LMFDB - Embedded newform 231.2.s.a.8.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.18
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32709 - 0.964186i) q^{2} +(-1.36346 + 1.06816i) q^{3} +(0.213475 - 0.657007i) q^{4} +(-1.68710 + 2.32209i) q^{5} +(-0.779526 + 2.73218i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.663628 + 2.04244i) q^{8} +(0.718055 - 2.91280i) q^{9} +O(q^{10})$	\(q+(1.32709 - 0.964186i) q^{2} +(-1.36346 + 1.06816i) q^{3} +(0.213475 - 0.657007i) q^{4} +(-1.68710 + 2.32209i) q^{5} +(-0.779526 + 2.73218i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.663628 + 2.04244i) q^{8} +(0.718055 - 2.91280i) q^{9} +4.70830i q^{10} +(0.00376805 + 3.31662i) q^{11} +(0.410727 + 1.12383i) q^{12} +(-0.129360 - 0.178049i) q^{13} +(1.56009 - 0.506903i) q^{14} +(-0.180079 - 4.96818i) q^{15} +(3.96775 + 2.88274i) q^{16} +(1.65312 + 1.20106i) q^{17} +(-1.85556 - 4.55788i) q^{18} +(-2.27859 + 0.740358i) q^{19} +(1.16548 + 1.60414i) q^{20} +(-1.62681 + 0.594551i) q^{21} +(3.20284 + 4.39782i) q^{22} -8.00809i q^{23} +(-3.08649 - 2.07592i) q^{24} +(-1.00072 - 3.07991i) q^{25} +(-0.343345 - 0.111560i) q^{26} +(2.13230 + 4.73849i) q^{27} +(0.406053 - 0.558884i) q^{28} +(2.22873 - 6.85932i) q^{29} +(-5.02923 - 6.41958i) q^{30} +(0.734413 - 0.533583i) q^{31} +3.74996 q^{32} +(-3.54783 - 4.51806i) q^{33} +3.35188 q^{34} +(-2.32209 + 1.68710i) q^{35} +(-1.76044 - 1.09358i) q^{36} +(0.606802 - 1.86754i) q^{37} +(-2.31005 + 3.17950i) q^{38} +(0.366563 + 0.104585i) q^{39} +(-5.86233 - 1.90479i) q^{40} +(-0.422906 - 1.30157i) q^{41} +(-1.58566 + 2.35757i) q^{42} +8.08879i q^{43} +(2.17985 + 0.705539i) q^{44} +(5.55235 + 6.58157i) q^{45} +(-7.72129 - 10.6274i) q^{46} +(4.10603 - 1.33413i) q^{47} +(-8.48911 + 0.307700i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-4.29765 - 3.12242i) q^{50} +(-3.53690 + 0.128200i) q^{51} +(-0.144595 + 0.0469817i) q^{52} +(6.13435 + 8.44321i) q^{53} +(7.39854 + 4.23246i) q^{54} +(-7.70786 - 5.58672i) q^{55} +2.14754i q^{56} +(2.31594 - 3.44335i) q^{57} +(-3.65594 - 11.2518i) q^{58} +(13.6851 + 4.44657i) q^{59} +(-3.30257 - 0.942267i) q^{60} +(7.04190 - 9.69234i) q^{61} +(0.460159 - 1.41622i) q^{62} +(1.58302 - 2.54835i) q^{63} +(-2.95897 + 2.14982i) q^{64} +0.631690 q^{65} +(-9.06454 - 2.57510i) q^{66} -3.50090 q^{67} +(1.14201 - 0.829716i) q^{68} +(8.55395 + 10.9187i) q^{69} +(-1.45494 + 4.47786i) q^{70} +(-5.87615 + 8.08782i) q^{71} +(6.42573 - 0.466432i) q^{72} +(-7.25057 - 2.35585i) q^{73} +(-0.995380 - 3.06346i) q^{74} +(4.65429 + 3.13040i) q^{75} +1.65510i q^{76} +(-1.02131 + 3.15546i) q^{77} +(0.587302 - 0.214641i) q^{78} +(6.21674 + 8.55660i) q^{79} +(-13.3880 + 4.35001i) q^{80} +(-7.96879 - 4.18310i) q^{81} +(-1.81619 - 1.31954i) q^{82} +(-4.31327 - 3.13378i) q^{83} +(0.0433416 + 1.19575i) q^{84} +(-5.57795 + 1.81239i) q^{85} +(7.79910 + 10.7345i) q^{86} +(4.28809 + 11.7331i) q^{87} +(-6.77149 + 2.20870i) q^{88} -17.0411i q^{89} +(13.7143 + 3.38082i) q^{90} +(-0.0680088 - 0.209309i) q^{91} +(-5.26137 - 1.70952i) q^{92} +(-0.431391 + 1.51199i) q^{93} +(4.16272 - 5.72949i) q^{94} +(2.12502 - 6.54015i) q^{95} +(-5.11293 + 4.00557i) q^{96} +(5.65434 - 4.10812i) q^{97} +1.64037 q^{98} +(9.66336 + 2.37054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.32709	−	0.964186i	0.938393	−	0.681783i	−0.00964018	−	0.999954i	$-0.503069\pi$
$2$	1.32709	−	0.964186i	0.938393	−	0.681783i	0.948033	+	0.318171i	$0.103069\pi$
$3$	−1.36346	+	1.06816i	−0.787195	+	0.616704i
$3$	−1.36346	+	1.06816i	−0.787195	+	0.616704i
$4$	0.213475	−	0.657007i	0.106737	−	0.328504i
$5$	−1.68710	+	2.32209i	−0.754493	+	1.03847i	0.243159	+	0.969986i	$0.421816\pi$
$5$	−1.68710	+	2.32209i	−0.754493	+	1.03847i	−0.997652	+	0.0684842i	$0.978184\pi$
$6$	−0.779526	+	2.73218i	−0.318240	+	1.11541i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.663628	+	2.04244i	0.234628	+	0.722110i
$9$	0.718055	−	2.91280i	0.239352	−	0.970933i
$10$			4.70830i			1.48889i
$11$	0.00376805	+	3.31662i	0.00113611	+	0.999999i
$11$	0.00376805	+	3.31662i	0.00113611	+	0.999999i
$12$	0.410727	+	1.12383i	0.118567	+	0.324422i
$13$	−0.129360	−	0.178049i	−0.0358781	−	0.0493820i	0.790701	−	0.612202i	$-0.209716\pi$
$13$	−0.129360	−	0.178049i	−0.0358781	−	0.0493820i	−0.826579	+	0.562820i	$0.809716\pi$
$14$	1.56009	−	0.506903i	0.416950	−	0.135475i
$15$	−0.180079	−	4.96818i	−0.0464962	−	1.28278i
$16$	3.96775	+	2.88274i	0.991937	+	0.720684i
$17$	1.65312	+	1.20106i	0.400941	+	0.291300i	0.769924	−	0.638136i	$-0.220294\pi$
$17$	1.65312	+	1.20106i	0.400941	+	0.291300i	−0.368983	+	0.929436i	$0.620294\pi$
$18$	−1.85556	−	4.55788i	−0.437359	−	1.07430i
$19$	−2.27859	+	0.740358i	−0.522744	+	0.169850i	−0.558490	−	0.829511i	$-0.688619\pi$
$19$	−2.27859	+	0.740358i	−0.522744	+	0.169850i	0.0357462	+	0.999361i	$0.488619\pi$
$20$	1.16548	+	1.60414i	0.260609	+	0.358697i
$21$	−1.62681	+	0.594551i	−0.354999	+	0.129742i
$22$	3.20284	+	4.39782i	0.682848	+	0.937618i
$23$		−	8.00809i		−	1.66980i	−0.550400	−	0.834901i	$-0.685525\pi$
$23$		−	8.00809i		−	1.66980i	0.550400	−	0.834901i	$-0.314475\pi$
$24$	−3.08649	−	2.07592i	−0.630026	−	0.423745i
$25$	−1.00072	−	3.07991i	−0.200144	−	0.615981i
$26$	−0.343345	−	0.111560i	−0.0673355	−	0.0218786i
$27$	2.13230	+	4.73849i	0.410362	+	0.911923i
$28$	0.406053	−	0.558884i	0.0767368	−	0.105619i
$29$	2.22873	−	6.85932i	0.413864	−	1.27374i	−0.499398	−	0.866373i	$-0.666446\pi$
$29$	2.22873	−	6.85932i	0.413864	−	1.27374i	0.913263	−	0.407371i	$-0.133554\pi$
$30$	−5.02923	−	6.41958i	−0.918207	−	1.17205i
$31$	0.734413	−	0.533583i	0.131905	−	0.0958343i	−0.519877	−	0.854241i	$-0.674022\pi$
$31$	0.734413	−	0.533583i	0.131905	−	0.0958343i	0.651781	+	0.758407i	$0.274022\pi$
$32$	3.74996			0.662906
$33$	−3.54783	−	4.51806i	−0.617598	−	0.786494i
$34$	3.35188			0.574843
$35$	−2.32209	+	1.68710i	−0.392505	+	0.285172i
$36$	−1.76044	−	1.09358i	−0.293407	−	0.182263i
$37$	0.606802	−	1.86754i	0.0997576	−	0.307022i	−0.888707	−	0.458476i	$-0.848395\pi$
$37$	0.606802	−	1.86754i	0.0997576	−	0.307022i	0.988464	+	0.151454i	$0.0483955\pi$
$38$	−2.31005	+	3.17950i	−0.374739	+	0.515784i
$39$	0.366563	+	0.104585i	0.0586971	+	0.0167471i
$40$	−5.86233	−	1.90479i	−0.926915	−	0.301173i
$41$	−0.422906	−	1.30157i	−0.0660468	−	0.203271i	0.912587	−	0.408883i	$-0.134082\pi$
$41$	−0.422906	−	1.30157i	−0.0660468	−	0.203271i	−0.978634	+	0.205612i	$0.934082\pi$
$42$	−1.58566	+	2.35757i	−0.244673	+	0.363781i
$43$			8.08879i			1.23353i	0.787148	+	0.616765i	$0.211557\pi$
$43$			8.08879i			1.23353i	−0.787148	+	0.616765i	$0.788443\pi$
$44$	2.17985	+	0.705539i	0.328625	+	0.106364i
$45$	5.55235	+	6.58157i	0.827696	+	0.981122i
$46$	−7.72129	−	10.6274i	−1.13844	−	1.56693i
$47$	4.10603	−	1.33413i	0.598926	−	0.194603i	0.00616480	−	0.999981i	$-0.498038\pi$
$47$	4.10603	−	1.33413i	0.598926	−	0.194603i	0.592762	+	0.805378i	$0.298038\pi$
$48$	−8.48911	+	0.307700i	−1.22530	+	0.0444127i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−4.29765	−	3.12242i	−0.607779	−	0.441578i
$51$	−3.53690	+	0.128200i	−0.495265	+	0.0179516i
$52$	−0.144595	+	0.0469817i	−0.0200517	+	0.00651519i
$53$	6.13435	+	8.44321i	0.842618	+	1.15976i	0.985441	+	0.170016i	$0.0543820\pi$
$53$	6.13435	+	8.44321i	0.842618	+	1.15976i	−0.142823	+	0.989748i	$0.545618\pi$
$54$	7.39854	+	4.23246i	1.00681	+	0.575964i
$55$	−7.70786	−	5.58672i	−1.03933	−	0.753313i
$56$			2.14754i			0.286978i
$57$	2.31594	−	3.44335i	0.306754	−	0.456083i
$58$	−3.65594	−	11.2518i	−0.480049	−	1.47744i
$59$	13.6851	+	4.44657i	1.78165	+	0.578894i	0.999048	−	0.0436266i	$-0.0138912\pi$
$59$	13.6851	+	4.44657i	1.78165	+	0.578894i	0.782604	+	0.622520i	$0.213891\pi$
$60$	−3.30257	−	0.942267i	−0.426360	−	0.121646i
$61$	7.04190	−	9.69234i	0.901622	−	1.24098i	−0.0683251	−	0.997663i	$-0.521766\pi$
$61$	7.04190	−	9.69234i	0.901622	−	1.24098i	0.969948	−	0.243314i	$-0.0782345\pi$
$62$	0.460159	−	1.41622i	0.0584402	−	0.179860i
$63$	1.58302	−	2.54835i	0.199441	−	0.321061i
$64$	−2.95897	+	2.14982i	−0.369871	+	0.268727i
$65$	0.631690			0.0783515
$66$	−9.06454	−	2.57510i	−1.11577	−	0.316973i
$67$	−3.50090			−0.427703			−0.213852	−	0.976866i	$-0.568601\pi$
$67$	−3.50090			−0.427703			−0.213852	+	0.976866i	$0.568601\pi$
$68$	1.14201	−	0.829716i	0.138489	−	0.100618i
$69$	8.55395	+	10.9187i	1.02977	+	1.31446i
$70$	−1.45494	+	4.47786i	−0.173899	+	0.535206i
$71$	−5.87615	+	8.08782i	−0.697370	+	0.959848i	0.302607	+	0.953115i	$0.402143\pi$
$71$	−5.87615	+	8.08782i	−0.697370	+	0.959848i	−0.999977	+	0.00673227i	$0.997857\pi$
$72$	6.42573	−	0.466432i	0.757279	−	0.0549696i
$73$	−7.25057	−	2.35585i	−0.848615	−	0.275732i	−0.147749	−	0.989025i	$-0.547203\pi$
$73$	−7.25057	−	2.35585i	−0.848615	−	0.275732i	−0.700866	+	0.713293i	$0.747203\pi$
$74$	−0.995380	−	3.06346i	−0.115711	−	0.356120i
$75$	4.65429	+	3.13040i	0.537431	+	0.361467i
$76$			1.65510i			0.189853i
$77$	−1.02131	+	3.15546i	−0.116389	+	0.359598i
$78$	0.587302	−	0.214641i	0.0664988	−	0.0243034i
