LMFDB - Embedded newform 630.2.bi.b.509.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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([1, 3, 1]))

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

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

chi := DirichletCharacter("630.479");

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.bi (of order $6$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.15
Character	$\chi$	$=$	630.509
Dual form			630.2.bi.b.479.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.630353 + 1.61327i) q^{3} +1.00000 q^{4} +(0.0611015 + 2.23523i) q^{5} +(0.630353 + 1.61327i) q^{6} +(1.83478 + 1.90619i) q^{7} +1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.630353 + 1.61327i) q^{3} +1.00000 q^{4} +(0.0611015 + 2.23523i) q^{5} +(0.630353 + 1.61327i) q^{6} +(1.83478 + 1.90619i) q^{7} +1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +(0.0611015 + 2.23523i) q^{10} +(-1.13018 - 0.652510i) q^{11} +(0.630353 + 1.61327i) q^{12} +(3.03357 - 5.25429i) q^{13} +(1.83478 + 1.90619i) q^{14} +(-3.56753 + 1.50756i) q^{15} +1.00000 q^{16} +(0.502991 - 0.290402i) q^{17} +(-2.20531 + 2.03386i) q^{18} +(-6.86424 - 3.96307i) q^{19} +(0.0611015 + 2.23523i) q^{20} +(-1.91866 + 4.16158i) q^{21} +(-1.13018 - 0.652510i) q^{22} +(3.28622 + 5.69190i) q^{23} +(0.630353 + 1.61327i) q^{24} +(-4.99253 + 0.273152i) q^{25} +(3.03357 - 5.25429i) q^{26} +(-4.67130 - 2.27572i) q^{27} +(1.83478 + 1.90619i) q^{28} +(-0.125548 + 0.0724850i) q^{29} +(-3.56753 + 1.50756i) q^{30} +1.38267i q^{31} +1.00000 q^{32} +(0.340266 - 2.23460i) q^{33} +(0.502991 - 0.290402i) q^{34} +(-4.14868 + 4.21764i) q^{35} +(-2.20531 + 2.03386i) q^{36} +(2.02863 + 1.17123i) q^{37} +(-6.86424 - 3.96307i) q^{38} +(10.3888 + 1.58192i) q^{39} +(0.0611015 + 2.23523i) q^{40} +(3.16905 - 5.48896i) q^{41} +(-1.91866 + 4.16158i) q^{42} +(10.0713 - 5.81466i) q^{43} +(-1.13018 - 0.652510i) q^{44} +(-4.68091 - 4.80511i) q^{45} +(3.28622 + 5.69190i) q^{46} -5.41619i q^{47} +(0.630353 + 1.61327i) q^{48} +(-0.267153 + 6.99490i) q^{49} +(-4.99253 + 0.273152i) q^{50} +(0.785560 + 0.628407i) q^{51} +(3.03357 - 5.25429i) q^{52} +(4.19068 + 7.25846i) q^{53} +(-4.67130 - 2.27572i) q^{54} +(1.38946 - 2.56609i) q^{55} +(1.83478 + 1.90619i) q^{56} +(2.06663 - 13.5720i) q^{57} +(-0.125548 + 0.0724850i) q^{58} -3.08716 q^{59} +(-3.56753 + 1.50756i) q^{60} +2.12053i q^{61} +1.38267i q^{62} +(-7.92320 - 0.472056i) q^{63} +1.00000 q^{64} +(11.9299 + 6.45968i) q^{65} +(0.340266 - 2.23460i) q^{66} -13.1972i q^{67} +(0.502991 - 0.290402i) q^{68} +(-7.11112 + 8.88948i) q^{69} +(-4.14868 + 4.21764i) q^{70} +10.3545i q^{71} +(-2.20531 + 2.03386i) q^{72} +(3.84599 + 6.66144i) q^{73} +(2.02863 + 1.17123i) q^{74} +(-3.58773 - 7.88215i) q^{75} +(-6.86424 - 3.96307i) q^{76} +(-0.829824 - 3.35156i) q^{77} +(10.3888 + 1.58192i) q^{78} -7.09192 q^{79} +(0.0611015 + 2.23523i) q^{80} +(0.726797 - 8.97061i) q^{81} +(3.16905 - 5.48896i) q^{82} +(-4.32983 + 2.49983i) q^{83} +(-1.91866 + 4.16158i) q^{84} +(0.679850 + 1.10656i) q^{85} +(10.0713 - 5.81466i) q^{86} +(-0.196078 - 0.156852i) q^{87} +(-1.13018 - 0.652510i) q^{88} +(1.35235 - 2.34234i) q^{89} +(-4.68091 - 4.80511i) q^{90} +(15.5816 - 3.85791i) q^{91} +(3.28622 + 5.69190i) q^{92} +(-2.23062 + 0.871568i) q^{93} -5.41619i q^{94} +(8.43897 - 15.5853i) q^{95} +(0.630353 + 1.61327i) q^{96} +(-5.76032 - 9.97717i) q^{97} +(-0.267153 + 6.99490i) q^{98} +(3.81952 - 0.859646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	0.630353	+	1.61327i	0.363934	+	0.931425i
$3$	0.630353	+	1.61327i	0.363934	+	0.931425i
$4$	1.00000			0.500000
$5$	0.0611015	+	2.23523i	0.0273254	+	0.999627i
$5$	0.0611015	+	2.23523i	0.0273254	+	0.999627i
$6$	0.630353	+	1.61327i	0.257340	+	0.658617i
$7$	1.83478	+	1.90619i	0.693482	+	0.720474i
$7$	1.83478	+	1.90619i	0.693482	+	0.720474i
$8$	1.00000			0.353553
$9$	−2.20531	+	2.03386i	−0.735104	+	0.677955i
$10$	0.0611015	+	2.23523i	0.0193220	+	0.706843i
$11$	−1.13018	−	0.652510i	−0.340762	−	0.196739i	0.319847	−	0.947469i	$-0.396369\pi$
$11$	−1.13018	−	0.652510i	−0.340762	−	0.196739i	−0.660609	+	0.750730i	$0.729702\pi$
$12$	0.630353	+	1.61327i	0.181967	+	0.465712i
$13$	3.03357	−	5.25429i	0.841360	−	1.45728i	−0.0473853	−	0.998877i	$-0.515089\pi$
$13$	3.03357	−	5.25429i	0.841360	−	1.45728i	0.888745	−	0.458402i	$-0.151578\pi$
$14$	1.83478	+	1.90619i	0.490366	+	0.509452i
$15$	−3.56753	+	1.50756i	−0.921132	+	0.389250i
$16$	1.00000			0.250000
$17$	0.502991	−	0.290402i	0.121993	−	0.0704328i	−0.437762	−	0.899091i	$-0.644229\pi$
$17$	0.502991	−	0.290402i	0.121993	−	0.0704328i	0.559755	+	0.828658i	$0.310895\pi$
$18$	−2.20531	+	2.03386i	−0.519797	+	0.479386i
$19$	−6.86424	−	3.96307i	−1.57476	−	0.909191i	−0.995572	−	0.0940001i	$-0.970035\pi$
$19$	−6.86424	−	3.96307i	−1.57476	−	0.909191i	−0.579193	−	0.815191i	$-0.696632\pi$
$20$	0.0611015	+	2.23523i	0.0136627	+	0.499813i
$21$	−1.91866	+	4.16158i	−0.418685	+	0.908131i
$22$	−1.13018	−	0.652510i	−0.240955	−	0.139116i
$23$	3.28622	+	5.69190i	0.685224	+	1.18684i	0.973366	+	0.229255i	$0.0736291\pi$
$23$	3.28622	+	5.69190i	0.685224	+	1.18684i	−0.288142	+	0.957588i	$0.593038\pi$
$24$	0.630353	+	1.61327i	0.128670	+	0.329308i
$25$	−4.99253	+	0.273152i	−0.998507	+	0.0546304i
$26$	3.03357	−	5.25429i	0.594931	−	1.03045i
$27$	−4.67130	−	2.27572i	−0.898993	−	0.437963i
$28$	1.83478	+	1.90619i	0.346741	+	0.360237i
$29$	−0.125548	+	0.0724850i	−0.0233136	+	0.0134601i	−0.511612	−	0.859217i	$-0.670951\pi$
$29$	−0.125548	+	0.0724850i	−0.0233136	+	0.0134601i	0.488298	+	0.872677i	$0.337618\pi$
$30$	−3.56753	+	1.50756i	−0.651339	+	0.275241i
$31$			1.38267i			0.248334i	0.992261	+	0.124167i	$0.0396259\pi$
$31$			1.38267i			0.248334i	−0.992261	+	0.124167i	$0.960374\pi$
$32$	1.00000			0.176777
$33$	0.340266	−	2.23460i	0.0592327	−	0.388995i
$34$	0.502991	−	0.290402i	0.0862622	−	0.0498035i
$35$	−4.14868	+	4.21764i	−0.701255	+	0.712911i
$36$	−2.20531	+	2.03386i	−0.367552	+	0.338977i
$37$	2.02863	+	1.17123i	0.333505	+	0.192549i	0.657396	−	0.753545i	$-0.271658\pi$
$37$	2.02863	+	1.17123i	0.333505	+	0.192549i	−0.323891	+	0.946094i	$0.604991\pi$
$38$	−6.86424	−	3.96307i	−1.11353	−	0.642895i
$39$	10.3888	+	1.58192i	1.66354	+	0.253310i
$40$	0.0611015	+	2.23523i	0.00966099	+	0.353421i
$41$	3.16905	−	5.48896i	0.494923	−	0.857232i	−0.505060	−	0.863084i	$-0.668530\pi$
$41$	3.16905	−	5.48896i	0.494923	−	0.857232i	0.999983	+	0.00585232i	$0.00186286\pi$
$42$	−1.91866	+	4.16158i	−0.296055	+	0.642146i
$43$	10.0713	−	5.81466i	1.53586	−	0.886728i	0.536783	−	0.843720i	$-0.319639\pi$
$43$	10.0713	−	5.81466i	1.53586	−	0.886728i	0.999075	−	0.0430080i	$-0.0136941\pi$
$44$	−1.13018	−	0.652510i	−0.170381	−	0.0983696i
$45$	−4.68091	−	4.80511i	−0.697788	−	0.716304i
$46$	3.28622	+	5.69190i	0.484527	+	0.839225i
$47$		−	5.41619i		−	0.790033i	−0.918674	−	0.395016i	$-0.870739\pi$
$47$		−	5.41619i		−	0.790033i	0.918674	−	0.395016i	$-0.129261\pi$
$48$	0.630353	+	1.61327i	0.0909835	+	0.232856i
$49$	−0.267153	+	6.99490i	−0.0381647	+	0.999271i
$50$	−4.99253	+	0.273152i	−0.706051	+	0.0386295i
$51$	0.785560	+	0.628407i	0.110000	+	0.0879946i
$52$	3.03357	−	5.25429i	0.420680	−	0.728639i
$53$	4.19068	+	7.25846i	0.575634	+	0.997027i	0.995972	+	0.0896594i	$0.0285779\pi$
$53$	4.19068	+	7.25846i	0.575634	+	0.997027i	−0.420339	+	0.907367i	$0.638089\pi$
$54$	−4.67130	−	2.27572i	−0.635684	−	0.309687i
$55$	1.38946	−	2.56609i	0.187354	−	0.346011i
$56$	1.83478	+	1.90619i	0.245183	+	0.254726i
$57$	2.06663	−	13.5720i	0.273732	−	1.79766i
$58$	−0.125548	+	0.0724850i	−0.0164852	+	0.00951775i
$59$	−3.08716			−0.401913			−0.200957	−	0.979600i	$-0.564405\pi$
$59$	−3.08716			−0.401913			−0.200957	+	0.979600i	$0.564405\pi$
$60$	−3.56753	+	1.50756i	−0.460566	+	0.194625i
$61$			2.12053i			0.271506i	0.990743	+	0.135753i	$0.0433453\pi$
$61$			2.12053i			0.271506i	−0.990743	+	0.135753i	$0.956655\pi$
$62$			1.38267i			0.175599i
$63$	−7.92320	−	0.472056i	−0.998230	−	0.0594735i
$64$	1.00000			0.125000
$65$	11.9299	+	6.45968i	1.47972	+	0.801225i
$66$	0.340266	−	2.23460i	0.0418838	−	0.275061i
$67$		−	13.1972i		−	1.61229i	−0.591717	−	0.806146i	$-0.701550\pi$
$67$		−	13.1972i		−	1.61229i	0.591717	−	0.806146i	$-0.298450\pi$
$68$	0.502991	−	0.290402i	0.0609966	−	0.0352164i
$69$	−7.11112	+	8.88948i	−0.856078	+	1.07017i
$70$	−4.14868	+	4.21764i	−0.495862	+	0.504104i
$71$			10.3545i			1.22885i	0.788975	+	0.614425i	$0.210612\pi$
$71$			10.3545i			1.22885i	−0.788975	+	0.614425i	$0.789388\pi$
$72$	−2.20531	+	2.03386i	−0.259898	+	0.239693i
$73$	3.84599	+	6.66144i	0.450139	+	0.779663i	0.998394	−	0.0566478i	$-0.0180412\pi$
$73$	3.84599	+	6.66144i	0.450139	+	0.779663i	−0.548256	+	0.836311i	$0.684708\pi$
$74$	2.02863	+	1.17123i	0.235824	+	0.136153i
$75$	−3.58773	−	7.88215i	−0.414275	−	0.910152i
$76$	−6.86424	−	3.96307i	−0.787382	−	0.454595i
$77$	−0.829824	−	3.35156i	−0.0945672	−	0.381945i
$78$	10.3888	+	1.58192i	1.17630	+	0.179117i
$79$	−7.09192			−0.797904			−0.398952	−	0.916972i	$-0.630626\pi$
