LMFDB - Embedded newform 630.2.i.i.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.5
Root			$-1.03843 - 1.38624i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.i.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.681302 + 1.59243i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.681302 - 1.59243i) q^{6} +(-1.52280 - 2.16358i) q^{7} -1.00000 q^{8} +(-2.07165 + 2.16985i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.681302 + 1.59243i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.681302 - 1.59243i) q^{6} +(-1.52280 - 2.16358i) q^{7} -1.00000 q^{8} +(-2.07165 + 2.16985i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.821620 - 1.42309i) q^{11} +(0.681302 + 1.59243i) q^{12} +(-2.49250 - 4.31714i) q^{13} +(1.52280 + 2.16358i) q^{14} +(1.71973 + 0.206189i) q^{15} +1.00000 q^{16} +(3.52620 - 6.10755i) q^{17} +(2.07165 - 2.16985i) q^{18} +(-3.51153 - 6.08215i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.40785 - 3.89901i) q^{21} +(0.821620 + 1.42309i) q^{22} +(-3.72617 + 6.45392i) q^{23} +(-0.681302 - 1.59243i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.49250 + 4.31714i) q^{26} +(-4.86675 - 1.82064i) q^{27} +(-1.52280 - 2.16358i) q^{28} +(-2.86866 + 4.96867i) q^{29} +(-1.71973 - 0.206189i) q^{30} +3.64324 q^{31} -1.00000 q^{32} +(1.70639 - 2.27792i) q^{33} +(-3.52620 + 6.10755i) q^{34} +(-2.63512 + 0.236999i) q^{35} +(-2.07165 + 2.16985i) q^{36} +(-2.87466 - 4.97906i) q^{37} +(3.51153 + 6.08215i) q^{38} +(5.17659 - 6.91042i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.30588 + 7.45800i) q^{41} +(-2.40785 + 3.89901i) q^{42} +(2.96195 - 5.13024i) q^{43} +(-0.821620 - 1.42309i) q^{44} +(0.843318 + 2.87903i) q^{45} +(3.72617 - 6.45392i) q^{46} +1.64116 q^{47} +(0.681302 + 1.59243i) q^{48} +(-2.36213 + 6.58941i) q^{49} +(0.500000 + 0.866025i) q^{50} +(12.1282 + 1.45413i) q^{51} +(-2.49250 - 4.31714i) q^{52} +(6.46391 - 11.1958i) q^{53} +(4.86675 + 1.82064i) q^{54} -1.64324 q^{55} +(1.52280 + 2.16358i) q^{56} +(7.29297 - 9.73564i) q^{57} +(2.86866 - 4.96867i) q^{58} +0.782167 q^{59} +(1.71973 + 0.206189i) q^{60} +4.76069 q^{61} -3.64324 q^{62} +(7.84936 + 1.17793i) q^{63} +1.00000 q^{64} -4.98501 q^{65} +(-1.70639 + 2.27792i) q^{66} -9.95545 q^{67} +(3.52620 - 6.10755i) q^{68} +(-12.8161 - 1.53659i) q^{69} +(2.63512 - 0.236999i) q^{70} -7.26549 q^{71} +(2.07165 - 2.16985i) q^{72} +(-0.392899 + 0.680521i) q^{73} +(2.87466 + 4.97906i) q^{74} +(1.03843 - 1.38624i) q^{75} +(-3.51153 - 6.08215i) q^{76} +(-1.82779 + 3.94472i) q^{77} +(-5.17659 + 6.91042i) q^{78} +5.86267 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.416496 - 8.99036i) q^{81} +(-4.30588 - 7.45800i) q^{82} +(3.28544 - 5.69055i) q^{83} +(2.40785 - 3.89901i) q^{84} +(-3.52620 - 6.10755i) q^{85} +(-2.96195 + 5.13024i) q^{86} +(-9.86667 - 1.18297i) q^{87} +(0.821620 + 1.42309i) q^{88} +(4.63848 + 8.03409i) q^{89} +(-0.843318 - 2.87903i) q^{90} +(-5.54488 + 11.9669i) q^{91} +(-3.72617 + 6.45392i) q^{92} +(2.48215 + 5.80160i) q^{93} -1.64116 q^{94} -7.02306 q^{95} +(-0.681302 - 1.59243i) q^{96} +(2.99028 - 5.17932i) q^{97} +(2.36213 - 6.58941i) q^{98} +(4.79000 + 1.16535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.681302	+	1.59243i	0.393350	+	0.919389i
$3$	0.681302	+	1.59243i	0.393350	+	0.919389i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.681302	−	1.59243i	−0.278140	−	0.650106i
$7$	−1.52280	−	2.16358i	−0.575566	−	0.817755i
$7$	−1.52280	−	2.16358i	−0.575566	−	0.817755i
$8$	−1.00000			−0.353553
$9$	−2.07165	+	2.16985i	−0.690551	+	0.723283i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.821620	−	1.42309i	−0.247728	−	0.429077i	0.715167	−	0.698953i	$-0.246351\pi$
$11$	−0.821620	−	1.42309i	−0.247728	−	0.429077i	−0.962895	+	0.269876i	$0.913017\pi$
$12$	0.681302	+	1.59243i	0.196675	+	0.459694i
$13$	−2.49250	−	4.31714i	−0.691296	−	1.19736i	−0.971413	−	0.237395i	$-0.923707\pi$
$13$	−2.49250	−	4.31714i	−0.691296	−	1.19736i	0.280117	−	0.959966i	$-0.409627\pi$
$14$	1.52280	+	2.16358i	0.406987	+	0.578240i
$15$	1.71973	+	0.206189i	0.444033	+	0.0532378i
$16$	1.00000			0.250000
$17$	3.52620	−	6.10755i	0.855229	−	1.48130i	−0.0212039	−	0.999775i	$-0.506750\pi$
$17$	3.52620	−	6.10755i	0.855229	−	1.48130i	0.876433	−	0.481524i	$-0.159917\pi$
$18$	2.07165	−	2.16985i	0.488294	−	0.511438i
$19$	−3.51153	−	6.08215i	−0.805601	−	1.39534i	−0.915885	−	0.401441i	$-0.868509\pi$
$19$	−3.51153	−	6.08215i	−0.805601	−	1.39534i	0.110284	−	0.993900i	$-0.464824\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.40785	−	3.89901i	0.525436	−	0.850833i
$22$	0.821620	+	1.42309i	0.175170	+	0.303403i
$23$	−3.72617	+	6.45392i	−0.776961	+	1.34574i	0.156724	+	0.987642i	$0.449907\pi$
$23$	−3.72617	+	6.45392i	−0.776961	+	1.34574i	−0.933686	+	0.358094i	$0.883427\pi$
$24$	−0.681302	−	1.59243i	−0.139070	−	0.325053i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.49250	+	4.31714i	0.488820	+	0.846662i
$27$	−4.86675	−	1.82064i	−0.936607	−	0.350382i
$28$	−1.52280	−	2.16358i	−0.287783	−	0.408878i
$29$	−2.86866	+	4.96867i	−0.532697	+	0.922658i	0.466574	+	0.884482i	$0.345488\pi$
$29$	−2.86866	+	4.96867i	−0.532697	+	0.922658i	−0.999271	+	0.0381762i	$0.987845\pi$
$30$	−1.71973	−	0.206189i	−0.313979	−	0.0376448i
$31$	3.64324			0.654345			0.327173	−	0.944965i	$-0.393904\pi$
$31$	3.64324			0.654345			0.327173	+	0.944965i	$0.393904\pi$
$32$	−1.00000			−0.176777
$33$	1.70639	−	2.27792i	0.297045	−	0.396536i
$34$	−3.52620	+	6.10755i	−0.604738	+	1.04744i
$35$	−2.63512	+	0.236999i	−0.445416	+	0.0400601i
$36$	−2.07165	+	2.16985i	−0.345276	+	0.361642i
$37$	−2.87466	−	4.97906i	−0.472592	−	0.818553i	0.526916	−	0.849917i	$-0.323348\pi$
$37$	−2.87466	−	4.97906i	−0.472592	−	0.818553i	−0.999508	+	0.0313643i	$0.990015\pi$
$38$	3.51153	+	6.08215i	0.569646	+	0.986655i
$39$	5.17659	−	6.91042i	0.828918	−	1.10655i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	4.30588	+	7.45800i	0.672465	+	1.16474i	0.977203	+	0.212307i	$0.0680977\pi$
$41$	4.30588	+	7.45800i	0.672465	+	1.16474i	−0.304738	+	0.952436i	$0.598569\pi$
$42$	−2.40785	+	3.89901i	−0.371539	+	0.601630i
$43$	2.96195	−	5.13024i	0.451692	−	0.782354i	−0.546799	−	0.837264i	$-0.684154\pi$
$43$	2.96195	−	5.13024i	0.451692	−	0.782354i	0.998491	+	0.0549098i	$0.0174871\pi$
$44$	−0.821620	−	1.42309i	−0.123864	−	0.214539i
$45$	0.843318	+	2.87903i	0.125714	+	0.429180i
$46$	3.72617	−	6.45392i	0.549394	−	0.951579i
$47$	1.64116			0.239388			0.119694	−	0.992811i	$-0.461809\pi$
$47$	1.64116			0.239388			0.119694	+	0.992811i	$0.461809\pi$
$48$	0.681302	+	1.59243i	0.0983375	+	0.229847i
$49$	−2.36213	+	6.58941i	−0.337448	+	0.941344i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	12.1282	+	1.45413i	1.69829	+	0.203618i
$52$	−2.49250	−	4.31714i	−0.345648	−	0.598680i
$53$	6.46391	−	11.1958i	0.887886	−	1.53786i	0.0455161	−	0.998964i	$-0.485507\pi$
$53$	6.46391	−	11.1958i	0.887886	−	1.53786i	0.842370	−	0.538900i	$-0.181160\pi$
$54$	4.86675	+	1.82064i	0.662281	+	0.247757i
$55$	−1.64324			−0.221575
$56$	1.52280	+	2.16358i	0.203493	+	0.289120i
$57$	7.29297	−	9.73564i	0.965978	−	1.28952i
$58$	2.86866	−	4.96867i	0.376674	−	0.652418i
$59$	0.782167			0.101829			0.0509147	−	0.998703i	$-0.483786\pi$
$59$	0.782167			0.101829			0.0509147	+	0.998703i	$0.483786\pi$
$60$	1.71973	+	0.206189i	0.222017	+	0.0266189i
$61$	4.76069			0.609543			0.304772	−	0.952425i	$-0.401420\pi$
$61$	4.76069			0.609543			0.304772	+	0.952425i	$0.401420\pi$
$62$	−3.64324			−0.462692
$63$	7.84936	+	1.17793i	0.988927	+	0.148405i
$64$	1.00000			0.125000
$65$	−4.98501			−0.618314
$66$	−1.70639	+	2.27792i	−0.210043	+	0.280393i
$67$	−9.95545			−1.21625			−0.608126	−	0.793841i	$-0.708078\pi$
$67$	−9.95545			−1.21625			−0.608126	+	0.793841i	$0.708078\pi$
$68$	3.52620	−	6.10755i	0.427614	−	0.740650i
$69$	−12.8161	−	1.53659i	−1.54287	−	0.184984i
$70$	2.63512	−	0.236999i	0.314956	−	0.0283268i
$71$	−7.26549			−0.862255			−0.431127	−	0.902291i	$-0.641884\pi$
$71$	−7.26549			−0.862255			−0.431127	+	0.902291i	$0.641884\pi$
$72$	2.07165	−	2.16985i	0.244147	−	0.255719i
$73$	−0.392899	+	0.680521i	−0.0459854	+	0.0796490i	−0.888102	−	0.459647i	$-0.847976\pi$
$73$	−0.392899	+	0.680521i	−0.0459854	+	0.0796490i	0.842117	+	0.539296i	$0.181309\pi$
$74$	2.87466	+	4.97906i	0.334173	+	0.578804i
$75$	1.03843	−	1.38624i	0.119908	−	0.160069i
$76$	−3.51153	−	6.08215i	−0.402800	−	0.697671i
$77$	−1.82779	+	3.94472i	−0.208296	+	0.449543i
$78$	−5.17659	+	6.91042i	−0.586134	+	0.782450i
$79$	5.86267			0.659602			0.329801	−	0.944050i	$-0.393018\pi$
$79$	5.86267			0.659602			0.329801	+	0.944050i	$0.393018\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.416496	−	8.99036i	−0.0462773	−	0.998929i
