$0.207078\pi$
$410$	5.18954	−	16.7201i	0.256293	−	0.825746i
$411$	−1.24809	−	4.65793i	−0.0615636	−	0.229759i
$412$	22.0662	−	10.8739i	1.08712	−	0.535718i
$413$	−10.8495	+	21.7225i	−0.533867	+	1.06889i
$414$	3.32610	+	4.64298i	0.163469	+	0.228190i
$415$	19.8244	−	8.06604i	0.973142	−	0.395946i
$416$	−2.14343	+	7.04760i	−0.105091	+	0.345537i
$417$	1.21842	−	4.54719i	0.0596661	−	0.222677i
$418$	−11.5578	+	14.0791i	−0.565312	+	0.688632i
$419$	−3.05027	+	3.05027i	−0.149016	+	0.149016i	−0.777678	−	0.628663i	$-0.783603\pi$
$419$	−3.05027	+	3.05027i	−0.149016	+	0.149016i	0.628663	+	0.777678i	$0.283603\pi$
$420$	−5.26576	+	6.69962i	−0.256943	+	0.326908i
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.998410	+	0.0563674i	$0.0179518\pi$
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.0563674	+	0.998410i	$0.482048\pi$
$422$	1.35213	+	13.7488i	0.0658208	+	0.669282i
$423$	23.0133	+	6.16640i	1.11895	+	0.299821i
$424$	0.489852	+	15.1647i	0.0237893	+	0.736461i
$425$	13.4341	−	7.53276i	0.651648	−	0.365392i
$426$	−2.42891	+	14.6984i	−0.117681	+	0.712142i
$427$	−12.9060	+	0.780286i	−0.624564	+	0.0377607i
$428$	−2.60671	+	7.67181i	−0.126000	+	0.370831i
$429$	3.62725	−	0.971918i	0.175125	−	0.0469246i
$430$	5.85022	−	18.8487i	0.282123	−	0.908966i
$431$	2.56467	+	4.44214i	0.123536	+	0.213970i	0.921160	−	0.389185i	$-0.127243\pi$
$431$	2.56467	+	4.44214i	0.123536	+	0.213970i	−0.797624	+	0.603155i	$0.793910\pi$
$432$	−14.5918	+	6.03424i	−0.702049	+	0.290322i
$433$	29.1874	+	29.1874i	1.40266	+	1.40266i	0.791540	+	0.611117i	$0.209280\pi$
$433$	29.1874	+	29.1874i	1.40266	+	1.40266i	0.611117	+	0.791540i	$0.290720\pi$
$434$	7.20637	−	18.8485i	0.345917	−	0.904756i
$435$	0.346358	+	2.76494i	0.0166066	+	0.132569i
$436$	2.41776	+	0.159171i	0.115790	+	0.00762290i
$437$	2.61774	+	4.53406i	0.125223	+	0.216893i
$438$	6.05282	+	2.74355i	0.289215	+	0.131092i
$439$	−27.2269	−	15.7195i	−1.29947	−	0.750250i	−0.319158	−	0.947701i	$-0.603400\pi$
$439$	−27.2269	−	15.7195i	−1.29947	−	0.750250i	−0.980313	+	0.197452i	$0.936733\pi$
$440$	9.07955	−	23.6410i	0.432851	−	1.12704i
$441$	13.8864	−	10.4337i	0.661258	−	0.496842i
$442$	4.61156	−	3.30359i	0.219350	−	0.157136i
$443$	7.19894	−	12.4689i	0.342032	−	0.592417i	−0.642778	−	0.766053i	$-0.722218\pi$
$443$	7.19894	−	12.4689i	0.342032	−	0.592417i	0.984810	+	0.173636i	$0.0555515\pi$
$444$	1.73172	−	0.343939i	0.0821837	−	0.0163226i
$445$	35.8714	+	4.95197i	1.70047	+	0.234746i
$446$	−8.29739	+	0.816009i	−0.392893	+	0.0386392i
$447$	3.33805	−	3.33805i	0.157884	−	0.157884i
$448$	7.98374	+	19.6025i	0.377196	+	0.926133i
$449$		−	24.3063i		−	1.14709i	−0.819175	−	0.573544i	$-0.805568\pi$
$449$		−	24.3063i		−	1.14709i	0.819175	−	0.573544i	$-0.194432\pi$
$450$	−15.8884	−	7.44371i	−0.748988	−	0.350900i
$451$	−5.73745	+	21.4125i	−0.270166	+	1.00827i
$452$	−30.2699	−	20.2384i	−1.42378	−	0.951934i
$453$	−5.35757	−	3.09319i	−0.251721	−	0.145331i
$454$	3.31443	−	20.0571i	0.155554	−	0.941328i
$455$	−7.57244	+	1.41714i	−0.355002	+	0.0664366i
$456$	−6.27110	+	1.89935i	−0.293671	+	0.0889451i
$457$	−2.79803	−	10.4424i	−0.130886	−	0.488474i	0.869095	−	0.494646i	$-0.164702\pi$
$457$	−2.79803	−	10.4424i	−0.130886	−	0.488474i	−0.999981	+	0.00617169i	$0.998035\pi$
$458$	2.32413	−	5.12750i	0.108600	−	0.239592i
$459$	11.7456	+	3.14723i	0.548239	+	0.146900i
$460$	−5.44082	−	4.83508i	−0.253679	−	0.225437i
$461$	9.72905	+	9.72905i	0.453127	+	0.453127i	0.896391	−	0.443264i	$-0.146180\pi$
$461$	9.72905	+	9.72905i	0.453127	+	0.453127i	−0.443264	+	0.896391i	$0.646180\pi$
$462$	6.33052	−	8.73774i	0.294522	−	0.406517i
$463$	−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
$465$	−8.60335	−	1.18767i	−0.398971	−	0.0550770i
$466$	−0.328436	+	0.724596i	−0.0152145	+	0.0335662i
$467$	−0.285082	−	0.164592i	−0.0131920	−	0.00761641i	0.493389	−	0.869808i	$-0.335758\pi$
$467$	−0.285082	−	0.164592i	−0.0131920	−	0.00761641i	−0.506582	+	0.862192i	$0.669091\pi$
$468$	−6.11882	−	2.07903i	−0.282843	−	0.0961034i
$469$	6.77827	+	20.3054i	0.312991	+	0.937616i
$470$	−30.3401	−	1.18844i	−1.39949	−	0.0548187i
$471$	14.1259	+	8.15561i	0.650888	+	0.375790i
$472$	17.7527	−	18.9379i	0.817135	−	0.871688i
$473$	−6.46789	+	24.1385i	−0.297394	+	1.10989i
$474$	9.12315	+	7.48938i	0.419040	+	0.343999i
$475$	−13.8267	−	8.21614i	−0.634412	−	0.376982i
$476$	4.30292	−	15.7216i	0.197224	−	0.720597i
$477$	−13.3107			−0.609453
$478$	−18.4333	−	15.1323i	−0.843122	−	0.692136i
$479$	8.80324	+	15.2477i	0.402230	+	0.696683i	0.993995	−	0.109428i	$-0.0349018\pi$
$479$	8.80324	+	15.2477i	0.402230	+	0.696683i	−0.591764	+	0.806111i	$0.701568\pi$
$480$	7.44176	−	5.25419i	0.339668	−	0.239820i
$481$	1.38233	+	0.798089i	0.0630289	+	0.0363897i
$482$	1.37705	−	8.33315i	0.0627228	−	0.379565i
$483$	−1.70988	−	2.58728i	−0.0778021	−	0.117725i
$484$	−3.23863	+	9.53164i	−0.147211	+	0.433256i
$485$	0.216352	−	0.513180i	0.00982405	−	0.0233023i
$486$	−7.54731	−	20.0615i	−0.342353	−	0.910009i
$487$	−15.7620	−	4.22342i	−0.714245	−	0.191381i	−0.116643	−	0.993174i	$-0.537213\pi$
