LMFDB - Embedded newform 630.2.r.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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([5, 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("630.59");

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.r (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			59.1
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.71289 + 0.256935i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.390088 - 2.20178i) q^{5} +(-0.633932 + 1.61187i) q^{6} +(0.160573 + 2.64087i) q^{7} -1.00000 q^{8} +(2.86797 - 0.880202i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71289 + 0.256935i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.390088 - 2.20178i) q^{5} +(-0.633932 + 1.61187i) q^{6} +(0.160573 + 2.64087i) q^{7} -1.00000 q^{8} +(2.86797 - 0.880202i) q^{9} +(-1.71175 - 1.43872i) q^{10} -1.17241i q^{11} +(1.07896 + 1.35494i) q^{12} +(2.14293 - 3.71166i) q^{13} +(2.36735 + 1.18138i) q^{14} +(-0.102462 + 3.87163i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.22349 - 3.59313i) q^{17} +(0.671707 - 2.92383i) q^{18} +(5.60709 - 3.23726i) q^{19} +(-2.10184 + 0.763064i) q^{20} +(-0.953576 - 4.48226i) q^{21} +(-1.01534 - 0.586205i) q^{22} -5.91309 q^{23} +(1.71289 - 0.256935i) q^{24} +(-4.69566 - 1.71777i) q^{25} +(-2.14293 - 3.71166i) q^{26} +(-4.68635 + 2.24457i) q^{27} +(2.20678 - 1.45950i) q^{28} +(-7.50426 + 4.33259i) q^{29} +(3.30170 + 2.02455i) q^{30} +(-1.82526 + 1.05382i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.301234 + 2.00821i) q^{33} +(-6.22349 + 3.59313i) q^{34} +(5.87726 + 0.676627i) q^{35} +(-2.19626 - 2.04363i) q^{36} +(-0.428534 + 0.247414i) q^{37} -6.47451i q^{38} +(-2.71694 + 6.90826i) q^{39} +(-0.390088 + 2.20178i) q^{40} +(5.59810 - 9.69620i) q^{41} +(-4.35854 - 1.41531i) q^{42} +(4.14896 - 2.39541i) q^{43} +(-1.01534 + 0.586205i) q^{44} +(-0.819251 - 6.65799i) q^{45} +(-2.95654 + 5.12089i) q^{46} +(-0.722267 - 0.417001i) q^{47} +(0.633932 - 1.61187i) q^{48} +(-6.94843 + 0.848104i) q^{49} +(-3.83547 + 3.20768i) q^{50} +(11.5833 + 4.55560i) q^{51} -4.28586 q^{52} +(2.38948 - 4.13870i) q^{53} +(-0.399323 + 5.18079i) q^{54} +(-2.58139 - 0.457343i) q^{55} +(-0.160573 - 2.64087i) q^{56} +(-8.77256 + 6.98572i) q^{57} +8.66517i q^{58} +(-1.54687 - 2.67926i) q^{59} +(3.40416 - 1.84708i) q^{60} +(-2.35021 - 1.35690i) q^{61} +2.10763i q^{62} +(2.78502 + 7.43261i) q^{63} +1.00000 q^{64} +(-7.33633 - 6.16613i) q^{65} +(1.88978 + 0.743228i) q^{66} +(-2.70732 + 1.56307i) q^{67} +7.18627i q^{68} +(10.1285 - 1.51928i) q^{69} +(3.52461 - 4.75154i) q^{70} -1.71924i q^{71} +(-2.86797 + 0.880202i) q^{72} +(2.77150 - 4.80038i) q^{73} +0.494829i q^{74} +(8.48450 + 1.73587i) q^{75} +(-5.60709 - 3.23726i) q^{76} +(3.09619 - 0.188257i) q^{77} +(4.62425 + 5.80707i) q^{78} +(2.82999 - 4.90169i) q^{79} +(1.71175 + 1.43872i) q^{80} +(7.45049 - 5.04878i) q^{81} +(-5.59810 - 9.69620i) q^{82} +(7.08726 - 4.09183i) q^{83} +(-3.40497 + 3.06695i) q^{84} +(-10.3390 + 12.3011i) q^{85} -4.79081i q^{86} +(11.7408 - 9.34934i) q^{87} +1.17241i q^{88} +(2.45588 + 4.25371i) q^{89} +(-6.17561 - 2.61950i) q^{90} +(10.1461 + 5.06322i) q^{91} +(2.95654 + 5.12089i) q^{92} +(2.85571 - 2.27404i) q^{93} +(-0.722267 + 0.417001i) q^{94} +(-4.94047 - 13.6084i) q^{95} +(-1.07896 - 1.35494i) q^{96} +(2.45459 + 4.25148i) q^{97} +(-2.73974 + 6.44157i) q^{98} +(-1.03196 - 3.36244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.71289	+	0.256935i	−0.988936	+	0.148342i
$3$	−1.71289	+	0.256935i	−0.988936	+	0.148342i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.390088	−	2.20178i	0.174452	−	0.984666i
$5$	0.390088	−	2.20178i	0.174452	−	0.984666i
$6$	−0.633932	+	1.61187i	−0.258801	+	0.658044i
$7$	0.160573	+	2.64087i	0.0606907	+	0.998157i
$7$	0.160573	+	2.64087i	0.0606907	+	0.998157i
$8$	−1.00000			−0.353553
$9$	2.86797	−	0.880202i	0.955990	−	0.293401i
$10$	−1.71175	−	1.43872i	−0.541304	−	0.454962i
$11$		−	1.17241i		−	0.353495i	−0.984256	−	0.176748i	$-0.943442\pi$
$11$		−	1.17241i		−	0.353495i	0.984256	−	0.176748i	$-0.0565576\pi$
$12$	1.07896	+	1.35494i	0.311468	+	0.391137i
$13$	2.14293	−	3.71166i	0.594342	−	1.02943i	−0.399298	−	0.916821i	$-0.630746\pi$
$13$	2.14293	−	3.71166i	0.594342	−	1.02943i	0.993639	−	0.112609i	$-0.0359207\pi$
$14$	2.36735	+	1.18138i	0.632701	+	0.315736i
$15$	−0.102462	+	3.87163i	−0.0264555	+	0.999650i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.22349	−	3.59313i	−1.50942	−	0.871463i	−0.999940	−	0.0109799i	$-0.996505\pi$
$17$	−6.22349	−	3.59313i	−1.50942	−	0.871463i	−0.509479	−	0.860483i	$-0.670162\pi$
$18$	0.671707	−	2.92383i	0.158323	−	0.689154i
$19$	5.60709	−	3.23726i	1.28636	−	0.742678i	0.308353	−	0.951272i	$-0.400222\pi$
$19$	5.60709	−	3.23726i	1.28636	−	0.742678i	0.978002	+	0.208594i	$0.0668888\pi$
$20$	−2.10184	+	0.763064i	−0.469986	+	0.170626i
$21$	−0.953576	−	4.48226i	−0.208087	−	0.978110i
$22$	−1.01534	−	0.586205i	−0.216471	−	0.124979i
$23$	−5.91309			−1.23296			−0.616482	−	0.787369i	$-0.711443\pi$
$23$	−5.91309			−1.23296			−0.616482	+	0.787369i	$0.711443\pi$
$24$	1.71289	−	0.256935i	0.349642	−	0.0524467i
$25$	−4.69566	−	1.71777i	−0.939133	−	0.343555i
$26$	−2.14293	−	3.71166i	−0.420263	−	0.727917i
$27$	−4.68635	+	2.24457i	−0.901889	+	0.431967i
$28$	2.20678	−	1.45950i	0.417042	−	0.275819i
$29$	−7.50426	+	4.33259i	−1.39351	+	0.804541i	−0.993701	−	0.112060i	$-0.964255\pi$
$29$	−7.50426	+	4.33259i	−1.39351	+	0.804541i	−0.399804	+	0.916601i	$0.630922\pi$
$30$	3.30170	+	2.02455i	0.602805	+	0.369630i
$31$	−1.82526	+	1.05382i	−0.327827	+	0.189271i	−0.654876	−	0.755736i	$-0.727279\pi$
$31$	−1.82526	+	1.05382i	−0.327827	+	0.189271i	0.327049	+	0.945007i	$0.393946\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.301234	+	2.00821i	0.0524380	+	0.349584i
$34$	−6.22349	+	3.59313i	−1.06732	+	0.616217i
$35$	5.87726	+	0.676627i	0.993438	+	0.114371i
$36$	−2.19626	−	2.04363i	−0.366044	−	0.340605i
$37$	−0.428534	+	0.247414i	−0.0704506	+	0.0406747i	−0.534812	−	0.844971i	$-0.679617\pi$
$37$	−0.428534	+	0.247414i	−0.0704506	+	0.0406747i	0.464361	+	0.885646i	$0.346284\pi$
$38$		−	6.47451i		−	1.05030i
$39$	−2.71694	+	6.90826i	−0.435059	+	1.10621i
$40$	−0.390088	+	2.20178i	−0.0616783	+	0.348132i
$41$	5.59810	−	9.69620i	0.874277	−	1.51429i	0.0167455	−	0.999860i	$-0.494670\pi$
$41$	5.59810	−	9.69620i	0.874277	−	1.51429i	0.857531	−	0.514432i	$-0.171997\pi$
$42$	−4.35854	−	1.41531i	−0.672538	−	0.218387i
$43$	4.14896	−	2.39541i	0.632711	−	0.365296i	−0.149090	−	0.988824i	$-0.547634\pi$
$43$	4.14896	−	2.39541i	0.632711	−	0.365296i	0.781801	+	0.623528i	$0.214301\pi$
$44$	−1.01534	+	0.586205i	−0.153068	+	0.0883738i
$45$	−0.819251	−	6.65799i	−0.122127	−	0.992515i
$46$	−2.95654	+	5.12089i	−0.435919	+	0.755033i
$47$	−0.722267	−	0.417001i	−0.105353	−	0.0608259i	0.446397	−	0.894835i	$-0.352707\pi$