$82$	−4.30588	−	7.45800i	−0.475504	−	0.823598i
$83$	3.28544	−	5.69055i	0.360624	−	0.624619i	−0.627440	−	0.778665i	$-0.715897\pi$
$83$	3.28544	−	5.69055i	0.360624	−	0.624619i	0.988064	+	0.154046i	$0.0492304\pi$
$84$	2.40785	−	3.89901i	0.262718	−	0.425417i
$85$	−3.52620	−	6.10755i	−0.382470	−	0.662457i
$86$	−2.96195	+	5.13024i	−0.319395	+	0.553208i
$87$	−9.86667	−	1.18297i	−1.05782	−	0.126828i
$88$	0.821620	+	1.42309i	0.0875850	+	0.151702i
$89$	4.63848	+	8.03409i	0.491678	+	0.851612i	0.999954	−	0.00958252i	$-0.00305026\pi$
$89$	4.63848	+	8.03409i	0.491678	+	0.851612i	−0.508276	+	0.861194i	$0.669717\pi$
$90$	−0.843318	−	2.87903i	−0.0888935	−	0.303476i
$91$	−5.54488	+	11.9669i	−0.581261	+	1.25447i
$92$	−3.72617	+	6.45392i	−0.388481	+	0.672868i
$93$	2.48215	+	5.80160i	0.257387	+	0.601598i
$94$	−1.64116			−0.169273
$95$	−7.02306			−0.720551
$96$	−0.681302	−	1.59243i	−0.0695351	−	0.162527i
$97$	2.99028	−	5.17932i	0.303617	−	0.525880i	−0.673335	−	0.739337i	$-0.735139\pi$
$97$	2.99028	−	5.17932i	0.303617	−	0.525880i	0.976953	+	0.213457i	$0.0684723\pi$
$98$	2.36213	−	6.58941i	0.238611	−	0.665631i
$99$	4.79000	+	1.16535i	0.481413	+	0.117123i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	2.33999	+	4.05298i	0.232838	+	0.403287i	0.958642	−	0.284614i	$-0.0918655\pi$
$101$	2.33999	+	4.05298i	0.232838	+	0.403287i	−0.725804	+	0.687901i	$0.758532\pi$
$102$	−12.1282	−	1.45413i	−1.20088	−	0.143980i
$103$	−2.79748	+	4.84537i	−0.275644	+	0.477429i	−0.970297	−	0.241915i	$-0.922224\pi$
$103$	−2.79748	+	4.84537i	−0.275644	+	0.477429i	0.694654	+	0.719344i	$0.255558\pi$
$104$	2.49250	+	4.31714i	0.244410	+	0.423331i
$105$	−2.17271	−	4.03476i	−0.212035	−	0.393753i
$106$	−6.46391	+	11.1958i	−0.627830	+	1.08743i
$107$	3.83855	+	6.64856i	0.371086	+	0.642740i	0.989733	−	0.142929i	$-0.0456521\pi$
$107$	3.83855	+	6.64856i	0.371086	+	0.642740i	−0.618647	+	0.785669i	$0.712319\pi$
$108$	−4.86675	−	1.82064i	−0.468303	−	0.175191i
$109$	9.68250	−	16.7706i	0.927415	−	1.60633i	0.139786	−	0.990182i	$-0.455359\pi$
$109$	9.68250	−	16.7706i	0.927415	−	1.60633i	0.787630	−	0.616149i	$-0.211308\pi$
$110$	1.64324			0.156677
$111$	5.97028	−	7.96994i	0.566674	−	0.756473i
$112$	−1.52280	−	2.16358i	−0.143891	−	0.204439i
$113$	−0.830795	−	1.43898i	−0.0781546	−	0.135368i	0.824299	−	0.566154i	$-0.191569\pi$
$113$	−0.830795	−	1.43898i	−0.0781546	−	0.135368i	−0.902454	+	0.430787i	$0.858236\pi$
$114$	−7.29297	+	9.73564i	−0.683050	+	0.911827i
$115$	3.72617	+	6.45392i	0.347468	+	0.601832i
$116$	−2.86866	+	4.96867i	−0.266349	+	0.461329i
$117$	14.5312	+	3.53527i	1.34341	+	0.326836i
$118$	−0.782167			−0.0720043
$119$	−18.5839	+	1.67141i	−1.70358	+	0.153218i
$120$	−1.71973	−	0.206189i	−0.156990	−	0.0188224i
$121$	4.14988	−	7.18780i	0.377262	−	0.653437i
$122$	−4.76069			−0.431012
$123$	−8.94272	+	11.9379i	−0.806338	+	1.07641i
$124$	3.64324			0.327173
$125$	−1.00000			−0.0894427
$126$	−7.84936	−	1.17793i	−0.699277	−	0.104938i
$127$	−16.4680			−1.46130			−0.730649	−	0.682754i	$-0.760782\pi$
$127$	−16.4680			−1.46130			−0.730649	+	0.682754i	$0.760782\pi$
$128$	−1.00000			−0.0883883
$129$	10.1875	+	1.22144i	0.896961	+	0.107542i
$130$	4.98501			0.437214
$131$	−6.83808	+	11.8439i	−0.597445	+	1.03481i	0.395751	+	0.918358i	$0.370484\pi$
$131$	−6.83808	+	11.8439i	−0.597445	+	1.03481i	−0.993197	+	0.116448i	$0.962849\pi$
$132$	1.70639	−	2.27792i	0.148523	−	0.198268i
$133$	−7.81183	+	16.8594i	−0.677371	+	1.46190i
$134$	9.95545			0.860020
$135$	−4.01009	+	3.30441i	−0.345134	+	0.284399i
$136$	−3.52620	+	6.10755i	−0.302369	+	0.523719i
$137$	−0.421767	−	0.730521i	−0.0360340	−	0.0624126i	0.847446	−	0.530882i	$-0.178139\pi$
$137$	−0.421767	−	0.730521i	−0.0360340	−	0.0624126i	−0.883480	+	0.468469i	$0.844806\pi$
$138$	12.8161	+	1.53659i	1.09098	+	0.130803i
$139$	2.92189	+	5.06087i	0.247832	+	0.429257i	0.962924	−	0.269773i	$-0.0869486\pi$
$139$	2.92189	+	5.06087i	0.247832	+	0.429257i	−0.715092	+	0.699030i	$0.753615\pi$
$140$	−2.63512	+	0.236999i	−0.222708	+	0.0200300i
$141$	1.11813	+	2.61343i	0.0941634	+	0.220091i
$142$	7.26549			0.609706
$143$	−4.09579	+	7.09411i	−0.342507	+	0.593239i
$144$	−2.07165	+	2.16985i	−0.172638	+	0.180821i
$145$	2.86866	+	4.96867i	0.238229	+	0.412625i
$146$	0.392899	−	0.680521i	0.0325166	−	0.0563203i
$147$	−12.1025	+	0.727853i	−0.998196	+	0.0600323i
$148$	−2.87466	−	4.97906i	−0.236296	−	0.409276i
$149$	6.83105	−	11.8317i	0.559622	−	0.969293i	−0.437906	−	0.899021i	$-0.644280\pi$
$149$	6.83105	−	11.8317i	0.559622	−	0.969293i	0.997528	−	0.0702723i	$-0.0223868\pi$
$150$	−1.03843	+	1.38624i	−0.0847876	+	0.113186i
$151$	0.289219	+	0.500943i	0.0235363	+	0.0407661i	0.877554	−	0.479478i	$-0.159174\pi$
$151$	0.289219	+	0.500943i	0.0235363	+	0.0407661i	−0.854017	+	0.520245i	$0.825841\pi$
$152$	3.51153	+	6.08215i	0.284823	+	0.493328i
$153$	5.94741	+	20.3041i	0.480820	+	1.64149i
$154$	1.82779	−	3.94472i	0.147288	−	0.317875i
$155$	1.82162	−	3.15514i	0.146316	−	0.253427i
$156$	5.17659	−	6.91042i	0.414459	−	0.553276i
$157$	−3.29826			−0.263230			−0.131615	−	0.991301i	$-0.542016\pi$
$157$	−3.29826			−0.263230			−0.131615	+	0.991301i	$0.542016\pi$
$158$	−5.86267			−0.466409
$159$	22.2324	+	2.66557i	1.76314	+	0.211394i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	19.6378	−	1.76620i	1.54768	−	0.139196i
$162$	0.416496	+	8.99036i	0.0327230	+	0.706349i
$163$	11.5863	+	20.0681i	0.907510	+	1.57185i	0.817512	+	0.575912i	$0.195353\pi$
$163$	11.5863	+	20.0681i	0.907510	+	1.57185i	0.0899989	+	0.995942i	$0.471314\pi$
$164$	4.30588	+	7.45800i	0.336232	+	0.582372i
$165$	−1.11954	−	2.61674i	−0.0871564	−	0.203713i
$166$	−3.28544	+	5.69055i	−0.255000	+	0.441673i
$167$	−6.21246	−	10.7603i	−0.480734	−	0.832656i	0.519021	−	0.854761i	$-0.326296\pi$
$167$	−6.21246	−	10.7603i	−0.480734	−	0.832656i	−0.999756	+	0.0221051i	$0.992963\pi$
$168$	−2.40785	+	3.89901i	−0.185770	+	0.300815i
$169$	−5.92516	+	10.2627i	−0.455782	+	0.789437i
$170$	3.52620	+	6.10755i	0.270447	+	0.468428i
$171$	20.4720	+	4.98062i	1.56554	+	0.380877i
$172$	2.96195	−	5.13024i	0.225846	−	0.391177i
$173$	−12.6529			−0.961983			−0.480992	−	0.876725i	$-0.659723\pi$
$173$	−12.6529			−0.961983			−0.480992	+	0.876725i	$0.659723\pi$
$174$	9.86667	+	1.18297i	0.747990	+	0.0896809i
$175$	−1.11231	+	2.40058i	−0.0840828	+	0.181466i
$176$	−0.821620	−	1.42309i	−0.0619320	−	0.107269i
$177$	0.532892	+	1.24554i	0.0400546	+	0.0936208i
$178$	−4.63848	−	8.03409i	−0.347669	−	0.602181i
$179$	4.33144	−	7.50227i	0.323747	−	0.560746i	−0.657511	−	0.753445i	$-0.728391\pi$
$179$	4.33144	−	7.50227i	0.323747	−	0.560746i	0.981258	+	0.192699i	$0.0617241\pi$
$180$	0.843318	+	2.87903i	0.0628572	+	0.214590i
$181$	−10.4358			−0.775688			−0.387844	−	0.921725i	$-0.626780\pi$
$181$	−10.4358			−0.775688			−0.387844	+	0.921725i	$0.626780\pi$
$182$	5.54488	−	11.9669i	0.411014	−	0.887045i
$183$	3.24347	+	7.58105i	0.239764	+	0.560407i
$184$	3.72617	−	6.45392i	0.274697	−	0.475790i
$185$	−5.74933			−0.422699
$186$	−2.48215	−	5.80160i	−0.182000	−	0.425394i
$187$	−11.5888			−0.847456
$188$	1.64116			0.119694
$189$	3.47202	+	13.3021i	0.252553	+	0.967583i
$190$	7.02306			0.509507
$191$	−17.9357			−1.29778			−0.648890	−	0.760882i	$-0.724767\pi$
$191$	−17.9357			−1.29778			−0.648890	+	0.760882i	$0.724767\pi$
$192$	0.681302	+	1.59243i	0.0491688	+	0.114924i
$193$	4.16116			0.299527			0.149763	−	0.988722i	$-0.452149\pi$
$193$	4.16116			0.299527			0.149763	+	0.988722i	$0.452149\pi$
$194$	−2.99028	+	5.17932i	−0.214690	+	0.371854i
$195$	−3.39630	−	7.93827i	−0.243214	−	0.568471i
$196$	−2.36213	+	6.58941i	−0.168724	+	0.470672i
$197$	−7.80338			−0.555967			−0.277984	−	0.960586i	$-0.589666\pi$
$197$	−7.80338			−0.555967			−0.277984	+	0.960586i	$0.589666\pi$
$198$	−4.79000	−	1.16535i	−0.340411	−	0.0828181i
$199$	−12.2477	+	21.2136i	−0.868214	+	1.50379i	−0.00439303	+	0.999990i	$0.501398\pi$
$199$	−12.2477	+	21.2136i	−0.868214	+	1.50379i	−0.863821	+	0.503800i	$0.831935\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−6.78267	−	15.8533i	−0.478413	−	1.11821i
$202$	−2.33999	−	4.05298i	−0.164641	−	0.285167i
$203$	15.1185	−	1.35974i	1.06111	−	0.0954349i
$204$	12.1282	+	1.45413i	0.849147	+	0.101809i
$205$	8.61175			0.601471
$206$	2.79748	−	4.84537i	0.194910	−	0.337593i
$207$	−6.28470	−	21.4555i	−0.436817	−	1.49126i
$208$	−2.49250	−	4.31714i	−0.172824	−	0.299340i
$209$	−5.77029	+	9.99444i	−0.399139	+	0.691330i
$210$	2.17271	+	4.03476i	0.149931	+	0.278425i
$211$	5.31753	+	9.21023i	0.366074	+	0.634059i	0.988948	−	0.148264i	$-0.0473684\pi$
$211$	5.31753	+	9.21023i	0.366074	+	0.634059i	−0.622874	+	0.782322i	$0.714035\pi$
$212$	6.46391	−	11.1958i	0.443943	−	0.768932i
$213$	−4.94999	−	11.5698i	−0.339168	−	0.792748i
