LMFDB - Embedded newform 630.2.bi.a.509.10

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			509.10
Character	$\chi$	$=$	630.509
Dual form			630.2.bi.a.479.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.630353 - 1.61327i) q^{3} +1.00000 q^{4} +(1.90522 + 1.17053i) q^{5} +(0.630353 + 1.61327i) q^{6} +(-1.83478 - 1.90619i) q^{7} -1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.630353 - 1.61327i) q^{3} +1.00000 q^{4} +(1.90522 + 1.17053i) q^{5} +(0.630353 + 1.61327i) q^{6} +(-1.83478 - 1.90619i) q^{7} -1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +(-1.90522 - 1.17053i) 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} +(0.687431 - 3.81149i) q^{15} +1.00000 q^{16} +(-0.502991 + 0.290402i) q^{17} +(2.20531 - 2.03386i) q^{18} +(-6.86424 - 3.96307i) q^{19} +(1.90522 + 1.17053i) 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} +(2.25971 + 4.46024i) 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} +(-0.687431 + 3.81149i) q^{30} +1.38267i q^{31} -1.00000 q^{32} +(-0.340266 + 2.23460i) q^{33} +(0.502991 - 0.290402i) q^{34} +(-1.26440 - 5.77939i) 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} +(-1.90522 - 1.17053i) 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} +(-6.58230 + 1.29357i) q^{45} +(3.28622 + 5.69190i) q^{46} +5.41619i q^{47} +(-0.630353 - 1.61327i) q^{48} +(-0.267153 + 6.99490i) q^{49} +(-2.25971 - 4.46024i) 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} +(0.687431 - 3.81149i) 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} +(1.26440 + 5.77939i) q^{70} +10.3545i q^{71} +(2.20531 - 2.03386i) q^{72} +(-3.84599 - 6.66144i) q^{73} +(2.02863 + 1.17123i) q^{74} +(5.77117 - 6.45705i) q^{75} +(-6.86424 - 3.96307i) q^{76} +(0.829824 + 3.35156i) q^{77} +(-10.3888 - 1.58192i) q^{78} -7.09192 q^{79} +(1.90522 + 1.17053i) 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} +(-1.29823 - 0.0354880i) 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} +(6.58230 - 1.29357i) 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} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 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} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 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} - 15 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 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * 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 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * 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 - 15 * 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
$5$	1.90522	+	1.17053i	0.852039	+	0.523478i
$5$	1.90522	+	1.17053i	0.852039	+	0.523478i
$6$	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
$10$	−1.90522	−	1.17053i	−0.602483	−	0.370155i
$11$	−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	$0.484911\pi$
$13$	−3.03357	+	5.25429i	−0.841360	+	1.45728i	−0.888745	+	0.458402i	$0.848422\pi$
$14$	1.83478	+	1.90619i	0.490366	+	0.509452i
$15$	0.687431	−	3.81149i	0.177494	−	0.984122i
$16$	1.00000			0.250000
$17$	−0.502991	+	0.290402i	−0.121993	+	0.0704328i	−0.559755	−	0.828658i	$-0.689105\pi$
$17$	−0.502991	+	0.290402i	−0.121993	+	0.0704328i	0.437762	+	0.899091i	$0.355771\pi$
$18$	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	$-0.696632\pi$
$20$	1.90522	+	1.17053i	0.426020	+	0.261739i
$21$	−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	$-0.926371\pi$
$23$	−3.28622	−	5.69190i	−0.685224	−	1.18684i	0.288142	−	0.957588i	$-0.406962\pi$
$24$	0.630353	+	1.61327i	0.128670	+	0.329308i
$25$	2.25971	+	4.46024i	0.451942	+	0.892047i
$26$	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	$0.337618\pi$
$30$	−0.687431	+	3.81149i	−0.125507	+	0.695879i
$31$			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
$35$	−1.26440	−	5.77939i	−0.213722	−	0.976894i
$36$	−2.20531	+	2.03386i	−0.367552	+	0.338977i
$37$	−2.02863	−	1.17123i	−0.333505	−	0.192549i	0.323891	−	0.946094i	$-0.395009\pi$
$37$	−2.02863	−	1.17123i	−0.333505	−	0.192549i	−0.657396	+	0.753545i	$0.728342\pi$
$38$	6.86424	+	3.96307i	1.11353	+	0.642895i
$39$	10.3888	+	1.58192i	1.66354	+	0.253310i
$40$	−1.90522	−	1.17053i	−0.301241	−	0.185077i
$41$	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	$0.680361\pi$
$43$	−10.0713	+	5.81466i	−1.53586	+	0.886728i	−0.999075	+	0.0430080i	$0.986306\pi$
$44$	−1.13018	−	0.652510i	−0.170381	−	0.0983696i
$45$	−6.58230	+	1.29357i	−0.981232	+	0.192833i
$46$	3.28622	+	5.69190i	0.484527	+	0.839225i
$47$			5.41619i			0.790033i	0.918674	+	0.395016i	$0.129261\pi$
$47$			5.41619i			0.790033i	−0.918674	+	0.395016i	$0.870739\pi$
$48$	−0.630353	−	1.61327i	−0.0909835	−	0.232856i
$49$	−0.267153	+	6.99490i	−0.0381647	+	0.999271i
$50$	−2.25971	−	4.46024i	−0.319571	−	0.630773i
$51$	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	$-0.971422\pi$
$53$	−4.19068	−	7.25846i	−0.575634	−	0.997027i	0.420339	−	0.907367i	$-0.361911\pi$
