LMFDB - Embedded newform 231.2.i.f.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$-2.57330i$ of defining polynomial
Character	$\chi$	$=$	231.100
Dual form			231.2.i.f.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.307468 + 0.532550i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.810927 + 1.40457i) q^{4} +(-0.747986 + 1.29555i) q^{5} -0.614936 q^{6} +(2.59895 - 0.495442i) q^{7} -2.22721 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.307468 + 0.532550i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.810927 + 1.40457i) q^{4} +(-0.747986 + 1.29555i) q^{5} -0.614936 q^{6} +(2.59895 - 0.495442i) q^{7} -2.22721 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.459963 - 0.796680i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.810927 + 1.40457i) q^{12} -1.27568 q^{13} +(-0.535246 + 1.53640i) q^{14} -1.49597 q^{15} +(-0.937059 + 1.62303i) q^{16} +(-0.307468 - 0.532550i) q^{17} +(-0.307468 - 0.532550i) q^{18} +(1.33037 - 2.30427i) q^{19} -2.42625 q^{20} +(1.72854 + 2.00304i) q^{21} +0.614936 q^{22} +(-0.937059 + 1.62303i) q^{23} +(-1.11360 - 1.92882i) q^{24} +(1.38104 + 2.39202i) q^{25} +(0.392231 - 0.679364i) q^{26} -1.00000 q^{27} +(2.80344 + 3.24863i) q^{28} +8.44902 q^{29} +(0.459963 - 0.796680i) q^{30} +(-2.31093 - 4.00264i) q^{31} +(-2.80344 - 4.85570i) q^{32} +(0.500000 - 0.866025i) q^{33} +0.378146 q^{34} +(-1.30211 + 3.73765i) q^{35} -1.62185 q^{36} +(-0.137079 + 0.237427i) q^{37} +(0.818094 + 1.41698i) q^{38} +(-0.637840 - 1.10477i) q^{39} +(1.66592 - 2.88546i) q^{40} -4.91993 q^{41} +(-1.59819 + 0.304665i) q^{42} +9.42511 q^{43} +(0.810927 - 1.40457i) q^{44} +(-0.747986 - 1.29555i) q^{45} +(-0.576231 - 0.998061i) q^{46} +(1.58106 - 2.73847i) q^{47} -1.87412 q^{48} +(6.50907 - 2.57526i) q^{49} -1.69850 q^{50} +(0.307468 - 0.532550i) q^{51} +(-1.03448 - 1.79178i) q^{52} +(-3.09416 - 5.35924i) q^{53} +(0.307468 - 0.532550i) q^{54} +1.49597 q^{55} +(-5.78840 + 1.10345i) q^{56} +2.66075 q^{57} +(-2.59780 + 4.49953i) q^{58} +(-0.937059 - 1.62303i) q^{59} +(-1.21312 - 2.10119i) q^{60} +(4.26322 - 7.38411i) q^{61} +2.84214 q^{62} +(-0.870409 + 2.49848i) q^{63} -0.300364 q^{64} +(0.954191 - 1.65271i) q^{65} +(0.307468 + 0.532550i) q^{66} +(-2.53122 - 4.38420i) q^{67} +(0.498668 - 0.863718i) q^{68} -1.87412 q^{69} +(-1.59013 - 1.84264i) q^{70} +16.0954 q^{71} +(1.11360 - 1.92882i) q^{72} +(-4.37866 - 7.58406i) q^{73} +(-0.0842945 - 0.146002i) q^{74} +(-1.38104 + 2.39202i) q^{75} +4.31534 q^{76} +(-1.72854 - 2.00304i) q^{77} +0.784462 q^{78} +(-4.72483 + 8.18365i) q^{79} +(-1.40181 - 2.42801i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.51272 - 2.62011i) q^{82} +9.00578 q^{83} +(-1.41168 + 4.05216i) q^{84} +0.919926 q^{85} +(-2.89792 + 5.01934i) q^{86} +(4.22451 + 7.31707i) q^{87} +(1.11360 + 1.92882i) q^{88} +(-5.33812 + 9.24589i) q^{89} +0.919926 q^{90} +(-3.31543 + 0.632026i) q^{91} -3.03954 q^{92} +(2.31093 - 4.00264i) q^{93} +(0.972248 + 1.68398i) q^{94} +(1.99020 + 3.44713i) q^{95} +(2.80344 - 4.85570i) q^{96} -17.6881 q^{97} +(-0.629878 + 4.25822i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.307468	+	0.532550i	−0.217413	+	0.376570i	−0.954016	−	0.299755i	$-0.903095\pi$
$2$	−0.307468	+	0.532550i	−0.217413	+	0.376570i	0.736604	+	0.676325i	$0.236428\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.810927	+	1.40457i	0.405463	+	0.702283i
$5$	−0.747986	+	1.29555i	−0.334509	+	0.579387i	−0.983390	−	0.181503i	$-0.941904\pi$
$5$	−0.747986	+	1.29555i	−0.334509	+	0.579387i	0.648881	+	0.760890i	$0.275237\pi$
$6$	−0.614936			−0.251047
$7$	2.59895	−	0.495442i	0.982310	−	0.187259i
$7$	2.59895	−	0.495442i	0.982310	−	0.187259i
$8$	−2.22721			−0.787437
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.459963	−	0.796680i	−0.145453	−	0.251932i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−0.810927	+	1.40457i	−0.234094	+	0.405463i
$13$	−1.27568			−0.353810			−0.176905	−	0.984228i	$-0.556609\pi$
$13$	−1.27568			−0.353810			−0.176905	+	0.984228i	$0.556609\pi$
$14$	−0.535246	+	1.53640i	−0.143050	+	0.410621i
$15$	−1.49597			−0.386258
$16$	−0.937059	+	1.62303i	−0.234265	+	0.405758i
$17$	−0.307468	−	0.532550i	−0.0745719	−	0.129162i	0.826328	−	0.563189i	$-0.190426\pi$
$17$	−0.307468	−	0.532550i	−0.0745719	−	0.129162i	−0.900900	+	0.434027i	$0.857092\pi$
$18$	−0.307468	−	0.532550i	−0.0724709	−	0.125523i
$19$	1.33037	−	2.30427i	0.305208	−	0.528636i	−0.672099	−	0.740461i	$-0.734607\pi$
$19$	1.33037	−	2.30427i	0.305208	−	0.528636i	0.977308	+	0.211825i	$0.0679405\pi$
$20$	−2.42625			−0.542525
$21$	1.72854	+	2.00304i	0.377198	+	0.437098i
$22$	0.614936			0.131105
$23$	−0.937059	+	1.62303i	−0.195390	+	0.338426i	−0.947028	−	0.321150i	$-0.895931\pi$
$23$	−0.937059	+	1.62303i	−0.195390	+	0.338426i	0.751638	+	0.659576i	$0.229264\pi$
$24$	−1.11360	−	1.92882i	−0.227313	−	0.393718i
$25$	1.38104	+	2.39202i	0.276207	+	0.478405i
$26$	0.392231	−	0.679364i	0.0769228	−	0.133234i
$27$	−1.00000			−0.192450
$28$	2.80344	+	3.24863i	0.529800	+	0.613933i
$29$	8.44902			1.56894			0.784472	−	0.620164i	$-0.212934\pi$
$29$	8.44902			1.56894			0.784472	+	0.620164i	$0.212934\pi$
$30$	0.459963	−	0.796680i	0.0839774	−	0.145453i
$31$	−2.31093	−	4.00264i	−0.415055	−	0.718896i	0.580379	−	0.814346i	$-0.302904\pi$
$31$	−2.31093	−	4.00264i	−0.415055	−	0.718896i	−0.995434	+	0.0954503i	$0.969571\pi$
$32$	−2.80344	−	4.85570i	−0.495583	−	0.858374i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	0.378146			0.0648515
$35$	−1.30211	+	3.73765i	−0.220096	+	0.631778i
$36$	−1.62185			−0.270309
$37$	−0.137079	+	0.237427i	−0.0225356	+	0.0390327i	−0.877073	−	0.480357i	$-0.840507\pi$
$37$	−0.137079	+	0.237427i	−0.0225356	+	0.0390327i	0.854538	+	0.519389i	$0.173841\pi$
$38$	0.818094	+	1.41698i	0.132712	+	0.229865i
$39$	−0.637840	−	1.10477i	−0.102136	−	0.176905i
$40$	1.66592	−	2.88546i	0.263405	−	0.456231i
$41$	−4.91993			−0.768363			−0.384182	−	0.923258i	$-0.625516\pi$
$41$	−4.91993			−0.768363			−0.384182	+	0.923258i	$0.625516\pi$
$42$	−1.59819	+	0.304665i	−0.246606	+	0.0470108i
$43$	9.42511			1.43732			0.718658	−	0.695364i	$-0.244757\pi$
$43$	9.42511			1.43732			0.718658	+	0.695364i	$0.244757\pi$
$44$	0.810927	−	1.40457i	0.122252	−	0.211746i
$45$	−0.747986	−	1.29555i	−0.111503	−	0.193129i
$46$	−0.576231	−	0.998061i	−0.0849606	−	0.147156i
$47$	1.58106	−	2.73847i	0.230621	−	0.399447i	−0.727370	−	0.686245i	$-0.759258\pi$
$47$	1.58106	−	2.73847i	0.230621	−	0.399447i	0.957991	+	0.286799i	$0.0925911\pi$
$48$	−1.87412			−0.270506
$49$	6.50907	−	2.57526i	0.929868	−	0.367894i
$50$	−1.69850			−0.240204
$51$	0.307468	−	0.532550i	0.0430541	−	0.0745719i
$52$	−1.03448	−	1.79178i	−0.143457	−	0.248475i
$53$	−3.09416	−	5.35924i	−0.425015	−	0.736148i	0.571407	−	0.820667i	$-0.306398\pi$
$53$	−3.09416	−	5.35924i	−0.425015	−	0.736148i	−0.996422	+	0.0845190i	$0.973065\pi$
$54$	0.307468	−	0.532550i	0.0418411	−	0.0724709i
$55$	1.49597			0.201717
$56$	−5.78840	+	1.10345i	−0.773508	+	0.147455i
$57$	2.66075			0.352424
$58$	−2.59780	+	4.49953i	−0.341108	+	0.590817i
$59$	−0.937059	−	1.62303i	−0.121995	−	0.211301i	0.798560	−	0.601916i	$-0.205596\pi$
$59$	−0.937059	−	1.62303i	−0.121995	−	0.211301i	−0.920554	+	0.390615i	$0.872262\pi$
$60$	−1.21312	−	2.10119i	−0.156614	−	0.271263i
$61$	4.26322	−	7.38411i	0.545849	−	0.945438i	−0.452704	−	0.891661i	$-0.649541\pi$
$61$	4.26322	−	7.38411i	0.545849	−	0.945438i	0.998553	−	0.0537772i	$-0.0171261\pi$
$62$	2.84214			0.360953
$63$	−0.870409	+	2.49848i	−0.109661	+	0.314779i
$64$	−0.300364			−0.0375455
$65$	0.954191	−	1.65271i	0.118353	−	0.204993i
$66$	0.307468	+	0.532550i	0.0378467	+	0.0655524i
$67$	−2.53122	−	4.38420i	−0.309237	−	0.535615i	0.668958	−	0.743300i	$-0.266740\pi$
$67$	−2.53122	−	4.38420i	−0.309237	−	0.535615i	−0.978196	+	0.207685i	$0.933407\pi$
$68$	0.498668	−	0.863718i	0.0604724	−	0.104741i
$69$	−1.87412			−0.225617
$70$	−1.59013	−	1.84264i	−0.190057	−	0.220238i
$71$	16.0954			1.91018			0.955088	−	0.296322i	$-0.0957600\pi$
$71$	16.0954			1.91018			0.955088	+	0.296322i	$0.0957600\pi$
$72$	1.11360	−	1.92882i	0.131239	−	0.227313i
$73$	−4.37866	−	7.58406i	−0.512483	−	0.887647i	−0.999895	−	0.0144749i	$-0.995392\pi$
$73$	−4.37866	−	7.58406i	−0.512483	−	0.887647i	0.487412	−	0.873172i	$-0.337941\pi$
$74$	−0.0842945	−	0.146002i	−0.00979904	−	0.0169724i
$75$	−1.38104	+	2.39202i	−0.159468	+	0.276207i
$76$	4.31534			0.495003
$77$	−1.72854	−	2.00304i	−0.196985	−	0.228267i
$78$	0.784462			0.0888228