$487$	−15.7620	−	4.22342i	−0.714245	−	0.191381i	−0.597603	+	0.801793i	$0.703880\pi$
$488$	13.4598	+	3.14455i	0.609297	+	0.142347i
$489$			15.2901i			0.691442i
$490$	−14.3242	+	16.8765i	−0.647102	+	0.762403i
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.972320	+	0.233652i	$0.0750676\pi$
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.233652	+	0.972320i	$0.424932\pi$
$492$	−5.99679	+	5.25598i	−0.270356	+	0.236958i
$493$	−2.66508	−	4.61606i	−0.120029	−	0.207897i
$494$	−5.39548	−	2.44560i	−0.242754	−	0.110033i
$495$	20.4719	+	8.63079i	0.920145	+	0.387925i
$496$	−13.1423	+	17.1069i	−0.590108	+	0.768124i
$497$	−7.74213	+	37.9178i	−0.347282	+	1.70084i
$498$	−9.61808	−	1.58938i	−0.430997	−	0.0712219i
$499$	38.6769	−	10.3634i	1.73142	−	0.463931i	0.750907	−	0.660408i	$-0.229617\pi$
$499$	38.6769	−	10.3634i	1.73142	−	0.463931i	0.980509	+	0.196476i	$0.0629499\pi$
$500$	21.8436	+	4.78112i	0.976873	+	0.213818i
$501$	−1.42471	+	5.31709i	−0.0636513	+	0.237550i
$502$	0.0831210	+	0.845195i	0.00370987	+	0.0377229i
$503$	−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
$507$	−4.07058	−	7.05045i	−0.180781	−	0.313122i
$508$	−21.9325	+	32.8037i	−0.973095	+	1.45543i
$509$	7.73911	+	28.8827i	0.343030	+	1.28020i	0.894897	+	0.446273i	$0.147249\pi$
$509$	7.73911	+	28.8827i	0.343030	+	1.28020i	−0.551867	+	0.833932i	$0.686084\pi$
$510$	−7.00992	−	0.274583i	−0.310405	−	0.0121587i
$511$	15.4441	+	7.71366i	0.683206	+	0.341232i
$512$	−2.18856	−	22.5213i	−0.0967215	−	0.995311i
$513$	−3.28654	−	12.2656i	−0.145105	−	0.541537i
$514$	−13.3386	−	6.04595i	−0.588339	−	0.266675i
$515$	−16.6057	−	21.9248i	−0.731736	−	0.966121i
$516$	−6.76024	+	5.92511i	−0.297603	+	0.260839i
$517$	38.4471			1.69090
$518$	4.52894	−	0.723518i	0.198990	−	0.0317896i
$519$	−18.6266			−0.817616
$520$	8.19056	+	0.862270i	0.359180	+	0.0378131i
$521$	15.0914	+	26.1390i	0.661165	+	1.14517i	0.980310	+	0.197465i	$0.0632708\pi$
$521$	15.0914	+	26.1390i	0.661165	+	1.14517i	−0.319145	+	0.947706i	$0.603396\pi$
$522$	−2.50679	+	5.53048i	−0.109719	+	0.242063i
$523$	7.76736	+	4.48449i	0.339643	+	0.196093i	0.660114	−	0.751165i	$-0.270508\pi$
$523$	7.76736	+	4.48449i	0.339643	+	0.196093i	−0.320471	+	0.947258i	$0.603841\pi$
$524$	−1.25246	−	2.54159i	−0.0547139	−	0.111030i
$525$	8.46904	+	4.36369i	0.369619	+	0.190447i
$526$	17.1628	+	23.9580i	0.748333	+	1.04462i
$527$	16.0467	−	4.29969i	0.699003	−	0.187297i
$528$	−9.15537	+	7.01675i	−0.398436	+	0.305365i
$529$	−17.6245	+	10.1755i	−0.766281	+	0.442413i
$530$	16.5447	−	3.74576i	0.718657	−	0.162706i
$531$	16.1025	+	16.1025i	0.698787	+	0.698787i
$532$	−16.4647	+	4.31735i	−0.713833	+	0.187181i
$533$	−7.20920			−0.312265
$534$	−12.7484	−	10.4654i	−0.551677	−	0.452883i
$535$	8.97384	+	1.23882i	0.387973	+	0.0535588i
$536$	−0.738847	−	22.8730i	−0.0319133	−	0.987962i
$537$	−2.84301	+	0.761783i	−0.122685	+	0.0328734i
$538$	−34.2389	+	24.5278i	−1.47615	+	1.05747i
$539$	17.2874	−	22.0631i	0.744623	−	0.950326i
$540$	9.71142	+	14.7429i	0.417913	+	0.634435i
$541$	−0.690427	−	2.57671i	−0.0296838	−	0.110781i	0.949494	−	0.313784i	$-0.101597\pi$
$541$	−0.690427	−	2.57671i	−0.0296838	−	0.110781i	−0.979178	+	0.203003i	$0.934930\pi$
$542$	−5.85081	+	2.20112i	−0.251314	+	0.0945464i
$543$	−9.80963	−	2.62848i	−0.420972	−	0.112799i
$544$	−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
$547$	−9.41386			−0.402508			−0.201254	−	0.979539i	$-0.564502\pi$
$547$	−9.41386			−0.402508			−0.201254	+	0.979539i	$0.564502\pi$
$548$	−0.879724	+	13.3628i	−0.0375800	+	0.570829i
$549$	−3.13845	+	11.7129i	−0.133946	+	0.499893i
$550$	−27.8747	−	4.96678i	−1.18858	−	0.211784i
$551$	−2.78305	+	4.82039i	−0.118562	+	0.205355i
$552$	0.961023	+	3.17302i	0.0409039	+	0.135053i
$553$	22.9503	+	20.3334i	0.975945	+	0.864664i
$554$	−1.95863	+	11.8526i	−0.0832144	+	0.503569i
$555$	−0.743923	−	1.82839i	−0.0315778	−	0.0776107i
$556$	−7.26629	+	10.8680i	−0.308159	+	0.460904i
$557$	−11.9097	−	20.6283i	−0.504632	−	0.874048i	−0.999986	−	0.00535649i	$-0.998295\pi$
$557$	−11.9097	−	20.6283i	−0.504632	−	0.874048i	0.495354	−	0.868691i	$-0.335038\pi$
$558$	−14.6276	−	12.0081i	−0.619235	−	0.508343i
$559$	−8.12700			−0.343735
$560$	19.8315	−	12.9116i	0.838035	−	0.545617i
$561$	8.88299			0.375040
$562$	−1.65685	−	1.36014i	−0.0698899	−	0.0573741i
$563$	−13.6305	−	23.6088i	−0.574459	−	0.994992i	−0.996100	−	0.0882292i	$-0.971879\pi$
$563$	−13.6305	−	23.6088i	−0.574459	−	0.994992i	0.421641	−	0.906763i	$-0.361454\pi$
$564$	11.4970	+	7.68689i	0.484113	+	0.323676i
$565$	−15.8151	+	37.5128i	−0.665345	+	1.57817i
$566$	−2.82779	+	17.1123i	−0.118861	+	0.719283i
$567$	−3.85451	−	11.5468i	−0.161874	−	0.484921i
$568$	19.5185	−	36.4785i	0.818979	−	1.53060i
$569$	−18.6660	+	32.3304i	−0.782519	+	1.35536i	0.147951	+	0.988995i	$0.452732\pi$
$569$	−18.6660	+	32.3304i	−0.782519	+	1.35536i	−0.930470	+	0.366368i	$0.880601\pi$
$570$	3.41179	+	6.48286i	0.142904	+	0.271537i
$571$	5.89295	−	21.9928i	0.246612	−	0.920369i	−0.725954	−	0.687743i	$-0.758602\pi$