$54$	−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	$0.564405\pi$
$60$	0.687431	−	3.81149i	0.0887469	−	0.492061i
$61$			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	$0.298450\pi$
$67$			13.1972i			1.61229i	−0.591717	+	0.806146i	$0.701550\pi$
$68$	−0.502991	+	0.290402i	−0.0609966	+	0.0352164i
$69$	−7.11112	+	8.88948i	−0.856078	+	1.07017i
$70$	1.26440	+	5.77939i	0.151124	+	0.690769i
$71$			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	0.548256	−	0.836311i	$-0.315292\pi$
$73$	−3.84599	−	6.66144i	−0.450139	−	0.779663i	−0.998394	+	0.0566478i	$0.981959\pi$
$74$	2.02863	+	1.17123i	0.235824	+	0.136153i
$75$	5.77117	−	6.45705i	0.666398	−	0.745596i
$76$	−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	$0.630626\pi$
$80$	1.90522	+	1.17053i	0.213010	+	0.130869i
$81$	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	−0.243178	−	0.969982i	$-0.578190\pi$
$83$	4.32983	−	2.49983i	0.475261	−	0.274392i	0.718439	+	0.695589i	$0.244857\pi$
$84$	−1.91866	+	4.16158i	−0.209343	+	0.454066i
$85$	−1.29823	−	0.0354880i	−0.140813	−	0.00384921i
$86$	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	$0.120879\pi$
$90$	6.58230	−	1.29357i	0.693835	−	0.136354i
$91$	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	$0.0321887\pi$
$97$	5.76032	+	9.97717i	0.584872	+	1.01303i	−0.410019	+	0.912077i	$0.634478\pi$
$98$	0.267153	−	6.99490i	0.0269865	−	0.706592i
$99$	3.81952	−	0.859646i	0.383876	−	0.0863976i
$100$	2.25971	+	4.46024i	0.225971	+	0.446024i
$101$	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	0.884416	−	0.466700i	$-0.154557\pi$
$103$	0.386002	+	0.668575i	0.0380339	+	0.0658766i	−0.846382	+	0.532577i	$0.821224\pi$
$104$	3.03357	−	5.25429i	0.297466	−	0.515226i
$105$	−8.52672	+	5.68287i	−0.832123	+	0.554591i
$106$	4.19068	+	7.25846i	0.407034	+	0.705004i
$107$	8.60622	−	14.9064i	0.831995	−	1.44106i	−0.0644590	−	0.997920i	$-0.520532\pi$
$107$	8.60622	−	14.9064i	0.831995	−	1.44106i	0.896454	−	0.443137i	$-0.146134\pi$
$108$	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	$0.358567\pi$
$113$	−6.02741	+	10.4398i	−0.567011	+	0.982092i	−0.996859	+	0.0791911i	$0.974766\pi$
$114$	2.06663	−	13.5720i	0.193558	−	1.27114i
$115$	0.401586	−	14.6909i	0.0374481	−	1.36994i
$116$	−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
$120$	−0.687431	+	3.81149i	−0.0627536	+	0.347940i
$121$	−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	$-0.772887\pi$
$127$		−	14.7512i		−	1.30896i	0.756079	−	0.654480i	$-0.227113\pi$
$128$	−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
$135$	6.23605	+	9.80366i	0.536714	+	0.843765i
$136$	0.502991	−	0.290402i	0.0431311	−	0.0249018i
$137$	4.42929	−	7.67175i	0.378419	−	0.655442i	−0.612413	−	0.790538i	$-0.709801\pi$
$137$	4.42929	−	7.67175i	0.378419	−	0.655442i	0.990832	+	0.135096i	$0.0431344\pi$
$138$	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	$0.688493\pi$
$140$	−1.26440	−	5.77939i	−0.106861	−	0.488447i
$141$	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
$145$	−0.324042	−	0.00885788i	−0.0269102	−	0.000735607i
$146$	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	$0.204788\pi$
$150$	−5.77117	+	6.45705i	−0.471214	+	0.527216i
$151$	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
$155$	−1.61846	+	2.63428i	−0.129998	+	0.211591i
$156$	10.3888	+	1.58192i	0.831772	+	0.126655i
$157$	3.39738			0.271140			0.135570	−	0.990768i	$-0.456713\pi$
$157$	3.39738			0.271140			0.135570	+	0.990768i	$0.456713\pi$
$158$	7.09192			0.564203
$159$	−9.06829	+	11.3361i	−0.719162	+	0.899011i
$160$	−1.90522	−	1.17053i	−0.150621	−	0.0925387i
$161$	−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	0.297183	−	0.954820i	$-0.403953\pi$
$163$	−4.86586	−	2.80931i	−0.381124	−	0.220042i	−0.678307	+	0.734778i	$0.737286\pi$
$164$	3.16905	−	5.48896i	0.247462	−	0.428616i
$165$	−3.26396	+	3.85911i	−0.254099	+	0.300432i
$166$	−4.32983	+	2.49983i	−0.336060	+	0.194025i
$167$	5.55272	+	3.20586i	0.429682	+	0.248077i	0.699211	−	0.714915i	$-0.253535\pi$
$167$	5.55272	+	3.20586i	0.429682	+	0.248077i	−0.269529	+	0.962992i	$0.586868\pi$
$168$	1.91866	−	4.16158i	0.148028	−	0.321073i
$169$	−11.9051	−	20.6202i	−0.915773	−	1.58617i
$170$	1.29823	+	0.0354880i	0.0995699	+	0.00272180i
$171$	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	$0.0986976\pi$
$173$			8.02653i			0.610246i	−0.952313	+	0.305123i	$0.901302\pi$
$174$	−0.196078	−	0.156852i	−0.0148646	−	0.0118909i
$175$	4.35600	−	12.4910i	0.329283	−	0.944231i
$176$	−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	$0.545203\pi$
$180$	−6.58230	+	1.29357i	−0.490616	+	0.0964167i
$181$		−	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	$0.0260422\pi$
$193$			2.27066i			0.163445i	−0.996655	+	0.0817227i	$0.973958\pi$
$194$	−5.76032	−	9.97717i	−0.413567	−	0.716319i
$195$	17.9413	+	15.1744i	1.28480	+	1.08666i
$196$	−0.267153	+	6.99490i	−0.0190824	+	0.499636i
$197$	−13.0144			−0.927240			−0.463620	−	0.886034i	$-0.653450\pi$