$214$	−3.83855	−	6.64856i	−0.262398	−	0.454486i
$215$	−2.96195	−	5.13024i	−0.202003	−	0.349879i
$216$	4.86675	+	1.82064i	0.331141	+	0.123879i
$217$	−5.54794	−	7.88243i	−0.376619	−	0.535094i
$218$	−9.68250	+	16.7706i	−0.655782	+	1.13585i
$219$	−1.35136	−	0.162023i	−0.0913167	−	0.0109485i
$220$	−1.64324			−0.110787
$221$	−35.1563			−2.36487
$222$	−5.97028	+	7.96994i	−0.400699	+	0.534907i
$223$	12.8215	−	22.2074i	0.858589	−	1.48712i	−0.0146860	−	0.999892i	$-0.504675\pi$
$223$	12.8215	−	22.2074i	0.858589	−	1.48712i	0.873275	−	0.487228i	$-0.161992\pi$
$224$	1.52280	+	2.16358i	0.101747	+	0.144560i
$225$	2.91497	+	0.709180i	0.194331	+	0.0472787i
$226$	0.830795	+	1.43898i	0.0552636	+	0.0957194i
$227$	9.49730	+	16.4498i	0.630358	+	1.09181i	0.987479	+	0.157753i	$0.0504251\pi$
$227$	9.49730	+	16.4498i	0.630358	+	1.09181i	−0.357121	+	0.934058i	$0.616242\pi$
$228$	7.29297	−	9.73564i	0.482989	−	0.644759i
$229$	−2.24447	+	3.88754i	−0.148319	+	0.256896i	−0.930606	−	0.366022i	$-0.880720\pi$
$229$	−2.24447	+	3.88754i	−0.148319	+	0.256896i	0.782287	+	0.622918i	$0.214053\pi$
$230$	−3.72617	−	6.45392i	−0.245697	−	0.425559i
$231$	−7.52697	−	0.223081i	−0.495238	−	0.0146777i
$232$	2.86866	−	4.96867i	0.188337	−	0.326209i
$233$	2.86866	+	4.96867i	0.187932	+	0.325508i	0.944561	−	0.328337i	$-0.106488\pi$
$233$	2.86866	+	4.96867i	0.187932	+	0.325508i	−0.756628	+	0.653845i	$0.773155\pi$
$234$	−14.5312	−	3.53527i	−0.949932	−	0.231108i
$235$	0.820581	−	1.42129i	0.0535288	−	0.0927147i
$236$	0.782167			0.0509147
$237$	3.99425	+	9.33588i	0.259455	+	0.606431i
$238$	18.5839	−	1.67141i	1.20461	−	0.108341i
$239$	−13.7619	−	23.8363i	−0.890183	−	1.54184i	−0.839656	−	0.543119i	$-0.817243\pi$
$239$	−13.7619	−	23.8363i	−0.890183	−	1.54184i	−0.0505270	−	0.998723i	$-0.516090\pi$
$240$	1.71973	+	0.206189i	0.111008	+	0.0133094i
$241$	10.0984	+	17.4909i	0.650492	+	1.12669i	0.983004	+	0.183586i	$0.0587706\pi$
$241$	10.0984	+	17.4909i	0.650492	+	1.12669i	−0.332512	+	0.943099i	$0.607896\pi$
$242$	−4.14988	+	7.18780i	−0.266764	+	0.462049i
$243$	14.0327	−	6.78839i	0.900201	−	0.435476i
$244$	4.76069			0.304772
$245$	4.52553	+	5.34037i	0.289126	+	0.341184i
$246$	8.94272	−	11.9379i	0.570167	−	0.761136i
$247$	−17.5050	+	30.3196i	−1.11382	+	1.92919i
$248$	−3.64324			−0.231346
$249$	11.3002	+	1.35484i	0.716120	+	0.0858597i
$250$	1.00000			0.0632456
$251$	24.3941			1.53974			0.769871	−	0.638200i	$-0.220321\pi$
$251$	24.3941			1.53974			0.769871	+	0.638200i	$0.220321\pi$
$252$	7.84936	+	1.17793i	0.494463	+	0.0742025i
$253$	12.2460			0.769900
$254$	16.4680			1.03329
$255$	7.32343	−	9.77631i	0.458611	−	0.612216i
$256$	1.00000			0.0625000
$257$	3.85742	−	6.68125i	0.240620	−	0.416765i	−0.720271	−	0.693692i	$-0.755983\pi$
$257$	3.85742	−	6.68125i	0.240620	−	0.416765i	0.960891	+	0.276927i	$0.0893161\pi$
$258$	−10.1875	−	1.22144i	−0.634247	−	0.0760436i
$259$	−6.39504	+	13.8017i	−0.397368	+	0.857596i
$260$	−4.98501			−0.309157
$261$	−4.83839	−	16.5179i	−0.299489	−	1.02243i
$262$	6.83808	−	11.8439i	0.422458	−	0.731718i
$263$	6.48658	+	11.2351i	0.399979	+	0.692785i	0.993723	−	0.111870i	$-0.0356839\pi$
$263$	6.48658	+	11.2351i	0.399979	+	0.692785i	−0.593743	+	0.804654i	$0.702351\pi$
$264$	−1.70639	+	2.27792i	−0.105021	+	0.140197i
$265$	−6.46391	−	11.1958i	−0.397075	−	0.687753i
$266$	7.81183	−	16.8594i	0.478974	−	1.03372i
$267$	−9.63350	+	12.8601i	−0.589561	+	0.787025i
$268$	−9.95545			−0.608126
$269$	10.5195	−	18.2203i	0.641384	−	1.11091i	−0.343741	−	0.939065i	$-0.611694\pi$
$269$	10.5195	−	18.2203i	0.641384	−	1.11091i	0.985124	−	0.171844i	$-0.0549726\pi$
$270$	4.01009	−	3.30441i	0.244047	−	0.201100i
$271$	−7.04460	−	12.2016i	−0.427929	−	0.741195i	0.568760	−	0.822503i	$-0.307423\pi$
$271$	−7.04460	−	12.2016i	−0.427929	−	0.741195i	−0.996689	+	0.0813089i	$0.974090\pi$
$272$	3.52620	−	6.10755i	0.213807	−	0.370325i
$273$	−22.8342	−	0.676749i	−1.38199	−	0.0409587i
$274$	0.421767	+	0.730521i	0.0254799	+	0.0441324i
$275$	−0.821620	+	1.42309i	−0.0495456	+	0.0858154i
$276$	−12.8161	−	1.53659i	−0.771436	−	0.0924920i
$277$	−3.39152	−	5.87428i	−0.203776	−	0.352951i	0.745966	−	0.665984i	$-0.231988\pi$
$277$	−3.39152	−	5.87428i	−0.203776	−	0.352951i	−0.949742	+	0.313033i	$0.898655\pi$
$278$	−2.92189	−	5.06087i	−0.175244	−	0.303531i
$279$	−7.54754	+	7.90529i	−0.451859	+	0.473277i
$280$	2.63512	−	0.236999i	0.157478	−	0.0141634i
$281$	5.76128	−	9.97883i	0.343689	−	0.595287i	−0.641426	−	0.767185i	$-0.721657\pi$
$281$	5.76128	−	9.97883i	0.343689	−	0.595287i	0.985115	+	0.171898i	$0.0549900\pi$
$282$	−1.11813	−	2.61343i	−0.0665836	−	0.155628i
$283$	4.93996			0.293650			0.146825	−	0.989162i	$-0.453095\pi$
$283$	4.93996			0.293650			0.146825	+	0.989162i	$0.453095\pi$
$284$	−7.26549			−0.431127
$285$	−4.78483	−	11.1837i	−0.283429	−	0.662467i
$286$	4.09579	−	7.09411i	0.242189	−	0.419483i
$287$	9.57894	−	20.6732i	0.565427	−	1.22030i
$288$	2.07165	−	2.16985i	0.122073	−	0.127860i
$289$	−16.3682	−	28.3505i	−0.962832	−	1.66767i
$290$	−2.86866	−	4.96867i	−0.168454	−	0.291770i
$291$	10.2850	+	1.23313i	0.602916	+	0.0722872i
$292$	−0.392899	+	0.680521i	−0.0229927	+	0.0398245i
$293$	1.17274	+	2.03124i	0.0685121	+	0.118667i	0.898247	−	0.439492i	$-0.144841\pi$
$293$	1.17274	+	2.03124i	0.0685121	+	0.118667i	−0.829734	+	0.558158i	$0.811508\pi$
$294$	12.1025	−	0.727853i	0.705831	−	0.0424492i
$295$	0.391083	−	0.677376i	0.0227698	−	0.0394384i
$296$	2.87466	+	4.97906i	0.167086	+	0.289402i
$297$	1.40770	+	8.42169i	0.0816828	+	0.488676i
$298$	−6.83105	+	11.8317i	−0.395712	+	0.685394i
$299$	37.1500			2.14844
$300$	1.03843	−	1.38624i	0.0599539	−	0.0800346i
$301$	−15.6101	+	1.40395i	−0.899753	+	0.0809226i
$302$	−0.289219	−	0.500943i	−0.0166427	−	0.0288260i
$303$	−4.85985	+	6.48758i	−0.279191	+	0.372702i
$304$	−3.51153	−	6.08215i	−0.201400	−	0.348835i
$305$	2.38034	−	4.12287i	0.136298	−	0.236075i
$306$	−5.94741	−	20.3041i	−0.339991	−	1.16071i
$307$	4.00934			0.228825			0.114412	−	0.993433i	$-0.463501\pi$
$307$	4.00934			0.228825			0.114412	+	0.993433i	$0.463501\pi$
$308$	−1.82779	+	3.94472i	−0.104148	+	0.224772i
$309$	−9.62184	−	1.15362i	−0.547367	−	0.0656271i
$310$	−1.82162	+	3.15514i	−0.103461	+	0.179200i
$311$	−17.9450			−1.01757			−0.508785	−	0.860894i	$-0.669905\pi$
$311$	−17.9450			−1.01757			−0.508785	+	0.860894i	$0.669905\pi$
$312$	−5.17659	+	6.91042i	−0.293067	+	0.391225i
$313$	−6.34031			−0.358375			−0.179188	−	0.983815i	$-0.557347\pi$
$313$	−6.34031			−0.358375			−0.179188	+	0.983815i	$0.557347\pi$
$314$	3.29826			0.186132
$315$	4.94480	−	6.20878i	0.278608	−	0.349825i
$316$	5.86267			0.329801
$317$	10.9145			0.613018			0.306509	−	0.951868i	$-0.400839\pi$
$317$	10.9145			0.613018			0.306509	+	0.951868i	$0.400839\pi$
$318$	−22.2324	−	2.66557i	−1.24673	−	0.149478i
$319$	9.42780			0.527856
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−7.97214	+	10.6423i	−0.444961	+	0.593995i
$322$	−19.6378	+	1.76620i	−1.09437	+	0.0984263i
$323$	−49.5294			−2.75589
$324$	−0.416496	−	8.99036i	−0.0231387	−	0.499464i
$325$	−2.49250	+	4.31714i	−0.138259	+	0.239472i
$326$	−11.5863	−	20.0681i	−0.641707	−	1.11147i
$327$	33.3027	+	3.99285i	1.84164	+	0.220805i
$328$	−4.30588	−	7.45800i	−0.237752	−	0.411799i
$329$	−2.49917	−	3.55078i	−0.137784	−	0.195761i
$330$	1.11954	+	2.61674i	0.0616288	+	0.144047i
$331$	26.2924			1.44516			0.722580	−	0.691288i	$-0.242956\pi$
$331$	26.2924			1.44516			0.722580	+	0.691288i	$0.242956\pi$
$332$	3.28544	−	5.69055i	0.180312	−	0.312310i
$333$	16.7591	+	4.07731i	0.918394	+	0.223435i
$334$	6.21246	+	10.7603i	0.339930	+	0.588777i
$335$	−4.97772	+	8.62167i	−0.271962	+	0.471052i
$336$	2.40785	−	3.89901i	0.131359	−	0.212708i
$337$	−8.15482	−	14.1246i	−0.444221	−	0.769414i	0.553776	−	0.832665i	$-0.313186\pi$
$337$	−8.15482	−	14.1246i	−0.444221	−	0.769414i	−0.997998	+	0.0632518i	$0.979853\pi$
$338$	5.92516	−	10.2627i	0.322286	−	0.558216i
$339$	1.72545	−	2.30336i	0.0937134	−	0.125101i
$340$	−3.52620	−	6.10755i	−0.191235	−	0.331229i
$341$	−2.99336	−	5.18465i	−0.162100	−	0.280765i
$342$	−20.4720	−	4.98062i	−1.10700	−	0.269321i
$343$	17.8538	−	4.92373i	0.964013	−	0.265856i
$344$	−2.96195	+	5.13024i	−0.159697	+	0.276604i
$345$	−7.73876	+	10.3307i	−0.416641	+	0.556188i
$346$	12.6529			0.680225
$347$	7.70803			0.413789			0.206894	−	0.978363i	$-0.433664\pi$
$347$	7.70803			0.413789			0.206894	+	0.978363i	$0.433664\pi$
$348$	−9.86667	−	1.18297i	−0.528909	−	0.0634140i
$349$	16.9427	−	29.3456i	0.906923	−	1.57084i	0.0886077	−	0.996067i	$-0.471758\pi$
$349$	16.9427	−	29.3456i	0.906923	−	1.57084i	0.818315	−	0.574770i	$-0.194908\pi$
$350$	1.11231	−	2.40058i	0.0594555	−	0.128316i
$351$	4.27045	+	25.5484i	0.227940	+	1.36367i
$352$	0.821620	+	1.42309i	0.0437925	+	0.0758509i