$79$	−7.09192			−0.797904			−0.398952	+	0.916972i	$0.630626\pi$
$80$	0.0611015	+	2.23523i	0.00683135	+	0.249907i
$81$	0.726797	−	8.97061i	0.0807552	−	0.996734i
$82$	3.16905	−	5.48896i	0.349964	−	0.606155i
$83$	−4.32983	+	2.49983i	−0.475261	+	0.274392i	−0.718439	−	0.695589i	$-0.755143\pi$
$83$	−4.32983	+	2.49983i	−0.475261	+	0.274392i	0.243178	+	0.969982i	$0.421810\pi$
$84$	−1.91866	+	4.16158i	−0.209343	+	0.454066i
$85$	0.679850	+	1.10656i	0.0737400	+	0.120023i
$86$	10.0713	−	5.81466i	1.08602	−	0.627011i
$87$	−0.196078	−	0.156852i	−0.0210217	−	0.0168163i
$88$	−1.13018	−	0.652510i	−0.120478	−	0.0695578i
$89$	1.35235	−	2.34234i	0.143349	−	0.248288i	−0.785407	−	0.618980i	$-0.787546\pi$
$89$	1.35235	−	2.34234i	0.143349	−	0.248288i	0.928756	+	0.370692i	$0.120879\pi$
$90$	−4.68091	−	4.80511i	−0.493411	−	0.506503i
$91$	15.5816	−	3.85791i	1.63340	−	0.404419i
$92$	3.28622	+	5.69190i	0.342612	+	0.593422i
$93$	−2.23062	+	0.871568i	−0.231305	+	0.0903774i
$94$		−	5.41619i		−	0.558638i
$95$	8.43897	−	15.5853i	0.865820	−	1.59902i
$96$	0.630353	+	1.61327i	0.0643351	+	0.164654i
$97$	−5.76032	−	9.97717i	−0.584872	−	1.01303i	−0.994891	−	0.100951i	$-0.967811\pi$
$97$	−5.76032	−	9.97717i	−0.584872	−	1.01303i	0.410019	−	0.912077i	$-0.365522\pi$
$98$	−0.267153	+	6.99490i	−0.0269865	+	0.706592i
$99$	3.81952	−	0.859646i	0.383876	−	0.0863976i
$100$	−4.99253	+	0.273152i	−0.499253	+	0.0273152i
$101$	7.17658	−	12.4302i	0.714097	−	1.23685i	−0.249210	−	0.968449i	$-0.580171\pi$
$101$	7.17658	−	12.4302i	0.714097	−	1.23685i	0.963307	−	0.268402i	$-0.0864956\pi$
$102$	0.785560	+	0.628407i	0.0777820	+	0.0622216i
$103$	−0.386002	−	0.668575i	−0.0380339	−	0.0658766i	0.846382	−	0.532577i	$-0.178776\pi$
$103$	−0.386002	−	0.668575i	−0.0380339	−	0.0658766i	−0.884416	+	0.466700i	$0.845443\pi$
$104$	3.03357	−	5.25429i	0.297466	−	0.515226i
$105$	−9.41934	−	4.03436i	−0.919233	−	0.393714i
$106$	4.19068	+	7.25846i	0.407034	+	0.705004i
$107$	−8.60622	+	14.9064i	−0.831995	+	1.44106i	0.0644590	+	0.997920i	$0.479468\pi$
$107$	−8.60622	+	14.9064i	−0.831995	+	1.44106i	−0.896454	+	0.443137i	$0.853866\pi$
$108$	−4.67130	−	2.27572i	−0.449497	−	0.218981i
$109$	−6.30827	−	10.9262i	−0.604223	−	1.04654i	−0.992174	−	0.124864i	$-0.960150\pi$
$109$	−6.30827	−	10.9262i	−0.604223	−	1.04654i	0.387951	−	0.921680i	$-0.373183\pi$
$110$	1.38946	−	2.56609i	0.132479	−	0.244667i
$111$	−0.610765	+	4.01103i	−0.0579712	+	0.380710i
$112$	1.83478	+	1.90619i	0.173371	+	0.180118i
$113$	6.02741	−	10.4398i	0.567011	−	0.982092i	−0.429848	−	0.902901i	$-0.641433\pi$
$113$	6.02741	−	10.4398i	0.567011	−	0.982092i	0.996859	−	0.0791911i	$-0.0252337\pi$
$114$	2.06663	−	13.5720i	0.193558	−	1.27114i
$115$	−12.5219	+	7.69325i	−1.16768	+	0.717399i
$116$	−0.125548	+	0.0724850i	−0.0116568	+	0.00673006i
$117$	3.99655	+	17.7572i	0.369482	+	1.64165i
$118$	−3.08716			−0.284196
$119$	1.47644	+	0.425974i	0.135345	+	0.0390490i
$120$	−3.56753	+	1.50756i	−0.325669	+	0.137621i
$121$	−4.64846	−	8.05137i	−0.422587	−	0.731943i
$122$			2.12053i			0.191984i
$123$	10.8528	+	1.65257i	0.978567	+	0.149008i
$124$			1.38267i			0.124167i
$125$	−0.915610	−	11.1428i	−0.0818946	−	0.996641i
$126$	−7.92320	−	0.472056i	−0.705855	−	0.0420541i
$127$			14.7512i			1.30896i	0.756079	+	0.654480i	$0.227113\pi$
$127$			14.7512i			1.30896i	−0.756079	+	0.654480i	$0.772887\pi$
$128$	1.00000			0.0883883
$129$	15.7291	+	12.5825i	1.38487	+	1.10783i
$130$	11.9299	+	6.45968i	1.04632	+	0.566552i
$131$	7.84610	+	13.5898i	0.685517	+	1.18735i	0.973274	+	0.229647i	$0.0737571\pi$
$131$	7.84610	+	13.5898i	0.685517	+	1.18735i	−0.287757	+	0.957703i	$0.592910\pi$
$132$	0.340266	−	2.23460i	0.0296164	−	0.194497i
$133$	−5.04000	−	20.3559i	−0.437023	−	1.76508i
$134$		−	13.1972i		−	1.14006i
$135$	4.80135	−	10.5805i	0.413234	−	0.910625i
$136$	0.502991	−	0.290402i	0.0431311	−	0.0249018i
$137$	−4.42929	+	7.67175i	−0.378419	+	0.655442i	−0.990832	−	0.135096i	$-0.956866\pi$
$137$	−4.42929	+	7.67175i	−0.378419	+	0.655442i	0.612413	+	0.790538i	$0.290199\pi$
$138$	−7.11112	+	8.88948i	−0.605339	+	0.756723i
$139$	−1.39913	−	0.807790i	−0.118673	−	0.0685158i	0.439489	−	0.898248i	$-0.355160\pi$
$139$	−1.39913	−	0.807790i	−0.118673	−	0.0685158i	−0.558161	+	0.829732i	$0.688493\pi$
$140$	−4.14868	+	4.21764i	−0.350627	+	0.356455i
$141$	8.73781	−	3.41411i	0.735856	−	0.287520i
$142$			10.3545i			0.868929i
$143$	−6.85696	+	3.95887i	−0.573408	+	0.331057i
$144$	−2.20531	+	2.03386i	−0.183776	+	0.169489i
$145$	−0.169692	−	0.276199i	−0.0140922	−	0.0229371i
$146$	3.84599	+	6.66144i	0.318296	+	0.551305i
$147$	−11.4531	+	3.97826i	−0.944636	+	0.328122i
$148$	2.02863	+	1.17123i	0.166753	+	0.0962746i
$149$	8.30790	−	4.79657i	0.680610	−	0.392950i	−0.119475	−	0.992837i	$-0.538121\pi$
$149$	8.30790	−	4.79657i	0.680610	−	0.392950i	0.800085	+	0.599887i	$0.204788\pi$
$150$	−3.58773	−	7.88215i	−0.292937	−	0.643575i
$151$	8.68275	−	15.0390i	0.706592	−	1.22385i	−0.259522	−	0.965737i	$-0.583565\pi$
$151$	8.68275	−	15.0390i	0.706592	−	1.22385i	0.966114	−	0.258116i	$-0.0831016\pi$
$152$	−6.86424	−	3.96307i	−0.556763	−	0.321448i
$153$	−0.518614	+	1.66344i	−0.0419274	+	0.134481i
$154$	−0.829824	−	3.35156i	−0.0668691	−	0.270076i
$155$	−3.09058	+	0.0844830i	−0.248242	+	0.00678584i
$156$	10.3888	+	1.58192i	0.831772	+	0.126655i
$157$	−3.39738			−0.271140			−0.135570	−	0.990768i	$-0.543287\pi$
$157$	−3.39738			−0.271140			−0.135570	+	0.990768i	$0.543287\pi$
$158$	−7.09192			−0.564203
$159$	−9.06829	+	11.3361i	−0.719162	+	0.899011i
$160$	0.0611015	+	2.23523i	0.00483050	+	0.176711i
$161$	−4.82037	+	16.7076i	−0.379898	+	1.31674i
$162$	0.726797	−	8.97061i	0.0571026	−	0.704797i
$163$	4.86586	+	2.80931i	0.381124	+	0.220042i	0.678307	−	0.734778i	$-0.262714\pi$
$163$	4.86586	+	2.80931i	0.381124	+	0.220042i	−0.297183	+	0.954820i	$0.596047\pi$
$164$	3.16905	−	5.48896i	0.247462	−	0.428616i
$165$	5.01565	+	0.624036i	0.390468	+	0.0485811i
$166$	−4.32983	+	2.49983i	−0.336060	+	0.194025i
$167$	−5.55272	−	3.20586i	−0.429682	−	0.248077i	0.269529	−	0.962992i	$-0.413132\pi$
$167$	−5.55272	−	3.20586i	−0.429682	−	0.248077i	−0.699211	+	0.714915i	$0.746465\pi$
$168$	−1.91866	+	4.16158i	−0.148028	+	0.321073i
$169$	−11.9051	−	20.6202i	−0.915773	−	1.58617i
$170$	0.679850	+	1.10656i	0.0521421	+	0.0848691i
$171$	23.1981	−	5.22112i	1.77401	−	0.399269i
$172$	10.0713	−	5.81466i	0.767929	−	0.443364i
$173$		−	8.02653i		−	0.610246i	−0.952313	−	0.305123i	$-0.901302\pi$
$173$		−	8.02653i		−	0.610246i	0.952313	−	0.305123i	$-0.0986976\pi$
$174$	−0.196078	−	0.156852i	−0.0148646	−	0.0118909i
$175$	−9.68089	−	9.01556i	−0.731806	−	0.681513i
$176$	−1.13018	−	0.652510i	−0.0851906	−	0.0491848i
$177$	−1.94600	−	4.98043i	−0.146270	−	0.374352i
$178$	1.35235	−	2.34234i	0.101363	−	0.175566i
$179$	−14.3104	+	8.26209i	−1.06961	+	0.617538i	−0.928074	−	0.372396i	$-0.878536\pi$
$179$	−14.3104	+	8.26209i	−1.06961	+	0.617538i	−0.141533	+	0.989934i	$0.545203\pi$
$180$	−4.68091	−	4.80511i	−0.348894	−	0.358152i
$181$		−	6.84621i		−	0.508875i	−0.967089	−	0.254437i	$-0.918110\pi$
$181$		−	6.84621i		−	0.508875i	0.967089	−	0.254437i	$-0.0818903\pi$
$182$	15.5816	−	3.85791i	1.15499	−	0.285967i
$183$	−3.42099	+	1.33668i	−0.252887	+	0.0988102i
$184$	3.28622	+	5.69190i	0.242263	+	0.419612i
$185$	−2.49402	+	4.60603i	−0.183364	+	0.338642i
$186$	−2.23062	+	0.871568i	−0.163557	+	0.0639064i
$187$	−0.757961			−0.0554276
$188$		−	5.41619i		−	0.395016i
$189$	−4.23286	−	13.0799i	−0.307895	−	0.951420i
$190$	8.43897	−	15.5853i	0.612227	−	1.13068i
$191$			8.46726i			0.612670i	0.951924	+	0.306335i	$0.0991027\pi$
$191$			8.46726i			0.612670i	−0.951924	+	0.306335i	$0.900897\pi$
$192$	0.630353	+	1.61327i	0.0454918	+	0.116428i
$193$		−	2.27066i		−	0.163445i	−0.996655	−	0.0817227i	$-0.973958\pi$
$193$		−	2.27066i		−	0.163445i	0.996655	−	0.0817227i	$-0.0260422\pi$
$194$	−5.76032	−	9.97717i	−0.413567	−	0.716319i
$195$	−2.90119	+	23.3181i	−0.207758	+	1.66985i
$196$	−0.267153	+	6.99490i	−0.0190824	+	0.499636i
$197$	13.0144			0.927240			0.463620	−	0.886034i	$-0.346550\pi$
$197$	13.0144			0.927240			0.463620	+	0.886034i	$0.346550\pi$
$198$	3.81952	−	0.859646i	0.271441	−	0.0610924i
$199$	−2.76888	+	1.59861i	−0.196280	+	0.113323i	−0.594919	−	0.803785i	$-0.702816\pi$
$199$	−2.76888	+	1.59861i	−0.196280	+	0.113323i	0.398639	+	0.917108i	$0.369483\pi$
$200$	−4.99253	+	0.273152i	−0.353025	+	0.0193148i
$201$	21.2907	−	8.31887i	1.50173	−	0.586768i
$202$	7.17658	−	12.4302i	0.504943	−	0.874586i
$203$	−0.368523	−	0.106324i	−0.0258653	−	0.00746249i
$204$	0.785560	+	0.628407i	0.0550002	+	0.0439973i
$205$	12.4627	+	6.74819i	0.870436	+	0.471314i
$206$	−0.386002	−	0.668575i	−0.0268940	−	0.0465818i
$207$	−18.8237	−	5.86869i	−1.30834	−	0.407902i
$208$	3.03357	−	5.25429i	0.210340	−	0.364320i
$209$	5.17189	+	8.95797i	0.357747	+	0.619636i
$210$	−9.41934	−	4.03436i	−0.649996	−	0.278398i
$211$	−5.05309	+	8.75221i	−0.347869	+	0.602527i	−0.985871	−	0.167508i	$-0.946428\pi$