$571$	5.89295	−	21.9928i	0.246612	−	0.920369i	0.972566	−	0.232626i	$-0.0747317\pi$
$572$	−10.4059	−	0.685064i	−0.435094	−	0.0286440i
$573$	−12.6881			−0.530051
$574$	−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
$577$	2.95800	+	0.792593i	0.123143	+	0.0329961i	0.319864	−	0.947463i	$-0.396363\pi$
$577$	2.95800	+	0.792593i	0.123143	+	0.0329961i	−0.196721	+	0.980459i	$0.563029\pi$
$578$	−9.94232	+	3.74038i	−0.413546	+	0.155579i
$579$	4.76949	+	17.8000i	0.198213	+	0.739742i
$580$	1.55953	−	7.57965i	0.0647558	−	0.314728i
$581$	−24.8119	−	5.06615i	−1.02937	−	0.210179i
$582$	−0.206215	+	0.147727i	−0.00854791	+	0.00612347i
$583$	−20.7478	+	5.55934i	−0.859284	+	0.230244i
$584$	−13.4643	−	12.6217i	−0.557157	−	0.522289i
$585$	−0.988047	+	7.15728i	−0.0408507	+	0.295917i
$586$	−0.924054	−	0.758576i	−0.0381723	−	0.0313365i
$587$	16.5240			0.682019			0.341010	−	0.940060i	$-0.389231\pi$
$587$	16.5240			0.682019			0.341010	+	0.940060i	$0.389231\pi$
$588$	9.58074	−	3.14130i	0.395103	−	0.129545i
$589$	−12.2670	−	12.2670i	−0.505451	−	0.505451i
$590$	−24.5462	−	15.4834i	−1.01055	−	0.637443i
$591$	11.7148	−	6.76357i	0.481884	−	0.278216i
$592$	−4.86071	−	0.642786i	−0.199774	−	0.0264184i
$593$	−34.5811	+	9.26597i	−1.42007	+	0.380508i	−0.885510	−	0.464620i	$-0.846191\pi$
$593$	−34.5811	+	9.26597i	−1.42007	+	0.380508i	−0.534564	+	0.845128i	$0.679524\pi$
$594$	−13.0182	−	18.1724i	−0.534141	−	0.745621i
$595$	−18.1700	−	1.39811i	−0.744897	−	0.0573171i
$596$	−11.7595	+	5.79489i	−0.481686	+	0.237368i
$597$	5.55830	+	3.20909i	0.227486	+	0.131339i
$598$	−1.23741	+	2.72998i	−0.0506017	+	0.111637i
$599$	−15.7308	−	27.2465i	−0.642742	−	1.11326i	−0.984818	−	0.173589i	$-0.944464\pi$
$599$	−15.7308	−	27.2465i	−0.642742	−	1.11326i	0.342077	−	0.939672i	$-0.388870\pi$
$600$	−7.34251	−	7.05836i	−0.299757	−	0.288157i
$601$	−42.9833			−1.75333			−0.876663	−	0.481104i	$-0.840236\pi$
$601$	−42.9833			−1.75333			−0.876663	+	0.481104i	$0.840236\pi$
$602$	−18.1280	+	14.7199i	−0.738841	+	0.599938i
$603$	20.0766			0.817581
$604$	11.3238	+	12.9199i	0.460761	+	0.525703i
$605$	11.1493	+	1.53914i	0.453284	+	0.0625749i
$606$	11.3958	+	5.16535i	0.462922	+	0.209828i
$607$	−3.38204	−	12.6219i	−0.137273	−	0.512308i	−0.999978	−	0.00660186i	$-0.997899\pi$
$607$	−3.38204	−	12.6219i	−0.137273	−	0.512308i	0.862706	−	0.505706i	$-0.168768\pi$
$608$	18.1863	+	0.608527i	0.737554	+	0.0246790i
$609$	1.47322	−	2.94964i	0.0596979	−	0.119526i
$610$	0.604870	−	15.4419i	0.0244905	−	0.625225i
$611$	3.23611	+	12.0773i	0.130919	+	0.488596i
$612$	−12.7081	−	8.49660i	−0.513694	−	0.343455i
$613$	18.6071	+	32.2284i	0.751534	+	1.30169i	0.947079	+	0.321000i	$0.104019\pi$
$613$	18.6071	+	32.2284i	0.751534	+	1.30169i	−0.195546	+	0.980695i	$0.562648\pi$
$614$	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	−0.719807	−	0.694174i	$-0.755770\pi$
$617$	−0.636726	+	0.636726i	−0.0256336	+	0.0256336i	0.694174	+	0.719807i	$0.255770\pi$
$618$	1.22610	+	12.4673i	0.0493210	+	0.501508i
$619$	−1.47025	+	5.48706i	−0.0590945	+	0.220544i	−0.989158	−	0.146855i	$-0.953085\pi$
$619$	−1.47025	+	5.48706i	−0.0590945	+	0.220544i	0.930064	+	0.367399i	$0.119752\pi$
$620$	21.5608	+	10.8093i	0.865903	+	0.434112i
$621$	−6.20607	+	1.66291i	−0.249041	+	0.0667303i
$622$	5.31593	+	0.878454i	0.213149	+	0.0352228i
$623$	−32.0700	−	28.4132i	−1.28486	−	1.13835i
$624$	−2.97478	−	2.28536i	−0.119086	−	0.0914877i
$625$	0.628039	−	24.9921i	0.0251216	−	0.999684i
$626$	−30.2761	−	13.7232i	−1.21007	−	0.548489i
$627$	−4.63810	−	8.03342i	−0.185228	−	0.320824i
$628$	−29.8568	−	34.0650i	−1.19141	−	1.35934i
$629$	2.66988	+	2.66988i	0.106455	+	0.106455i
$630$	10.7596	+	17.7545i	0.428672	+	0.707357i
$631$		−	32.0044i		−	1.27408i	−0.770832	−	0.637038i	$-0.780159\pi$
$631$		−	32.0044i		−	1.27408i	0.770832	−	0.637038i	$-0.219841\pi$
$632$	−17.2975	−	27.8436i	−0.688058	−	1.10756i
$633$	−6.79560	−	1.82087i	−0.270101	−	0.0723733i
$634$	−0.0141854	−	0.0377063i	−0.000563374	−	0.00149751i
$635$	40.6528	+	17.1389i	1.61326	+	0.680136i
$636$	−7.31582	−	2.48575i	−0.290091	−	0.0985663i
$637$	8.38576	+	3.57342i	0.332256	+	0.141584i
$638$	−1.59755	+	9.66753i	−0.0632477	+	0.382741i
$639$	31.4325	+	18.1476i	1.24345	+	0.717907i
$640$	−24.2618	+	7.16692i	−0.959032	+	0.283297i
$641$	−16.6572	−	28.8512i	−0.657921	−	1.13955i	−0.981153	−	0.193233i	$-0.938103\pi$
$641$	−16.6572	−	28.8512i	−0.657921	−	1.13955i	0.323231	−	0.946320i	$-0.395231\pi$
$642$	−3.18922	−	2.61810i	−0.125869	−	0.103328i
$643$	−5.26026			−0.207444			−0.103722	−	0.994606i	$-0.533075\pi$
$643$	−5.26026			−0.207444			−0.103722	+	0.994606i	$0.533075\pi$
$644$	2.18448	+	8.33071i	0.0860804	+	0.328276i
$645$	7.93490	+	6.16823i	0.312436	+	0.242874i
$646$	−10.8309	−	8.89132i	−0.426136	−	0.349824i
$647$	−11.1178	+	41.4921i	−0.437085	+	1.63122i	0.298942	+	0.954271i	$0.403366\pi$
$647$	−11.1178	+	41.4921i	−0.437085	+	1.63122i	−0.736027	+	0.676952i	$0.763301\pi$
$648$	0.420151	+	13.0069i	0.0165051	+	0.510959i
$649$	31.8248	+	18.3740i	1.24923	+	0.721244i
$650$	−0.786026	−	9.17432i	−0.0308305	−	0.359846i