$353$	−5.99417	−	10.3822i	−0.319038	−	0.552589i	0.661250	−	0.750166i	$-0.270026\pi$
$353$	−5.99417	−	10.3822i	−0.319038	−	0.552589i	−0.980287	+	0.197576i	$0.936693\pi$
$354$	−0.532892	−	1.24554i	−0.0283229	−	0.0661999i
$355$	−3.63274	+	6.29210i	−0.192806	+	0.333950i
$356$	4.63848	+	8.03409i	0.245839	+	0.425806i
$357$	−15.3228	−	28.4548i	−0.810971	−	1.50599i
$358$	−4.33144	+	7.50227i	−0.228924	+	0.396507i
$359$	−6.92259	−	11.9903i	−0.365360	−	0.632823i	0.623474	−	0.781844i	$-0.285721\pi$
$359$	−6.92259	−	11.9903i	−0.365360	−	0.632823i	−0.988834	+	0.149022i	$0.952388\pi$
$360$	−0.843318	−	2.87903i	−0.0444468	−	0.151738i
$361$	−15.1617	+	26.2608i	−0.797985	+	1.38215i
$362$	10.4358			0.548494
$363$	14.2734	+	1.71132i	0.749158	+	0.0898209i
$364$	−5.54488	+	11.9669i	−0.290631	+	0.627236i
$365$	0.392899	+	0.680521i	0.0205653	+	0.0356201i
$366$	−3.24347	−	7.58105i	−0.169539	−	0.396268i
$367$	8.64239	+	14.9691i	0.451129	+	0.781379i	0.998456	−	0.0555400i	$-0.0176880\pi$
$367$	8.64239	+	14.9691i	0.451129	+	0.781379i	−0.547327	+	0.836919i	$0.684355\pi$
$368$	−3.72617	+	6.45392i	−0.194240	+	0.336434i
$369$	−25.1030	−	6.10729i	−1.30681	−	0.317933i
$370$	5.74933			0.298893
$371$	−34.0663	+	3.06388i	−1.76863	+	0.159068i
$372$	2.48215	+	5.80160i	0.128693	+	0.300799i
$373$	7.77130	−	13.4603i	0.402383	−	0.696947i	−0.591630	−	0.806209i	$-0.701515\pi$
$373$	7.77130	−	13.4603i	0.402383	−	0.696947i	0.994013	+	0.109262i	$0.0348488\pi$
$374$	11.5888			0.599242
$375$	−0.681302	−	1.59243i	−0.0351823	−	0.0822326i
$376$	−1.64116			−0.0846365
$377$	28.6006			1.47301
$378$	−3.47202	−	13.3021i	−0.178582	−	0.684185i
$379$	21.7020			1.11476			0.557379	−	0.830259i	$-0.311807\pi$
$379$	21.7020			1.11476			0.557379	+	0.830259i	$0.311807\pi$
$380$	−7.02306			−0.360276
$381$	−11.2197	−	26.2241i	−0.574801	−	1.34350i
$382$	17.9357			0.917669
$383$	12.7077	−	22.0104i	0.649334	−	1.12468i	−0.333948	−	0.942592i	$-0.608381\pi$
$383$	12.7077	−	22.0104i	0.649334	−	1.12468i	0.983282	−	0.182089i	$-0.0582858\pi$
$384$	−0.681302	−	1.59243i	−0.0347676	−	0.0812633i
$385$	2.50233	+	3.55528i	0.127531	+	0.181194i
$386$	−4.16116			−0.211797
$387$	4.99572	+	17.0551i	0.253947	+	0.866957i
$388$	2.99028	−	5.17932i	0.151809	−	0.262940i
$389$	5.19770	+	9.00269i	0.263534	+	0.456454i	0.967179	−	0.254098i	$-0.0817785\pi$
$389$	5.19770	+	9.00269i	0.263534	+	0.456454i	−0.703644	+	0.710552i	$0.748445\pi$
$390$	3.39630	+	7.93827i	0.171978	+	0.401970i
$391$	26.2785	+	45.5156i	1.32896	+	2.30182i
$392$	2.36213	−	6.58941i	0.119306	−	0.332815i
$393$	−23.5193	−	2.81987i	−1.18639	−	0.142244i
$394$	7.80338			0.393128
$395$	2.93134	−	5.07722i	0.147492	−	0.255463i
$396$	4.79000	+	1.16535i	0.240707	+	0.0585613i
$397$	1.36768	+	2.36890i	0.0686421	+	0.118892i	0.898304	−	0.439375i	$-0.144800\pi$
$397$	1.36768	+	2.36890i	0.0686421	+	0.118892i	−0.829662	+	0.558266i	$0.811467\pi$
$398$	12.2477	−	21.2136i	0.613920	−	1.06334i
$399$	−32.1696	−	0.953429i	−1.61049	−	0.0477311i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.0177095	−	0.0306738i	0.000884372	−	0.00153178i	−0.865583	−	0.500766i	$-0.833052\pi$
$401$	0.0177095	−	0.0306738i	0.000884372	−	0.00153178i	0.866467	+	0.499234i	$0.166385\pi$
$402$	6.78267	+	15.8533i	0.338289	+	0.790693i
$403$	−9.08079	−	15.7284i	−0.452347	−	0.783487i
$404$	2.33999	+	4.05298i	0.116419	+	0.201644i
$405$	−7.99413	−	4.13448i	−0.397231	−	0.205444i
$406$	−15.1185	+	1.35974i	−0.750319	+	0.0674827i
$407$	−4.72376	+	8.18180i	−0.234148	+	0.405557i
$408$	−12.1282	−	1.45413i	−0.600438	−	0.0719900i
$409$	16.3458			0.808250			0.404125	−	0.914704i	$-0.367576\pi$
$409$	16.3458			0.808250			0.404125	+	0.914704i	$0.367576\pi$
$410$	−8.61175			−0.425304
$411$	0.875952	−	1.16934i	0.0432075	−	0.0576792i
$412$	−2.79748	+	4.84537i	−0.137822	+	0.238714i
$413$	−1.19109	−	1.69228i	−0.0586096	−	0.0832716i
$414$	6.28470	+	21.4555i	0.308876	+	1.05448i
$415$	−3.28544	−	5.69055i	−0.161276	−	0.279338i
$416$	2.49250	+	4.31714i	0.122205	+	0.211665i
$417$	−6.06838	+	8.10089i	−0.297170	+	0.396702i
$418$	5.77029	−	9.99444i	0.282234	−	0.488844i
$419$	−4.00800	−	6.94206i	−0.195804	−	0.339142i	0.751360	−	0.659892i	$-0.229398\pi$
$419$	−4.00800	−	6.94206i	−0.195804	−	0.339142i	−0.947164	+	0.320751i	$0.896065\pi$
$420$	−2.17271	−	4.03476i	−0.106018	−	0.196876i
$421$	16.7469	−	29.0066i	0.816196	−	1.41369i	−0.0922696	−	0.995734i	$-0.529412\pi$
$421$	16.7469	−	29.0066i	0.816196	−	1.41369i	0.908466	−	0.417959i	$-0.137255\pi$
$422$	−5.31753	−	9.21023i	−0.258853	−	0.448347i
$423$	−3.39992	+	3.56108i	−0.165310	+	0.173145i
$424$	−6.46391	+	11.1958i	−0.313915	+	0.543717i
$425$	−7.05240			−0.342091
$426$	4.94999	+	11.5698i	0.239828	+	0.560557i
$427$	−7.24959	−	10.3001i	−0.350832	−	0.498457i
$428$	3.83855	+	6.64856i	0.185543	+	0.321370i
$429$	−14.0873	−	1.68901i	−0.680142	−	0.0815462i
$430$	2.96195	+	5.13024i	0.142838	+	0.247402i
$431$	−12.2779	+	21.2660i	−0.591406	+	1.02434i	0.402638	+	0.915360i	$0.368094\pi$
$431$	−12.2779	+	21.2660i	−0.591406	+	1.02434i	−0.994043	+	0.108985i	$0.965240\pi$
$432$	−4.86675	−	1.82064i	−0.234152	−	0.0875954i
$433$	25.8917			1.24428			0.622138	−	0.782907i	$-0.286264\pi$
$433$	25.8917			1.24428			0.622138	+	0.782907i	$0.286264\pi$
$434$	5.54794	+	7.88243i	0.266310	+	0.378369i
$435$	−5.95782	+	7.95330i	−0.285656	+	0.381332i
$436$	9.68250	−	16.7706i	0.463708	−	0.803165i
$437$	52.3383			2.50368
$438$	1.35136	+	0.162023i	0.0645707	+	0.00774175i
$439$	−12.0363			−0.574460			−0.287230	−	0.957862i	$-0.592734\pi$
$439$	−12.0363			−0.574460			−0.287230	+	0.957862i	$0.592734\pi$
$440$	1.64324			0.0783384
$441$	−9.40451	−	18.7765i	−0.447834	−	0.894117i
$442$	35.1563			1.67221
$443$	2.01540			0.0957545			0.0478773	−	0.998853i	$-0.484754\pi$
$443$	2.01540			0.0957545			0.0478773	+	0.998853i	$0.484754\pi$
$444$	5.97028	−	7.96994i	0.283337	−	0.378237i
$445$	9.27697			0.439770
$446$	−12.8215	+	22.2074i	−0.607114	+	1.05155i
$447$	23.4952	+	2.81697i	1.11128	+	0.133238i
$448$	−1.52280	−	2.16358i	−0.0719457	−	0.102219i
$449$	−0.742369			−0.0350346			−0.0175173	−	0.999847i	$-0.505576\pi$
$449$	−0.742369			−0.0350346			−0.0175173	+	0.999847i	$0.505576\pi$
$450$	−2.91497	−	0.709180i	−0.137413	−	0.0334311i
$451$	7.07559	−	12.2553i	0.333177	−	0.577079i
$452$	−0.830795	−	1.43898i	−0.0390773	−	0.0676839i
$453$	−0.600669	+	0.801854i	−0.0282219	+	0.0376744i
$454$	−9.49730	−	16.4498i	−0.445730	−	0.772027i
$455$	7.59119	+	10.7855i	0.355881	+	0.505630i
$456$	−7.29297	+	9.73564i	−0.341525	+	0.455913i
$457$	−11.2275			−0.525199			−0.262600	−	0.964905i	$-0.584580\pi$
$457$	−11.2275			−0.525199			−0.262600	+	0.964905i	$0.584580\pi$
$458$	2.24447	−	3.88754i	0.104877	−	0.181653i
$459$	−28.2808	+	23.3040i	−1.32003	+	1.08774i
$460$	3.72617	+	6.45392i	0.173734	+	0.300916i
$461$	9.12633	−	15.8073i	0.425056	−	0.736218i	−0.571370	−	0.820693i	$-0.693588\pi$
$461$	9.12633	−	15.8073i	0.425056	−	0.736218i	0.996426	+	0.0844747i	$0.0269212\pi$
$462$	7.52697	+	0.223081i	0.350186	+	0.0103787i
$463$	14.5347	+	25.1748i	0.675484	+	1.16997i	0.976327	+	0.216299i	$0.0693985\pi$
$463$	14.5347	+	25.1748i	0.675484	+	1.16997i	−0.300843	+	0.953674i	$0.597268\pi$
$464$	−2.86866	+	4.96867i	−0.133174	+	0.230665i
$465$	6.26541	+	0.751196i	0.290551	+	0.0348359i
$466$	−2.86866	−	4.96867i	−0.132888	−	0.230169i
$467$	−3.65873	−	6.33711i	−0.169306	−	0.293246i	0.768870	−	0.639405i	$-0.220819\pi$
$467$	−3.65873	−	6.33711i	−0.169306	−	0.293246i	−0.938176	+	0.346159i	$0.887486\pi$
$468$	14.5312	+	3.53527i	0.671703	+	0.163418i
$469$	15.1602	+	21.5394i	0.700033	+	0.994596i
$470$	−0.820581	+	1.42129i	−0.0378506	+	0.0655592i
$471$	−2.24711	−	5.25224i	−0.103542	−	0.242011i
$472$	−0.782167			−0.0360021
$473$	−9.73438			−0.447587
$474$	−3.99425	−	9.33588i	−0.183462	−	0.428811i
$475$	−3.51153	+	6.08215i	−0.161120	+	0.279068i
$476$	−18.5839	+	1.67141i	−0.851791	+	0.0766089i
$477$	10.9023	+	37.2196i	0.499180	+	1.70417i
$478$	13.7619	+	23.8363i	0.629454	+	1.09025i
$479$	−3.08835	−	5.34918i	−0.141110	−	0.244410i	0.786805	−	0.617202i	$-0.211734\pi$
$479$	−3.08835	−	5.34918i	−0.141110	−	0.244410i	−0.927915	+	0.372792i	$0.878401\pi$
$480$	−1.71973	−	0.206189i	−0.0784948	−	0.00941120i
$481$	−14.3302	+	24.8207i	−0.653402	+	1.13173i
$482$	−10.0984	−	17.4909i	−0.459967	−	0.796687i
$483$	16.1918	+	30.0685i	0.736753	+	1.36816i
$484$	4.14988	−	7.18780i	0.188631	−	0.326718i
$485$	−2.99028	−	5.17932i	−0.135782	−	0.235181i
$486$	−14.0327	+	6.78839i	−0.636538	+	0.307928i
$487$	3.11014	−	5.38693i	0.140934	−	0.244105i	−0.786915	−	0.617062i	$-0.788323\pi$
$487$	3.11014	−	5.38693i	0.140934	−	0.244105i	0.927849	+	0.372957i	$0.121656\pi$
$488$	−4.76069			−0.215506
$489$	−24.0632	+	32.1228i	−1.08818	+	1.45264i
