LMFDB - Embedded newform 231.2.j.g.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.2
Root			$0.705143 - 0.512316i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.g.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.705143 - 0.512316i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.383276 - 1.17960i) q^{4} +(3.28814 - 2.38897i) q^{5} +(-0.705143 + 0.512316i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.872746 + 2.68604i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.54252 q^{10} +(-2.96738 + 1.48143i) q^{11} -1.24031 q^{12} +(4.92697 + 3.57965i) q^{13} +(-0.269341 + 0.828945i) q^{14} +(-1.25596 - 3.86544i) q^{15} +(-0.0153474 + 0.0111506i) q^{16} +(-1.37664 + 1.00019i) q^{17} +(0.269341 + 0.828945i) q^{18} +(1.68634 - 5.19003i) q^{19} +(-4.07830 - 2.96306i) q^{20} -1.00000 q^{21} +(2.85139 + 0.475616i) q^{22} -6.39153 q^{23} +(2.28488 + 1.66006i) q^{24} +(3.55958 - 10.9553i) q^{25} +(-1.64030 - 5.04833i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.00343 + 0.729034i) q^{28} +(1.46763 + 4.51690i) q^{29} +(-1.09470 + 3.36913i) q^{30} +(3.52981 + 2.56456i) q^{31} +5.66506 q^{32} +(0.491955 + 3.27994i) q^{33} +1.48314 q^{34} +(-3.28814 - 2.38897i) q^{35} +(-0.383276 + 1.17960i) q^{36} +(0.753854 + 2.32012i) q^{37} +(-3.84805 + 2.79577i) q^{38} +(4.92697 - 3.57965i) q^{39} +(3.54716 + 10.9170i) q^{40} +(-0.992058 + 3.05324i) q^{41} +(0.705143 + 0.512316i) q^{42} +0.127191 q^{43} +(2.88483 + 2.93253i) q^{44} -4.06436 q^{45} +(4.50694 + 3.27449i) q^{46} +(2.61671 - 8.05340i) q^{47} +(0.00586220 + 0.0180420i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.12258 + 5.90140i) q^{50} +(0.525831 + 1.61834i) q^{51} +(2.33417 - 7.18385i) q^{52} +(3.81374 + 2.77084i) q^{53} +0.871604 q^{54} +(-6.21806 + 11.9602i) q^{55} +2.82426 q^{56} +(-4.41490 - 3.20761i) q^{57} +(1.27919 - 3.93695i) q^{58} +(1.43188 + 4.40689i) q^{59} +(-4.07830 + 2.96306i) q^{60} +(-4.29654 + 3.12162i) q^{61} +(-1.17516 - 3.61676i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-3.96398 - 2.88000i) q^{64} +24.7522 q^{65} +(1.33347 - 2.56486i) q^{66} +14.0686 q^{67} +(1.70746 + 1.24054i) q^{68} +(-1.97509 + 6.07871i) q^{69} +(1.09470 + 3.36913i) q^{70} +(-1.79507 + 1.30420i) q^{71} +(2.28488 - 1.66006i) q^{72} +(-1.72244 - 5.30112i) q^{73} +(0.657063 - 2.02223i) q^{74} +(-9.31911 - 6.77073i) q^{75} -6.76849 q^{76} +(2.32590 + 2.36436i) q^{77} -5.30813 q^{78} +(-5.07362 - 3.68620i) q^{79} +(-0.0238261 + 0.0733293i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.26377 - 1.64472i) q^{82} +(0.103329 - 0.0750731i) q^{83} +(0.383276 + 1.17960i) q^{84} +(-2.13717 + 6.57753i) q^{85} +(-0.0896877 - 0.0651619i) q^{86} +4.74935 q^{87} +(-1.38941 - 9.26341i) q^{88} -8.12736 q^{89} +(2.86596 + 2.08224i) q^{90} +(1.88193 - 5.79200i) q^{91} +(2.44972 + 7.53946i) q^{92} +(3.52981 - 2.56456i) q^{93} +(-5.97104 + 4.33821i) q^{94} +(-6.85391 - 21.0942i) q^{95} +(1.75060 - 5.38780i) q^{96} +(2.10118 + 1.52660i) q^{97} +0.871604 q^{98} +(3.27143 + 0.545679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25}+ \cdots - q^{99}+O(q^{100}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.705143	−	0.512316i	−0.498611	−	0.362262i	0.309875	−	0.950777i	$-0.399713\pi$
$2$	−0.705143	−	0.512316i	−0.498611	−	0.362262i	−0.808486	+	0.588515i	$0.799713\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.383276	−	1.17960i	−0.191638	−	0.589800i
$5$	3.28814	−	2.38897i	1.47050	−	1.06838i	0.490033	−	0.871704i	$-0.336985\pi$
$5$	3.28814	−	2.38897i	1.47050	−	1.06838i	0.980468	−	0.196677i	$-0.0630151\pi$
$6$	−0.705143	+	0.512316i	−0.287873	+	0.209152i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.872746	+	2.68604i	−0.308562	+	0.949657i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−3.54252			−1.12024
$11$	−2.96738	+	1.48143i	−0.894699	+	0.446669i
$11$	−2.96738	+	1.48143i	−0.894699	+	0.446669i
$12$	−1.24031			−0.358045
$13$	4.92697	+	3.57965i	1.36649	+	0.992816i	0.998002	+	0.0631857i	$0.0201260\pi$
$13$	4.92697	+	3.57965i	1.36649	+	0.992816i	0.368493	+	0.929631i	$0.379874\pi$
$14$	−0.269341	+	0.828945i	−0.0719843	+	0.221545i
$15$	−1.25596	−	3.86544i	−0.324287	−	0.998052i
$16$	−0.0153474	+	0.0111506i	−0.00383686	+	0.00278764i
$17$	−1.37664	+	1.00019i	−0.333885	+	0.242582i	−0.742077	−	0.670314i	$-0.766159\pi$
$17$	−1.37664	+	1.00019i	−0.333885	+	0.242582i	0.408192	+	0.912896i	$0.366159\pi$
$18$	0.269341	+	0.828945i	0.0634842	+	0.195384i
$19$	1.68634	−	5.19003i	0.386873	−	1.19067i	−0.548239	−	0.836322i	$-0.684702\pi$
$19$	1.68634	−	5.19003i	0.386873	−	1.19067i	0.935112	−	0.354352i	$-0.115298\pi$
$20$	−4.07830	−	2.96306i	−0.911935	−	0.662560i
$21$	−1.00000			−0.218218
$22$	2.85139	+	0.475616i	0.607918	+	0.101402i
$23$	−6.39153			−1.33273			−0.666363	−	0.745627i	$-0.732150\pi$
$23$	−6.39153			−1.33273			−0.666363	+	0.745627i	$0.732150\pi$
$24$	2.28488	+	1.66006i	0.466399	+	0.338859i
$25$	3.55958	−	10.9553i	0.711917	−	2.19106i
$26$	−1.64030	−	5.04833i	−0.321690	−	0.990059i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.00343	+	0.729034i	−0.189630	+	0.137774i
$29$	1.46763	+	4.51690i	0.272532	+	0.838767i	0.989862	+	0.142033i	$0.0453640\pi$
$29$	1.46763	+	4.51690i	0.272532	+	0.838767i	−0.717330	+	0.696733i	$0.754636\pi$
$30$	−1.09470	+	3.36913i	−0.199864	+	0.615117i
$31$	3.52981	+	2.56456i	0.633973	+	0.460608i	0.857774	−	0.514026i	$-0.171847\pi$
$31$	3.52981	+	2.56456i	0.633973	+	0.460608i	−0.223801	+	0.974635i	$0.571847\pi$
$32$	5.66506			1.00145
$33$	0.491955	+	3.27994i	0.0856384	+	0.570964i
$34$	1.48314			0.254357
$35$	−3.28814	−	2.38897i	−0.555797	−	0.403810i
$36$	−0.383276	+	1.17960i	−0.0638793	+	0.196600i
$37$	0.753854	+	2.32012i	0.123933	+	0.381426i	0.993705	−	0.112027i	$-0.0357344\pi$
$37$	0.753854	+	2.32012i	0.123933	+	0.381426i	−0.869772	+	0.493453i	$0.835734\pi$
$38$	−3.84805	+	2.79577i	−0.624236	+	0.453534i
$39$	4.92697	−	3.57965i	0.788946	−	0.573203i
$40$	3.54716	+	10.9170i	0.560855	+	1.72613i
$41$	−0.992058	+	3.05324i	−0.154933	+	0.476836i	−0.998154	−	0.0607314i	$-0.980657\pi$
$41$	−0.992058	+	3.05324i	−0.154933	+	0.476836i	0.843221	+	0.537568i	$0.180657\pi$
$42$	0.705143	+	0.512316i	0.108806	+	0.0790521i
$43$	0.127191			0.0193964			0.00969821	−	0.999953i	$-0.496913\pi$
$43$	0.127191			0.0193964			0.00969821	+	0.999953i	$0.496913\pi$
$44$	2.88483	+	2.93253i	0.434904	+	0.442095i
$45$	−4.06436			−0.605880
$46$	4.50694	+	3.27449i	0.664512	+	0.482797i
$47$	2.61671	−	8.05340i	0.381686	−	1.17471i	−0.557170	−	0.830399i	$-0.688113\pi$
$47$	2.61671	−	8.05340i	0.381686	−	1.17471i	0.938856	−	0.344310i	$-0.111887\pi$
$48$	0.00586220	+	0.0180420i	0.000846136	+	0.00260414i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−8.12258	+	5.90140i	−1.14871	+	0.834584i
$51$	0.525831	+	1.61834i	0.0736311	+	0.226613i
$52$	2.33417	−	7.18385i	0.323692	−	0.996220i
$53$	3.81374	+	2.77084i	0.523857	+	0.380604i	0.818055	−	0.575140i	$-0.195052\pi$
$53$	3.81374	+	2.77084i	0.523857	+	0.380604i	−0.294198	+	0.955745i	$0.595052\pi$
$54$	0.871604			0.118610
$55$	−6.21806	+	11.9602i	−0.838443	+	1.61271i
$56$	2.82426			0.377408
$57$	−4.41490	−	3.20761i	−0.584768	−	0.424859i
$58$	1.27919	−	3.93695i	0.167966	−	0.516946i
$59$	1.43188	+	4.40689i	0.186416	+	0.573728i	0.999970	−	0.00776089i	$-0.00247039\pi$
$59$	1.43188	+	4.40689i	0.186416	+	0.573728i	−0.813554	+	0.581489i	$0.802470\pi$
$60$	−4.07830	+	2.96306i	−0.526506	+	0.382529i
$61$	−4.29654	+	3.12162i	−0.550115	+	0.399682i	−0.827828	−	0.560982i	$-0.810424\pi$
$61$	−4.29654	+	3.12162i	−0.550115	+	0.399682i	0.277713	+	0.960664i	$0.410424\pi$
$62$	−1.17516	−	3.61676i	−0.149245	−	0.459329i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−3.96398	−	2.88000i	−0.495498	−	0.360000i
$65$	24.7522			3.07014
$66$	1.33347	−	2.56486i	0.164138	−	0.315712i
$67$	14.0686			1.71876			0.859379	−	0.511340i	$-0.170851\pi$
$67$	14.0686			1.71876			0.859379	+	0.511340i	$0.170851\pi$
$68$	1.70746	+	1.24054i	0.207060	+	0.150438i
$69$	−1.97509	+	6.07871i	−0.237773	+	0.731790i
$70$	1.09470	+	3.36913i	0.130841	+	0.402689i
$71$	−1.79507	+	1.30420i	−0.213036	+	0.154780i	−0.689186	−	0.724584i	$-0.742032\pi$
$71$	−1.79507	+	1.30420i	−0.213036	+	0.154780i	0.476150	+	0.879364i	$0.342032\pi$
$72$	2.28488	−	1.66006i	0.269275	−	0.195640i
$73$	−1.72244	−	5.30112i	−0.201596	−	0.620449i	−0.999836	−	0.0181095i	$-0.994235\pi$
$73$	−1.72244	−	5.30112i	−0.201596	−	0.620449i	0.798240	−	0.602340i	$-0.205765\pi$
$74$	0.657063	−	2.02223i	0.0763820	−	0.235080i
$75$	−9.31911	−	6.77073i	−1.07608	−	0.781817i
$76$	−6.76849			−0.776400
$77$	2.32590	+	2.36436i	0.265061	+	0.269444i
$78$	−5.30813			−0.601027
$79$	−5.07362	−	3.68620i	−0.570827	−	0.414730i	0.264579	−	0.964364i	$-0.414767\pi$
$79$	−5.07362	−	3.68620i	−0.570827	−	0.414730i	−0.835406	+	0.549634i	$0.814767\pi$