$651$	7.69161	+	6.81458i	0.301458	+	0.267084i
$652$	13.6605	−	40.2043i	0.534986	−	1.57452i
$653$	−17.2860	−	9.98010i	−0.676455	−	0.390552i	0.122063	−	0.992522i	$-0.461049\pi$
$653$	−17.2860	−	9.98010i	−0.676455	−	0.390552i	−0.798518	+	0.601971i	$0.794382\pi$
$654$	−0.509402	+	1.12384i	−0.0199192	+	0.0439457i
$655$	−2.52531	+	1.91266i	−0.0986719	+	0.0747336i
$656$	20.4639	−	8.46257i	0.798983	−	0.330408i
$657$	11.4484	−	11.4484i	0.446644	−	0.446644i
$658$	29.0933	+	21.0782i	1.13417	+	0.821713i
$659$	29.6719	+	29.6719i	1.15585	+	1.15585i	0.985359	+	0.170494i	$0.0545363\pi$
$659$	29.6719	+	29.6719i	1.15585	+	1.15585i	0.170494	+	0.985359i	$0.445464\pi$
$660$	9.64002	+	8.56677i	0.375237	+	0.333461i
$661$	11.8427	+	3.17323i	0.460626	+	0.123424i	0.481667	−	0.876354i	$-0.340031\pi$
$661$	11.8427	+	3.17323i	0.460626	+	0.123424i	−0.0210412	+	0.999779i	$0.506698\pi$
$662$	−0.773009	+	1.70541i	−0.0300438	+	0.0662827i
$663$	0.747686	+	2.79040i	0.0290377	+	0.108370i
$664$	23.8701	+	12.7722i	0.926339	+	0.495656i
$665$	8.22275	+	17.1622i	0.318865	+	0.665522i
$666$	0.701285	−	4.24380i	0.0271742	−	0.164444i
$667$	2.43900	+	1.40816i	0.0944384	+	0.0545240i
$668$	8.49656	−	12.7080i	0.328742	−	0.491689i
$669$	1.09889	−	4.10113i	0.0424857	−	0.158559i
$670$	−24.9545	+	5.64976i	−0.964077	+	0.218269i
$671$			19.5680i			0.755415i
$672$	−10.7748	+	0.290318i	−0.415648	+	0.0111992i
$673$	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
$675$	14.1310	−	13.7803i	0.543902	−	0.530406i
$676$	4.40430	+	22.1754i	0.169396	+	0.852901i
$677$	3.51471	−	6.08766i	0.135081	−	0.233968i	−0.790547	−	0.612401i	$-0.790204\pi$
$677$	3.51471	−	6.08766i	0.135081	−	0.233968i	0.925629	+	0.378433i	$0.123537\pi$
$678$	15.0741	−	10.7986i	0.578917	−	0.414719i
$679$	−0.549751	+	0.363318i	−0.0210975	+	0.0139429i
$680$	18.1868	+	6.98480i	0.697431	+	0.267855i
$681$	8.96558	+	5.17628i	0.343562	+	0.198355i
$682$	−27.8158	−	12.6080i	−1.06512	−	0.482786i
$683$	−23.8074	−	41.2356i	−0.910965	−	1.57784i	−0.812704	−	0.582677i	$-0.802005\pi$
$683$	−23.8074	−	41.2356i	−0.910965	−	1.57784i	−0.0982608	−	0.995161i	$-0.531328\pi$
$684$	−1.04867	+	15.9290i	−0.0400970	+	0.609062i
$685$	14.8563	−	1.86101i	0.567628	−	0.0711055i
$686$	25.1775	−	7.21774i	0.961280	−	0.275575i
$687$	2.02719	+	2.02719i	0.0773420	+	0.0773420i
$688$	23.0692	−	9.53994i	0.879505	−	0.363707i
$689$	−3.49270	−	6.04953i	−0.133061	−	0.230469i
$690$	3.28017	−	1.72628i	0.124874	−	0.0657184i
$691$	−22.1174	+	5.92635i	−0.841387	+	0.225449i	−0.653675	−	0.756775i	$-0.726774\pi$
$691$	−22.1174	+	5.92635i	−0.841387	+	0.225449i	−0.187712	+	0.982224i	$0.560107\pi$
$692$	48.9773	+	16.6413i	1.86184	+	0.632609i
$693$	−14.4936	−	21.9308i	−0.550567	−	0.833084i
$694$	−1.96175	+	11.8715i	−0.0744670	+	0.450634i
$695$	13.4684	+	5.67817i	0.510886	+	0.215385i
$696$	−2.41060	+	2.57153i	−0.0913734	+	0.0974736i
$697$	−16.4724	−	4.41376i	−0.623936	−	0.167183i
$698$	4.11514	+	41.8437i	0.155760	+	1.58381i
$699$	−0.286473	−	0.286473i	−0.0108354	−	0.0108354i
$700$	−18.3701	−	19.0404i	−0.694326	−	0.719661i
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	−0.258757	−	0.965942i	$-0.583313\pi$
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	0.965942	+	0.258757i	$0.0833130\pi$
$702$	4.61272	−	5.61896i	0.174096	−	0.212074i
$703$	1.02050	−	3.80857i	0.0384890	−	0.143643i
$704$	30.3423	−	10.2705i	1.14357	−	0.387083i
$705$	6.00684	−	14.2480i	0.226231	−	0.536611i
$706$	11.5132	+	16.0716i	0.433305	+	0.604862i
$707$	29.0770	+	14.5227i	1.09355	+	0.546182i
$708$	5.84314	+	11.8574i	0.219599	+	0.445627i
$709$	−4.93857	−	18.4310i	−0.185472	−	0.692190i	−0.994529	−	0.104460i	$-0.966688\pi$
$709$	−4.93857	−	18.4310i	−0.185472	−	0.692190i	0.809057	−	0.587730i	$-0.199978\pi$
$710$	−44.1765	−	13.7114i	−1.65792	−	0.514580i
$711$	24.9040	−	14.3783i	0.933971	−	0.539229i
$712$	24.1710	+	38.9078i	0.905846	+	1.45813i
$713$	−6.20678	+	6.20678i	−0.232446	+	0.232446i
$714$	6.72185	+	4.87000i	0.251559	+	0.182255i
$715$	1.44922	+	11.5689i	0.0541976	+	0.432654i
$716$	8.15610	+	0.536949i	0.304808	+	0.0200667i
$717$	10.5179	−	6.07252i	0.392799	−	0.226782i
$718$	−11.6295	−	30.9123i	−0.434007	−	1.15364i
$719$	7.09781	−	12.2938i	0.264704	−	0.458480i	−0.702782	−	0.711405i	$-0.748059\pi$
$719$	7.09781	−	12.2938i	0.264704	−	0.458480i	0.967486	+	0.252925i	$0.0813925\pi$
$720$	−5.59697	−	21.4764i	−0.208587	−	0.800378i
$721$	1.96392	+	32.4833i	0.0731401	+	1.20974i
$722$	1.99506	−	12.0730i	0.0742485	−	0.449312i
$723$	3.72493	+	2.15059i	0.138532	+	0.0799814i
$724$	23.4454	+	15.6755i	0.871342	+	0.582577i
$725$	−8.65114	−	0.108682i	−0.321295	−	0.00403636i
$726$	−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	$0.797669\pi$
$728$	−7.49870	−	6.22333i	−0.277920	−	0.230652i
$729$	−2.88776			−0.106954
$730$	−11.0083	+	17.4517i	−0.407435	+	0.645916i
$731$	−18.5695	−	4.97568i	−0.686817	−	0.184032i
$732$	−3.91232	+	5.85154i	−0.144604	+	0.216279i
$733$	6.37528	−	11.0423i	0.235476	−	0.407857i	−0.723935	−	0.689869i	$-0.757668\pi$