$490$	−4.52553	−	5.34037i	−0.204443	−	0.241253i
$491$	−3.94447	−	6.83202i	−0.178011	−	0.308325i	0.763188	−	0.646177i	$-0.223633\pi$
$491$	−3.94447	−	6.83202i	−0.178011	−	0.308325i	−0.941199	+	0.337852i	$0.890300\pi$
$492$	−8.94272	+	11.9379i	−0.403169	+	0.538204i
$493$	20.2309	+	35.0410i	0.911156	+	1.57817i
$494$	17.5050	−	30.3196i	0.787588	−	1.36414i
$495$	3.40423	−	3.56559i	0.153009	−	0.160261i
$496$	3.64324			0.163586
$497$	11.0639	+	15.7194i	0.496285	+	0.705114i
$498$	−11.3002	−	1.35484i	−0.506373	−	0.0607120i
$499$	−4.34473	+	7.52530i	−0.194497	+	0.336879i	−0.946735	−	0.322012i	$-0.895641\pi$
$499$	−4.34473	+	7.52530i	−0.194497	+	0.336879i	0.752239	+	0.658891i	$0.228974\pi$
$500$	−1.00000			−0.0447214
$501$	12.9024	−	17.2239i	0.576438	−	0.769507i
$502$	−24.3941			−1.08876
$503$	23.0236			1.02657			0.513285	−	0.858218i	$-0.328428\pi$
$503$	23.0236			1.02657			0.513285	+	0.858218i	$0.328428\pi$
$504$	−7.84936	−	1.17793i	−0.349638	−	0.0524691i
$505$	4.67998			0.208257
$506$	−12.2460			−0.544401
$507$	−20.3794	−	2.44340i	−0.905081	−	0.108515i
$508$	−16.4680			−0.730649
$509$	−8.29698	+	14.3708i	−0.367757	+	0.636974i	−0.989215	−	0.146474i	$-0.953208\pi$
$509$	−8.29698	+	14.3708i	−0.367757	+	0.636974i	0.621457	+	0.783448i	$0.286541\pi$
$510$	−7.32343	+	9.77631i	−0.324287	+	0.432902i
$511$	2.07067	−	0.186233i	0.0916010	−	0.00823847i
$512$	−1.00000			−0.0441942
$513$	6.01637	+	35.9935i	0.265629	+	1.58915i
$514$	−3.85742	+	6.68125i	−0.170144	+	0.294698i
$515$	2.79748	+	4.84537i	0.123272	+	0.213513i
$516$	10.1875	+	1.22144i	0.448480	+	0.0537709i
$517$	−1.34841	−	2.33552i	−0.0593031	−	0.102716i
$518$	6.39504	−	13.8017i	0.280982	−	0.606412i
$519$	−8.62046	−	20.1489i	−0.378396	−	0.884436i
$520$	4.98501			0.218607
$521$	−0.696803	+	1.20690i	−0.0305275	+	0.0528751i	−0.880886	−	0.473329i	$-0.843052\pi$
$521$	−0.696803	+	1.20690i	−0.0305275	+	0.0528751i	0.850358	+	0.526205i	$0.176385\pi$
$522$	4.83839	+	16.5179i	0.211770	+	0.722970i
$523$	−7.36346	−	12.7539i	−0.321982	−	0.557689i	0.658915	−	0.752217i	$-0.271016\pi$
$523$	−7.36346	−	12.7539i	−0.321982	−	0.557689i	−0.980897	+	0.194529i	$0.937682\pi$
$524$	−6.83808	+	11.8439i	−0.298723	+	0.517403i
$525$	−4.58056	−	0.135757i	−0.199912	−	0.00592491i
$526$	−6.48658	−	11.2351i	−0.282828	−	0.489873i
$527$	12.8468	−	22.2513i	0.559615	−	0.969282i
$528$	1.70639	−	2.27792i	0.0742613	−	0.0991339i
$529$	−16.2688	−	28.1783i	−0.707337	−	1.22514i
$530$	6.46391	+	11.1958i	0.280774	+	0.486315i
$531$	−1.62038	+	1.69718i	−0.0703185	+	0.0736515i
$532$	−7.81183	+	16.8594i	−0.338686	+	0.730948i
$533$	21.4648	−	37.1782i	0.929745	−	1.61037i
$534$	9.63350	−	12.8601i	0.416882	−	0.556511i
$535$	7.67709			0.331910
$536$	9.95545			0.430010
$537$	14.8978	+	1.78619i	0.642889	+	0.0770798i
$538$	−10.5195	+	18.2203i	−0.453527	+	0.785531i
$539$	11.3181	−	2.05247i	0.487505	−	0.0884061i
$540$	−4.01009	+	3.30441i	−0.172567	+	0.142199i
$541$	12.5237	+	21.6917i	0.538437	+	0.932601i	0.998988	+	0.0449675i	$0.0143184\pi$
$541$	12.5237	+	21.6917i	0.538437	+	0.932601i	−0.460551	+	0.887633i	$0.652348\pi$
$542$	7.04460	+	12.2016i	0.302591	+	0.524104i
$543$	−7.10994	−	16.6183i	−0.305117	−	0.713159i
$544$	−3.52620	+	6.10755i	−0.151185	+	0.261859i
$545$	−9.68250	−	16.7706i	−0.414753	−	0.718373i
$546$	22.8342	+	0.676749i	0.977212	+	0.0289622i
$547$	5.32171	−	9.21747i	0.227540	−	0.394110i	−0.729539	−	0.683940i	$-0.760265\pi$
$547$	5.32171	−	9.21747i	0.227540	−	0.394110i	0.957078	+	0.289829i	$0.0935985\pi$
$548$	−0.421767	−	0.730521i	−0.0180170	−	0.0312063i
$549$	−9.86250	+	10.3300i	−0.420921	+	0.440872i
$550$	0.821620	−	1.42309i	0.0350340	−	0.0606807i
$551$	40.2936			1.71656
$552$	12.8161	+	1.53659i	0.545488	+	0.0654017i
$553$	−8.92770	−	12.6843i	−0.379645	−	0.539393i
$554$	3.39152	+	5.87428i	0.144092	+	0.249574i
$555$	−3.91703	−	9.15539i	−0.166269	−	0.388625i
$556$	2.92189	+	5.06087i	0.123916	+	0.214629i
$557$	−21.3732	+	37.0195i	−0.905613	+	1.56857i	−0.0855219	+	0.996336i	$0.527256\pi$
$557$	−21.3732	+	37.0195i	−0.905613	+	1.56857i	−0.820092	+	0.572232i	$0.806078\pi$
$558$	7.54754	−	7.90529i	0.319513	−	0.334657i
$559$	−29.5306			−1.24901
$560$	−2.63512	+	0.236999i	−0.111354	+	0.0100150i
$561$	−7.89547	−	18.4543i	−0.333347	−	0.779141i
$562$	−5.76128	+	9.97883i	−0.243025	+	0.420932i
$563$	−13.1487			−0.554154			−0.277077	−	0.960848i	$-0.589366\pi$
$563$	−13.1487			−0.554154			−0.277077	+	0.960848i	$0.589366\pi$
$564$	1.11813	+	2.61343i	0.0470817	+	0.110045i
$565$	−1.66159			−0.0699036
$566$	−4.93996			−0.207642
$567$	−18.8171	+	14.5917i	−0.790244	+	0.612793i
$568$	7.26549			0.304853
$569$	−2.34989			−0.0985126			−0.0492563	−	0.998786i	$-0.515685\pi$
$569$	−2.34989			−0.0985126			−0.0492563	+	0.998786i	$0.515685\pi$
$570$	4.78483	+	11.1837i	0.200414	+	0.468435i
$571$	−14.6129			−0.611532			−0.305766	−	0.952107i	$-0.598913\pi$
$571$	−14.6129			−0.611532			−0.305766	+	0.952107i	$0.598913\pi$
$572$	−4.09579	+	7.09411i	−0.171253	+	0.296620i
$573$	−12.2196	−	28.5613i	−0.510482	−	1.19316i
$574$	−9.57894	+	20.6732i	−0.399817	+	0.862881i
$575$	7.45235			0.310784
$576$	−2.07165	+	2.16985i	−0.0863189	+	0.0904104i
$577$	4.53371	−	7.85261i	0.188741	−	0.326909i	−0.756090	−	0.654468i	$-0.772893\pi$
$577$	4.53371	−	7.85261i	0.188741	−	0.326909i	0.944831	+	0.327559i	$0.106226\pi$
$578$	16.3682	+	28.3505i	0.680825	+	1.17922i
$579$	2.83501	+	6.62634i	0.117819	+	0.275381i
$580$	2.86866	+	4.96867i	0.119115	+	0.206313i
$581$	−17.3150	+	1.55729i	−0.718349	+	0.0646073i
$582$	−10.2850	−	1.23313i	−0.426326	−	0.0511147i
$583$	−21.2435			−0.879816
$584$	0.392899	−	0.680521i	0.0162583	−	0.0281602i
$585$	10.3272	−	10.8167i	0.426978	−	0.447216i
$586$	−1.17274	−	2.03124i	−0.0484454	−	0.0839099i
$587$	−19.8453	+	34.3730i	−0.819103	+	1.41873i	0.0872417	+	0.996187i	$0.472195\pi$
$587$	−19.8453	+	34.3730i	−0.819103	+	1.41873i	−0.906344	+	0.422540i	$0.861139\pi$
$588$	−12.1025	+	0.727853i	−0.499098	+	0.0300162i
$589$	−12.7934	−	22.1587i	−0.527141	−	0.913035i
$590$	−0.391083	+	0.677376i	−0.0161006	+	0.0278871i
$591$	−5.31646	−	12.4263i	−0.218690	−	0.511150i
$592$	−2.87466	−	4.97906i	−0.118148	−	0.204638i
$593$	17.8017	+	30.8334i	0.731028	+	1.26618i	0.956444	+	0.291915i	$0.0942925\pi$
$593$	17.8017	+	30.8334i	0.731028	+	1.26618i	−0.225416	+	0.974263i	$0.572374\pi$
$594$	−1.40770	−	8.42169i	−0.0577585	−	0.345546i
$595$	−7.84446	+	16.9298i	−0.321591	+	0.694055i
$596$	6.83105	−	11.8317i	0.279811	−	0.484646i
$597$	−42.1254	−	5.05066i	−1.72408	−	0.206710i
$598$	−37.1500			−1.51918
$599$	2.22423			0.0908795			0.0454398	−	0.998967i	$-0.485531\pi$
$599$	2.22423			0.0908795			0.0454398	+	0.998967i	$0.485531\pi$
$600$	−1.03843	+	1.38624i	−0.0423938	+	0.0565930i
$601$	2.28720	−	3.96154i	0.0932967	−	0.161595i	−0.815600	−	0.578616i	$-0.803593\pi$
$601$	2.28720	−	3.96154i	0.0932967	−	0.161595i	0.908896	+	0.417022i	$0.136926\pi$
$602$	15.6101	−	1.40395i	0.636222	−	0.0572209i
$603$	20.6242	−	21.6018i	0.839884	−	0.879694i
$604$	0.289219	+	0.500943i	0.0117682	+	0.0203831i
$605$	−4.14988	−	7.18780i	−0.168717	−	0.292226i
$606$	4.85985	−	6.48758i	0.197418	−	0.263540i
$607$	−15.1379	+	26.2195i	−0.614427	+	1.06422i	0.376058	+	0.926596i	$0.377279\pi$
$607$	−15.1379	+	26.2195i	−0.614427	+	1.06422i	−0.990485	+	0.137622i	$0.956054\pi$
$608$	3.51153	+	6.08215i	0.142411	+	0.246664i
$609$	12.4656	+	23.1487i	0.505130	+	0.938034i
$610$	−2.38034	+	4.12287i	−0.0963773	+	0.166930i
$611$	−4.09061	−	7.08514i	−0.165488	−	0.286634i
$612$	5.94741	+	20.3041i	0.240410	+	0.820743i
$613$	−2.43790	+	4.22257i	−0.0984660	+	0.170548i	−0.911050	−	0.412296i	$-0.864727\pi$
$613$	−2.43790	+	4.22257i	−0.0984660	+	0.170548i	0.812584	+	0.582844i	$0.198060\pi$
$614$	−4.00934			−0.161804
$615$	5.86721	+	13.7136i	0.236589	+	0.552986i
$616$	1.82779	−	3.94472i	0.0736439	−	0.158937i
$617$	12.4725	+	21.6030i	0.502125	+	0.869705i	0.999997	+	0.00245498i	$0.000781445\pi$
$617$	12.4725	+	21.6030i	0.502125	+	0.869705i	−0.497872	+	0.867250i	$0.665885\pi$
$618$	9.62184	+	1.15362i	0.387047	+	0.0464053i
$619$	−18.5471	−	32.1246i	−0.745472	−	1.29120i	−0.949974	−	0.312329i	$-0.898891\pi$
$619$	−18.5471	−	32.1246i	−0.745472	−	1.29120i	0.204502	−	0.978866i	$-0.434442\pi$
$620$	1.82162	−	3.15514i	0.0731580	−	0.126713i
$621$	29.8846	−	24.6256i	1.19923	−	0.988193i
$622$	17.9450			0.719531
$623$	10.3189	−	22.2701i	0.413417	−	0.892231i
$624$	5.17659	−	6.91042i	0.207230	−	0.276638i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.34031			0.253410
$627$	−19.8467	−	2.37954i	−0.792602	−	0.0950297i
$628$	−3.29826			−0.131615
$629$	−40.5465			−1.61670
$630$	−4.94480	+	6.20878i	−0.197005	+	0.247364i
$631$	−21.4560			−0.854152			−0.427076	−	0.904216i	$-0.640456\pi$