$47$	−0.722267	−	0.417001i	−0.105353	−	0.0608259i	−0.551751	+	0.834009i	$0.686040\pi$
$48$	0.633932	−	1.61187i	0.0915001	−	0.232654i
$49$	−6.94843	+	0.848104i	−0.992633	+	0.121158i
$50$	−3.83547	+	3.20768i	−0.542417	+	0.453634i
$51$	11.5833	+	4.55560i	1.62199	+	0.637912i
$52$	−4.28586			−0.594342
$53$	2.38948	−	4.13870i	0.328220	−	0.568494i	−0.653939	−	0.756548i	$-0.726885\pi$
$53$	2.38948	−	4.13870i	0.328220	−	0.568494i	0.982159	+	0.188054i	$0.0602179\pi$
$54$	−0.399323	+	5.18079i	−0.0543410	+	0.705016i
$55$	−2.58139	−	0.457343i	−0.348075	−	0.0616681i
$56$	−0.160573	−	2.64087i	−0.0214574	−	0.352902i
$57$	−8.77256	+	6.98572i	−1.16195	+	0.925281i
$58$			8.66517i			1.13779i
$59$	−1.54687	−	2.67926i	−0.201386	−	0.348810i	0.747590	−	0.664161i	$-0.231211\pi$
$59$	−1.54687	−	2.67926i	−0.201386	−	0.348810i	−0.948975	+	0.315351i	$0.897878\pi$
$60$	3.40416	−	1.84708i	0.439475	−	0.238457i
$61$	−2.35021	−	1.35690i	−0.300914	−	0.173733i	0.341939	−	0.939722i	$-0.388916\pi$
$61$	−2.35021	−	1.35690i	−0.300914	−	0.173733i	−0.642853	+	0.765989i	$0.722250\pi$
$62$			2.10763i			0.267669i
$63$	2.78502	+	7.43261i	0.350880	+	0.936421i
$64$	1.00000			0.125000
$65$	−7.33633	−	6.16613i	−0.909960	−	0.764815i
$66$	1.88978	+	0.743228i	0.232615	+	0.0914851i
$67$	−2.70732	+	1.56307i	−0.330751	+	0.190959i	−0.656175	−	0.754609i	$-0.727827\pi$
$67$	−2.70732	+	1.56307i	−0.330751	+	0.190959i	0.325423	+	0.945568i	$0.394493\pi$
$68$			7.18627i			0.871463i
$69$	10.1285	−	1.51928i	1.21932	−	0.182900i
$70$	3.52461	−	4.75154i	0.421271	−	0.567918i
$71$		−	1.71924i		−	0.204036i	−0.994783	−	0.102018i	$-0.967470\pi$
$71$		−	1.71924i		−	0.204036i	0.994783	−	0.102018i	$-0.0325300\pi$
$72$	−2.86797	+	0.880202i	−0.337993	+	0.103733i
$73$	2.77150	−	4.80038i	0.324379	−	0.561841i	−0.657007	−	0.753884i	$-0.728178\pi$
$73$	2.77150	−	4.80038i	0.324379	−	0.561841i	0.981387	+	0.192043i	$0.0615112\pi$
$74$			0.494829i			0.0575227i
$75$	8.48450	+	1.73587i	0.979706	+	0.200441i
$76$	−5.60709	−	3.23726i	−0.643178	−	0.371339i
$77$	3.09619	−	0.188257i	0.352844	−	0.0214539i
$78$	4.62425	+	5.80707i	0.523594	+	0.657521i
$79$	2.82999	−	4.90169i	0.318399	−	0.551483i	−0.661755	−	0.749720i	$-0.730188\pi$
$79$	2.82999	−	4.90169i	0.318399	−	0.551483i	0.980154	+	0.198237i	$0.0635215\pi$
$80$	1.71175	+	1.43872i	0.191380	+	0.160853i
$81$	7.45049	−	5.04878i	0.827832	−	0.560976i
$82$	−5.59810	−	9.69620i	−0.618207	−	1.07077i
$83$	7.08726	−	4.09183i	0.777927	−	0.449137i	−0.0577679	−	0.998330i	$-0.518398\pi$
$83$	7.08726	−	4.09183i	0.777927	−	0.449137i	0.835695	+	0.549193i	$0.185065\pi$
$84$	−3.40497	+	3.06695i	−0.371512	+	0.334632i
$85$	−10.3390	+	12.3011i	−1.12142	+	1.33424i
$86$		−	4.79081i		−	0.516606i
$87$	11.7408	−	9.34934i	1.25874	−	1.00235i
$88$			1.17241i			0.124979i
$89$	2.45588	+	4.25371i	0.260323	+	0.450893i	0.966328	−	0.257314i	$-0.0828376\pi$
$89$	2.45588	+	4.25371i	0.260323	+	0.450893i	−0.706005	+	0.708207i	$0.749504\pi$
$90$	−6.17561	−	2.61950i	−0.650967	−	0.276120i
$91$	10.1461	+	5.06322i	1.06360	+	0.530769i
$92$	2.95654	+	5.12089i	0.308241	+	0.533889i
$93$	2.85571	−	2.27404i	0.296123	−	0.235807i
$94$	−0.722267	+	0.417001i	−0.0744961	+	0.0430104i
$95$	−4.94047	−	13.6084i	−0.506881	−	1.39619i
$96$	−1.07896	−	1.35494i	−0.110121	−	0.138288i
$97$	2.45459	+	4.25148i	0.249226	+	0.431673i	0.963311	−	0.268386i	$-0.0864904\pi$
$97$	2.45459	+	4.25148i	0.249226	+	0.431673i	−0.714085	+	0.700059i	$0.753157\pi$
$98$	−2.73974	+	6.44157i	−0.276755	+	0.650697i
$99$	−1.03196	−	3.36244i	−0.103716	−	0.337938i
$100$	0.860196	+	4.92545i	0.0860196	+	0.492545i
$101$	7.98647			0.794683			0.397342	−	0.917671i	$-0.369933\pi$
$101$	7.98647			0.794683			0.397342	+	0.917671i	$0.369933\pi$
$102$	9.73694	−	7.75367i	0.964101	−	0.767728i
$103$	15.2058			1.49827			0.749135	−	0.662418i	$-0.230470\pi$
$103$	15.2058			1.49827			0.749135	+	0.662418i	$0.230470\pi$
$104$	−2.14293	+	3.71166i	−0.210132	+	0.363959i
$105$	−10.2409	+	0.351089i	−0.999413	+	0.0342627i
$106$	−2.38948	−	4.13870i	−0.232087	−	0.401986i
$107$	9.09652	+	15.7556i	0.879393	+	1.52315i	0.852008	+	0.523529i	$0.175385\pi$
$107$	9.09652	+	15.7556i	0.879393	+	1.52315i	0.0273858	+	0.999625i	$0.491282\pi$
$108$	4.28703	+	2.93622i	0.412520	+	0.282538i
$109$	−3.71187	+	6.42915i	−0.355533	+	0.615801i	−0.987209	−	0.159431i	$-0.949034\pi$
$109$	−3.71187	+	6.42915i	−0.355533	+	0.615801i	0.631676	+	0.775232i	$0.282367\pi$
$110$	−1.68677	+	2.00688i	−0.160827	+	0.191348i
$111$	0.670461	−	0.533898i	0.0636374	−	0.0506754i
$112$	−2.36735	−	1.18138i	−0.223694	−	0.111630i
$113$	2.85988	−	4.95345i	0.269035	−	0.465982i	−0.699578	−	0.714556i	$-0.746629\pi$
$113$	2.85988	−	4.95345i	0.269035	−	0.465982i	0.968613	+	0.248574i	$0.0799620\pi$
$114$	1.66353	+	11.0901i	0.155804	+	1.03868i
$115$	−2.30662	+	13.0193i	−0.215094	+	1.21406i
$116$	7.50426	+	4.33259i	0.696753	+	0.402270i
$117$	2.87884	−	12.5311i	0.266149	−	1.15850i
$118$	−3.09374			−0.284802
$119$	8.48969	−	17.0124i	0.778249	−	1.55953i
$120$	0.102462	−	3.87163i	0.00935344	−	0.353430i
$121$	9.62545			0.875041
$122$	−2.35021	+	1.35690i	−0.212778	+	0.122848i
$123$	−7.09763	+	18.0468i	−0.639972	+	1.62723i
$124$	1.82526	+	1.05382i	0.163913	+	0.0946354i
$125$	−5.61388	+	9.66873i	−0.502120	+	0.864798i
$126$	7.82934	+	1.30441i	0.697493	+	0.116206i
$127$			12.2323i			1.08544i	0.839914	+	0.542719i	$0.182605\pi$
$127$			12.2323i			1.08544i	−0.839914	+	0.542719i	$0.817395\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.49125	+	5.16908i	−0.571522	+	0.455112i
$130$	−9.00819	+	3.27038i	−0.790071	+	0.286832i
$131$	−8.86802			−0.774802			−0.387401	−	0.921911i	$-0.626627\pi$
$131$	−8.86802			−0.774802			−0.387401	+	0.921911i	$0.626627\pi$
$132$	1.58854	−	1.26498i	0.138265	−	0.110102i
$133$	9.44953	+	14.2878i	0.819379	+	1.23891i
$134$			3.12614i			0.270057i
$135$	3.11396	+	11.1939i	0.268007	+	0.963417i
$136$	6.22349	+	3.59313i	0.533660	+	0.308109i
$137$	0.675059			0.0576742			0.0288371	−	0.999584i	$-0.490820\pi$
$137$	0.675059			0.0576742			0.0288371	+	0.999584i	$0.490820\pi$
$138$	3.74849	−	9.53114i	0.319093	−	0.811345i
$139$	−19.0670	−	11.0084i	−1.61724	−	0.933717i	−0.987629	−	0.156810i	$-0.949879\pi$
$139$	−19.0670	−	11.0084i	−1.61724	−	0.933717i	−0.629616	−	0.776906i	$-0.716788\pi$
$140$	−2.35265	−	5.42817i	−0.198836	−	0.458764i
$141$	1.34430	+	0.528700i	0.113211	+	0.0445246i
$142$	−1.48891	−	0.859621i	−0.124946	−	0.0721378i
$143$	−4.35159	−	2.51239i	−0.363899	−	0.210097i
$144$	−0.671707	+	2.92383i	−0.0559756	+	0.243653i
$145$	6.61208	+	18.2128i	0.549103	+	1.51249i
$146$	−2.77150	−	4.80038i	−0.229371	−	0.397282i
$147$	11.6840	−	3.23800i	0.963678	−	0.267066i
$148$	0.428534	+	0.247414i	0.0352253	+	0.0203373i
$149$		−	10.4640i		−	0.857248i	−0.903483	−	0.428624i	$-0.858998\pi$
$149$		−	10.4640i		−	0.857248i	0.903483	−	0.428624i	$-0.141002\pi$