$79$	−4.72483	+	8.18365i	−0.531585	+	0.920732i	0.467735	+	0.883869i	$0.345070\pi$
$79$	−4.72483	+	8.18365i	−0.531585	+	0.920732i	−0.999320	+	0.0368638i	$0.988263\pi$
$80$	−1.40181	−	2.42801i	−0.156727	−	0.271460i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.51272	−	2.62011i	0.167052	−	0.289342i
$83$	9.00578			0.988513			0.494256	−	0.869316i	$-0.335440\pi$
$83$	9.00578			0.988513			0.494256	+	0.869316i	$0.335440\pi$
$84$	−1.41168	+	4.05216i	−0.154027	+	0.442127i
$85$	0.919926			0.0997800
$86$	−2.89792	+	5.01934i	−0.312491	+	0.541250i
$87$	4.22451	+	7.31707i	0.452915	+	0.784472i
$88$	1.11360	+	1.92882i	0.118711	+	0.205613i
$89$	−5.33812	+	9.24589i	−0.565839	+	0.980062i	0.431132	+	0.902289i	$0.358114\pi$
$89$	−5.33812	+	9.24589i	−0.565839	+	0.980062i	−0.996971	+	0.0777732i	$0.975219\pi$
$90$	0.919926			0.0969688
$91$	−3.31543	+	0.632026i	−0.347552	+	0.0662543i
$92$	−3.03954			−0.316894
$93$	2.31093	−	4.00264i	0.239632	−	0.415055i
$94$	0.972248	+	1.68398i	0.100280	+	0.173689i
$95$	1.99020	+	3.44713i	0.204190	+	0.353668i
$96$	2.80344	−	4.85570i	0.286125	−	0.495583i
$97$	−17.6881			−1.79595			−0.897977	−	0.440042i	$-0.854964\pi$
$97$	−17.6881			−1.79595			−0.897977	+	0.440042i	$0.854964\pi$
$98$	−0.629878	+	4.25822i	−0.0636273	+	0.430145i
$99$	1.00000			0.100504
$100$	−2.23984	+	3.87951i	−0.223984	+	0.387951i
$101$	−2.35039	−	4.07100i	−0.233873	−	0.405080i	0.725072	−	0.688673i	$-0.241807\pi$
$101$	−2.35039	−	4.07100i	−0.233873	−	0.405080i	−0.958945	+	0.283594i	$0.908473\pi$
$102$	0.189073	+	0.327484i	0.0187210	+	0.0324258i
$103$	−8.78209	+	15.2110i	−0.865325	+	1.49879i	0.00139871	+	0.999999i	$0.499555\pi$
$103$	−8.78209	+	15.2110i	−0.865325	+	1.49879i	−0.866724	+	0.498788i	$0.833779\pi$
$104$	2.84121			0.278603
$105$	−3.88795	+	0.741167i	−0.379425	+	0.0723305i
$106$	3.80542			0.369615
$107$	−5.91704	+	10.2486i	−0.572022	+	0.990771i	0.424336	+	0.905505i	$0.360508\pi$
$107$	−5.91704	+	10.2486i	−0.572022	+	0.990771i	−0.996358	+	0.0852666i	$0.972826\pi$
$108$	−0.810927	−	1.40457i	−0.0780315	−	0.135154i
$109$	0.511958	+	0.886737i	0.0490367	+	0.0849340i	0.889502	−	0.456931i	$-0.151052\pi$
$109$	0.511958	+	0.886737i	0.0490367	+	0.0849340i	−0.840465	+	0.541865i	$0.817718\pi$
$110$	−0.459963	+	0.796680i	−0.0438558	+	0.0759604i
$111$	−0.274157			−0.0260218
$112$	−1.63125	+	4.68244i	−0.154139	+	0.442449i
$113$	6.28526			0.591268			0.295634	−	0.955301i	$-0.404469\pi$
$113$	6.28526			0.591268			0.295634	+	0.955301i	$0.404469\pi$
$114$	−0.818094	+	1.41698i	−0.0766215	+	0.132712i
$115$	−1.40181	−	2.42801i	−0.130720	−	0.226413i
$116$	6.85154	+	11.8672i	0.636149	+	1.10184i
$117$	0.637840	−	1.10477i	0.0589684	−	0.102136i
$118$	1.15246			0.106093
$119$	−1.06294	−	1.23174i	−0.0974397	−	0.112913i
$120$	3.33184			0.304154
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.62160	+	4.54075i	0.237349	+	0.411100i
$123$	−2.45996	−	4.26078i	−0.221807	−	0.384182i
$124$	3.74799	−	6.49170i	0.336579	−	0.582972i
$125$	−11.6118			−1.03859
$126$	−1.06294	−	1.23174i	−0.0946943	−	0.109732i
$127$	−19.7328			−1.75100			−0.875500	−	0.483218i	$-0.839468\pi$
$127$	−19.7328			−1.75100			−0.875500	+	0.483218i	$0.839468\pi$
$128$	5.69923	−	9.87136i	0.503746	−	0.872513i
$129$	4.71255	+	8.16238i	0.414917	+	0.718658i
$130$	0.586766	+	1.01631i	0.0514628	+	0.0891362i
$131$	2.65786	−	4.60355i	0.232218	−	0.402214i	−0.726242	−	0.687439i	$-0.758735\pi$
$131$	2.65786	−	4.60355i	0.232218	−	0.402214i	0.958461	+	0.285225i	$0.0920682\pi$
$132$	1.62185			0.141164
$133$	2.31594	−	6.64781i	0.200817	−	0.576438i
$134$	3.11307			0.268929
$135$	0.747986	−	1.29555i	0.0643763	−	0.111503i
$136$	0.684795	+	1.18610i	0.0587207	+	0.101707i
$137$	−1.19408	−	2.06821i	−0.102017	−	0.176699i	0.810498	−	0.585741i	$-0.199196\pi$
$137$	−1.19408	−	2.06821i	−0.102017	−	0.176699i	−0.912516	+	0.409042i	$0.865863\pi$
$138$	0.576231	−	0.998061i	0.0490520	−	0.0849606i
$139$	12.4948			1.05980			0.529899	−	0.848061i	$-0.322230\pi$
$139$	12.4948			1.05980			0.529899	+	0.848061i	$0.322230\pi$
$140$	−6.30569	+	1.20206i	−0.532928	+	0.101593i
$141$	3.16211			0.266298
$142$	−4.94883	+	8.57163i	−0.415297	+	0.719315i
$143$	0.637840	+	1.10477i	0.0533389	+	0.0923857i
$144$	−0.937059	−	1.62303i	−0.0780882	−	0.135253i
$145$	−6.31975	+	10.9461i	−0.524826	+	0.909026i
$146$	5.38519			0.445681
$147$	5.48478	+	4.34940i	0.452377	+	0.358732i
$148$	−0.444643			−0.0365494
$149$	3.35328	−	5.80805i	0.274711	−	0.475814i	−0.695351	−	0.718670i	$-0.744751\pi$
$149$	3.35328	−	5.80805i	0.274711	−	0.475814i	0.970062	+	0.242857i	$0.0780844\pi$
$150$	−0.849248	−	1.47094i	−0.0693408	−	0.120102i
$151$	5.08451	+	8.80664i	0.413772	+	0.716674i	0.995299	−	0.0968533i	$-0.0308778\pi$
$151$	5.08451	+	8.80664i	0.413772	+	0.716674i	−0.581527	+	0.813527i	$0.697544\pi$
$152$	−2.96302	+	5.13209i	−0.240332	+	0.416268i
$153$	0.614936			0.0497146
$154$	1.59819	−	0.304665i	0.128786	−	0.0245506i
$155$	6.91416			0.555359
$156$	1.03448	−	1.79178i	0.0828250	−	0.143457i
$157$	−10.9382	−	18.9455i	−0.872964	−	1.51202i	−0.858916	−	0.512117i	$-0.828861\pi$
$157$	−10.9382	−	18.9455i	−0.872964	−	1.51202i	−0.0140485	−	0.999901i	$-0.504472\pi$
$158$	−2.90547	−	5.03242i	−0.231147	−	0.400358i
$159$	3.09416	−	5.35924i	0.245383	−	0.425015i
$160$	8.38773			0.663108
$161$	−1.63125	+	4.68244i	−0.128560	+	0.369028i
$162$	0.614936			0.0483139
$163$	−8.63594	+	14.9579i	−0.676419	+	1.17159i	0.299633	+	0.954055i	$0.403136\pi$
$163$	−8.63594	+	14.9579i	−0.676419	+	1.17159i	−0.976052	+	0.217537i	$0.930198\pi$
$164$	−3.98970	−	6.91036i	−0.311543	−	0.539609i
$165$	0.747986	+	1.29555i	0.0582306	+	0.100858i
$166$	−2.76899	+	4.79603i	−0.214915	+	0.372244i
$167$	−13.4655			−1.04199			−0.520997	−	0.853559i	$-0.674440\pi$
$167$	−13.4655			−1.04199			−0.520997	+	0.853559i	$0.674440\pi$
$168$	−3.84982	−	4.46118i	−0.297020	−	0.344187i
$169$	−11.3726			−0.874818
$170$	−0.282848	+	0.489907i	−0.0216934	+	0.0375741i
$171$	1.33037	+	2.30427i	0.101736	+	0.176212i
$172$	7.64307	+	13.2382i	0.582779	+	1.00940i
$173$	9.02795	−	15.6369i	0.686382	−	1.18885i	−0.286618	−	0.958045i	$-0.592531\pi$
$173$	9.02795	−	15.6369i	0.686382	−	1.18885i	0.973000	−	0.230804i	$-0.0741357\pi$
$174$	−5.19561			−0.393878
$175$	4.77435	+	5.53252i	0.360907	+	0.418219i
$176$	1.87412			0.141267
$177$	0.937059	−	1.62303i	0.0704336	−	0.121995i
$178$	−3.28260	−	5.68563i	−0.246041	−	0.426156i
$179$	8.73467	+	15.1289i	0.652860	+	1.13079i	0.982426	+	0.186654i	$0.0597642\pi$
$179$	8.73467	+	15.1289i	0.652860	+	1.13079i	−0.329566	+	0.944133i	$0.606902\pi$
$180$	1.21312	−	2.10119i	0.0904209	−	0.156614i
$181$	−2.68530			−0.199597			−0.0997985	−	0.995008i	$-0.531820\pi$
$181$	−2.68530			−0.199597			−0.0997985	+	0.995008i	$0.531820\pi$
$182$	0.682803	−	1.95996i	0.0506127	−	0.145282i
$183$	8.52643			0.630292
$184$	2.08702	−	3.61483i	0.153857	−	0.266489i
$185$	−0.205065	−	0.355184i	−0.0150767	−	0.0261136i
$186$	1.42107	+	2.46137i	0.104198	+	0.180476i
$187$	−0.307468	+	0.532550i	−0.0224843	+	0.0389439i
$188$	5.12848			0.374033
$189$	−2.59895	+	0.495442i	−0.189046	+	0.0360381i
$190$	−2.44769			−0.177574
$191$	9.41971	−	16.3154i	0.681586	−	1.18054i	−0.292910	−	0.956140i	$-0.594624\pi$
$191$	9.41971	−	16.3154i	0.681586	−	1.18054i	0.974497	−	0.224402i	$-0.0720430\pi$
$192$	−0.150182	−	0.260123i	−0.0108384	−	0.0187727i
$193$	−7.12135	−	12.3345i	−0.512606	−	0.887859i	−0.999893	−	0.0146175i	$-0.995347\pi$
$193$	−7.12135	−	12.3345i	−0.512606	−	0.887859i	0.487287	−	0.873242i	$-0.337986\pi$
$194$	5.43853	−	9.41980i	0.390463	−	0.676302i
$195$	1.90838			0.136662
$196$	8.89550	+	7.05408i	0.635393	+	0.503863i
$197$	−13.5291			−0.963908			−0.481954	−	0.876196i	$-0.660073\pi$
$197$	−13.5291			−0.963908			−0.481954	+	0.876196i	$0.660073\pi$
$198$	−0.307468	+	0.532550i	−0.0218508	+	0.0378467i
$199$	−7.11782	−	12.3284i	−0.504569	−	0.873940i	−0.999986	−	0.00528415i	$-0.998318\pi$
$199$	−7.11782	−	12.3284i	−0.504569	−	0.873940i	0.495417	−	0.868655i	$-0.335015\pi$
$200$	−3.07585	−	5.32753i	−0.217496	−	0.376713i
$201$	2.53122	−	4.38420i	0.178538	−	0.309237i
$202$	2.89068			0.203388
$203$	21.9586	−	4.18600i	1.54119	−	0.293800i
$204$	0.997336			0.0698275
$205$	3.68003	−	6.37401i	0.257025	−	0.445180i
$206$	−5.40042	−	9.35381i	−0.376265	−	0.651711i
$207$	−0.937059	−	1.62303i	−0.0651301	−	0.112809i
$208$	1.19539	−	2.07047i	0.0828852	−	0.143561i
$209$	−2.66075			−0.184048
$210$	0.800712	−	2.29842i	0.0552544	−	0.158606i
$211$	1.50124			0.103350			0.0516748	−	0.998664i	$-0.483544\pi$