$79$	6.21674	+	8.55660i	0.699438	+	0.962693i	0.999960	+	0.00891856i	$0.00283890\pi$
$79$	6.21674	+	8.55660i	0.699438	+	0.962693i	−0.300523	+	0.953775i	$0.597161\pi$
$80$	−13.3880	+	4.35001i	−1.49682	+	0.486346i
$81$	−7.96879	−	4.18310i	−0.885422	−	0.464789i
$82$	−1.81619	−	1.31954i	−0.200565	−	0.145719i
$83$	−4.31327	−	3.13378i	−0.473443	−	0.343977i	0.325338	−	0.945598i	$-0.394522\pi$
$83$	−4.31327	−	3.13378i	−0.473443	−	0.343977i	−0.798782	+	0.601621i	$0.794522\pi$
$84$	0.0433416	+	1.19575i	0.00472896	+	0.130467i
$85$	−5.57795	+	1.81239i	−0.605014	+	0.196581i
$86$	7.79910	+	10.7345i	0.840999	+	1.15754i
$87$	4.28809	+	11.7331i	0.459731	+	1.25792i
$88$	−6.77149	+	2.20870i	−0.721843	+	0.235448i
$89$		−	17.0411i		−	1.80635i	−0.429268	−	0.903177i	$-0.641229\pi$
$89$		−	17.0411i		−	1.80635i	0.429268	−	0.903177i	$-0.358771\pi$
$90$	13.7143	+	3.38082i	1.44562	+	0.356369i
$91$	−0.0680088	−	0.209309i	−0.00712925	−	0.0219416i
$92$	−5.26137	−	1.70952i	−0.548536	−	0.178230i
$93$	−0.431391	+	1.51199i	−0.0447332	+	0.156786i
$94$	4.16272	−	5.72949i	0.429351	−	0.590952i
$95$	2.12502	−	6.54015i	0.218023	−	0.671005i
$96$	−5.11293	+	4.00557i	−0.521836	+	0.408817i
$97$	5.65434	−	4.10812i	0.574111	−	0.417116i	−0.262485	−	0.964936i	$-0.584542\pi$
$97$	5.65434	−	4.10812i	0.574111	−	0.417116i	0.836596	+	0.547820i	$0.184542\pi$
$98$	1.64037			0.165703
$99$	9.66336	+	2.37054i	0.971204	+	0.238248i
$100$	−2.23715			−0.223715
$101$	−3.27138	+	2.37679i	−0.325514	+	0.236500i	−0.738525	−	0.674226i	$-0.764477\pi$
$101$	−3.27138	+	2.37679i	−0.325514	+	0.236500i	0.413011	+	0.910726i	$0.364477\pi$
$102$	−4.57017	+	3.58036i	−0.452514	+	0.354508i
$103$	−0.586943	+	1.80642i	−0.0578332	+	0.177992i	−0.975800	−	0.218665i	$-0.929830\pi$
$103$	−0.586943	+	1.80642i	−0.0578332	+	0.177992i	0.917967	+	0.396657i	$0.129830\pi$
$104$	0.277807	−	0.382369i	0.0272412	−	0.0374943i
$105$	1.36399	−	4.78066i	0.133111	−	0.466545i
$106$	16.2817	+	5.29023i	1.58141	+	0.513833i
$107$	−1.94668	−	5.99126i	−0.188192	−	0.579197i	0.811796	−	0.583941i	$-0.198490\pi$
$107$	−1.94668	−	5.99126i	−0.188192	−	0.579197i	−0.999989	+	0.00474403i	$0.998490\pi$
$108$	3.56841	−	0.389392i	0.343371	−	0.0374693i
$109$		−	16.4195i		−	1.57270i	−0.617781	−	0.786350i	$-0.711968\pi$
$109$		−	16.4195i		−	1.57270i	0.617781	−	0.786350i	$-0.288032\pi$
$110$	−15.6156	+	0.0177411i	−1.48889	+	0.00169155i
$111$	1.16749	+	3.19449i	0.110813	+	0.303207i
$112$	2.88274	+	3.96775i	0.272393	+	0.374917i
$113$	6.01352	−	1.95391i	0.565704	−	0.183808i	−0.0121820	−	0.999926i	$-0.503878\pi$
$113$	6.01352	−	1.95391i	0.565704	−	0.183808i	0.577886	+	0.816117i	$0.303878\pi$
$114$	−0.246572	−	6.80264i	−0.0230935	−	0.637125i
$115$	18.5955	+	13.5104i	1.73404	+	1.25985i
$116$	−4.03085	−	2.92858i	−0.374255	−	0.271912i
$117$	−0.611509	+	0.248951i	−0.0565341	+	0.0230156i
$118$	22.4487	−	7.29402i	2.06657	−	0.671469i
$119$	1.20106	+	1.65312i	0.110101	+	0.151541i
$120$	10.0277	−	3.66482i	0.915398	−	0.334551i
$121$	−11.0000	+	0.0249944i	−0.999997	+	0.00227222i
$122$		−	19.6523i		−	1.77923i
$123$	1.96690	+	1.32291i	0.177350	+	0.119283i
$124$	−0.193789	−	0.596421i	−0.0174028	−	0.0535602i
$125$	−4.80877	−	1.56246i	−0.430110	−	0.139751i
$126$	−0.356278	−	4.90820i	−0.0317398	−	0.437257i
$127$	−8.08026	+	11.1215i	−0.717007	+	0.986875i	0.282611	+	0.959235i	$0.408799\pi$
$127$	−8.08026	+	11.1215i	−0.717007	+	0.986875i	−0.999618	+	0.0276407i	$0.991201\pi$
$128$	−4.17159	+	12.8388i	−0.368720	+	1.13480i
$129$	−8.64015	−	11.0288i	−0.760723	−	0.971028i
$130$	0.838308	−	0.609067i	0.0735245	−	0.0534187i
$131$	−8.79354			−0.768295			−0.384148	−	0.923272i	$-0.625505\pi$
$131$	−8.79354			−0.768295			−0.384148	+	0.923272i	$0.625505\pi$
$132$	−3.72577	+	1.36646i	−0.324287	+	0.118935i
$133$	−2.39585			−0.207747
$134$	−4.64600	+	3.37552i	−0.401354	+	0.291600i
$135$	−14.6006	−	3.04289i	−1.25662	−	0.261890i
$136$	−1.35604	+	4.17345i	−0.116279	+	0.357870i
$137$	7.91272	−	10.8909i	0.676030	−	0.930475i	−0.323848	−	0.946109i	$-0.604977\pi$
$137$	7.91272	−	10.8909i	0.676030	−	0.930475i	0.999878	+	0.0156341i	$0.00497670\pi$
$138$	21.8795	+	6.24251i	1.86251	+	0.531398i
$139$	−4.63434	−	1.50579i	−0.393080	−	0.127719i	0.105807	−	0.994387i	$-0.466258\pi$
$139$	−4.63434	−	1.50579i	−0.393080	−	0.127719i	−0.498887	+	0.866667i	$0.666258\pi$
$140$	0.612728	+	1.88578i	0.0517850	+	0.159378i
$141$	−4.17335	+	6.20495i	−0.351459	+	0.522551i
$142$			16.3989i			1.37617i
$143$	0.590035	−	0.429710i	0.0493412	−	0.0359342i
$144$	11.2459	−	9.48729i	0.937158	−	0.790607i
$145$	12.1679	+	16.7477i	1.01049	+	1.39082i
$146$	−11.8936	+	3.86447i	−0.984323	+	0.319826i
$147$	−1.73091	+	0.0627395i	−0.142763	+	0.00517467i
$148$	−1.09745	−	0.797346i	−0.0902101	−	0.0655414i
$149$	9.88388	+	7.18106i	0.809719	+	0.588295i	0.913749	−	0.406279i	$-0.133174\pi$
$149$	9.88388	+	7.18106i	0.809719	+	0.588295i	−0.104030	+	0.994574i	$0.533174\pi$
$150$	9.19494	−	0.333284i	0.750764	−	0.0272125i
$151$	15.3964	−	5.00260i	1.25294	−	0.407106i	0.393968	−	0.919124i	$-0.371102\pi$
$151$	15.3964	−	5.00260i	1.25294	−	0.407106i	0.858975	+	0.512018i	$0.171102\pi$
$152$	−3.02427	−	4.16255i	−0.245301	−	0.337627i
$153$	4.68548	−	3.95278i	0.378799	−	0.319563i
$154$	1.68708	+	5.17231i	0.135949	+	0.416796i
$155$			2.60558i			0.209285i
$156$	0.146965	−	0.218509i	0.0117666	−	0.0174947i
$157$	2.60374	+	8.01350i	0.207801	+	0.639547i	0.999587	+	0.0287473i	$0.00915180\pi$
$157$	2.60374	+	8.01350i	0.207801	+	0.639547i	−0.791785	+	0.610799i	$0.790848\pi$
$158$	16.5003	+	5.36128i	1.31269	+	0.426520i
$159$	−17.3827	−	4.95951i	−1.37854	−	0.393314i
$160$	−6.32655	+	8.70775i	−0.500158	+	0.688408i
$161$	2.47464	−	7.61615i	0.195029	−	0.600236i
$162$	−14.6086	+	2.13206i	−1.14776	+	0.167510i
$163$	−18.7782	+	13.6432i	−1.47082	+	1.06862i	−0.490449	+	0.871470i	$0.663167\pi$
$163$	−18.7782	+	13.6432i	−1.47082	+	1.06862i	−0.980374	+	0.197146i	$0.936833\pi$
$164$	−0.945421			−0.0738249
$165$	16.4769	−	0.615974i	1.28272	−	0.0479535i
$166$	−8.74564			−0.678793
$167$	−13.4156	+	9.74702i	−1.03813	+	0.754247i	−0.969920	−	0.243424i	$-0.921729\pi$
$167$	−13.4156	+	9.74702i	−1.03813	+	0.754247i	−0.0682117	+	0.997671i	$0.521729\pi$
$168$	−2.29393	−	2.92809i	−0.176980	−	0.225907i
$169$	4.00225	−	12.3177i	0.307866	−	0.947513i
$170$	−5.65496	+	7.78338i	−0.433715	+	0.596958i
$171$	0.520363	+	7.16869i	0.0397931	+	0.548203i
$172$	5.31440	+	1.72675i	0.405219	+	0.131664i
$173$	3.23623	+	9.96008i	0.246046	+	0.757251i	0.995463	+	0.0951527i	$0.0303339\pi$
$173$	3.23623	+	9.96008i	0.246046	+	0.757251i	−0.749417	+	0.662098i	$0.769666\pi$
$174$	17.0035	+	11.4363i	1.28903	+	0.866984i
$175$		−	3.23840i		−	0.244800i
$176$	−9.54600	+	13.1704i	−0.719557	+	0.992755i
$177$	−23.4088	+	8.55522i	−1.75951	+	0.643050i
$178$	−16.4308	−	22.6151i	−1.23154	−	1.69507i
$179$	−8.81100	+	2.86287i	−0.658565	+	0.213981i	−0.619187	−	0.785244i	$-0.712538\pi$
$179$	−8.81100	+	2.86287i	−0.658565	+	0.213981i	−0.0393782	+	0.999224i	$0.512538\pi$
$180$	5.50942	−	2.24294i	0.410648	−	0.167179i
$181$	−14.2545	−	10.3565i	−1.05953	−	0.769794i	−0.0855289	−	0.996336i	$-0.527258\pi$
$181$	−14.2545	−	10.3565i	−1.05953	−	0.769794i	−0.974001	+	0.226542i	$0.927258\pi$
$182$	−0.292067	−	0.212199i	−0.0216494	−	0.0157292i
$183$	0.751644	+	20.7370i	0.0555631	+	1.53293i
$184$	16.3560	−	5.31439i	1.20578	−	0.391782i
$185$	3.31287	+	4.55978i	0.243567	+	0.335241i
$186$	0.885348	+	2.42249i	0.0649169	+	0.177626i
$187$	−3.97724	+	5.48730i	−0.290845	+	0.401271i
$188$		−	2.98250i		−	0.217521i
$189$	0.563668	+	5.16549i	0.0410008	+	0.375734i
$190$	−3.48583	−	10.7283i	−0.252888	−	0.778311i
$191$	−3.65072	−	1.18619i	−0.264157	−	0.0858298i	0.173944	−	0.984756i	$-0.444349\pi$
$191$	−3.65072	−	1.18619i	−0.264157	−	0.0858298i	−0.438101	+	0.898926i	$0.644349\pi$
$192$	1.73809	−	6.09185i	0.125435	−	0.439642i
$193$	−6.39754	+	8.80546i	−0.460505	+	0.633831i	−0.974613	−	0.223894i	$-0.928123\pi$
$193$	−6.39754	+	8.80546i	−0.460505	+	0.633831i	0.514108	+	0.857725i	$0.328123\pi$
$194$	3.54282	−	10.9037i	0.254359	−	0.782838i
$195$	−0.861285	+	0.674748i	−0.0616779	+	0.0483197i
$196$	0.558884	−	0.406053i	0.0399203	−	0.0290038i
$197$	14.4054			1.02634			0.513170	−	0.858287i	$-0.328471\pi$
$197$	14.4054			1.02634			0.513170	+	0.858287i	$0.328471\pi$
$198$	15.1098	−	6.17136i	1.07381	−	0.438579i
$199$	9.57277			0.678595			0.339298	−	0.940679i	$-0.389811\pi$
$199$	9.57277			0.678595			0.339298	+	0.940679i	$0.389811\pi$
$200$	5.62640	−	4.08782i	0.397847	−	0.289053i
$201$	4.77334	−	3.73953i	0.336686	−	0.263766i
$202$	−2.04973	+	6.30843i	−0.144219	+	0.443860i
$203$	4.23929	−	5.83489i	0.297540	−	0.409529i
$204$	−0.670809	+	2.35113i	−0.0469660	+	0.164612i
$205$	3.73585	+	1.21385i	0.260923	+	0.0847790i
$206$	0.962804	+	2.96321i	0.0670817	+	0.206456i
$207$	−23.3260	−	5.75025i	−1.62127	−	0.399670i
$208$		−	1.07937i		−	0.0748406i
$209$	−2.46408	−	7.55443i	−0.170444	−	0.522551i
$210$	−2.79932	−	7.65950i	−0.193171	−	0.528556i
$211$	−13.2894	−	18.2913i	−0.914880	−	1.25922i	−0.965473	−	0.260504i	$-0.916111\pi$