$150$	5.74556	−	6.47986i	0.469123	−	0.529078i
$151$	−11.6689			−0.949598			−0.474799	−	0.880094i	$-0.657479\pi$
$151$	−11.6689			−0.949598			−0.474799	+	0.880094i	$0.657479\pi$
$152$	−5.60709	+	3.23726i	−0.454795	+	0.262576i
$153$	−21.0115	−	4.82707i	−1.69868	−	0.390245i
$154$	1.38506	−	2.77551i	0.111611	−	0.223657i
$155$	1.60826	+	4.42990i	0.129178	+	0.355818i
$156$	7.34120	−	1.10119i	0.587766	−	0.0881656i
$157$	11.7137	+	20.2887i	0.934852	+	1.61921i	0.774898	+	0.632086i	$0.217801\pi$
$157$	11.7137	+	20.2887i	0.934852	+	1.61921i	0.159954	+	0.987125i	$0.448866\pi$
$158$	−2.82999	−	4.90169i	−0.225142	−	0.389958i
$159$	−3.02953	+	7.70306i	−0.240257	+	0.610893i
$160$	2.10184	−	0.763064i	0.166165	−	0.0603255i
$161$	−0.949480	−	15.6157i	−0.0748295	−	1.23069i
$162$	−0.647130	−	8.97670i	−0.0508433	−	0.705277i
$163$	14.0391	−	8.10545i	1.09962	−	0.634868i	0.163502	−	0.986543i	$-0.447721\pi$
$163$	14.0391	−	8.10545i	1.09962	−	0.634868i	0.936122	+	0.351675i	$0.114388\pi$
$164$	−11.1962			−0.874277
$165$	4.53914	+	0.120127i	0.353371	+	0.00935191i
$166$		−	8.18366i		−	0.635175i
$167$	−11.8916	−	6.86564i	−0.920202	−	0.531279i	−0.0365024	−	0.999334i	$-0.511622\pi$
$167$	−11.8916	−	6.86564i	−0.920202	−	0.531279i	−0.883699	+	0.468055i	$0.844955\pi$
$168$	0.953576	+	4.48226i	0.0735700	+	0.345814i
$169$	−2.68430	−	4.64934i	−0.206484	−	0.357641i
$170$	5.48358	+	15.1044i	0.420572	+	1.15845i
$171$	13.2315	−	14.2197i	1.01184	−	1.08741i
$172$	−4.14896	−	2.39541i	−0.316356	−	0.182648i
$173$	0.365628	+	0.211095i	0.0277981	+	0.0160493i	0.513835	−	0.857889i	$-0.328224\pi$
$173$	0.365628	+	0.211095i	0.0277981	+	0.0160493i	−0.486037	+	0.873938i	$0.661558\pi$
$174$	−2.22639	−	14.8425i	−0.168782	−	1.12520i
$175$	3.78243	−	12.6765i	0.285925	−	0.958252i
$176$	1.01534	+	0.586205i	0.0765340	+	0.0441869i
$177$	3.33801	+	4.19183i	0.250900	+	0.315077i
$178$	4.91177			0.368152
$179$	18.7039	+	10.7987i	1.39800	+	0.807133i	0.994183	−	0.107708i	$-0.0343511\pi$
$179$	18.7039	+	10.7987i	1.39800	+	0.807133i	0.403813	+	0.914841i	$0.367684\pi$
$180$	−5.35636	+	4.03849i	−0.399240	+	0.301011i
$181$		−	14.2098i		−	1.05621i	−0.849179	−	0.528105i	$-0.822903\pi$
$181$		−	14.2098i		−	1.05621i	0.849179	−	0.528105i	$-0.177097\pi$
$182$	9.45794	−	6.25520i	0.701069	−	0.463666i
$183$	4.37429	+	1.72036i	0.323357	+	0.127173i
$184$	5.91309			0.435919
$185$	0.377586	+	1.04005i	0.0277607	+	0.0764660i
$186$	−0.541524	−	3.61014i	−0.0397065	−	0.264708i
$187$	−4.21263	+	7.29649i	−0.308058	+	0.533572i
$188$			0.834002i			0.0608259i
$189$	−6.68012	−	12.0157i	−0.485908	−	0.874010i
$190$	−14.2555	−	2.52563i	−1.03420	−	0.183228i
$191$	6.42249	+	3.70803i	0.464715	+	0.268303i	0.714025	−	0.700120i	$-0.246870\pi$
$191$	6.42249	+	3.70803i	0.464715	+	0.268303i	−0.249310	+	0.968424i	$0.580204\pi$
$192$	−1.71289	+	0.256935i	−0.123617	+	0.0185427i
$193$	−15.1338	+	8.73749i	−1.08935	+	0.628938i	−0.933404	−	0.358827i	$-0.883177\pi$
$193$	−15.1338	+	8.73749i	−1.08935	+	0.628938i	−0.155949	+	0.987765i	$0.549844\pi$
$194$	4.90919			0.352459
$195$	14.1506	+	8.67693i	1.01335	+	0.621368i
$196$	4.20870	+	5.59347i	0.300621	+	0.399533i
$197$	18.8501			1.34302			0.671508	−	0.740997i	$-0.265647\pi$
$197$	18.8501			1.34302			0.671508	+	0.740997i	$0.265647\pi$
$198$	−3.42794	−	0.787517i	−0.243613	−	0.0559664i
$199$	5.56129	+	3.21081i	0.394230	+	0.227609i	0.683991	−	0.729490i	$-0.260243\pi$
$199$	5.56129	+	3.21081i	0.394230	+	0.227609i	−0.289762	+	0.957099i	$0.593576\pi$
$200$	4.69566	+	1.71777i	0.332034	+	0.121465i
$201$	4.23572	−	3.37297i	0.298765	−	0.237911i
$202$	3.99323	−	6.91648i	0.280963	−	0.486642i
$203$	−12.6468	−	19.1221i	−0.887631	−	1.34211i
$204$	−1.84640	−	12.3093i	−0.129274	−	0.861821i
$205$	−19.1651	−	16.1082i	−1.33855	−	1.12504i
$206$	7.60289	−	13.1686i	0.529718	−	0.917499i
$207$	−16.9586	+	5.20471i	−1.17870	+	0.361753i
$208$	2.14293	+	3.71166i	0.148585	+	0.257358i
$209$	−3.79540	−	6.57382i	−0.262533	−	0.454721i
$210$	−4.81642	+	9.04445i	−0.332364	+	0.624127i
$211$	−4.56527	+	7.90727i	−0.314286	+	0.544359i	−0.979285	−	0.202485i	$-0.935098\pi$
$211$	−4.56527	+	7.90727i	−0.314286	+	0.544359i	0.665000	+	0.746844i	$0.268432\pi$
$212$	−4.77896			−0.328220
$213$	0.441733	+	2.94487i	0.0302671	+	0.201779i
$214$	18.1930			1.24365
$215$	−3.65570	−	10.0695i	−0.249316	−	0.686736i
$216$	4.68635	−	2.24457i	0.318866	−	0.152724i
$217$	−3.07608	−	4.65107i	−0.208818	−	0.315735i
$218$	3.71187	+	6.42915i	0.251400	+	0.435437i
$219$	−3.51388	+	8.93460i	−0.237446	+	0.603744i
$220$	0.894624	+	2.46422i	0.0603156	+	0.166138i
$221$	−26.6730	+	15.3997i	−1.79422	+	1.03589i
$222$	−0.127139	−	0.847586i	−0.00853300	−	0.0568862i
$223$	−5.48740	−	9.50446i	−0.367464	−	0.636466i	0.621705	−	0.783252i	$-0.286440\pi$
$223$	−5.48740	−	9.50446i	−0.367464	−	0.636466i	−0.989168	+	0.146786i	$0.953107\pi$
$224$	−2.20678	+	1.45950i	−0.147447	+	0.0975167i
$225$	−14.9790	−	0.793388i	−0.998600	−	0.0528926i
$226$	−2.85988	−	4.95345i	−0.190236	−	0.329499i
$227$			7.62205i			0.505893i	0.967480	+	0.252947i	$0.0813997\pi$
$227$			7.62205i			0.505893i	−0.967480	+	0.252947i	$0.918600\pi$
$228$	10.4361	+	4.10440i	0.691147	+	0.271820i
$229$		−	12.5256i		−	0.827712i	−0.910342	−	0.413856i	$-0.864182\pi$
$229$		−	12.5256i		−	0.827712i	0.910342	−	0.413856i	$-0.135818\pi$
$230$	10.1217	+	8.50725i	0.667408	+	0.560952i
$231$	−5.25506	+	1.11798i	−0.345757	+	0.0735579i
$232$	7.50426	−	4.33259i	0.492679	−	0.284448i
$233$	−10.0310	−	17.3742i	−0.657152	−	1.13822i	−0.981350	−	0.192232i	$-0.938427\pi$
$233$	−10.0310	−	17.3742i	−0.657152	−	1.13822i	0.324197	−	0.945989i	$-0.394906\pi$
$234$	−9.41287	−	8.75872i	−0.615338	−	0.572576i
$235$	−1.19989	+	1.42761i	−0.0782723	+	0.0931267i
$236$	−1.54687	+	2.67926i	−0.100693	+	0.174405i
$237$	−3.58804	+	9.12317i	−0.233068	+	0.592614i
$238$	−10.4883	−	15.8585i	−0.679858	−	1.02795i
$239$	10.8229	+	6.24858i	0.700073	+	0.404187i	0.807374	−	0.590039i	$-0.200888\pi$
$239$	10.8229	+	6.24858i	0.700073	+	0.404187i	−0.107302	+	0.994226i	$0.534221\pi$
$240$	−3.30170	−	2.02455i	−0.213124	−	0.130684i
$241$		−	17.0829i		−	1.10040i	−0.835031	−	0.550202i	$-0.814551\pi$
$241$		−	17.0829i		−	1.10040i	0.835031	−	0.550202i	$-0.185449\pi$
$242$	4.81273	−	8.33589i	0.309374	−	0.535851i
$243$	−11.4646	+	10.5623i	−0.735457	+	0.677571i
$244$			2.71379i			0.173733i
$245$	−0.843159	+	15.6297i	−0.0538675	+	0.998548i
$246$	12.0802	+	15.1701i	0.770206	+	0.967213i
$247$		−	27.7489i		−	1.76562i
$248$	1.82526	−	1.05382i	0.115904	−	0.0669174i
$249$	−11.0883	+	8.82981i	−0.702695	+	0.559566i
$250$	5.56643	+	9.69613i	0.352052	+	0.613237i
$251$	−9.66146			−0.609826			−0.304913	−	0.952380i	$-0.598627\pi$
$251$	−9.66146			−0.609826			−0.304913	+	0.952380i	$0.598627\pi$
$252$	5.04432	−	6.12820i	0.317762	−	0.386040i
$253$			6.93257i			0.435847i
$254$	10.5935	+	6.11613i	0.664693	+	0.383760i