$80$	−0.0238261	+	0.0733293i	−0.00266384	+	0.00819846i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.26377	−	1.64472i	0.249991	−	0.181629i
$83$	0.103329	−	0.0750731i	0.0113419	−	0.00824034i	−0.582100	−	0.813117i	$-0.697769\pi$
$83$	0.103329	−	0.0750731i	0.0113419	−	0.00824034i	0.593442	+	0.804877i	$0.297769\pi$
$84$	0.383276	+	1.17960i	0.0418188	+	0.128705i
$85$	−2.13717	+	6.57753i	−0.231809	+	0.713433i
$86$	−0.0896877	−	0.0651619i	−0.00967127	−	0.00702659i
$87$	4.74935			0.509183
$88$	−1.38941	−	9.26341i	−0.148112	−	0.987483i
$89$	−8.12736			−0.861498			−0.430749	−	0.902472i	$-0.641751\pi$
$89$	−8.12736			−0.861498			−0.430749	+	0.902472i	$0.641751\pi$
$90$	2.86596	+	2.08224i	0.302098	+	0.219487i
$91$	1.88193	−	5.79200i	0.197280	−	0.607166i
$92$	2.44972	+	7.53946i	0.255401	+	0.786043i
$93$	3.52981	−	2.56456i	0.366025	−	0.265932i
$94$	−5.97104	+	4.33821i	−0.615866	+	0.447453i
$95$	−6.85391	−	21.0942i	−0.703196	−	2.16422i
$96$	1.75060	−	5.38780i	0.178670	−	0.549890i
$97$	2.10118	+	1.52660i	0.213343	+	0.155003i	0.689325	−	0.724452i	$-0.257907\pi$
$97$	2.10118	+	1.52660i	0.213343	+	0.155003i	−0.475982	+	0.879455i	$0.657907\pi$
$98$	0.871604			0.0880453
$99$	3.27143	+	0.545679i	0.328791	+	0.0548428i
$100$	−14.2872			−1.42872
$101$	4.87492	+	3.54184i	0.485073	+	0.352426i	0.803286	−	0.595593i	$-0.203083\pi$
$101$	4.87492	+	3.54184i	0.485073	+	0.352426i	−0.318214	+	0.948019i	$0.603083\pi$
$102$	0.458317	−	1.41055i	0.0453801	−	0.139666i
$103$	3.98440	+	12.2627i	0.392595	+	1.20828i	0.930819	+	0.365481i	$0.119095\pi$
$103$	3.98440	+	12.2627i	0.392595	+	1.20828i	−0.538224	+	0.842802i	$0.680905\pi$
$104$	−13.9151	+	10.1099i	−1.36448	+	0.991355i
$105$	−3.28814	+	2.38897i	−0.320890	+	0.233140i
$106$	−1.26968	−	3.90768i	−0.123322	−	0.379547i
$107$	−1.65250	+	5.08587i	−0.159753	+	0.491669i	−0.998611	−	0.0526805i	$-0.983224\pi$
$107$	−1.65250	+	5.08587i	−0.159753	+	0.491669i	0.838858	+	0.544350i	$0.183224\pi$
$108$	1.00343	+	0.729034i	0.0965550	+	0.0701513i
$109$	−1.44173			−0.138093			−0.0690465	−	0.997613i	$-0.521996\pi$
$109$	−1.44173			−0.138093			−0.0690465	+	0.997613i	$0.521996\pi$
$110$	10.5120	−	5.24800i	1.00228	−	0.500377i
$111$	2.43952			0.231549
$112$	0.0153474	+	0.0111506i	0.00145020	+	0.00105363i
$113$	6.03121	−	18.5621i	0.567368	−	1.74618i	−0.0934402	−	0.995625i	$-0.529786\pi$
$113$	6.03121	−	18.5621i	0.567368	−	1.74618i	0.660808	−	0.750555i	$-0.270214\pi$
$114$	1.46982	+	4.52365i	0.137662	+	0.423679i
$115$	−21.0163	+	15.2692i	−1.95978	+	1.42386i
$116$	4.76563	−	3.46243i	0.442478	−	0.321479i
$117$	−1.88193	−	5.79200i	−0.173985	−	0.535470i
$118$	1.24804	−	3.84106i	0.114891	−	0.353598i
$119$	1.37664	+	1.00019i	0.126197	+	0.0916873i
$120$	11.4788			1.04787
$121$	6.61071	−	8.79196i	0.600974	−	0.799269i
$122$	4.62893			0.419083
$123$	2.59724	+	1.88701i	0.234185	+	0.170146i
$124$	1.67227	−	5.14670i	0.150174	−	0.462188i
$125$	−8.18766	−	25.1990i	−0.732327	−	2.25387i
$126$	0.705143	−	0.512316i	0.0628191	−	0.0456408i
$127$	0.519157	−	0.377189i	0.0460677	−	0.0334701i	−0.564513	−	0.825424i	$-0.690936\pi$
$127$	0.519157	−	0.377189i	0.0460677	−	0.0334701i	0.610581	+	0.791954i	$0.290936\pi$
$128$	−2.18150	−	6.71397i	−0.192819	−	0.593436i
$129$	0.0393041	−	0.120966i	0.00346053	−	0.0106504i
$130$	−17.4539	−	12.6810i	−1.53081	−	1.11220i
$131$	−13.9987			−1.22307			−0.611537	−	0.791216i	$-0.709448\pi$
$131$	−13.9987			−1.22307			−0.611537	+	0.791216i	$0.709448\pi$
$132$	3.68046	−	1.83743i	0.320343	−	0.159928i
$133$	−5.45712			−0.473192
$134$	−9.92039	−	7.20759i	−0.856992	−	0.622641i
$135$	−1.25596	+	3.86544i	−0.108096	+	0.332684i
$136$	−1.48509	−	4.57062i	−0.127345	−	0.391928i
$137$	2.18449	−	1.58712i	0.186633	−	0.135597i	−0.490545	−	0.871416i	$-0.663202\pi$
$137$	2.18449	−	1.58712i	0.186633	−	0.135597i	0.677179	+	0.735819i	$0.263202\pi$
$138$	4.50694	−	3.27449i	0.383656	−	0.278743i
$139$	−0.637168	−	1.96100i	−0.0540439	−	0.166330i	0.920391	−	0.390998i	$-0.127870\pi$
$139$	−0.637168	−	1.96100i	−0.0540439	−	0.166330i	−0.974435	+	0.224668i	$0.927870\pi$
$140$	−1.55777	+	4.79433i	−0.131656	+	0.405195i
$141$	−6.85063	−	4.97727i	−0.576927	−	0.419162i
$142$	1.93395			0.162293
$143$	−19.9232	−	3.32322i	−1.66606	−	0.277902i
$144$	0.0189705			0.00158087
$145$	15.6165	+	11.3461i	1.29688	+	0.942239i
$146$	−1.50128	+	4.62048i	−0.124247	+	0.382394i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	2.44789	−	1.77849i	0.201215	−	0.146191i
$149$	−8.15727	+	5.92661i	−0.668270	+	0.485526i	−0.869446	−	0.494029i	$-0.835524\pi$
$149$	−8.15727	+	5.92661i	−0.668270	+	0.485526i	0.201176	+	0.979555i	$0.435524\pi$
$150$	3.10255	+	9.54867i	0.253322	+	0.779645i
$151$	−4.62410	+	14.2315i	−0.376304	+	1.15815i	0.566290	+	0.824206i	$0.308378\pi$
$151$	−4.62410	+	14.2315i	−0.376304	+	1.15815i	−0.942595	+	0.333939i	$0.891622\pi$
$152$	12.4688	+	9.05915i	1.01136	+	0.734794i
$153$	1.70162			0.137568
$154$	−0.428790	−	2.85881i	−0.0345529	−	0.230369i
$155$	17.7332			1.42436
$156$	−6.11094	−	4.43986i	−0.489267	−	0.355473i
$157$	6.01162	−	18.5019i	0.479780	−	1.47661i	−0.359622	−	0.933098i	$-0.617094\pi$
$157$	6.01162	−	18.5019i	0.479780	−	1.47661i	0.839401	−	0.543512i	$-0.182906\pi$
$158$	1.68913	+	5.19860i	0.134380	+	0.413578i
$159$	3.81374	−	2.77084i	0.302449	−	0.219742i
$160$	18.6275	−	13.5337i	1.47264	−	1.06993i
$161$	1.97509	+	6.07871i	0.155659	+	0.479069i
$162$	0.269341	−	0.828945i	0.0211614	−	0.0651281i
$163$	−9.79754	−	7.11833i	−0.767403	−	0.557551i	0.133769	−	0.991013i	$-0.457292\pi$
$163$	−9.79754	−	7.11833i	−0.767403	−	0.557551i	−0.901172	+	0.433462i	$0.857292\pi$
$164$	3.98184			0.310929
$165$	9.45330	+	9.60962i	0.735938	+	0.748108i
$166$	−0.111323			−0.00864034
$167$	10.6531	+	7.73994i	0.824363	+	0.598935i	0.917959	−	0.396675i	$-0.129836\pi$
$167$	10.6531	+	7.73994i	0.824363	+	0.598935i	−0.0935958	+	0.995610i	$0.529836\pi$
$168$	0.872746	−	2.68604i	0.0673338	−	0.207232i
$169$	7.44388	+	22.9099i	0.572606	+	1.76230i
$170$	4.87678	−	3.54319i	0.374032	−	0.271750i
$171$	−4.41490	+	3.20761i	−0.337616	+	0.245292i
$172$	−0.0487491	−	0.150034i	−0.00371709	−	0.0114400i
$173$	−4.54809	+	13.9976i	−0.345785	+	1.06422i	0.615377	+	0.788233i	$0.289004\pi$
$173$	−4.54809	+	13.9976i	−0.345785	+	1.06422i	−0.961162	+	0.275984i	$0.910996\pi$
$174$	−3.34897	−	2.43317i	−0.253885	−	0.184458i
$175$	−11.5191			−0.870759
$176$	0.0290229	−	0.0558242i	0.00218768	−	0.00420791i
$177$	4.63368			0.348288
$178$	5.73095	+	4.16378i	0.429553	+	0.312088i
$179$	−3.61252	+	11.1182i	−0.270013	+	0.831014i	0.720483	+	0.693472i	$0.243920\pi$
$179$	−3.61252	+	11.1182i	−0.270013	+	0.831014i	−0.990496	+	0.137541i	$0.956080\pi$
$180$	1.55777	+	4.79433i	0.116109	+	0.357348i
$181$	−15.9378	+	11.5795i	−1.18465	+	0.860698i	−0.992689	−	0.120704i	$-0.961485\pi$
$181$	−15.9378	+	11.5795i	−1.18465	+	0.860698i	−0.191961	+	0.981403i	$0.561485\pi$
$182$	−4.29436	+	3.12004i	−0.318319	+	0.231273i
$183$	1.64113	+	5.05088i	0.121316	+	0.373372i
$184$	5.57818	−	17.1679i	0.411229	−	1.26563i
$185$	8.02149	+	5.82796i	0.589752	+	0.428480i
$186$	−3.80289			−0.278841
$187$	2.60331	−	5.00735i	0.190373	−	0.366174i
$188$	−10.5027			−0.765989
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	−5.97390	+	18.3858i	−0.433392	+	1.33384i
$191$	2.15136	+	6.62120i	0.155667	+	0.479093i	0.998228	−	0.0595077i	$-0.0189531\pi$
$191$	2.15136	+	6.62120i	0.155667	+	0.479093i	−0.842561	+	0.538601i	$0.818953\pi$
$192$	−3.96398	+	2.88000i	−0.286076	+	0.207846i
$193$	−13.6427	+	9.91199i	−0.982022	+	0.713481i	−0.958160	−	0.286234i	$-0.907596\pi$
$193$	−13.6427	+	9.91199i	−0.982022	+	0.713481i	−0.0238626	+	0.999715i	$0.507596\pi$
$194$	−0.699533	−	2.15294i	−0.0502235	−	0.154572i
$195$	7.64886	−	23.5408i	0.547747	−	1.68579i
$196$	1.00343	+	0.729034i	0.0716735	+	0.0520738i
$197$	6.42145			0.457510			0.228755	−	0.973484i	$-0.426535\pi$
$197$	6.42145			0.457510			0.228755	+	0.973484i	$0.426535\pi$
$198$	−2.02726	−	2.06079i	−0.144071	−	0.146454i
$199$	−13.2645			−0.940297			−0.470149	−	0.882587i	$-0.655800\pi$
$199$	−13.2645			−0.940297			−0.470149	+	0.882587i	$0.655800\pi$
$200$	26.3196	+	19.1223i	1.86108	+	1.35215i
$201$	4.34745	−	13.3801i	0.306645	−	0.943757i
$202$	−1.62297	−	4.99500i	−0.114192	−	0.351447i
$203$	3.84230	−	2.79160i	0.269677	−	0.195932i
$204$	1.70746	−	1.24054i	0.119546	−	0.0868553i
$205$	4.03209	+	12.4095i	0.281613	+	0.866716i
$206$	3.47282	−	10.6882i	0.241963	−	0.744685i
$207$	5.17086	+	3.75685i	0.359399	+	0.261119i
$208$	−0.115531			−0.00801067
$209$	2.68466	+	17.8990i	0.185702	+	1.23810i
$210$	3.54252			0.244457
$211$	−2.35552	−	1.71139i	−0.162161	−	0.117817i	0.503746	−	0.863852i	$-0.331955\pi$
$211$	−2.35552	−	1.71139i	−0.162161	−	0.117817i	−0.665906	+	0.746035i	$0.731955\pi$
$212$	1.80678	−	5.56068i	0.124090	−	0.381909i
$213$	0.685658	+	2.11024i	0.0469805	+	0.144591i