$211$	−13.2894	−	18.2913i	−0.914880	−	1.25922i	0.0505931	−	0.998719i	$-0.483889\pi$
$212$	6.85678	−	2.22790i	0.470926	−	0.153013i
$213$	−0.627213	−	17.3041i	−0.0429759	−	1.18566i
$214$	−8.36010	−	6.07397i	−0.571485	−	0.415208i
$215$	−18.7829	−	13.6466i	−1.28098	−	0.930689i
$216$	−8.26300	+	7.49969i	−0.562226	+	0.510289i
$217$	0.863355	−	0.280521i	0.0586083	−	0.0190430i
$218$	−15.8314	−	21.7901i	−1.07224	−	1.47581i
$219$	12.4023	−	4.53267i	0.838070	−	0.306290i
$220$	−5.31594	+	3.87150i	−0.358401	+	0.261016i
$221$		−	0.449707i		−	0.0302505i
$222$	4.62944	+	3.11369i	0.310708	+	0.208977i
$223$	2.59404	+	7.98363i	0.173710	+	0.534623i	0.999572	−	0.0292483i	$-0.00931135\pi$
$223$	2.59404	+	7.98363i	0.173710	+	0.534623i	−0.825863	+	0.563871i	$0.809311\pi$
$224$	3.56642	+	1.15880i	0.238292	+	0.0774257i
$225$	−9.68972	+	0.703360i	−0.645981	+	0.0468907i
$226$	6.09654	−	8.39116i	0.405536	−	0.558172i
$227$	6.78293	−	20.8757i	0.450199	−	1.38557i	−0.426482	−	0.904496i	$-0.640247\pi$
$227$	6.78293	−	20.8757i	0.450199	−	1.38557i	0.876680	−	0.481073i	$-0.159753\pi$
$228$	−1.76791	−	2.25666i	−0.117083	−	0.149451i
$229$	5.13433	−	3.73031i	0.339286	−	0.246506i	−0.405075	−	0.914284i	$-0.632754\pi$
$229$	5.13433	−	3.73031i	0.339286	−	0.246506i	0.744361	+	0.667778i	$0.232754\pi$
$230$	37.7045			2.48616
$231$	−1.97803	−	5.39327i	−0.130145	−	0.354851i
$232$	15.4888			1.01689
$233$	−4.95604	+	3.60077i	−0.324681	+	0.235894i	−0.738170	−	0.674615i	$-0.764310\pi$
$233$	−4.95604	+	3.60077i	−0.324681	+	0.235894i	0.413489	+	0.910509i	$0.364310\pi$
$234$	−0.571491	+	0.919990i	−0.0373596	+	0.0601416i
$235$	−3.82930	+	11.7854i	−0.249796	+	0.768794i
$236$	5.84285	−	8.04200i	0.380337	−	0.523489i
$237$	−17.6161	−	5.02611i	−1.14429	−	0.326481i
$238$	3.18783	+	1.03579i	0.206636	+	0.0671402i
$239$	−5.23636	−	16.1158i	−0.338712	−	1.04245i	−0.964865	−	0.262747i	$-0.915372\pi$
$239$	−5.23636	−	16.1158i	−0.338712	−	1.04245i	0.626153	−	0.779700i	$-0.284628\pi$
$240$	13.6074	−	20.2316i	0.878357	−	1.30594i
$241$		−	28.3577i		−	1.82668i	−0.407200	−	0.913339i	$-0.633495\pi$
$241$		−	28.3577i		−	1.82668i	0.407200	−	0.913339i	$-0.366505\pi$
$242$	−14.5738	+	10.6392i	−0.936842	+	0.683913i
$243$	15.3334	−	2.80848i	0.983637	−	0.180164i
$244$	−4.86467	−	6.69565i	−0.311429	−	0.428645i
$245$	−2.72978	+	0.886960i	−0.174399	+	0.0566658i
$246$	3.88579	−	0.140846i	0.247749	−	0.00898001i
$247$	0.426579	+	0.309928i	0.0271426	+	0.0197202i
$248$	1.57719	+	1.14589i	0.100151	+	0.0727642i
$249$	9.22837	−	0.334496i	0.584824	−	0.0211978i
$250$	−7.88817	+	2.56302i	−0.498892	+	0.162100i
$251$	−5.02113	−	6.91099i	−0.316931	−	0.436218i	0.620596	−	0.784130i	$-0.286891\pi$
$251$	−5.02113	−	6.91099i	−0.316931	−	0.436218i	−0.937527	+	0.347912i	$0.886891\pi$
$252$	−1.33635	−	1.58406i	−0.0841820	−	0.0997864i
$253$	26.5598	−	0.0301749i	1.66980	−	0.00189708i
$254$			22.5501i			1.41492i
$255$	5.66940	−	8.42928i	0.355031	−	0.527862i
$256$	4.58251	+	14.1035i	0.286407	+	0.881470i
$257$	−9.30605	−	3.02372i	−0.580495	−	0.188614i	0.00402714	−	0.999992i	$-0.498718\pi$
$257$	−9.30605	−	3.02372i	−0.580495	−	0.188614i	−0.584522	+	0.811378i	$0.698718\pi$
$258$	−22.1000	−	6.30542i	−1.37589	−	0.392559i
$259$	1.15421	−	1.58863i	0.0717188	−	0.0987125i
$260$	0.134850	−	0.415025i	0.00836303	−	0.0257388i
$261$	−18.3795	−	11.4172i	−1.13766	−	0.706707i
$262$	−11.6698	+	8.47861i	−0.720963	+	0.523810i
$263$	−16.0094			−0.987180			−0.493590	−	0.869695i	$-0.664316\pi$
$263$	−16.0094			−0.987180			−0.493590	+	0.869695i	$0.664316\pi$
$264$	6.87341	−	10.2445i	0.423029	−	0.630507i
$265$	−29.9552			−1.84013
$266$	−3.17950	+	2.31005i	−0.194948	+	0.141638i
$267$	18.2027	+	23.2349i	1.11399	+	1.42195i
$268$	−0.747353	+	2.30012i	−0.0456519	+	0.140502i
$269$	−15.1500	+	20.8522i	−0.923715	+	1.27138i	0.0385467	+	0.999257i	$0.487727\pi$
$269$	−15.1500	+	20.8522i	−0.923715	+	1.27138i	−0.962261	+	0.272127i	$0.912273\pi$
$270$	−22.3102	+	10.0395i	−1.35776	+	0.610986i
$271$	22.6559	+	7.36136i	1.37625	+	0.447171i	0.901435	−	0.432915i	$-0.142515\pi$
$271$	22.6559	+	7.36136i	1.37625	+	0.447171i	0.474815	+	0.880086i	$0.342515\pi$
$272$	3.09682	+	9.53103i	0.187772	+	0.577903i
$273$	0.316304	+	0.212741i	0.0191436	+	0.0128757i
$274$		−	22.0826i		−	1.33406i
$275$	10.2111	−	3.33062i	0.615753	−	0.200844i
$276$	8.99973	−	3.28913i	0.541720	−	0.197983i
$277$	−0.603624	−	0.830817i	−0.0362682	−	0.0499189i	0.790498	−	0.612465i	$-0.209822\pi$
$277$	−0.603624	−	0.830817i	−0.0362682	−	0.0499189i	−0.826766	+	0.562546i	$0.809822\pi$
$278$	−7.60205	+	2.47005i	−0.455940	+	0.148144i
$279$	−1.02687	−	2.52234i	−0.0614771	−	0.151009i
$280$	−4.98679	−	3.62312i	−0.298018	−	0.216523i
$281$	5.58584	+	4.05835i	0.333224	+	0.242101i	0.741797	−	0.670624i	$-0.233974\pi$
$281$	5.58584	+	4.05835i	0.333224	+	0.242101i	−0.408574	+	0.912725i	$0.633974\pi$
$282$	0.444323	+	12.2584i	0.0264591	+	0.729977i
$283$	−0.522455	+	0.169756i	−0.0310568	+	0.0100909i	−0.324504	−	0.945884i	$-0.605197\pi$
$283$	−0.522455	+	0.169756i	−0.0310568	+	0.0100909i	0.293447	+	0.955975i	$0.405197\pi$
$284$	4.05935	+	5.58721i	0.240878	+	0.331540i
$285$	4.08856	+	11.1871i	0.242185	+	0.662667i
$286$	0.368707	−	1.13917i	0.0218021	−	0.0673603i
$287$		−	1.36855i		−	0.0807831i
$288$	2.69268	−	10.9229i	0.158668	−	0.643637i
$289$	−3.96303	−	12.1970i	−0.233120	−	0.717468i
$290$	32.2957	+	10.4935i	1.89647	+	0.616200i
$291$	−3.32133	+	11.6410i	−0.194700	+	0.682408i
$292$	−3.09562	+	4.26076i	−0.181158	+	0.249342i
$293$	0.224324	−	0.690398i	0.0131051	−	0.0403335i	−0.944290	−	0.329114i	$-0.893250\pi$
$293$	0.224324	−	0.690398i	0.0131051	−	0.0403335i	0.957395	+	0.288781i	$0.0932499\pi$
$294$	−2.23658	+	1.75218i	−0.130440	+	0.102189i
$295$	−33.4135	+	24.2763i	−1.94541	+	1.41342i
$296$	4.21703			0.245110
$297$	−15.7077	+	7.08990i	−0.911456	+	0.411398i
$298$	20.0407			1.16092
$299$	−1.42583	+	1.03593i	−0.0824581	+	0.0599093i
$300$	3.05027	−	2.38964i	0.176107	−	0.137966i
$301$	−2.49957	+	7.69290i	−0.144073	+	0.443411i
$302$	15.6090	−	21.4839i	0.898195	−	1.23626i
$303$	1.92159	−	6.73503i	0.110393	−	0.386917i
$304$	−11.1751	−	3.63102i	−0.640937	−	0.208253i
$305$	10.6261	+	32.7038i	0.608450	+	1.87262i
$306$	2.40684	−	9.76337i	0.137590	−	0.558134i
$307$		−	3.91111i		−	0.223219i	−0.993752	−	0.111609i	$-0.964399\pi$
$307$		−	3.91111i		−	0.223219i	0.993752	−	0.111609i	$-0.0356005\pi$
$308$	1.85514	+	1.34462i	0.105706	+	0.0766167i
$309$	−1.12928	−	3.08994i	−0.0642426	−	0.175781i
$310$	2.51226	+	3.45784i	0.142687	+	0.196392i
$311$	22.8125	−	7.41222i	1.29358	−	0.420309i	0.420235	−	0.907415i	$-0.361948\pi$
$311$	22.8125	−	7.41222i	1.29358	−	0.420309i	0.873342	+	0.487107i	$0.161948\pi$
$312$	0.0296528	+	0.818088i	0.00167876	+	0.0463151i
$313$	9.85137	+	7.15744i	0.556833	+	0.404563i	0.830298	−	0.557319i	$-0.188170\pi$
$313$	9.85137	+	7.15744i	0.556833	+	0.404563i	−0.273466	+	0.961882i	$0.588170\pi$
$314$	11.1819	+	8.12412i	0.631031	+	0.458471i
$315$	3.24679	+	7.97521i	0.182936	+	0.449352i
$316$	6.94887	−	2.25782i	0.390904	−	0.127013i
$317$	4.31144	+	5.93419i	0.242155	+	0.333297i	0.912744	−	0.408531i	$-0.133959\pi$
$317$	4.31144	+	5.93419i	0.242155	+	0.333297i	−0.670590	+	0.741828i	$0.733959\pi$
$318$	−27.8502	+	10.1784i	−1.56176	+	0.570778i
$319$	22.7582	+	7.36600i	1.27421	+	0.412417i
$320$		−	10.4979i		−	0.586853i
$321$	9.05386	+	6.08948i	0.505337	+	0.339882i
$322$	−4.05932	−	12.4933i	−0.226217	−	0.696225i
$323$	−4.65600	−	1.51283i	−0.259067	−	0.0841759i
$324$	−4.44946	+	4.34257i	−0.247192	+	0.241254i
$325$	−0.418921	+	0.576595i	−0.0232376	+	0.0319838i
$326$	−11.7658	+	36.2114i	−0.651647	+	2.00556i
$327$	17.5387	+	22.3873i	0.969891	+	1.23802i
$328$	2.37772	−	1.72752i	0.131288	−	0.0953861i
$329$	4.31734			0.238023
$330$	21.2724	−	16.7042i	1.17101	−	0.919538i
$331$	5.37717			0.295556			0.147778	−	0.989021i	$-0.452788\pi$
$331$	5.37717			0.295556			0.147778	+	0.989021i	$0.452788\pi$
$332$	−2.97969	+	2.16487i	−0.163532	+	0.118813i
$333$	−5.00406	−	3.10849i	−0.274221	−	0.170344i
$334$	−8.40577	+	25.8703i	−0.459943	+	1.41556i
$335$	5.90636	−	8.12941i	0.322699	−	0.444157i
$336$	−8.16870	−	2.33064i	−0.445639	−	0.127147i
$337$	−15.7544	−	5.11891i	−0.858197	−	0.278845i	−0.153322	−	0.988176i	$-0.548997\pi$
$337$	−15.7544	−	5.11891i	−0.858197	−	0.278845i	−0.704875	+	0.709331i	$0.748997\pi$
$338$	−6.56518	−	20.2056i	−0.357099	−	1.09904i
$339$	−6.11211	+	9.08750i	−0.331964	+	0.493565i
$340$			4.05165i			0.219732i
$341$	1.77246	+	2.43376i	0.0959841	+	0.131796i
$342$	7.60252	+	9.01176i	0.411097	+	0.487300i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−16.5208	+	5.36795i	−0.890744	+	0.289420i
$345$	−39.7856	+	1.44209i	−2.14199	+	0.0776394i
$346$	13.8981	+	10.0976i	0.747168	+	0.542850i
$347$	8.58168	+	6.23496i	0.460689	+	0.334710i	0.793801	−	0.608177i	$-0.208099\pi$
$347$	8.58168	+	6.23496i	0.460689	+	0.334710i	−0.333113	+	0.942887i	$0.608099\pi$
$348$	8.62411	−	0.312593i	0.462301	−	0.0167568i