$211$	1.50124			0.103350			0.0516748	+	0.998664i	$0.483544\pi$
$212$	5.01827	−	8.69190i	0.344656	−	0.596962i
$213$	8.04772	+	13.9391i	0.551420	+	0.955088i
$214$	−3.63860	−	6.30224i	−0.248730	−	0.430813i
$215$	−7.04984	+	12.2107i	−0.480795	+	0.832762i
$216$	2.22721			0.151542
$217$	−7.98906	−	9.25774i	−0.542333	−	0.628456i
$218$	−0.629642			−0.0426448
$219$	4.37866	−	7.58406i	0.295882	−	0.512483i
$220$	1.21312	+	2.10119i	0.0817888	+	0.141662i
$221$	0.392231	+	0.679364i	0.0263843	+	0.0456990i
$222$	0.0842945	−	0.146002i	0.00565748	−	0.00979904i
$223$	7.22937			0.484115			0.242057	−	0.970262i	$-0.422178\pi$
$223$	7.22937			0.484115			0.242057	+	0.970262i	$0.422178\pi$
$224$	−9.69171	−	11.2308i	−0.647555	−	0.750388i
$225$	−2.76207			−0.184138
$226$	−1.93252	+	3.34722i	−0.128549	+	0.222654i
$227$	0.400040	+	0.692889i	0.0265516	+	0.0459887i	0.878996	−	0.476829i	$-0.158214\pi$
$227$	0.400040	+	0.692889i	0.0265516	+	0.0459887i	−0.852444	+	0.522818i	$0.824881\pi$
$228$	2.15767	+	3.73719i	0.142895	+	0.247502i
$229$	4.27114	−	7.39784i	0.282245	−	0.488863i	−0.689692	−	0.724103i	$-0.742254\pi$
$229$	4.27114	−	7.39784i	0.282245	−	0.488863i	0.971937	+	0.235240i	$0.0755875\pi$
$230$	1.72405			0.113680
$231$	0.870409	−	2.49848i	0.0572687	−	0.164388i
$232$	−18.8177			−1.23544
$233$	−0.919521	+	1.59266i	−0.0602398	+	0.104338i	−0.894573	−	0.446923i	$-0.852520\pi$
$233$	−0.919521	+	1.59266i	−0.0602398	+	0.104338i	0.834333	+	0.551261i	$0.185853\pi$
$234$	0.392231	+	0.679364i	0.0256409	+	0.0444114i
$235$	2.36521	+	4.09667i	0.154289	+	0.267237i
$236$	1.51977	−	2.63232i	0.0989287	−	0.171350i
$237$	−9.44966			−0.613822
$238$	0.982783	−	0.187349i	0.0637043	−	0.0121441i
$239$	−8.71500			−0.563726			−0.281863	−	0.959455i	$-0.590952\pi$
$239$	−8.71500			−0.563726			−0.281863	+	0.959455i	$0.590952\pi$
$240$	1.40181	−	2.42801i	0.0904866	−	0.156727i
$241$	−0.540256	−	0.935751i	−0.0348010	−	0.0602770i	0.848100	−	0.529836i	$-0.177746\pi$
$241$	−0.540256	−	0.935751i	−0.0348010	−	0.0602770i	−0.882901	+	0.469559i	$0.844413\pi$
$242$	−0.307468	−	0.532550i	−0.0197648	−	0.0342336i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	13.8286			0.885287
$245$	−1.53232	+	10.3591i	−0.0978965	+	0.661817i
$246$	3.02544			0.192895
$247$	−1.69713	+	2.93952i	−0.107986	+	0.187037i
$248$	5.14691	+	8.91472i	0.326829	+	0.566085i
$249$	4.50289	+	7.79923i	0.285359	+	0.494256i
$250$	3.57027	−	6.18388i	0.225803	−	0.391103i
$251$	−8.63296			−0.544908			−0.272454	−	0.962169i	$-0.587835\pi$
$251$	−8.63296			−0.544908			−0.272454	+	0.962169i	$0.587835\pi$
$252$	−4.21512	+	0.803534i	−0.265527	+	0.0506179i
$253$	1.87412			0.117825
$254$	6.06720	−	10.5087i	0.380690	−	0.659374i
$255$	0.459963	+	0.796680i	0.0288040	+	0.0498900i
$256$	3.20430	+	5.55001i	0.200269	+	0.346875i
$257$	−7.35575	+	12.7405i	−0.458839	+	0.794733i	−0.998900	−	0.0468931i	$-0.985068\pi$
$257$	−7.35575	+	12.7405i	−0.458839	+	0.794733i	0.540061	+	0.841626i	$0.318401\pi$
$258$	−5.79584			−0.360833
$259$	−0.238629	+	0.684975i	−0.0148277	+	0.0425623i
$260$	3.09512			0.191951
$261$	−4.22451	+	7.31707i	−0.261491	+	0.452915i
$262$	1.63441	+	2.83089i	0.100974	+	0.174893i
$263$	−15.4640	−	26.7844i	−0.953551	−	1.65160i	−0.737650	−	0.675183i	$-0.764064\pi$
$263$	−15.4640	−	26.7844i	−0.953551	−	1.65160i	−0.215901	−	0.976415i	$-0.569269\pi$
$264$	−1.11360	+	1.92882i	−0.0685376	+	0.118711i
$265$	9.25754			0.568686
$266$	2.82822	+	3.27734i	0.173409	+	0.200947i
$267$	−10.6762			−0.653375
$268$	4.10526	−	7.11053i	0.250769	−	0.434344i
$269$	15.5582	+	26.9475i	0.948598	+	1.64302i	0.748383	+	0.663267i	$0.230831\pi$
$269$	15.5582	+	26.9475i	0.948598	+	1.64302i	0.200215	+	0.979752i	$0.435836\pi$
$270$	0.459963	+	0.796680i	0.0279925	+	0.0484844i
$271$	−1.38484	+	2.39862i	−0.0841233	+	0.145706i	−0.905017	−	0.425375i	$-0.860142\pi$
$271$	−1.38484	+	2.39862i	−0.0841233	+	0.145706i	0.820894	+	0.571081i	$0.193476\pi$
$272$	1.15246			0.0698783
$273$	−2.20507	−	2.55523i	−0.133457	−	0.154650i
$274$	1.46857			0.0887195
$275$	1.38104	−	2.39202i	0.0832796	−	0.144244i
$276$	−1.51977	−	2.63232i	−0.0914795	−	0.158447i
$277$	−9.65146	−	16.7168i	−0.579900	−	1.00442i	−0.995490	−	0.0948641i	$-0.969758\pi$
$277$	−9.65146	−	16.7168i	−0.579900	−	1.00442i	0.415590	−	0.909552i	$-0.363575\pi$
$278$	−3.84176	+	6.65412i	−0.230413	+	0.399088i
$279$	4.62185			0.276703
$280$	2.90006	−	8.32452i	0.173312	−	0.497485i
$281$	−7.96061			−0.474890			−0.237445	−	0.971401i	$-0.576310\pi$
$281$	−7.96061			−0.474890			−0.237445	+	0.971401i	$0.576310\pi$
$282$	−0.972248	+	1.68398i	−0.0578965	+	0.100280i
$283$	4.27898	+	7.41142i	0.254359	+	0.440563i	0.964721	−	0.263273i	$-0.0848021\pi$
$283$	4.27898	+	7.41142i	0.254359	+	0.440563i	−0.710362	+	0.703836i	$0.751469\pi$
$284$	13.0522	+	22.6071i	0.774507	+	1.34149i
$285$	−1.99020	+	3.44713i	−0.117889	+	0.204190i
$286$	−0.784462			−0.0463862
$287$	−12.7866	+	2.43754i	−0.754771	+	0.143883i
$288$	5.60688			0.330388
$289$	8.31093	−	14.3949i	0.488878	−	0.846762i
$290$	−3.88624	−	6.73116i	−0.228208	−	0.395268i
$291$	−8.84405	−	15.3183i	−0.518447	−	0.897977i
$292$	7.10154	−	12.3002i	0.415586	−	0.719817i
$293$	−28.2280			−1.64910			−0.824548	−	0.565792i	$-0.808571\pi$
$293$	−28.2280			−1.64910			−0.824548	+	0.565792i	$0.808571\pi$
$294$	−4.00266	+	1.58362i	−0.233440	+	0.0923585i
$295$	2.80363			0.163233
$296$	0.305302	−	0.528799i	0.0177453	−	0.0307358i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	2.06205	+	3.57158i	0.119451	+	0.206896i
$299$	1.19539	−	2.07047i	0.0691311	−	0.119739i
$300$	−4.47967			−0.258634
$301$	24.4954	−	4.66959i	1.41189	−	0.269151i
$302$	−6.25330			−0.359837
$303$	2.35039	−	4.07100i	0.135027	−	0.233873i
$304$	2.49327	+	4.31848i	0.142999	+	0.247682i
$305$	6.37765	+	11.0464i	0.365183	+	0.632516i
$306$	−0.189073	+	0.327484i	−0.0108086	+	0.0187210i
$307$	8.29757			0.473568			0.236784	−	0.971562i	$-0.423907\pi$
$307$	8.29757			0.473568			0.236784	+	0.971562i	$0.423907\pi$
$308$	1.41168	−	4.05216i	0.0804377	−	0.230894i
$309$	−17.5642			−0.999191
$310$	−2.12588	+	3.68214i	−0.120742	+	0.209131i
$311$	17.3610	+	30.0702i	0.984453	+	1.70512i	0.644340	+	0.764739i	$0.277132\pi$
$311$	17.3610	+	30.0702i	0.984453	+	1.70512i	0.340113	+	0.940385i	$0.389535\pi$
$312$	1.42060	+	2.46056i	0.0804258	+	0.139302i
$313$	−16.0970	+	27.8809i	−0.909859	+	1.57592i	−0.0956001	+	0.995420i	$0.530477\pi$
$313$	−16.0970	+	27.8809i	−0.909859	+	1.57592i	−0.814259	+	0.580502i	$0.802856\pi$
$314$	13.4526			0.759174
$315$	−2.58585	−	2.99648i	−0.145696	−	0.168833i
$316$	−15.3260			−0.862153
$317$	5.50543	−	9.53568i	0.309216	−	0.535577i	−0.668975	−	0.743285i	$-0.733267\pi$
$317$	5.50543	−	9.53568i	0.309216	−	0.535577i	0.978191	+	0.207707i	$0.0666002\pi$
$318$	1.90271	+	3.29559i	0.106699	+	0.184807i
$319$	−4.22451	−	7.31707i	−0.236527	−	0.409677i
$320$	0.224668	−	0.389136i	0.0125593	−	0.0217534i
$321$	−11.8341			−0.660514
$322$	−1.99208	−	2.30842i	−0.111014	−	0.128643i
$323$	−1.63619			−0.0910399
$324$	0.810927	−	1.40457i	0.0450515	−	0.0780315i
$325$	−1.76176	−	3.05146i	−0.0977249	−	0.169264i
$326$	−5.31055	−	9.19814i	−0.294124	−	0.509438i
$327$	−0.511958	+	0.886737i	−0.0283113	+	0.0490367i
$328$	10.9577			0.605038
$329$	2.75233	−	7.90046i	0.151741	−	0.435566i
$330$	−0.919926			−0.0506403
$331$	−7.20065	+	12.4719i	−0.395784	+	0.685517i	−0.993201	−	0.116413i	$-0.962860\pi$
$331$	−7.20065	+	12.4719i	−0.395784	+	0.685517i	0.597417	+	0.801931i	$0.296194\pi$
$332$	7.30303	+	12.6492i	0.400806	+	0.694216i
$333$	−0.137079	−	0.237427i	−0.00751186	−	0.0130109i
$334$	4.14022	−	7.17107i	0.226543	−	0.392383i
$335$	7.57326			0.413771
$336$	−4.87074	+	0.928516i	−0.265720	+	0.0506547i
$337$	−19.0458			−1.03749			−0.518746	−	0.854928i	$-0.673601\pi$
$337$	−19.0458			−1.03749			−0.518746	+	0.854928i	$0.673601\pi$
$338$	3.49672	−	6.05650i	0.190197	−	0.329430i
$339$	3.14263	+	5.44320i	0.170684	+	0.295634i
$340$	0.745993	+	1.29210i	0.0404572	+	0.0700738i
$341$	−2.31093	+	4.00264i	−0.125144	+	0.216755i
$342$	−1.63619			−0.0884749
$343$	15.6409	−	9.91783i	0.844527	−	0.535513i
$344$	−20.9917			−1.13180
$345$	1.40181	−	2.42801i	0.0754711	−	0.130720i
$346$	5.55161	+	9.61567i	0.298456	+	0.516942i
$347$	8.74256	+	15.1426i	0.469325	+	0.812895i	0.999385	−	0.0350650i	$-0.0111638\pi$
$347$	8.74256	+	15.1426i	0.469325	+	0.812895i	−0.530060	+	0.847960i	$0.677830\pi$
$348$	−6.85154	+	11.8672i	−0.367281	+	0.636149i
$349$	31.9333			1.70935			0.854676	−	0.519162i	$-0.173756\pi$