$214$	3.77082	−	2.73966i	0.257768	−	0.187279i
$215$	0.418221	−	0.303855i	0.0285224	−	0.0207228i
$216$	−0.872746	−	2.68604i	−0.0593828	−	0.182762i
$217$	1.34827	−	4.14954i	0.0915264	−	0.281689i
$218$	1.01663	+	0.738623i	0.0688547	+	0.0500259i
$219$	−5.57393			−0.376651
$220$	16.4914	+	2.75080i	1.11185	+	0.185459i
$221$	−10.3630			−0.697091
$222$	−1.72021	−	1.24981i	−0.115453	−	0.0838816i
$223$	−1.03697	+	3.19146i	−0.0694406	+	0.213716i	−0.979755	−	0.200202i	$-0.935840\pi$
$223$	−1.03697	+	3.19146i	−0.0694406	+	0.213716i	0.910314	+	0.413918i	$0.135840\pi$
$224$	−1.75060	−	5.38780i	−0.116967	−	0.359987i
$225$	−9.31911	+	6.77073i	−0.621274	+	0.451382i
$226$	−13.7625	+	9.99908i	−0.915471	+	0.665129i
$227$	1.03147	+	3.17454i	0.0684612	+	0.210702i	0.979434	−	0.201764i	$-0.0646675\pi$
$227$	1.03147	+	3.17454i	0.0684612	+	0.210702i	−0.910973	+	0.412466i	$0.864668\pi$
$228$	−2.09158	+	6.43722i	−0.138518	+	0.426315i
$229$	−5.50248	−	3.99778i	−0.363614	−	0.264181i	0.390944	−	0.920414i	$-0.372149\pi$
$229$	−5.50248	−	3.99778i	−0.363614	−	0.264181i	−0.754558	+	0.656234i	$0.772149\pi$
$230$	22.6421			1.49298
$231$	2.96738	−	1.48143i	0.195239	−	0.0974711i
$232$	−13.4134			−0.880634
$233$	−5.00420	−	3.63576i	−0.327836	−	0.238187i	0.411676	−	0.911330i	$-0.364944\pi$
$233$	−5.00420	−	3.63576i	−0.327836	−	0.238187i	−0.739512	+	0.673144i	$0.764944\pi$
$234$	−1.64030	+	5.04833i	−0.107230	+	0.330020i
$235$	−10.6353	−	32.7319i	−0.693767	−	2.13520i
$236$	4.64956	−	3.37811i	0.302661	−	0.219896i
$237$	−5.07362	+	3.68620i	−0.329567	+	0.239444i
$238$	−0.458317	−	1.41055i	−0.0297082	−	0.0914326i
$239$	6.32817	−	19.4761i	0.409335	−	1.25980i	−0.507885	−	0.861425i	$-0.669573\pi$
$239$	6.32817	−	19.4761i	0.409335	−	1.25980i	0.917220	−	0.398380i	$-0.130427\pi$
$240$	0.0623776	+	0.0453200i	0.00402646	+	0.00292539i
$241$	1.04113			0.0670653			0.0335326	−	0.999438i	$-0.489324\pi$
$241$	1.04113			0.0670653			0.0335326	+	0.999438i	$0.489324\pi$
$242$	−9.16576	+	2.81281i	−0.589197	+	0.180814i
$243$	1.00000			0.0641500
$244$	5.32902	+	3.87176i	0.341155	+	0.247864i
$245$	−1.25596	+	3.86544i	−0.0802402	+	0.246954i
$246$	−0.864682	−	2.66122i	−0.0551301	−	0.169673i
$247$	26.8870	−	19.5346i	1.71078	−	1.24295i
$248$	−9.96913	+	7.24299i	−0.633040	+	0.459931i
$249$	−0.0394683	−	0.121471i	−0.00250120	−	0.00769790i
$250$	−7.13640	+	21.9636i	−0.451346	+	1.38910i
$251$	−5.36621	−	3.89878i	−0.338712	−	0.246089i	0.405406	−	0.914137i	$-0.367130\pi$
$251$	−5.36621	−	3.89878i	−0.338712	−	0.246089i	−0.744118	+	0.668048i	$0.767130\pi$
$252$	1.24031			0.0781319
$253$	18.9661	−	9.46863i	1.19239	−	0.595287i
$254$	−0.559320			−0.0350948
$255$	5.59518	+	4.06514i	0.350384	+	0.254569i
$256$	−4.92962	+	15.1718i	−0.308101	+	0.948238i
$257$	0.890729	+	2.74138i	0.0555622	+	0.171003i	0.974986	−	0.222264i	$-0.0713448\pi$
$257$	0.890729	+	2.74138i	0.0555622	+	0.171003i	−0.919424	+	0.393267i	$0.871345\pi$
$258$	−0.0896877	+	0.0651619i	−0.00558371	+	0.00405680i
$259$	1.97362	−	1.43392i	0.122635	−	0.0890992i
$260$	−9.48693	−	29.1978i	−0.588354	−	1.81077i
$261$	1.46763	−	4.51690i	0.0908439	−	0.279589i
$262$	9.87109	+	7.17177i	0.609838	+	0.443073i
$263$	−21.1018			−1.30119			−0.650595	−	0.759425i	$-0.725480\pi$
$263$	−21.1018			−1.30119			−0.650595	+	0.759425i	$0.725480\pi$
$264$	−9.23938	−	1.54114i	−0.568644	−	0.0948507i
$265$	19.1596			1.17696
$266$	3.84805	+	2.79577i	0.235939	+	0.171420i
$267$	−2.51149	+	7.72958i	−0.153701	+	0.473042i
$268$	−5.39216	−	16.5954i	−0.329379	−	1.01372i
$269$	13.8597	−	10.0696i	0.845040	−	0.613957i	−0.0787342	−	0.996896i	$-0.525088\pi$
$269$	13.8597	−	10.0696i	0.845040	−	0.613957i	0.923774	+	0.382938i	$0.125088\pi$
$270$	2.86596	−	2.08224i	0.174417	−	0.126721i
$271$	5.05547	+	15.5591i	0.307098	+	0.945151i	0.978886	+	0.204407i	$0.0655266\pi$
$271$	5.05547	+	15.5591i	0.307098	+	0.945151i	−0.671788	+	0.740744i	$0.734473\pi$
$272$	0.00997527	−	0.0307007i	0.000604839	−	0.00186150i
$273$	−4.92697	−	3.57965i	−0.298194	−	0.216650i
$274$	−2.35348			−0.142179
$275$	5.66686	+	37.7818i	0.341725	+	2.27833i
$276$	7.92745			0.477177
$277$	2.00516	+	1.45684i	0.120479	+	0.0875329i	0.646393	−	0.763005i	$-0.276277\pi$
$277$	2.00516	+	1.45684i	0.120479	+	0.0875329i	−0.525914	+	0.850538i	$0.676277\pi$
$278$	−0.555358	+	1.70922i	−0.0333082	+	0.102512i
$279$	−1.34827	−	4.14954i	−0.0807187	−	0.248427i
$280$	9.28658	−	6.74709i	0.554979	−	0.403216i
$281$	−19.5740	+	14.2214i	−1.16769	+	0.848375i	−0.990730	−	0.135843i	$-0.956626\pi$
$281$	−19.5740	+	14.2214i	−1.16769	+	0.848375i	−0.176958	+	0.984218i	$0.556626\pi$
$282$	2.28073	+	7.01938i	0.135816	+	0.417998i
$283$	−9.01893	+	27.7574i	−0.536119	+	1.65001i	0.205098	+	0.978741i	$0.434249\pi$
$283$	−9.01893	+	27.7574i	−0.536119	+	1.65001i	−0.741218	+	0.671265i	$0.765751\pi$
$284$	2.22644	+	1.61760i	0.132115	+	0.0959872i
$285$	−22.1797			−1.31381
$286$	12.3462	+	12.5503i	0.730044	+	0.742116i
$287$	3.21037			0.189502
$288$	−4.58313	−	3.32984i	−0.270064	−	0.196213i
$289$	−4.35852	+	13.4142i	−0.256384	+	0.789068i
$290$	−5.19910	−	16.0012i	−0.305302	−	0.939622i
$291$	2.10118	−	1.52660i	0.123174	−	0.0894908i
$292$	−5.59304	+	4.06358i	−0.327308	+	0.237803i
$293$	−8.40272	−	25.8609i	−0.490892	−	1.51081i	−0.823262	−	0.567662i	$-0.807848\pi$
$293$	−8.40272	−	25.8609i	−0.490892	−	1.51081i	0.332369	−	0.943149i	$-0.392152\pi$
$294$	0.269341	−	0.828945i	0.0157083	−	0.0483451i
$295$	15.2362	+	11.0697i	0.887085	+	0.644505i
$296$	−6.88986			−0.400465
$297$	1.52990	−	2.94269i	0.0887737	−	0.170752i
$298$	8.78834			0.509095
$299$	−31.4909	−	22.8794i	−1.82116	−	1.32315i
$300$	−4.41497	+	13.5879i	−0.254899	+	0.784497i
$301$	−0.0393041	−	0.120966i	−0.00226545	−	0.00697234i
$302$	10.5517	−	7.66625i	0.607182	−	0.441143i
$303$	4.87492	−	3.54184i	0.280057	−	0.203473i
$304$	0.0319907	+	0.0984573i	0.00183479	+	0.00564691i
$305$	−6.67015	+	20.5286i	−0.381932	+	1.17547i
$306$	−1.19989	−	0.871770i	−0.0685931	−	0.0498358i
$307$	−9.95364			−0.568084			−0.284042	−	0.958812i	$-0.591676\pi$
$307$	−9.95364			−0.568084			−0.284042	+	0.958812i	$0.591676\pi$
$308$	1.89754	−	3.64983i	0.108122	−	0.207969i
$309$	12.8938			0.733502
$310$	−12.5044	−	9.08500i	−0.710204	−	0.515993i
$311$	5.01864	−	15.4458i	0.284581	−	0.875850i	−0.701943	−	0.712233i	$-0.747684\pi$
$311$	5.01864	−	15.4458i	0.284581	−	0.875850i	0.986524	−	0.163617i	$-0.0523161\pi$
$312$	5.31508	+	16.3581i	0.300907	+	0.926097i
$313$	−13.4417	+	9.76594i	−0.759768	+	0.552004i	−0.898839	−	0.438279i	$-0.855588\pi$
$313$	−13.4417	+	9.76594i	−0.759768	+	0.552004i	0.139071	+	0.990282i	$0.455588\pi$
$314$	−13.7179	+	9.96661i	−0.774144	+	0.562448i
$315$	1.25596	+	3.86544i	0.0707652	+	0.217793i
$316$	−2.40365	+	7.39768i	−0.135216	+	0.416152i
$317$	−6.55305	−	4.76107i	−0.368056	−	0.267408i	0.388348	−	0.921513i	$-0.373046\pi$
$317$	−6.55305	−	4.76107i	−0.368056	−	0.267408i	−0.756404	+	0.654104i	$0.773046\pi$
$318$	−4.10878			−0.230409
$319$	−11.0465	−	11.2292i	−0.618485	−	0.628713i
$320$	−19.9144			−1.11325
$321$	4.32630	+	3.14324i	0.241470	+	0.175438i
$322$	1.72150	−	5.29823i	0.0959354	−	0.295259i
$323$	2.86952	+	8.83148i	0.159664	+	0.491397i
$324$	1.00343	−	0.729034i	0.0557460	−	0.0405019i
$325$	56.7540	−	41.2342i	3.14815	−	2.28726i
$326$	3.26183	+	10.0389i	0.180656	+	0.556002i
$327$	−0.445520	+	1.37117i	−0.0246373	+	0.0758258i
$328$	−7.33530	−	5.32941i	−0.405024	−	0.294267i
$329$	−8.46784			−0.466847
$330$	−1.74276	−	11.6192i	−0.0959358	−	0.639618i
$331$	−6.64605			−0.365300			−0.182650	−	0.983178i	$-0.558468\pi$
$331$	−6.64605			−0.365300			−0.182650	+	0.983178i	$0.558468\pi$
$332$	−0.128160	−	0.0931136i	−0.00703369	−	0.00511027i
$333$	0.753854	−	2.32012i	0.0413110	−	0.127142i
$334$	−3.54667	−	10.9155i	−0.194065	−	0.597271i
$335$	46.2596	−	33.6096i	2.52743	−	1.83629i
$336$	0.0153474	−	0.0111506i	0.000837272	−	0.000608313i
$337$	−6.47454	−	19.9266i	−0.352691	−	1.08547i	−0.957336	−	0.288976i	$-0.906685\pi$
$337$	−6.47454	−	19.9266i	−0.352691	−	1.08547i	0.604646	−	0.796494i	$-0.293315\pi$
$338$	6.48811	−	19.9684i	0.352907	−	1.08614i
$339$	−15.7899	−	11.4720i	−0.857590	−	0.623075i
$340$	8.57798			0.465207
$341$	−14.2735	−	2.38084i	−0.772955	−	0.128930i
$342$	4.75645			0.257199
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−0.111005	+	0.341639i	−0.00598500	+	0.0184199i
$345$	8.02749	+	24.7061i	0.432186	+	1.33013i
$346$	10.3782	−	7.54023i	0.557938	−	0.405365i
$347$	14.3901	−	10.4550i	0.772500	−	0.561254i	−0.130219	−	0.991485i	$-0.541568\pi$
$347$	14.3901	−	10.4550i	0.772500	−	0.561254i	0.902719	+	0.430231i	$0.141568\pi$
$348$	−1.82031	−	5.60233i	−0.0975788	−	0.300317i
$349$	3.62603	−	11.1598i	0.194097	−	0.597368i	−0.805889	−	0.592066i	$-0.798312\pi$
$349$	3.62603	−	11.1598i	0.194097	−	0.597368i	0.999986	−	0.00530193i	$-0.00168767\pi$