$349$	16.1272	−	5.24006i	0.863271	−	0.280494i	0.156277	−	0.987713i	$-0.450051\pi$
$349$	16.1272	−	5.24006i	0.863271	−	0.280494i	0.706994	+	0.707219i	$0.250051\pi$
$350$	−3.12242	−	4.29765i	−0.166901	−	0.229719i
$351$	0.567849	−	0.992628i	0.0303095	−	0.0529825i
$352$	0.0141301	+	12.4372i	0.000753135	+	0.662905i
$353$			16.9322i			0.901209i	0.892724	+	0.450605i	$0.148792\pi$
$353$			16.9322i			0.901209i	−0.892724	+	0.450605i	$0.851208\pi$
$354$	−22.8167	+	33.9240i	−1.21270	+	1.80304i
$355$	−8.86702	−	27.2899i	−0.470613	−	1.44840i
$356$	−11.1961	−	3.63784i	−0.593394	−	0.192805i
$357$	−3.40340	−	0.971036i	−0.180127	−	0.0513927i
$358$	−8.93264	+	12.2947i	−0.472105	+	0.649796i
$359$	4.57288	−	14.0739i	0.241347	−	0.742791i	−0.754869	−	0.655876i	$-0.772299\pi$
$359$	4.57288	−	14.0739i	0.241347	−	0.742791i	0.996216	−	0.0869144i	$-0.0277007\pi$
$360$	−9.75773	+	15.7080i	−0.514277	+	0.827886i
$361$	−10.7275	+	7.79398i	−0.564605	+	0.410209i
$362$	−28.9026			−1.51909
$363$	14.9713	−	11.7838i	0.785792	−	0.618491i
$364$	−0.152036			−0.00796885
$365$	17.7029	−	12.8619i	0.926613	−	0.673224i
$366$	20.9919	+	26.7951i	1.09726	+	1.40060i
$367$	7.21925	−	22.2186i	0.376842	−	1.15980i	−0.565386	−	0.824826i	$-0.691273\pi$
$367$	7.21925	−	22.2186i	0.376842	−	1.15980i	0.942228	−	0.334973i	$-0.108727\pi$
$368$	23.0852	−	31.7741i	1.20340	−	1.65634i
$369$	−4.09488	+	0.297240i	−0.213171	+	0.0154737i
$370$	8.79295	+	2.85700i	0.457123	+	0.148528i
$371$	3.22502	+	9.92559i	0.167435	+	0.515311i
$372$	0.901299	+	0.606199i	0.0467302	+	0.0314300i
$373$			5.32980i			0.275966i	0.990435	+	0.137983i	$0.0440620\pi$
$373$			5.32980i			0.275966i	−0.990435	+	0.137983i	$0.955938\pi$
$374$	0.0126301	+	11.1169i	0.000653086	+	0.574843i
$375$	8.22554	−	3.00619i	0.424765	−	0.155239i
$376$	5.44975	+	7.50094i	0.281050	+	0.386831i
$377$	−1.50961	+	0.490501i	−0.0777487	+	0.0252621i
$378$	5.72853	+	6.31158i	0.294644	+	0.324633i
$379$	3.38648	+	2.46042i	0.173952	+	0.126383i	0.671355	−	0.741136i	$-0.265713\pi$
$379$	3.38648	+	2.46042i	0.173952	+	0.126383i	−0.497403	+	0.867520i	$0.665713\pi$
$380$	−3.84329	−	2.79231i	−0.197156	−	0.143243i
$381$	−0.862477	−	23.7948i	−0.0441860	−	1.21904i
$382$	−5.98854	+	1.94579i	−0.306400	+	0.0995555i
$383$	17.0331	+	23.4441i	0.870353	+	1.19794i	0.979001	+	0.203857i	$0.0653479\pi$
$383$	17.0331	+	23.4441i	0.870353	+	1.19794i	−0.108648	+	0.994080i	$0.534652\pi$
$384$	−8.02617	−	21.9612i	−0.409584	−	1.12070i
$385$	−5.60422	−	7.69514i	−0.285617	−	0.392181i
$386$			17.8540i			0.908747i
$387$	23.5610	+	5.80820i	1.19767	+	0.295247i
$388$	−1.49200	−	4.59192i	−0.0757451	−	0.233119i
$389$	−4.25029	−	1.38100i	−0.215498	−	0.0700197i	0.199278	−	0.979943i	$-0.436140\pi$
$389$	−4.25029	−	1.38100i	−0.215498	−	0.0700197i	−0.414777	+	0.909923i	$0.636140\pi$
$390$	−0.492419	+	1.72589i	−0.0249346	+	0.0873938i
$391$	9.61821	−	13.2383i	0.486414	−	0.669491i
$392$	−0.663628	+	2.04244i	−0.0335183	+	0.103159i
$393$	11.9897	−	9.39294i	0.604798	−	0.473811i
$394$	19.1172	−	13.8895i	0.963111	−	0.699741i
$395$	−30.3575			−1.52745
$396$	3.62035	−	5.84285i	0.181929	−	0.293614i
$397$	−7.15730			−0.359214			−0.179607	−	0.983738i	$-0.557483\pi$
$397$	−7.15730			−0.359214			−0.179607	+	0.983738i	$0.557483\pi$
$398$	12.7039	−	9.22993i	0.636789	−	0.462655i
$399$	3.26665	−	2.55916i	0.163537	−	0.128118i
$400$	4.90795	−	15.1051i	0.245397	−	0.755255i
$401$	−4.02578	+	5.54101i	−0.201038	+	0.276705i	−0.897618	−	0.440774i	$-0.854704\pi$
$401$	−4.02578	+	5.54101i	−0.201038	+	0.276705i	0.696580	+	0.717479i	$0.254704\pi$
$402$	2.72904	−	9.56508i	0.136112	−	0.477063i
$403$	−0.190008	−	0.0617373i	−0.00946497	−	0.00307536i
$404$	0.863215	+	2.65670i	0.0429466	+	0.132176i
$405$	23.1577	−	11.4470i	1.15071	−	0.568804i
$406$		−	11.8309i		−	0.587157i
$407$	6.19622	+	2.00549i	0.307135	+	0.0994087i
$408$	−2.60902	−	7.13881i	−0.129166	−	0.353424i
$409$	2.96381	+	4.07934i	0.146551	+	0.201710i	0.875981	−	0.482345i	$-0.160215\pi$
$409$	2.96381	+	4.07934i	0.146551	+	0.201710i	−0.729430	+	0.684055i	$0.760215\pi$
$410$	6.12818	−	1.99117i	0.302649	−	0.0983366i
$411$	0.844595	+	23.3014i	0.0416608	+	1.14938i
$412$	1.06154	+	0.771251i	0.0522981	+	0.0379968i
$413$	11.6413	+	8.45787i	0.572829	+	0.416185i
$414$	−36.4999	+	14.8595i	−1.79387	+	0.730303i
$415$	14.5538	−	4.72882i	0.714419	−	0.232129i
$416$	−0.485096	−	0.667678i	−0.0237838	−	0.0327356i
$417$	7.92718	−	2.89715i	0.388196	−	0.141874i
$418$	−10.5539	−	7.64957i	−0.516209	−	0.374153i
$419$			11.7034i			0.571749i	0.958267	+	0.285874i	$0.0922840\pi$
$419$			11.7034i			0.571749i	−0.958267	+	0.285874i	$0.907716\pi$
$420$	−2.84976	−	1.91670i	−0.139054	−	0.0935253i
$421$	−2.81069	−	8.65042i	−0.136985	−	0.421596i	0.858909	−	0.512129i	$-0.171143\pi$
$421$	−2.81069	−	8.65042i	−0.136985	−	0.421596i	−0.995893	+	0.0905330i	$0.971143\pi$
$422$	−35.2724	−	11.4607i	−1.71703	−	0.557898i
$423$	−0.937697	−	12.9180i	−0.0455924	−	0.628096i
$424$	−13.1738	+	18.1322i	−0.639776	+	0.880576i
$425$	2.04484	−	6.29338i	0.0991895	−	0.305274i
$426$	−17.5168	−	22.3593i	−0.848689	−	1.08331i
$427$	9.69234	−	7.04190i	0.469045	−	0.340781i
$428$	−4.35187			−0.210355
$429$	−0.345489	+	1.21615i	−0.0166804	+	0.0587161i
$430$	−38.0844			−1.83659
$431$	18.7399	−	13.6153i	0.902669	−	0.655827i	−0.0364814	−	0.999334i	$-0.511615\pi$
$431$	18.7399	−	13.6153i	0.902669	−	0.655827i	0.939150	+	0.343507i	$0.111615\pi$
$432$	−5.19938	+	24.9480i	−0.250155	+	1.20031i
$433$	−11.8799	+	36.5625i	−0.570911	+	1.75708i	0.0787886	+	0.996891i	$0.474895\pi$
$433$	−11.8799	+	36.5625i	−0.570911	+	1.75708i	−0.649699	+	0.760191i	$0.725105\pi$
$434$	0.875274	−	1.20471i	0.0420145	−	0.0578280i
$435$	−34.4797	−	9.83750i	−1.65317	−	0.471672i
$436$	−10.7877	−	3.50514i	−0.516638	−	0.167866i
$437$	5.92886	+	18.2471i	0.283616	+	0.872879i
$438$	12.0886	−	17.9734i	0.577616	−	0.858802i
$439$		−	18.1948i		−	0.868390i	−0.900819	−	0.434195i	$-0.857033\pi$
$439$		−	18.1948i		−	0.868390i	0.900819	−	0.434195i	$-0.142967\pi$
$440$	6.29536	−	19.4503i	0.300120	−	0.927257i
$441$	2.29302	−	1.93444i	0.109191	−	0.0921163i
$442$	−0.433601	−	0.596800i	−0.0206243	−	0.0283869i
$443$	25.0319	−	8.13334i	1.18930	−	0.386427i	0.353486	−	0.935440i	$-0.384996\pi$
$443$	25.0319	−	8.13334i	1.18930	−	0.386427i	0.835814	+	0.549013i	$0.184996\pi$
$444$	2.34803	−	0.0851078i	0.111433	−	0.00403904i
$445$	39.5710	+	28.7500i	1.87585	+	1.36288i
$446$	11.1402	+	8.09384i	0.527505	+	0.383255i
$447$	−21.1468	+	0.766498i	−1.00021	+	0.0362541i
$448$	−3.47848	+	1.13023i	−0.164343	+	0.0533981i
$449$	−0.161902	−	0.222838i	−0.00764061	−	0.0105164i	0.805180	−	0.593031i	$-0.202069\pi$
$449$	−0.161902	−	0.222838i	−0.00764061	−	0.0105164i	−0.812820	+	0.582515i	$0.802069\pi$
$450$	−12.1809	+	10.2761i	−0.574215	+	0.484421i
$451$	4.31522	−	1.40752i	0.203196	−	0.0662777i
$452$		−	4.36804i		−	0.205455i
$453$	−15.6488	+	23.2667i	−0.735246	+	1.09317i
$454$	−11.1265	−	34.2439i	−0.522194	−	1.60715i
$455$	0.600773	+	0.195203i	0.0281647	+	0.00915126i
$456$	8.56976	+	2.44506i	0.401316	+	0.114501i
$457$	2.84632	−	3.91762i	0.133145	−	0.183259i	−0.737239	−	0.675632i	$-0.763871\pi$
$457$	2.84632	−	3.91762i	0.133145	−	0.183259i	0.870384	+	0.492374i	$0.163871\pi$
$458$	3.21700	−	9.90090i	0.150320	−	0.462639i
$459$	−2.16627	+	10.3943i	−0.101113	+	0.485165i
$460$	12.8461	−	9.33325i	0.598953	−	0.435165i
$461$	−26.2389			−1.22207			−0.611034	−	0.791604i	$-0.709246\pi$
$461$	−26.2389			−1.22207			−0.611034	+	0.791604i	$0.709246\pi$
$462$	−7.82514	−	5.25016i	−0.364058	−	0.244260i
$463$	10.7389			0.499080			0.249540	−	0.968365i	$-0.419721\pi$
$463$	10.7389			0.499080			0.249540	+	0.968365i	$0.419721\pi$
$464$	28.6167	−	20.7912i	1.32849	−	0.965208i
$465$	−2.78319	−	3.55261i	−0.129067	−	0.164748i
$466$	−3.10528	+	9.55708i	−0.143850	+	0.442723i
$467$	−1.88395	+	2.59304i	−0.0871789	+	0.119991i	−0.850379	−	0.526171i	$-0.823627\pi$
$467$	−1.88395	+	2.59304i	−0.0871789	+	0.119991i	0.763200	+	0.646162i	$0.223627\pi$
$468$	0.0330212	+	0.454911i	0.00152641	+	0.0210283i
$469$	−3.32955	−	1.08184i	−0.153745	−	0.0499546i
$470$	6.28148	+	19.3324i	0.289743	+	0.891738i
$471$	−12.1098	−	8.14487i	−0.557991	−	0.375296i
$472$			30.9019i			1.42237i
$473$	−26.8275	+	0.0304790i	−1.23353	+	0.00140143i
$474$	−28.2243	+	10.3151i	−1.29638	+	0.473790i
$475$	4.56047	+	6.27695i	0.209249	+	0.288006i
$476$	1.34251	−	0.436207i	0.0615338	−	0.0199935i
$477$	28.9982	−	11.8054i	1.32774	−	0.540534i
$478$	−22.4878	−	16.3383i	−1.02857	−	0.747298i
$479$	−27.7599	−	20.1688i	−1.26838	−	0.921535i	−0.269247	−	0.963071i	$-0.586775\pi$
$479$	−27.7599	−	20.1688i	−1.26838	−	0.921535i	−0.999137	+	0.0415361i	$0.986775\pi$
$480$	−0.675288	−	18.6305i	−0.0308226	−	0.850361i
$481$	−0.411011	+	0.133545i	−0.0187405	+	0.00608915i
$482$	−27.3421	−	37.6331i	−1.24540	−	1.71414i
$483$	4.76122	+	13.0276i	0.216643	+	0.592778i
$484$	−2.33179	+	7.23240i	−0.105991	+	0.328745i
$485$			20.0607i			0.910908i
$486$	17.6409	−	18.5113i	0.800205	−	0.839691i
$487$	2.69926	+	8.30748i	0.122315	+	0.376448i	0.993402	−	0.114681i	$-0.0365845\pi$