$631$	−21.4560			−0.854152			−0.427076	+	0.904216i	$0.640456\pi$
$632$	−5.86267			−0.233205
$633$	−11.0438	+	14.7427i	−0.438951	+	0.585971i
$634$	−10.9145			−0.433469
$635$	−8.23399	+	14.2617i	−0.326756	+	0.565958i
$636$	22.2324	+	2.66557i	0.881572	+	0.105697i
$637$	34.3351	−	6.22646i	1.36040	−	0.246702i
$638$	−9.42780			−0.373250
$639$	15.0516	−	15.7650i	0.595431	−	0.623655i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	21.3821	+	37.0349i	0.844542	+	1.46279i	0.886019	+	0.463649i	$0.153460\pi$
$641$	21.3821	+	37.0349i	0.844542	+	1.46279i	−0.0414772	+	0.999139i	$0.513206\pi$
$642$	7.97214	−	10.6423i	0.314635	−	0.420018i
$643$	−9.01808	−	15.6198i	−0.355638	−	0.615983i	0.631589	−	0.775304i	$-0.282403\pi$
$643$	−9.01808	−	15.6198i	−0.355638	−	0.615983i	−0.987227	+	0.159320i	$0.949070\pi$
$644$	19.6378	−	1.76620i	0.773838	−	0.0695979i
$645$	6.15156	−	8.21193i	0.242217	−	0.323344i
$646$	49.5294			1.94871
$647$	13.8584	−	24.0035i	0.544831	−	0.943676i	−0.453786	−	0.891111i	$-0.649927\pi$
$647$	13.8584	−	24.0035i	0.544831	−	0.943676i	0.998618	−	0.0525650i	$-0.0167397\pi$
$648$	0.416496	+	8.99036i	0.0163615	+	0.353175i
$649$	−0.642644	−	1.11309i	−0.0252260	−	0.0436927i
$650$	2.49250	−	4.31714i	0.0977641	−	0.169332i
$651$	8.77238	−	14.2050i	0.343817	−	0.556739i
$652$	11.5863	+	20.0681i	0.453755	+	0.785927i
$653$	5.80425	−	10.0533i	0.227138	−	0.393414i	−0.729821	−	0.683638i	$-0.760397\pi$
$653$	5.80425	−	10.0533i	0.227138	−	0.393414i	0.956959	+	0.290224i	$0.0937299\pi$
$654$	−33.3027	−	3.99285i	−1.30224	−	0.156133i
$655$	6.83808	+	11.8439i	0.267186	+	0.462779i
$656$	4.30588	+	7.45800i	0.168116	+	0.291186i
$657$	−0.662677	−	2.26234i	−0.0258535	−	0.0882621i
$658$	2.49917	+	3.55078i	0.0974278	+	0.138424i
$659$	−2.05194	+	3.55407i	−0.0799324	+	0.138447i	−0.903221	−	0.429177i	$-0.858804\pi$
$659$	−2.05194	+	3.55407i	−0.0799324	+	0.138447i	0.823288	+	0.567624i	$0.192137\pi$
$660$	−1.11954	−	2.61674i	−0.0435782	−	0.101857i
$661$	16.1112			0.626654			0.313327	−	0.949645i	$-0.398556\pi$
$661$	16.1112			0.626654			0.313327	+	0.949645i	$0.398556\pi$
$662$	−26.2924			−1.02188
$663$	−23.9520	−	55.9838i	−0.930220	−	2.17423i
$664$	−3.28544	+	5.69055i	−0.127500	+	0.220836i
$665$	10.6948	+	15.1949i	0.414725	+	0.589234i
$666$	−16.7591	−	4.07731i	−0.649403	−	0.157993i
$667$	−21.3783	−	37.0282i	−0.827770	−	1.43374i
$668$	−6.21246	−	10.7603i	−0.240367	−	0.416328i
$669$	44.0990	+	5.28729i	1.70497	+	0.204418i
$670$	4.97772	−	8.62167i	0.192306	−	0.333084i
$671$	−3.91148	−	6.77488i	−0.151001	−	0.261541i
$672$	−2.40785	+	3.89901i	−0.0928849	+	0.150407i
$673$	18.0611	−	31.2827i	0.696203	−	1.20586i	−0.273571	−	0.961852i	$-0.588205\pi$
$673$	18.0611	−	31.2827i	0.696203	−	1.20586i	0.969774	−	0.244007i	$-0.0784619\pi$
$674$	8.15482	+	14.1246i	0.314112	+	0.544058i
$675$	0.856658	+	5.12505i	0.0329728	+	0.197263i
$676$	−5.92516	+	10.2627i	−0.227891	+	0.394718i
$677$	0.0536824			0.00206318			0.00103159	−	0.999999i	$-0.499672\pi$
$677$	0.0536824			0.00206318			0.00103159	+	0.999999i	$0.499672\pi$
$678$	−1.72545	+	2.30336i	−0.0662654	+	0.0884600i
$679$	−15.7595	+	1.41739i	−0.604793	+	0.0543943i
$680$	3.52620	+	6.10755i	0.135224	+	0.234214i
$681$	−19.7246	+	26.3311i	−0.755848	+	1.00901i
$682$	2.99336	+	5.18465i	0.114622	+	0.198531i
$683$	−7.74990	+	13.4232i	−0.296542	+	0.513625i	−0.975342	−	0.220697i	$-0.929167\pi$
$683$	−7.74990	+	13.4232i	−0.296542	+	0.513625i	0.678801	+	0.734323i	$0.262500\pi$
$684$	20.4720	+	4.98062i	0.782768	+	0.190439i
$685$	−0.843533			−0.0322298
$686$	−17.8538	+	4.92373i	−0.681660	+	0.187989i
$687$	−7.71979	−	0.925571i	−0.294529	−	0.0353127i
$688$	2.96195	−	5.13024i	0.112923	−	0.195589i
$689$	−64.4453			−2.45517
$690$	7.73876	−	10.3307i	0.294609	−	0.393284i
$691$	32.7602			1.24626			0.623129	−	0.782119i	$-0.285861\pi$
$691$	32.7602			1.24626			0.623129	+	0.782119i	$0.285861\pi$
$692$	−12.6529			−0.480992
$693$	−4.77290	−	12.1381i	−0.181308	−	0.461090i
$694$	−7.70803			−0.292593
$695$	5.84379			0.221668
$696$	9.86667	+	1.18297i	0.373995	+	0.0448405i
$697$	60.7335			2.30044
$698$	−16.9427	+	29.3456i	−0.641291	+	1.11075i
$699$	−5.95782	+	7.95330i	−0.225346	+	0.300822i
$700$	−1.11231	+	2.40058i	−0.0420414	+	0.0907332i
$701$	−20.2343			−0.764237			−0.382119	−	0.924113i	$-0.624805\pi$
$701$	−20.2343			−0.764237			−0.382119	+	0.924113i	$0.624805\pi$
$702$	−4.27045	−	25.5484i	−0.161178	−	0.964263i
$703$	−20.1889	+	34.9683i	−0.761440	+	1.31885i
$704$	−0.821620	−	1.42309i	−0.0309660	−	0.0536347i
$705$	2.82236	+	0.338390i	0.106296	+	0.0127445i
$706$	5.99417	+	10.3822i	0.225594	+	0.390740i
$707$	5.20560	−	11.2347i	0.195777	−	0.422523i
$708$	0.532892	+	1.24554i	0.0200273	+	0.0468104i
$709$	−25.5671			−0.960194			−0.480097	−	0.877215i	$-0.659399\pi$
$709$	−25.5671			−0.960194			−0.480097	+	0.877215i	$0.659399\pi$
$710$	3.63274	−	6.29210i	0.136334	−	0.236138i
$711$	−12.1454	+	12.7211i	−0.455489	+	0.477079i
$712$	−4.63848	−	8.03409i	−0.173835	−	0.301090i
$713$	−13.5754	+	23.5132i	−0.508401	+	0.880576i
$714$	15.3228	+	28.4548i	0.573443	+	1.06489i
$715$	4.09579	+	7.09411i	0.153174	+	0.265305i
$716$	4.33144	−	7.50227i	0.161873	−	0.280373i
$717$	28.5816	−	38.1545i	1.06740	−	1.42491i
$718$	6.92259	+	11.9903i	0.258349	+	0.447473i
$719$	10.0236	+	17.3614i	0.373818	+	0.647472i	0.990149	−	0.140015i	$-0.0447151\pi$
$719$	10.0236	+	17.3614i	0.373818	+	0.647472i	−0.616331	+	0.787487i	$0.711382\pi$
$720$	0.843318	+	2.87903i	0.0314286	+	0.107295i
$721$	14.7434	−	1.32600i	0.549071	−	0.0493827i
$722$	15.1617	−	26.2608i	0.564260	−	0.977328i
$723$	−20.9729	+	27.9975i	−0.779991	+	1.04124i
$724$	−10.4358			−0.387844
$725$	5.73732			0.213079
$726$	−14.2734	−	1.71132i	−0.529735	−	0.0635130i
$727$	5.67928	−	9.83680i	0.210633	−	0.364827i	−0.741280	−	0.671196i	$-0.765781\pi$
$727$	5.67928	−	9.83680i	0.210633	−	0.364827i	0.951913	+	0.306369i	$0.0991142\pi$
$728$	5.54488	−	11.9669i	0.205507	−	0.443523i
$729$	20.3706	+	17.7212i	0.754465	+	0.656340i
$730$	−0.392899	−	0.680521i	−0.0145418	−	0.0251872i
$731$	−20.8888	−	36.1805i	−0.772601	−	1.33818i
$732$	3.24347	+	7.58105i	0.119882	+	0.280204i
$733$	16.6683	−	28.8703i	0.615657	−	1.06635i	−0.374612	−	0.927182i	$-0.622224\pi$
$733$	16.6683	−	28.8703i	0.615657	−	1.06635i	0.990269	−	0.139168i	$-0.0444427\pi$
$734$	−8.64239	−	14.9691i	−0.318997	−	0.552518i
$735$	−5.42091	+	10.8450i	−0.199953	+	0.400023i
$736$	3.72617	−	6.45392i	0.137349	−	0.237895i
$737$	8.17960	+	14.1675i	0.301299	+	0.521866i
$738$	25.1030	+	6.10729i	0.924055	+	0.224812i
$739$	20.5958	−	35.6730i	0.757630	−	1.31225i	−0.186427	−	0.982469i	$-0.559691\pi$
$739$	20.5958	−	35.6730i	0.757630	−	1.31225i	0.944056	−	0.329784i	$-0.106976\pi$
$740$	−5.74933			−0.211349
$741$	−60.2080	−	7.21868i	−2.21179	−	0.265185i
$742$	34.0663	−	3.06388i	1.25061	−	0.112478i
$743$	−12.2773	−	21.2649i	−0.450410	−	0.780133i	0.548001	−	0.836478i	$-0.315389\pi$
$743$	−12.2773	−	21.2649i	−0.450410	−	0.780133i	−0.998411	+	0.0563442i	$0.982056\pi$
$744$	−2.48215	−	5.80160i	−0.0910000	−	0.212697i
$745$	−6.83105	−	11.8317i	−0.250270	−	0.433481i
$746$	−7.77130	+	13.4603i	−0.284528	+	0.492816i
$747$	5.54134	+	18.9178i	0.202747	+	0.692165i
$748$	−11.5888			−0.423728
$749$	8.53931	−	18.4294i	0.312020	−	0.673397i
$750$	0.681302	+	1.59243i	0.0248776	+	0.0581473i
$751$	6.16195	−	10.6728i	0.224853	−	0.389457i	−0.731422	−	0.681925i	$-0.761143\pi$
$751$	6.16195	−	10.6728i	0.224853	−	0.389457i	0.956275	+	0.292468i	$0.0944765\pi$
$752$	1.64116			0.0598471
$753$	16.6197	+	38.8458i	0.605657	+	1.41562i
$754$	−28.6006			−1.04157
$755$	0.578439			0.0210515
$756$	3.47202	+	13.3021i	0.126276	+	0.483792i
$757$	−16.4874			−0.599245			−0.299622	−	0.954058i	$-0.596861\pi$
$757$	−16.4874			−0.599245			−0.299622	+	0.954058i	$0.596861\pi$
$758$	−21.7020			−0.788252
$759$	8.34323	+	19.5009i	0.302840	+	0.707837i
$760$	7.02306			0.254753
$761$	−20.0239	+	34.6823i	−0.725864	+	1.25723i	0.232753	+	0.972536i	$0.425227\pi$
$761$	−20.0239	+	34.6823i	−0.725864	+	1.25723i	−0.958617	+	0.284698i	$0.908107\pi$
$762$	11.2197	+	26.2241i	0.406446	+	0.949998i
$763$	−51.0290	+	4.58948i	−1.84737	+	0.166150i
$764$	−17.9357			−0.648890
$765$	20.5575	+	5.00142i	0.743259	+	0.180827i
$766$	−12.7077	+	22.0104i	−0.459149	+	0.795269i
$767$	−1.94955	−	3.37673i	−0.0703943	−	0.121927i
$768$	0.681302	+	1.59243i	0.0245844	+	0.0574618i
$769$	−3.91652	−	6.78361i	−0.141233	−	0.244623i	0.786728	−	0.617300i	$-0.211773\pi$
$769$	−3.91652	−	6.78361i	−0.141233	−	0.244623i	−0.927961	+	0.372677i	$0.878440\pi$
$770$	−2.50233	−	3.55528i	−0.0901779	−	0.128123i
$771$	13.2675	+	1.59072i	0.477817	+	0.0572883i
$772$	4.16116			0.149763