$255$	14.5490	−	23.7269i	0.911091	−	1.48584i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	8.46428i		−	0.527987i	−0.964524	−	0.263994i	$-0.914960\pi$
$257$		−	8.46428i		−	0.527987i	0.964524	−	0.263994i	$-0.0850398\pi$
$258$	1.23093	+	8.20612i	0.0766342	+	0.510891i
$259$	−0.722201	−	1.09198i	−0.0448754	−	0.0678521i
$260$	−1.67186	+	9.43652i	−0.103684	+	0.585228i
$261$	−17.7084	+	19.0310i	−1.09612	+	1.17799i
$262$	−4.43401	+	7.67993i	−0.273934	+	0.474468i
$263$	15.9223			0.981810			0.490905	−	0.871213i	$-0.336666\pi$
$263$	15.9223			0.981810			0.490905	+	0.871213i	$0.336666\pi$
$264$	−0.301234	−	2.00821i	−0.0185396	−	0.123597i
$265$	−8.18039	−	6.87556i	−0.502517	−	0.422362i
$266$	17.0984	−	1.03963i	1.04837	−	0.0637438i
$267$	−5.29958	−	6.65513i	−0.324329	−	0.407288i
$268$	2.70732	+	1.56307i	0.165376	+	0.0954797i
$269$	−13.0701	+	22.6380i	−0.796897	+	1.38027i	0.124731	+	0.992191i	$0.460193\pi$
$269$	−13.0701	+	22.6380i	−0.796897	+	1.38027i	−0.921628	+	0.388075i	$0.873140\pi$
$270$	11.2512	+	2.90018i	0.684725	+	0.176499i
$271$	1.07493	−	0.620610i	0.0652972	−	0.0376994i	−0.466996	−	0.884259i	$-0.654664\pi$
$271$	1.07493	−	0.620610i	0.0652972	−	0.0376994i	0.532293	+	0.846560i	$0.321330\pi$
$272$	6.22349	−	3.59313i	0.377355	−	0.217866i
$273$	−18.6801	−	6.06582i	−1.13057	−	0.367120i
$274$	0.337529	−	0.584618i	0.0203909	−	0.0353181i
$275$	−2.01394	+	5.50525i	−0.121445	+	0.331979i
$276$	−6.37996	−	8.01186i	−0.384029	−	0.482257i
$277$			4.23547i			0.254485i	0.991872	+	0.127242i	$0.0406126\pi$
$277$			4.23547i			0.254485i	−0.991872	+	0.127242i	$0.959387\pi$
$278$	−19.0670	+	11.0084i	−1.14356	+	0.660237i
$279$	−4.30722	+	4.62891i	−0.257867	+	0.277126i
$280$	−5.87726	−	0.676627i	−0.351233	−	0.0404362i
$281$	2.44426	−	1.41119i	0.145812	−	0.0841848i	−0.425319	−	0.905044i	$-0.639838\pi$
$281$	2.44426	−	1.41119i	0.145812	−	0.0841848i	0.571131	+	0.820859i	$0.306505\pi$
$282$	1.13002	−	0.899852i	0.0672917	−	0.0535854i
$283$	6.17710	+	10.6990i	0.367190	+	0.635992i	0.989125	−	0.147077i	$-0.0469864\pi$
$283$	6.17710	+	10.6990i	0.367190	+	0.635992i	−0.621935	+	0.783069i	$0.713653\pi$
$284$	−1.48891	+	0.859621i	−0.0883503	+	0.0510091i
$285$	11.9589	+	22.0403i	0.708387	+	1.30555i
$286$	−4.35159	+	2.51239i	−0.257315	+	0.148561i
$287$	26.5053	+	13.2269i	1.56456	+	0.780762i
$288$	2.19626	+	2.04363i	0.129416	+	0.120422i
$289$	17.3212	+	30.0013i	1.01890	+	1.76478i
$290$	19.0788	+	3.38018i	1.12035	+	0.198491i
$291$	−5.29680	−	6.65164i	−0.310504	−	0.389926i
$292$	−5.54300			−0.324379
$293$	7.31257	+	4.22192i	0.427205	+	0.246647i	0.698155	−	0.715946i	$-0.254005\pi$
$293$	7.31257	+	4.22192i	0.427205	+	0.246647i	−0.270950	+	0.962593i	$0.587338\pi$
$294$	3.03780	−	11.7376i	0.177168	−	0.684552i
$295$	−6.50256	+	2.36072i	−0.378593	+	0.137447i
$296$	0.428534	−	0.247414i	0.0249080	−	0.0143807i
$297$	2.63156	+	5.49433i	0.152698	+	0.318814i
$298$	−9.06213	−	5.23202i	−0.524955	−	0.303083i
$299$	−12.6713	+	21.9474i	−0.732802	+	1.26925i
$300$	−2.73894	−	8.21573i	−0.158133	−	0.474335i
$301$	6.99218	+	10.5723i	0.403022	+	0.609375i
$302$	−5.83443	+	10.1055i	−0.335734	+	0.581508i
$303$	−13.6799	+	2.05200i	−0.785891	+	0.117885i
$304$			6.47451i			0.371339i
$305$	−3.90438	+	4.64534i	−0.223564	+	0.265992i
$306$	−14.6861	+	15.7829i	−0.839548	+	0.902250i
$307$	10.5837			0.604042			0.302021	−	0.953301i	$-0.402339\pi$
$307$	10.5837			0.604042			0.302021	+	0.953301i	$0.402339\pi$
$308$	−1.71113	−	2.58725i	−0.0975007	−	0.147422i
$309$	−26.0458	+	3.90690i	−1.48169	+	0.222256i
$310$	4.64054	+	0.822161i	0.263565	+	0.0466956i
$311$	10.5647	+	18.2986i	0.599068	+	1.03762i	0.992959	+	0.118459i	$0.0377954\pi$
$311$	10.5647	+	18.2986i	0.599068	+	1.03762i	−0.393891	+	0.919157i	$0.628871\pi$
$312$	2.71694	−	6.90826i	0.153817	−	0.391103i
$313$	4.08549	−	7.07628i	0.230926	−	0.399975i	−0.727155	−	0.686473i	$-0.759158\pi$
$313$	4.08549	−	7.07628i	0.230926	−	0.399975i	0.958081	+	0.286498i	$0.0924912\pi$
$314$	23.4273			1.32208
$315$	17.4514	−	3.23263i	0.983273	−	0.182138i
$316$	−5.65999			−0.318399
$317$	15.7479	−	27.2761i	0.884490	−	1.53198i	0.0381920	−	0.999270i	$-0.487840\pi$
$317$	15.7479	−	27.2761i	0.884490	−	1.53198i	0.846298	−	0.532710i	$-0.178827\pi$
$318$	5.15628	+	6.47518i	0.289150	+	0.363110i
$319$	5.07957	+	8.79807i	0.284401	+	0.492598i
$320$	0.390088	−	2.20178i	0.0218066	−	0.123083i
$321$	−19.6295	−	24.6504i	−1.09561	−	1.37585i
$322$	−13.9984	−	6.98559i	−0.780098	−	0.389292i
$323$	−46.5276			−2.58887
$324$	−8.09762	−	3.92792i	−0.449868	−	0.218218i
$325$	−16.4383	+	13.7477i	−0.911831	+	0.762583i
$326$		−	16.2109i		−	0.897839i
$327$	4.70615	−	11.9661i	0.260251	−	0.661728i
$328$	−5.59810	+	9.69620i	−0.309103	+	0.535383i
$329$	0.985271	−	1.97438i	0.0543197	−	0.108851i
$330$	2.37360	−	3.87095i	0.130663	−	0.213089i
$331$	4.62879	−	8.01729i	0.254421	−	0.440670i	−0.710317	−	0.703882i	$-0.751448\pi$
$331$	4.62879	−	8.01729i	0.254421	−	0.440670i	0.964738	+	0.263212i	$0.0847818\pi$
$332$	−7.08726	−	4.09183i	−0.388964	−	0.224568i
$333$	−1.01125	+	1.08677i	−0.0554160	+	0.0595548i
$334$	−11.8916	+	6.86564i	−0.650681	+	0.375671i
$335$	2.38545	+	6.57065i	0.130331	+	0.358993i
$336$	4.35854	+	1.41531i	0.237778	+	0.0772115i
$337$	1.22970	+	0.709968i	0.0669860	+	0.0386744i	0.533119	−	0.846040i	$-0.321020\pi$
$337$	1.22970	+	0.709968i	0.0669860	+	0.0386744i	−0.466133	+	0.884715i	$0.654353\pi$
$338$	−5.36859			−0.292013
$339$	−3.62593	+	9.21951i	−0.196934	+	0.500735i
$340$	15.8226	+	2.80327i	0.858100	+	0.152029i
$341$	1.23550	+	2.13996i	0.0669063	+	0.115885i
$342$	−5.69888	−	18.5687i	−0.308160	−	1.00408i
$343$	−3.35546	−	18.2138i	−0.181178	−	0.983450i
$344$	−4.14896	+	2.39541i	−0.223697	+	0.129152i
$345$	0.605866	−	22.8933i	0.0326187	−	1.23253i
$346$	0.365628	−	0.211095i	0.0196563	−	0.0113485i
$347$	−2.79817	−	4.84657i	−0.150214	−	0.260177i	0.781092	−	0.624416i	$-0.214663\pi$
$347$	−2.79817	−	4.84657i	−0.150214	−	0.260177i	−0.931306	+	0.364238i	$0.881329\pi$
$348$	−13.9671	−	5.49313i	−0.748718	−	0.294462i
$349$	19.8352	−	11.4519i	1.06176	−	0.613005i	0.135839	−	0.990731i	$-0.456627\pi$
$349$	19.8352	−	11.4519i	1.06176	−	0.613005i	0.925918	+	0.377726i	$0.123294\pi$
$350$	−9.08694	−	9.61392i	−0.485718	−	0.513886i
$351$	−1.71144	+	22.2041i	−0.0913501	+	1.18517i
$352$	1.01534	−	0.586205i	0.0541177	−	0.0312449i
$353$		−	27.2427i		−	1.44998i	−0.688759	−	0.724990i	$-0.741844\pi$
$353$		−	27.2427i		−	1.44998i	0.688759	−	0.724990i	$-0.258156\pi$
$354$	5.29924	−	0.794891i	0.281651	−	0.0422480i
$355$	−3.78539	−	0.670655i	−0.200908	−	0.0355946i
$356$	2.45588	−	4.25371i	0.130162	−	0.225446i
$357$	−10.1708	+	31.3217i	−0.538296	+	1.65772i
$358$	18.7039	−	10.7987i	0.988532	−	0.570729i
$359$	−8.75688	+	5.05579i	−0.462171	+	0.266834i	−0.712957	−	0.701208i	$-0.752644\pi$