$487$	2.69926	+	8.30748i	0.122315	+	0.376448i	−0.871087	+	0.491129i	$0.836585\pi$
$488$	24.4692	+	7.95052i	1.10767	+	0.359903i
$489$	11.0302	−	38.6601i	0.498805	−	1.74827i
$490$	−2.76747	+	3.80909i	−0.125021	+	0.172077i
$491$	−0.0459768	+	0.141502i	−0.00207490	+	0.00638590i	−0.952089	−	0.305822i	$-0.901069\pi$
$491$	−0.0459768	+	0.141502i	−0.00207490	+	0.00638590i	0.950014	+	0.312208i	$0.101069\pi$
$492$	1.28904	−	1.00986i	0.0581146	−	0.0455282i
$493$	11.9228	−	8.66244i	0.536977	−	0.390137i
$494$	0.864937			0.0389153
$495$	−21.8076	+	18.4399i	−0.980181	+	0.828810i
$496$	4.45215			0.199907
$497$	−8.08782	+	5.87615i	−0.362788	+	0.263581i
$498$	11.9243	−	9.34177i	0.534343	−	0.418615i
$499$	4.98532	−	15.3432i	0.223173	−	0.686857i	−0.775298	−	0.631595i	$-0.782401\pi$
$499$	4.98532	−	15.3432i	0.223173	−	0.686857i	0.998472	−	0.0552622i	$-0.0175995\pi$
$500$	−2.05310	+	2.82585i	−0.0918175	+	0.126376i
$501$	7.88028	−	27.6198i	0.352065	−	1.23396i
$502$	−13.3270	−	4.33019i	−0.594812	−	0.193266i
$503$	−0.498919	−	1.53552i	−0.0222457	−	0.0684653i	0.939317	−	0.343049i	$-0.111460\pi$
$503$	−0.498919	−	1.53552i	−0.0222457	−	0.0684653i	−0.961563	+	0.274584i	$0.911460\pi$
$504$	6.25536	+	1.54205i	0.278636	+	0.0686886i
$505$		−	11.6063i		−	0.516474i
$506$	35.2181	−	25.6486i	1.56564	−	1.14022i
$507$	7.70036	+	21.0697i	0.341985	+	0.935740i
$508$	5.58199	+	7.68295i	0.247661	+	0.340876i
$509$	19.6402	−	6.38150i	0.870538	−	0.282855i	0.160515	−	0.987033i	$-0.448685\pi$
$509$	19.6402	−	6.38150i	0.870538	−	0.282855i	0.710023	+	0.704179i	$0.248685\pi$
$510$	−0.603603	−	16.6528i	−0.0267280	−	0.737396i
$511$	−6.16770	−	4.48110i	−0.272843	−	0.198232i
$512$	−2.16293	−	1.57146i	−0.0955890	−	0.0694495i
$513$	−8.36682	−	9.21840i	−0.369404	−	0.407002i
$514$	−15.2654	+	4.96002i	−0.673327	+	0.218777i
$515$	−3.20445	−	4.41055i	−0.141205	−	0.194352i
$516$	−9.09043	+	3.32228i	−0.400184	+	0.146255i
$517$	4.44028	+	13.6131i	0.195283	+	0.598705i
$518$		−	3.22112i		−	0.141528i
$519$	−15.0515	−	10.1234i	−0.660686	−	0.444367i
$520$	0.419207	+	1.29019i	0.0183834	+	0.0565784i
$521$	13.8202	+	4.49045i	0.605473	+	0.196730i	0.595680	−	0.803222i	$-0.296883\pi$
$521$	13.8202	+	4.49045i	0.605473	+	0.196730i	0.00979328	+	0.999952i	$0.496883\pi$
$522$	−35.3995	+	2.56959i	−1.54939	+	0.112468i
$523$	16.7933	−	23.1140i	0.734320	−	1.01070i	−0.264605	−	0.964357i	$-0.585242\pi$
$523$	16.7933	−	23.1140i	0.734320	−	1.01070i	0.998925	−	0.0463481i	$-0.0147583\pi$
$524$	−1.87720	+	5.77742i	−0.0820058	+	0.252388i
$525$	3.45914	+	4.41544i	0.150969	+	0.192706i
$526$	−21.2458	+	15.4360i	−0.926363	+	0.673042i
$527$	1.85494			0.0808024
$528$	−1.05251	−	28.1540i	−0.0458047	−	1.22525i
$529$	−41.1295			−1.78824
$530$	−39.7531	+	28.8823i	−1.72677	+	1.25457i
$531$	22.7786	−	36.6691i	0.988508	−	1.59131i
$532$	−0.511453	+	1.57409i	−0.0221743	+	0.0682455i
$533$	−0.177036	+	0.243670i	−0.00766829	+	0.0105545i
$534$	46.5593	+	13.2840i	2.01482	+	0.574854i
$535$	17.1965	+	5.58747i	0.743468	+	0.241568i
$536$	−2.32329	−	7.15037i	−0.100351	−	0.308849i
$537$	8.95545	−	13.3150i	0.386456	−	0.574585i
$538$			42.2802i			1.82283i
$539$	−1.94641	+	2.68542i	−0.0838380	+	0.115669i
$540$	−5.11606	+	8.94312i	−0.220160	+	0.384851i
$541$	1.77876	+	2.44825i	0.0764749	+	0.105259i	0.845541	−	0.533911i	$-0.179278\pi$
$541$	1.77876	+	2.44825i	0.0764749	+	0.105259i	−0.769066	+	0.639169i	$0.779278\pi$
$542$	37.1641	−	12.0754i	1.59634	−	0.518681i
$543$	30.4979	−	1.10544i	1.30879	−	0.0474391i
$544$	6.19914	+	4.50394i	0.265786	+	0.193105i
$545$	38.1275	+	27.7013i	1.63320	+	1.18659i
$546$	0.624885	−	0.0226499i	0.0267426	−	0.000969325i
$547$	−3.67916	+	1.19543i	−0.157310	+	0.0511130i	−0.386613	−	0.922242i	$-0.626355\pi$
$547$	−3.67916	+	1.19543i	−0.157310	+	0.0511130i	0.229304	+	0.973355i	$0.426355\pi$
$548$	−5.46625	−	7.52365i	−0.233507	−	0.321395i
$549$	−23.1754	−	27.4713i	−0.989100	−	1.17244i
$550$	10.3397	−	14.2654i	0.440887	−	0.608281i
$551$			17.2796i			0.736137i
$552$	−16.6242	+	24.7169i	−0.707571	+	1.05202i
$553$	3.26833	+	10.0589i	0.138984	+	0.427748i
$554$	−1.60212	−	0.520562i	−0.0680677	−	0.0221165i
$555$	−9.38756	−	2.67839i	−0.398480	−	0.113691i
$556$	−1.97863	+	2.72335i	−0.0839126	+	0.115496i
$557$	3.69104	−	11.3598i	0.156394	−	0.481332i	−0.841905	−	0.539625i	$-0.818566\pi$
$557$	3.69104	−	11.3598i	0.156394	−	0.481332i	0.998299	+	0.0582934i	$0.0185659\pi$
$558$	−3.79475	−	2.35728i	−0.160645	−	0.0997914i
$559$	1.44020	−	1.04637i	0.0609141	−	0.0442567i
$560$	−14.0769			−0.594859
$561$	−0.438518	−	11.7301i	−0.0185143	−	0.495244i
$562$	11.3259			0.477755
$563$	−33.9734	+	24.6831i	−1.43181	+	1.04027i	−0.442129	+	0.896951i	$0.645777\pi$
$563$	−33.9734	+	24.6831i	−1.43181	+	1.04027i	−0.989677	+	0.143317i	$0.954223\pi$
$564$	3.18579	+	4.06652i	0.134146	+	0.171231i
$565$	−5.60824	+	17.2604i	−0.235940	+	0.726149i
$566$	−0.529668	+	0.729026i	−0.0222636	+	0.0306432i
$567$	−6.28612	−	6.44086i	−0.263992	−	0.270491i
$568$	−20.4184	−	6.63435i	−0.856738	−	0.278371i
$569$	−4.90354	−	15.0916i	−0.205567	−	0.632671i	−0.999690	−	0.0249130i	$-0.992069\pi$
$569$	−4.90354	−	15.0916i	−0.205567	−	0.632671i	0.794122	−	0.607758i	$-0.207931\pi$
$570$	16.2123	+	10.9042i	0.679060	+	0.456725i
$571$			7.54472i			0.315737i	0.987460	+	0.157868i	$0.0504622\pi$
$571$			7.54472i			0.315737i	−0.987460	+	0.157868i	$0.949538\pi$
$572$	−0.156365	−	0.479389i	−0.00653797	−	0.0200443i
$573$	6.24466	−	2.28224i	0.260875	−	0.0953419i
$574$	−1.31954	−	1.81619i	−0.0550765	−	0.0758063i
$575$	−24.6642	+	8.01387i	−1.02857	+	0.334202i
$576$	4.13728	+	10.1626i	0.172387	+	0.423440i
$577$	11.0384	+	8.01990i	0.459536	+	0.333873i	0.793349	−	0.608767i	$-0.208335\pi$
$577$	11.0384	+	8.01990i	0.459536	+	0.333873i	−0.333813	+	0.942639i	$0.608335\pi$
$578$	−17.0194	−	12.3653i	−0.707915	−	0.514330i
$579$	−0.682866	−	18.8395i	−0.0283789	−	0.782944i
$580$	13.6009	−	4.41919i	0.564745	−	0.183497i
$581$	−3.13378	−	4.31327i	−0.130011	−	0.178945i
$582$	6.81640	+	18.6510i	0.282549	+	0.773110i
$583$	−27.9798	+	20.3771i	−1.15881	+	0.843935i
$584$		−	16.3722i		−	0.677488i
$585$	0.453588	−	1.83999i	0.0187536	−	0.0760741i
$586$	−0.367975	−	1.13251i	−0.0152009	−	0.0467835i
$587$	−25.4569	−	8.27144i	−1.05072	−	0.341399i	−0.267768	−	0.963483i	$-0.586286\pi$
$587$	−25.4569	−	8.27144i	−1.05072	−	0.341399i	−0.782950	+	0.622085i	$0.786286\pi$
$588$	−0.328286	+	1.15062i	−0.0135383	+	0.0474506i
$589$	−1.27838	+	1.75954i	−0.0526749	+	0.0725008i
$590$	−20.9358	+	64.4336i	−0.861911	+	2.65269i
$591$	−19.6412	+	15.3873i	−0.807930	+	0.632949i
$592$	7.79127	−	5.66069i	0.320219	−	0.232653i
$593$	−11.5269			−0.473353			−0.236677	−	0.971589i	$-0.576058\pi$
$593$	−11.5269			−0.473353			−0.236677	+	0.971589i	$0.576058\pi$
$594$	−14.0096	+	24.5541i	−0.574820	+	1.00747i
$595$	−5.86501			−0.240442
$596$	6.82797	−	4.96081i	0.279684	−	0.203203i
$597$	−13.0521	+	10.2253i	−0.534187	+	0.418493i
$598$	−0.893379	+	2.74954i	−0.0365330	+	0.112437i
$599$	−14.1817	+	19.5195i	−0.579449	+	0.797544i	−0.993635	−	0.112649i	$-0.964066\pi$
$599$	−14.1817	+	19.5195i	−0.579449	+	0.797544i	0.414185	+	0.910192i	$0.364066\pi$
$600$	−3.30492	+	11.5835i	−0.134923	+	0.472895i
$601$	13.8351	+	4.49528i	0.564344	+	0.183366i	0.577275	−	0.816550i	$-0.304116\pi$
$601$	13.8351	+	4.49528i	0.564344	+	0.183366i	−0.0129308	+	0.999916i	$0.504116\pi$
$602$	4.10023	+	12.6192i	0.167113	+	0.514321i
$603$	−2.51384	+	10.1974i	−0.102371	+	0.415271i
$604$		−	11.1835i		−	0.455050i
$605$	18.5000	−	25.5851i	0.752131	−	1.04018i
$606$	−3.94370	−	10.7908i	−0.160202	−	0.438344i
$607$	−24.8605	−	34.2176i	−1.00906	−	1.38885i	−0.919599	−	0.392859i	$-0.871486\pi$
$607$	−24.8605	−	34.2176i	−1.00906	−	1.38885i	−0.0894595	−	0.995990i	$-0.528514\pi$
$608$	−8.54462	+	2.77631i	−0.346530	+	0.112594i
$609$	0.452497	+	12.4839i	0.0183361	+	0.505873i
$610$	45.6344	+	33.1553i	1.84768	+	1.34242i
$611$	−0.768699	−	0.558492i	−0.0310982	−	0.0225942i
$612$	−1.59677	−	3.92222i	−0.0645457	−	0.158546i
$613$	−1.32415	+	0.430244i	−0.0534821	+	0.0173774i	−0.335636	−	0.941992i	$-0.608951\pi$
$613$	−1.32415	+	0.430244i	−0.0534821	+	0.0173774i	0.282154	+	0.959369i	$0.408951\pi$
$614$	−3.77104	−	5.19039i	−0.152187	−	0.209467i
$615$	−6.39027	+	2.33546i	−0.257681	+	0.0941747i
$616$	−7.12259	+	0.00809206i	−0.286977	+	0.000326039i
$617$			15.3913i			0.619631i	0.950797	+	0.309815i	$0.100267\pi$
$617$			15.3913i			0.619631i	−0.950797	+	0.309815i	$0.899733\pi$
$618$	−4.47793	−	3.01179i	−0.180129	−	0.121152i
$619$	6.58909	+	20.2791i	0.264838	+	0.815087i	0.991731	+	0.128336i	$0.0409637\pi$
$619$	6.58909	+	20.2791i	0.264838	+	0.815087i	−0.726893	+	0.686751i	$0.759036\pi$
$620$	1.71189	+	0.556225i	0.0687510	+	0.0223385i
$621$	37.9462	−	17.0757i	1.52273	−	0.685223i
$622$	23.1274	−	31.8322i	0.927325	−	1.27635i
$623$	5.26599	−	16.2071i	0.210978	−	0.649322i
$624$	1.15294	+	1.47167i	0.0461545	+	0.0589141i
$625$	24.8407	−	18.0478i	0.993627	−	0.721912i
$626$	19.9748			0.798352