$733$	6.37528	−	11.0423i	0.235476	−	0.407857i	0.959411	+	0.282012i	$0.0910017\pi$
$734$	8.08602	−	5.79259i	0.298461	−	0.213808i
$735$	−5.47539	−	9.85358i	−0.201963	−	0.363455i
$736$	0.307900	−	9.20184i	0.0113493	−	0.339185i
$737$	31.2940	−	8.38520i	1.15273	−	0.308873i
$738$	6.84061	+	18.1830i	0.251806	+	0.669327i
$739$	2.78670	−	10.4001i	0.102510	−	0.382574i	−0.895540	−	0.444980i	$-0.853211\pi$
$739$	2.78670	−	10.4001i	0.102510	−	0.382574i	0.998051	+	0.0624060i	$0.0198774\pi$
$740$	0.322576	+	5.47226i	0.0118581	+	0.201164i
$741$	2.13314	−	2.13314i	0.0783628	−	0.0783628i
$742$	−18.7479	−	7.16791i	−0.688257	−	0.263142i
$743$	−12.8147	−	12.8147i	−0.470126	−	0.470126i	0.431829	−	0.901955i	$-0.357868\pi$
$743$	−12.8147	−	12.8147i	−0.470126	−	0.470126i	−0.901955	+	0.431829i	$0.857868\pi$
$744$	−5.79713	−	9.33158i	−0.212533	−	0.342112i
$745$	8.84949	+	11.6841i	0.324220	+	0.428073i
$746$	−14.3070	−	38.0294i	−0.523816	−	1.39236i
$747$	−11.8751	+	20.5682i	−0.434485	+	0.752551i
$748$	−23.3572	−	7.93624i	−0.854024	−	0.290178i
$749$	−8.02285	−	7.10804i	−0.293148	−	0.259722i
$750$	−6.19568	+	9.55405i	−0.226234	+	0.348864i
$751$	−25.4233	+	44.0345i	−0.927711	+	1.60684i	−0.140569	+	0.990071i	$0.544893\pi$
$751$	−25.4233	+	44.0345i	−0.927711	+	1.60684i	−0.787142	+	0.616772i	$0.788440\pi$
$752$	−23.3631	−	30.4838i	−0.851963	−	1.11163i
$753$	−0.417753	−	0.111937i	−0.0152238	−	0.00407919i
$754$	−3.17132	+	0.311884i	−0.115493	+	0.0113582i
$755$	11.7885	−	15.1649i	0.429027	−	0.551906i
$756$	0.111824	−	20.8883i	0.00406701	−	0.759699i
$757$		−	16.7501i		−	0.608791i	−0.952546	−	0.304396i	$-0.901546\pi$
$757$		−	16.7501i		−	0.608791i	0.952546	−	0.304396i	$-0.0984545\pi$
$758$	2.40222	+	24.4264i	0.0872525	+	0.887205i
$759$	−4.06471	+	2.34676i	−0.147540	+	0.0851821i
$760$	−3.17914	−	20.0944i	−0.115319	−	0.728901i
$761$	3.95436	−	6.84916i	0.143346	−	0.248282i	−0.785409	−	0.618977i	$-0.787547\pi$
$761$	3.95436	−	6.84916i	0.143346	−	0.248282i	0.928754	+	0.370695i	$0.120881\pi$
$762$	−11.7025	−	16.3359i	−0.423939	−	0.591786i
$763$	−1.43222	+	2.86755i	−0.0518497	+	0.103812i
$764$	33.3624	+	11.3358i	1.20701	+	0.410114i
$765$	−6.63958	+	15.7488i	−0.240054	+	0.569400i
$766$	8.76585	−	19.3392i	0.316723	−	0.698754i
$767$	−3.09311	+	11.5436i	−0.111686	+	0.416816i
$768$	11.1269	+	2.99524i	0.401506	+	0.108081i
$769$	−32.4594			−1.17052			−0.585258	−	0.810847i	$-0.699007\pi$
$769$	−32.4594			−1.17052			−0.585258	+	0.810847i	$0.699007\pi$
$770$	24.1867	+	23.1807i	0.871627	+	0.835373i
$771$	5.27348	−	5.27348i	0.189920	−	0.189920i
$772$	3.36181	−	51.0650i	0.120994	−	1.83787i
$773$	−1.57871	+	0.911466i	−0.0567821	+	0.0327832i	−0.528122	−	0.849168i	$-0.677104\pi$
$773$	−1.57871	+	0.911466i	−0.0567821	+	0.0327832i	0.471340	+	0.881951i	$0.343770\pi$
$774$	7.71148	+	20.4979i	0.277183	+	0.736782i
$775$	7.30582	−	25.9569i	0.262433	−	0.932401i
$776$	0.674211	−	0.204200i	0.0242028	−	0.00733037i
$777$	−0.467246	+	2.28838i	−0.0167624	+	0.0820951i
$778$	29.0448	−	20.8068i	1.04131	−	0.745961i
$779$	4.60914	+	17.2015i	0.165140	+	0.616309i
$780$	−1.87966	+	3.74928i	−0.0673027	+	0.134246i
$781$	56.5744	+	15.1591i	2.02439	+	0.542434i
$782$	−4.49879	+	5.48017i	−0.160876	+	0.195971i
$783$	−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
$787$	−28.6835	+	16.5605i	−1.02246	+	0.590316i	−0.914815	−	0.403873i	$-0.867664\pi$
$787$	−28.6835	+	16.5605i	−1.02246	+	0.590316i	−0.107643	+	0.994190i	$0.534330\pi$
$788$	−36.8461	+	7.31806i	−1.31259	+	0.260695i
$789$	−14.4967	+	3.88437i	−0.516095	+	0.138287i
$790$	−26.9086	+	24.8800i	−0.957366	+	0.885191i
$791$	40.1861	−	26.5581i	1.42885	−	0.944298i
$792$	8.14602	+	26.8959i	0.289456	+	0.955703i
$793$	−6.14688	+	1.64705i	−0.218282	+	0.0584885i
$794$	−16.1345	+	6.06994i	−0.572593	+	0.215414i
$795$	−1.18133	+	8.55743i	−0.0418976	+	0.303501i
$796$	−11.7481	−	13.4040i	−0.416400	−	0.475091i
$797$		−	37.6739i		−	1.33448i	−0.744844	−	0.667238i	$-0.767476\pi$
$797$		−	37.6739i		−	1.33448i	0.744844	−	0.667238i	$-0.232524\pi$
$798$	0.894537	−	8.62176i	0.0316663	−	0.305207i
$799$			29.5769i			1.04636i
$800$	13.0005	+	25.1194i	0.459639	+	0.888106i
$801$	−34.8000	+	20.0918i	−1.22960	+	0.709908i
$802$	−17.7834	−	47.2700i	−0.627953	−	1.66916i
$803$	13.0634	−	22.6265i	0.460998	−	0.798472i
$804$	11.0345	+	3.74927i	0.389157	+	0.132227i
$805$	8.68366	−	4.16051i	0.306059	−	0.146639i
$806$	1.61927	−	9.79896i	0.0570364	−	0.345154i
$807$	−5.55126	−	20.7176i	−0.195414	−	0.729293i
$808$	−25.3496	−	23.7632i	−0.891796	−	0.835985i
$809$	0.337958	+	0.585360i	0.0118820	+	0.0205802i	0.871905	−	0.489675i	$-0.162884\pi$
$809$	0.337958	+	0.585360i	0.0118820	+	0.0205802i	−0.860023	+	0.510255i	$0.829551\pi$
$810$	14.1906	−	3.21278i	0.498606	−	0.112886i
$811$	8.03712	−	8.03712i	0.282222	−	0.282222i	−0.551773	−	0.833994i	$-0.686048\pi$
$811$	8.03712	−	8.03712i	0.282222	−	0.282222i	0.833994	+	0.551773i	$0.186048\pi$
$812$	−6.50900	+	6.43968i	−0.228421	+	0.225989i
$813$		−	3.18338i		−	0.111646i
$814$	−0.679354	−	6.90784i	−0.0238114	−	0.242120i
$815$	−47.0276	−	6.49205i	−1.64730	−	0.227407i