$349$	31.9333			1.70935			0.854676	+	0.519162i	$0.173756\pi$
$350$	−4.41431	+	0.841506i	−0.235955	+	0.0449804i
$351$	1.27568			0.0680908
$352$	−2.80344	+	4.85570i	−0.149424	+	0.258810i
$353$	13.8765	+	24.0349i	0.738574	+	1.27925i	0.953137	+	0.302537i	$0.0978337\pi$
$353$	13.8765	+	24.0349i	0.738574	+	1.27925i	−0.214564	+	0.976710i	$0.568833\pi$
$354$	0.576231	+	0.998061i	0.0306263	+	0.0530464i
$355$	−12.0392	+	20.8524i	−0.638972	+	1.10673i
$356$	−17.3153			−0.917708
$357$	0.535246	−	1.53640i	0.0283282	−	0.0813151i
$358$	−10.7425			−0.567760
$359$	−3.30325	+	5.72139i	−0.174339	+	0.301964i	−0.939932	−	0.341361i	$-0.889112\pi$
$359$	−3.30325	+	5.72139i	−0.174339	+	0.301964i	0.765594	+	0.643325i	$0.222445\pi$
$360$	1.66592	+	2.88546i	0.0878017	+	0.152077i
$361$	5.96022	+	10.3234i	0.313696	+	0.543337i
$362$	0.825644	−	1.43006i	0.0433949	−	0.0751622i
$363$	−1.00000			−0.0524864
$364$	−3.57629	−	4.14422i	−0.187449	−	0.217216i
$365$	13.1007			0.685722
$366$	−2.62160	+	4.54075i	−0.137033	+	0.237349i
$367$	13.1226	+	22.7290i	0.684995	+	1.18645i	0.973438	+	0.228950i	$0.0735291\pi$
$367$	13.1226	+	22.7290i	0.684995	+	1.18645i	−0.288443	+	0.957497i	$0.593138\pi$
$368$	−1.75616	−	3.04175i	−0.0915461	−	0.158562i
$369$	2.45996	−	4.26078i	0.128061	−	0.221807i
$370$	0.252204			0.0131115
$371$	−10.6968	−	12.3954i	−0.555348	−	0.643538i
$372$	7.49597			0.388648
$373$	3.88116	−	6.72237i	0.200959	−	0.348071i	−0.747879	−	0.663835i	$-0.768928\pi$
$373$	3.88116	−	6.72237i	0.200959	−	0.348071i	0.948838	+	0.315764i	$0.102261\pi$
$374$	−0.189073	−	0.327484i	−0.00977674	−	0.0169338i
$375$	−5.80592	−	10.0561i	−0.299816	−	0.519297i
$376$	−3.52134	+	6.09914i	−0.181599	+	0.314539i
$377$	−10.7783			−0.555108
$378$	0.535246	−	1.53640i	0.0275301	−	0.0790241i
$379$	15.4636			0.794310			0.397155	−	0.917752i	$-0.369998\pi$
$379$	15.4636			0.794310			0.397155	+	0.917752i	$0.369998\pi$
$380$	−3.22781	+	5.59073i	−0.165583	+	0.286799i
$381$	−9.86639	−	17.0891i	−0.505470	−	0.875500i
$382$	5.79252	+	10.0329i	0.296371	+	0.513330i
$383$	13.3787	−	23.1725i	0.683618	−	1.18406i	−0.290251	−	0.956950i	$-0.593739\pi$
$383$	13.3787	−	23.1725i	0.683618	−	1.18406i	0.973869	−	0.227110i	$-0.0729278\pi$
$384$	11.3985			0.581675
$385$	3.88795	−	0.741167i	0.198148	−	0.0377734i
$386$	8.75834			0.445788
$387$	−4.71255	+	8.16238i	−0.239553	+	0.414917i
$388$	−14.3438	−	24.8441i	−0.728194	−	1.26127i
$389$	−9.88948	−	17.1291i	−0.501416	−	0.868479i	−0.999999	−	0.00163628i	$-0.999479\pi$
$389$	−9.88948	−	17.1291i	−0.501416	−	0.868479i	0.498582	−	0.866842i	$-0.333854\pi$
$390$	−0.586766	+	1.01631i	−0.0297121	+	0.0514628i
$391$	1.15246			0.0582825
$392$	−14.4971	+	5.73563i	−0.732212	+	0.289693i
$393$	5.31572			0.268143
$394$	4.15976	−	7.20492i	0.209566	−	0.362979i
$395$	−7.06821	−	12.2425i	−0.355640	−	0.615987i
$396$	0.810927	+	1.40457i	0.0407506	+	0.0705821i
$397$	0.124394	−	0.215457i	0.00624316	−	0.0108135i	−0.862887	−	0.505397i	$-0.831346\pi$
$397$	0.124394	−	0.215457i	0.00624316	−	0.0108135i	0.869130	+	0.494584i	$0.164679\pi$
$398$	8.75401			0.438799
$399$	6.91514	−	1.31824i	0.346190	−	0.0659948i
$400$	−5.17644			−0.258822
$401$	−17.3938	+	30.1269i	−0.868603	+	1.50446i	−0.00517891	+	0.999987i	$0.501649\pi$
$401$	−17.3938	+	30.1269i	−0.868603	+	1.50446i	−0.863424	+	0.504478i	$0.831685\pi$
$402$	1.55654	+	2.69600i	0.0776330	+	0.134464i
$403$	2.94801	+	5.10610i	0.146851	+	0.254353i
$404$	3.81200	−	6.60257i	0.189654	−	0.328490i
$405$	1.49597			0.0743354
$406$	−4.52230	+	12.9811i	−0.224438	+	0.644241i
$407$	0.274157			0.0135895
$408$	−0.684795	+	1.18610i	−0.0339024	+	0.0587207i
$409$	0.903940	+	1.56567i	0.0446969	+	0.0774174i	0.887508	−	0.460792i	$-0.152434\pi$
$409$	0.903940	+	1.56567i	0.0446969	+	0.0774174i	−0.842811	+	0.538209i	$0.819101\pi$
$410$	2.26299	+	3.91961i	0.111761	+	0.193576i
$411$	1.19408	−	2.06821i	0.0588998	−	0.102017i
$412$	−28.4865			−1.40343
$413$	−3.23949	−	3.75392i	−0.159405	−	0.184718i
$414$	1.15246			0.0566404
$415$	−6.73619	+	11.6674i	−0.330667	+	0.572731i
$416$	3.57629	+	6.19432i	0.175342	+	0.303702i
$417$	6.24742	+	10.8208i	0.305937	+	0.529899i
$418$	0.818094	−	1.41698i	0.0400143	−	0.0693068i
$419$	25.7007			1.25556			0.627780	−	0.778391i	$-0.283964\pi$
$419$	25.7007			1.25556			0.627780	+	0.778391i	$0.283964\pi$
$420$	−4.19386	−	4.85986i	−0.204640	−	0.237137i
$421$	25.2666			1.23142			0.615710	−	0.787973i	$-0.288869\pi$
$421$	25.2666			1.23142			0.615710	+	0.787973i	$0.288869\pi$
$422$	−0.461583	+	0.799485i	−0.0224695	+	0.0389183i
$423$	1.58106	+	2.73847i	0.0768735	+	0.133149i
$424$	6.89133	+	11.9361i	0.334673	+	0.579670i
$425$	0.849248	−	1.47094i	0.0411946	−	0.0713511i
$426$	−9.89766			−0.479543
$427$	7.42149	−	21.3031i	0.359151	−	1.03093i
$428$	−19.1932			−0.927736
$429$	−0.637840	+	1.10477i	−0.0307952	+	0.0533389i
$430$	−4.33520	−	7.50879i	−0.209062	−	0.362106i
$431$	−16.5150	−	28.6048i	−0.795499	−	1.37784i	−0.922522	−	0.385944i	$-0.873876\pi$
$431$	−16.5150	−	28.6048i	−0.795499	−	1.37784i	0.127023	−	0.991900i	$-0.459458\pi$
$432$	0.937059	−	1.62303i	0.0450843	−	0.0780882i
$433$	15.9029			0.764243			0.382122	−	0.924112i	$-0.375194\pi$
$433$	15.9029			0.764243			0.382122	+	0.924112i	$0.375194\pi$
$434$	7.38659	−	1.40812i	0.354568	−	0.0675918i
$435$	−12.6395			−0.606017
$436$	−0.830321	+	1.43816i	−0.0397651	+	0.0688753i
$437$	2.49327	+	4.31848i	0.119269	+	0.206581i
$438$	2.69259	+	4.66371i	0.128657	+	0.222841i
$439$	−2.23812	+	3.87653i	−0.106819	+	0.185017i	−0.914480	−	0.404631i	$-0.867400\pi$
$439$	−2.23812	+	3.87653i	−0.106819	+	0.185017i	0.807661	+	0.589648i	$0.200733\pi$
$440$	−3.33184			−0.158839
$441$	−1.02430	+	6.92465i	−0.0487762	+	0.329745i
$442$	−0.482394			−0.0229451
$443$	0.818736	−	1.41809i	0.0388993	−	0.0673756i	−0.845920	−	0.533309i	$-0.820948\pi$
$443$	0.818736	−	1.41809i	0.0388993	−	0.0673756i	0.884820	+	0.465934i	$0.154282\pi$
$444$	−0.222321	−	0.385072i	−0.0105509	−	0.0182747i
$445$	−7.98567	−	13.8316i	−0.378557	−	0.655680i
$446$	−2.22280	+	3.85000i	−0.105253	+	0.182303i
$447$	6.70655			0.317209
$448$	−0.780630	+	0.148813i	−0.0368813	+	0.00703075i
$449$	−2.45974			−0.116082			−0.0580412	−	0.998314i	$-0.518485\pi$
$449$	−2.45974			−0.116082			−0.0580412	+	0.998314i	$0.518485\pi$
$450$	0.849248	−	1.47094i	0.0400339	−	0.0693408i
$451$	2.45996	+	4.26078i	0.115835	+	0.200632i
$452$	5.09689	+	8.82807i	0.239737	+	0.415237i
$453$	−5.08451	+	8.80664i	−0.238891	+	0.413772i
$454$	−0.491998			−0.0230906
$455$	1.66107	−	4.76805i	0.0778723	−	0.223530i
$456$	−5.92603			−0.277512
$457$	15.4981	−	26.8436i	0.724972	−	1.25569i	−0.234013	−	0.972233i	$-0.575186\pi$
$457$	15.4981	−	26.8436i	0.724972	−	1.25569i	0.958985	−	0.283455i	$-0.0914807\pi$
$458$	2.62648	+	4.54920i	0.122727	+	0.212570i
$459$	0.307468	+	0.532550i	0.0143514	+	0.0248573i
$460$	2.27354	−	3.93788i	0.106004	−	0.183605i
$461$	−17.0555			−0.794355			−0.397177	−	0.917742i	$-0.630010\pi$
$461$	−17.0555			−0.794355			−0.397177	+	0.917742i	$0.630010\pi$
$462$	1.06294	+	1.23174i	0.0494525	+	0.0573057i
$463$	13.9963			0.650461			0.325231	−	0.945635i	$-0.394558\pi$
$463$	13.9963			0.650461			0.325231	+	0.945635i	$0.394558\pi$
$464$	−7.91723	+	13.7130i	−0.367548	+	0.636612i
$465$	3.45708	+	5.98784i	0.160318	+	0.277679i
$466$	−0.565446	−	0.979382i	−0.0261938	−	0.0453690i
$467$	−18.8191	+	32.5957i	−0.870845	+	1.50835i	−0.00972103	+	0.999953i	$0.503094\pi$
$467$	−18.8191	+	32.5957i	−0.870845	+	1.50835i	−0.861124	+	0.508395i	$0.830239\pi$
$468$	2.06897			0.0956381
$469$	−8.75062	−	10.1402i	−0.404066	−	0.468232i
$470$	−2.90891			−0.134178
$471$	10.9382	−	18.9455i	0.504006	−	0.872964i
$472$	2.08702	+	3.61483i	0.0960631	+	0.166386i
$473$	−4.71255	−	8.16238i	−0.216683	−	0.375307i
$474$	2.90547	−	5.03242i	0.133453	−	0.231147i
$475$	7.34916			0.337203
$476$	0.868091	−	2.49182i	0.0397889	−	0.114212i
$477$	6.18832			0.283344
$478$	2.67958	−	4.64117i	0.122561	−	0.212282i
$479$	−17.2495	−	29.8770i	−0.788149	−	1.36511i	−0.927100	−	0.374815i	$-0.877706\pi$
$479$	−17.2495	−	29.8770i	−0.788149	−	1.36511i	0.138951	−	0.990299i	$-0.455627\pi$
$480$	4.19386	+	7.26399i	0.191423	+	0.331554i
$481$	0.174868	−	0.302881i	0.00797331	−	0.0138102i
$482$	0.664446			0.0302647
$483$	−4.87074	+	0.928516i	−0.221626	+	0.0422490i
$484$	−1.62185			−0.0737206
$485$	13.2304	−	22.9158i	0.600764	−	1.04055i
$486$	0.307468	+	0.532550i	0.0139470	+	0.0241570i
$487$	1.03741	+	1.79685i	0.0470096	+	0.0814230i	0.888573	−	0.458736i	$-0.151698\pi$