$773$	16.2391	−	28.1269i	0.584079	−	1.01165i	−0.410911	−	0.911676i	$-0.634789\pi$
$773$	16.2391	−	28.1269i	0.584079	−	1.01165i	0.994990	−	0.0999786i	$-0.0318774\pi$
$774$	−4.99572	−	17.0551i	−0.179568	−	0.613031i
$775$	−1.82162	−	3.15514i	−0.0654345	−	0.113336i
$776$	−2.99028	+	5.17932i	−0.107345	+	0.185927i
$777$	−26.3352	−	0.780510i	−0.944769	−	0.0280006i
$778$	−5.19770	−	9.00269i	−0.186347	−	0.322762i
$779$	30.2404	−	52.3780i	1.08348	−	1.87664i
$780$	−3.39630	−	7.93827i	−0.121607	−	0.284236i
$781$	5.96947	+	10.3394i	0.213605	+	0.369974i
$782$	−26.2785	−	45.5156i	−0.939716	−	1.62764i
$783$	23.0072	−	18.9585i	0.822210	−	0.677521i
$784$	−2.36213	+	6.58941i	−0.0843619	+	0.235336i
$785$	−1.64913	+	2.85638i	−0.0588600	+	0.101949i
$786$	23.5193	+	2.81987i	0.838907	+	0.100581i
$787$	17.5739			0.626443			0.313221	−	0.949680i	$-0.398592\pi$
$787$	17.5739			0.626443			0.313221	+	0.949680i	$0.398592\pi$
$788$	−7.80338			−0.277984
$789$	−13.4717	+	17.9839i	−0.479607	+	0.640243i
$790$	−2.93134	+	5.07722i	−0.104292	+	0.180640i
$791$	−1.84820	+	3.98877i	−0.0657145	+	0.141824i
$792$	−4.79000	−	1.16535i	−0.170205	−	0.0414091i
$793$	−11.8660	−	20.5526i	−0.421375	−	0.729843i
$794$	−1.36768	−	2.36890i	−0.0485373	−	0.0840690i
$795$	13.4247	−	17.9210i	0.476123	−	0.635594i
$796$	−12.2477	+	21.2136i	−0.434107	+	0.751895i
$797$	27.9349	+	48.3847i	0.989506	+	1.71388i	0.619884	+	0.784694i	$0.287180\pi$
$797$	27.9349	+	48.3847i	0.989506	+	1.71388i	0.369623	+	0.929182i	$0.379487\pi$
$798$	32.1696	+	0.953429i	1.13879	+	0.0337510i
$799$	5.78707	−	10.0235i	0.204732	−	0.354606i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−27.0421	−	6.57904i	−0.955486	−	0.232459i
$802$	−0.0177095	+	0.0306738i	−0.000625345	+	0.00108313i
$803$	1.29126			0.0455674
$804$	−6.78267	−	15.8533i	−0.239206	−	0.559104i
$805$	8.28933	−	17.8899i	0.292160	−	0.630537i
$806$	9.08079	+	15.7284i	0.319857	+	0.554009i
$807$	36.1814	+	4.33800i	1.27365	+	0.152705i
$808$	−2.33999	−	4.05298i	−0.0823206	−	0.142584i
$809$	17.3337	−	30.0228i	0.609420	−	1.05555i	−0.381917	−	0.924197i	$-0.624736\pi$
$809$	17.3337	−	30.0228i	0.609420	−	1.05555i	0.991336	−	0.131349i	$-0.0419309\pi$
$810$	7.99413	+	4.13448i	0.280885	+	0.145271i
$811$	32.8549			1.15369			0.576845	−	0.816854i	$-0.304284\pi$
$811$	32.8549			1.15369			0.576845	+	0.816854i	$0.304284\pi$
$812$	15.1185	−	1.35974i	0.530556	−	0.0477175i
$813$	14.6307	−	19.5310i	0.513120	−	0.684982i
$814$	4.72376	−	8.18180i	0.165568	−	0.286772i
$815$	23.1726			0.811702
$816$	12.1282	+	1.45413i	0.424574	+	0.0509046i
$817$	−41.6039			−1.45553
$818$	−16.3458			−0.571519
$819$	−14.4793	−	36.8228i	−0.505947	−	1.28669i
$820$	8.61175			0.300735
$821$	−13.6370			−0.475936			−0.237968	−	0.971273i	$-0.576481\pi$
$821$	−13.6370			−0.475936			−0.237968	+	0.971273i	$0.576481\pi$
$822$	−0.875952	+	1.16934i	−0.0305523	+	0.0407854i
$823$	−2.08549			−0.0726957			−0.0363478	−	0.999339i	$-0.511572\pi$
$823$	−2.08549			−0.0726957			−0.0363478	+	0.999339i	$0.511572\pi$
$824$	2.79748	−	4.84537i	0.0974548	−	0.168797i
$825$	−2.82594	−	0.338818i	−0.0983865	−	0.0117961i
$826$	1.19109	+	1.69228i	0.0414432	+	0.0588819i
$827$	−4.20031			−0.146059			−0.0730295	−	0.997330i	$-0.523267\pi$
$827$	−4.20031			−0.146059			−0.0730295	+	0.997330i	$0.523267\pi$
$828$	−6.28470	−	21.4555i	−0.218408	−	0.745632i
$829$	13.2645	−	22.9747i	0.460694	−	0.797945i	−0.538302	−	0.842752i	$-0.680934\pi$
$829$	13.2645	−	22.9747i	0.460694	−	0.797945i	0.998996	+	0.0448071i	$0.0142673\pi$
$830$	3.28544	+	5.69055i	0.114039	+	0.197522i
$831$	7.04372	−	9.40290i	0.244344	−	0.326183i
$832$	−2.49250	−	4.31714i	−0.0864121	−	0.149670i
$833$	31.9158	+	37.6624i	1.10582	+	1.30493i
$834$	6.06838	−	8.10089i	0.210131	−	0.280511i
$835$	−12.4249			−0.429982
$836$	−5.77029	+	9.99444i	−0.199570	+	0.345665i
$837$	−17.7308	−	6.63302i	−0.612864	−	0.229271i
$838$	4.00800	+	6.94206i	0.138454	+	0.239810i
$839$	2.18181	−	3.77901i	0.0753244	−	0.130466i	−0.825903	−	0.563812i	$-0.809334\pi$
$839$	2.18181	−	3.77901i	0.0753244	−	0.130466i	0.901227	+	0.433347i	$0.142667\pi$
$840$	2.17271	+	4.03476i	0.0749657	+	0.139213i
$841$	−1.95844	−	3.39211i	−0.0675323	−	0.116969i
$842$	−16.7469	+	29.0066i	−0.577138	+	0.999632i
$843$	19.8157	+	2.37582i	0.682490	+	0.0818278i
$844$	5.31753	+	9.21023i	0.183037	+	0.317029i
$845$	5.92516	+	10.2627i	0.203832	+	0.353047i
$846$	3.39992	−	3.56108i	0.116892	−	0.122432i
$847$	−21.8708	+	1.96703i	−0.751490	+	0.0675880i
$848$	6.46391	−	11.1958i	0.221971	−	0.384466i
$849$	3.36561	+	7.86653i	0.115507	+	0.269979i
$850$	7.05240			0.241895
$851$	42.8460			1.46874
$852$	−4.94999	−	11.5698i	−0.169584	−	0.396374i
$853$	−13.9693	+	24.1956i	−0.478300	+	0.828440i	−0.999690	−	0.0248783i	$-0.992080\pi$
$853$	−13.9693	+	24.1956i	−0.478300	+	0.828440i	0.521390	+	0.853318i	$0.325414\pi$
$854$	7.24959	+	10.3001i	0.248076	+	0.352463i
$855$	14.5494	−	15.2390i	0.497578	−	0.521163i
$856$	−3.83855	−	6.64856i	−0.131199	−	0.227243i
$857$	2.26944	+	3.93078i	0.0775225	+	0.134273i	0.902180	−	0.431359i	$-0.141966\pi$
$857$	2.26944	+	3.93078i	0.0775225	+	0.134273i	−0.824658	+	0.565632i	$0.808632\pi$
$858$	14.0873	+	1.68901i	0.480933	+	0.0576619i
$859$	7.34136	−	12.7156i	0.250484	−	0.433851i	−0.713175	−	0.700986i	$-0.752744\pi$
$859$	7.34136	−	12.7156i	0.250484	−	0.433851i	0.963659	+	0.267135i	$0.0860769\pi$
$860$	−2.96195	−	5.13024i	−0.101001	−	0.174940i
$861$	39.4467	+	1.16910i	1.34434	+	0.0398430i
$862$	12.2779	−	21.2660i	0.418187	−	0.724321i
$863$	14.6627	+	25.3966i	0.499125	+	0.864510i	0.999999	−	0.00100981i	$-0.000321432\pi$
$863$	14.6627	+	25.3966i	0.499125	+	0.864510i	−0.500874	+	0.865520i	$0.666988\pi$
$864$	4.86675	+	1.82064i	0.165570	+	0.0619393i
$865$	−6.32646	+	10.9577i	−0.215106	+	0.372574i
$866$	−25.8917			−0.879836
$867$	33.9944	−	45.3803i	1.15451	−	1.54120i
$868$	−5.54794	−	7.88243i	−0.188309	−	0.267547i
$869$	−4.81689	−	8.34310i	−0.163402	−	0.283020i
$870$	5.95782	−	7.95330i	0.201989	−	0.269642i
$871$	24.8140	+	42.9791i	0.840790	+	1.45629i
$872$	−9.68250	+	16.7706i	−0.327891	+	0.567924i
$873$	5.04352	+	17.2182i	0.170697	+	0.582749i
$874$	−52.3383			−1.77037
$875$	1.52280	+	2.16358i	0.0514802	+	0.0731423i
$876$	−1.35136	−	0.162023i	−0.0456584	−	0.00547425i
$877$	−17.7842	+	30.8031i	−0.600529	+	1.04015i	0.392212	+	0.919875i	$0.371710\pi$
$877$	−17.7842	+	30.8031i	−0.600529	+	1.04015i	−0.992741	+	0.120272i	$0.961623\pi$
$878$	12.0363			0.406204
$879$	−2.43562	+	3.25139i	−0.0821514	+	0.109667i
$880$	−1.64324			−0.0553936
$881$	5.92938			0.199766			0.0998829	−	0.994999i	$-0.468153\pi$
$881$	5.92938			0.199766			0.0998829	+	0.994999i	$0.468153\pi$
$882$	9.40451	+	18.7765i	0.316666	+	0.632236i
$883$	11.3953			0.383483			0.191742	−	0.981445i	$-0.438586\pi$
$883$	11.3953			0.383483			0.191742	+	0.981445i	$0.438586\pi$
$884$	−35.1563			−1.18243
$885$	1.34512	+	0.161274i	0.0452157	+	0.00542117i
$886$	−2.01540			−0.0677087
$887$	−3.92461	+	6.79762i	−0.131775	+	0.228242i	−0.924361	−	0.381519i	$-0.875401\pi$
$887$	−3.92461	+	6.79762i	−0.131775	+	0.228242i	0.792586	+	0.609761i	$0.208734\pi$
$888$	−5.97028	+	7.96994i	−0.200350	+	0.267454i
$889$	25.0775	+	35.6298i	0.841073	+	1.19498i
$890$	−9.27697			−0.310965
$891$	−12.4519	+	7.97937i	−0.417153	+	0.267319i
$892$	12.8215	−	22.2074i	0.429295	−	0.743560i
$893$	−5.76300	−	9.98180i	−0.192851	−	0.334028i
$894$	−23.4952	−	2.81697i	−0.785797	−	0.0942137i
$895$	−4.33144	−	7.50227i	−0.144784	−	0.250773i
$896$	1.52280	+	2.16358i	0.0508733	+	0.0722800i
$897$	25.3104	+	59.1588i	0.845090	+	1.97525i
$898$	0.742369			0.0247732
$899$	−10.4512	+	18.1021i	−0.348568	+	0.603737i
$900$	2.91497	+	0.709180i	0.0971657	+	0.0236393i
$901$	−45.5860	−	78.9573i	−1.51869	−	2.63045i
$902$	−7.07559	+	12.2553i	−0.235591	+	0.408056i
$903$	−12.8709	−	23.9015i	−0.428317	−	0.795392i
$904$	0.830795	+	1.43898i	0.0276318	+	0.0478597i
$905$	−5.21791	+	9.03768i	−0.173449	+	0.300423i
$906$	0.600669	−	0.801854i	0.0199559	−	0.0266398i
$907$	−9.89508	−	17.1388i	−0.328561	−	0.569084i	0.653666	−	0.756783i	$-0.273230\pi$
$907$	−9.89508	−	17.1388i	−0.328561	−	0.569084i	−0.982226	+	0.187700i	$0.939897\pi$
$908$	9.49730	+	16.4498i	0.315179	+	0.545906i
$909$	−13.6420	−	3.31895i	−0.452477	−	0.110083i
$910$	−7.59119	−	10.7855i	−0.251646	−	0.357534i
$911$	−0.911882	+	1.57943i	−0.0302120	+	0.0523287i	−0.880736	−	0.473607i	$-0.842952\pi$
$911$	−0.911882	+	1.57943i	−0.0302120	+	0.0523287i	0.850524	+	0.525936i	$0.176285\pi$
$912$	7.29297	−	9.73564i	0.241494	−	0.322379i
$913$	−10.7975			−0.357347
$914$	11.2275			0.371372
$915$	8.18711	+	0.981601i	0.270658	+	0.0324507i
$916$	−2.24447	+	3.88754i	−0.0741595	+	0.128448i
$917$	36.0382	−	3.24123i	1.19009	−	0.107035i