$350$	8.12258	+	5.90140i	0.434170	+	0.315443i
$351$	−6.09006			−0.325064
$352$	−16.8104	+	8.39241i	−0.895998	+	0.447317i
$353$	15.2682			0.812642			0.406321	−	0.913730i	$-0.366811\pi$
$353$	15.2682			0.812642			0.406321	+	0.913730i	$0.366811\pi$
$354$	−3.26740	−	2.37391i	−0.173661	−	0.126172i
$355$	−2.78676	+	8.57677i	−0.147906	+	0.455208i
$356$	3.11502	+	9.58704i	0.165096	+	0.508112i
$357$	1.37664	−	1.00019i	0.0728597	−	0.0529357i
$358$	8.24338	−	5.98917i	0.435676	−	0.316537i
$359$	2.08338	+	6.41200i	0.109957	+	0.338412i	0.990862	−	0.134881i	$-0.0430651\pi$
$359$	2.08338	+	6.41200i	0.109957	+	0.338412i	−0.880905	+	0.473293i	$0.843065\pi$
$360$	3.54716	−	10.9170i	0.186952	−	0.575378i
$361$	−8.72130	−	6.33640i	−0.459016	−	0.333495i
$362$	17.1708			0.902478
$363$	−6.31882	−	9.00402i	−0.331652	−	0.472589i
$364$	−7.55354			−0.395913
$365$	−18.3279	−	13.3160i	−0.959324	−	0.696989i
$366$	1.43042	−	4.40237i	0.0747691	−	0.230116i
$367$	−6.48141	−	19.9477i	−0.338327	−	1.04126i	−0.965060	−	0.262029i	$-0.915608\pi$
$367$	−6.48141	−	19.9477i	−0.338327	−	1.04126i	0.626733	−	0.779234i	$-0.284392\pi$
$368$	0.0980937	−	0.0712692i	0.00511349	−	0.00371516i
$369$	2.59724	−	1.88701i	0.135207	−	0.0982337i
$370$	−2.67054	−	8.21908i	−0.138835	−	0.427290i
$371$	1.45672	−	4.48332i	0.0756290	−	0.232762i
$372$	−4.37805	−	3.18084i	−0.226991	−	0.164919i
$373$	29.1253			1.50805			0.754027	−	0.656844i	$-0.228109\pi$
$373$	29.1253			1.50805			0.754027	+	0.656844i	$0.228109\pi$
$374$	−4.40105	+	2.19718i	−0.227573	+	0.113613i
$375$	−26.4958			−1.36824
$376$	19.3480	+	14.0571i	0.997796	+	0.724942i
$377$	−8.93795	+	27.5082i	−0.460328	+	1.41674i
$378$	−0.269341	−	0.828945i	−0.0138534	−	0.0426363i
$379$	−25.8362	+	18.7711i	−1.32712	+	0.964207i	−0.327303	+	0.944919i	$0.606140\pi$
$379$	−25.8362	+	18.7711i	−1.32712	+	0.964207i	−0.999814	+	0.0192874i	$0.993860\pi$
$380$	−22.2558	+	16.1698i	−1.14170	+	0.829491i
$381$	−0.198300	−	0.610305i	−0.0101592	−	0.0312669i
$382$	1.87513	−	5.77107i	0.0959402	−	0.295273i
$383$	−2.90411	−	2.10996i	−0.148393	−	0.107814i	0.511111	−	0.859514i	$-0.329234\pi$
$383$	−2.90411	−	2.10996i	−0.148393	−	0.107814i	−0.659505	+	0.751700i	$0.729234\pi$
$384$	−7.05948			−0.360253
$385$	13.2963	+	2.21784i	0.677641	+	0.113031i
$386$	14.6981			0.748115
$387$	−0.102900	−	0.0747609i	−0.00523068	−	0.00380031i
$388$	0.995445	−	3.06367i	0.0505361	−	0.155534i
$389$	3.23572	+	9.95853i	0.164058	+	0.504917i	0.998966	−	0.0454722i	$-0.0144792\pi$
$389$	3.23572	+	9.95853i	0.164058	+	0.504917i	−0.834908	+	0.550389i	$0.814479\pi$
$390$	−17.4539	+	12.6810i	−0.883811	+	0.642126i
$391$	8.79886	−	6.39275i	0.444977	−	0.323295i
$392$	−0.872746	−	2.68604i	−0.0440803	−	0.135665i
$393$	−4.32584	+	13.3136i	−0.218210	+	0.671581i
$394$	−4.52804	−	3.28981i	−0.228119	−	0.165738i
$395$	−25.4890			−1.28249
$396$	−0.610175	−	4.06812i	−0.0306624	−	0.204431i
$397$	17.7269			0.889686			0.444843	−	0.895609i	$-0.353259\pi$
$397$	17.7269			0.889686			0.444843	+	0.895609i	$0.353259\pi$
$398$	9.35338	+	6.79563i	0.468843	+	0.340634i
$399$	−1.68634	+	5.19003i	−0.0844227	+	0.259826i
$400$	0.0675270	+	0.207827i	0.00337635	+	0.0103913i
$401$	−6.53714	+	4.74951i	−0.326449	+	0.237179i	−0.738922	−	0.673791i	$-0.764665\pi$
$401$	−6.53714	+	4.74951i	−0.326449	+	0.237179i	0.412473	+	0.910970i	$0.364665\pi$
$402$	−9.92039	+	7.20759i	−0.494784	+	0.359482i
$403$	8.21104	+	25.2710i	0.409021	+	1.25884i
$404$	2.30952	−	7.10796i	0.114903	−	0.353634i
$405$	3.28814	+	2.38897i	0.163389	+	0.118709i
$406$	−4.13955			−0.205442
$407$	−5.67408	−	5.76791i	−0.281254	−	0.285905i
$408$	−4.80584			−0.237924
$409$	−32.1090	−	23.3286i	−1.58769	−	1.15352i	−0.907148	−	0.420811i	$-0.861746\pi$
$409$	−32.1090	−	23.3286i	−1.58769	−	1.15352i	−0.680539	−	0.732712i	$-0.738254\pi$
$410$	3.51438	−	10.8162i	0.173563	−	0.534172i
$411$	−0.834399	−	2.56802i	−0.0411579	−	0.126671i
$412$	12.9380	−	9.40001i	0.637409	−	0.463105i
$413$	3.74872	−	2.72361i	0.184463	−	0.134020i
$414$	−1.72150	−	5.29823i	−0.0846070	−	0.260394i
$415$	0.160413	−	0.493702i	0.00787438	−	0.0242349i
$416$	27.9116	+	20.2789i	1.36848	+	0.994257i
$417$	−2.06192			−0.100973
$418$	7.27688	−	13.9967i	0.355924	−	0.684603i
$419$	16.1715			0.790028			0.395014	−	0.918675i	$-0.370740\pi$
$419$	16.1715			0.790028			0.395014	+	0.918675i	$0.370740\pi$
$420$	4.07830	+	2.96306i	0.199001	+	0.144582i
$421$	7.66622	−	23.5942i	0.373629	−	1.14991i	−0.570770	−	0.821110i	$-0.693355\pi$
$421$	7.66622	−	23.5942i	0.373629	−	1.14991i	0.944399	−	0.328802i	$-0.106645\pi$
$422$	0.784207	+	2.41354i	0.0381746	+	0.117489i
$423$	−6.85063	+	4.97727i	−0.333089	+	0.242003i
$424$	−10.7710	+	7.82559i	−0.523086	+	0.380044i
$425$	6.05708	+	18.6418i	0.293811	+	0.904259i
$426$	0.597622	−	1.83929i	0.0289549	−	0.0891140i
$427$	4.29654	+	3.12162i	0.207924	+	0.151066i
$428$	6.63265			0.320601
$429$	−9.31718	+	17.9212i	−0.449838	+	0.865242i
$430$	−0.450576			−0.0217287
$431$	−17.7030	−	12.8620i	−0.852724	−	0.619540i	0.0731719	−	0.997319i	$-0.476688\pi$
$431$	−17.7030	−	12.8620i	−0.852724	−	0.619540i	−0.925896	+	0.377779i	$0.876688\pi$
$432$	0.00586220	−	0.0180420i	0.000282045	−	0.000868046i
$433$	12.1579	+	37.4183i	0.584273	+	1.79821i	0.602170	+	0.798368i	$0.294303\pi$
$433$	12.1579	+	37.4183i	0.584273	+	1.79821i	−0.0178973	+	0.999840i	$0.505697\pi$
$434$	−3.07660	+	2.23528i	−0.147682	+	0.107297i
$435$	15.6165	−	11.3461i	0.748755	−	0.544002i
$436$	0.552581	+	1.70067i	0.0264638	+	0.0814473i
$437$	−10.7783	+	33.1722i	−0.515596	+	1.58684i
$438$	3.93041	+	2.85561i	0.187802	+	0.136446i
$439$	9.59194			0.457799			0.228899	−	0.973450i	$-0.426487\pi$
$439$	9.59194			0.457799			0.228899	+	0.973450i	$0.426487\pi$
$440$	−26.6986	−	27.1401i	−1.27281	−	1.29385i
$441$	1.00000			0.0476190
$442$	7.30740	+	5.30914i	0.347577	+	0.252530i
$443$	−0.194414	+	0.598344i	−0.00923687	+	0.0284282i	−0.955569	−	0.294768i	$-0.904758\pi$
$443$	−0.194414	+	0.598344i	−0.00923687	+	0.0284282i	0.946332	+	0.323197i	$0.104758\pi$
$444$	−0.935010	−	2.87766i	−0.0443736	−	0.136568i
$445$	−26.7239	+	19.4160i	−1.26683	+	0.920409i
$446$	2.36625	−	1.71918i	0.112045	−	0.0814055i
$447$	3.11580	+	9.58945i	0.147372	+	0.453565i
$448$	−1.51411	+	4.65994i	−0.0715348	+	0.220162i
$449$	14.0254	+	10.1901i	0.661900	+	0.480899i	0.867304	−	0.497779i	$-0.165851\pi$
$449$	14.0254	+	10.1901i	0.661900	+	0.480899i	−0.205404	+	0.978677i	$0.565851\pi$
$450$	10.0401			0.473293
$451$	−1.57936	−	10.5298i	−0.0743690	−	0.495829i
$452$	−24.2075			−1.13863
$453$	12.1061	+	8.79557i	0.568792	+	0.413252i
$454$	0.899035	−	2.76695i	0.0421938	−	0.129859i
$455$	−7.64886	−	23.5408i	−0.358584	−	1.10361i
$456$	12.4688	−	9.05915i	0.583907	−	0.424233i
$457$	23.5549	−	17.1136i	1.10185	−	0.800541i	0.120489	−	0.992715i	$-0.461554\pi$
$457$	23.5549	−	17.1136i	1.10185	−	0.800541i	0.981361	+	0.192174i	$0.0615539\pi$
$458$	1.83190	+	5.63801i	0.0855991	+	0.263447i
$459$	0.525831	−	1.61834i	0.0245437	−	0.0755377i
$460$	26.0666	+	18.9385i	1.21536	+	0.883011i
$461$	15.1850			0.707236			0.353618	−	0.935390i	$-0.384951\pi$
$461$	15.1850			0.707236			0.353618	+	0.935390i	$0.384951\pi$
$462$	−2.85139	−	0.475616i	−0.132659	−	0.0221277i
$463$	17.8886			0.831355			0.415677	−	0.909512i	$-0.363545\pi$
$463$	17.8886			0.831355			0.415677	+	0.909512i	$0.363545\pi$
$464$	−0.0728903	−	0.0529579i	−0.00338385	−	0.00245851i
$465$	5.47985	−	16.8653i	0.254122	−	0.782108i
$466$	1.66601	+	5.12747i	0.0771766	+	0.237525i
$467$	24.5214	−	17.8158i	1.13472	−	0.824419i	0.148341	−	0.988936i	$-0.452607\pi$
$467$	24.5214	−	17.8158i	1.13472	−	0.824419i	0.986374	+	0.164517i	$0.0526067\pi$
$468$	−6.11094	+	4.43986i	−0.282479	+	0.205233i
$469$	−4.34745	−	13.3801i	−0.200746	−	0.617834i
$470$	−9.26973	+	28.5293i	−0.427581	+	1.31596i
$471$	−15.7386	−	11.4348i	−0.725198	−	0.526887i
$472$	−13.0867			−0.602366
$473$	−0.377424	+	0.188425i	−0.0173540	+	0.00866377i
$474$	5.46613			0.251068
$475$	−50.8555	−	36.9487i	−2.33341	−	1.69532i
$476$	0.652191	−	2.00724i	0.0298931	−	0.0920016i
$477$	−1.45672	−	4.48332i	−0.0666985	−	0.205277i
$478$	−14.4402	+	10.4914i	−0.660479	+	0.479866i
$479$	6.42966	−	4.67142i	0.293779	−	0.213443i	−0.431126	−	0.902292i	$-0.641884\pi$
$479$	6.42966	−	4.67142i	0.293779	−	0.213443i	0.724905	+	0.688849i	$0.241884\pi$
$480$	−7.11508	−	21.8980i	−0.324758	−	0.999501i
$481$	−4.59102	+	14.1297i	−0.209333	+	0.644259i
$482$	−0.734147	−	0.533389i	−0.0334395	−	0.0242952i
$483$	6.39153			0.290825
$484$	−12.9047	−	4.42826i	−0.586578	−	0.201285i
$485$	10.5560			0.479323
$486$	−0.705143	−	0.512316i	−0.0319859	−	0.0232391i
$487$	−3.14304	+	9.67329i	−0.142425	+	0.438338i	−0.996671	−	0.0815305i	$-0.974019\pi$
$487$	−3.14304	+	9.67329i	−0.142425	+	0.438338i	0.854246	+	0.519869i	$0.174019\pi$
$488$	−4.63499	−	14.2650i	−0.209816	−	0.645747i