$627$	11.4290	+	7.66814i	0.456432	+	0.306236i
$628$	5.82076			0.232274
$629$	3.24615	−	2.35847i	0.129433	−	0.0940382i
$630$	11.9984	+	7.45330i	0.478026	+	0.296947i
$631$	0.329619	−	1.01446i	0.0131219	−	0.0403851i	−0.944281	−	0.329140i	$-0.893241\pi$
$631$	0.329619	−	1.01446i	0.0131219	−	0.0403851i	0.957403	+	0.288755i	$0.0932412\pi$
$632$	−13.3507	+	18.3757i	−0.531063	+	0.730946i
$633$	37.6576	+	10.7442i	1.49676	+	0.427044i
$634$	11.4433	+	3.71816i	0.454472	+	0.147667i
$635$	−12.1930	−	37.5262i	−0.483864	−	1.48918i
$636$	−6.96919	+	10.3618i	−0.276346	+	0.410873i
$637$		−	0.220081i		−	0.00871992i
$638$	37.3043	−	12.1678i	1.47689	−	0.481727i
$639$	19.3388	+	22.9235i	0.765031	+	0.906841i
$640$	−22.7751	−	31.3472i	−0.900264	−	1.23911i
$641$	−0.658016	+	0.213802i	−0.0259901	+	0.00844468i	−0.321983	−	0.946745i	$-0.604349\pi$
$641$	−0.658016	+	0.213802i	−0.0259901	+	0.00844468i	0.295993	+	0.955190i	$0.404349\pi$
$642$	17.8867	−	0.648328i	0.705930	−	0.0255875i
$643$	−0.214019	−	0.155494i	−0.00844009	−	0.00613209i	0.583557	−	0.812072i	$-0.301660\pi$
$643$	−0.214019	−	0.155494i	−0.00844009	−	0.00613209i	−0.591997	+	0.805940i	$0.701660\pi$
$644$	−4.47559	−	3.25171i	−0.176363	−	0.128135i
$645$	40.1866	−	1.45662i	1.58234	−	0.0573544i
$646$	−7.63757	+	2.48160i	−0.300496	+	0.0976371i
$647$	−10.7953	−	14.8585i	−0.424408	−	0.584148i	0.542250	−	0.840217i	$-0.317572\pi$
$647$	−10.7953	−	14.8585i	−0.424408	−	0.584148i	−0.966658	+	0.256069i	$0.917572\pi$
$648$	3.25540	−	19.0518i	0.127884	−	0.748424i
$649$	−14.6960	+	45.4052i	−0.576869	+	1.78231i
$650$			1.16911i			0.0458563i
$651$	−0.877509	+	1.30468i	−0.0343923	+	0.0511346i
$652$	4.95499	+	15.2499i	0.194052	+	0.597232i
$653$	−36.4445	−	11.8415i	−1.42618	−	0.463395i	−0.508622	−	0.860990i	$-0.669845\pi$
$653$	−36.4445	−	11.8415i	−1.42618	−	0.463395i	−0.917561	+	0.397595i	$0.869845\pi$
$654$	44.8609	+	12.7994i	1.75420	+	0.500496i
$655$	14.8356	−	20.4194i	0.579674	−	0.797852i
$656$	2.07410	−	6.38343i	0.0809801	−	0.249231i
$657$	−12.0684	+	19.4278i	−0.470834	+	0.757951i
$658$	5.72949	−	4.16272i	0.223359	−	0.162280i
$659$	−36.9613			−1.43981			−0.719903	−	0.694075i	$-0.755814\pi$
$659$	−36.9613			−1.43981			−0.719903	+	0.694075i	$0.755814\pi$
$660$	3.11270	−	10.9569i	0.121162	−	0.426498i
$661$	39.6307			1.54145			0.770727	−	0.637165i	$-0.219893\pi$
$661$	39.6307			1.54145			0.770727	+	0.637165i	$0.219893\pi$
$662$	7.13598	−	5.18459i	0.277348	−	0.201505i
$663$	0.480360	+	0.613158i	0.0186556	+	0.0238131i
$664$	3.53813	−	10.8892i	0.137306	−	0.422585i
$665$	4.04203	−	5.56338i	0.156743	−	0.215739i
$666$	−9.63799	+	0.699605i	−0.373465	+	0.0271092i
$667$	−54.9301	−	17.8479i	−2.12690	−	0.691072i
$668$	3.53997	+	10.8949i	0.136965	+	0.421536i
$669$	−12.0647	−	8.11451i	−0.466448	−	0.313725i
$670$		−	16.4833i		−	0.636805i
$671$	32.1724	+	23.3188i	1.24200	+	0.900212i
$672$	−6.10047	+	2.22954i	−0.235331	+	0.0860064i
$673$	−20.3047	−	27.9470i	−0.782687	−	1.07728i	−0.994980	−	0.100070i	$-0.968093\pi$
$673$	−20.3047	−	27.9470i	−0.782687	−	1.07728i	0.212293	−	0.977206i	$-0.431907\pi$
$674$	−25.8431	+	8.39692i	−0.995438	+	0.323437i
$675$	12.4603	−	11.3092i	0.479595	−	0.435291i
$676$	−7.23842	−	5.25902i	−0.278401	−	0.202270i
$677$	−12.6540	−	9.19365i	−0.486331	−	0.353340i	0.317440	−	0.948278i	$-0.397177\pi$
$677$	−12.6540	−	9.19365i	−0.486331	−	0.353340i	−0.803772	+	0.594938i	$0.797177\pi$
$678$	0.650737	+	17.9531i	0.0249914	+	0.689486i
$679$	6.64707	−	2.15976i	0.255091	−	0.0828842i
$680$	−7.40337	−	10.1899i	−0.283906	−	0.390763i
$681$	13.0504	+	35.7085i	0.500092	+	1.36835i
$682$	4.69881	+	1.52084i	0.179927	+	0.0582358i
$683$			22.7298i			0.869731i	0.900495	+	0.434865i	$0.143204\pi$
$683$			22.7298i			0.869731i	−0.900495	+	0.434865i	$0.856796\pi$
$684$	4.82096	+	1.18845i	0.184334	+	0.0454416i
$685$	11.9402	+	36.7481i	0.456211	+	1.40407i
$686$	1.56009	+	0.506903i	0.0595644	+	0.0193536i
$687$	−3.01588	+	10.5704i	−0.115063	+	0.403287i
$688$	−23.3179	+	32.0943i	−0.888985	+	1.22358i
$689$	0.709766	−	2.18443i	0.0270399	−	0.0832203i
$690$	−51.4086	+	40.2745i	−1.95709	+	1.53322i
$691$	13.7667	−	10.0021i	0.523711	−	0.380498i	−0.294289	−	0.955716i	$-0.595083\pi$
$691$	13.7667	−	10.0021i	0.523711	−	0.380498i	0.818000	+	0.575218i	$0.195083\pi$
$692$	7.23470			0.275022
$693$	8.45786	+	5.24066i	0.321288	+	0.199076i
$694$	17.4003			0.660507
$695$	11.3152	−	8.22095i	0.429209	−	0.311839i
$696$	−21.1183	+	16.5445i	−0.800489	+	0.627119i
$697$	0.864153	−	2.65959i	0.0327321	−	0.100739i
$698$	16.3499	−	22.5037i	0.618852	−	0.851777i
$699$	2.91115	−	10.2034i	0.110110	−	0.385927i
$700$	−2.12766	−	0.691317i	−0.0804178	−	0.0261293i
$701$	−7.14174	−	21.9800i	−0.269740	−	0.830174i	−0.990563	−	0.137055i	$-0.956236\pi$
$701$	−7.14174	−	21.9800i	−0.269740	−	0.830174i	0.720824	−	0.693119i	$-0.243764\pi$
$702$	−0.203492	−	1.86482i	−0.00768032	−	0.0703830i
$703$			4.70461i			0.177438i
$704$	−7.14128	−	9.80568i	−0.269147	−	0.369566i
$705$	−7.36761	−	20.1592i	−0.277480	−	0.759241i
$706$	16.3258	+	22.4705i	0.614429	+	0.845689i
$707$	−3.84573	+	1.24955i	−0.144634	+	0.0469943i
$708$	0.623659	+	17.2061i	0.0234386	+	0.646644i
$709$	3.54318	+	2.57427i	0.133067	+	0.0966788i	0.652328	−	0.757937i	$-0.273793\pi$
$709$	3.54318	+	2.57427i	0.133067	+	0.0966788i	−0.519261	+	0.854616i	$0.673793\pi$
$710$	−38.0798	−	27.6666i	−1.42911	−	1.03831i
$711$	29.3876	−	11.9640i	1.10212	−	0.448685i
$712$	34.8054	−	11.3090i	1.30439	−	0.423821i
$713$	−4.27298	−	5.88125i	−0.160024	−	0.220255i
$714$	−5.45288	+	1.99287i	−0.204069	+	0.0745811i
$715$	0.00238024	+	2.09508i	8.90160e−5	+	0.0783515i
$716$			6.40004i			0.239181i
$717$	24.3539	+	16.3801i	0.909514	+	0.611724i
$718$	−7.50122	−	23.0864i	−0.279943	−	0.861576i
$719$	44.5949	+	14.4897i	1.66311	+	0.540376i	0.981520	−	0.191360i	$-0.0612899\pi$
$719$	44.5949	+	14.4897i	1.66311	+	0.540376i	0.681588	+	0.731737i	$0.261290\pi$
$720$	3.05742	+	42.1200i	0.113943	+	1.56972i
$721$	−1.11643	+	1.53664i	−0.0415781	+	0.0572273i
$722$	−6.72148	+	20.6866i	−0.250148	+	0.769875i
$723$	30.2906	+	38.6646i	1.12652	+	1.43795i
$724$	−9.84729	+	7.15447i	−0.365971	+	0.265894i
$725$	−23.3564			−0.867435
$726$	8.50647	−	30.0734i	0.315705	−	1.11613i
$727$	−41.0573			−1.52273			−0.761365	−	0.648324i	$-0.775470\pi$
$727$	−41.0573			−1.52273			−0.761365	+	0.648324i	$0.775470\pi$
$728$	0.382369	−	0.277807i	0.0141715	−	0.0102962i
$729$	−17.9066	+	20.2078i	−0.663206	+	0.748437i
$730$	11.0920	−	34.1378i	0.410535	−	1.26350i
$731$	−9.71514	+	13.3717i	−0.359328	+	0.494572i
$732$	13.7848	+	3.93299i	0.509502	+	0.145368i
$733$	4.28637	+	1.39273i	0.158321	+	0.0514415i	0.387105	−	0.922036i	$-0.373475\pi$
$733$	4.28637	+	1.39273i	0.158321	+	0.0514415i	−0.228784	+	0.973477i	$0.573475\pi$
$734$	−11.8422	−	36.4467i	−0.437105	−	1.34527i
$735$	2.77453	−	4.12519i	0.102340	−	0.152160i
$736$		−	30.0300i		−	1.10692i
$737$	−0.0131916	−	11.6112i	−0.000485918	−	0.427703i
$738$	−5.14767	+	4.34269i	−0.189488	+	0.159857i
$739$	−30.3495	−	41.7725i	−1.11642	−	1.53662i	−0.811598	−	0.584217i	$-0.801402\pi$
$739$	−30.3495	−	41.7725i	−1.11642	−	1.53662i	−0.304826	−	0.952408i	$-0.598598\pi$
$740$	3.70302	−	1.20318i	0.136126	−	0.0442299i
$741$	−0.912678	+	0.0330813i	−0.0335281	+	0.00121527i
$742$	13.8500	+	10.0626i	0.508450	+	0.369410i
$743$	20.9848	+	15.2463i	0.769857	+	0.559334i	0.901918	−	0.431908i	$-0.142159\pi$
$743$	20.9848	+	15.2463i	0.769857	+	0.559334i	−0.132061	+	0.991242i	$0.542159\pi$
$744$	−3.37443	+	0.122311i	−0.123713	+	0.00448415i
$745$	−33.3501	+	10.8361i	−1.22185	+	0.397005i
$746$	5.13892	+	7.07311i	0.188149	+	0.258965i
$747$	−12.2252	+	10.3135i	−0.447298	+	0.377350i
$748$	2.75616	+	3.78448i	0.100775	+	0.138374i
$749$		−	6.29958i		−	0.230182i
$750$	8.01749	−	11.9204i	0.292757	−	0.435273i
$751$	7.28139	+	22.4098i	0.265702	+	0.817746i	0.991531	+	0.129871i	$0.0414564\pi$
$751$	7.28139	+	22.4098i	0.265702	+	0.817746i	−0.725829	+	0.687875i	$0.758544\pi$
$752$	20.1377	+	6.54312i	0.734345	+	0.238603i
$753$	14.2282	+	4.05949i	0.518504	+	0.147936i
$754$	−1.53045	+	2.10648i	−0.0557356	+	0.0767134i
$755$	−14.3588	+	44.1918i	−0.522569	+	1.60830i
$756$	3.51409	+	0.732367i	0.127806	+	0.0266359i
$757$	25.4379	−	18.4817i	0.924556	−	0.671729i	−0.0200979	−	0.999798i	$-0.506398\pi$
$757$	25.4379	−	18.4817i	0.924556	−	0.671729i	0.944654	+	0.328069i	$0.106398\pi$
$758$	6.86647			0.249401
$759$	−36.1811	+	28.4114i	−1.31329	+	1.03127i
$760$	14.7681			0.535694
$761$	16.0865	−	11.6875i	0.583136	−	0.423673i	−0.256717	−	0.966487i	$-0.582641\pi$
$761$	16.0865	−	11.6875i	0.583136	−	0.423673i	0.839853	+	0.542813i	$0.182641\pi$
$762$	−24.0872	−	30.7462i	−0.872587	−	1.11382i
$763$	5.07390	−	15.6158i	0.183687	−	0.565332i
$764$	−1.55867	+	2.14533i	−0.0563908	+	0.0776153i
$765$	1.27384	+	17.5488i	0.0460558	+	0.634480i
$766$	45.2090	+	14.6893i	1.63347	+	0.530745i
$767$	−0.978605	−	3.01184i	−0.0353354	−	0.108751i
$768$	−21.3129	−	14.3347i	−0.769064	−	0.517260i
$769$			19.1944i			0.692167i	0.938204	+	0.346083i	$0.112489\pi$