$211$	−5.05309	+	8.75221i	−0.347869	+	0.602527i	0.638002	+	0.770035i	$0.279761\pi$
$212$	4.19068	+	7.25846i	0.287817	+	0.498513i
$213$	−16.7046	+	6.52697i	−1.14458	+	0.447221i
$214$	−8.60622	+	14.9064i	−0.588309	+	1.01898i
$215$	13.6125	+	22.1564i	0.928365	+	1.51105i
$216$	−4.67130	−	2.27572i	−0.317842	−	0.154843i
$217$	−2.63563	+	2.53689i	−0.178918	+	0.172215i
$218$	−6.30827	−	10.9262i	−0.427250	−	0.740019i
$219$	−8.32241	+	10.4037i	−0.562377	+	0.703016i
$220$	1.38946	−	2.56609i	0.0936772	−	0.173006i
$221$		−	3.52381i		−	0.237037i
$222$	−0.610765	+	4.01103i	−0.0409918	+	0.269203i
$223$	−1.58167	−	2.73954i	−0.105917	−	0.183453i	0.808196	−	0.588914i	$-0.200444\pi$
$223$	−1.58167	−	2.73954i	−0.105917	−	0.183453i	−0.914112	+	0.405461i	$0.867111\pi$
$224$	1.83478	+	1.90619i	0.122592	+	0.127363i
$225$	10.4545	−	10.7565i	0.696969	−	0.717101i
$226$	6.02741	−	10.4398i	0.400938	−	0.694444i
$227$	8.30806	+	4.79666i	0.551425	+	0.318365i	0.749697	−	0.661782i	$-0.230199\pi$
$227$	8.30806	+	4.79666i	0.551425	+	0.318365i	−0.198272	+	0.980147i	$0.563533\pi$
$228$	2.06663	−	13.5720i	0.136866	−	0.898830i
$229$	3.11351	−	1.79758i	0.205746	−	0.118788i	−0.393587	−	0.919288i	$-0.628766\pi$
$229$	3.11351	−	1.79758i	0.205746	−	0.118788i	0.599333	+	0.800500i	$0.295433\pi$
$230$	−12.5219	+	7.69325i	−0.825672	+	0.507278i
$231$	4.88390	−	3.45140i	0.321337	−	0.227085i
$232$	−0.125548	+	0.0724850i	−0.00824261	+	0.00475887i
$233$	−2.91309	+	5.04563i	−0.190843	+	0.330550i	−0.945530	−	0.325535i	$-0.894456\pi$
$233$	−2.91309	+	5.04563i	−0.190843	+	0.330550i	0.754687	+	0.656085i	$0.227789\pi$
$234$	3.99655	+	17.7572i	0.261263	+	1.16083i
$235$	12.1065	−	0.330937i	0.789738	−	0.0215880i
$236$	−3.08716			−0.200957
$237$	−4.47041	−	11.4412i	−0.290384	−	0.743187i
$238$	1.47644	+	0.425974i	0.0957035	+	0.0276118i
$239$	−19.9340	−	11.5089i	−1.28942	−	0.744448i	−0.310870	−	0.950452i	$-0.600621\pi$
$239$	−19.9340	−	11.5089i	−1.28942	−	0.744448i	−0.978551	+	0.206005i	$0.933954\pi$
$240$	−3.56753	+	1.50756i	−0.230283	+	0.0973125i
$241$	−5.92882	−	3.42300i	−0.381909	−	0.220495i	0.296740	−	0.954958i	$-0.404101\pi$
$241$	−5.92882	−	3.42300i	−0.381909	−	0.220495i	−0.678648	+	0.734463i	$0.737434\pi$
$242$	−4.64846	−	8.05137i	−0.298814	−	0.517562i
$243$	14.9302	−	4.48212i	0.957772	−	0.287528i
$244$			2.12053i			0.135753i
$245$	−15.6516	−	0.169750i	−0.999941	−	0.0108449i
$246$	10.8528	+	1.65257i	0.691951	+	0.105364i
$247$	−41.6463	+	24.0445i	−2.64989	+	1.52991i
$248$			1.38267i			0.0877995i
$249$	−6.76224	−	5.40944i	−0.428539	−	0.342809i
$250$	−0.915610	−	11.1428i	−0.0579082	−	0.704732i
$251$	−12.2160			−0.771068			−0.385534	−	0.922694i	$-0.625983\pi$
$251$	−12.2160			−0.771068			−0.385534	+	0.922694i	$0.625983\pi$
$252$	−7.92320	−	0.472056i	−0.499115	−	0.0297367i
$253$		−	8.57717i		−	0.539242i
$254$			14.7512i			0.925575i
$255$	−1.35664	+	1.79431i	−0.0849559	+	0.112364i
$256$	1.00000			0.0625000
$257$	−22.8388	+	13.1860i	−1.42465	+	0.822520i	−0.996691	−	0.0812807i	$-0.974099\pi$
$257$	−22.8388	+	13.1860i	−1.42465	+	0.822520i	−0.427954	+	0.903800i	$0.640766\pi$
$258$	15.7291	+	12.5825i	0.979252	+	0.783351i
$259$	1.48950	+	6.01592i	0.0925532	+	0.373811i
$260$	11.9299	+	6.45968i	0.739862	+	0.400613i
$261$	0.129447	−	0.415199i	0.00801258	−	0.0257002i
$262$	7.84610	+	13.5898i	0.484734	+	0.839583i
$263$	−10.3480	+	17.9233i	−0.638088	+	1.10520i	0.347764	+	0.937582i	$0.386941\pi$
$263$	−10.3480	+	17.9233i	−0.638088	+	1.10520i	−0.985852	+	0.167619i	$0.946392\pi$
$264$	0.340266	−	2.23460i	0.0209419	−	0.137530i
$265$	−15.9683	+	9.81064i	−0.980925	+	0.602663i
$266$	−5.04000	−	20.3559i	−0.309022	−	1.24810i
$267$	4.63130	+	0.705215i	0.283431	+	0.0431584i
$268$		−	13.1972i		−	0.806146i
$269$	−4.69521	−	8.13233i	−0.286272	−	0.495837i	0.686645	−	0.726993i	$-0.259083\pi$
$269$	−4.69521	−	8.13233i	−0.286272	−	0.495837i	−0.972917	+	0.231156i	$0.925749\pi$
$270$	4.80135	−	10.5805i	0.292201	−	0.643909i
$271$	−2.94143	−	1.69824i	−0.178679	−	0.103161i	0.407993	−	0.912985i	$-0.366229\pi$
$271$	−2.94143	−	1.69824i	−0.178679	−	0.103161i	−0.586672	+	0.809825i	$0.699562\pi$
$272$	0.502991	−	0.290402i	0.0304983	−	0.0176082i
$273$	16.0458	+	22.7056i	0.971135	+	1.37421i
$274$	−4.42929	+	7.67175i	−0.267583	+	0.463467i
$275$	5.82070	+	2.94897i	0.351001	+	0.177829i
$276$	−7.11112	+	8.88948i	−0.428039	+	0.535084i
$277$	18.1450	+	10.4760i	1.09023	+	0.629442i	0.933637	−	0.358221i	$-0.116617\pi$
$277$	18.1450	+	10.4760i	1.09023	+	0.629442i	0.156590	+	0.987664i	$0.449950\pi$
$278$	−1.39913	−	0.807790i	−0.0839144	−	0.0484480i
$279$	−2.81216	−	3.04921i	−0.168359	−	0.182552i
$280$	−4.14868	+	4.21764i	−0.247931	+	0.252052i
$281$	0.919808	−	0.531051i	0.0548712	−	0.0316799i	−0.472313	−	0.881431i	$-0.656581\pi$
$281$	0.919808	−	0.531051i	0.0548712	−	0.0316799i	0.527185	+	0.849751i	$0.323248\pi$
$282$	8.73781	−	3.41411i	0.520329	−	0.203307i
$283$	20.9648			1.24623			0.623113	−	0.782132i	$-0.285868\pi$
$283$	20.9648			1.24623			0.623113	+	0.782132i	$0.285868\pi$
$284$			10.3545i			0.614425i
$285$	30.4629	+	3.79013i	1.80447	+	0.224508i
$286$	−6.85696	+	3.95887i	−0.405460	+	0.234093i
$287$	16.2776	−	4.03022i	0.960834	−	0.237896i
$288$	−2.20531	+	2.03386i	−0.129949	+	0.119847i
$289$	−8.33133	+	14.4303i	−0.490078	+	0.848841i
$290$	−0.169692	−	0.276199i	−0.00996466	−	0.0162190i
$291$	12.4649	−	15.5821i	0.730705	−	0.913440i
$292$	3.84599	+	6.66144i	0.225069	+	0.389832i
$293$	−19.5706	−	11.2991i	−1.14332	−	0.660099i	−0.196073	−	0.980589i	$-0.562819\pi$
$293$	−19.5706	−	11.2991i	−1.14332	−	0.660099i	−0.947252	+	0.320491i	$0.896152\pi$
$294$	−11.4531	+	3.97826i	−0.667958	+	0.232017i
$295$	−0.188630	−	6.90051i	−0.0109825	−	0.401763i
$296$	2.02863	+	1.17123i	0.117912	+	0.0680764i
$297$	3.79449	+	5.62005i	0.220178	+	0.326108i
$298$	8.30790	−	4.79657i	0.481264	−	0.277858i
$299$	39.8759			2.30608
$300$	−3.58773	−	7.88215i	−0.207137	−	0.455076i
$301$	29.5625	+	8.52920i	1.70395	+	0.491615i
$302$	8.68275	−	15.0390i	0.499636	−	0.865395i
$303$	24.5771	+	3.74239i	1.41192	+	0.214995i
$304$	−6.86424	−	3.96307i	−0.393691	−	0.227298i
$305$	−4.73987	+	0.129567i	−0.271404	+	0.00741901i
$306$	−0.518614	+	1.66344i	−0.0296472	+	0.0950926i
$307$	−29.2086			−1.66702			−0.833512	−	0.552501i	$-0.813674\pi$
$307$	−29.2086			−1.66702			−0.833512	+	0.552501i	$0.813674\pi$
$308$	−0.829824	−	3.35156i	−0.0472836	−	0.190973i
$309$	0.835278	−	1.04416i	0.0475173	−	0.0594005i
$310$	−3.09058	+	0.0844830i	−0.175533	+	0.00479831i
$311$	−13.0106			−0.737764			−0.368882	−	0.929476i	$-0.620259\pi$
$311$	−13.0106			−0.737764			−0.368882	+	0.929476i	$0.620259\pi$
$312$	10.3888	+	1.58192i	0.588152	+	0.0895586i
$313$	−7.25446			−0.410047			−0.205023	−	0.978757i	$-0.565727\pi$
$313$	−7.25446			−0.410047			−0.205023	+	0.978757i	$0.565727\pi$
$314$	−3.39738			−0.191725
$315$	0.571036	−	17.7391i	0.0321742	−	0.999482i
$316$	−7.09192			−0.398952
$317$	28.5206			1.60188			0.800939	−	0.598746i	$-0.204334\pi$
$317$	28.5206			1.60188			0.800939	+	0.598746i	$0.204334\pi$
$318$	−9.06829	+	11.3361i	−0.508525	+	0.635697i
$319$	0.189189			0.0105925
$320$	0.0611015	+	2.23523i	0.00341568	+	0.124953i
$321$	−29.4731	−	4.48791i	−1.64503	−	0.250490i
$322$	−4.82037	+	16.7076i	−0.268629	+	0.931076i
$323$	−4.60353			−0.256147
$324$	0.726797	−	8.97061i	0.0403776	−	0.498367i
$325$	−13.7100	+	27.0608i	−0.760492	+	1.50107i
$326$	4.86586	+	2.80931i	0.269495	+	0.155593i
$327$	13.6506	−	17.0644i	0.754880	−	0.943661i
$328$	3.16905	−	5.48896i	0.174982	−	0.303077i
$329$	10.3243	−	9.93753i	0.569198	−	0.547874i
$330$	5.01565	+	0.624036i	0.276103	+	0.0343521i
$331$	24.7022			1.35775			0.678877	−	0.734252i	$-0.262467\pi$
$331$	24.7022			1.35775			0.678877	+	0.734252i	$0.262467\pi$
$332$	−4.32983	+	2.49983i	−0.237631	+	0.137196i
$333$	−6.85589	+	1.54303i	−0.375700	+	0.0845576i
$334$	−5.55272	−	3.20586i	−0.303831	−	0.175417i
$335$	29.4988	−	0.806367i	1.61169	−	0.0440565i
$336$	−1.91866	+	4.16158i	−0.104671	+	0.227033i
$337$	6.13756	+	3.54352i	0.334334	+	0.193028i	0.657764	−	0.753224i	$-0.271503\pi$
$337$	6.13756	+	3.54352i	0.334334	+	0.193028i	−0.323430	+	0.946252i	$0.604836\pi$
$338$	−11.9051	−	20.6202i	−0.647549	−	1.12159i
$339$	20.6416	+	3.14313i	1.12110	+	0.170711i
$340$	0.679850	+	1.10656i	0.0368700	+	0.0600115i
$341$	0.902204	−	1.56266i	0.0488571	−	0.0846230i
$342$	23.1981	−	5.22112i	1.25441	−	0.282326i
$343$	−13.8238	+	12.3249i	−0.746415	+	0.665480i
$344$	10.0713	−	5.81466i	0.543008	−	0.313506i
$345$	−20.3046	−	15.3519i	−1.09316	−	0.826516i
$346$		−	8.02653i		−	0.431509i
$347$	7.75645			0.416388			0.208194	−	0.978088i	$-0.433241\pi$
$347$	7.75645			0.416388			0.208194	+	0.978088i	$0.433241\pi$
$348$	−0.196078	−	0.156852i	−0.0105109	−	0.00840814i
$349$	−8.89557	+	5.13586i	−0.476169	+	0.274916i	−0.718819	−	0.695198i	$-0.755317\pi$
$349$	−8.89557	+	5.13586i	−0.476169	+	0.274916i	0.242650	+	0.970114i	$0.421983\pi$
$350$	−9.68089	−	9.01556i	−0.517465	−	0.481902i
$351$	−26.1280	+	17.6408i	−1.39461	+	0.941598i