$489$	−9.79754	+	7.11833i	−0.443060	+	0.321902i
$490$	2.86596	−	2.08224i	0.129471	−	0.0940660i
$491$	0.332923	+	1.02463i	0.0150246	+	0.0462409i	0.958288	−	0.285805i	$-0.0922610\pi$
$491$	0.332923	+	1.02463i	0.0150246	+	0.0462409i	−0.943263	+	0.332046i	$0.892261\pi$
$492$	1.23046	−	3.78695i	0.0554732	−	0.170729i
$493$	−6.53816	−	4.75025i	−0.294464	−	0.213940i
$494$	−28.9671			−1.30329
$495$	12.0605	−	6.02108i	0.542080	−	0.270628i
$496$	−0.0827699			−0.00371648
$497$	1.79507	+	1.30420i	0.0805201	+	0.0585013i
$498$	−0.0344007	+	0.105874i	−0.00154153	+	0.00474435i
$499$	10.6969	+	32.9217i	0.478859	+	1.47378i	0.840682	+	0.541530i	$0.182155\pi$
$499$	10.6969	+	32.9217i	0.478859	+	1.47378i	−0.361823	+	0.932247i	$0.617845\pi$
$500$	−26.5867	+	19.3163i	−1.18899	+	0.863853i
$501$	10.6531	−	7.73994i	0.475946	−	0.345795i
$502$	1.78654	+	5.49840i	0.0797371	+	0.245405i
$503$	0.852636	−	2.62414i	0.0380172	−	0.117005i	−0.930247	−	0.366934i	$-0.880407\pi$
$503$	0.852636	−	2.62414i	0.0380172	−	0.117005i	0.968264	+	0.249929i	$0.0804074\pi$
$504$	−2.28488	−	1.66006i	−0.101777	−	0.0739450i
$505$	24.4908			1.08982
$506$	−18.2247	−	3.03991i	−0.810189	−	0.135141i
$507$	24.0889			1.06983
$508$	−0.643913	−	0.467830i	−0.0285690	−	0.0207566i
$509$	4.50899	−	13.8773i	0.199858	−	0.615099i	−0.800028	−	0.599963i	$-0.795182\pi$
$509$	4.50899	−	13.8773i	0.199858	−	0.615099i	0.999885	−	0.0151357i	$-0.00481803\pi$
$510$	−1.86277	−	5.73300i	−0.0824846	−	0.253862i
$511$	−4.50940	+	3.27627i	−0.199484	+	0.144934i
$512$	−0.173635	+	0.126153i	−0.00767364	+	0.00557523i
$513$	1.68634	+	5.19003i	0.0744538	+	0.229145i
$514$	0.776364	−	2.38940i	0.0342439	−	0.105392i
$515$	42.3966	+	30.8029i	1.86822	+	1.35734i
$516$	−0.157755			−0.00694480
$517$	4.16580	+	27.7740i	0.183212	+	1.22150i
$518$	−2.12630			−0.0934242
$519$	11.9071	+	8.65098i	0.522662	+	0.379736i
$520$	−21.6024	+	66.4854i	−0.947329	+	2.91558i
$521$	−4.24334	−	13.0597i	−0.185904	−	0.572154i	0.814059	−	0.580783i	$-0.197253\pi$
$521$	−4.24334	−	13.0597i	−0.185904	−	0.572154i	−0.999963	+	0.00862850i	$0.997253\pi$
$522$	−3.34897	+	2.43317i	−0.146580	+	0.106497i
$523$	−6.10491	+	4.43548i	−0.266949	+	0.193950i	−0.713205	−	0.700956i	$-0.752757\pi$
$523$	−6.10491	+	4.43548i	−0.266949	+	0.193950i	0.446256	+	0.894905i	$0.352757\pi$
$524$	5.36537	+	16.5129i	0.234387	+	0.721369i
$525$	−3.55958	+	10.9553i	−0.155353	+	0.478127i
$526$	14.8798	+	10.8108i	0.648788	+	0.471372i
$527$	−7.42434			−0.323409
$528$	−0.0441234	−	0.0448530i	−0.00192022	−	0.00195198i
$529$	17.8517			0.776160
$530$	−13.5102	−	9.81576i	−0.586847	−	0.426369i
$531$	1.43188	−	4.40689i	0.0621385	−	0.191243i
$532$	2.09158	+	6.43722i	0.0906815	+	0.279089i
$533$	−15.8174	+	11.4920i	−0.685126	+	0.497774i
$534$	5.73095	−	4.16378i	0.248002	−	0.180184i
$535$	6.71635	+	20.6708i	0.290373	+	0.893677i
$536$	−12.2783	+	37.7888i	−0.530344	+	1.63223i
$537$	9.45771	+	6.87143i	0.408130	+	0.296524i
$538$	−14.9319			−0.643760
$539$	1.52990	−	2.94269i	0.0658974	−	0.126751i
$540$	5.04106			0.216932
$541$	1.63162	+	1.18544i	0.0701486	+	0.0509659i	0.622307	−	0.782773i	$-0.286196\pi$
$541$	1.63162	+	1.18544i	0.0701486	+	0.0509659i	−0.552158	+	0.833739i	$0.686196\pi$
$542$	4.40637	−	13.5614i	0.189270	−	0.582513i
$543$	6.08771	+	18.7360i	0.261249	+	0.804041i
$544$	−7.79877	+	5.66614i	−0.334370	+	0.242934i
$545$	−4.74062	+	3.44426i	−0.203066	+	0.147536i
$546$	1.64030	+	5.04833i	0.0701984	+	0.216049i
$547$	12.7165	−	39.1373i	0.543718	−	1.67339i	−0.180301	−	0.983612i	$-0.557707\pi$
$547$	12.7165	−	39.1373i	0.543718	−	1.67339i	0.724019	−	0.689780i	$-0.242293\pi$
$548$	−2.70943	−	1.96852i	−0.115741	−	0.0840908i
$549$	5.31081			0.226660
$550$	15.3603	−	29.5448i	0.654964	−	1.25979i
$551$	25.9177			1.10413
$552$	−14.6039	−	10.6103i	−0.621582	−	0.451606i
$553$	−1.93795	+	5.96440i	−0.0824100	+	0.253632i
$554$	−0.667566	−	2.05456i	−0.0283622	−	0.0872897i
$555$	8.02149	−	5.82796i	0.340493	−	0.247383i
$556$	−2.06899	+	1.50321i	−0.0877446	+	0.0637502i
$557$	−5.70473	−	17.5574i	−0.241717	−	0.743930i	−0.996159	−	0.0875624i	$-0.972092\pi$
$557$	−5.70473	−	17.5574i	−0.241717	−	0.743930i	0.754442	−	0.656367i	$-0.227908\pi$
$558$	−1.17516	+	3.61676i	−0.0497483	+	0.153110i
$559$	0.626665	+	0.455299i	0.0265051	+	0.0192571i
$560$	0.0771030			0.00325819
$561$	−3.95781	−	4.02325i	−0.167099	−	0.169862i
$562$	21.0883			0.889557
$563$	23.0694	+	16.7609i	0.972260	+	0.706388i	0.955966	−	0.293479i	$-0.0948131\pi$
$563$	23.0694	+	16.7609i	0.972260	+	0.706388i	0.0162945	+	0.999867i	$0.494813\pi$
$564$	−3.24552	+	9.98868i	−0.136661	+	0.420599i
$565$	−24.5130	−	75.4433i	−1.03127	−	3.17392i
$566$	20.5802	−	14.9524i	0.865050	−	0.628496i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−1.93648	−	5.95987i	−0.0812528	−	0.250070i
$569$	5.48146	−	16.8702i	0.229795	−	0.707235i	−0.767975	−	0.640480i	$-0.778735\pi$
$569$	5.48146	−	16.8702i	0.229795	−	0.707235i	0.997769	−	0.0667550i	$-0.0212646\pi$
$570$	15.6399	+	11.3630i	0.655082	+	0.475945i
$571$	−20.8488			−0.872496			−0.436248	−	0.899827i	$-0.643693\pi$
$571$	−20.8488			−0.872496			−0.436248	+	0.899827i	$0.643693\pi$
$572$	3.71600	+	24.7751i	0.155374	+	1.03590i
$573$	6.96194			0.290839
$574$	−2.26377	−	1.64472i	−0.0944878	−	0.0686494i
$575$	−22.7512	+	70.0210i	−0.948791	+	2.92008i
$576$	1.51411	+	4.65994i	0.0630878	+	0.194164i
$577$	−17.2311	+	12.5191i	−0.717339	+	0.521178i	−0.885533	−	0.464576i	$-0.846207\pi$
$577$	−17.2311	+	12.5191i	−0.717339	+	0.521178i	0.168194	+	0.985754i	$0.446207\pi$
$578$	9.94567	−	7.22595i	0.413685	−	0.300560i
$579$	5.21104	+	16.0379i	0.216564	+	0.666514i
$580$	7.39840	−	22.7699i	0.307202	−	0.945470i
$581$	−0.103329	−	0.0750731i	−0.00428682	−	0.00311456i
$582$	−2.26374			−0.0938349
$583$	−15.4216	−	2.57235i	−0.638699	−	0.106536i
$584$	15.7422			0.651419
$585$	−20.0250	−	14.5490i	−0.827931	−	0.601527i
$586$	−7.32385	+	22.5405i	−0.302545	+	0.931139i
$587$	9.01940	+	27.7589i	0.372271	+	1.14573i	0.945302	+	0.326197i	$0.105767\pi$
$587$	9.01940	+	27.7589i	0.372271	+	1.14573i	−0.573031	+	0.819534i	$0.694233\pi$
$588$	1.00343	−	0.729034i	0.0413807	−	0.0300648i
$589$	19.2626	−	13.9951i	0.793702	−	0.576658i
$590$	−5.07248	−	15.6115i	−0.208831	−	0.642714i
$591$	1.98434	−	6.10717i	0.0816248	−	0.251215i
$592$	−0.0374404	−	0.0272021i	−0.00153879	−	0.00111800i
$593$	−37.3094			−1.53212			−0.766058	−	0.642772i	$-0.777784\pi$
$593$	−37.3094			−1.53212			−0.766058	+	0.642772i	$0.777784\pi$
$594$	−2.58638	+	1.29122i	−0.106121	+	0.0529795i
$595$	6.91602			0.283529
$596$	10.1175	+	7.35080i	0.414430	+	0.301101i
$597$	−4.09896	+	12.6153i	−0.167759	+	0.516310i
$598$	10.4840	+	32.2666i	0.428724	+	1.31948i
$599$	4.00761	−	2.91170i	0.163747	−	0.118969i	−0.502894	−	0.864348i	$-0.667731\pi$
$599$	4.00761	−	2.91170i	0.163747	−	0.118969i	0.666641	+	0.745379i	$0.267731\pi$
$600$	26.3196	−	19.1223i	1.07450	−	0.780666i
$601$	9.10277	+	28.0155i	0.371310	+	1.14277i	0.945935	+	0.324357i	$0.105148\pi$
$601$	9.10277	+	28.0155i	0.371310	+	1.14277i	−0.574625	+	0.818417i	$0.694852\pi$
$602$	−0.0342576	+	0.105434i	−0.00139624	+	0.00429718i
$603$	−11.3818	−	8.26933i	−0.463501	−	0.336753i
$604$	18.5598			0.755189
$605$	0.733195	−	44.7020i	0.0298086	−	1.81739i
$606$	−5.25205			−0.213350
$607$	21.3116	+	15.4838i	0.865011	+	0.628467i	0.929243	−	0.369468i	$-0.120460\pi$
$607$	21.3116	+	15.4838i	0.865011	+	0.628467i	−0.0642329	+	0.997935i	$0.520460\pi$
$608$	9.55323	−	29.4018i	0.387435	−	1.19240i
$609$	−1.46763	−	4.51690i	−0.0594713	−	0.183034i
$610$	15.2206	−	11.0584i	0.616262	−	0.447741i
$611$	41.7208	−	30.3119i	1.68784	−	1.22629i
$612$	−0.652191	−	2.00724i	−0.0263633	−	0.0811378i
$613$	14.8974	−	45.8494i	0.601699	−	1.85184i	0.0836366	−	0.996496i	$-0.473347\pi$
$613$	14.8974	−	45.8494i	0.601699	−	1.85184i	0.518062	−	0.855343i	$-0.326653\pi$
$614$	7.01873	+	5.09941i	0.283253	+	0.205795i
$615$	13.0481			0.526150
$616$	−8.38067	+	4.18396i	−0.337667	+	0.168577i
$617$	−29.2376			−1.17706			−0.588532	−	0.808474i	$-0.700294\pi$
$617$	−29.2376			−1.17706			−0.588532	+	0.808474i	$0.700294\pi$
$618$	−9.09196	−	6.60570i	−0.365732	−	0.265720i
$619$	1.89856	−	5.84318i	0.0763097	−	0.234857i	−0.905624	−	0.424081i	$-0.860597\pi$
$619$	1.89856	−	5.84318i	0.0763097	−	0.234857i	0.981934	+	0.189224i	$0.0605972\pi$
$620$	−6.79670	−	20.9181i	−0.272962	−	0.840090i
$621$	5.17086	−	3.75685i	0.207499	−	0.150757i
$622$	−11.4520	+	8.32035i	−0.459183	+	0.333616i
$623$	2.51149	+	7.72958i	0.100621	+	0.309679i
$624$	−0.0357012	+	0.109877i	−0.00142919	+	0.00439860i
$625$	−40.5264	−	29.4442i	−1.62106	−	1.17777i
$626$	14.4815			0.578799
$627$	17.8526	+	2.97783i	0.712963	+	0.118923i
$628$	−24.1289			−0.962849
$629$	−3.35835	−	2.43999i	−0.133906	−	0.0972886i
$630$	1.09470	−	3.36913i	0.0436138	−	0.134230i