$359$	−8.75688	+	5.05579i	−0.462171	+	0.266834i	0.250786	+	0.968043i	$0.419311\pi$
$360$	0.819251	+	6.65799i	0.0431783	+	0.350907i
$361$	11.4597	−	19.8487i	0.603140	−	1.04467i
$362$	−12.3061	−	7.10492i	−0.646793	−	0.373426i
$363$	−16.4873	+	2.47312i	−0.865360	+	0.129805i
$364$	−0.688192	−	11.3184i	−0.0360710	−	0.593246i
$365$	−9.48824	−	7.97479i	−0.496637	−	0.417420i
$366$	3.67702	−	2.92806i	0.192201	−	0.153052i
$367$	−21.9413			−1.14532			−0.572662	−	0.819792i	$-0.694089\pi$
$367$	−21.9413			−1.14532			−0.572662	+	0.819792i	$0.694089\pi$
$368$	2.95654	−	5.12089i	0.154121	−	0.266945i
$369$	7.52057	−	32.7359i	0.391505	−	1.70416i
$370$	1.08950	+	0.193026i	0.0566406	+	0.0100350i
$371$	11.3135	+	5.64575i	0.587366	+	0.293113i
$372$	−3.39723	−	1.33609i	−0.176138	−	0.0692732i
$373$			10.8314i			0.560829i	0.959879	+	0.280414i	$0.0904719\pi$
$373$			10.8314i			0.560829i	−0.959879	+	0.280414i	$0.909528\pi$
$374$	4.21263	+	7.29649i	0.217830	+	0.377293i
$375$	7.13171	−	18.0039i	0.368280	−	0.929715i
$376$	0.722267	+	0.417001i	0.0372481	+	0.0215052i
$377$			37.1377i			1.91269i
$378$	−13.7459	−	0.222670i	−0.707014	−	0.0114529i
$379$	14.1460			0.726629			0.363315	−	0.931667i	$-0.381645\pi$
$379$	14.1460			0.726629			0.363315	+	0.931667i	$0.381645\pi$
$380$	−9.31498	+	11.0828i	−0.477849	+	0.568534i
$381$	−3.14290	−	20.9525i	−0.161016	−	1.07343i
$382$	6.42249	−	3.70803i	0.328603	−	0.189719i
$383$			3.82263i			0.195327i	0.995219	+	0.0976637i	$0.0311369\pi$
$383$			3.82263i			0.195327i	−0.995219	+	0.0976637i	$0.968863\pi$
$384$	−0.633932	+	1.61187i	−0.0323502	+	0.0822555i
$385$	0.793285	−	6.89056i	0.0404295	−	0.351176i
$386$			17.4750i			0.889453i
$387$	9.79066	−	10.5219i	0.497687	−	0.534857i
$388$	2.45459	−	4.25148i	0.124613	−	0.215836i
$389$			6.79087i			0.344311i	0.985070	+	0.172155i	$0.0550731\pi$
$389$			6.79087i			0.344311i	−0.985070	+	0.172155i	$0.944927\pi$
$390$	14.5897	−	7.91632i	0.738781	−	0.400859i
$391$	36.8001	+	21.2465i	1.86106	+	1.07448i
$392$	6.94843	−	0.848104i	0.350949	−	0.0428357i
$393$	15.1899	−	2.27851i	0.766230	−	0.114935i
$394$	9.42507	−	16.3247i	0.474828	−	0.822426i
$395$	−9.68850	−	8.14311i	−0.487481	−	0.409724i
$396$	−2.39598	+	2.57492i	−0.120402	+	0.129395i
$397$	−9.26588	−	16.0490i	−0.465041	−	0.805475i	0.534162	−	0.845382i	$-0.320627\pi$
$397$	−9.26588	−	16.0490i	−0.465041	−	0.805475i	−0.999203	+	0.0399072i	$0.987294\pi$
$398$	5.56129	−	3.21081i	0.278762	−	0.160944i
$399$	−19.8570	−	22.0455i	−0.994095	−	1.10366i
$400$	3.83547	−	3.20768i	0.191773	−	0.160384i
$401$			11.5263i			0.575594i	0.957691	+	0.287797i	$0.0929228\pi$
$401$			11.5263i			0.575594i	−0.957691	+	0.287797i	$0.907077\pi$
$402$	−0.803215	−	5.35473i	−0.0400607	−	0.267070i
$403$			9.03301i			0.449966i
$404$	−3.99323	−	6.91648i	−0.198671	−	0.344108i
$405$	−8.20996	−	18.3738i	−0.407956	−	0.913001i
$406$	−22.8836	+	1.39139i	−1.13570	+	0.0690535i
$407$	0.290071	+	0.502418i	0.0143783	+	0.0249039i
$408$	−11.5833	−	4.55560i	−0.573461	−	0.225536i
$409$	−4.22950	+	2.44190i	−0.209135	+	0.120744i	−0.600909	−	0.799317i	$-0.705195\pi$
$409$	−4.22950	+	2.44190i	−0.209135	+	0.120744i	0.391774	+	0.920061i	$0.371861\pi$
$410$	−23.5326	+	8.54342i	−1.16219	+	0.421929i
$411$	−1.15630	+	0.173446i	−0.0570361	+	0.00855548i
$412$	−7.60289	−	13.1686i	−0.374567	−	0.648770i
$413$	6.82720	−	4.51531i	0.335945	−	0.222184i
$414$	−3.97186	+	17.2889i	−0.195206	+	0.849703i
$415$	−6.24465	−	17.2007i	−0.306538	−	0.844351i
$416$	4.28586			0.210132
$417$	35.4881	+	13.9571i	1.73786	+	0.683482i
$418$	−7.59079			−0.371278
$419$	−15.6980	+	27.1897i	−0.766897	+	1.32830i	0.172341	+	0.985037i	$0.444867\pi$
$419$	−15.6980	+	27.1897i	−0.766897	+	1.32830i	−0.939238	+	0.343267i	$0.888466\pi$
$420$	5.42452	+	8.69337i	0.264689	+	0.424193i
$421$	9.58537	+	16.6023i	0.467162	+	0.809149i	0.999296	−	0.0375115i	$-0.0119431\pi$
$421$	9.58537	+	16.6023i	0.467162	+	0.809149i	−0.532134	+	0.846660i	$0.678610\pi$
$422$	4.56527	+	7.90727i	0.222234	+	0.384920i
$423$	−2.43848	−	0.560205i	−0.118563	−	0.0272381i
$424$	−2.38948	+	4.13870i	−0.116043	+	0.200993i
$425$	23.0512	+	27.5627i	1.11815	+	1.33699i
$426$	2.77120	+	1.08988i	0.134265	+	0.0528049i
$427$	3.20601	−	6.42450i	0.155150	−	0.310903i
$428$	9.09652	−	15.7556i	0.439697	−	0.761577i
$429$	8.09932	+	3.18537i	0.391039	+	0.153791i
$430$	−10.5483	−	1.86884i	−0.508685	−	0.0901233i
$431$	0.601870	+	0.347490i	0.0289911	+	0.0167380i	0.514425	−	0.857535i	$-0.328005\pi$
$431$	0.601870	+	0.347490i	0.0289911	+	0.0167380i	−0.485434	+	0.874273i	$0.661339\pi$
$432$	0.399323	−	5.18079i	0.0192124	−	0.249261i
$433$	30.7847			1.47942			0.739709	−	0.672927i	$-0.234963\pi$
$433$	30.7847			1.47942			0.739709	+	0.672927i	$0.234963\pi$
$434$	−5.56599	+	0.338428i	−0.267176	+	0.0162451i
$435$	−16.0053	−	29.4976i	−0.767393	−	1.41430i
$436$	7.42375			0.355533
$437$	−33.1552	+	19.1422i	−1.58603	+	0.915695i
$438$	5.98065	+	7.51041i	0.285767	+	0.358861i
$439$	−25.5026	−	14.7240i	−1.21717	−	0.702736i	−0.252862	−	0.967502i	$-0.581372\pi$
$439$	−25.5026	−	14.7240i	−1.21717	−	0.702736i	−0.964313	+	0.264766i	$0.914705\pi$
$440$	2.58139	+	0.457343i	0.123063	+	0.0218030i
$441$	−19.1814	+	8.54836i	−0.913399	+	0.407065i
$442$			30.7993i			1.46498i
$443$	0.807475	−	1.39859i	0.0383643	−	0.0664489i	−0.846206	−	0.532856i	$-0.821119\pi$
$443$	0.807475	−	1.39859i	0.0383643	−	0.0664489i	0.884570	+	0.466407i	$0.154452\pi$
$444$	−0.797600	−	0.313687i	−0.0378524	−	0.0148869i
$445$	10.3238	−	3.74799i	0.489393	−	0.177672i
$446$	−10.9748			−0.519672
$447$	2.68858	+	17.9237i	0.127166	+	0.847764i
$448$	0.160573	+	2.64087i	0.00758634	+	0.124770i
$449$		−	34.9051i		−	1.64727i	−0.567119	−	0.823636i	$-0.691942\pi$
$449$		−	34.9051i		−	1.64727i	0.567119	−	0.823636i	$-0.308058\pi$
$450$	−8.17660	+	12.5755i	−0.385448	+	0.592815i
$451$	−11.3679	−	6.56328i	−0.535295	−	0.309053i
$452$	−5.71976			−0.269035
$453$	19.9874	−	2.99814i	0.939092	−	0.140865i
$454$	6.60089	+	3.81103i	0.309795	+	0.178860i
$455$	15.1060	−	20.3644i	0.708179	−	0.954700i
$456$	8.77256	−	6.98572i	0.410813	−	0.327136i
$457$	0.249715	+	0.144173i	0.0116812	+	0.00674413i	0.505829	−	0.862634i	$-0.331187\pi$
$457$	0.249715	+	0.144173i	0.0116812	+	0.00674413i	−0.494148	+	0.869378i	$0.664520\pi$
$458$	−10.8475	−	6.26278i	−0.506868	−	0.292640i
$459$	37.2305	+	2.86964i	1.73777	+	0.133944i
$460$	12.4284	−	4.51207i	0.579476	−	0.210376i
$461$	−7.61142	−	13.1834i	−0.354499	−	0.614011i	0.632533	−	0.774534i	$-0.282015\pi$
$461$	−7.61142	−	13.1834i	−0.354499	−	0.614011i	−0.987032	+	0.160523i	$0.948682\pi$
$462$	−1.65933	+	5.11000i	−0.0771988	+	0.237739i
$463$	−19.2284	−	11.1015i	−0.893618	−	0.515931i	−0.0184941	−	0.999829i	$-0.505887\pi$
$463$	−19.2284	−	11.1015i	−0.893618	−	0.515931i	−0.875124	+	0.483898i	$0.839221\pi$
$464$		−	8.66517i		−	0.402270i
$465$	−3.89296	−	7.17471i	−0.180532	−	0.332719i
$466$	−20.0620			−0.929354