$487$	1.03741	+	1.79685i	0.0470096	+	0.0814230i	−0.841563	+	0.540159i	$0.818364\pi$
$488$	−9.49507	+	16.4459i	−0.429822	+	0.744473i
$489$	−17.2719			−0.781061
$490$	−5.04559	−	4.00112i	−0.227937	−	0.180752i
$491$	−29.9003			−1.34938			−0.674692	−	0.738100i	$-0.735723\pi$
$491$	−29.9003			−1.34938			−0.674692	+	0.738100i	$0.735723\pi$
$492$	3.98970	−	6.91036i	0.179870	−	0.311543i
$493$	−2.59780	−	4.49953i	−0.116999	−	0.202649i
$494$	−1.04363	−	1.80761i	−0.0469550	−	0.0813284i
$495$	−0.747986	+	1.29555i	−0.0336195	+	0.0582306i
$496$	8.66190			0.388931
$497$	41.8312	−	7.97435i	1.87639	−	0.357699i
$498$	−5.53798			−0.248163
$499$	−0.689073	+	1.19351i	−0.0308471	+	0.0534288i	−0.881037	−	0.473048i	$-0.843154\pi$
$499$	−0.689073	+	1.19351i	−0.0308471	+	0.0534288i	0.850190	+	0.526476i	$0.176487\pi$
$500$	−9.41635	−	16.3096i	−0.421112	−	0.729387i
$501$	−6.73276	−	11.6615i	−0.300798	−	0.520997i
$502$	2.65436	−	4.59748i	0.118470	−	0.205196i
$503$	34.3693			1.53245			0.766226	−	0.642571i	$-0.222132\pi$
$503$	34.3693			1.53245			0.766226	+	0.642571i	$0.222132\pi$
$504$	1.93858	−	5.56463i	0.0863513	−	0.247868i
$505$	7.03224			0.312931
$506$	−0.576231	+	0.998061i	−0.0256166	+	0.0443692i
$507$	−5.68632	−	9.84899i	−0.252538	−	0.437409i
$508$	−16.0018	−	27.7160i	−0.709967	−	1.22970i
$509$	16.0981	−	27.8827i	0.713536	−	1.23588i	−0.249986	−	0.968249i	$-0.580426\pi$
$509$	16.0981	−	27.8827i	0.713536	−	1.23588i	0.963522	−	0.267630i	$-0.0862406\pi$
$510$	−0.565696			−0.0250494
$511$	−15.1374	−	17.5412i	−0.669638	−	0.775978i
$512$	18.8560			0.833327
$513$	−1.33037	+	2.30427i	−0.0587374	+	0.101736i
$514$	−4.52332	−	7.83462i	−0.199515	−	0.345570i
$515$	−13.1378	−	22.7553i	−0.578919	−	1.00272i
$516$	−7.64307	+	13.2382i	−0.336468	+	0.582779i
$517$	−3.16211			−0.139069
$518$	−0.291413	−	0.337690i	−0.0128039	−	0.0148372i
$519$	18.0559			0.792566
$520$	−2.12518	+	3.68092i	−0.0931954	+	0.161419i
$521$	−13.5887	−	23.5364i	−0.595334	−	1.03115i	−0.993500	−	0.113835i	$-0.963687\pi$
$521$	−13.5887	−	23.5364i	−0.595334	−	1.03115i	0.398166	−	0.917313i	$-0.369647\pi$
$522$	−2.59780	−	4.49953i	−0.113703	−	0.196939i
$523$	0.494960	−	0.857296i	0.0216431	−	0.0374869i	−0.855001	−	0.518626i	$-0.826444\pi$
$523$	0.494960	−	0.857296i	0.0216431	−	0.0374869i	0.876644	+	0.481139i	$0.159777\pi$
$524$	8.62133			0.376624
$525$	−2.40413	+	6.90097i	−0.104925	+	0.301183i
$526$	19.0187			0.829256
$527$	−1.42107	+	2.46137i	−0.0619029	+	0.107219i
$528$	0.937059	+	1.62303i	0.0407802	+	0.0706335i
$529$	9.74384	+	16.8768i	0.423645	+	0.733775i
$530$	−2.84640	+	4.93011i	−0.123640	+	0.214150i
$531$	1.87412			0.0813298
$532$	11.2153	−	2.13800i	0.486247	−	0.0926941i
$533$	6.27626			0.271855
$534$	3.28260	−	5.68563i	0.142052	−	0.246041i
$535$	−8.85173	−	15.3316i	−0.382693	−	0.662845i
$536$	5.63755	+	9.76452i	0.243505	+	0.421763i
$537$	−8.73467	+	15.1289i	−0.376929	+	0.652860i
$538$	−19.1345			−0.824949
$539$	−5.48478	−	4.34940i	−0.236246	−	0.187342i
$540$	2.42625			0.104409
$541$	12.7729	−	22.1234i	0.549151	−	0.951158i	−0.449182	−	0.893440i	$-0.648284\pi$
$541$	12.7729	−	22.1234i	0.549151	−	0.951158i	0.998333	−	0.0577174i	$-0.0183822\pi$
$542$	−0.851591	−	1.47500i	−0.0365790	−	0.0633566i
$543$	−1.34265	−	2.32554i	−0.0576187	−	0.0997985i
$544$	−1.72394	+	2.98594i	−0.0739131	+	0.128021i
$545$	−1.53175			−0.0656129
$546$	2.03878	−	0.388655i	0.0872516	−	0.0166329i
$547$	−5.97544			−0.255491			−0.127746	−	0.991807i	$-0.540774\pi$
$547$	−5.97544			−0.255491			−0.127746	+	0.991807i	$0.540774\pi$
$548$	1.93663	−	3.35434i	0.0827287	−	0.143290i
$549$	4.26322	+	7.38411i	0.181950	+	0.315146i
$550$	0.849248	+	1.47094i	0.0362121	+	0.0627211i
$551$	11.2403	−	19.4689i	0.478855	−	0.829401i
$552$	4.17405			0.177659
$553$	−8.22508	+	23.6098i	−0.349766	+	1.00399i
$554$	11.8701			0.504310
$555$	0.205065	−	0.355184i	0.00870454	−	0.0150767i
$556$	10.1324	+	17.5498i	0.429709	+	0.744278i
$557$	7.48068	+	12.9569i	0.316967	+	0.549002i	0.979854	−	0.199717i	$-0.0640023\pi$
$557$	7.48068	+	12.9569i	0.316967	+	0.549002i	−0.662887	+	0.748720i	$0.730669\pi$
$558$	−1.42107	+	2.46137i	−0.0601588	+	0.104198i
$559$	−12.0234			−0.508537
$560$	−4.84618	−	5.61576i	−0.204788	−	0.237309i
$561$	−0.614936			−0.0259626
$562$	2.44763	−	4.23942i	0.103247	−	0.178829i
$563$	19.1138	+	33.1061i	0.805551	+	1.39525i	0.915919	+	0.401364i	$0.131464\pi$
$563$	19.1138	+	33.1061i	0.805551	+	1.39525i	−0.110368	+	0.993891i	$0.535203\pi$
$564$	2.56424	+	4.44139i	0.107974	+	0.187016i
$565$	−4.70129	+	8.14287i	−0.197785	+	0.342573i
$566$	−5.26260			−0.221204
$567$	−1.72854	−	2.00304i	−0.0725919	−	0.0841196i
$568$	−35.8479			−1.50414
$569$	−4.97944	+	8.62465i	−0.208749	+	0.361564i	−0.951321	−	0.308203i	$-0.900273\pi$
$569$	−4.97944	+	8.62465i	−0.208749	+	0.361564i	0.742572	+	0.669767i	$0.233606\pi$
$570$	−1.22384	−	2.11976i	−0.0512612	−	0.0887870i
$571$	13.1256	+	22.7341i	0.549288	+	0.951395i	0.998324	+	0.0578807i	$0.0184343\pi$
$571$	13.1256	+	22.7341i	0.549288	+	0.951395i	−0.449036	+	0.893514i	$0.648232\pi$
$572$	−1.03448	+	1.79178i	−0.0432539	+	0.0749180i
$573$	18.8394			0.787028
$574$	2.63337	−	7.55899i	0.109915	−	0.315506i
$575$	−5.17644			−0.215873
$576$	0.150182	−	0.260123i	0.00625758	−	0.0108384i
$577$	−5.75328	−	9.96497i	−0.239512	−	0.414847i	0.721062	−	0.692870i	$-0.243654\pi$
$577$	−5.75328	−	9.96497i	−0.239512	−	0.414847i	−0.960574	+	0.278023i	$0.910321\pi$
$578$	5.11069	+	8.85197i	0.212577	+	0.368193i
$579$	7.12135	−	12.3345i	0.295953	−	0.512606i
$580$	−20.4994			−0.851192
$581$	23.4056	−	4.46184i	0.971026	−	0.185108i
$582$	10.8771			0.450868
$583$	−3.09416	+	5.35924i	−0.128147	+	0.221957i
$584$	9.75218	+	16.8913i	0.403548	+	0.698966i
$585$	0.954191	+	1.65271i	0.0394509	+	0.0683310i
$586$	8.67920	−	15.0328i	0.358534	−	0.621000i
$587$	21.1030			0.871013			0.435506	−	0.900186i	$-0.356569\pi$
$587$	21.1030			0.871013			0.435506	+	0.900186i	$0.356569\pi$
$588$	−1.66126	+	11.2308i	−0.0685094	+	0.463149i
$589$	−12.2976			−0.506713
$590$	−0.862025	+	1.49307i	−0.0354890	+	0.0614688i
$591$	−6.76455	−	11.7165i	−0.278256	−	0.481954i
$592$	−0.256901	−	0.444966i	−0.0105586	−	0.0182880i
$593$	−9.70501	+	16.8096i	−0.398537	+	0.690286i	−0.993546	−	0.113433i	$-0.963815\pi$
$593$	−9.70501	+	16.8096i	−0.398537	+	0.690286i	0.595009	+	0.803719i	$0.297149\pi$
$594$	−0.614936			−0.0252311
$595$	2.39084	−	0.455770i	0.0980150	−	0.0186848i
$596$	10.8771			0.445541
$597$	7.11782	−	12.3284i	0.291313	−	0.504569i
$598$	0.735087	+	1.27321i	0.0300599	+	0.0520653i
$599$	−3.70230	−	6.41257i	−0.151272	−	0.262011i	0.780423	−	0.625251i	$-0.215004\pi$
$599$	−3.70230	−	6.41257i	−0.151272	−	0.262011i	−0.931695	+	0.363241i	$0.881670\pi$
$600$	3.07585	−	5.32753i	0.125571	−	0.217496i
$601$	−11.5056			−0.469322			−0.234661	−	0.972077i	$-0.575398\pi$
$601$	−11.5056			−0.469322			−0.234661	+	0.972077i	$0.575398\pi$
$602$	−5.04475	+	14.4808i	−0.205609	+	0.590192i
$603$	5.06243			0.206158
$604$	−8.24634	+	14.2831i	−0.335539	+	0.581170i
$605$	−0.747986	−	1.29555i	−0.0304099	−	0.0526716i
$606$	1.44534	+	2.50341i	0.0587130	+	0.101694i
$607$	−22.5141	+	38.9956i	−0.913821	+	1.58278i	−0.105202	+	0.994451i	$0.533549\pi$
$607$	−22.5141	+	38.9956i	−0.913821	+	1.58278i	−0.808619	+	0.588333i	$0.799785\pi$
$608$	−14.9185			−0.605024
$609$	14.6045	+	16.9237i	0.591803	+	0.685782i
$610$	−7.84369			−0.317582
$611$	−2.01692	+	3.49341i	−0.0815959	+	0.141328i
$612$	0.498668	+	0.863718i	0.0201575	+	0.0349137i
$613$	8.92108	+	15.4518i	0.360319	+	0.624091i	0.988013	−	0.154369i	$-0.0493345\pi$
$613$	8.92108	+	15.4518i	0.360319	+	0.624091i	−0.627694	+	0.778460i	$0.716001\pi$
$614$	−2.55124	+	4.41887i	−0.102960	+	0.178331i
$615$	7.36007			0.296787
$616$	3.84982	+	4.46118i	0.155114	+	0.179746i
$617$	11.7052			0.471235			0.235617	−	0.971846i	$-0.424289\pi$
$617$	11.7052			0.471235			0.235617	+	0.971846i	$0.424289\pi$
$618$	5.40042	−	9.35381i	0.217237	−	0.376265i
$619$	3.75957	+	6.51176i	0.151110	+	0.261730i	0.931636	−	0.363394i	$-0.118382\pi$
$619$	3.75957	+	6.51176i	0.151110	+	0.261730i	−0.780526	+	0.625123i	$0.785049\pi$
$620$	5.60688	+	9.71140i	0.225178	+	0.390019i
$621$	0.937059	−	1.62303i	0.0376029	−	0.0651301i
$622$	−21.3518			−0.856131
$623$	−9.29269	+	26.6743i	−0.372304	+	1.06868i
$624$	2.39078			0.0957076
$625$	1.78031	−	3.08358i	0.0712123	−	0.123343i
$626$	−9.89865	−	17.1450i	−0.395630	−	0.685251i
$627$	−1.33037	−	2.30427i	−0.0531300	−	0.0920238i
$628$	17.7402	−	30.7269i	0.707910	−	1.22614i
$629$	0.168589			0.00672208