$631$	12.5351	+	38.5792i	0.499016	+	1.53581i	0.810603	+	0.585596i	$0.199139\pi$
$631$	12.5351	+	38.5792i	0.499016	+	1.53581i	−0.311587	+	0.950217i	$0.600861\pi$
$632$	14.3292	−	10.4108i	0.569987	−	0.414120i
$633$	−2.35552	+	1.71139i	−0.0936235	+	0.0680215i
$634$	2.18166	+	6.71447i	0.0866449	+	0.266666i
$635$	0.805964	−	2.48050i	0.0319837	−	0.0984357i
$636$	−4.73020	−	3.43669i	−0.187565	−	0.136274i
$637$	−6.09006			−0.241297
$638$	2.03647	+	13.5775i	0.0806248	+	0.537537i
$639$	2.21883			0.0877757
$640$	−23.2126	−	16.8649i	−0.917557	−	0.666644i
$641$	7.27011	−	22.3751i	0.287152	−	0.883763i	−0.698593	−	0.715519i	$-0.746190\pi$
$641$	7.27011	−	22.3751i	0.287152	−	0.883763i	0.985745	−	0.168244i	$-0.0538097\pi$
$642$	−1.44032	−	4.43286i	−0.0568451	−	0.174951i
$643$	17.0009	−	12.3519i	0.670452	−	0.487112i	−0.199725	−	0.979852i	$-0.564005\pi$
$643$	17.0009	−	12.3519i	0.670452	−	0.487112i	0.870176	+	0.492740i	$0.164005\pi$
$644$	6.41345	−	4.65964i	0.252725	−	0.183616i
$645$	−0.159746	−	0.491648i	−0.00629000	−	0.0193586i
$646$	2.50109	−	7.69755i	0.0984040	−	0.302856i
$647$	−0.366260	−	0.266103i	−0.0143992	−	0.0104616i	0.580562	−	0.814216i	$-0.302833\pi$
$647$	−0.366260	−	0.266103i	−0.0143992	−	0.0104616i	−0.594962	+	0.803754i	$0.702833\pi$
$648$	−2.82426			−0.110948
$649$	−10.7775	−	10.9557i	−0.423052	−	0.430048i
$650$	−61.1446			−2.39829
$651$	−3.52981	−	2.56456i	−0.138344	−	0.100513i
$652$	−4.64163	+	14.2855i	−0.181780	+	0.559462i
$653$	−6.81098	−	20.9620i	−0.266534	−	0.820308i	−0.991336	−	0.131350i	$-0.958069\pi$
$653$	−6.81098	−	20.9620i	−0.266534	−	0.820308i	0.724802	−	0.688957i	$-0.241931\pi$
$654$	1.01663	−	0.738623i	0.0397533	−	0.0288824i
$655$	−46.0297	+	33.4426i	−1.79853	+	1.30671i
$656$	−0.0188198	−	0.0579215i	−0.000734791	−	0.00226145i
$657$	−1.72244	+	5.30112i	−0.0671987	+	0.206816i
$658$	5.97104	+	4.33821i	0.232775	+	0.169121i
$659$	18.3859			0.716215			0.358107	−	0.933680i	$-0.383422\pi$
$659$	18.3859			0.716215			0.358107	+	0.933680i	$0.383422\pi$
$660$	7.71230	−	14.8343i	0.300201	−	0.577422i
$661$	−45.9605			−1.78766			−0.893829	−	0.448408i	$-0.851991\pi$
$661$	−45.9605			−1.78766			−0.893829	+	0.448408i	$0.851991\pi$
$662$	4.68641	+	3.40488i	0.182143	+	0.132334i
$663$	−3.20234	+	9.85580i	−0.124369	+	0.382768i
$664$	0.111469	+	0.343066i	0.00432583	+	0.0133135i
$665$	−17.9438	+	13.0369i	−0.695829	+	0.505550i
$666$	−1.72021	+	1.24981i	−0.0666569	+	0.0484290i
$667$	−9.38040	−	28.8699i	−0.363210	−	1.11785i
$668$	5.04697	−	15.5330i	0.195273	−	0.600988i
$669$	2.71482	+	1.97243i	0.104961	+	0.0762586i
$670$	−49.8384			−1.92542
$671$	8.12500	−	15.6281i	0.313662	−	0.603315i
$672$	−5.66506			−0.218535
$673$	−24.0603	−	17.4808i	−0.927457	−	0.673837i	0.0179118	−	0.999840i	$-0.494298\pi$
$673$	−24.0603	−	17.4808i	−0.927457	−	0.673837i	−0.945369	+	0.326003i	$0.894298\pi$
$674$	−5.64324	+	17.3681i	−0.217369	+	0.668994i
$675$	3.55958	+	10.9553i	0.137008	+	0.421669i
$676$	24.1715	−	17.5616i	0.929672	−	0.675446i
$677$	−22.4767	+	16.3303i	−0.863851	+	0.627624i	−0.928930	−	0.370256i	$-0.879270\pi$
$677$	−22.4767	+	16.3303i	−0.863851	+	0.627624i	0.0650791	+	0.997880i	$0.479270\pi$
$678$	5.25683	+	16.1788i	0.201887	+	0.621345i
$679$	0.802581	−	2.47009i	0.0308002	−	0.0947933i
$680$	−15.8023	−	11.4810i	−0.605989	−	0.440277i
$681$	3.33791			0.127909
$682$	8.84513	+	8.99139i	0.338697	+	0.344298i
$683$	40.8297			1.56231			0.781153	−	0.624339i	$-0.214632\pi$
$683$	40.8297			1.56231			0.781153	+	0.624339i	$0.214632\pi$
$684$	5.47583	+	3.97842i	0.209373	+	0.152119i
$685$	3.39130	−	10.4374i	0.129575	−	0.398791i
$686$	−0.269341	−	0.828945i	−0.0102835	−	0.0316493i
$687$	−5.50248	+	3.99778i	−0.209933	+	0.152525i
$688$	−0.00195205	+	0.00141825i	−7.44213e−5	+	5.40703e-5i
$689$	8.87151	+	27.3037i	0.337977	+	1.04019i
$690$	6.99680	−	21.5339i	0.266364	−	0.819783i
$691$	−30.5934	−	22.2274i	−1.16383	−	0.845571i	−0.173572	−	0.984821i	$-0.555531\pi$
$691$	−30.5934	−	22.2274i	−1.16383	−	0.845571i	−0.990257	+	0.139250i	$0.955531\pi$
$692$	18.2547			0.693941
$693$	−0.491955	−	3.27994i	−0.0186878	−	0.124594i
$694$	−15.5033			−0.588498
$695$	−6.77988	−	4.92587i	−0.257175	−	0.186849i
$696$	−4.14497	+	12.7569i	−0.157115	+	0.483549i
$697$	−1.68811	−	5.19547i	−0.0639418	−	0.196792i
$698$	−8.27419	+	6.01155i	−0.313183	+	0.227541i
$699$	−5.00420	+	3.63576i	−0.189276	+	0.137517i
$700$	4.41497	+	13.5879i	0.166870	+	0.513574i
$701$	8.47498	−	26.0833i	0.320096	−	0.985153i	−0.653510	−	0.756918i	$-0.726704\pi$
$701$	8.47498	−	26.0833i	0.320096	−	0.985153i	0.973606	−	0.228235i	$-0.0732956\pi$
$702$	4.29436	+	3.12004i	0.162080	+	0.117758i
$703$	13.3128			0.502100
$704$	16.0292	+	2.67369i	0.604123	+	0.100769i
$705$	−34.4164			−1.29620
$706$	−10.7662	−	7.82213i	−0.405192	−	0.294390i
$707$	1.86205	−	5.73081i	0.0700297	−	0.215529i
$708$	−1.77598	−	5.46589i	−0.0667452	−	0.205421i
$709$	25.7623	−	18.7174i	0.967522	−	0.702946i	0.0126366	−	0.999920i	$-0.495978\pi$
$709$	25.7623	−	18.7174i	0.967522	−	0.702946i	0.954885	+	0.296974i	$0.0959775\pi$
$710$	6.35908	−	4.62014i	0.238652	−	0.173391i
$711$	1.93795	+	5.96440i	0.0726788	+	0.223682i
$712$	7.09312	−	21.8304i	0.265826	−	0.818128i
$713$	−22.5609	−	16.3915i	−0.844913	−	0.613865i
$714$	−1.48314			−0.0555053
$715$	−73.4494	+	36.6688i	−2.74685	+	1.37134i
$716$	14.4996			0.541877
$717$	−16.5674	−	12.0369i	−0.618720	−	0.449526i
$718$	1.81589	−	5.58873i	0.0677683	−	0.208569i
$719$	−4.71151	−	14.5005i	−0.175710	−	0.540778i	0.823956	−	0.566654i	$-0.191763\pi$
$719$	−4.71151	−	14.5005i	−0.175710	−	0.540778i	−0.999665	+	0.0258760i	$0.991763\pi$
$720$	0.0623776	−	0.0453200i	0.00232468	−	0.00168898i
$721$	10.4313	−	7.57878i	0.388482	−	0.282249i
$722$	2.90352	+	8.93613i	0.108058	+	0.332568i
$723$	0.321728	−	0.990176i	0.0119652	−	0.0368250i
$724$	19.7678	+	14.3621i	0.734664	+	0.533765i
$725$	54.7080			2.03180
$726$	−0.157234	+	9.58636i	−0.00583550	+	0.355783i
$727$	−33.7158			−1.25045			−0.625225	−	0.780445i	$-0.714993\pi$
$727$	−33.7158			−1.25045			−0.625225	+	0.780445i	$0.714993\pi$
$728$	13.9151	+	10.1099i	0.515726	+	0.374697i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	6.10177	+	18.7793i	0.225837	+	0.695054i
$731$	−0.175096	+	0.127215i	−0.00647617	+	0.00470521i
$732$	5.32902	−	3.87176i	0.196966	−	0.143104i
$733$	−1.39567	−	4.29543i	−0.0515503	−	0.158655i	0.921967	−	0.387268i	$-0.126581\pi$
$733$	−1.39567	−	4.29543i	−0.0515503	−	0.158655i	−0.973518	+	0.228612i	$0.926581\pi$
$734$	−5.64923	+	17.3865i	−0.208517	+	0.641749i
$735$	3.28814	+	2.38897i	0.121285	+	0.0881186i
$736$	−36.2084			−1.33466
$737$	−41.7470	+	20.8417i	−1.53777	+	0.767715i
$738$	−2.79817			−0.103002
$739$	−8.12253	−	5.90136i	−0.298792	−	0.217085i	0.428280	−	0.903646i	$-0.359120\pi$
$739$	−8.12253	−	5.90136i	−0.298792	−	0.217085i	−0.727072	+	0.686561i	$0.759120\pi$
$740$	3.80022	−	11.6959i	0.139699	−	0.429949i
$741$	−10.2699	−	31.6076i	−0.377275	−	1.16113i
$742$	−3.32407	+	2.41508i	−0.122030	+	0.0886603i
$743$	12.7037	−	9.22981i	0.466055	−	0.338609i	−0.329847	−	0.944035i	$-0.606997\pi$
$743$	12.7037	−	9.22981i	0.466055	−	0.338609i	0.795902	+	0.605426i	$0.206997\pi$
$744$	3.80787	+	11.7194i	0.139603	+	0.429654i
$745$	−12.6638	+	38.9750i	−0.463964	+	1.42793i
$746$	−20.5375	−	14.9214i	−0.751932	−	0.546311i
$747$	−0.127722			−0.00467310
$748$	−6.90446	−	1.15167i	−0.252452	−	0.0421094i
$749$	5.34760			0.195397
$750$	18.6833	+	13.5742i	0.682219	+	0.495661i
$751$	5.95724	−	18.3345i	0.217383	−	0.669036i	−0.781593	−	0.623789i	$-0.785593\pi$
$751$	5.95724	−	18.3345i	0.217383	−	0.669036i	0.998976	−	0.0452468i	$-0.0144074\pi$
$752$	0.0496402	+	0.152777i	0.00181019	+	0.00557120i
$753$	−5.36621	+	3.89878i	−0.195556	+	0.142080i
$754$	20.3954	−	14.8181i	0.742758	−	0.539645i
$755$	18.7940	+	57.8421i	0.683985	+	2.10509i
$756$	0.383276	−	1.17960i	0.0139396	−	0.0429017i
$757$	−30.3730	−	22.0673i	−1.10393	−	0.802049i	−0.122229	−	0.992502i	$-0.539004\pi$
$757$	−30.3730	−	22.0673i	−1.10393	−	0.802049i	−0.981696	+	0.190453i	$0.939004\pi$
$758$	27.8350			1.01101
$759$	−3.14435	−	20.9638i	−0.114133	−	0.760938i
$760$	62.6414			2.27224
$761$	31.3469	+	22.7749i	1.13633	+	0.825588i	0.986603	−	0.163140i	$-0.0521621\pi$
$761$	31.3469	+	22.7749i	1.13633	+	0.825588i	0.149722	+	0.988728i	$0.452162\pi$
$762$	−0.172839	+	0.531945i	−0.00626131	+	0.0192703i
$763$	0.445520	+	1.37117i	0.0161289	+	0.0496397i
$764$	6.98581	−	5.07549i	0.252738	−	0.183625i
$765$	5.59518	−	4.06514i	0.202294	−	0.146975i
$766$	0.966847	+	2.97565i	0.0349336	+	0.107515i
$767$	−8.72027	+	26.8382i	−0.314871	+	0.969072i
$768$	12.9059	+	9.37669i	0.465702	+	0.338352i
$769$	−24.0014			−0.865513			−0.432756	−	0.901511i	$-0.642459\pi$
$769$	−24.0014			−0.865513			−0.432756	+	0.901511i	$0.642459\pi$
$770$	−8.23954	−	8.37579i	−0.296932	−	0.301842i
$771$	2.88246			0.103809