$769$			19.1944i			0.692167i	−0.938204	+	0.346083i	$0.887511\pi$
$770$	−14.8568	−	4.80863i	−0.535403	−	0.173291i
$771$	15.9183	−	5.81765i	0.573282	−	0.209518i
$772$	4.41954	+	6.08297i	0.159063	+	0.218931i
$773$	−34.2151	+	11.1172i	−1.23063	+	0.399857i	−0.850943	−	0.525258i	$-0.823969\pi$
$773$	−34.2151	+	11.1172i	−1.23063	+	0.399857i	−0.379689	+	0.925114i	$0.623969\pi$
$774$	36.8677	−	15.0092i	1.32518	−	0.539495i
$775$	−2.37833	−	1.72796i	−0.0854321	−	0.0620700i
$776$	12.1429	+	8.82236i	0.435906	+	0.316704i
$777$	0.123198	+	3.39891i	0.00441972	+	0.121935i
$778$	−6.97206	+	2.26536i	−0.249960	+	0.0812171i
$779$	1.92726	+	2.65264i	0.0690511	+	0.0950407i
$780$	0.259452	+	0.709912i	0.00928987	+	0.0254189i
$781$	−26.8464	−	19.4585i	−0.960639	−	0.696279i
$782$		−	26.8422i		−	0.959875i
$783$	37.2551	−	4.06535i	1.33139	−	0.145284i
$784$	1.51555	+	4.66437i	0.0541266	+	0.166585i
$785$	−23.0008	−	7.47342i	−0.820935	−	0.266738i
$786$	6.85480	−	24.0255i	0.244502	−	0.856962i
$787$	−10.1732	+	14.0022i	−0.362634	+	0.499123i	−0.950880	−	0.309559i	$-0.899819\pi$
$787$	−10.1732	+	14.0022i	−0.362634	+	0.499123i	0.588246	+	0.808682i	$0.299819\pi$
$788$	3.07518	−	9.46444i	0.109549	−	0.337157i
$789$	21.8282	−	17.1006i	0.777103	−	0.608798i
$790$	−40.2870	+	29.2702i	−1.43335	+	1.04139i
$791$	6.32299			0.224820
$792$	1.57119	+	21.3100i	0.0558299	+	0.757216i
$793$	−2.63666			−0.0936304
$794$	−9.49836	+	6.90097i	−0.337084	+	0.244906i
$795$	40.8427	−	31.9970i	1.44854	−	1.13482i
$796$	2.04354	−	6.28938i	0.0724315	−	0.222921i
$797$	−17.3697	+	23.9073i	−0.615265	+	0.846839i	−0.996998	−	0.0774335i	$-0.975327\pi$
$797$	−17.3697	+	23.9073i	−0.615265	+	0.846839i	0.381733	+	0.924273i	$0.375327\pi$
$798$	1.86763	−	6.54589i	0.0661133	−	0.231722i
$799$	8.39014	+	2.72612i	0.296822	+	0.0964432i
$800$	−3.75267	−	11.5495i	−0.132677	−	0.408337i
$801$	−49.6373	−	12.2365i	−1.75385	−	0.432354i
$802$			11.2350i			0.396722i
$803$	7.78615	−	24.0563i	0.274767	−	0.848927i
$804$	−1.43791	−	3.93442i	−0.0507113	−	0.138756i
$805$	13.5104	+	18.5955i	0.476180	+	0.655406i
$806$	−0.311684	+	0.101272i	−0.0109786	+	0.00356716i
$807$	−1.61710	−	44.6140i	−0.0569245	−	1.57049i
$808$	−7.02543	−	5.10427i	−0.247154	−	0.179568i
$809$	12.8575	+	9.34149i	0.452044	+	0.328429i	0.790402	−	0.612588i	$-0.209872\pi$
$809$	12.8575	+	9.34149i	0.452044	+	0.328429i	−0.338358	+	0.941017i	$0.609872\pi$
$810$	19.6953	−	37.5194i	0.692021	−	1.31830i
$811$	−43.2957	+	14.0676i	−1.52032	+	0.493981i	−0.945866	−	0.324557i	$-0.894785\pi$
$811$	−43.2957	+	14.0676i	−1.52032	+	0.493981i	−0.574452	+	0.818538i	$0.694785\pi$
$812$	−2.92858	−	4.03085i	−0.102773	−	0.141455i
$813$	−38.7536	+	14.1633i	−1.35915	+	0.496729i
$814$	10.1566	−	3.31284i	0.355989	−	0.116115i
$815$		−	66.6221i		−	2.33367i
$816$	−14.4031	−	9.68728i	−0.504209	−	0.339123i
$817$	−5.98861	−	18.4310i	−0.209515	−	0.644820i
$818$	7.86648	+	2.55597i	0.275045	+	0.0893675i
$819$	−0.658510	+	0.0478001i	−0.0230102	+	0.00167027i
$820$	1.59502	−	2.19535i	0.0557004	−	0.0766650i
$821$	−13.5724	+	41.7715i	−0.473680	+	1.45784i	0.374051	+	0.927408i	$0.377969\pi$
$821$	−13.5724	+	41.7715i	−0.473680	+	1.45784i	−0.847730	+	0.530428i	$0.822031\pi$
$822$	23.5878	+	30.1087i	0.822718	+	1.05016i
$823$	−20.7867	+	15.1024i	−0.724579	+	0.526437i	−0.887844	−	0.460145i	$-0.847797\pi$
$823$	−20.7867	+	15.1024i	−0.724579	+	0.526437i	0.163265	+	0.986582i	$0.447797\pi$
$824$	−4.07902			−0.142099
$825$	−10.3648	+	15.4483i	−0.360856	+	0.537841i
$826$	23.6039			0.821286
$827$	37.7072	−	27.3959i	1.31121	−	0.952647i	0.311209	−	0.950341i	$-0.399266\pi$
$827$	37.7072	−	27.3959i	1.31121	−	0.952647i	0.999997	−	0.00230585i	$-0.000733974\pi$
$828$	−8.75745	+	14.0978i	−0.304343	+	0.489932i
$829$	−8.68518	+	26.7302i	−0.301649	+	0.928380i	0.679258	+	0.733900i	$0.262302\pi$
$829$	−8.68518	+	26.7302i	−0.301649	+	0.928380i	−0.980907	+	0.194480i	$0.937698\pi$
$830$	14.7547	−	20.3082i	0.512145	−	0.704907i
$831$	1.71047	+	0.488018i	0.0593354	+	0.0169292i
$832$	0.765546	+	0.248741i	0.0265405	+	0.00862355i
$833$	0.631436	+	1.94336i	0.0218780	+	0.0673334i
$834$	7.72668	−	11.4880i	0.267553	−	0.397799i
$835$		−	47.5965i		−	1.64714i
$836$	−5.48933	+	0.00623650i	−0.189853	+	0.000215694i
$837$	4.09437	+	2.34225i	0.141522	+	0.0809600i
$838$	11.2843	+	15.5314i	0.389808	+	0.536525i
$839$	6.47212	−	2.10292i	0.223443	−	0.0726009i	−0.195156	−	0.980772i	$-0.562521\pi$
$839$	6.47212	−	2.10292i	0.223443	−	0.0726009i	0.418599	+	0.908171i	$0.362521\pi$
$840$	10.6694	−	0.386727i	0.368129	−	0.0133434i
$841$	−18.6216	−	13.5294i	−0.642123	−	0.466529i
$842$	−12.0707	−	8.76984i	−0.415982	−	0.302229i
$843$	−11.9511	+	0.433184i	−0.411617	+	0.0149196i
$844$	−14.8545	+	4.82650i	−0.511311	+	0.166135i
$845$	21.8506	+	30.0747i	0.751682	+	1.03460i
$846$	−13.6998	−	16.2392i	−0.471008	−	0.558317i
$847$	−10.4693	−	3.37541i	−0.359730	−	0.115980i
$848$			51.1843i			1.75768i
$849$	0.531021	−	0.789523i	0.0182246	−	0.0270964i
$850$	−3.35430	−	10.3235i	−0.115052	−	0.354093i
$851$	−14.9555	−	4.85932i	−0.512666	−	0.166575i
$852$	−11.5028	−	3.28191i	−0.394080	−	0.112436i
$853$	6.58770	−	9.06718i	0.225558	−	0.310454i	−0.681206	−	0.732091i	$-0.738544\pi$
$853$	6.58770	−	9.06718i	0.225558	−	0.310454i	0.906765	+	0.421637i	$0.138544\pi$
$854$	6.07289	−	18.6904i	0.207810	−	0.639574i
$855$	−17.5242	−	10.8859i	−0.599317	−	0.372292i
$856$	10.9449	−	7.95193i	0.374089	−	0.271791i
$857$	12.1069			0.413562			0.206781	−	0.978387i	$-0.433701\pi$
$857$	12.1069			0.413562			0.206781	+	0.978387i	$0.433701\pi$
$858$	0.714098	+	1.94705i	0.0243789	+	0.0664712i
$859$	−13.3236			−0.454595			−0.227298	−	0.973825i	$-0.572989\pi$
$859$	−13.3236			−0.454595			−0.227298	+	0.973825i	$0.572989\pi$
$860$	−12.9756	+	9.42731i	−0.442464	+	0.321469i
$861$	1.46184	+	1.86597i	0.0498193	+	0.0635920i
$862$	11.7418	−	36.1375i	0.399927	−	1.23085i
$863$	−22.3070	+	30.7030i	−0.759340	+	1.04514i	0.237929	+	0.971283i	$0.423531\pi$
$863$	−22.3070	+	30.7030i	−0.759340	+	1.04514i	−0.997269	+	0.0738588i	$0.976469\pi$
$864$	7.99605	+	17.7691i	0.272031	+	0.604519i
$865$	−28.5880	−	9.28882i	−0.972023	−	0.315829i
$866$	19.4874	+	59.9761i	0.662210	+	2.03807i
$867$	18.4318	+	12.3969i	0.625976	+	0.421022i
$868$		−	0.627114i		−	0.0212857i
$869$	−28.3556	+	20.6508i	−0.961898	+	0.700531i
$870$	−55.2427	+	20.1896i	−1.87290	+	0.684491i
$871$	0.452878	+	0.623333i	0.0153452	+	0.0211208i
$872$	33.5357	−	10.8964i	1.13566	−	0.368999i
$873$	−7.90599	−	19.4198i	−0.267577	−	0.657261i
$874$	25.4618	+	18.4991i	0.861257	+	0.625740i
$875$	−4.09059	−	2.97198i	−0.138287	−	0.100471i
$876$	−0.330423	−	9.11601i	−0.0111640	−	0.308002i
$877$	5.97361	−	1.94094i	0.201715	−	0.0655410i	−0.206417	−	0.978464i	$-0.566180\pi$
$877$	5.97361	−	1.94094i	0.201715	−	0.0655410i	0.408132	+	0.912923i	$0.366180\pi$
$878$	−17.5432	−	24.1461i	−0.592053	−	0.814891i
$879$	0.431601	+	1.18095i	0.0145575	+	0.0398323i
$880$	−14.4778	−	44.3864i	−0.488046	−	1.49627i
$881$			49.3575i			1.66290i	0.555603	+	0.831448i	$0.312488\pi$
$881$			49.3575i			1.66290i	−0.555603	+	0.831448i	$0.687512\pi$
$882$	1.17788	−	4.77807i	0.0396612	−	0.160886i
$883$	10.6981	+	32.9253i	0.360019	+	1.10802i	0.953042	+	0.302839i	$0.0979343\pi$
$883$	10.6981	+	32.9253i	0.360019	+	1.10802i	−0.593023	+	0.805186i	$0.702066\pi$
$884$	−0.295461	−	0.0960009i	−0.00993741	−	0.00322886i
$885$	19.6269	−	68.7909i	0.659752	−	2.31238i
$886$	25.3774	−	34.9290i	0.852571	−	1.17346i
$887$	−11.7732	+	36.2343i	−0.395307	+	1.21663i	0.533416	+	0.845853i	$0.320908\pi$
$887$	−11.7732	+	36.2343i	−0.395307	+	1.21663i	−0.928722	+	0.370776i	$0.879092\pi$
$888$	−5.74975	+	4.50447i	−0.192949	+	0.151160i
$889$	−11.1215	+	8.08026i	−0.373004	+	0.271003i
$890$	80.2346			2.68947
$891$	13.8437	−	26.4452i	0.463783	−	0.885949i
$892$	5.79906			0.194167
$893$	−8.36822	+	6.07987i	−0.280032	+	0.203455i
$894$	−27.3247	+	21.4067i	−0.913874	+	0.715947i
$895$	8.21718	−	25.2899i	0.274670	−	0.845348i
$896$	−7.93484	+	10.9214i	−0.265084	+	0.364857i
$897$	0.837529	−	2.93547i	0.0279643	−	0.0980126i
$898$	−0.429715	−	0.139623i	−0.0143398	−	0.00465928i
$899$	−2.02321	−	6.22679i	−0.0674777	−	0.207675i
$900$	−1.60640	+	6.51637i	−0.0535465	+	0.217212i
$901$			21.3254i			0.710452i
$902$	4.36957	−	6.02859i	0.145491	−	0.200730i
$903$	−4.80920	−	13.1589i	−0.160040	−	0.437902i
$904$	7.98147	+	10.9856i	0.265460	+	0.365374i
$905$	48.0975	−	15.6278i	1.59882	−	0.519487i
$906$	1.66608	+	45.9654i	0.0553519	+	1.52710i
$907$	−29.3789	−	21.3450i	−0.975511	−	0.708750i	−0.0188099	−	0.999823i	$-0.505988\pi$
$907$	−29.3789	−	21.3450i	−0.975511	−	0.708750i	−0.956701	+	0.291073i	$0.905988\pi$
$908$	−12.2675	−	8.91287i	−0.407112	−	0.295784i
$909$	4.57409	+	11.2355i	0.151713	+	0.372659i
$910$	0.985491	−	0.320205i	0.0326687	−	0.0106147i
$911$	0.748051	+	1.02960i	0.0247840	+	0.0341123i	0.821229	−	0.570598i	$-0.193289\pi$
$911$	0.748051	+	1.02960i	0.0247840	+	0.0341123i	−0.796445	+	0.604711i	$0.793289\pi$
$912$	19.1154	−	6.98610i	0.632973	−	0.231333i