$352$	−1.13018	−	0.652510i	−0.0602388	−	0.0347789i
$353$	−18.2499	−	10.5366i	−0.971346	−	0.560807i	−0.0716994	−	0.997426i	$-0.522842\pi$
$353$	−18.2499	−	10.5366i	−0.971346	−	0.560807i	−0.899646	+	0.436620i	$0.856176\pi$
$354$	−1.94600	−	4.98043i	−0.103429	−	0.264707i
$355$	−23.1447	+	0.632674i	−1.22839	+	0.0335789i
$356$	1.35235	−	2.34234i	0.0716746	−	0.124144i
$357$	0.243465	+	2.65042i	0.0128855	+	0.140275i
$358$	−14.3104	+	8.26209i	−0.756326	+	0.436665i
$359$	15.0004	+	8.66050i	0.791692	+	0.457084i	0.840558	−	0.541722i	$-0.182227\pi$
$359$	15.0004	+	8.66050i	0.791692	+	0.457084i	−0.0488656	+	0.998805i	$0.515561\pi$
$360$	−4.68091	−	4.80511i	−0.246705	−	0.253252i
$361$	21.9119	+	37.9525i	1.15326	+	1.99750i
$362$		−	6.84621i		−	0.359829i
$363$	10.0589	−	12.5744i	0.527956	−	0.659987i
$364$	15.5816	−	3.85791i	0.816699	−	0.202209i
$365$	−14.6549	+	9.00370i	−0.767072	+	0.471275i
$366$	−3.42099	+	1.33668i	−0.178818	+	0.0698694i
$367$	−3.49830	+	6.05923i	−0.182610	+	0.316289i	−0.942768	−	0.333448i	$-0.891788\pi$
$367$	−3.49830	+	6.05923i	−0.182610	+	0.316289i	0.760159	+	0.649737i	$0.225121\pi$
$368$	3.28622	+	5.69190i	0.171306	+	0.296711i
$369$	4.17505	+	18.5503i	0.217345	+	0.965690i
$370$	−2.49402	+	4.60603i	−0.129658	+	0.239456i
$371$	−6.14707	+	21.3059i	−0.319140	+	1.10615i
$372$	−2.23062	+	0.871568i	−0.115652	+	0.0451887i
$373$	12.9529	−	7.47838i	0.670678	−	0.387216i	−0.125656	−	0.992074i	$-0.540103\pi$
$373$	12.9529	−	7.47838i	0.670678	−	0.387216i	0.796333	+	0.604858i	$0.206770\pi$
$374$	−0.757961			−0.0391932
$375$	17.3992	−	8.50101i	0.898492	−	0.438990i
$376$		−	5.41619i		−	0.279319i
$377$			0.879552i			0.0452992i
$378$	−4.23286	−	13.0799i	−0.217715	−	0.672756i
$379$	1.81688			0.0933268			0.0466634	−	0.998911i	$-0.485141\pi$
$379$	1.81688			0.0933268			0.0466634	+	0.998911i	$0.485141\pi$
$380$	8.43897	−	15.5853i	0.432910	−	0.799510i
$381$	−23.7978	+	9.29848i	−1.21920	+	0.476376i
$382$			8.46726i			0.433223i
$383$	−3.98546	+	2.30101i	−0.203647	+	0.117576i	−0.598356	−	0.801231i	$-0.704179\pi$
$383$	−3.98546	+	2.30101i	−0.203647	+	0.117576i	0.394708	+	0.918807i	$0.370846\pi$
$384$	0.630353	+	1.61327i	0.0321675	+	0.0823271i
$385$	7.44081	−	2.05963i	0.379219	−	0.104969i
$386$		−	2.27066i		−	0.115573i
$387$	−10.3841	+	33.3068i	−0.527854	+	1.69308i
$388$	−5.76032	−	9.97717i	−0.292436	−	0.506514i
$389$	−14.8244	−	8.55885i	−0.751625	−	0.433951i	0.0746556	−	0.997209i	$-0.476214\pi$
$389$	−14.8244	−	8.55885i	−0.751625	−	0.433951i	−0.826281	+	0.563258i	$0.809548\pi$
$390$	−2.90119	+	23.3181i	−0.146907	+	1.18076i
$391$	3.30588	+	1.90865i	0.167185	+	0.0965245i
$392$	−0.267153	+	6.99490i	−0.0134933	+	0.353296i
$393$	−16.9783	+	21.2243i	−0.856444	+	1.07062i
$394$	13.0144			0.655657
$395$	−0.433327	−	15.8521i	−0.0218031	−	0.797606i
$396$	3.81952	−	0.859646i	0.191938	−	0.0431988i
$397$	7.42358	−	12.8580i	0.372579	−	0.645325i	−0.617383	−	0.786663i	$-0.711807\pi$
$397$	7.42358	−	12.8580i	0.372579	−	0.645325i	0.989961	+	0.141338i	$0.0451403\pi$
$398$	−2.76888	+	1.59861i	−0.138791	+	0.0801312i
$399$	29.6628	−	20.9623i	1.48500	−	1.04943i
$400$	−4.99253	+	0.273152i	−0.249627	+	0.0136576i
$401$	−8.29051	+	4.78653i	−0.414008	+	0.239028i	−0.692511	−	0.721408i	$-0.743495\pi$
$401$	−8.29051	+	4.78653i	−0.414008	+	0.239028i	0.278502	+	0.960436i	$0.410162\pi$
$402$	21.2907	−	8.31887i	1.06188	−	0.414908i
$403$	7.26494	+	4.19441i	0.361892	+	0.208939i
$404$	7.17658	−	12.4302i	0.357048	−	0.618426i
$405$	20.0958	+	1.07644i	0.998568	+	0.0534889i
$406$	−0.368523	−	0.106324i	−0.0182895	−	0.00527678i
$407$	−1.52848	−	2.64741i	−0.0757640	−	0.131227i
$408$	0.785560	+	0.628407i	0.0388910	+	0.0311108i
$409$			38.6251i			1.90989i	0.296787	+	0.954944i	$0.404085\pi$
$409$			38.6251i			1.90989i	−0.296787	+	0.954944i	$0.595915\pi$
$410$	12.4627	+	6.74819i	0.615491	+	0.333269i
$411$	−15.1687	−	2.30975i	−0.748214	−	0.113932i
$412$	−0.386002	−	0.668575i	−0.0190169	−	0.0329383i
$413$	−5.66426	−	5.88472i	−0.278720	−	0.289568i
$414$	−18.8237	−	5.86869i	−0.925134	−	0.288430i
$415$	−5.85226	−	9.52544i	−0.287276	−	0.467586i
$416$	3.03357	−	5.25429i	0.148733	−	0.257613i
$417$	0.421240	−	2.76638i	0.0206282	−	0.135470i
$418$	5.17189	+	8.95797i	0.252965	+	0.438149i
$419$	−6.88512	+	11.9254i	−0.336360	+	0.582593i	−0.983745	−	0.179570i	$-0.942529\pi$
$419$	−6.88512	+	11.9254i	−0.336360	+	0.582593i	0.647385	+	0.762163i	$0.275863\pi$
$420$	−9.41934	−	4.03436i	−0.459617	−	0.196857i
$421$	−9.44758	−	16.3637i	−0.460447	−	0.797517i	0.538536	−	0.842602i	$-0.318977\pi$
$421$	−9.44758	−	16.3637i	−0.460447	−	0.797517i	−0.998983	+	0.0450850i	$0.985644\pi$
$422$	−5.05309	+	8.75221i	−0.245981	+	0.426051i
$423$	11.0158	+	11.9444i	0.535606	+	0.580756i
$424$	4.19068	+	7.25846i	0.203517	+	0.352502i
$425$	−2.43188	+	1.58723i	−0.117963	+	0.0769922i
$426$	−16.7046	+	6.52697i	−0.809342	+	0.316233i
$427$	−4.04214	+	3.89070i	−0.195613	+	0.188284i
$428$	−8.60622	+	14.9064i	−0.415997	+	0.720529i
$429$	−10.7090	−	8.56668i	−0.517037	−	0.413603i
$430$	13.6125	+	22.1564i	0.656453	+	1.06848i
$431$	−29.2156	+	16.8676i	−1.40726	+	0.812485i	−0.995124	−	0.0986352i	$-0.968552\pi$
$431$	−29.2156	+	16.8676i	−1.40726	+	0.812485i	−0.412141	+	0.911120i	$0.635219\pi$
$432$	−4.67130	−	2.27572i	−0.224748	−	0.109491i
$433$	−7.29213			−0.350437			−0.175219	−	0.984530i	$-0.556063\pi$
$433$	−7.29213			−0.350437			−0.175219	+	0.984530i	$0.556063\pi$
$434$	−2.63563	+	2.53689i	−0.126514	+	0.121775i
$435$	0.338620	−	0.447863i	0.0162356	−	0.0214734i
$436$	−6.30827	−	10.9262i	−0.302111	−	0.523272i
$437$		−	52.0941i		−	2.49200i
$438$	−8.32241	+	10.4037i	−0.397660	+	0.497108i
$439$			2.64782i			0.126374i	0.998002	+	0.0631868i	$0.0201264\pi$
$439$			2.64782i			0.126374i	−0.998002	+	0.0631868i	$0.979874\pi$
$440$	1.38946	−	2.56609i	0.0662397	−	0.122333i
$441$	−13.6375	−	15.9693i	−0.649406	−	0.760442i
$442$		−	3.52381i		−	0.167611i
$443$	−25.9087			−1.23096			−0.615480	−	0.788153i	$-0.711038\pi$
$443$	−25.9087			−1.23096			−0.615480	+	0.788153i	$0.711038\pi$
$444$	−0.610765	+	4.01103i	−0.0289856	+	0.190355i
$445$	5.31832	+	2.87970i	0.252112	+	0.136511i
$446$	−1.58167	−	2.73954i	−0.0748943	−	0.129721i
$447$	12.9751	+	10.3794i	0.613701	+	0.490929i
$448$	1.83478	+	1.90619i	0.0866853	+	0.0900592i
$449$		−	11.3781i		−	0.536965i	−0.963285	−	0.268482i	$-0.913478\pi$
$449$		−	11.3781i		−	0.536965i	0.963285	−	0.268482i	$-0.0865221\pi$
$450$	10.4545	−	10.7565i	0.492832	−	0.507067i
$451$	−7.16321	+	4.13568i	−0.337302	+	0.194742i
$452$	6.02741	−	10.4398i	0.283506	−	0.491046i
$453$	29.7352	+	4.52781i	1.39708	+	0.212735i
$454$	8.30806	+	4.79666i	0.389916	+	0.225118i
$455$	9.57539	+	34.5929i	0.448901	+	1.62174i
$456$	2.06663	−	13.5720i	0.0967789	−	0.635569i
$457$		−	11.4929i		−	0.537617i	−0.963194	−	0.268808i	$-0.913370\pi$
$457$		−	11.4929i		−	0.537617i	0.963194	−	0.268808i	$-0.0866298\pi$
$458$	3.11351	−	1.79758i	0.145485	−	0.0839956i
$459$	−3.01050	+	0.211888i	−0.140518	+	0.00989010i
$460$	−12.5219	+	7.69325i	−0.583838	+	0.358700i
$461$	−0.576578	−	0.998663i	−0.0268539	−	0.0465124i	0.852286	−	0.523076i	$-0.175216\pi$
$461$	−0.576578	−	0.998663i	−0.0268539	−	0.0465124i	−0.879140	+	0.476564i	$0.841882\pi$
$462$	4.88390	−	3.45140i	0.227220	−	0.160574i
$463$	15.2816	+	8.82285i	0.710197	+	0.410033i	0.811134	−	0.584860i	$-0.198851\pi$
$463$	15.2816	+	8.82285i	0.710197	+	0.410033i	−0.100937	+	0.994893i	$0.532184\pi$
$464$	−0.125548	+	0.0724850i	−0.00582841	+	0.00336503i
$465$	−2.08445	−	4.93271i	−0.0966641	−	0.228749i
$466$	−2.91309	+	5.04563i	−0.134946	+	0.233734i
$467$	−16.2441	−	9.37851i	−0.751685	−	0.433986i	0.0746173	−	0.997212i	$-0.476226\pi$
$467$	−16.2441	−	9.37851i	−0.751685	−	0.433986i	−0.826302	+	0.563227i	$0.809560\pi$
$468$	3.99655	+	17.7572i	0.184741	+	0.820827i
$469$	25.1564	−	24.2139i	1.16161	−	1.11810i
$470$	12.1065	−	0.330937i	0.558429	−	0.0152650i
$471$	−2.14155	−	5.48090i	−0.0986772	−	0.252547i
$472$	−3.08716			−0.142098
$473$	−15.1765			−0.697817
$474$	−4.47041	−	11.4412i	−0.205333	−	0.525513i
$475$	35.3525	+	17.9108i	1.62208	+	0.821803i
$476$	1.47644	+	0.425974i	0.0676726	+	0.0195245i
$477$	−24.0045	−	7.48391i	−1.09909	−	0.342665i
$478$	−19.9340	−	11.5089i	−0.911759	−	0.526404i
$479$	−0.0620969	+	0.107555i	−0.00283728	+	0.00491432i	−0.867441	−	0.497541i	$-0.834236\pi$
$479$	−0.0620969	+	0.107555i	−0.00283728	+	0.00491432i	0.864603	+	0.502455i	$0.167570\pi$
$480$	−3.56753	+	1.50756i	−0.162835	+	0.0688103i
$481$	12.3080	−	7.10601i	0.561196	−	0.324006i
$482$	−5.92882	−	3.42300i	−0.270050	−	0.155914i
$483$	−29.9924	+	2.75507i	−1.36470	+	0.125360i
$484$	−4.64846	−	8.05137i	−0.211294	−	0.365971i
$485$	21.9493	−	13.4853i	0.996668	−	0.612335i
$486$	14.9302	−	4.48212i	0.677247	−	0.203313i
$487$	−22.4789	+	12.9782i	−1.01862	+	0.588099i	−0.913703	−	0.406382i	$-0.866790\pi$
$487$	−22.4789	+	12.9782i	−1.01862	+	0.588099i	−0.104914	+	0.994481i	$0.533457\pi$
$488$			2.12053i			0.0959918i
$489$	−1.46498	+	9.62083i	−0.0662485	+	0.435069i