$630$	2.39084	−	0.455770i	0.0952534	−	0.0181583i
$631$	27.1694			1.08159			0.540797	−	0.841153i	$-0.318123\pi$
$631$	27.1694			1.08159			0.540797	+	0.841153i	$0.318123\pi$
$632$	10.5232	−	18.2267i	0.418590	−	0.725019i
$633$	0.750620	+	1.30011i	0.0298345	+	0.0516748i
$634$	3.38549	+	5.86383i	0.134455	+	0.232883i
$635$	14.7598	−	25.5648i	0.585726	−	1.01451i
$636$	10.0365			0.397975
$637$	−8.30350	+	3.28521i	−0.328997	+	0.130165i
$638$	5.19561			0.205696
$639$	−8.04772	+	13.9391i	−0.318363	+	0.551420i
$640$	8.52588	+	14.7673i	0.337015	+	0.583727i
$641$	6.17690	+	10.6987i	0.243973	+	0.422573i	0.961842	−	0.273604i	$-0.0882159\pi$
$641$	6.17690	+	10.6987i	0.243973	+	0.422573i	−0.717870	+	0.696178i	$0.754883\pi$
$642$	3.63860	−	6.30224i	0.143604	−	0.248730i
$643$	−21.3948			−0.843728			−0.421864	−	0.906659i	$-0.638624\pi$
$643$	−21.3948			−0.843728			−0.421864	+	0.906659i	$0.638624\pi$
$644$	−7.89962	+	1.50592i	−0.311289	+	0.0593415i
$645$	−14.0997			−0.555175
$646$	0.503075	−	0.871352i	0.0197932	−	0.0342829i
$647$	−1.37765	−	2.38616i	−0.0541609	−	0.0938095i	0.837674	−	0.546171i	$-0.183915\pi$
$647$	−1.37765	−	2.38616i	−0.0541609	−	0.0938095i	−0.891835	+	0.452361i	$0.850582\pi$
$648$	1.11360	+	1.92882i	0.0437465	+	0.0757712i
$649$	−0.937059	+	1.62303i	−0.0367828	+	0.0637096i
$650$	2.16674			0.0849865
$651$	4.02290	−	11.5476i	0.157670	−	0.452586i
$652$	−28.0125			−1.09705
$653$	4.33349	−	7.50582i	0.169583	−	0.293726i	−0.768691	−	0.639621i	$-0.779091\pi$
$653$	4.33349	−	7.50582i	0.169583	−	0.293726i	0.938273	+	0.345895i	$0.112425\pi$
$654$	−0.314821	−	0.545286i	−0.0123105	−	0.0213224i
$655$	3.97608	+	6.88678i	0.155358	+	0.269089i
$656$	4.61026	−	7.98520i	0.180000	−	0.311770i
$657$	8.75732			0.341656
$658$	3.36114	+	3.89489i	0.131031	+	0.151839i
$659$	−32.2924			−1.25793			−0.628967	−	0.777432i	$-0.716522\pi$
$659$	−32.2924			−1.25793			−0.628967	+	0.777432i	$0.716522\pi$
$660$	−1.21312	+	2.10119i	−0.0472208	+	0.0817888i
$661$	6.37793	+	11.0469i	0.248073	+	0.429675i	0.962991	−	0.269533i	$-0.0868694\pi$
$661$	6.37793	+	11.0469i	0.248073	+	0.429675i	−0.714918	+	0.699208i	$0.753536\pi$
$662$	−4.42794	−	7.66942i	−0.172097	−	0.298080i
$663$	−0.392231	+	0.679364i	−0.0152330	+	0.0263843i
$664$	−20.0577			−0.778391
$665$	6.88028	+	7.97288i	0.266806	+	0.309175i
$666$	0.168589			0.00653269
$667$	−7.91723	+	13.7130i	−0.306556	+	0.530971i
$668$	−10.9196	−	18.9132i	−0.422490	−	0.731775i
$669$	3.61469	+	6.26082i	0.139752	+	0.242057i
$670$	−2.32853	+	4.03314i	−0.0899591	+	0.155814i
$671$	−8.52643			−0.329159
$672$	4.88028	−	14.0087i	0.188261	−	0.540396i
$673$	43.6075			1.68095			0.840473	−	0.541853i	$-0.182277\pi$
$673$	43.6075			1.68095			0.840473	+	0.541853i	$0.182277\pi$
$674$	5.85598	−	10.1429i	0.225564	−	0.390688i
$675$	−1.38104	−	2.39202i	−0.0531561	−	0.0920690i
$676$	−9.22238	−	15.9736i	−0.354707	−	0.614370i
$677$	−1.08387	+	1.87732i	−0.0416566	+	0.0721513i	−0.886102	−	0.463490i	$-0.846597\pi$
$677$	−1.08387	+	1.87732i	−0.0416566	+	0.0721513i	0.844445	+	0.535642i	$0.179930\pi$
$678$	−3.86503			−0.148436
$679$	−45.9705	+	8.76343i	−1.76419	+	0.336310i
$680$	−2.04887			−0.0785705
$681$	−0.400040	+	0.692889i	−0.0153296	+	0.0265516i
$682$	−1.42107	−	2.46137i	−0.0544157	−	0.0942507i
$683$	−11.9795	−	20.7491i	−0.458383	−	0.793943i	0.540492	−	0.841349i	$-0.318238\pi$
$683$	−11.9795	−	20.7491i	−0.458383	−	0.793943i	−0.998876	+	0.0474056i	$0.984905\pi$
$684$	−2.15767	+	3.73719i	−0.0825006	+	0.142895i
$685$	3.57263			0.136503
$686$	0.472678	+	11.3790i	0.0180469	+	0.434451i
$687$	8.54229			0.325909
$688$	−8.83188	+	15.2973i	−0.336712	+	0.583203i
$689$	3.94716	+	6.83668i	0.150375	+	0.260457i
$690$	0.862025	+	1.49307i	0.0328167	+	0.0568402i
$691$	−2.52944	+	4.38113i	−0.0962246	+	0.166666i	−0.910119	−	0.414347i	$-0.864010\pi$
$691$	−2.52944	+	4.38113i	−0.0962246	+	0.166666i	0.813894	+	0.581013i	$0.197343\pi$
$692$	29.2840			1.11321
$693$	2.59895	−	0.495442i	0.0987259	−	0.0188203i
$694$	−10.7522			−0.408149
$695$	−9.34595	+	16.1877i	−0.354512	+	0.614033i
$696$	−9.40887	−	16.2966i	−0.356642	−	0.617722i
$697$	1.51272	+	2.62011i	0.0572983	+	0.0992436i
$698$	−9.81848	+	17.0061i	−0.371635	+	0.643690i
$699$	−1.83904			−0.0695589
$700$	−3.89915	+	11.1924i	−0.147374	+	0.423032i
$701$	−21.7177			−0.820265			−0.410132	−	0.912026i	$-0.634517\pi$
$701$	−21.7177			−0.820265			−0.410132	+	0.912026i	$0.634517\pi$
$702$	−0.392231	+	0.679364i	−0.0148038	+	0.0256409i
$703$	0.364731	+	0.631733i	0.0137561	+	0.0238262i
$704$	0.150182	+	0.260123i	0.00566019	+	0.00980374i
$705$	−2.36521	+	4.09667i	−0.0890791	+	0.154289i
$706$	−17.0664			−0.642301
$707$	−8.12550	−	9.41584i	−0.305591	−	0.354119i
$708$	3.03954			0.114233
$709$	−2.79595	+	4.84273i	−0.105004	+	0.181873i	−0.913740	−	0.406300i	$-0.866819\pi$
$709$	−2.79595	+	4.84273i	−0.105004	+	0.181873i	0.808736	+	0.588172i	$0.200152\pi$
$710$	−7.40331	−	12.8229i	−0.277841	−	0.481235i
$711$	−4.72483	−	8.18365i	−0.177195	−	0.306911i
$712$	11.8891	−	20.5925i	0.445563	−	0.771737i
$713$	8.66190			0.324391
$714$	0.653641	+	0.757440i	0.0244619	+	0.0283465i
$715$	−1.90838			−0.0713694
$716$	−14.1664	+	24.5368i	−0.529422	+	0.916985i
$717$	−4.35750	−	7.54741i	−0.162734	−	0.281863i
$718$	−2.03129	−	3.51829i	−0.0758069	−	0.131301i
$719$	−3.86213	+	6.68941i	−0.144033	+	0.249473i	−0.929012	−	0.370050i	$-0.879341\pi$
$719$	−3.86213	+	6.68941i	−0.144033	+	0.249473i	0.784979	+	0.619523i	$0.212674\pi$
$720$	2.80363			0.104485
$721$	−15.2880	+	43.8837i	−0.569356	+	1.63431i
$722$	−7.33030			−0.272806
$723$	0.540256	−	0.935751i	0.0200923	−	0.0348010i
$724$	−2.17758	−	3.77169i	−0.0809293	−	0.140174i
$725$	11.6684	+	20.2103i	0.433353	+	0.750590i
$726$	0.307468	−	0.532550i	0.0114112	−	0.0197648i
$727$	−35.7990			−1.32771			−0.663855	−	0.747861i	$-0.731081\pi$
$727$	−35.7990			−1.32771			−0.663855	+	0.747861i	$0.731081\pi$
$728$	7.38415	−	1.40765i	0.273675	−	0.0521711i
$729$	1.00000			0.0370370
$730$	−4.02804	+	6.97678i	−0.149085	+	0.258222i
$731$	−2.89792	−	5.01934i	−0.107183	−	0.185647i
$732$	6.91431	+	11.9759i	0.255560	+	0.442644i
$733$	−8.12689	+	14.0762i	−0.300174	+	0.519916i	−0.976175	−	0.216984i	$-0.930378\pi$
$733$	−8.12689	+	14.0762i	−0.300174	+	0.519916i	0.676001	+	0.736900i	$0.263711\pi$
$734$	−16.1391			−0.595707
$735$	−9.73739	+	3.85251i	−0.359169	+	0.142102i
$736$	10.5079			0.387328
$737$	−2.53122	+	4.38420i	−0.0932386	+	0.161494i
$738$	1.51272	+	2.62011i	0.0556840	+	0.0964475i
$739$	−0.287041	−	0.497169i	−0.0105590	−	0.0182887i	0.860698	−	0.509116i	$-0.170028\pi$
$739$	−0.287041	−	0.497169i	−0.0105590	−	0.0182887i	−0.871257	+	0.490828i	$0.836694\pi$
$740$	0.332586	−	0.576056i	0.0122261	−	0.0211762i
$741$	−3.39426			−0.124691
$742$	9.89009	−	1.88536i	0.363077	−	0.0692139i
$743$	25.6448			0.940818			0.470409	−	0.882449i	$-0.344106\pi$
$743$	25.6448			0.940818			0.470409	+	0.882449i	$0.344106\pi$
$744$	−5.14691	+	8.91472i	−0.188695	+	0.326829i
$745$	5.01641	+	8.68867i	0.183787	+	0.318328i
$746$	2.38667	+	4.13383i	0.0873821	+	0.151350i
$747$	−4.50289	+	7.79923i	−0.164752	+	0.285359i
$748$	−0.997336			−0.0364662
$749$	−10.3005	+	29.5672i	−0.376372	+	1.08036i
$750$	7.14053			0.260735
$751$	−14.9561	+	25.9047i	−0.545755	+	0.945275i	0.452804	+	0.891610i	$0.350424\pi$
$751$	−14.9561	+	25.9047i	−0.545755	+	0.945275i	−0.998559	+	0.0536652i	$0.982910\pi$
$752$	2.96308	+	5.13221i	0.108053	+	0.187152i
$753$	−4.31648	−	7.47636i	−0.157301	−	0.272454i
$754$	3.31397	−	5.73996i	0.120688	−	0.209037i
$755$	−15.2126			−0.553642
$756$	−2.80344	−	3.24863i	−0.101960	−	0.118152i
$757$	13.9358			0.506505			0.253252	−	0.967400i	$-0.418500\pi$
$757$	13.9358			0.506505			0.253252	+	0.967400i	$0.418500\pi$
$758$	−4.75455	+	8.23512i	−0.172693	+	0.299113i
$759$	0.937059	+	1.62303i	0.0340131	+	0.0589124i
$760$	−4.43259	−	7.67747i	−0.160787	−	0.278491i
$761$	18.2281	−	31.5721i	0.660770	−	1.14449i	−0.319644	−	0.947538i	$-0.603563\pi$
$761$	18.2281	−	31.5721i	0.660770	−	1.14449i	0.980414	−	0.196949i	$-0.0631033\pi$
$762$	12.1344			0.439583
$763$	1.76988	+	2.05094i	0.0640739	+	0.0742490i
$764$	30.5548			1.10543
$765$	−0.459963	+	0.796680i	−0.0166300	+	0.0288040i
$766$	8.22702	+	14.2496i	0.297254	+	0.514860i
$767$	1.19539	+	2.07047i	0.0431630	+	0.0747604i
$768$	−3.20430	+	5.55001i	−0.115625	+	0.200269i
$769$	−10.7416			−0.387354			−0.193677	−	0.981065i	$-0.562041\pi$
$769$	−10.7416			−0.387354			−0.193677	+	0.981065i	$0.562041\pi$
$770$	−0.800712	+	2.29842i	−0.0288557	+	0.0828291i
$771$	−14.7115			−0.529822