$197$	−13.0144			−0.927240			−0.463620	+	0.886034i	$0.653450\pi$
$198$	−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	$0.369483\pi$
$200$	−2.25971	−	4.46024i	−0.159786	−	0.315386i
$201$	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
$210$	8.52672	−	5.68287i	0.588400	−	0.392155i
$211$	−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
$215$	−25.9943	−	0.710569i	−1.77279	−	0.0484604i
$216$	−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	0.914112	−	0.405461i	$-0.132889\pi$
$223$	1.58167	+	2.73954i	0.105917	+	0.183453i	−0.808196	+	0.588914i	$0.799556\pi$
$224$	1.83478	+	1.90619i	0.122592	+	0.127363i
$225$	−14.0549	−	5.24027i	−0.936992	−	0.349351i
$226$	6.02741	−	10.4398i	0.400938	−	0.694444i
$227$	−8.30806	−	4.79666i	−0.551425	−	0.318365i	0.198272	−	0.980147i	$-0.436467\pi$
$227$	−8.30806	−	4.79666i	−0.551425	−	0.318365i	−0.749697	+	0.661782i	$0.769801\pi$
$228$	−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	$0.295433\pi$
$230$	−0.401586	+	14.6909i	−0.0264798	+	0.968691i
$231$	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	−0.754687	−	0.656085i	$-0.772211\pi$
$233$	2.91309	−	5.04563i	0.190843	−	0.330550i	0.945530	+	0.325535i	$0.105544\pi$
$234$	3.99655	+	17.7572i	0.261263	+	1.16083i
$235$	−6.33983	+	10.3190i	−0.413565	+	0.673139i
$236$	−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	$0.933954\pi$
$240$	0.687431	−	3.81149i	0.0443735	−	0.246030i
$241$	−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
$245$	−8.69674	+	13.0141i	−0.555614	+	0.831440i
$246$	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
$255$	0.761092	+	2.11678i	0.0476614	+	0.132558i
$256$	1.00000			0.0625000
$257$	22.8388	−	13.1860i	1.42465	−	0.822520i	0.427954	−	0.903800i	$-0.359234\pi$
$257$	22.8388	−	13.1860i	1.42465	−	0.822520i	0.996691	+	0.0812807i	$0.0259010\pi$
$258$	−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	$-0.613059\pi$
$263$	10.3480	−	17.9233i	0.638088	−	1.10520i	0.985852	−	0.167619i	$-0.0536077\pi$
$264$	0.340266	−	2.23460i	0.0209419	−	0.137530i
$265$	0.512113	−	18.7343i	0.0314589	−	1.15084i
$266$	−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	$0.925749\pi$
$270$	−6.23605	−	9.80366i	−0.379514	−	0.596632i
$271$	−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
$275$	0.356469	−	6.51536i	0.0214959	−	0.392891i
$276$	−7.11112	+	8.88948i	−0.428039	+	0.535084i
$277$	−18.1450	−	10.4760i	−1.09023	−	0.629442i	−0.156590	−	0.987664i	$-0.550050\pi$
$277$	−18.1450	−	10.4760i	−1.09023	−	0.629442i	−0.933637	+	0.358221i	$0.883383\pi$
$278$	1.39913	+	0.807790i	0.0839144	+	0.0484480i
$279$	−2.81216	−	3.04921i	−0.168359	−	0.182552i
$280$	1.26440	+	5.77939i	0.0755622	+	0.345384i
$281$	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	$-0.714132\pi$
$283$	−20.9648			−1.24623			−0.623113	+	0.782132i	$0.714132\pi$
$284$			10.3545i			0.614425i
$285$	−19.8239	+	23.4386i	−1.17427	+	1.38838i
$286$	−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
$290$	0.324042	+	0.00885788i	0.0190284	+	0.000520153i
$291$	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	0.947252	−	0.320491i	$-0.103848\pi$
$293$	19.5706	+	11.2991i	1.14332	+	0.660099i	0.196073	+	0.980589i	$0.437181\pi$
$294$	−11.4531	+	3.97826i	−0.667958	+	0.232017i
$295$	−5.88170	−	3.61361i	−0.342446	−	0.210393i
$296$	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
$300$	5.77117	−	6.45705i	0.333199	−	0.372798i
$301$	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
$305$	−2.48214	+	4.04007i	−0.142127	+	0.231334i
$306$	−0.518614	+	1.66344i	−0.0296472	+	0.0950926i
$307$	29.2086			1.66702			0.833512	−	0.552501i	$-0.186326\pi$
$307$	29.2086			1.66702			0.833512	+	0.552501i	$0.186326\pi$
$308$	0.829824	+	3.35156i	0.0472836	+	0.190973i
$309$	0.835278	−	1.04416i	0.0475173	−	0.0594005i
$310$	1.61846	−	2.63428i	0.0919221	−	0.149617i
$311$	−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	$-0.434273\pi$
$313$	7.25446			0.410047			0.205023	+	0.978757i	$0.434273\pi$
$314$	−3.39738			−0.191725
$315$	14.5429	+	10.1737i	0.819398	+	0.573225i
$316$	−7.09192			−0.398952
$317$	−28.5206			−1.60188			−0.800939	−	0.598746i	$-0.795666\pi$
$317$	−28.5206			−1.60188			−0.800939	+	0.598746i	$0.795666\pi$
$318$	9.06829	−	11.3361i	0.508525	−	0.635697i
$319$	0.189189			0.0105925
$320$	1.90522	+	1.17053i	0.106505	+	0.0654347i
$321$	−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
$325$	−30.2904	−	1.65725i	−1.68021	−	0.0919277i
$326$	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
$330$	3.26396	−	3.85911i	0.179675	−	0.212437i
$331$	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
$335$	−15.4477	+	25.1435i	−0.843999	+	1.37374i
$336$	−1.91866	+	4.16158i	−0.104671	+	0.227033i
$337$	−6.13756	−	3.54352i	−0.334334	−	0.193028i	0.323430	−	0.946252i	$-0.395164\pi$
$337$	−6.13756	−	3.54352i	−0.334334	−	0.193028i	−0.657764	+	0.753224i	$0.728497\pi$
$338$	11.9051	+	20.6202i	0.647549	+	1.12159i
$339$	20.6416	+	3.14313i	1.12110	+	0.170711i
$340$	−1.29823	−	0.0354880i	−0.0704065	−	0.00192461i