$816$	−5.39791	−	7.04313i	−0.188965	−	0.246559i
$817$	5.19593	+	19.3915i	0.181782	+	0.678421i
$818$	3.60285	−	21.8025i	0.125971	−	0.762308i
$819$	5.66917	−	6.39879i	0.198097	−	0.223592i
$820$	−13.6196	−	20.6759i	−0.475615	−	0.722034i
$821$	−24.7397	+	6.62898i	−0.863421	+	0.231353i	−0.663241	−	0.748406i	$-0.730819\pi$
$821$	−24.7397	+	6.62898i	−0.863421	+	0.231353i	−0.200180	+	0.979759i	$0.564153\pi$
$822$	−6.21139	−	2.81543i	−0.216647	−	0.0981993i
$823$	−2.10830	+	7.86830i	−0.0734909	+	0.274272i	−0.992887	−	0.119062i	$-0.962011\pi$
$823$	−2.10830	+	7.86830i	−0.0734909	+	0.274272i	0.919396	+	0.393333i	$0.128678\pi$
$824$	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
$827$			24.7546i			0.860801i	0.902638	+	0.430400i	$0.141628\pi$
$827$			24.7546i			0.860801i	−0.902638	+	0.430400i	$0.858372\pi$
$828$	8.05971	+	0.530603i	0.280094	+	0.0184397i
$829$	−22.3099	−	5.97792i	−0.774854	−	0.207622i	−0.150339	−	0.988634i	$-0.548037\pi$
$829$	−22.3099	−	5.97792i	−0.774854	−	0.207622i	−0.624515	+	0.781013i	$0.714703\pi$
$830$	8.97220	−	28.9074i	0.311430	−	1.00339i
$831$	−5.29813	−	3.05888i	−0.183790	−	0.106111i
$832$	5.78018	+	8.66692i	0.200392	+	0.300472i
$833$	16.9729	+	13.2990i	0.588077	+	0.460785i
$834$	−3.87709	−	5.41213i	−0.134253	−	0.187407i
$835$	−15.7488	−	6.63955i	−0.545009	−	0.229771i
$836$	5.01834	+	25.2671i	0.173563	+	0.873881i
$837$	18.4374	−	10.6448i	0.637288	−	0.367939i
$838$	0.597080	+	6.07126i	0.0206258	+	0.209728i
$839$		−	9.36329i		−	0.323257i	−0.986852	−	0.161628i	$-0.948325\pi$
$839$		−	9.36329i		−	0.323257i	0.986852	−	0.161628i	$-0.0516746\pi$
$840$	2.59806	+	11.7676i	0.0896417	+	0.406021i
$841$		−	26.0058i		−	0.896753i
$842$	43.0766	−	4.23639i	1.48452	−	0.145996i
$843$	0.945384	−	0.545817i	0.0325607	−	0.0187990i
$844$	16.2417	+	10.8592i	0.559064	+	0.373789i
$845$	23.4133	−	9.52627i	0.805443	−	0.327714i
$846$	27.3908	−	19.6219i	0.941714	−	0.674616i
$847$	−9.96777	−	8.83120i	−0.342497	−	0.303444i
$848$	17.0156	+	13.0722i	0.584319	+	0.448901i
$849$	−7.64923	−	4.41628i	−0.262521	−	0.151566i
$850$	3.82089	−	21.4437i	0.131055	−	0.735514i
$851$	−1.92704	−	0.516349i	−0.0660582	−	0.0177002i
$852$	13.8869	+	15.8443i	0.475759	+	0.542816i
$853$		−	14.6246i		−	0.500735i	−0.968151	−	0.250368i	$-0.919449\pi$
$853$		−	14.6246i		−	0.500735i	0.968151	−	0.250368i	$-0.0805515\pi$
$854$	−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
$857$	−10.1631	+	37.9291i	−0.347164	+	1.29563i	0.542900	+	0.839798i	$0.317326\pi$
$857$	−10.1631	+	37.9291i	−0.347164	+	1.29563i	−0.890064	+	0.455836i	$0.849340\pi$
$858$	2.19245	−	4.83697i	0.0748489	−	0.165131i
$859$	28.7522	−	7.70414i	0.981013	−	0.262862i	0.267542	−	0.963546i	$-0.413789\pi$
$859$	28.7522	−	7.70414i	0.981013	−	0.262862i	0.713471	+	0.700684i	$0.247122\pi$
$860$	−15.3535	−	23.3081i	−0.523548	−	0.794801i
$861$	−3.34017	−	10.0060i	−0.113833	−	0.341004i
$862$	7.15692	+	1.18268i	0.243766	+	0.0402821i
$863$	2.61211	+	9.74854i	0.0889174	+	0.331844i	0.996027	−	0.0890498i	$-0.0283830\pi$
$863$	2.61211	+	9.74854i	0.0889174	+	0.331844i	−0.907110	+	0.420894i	$0.861716\pi$
$864$	−6.49775	+	21.3646i	−0.221058	+	0.726838i
$865$	7.90869	−	57.2895i	0.268903	−	1.94790i
$866$	58.0946	−	5.71333i	1.97413	−	0.194147i
$867$		−	5.40954i		−	0.183718i
$868$	−14.1363	−	24.7903i	−0.479817	−	0.841438i
$869$	32.8133	−	32.8133i	1.11312	−	1.11312i
$870$	3.33307	+	2.10246i	0.113002	+	0.0712799i
$871$	5.26806	+	9.12455i	0.178501	+	0.309174i
$872$	2.34350	−	2.49996i	0.0793610	−	0.0846592i
$873$	0.159952	+	0.596950i	0.00541357	+	0.0202037i
$874$	7.30502	+	1.20715i	0.247096	+	0.0408324i
$875$	−17.0172	+	24.1953i	−0.575288	+	0.817951i
$876$	8.43025	−	4.15431i	0.284832	−	0.140361i
$877$	−12.3785	+	21.4403i	−0.417994	+	0.723986i	−0.995738	−	0.0922319i	$-0.970600\pi$
$877$	−12.3785	+	21.4403i	−0.417994	+	0.723986i	0.577744	+	0.816218i	$0.303933\pi$
$878$	−41.6140	+	15.6555i	−1.40440	+	0.528348i
$879$	0.527258	−	0.304412i	0.0177840	−	0.0102676i
$880$	−17.6940	−	31.1383i	−0.596466	−	1.04967i
$881$		−	32.4793i		−	1.09426i	−0.837049	−	0.547128i	$-0.815721\pi$
$881$		−	32.4793i		−	1.09426i	0.837049	−	0.547128i	$-0.184279\pi$
$882$	1.05587	−	24.5413i	0.0355530	−	0.826347i
$883$			5.96843i			0.200854i	0.994944	+	0.100427i	$0.0320209\pi$
$883$			5.96843i			0.200854i	−0.994944	+	0.100427i	$0.967979\pi$
$884$	0.527012	−	8.00517i	0.0177253	−	0.269243i
$885$	11.7814	−	8.92317i	0.396027	−	0.299949i
$886$	−7.16965	−	19.0577i	−0.240869	−	0.640255i
$887$	−23.9104	+	6.40678i	−0.802833	+	0.215118i	−0.636827	−	0.771006i	$-0.719754\pi$
$887$	−23.9104	+	6.40678i	−0.802833	+	0.215118i	−0.166006	+	0.986125i	$0.553087\pi$
$888$	1.17796	−	2.20152i	0.0395299	−	0.0738781i
$889$	−28.7812	−	43.5499i	−0.965290	−	1.46062i
$890$	37.6012	−	34.7665i	1.26040	−	1.16538i
$891$	−17.7956	+	4.76831i	−0.596174	+	0.159744i
$892$	−6.55350	+	9.80187i	−0.219427	+	0.328191i
$893$	26.7482	−	15.4431i	0.895094	−	0.516783i
$894$	−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