$490$	−15.6516	−	0.169750i	−0.707065	−	0.00766854i
$491$	17.4877	+	10.0965i	0.789210	+	0.455651i	0.839684	−	0.543075i	$-0.182740\pi$
$491$	17.4877	+	10.0965i	0.789210	+	0.455651i	−0.0504742	+	0.998725i	$0.516073\pi$
$492$	10.8528	+	1.65257i	0.489283	+	0.0745038i
$493$	−0.0420996	+	0.0729186i	−0.00189607	+	0.00328409i
$494$	−41.6463	+	24.0445i	−1.87375	+	1.08181i
$495$	2.15489	+	8.48499i	0.0968549	+	0.381372i
$496$			1.38267i			0.0620836i
$497$	−19.7376	+	18.9982i	−0.885355	+	0.852186i
$498$	−6.76224	−	5.40944i	−0.303023	−	0.242403i
$499$	3.80999	+	6.59910i	0.170559	+	0.295416i	0.938615	−	0.344966i	$-0.112109\pi$
$499$	3.80999	+	6.59910i	0.170559	+	0.295416i	−0.768057	+	0.640382i	$0.778776\pi$
$500$	−0.915610	−	11.1428i	−0.0409473	−	0.498320i
$501$	1.67177	−	10.9789i	0.0746891	−	0.490500i
$502$	−12.2160			−0.545228
$503$		−	20.5824i		−	0.917723i	−0.888508	−	0.458861i	$-0.848257\pi$
$503$		−	20.5824i		−	0.917723i	0.888508	−	0.458861i	$-0.151743\pi$
$504$	−7.92320	−	0.472056i	−0.352928	−	0.0210271i
$505$	28.2229	+	15.2818i	1.25590	+	0.680032i
$506$		−	8.57717i		−	0.381302i
$507$	25.7616	−	32.2041i	1.14411	−	1.43023i
$508$			14.7512i			0.654480i
$509$	1.28951	+	2.23350i	0.0571567	+	0.0989983i	0.893188	−	0.449683i	$-0.148463\pi$
$509$	1.28951	+	2.23350i	0.0571567	+	0.0989983i	−0.836031	+	0.548682i	$0.815130\pi$
$510$	−1.35664	+	1.79431i	−0.0600729	+	0.0794532i
$511$	−5.64146	+	19.5535i	−0.249564	+	0.864996i
$512$	1.00000			0.0441942
$513$	23.0461	+	34.1338i	1.01751	+	1.50704i
$514$	−22.8388	+	13.1860i	−1.00738	+	0.581609i
$515$	1.47083	−	0.903655i	0.0648127	−	0.0398198i
$516$	15.7291	+	12.5825i	0.692436	+	0.553913i
$517$	−3.53412	+	6.12128i	−0.155430	+	0.269213i
$518$	1.48950	+	6.01592i	0.0654450	+	0.264324i
$519$	12.9490	−	5.05955i	0.568398	−	0.222089i
$520$	11.9299	+	6.45968i	0.523162	+	0.283276i
$521$	−16.7954	−	29.0904i	−0.735818	−	1.27447i	−0.954363	−	0.298648i	$-0.903464\pi$
$521$	−16.7954	−	29.0904i	−0.735818	−	1.27447i	0.218545	−	0.975827i	$-0.429869\pi$
$522$	0.129447	−	0.415199i	0.00566575	−	0.0181728i
$523$	−1.28600	+	2.22742i	−0.0562330	+	0.0973984i	−0.892772	−	0.450510i	$-0.851242\pi$
$523$	−1.28600	+	2.22742i	−0.0562330	+	0.0973984i	0.836539	+	0.547908i	$0.184576\pi$
$524$	7.84610	+	13.5898i	0.342758	+	0.593675i
$525$	8.44221	−	21.3009i	0.368448	−	0.929648i
$526$	−10.3480	+	17.9233i	−0.451196	+	0.781495i
$527$	0.401529	+	0.695469i	0.0174909	+	0.0302951i
$528$	0.340266	−	2.23460i	0.0148082	−	0.0972487i
$529$	−10.0985	+	17.4911i	−0.439064	+	0.760482i
$530$	−15.9683	+	9.81064i	−0.693619	+	0.426147i
$531$	6.80814	−	6.27885i	0.295448	−	0.272479i
$532$	−5.04000	−	20.3559i	−0.218512	−	0.882542i
$533$	−19.2271	−	33.3023i	−0.832817	−	1.44248i
$534$	4.63130	+	0.705215i	0.200416	+	0.0305176i
$535$	−33.8452	−	18.3261i	−1.46325	−	0.792307i
$536$		−	13.1972i		−	0.570031i
$537$	−22.3496	−	17.8785i	−0.964456	−	0.771515i
$538$	−4.69521	−	8.13233i	−0.202425	−	0.350610i
$539$	4.86618	−	7.73118i	0.209601	−	0.333006i
$540$	4.80135	−	10.5805i	0.206617	−	0.455312i
$541$	−15.6121	+	27.0410i	−0.671218	+	1.16258i	0.306341	+	0.951922i	$0.400895\pi$
$541$	−15.6121	+	27.0410i	−0.671218	+	1.16258i	−0.977559	+	0.210662i	$0.932438\pi$
$542$	−2.94143	−	1.69824i	−0.126345	−	0.0729455i
$543$	11.0448	−	4.31552i	0.473978	−	0.185197i
$544$	0.502991	−	0.290402i	0.0215656	−	0.0124509i
$545$	24.0373	−	14.7681i	1.02964	−	0.632594i
$546$	16.0458	+	22.7056i	0.686696	+	0.971710i
$547$	18.7975	−	10.8527i	0.803721	−	0.464029i	−0.0410494	−	0.999157i	$-0.513070\pi$
$547$	18.7975	−	10.8527i	0.803721	−	0.464029i	0.844771	+	0.535128i	$0.179737\pi$
$548$	−4.42929	+	7.67175i	−0.189210	+	0.327721i
$549$	−4.31286	−	4.67642i	−0.184069	−	0.199585i
$550$	5.82070	+	2.94897i	0.248195	+	0.125744i
$551$	1.14905			0.0489513
$552$	−7.11112	+	8.88948i	−0.302669	+	0.378361i
$553$	−13.0121	−	13.5186i	−0.553332	−	0.574869i
$554$	18.1450	+	10.4760i	0.770906	+	0.445083i
$555$	−9.00290	−	1.12012i	−0.382152	−	0.0475465i
$556$	−1.39913	−	0.807790i	−0.0593365	−	0.0342579i
$557$	−6.54619	−	11.3383i	−0.277371	−	0.480421i	0.693360	−	0.720592i	$-0.256130\pi$
$557$	−6.54619	−	11.3383i	−0.277371	−	0.480421i	−0.970731	+	0.240171i	$0.922796\pi$
$558$	−2.81216	−	3.04921i	−0.119048	−	0.129083i
$559$		−	70.5567i		−	2.98423i
$560$	−4.14868	+	4.21764i	−0.175314	+	0.178228i
$561$	−0.477783	−	1.22280i	−0.0201720	−	0.0516266i
$562$	0.919808	−	0.531051i	0.0387998	−	0.0224011i
$563$		−	5.73737i		−	0.241801i	−0.992665	−	0.120901i	$-0.961422\pi$
$563$		−	5.73737i		−	0.241801i	0.992665	−	0.120901i	$-0.0385783\pi$
$564$	8.73781	−	3.41411i	0.367928	−	0.143760i
$565$	23.7036	+	12.8348i	0.997219	+	0.539963i
$566$	20.9648			0.881214
$567$	18.4332	−	15.0737i	0.774123	−	0.633035i
$568$			10.3545i			0.434464i
$569$		−	42.6276i		−	1.78704i	−0.449021	−	0.893521i	$-0.648227\pi$
$569$		−	42.6276i		−	1.78704i	0.449021	−	0.893521i	$-0.351773\pi$
$570$	30.4629	+	3.79013i	1.27595	+	0.158751i
$571$	−33.8548			−1.41678			−0.708390	−	0.705821i	$-0.750578\pi$
$571$	−33.8548			−1.41678			−0.708390	+	0.705821i	$0.750578\pi$
$572$	−6.85696	+	3.95887i	−0.286704	+	0.165529i
$573$	−13.6600	+	5.33736i	−0.570656	+	0.222971i
$574$	16.2776	−	4.03022i	0.679412	−	0.168218i
$575$	−17.9613	−	27.5194i	−0.749039	−	1.14764i
$576$	−2.20531	+	2.03386i	−0.0918880	+	0.0847443i
$577$	6.51191	+	11.2790i	0.271095	+	0.469549i	0.969142	−	0.246502i	$-0.0792811\pi$
$577$	6.51191	+	11.2790i	0.271095	+	0.469549i	−0.698048	+	0.716051i	$0.745948\pi$
$578$	−8.33133	+	14.4303i	−0.346538	+	0.600221i
$579$	3.66319	−	1.43131i	0.152237	−	0.0594833i
$580$	−0.169692	−	0.276199i	−0.00704608	−	0.0114686i
$581$	−12.7095	−	3.66686i	−0.527277	−	0.152127i
$582$	12.4649	−	15.5821i	0.516686	−	0.645900i
$583$		−	10.9378i		−	0.452999i
$584$	3.84599	+	6.66144i	0.159148	+	0.275653i
$585$	−39.4473	+	10.0182i	−1.63095	+	0.414202i
$586$	−19.5706	−	11.2991i	−0.808452	−	0.466760i
$587$	33.7149	−	19.4653i	1.39156	−	0.803419i	0.398075	−	0.917353i	$-0.369678\pi$
$587$	33.7149	−	19.4653i	1.39156	−	0.803419i	0.993488	+	0.113934i	$0.0363451\pi$
$588$	−11.4531	+	3.97826i	−0.472318	+	0.164061i
$589$	5.47961	−	9.49096i	0.225783	−	0.391068i
$590$	−0.188630	−	6.90051i	−0.00776577	−	0.284090i
$591$	8.20368	+	20.9959i	0.337454	+	0.863654i
$592$	2.02863	+	1.17123i	0.0833763	+	0.0481373i
$593$	22.4867	+	12.9827i	0.923419	+	0.533136i	0.884724	−	0.466115i	$-0.154347\pi$
$593$	22.4867	+	12.9827i	0.923419	+	0.533136i	0.0386950	+	0.999251i	$0.487680\pi$
$594$	3.79449	+	5.62005i	0.155690	+	0.230594i
$595$	−0.861939	+	3.32622i	−0.0353361	+	0.136362i
$596$	8.30790	−	4.79657i	0.340305	−	0.196475i
$597$	−4.32437	−	3.45927i	−0.176985	−	0.141579i
$598$	39.8759			1.63065
$599$		−	25.5862i		−	1.04542i	−0.852509	−	0.522712i	$-0.824920\pi$
$599$		−	25.5862i		−	1.04542i	0.852509	−	0.522712i	$-0.175080\pi$
$600$	−3.58773	−	7.88215i	−0.146468	−	0.321787i
$601$	29.1769	−	16.8453i	1.19015	−	0.687133i	0.231809	−	0.972761i	$-0.425536\pi$
$601$	29.1769	−	16.8453i	1.19015	−	0.687133i	0.958340	+	0.285629i	$0.0922024\pi$
$602$	29.5625	+	8.52920i	1.20488	+	0.347624i
$603$	26.8413	+	29.1039i	1.09306	+	1.18520i
$604$	8.68275	−	15.0390i	0.353296	−	0.611927i
$605$	17.7127	−	10.8823i	0.720122	−	0.442430i
$606$	24.5771	+	3.74239i	0.998377	+	0.152024i
$607$	−13.9082	−	24.0897i	−0.564517	−	0.977771i	−0.997094	−	0.0761748i	$-0.975729\pi$
$607$	−13.9082	−	24.0897i	−0.564517	−	0.977771i	0.432578	−	0.901597i	$-0.357604\pi$
$608$	−6.86424	−	3.96307i	−0.278382	−	0.160724i
$609$	−0.0607694	−	0.661551i	−0.00246250	−	0.0268074i
$610$	−4.73987	+	0.129567i	−0.191912	+	0.00524603i
$611$	−28.4582	−	16.4304i	−1.15130	−	0.664702i
$612$	−0.518614	+	1.66344i	−0.0209637	+	0.0672406i
$613$	24.9598	−	14.4106i	1.00812	−	0.582037i	0.0974774	−	0.995238i	$-0.468923\pi$
$613$	24.9598	−	14.4106i	1.00812	−	0.582037i	0.910640	+	0.413201i	$0.135589\pi$
$614$	−29.2086			−1.17876
$615$	−3.03076	+	24.3596i	−0.122212	+	0.982273i
$616$	−0.829824	−	3.35156i	−0.0334346	−	0.135038i
$617$	−5.31220	+	9.20099i	−0.213861	+	0.370418i	−0.952920	−	0.303223i	$-0.901937\pi$
$617$	−5.31220	+	9.20099i	−0.213861	+	0.370418i	0.739059	+	0.673641i	$0.235271\pi$
$618$	0.835278	−	1.04416i	0.0335998	−	0.0420025i
$619$	29.9975	+	17.3190i	1.20570	+	0.696111i	0.961817	−	0.273694i	$-0.0882455\pi$
$619$	29.9975	+	17.3190i	1.20570	+	0.696111i	0.243883	+	0.969805i	$0.421579\pi$
$620$	−3.09058	+	0.0844830i	−0.124121	+	0.00339292i
$621$	−2.39775	−	34.0671i	−0.0962184	−	1.36707i
$622$	−13.0106			−0.521678
$623$	6.94623	−	1.71984i	0.278295	−	0.0689040i
$624$	10.3888	+	1.58192i	0.415886	+	0.0633275i
$625$	24.8508	−	2.72744i	0.994031	−	0.109098i
$626$	−7.25446			−0.289947
$627$	−11.1916	+	13.9904i	−0.446948	+	0.558721i
$628$	−3.39738			−0.135570
$629$	1.36051			0.0542471
$630$	0.571036	−	17.7391i	0.0227506	−	0.706741i
$631$	−17.6726			−0.703534			−0.351767	−	0.936088i	$-0.614419\pi$
$631$	−17.6726			−0.703534			−0.351767	+	0.936088i	$0.614419\pi$
$632$	−7.09192			−0.282102
$633$	−17.3049	−	2.63505i	−0.687810	−	0.104734i