$341$	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
$345$	−23.9537	+	8.61260i	−1.28962	+	0.463687i
$346$		−	8.02653i		−	0.431509i
$347$	−7.75645			−0.416388			−0.208194	−	0.978088i	$-0.566759\pi$
$347$	−7.75645			−0.416388			−0.208194	+	0.978088i	$0.566759\pi$
$348$	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	$0.421983\pi$
$350$	−4.35600	+	12.4910i	−0.232838	+	0.667672i
$351$	−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	0.899646	−	0.436620i	$-0.143824\pi$
$353$	18.2499	+	10.5366i	0.971346	+	0.560807i	0.0716994	+	0.997426i	$0.477158\pi$
$354$	−1.94600	−	4.98043i	−0.103429	−	0.264707i
$355$	−12.1202	+	19.7275i	−0.643276	+	1.04703i
$356$	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	$0.515561\pi$
$360$	6.58230	−	1.29357i	0.346918	−	0.0681769i
$361$	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
$365$	0.469991	−	17.1934i	0.0246005	−	0.899941i
$366$	−3.42099	+	1.33668i	−0.178818	+	0.0698694i
$367$	3.49830	−	6.05923i	0.182610	−	0.316289i	−0.760159	−	0.649737i	$-0.774879\pi$
$367$	3.49830	−	6.05923i	0.182610	−	0.316289i	0.942768	+	0.333448i	$0.108212\pi$
$368$	−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	−0.796333	−	0.604858i	$-0.793230\pi$
$373$	−12.9529	+	7.47838i	−0.670678	+	0.387216i	0.125656	+	0.992074i	$0.459897\pi$
$374$	−0.757961			−0.0391932
$375$	18.5535	−	5.54675i	0.958100	−	0.286433i
$376$		−	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	−0.394708	−	0.918807i	$-0.629154\pi$
$383$	3.98546	−	2.30101i	0.203647	−	0.117576i	0.598356	+	0.801231i	$0.295821\pi$
$384$	0.630353	+	1.61327i	0.0321675	+	0.0823271i
$385$	−2.34211	+	7.35678i	−0.119365	+	0.374936i
$386$		−	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	$0.809548\pi$
$390$	−17.9413	−	15.1744i	−0.908493	−	0.768384i
$391$	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
$395$	−13.5117	−	8.30132i	−0.679845	−	0.417685i
$396$	3.81952	−	0.859646i	0.191938	−	0.0431988i
$397$	−7.42358	+	12.8580i	−0.372579	+	0.645325i	−0.989961	−	0.141338i	$-0.954860\pi$
$397$	−7.42358	+	12.8580i	−0.372579	+	0.645325i	0.617383	+	0.786663i	$0.288193\pi$
$398$	2.76888	−	1.59861i	0.138791	−	0.0801312i
$399$	29.6628	−	20.9623i	1.48500	−	1.04943i
$400$	2.25971	+	4.46024i	0.112985	+	0.223012i
$401$	−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
$405$	11.8851	−	16.2402i	0.590575	−	0.806983i
$406$	−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
$415$	11.1754	+	0.305487i	0.548579	+	0.0149958i
$416$	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	$0.275863\pi$
$420$	−8.52672	+	5.68287i	−0.416061	+	0.277296i
$421$	−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
$430$	25.9943	+	0.710569i	1.25355	+	0.0342667i
$431$	−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	$-0.443937\pi$
$433$	7.29213			0.350437			0.175219	+	0.984530i	$0.443937\pi$
$434$	−2.63563	+	2.53689i	−0.126514	+	0.121775i
$435$	0.189970	+	0.528352i	0.00910838	+	0.0253325i
$436$	−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	$-0.288962\pi$
$443$	25.9087			1.23096			0.615480	+	0.788153i	$0.288962\pi$
$444$	−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	$-0.0865221\pi$
$450$	14.0549	+	5.24027i	0.662553	+	0.247029i
$451$	−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
$455$	34.2022	+	10.8886i	1.60342	+	0.510467i
$456$	2.06663	−	13.5720i	0.0967789	−	0.635569i
$457$			11.4929i			0.537617i	0.963194	+	0.268808i	$0.0866298\pi$
$457$			11.4929i			0.537617i	−0.963194	+	0.268808i	$0.913370\pi$
$458$	−3.11351	+	1.79758i	−0.145485	+	0.0839956i
$459$	−3.01050	+	0.211888i	−0.140518	+	0.00989010i
$460$	0.401586	−	14.6909i	0.0187240	−	0.684968i
$461$	−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	0.100937	−	0.994893i	$-0.467816\pi$
$463$	−15.2816	−	8.82285i	−0.710197	−	0.410033i	−0.811134	+	0.584860i	$0.801149\pi$
$464$	−0.125548	+	0.0724850i	−0.00582841	+	0.00336503i
$465$	5.27002	+	0.950488i	0.244391	+	0.0440778i
$466$	−2.91309	+	5.04563i	−0.134946	+	0.233734i
$467$	16.2441	+	9.37851i	0.751685	+	0.433986i	0.826302	−	0.563227i	$-0.190440\pi$
$467$	16.2441	+	9.37851i	0.751685	+	0.433986i	−0.0746173	+	0.997212i	$0.523774\pi$
$468$	−3.99655	−	17.7572i	−0.184741	−	0.820827i
$469$	25.1564	−	24.2139i	1.16161	−	1.11810i
$470$	6.33983	−	10.3190i	0.292434	−	0.475981i
$471$	−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
$475$	2.16504	−	39.5715i	0.0993390	−	1.81567i
$476$	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	$0.167570\pi$
$480$	−0.687431	+	3.81149i	−0.0313768	+	0.173970i
$481$	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
$485$	−0.703929	+	25.7513i	−0.0319638	+	1.16931i
$486$	14.9302	−	4.48212i	0.677247	−	0.203313i
$487$	22.4789	−	12.9782i	1.01862	−	0.588099i	0.104914	−	0.994481i	$-0.466543\pi$
$487$	22.4789	−	12.9782i	1.01862	−	0.588099i	0.913703	+	0.406382i	$0.133210\pi$
$488$		−	2.12053i		−	0.0959918i
$489$	−1.46498	+	9.62083i	−0.0662485	+	0.435069i