$913$	10.3773	−	14.3173i	0.343439	−	0.473834i
$914$		−	7.94341i		−	0.262745i
$915$	−49.4214	−	33.2400i	−1.63382	−	1.09888i
$916$	−1.35479	−	4.16962i	−0.0447635	−	0.137768i
$917$	−8.36316	−	2.71735i	−0.276176	−	0.0897350i
$918$	7.14724	+	15.8829i	0.235894	+	0.524213i
$919$	−5.06172	+	6.96686i	−0.166971	+	0.229815i	−0.884300	−	0.466918i	$-0.845364\pi$
$919$	−5.06172	+	6.96686i	−0.166971	+	0.229815i	0.717330	+	0.696734i	$0.245364\pi$
$920$	−15.2537	+	46.9460i	−0.502899	+	1.54776i
$921$	4.17770	+	5.33265i	0.137660	+	0.175717i
$922$	−34.8214	+	25.2992i	−1.14678	+	0.833185i
$923$	2.20017			0.0724195
$924$	−3.96568	+	0.148253i	−0.130461	+	0.00487718i
$925$	−6.35910			−0.209086
$926$	14.2515	−	10.3543i	0.468333	−	0.340264i
$927$	4.84029	+	3.00676i	0.158976	+	0.0987549i
$928$	8.35764	−	25.7222i	0.274353	−	0.844372i
$929$	16.8391	−	23.1771i	0.552474	−	0.760415i	−0.437871	−	0.899038i	$-0.644268\pi$
$929$	16.8391	−	23.1771i	0.552474	−	0.760415i	0.990345	+	0.138623i	$0.0442675\pi$
$930$	−7.11891	−	2.03112i	−0.233438	−	0.0666030i
$931$	−2.27859	−	0.740358i	−0.0746777	−	0.0242643i
$932$	1.30775	+	4.02483i	0.0428366	+	0.131838i
$933$	−23.1865	+	34.4737i	−0.759091	+	1.12862i
$934$			5.25767i			0.172036i
$935$	−6.03202	−	18.4931i	−0.197268	−	0.604790i
$936$	−0.914282	−	1.08376i	−0.0298842	−	0.0354237i
$937$	2.67017	+	3.67517i	0.0872305	+	0.120062i	0.850402	−	0.526134i	$-0.176359\pi$
$937$	2.67017	+	3.67517i	0.0872305	+	0.120062i	−0.763171	+	0.646196i	$0.776359\pi$
$938$	−5.46171	+	1.77462i	−0.178331	+	0.0579433i
$939$	−21.0773	+	0.763977i	−0.687831	+	0.0249314i
$940$	6.92563	+	5.03176i	0.225889	+	0.164118i
$941$	9.69130	+	7.04114i	0.315927	+	0.229535i	0.734436	−	0.678678i	$-0.237447\pi$
$941$	9.69130	+	7.04114i	0.315927	+	0.229535i	−0.418508	+	0.908213i	$0.637447\pi$
$942$	−23.9240	+	0.867159i	−0.779485	+	0.0282536i
$943$	−10.4231	+	3.38667i	−0.339422	+	0.110285i
$944$	41.4808	+	57.0935i	1.35009	+	1.85823i
$945$	−12.9457	−	7.40580i	−0.421124	−	0.240911i
$946$	−35.5730	+	25.9071i	−1.15658	+	0.842313i
$947$		−	18.8859i		−	0.613710i	−0.951756	−	0.306855i	$-0.900723\pi$
$947$		−	18.8859i		−	0.613710i	0.951756	−	0.306855i	$-0.0992767\pi$
$948$	−7.06279	+	10.5010i	−0.229389	+	0.341056i
$949$	0.518478	+	1.59571i	0.0168305	+	0.0517990i
$950$	12.1043	+	3.93292i	0.392715	+	0.127601i
$951$	−12.2172	−	3.48572i	−0.396169	−	0.113032i
$952$	−2.57933	+	3.55015i	−0.0835967	+	0.115061i
$953$	13.5555	−	41.7195i	0.439106	−	1.35143i	−0.449715	−	0.893172i	$-0.648474\pi$
$953$	13.5555	−	41.7195i	0.439106	−	1.35143i	0.888820	−	0.458256i	$-0.151526\pi$
$954$	27.1005	−	43.6265i	0.877411	−	1.41246i
$955$	8.91357	−	6.47609i	0.288436	−	0.209561i
$956$	−11.7061			−0.378601
$957$	−38.8980	+	14.2662i	−1.25739	+	0.461160i
$958$	−56.2864			−1.81853
$959$	10.8909	−	7.91272i	0.351686	−	0.255515i
$960$	11.2135	+	14.3135i	0.361915	+	0.461968i
$961$	−9.32487	+	28.6990i	−0.300802	+	0.925775i
$962$	−0.416685	+	0.573517i	−0.0134345	+	0.0184909i
$963$	−18.8491	+	1.36823i	−0.607405	+	0.0440905i
$964$	−18.6312	−	6.05364i	−0.600070	−	0.194975i
$965$	−9.65380	−	29.7113i	−0.310767	−	0.956442i
$966$	18.8796	+	12.6981i	0.607442	+	0.408556i
$967$			21.3303i			0.685936i	0.939347	+	0.342968i	$0.111432\pi$
$967$			21.3303i			0.685936i	−0.939347	+	0.342968i	$0.888568\pi$
$968$	−7.35093	−	22.4501i	−0.236268	−	0.721575i
$969$	7.96422	−	2.91069i	0.255848	−	0.0935047i
$970$	19.3422	+	26.6223i	0.621041	+	0.854790i
$971$	−17.4856	+	5.68143i	−0.561141	+	0.182326i	−0.575835	−	0.817566i	$-0.695323\pi$
$971$	−17.4856	+	5.68143i	−0.561141	+	0.182326i	0.0146935	+	0.999892i	$0.495323\pi$
$972$	1.42810	−	10.6737i	0.0458063	−	0.342358i
$973$	−3.94221	−	2.86418i	−0.126381	−	0.0918215i
$974$	11.5921	+	8.42217i	0.371435	+	0.269864i
$975$	−0.0447151	−	1.23364i	−0.00143203	−	0.0395082i
$976$	55.8809	−	18.1568i	1.78871	−	0.581186i
$977$	−14.5389	−	20.0111i	−0.465142	−	0.640213i	0.510423	−	0.859923i	$-0.329489\pi$
$977$	−14.5389	−	20.0111i	−0.465142	−	0.640213i	−0.975565	+	0.219710i	$0.929489\pi$
$978$	−22.6375	−	61.9406i	−0.723866	−	1.98064i
$979$	56.5189	−	0.0642118i	1.80635	−	0.00205222i
$980$			1.98283i			0.0633392i
$981$	−47.8266	−	11.7901i	−1.52699	−	0.376428i
$982$	0.0754190	+	0.232116i	0.00240672	+	0.00740712i
$983$	35.6117	+	11.5709i	1.13584	+	0.369056i	0.815791	−	0.578346i	$-0.196302\pi$
$983$	35.6117	+	11.5709i	1.13584	+	0.369056i	0.320045	+	0.947402i	$0.396302\pi$
$984$	−1.39666	+	4.89520i	−0.0445240	+	0.156053i
$985$	−24.3033	+	33.4506i	−0.774367	+	1.06582i
$986$	7.47044	−	22.9916i	0.237907	−	0.732203i
$987$	−5.88652	+	4.61162i	−0.187370	+	0.146790i
$988$	0.294689	−	0.214104i	0.00937530	−	0.00681155i
$989$	64.7758			2.05975
$990$	−11.1612	+	45.4980i	−0.354727	+	1.44602i
$991$	−13.8553			−0.440128			−0.220064	−	0.975485i	$-0.570627\pi$
$991$	−13.8553			−0.440128			−0.220064	+	0.975485i	$0.570627\pi$
$992$	2.75402	−	2.00091i	0.0874403	−	0.0635291i
$993$	−7.33156	+	5.74369i	−0.232660	+	0.182271i
$994$	−5.06755	+	15.5963i	−0.160733	+	0.494685i
$995$	−16.1502	+	22.2288i	−0.511996	+	0.704701i
$996$	1.75026	−	6.13451i	0.0554590	−	0.194379i
$997$	7.88343	+	2.56148i	0.249671	+	0.0811229i	0.431179	−	0.902267i	$-0.358098\pi$
$997$	7.88343	+	2.56148i	0.249671	+	0.0811229i	−0.181508	+	0.983389i	$0.558098\pi$
$998$	−8.17777	−	25.1686i	−0.258863	−	0.796698i
$999$	10.1432	−	1.10685i	0.320917	−	0.0350191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.18	yes	96
3.2	odd	2	inner	231.2.s.a.8.7	✓	96
11.7	odd	10	inner	231.2.s.a.29.7	yes	96
33.29	even	10	inner	231.2.s.a.29.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.7	✓	96	3.2	odd	2	inner
231.2.s.a.8.18	yes	96	1.1	even	1	trivial
231.2.s.a.29.7	yes	96	11.7	odd	10	inner
231.2.s.a.29.18	yes	96	33.29	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32709 - 0.964186i) q^{2} +(-1.36346 + 1.06816i) q^{3} +(0.213475 - 0.657007i) q^{4} +(-1.68710 + 2.32209i) q^{5} +(-0.779526 + 2.73218i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.663628 + 2.04244i) q^{8} +(0.718055 - 2.91280i) q^{9} +O(q^{10})\)	\(q+(1.32709 - 0.964186i) q^{2} +(-1.36346 + 1.06816i) q^{3} +(0.213475 - 0.657007i) q^{4} +(-1.68710 + 2.32209i) q^{5} +(-0.779526 + 2.73218i) q^{6} +(0.951057 + 0.309017i) q^{7} +(0.663628 + 2.04244i) q^{8} +(0.718055 - 2.91280i) q^{9} +4.70830i q^{10} +(0.00376805 + 3.31662i) q^{11} +(0.410727 + 1.12383i) q^{12} +(-0.129360 - 0.178049i) q^{13} +(1.56009 - 0.506903i) q^{14} +(-0.180079 - 4.96818i) q^{15} +(3.96775 + 2.88274i) q^{16} +(1.65312 + 1.20106i) q^{17} +(-1.85556 - 4.55788i) q^{18} +(-2.27859 + 0.740358i) q^{19} +(1.16548 + 1.60414i) q^{20} +(-1.62681 + 0.594551i) q^{21} +(3.20284 + 4.39782i) q^{22} -8.00809i q^{23} +(-3.08649 - 2.07592i) q^{24} +(-1.00072 - 3.07991i) q^{25} +(-0.343345 - 0.111560i) q^{26} +(2.13230 + 4.73849i) q^{27} +(0.406053 - 0.558884i) q^{28} +(2.22873 - 6.85932i) q^{29} +(-5.02923 - 6.41958i) q^{30} +(0.734413 - 0.533583i) q^{31} +3.74996 q^{32} +(-3.54783 - 4.51806i) q^{33} +3.35188 q^{34} +(-2.32209 + 1.68710i) q^{35} +(-1.76044 - 1.09358i) q^{36} +(0.606802 - 1.86754i) q^{37} +(-2.31005 + 3.17950i) q^{38} +(0.366563 + 0.104585i) q^{39} +(-5.86233 - 1.90479i) q^{40} +(-0.422906 - 1.30157i) q^{41} +(-1.58566 + 2.35757i) q^{42} +8.08879i q^{43} +(2.17985 + 0.705539i) q^{44} +(5.55235 + 6.58157i) q^{45} +(-7.72129 - 10.6274i) q^{46} +(4.10603 - 1.33413i) q^{47} +(-8.48911 + 0.307700i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-4.29765 - 3.12242i) q^{50} +(-3.53690 + 0.128200i) q^{51} +(-0.144595 + 0.0469817i) q^{52} +(6.13435 + 8.44321i) q^{53} +(7.39854 + 4.23246i) q^{54} +(-7.70786 - 5.58672i) q^{55} +2.14754i q^{56} +(2.31594 - 3.44335i) q^{57} +(-3.65594 - 11.2518i) q^{58} +(13.6851 + 4.44657i) q^{59} +(-3.30257 - 0.942267i) q^{60} +(7.04190 - 9.69234i) q^{61} +(0.460159 - 1.41622i) q^{62} +(1.58302 - 2.54835i) q^{63} +(-2.95897 + 2.14982i) q^{64} +0.631690 q^{65} +(-9.06454 - 2.57510i) q^{66} -3.50090 q^{67} +(1.14201 - 0.829716i) q^{68} +(8.55395 + 10.9187i) q^{69} +(-1.45494 + 4.47786i) q^{70} +(-5.87615 + 8.08782i) q^{71} +(6.42573 - 0.466432i) q^{72} +(-7.25057 - 2.35585i) q^{73} +(-0.995380 - 3.06346i) q^{74} +(4.65429 + 3.13040i) q^{75} +1.65510i q^{76} +(-1.02131 + 3.15546i) q^{77} +(0.587302 - 0.214641i) q^{78} +(6.21674 + 8.55660i) q^{79} +(-13.3880 + 4.35001i) q^{80} +(-7.96879 - 4.18310i) q^{81} +(-1.81619 - 1.31954i) q^{82} +(-4.31327 - 3.13378i) q^{83} +(0.0433416 + 1.19575i) q^{84} +(-5.57795 + 1.81239i) q^{85} +(7.79910 + 10.7345i) q^{86} +(4.28809 + 11.7331i) q^{87} +(-6.77149 + 2.20870i) q^{88} -17.0411i q^{89} +(13.7143 + 3.38082i) q^{90} +(-0.0680088 - 0.209309i) q^{91} +(-5.26137 - 1.70952i) q^{92} +(-0.431391 + 1.51199i) q^{93} +(4.16272 - 5.72949i) q^{94} +(2.12502 - 6.54015i) q^{95} +(-5.11293 + 4.00557i) q^{96} +(5.65434 - 4.10812i) q^{97} +1.64037 q^{98} +(9.66336 + 2.37054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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