$634$	28.5206			1.13270
$635$	−32.9725	+	0.901323i	−1.30847	+	0.0357679i
$636$	−9.06829	+	11.3361i	−0.359581	+	0.449506i
$637$	35.9428	+	22.6232i	1.42411	+	0.896364i
$638$	0.189189			0.00749006
$639$	−21.0596	−	22.8349i	−0.833105	−	0.903333i
$640$	0.0611015	+	2.23523i	0.00241525	+	0.0883553i
$641$	11.8920	+	6.86584i	0.469705	+	0.271185i	0.716116	−	0.697981i	$-0.245918\pi$
$641$	11.8920	+	6.86584i	0.469705	+	0.271185i	−0.246411	+	0.969165i	$0.579251\pi$
$642$	−29.4731	−	4.48791i	−1.16321	−	0.177124i
$643$	7.15031	−	12.3847i	0.281981	−	0.488405i	−0.689892	−	0.723912i	$-0.742342\pi$
$643$	7.15031	−	12.3847i	0.281981	−	0.488405i	0.971872	+	0.235508i	$0.0756753\pi$
$644$	−4.82037	+	16.7076i	−0.189949	+	0.658370i
$645$	−27.1637	+	35.9271i	−1.06957	+	1.41463i
$646$	−4.60353			−0.181124
$647$	−18.0964	+	10.4480i	−0.711443	+	0.410752i	−0.811595	−	0.584220i	$-0.801400\pi$
$647$	−18.0964	+	10.4480i	−0.711443	+	0.410752i	0.100152	+	0.994972i	$0.468067\pi$
$648$	0.726797	−	8.97061i	0.0285513	−	0.352399i
$649$	3.48904	+	2.01440i	0.136957	+	0.0790721i
$650$	−13.7100	+	27.0608i	−0.537749	+	1.06141i
$651$	−5.75408	−	2.65286i	−0.225520	−	0.103974i
$652$	4.86586	+	2.80931i	0.190562	+	0.110021i
$653$	−0.641461	−	1.11104i	−0.0251023	−	0.0434785i	0.853201	−	0.521582i	$-0.174658\pi$
$653$	−0.641461	−	1.11104i	−0.0251023	−	0.0434785i	−0.878304	+	0.478103i	$0.841324\pi$
$654$	13.6506	−	17.0644i	0.533781	−	0.667269i
$655$	−29.8971	+	18.3682i	−1.16817	+	0.717706i
$656$	3.16905	−	5.48896i	0.123731	−	0.214308i
$657$	−22.0301	−	6.86835i	−0.859475	−	0.267960i
$658$	10.3243	−	9.93753i	0.402484	−	0.387405i
$659$	−4.33134	+	2.50070i	−0.168725	+	0.0974136i	−0.581985	−	0.813200i	$-0.697724\pi$
$659$	−4.33134	+	2.50070i	−0.168725	+	0.0974136i	0.413259	+	0.910613i	$0.364390\pi$
$660$	5.01565	+	0.624036i	0.195234	+	0.0242906i
$661$			10.0060i			0.389190i	0.980884	+	0.194595i	$0.0623393\pi$
$661$			10.0060i			0.389190i	−0.980884	+	0.194595i	$0.937661\pi$
$662$	24.7022			0.960077
$663$	5.68488	−	2.22125i	0.220782	−	0.0862660i
$664$	−4.32983	+	2.49983i	−0.168030	+	0.0970123i
$665$	45.1923	−	12.5094i	1.75248	−	0.485092i
$666$	−6.85589	+	1.54303i	−0.265660	+	0.0597912i
$667$	−0.825155	−	0.476403i	−0.0319501	−	0.0184464i
$668$	−5.55272	−	3.20586i	−0.214841	−	0.124039i
$669$	3.42261	−	4.27854i	0.132326	−	0.165418i
$670$	29.4988	−	0.806367i	1.13964	−	0.0311527i
$671$	1.38367	−	2.39658i	0.0534158	−	0.0925189i
$672$	−1.91866	+	4.16158i	−0.0740138	+	0.160536i
$673$	−2.63843	+	1.52330i	−0.101704	+	0.0587189i	−0.549989	−	0.835172i	$-0.685368\pi$
$673$	−2.63843	+	1.52330i	−0.101704	+	0.0587189i	0.448285	+	0.893891i	$0.352035\pi$
$674$	6.13756	+	3.54352i	0.236410	+	0.136491i
$675$	23.9433	+	10.0856i	0.921577	+	0.388197i
$676$	−11.9051	−	20.6202i	−0.457887	−	0.793083i
$677$		−	8.97285i		−	0.344855i	−0.985022	−	0.172427i	$-0.944839\pi$
$677$		−	8.97285i		−	0.344855i	0.985022	−	0.172427i	$-0.0551610\pi$
$678$	20.6416	+	3.14313i	0.792737	+	0.120711i
$679$	8.44949	−	29.2862i	0.324262	−	1.12390i
$680$	0.679850	+	1.10656i	0.0260710	+	0.0424346i
$681$	−2.50132	+	16.4268i	−0.0958509	+	0.629475i
$682$	0.902204	−	1.56266i	0.0345472	−	0.0598375i
$683$	−0.499734	−	0.865564i	−0.0191218	−	0.0331199i	0.856306	−	0.516469i	$-0.172754\pi$
$683$	−0.499734	−	0.865564i	−0.0191218	−	0.0331199i	−0.875428	+	0.483349i	$0.839420\pi$
$684$	23.1981	−	5.22112i	0.887003	−	0.199635i
$685$	−17.4188	−	9.43173i	−0.665537	−	0.360368i
$686$	−13.8238	+	12.3249i	−0.527795	+	0.470566i
$687$	4.86260	+	3.88983i	0.185520	+	0.148406i
$688$	10.0713	−	5.81466i	0.383965	−	0.221682i
$689$	50.8508			1.93726
$690$	−20.3046	−	15.3519i	−0.772981	−	0.584435i
$691$		−	17.0779i		−	0.649673i	−0.945770	−	0.324836i	$-0.894691\pi$
$691$		−	17.0779i		−	0.649673i	0.945770	−	0.324836i	$-0.105309\pi$
$692$		−	8.02653i		−	0.305123i
$693$	8.64663	+	5.70348i	0.328458	+	0.216657i
$694$	7.75645			0.294431
$695$	1.72011	−	3.17675i	0.0652475	−	0.120501i
$696$	−0.196078	−	0.156852i	−0.00743230	−	0.00594545i
$697$		−	3.68120i		−	0.139435i
$698$	−8.89557	+	5.13586i	−0.336702	+	0.194395i
$699$	−9.97626	−	1.51910i	−0.377337	−	0.0574575i
$700$	−9.68089	−	9.01556i	−0.365903	−	0.340756i
$701$			10.9031i			0.411803i	0.978573	+	0.205902i	$0.0660127\pi$
$701$			10.9031i			0.411803i	−0.978573	+	0.205902i	$0.933987\pi$
$702$	−26.1280	+	17.6408i	−0.986139	+	0.665811i
$703$	−9.28334	−	16.0792i	−0.350128	−	0.606439i
$704$	−1.13018	−	0.652510i	−0.0425953	−	0.0245924i
$705$	8.16522	+	19.3224i	0.307520	+	0.727725i
$706$	−18.2499	−	10.5366i	−0.686845	−	0.396550i
$707$	36.8618	−	9.12675i	1.38633	−	0.343247i
$708$	−1.94600	−	4.98043i	−0.0731350	−	0.187176i
$709$	−46.5248			−1.74728			−0.873638	−	0.486577i	$-0.838245\pi$
$709$	−46.5248			−1.74728			−0.873638	+	0.486577i	$0.838245\pi$
$710$	−23.1447	+	0.632674i	−0.868604	+	0.0237438i
$711$	15.6399	−	14.4240i	0.586542	−	0.540943i
$712$	1.35235	−	2.34234i	0.0506816	−	0.0877830i
$713$	−7.87000	+	4.54375i	−0.294734	+	0.170165i
$714$	0.243465	+	2.65042i	0.00911144	+	0.0991894i
$715$	−9.26796	−	15.0850i	−0.346602	−	0.564147i
$716$	−14.3104	+	8.26209i	−0.534803	+	0.308769i
$717$	6.00156	−	39.4136i	0.224132	−	1.47193i
$718$	15.0004	+	8.66050i	0.559811	+	0.323207i
$719$	−8.48584	+	14.6979i	−0.316468	+	0.548139i	−0.979749	−	0.200232i	$-0.935830\pi$
$719$	−8.48584	+	14.6979i	−0.316468	+	0.548139i	0.663280	+	0.748371i	$0.269164\pi$
$720$	−4.68091	−	4.80511i	−0.174447	−	0.179076i
$721$	0.566204	−	1.96248i	0.0210865	−	0.0730867i
$722$	21.9119	+	37.9525i	0.815475	+	1.41244i
$723$	1.78500	−	11.7225i	0.0663849	−	0.435965i
$724$		−	6.84621i		−	0.254437i
$725$	0.607002	−	0.396177i	0.0225435	−	0.0147137i
$726$	10.0589	−	12.5744i	0.373321	−	0.466681i
$727$	19.9409	+	34.5386i	0.739567	+	1.28097i	0.952691	+	0.303942i	$0.0983029\pi$
$727$	19.9409	+	34.5386i	0.739567	+	1.28097i	−0.213124	+	0.977025i	$0.568364\pi$
$728$	15.5816	−	3.85791i	0.577494	−	0.142984i
$729$	16.6422	+	21.2612i	0.616377	+	0.787451i
$730$	−14.6549	+	9.00370i	−0.542402	+	0.333242i
$731$	3.37718	−	5.84945i	0.124910	−	0.216350i
$732$	−3.42099	+	1.33668i	−0.126444	+	0.0494051i
$733$	−7.10271	−	12.3023i	−0.262345	−	0.454394i	0.704520	−	0.709684i	$-0.251162\pi$
$733$	−7.10271	−	12.3023i	−0.262345	−	0.454394i	−0.966865	+	0.255290i	$0.917829\pi$
$734$	−3.49830	+	6.05923i	−0.129125	+	0.223650i
$735$	−9.59214	−	25.3573i	−0.353812	−	0.935317i
$736$	3.28622	+	5.69190i	0.121132	+	0.209806i
$737$	−8.61129	+	14.9152i	−0.317201	+	0.549408i
$738$	4.17505	+	18.5503i	0.153686	+	0.682846i
$739$	15.4922	+	26.8333i	0.569891	+	0.987080i	0.996576	+	0.0826801i	$0.0263480\pi$
$739$	15.4922	+	26.8333i	0.569891	+	0.987080i	−0.426685	+	0.904400i	$0.640319\pi$
$740$	−2.49402	+	4.60603i	−0.0916821	+	0.169321i
$741$	−65.0422	−	52.0304i	−2.38938	−	1.91138i
$742$	−6.14707	+	21.3059i	−0.225666	+	0.782166i
$743$	25.1293	−	43.5252i	0.921904	−	1.59678i	0.125437	−	0.992102i	$-0.459967\pi$
$743$	25.1293	−	43.5252i	0.921904	−	1.59678i	0.796467	−	0.604682i	$-0.206700\pi$
$744$	−2.23062	+	0.871568i	−0.0817786	+	0.0319532i
$745$	11.2291	+	18.2770i	0.411402	+	0.669618i
$746$	12.9529	−	7.47838i	0.474241	−	0.273803i
$747$	4.46432	−	14.3192i	0.163341	−	0.523912i
$748$	−0.757961			−0.0277138
$749$	−44.2051	+	10.9449i	−1.61522	+	0.399917i
$750$	17.3992	−	8.50101i	0.635330	−	0.310413i
$751$	−13.9963	−	24.2423i	−0.510732	−	0.884613i	−0.999923	−	0.0124365i	$-0.996041\pi$
$751$	−13.9963	−	24.2423i	−0.510732	−	0.884613i	0.489191	−	0.872177i	$-0.337292\pi$
$752$		−	5.41619i		−	0.197508i
$753$	−7.70040	−	19.7078i	−0.280618	−	0.718192i
$754$			0.879552i			0.0320314i
$755$	34.1461	+	18.4891i	1.24270	+	0.672886i
$756$	−4.23286	−	13.0799i	−0.153947	−	0.475710i
$757$		−	17.6703i		−	0.642238i	−0.947039	−	0.321119i	$-0.895941\pi$
$757$		−	17.6703i		−	0.642238i	0.947039	−	0.321119i	$-0.104059\pi$
$758$	1.81688			0.0659920
$759$	13.8373	−	5.40664i	0.502263	−	0.196249i
$760$	8.43897	−	15.5853i	0.306114	−	0.565339i
$761$	1.02863	+	1.78164i	0.0372879	+	0.0645846i	0.884067	−	0.467360i	$-0.154795\pi$
$761$	1.02863	+	1.78164i	0.0372879	+	0.0645846i	−0.846779	+	0.531945i	$0.821461\pi$
$762$	−23.7978	+	9.29848i	−0.862103	+	0.336848i
$763$	9.25325	−	32.0721i	0.334990	−	1.16109i
$764$			8.46726i			0.306335i
$765$	−3.74987	−	1.05758i	−0.135577	−	0.0382370i
$766$	−3.98546	+	2.30101i	−0.144000	+	0.0831387i
$767$	−9.36509	+	16.2208i	−0.338154	+	0.585700i
$768$	0.630353	+	1.61327i	0.0227459	+	0.0582140i
$769$	12.1169	+	6.99571i	0.436947	+	0.252272i	0.702302	−	0.711879i	$-0.252156\pi$
$769$	12.1169	+	6.99571i	0.436947	+	0.252272i	−0.265355	+	0.964151i	$0.585489\pi$
$770$	7.44081	−	2.05963i	0.268148	−	0.0742241i
$771$	−35.6691	−	28.5335i	−1.28459	−	1.02761i
$772$		−	2.27066i		−	0.0817227i
$773$	−36.5855	+	21.1226i	−1.31589	+	0.759728i	−0.983064	−	0.183261i	$-0.941335\pi$
$773$	−36.5855	+	21.1226i	−1.31589	+	0.759728i	−0.332824	+	0.942989i	$0.608001\pi$
$774$	−10.3841	+	33.3068i	−0.373249	+	1.19719i