$490$	8.69674	−	13.0141i	0.392879	−	0.587917i
$491$	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
$495$	8.28326	+	2.83306i	0.372305	+	0.127336i
$496$			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	$0.151743\pi$
$503$			20.5824i			0.917723i	−0.888508	+	0.458861i	$0.848257\pi$
$504$	−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	$0.815130\pi$
$510$	−0.761092	−	2.11678i	−0.0337017	−	0.0937324i
$511$	−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
$515$	−0.0471706	+	1.72561i	−0.00207858	+	0.0760394i
$516$	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	−0.836539	−	0.547908i	$-0.815424\pi$
$523$	1.28600	−	2.22742i	0.0562330	−	0.0973984i	0.892772	+	0.450510i	$0.148758\pi$
$524$	7.84610	+	13.5898i	0.342758	+	0.593675i
$525$	−22.8972	+	0.846307i	−0.999318	+	0.0369359i
$526$	−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
$530$	−0.512113	+	18.7343i	−0.0222448	+	0.813765i
$531$	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
$540$	6.23605	+	9.80366i	0.268357	+	0.421882i
$541$	−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
$545$	0.770889	−	28.2009i	0.0330213	−	1.20799i
$546$	16.0458	+	22.7056i	0.686696	+	0.971710i
$547$	−18.7975	+	10.8527i	−0.803721	+	0.464029i	−0.844771	−	0.535128i	$-0.820263\pi$
$547$	−18.7975	+	10.8527i	−0.803721	+	0.464029i	0.0410494	+	0.999157i	$0.486930\pi$
$548$	4.42929	−	7.67175i	0.189210	−	0.327721i
$549$	−4.31286	−	4.67642i	−0.184069	−	0.199585i
$550$	−0.356469	+	6.51536i	−0.0151999	+	0.277816i
$551$	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
$555$	−5.85868	+	6.92696i	−0.248687	+	0.294033i
$556$	−1.39913	−	0.807790i	−0.0593365	−	0.0342579i
$557$	6.54619	+	11.3383i	0.277371	+	0.480421i	0.970731	−	0.240171i	$-0.0772035\pi$
$557$	6.54619	+	11.3383i	0.277371	+	0.480421i	−0.693360	+	0.720592i	$0.743870\pi$
$558$	2.81216	+	3.04921i	0.119048	+	0.129083i
$559$		−	70.5567i		−	2.98423i
$560$	−1.26440	−	5.77939i	−0.0534305	−	0.244224i
$561$	−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	$0.0385783\pi$
$563$			5.73737i			0.241801i	−0.992665	+	0.120901i	$0.961422\pi$
$564$	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	$-0.351773\pi$
$570$	19.8239	−	23.4386i	0.830331	−	0.981736i
$571$	−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	0.698048	−	0.716051i	$-0.254052\pi$
$577$	−6.51191	−	11.2790i	−0.271095	−	0.469549i	−0.969142	+	0.246502i	$0.920719\pi$
$578$	8.33133	−	14.4303i	0.346538	−	0.600221i
$579$	3.66319	−	1.43131i	0.152237	−	0.0594833i
$580$	−0.324042	−	0.00885788i	−0.0134551	−	0.000367804i
$581$	−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
$585$	13.1711	−	38.5094i	0.544557	−	1.59217i
$586$	−19.5706	−	11.2991i	−0.808452	−	0.466760i
$587$	−33.7149	+	19.4653i	−1.39156	+	0.803419i	−0.993488	−	0.113934i	$-0.963655\pi$
$587$	−33.7149	+	19.4653i	−1.39156	+	0.803419i	−0.398075	+	0.917353i	$0.630322\pi$
$588$	11.4531	−	3.97826i	0.472318	−	0.164061i
$589$	5.47961	−	9.49096i	0.225783	−	0.391068i
$590$	5.88170	+	3.61361i	0.242146	+	0.148770i
$591$	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	−0.0386950	−	0.999251i	$-0.512320\pi$
$593$	−22.4867	−	12.9827i	−0.923419	−	0.533136i	−0.884724	+	0.466115i	$0.845653\pi$
$594$	3.79449	+	5.62005i	0.155690	+	0.230594i
$595$	2.31433	+	2.53980i	0.0948781	+	0.104121i
$596$	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	$-0.175080\pi$
$600$	−5.77117	+	6.45705i	−0.235607	+	0.263608i
$601$	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
$605$	0.568056	−	20.7808i	0.0230947	−	0.844859i
$606$	24.5771	+	3.74239i	0.998377	+	0.152024i
$607$	13.9082	+	24.0897i	0.564517	+	0.977771i	0.997094	+	0.0761748i	$0.0242707\pi$
$607$	13.9082	+	24.0897i	0.564517	+	0.977771i	−0.432578	+	0.901597i	$0.642396\pi$
$608$	6.86424	+	3.96307i	0.278382	+	0.160724i
$609$	−0.0607694	−	0.661551i	−0.00246250	−	0.0268074i
$610$	2.48214	−	4.04007i	0.100499	−	0.163577i
$611$	−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	−0.910640	−	0.413201i	$-0.864411\pi$
$613$	−24.9598	+	14.4106i	−1.00812	+	0.582037i	−0.0974774	+	0.995238i	$0.531077\pi$
$614$	−29.2086			−1.17876
$615$	−18.7426	−	15.8521i	−0.755775	−	0.639218i
$616$	−0.829824	−	3.35156i	−0.0334346	−	0.135038i
$617$	5.31220	−	9.20099i	0.213861	−	0.370418i	−0.739059	−	0.673641i	$-0.764729\pi$
$617$	5.31220	−	9.20099i	0.213861	−	0.370418i	0.952920	+	0.303223i	$0.0980627\pi$
$618$	−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	$0.421579\pi$
$620$	−1.61846	+	2.63428i	−0.0649988	+	0.105795i
$621$	−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
$625$	−14.7874	+	20.1577i	−0.591497	+	0.806307i
$626$	−7.25446			−0.289947
$627$	11.1916	−	13.9904i	0.446948	−	0.558721i
$628$	3.39738			0.135570
$629$	1.36051			0.0542471
$630$	−14.5429	−	10.1737i	−0.579402	−	0.405331i
$631$	−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
$635$	17.2668	−	28.1043i	0.685212	−	1.11529i
$636$	−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
$640$	−1.90522	−	1.17053i	−0.0753103	−	0.0462693i