$772$	11.5498	−	20.0048i	0.415686	−	0.719989i
$773$	0.911869	+	1.57940i	0.0327976	+	0.0568072i	0.881958	−	0.471327i	$-0.156225\pi$
$773$	0.911869	+	1.57940i	0.0327976	+	0.0568072i	−0.849161	+	0.528135i	$0.822892\pi$
$774$	−2.89792	−	5.01934i	−0.104164	−	0.180417i
$775$	6.38294	−	11.0556i	0.229282	−	0.397128i
$776$	39.3951			1.41420
$777$	−0.712520	+	0.135829i	−0.0255615	+	0.00487283i
$778$	12.1628			0.436057
$779$	−6.54533	+	11.3369i	−0.234511	+	0.406185i
$780$	1.54756	+	2.68045i	0.0554115	+	0.0959755i
$781$	−8.04772	−	13.9391i	−0.287970	−	0.498779i
$782$	−0.354345	+	0.613744i	−0.0126714	+	0.0219474i
$783$	−8.44902			−0.301943
$784$	−1.91966	+	12.9776i	−0.0685592	+	0.463486i
$785$	32.7265			1.16806
$786$	−1.63441	+	2.83089i	−0.0582976	+	0.100974i
$787$	−12.4967	−	21.6449i	−0.445458	−	0.771556i	0.552626	−	0.833429i	$-0.313626\pi$
$787$	−12.4967	−	21.6449i	−0.445458	−	0.771556i	−0.998084	+	0.0618734i	$0.980292\pi$
$788$	−10.9711	−	19.0025i	−0.390830	−	0.676937i
$789$	15.4640	−	26.7844i	0.550533	−	0.953551i
$790$	8.69300			0.309283
$791$	16.3351	−	3.11398i	0.580809	−	0.110720i
$792$	−2.22721			−0.0791404
$793$	−5.43850	+	9.41976i	−0.193127	+	0.334506i
$794$	0.0764944	+	0.132492i	0.00271468	+	0.00470197i
$795$	4.62877	+	8.01727i	0.164166	+	0.284343i
$796$	11.5441	−	19.9949i	0.409169	−	0.708701i
$797$	−14.0330			−0.497074			−0.248537	−	0.968622i	$-0.579950\pi$
$797$	−14.0330			−0.497074			−0.248537	+	0.968622i	$0.579950\pi$
$798$	−1.42415	+	4.08798i	−0.0504145	+	0.144713i
$799$	−1.94450			−0.0687913
$800$	7.74330	−	13.4118i	0.273767	−	0.474178i
$801$	−5.33812	−	9.24589i	−0.188613	−	0.326687i
$802$	−10.6961	−	18.5261i	−0.377691	−	0.654180i
$803$	−4.37866	+	7.58406i	−0.154520	+	0.267636i
$804$	8.21053			0.289563
$805$	−4.84618	−	5.61576i	−0.170805	−	0.197930i
$806$	−3.62567			−0.127709
$807$	−15.5582	+	26.9475i	−0.547673	+	0.948598i
$808$	5.23482	+	9.06697i	0.184160	+	0.318975i
$809$	19.7742	+	34.2499i	0.695223	+	1.20416i	0.970106	+	0.242683i	$0.0780275\pi$
$809$	19.7742	+	34.2499i	0.695223	+	1.20416i	−0.274883	+	0.961478i	$0.588639\pi$
$810$	−0.459963	+	0.796680i	−0.0161615	+	0.0279925i
$811$	19.9504			0.700555			0.350277	−	0.936646i	$-0.386087\pi$
$811$	19.9504			0.700555			0.350277	+	0.936646i	$0.386087\pi$
$812$	23.6863	+	27.4477i	0.831227	+	0.963227i
$813$	−2.76969			−0.0971372
$814$	−0.0842945	+	0.146002i	−0.00295452	+	0.00511738i
$815$	−12.9191	−	22.3766i	−0.452537	−	0.783817i
$816$	0.576231	+	0.998061i	0.0201721	+	0.0349391i
$817$	12.5389	−	21.7180i	0.438681	−	0.759817i
$818$	−1.11173			−0.0388707
$819$	1.11036	−	3.18726i	0.0387993	−	0.111372i
$820$	11.9370			0.416857
$821$	−0.517645	+	0.896588i	−0.0180659	+	0.0312911i	−0.874917	−	0.484273i	$-0.839084\pi$
$821$	−0.517645	+	0.896588i	−0.0180659	+	0.0312911i	0.856851	+	0.515564i	$0.172418\pi$
$822$	0.734285	+	1.27182i	0.0256111	+	0.0443598i
$823$	−3.95013	−	6.84182i	−0.137693	−	0.238491i	0.788930	−	0.614483i	$-0.210635\pi$
$823$	−3.95013	−	6.84182i	−0.137693	−	0.238491i	−0.926623	+	0.375992i	$0.877302\pi$
$824$	19.5595	−	33.8781i	0.681389	−	1.18020i
$825$	2.76207			0.0961629
$826$	2.99519	−	0.570978i	0.104216	−	0.0198669i
$827$	−19.4794			−0.677364			−0.338682	−	0.940901i	$-0.609981\pi$
$827$	−19.4794			−0.677364			−0.338682	+	0.940901i	$0.609981\pi$
$828$	1.51977	−	2.63232i	0.0528157	−	0.0914795i
$829$	−12.7817	−	22.1386i	−0.443927	−	0.768904i	0.554050	−	0.832484i	$-0.313082\pi$
$829$	−12.7817	−	22.1386i	−0.443927	−	0.768904i	−0.997977	+	0.0635793i	$0.979748\pi$
$830$	−4.14233	−	7.17472i	−0.143782	−	0.249038i
$831$	9.65146	−	16.7168i	0.334805	−	0.579900i
$832$	0.383168			0.0132840
$833$	−3.37279	−	2.67460i	−0.116860	−	0.0926694i
$834$	−7.68352			−0.266059
$835$	10.0720	−	17.4452i	0.348556	−	0.603718i
$836$	−2.15767	−	3.73719i	−0.0746246	−	0.129254i
$837$	2.31093	+	4.00264i	0.0798773	+	0.138352i
$838$	−7.90213	+	13.6869i	−0.272974	+	0.472806i
$839$	29.1936			1.00787			0.503937	−	0.863740i	$-0.331884\pi$
$839$	29.1936			1.00787			0.503937	+	0.863740i	$0.331884\pi$
$840$	8.65928	−	1.65073i	0.298774	−	0.0569557i
$841$	42.3860			1.46159
$842$	−7.76868	+	13.4557i	−0.267726	+	0.463715i
$843$	−3.98031	−	6.89409i	−0.137089	−	0.237445i
$844$	1.21740	+	2.10859i	0.0419045	+	0.0725807i
$845$	8.50657	−	14.7338i	0.292635	−	0.506858i
$846$	−1.94450			−0.0668531
$847$	−0.870409	+	2.49848i	−0.0299076	+	0.0858487i
$848$	11.5976			0.398264
$849$	−4.27898	+	7.41142i	−0.146854	+	0.254359i
$850$	0.522233	+	0.904534i	0.0179125	+	0.0310253i
$851$	−0.256901	−	0.444966i	−0.00880646	−	0.0152532i
$852$	−13.0522	+	22.6071i	−0.447162	+	0.774507i
$853$	3.81162			0.130507			0.0652536	−	0.997869i	$-0.479214\pi$
$853$	3.81162			0.130507			0.0652536	+	0.997869i	$0.479214\pi$
$854$	9.06310	+	10.5023i	0.310133	+	0.359382i
$855$	−3.98040			−0.136127
$856$	13.1785	−	22.8258i	0.450431	−	0.780170i
$857$	17.3435	+	30.0398i	0.592442	+	1.02614i	0.993902	+	0.110264i	$0.0351695\pi$
$857$	17.3435	+	30.0398i	0.592442	+	1.02614i	−0.401460	+	0.915876i	$0.631497\pi$
$858$	−0.392231	−	0.679364i	−0.0133905	−	0.0231931i
$859$	24.3029	−	42.0939i	0.829205	−	1.43622i	−0.0694582	−	0.997585i	$-0.522127\pi$
$859$	24.3029	−	42.0939i	0.829205	−	1.43622i	0.898663	−	0.438640i	$-0.144540\pi$
$860$	−22.8676			−0.779780
$861$	−8.50429	−	9.85479i	−0.289825	−	0.335850i
$862$	20.3113			0.691806
$863$	−10.8282	+	18.7550i	−0.368596	+	0.638426i	−0.989346	−	0.145582i	$-0.953495\pi$
$863$	−10.8282	+	18.7550i	−0.368596	+	0.638426i	0.620751	+	0.784008i	$0.286828\pi$
$864$	2.80344	+	4.85570i	0.0953749	+	0.165194i
$865$	13.5056	+	23.3923i	0.459203	+	0.795362i
$866$	−4.88962	+	8.46908i	−0.166156	+	0.287791i
$867$	16.6219			0.564508
$868$	6.52456	−	18.7285i	0.221458	−	0.635687i
$869$	9.44966			0.320558
$870$	3.88624	−	6.73116i	0.131756	−	0.228208i
$871$	3.22903	+	5.59284i	0.109411	+	0.189506i
$872$	−1.14024	−	1.97495i	−0.0386133	−	0.0668802i
$873$	8.84405	−	15.3183i	0.299326	−	0.518447i
$874$	−3.06641			−0.103723
$875$	−30.1786	+	5.75299i	−1.02022	+	0.194487i
$876$	14.2031			0.479878
$877$	8.00130	−	13.8587i	0.270185	−	0.467974i	−0.698724	−	0.715391i	$-0.746249\pi$
$877$	8.00130	−	13.8587i	0.270185	−	0.467974i	0.968909	+	0.247417i	$0.0795818\pi$
$878$	−1.37630	−	2.38382i	−0.0464478	−	0.0804500i
$879$	−14.1140	−	24.4461i	−0.476053	−	0.824548i
$880$	−1.40181	+	2.42801i	−0.0472551	+	0.0818482i
$881$	−36.2250			−1.22045			−0.610226	−	0.792228i	$-0.708921\pi$
$881$	−36.2250			−1.22045			−0.610226	+	0.792228i	$0.708921\pi$
$882$	−3.37279	−	2.67460i	−0.113568	−	0.0900584i
$883$	−4.78873			−0.161154			−0.0805768	−	0.996748i	$-0.525676\pi$
$883$	−4.78873			−0.161154			−0.0805768	+	0.996748i	$0.525676\pi$
$884$	−0.636141	+	1.10183i	−0.0213957	+	0.0370585i
$885$	1.40181	+	2.42801i	0.0471214	+	0.0816167i
$886$	0.503470	+	0.872035i	0.0169144	+	0.0292966i
$887$	27.2066	−	47.1231i	0.913507	−	1.58224i	0.104434	−	0.994532i	$-0.466697\pi$
$887$	27.2066	−	47.1231i	0.913507	−	1.58224i	0.809073	−	0.587709i	$-0.199970\pi$
$888$	0.610605			0.0204906
$889$	−51.2845	+	9.77644i	−1.72003	+	0.327891i
$890$	9.82135			0.329212
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	5.86249	+	10.1541i	0.196291	+	0.339986i
$893$	−4.20678	−	7.28636i	−0.140775	−	0.243829i
$894$	−2.06205	+	3.57158i	−0.0689653	+	0.119451i
$895$	−26.1336			−0.873551
$896$	9.92133	−	28.4788i	0.331448	−	0.951410i
$897$	2.39078			0.0798257
$898$	0.756292	−	1.30994i	0.0252378	−	0.0437132i
$899$	−19.5251	−	33.8184i	−0.651198	−	1.12791i
$900$	−2.23984	−	3.87951i	−0.0746612	−	0.129317i
$901$	−1.90271	+	3.29559i	−0.0633884	+	0.109792i
$902$	−3.02544			−0.100736
$903$	16.2917	+	18.8788i	0.542153	+	0.628248i
$904$	−13.9986			−0.465586
$905$	2.00857	−	3.47894i	0.0667670	−	0.115644i
$906$	−3.12665	−	5.41552i	−0.103876	−	0.179919i
$907$	−26.9300	−	46.6441i	−0.894196	−	1.54879i	−0.834796	−	0.550559i	$-0.814415\pi$
$907$	−26.9300	−	46.6441i	−0.894196	−	1.54879i	−0.0593996	−	0.998234i	$-0.518919\pi$
$908$	−0.648806	+	1.12376i	−0.0215314	+	0.0372934i
$909$	4.70079			0.155915
$910$	2.02850	+	2.35063i	0.0672441	+	0.0779225i
$911$	−22.0506			−0.730571			−0.365285	−	0.930896i	$-0.619029\pi$
$911$	−22.0506			−0.730571			−0.365285	+	0.930896i	$0.619029\pi$
$912$	−2.49327	+	4.31848i	−0.0825606	+	0.142999i
$913$	−4.50289	−	7.79923i	−0.149024	−	0.258117i
$914$	9.53036	+	16.5071i	0.315236	+	0.546005i
$915$	−6.37765	+	11.0464i	−0.210839	+	0.365183i
$916$	13.8543			0.457760
$917$	4.62686	−	13.2812i	0.152792	−	0.438584i