$772$	16.9211	+	12.2939i	0.609004	+	0.442467i
$773$	−12.1355	+	37.3493i	−0.436485	+	1.34336i	0.455072	+	0.890455i	$0.349613\pi$
$773$	−12.1355	+	37.3493i	−0.436485	+	1.34336i	−0.891557	+	0.452908i	$0.850387\pi$
$774$	0.0342576	+	0.105434i	0.00123137	+	0.00378975i
$775$	40.6601	−	29.5413i	1.46055	−	1.06116i
$776$	−5.93430	+	4.31152i	−0.213029	+	0.154775i
$777$	−0.753854	−	2.32012i	−0.0270444	−	0.0832340i
$778$	2.82027	−	8.67989i	0.101112	−	0.311189i
$779$	14.1735	+	10.2976i	0.507817	+	0.368950i
$780$	−30.7004			−1.09925
$781$	3.39459	−	6.52934i	0.121468	−	0.233638i
$782$	−9.47956			−0.338988
$783$	−3.84230	−	2.79160i	−0.137313	−	0.0997635i
$784$	0.00586220	−	0.0180420i	0.000209364	−	0.000644357i
$785$	−24.4334	−	75.1983i	−0.872066	−	2.68394i
$786$	9.87109	−	7.17177i	0.352090	−	0.255809i
$787$	−20.5681	+	14.9436i	−0.733172	+	0.532681i	−0.890565	−	0.454855i	$-0.849691\pi$
$787$	−20.5681	+	14.9436i	−0.733172	+	0.532681i	0.157393	+	0.987536i	$0.449691\pi$
$788$	−2.46119	−	7.57475i	−0.0876761	−	0.269839i
$789$	−6.52080	+	20.0690i	−0.232147	+	0.714474i
$790$	17.9734	+	13.0584i	0.639465	+	0.464598i
$791$	−19.5174			−0.693959
$792$	−4.32084	+	8.31093i	−0.153534	+	0.295316i
$793$	−32.3432			−1.14854
$794$	−12.5000	−	9.08176i	−0.443607	−	0.322300i
$795$	5.92063	−	18.2218i	0.209983	−	0.646262i
$796$	5.08397	+	15.6468i	0.180197	+	0.554588i
$797$	29.7416	−	21.6085i	1.05350	−	0.765413i	0.0806252	−	0.996744i	$-0.474308\pi$
$797$	29.7416	−	21.6085i	1.05350	−	0.765413i	0.972875	+	0.231332i	$0.0743083\pi$
$798$	3.84805	−	2.79577i	0.136219	−	0.0989692i
$799$	4.45265	+	13.7039i	0.157524	+	0.484808i
$800$	20.1653	−	62.0623i	0.712950	−	2.19424i
$801$	6.57517	+	4.77714i	0.232322	+	0.168792i
$802$	7.04287			0.248692
$803$	12.9644	+	13.1788i	0.457503	+	0.465069i
$804$	−17.4494			−0.615393
$805$	21.0163	+	15.2692i	0.740726	+	0.538169i
$806$	7.15678	−	22.0263i	0.252087	−	0.775844i
$807$	−5.29393	−	16.2930i	−0.186355	−	0.573542i
$808$	−13.7681	+	10.0031i	−0.484359	+	0.351907i
$809$	32.7478	−	23.7926i	1.15135	−	0.836505i	0.162690	−	0.986677i	$-0.447983\pi$
$809$	32.7478	−	23.7926i	1.15135	−	0.836505i	0.988660	+	0.150172i	$0.0479828\pi$
$810$	−1.09470	−	3.36913i	−0.0384638	−	0.118379i
$811$	−2.95118	+	9.08279i	−0.103630	+	0.318940i	−0.989406	−	0.145172i	$-0.953626\pi$
$811$	−2.95118	+	9.08279i	−0.103630	+	0.318940i	0.885777	+	0.464112i	$0.153626\pi$
$812$	−4.76563	−	3.46243i	−0.167241	−	0.121508i
$813$	16.3599			0.573765
$814$	1.04604	+	6.97412i	0.0366638	+	0.244443i
$815$	−49.2212			−1.72414
$816$	−0.0261156	−	0.0189741i	−0.000914228	−	0.000664226i
$817$	0.214487	−	0.660124i	0.00750395	−	0.0230948i
$818$	10.6898	+	32.8999i	0.373761	+	1.15032i
$819$	−4.92697	+	3.57965i	−0.172162	+	0.125083i
$820$	13.0928	−	9.51251i	0.457222	−	0.332191i
$821$	−11.2046	−	34.4843i	−0.391044	−	1.20351i	−0.932000	−	0.362458i	$-0.881938\pi$
$821$	−11.2046	−	34.4843i	−0.391044	−	1.20351i	0.540956	−	0.841051i	$-0.318062\pi$
$822$	−0.727266	+	2.23829i	−0.0253663	+	0.0780695i
$823$	33.7670	+	24.5332i	1.17704	+	0.855173i	0.991835	−	0.127526i	$-0.0407037\pi$
$823$	33.7670	+	24.5332i	1.17704	+	0.855173i	0.185209	+	0.982699i	$0.440704\pi$
$824$	−36.4155			−1.26859
$825$	37.6838	+	6.28571i	1.31198	+	0.218840i
$826$	−4.03873			−0.140525
$827$	−22.8676	−	16.6143i	−0.795183	−	0.577735i	0.114314	−	0.993445i	$-0.463533\pi$
$827$	−22.8676	−	16.6143i	−0.795183	−	0.577735i	−0.909497	+	0.415710i	$0.863533\pi$
$828$	2.44972	−	7.53946i	0.0851336	−	0.262014i
$829$	−0.621234	−	1.91196i	−0.0215764	−	0.0664052i	0.939689	−	0.342031i	$-0.111115\pi$
$829$	−0.621234	−	1.91196i	−0.0215764	−	0.0664052i	−0.961265	+	0.275626i	$0.911115\pi$
$830$	−0.366046	+	0.265948i	−0.0127056	+	0.00923118i
$831$	2.00516	−	1.45684i	0.0695584	−	0.0505371i
$832$	−9.22101	−	28.3794i	−0.319681	−	0.983877i
$833$	0.525831	−	1.61834i	0.0182190	−	0.0560722i
$834$	1.45395	+	1.05635i	0.0503461	+	0.0365785i
$835$	53.5195			1.85212
$836$	20.0847	−	10.0271i	0.694644	−	0.346794i
$837$	−4.36309			−0.150810
$838$	−11.4032	−	8.28491i	−0.393917	−	0.286197i
$839$	−7.48127	+	23.0250i	−0.258282	+	0.794911i	0.734883	+	0.678194i	$0.237237\pi$
$839$	−7.48127	+	23.0250i	−0.258282	+	0.794911i	−0.993165	+	0.116717i	$0.962763\pi$
$840$	−3.54716	−	10.9170i	−0.122389	−	0.376673i
$841$	5.21307	−	3.78752i	0.179761	−	0.130604i
$842$	−17.4935	+	12.7098i	−0.602865	+	0.438007i
$843$	7.47661	+	23.0106i	0.257508	+	0.792529i
$844$	−1.11594	+	3.43451i	−0.0384122	+	0.118221i
$845$	79.2076	+	57.5477i	2.72483	+	1.97970i
$846$	7.38061			0.253751
$847$	−10.4045	−	3.57030i	−0.357502	−	0.122677i
$848$	−0.0894276			−0.00307096
$849$	23.6119	+	17.1550i	0.810357	+	0.588759i
$850$	5.27938	−	16.2482i	0.181081	−	0.557310i
$851$	−4.81828	−	14.8291i	−0.165169	−	0.508337i
$852$	2.22644	−	1.61760i	0.0762766	−	0.0554182i
$853$	−16.2959	+	11.8397i	−0.557963	+	0.405384i	−0.830713	−	0.556701i	$-0.812067\pi$
$853$	−16.2959	+	11.8397i	−0.557963	+	0.405384i	0.272750	+	0.962085i	$0.412067\pi$
$854$	−1.43042	−	4.40237i	−0.0489479	−	0.150646i
$855$	−6.85391	+	21.0942i	−0.234399	+	0.721405i
$856$	−12.2186	−	8.87734i	−0.417623	−	0.303421i
$857$	−26.6092			−0.908953			−0.454477	−	0.890759i	$-0.650174\pi$
$857$	−26.6092			−0.908953			−0.454477	+	0.890759i	$0.650174\pi$
$858$	15.7512	−	7.86364i	0.537738	−	0.268460i
$859$	14.4645			0.493522			0.246761	−	0.969076i	$-0.420634\pi$
$859$	14.4645			0.493522			0.246761	+	0.969076i	$0.420634\pi$
$860$	−0.518722	−	0.376874i	−0.0176883	−	0.0128513i
$861$	0.992058	−	3.05324i	0.0338093	−	0.104054i
$862$	5.89374	+	18.1391i	0.200742	+	0.617819i
$863$	−22.9456	+	16.6710i	−0.781078	+	0.567487i	−0.905302	−	0.424768i	$-0.860356\pi$
$863$	−22.9456	+	16.6710i	−0.781078	+	0.567487i	0.124224	+	0.992254i	$0.460356\pi$
$864$	−4.58313	+	3.32984i	−0.155921	+	0.113283i
$865$	18.4851	+	56.8913i	0.628512	+	1.93436i
$866$	10.5969	−	32.6139i	0.360098	−	1.10827i
$867$	11.4108	+	8.29040i	0.387530	+	0.281557i
$868$	−5.41156			−0.183680
$869$	20.5162	+	3.42214i	0.695965	+	0.116088i
$870$	−16.8246			−0.570409
$871$	69.3157	+	50.3608i	2.34867	+	1.70641i
$872$	1.25827	−	3.87255i	0.0426103	−	0.131141i
$873$	−0.802581	−	2.47009i	−0.0271632	−	0.0835999i
$874$	24.5949	−	17.8692i	0.831935	−	0.604436i
$875$	−21.4356	+	15.5739i	−0.724655	+	0.526493i
$876$	2.13635	+	6.57501i	0.0721806	+	0.222149i
$877$	3.13396	−	9.64535i	0.105826	−	0.325700i	−0.884097	−	0.467303i	$-0.845226\pi$
$877$	3.13396	−	9.64535i	0.105826	−	0.325700i	0.989924	+	0.141603i	$0.0452256\pi$
$878$	−6.76369	−	4.91411i	−0.228263	−	0.165843i
$879$	−27.1918			−0.917156
$880$	−0.0379312	−	0.252893i	−0.00127866	−	0.00852501i
$881$	−3.71883			−0.125291			−0.0626453	−	0.998036i	$-0.519954\pi$
$881$	−3.71883			−0.125291			−0.0626453	+	0.998036i	$0.519954\pi$
$882$	−0.705143	−	0.512316i	−0.0237434	−	0.0172506i
$883$	5.35542	−	16.4823i	0.180224	−	0.554673i	−0.819609	−	0.572923i	$-0.805809\pi$
$883$	5.35542	−	16.4823i	0.180224	−	0.554673i	0.999833	+	0.0182500i	$0.00580947\pi$
$884$	3.97189	+	12.2242i	0.133589	+	0.411145i
$885$	15.2362	−	11.0697i	0.512158	−	0.372105i
$886$	0.443631	−	0.322316i	0.0149041	−	0.0108284i
$887$	−1.67084	−	5.14232i	−0.0561014	−	0.172662i	0.919079	−	0.394072i	$-0.128934\pi$
$887$	−1.67084	−	5.14232i	−0.0561014	−	0.172662i	−0.975181	+	0.221410i	$0.928934\pi$
$888$	−2.12908	+	6.55265i	−0.0714474	+	0.219892i
$889$	−0.519157	−	0.377189i	−0.0174120	−	0.0126505i
$890$	28.7913			0.965087
$891$	−2.32590	−	2.36436i	−0.0779205	−	0.0792090i
$892$	4.16210			0.139357
$893$	−37.3847	−	27.1616i	−1.25103	−	0.908927i
$894$	2.71575	−	8.35821i	0.0908281	−	0.279540i
$895$	14.6826	+	45.1884i	0.490786	+	1.51048i
$896$	−5.71124	+	4.14946i	−0.190799	+	0.138624i
$897$	−31.4909	+	22.8794i	−1.05145	+	0.763923i
$898$	−4.66939	−	14.3709i	−0.155819	−	0.479563i
$899$	−6.40339	+	19.7076i	−0.213565	+	0.657286i
$900$	11.5586	+	8.39778i	0.385285	+	0.279926i
$901$	−8.02152			−0.267236
$902$	−4.28092	+	8.23414i	−0.142539	+	0.274167i
$903$	−0.127191			−0.00423264
$904$	44.5949	+	32.4001i	1.48320	+	1.07761i
$905$	−24.7427	+	76.1501i	−0.822474	+	2.53132i
$906$	−4.03039	−	12.4043i	−0.133901	−	0.412104i
$907$	8.65808	−	6.29046i	0.287487	−	0.208871i	−0.434690	−	0.900580i	$-0.643142\pi$
$907$	8.65808	−	6.29046i	0.287487	−	0.208871i	0.722176	+	0.691709i	$0.243142\pi$
$908$	3.34936	−	2.43345i	0.111152	−	0.0807569i
$909$	−1.86205	−	5.73081i	−0.0617604	−	0.190079i
$910$	−6.66678	+	20.5182i	−0.221002	+	0.680173i
$911$	22.3053	+	16.2057i	0.739007	+	0.536920i	0.892400	−	0.451245i	$-0.149020\pi$
$911$	22.3053	+	16.2057i	0.739007	+	0.536920i	−0.153393	+	0.988165i	$0.549020\pi$
$912$	0.103524			0.00342803
$913$	−0.195402	+	0.375846i	−0.00646685	+	0.0124387i
$914$	−25.3771			−0.839400
$915$	17.4627	+	12.6874i	0.577299	+	0.419432i
$916$	−2.60682	+	8.02298i	−0.0861319	+	0.265087i