$775$	−0.377678	−	6.90301i	−0.0135666	−	0.247963i
$776$	−5.76032	−	9.97717i	−0.206784	−	0.358160i
$777$	−8.76642	+	6.19513i	−0.314494	+	0.222249i
$778$	−14.8244	−	8.55885i	−0.531479	−	0.306850i
$779$	−43.5063	+	25.1184i	−1.55878	+	0.899959i
$780$	−2.90119	+	23.3181i	−0.103879	+	0.834923i
$781$	6.75640	−	11.7024i	0.241763	−	0.418746i
$782$	3.30588	+	1.90865i	0.118218	+	0.0682532i
$783$	0.751427	−	0.0528878i	0.0268538	−	0.00189006i
$784$	−0.267153	+	6.99490i	−0.00954118	+	0.249818i
$785$	−0.207585	−	7.59393i	−0.00740902	−	0.271039i
$786$	−16.9783	+	21.2243i	−0.605598	+	0.757046i
$787$	44.8213			1.59771			0.798854	−	0.601525i	$-0.205440\pi$
$787$	44.8213			1.59771			0.798854	+	0.601525i	$0.205440\pi$
$788$	13.0144			0.463620
$789$	−35.4382	−	5.39622i	−1.26163	−	0.192111i
$790$	−0.433327	−	15.8521i	−0.0154171	−	0.563993i
$791$	30.9592	−	7.66531i	1.10078	−	0.272547i
$792$	3.81952	−	0.859646i	0.135721	−	0.0305462i
$793$	11.1419	+	6.43276i	0.395659	+	0.228434i
$794$	7.42358	−	12.8580i	0.263453	−	0.456314i
$795$	−25.8929	−	19.5771i	−0.918327	−	0.694328i
$796$	−2.76888	+	1.59861i	−0.0981402	+	0.0566613i
$797$	33.4229	+	19.2967i	1.18390	+	0.683524i	0.956913	−	0.290374i	$-0.0937796\pi$
$797$	33.4229	+	19.2967i	1.18390	+	0.683524i	0.226986	+	0.973898i	$0.427113\pi$
$798$	29.6628	−	20.9623i	1.05005	−	0.742058i
$799$	−1.57287	−	2.72430i	−0.0556442	−	0.0963786i
$800$	−4.99253	+	0.273152i	−0.176513	+	0.00965739i
$801$	1.78165	+	7.91610i	0.0629515	+	0.279702i
$802$	−8.29051	+	4.78653i	−0.292748	+	0.169018i
$803$		−	10.0382i		−	0.354240i
$804$	21.2907	−	8.31887i	0.750864	−	0.293384i
$805$	−37.6398	−	9.75379i	−1.32663	−	0.343776i
$806$	7.26494	+	4.19441i	0.255896	+	0.147742i
$807$	10.1601	−	12.7009i	0.357651	−	0.447093i
$808$	7.17658	−	12.4302i	0.252471	−	0.437293i
$809$	12.0653	−	6.96590i	0.424193	−	0.244908i	−0.272677	−	0.962106i	$-0.587909\pi$
$809$	12.0653	−	6.96590i	0.424193	−	0.244908i	0.696870	+	0.717198i	$0.254576\pi$
$810$	20.0958	+	1.07644i	0.706095	+	0.0378223i
$811$			50.7243i			1.78117i	0.454815	+	0.890586i	$0.349705\pi$
$811$			50.7243i			1.78117i	−0.454815	+	0.890586i	$0.650295\pi$
$812$	−0.368523	−	0.106324i	−0.0129326	−	0.00373125i
$813$	0.885584	−	5.81583i	0.0310588	−	0.203970i
$814$	−1.52848	−	2.64741i	−0.0535732	−	0.0927915i
$815$	−5.98215	+	11.0480i	−0.209545	+	0.386994i
$816$	0.785560	+	0.628407i	0.0275001	+	0.0219986i
$817$	−92.1757			−3.22482
$818$			38.6251i			1.35049i
$819$	−26.5159	+	40.1988i	−0.926540	+	1.40466i
$820$	12.4627	+	6.74819i	0.435218	+	0.235657i
$821$			24.8097i			0.865863i	0.901427	+	0.432932i	$0.142521\pi$
$821$			24.8097i			0.865863i	−0.901427	+	0.432932i	$0.857479\pi$
$822$	−15.1687	−	2.30975i	−0.529067	−	0.0805618i
$823$		−	9.96359i		−	0.347309i	−0.984807	−	0.173654i	$-0.944442\pi$
$823$		−	9.96359i		−	0.347309i	0.984807	−	0.173654i	$-0.0555576\pi$
$824$	−0.386002	−	0.668575i	−0.0134470	−	0.0232909i
$825$	−1.08840	+	11.2493i	−0.0378933	+	0.391650i
$826$	−5.66426	−	5.88472i	−0.197085	−	0.204756i
$827$	−36.2819			−1.26165			−0.630823	−	0.775926i	$-0.717283\pi$
$827$	−36.2819			−1.26165			−0.630823	+	0.775926i	$0.717283\pi$
$828$	−18.8237	−	5.86869i	−0.654168	−	0.203951i
$829$	−16.8402	+	9.72267i	−0.584883	+	0.337682i	−0.763071	−	0.646314i	$-0.776310\pi$
$829$	−16.8402	+	9.72267i	−0.584883	+	0.337682i	0.178189	+	0.983996i	$0.442976\pi$
$830$	−5.85226	−	9.52544i	−0.203135	−	0.330633i
$831$	−5.46295	+	35.8764i	−0.189508	+	1.24454i
$832$	3.03357	−	5.25429i	0.105170	−	0.182160i
$833$	1.89696	+	3.59595i	0.0657257	+	0.124592i
$834$	0.421240	−	2.76638i	0.0145863	−	0.0957919i
$835$	6.82657	−	12.6075i	0.236243	−	0.436301i
$836$	5.17189	+	8.95797i	0.178874	+	0.309818i
$837$	3.14657	−	6.45886i	0.108761	−	0.223251i
$838$	−6.88512	+	11.9254i	−0.237843	+	0.411956i
$839$	21.1582	+	36.6471i	0.730463	+	1.26520i	0.956686	+	0.291123i	$0.0940288\pi$
$839$	21.1582	+	36.6471i	0.730463	+	1.26520i	−0.226223	+	0.974075i	$0.572638\pi$
$840$	−9.41934	−	4.03436i	−0.324998	−	0.139199i
$841$	−14.4895	+	25.0965i	−0.499638	+	0.865398i
$842$	−9.44758	−	16.3637i	−0.325585	−	0.563930i
$843$	1.43654	+	1.14915i	0.0494769	+	0.0395790i
$844$	−5.05309	+	8.75221i	−0.173935	+	0.301263i
$845$	45.3634	−	27.8705i	1.56055	−	0.958774i
$846$	11.0158	+	11.9444i	0.378731	+	0.410657i
$847$	6.81857	−	23.6334i	0.234289	−	0.812052i
$848$	4.19068	+	7.25846i	0.143908	+	0.249257i
$849$	13.2152	+	33.8219i	0.453544	+	1.16076i
$850$	−2.43188	+	1.58723i	−0.0834126	+	0.0544417i
$851$			15.3957i			0.527757i
$852$	−16.7046	+	6.52697i	−0.572291	+	0.223610i
$853$	4.70765	+	8.15389i	0.161187	+	0.279184i	0.935295	−	0.353870i	$-0.115134\pi$
$853$	4.70765	+	8.15389i	0.161187	+	0.279184i	−0.774108	+	0.633054i	$0.781801\pi$
$854$	−4.04214	+	3.89070i	−0.138319	+	0.133137i
$855$	13.0879	+	51.5342i	0.447596	+	1.76243i
$856$	−8.60622	+	14.9064i	−0.294155	+	0.509491i
$857$	31.6377	+	18.2660i	1.08072	+	0.623956i	0.931092	−	0.364786i	$-0.118858\pi$
$857$	31.6377	+	18.2660i	1.08072	+	0.623956i	0.149632	+	0.988742i	$0.452191\pi$
$858$	−10.7090	−	8.56668i	−0.365601	−	0.292461i
$859$	−22.4507	+	12.9619i	−0.766007	+	0.442254i	−0.831448	−	0.555602i	$-0.812488\pi$
$859$	−22.4507	+	12.9619i	−0.766007	+	0.442254i	0.0654412	+	0.997856i	$0.479155\pi$
$860$	13.6125	+	22.1564i	0.464182	+	0.755527i
$861$	16.7624	+	23.7197i	0.571263	+	0.808366i
$862$	−29.2156	+	16.8676i	−0.995087	+	0.574513i
$863$	11.4281	−	19.7941i	0.389018	−	0.673800i	−0.603299	−	0.797515i	$-0.706148\pi$
$863$	11.4281	−	19.7941i	0.389018	−	0.673800i	0.992318	+	0.123715i	$0.0394809\pi$
$864$	−4.67130	−	2.27572i	−0.158921	−	0.0774216i
$865$	17.9412	−	0.490433i	0.610018	−	0.0166752i
$866$	−7.29213			−0.247797
$867$	−28.5317	−	4.34456i	−0.968988	−	0.147549i
$868$	−2.63563	+	2.53689i	−0.0894592	+	0.0861077i
$869$	8.01516	+	4.62755i	0.271896	+	0.156979i
$870$	0.338620	−	0.447863i	0.0114803	−	0.0151840i
$871$	−69.3418	−	40.0345i	−2.34956	−	1.35652i
$872$	−6.30827	−	10.9262i	−0.213625	−	0.370009i
$873$	32.9955	+	10.2871i	1.11673	+	0.348164i
$874$		−	52.0941i		−	1.76211i
$875$	19.5604	−	22.1899i	0.661261	−	0.750156i
$876$	−8.32241	+	10.4037i	−0.281188	+	0.351508i
$877$	−4.24658	+	2.45176i	−0.143397	+	0.0827901i	−0.569982	−	0.821657i	$-0.693050\pi$
$877$	−4.24658	+	2.45176i	−0.143397	+	0.0827901i	0.426585	+	0.904447i	$0.359716\pi$
$878$			2.64782i			0.0893596i
$879$	5.89215	−	38.6951i	0.198737	−	1.30515i
$880$	1.38946	−	2.56609i	0.0468386	−	0.0865028i
$881$	42.9169			1.44591			0.722953	−	0.690897i	$-0.242784\pi$
$881$	42.9169			1.44591			0.722953	+	0.690897i	$0.242784\pi$
$882$	−13.6375	−	15.9693i	−0.459199	−	0.537714i
$883$			39.4640i			1.32807i	0.747701	+	0.664035i	$0.231157\pi$
$883$			39.4640i			1.32807i	−0.747701	+	0.664035i	$0.768843\pi$
$884$		−	3.52381i		−	0.118519i
$885$	11.0135	−	4.65407i	0.370215	−	0.156445i
$886$	−25.9087			−0.870420
$887$	−24.0226	+	13.8694i	−0.806599	+	0.465690i	−0.845773	−	0.533542i	$-0.820861\pi$
$887$	−24.0226	+	13.8694i	−0.806599	+	0.465690i	0.0391745	+	0.999232i	$0.487527\pi$
$888$	−0.610765	+	4.01103i	−0.0204959	+	0.134601i
$889$	−28.1187	+	27.0653i	−0.943072	+	0.907741i
$890$	5.31832	+	2.87970i	0.178270	+	0.0965279i
$891$	−6.67482	+	9.66416i	−0.223615	+	0.323762i
$892$	−1.58167	−	2.73954i	−0.0529583	−	0.0917264i
$893$	−21.4648	+	37.1780i	−0.718291	+	1.24412i
$894$	12.9751	+	10.3794i	0.433952	+	0.347139i
$895$	−19.3421	−	31.4822i	−0.646535	−	1.05233i
$896$	1.83478	+	1.90619i	0.0612958	+	0.0636815i
$897$	25.1359	+	64.3307i	0.839262	+	2.14794i
$898$		−	11.3781i		−	0.379691i
$899$	−0.100223	−	0.173591i	−0.00334261	−	0.00578957i
$900$	10.4545	−	10.7565i	0.348485	−	0.358551i
$901$	4.21574	+	2.43396i	0.140447	+	0.0810870i
$902$	−7.16321	+	4.13568i	−0.238509	+	0.137703i
$903$	4.87485	+	53.0689i	0.162225	+	1.76602i
$904$	6.02741	−	10.4398i	0.200469	−	0.347222i
$905$	15.3029	−	0.418313i	0.508685	−	0.0139052i
$906$	29.7352	+	4.52781i	0.987885	+	0.150426i
$907$	−38.6625	−	22.3218i	−1.28377	−	0.741183i	−0.306231	−	0.951957i	$-0.599068\pi$
$907$	−38.6625	−	22.3218i	−1.28377	−	0.741183i	−0.977535	+	0.210774i	$0.932401\pi$
$908$	8.30806	+	4.79666i	0.275713	+	0.159183i
$909$	9.45474	+	42.0087i	0.313594	+	1.39334i
$910$	9.57539	+	34.5929i	0.317421	+	1.14674i
$911$	−14.1534	+	8.17148i	−0.468924	+	0.270733i	−0.715789	−	0.698317i	$-0.753933\pi$
$911$	−14.1534	+	8.17148i	−0.468924	+	0.270733i	0.246865	+	0.969050i	$0.420599\pi$
$912$	2.06663	−	13.5720i	0.0684330	−	0.449415i
$913$	6.52466			0.215935
$914$		−	11.4929i		−	0.380152i
$915$	−3.19682	−	7.56504i	−0.105684	−	0.250093i
$916$	3.11351	−	1.79758i	0.102873	−	0.0593939i
$917$	−11.5090	+	39.8906i	−0.380061	+	1.31730i
$918$	−3.01050	+	0.211888i	−0.0993612	+	0.00699336i
$919$	19.1208	−	33.1181i	0.630736	−	1.09247i	−0.356666	−	0.934232i	$-0.616087\pi$
$919$	19.1208	−	33.1181i	0.630736	−	1.09247i	0.987402	−	0.158234i	$-0.0505801\pi$
$920$	−12.5219	+	7.69325i	−0.412836	+	0.253639i
$921$	−18.4117	−	47.1215i	−0.606687	−	1.55271i
$922$	−0.576578	−	0.998663i	−0.0189886	−	0.0328892i