$898$	−26.5686	−	21.8107i	−0.886605	−	0.727833i
$899$	−9.01405	−	2.41531i	−0.300635	−	0.0805550i
$900$	−22.3936	+	10.6878i	−0.746454	+	0.356259i
$901$	−4.27674	−	15.9610i	−0.142479	−	0.531739i
$902$	18.2570	+	25.4854i	0.607892	+	0.848571i
$903$	−3.76540	−	11.2799i	−0.125305	−	0.375371i
$904$	−49.2840	+	14.9268i	−1.63916	+	0.496457i
$905$	12.2495	−	29.0553i	0.407187	−	0.965832i
$906$	−8.18857	+	3.08061i	−0.272047	+	0.102346i
$907$	43.7978	−	25.2867i	1.45428	−	0.839630i	0.455561	−	0.890204i	$-0.349439\pi$
$907$	43.7978	−	25.2867i	1.45428	−	0.839630i	0.998720	+	0.0505746i	$0.0161053\pi$
$908$	−18.9498	−	21.6207i	−0.628871	−	0.717508i
$909$	21.5542	−	21.5542i	0.714907	−	0.714907i
$910$	−5.24591	+	9.54886i	−0.173900	+	0.316542i
$911$	−29.4944			−0.977193			−0.488597	−	0.872510i	$-0.662491\pi$
$911$	−29.4944			−0.977193			−0.488597	+	0.872510i	$0.662491\pi$
$912$	−3.55110	+	8.55910i	−0.117589	+	0.283420i
$913$	−9.91949	+	37.0200i	−0.328287	+	1.22518i
$914$	−13.9250	−	6.31177i	−0.460599	−	0.208775i
$915$	7.25167	+	3.05724i	0.239733	+	0.101069i
$916$	−3.51922	−	7.14148i	−0.116278	−	0.235961i
$917$	3.74145	−	0.226205i	0.123553	−	0.00746995i
$918$	13.9798	−	10.0147i	0.461402	−	0.330535i
$919$	6.17836	−	10.7012i	0.203805	−	0.353001i	−0.745946	−	0.666006i	$-0.768002\pi$
$919$	6.17836	−	10.7012i	0.203805	−	0.353001i	0.949751	+	0.313005i	$0.101336\pi$
$920$	−10.1673	+	1.60857i	−0.335205	+	0.0530328i
$921$	−10.1572	+	5.86426i	−0.334691	+	0.193234i
$922$	19.3647	−	1.90443i	0.637742	−	0.0627190i
$923$			19.0476i			0.626959i
$924$	−3.87044	−	14.7603i	−0.127328	−	0.485579i
$925$	5.93941	−	1.51176i	0.195287	−	0.0497063i
$926$	3.49454	+	35.5334i	0.114838	+	1.16770i
$927$	29.4804	+	7.89924i	0.968263	+	0.259445i
$928$	8.63595	−	4.60799i	0.283489	−	0.151265i
$929$	−29.2360	+	50.6382i	−0.959201	+	1.66138i	−0.234753	+	0.972055i	$0.575428\pi$
$929$	−29.2360	+	50.6382i	−0.959201	+	1.66138i	−0.724448	+	0.689330i	$0.757905\pi$
$930$	−9.01822	+	8.33835i	−0.295719	+	0.273425i
$931$	3.16502	−	22.2935i	0.103729	−	0.730640i
$932$	0.497321	+	1.00920i	0.0162903	+	0.0330575i
$933$	−1.37192	+	2.37623i	−0.0449146	+	0.0777943i
$934$	−0.435722	+	0.163922i	−0.0142573	+	0.00536370i
$935$	−3.77164	+	27.3213i	−0.123346	+	0.893502i
$936$	−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	$0.724633\pi$
$938$	28.2776	+	10.8114i	0.923295	+	0.353005i
$939$	11.9698	−	11.9698i	0.390621	−	0.390621i
$940$	−28.5240	+	32.0975i	−0.930351	+	1.04691i
$941$	9.99642	−	37.3071i	0.325874	−	1.21618i	−0.587557	−	0.809183i	$-0.699910\pi$
$941$	9.99642	−	37.3071i	0.325874	−	1.21618i	0.913430	−	0.406995i	$-0.133423\pi$
$942$	21.5902	−	8.12242i	0.703447	−	0.264643i
$943$	8.70356	−	2.33211i	0.283427	−	0.0759440i
$944$	−4.77053	−	36.3985i	−0.155267	−	1.18467i
$945$	−22.9556	+	4.29601i	−0.746746	+	0.139749i
$946$	20.5813	+	28.7299i	0.669156	+	0.934091i
$947$	−1.29120	+	2.23642i	−0.0419582	+	0.0726737i	−0.886242	−	0.463223i	$-0.846693\pi$
$947$	−1.29120	+	2.23642i	−0.0419582	+	0.0726737i	0.844284	+	0.535897i	$0.180026\pi$
$948$	16.3729	−	3.25184i	0.531766	−	0.105615i
$949$	8.20719	+	2.19911i	0.266417	+	0.0713862i
$950$	−21.3879	+	7.74102i	−0.693915	+	0.251152i
$951$	0.0205157			0.000665267
$952$	−13.3237	−	18.8108i	−0.431823	−	0.609660i
$953$	19.3433	+	19.3433i	0.626592	+	0.626592i	0.947209	−	0.320617i	$-0.103890\pi$
$953$	19.3433	+	19.3433i	0.626592	+	0.626592i	−0.320617	+	0.947209i	$0.603890\pi$
$954$	−11.9440	+	14.5495i	−0.386701	+	0.471058i
$955$	5.38725	−	39.0245i	0.174327	−	1.26280i
$956$	−33.0814	+	6.57036i	−1.06993	+	0.212501i
$957$	−4.32140	−	2.49496i	−0.139691	−	0.0806507i
$958$	24.5662	+	4.05954i	0.793697	+	0.131158i
$959$	−15.8487	−	7.91574i	−0.511781	−	0.255613i
$960$	0.934472	−	12.8491i	0.0301600	−	0.414703i
$961$	−0.957251	+	1.65801i	−0.0308791	+	0.0534841i
$962$	2.11277	−	0.794842i	0.0681185	−	0.0256267i
$963$	−8.70580	+	5.02630i	−0.280541	+	0.161970i
$964$	−7.87307	−	8.98276i	−0.253575	−	0.289315i
$965$	−56.7723	+	7.11174i	−1.82756	+	0.228935i
$966$	−4.36240	−	0.452614i	−0.140358	−	0.0145626i
$967$	17.8010	−	17.8010i	0.572442	−	0.572442i	−0.360368	−	0.932810i	$-0.617349\pi$
$967$	17.8010	−	17.8010i	0.572442	−	0.572442i	0.932810	+	0.360368i	$0.117349\pi$
$968$	7.51266	+	12.0930i	0.241466	+	0.388685i
$969$	6.18003	−	3.56804i	0.198531	−	0.114622i
$970$	−0.366804	−	0.696978i	−0.0117774	−	0.0223786i
$971$	12.0452	+	44.9534i	0.386550	+	1.44262i	0.835710	+	0.549171i	$0.185057\pi$
$971$	12.0452	+	44.9534i	0.386550	+	1.44262i	−0.449160	+	0.893451i	$0.648277\pi$
$972$	−28.7011	−	9.75197i	−0.920588	−	0.312795i
$973$	−9.53530	−	14.4282i	−0.305688	−	0.462548i
$974$	−18.7602	+	13.4392i	−0.601114	+	0.430621i
$975$	4.51373	+	1.27043i	0.144555	+	0.0406864i
$976$	15.5151	−	11.8909i	0.496625	−	0.380617i
$977$	−7.73241	+	28.8578i	−0.247382	+	0.923241i	0.724790	+	0.688970i	$0.241937\pi$
$977$	−7.73241	+	28.8578i	−0.247382	+	0.923241i	−0.972171	+	0.234271i	$0.924730\pi$
$978$	16.7132	+	13.7202i	0.534429	+	0.438724i
$979$	−45.8523	+	45.8523i	−1.46545	+	1.46545i