$641$	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	−0.971872	−	0.235508i	$-0.924325\pi$
$643$	−7.15031	+	12.3847i	−0.281981	+	0.488405i	0.689892	+	0.723912i	$0.257658\pi$
$644$	−4.82037	+	16.7076i	−0.189949	+	0.658370i
$645$	15.2392	+	42.3838i	0.600043	+	1.66886i
$646$	−4.60353			−0.181124
$647$	18.0964	−	10.4480i	0.711443	−	0.410752i	−0.100152	−	0.994972i	$-0.531933\pi$
$647$	18.0964	−	10.4480i	0.711443	−	0.410752i	0.811595	+	0.584220i	$0.198600\pi$
$648$	−0.726797	+	8.97061i	−0.0285513	+	0.352399i
$649$	3.48904	+	2.01440i	0.136957	+	0.0790721i
$650$	30.2904	+	1.65725i	1.18809	+	0.0650027i
$651$	−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	0.878304	−	0.478103i	$-0.158676\pi$
$653$	0.641461	+	1.11104i	0.0251023	+	0.0434785i	−0.853201	+	0.521582i	$0.825342\pi$
$654$	13.6506	−	17.0644i	0.533781	−	0.667269i
$655$	−0.958817	+	35.0757i	−0.0374641	+	1.37052i
$656$	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	$0.364390\pi$
$660$	−3.26396	+	3.85911i	−0.127049	+	0.150216i
$661$			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
$665$	−14.2250	+	44.6820i	−0.551621	+	1.73269i
$666$	−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
$670$	15.4477	−	25.1435i	0.596797	−	0.971378i
$671$	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	−0.448285	−	0.893891i	$-0.647965\pi$
$673$	2.63843	−	1.52330i	0.101704	−	0.0587189i	0.549989	+	0.835172i	$0.314632\pi$
$674$	6.13756	+	3.54352i	0.236410	+	0.136491i
$675$	0.405534	+	25.9776i	0.0156090	+	0.999878i
$676$	−11.9051	−	20.6202i	−0.457887	−	0.793083i
$677$			8.97285i			0.344855i	0.985022	+	0.172427i	$0.0551610\pi$
$677$			8.97285i			0.344855i	−0.985022	+	0.172427i	$0.944839\pi$
$678$	−20.6416	−	3.14313i	−0.792737	−	0.120711i
$679$	8.44949	−	29.2862i	0.324262	−	1.12390i
$680$	1.29823	+	0.0354880i	0.0497849	+	0.00136090i
$681$	−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	0.875428	−	0.483349i	$-0.160580\pi$
$683$	0.499734	+	0.865564i	0.0191218	+	0.0331199i	−0.856306	+	0.516469i	$0.827246\pi$
$684$	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
$690$	23.9537	−	8.61260i	0.911900	−	0.327876i
$691$		−	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
$700$	4.35600	−	12.4910i	0.164641	−	0.472116i
$701$			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
$705$	20.6437	+	3.72326i	0.777489	+	0.140226i
$706$	−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	$0.838245\pi$
$710$	12.1202	−	19.7275i	0.454865	−	0.740361i
$711$	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
$715$	17.6980	+	0.483785i	0.661867	+	0.0180925i
$716$	−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	$0.269164\pi$
$720$	−6.58230	+	1.29357i	−0.245308	+	0.0482084i
$721$	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	$-0.901697\pi$
$727$	−19.9409	−	34.5386i	−0.739567	−	1.28097i	0.213124	−	0.977025i	$-0.431636\pi$
$728$	−15.5816	+	3.85791i	−0.577494	+	0.142984i
$729$	16.6422	+	21.2612i	0.616377	+	0.787451i
$730$	−0.469991	+	17.1934i	−0.0173951	+	0.636355i
$731$	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	0.966865	−	0.255290i	$-0.0821709\pi$
$733$	7.10271	+	12.3023i	0.262345	+	0.454394i	−0.704520	+	0.709684i	$0.748838\pi$
$734$	−3.49830	+	6.05923i	−0.129125	+	0.223650i
$735$	26.4773	+	5.82676i	0.976631	+	0.214923i
$736$	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	$0.540033\pi$
$743$	−25.1293	+	43.5252i	−0.921904	+	1.59678i	−0.796467	+	0.604682i	$0.793300\pi$
$744$	−2.23062	+	0.871568i	−0.0817786	+	0.0319532i
$745$	21.4429	+	0.586155i	0.785607	+	0.0214751i
$746$	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
$750$	−18.5535	+	5.54675i	−0.677479	+	0.202539i
$751$	−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	$0.104059\pi$
$757$			17.6703i			0.642238i	−0.947039	+	0.321119i	$0.895941\pi$
$758$	−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
$765$	2.93518	−	2.56216i	0.106122	−	0.0926353i
$766$	−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	$0.585489\pi$
$770$	2.34211	−	7.35678i	0.0844038	−	0.265120i
$771$	−35.6691	−	28.5335i	−1.28459	−	1.02761i
$772$			2.27066i			0.0817227i
$773$	36.5855	−	21.1226i	1.31589	−	0.759728i	0.332824	−	0.942989i	$-0.391999\pi$
$773$	36.5855	−	21.1226i	1.31589	−	0.759728i	0.983064	+	0.183261i	$0.0586652\pi$
$774$	−10.3841	+	33.3068i	−0.373249	+	1.19719i
$775$	−6.16702	+	3.12443i	−0.221526	+	0.112233i
$776$	−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
$780$	17.9413	+	15.1744i	0.642402	+	0.543329i
$781$	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
$785$	6.47274	+	3.97674i	0.231022	+	0.141936i
$786$	−16.9783	+	21.2243i	−0.605598	+	0.757046i
$787$	−44.8213			−1.59771			−0.798854	−	0.601525i	$-0.794560\pi$
$787$	−44.8213			−1.59771			−0.798854	+	0.601525i	$0.794560\pi$
$788$	−13.0144			−0.463620
$789$	−35.4382	−	5.39622i	−1.26163	−	0.192111i
$790$	13.5117	+	8.30132i	0.480723	+	0.295348i
$791$	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