$467$	−22.8739	+	13.2062i	−1.05848	+	0.611112i	−0.925011	−	0.379941i	$-0.875944\pi$
$467$	−22.8739	+	13.2062i	−1.05848	+	0.611112i	−0.133466	+	0.991053i	$0.542611\pi$
$468$	−12.2917	+	3.77242i	−0.568185	+	0.174380i
$469$	−4.56259	−	6.89870i	−0.210681	−	0.318552i
$470$	0.636397	+	1.75294i	0.0293548	+	0.0808571i
$471$	−25.2770	−	31.7425i	−1.16470	−	1.46262i
$472$	1.54687	+	2.67926i	0.0712005	+	0.123323i
$473$	−2.80840	−	4.86429i	−0.129130	−	0.223660i
$474$	6.10688	+	7.66892i	0.280498	+	0.352245i
$475$	−31.8899	+	5.56935i	−1.46321	+	0.255539i
$476$	−18.9780	+	1.15392i	−0.869857	+	0.0528897i
$477$	3.21006	−	13.9729i	0.146978	−	0.639774i
$478$	10.8229	−	6.24858i	0.495026	−	0.285803i
$479$	39.4823			1.80399			0.901997	−	0.431743i	$-0.142101\pi$
$479$	39.4823			1.80399			0.901997	+	0.431743i	$0.142101\pi$
$480$	−3.40416	+	1.84708i	−0.155378	+	0.0843073i
$481$			2.12077i			0.0966986i
$482$	−14.7942	−	8.54144i	−0.673857	−	0.389052i
$483$	5.63858	+	26.5040i	0.256564	+	1.20598i
$484$	−4.81273	−	8.33589i	−0.218760	−	0.378904i
$485$	10.3183	−	3.74602i	0.468531	−	0.170098i
$486$	3.41489	+	15.2098i	0.154903	+	0.689931i
$487$	−21.3058	−	12.3009i	−0.965458	−	0.557408i	−0.0676098	−	0.997712i	$-0.521537\pi$
$487$	−21.3058	−	12.3009i	−0.965458	−	0.557408i	−0.897849	+	0.440304i	$0.854871\pi$
$488$	2.35021	+	1.35690i	0.106389	+	0.0614238i
$489$	−21.9648	+	17.4909i	−0.993281	+	0.790964i
$490$	13.1142	+	8.54507i	0.592438	+	0.386027i
$491$	−13.3649	−	7.71621i	−0.603148	−	0.348228i	0.167131	−	0.985935i	$-0.446550\pi$
$491$	−13.3649	−	7.71621i	−0.603148	−	0.348228i	−0.770279	+	0.637707i	$0.779883\pi$
$492$	19.1778	−	2.87670i	0.864604	−	0.129692i
$493$	62.2702			2.80451
$494$	−24.0312	−	13.8744i	−1.08122	−	0.624240i
$495$	−7.80590	+	0.960499i	−0.350849	+	0.0431712i
$496$		−	2.10763i		−	0.0946354i
$497$	4.54030	−	0.276063i	0.203660	−	0.0123831i
$498$	2.10267	+	14.0177i	0.0942228	+	0.628148i
$499$	10.6991			0.478957			0.239479	−	0.970902i	$-0.423024\pi$
$499$	10.6991			0.478957			0.239479	+	0.970902i	$0.423024\pi$
$500$	11.1803	+	0.0273945i	0.499998	+	0.00122512i
$501$	22.1330	+	8.70469i	0.988832	+	0.388897i
$502$	−4.83073	+	8.36707i	−0.215606	+	0.373440i
$503$			13.1731i			0.587361i	0.955904	+	0.293680i	$0.0948802\pi$
$503$			13.1731i			0.587361i	−0.955904	+	0.293680i	$0.905120\pi$
$504$	−2.78502	−	7.43261i	−0.124055	−	0.331075i
$505$	3.11542	−	17.5844i	0.138634	−	0.782497i
$506$	6.00378	+	3.46629i	0.266901	+	0.154095i
$507$	5.79248	+	7.27410i	0.257253	+	0.323054i
$508$	10.5935	−	6.11613i	0.470009	−	0.271360i
$509$	39.0491			1.73082			0.865410	−	0.501064i	$-0.167058\pi$
$509$	39.0491			1.73082			0.865410	+	0.501064i	$0.167058\pi$
$510$	−13.2736	−	24.4632i	−0.587765	−	1.08325i
$511$	13.1222	+	6.54837i	0.580493	+	0.289683i
$512$	−1.00000			−0.0441942
$513$	−19.0106	+	27.7564i	−0.839338	+	1.22548i
$514$	−7.33028	−	4.23214i	−0.323325	−	0.186672i
$515$	5.93158	−	33.4798i	0.261377	−	1.47529i
$516$	7.72217	+	3.03705i	0.339950	+	0.133699i
$517$	−0.488897	+	0.846794i	−0.0215016	+	0.0372419i
$518$	−1.30678	+	0.0794559i	−0.0574166	+	0.00349109i
$519$	−0.680517	−	0.267640i	−0.0298714	−	0.0117481i
$520$	7.33633	+	6.16613i	0.321719	+	0.270403i
$521$	−3.75669	+	6.50678i	−0.164584	+	0.285067i	−0.936507	−	0.350648i	$-0.885961\pi$
$521$	−3.75669	+	6.50678i	−0.164584	+	0.285067i	0.771924	+	0.635715i	$0.219295\pi$
$522$	7.62710	+	24.8514i	0.333829	+	1.08772i
$523$	6.93702	+	12.0153i	0.303335	+	0.525391i	0.976889	−	0.213747i	$-0.0685667\pi$
$523$	6.93702	+	12.0153i	0.303335	+	0.525391i	−0.673555	+	0.739138i	$0.735233\pi$
$524$	4.43401	+	7.67993i	0.193701	+	0.335499i
$525$	−3.22184	+	22.6852i	−0.140613	+	0.990065i
$526$	7.96114	−	13.7891i	0.347122	−	0.601233i
$527$	15.1460			0.659770
$528$	−1.88978	−	0.743228i	−0.0822420	−	0.0323449i
$529$	11.9646			0.520201
$530$	−10.0446	+	3.64665i	−0.436310	+	0.158400i
$531$	−6.79467	−	6.32248i	−0.294864	−	0.274372i
$532$	7.64884	−	15.3274i	0.331619	−	0.664529i
$533$	−23.9927	−	41.5565i	−1.03924	−	1.80001i
$534$	−8.41331	+	1.26201i	−0.364079	+	0.0546123i
$535$	38.2389	−	13.8824i	1.65321	−	0.600191i
$536$	2.70732	−	1.56307i	0.116938	−	0.0675144i
$537$	−34.8123	−	13.6913i	−1.50226	−	0.590823i
$538$	13.0701	+	22.6380i	0.563491	+	0.975995i
$539$	0.994327	+	8.14642i	0.0428287	+	0.350891i
$540$	8.13722	−	8.29371i	0.350170	−	0.356905i
$541$	−13.2014	−	22.8655i	−0.567572	−	0.983063i	−0.996805	−	0.0798694i	$-0.974550\pi$
$541$	−13.2014	−	22.8655i	−0.567572	−	0.983063i	0.429234	−	0.903193i	$-0.358784\pi$
$542$		−	1.24122i		−	0.0533150i
$543$	3.65101	+	24.3399i	0.156680	+	1.04452i
$544$		−	7.18627i		−	0.308109i
$545$	12.7076	+	10.6807i	0.544335	+	0.457509i
$546$	−14.5932	+	13.1445i	−0.624532	+	0.562534i
$547$	20.7304	−	11.9687i	0.886366	−	0.511744i	0.0136139	−	0.999907i	$-0.495666\pi$
$547$	20.7304	−	11.9687i	0.886366	−	0.511744i	0.872752	+	0.488164i	$0.162333\pi$
$548$	−0.337529	−	0.584618i	−0.0144185	−	0.0249737i
$549$	−7.93468	−	1.82287i	−0.338644	−	0.0777984i
$550$	3.76072	+	4.49674i	0.160357	+	0.191742i
$551$	−28.0514	+	48.5864i	−1.19503	+	2.06985i
$552$	−10.1285	+	1.51928i	−0.431096	+	0.0646649i
$553$	13.3992	+	6.68658i	0.569791	+	0.284342i
$554$	3.66803	+	2.11774i	0.155840	+	0.0899740i
$555$	−0.913988	−	1.68448i	−0.0387966	−	0.0715020i
$556$			22.0167i			0.933717i
$557$	11.8187	−	20.4706i	0.500775	−	0.867369i	−0.499224	−	0.866473i	$-0.666382\pi$
$557$	11.8187	−	20.4706i	0.500775	−	0.867369i	1.00000		0.000895644i	$-0.000285092\pi$
$558$	1.85514	+	6.04462i	0.0785344	+	0.255889i
$559$		−	20.5327i		−	0.868443i
$560$	−3.52461	+	4.75154i	−0.148942	+	0.200789i
$561$	5.34104	−	13.5804i	0.225499	−	0.573367i
$562$		−	2.82239i		−	0.119055i
$563$	−32.8465	+	18.9640i	−1.38432	+	0.799235i	−0.992667	−	0.120880i	$-0.961429\pi$
$563$	−32.8465	+	18.9640i	−1.38432	+	0.799235i	−0.391649	+	0.920115i	$0.628095\pi$
$564$	−0.214284	−	1.42855i	−0.00902300	−	0.0601529i
$565$	−9.79081	−	8.22910i	−0.411902	−	0.346201i
$566$	12.3542			0.519286
$567$	14.5295	+	18.8651i	0.610184	+	0.792260i
$568$			1.71924i			0.0721378i
$569$	−5.79585	−	3.34624i	−0.242975	−	0.140281i	0.373569	−	0.927603i	$-0.378134\pi$
$569$	−5.79585	−	3.34624i	−0.242975	−	0.140281i	−0.616543	+	0.787321i	$0.711467\pi$
$570$	25.0669	+	0.663391i	1.04994	+	0.0277864i
$571$	16.7631	+	29.0346i	0.701515	+	1.21506i	0.967934	+	0.251203i	$0.0808261\pi$
$571$	16.7631	+	29.0346i	0.701515	+	1.21506i	−0.266419	+	0.963857i	$0.585841\pi$
$572$			5.02479i			0.210097i
$573$	−11.9537	−	4.70127i	−0.499374	−	0.196398i
$574$	24.7075	−	16.3408i	1.03127	−	0.682053i
$575$	27.7659	+	10.1573i	1.15792	+	0.423591i
$576$	2.86797	−	0.880202i	0.119499	−	0.0366751i
$577$	−19.1880	+	33.2346i	−0.798807	+	1.38357i	0.121586	+	0.992581i	$0.461202\pi$
$577$	−19.1880	+	33.2346i	−0.798807	+	1.38357i	−0.920393	+	0.390994i	$0.872131\pi$