$918$	28.2808	−	23.3040i	0.933405	−	0.769148i
$919$	16.5671	+	28.6951i	0.546499	+	0.946564i	0.998511	+	0.0545518i	$0.0173730\pi$
$919$	16.5671	+	28.6951i	0.546499	+	0.946564i	−0.452012	+	0.892012i	$0.649294\pi$
$920$	−3.72617	−	6.45392i	−0.122848	−	0.212780i
$921$	2.73157	+	6.38458i	0.0900083	+	0.210379i
$922$	−9.12633	+	15.8073i	−0.300560	+	0.520585i
$923$	18.1093	+	31.3662i	0.596074	+	1.03243i
$924$	−7.52697	−	0.223081i	−0.247619	−	0.00733883i
$925$	−2.87466	+	4.97906i	−0.0945183	+	0.163711i
$926$	−14.5347	−	25.1748i	−0.477639	−	0.827295i
$927$	−4.71833	−	16.1080i	−0.154970	−	0.529058i
$928$	2.86866	−	4.96867i	0.0941684	−	0.163104i
$929$	−1.47951			−0.0485413			−0.0242706	−	0.999705i	$-0.507726\pi$
$929$	−1.47951			−0.0485413			−0.0242706	+	0.999705i	$0.507726\pi$
$930$	−6.26541	−	0.751196i	−0.205451	−	0.0246327i
$931$	48.3725	−	8.77207i	1.58534	−	0.287493i
$932$	2.86866	+	4.96867i	0.0939662	+	0.162754i
$933$	−12.2260	−	28.5762i	−0.400261	−	0.935543i
$934$	3.65873	+	6.33711i	0.119717	+	0.207356i
$935$	−5.79439	+	10.0362i	−0.189497	+	0.328218i
$936$	−14.5312	−	3.53527i	−0.474966	−	0.115554i
$937$	−31.9616			−1.04414			−0.522070	−	0.852902i	$-0.674840\pi$
$937$	−31.9616			−1.04414			−0.522070	+	0.852902i	$0.674840\pi$
$938$	−15.1602	−	21.5394i	−0.494998	−	0.703286i
$939$	−4.31967	−	10.0965i	−0.140967	−	0.329486i
$940$	0.820581	−	1.42129i	0.0267644	−	0.0463573i
$941$	−18.7812			−0.612250			−0.306125	−	0.951991i	$-0.599033\pi$
$941$	−18.7812			−0.612250			−0.306125	+	0.951991i	$0.599033\pi$
$942$	2.24711	+	5.25224i	0.0732149	+	0.171127i
$943$	−64.1778			−2.08992
$944$	0.782167			0.0254574
$945$	13.2559	+	3.64417i	0.431216	+	0.118545i
$946$	9.73438			0.316492
$947$	−12.8339			−0.417047			−0.208523	−	0.978017i	$-0.566866\pi$
$947$	−12.8339			−0.417047			−0.208523	+	0.978017i	$0.566866\pi$
$948$	3.99425	+	9.33588i	0.129727	+	0.303215i
$949$	3.91721			0.127158
$950$	3.51153	−	6.08215i	0.113929	−	0.197331i
$951$	7.43606	+	17.3805i	0.241131	+	0.563602i
$952$	18.5839	−	1.67141i	0.602307	−	0.0541707i
$953$	−34.9964			−1.13364			−0.566822	−	0.823841i	$-0.691827\pi$
$953$	−34.9964			−1.13364			−0.566822	+	0.823841i	$0.691827\pi$
$954$	−10.9023	−	37.2196i	−0.352974	−	1.20503i
$955$	−8.96784	+	15.5328i	−0.290193	+	0.502628i
$956$	−13.7619	−	23.8363i	−0.445091	−	0.770921i
$957$	6.42318	+	15.0131i	0.207632	+	0.485304i
$958$	3.08835	+	5.34918i	0.0997802	+	0.172824i
$959$	−0.938271	+	2.02497i	−0.0302984	+	0.0653896i
$960$	1.71973	+	0.206189i	0.0555042	+	0.00665472i
$961$	−17.7268			−0.571832
$962$	14.3302	−	24.8207i	0.462025	−	0.800251i
$963$	−22.3785	−	5.44444i	−0.721138	−	0.175445i
$964$	10.0984	+	17.4909i	0.325246	+	0.563343i
$965$	2.08058	−	3.60367i	0.0669762	−	0.116006i
$966$	−16.1918	−	30.0685i	−0.520963	−	0.967437i
$967$	−13.2132	−	22.8860i	−0.424908	−	0.735963i	0.571503	−	0.820600i	$-0.306360\pi$
$967$	−13.2132	−	22.8860i	−0.424908	−	0.735963i	−0.996412	+	0.0846367i	$0.973027\pi$
$968$	−4.14988	+	7.18780i	−0.133382	+	0.231025i
$969$	−33.7445	−	78.8721i	−1.08403	−	2.53374i
$970$	2.99028	+	5.17932i	0.0960122	+	0.166298i
$971$	−16.2985	−	28.2298i	−0.523043	−	0.905938i	−0.999640	−	0.0268157i	$-0.991463\pi$
$971$	−16.2985	−	28.2298i	−0.523043	−	0.905938i	0.476597	−	0.879122i	$-0.341870\pi$
$972$	14.0327	−	6.78839i	0.450100	−	0.217738i
$973$	6.50011	−	14.0285i	0.208384	−	0.449732i
$974$	−3.11014	+	5.38693i	−0.0996554	+	0.172608i
$975$	−8.57289	−	1.02785i	−0.274552	−	0.0329177i
$976$	4.76069			0.152386
$977$	40.9644			1.31057			0.655284	−	0.755383i	$-0.272549\pi$
$977$	40.9644			1.31057			0.655284	+	0.755383i	$0.272549\pi$
$978$	24.0632	−	32.1228i	0.769456	−	1.02717i
$979$	7.62215	−	13.2019i	0.243605	−	0.421936i
$980$	4.52553	+	5.34037i	0.144563	+	0.170592i
$981$	16.3309	+	55.7524i	0.521404	+	1.78004i
$982$	3.94447	+	6.83202i	0.125873	+	0.218019i
$983$	−7.67599	−	13.2952i	−0.244826	−	0.424051i	0.717257	−	0.696809i	$-0.245398\pi$
$983$	−7.67599	−	13.2952i	−0.244826	−	0.424051i	−0.962083	+	0.272758i	$0.912064\pi$
$984$	8.94272	−	11.9379i	0.285083	−	0.380568i
$985$	−3.90169	+	6.75792i	−0.124318	+	0.215325i
$986$	−20.2309	−	35.0410i	−0.644284	−	1.11593i
$987$	3.95168	−	6.39891i	0.125783	−	0.203679i
$988$	−17.5050	+	30.3196i	−0.556909	+	0.964594i
$989$	22.0734	+	38.2323i	0.701895	+	1.21572i
$990$	−3.40423	+	3.56559i	−0.108193	+	0.113322i
$991$	−4.62129	+	8.00431i	−0.146800	+	0.254265i	−0.930043	−	0.367450i	$-0.880231\pi$
$991$	−4.62129	+	8.00431i	−0.146800	+	0.254265i	0.783243	+	0.621716i	$0.213564\pi$
$992$	−3.64324			−0.115673
$993$	17.9131	+	41.8687i	0.568454	+	1.32866i
$994$	−11.0639	−	15.7194i	−0.350926	−	0.498591i
$995$	12.2477	+	21.2136i	0.388277	+	0.672515i
$996$	11.3002	+	1.35484i	0.358060	+	0.0429299i
$997$	5.36626	+	9.29463i	0.169951	+	0.294364i	0.938402	−	0.345544i	$-0.112306\pi$
$997$	5.36626	+	9.29463i	0.169951	+	0.294364i	−0.768451	+	0.639908i	$0.778972\pi$
$998$	4.34473	−	7.52530i	0.137530	−	0.238209i
$999$	4.92521	+	29.4656i	0.155827	+	0.932250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.i.151.5	yes	16
3.2	odd	2		1890.2.i.i.991.2		16
7.2	even	3		630.2.l.i.331.2	yes	16
9.4	even	3		630.2.l.i.571.2	yes	16
9.5	odd	6		1890.2.l.i.361.8		16
21.2	odd	6		1890.2.l.i.1801.8		16
63.23	odd	6		1890.2.i.i.1171.2		16
63.58	even	3	inner	630.2.i.i.121.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.5	✓	16	63.58	even	3	inner
630.2.i.i.151.5	yes	16	1.1	even	1	trivial
630.2.l.i.331.2	yes	16	7.2	even	3
630.2.l.i.571.2	yes	16	9.4	even	3
1890.2.i.i.991.2		16	3.2	odd	2
1890.2.i.i.1171.2		16	63.23	odd	6
1890.2.l.i.361.8		16	9.5	odd	6
1890.2.l.i.1801.8		16	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.681302 + 1.59243i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.681302 - 1.59243i) q^{6} +(-1.52280 - 2.16358i) q^{7} -1.00000 q^{8} +(-2.07165 + 2.16985i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.681302 + 1.59243i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.681302 - 1.59243i) q^{6} +(-1.52280 - 2.16358i) q^{7} -1.00000 q^{8} +(-2.07165 + 2.16985i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.821620 - 1.42309i) q^{11} +(0.681302 + 1.59243i) q^{12} +(-2.49250 - 4.31714i) q^{13} +(1.52280 + 2.16358i) q^{14} +(1.71973 + 0.206189i) q^{15} +1.00000 q^{16} +(3.52620 - 6.10755i) q^{17} +(2.07165 - 2.16985i) q^{18} +(-3.51153 - 6.08215i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.40785 - 3.89901i) q^{21} +(0.821620 + 1.42309i) q^{22} +(-3.72617 + 6.45392i) q^{23} +(-0.681302 - 1.59243i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.49250 + 4.31714i) q^{26} +(-4.86675 - 1.82064i) q^{27} +(-1.52280 - 2.16358i) q^{28} +(-2.86866 + 4.96867i) q^{29} +(-1.71973 - 0.206189i) q^{30} +3.64324 q^{31} -1.00000 q^{32} +(1.70639 - 2.27792i) q^{33} +(-3.52620 + 6.10755i) q^{34} +(-2.63512 + 0.236999i) q^{35} +(-2.07165 + 2.16985i) q^{36} +(-2.87466 - 4.97906i) q^{37} +(3.51153 + 6.08215i) q^{38} +(5.17659 - 6.91042i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.30588 + 7.45800i) q^{41} +(-2.40785 + 3.89901i) q^{42} +(2.96195 - 5.13024i) q^{43} +(-0.821620 - 1.42309i) q^{44} +(0.843318 + 2.87903i) q^{45} +(3.72617 - 6.45392i) q^{46} +1.64116 q^{47} +(0.681302 + 1.59243i) q^{48} +(-2.36213 + 6.58941i) q^{49} +(0.500000 + 0.866025i) q^{50} +(12.1282 + 1.45413i) q^{51} +(-2.49250 - 4.31714i) q^{52} +(6.46391 - 11.1958i) q^{53} +(4.86675 + 1.82064i) q^{54} -1.64324 q^{55} +(1.52280 + 2.16358i) q^{56} +(7.29297 - 9.73564i) q^{57} +(2.86866 - 4.96867i) q^{58} +0.782167 q^{59} +(1.71973 + 0.206189i) q^{60} +4.76069 q^{61} -3.64324 q^{62} +(7.84936 + 1.17793i) q^{63} +1.00000 q^{64} -4.98501 q^{65} +(-1.70639 + 2.27792i) q^{66} -9.95545 q^{67} +(3.52620 - 6.10755i) q^{68} +(-12.8161 - 1.53659i) q^{69} +(2.63512 - 0.236999i) q^{70} -7.26549 q^{71} +(2.07165 - 2.16985i) q^{72} +(-0.392899 + 0.680521i) q^{73} +(2.87466 + 4.97906i) q^{74} +(1.03843 - 1.38624i) q^{75} +(-3.51153 - 6.08215i) q^{76} +(-1.82779 + 3.94472i) q^{77} +(-5.17659 + 6.91042i) q^{78} +5.86267 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.416496 - 8.99036i) q^{81} +(-4.30588 - 7.45800i) q^{82} +(3.28544 - 5.69055i) q^{83} +(2.40785 - 3.89901i) q^{84} +(-3.52620 - 6.10755i) q^{85} +(-2.96195 + 5.13024i) q^{86} +(-9.86667 - 1.18297i) q^{87} +(0.821620 + 1.42309i) q^{88} +(4.63848 + 8.03409i) q^{89} +(-0.843318 - 2.87903i) q^{90} +(-5.54488 + 11.9669i) q^{91} +(-3.72617 + 6.45392i) q^{92} +(2.48215 + 5.80160i) q^{93} -1.64116 q^{94} -7.02306 q^{95} +(-0.681302 - 1.59243i) q^{96} +(2.99028 - 5.17932i) q^{97} +(2.36213 - 6.58941i) q^{98} +(4.79000 + 1.16535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

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