$795$	−30.5463	+	10.9830i	−1.08337	+	0.389527i
$796$	−2.76888	+	1.59861i	−0.0981402	+	0.0566613i
$797$	−33.4229	−	19.2967i	−1.18390	−	0.683524i	−0.226986	−	0.973898i	$-0.572887\pi$
$797$	−33.4229	−	19.2967i	−1.18390	−	0.683524i	−0.956913	+	0.290374i	$0.906220\pi$
$798$	−29.6628	+	20.9623i	−1.05005	+	0.742058i
$799$	−1.57287	−	2.72430i	−0.0556442	−	0.0963786i
$800$	−2.25971	−	4.46024i	−0.0798928	−	0.157693i
$801$	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
$805$	−28.7406	+	26.1892i	−1.01297	+	0.923046i
$806$	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	$0.254576\pi$
$810$	−11.8851	+	16.2402i	−0.417599	+	0.570623i
$811$			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	$0.0555576\pi$
$823$			9.96359i			0.347309i	−0.984807	+	0.173654i	$0.944442\pi$
$824$	−0.386002	−	0.668575i	−0.0134470	−	0.0232909i
$825$	−10.7358	+	3.53189i	−0.373771	+	0.122965i
$826$	−5.66426	−	5.88472i	−0.197085	−	0.204756i
$827$	36.2819			1.26165			0.630823	−	0.775926i	$-0.282717\pi$
$827$	36.2819			1.26165			0.630823	+	0.775926i	$0.282717\pi$
$828$	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	$0.442976\pi$
$830$	−11.1754	−	0.305487i	−0.387904	−	0.0106036i
$831$	−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	$0.572638\pi$
$840$	8.52672	−	5.68287i	0.294200	−	0.196078i
$841$	−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
$845$	1.45483	−	53.2211i	0.0500478	−	1.83086i
$846$	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	0.774108	−	0.633054i	$-0.218199\pi$
$853$	−4.70765	−	8.15389i	−0.161187	−	0.279184i	−0.935295	+	0.353870i	$0.884866\pi$
$854$	−4.04214	+	3.89070i	−0.138319	+	0.133137i
$855$	50.3090	+	17.2068i	1.72053	+	0.588459i
$856$	−8.60622	+	14.9064i	−0.294155	+	0.509491i
$857$	−31.6377	−	18.2660i	−1.08072	−	0.623956i	−0.149632	−	0.988742i	$-0.547809\pi$
$857$	−31.6377	−	18.2660i	−1.08072	−	0.623956i	−0.931092	+	0.364786i	$0.881142\pi$
$858$	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	$0.479155\pi$
$860$	−25.9943	−	0.710569i	−0.886397	−	0.0242302i
$861$	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	−0.992318	−	0.123715i	$-0.960519\pi$
$863$	−11.4281	+	19.7941i	−0.389018	+	0.673800i	0.603299	+	0.797515i	$0.293852\pi$
$864$	−4.67130	−	2.27572i	−0.158921	−	0.0774216i
$865$	−9.39531	+	15.2923i	−0.319450	+	0.519954i
$866$	−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
$870$	−0.189970	−	0.528352i	−0.00644060	−	0.0179128i
$871$	−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
$875$	22.9203	−	18.6992i	0.774846	−	0.632150i
$876$	−8.32241	+	10.4037i	−0.281188	+	0.351508i
$877$	4.24658	−	2.45176i	0.143397	−	0.0827901i	−0.426585	−	0.904447i	$-0.640284\pi$
$877$	4.24658	−	2.45176i	0.143397	−	0.0827901i	0.569982	+	0.821657i	$0.306950\pi$
$878$		−	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	$-0.768843\pi$
$883$		−	39.4640i		−	1.32807i	0.747701	−	0.664035i	$-0.231157\pi$
$884$		−	3.52381i		−	0.118519i
$885$	−2.12221	+	11.7667i	−0.0713372	+	0.395532i
$886$	−25.9087			−0.870420
$887$	24.0226	−	13.8694i	0.806599	−	0.465690i	−0.0391745	−	0.999232i	$-0.512473\pi$
$887$	24.0226	−	13.8694i	0.806599	−	0.465690i	0.845773	+	0.533542i	$0.179139\pi$
$888$	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
$895$	−36.9354	−	1.00965i	−1.23461	−	0.0337489i
$896$	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
$900$	−14.0549	−	5.24027i	−0.468496	−	0.174676i
$901$	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
$905$	8.01371	−	13.0435i	0.266385	−	0.433581i
$906$	29.7352	+	4.52781i	0.987885	+	0.150426i
$907$	38.6625	+	22.3218i	1.28377	+	0.741183i	0.977535	−	0.210774i	$-0.0675985\pi$
$907$	38.6625	+	22.3218i	1.28377	+	0.741183i	0.306231	+	0.951957i	$0.400932\pi$
$908$	−8.30806	−	4.79666i	−0.275713	−	0.159183i
$909$	9.45474	+	42.0087i	0.313594	+	1.39334i
$910$	−34.2022	−	10.8886i	−1.13379	−	0.360955i
$911$	−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
$915$	8.08236	+	1.45772i	0.267195	+	0.0481906i
$916$	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	$-0.0505801\pi$
$920$	−0.401586	+	14.6909i	−0.0132399	+	0.484346i
$921$	−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
$925$	0.639849	−	11.6948i	0.0210381	−	0.384523i
$926$	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	$0.513568\pi$
$930$	−5.27002	−	0.950488i	−0.172811	−	0.0311677i
$931$	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
$935$	1.44408	+	0.887218i	0.0472265	+	0.0290151i
$936$	3.99655	+	17.7572i	0.130631	+	0.580413i
$937$	−55.8623			−1.82494			−0.912472	−	0.409140i	$-0.865829\pi$
$937$	−55.8623			−1.82494			−0.912472	+	0.409140i	$0.865829\pi$
$938$	−25.1564	+	24.2139i	−0.821385	+	0.790613i
$939$	−4.57287	−	11.7034i	−0.149230	−	0.381928i
$940$	−6.33983	+	10.3190i	−0.206782	+	0.336569i
$941$	−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
$945$	7.24589	−	29.8747i	0.235709	−	0.971824i
$946$	−15.1765			−0.493431
$947$	−20.5459			−0.667652			−0.333826	−	0.942635i	$-0.608340\pi$