$980$	5.59376	+	30.8011i	0.178686	+	0.983906i
$981$	2.12565	+	2.12565i	0.0678669	+	0.0678669i
$982$	53.1885	−	5.23084i	1.69731	−	0.166923i
$983$	6.59494	+	1.76711i	0.210346	+	0.0563620i	0.362453	−	0.932002i	$-0.381939\pi$
$983$	6.59494	+	1.76711i	0.210346	+	0.0563620i	−0.152107	+	0.988364i	$0.548606\pi$
$984$	0.364086	+	11.2712i	0.0116066	+	0.359314i
$985$	15.8286	+	38.9029i	0.504341	+	1.23955i
$986$	−7.43713	−	1.22898i	−0.236846	−	0.0391387i
$987$	−15.2634	+	10.0872i	−0.485839	+	0.321080i
$988$	−7.51473	+	3.70315i	−0.239075	+	0.117813i
$989$	9.81160	−	2.62901i	0.311991	−	0.0835977i
$990$	27.8041	−	14.6327i	0.883671	−	0.465056i
$991$	−22.3880	−	38.7772i	−0.711179	−	1.23180i	−0.964415	−	0.264394i	$-0.914828\pi$
$991$	−22.3880	−	38.7772i	−0.711179	−	1.23180i	0.253236	−	0.967405i	$-0.418505\pi$
$992$	6.90614	+	29.7160i	0.219270	+	0.943484i
$993$	−0.674245	−	0.674245i	−0.0213965	−	0.0213965i
$994$	34.4996	+	42.4873i	1.09426	+	1.34762i
$995$	−12.2302	+	15.7330i	−0.387722	+	0.498771i
$996$	−10.3679	+	9.08707i	−0.328518	+	0.287935i
$997$	−17.2135	−	29.8147i	−0.545159	−	0.944242i	−0.998597	−	0.0529547i	$-0.983136\pi$
$997$	−17.2135	−	29.8147i	−0.545159	−	0.944242i	0.453438	−	0.891288i	$-0.350197\pi$
$998$	23.3778	−	51.5760i	0.740011	−	1.63261i
$999$	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.ch.c.117.64	✓	360
5.3	odd	4		560.2.cz.c.453.20	yes	360
7.3	odd	6	inner	560.2.ch.c.437.56	yes	360
16.13	even	4		560.2.cz.c.397.79	yes	360
35.3	even	12		560.2.cz.c.213.79	yes	360
80.13	odd	4	inner	560.2.ch.c.173.56	yes	360
112.45	odd	12		560.2.cz.c.157.20	yes	360
560.493	even	12	inner	560.2.ch.c.493.64	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.64	✓	360	1.1	even	1	trivial
560.2.ch.c.173.56	yes	360	80.13	odd	4	inner
560.2.ch.c.437.56	yes	360	7.3	odd	6	inner
560.2.ch.c.493.64	yes	360	560.493	even	12	inner
560.2.cz.c.157.20	yes	360	112.45	odd	12
560.2.cz.c.213.79	yes	360	35.3	even	12
560.2.cz.c.397.79	yes	360	16.13	even	4
560.2.cz.c.453.20	yes	360	5.3	odd	4

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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.897326 - 1.09307i) q^{2} +(0.360092 + 0.623698i) q^{3} +(-0.389613 - 1.96168i) q^{4} +(-2.07119 + 0.842714i) q^{5} +(1.00487 + 0.166053i) q^{6} +(2.59227 + 0.529295i) q^{7} +(-2.49387 - 1.33439i) q^{8} +(1.24067 - 2.14890i) q^{9} +(-0.937387 + 3.02015i) q^{10} +(1.03636 - 3.86774i) q^{11} +(1.08320 - 0.949387i) q^{12} +1.30220 q^{13} +(2.90466 - 2.35858i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(-3.69640 + 1.52860i) q^{16} +(2.97541 + 0.797258i) q^{17} +(-1.23562 - 3.28440i) q^{18} +(-0.832549 - 3.10711i) q^{19} +(2.46010 + 3.73469i) q^{20} +(0.603335 + 1.80739i) q^{21} +(-3.29776 - 4.60343i) q^{22} +(-1.57212 + 0.421249i) q^{23} +(-0.0657649 - 2.03593i) q^{24} +(3.57967 - 3.49084i) q^{25} +(1.16850 - 1.42340i) q^{26} +3.94757 q^{27} +(0.0283273 - 5.29143i) q^{28} +(-1.22355 - 1.22355i) q^{29} +(-2.22121 + 0.502886i) q^{30} +(4.67056 - 2.69655i) q^{31} +(-1.64601 + 5.41208i) q^{32} +(2.78548 - 0.746367i) q^{33} +(3.54137 - 2.53693i) q^{34} +(-5.81512 + 1.08827i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(1.06154 + 0.612879i) q^{37} +(-4.14337 - 1.87806i) q^{38} +(0.468911 + 0.812178i) q^{39} +(6.28980 + 0.662165i) q^{40} -5.53618 q^{41} +(2.51699 + 0.962325i) q^{42} -6.24099 q^{43} +(-7.99105 - 0.526083i) q^{44} +(-0.758753 + 5.49631i) q^{45} +(-0.950251 + 2.09644i) q^{46} +(2.48511 + 9.27457i) q^{47} +(-2.28443 - 1.75500i) q^{48} +(6.43969 + 2.74415i) q^{49} +(-0.603615 - 7.04526i) q^{50} +(0.574172 + 2.14284i) q^{51} +(-0.507353 - 2.55450i) q^{52} +(-2.68216 - 4.64563i) 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} +(-2.43536 + 0.239506i) q^{58} +(-2.37530 + 8.86473i) q^{59} +(-1.44345 + 2.87919i) q^{60} +(-4.72039 + 1.26482i) q^{61} +(1.24349 - 7.52494i) q^{62} +(4.35354 - 4.91384i) q^{63} +(4.43879 + 6.65561i) q^{64} +(-2.69710 + 1.09738i) q^{65} +(1.68365 - 3.71447i) q^{66} +(4.04552 + 7.00704i) q^{67} +(0.404710 - 6.14743i) q^{68} +(-0.828841 - 0.828841i) q^{69} +(-4.02851 + 7.33288i) q^{70} +14.6273i q^{71} +(-5.96154 + 3.70354i) q^{72} +(6.30257 + 1.68877i) q^{73} +(1.62247 - 0.610385i) q^{74} +(3.46624 + 0.975606i) q^{75} +(-5.77080 + 2.84377i) q^{76} +(4.73368 - 9.47766i) q^{77} +(1.30853 + 0.216234i) q^{78} +(10.0365 + 5.79459i) q^{79} +(6.36779 - 6.28102i) q^{80} +(-2.30051 - 3.98461i) q^{81} +(-4.96775 + 6.05144i) q^{82} -9.57150 q^{83} +(3.31045 - 1.88773i) q^{84} +(-6.83450 + 0.856142i) q^{85} +(-5.60020 + 6.82185i) q^{86} +(0.322536 - 1.20372i) q^{87} +(-7.74562 + 8.26273i) q^{88} +(-14.0247 - 8.09717i) q^{89} +(5.32701 + 5.76135i) q^{90} +(3.37564 + 0.689246i) q^{91} +(1.43888 + 2.91988i) q^{92} +(3.36366 + 1.94201i) q^{93} +(12.3677 + 5.60590i) q^{94} +(4.34278 + 5.73383i) q^{95} +(-3.96822 + 0.922233i) q^{96} +(-0.176114 + 0.176114i) q^{97} +(8.77805 - 4.57666i) q^{98} +(-7.02560 - 7.02560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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