$578$	34.6425			1.44094
$579$	23.6775	−	18.8547i	0.984003	−	0.783576i
$580$	12.4667	−	14.8326i	0.517652	−	0.615891i
$581$	11.9440	+	18.0595i	0.495522	+	0.749235i
$582$	−8.40889	+	1.26134i	−0.348560	+	0.0522843i
$583$	−4.85225	−	2.80145i	−0.200960	−	0.116024i
$584$	−2.77150	+	4.80038i	−0.114685	+	0.198641i
$585$	−26.4678	−	11.2268i	−1.09431	−	0.464172i
$586$	7.31257	−	4.22192i	0.302080	−	0.174406i
$587$	−30.4845	+	17.6002i	−1.25823	+	0.726439i	−0.972730	−	0.231940i	$-0.925493\pi$
$587$	−30.4845	+	17.6002i	−1.25823	+	0.726439i	−0.285499	+	0.958379i	$0.592159\pi$
$588$	−8.64618	−	8.49962i	−0.356563	−	0.350518i
$589$	−6.82294	+	11.8177i	−0.281134	+	0.486939i
$590$	−1.20683	+	6.81174i	−0.0496844	+	0.280435i
$591$	−32.2882	+	4.84326i	−1.32816	+	0.199225i
$592$		−	0.494829i		−	0.0203373i
$593$	9.49935	−	5.48445i	0.390092	−	0.225219i	−0.292108	−	0.956385i	$-0.594357\pi$
$593$	9.49935	−	5.48445i	0.390092	−	0.225219i	0.682200	+	0.731166i	$0.261023\pi$
$594$	6.07401	+	0.468171i	0.249220	+	0.0192093i
$595$	−34.1459	−	25.3288i	−1.39984	−	1.03838i
$596$	−9.06213	+	5.23202i	−0.371199	+	0.214312i
$597$	−10.3508	−	4.07087i	−0.423632	−	0.166610i
$598$	12.6713	+	21.9474i	0.518169	+	0.897496i
$599$	−25.5205	+	14.7343i	−1.04274	+	0.602026i	−0.920608	−	0.390488i	$-0.872306\pi$
$599$	−25.5205	+	14.7343i	−1.04274	+	0.602026i	−0.122131	+	0.992514i	$0.538973\pi$
$600$	−8.48450	−	1.73587i	−0.346378	−	0.0708667i
$601$	21.1142	−	12.1903i	0.861266	−	0.497252i	−0.00317008	−	0.999995i	$-0.501009\pi$
$601$	21.1142	−	12.1903i	0.861266	−	0.497252i	0.864436	+	0.502743i	$0.167676\pi$
$602$	12.6519	−	0.769273i	0.515654	−	0.0313532i
$603$	−6.38868	+	6.86582i	−0.260167	+	0.279598i
$604$	5.83443	+	10.1055i	0.237400	+	0.411188i
$605$	3.75477	−	21.1931i	0.152653	−	0.861623i
$606$	−5.06287	+	12.8732i	−0.205665	+	0.522936i
$607$	42.2934			1.71664			0.858319	−	0.513116i	$-0.171509\pi$
$607$	42.2934			1.71664			0.858319	+	0.513116i	$0.171509\pi$
$608$	5.60709	+	3.23726i	0.227398	+	0.131288i
$609$	26.5757	+	29.5046i	1.07690	+	1.19559i
$610$	2.07080	+	5.70396i	0.0838442	+	0.230947i
$611$	−3.09553	+	1.78721i	−0.125232	+	0.0723027i
$612$	6.32537	+	20.6100i	0.255688	+	0.833110i
$613$	−34.6428	−	20.0010i	−1.39921	−	0.807833i	−0.404898	−	0.914362i	$-0.632693\pi$
$613$	−34.6428	−	20.0010i	−1.39921	−	0.807833i	−0.994310	+	0.106529i	$0.966026\pi$
$614$	5.29184	−	9.16573i	0.213561	−	0.369899i
$615$	36.9665	+	22.6673i	1.49063	+	0.914032i
$616$	−3.09619	+	0.188257i	−0.124749	+	0.00758509i
$617$	−3.01056	+	5.21444i	−0.121200	+	0.209925i	−0.920241	−	0.391351i	$-0.872008\pi$
$617$	−3.01056	+	5.21444i	−0.121200	+	0.209925i	0.799041	+	0.601277i	$0.205341\pi$
$618$	−9.63942	+	24.5098i	−0.387754	+	0.985927i
$619$		−	15.1993i		−	0.610913i	−0.952206	−	0.305457i	$-0.901191\pi$
$619$		−	15.1993i		−	0.610913i	0.952206	−	0.305457i	$-0.0988091\pi$
$620$	3.03228	−	3.60774i	0.121779	−	0.144890i
$621$	27.7108	−	13.2723i	1.11200	−	0.532601i
$622$	21.1294			0.847210
$623$	−10.8392	+	7.16871i	−0.434263	+	0.287208i
$624$	−4.62425	−	5.80707i	−0.185118	−	0.232469i
$625$	19.0985	+	16.1322i	0.763940	+	0.645287i
$626$	−4.08549	−	7.07628i	−0.163289	−	0.282825i
$627$	8.19013	+	10.2850i	0.327082	+	0.410745i
$628$	11.7137	−	20.2887i	0.467426	−	0.809605i
$629$	3.55597			0.141786
$630$	5.92614	−	16.7296i	0.236103	−	0.666525i
$631$	17.7980			0.708525			0.354263	−	0.935146i	$-0.384732\pi$
$631$	17.7980			0.708525			0.354263	+	0.935146i	$0.384732\pi$
$632$	−2.82999	+	4.90169i	−0.112571	+	0.194979i
$633$	5.78813	−	14.7172i	0.230058	−	0.584958i
$634$	−15.7479	−	27.2761i	−0.625429	−	1.08327i
$635$	26.9328	+	4.77166i	1.06879	+	0.189357i
$636$	8.18581	−	1.22788i	0.324589	−	0.0486887i
$637$	−11.7421	+	27.6077i	−0.465240	+	1.09386i
$638$	10.1591			0.402204
$639$	−1.51328	−	4.93073i	−0.0598644	−	0.195057i
$640$	−1.71175	−	1.43872i	−0.0676630	−	0.0568702i
$641$		−	4.84232i		−	0.191260i	−0.995417	−	0.0956300i	$-0.969513\pi$
$641$		−	4.84232i		−	0.191260i	0.995417	−	0.0956300i	$-0.0304866\pi$
$642$	−31.1626	+	4.67443i	−1.22989	+	0.184485i
$643$	16.6814	−	28.8931i	0.657851	−	1.13943i	−0.323320	−	0.946290i	$-0.604799\pi$
$643$	16.6814	−	28.8931i	0.657851	−	1.13943i	0.981171	−	0.193141i	$-0.0618675\pi$
$644$	−13.0489	+	8.63014i	−0.514198	+	0.340075i
$645$	8.84901	+	16.3087i	0.348429	+	0.642154i
$646$	−23.2638	+	40.2941i	−0.915302	+	1.58535i
$647$	9.93502	+	5.73598i	0.390586	+	0.225505i	0.682414	−	0.730966i	$-0.260930\pi$
$647$	9.93502	+	5.73598i	0.390586	+	0.225505i	−0.291828	+	0.956471i	$0.594264\pi$
$648$	−7.45049	+	5.04878i	−0.292683	+	0.198335i
$649$	−3.14119	+	1.81357i	−0.123303	+	0.0711888i
$650$	3.68668	+	21.1098i	0.144604	+	0.827994i
$651$	6.46401	+	7.17641i	0.253344	+	0.281266i
$652$	−14.0391	−	8.10545i	−0.549812	−	0.317434i
$653$	28.4926			1.11500			0.557502	−	0.830176i	$-0.311760\pi$
$653$	28.4926			1.11500			0.557502	+	0.830176i	$0.311760\pi$
$654$	−8.00990	−	10.0587i	−0.313212	−	0.393327i
$655$	−3.45930	+	19.5254i	−0.135166	+	0.762921i
$656$	5.59810	+	9.69620i	0.218569	+	0.378573i
$657$	3.72327	−	16.2068i	0.145259	−	0.632288i
$658$	−1.21722	−	1.84046i	−0.0474523	−	0.0717485i
$659$	38.6573	−	22.3188i	1.50588	−	0.869418i	0.505899	−	0.862593i	$-0.331161\pi$
$659$	38.6573	−	22.3188i	1.50588	−	0.869418i	0.999977	−	0.00682541i	$-0.00217261\pi$
$660$	−2.16554	−	3.99107i	−0.0842934	−	0.155352i
$661$	−22.7752	+	13.1493i	−0.885853	+	0.511448i	−0.872584	−	0.488464i	$-0.837557\pi$
$661$	−22.7752	+	13.1493i	−0.885853	+	0.511448i	−0.0132693	+	0.999912i	$0.504224\pi$
$662$	−4.62879	−	8.01729i	−0.179903	−	0.311601i
$663$	41.7312	−	33.2311i	1.62070	−	1.29059i
$664$	−7.08726	+	4.09183i	−0.275039	+	0.158794i
$665$	35.1448	−	15.2323i	1.36286	−	0.590683i
$666$	0.435549	+	1.41915i	0.0168772	+	0.0549911i
$667$	44.3733	−	25.6190i	1.71814	−	0.991970i
$668$			13.7313i			0.531279i
$669$	11.8413	+	14.8702i	0.457813	+	0.574914i
$670$	6.88307	+	1.21947i	0.265916	+	0.0471122i
$671$	−1.59084	+	2.75542i	−0.0614137	+	0.106372i
$672$	3.40497	−	3.06695i	0.131349	−	0.118310i
$673$	6.25246	−	3.60986i	0.241015	−	0.139150i	−0.374628	−	0.927175i	$-0.622230\pi$
$673$	6.25246	−	3.60986i	0.241015	−	0.139150i	0.615643	+	0.788025i	$0.288896\pi$
$674$	1.22970	−	0.709968i	0.0473663	−	0.0273469i
$675$	25.8612	−	2.48965i	0.995398	−	0.0958265i
$676$	−2.68430	+	4.64934i	−0.103242	+	0.178821i
$677$	8.94210	+	5.16272i	0.343673	+	0.198419i	0.661895	−	0.749597i	$-0.269752\pi$
$677$	8.94210	+	5.16272i	0.343673	+	0.198419i	−0.318222	+	0.948016i	$0.603086\pi$
$678$	6.17137	+	7.74991i	0.237010	+	0.297633i
$679$	−10.8335	+	7.16495i	−0.415751	+	0.274965i
$680$	10.3390	−	12.3011i	0.396482	−	0.471726i
$681$	−1.95837	−	13.0557i	−0.0750450	−	0.500296i
$682$	2.47101			0.0946199
$683$	17.4703	−	30.2595i	0.668483	−	1.15785i	−0.309846	−	0.950787i	$-0.600277\pi$