$947$	−20.5459			−0.667652			−0.333826	+	0.942635i	$0.608340\pi$
$948$	4.47041	+	11.4412i	0.145192	+	0.371594i
$949$	46.6682			1.51491
$950$	−2.16504	+	39.5715i	−0.0702433	+	1.28387i
$951$	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	$-0.219146\pi$
$953$	47.6780			1.54444			0.772220	+	0.635355i	$0.219146\pi$
$954$	−24.0045	−	7.48391i	−0.777173	−	0.242300i
$955$	−9.91120	+	16.1320i	−0.320719	+	0.522019i
$956$	−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
$960$	0.687431	−	3.81149i	0.0221867	−	0.123015i
$961$	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
$965$	−2.65787	+	4.32609i	−0.0855600	+	0.139262i
$966$	−29.9924	+	2.75507i	−0.964991	+	0.0886430i
$967$	−8.54536	−	4.93367i	−0.274800	−	0.158656i	0.356267	−	0.934384i	$-0.384049\pi$
$967$	−8.54536	−	4.93367i	−0.274800	−	0.158656i	−0.631067	+	0.775728i	$0.717383\pi$
$968$	4.64846	+	8.05137i	0.149407	+	0.258781i
$969$	−2.90185	−	7.42677i	−0.0932208	−	0.238582i
$970$	0.703929	−	25.7513i	0.0226018	−	0.826825i
$971$	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
$975$	16.4200	+	49.9113i	0.525861	+	1.59844i
$976$			2.12053i			0.0678764i
$977$	11.2497			0.359910			0.179955	−	0.983675i	$-0.442405\pi$
$977$	11.2497			0.359910			0.179955	+	0.983675i	$0.442405\pi$
$978$	1.46498	−	9.62083i	0.0468448	−	0.307640i
$979$	−3.05681	+	1.76485i	−0.0976960	+	0.0564048i
$980$	−8.69674	+	13.0141i	−0.277807	+	0.415720i
$981$	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	−0.327721	−	0.944775i	$-0.606281\pi$
$983$	−41.0653	−	23.7091i	−1.30978	−	0.756202i	−0.982059	+	0.188573i	$0.939614\pi$
$984$	10.8528	+	1.65257i	0.345976	+	0.0526821i
$985$	−24.7953	−	15.2338i	−0.790045	−	0.485389i
$986$	−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
$990$	−8.28326	−	2.83306i	−0.263259	−	0.0900404i
$991$	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
$995$	−7.14654	−	0.195355i	−0.226561	−	0.00619317i
$996$	−6.76224	−	5.40944i	−0.214270	−	0.171405i
$997$	−8.39742	+	14.5447i	−0.265949	+	0.460637i	−0.967812	−	0.251675i	$-0.919019\pi$
$997$	−8.39742	+	14.5447i	−0.265949	+	0.460637i	0.701863	+	0.712312i	$0.252352\pi$
$998$	−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.a.509.10	yes	48
3.2	odd	2		1890.2.bi.b.719.5		48
5.4	even	2		630.2.bi.b.509.15	yes	48
7.3	odd	6		630.2.r.b.59.17	yes	48
9.2	odd	6		630.2.r.a.299.8	yes	48
9.7	even	3		1890.2.r.b.89.5		48
15.14	odd	2		1890.2.bi.a.719.13		48
21.17	even	6		1890.2.r.a.1529.5		48
35.24	odd	6		630.2.r.a.59.8	✓	48
45.29	odd	6		630.2.r.b.299.17	yes	48
45.34	even	6		1890.2.r.a.89.5		48
63.38	even	6		630.2.bi.b.479.15	yes	48
63.52	odd	6		1890.2.bi.a.899.13		48
105.59	even	6		1890.2.r.b.1529.5		48
315.164	even	6	inner	630.2.bi.a.479.10	yes	48
315.304	odd	6		1890.2.bi.b.899.5		48

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.630353 - 1.61327i) q^{3} +1.00000 q^{4} +(1.90522 + 1.17053i) q^{5} +(0.630353 + 1.61327i) q^{6} +(-1.83478 - 1.90619i) q^{7} -1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.630353 - 1.61327i) q^{3} +1.00000 q^{4} +(1.90522 + 1.17053i) q^{5} +(0.630353 + 1.61327i) q^{6} +(-1.83478 - 1.90619i) q^{7} -1.00000 q^{8} +(-2.20531 + 2.03386i) q^{9} +(-1.90522 - 1.17053i) 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} +(0.687431 - 3.81149i) q^{15} +1.00000 q^{16} +(-0.502991 + 0.290402i) q^{17} +(2.20531 - 2.03386i) q^{18} +(-6.86424 - 3.96307i) q^{19} +(1.90522 + 1.17053i) 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} +(2.25971 + 4.46024i) 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} +(-0.687431 + 3.81149i) q^{30} +1.38267i q^{31} -1.00000 q^{32} +(-0.340266 + 2.23460i) q^{33} +(0.502991 - 0.290402i) q^{34} +(-1.26440 - 5.77939i) 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} +(-1.90522 - 1.17053i) 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} +(-6.58230 + 1.29357i) q^{45} +(3.28622 + 5.69190i) q^{46} +5.41619i q^{47} +(-0.630353 - 1.61327i) q^{48} +(-0.267153 + 6.99490i) q^{49} +(-2.25971 - 4.46024i) 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} +(0.687431 - 3.81149i) 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} +(1.26440 + 5.77939i) q^{70} +10.3545i q^{71} +(2.20531 - 2.03386i) q^{72} +(-3.84599 - 6.66144i) q^{73} +(2.02863 + 1.17123i) q^{74} +(5.77117 - 6.45705i) q^{75} +(-6.86424 - 3.96307i) q^{76} +(0.829824 + 3.35156i) q^{77} +(-10.3888 - 1.58192i) q^{78} -7.09192 q^{79} +(1.90522 + 1.17053i) 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} +(-1.29823 - 0.0354880i) 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} +(6.58230 - 1.29357i) 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	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * 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 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * 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 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

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