$923$	54.4054	+	31.4110i	1.79078	+	1.03391i
$924$	4.88390	−	3.45140i	0.160669	−	0.113543i
$925$	−10.4479	−	5.29329i	−0.343526	−	0.174042i
$926$	15.2816	+	8.82285i	0.502185	+	0.289937i
$927$	2.21104	+	0.689340i	0.0726202	+	0.0226409i
$928$	−0.125548	+	0.0724850i	−0.00412131	+	0.00237944i
$929$	−2.59756			−0.0852231			−0.0426115	−	0.999092i	$-0.513568\pi$
$929$	−2.59756			−0.0852231			−0.0426115	+	0.999092i	$0.513568\pi$
$930$	−2.08445	−	4.93271i	−0.0683518	−	0.161750i
$931$	29.5551	−	46.9559i	0.968629	−	1.53892i
$932$	−2.91309	+	5.04563i	−0.0954215	+	0.165275i
$933$	−8.20128	−	20.9897i	−0.268498	−	0.687172i
$934$	−16.2441	−	9.37851i	−0.531522	−	0.306874i
$935$	−0.0463125	−	1.69422i	−0.00151458	−	0.0554069i
$936$	3.99655	+	17.7572i	0.130631	+	0.580413i
$937$	55.8623			1.82494			0.912472	−	0.409140i	$-0.134171\pi$
$937$	55.8623			1.82494			0.912472	+	0.409140i	$0.134171\pi$
$938$	25.1564	−	24.2139i	0.821385	−	0.790613i
$939$	−4.57287	−	11.7034i	−0.149230	−	0.381928i
$940$	12.1065	−	0.330937i	0.394869	−	0.0107940i
$941$	−21.4380			−0.698860			−0.349430	−	0.936962i	$-0.613625\pi$
$941$	−21.4380			−0.698860			−0.349430	+	0.936962i	$0.613625\pi$
$942$	−2.14155	−	5.48090i	−0.0697753	−	0.178577i
$943$	41.6568			1.35653
$944$	−3.08716			−0.100478
$945$	28.9779	−	10.2606i	0.942652	−	0.333778i
$946$	−15.1765			−0.493431
$947$	20.5459			0.667652			0.333826	−	0.942635i	$-0.391660\pi$
$947$	20.5459			0.667652			0.333826	+	0.942635i	$0.391660\pi$
$948$	−4.47041	−	11.4412i	−0.145192	−	0.371594i
$949$	46.6682			1.51491
$950$	35.3525	+	17.9108i	1.14699	+	0.581102i
$951$	17.9781	+	46.0116i	0.582978	+	1.49203i
$952$	1.47644	+	0.425974i	0.0478517	+	0.0138059i
$953$	−47.6780			−1.54444			−0.772220	−	0.635355i	$-0.780854\pi$
$953$	−47.6780			−1.54444			−0.772220	+	0.635355i	$0.780854\pi$
$954$	−24.0045	−	7.48391i	−0.777173	−	0.242300i
$955$	−18.9263	+	0.517362i	−0.612441	+	0.0167415i
$956$	−19.9340	−	11.5089i	−0.644711	−	0.372224i
$957$	0.119256	+	0.305214i	0.00385499	+	0.00986615i
$958$	−0.0620969	+	0.107555i	−0.00200626	+	0.00347495i
$959$	−22.7506	+	5.63290i	−0.734656	+	0.181896i
$960$	−3.56753	+	1.50756i	−0.115142	+	0.0486562i
$961$	29.0882			0.938330
$962$	12.3080	−	7.10601i	0.396825	−	0.229107i
$963$	−11.3382	−	50.3772i	−0.365369	−	1.62338i
$964$	−5.92882	−	3.42300i	−0.190954	−	0.110248i
$965$	5.07544	−	0.138740i	0.163384	−	0.00446621i
$966$	−29.9924	+	2.75507i	−0.964991	+	0.0886430i
$967$	8.54536	+	4.93367i	0.274800	+	0.158656i	0.631067	−	0.775728i	$-0.282617\pi$
$967$	8.54536	+	4.93367i	0.274800	+	0.158656i	−0.356267	+	0.934384i	$0.615951\pi$
$968$	−4.64846	−	8.05137i	−0.149407	−	0.258781i
$969$	−2.90185	−	7.42677i	−0.0932208	−	0.238582i
$970$	21.9493	−	13.4853i	0.704751	−	0.432986i
$971$	25.6986	−	44.5114i	0.824709	−	1.42844i	−0.0774332	−	0.996998i	$-0.524672\pi$
$971$	25.6986	−	44.5114i	0.824709	−	1.42844i	0.902142	−	0.431440i	$-0.141994\pi$
$972$	14.9302	−	4.48212i	0.478886	−	0.143764i
$973$	−1.02730	−	4.14914i	−0.0329337	−	0.133015i
$974$	−22.4789	+	12.9782i	−0.720271	+	0.415849i
$975$	−52.2987	−	5.06006i	−1.67490	−	0.162052i
$976$			2.12053i			0.0678764i
$977$	−11.2497			−0.359910			−0.179955	−	0.983675i	$-0.557595\pi$
$977$	−11.2497			−0.359910			−0.179955	+	0.983675i	$0.557595\pi$
$978$	−1.46498	+	9.62083i	−0.0468448	+	0.307640i
$979$	−3.05681	+	1.76485i	−0.0976960	+	0.0564048i
$980$	−15.6516	−	0.169750i	−0.499971	−	0.00542247i
$981$	36.1342	+	11.2656i	1.15368	+	0.359683i
$982$	17.4877	+	10.0965i	0.558056	+	0.322194i
$983$	41.0653	+	23.7091i	1.30978	+	0.756202i	0.982059	−	0.188573i	$-0.0603861\pi$
$983$	41.0653	+	23.7091i	1.30978	+	0.756202i	0.327721	+	0.944775i	$0.393719\pi$
$984$	10.8528	+	1.65257i	0.345976	+	0.0526821i
$985$	0.795201	+	29.0903i	0.0253372	+	0.926893i
$986$	−0.0420996	+	0.0729186i	−0.00134072	+	0.00232220i
$987$	22.5399	+	10.3918i	0.717454	+	0.330775i
$988$	−41.6463	+	24.0445i	−1.32494	+	0.764957i
$989$	66.1930	+	38.2165i	2.10481	+	1.21522i
$990$	2.15489	+	8.48499i	0.0684868	+	0.269671i
$991$	16.8939	+	29.2611i	0.536653	+	0.929511i	0.999081	+	0.0428538i	$0.0136450\pi$
$991$	16.8939	+	29.2611i	0.536653	+	0.929511i	−0.462428	+	0.886657i	$0.653022\pi$
$992$			1.38267i			0.0438997i
$993$	15.5711	+	39.8514i	0.494133	+	1.26464i
$994$	−19.7376	+	18.9982i	−0.626040	+	0.602587i
$995$	−3.74245	−	6.09141i	−0.118644	−	0.193111i
$996$	−6.76224	−	5.40944i	−0.214270	−	0.171405i
$997$	8.39742	−	14.5447i	0.265949	−	0.460637i	−0.701863	−	0.712312i	$-0.747648\pi$
$997$	8.39742	−	14.5447i	0.265949	−	0.460637i	0.967812	+	0.251675i	$0.0809815\pi$
$998$	3.80999	+	6.59910i	0.120603	+	0.208891i
$999$	−6.81096	−	10.0878i	−0.215489	−	0.319163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.509.15	yes	48
3.2	odd	2		1890.2.bi.a.719.13		48
5.4	even	2		630.2.bi.a.509.10	yes	48
7.3	odd	6		630.2.r.a.59.8	✓	48
9.2	odd	6		630.2.r.b.299.17	yes	48
9.7	even	3		1890.2.r.a.89.5		48
15.14	odd	2		1890.2.bi.b.719.5		48
21.17	even	6		1890.2.r.b.1529.5		48
35.24	odd	6		630.2.r.b.59.17	yes	48
45.29	odd	6		630.2.r.a.299.8	yes	48
45.34	even	6		1890.2.r.b.89.5		48
63.38	even	6		630.2.bi.a.479.10	yes	48
63.52	odd	6		1890.2.bi.b.899.5		48
105.59	even	6		1890.2.r.a.1529.5		48
315.164	even	6	inner	630.2.bi.b.479.15	yes	48
315.304	odd	6		1890.2.bi.a.899.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.8	✓	48	7.3	odd	6
630.2.r.a.299.8	yes	48	45.29	odd	6
630.2.r.b.59.17	yes	48	35.24	odd	6
630.2.r.b.299.17	yes	48	9.2	odd	6
630.2.bi.a.479.10	yes	48	63.38	even	6
630.2.bi.a.509.10	yes	48	5.4	even	2
630.2.bi.b.479.15	yes	48	315.164	even	6	inner
630.2.bi.b.509.15	yes	48	1.1	even	1	trivial
1890.2.r.a.89.5		48	9.7	even	3
1890.2.r.a.1529.5		48	105.59	even	6
1890.2.r.b.89.5		48	45.34	even	6
1890.2.r.b.1529.5		48	21.17	even	6
1890.2.bi.a.719.13		48	3.2	odd	2
1890.2.bi.a.899.13		48	315.304	odd	6
1890.2.bi.b.719.5		48	15.14	odd	2
1890.2.bi.b.899.5		48	63.52	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.630353 + 1.61327i) q^{3} +1.00000 q^{4} +(0.0611015 + 2.23523i) q^{5} +(0.630353 + 1.61327i) q^{6} +(1.83478 + 1.90619i) q^{7} +1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.630353 + 1.61327i) q^{3} +1.00000 q^{4} +(0.0611015 + 2.23523i) q^{5} +(0.630353 + 1.61327i) q^{6} +(1.83478 + 1.90619i) q^{7} +1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +(0.0611015 + 2.23523i) q^{10} +(-1.13018 - 0.652510i) q^{11} +(0.630353 + 1.61327i) q^{12} +(3.03357 - 5.25429i) q^{13} +(1.83478 + 1.90619i) q^{14} +(-3.56753 + 1.50756i) q^{15} +1.00000 q^{16} +(0.502991 - 0.290402i) q^{17} +(-2.20531 + 2.03386i) q^{18} +(-6.86424 - 3.96307i) q^{19} +(0.0611015 + 2.23523i) q^{20} +(-1.91866 + 4.16158i) q^{21} +(-1.13018 - 0.652510i) q^{22} +(3.28622 + 5.69190i) q^{23} +(0.630353 + 1.61327i) q^{24} +(-4.99253 + 0.273152i) q^{25} +(3.03357 - 5.25429i) q^{26} +(-4.67130 - 2.27572i) q^{27} +(1.83478 + 1.90619i) q^{28} +(-0.125548 + 0.0724850i) q^{29} +(-3.56753 + 1.50756i) q^{30} +1.38267i q^{31} +1.00000 q^{32} +(0.340266 - 2.23460i) q^{33} +(0.502991 - 0.290402i) q^{34} +(-4.14868 + 4.21764i) q^{35} +(-2.20531 + 2.03386i) q^{36} +(2.02863 + 1.17123i) q^{37} +(-6.86424 - 3.96307i) q^{38} +(10.3888 + 1.58192i) q^{39} +(0.0611015 + 2.23523i) q^{40} +(3.16905 - 5.48896i) q^{41} +(-1.91866 + 4.16158i) q^{42} +(10.0713 - 5.81466i) q^{43} +(-1.13018 - 0.652510i) q^{44} +(-4.68091 - 4.80511i) q^{45} +(3.28622 + 5.69190i) q^{46} -5.41619i q^{47} +(0.630353 + 1.61327i) q^{48} +(-0.267153 + 6.99490i) q^{49} +(-4.99253 + 0.273152i) q^{50} +(0.785560 + 0.628407i) q^{51} +(3.03357 - 5.25429i) q^{52} +(4.19068 + 7.25846i) q^{53} +(-4.67130 - 2.27572i) q^{54} +(1.38946 - 2.56609i) q^{55} +(1.83478 + 1.90619i) q^{56} +(2.06663 - 13.5720i) q^{57} +(-0.125548 + 0.0724850i) q^{58} -3.08716 q^{59} +(-3.56753 + 1.50756i) q^{60} +2.12053i q^{61} +1.38267i q^{62} +(-7.92320 - 0.472056i) q^{63} +1.00000 q^{64} +(11.9299 + 6.45968i) q^{65} +(0.340266 - 2.23460i) q^{66} -13.1972i q^{67} +(0.502991 - 0.290402i) q^{68} +(-7.11112 + 8.88948i) q^{69} +(-4.14868 + 4.21764i) q^{70} +10.3545i q^{71} +(-2.20531 + 2.03386i) q^{72} +(3.84599 + 6.66144i) q^{73} +(2.02863 + 1.17123i) q^{74} +(-3.58773 - 7.88215i) q^{75} +(-6.86424 - 3.96307i) q^{76} +(-0.829824 - 3.35156i) q^{77} +(10.3888 + 1.58192i) q^{78} -7.09192 q^{79} +(0.0611015 + 2.23523i) q^{80} +(0.726797 - 8.97061i) q^{81} +(3.16905 - 5.48896i) q^{82} +(-4.32983 + 2.49983i) q^{83} +(-1.91866 + 4.16158i) q^{84} +(0.679850 + 1.10656i) q^{85} +(10.0713 - 5.81466i) q^{86} +(-0.196078 - 0.156852i) q^{87} +(-1.13018 - 0.652510i) q^{88} +(1.35235 - 2.34234i) q^{89} +(-4.68091 - 4.80511i) q^{90} +(15.5816 - 3.85791i) q^{91} +(3.28622 + 5.69190i) q^{92} +(-2.23062 + 0.871568i) q^{93} -5.41619i q^{94} +(8.43897 - 15.5853i) q^{95} +(0.630353 + 1.61327i) q^{96} +(-5.76032 - 9.97717i) q^{97} +(-0.267153 + 6.99490i) q^{98} +(3.81952 - 0.859646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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