$917$	4.32584	+	13.3136i	0.142852	+	0.439653i
$918$	−1.19989	+	0.871770i	−0.0396022	+	0.0287727i
$919$	−29.4499	+	21.3966i	−0.971464	+	0.705810i	−0.955785	−	0.294067i	$-0.904991\pi$
$919$	−29.4499	+	21.3966i	−0.971464	+	0.705810i	−0.0156789	+	0.999877i	$0.504991\pi$
$920$	−22.6718	−	69.7765i	−0.747466	−	2.30046i
$921$	−3.07584	+	9.46647i	−0.101352	+	0.311931i
$922$	−10.7076	−	7.77952i	−0.352636	−	0.256205i
$923$	−13.5128			−0.444781
$924$	−2.88483	−	2.93253i	−0.0949038	−	0.0964731i
$925$	28.1010			0.923956
$926$	−12.6140	−	9.16463i	−0.414523	−	0.301168i
$927$	3.98440	−	12.2627i	0.130865	−	0.402761i
$928$	8.31421	+	25.5885i	0.272927	+	0.839984i
$929$	−21.2287	+	15.4235i	−0.696491	+	0.506030i	−0.878787	−	0.477214i	$-0.841647\pi$
$929$	−21.2287	+	15.4235i	−0.696491	+	0.506030i	0.182297	+	0.983244i	$0.441647\pi$
$930$	−12.5044	+	9.08500i	−0.410036	+	0.297909i
$931$	1.68634	+	5.19003i	0.0552676	+	0.170096i
$932$	−2.37076	+	7.29646i	−0.0776569	+	0.239003i
$933$	−13.1390	−	9.54602i	−0.430150	−	0.312523i
$934$	−26.4184			−0.864437
$935$	−3.40237	−	22.6841i	−0.111270	−	0.741850i
$936$	17.2000			0.562198
$937$	−19.3192	−	14.0362i	−0.631131	−	0.458544i	0.225661	−	0.974206i	$-0.427546\pi$
$937$	−19.3192	−	14.0362i	−0.631131	−	0.458544i	−0.856792	+	0.515662i	$0.827546\pi$
$938$	−3.78925	+	11.6621i	−0.123724	+	0.380782i
$939$	5.13426	+	15.8016i	0.167550	+	0.515667i
$940$	−34.5344	+	25.0907i	−1.12639	+	0.818369i
$941$	−14.3837	+	10.4504i	−0.468896	+	0.340673i	−0.797011	−	0.603965i	$-0.793587\pi$
$941$	−14.3837	+	10.4504i	−0.468896	+	0.340673i	0.328115	+	0.944638i	$0.393587\pi$
$942$	5.23976	+	16.1263i	0.170720	+	0.525424i
$943$	6.34077	−	19.5149i	0.206484	−	0.635492i
$944$	−0.0711151	−	0.0516681i	−0.00231460	−	0.00168165i
$945$	4.06436			0.132214
$946$	0.362671	+	0.0604940i	0.0117914	+	0.00196683i
$947$	31.7071			1.03034			0.515171	−	0.857088i	$-0.327729\pi$
$947$	31.7071			1.03034			0.515171	+	0.857088i	$0.327729\pi$
$948$	6.29284	+	4.57202i	0.204382	+	0.148492i
$949$	10.4898	−	32.2842i	0.340512	−	1.04799i
$950$	16.9310	+	52.1082i	0.549313	+	1.69061i
$951$	−6.55305	+	4.76107i	−0.212497	+	0.154388i
$952$	−3.88801	+	2.82480i	−0.126011	+	0.0915523i
$953$	−1.01423	−	3.12149i	−0.0328543	−	0.101115i	0.933285	−	0.359138i	$-0.116929\pi$
$953$	−1.01423	−	3.12149i	−0.0328543	−	0.101115i	−0.966139	+	0.258023i	$0.916929\pi$
$954$	−1.26968	+	3.90768i	−0.0411075	+	0.126516i
$955$	22.8918	+	16.6319i	0.740762	+	0.538195i
$956$	−25.3995			−0.821478
$957$	−14.0931	+	7.03584i	−0.455566	+	0.227436i
$958$	−6.92707			−0.223804
$959$	−2.18449	−	1.58712i	−0.0705407	−	0.0512508i
$960$	−6.15388	+	18.9397i	−0.198616	+	0.611276i
$961$	−3.69691	−	11.3779i	−0.119255	−	0.367030i
$962$	10.4762	−	7.61141i	0.337766	−	0.245402i
$963$	4.32630	−	3.14324i	0.139413	−	0.101289i
$964$	−0.399041	−	1.22812i	−0.0128522	−	0.0395551i
$965$	−21.1796	+	65.1840i	−0.681795	+	2.09835i
$966$	−4.50694	−	3.27449i	−0.145008	−	0.105355i
$967$	−3.83683			−0.123384			−0.0616921	−	0.998095i	$-0.519650\pi$
$967$	−3.83683			−0.123384			−0.0616921	+	0.998095i	$0.519650\pi$
$968$	17.8460	+	25.4297i	0.573593	+	0.817343i
$969$	9.28597			0.298308
$970$	−7.44348	−	5.40800i	−0.238996	−	0.173641i
$971$	13.6977	−	42.1573i	0.439581	−	1.35289i	−0.448738	−	0.893663i	$-0.648126\pi$
$971$	13.6977	−	42.1573i	0.439581	−	1.35289i	0.888319	−	0.459228i	$-0.151874\pi$
$972$	−0.383276	−	1.17960i	−0.0122936	−	0.0378357i
$973$	−1.66813	+	1.21197i	−0.0534777	+	0.0388538i
$974$	7.17207	−	5.21082i	0.229808	−	0.166965i
$975$	−21.6781	−	66.7183i	−0.694255	−	2.13670i
$976$	0.0311330	−	0.0958176i	0.000996544	−	0.00306705i
$977$	−7.84564	−	5.70019i	−0.251004	−	0.182365i	0.455168	−	0.890406i	$-0.349579\pi$
$977$	−7.84564	−	5.70019i	−0.251004	−	0.182365i	−0.706172	+	0.708041i	$0.749579\pi$
$978$	10.5555			0.337528
$979$	24.1170	−	12.0401i	0.770782	−	0.384804i
$980$	5.04106			0.161031
$981$	1.16639	+	0.847429i	0.0372399	+	0.0270563i
$982$	0.290177	−	0.893073i	0.00925992	−	0.0284991i
$983$	8.86112	+	27.2717i	0.282626	+	0.869833i	0.987100	+	0.160104i	$0.0511829\pi$
$983$	8.86112	+	27.2717i	0.282626	+	0.869833i	−0.704474	+	0.709730i	$0.748817\pi$
$984$	−7.33530	+	5.32941i	−0.233841	+	0.169895i
$985$	21.1146	−	15.3407i	0.672768	−	0.488795i
$986$	2.17670	+	6.69921i	0.0693204	+	0.213346i
$987$	−2.61671	+	8.05340i	−0.0832907	+	0.256342i
$988$	−33.3481	−	24.2288i	−1.06095	−	0.770822i
$989$	−0.812944			−0.0258501
$990$	−11.5891	−	1.93308i	−0.368325	−	0.0614372i
$991$	−14.0455			−0.446170			−0.223085	−	0.974799i	$-0.571613\pi$
$991$	−14.0455			−0.446170			−0.223085	+	0.974799i	$0.571613\pi$
$992$	19.9966	+	14.5284i	0.634893	+	0.461277i
$993$	−2.05374	+	6.32077i	−0.0651736	+	0.200584i
$994$	−0.597622	−	1.83929i	−0.0189554	−	0.0583388i
$995$	−43.6156	+	31.6886i	−1.38271	+	1.00460i
$996$	−0.128160	+	0.0931136i	−0.00406090	+	0.00295042i
$997$	−11.1896	−	34.4379i	−0.354377	−	1.09066i	−0.956370	−	0.292159i	$-0.905626\pi$
$997$	−11.1896	−	34.4379i	−0.354377	−	1.09066i	0.601993	−	0.798501i	$-0.294374\pi$
$998$	9.32347	−	28.6947i	0.295129	−	0.908314i
$999$	−1.97362	−	1.43392i	−0.0624424	−	0.0453671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.169.2	✓	20
3.2	odd	2		693.2.m.j.631.4		20
11.3	even	5	inner	231.2.j.g.190.2	yes	20
11.5	even	5		2541.2.a.bq.1.7		10
11.6	odd	10		2541.2.a.br.1.4		10
33.5	odd	10		7623.2.a.cx.1.4		10
33.14	odd	10		693.2.m.j.190.4		20
33.17	even	10		7623.2.a.cy.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.2	✓	20	1.1	even	1	trivial
231.2.j.g.190.2	yes	20	11.3	even	5	inner
693.2.m.j.190.4		20	33.14	odd	10
693.2.m.j.631.4		20	3.2	odd	2
2541.2.a.bq.1.7		10	11.5	even	5
2541.2.a.br.1.4		10	11.6	odd	10
7623.2.a.cx.1.4		10	33.5	odd	10
7623.2.a.cy.1.7		10	33.17	even	10

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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.705143 - 0.512316i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.383276 - 1.17960i) q^{4} +(3.28814 - 2.38897i) q^{5} +(-0.705143 + 0.512316i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.872746 + 2.68604i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.54252 q^{10} +(-2.96738 + 1.48143i) q^{11} -1.24031 q^{12} +(4.92697 + 3.57965i) q^{13} +(-0.269341 + 0.828945i) q^{14} +(-1.25596 - 3.86544i) q^{15} +(-0.0153474 + 0.0111506i) q^{16} +(-1.37664 + 1.00019i) q^{17} +(0.269341 + 0.828945i) q^{18} +(1.68634 - 5.19003i) q^{19} +(-4.07830 - 2.96306i) q^{20} -1.00000 q^{21} +(2.85139 + 0.475616i) q^{22} -6.39153 q^{23} +(2.28488 + 1.66006i) q^{24} +(3.55958 - 10.9553i) q^{25} +(-1.64030 - 5.04833i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.00343 + 0.729034i) q^{28} +(1.46763 + 4.51690i) q^{29} +(-1.09470 + 3.36913i) q^{30} +(3.52981 + 2.56456i) q^{31} +5.66506 q^{32} +(0.491955 + 3.27994i) q^{33} +1.48314 q^{34} +(-3.28814 - 2.38897i) q^{35} +(-0.383276 + 1.17960i) q^{36} +(0.753854 + 2.32012i) q^{37} +(-3.84805 + 2.79577i) q^{38} +(4.92697 - 3.57965i) q^{39} +(3.54716 + 10.9170i) q^{40} +(-0.992058 + 3.05324i) q^{41} +(0.705143 + 0.512316i) q^{42} +0.127191 q^{43} +(2.88483 + 2.93253i) q^{44} -4.06436 q^{45} +(4.50694 + 3.27449i) q^{46} +(2.61671 - 8.05340i) q^{47} +(0.00586220 + 0.0180420i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.12258 + 5.90140i) q^{50} +(0.525831 + 1.61834i) q^{51} +(2.33417 - 7.18385i) q^{52} +(3.81374 + 2.77084i) q^{53} +0.871604 q^{54} +(-6.21806 + 11.9602i) q^{55} +2.82426 q^{56} +(-4.41490 - 3.20761i) q^{57} +(1.27919 - 3.93695i) q^{58} +(1.43188 + 4.40689i) q^{59} +(-4.07830 + 2.96306i) q^{60} +(-4.29654 + 3.12162i) q^{61} +(-1.17516 - 3.61676i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-3.96398 - 2.88000i) q^{64} +24.7522 q^{65} +(1.33347 - 2.56486i) q^{66} +14.0686 q^{67} +(1.70746 + 1.24054i) q^{68} +(-1.97509 + 6.07871i) q^{69} +(1.09470 + 3.36913i) q^{70} +(-1.79507 + 1.30420i) q^{71} +(2.28488 - 1.66006i) q^{72} +(-1.72244 - 5.30112i) q^{73} +(0.657063 - 2.02223i) q^{74} +(-9.31911 - 6.77073i) q^{75} -6.76849 q^{76} +(2.32590 + 2.36436i) q^{77} -5.30813 q^{78} +(-5.07362 - 3.68620i) q^{79} +(-0.0238261 + 0.0733293i) q^{80} +(0.309017 + 0.951057i) q^{81} +(2.26377 - 1.64472i) q^{82} +(0.103329 - 0.0750731i) q^{83} +(0.383276 + 1.17960i) q^{84} +(-2.13717 + 6.57753i) q^{85} +(-0.0896877 - 0.0651619i) q^{86} +4.74935 q^{87} +(-1.38941 - 9.26341i) q^{88} -8.12736 q^{89} +(2.86596 + 2.08224i) q^{90} +(1.88193 - 5.79200i) q^{91} +(2.44972 + 7.53946i) q^{92} +(3.52981 - 2.56456i) q^{93} +(-5.97104 + 4.33821i) q^{94} +(-6.85391 - 21.0942i) q^{95} +(1.75060 - 5.38780i) q^{96} +(2.10118 + 1.52660i) q^{97} +0.871604 q^{98} +(3.27143 + 0.545679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25}+ \cdots - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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