$918$	−0.378146			−0.0124807
$919$	−3.17454	+	5.49846i	−0.104718	+	0.181378i	−0.913623	−	0.406562i	$-0.866727\pi$
$919$	−3.17454	+	5.49846i	−0.104718	+	0.181378i	0.808905	+	0.587940i	$0.200061\pi$
$920$	3.12213	+	5.40769i	0.102934	+	0.178286i
$921$	4.14879	+	7.18591i	0.136707	+	0.236784i
$922$	5.24402	−	9.08292i	0.172703	−	0.299130i
$923$	−20.5326			−0.675840
$924$	4.21512	−	0.803534i	0.138667	−	0.0264343i
$925$	−0.757241			−0.0248979
$926$	−4.30340	+	7.45371i	−0.141419	+	0.244944i
$927$	−8.78209	−	15.2110i	−0.288442	−	0.499596i
$928$	−23.6863	−	41.0259i	−0.777542	−	1.34674i
$929$	−28.9332	+	50.1138i	−0.949268	+	1.64418i	−0.202296	+	0.979324i	$0.564840\pi$
$929$	−28.9332	+	50.1138i	−0.949268	+	1.64418i	−0.746972	+	0.664856i	$0.768493\pi$
$930$	−4.25177			−0.139421
$931$	2.72540	−	18.4247i	0.0893213	−	0.603846i
$932$	−2.98266			−0.0977001
$933$	−17.3610	+	30.0702i	−0.568374	+	0.984453i
$934$	−11.5726	−	20.0442i	−0.378665	−	0.655868i
$935$	−0.459963	−	0.796680i	−0.0150424	−	0.0260542i
$936$	−1.42060	+	2.46056i	−0.0464339	+	0.0804258i
$937$	16.1657			0.528110			0.264055	−	0.964508i	$-0.414940\pi$
$937$	16.1657			0.528110			0.264055	+	0.964508i	$0.414940\pi$
$938$	8.09072	−	1.54235i	0.264171	−	0.0503594i
$939$	−32.1941			−1.05061
$940$	−3.83603	+	6.64420i	−0.125117	+	0.216710i
$941$	−26.5775	−	46.0336i	−0.866401	−	1.50065i	−0.865649	−	0.500651i	$-0.833094\pi$
$941$	−26.5775	−	46.0336i	−0.866401	−	1.50065i	−0.000752355	−	1.00000i	$-0.500239\pi$
$942$	6.72630	+	11.6503i	0.219155	+	0.379587i
$943$	4.61026	−	7.98520i	0.150131	−	0.260034i
$944$	3.51232			0.114316
$945$	1.30211	−	3.73765i	0.0423575	−	0.121586i
$946$	5.79584			0.188439
$947$	7.54598	−	13.0700i	0.245211	−	0.424719i	−0.716980	−	0.697094i	$-0.754476\pi$
$947$	7.54598	−	13.0700i	0.245211	−	0.424719i	0.962191	+	0.272376i	$0.0878093\pi$
$948$	−7.66299	−	13.2727i	−0.248882	−	0.431077i
$949$	5.58577	+	9.67484i	0.181322	+	0.314059i
$950$	−2.25963	+	3.91380i	−0.0733122	+	0.126980i
$951$	11.0109			0.357052
$952$	2.36739	+	2.74334i	0.0767276	+	0.0889121i
$953$	−27.2774			−0.883602			−0.441801	−	0.897113i	$-0.645660\pi$
$953$	−27.2774			−0.883602			−0.441801	+	0.897113i	$0.645660\pi$
$954$	−1.90271	+	3.29559i	−0.0616025	+	0.106699i
$955$	14.0916	+	24.4074i	0.455994	+	0.789805i
$956$	−7.06722	−	12.2408i	−0.228570	−	0.395896i
$957$	4.22451	−	7.31707i	0.136559	−	0.236527i
$958$	21.2147			0.685414
$959$	−4.12804	−	4.78358i	−0.133301	−	0.154470i
$960$	0.449336			0.0145022
$961$	4.81923	−	8.34716i	0.155459	−	0.269263i
$962$	0.107533	+	0.186252i	0.00346700	+	0.00600502i
$963$	−5.91704	−	10.2486i	−0.190674	−	0.330257i
$964$	0.876217	−	1.51765i	0.0282210	−	0.0488803i
$965$	21.3067			0.685886
$966$	1.00311	−	2.87940i	0.0322747	−	0.0926432i
$967$	47.7400			1.53521			0.767607	−	0.640920i	$-0.221447\pi$
$967$	47.7400			1.53521			0.767607	+	0.640920i	$0.221447\pi$
$968$	1.11360	−	1.92882i	0.0357926	−	0.0619946i
$969$	−0.818094	−	1.41698i	−0.0262810	−	0.0455200i
$970$	8.13588	+	14.0918i	0.261227	+	0.452459i
$971$	13.8483	−	23.9859i	0.444413	−	0.769746i	−0.553598	−	0.832784i	$-0.686746\pi$
$971$	13.8483	−	23.9859i	0.444413	−	0.769746i	0.998011	+	0.0630381i	$0.0200790\pi$
$972$	1.62185			0.0520210
$973$	32.4734	−	6.19046i	1.04105	−	0.198457i
$974$	−1.27588			−0.0408819
$975$	1.76176	−	3.05146i	0.0564215	−	0.0977249i
$976$	7.98977	+	13.8387i	0.255746	+	0.442965i
$977$	−8.96009	−	15.5193i	−0.286659	−	0.496508i	0.686351	−	0.727270i	$-0.259211\pi$
$977$	−8.96009	−	15.5193i	−0.286659	−	0.496508i	−0.973010	+	0.230763i	$0.925878\pi$
$978$	5.31055	−	9.19814i	0.169813	−	0.294124i
$979$	10.6762			0.341214
$980$	−15.7926	+	6.24821i	−0.504477	+	0.199592i
$981$	−1.02392			−0.0326911
$982$	9.19340	−	15.9234i	0.293373	−	0.508137i
$983$	−15.2096	−	26.3438i	−0.485110	−	0.840235i	0.514743	−	0.857344i	$-0.327887\pi$
$983$	−15.2096	−	26.3438i	−0.485110	−	0.840235i	−0.999854	+	0.0171088i	$0.994554\pi$
$984$	5.47885	+	9.48965i	0.174659	+	0.302519i
$985$	10.1196	−	17.5276i	0.322436	−	0.558476i
$986$	3.19497			0.101748
$987$	8.21816	−	1.56664i	0.261587	−	0.0498668i
$988$	−5.50500			−0.175137
$989$	−8.83188	+	15.2973i	−0.280837	+	0.486425i
$990$	−0.459963	−	0.796680i	−0.0146186	−	0.0253201i
$991$	−7.10473	−	12.3058i	−0.225689	−	0.390905i	0.730837	−	0.682552i	$-0.239130\pi$
$991$	−7.10473	−	12.3058i	−0.225689	−	0.390905i	−0.956526	+	0.291647i	$0.905797\pi$
$992$	−12.9571	+	22.4423i	−0.411388	+	0.712545i
$993$	−14.4013			−0.457012
$994$	−8.61502	+	24.7291i	−0.273252	+	0.784359i
$995$	21.2961			0.675132
$996$	−7.30303	+	12.6492i	−0.231405	+	0.400806i
$997$	0.498726	+	0.863818i	0.0157948	+	0.0273574i	0.873815	−	0.486259i	$-0.161639\pi$
$997$	0.498726	+	0.863818i	0.0157948	+	0.0273574i	−0.858020	+	0.513616i	$0.828305\pi$
$998$	−0.423736	−	0.733932i	−0.0134131	−	0.0232322i
$999$	0.137079	−	0.237427i	0.00433697	−	0.00751186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.f.100.3	yes	10
3.2	odd	2		693.2.i.j.100.3		10
7.2	even	3		1617.2.a.ba.1.3		5
7.4	even	3	inner	231.2.i.f.67.3	✓	10
7.5	odd	6		1617.2.a.bb.1.3		5
21.2	odd	6		4851.2.a.ca.1.3		5
21.5	even	6		4851.2.a.bz.1.3		5
21.11	odd	6		693.2.i.j.298.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.3	✓	10	7.4	even	3	inner
231.2.i.f.100.3	yes	10	1.1	even	1	trivial
693.2.i.j.100.3		10	3.2	odd	2
693.2.i.j.298.3		10	21.11	odd	6
1617.2.a.ba.1.3		5	7.2	even	3
1617.2.a.bb.1.3		5	7.5	odd	6
4851.2.a.bz.1.3		5	21.5	even	6
4851.2.a.ca.1.3		5	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.307468 + 0.532550i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.810927 + 1.40457i) q^{4} +(-0.747986 + 1.29555i) q^{5} -0.614936 q^{6} +(2.59895 - 0.495442i) q^{7} -2.22721 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.307468 + 0.532550i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.810927 + 1.40457i) q^{4} +(-0.747986 + 1.29555i) q^{5} -0.614936 q^{6} +(2.59895 - 0.495442i) q^{7} -2.22721 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.459963 - 0.796680i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.810927 + 1.40457i) q^{12} -1.27568 q^{13} +(-0.535246 + 1.53640i) q^{14} -1.49597 q^{15} +(-0.937059 + 1.62303i) q^{16} +(-0.307468 - 0.532550i) q^{17} +(-0.307468 - 0.532550i) q^{18} +(1.33037 - 2.30427i) q^{19} -2.42625 q^{20} +(1.72854 + 2.00304i) q^{21} +0.614936 q^{22} +(-0.937059 + 1.62303i) q^{23} +(-1.11360 - 1.92882i) q^{24} +(1.38104 + 2.39202i) q^{25} +(0.392231 - 0.679364i) q^{26} -1.00000 q^{27} +(2.80344 + 3.24863i) q^{28} +8.44902 q^{29} +(0.459963 - 0.796680i) q^{30} +(-2.31093 - 4.00264i) q^{31} +(-2.80344 - 4.85570i) q^{32} +(0.500000 - 0.866025i) q^{33} +0.378146 q^{34} +(-1.30211 + 3.73765i) q^{35} -1.62185 q^{36} +(-0.137079 + 0.237427i) q^{37} +(0.818094 + 1.41698i) q^{38} +(-0.637840 - 1.10477i) q^{39} +(1.66592 - 2.88546i) q^{40} -4.91993 q^{41} +(-1.59819 + 0.304665i) q^{42} +9.42511 q^{43} +(0.810927 - 1.40457i) q^{44} +(-0.747986 - 1.29555i) q^{45} +(-0.576231 - 0.998061i) q^{46} +(1.58106 - 2.73847i) q^{47} -1.87412 q^{48} +(6.50907 - 2.57526i) q^{49} -1.69850 q^{50} +(0.307468 - 0.532550i) q^{51} +(-1.03448 - 1.79178i) q^{52} +(-3.09416 - 5.35924i) q^{53} +(0.307468 - 0.532550i) q^{54} +1.49597 q^{55} +(-5.78840 + 1.10345i) q^{56} +2.66075 q^{57} +(-2.59780 + 4.49953i) q^{58} +(-0.937059 - 1.62303i) q^{59} +(-1.21312 - 2.10119i) q^{60} +(4.26322 - 7.38411i) q^{61} +2.84214 q^{62} +(-0.870409 + 2.49848i) q^{63} -0.300364 q^{64} +(0.954191 - 1.65271i) q^{65} +(0.307468 + 0.532550i) q^{66} +(-2.53122 - 4.38420i) q^{67} +(0.498668 - 0.863718i) q^{68} -1.87412 q^{69} +(-1.59013 - 1.84264i) q^{70} +16.0954 q^{71} +(1.11360 - 1.92882i) q^{72} +(-4.37866 - 7.58406i) q^{73} +(-0.0842945 - 0.146002i) q^{74} +(-1.38104 + 2.39202i) q^{75} +4.31534 q^{76} +(-1.72854 - 2.00304i) q^{77} +0.784462 q^{78} +(-4.72483 + 8.18365i) q^{79} +(-1.40181 - 2.42801i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.51272 - 2.62011i) q^{82} +9.00578 q^{83} +(-1.41168 + 4.05216i) q^{84} +0.919926 q^{85} +(-2.89792 + 5.01934i) q^{86} +(4.22451 + 7.31707i) q^{87} +(1.11360 + 1.92882i) q^{88} +(-5.33812 + 9.24589i) q^{89} +0.919926 q^{90} +(-3.31543 + 0.632026i) q^{91} -3.03954 q^{92} +(2.31093 - 4.00264i) q^{93} +(0.972248 + 1.68398i) q^{94} +(1.99020 + 3.44713i) q^{95} +(2.80344 - 4.85570i) q^{96} -17.6881 q^{97} +(-0.629878 + 4.25822i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Introduction

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