$683$	17.4703	−	30.2595i	0.668483	−	1.15785i	0.978328	−	0.207059i	$-0.0663893\pi$
$684$	−18.9304	−	4.34898i	−0.723822	−	0.166287i
$685$	0.263332	−	1.48633i	0.0100614	−	0.0567898i
$686$	−17.4513	−	6.20096i	−0.666294	−	0.236754i
$687$	3.21826	+	21.4549i	0.122784	+	0.818555i
$688$			4.79081i			0.182648i
$689$	−10.2410	−	17.7379i	−0.390150	−	0.675759i
$690$	−19.5232	−	11.9713i	−0.743237	−	0.455741i
$691$	−22.8320	−	13.1820i	−0.868569	−	0.501469i	−0.00169652	−	0.999999i	$-0.500540\pi$
$691$	−22.8320	−	13.1820i	−0.868569	−	0.501469i	−0.866872	+	0.498530i	$0.833873\pi$
$692$		−	0.422190i		−	0.0160493i
$693$	8.71407	−	3.26519i	0.331020	−	0.124034i
$694$	−5.59634			−0.212434
$695$	−31.6758	+	37.6872i	−1.20153	+	1.42956i
$696$	−11.7408	+	9.34934i	−0.445032	+	0.354386i
$697$	−69.6795	+	40.2295i	−2.63930	+	1.52380i
$698$		−	22.9038i		−	0.866920i
$699$	21.6460	+	27.1827i	0.818727	+	1.02815i
$700$	−12.8694	+	3.06256i	−0.486417	+	0.115754i
$701$			32.4691i			1.22634i	0.789951	+	0.613170i	$0.210106\pi$
$701$			32.4691i			1.22634i	−0.789951	+	0.613170i	$0.789894\pi$
$702$	18.3736	+	12.5842i	0.693467	+	0.474961i
$703$	−1.60189	+	2.77455i	−0.0604163	+	0.104644i
$704$		−	1.17241i		−	0.0441869i
$705$	1.68848	−	2.75362i	0.0635917	−	0.103707i
$706$	−23.5928	−	13.6213i	−0.887928	−	0.512646i
$707$	1.28241	+	21.0913i	0.0482299	+	0.793218i
$708$	1.96122	−	4.98672i	0.0737072	−	0.187412i
$709$	−4.78868	+	8.29424i	−0.179843	+	0.311497i	−0.941827	−	0.336099i	$-0.890892\pi$
$709$	−4.78868	+	8.29424i	−0.179843	+	0.311497i	0.761984	+	0.647596i	$0.224226\pi$
$710$	−2.47350	+	2.94292i	−0.0928287	+	0.110446i
$711$	3.80185	−	16.5489i	0.142581	−	0.620631i
$712$	−2.45588	−	4.25371i	−0.0920381	−	0.159415i
$713$	10.7929	−	6.23131i	0.404199	−	0.233364i
$714$	22.0400	+	24.4690i	0.824824	+	0.915730i
$715$	−7.22924	+	8.60120i	−0.270358	+	0.321667i
$716$		−	21.5974i		−	0.807133i
$717$	−20.1438	−	7.92235i	−0.752285	−	0.295865i
$718$			10.1116i			0.377361i
$719$	−2.90254	−	5.02734i	−0.108246	−	0.187488i	0.806814	−	0.590806i	$-0.201190\pi$
$719$	−2.90254	−	5.02734i	−0.108246	−	0.187488i	−0.915060	+	0.403318i	$0.867857\pi$
$720$	6.17561	+	2.61950i	0.230152	+	0.0976231i
$721$	2.44163	+	40.1565i	0.0909311	+	1.49551i
$722$	−11.4597	−	19.8487i	−0.426485	−	0.738693i
$723$	4.38919	+	29.2610i	0.163236	+	1.08823i
$724$	−12.3061	+	7.10492i	−0.457352	+	0.264052i
$725$	42.6799	−	7.45375i	1.58509	−	0.276825i
$726$	−6.10188	+	15.5150i	−0.226462	+	0.575815i
$727$	−8.93125	−	15.4694i	−0.331242	−	0.573728i	0.651514	−	0.758637i	$-0.274134\pi$
$727$	−8.93125	−	15.4694i	−0.331242	−	0.573728i	−0.982756	+	0.184909i	$0.940801\pi$
$728$	−10.1461	−	5.06322i	−0.376041	−	0.187655i
$729$	16.9238	−	21.0377i	0.626808	−	0.779174i
$730$	−11.6505	+	4.22966i	−0.431204	+	0.156547i
$731$	−34.4281			−1.27337
$732$	−0.697269	−	4.64842i	−0.0257718	−	0.171811i
$733$	−9.51136			−0.351310			−0.175655	−	0.984452i	$-0.556204\pi$
$733$	−9.51136			−0.351310			−0.175655	+	0.984452i	$0.556204\pi$
$734$	−10.9706	+	19.0017i	−0.404933	+	0.701365i
$735$	−2.57159	−	26.9886i	−0.0948547	−	0.995491i
$736$	−2.95654	−	5.12089i	−0.108980	−	0.188758i
$737$	1.83256	+	3.17409i	0.0675032	+	0.116919i
$738$	−24.5898	−	22.8809i	−0.905163	−	0.842259i
$739$	−5.18196	+	8.97542i	−0.190622	+	0.330166i	−0.945456	−	0.325749i	$-0.894384\pi$
$739$	−5.18196	+	8.97542i	−0.190622	+	0.330166i	0.754835	+	0.655915i	$0.227717\pi$
$740$	0.711917	−	0.847024i	0.0261706	−	0.0311372i
$741$	7.12966	+	47.5307i	0.261914	+	1.74608i
$742$	10.5461	−	6.97487i	0.387159	−	0.256056i
$743$	−18.0132	+	31.1998i	−0.660840	+	1.14461i	0.319555	+	0.947568i	$0.396466\pi$
$743$	−18.0132	+	31.1998i	−0.660840	+	1.14461i	−0.980395	+	0.197041i	$0.936867\pi$
$744$	−2.85571	+	2.27404i	−0.104695	+	0.0833704i
$745$	−23.0395	−	4.08190i	−0.844103	−	0.149549i
$746$	9.38027	+	5.41570i	0.343436	+	0.198283i
$747$	16.7244	−	17.9735i	0.611913	−	0.657614i
$748$	8.42526			0.308058
$749$	−40.1480	+	26.5527i	−1.46698	+	0.970214i
$750$	−12.0259	−	15.1782i	−0.439125	−	0.554228i
$751$	−31.2098			−1.13886			−0.569431	−	0.822039i	$-0.692837\pi$
$751$	−31.2098			−1.13886			−0.569431	+	0.822039i	$0.692837\pi$
$752$	0.722267	−	0.417001i	0.0263384	−	0.0152065i
$753$	16.5490	−	2.48237i	0.603079	−	0.0904625i
$754$	32.1622	+	18.5689i	1.17128	+	0.676238i
$755$	−4.55188	+	25.6923i	−0.165660	+	0.935037i
$756$	−7.06580	+	11.7930i	−0.256981	+	0.428907i
$757$			13.3600i			0.485577i	0.970079	+	0.242788i	$0.0780621\pi$
$757$			13.3600i			0.485577i	−0.970079	+	0.242788i	$0.921938\pi$
$758$	7.07298	−	12.2508i	0.256902	−	0.444968i
$759$	−1.78122	−	11.8747i	−0.0646542	−	0.431025i
$760$	4.94047	+	13.6084i	0.179210	+	0.493628i
$761$	2.26962			0.0822736			0.0411368	−	0.999154i	$-0.486902\pi$
$761$	2.26962			0.0822736			0.0411368	+	0.999154i	$0.486902\pi$
$762$	−19.7169	−	7.75442i	−0.714266	−	0.280913i
$763$	−17.5746	−	8.77024i	−0.636244	−	0.317504i
$764$		−	7.41605i		−	0.268303i
$765$	−18.8244	+	44.3796i	−0.680599	+	1.60455i
$766$	3.31050	+	1.91132i	0.119613	+	0.0690586i
$767$	−13.2594			−0.478767
$768$	1.07896	+	1.35494i	0.0389335	+	0.0488921i
$769$	−17.0906	−	9.86724i	−0.616301	−	0.355822i	0.159126	−	0.987258i	$-0.449132\pi$
$769$	−17.0906	−	9.86724i	−0.616301	−	0.355822i	−0.775428	+	0.631436i	$0.782466\pi$
$770$	−5.57076	−	4.13229i	−0.200756	−	0.148917i
$771$	2.17477	+	14.4984i	0.0783224	+	0.522146i
$772$	15.1338	+	8.73749i	0.544677	+	0.314469i
$773$	−24.4085	−	14.0923i	−0.877913	−	0.506863i	−0.00794325	−	0.999968i	$-0.502528\pi$
$773$	−24.4085	−	14.0923i	−0.877913	−	0.506863i	−0.869970	+	0.493105i	$0.835862\pi$
$774$	−4.21688	−	13.7399i	−0.151573	−	0.493870i
$775$	10.3810	−	1.81298i	0.372898	−	0.0651240i
$776$	−2.45459	−	4.25148i	−0.0881148	−	0.152619i
$777$	1.51762	+	1.68487i	0.0544442	+	0.0604445i
$778$	5.88106	+	3.39543i	0.210846	+	0.121732i
$779$		−	72.4900i		−	2.59722i
$780$	0.439137	−	16.5933i	0.0157236	−	0.594134i
$781$	−2.01566			−0.0721259
$782$	36.8001	−	21.2465i	1.31597	−	0.759774i
$783$	25.4428	−	37.1479i	0.909252	−	1.32756i
$784$	2.73974	−	6.44157i	0.0978477	−	0.230056i
$785$	49.2405	−	17.8765i	1.75747	−	0.638041i
$786$	5.62172	−	14.2941i	0.200520	−	0.509854i
$787$	−0.487574	−	0.844503i	−0.0173801	−	0.0301033i	0.857205	−	0.514976i	$-0.172199\pi$
$787$	−0.487574	−	0.844503i	−0.0173801	−	0.0301033i	−0.874585	+	0.484873i	$0.838866\pi$
$788$	−9.42507	−	16.3247i	−0.335754	−	0.581543i
$789$	−27.2731	+	4.09099i	−0.970947	+	0.145643i
$790$	−11.8964	+	4.31893i	−0.423254	+	0.153661i
$791$	13.5407	+	6.75719i	0.481451	+	0.240258i
$792$	1.03196	+	3.36244i	0.0366690	+	0.119479i
$793$	−10.0727	+	5.81547i	−0.357692	+	0.206513i
$794$	−18.5318			−0.657667
$795$	15.7787	+	9.67523i	0.559612	+	0.343145i
$796$		−	6.42163i		−	0.227609i
$797$	36.9701	+	21.3447i	1.30955	+	0.756068i	0.982021	−	0.188774i	$-0.0604513\pi$
$797$	36.9701	+	21.3447i	1.30955	+	0.756068i	0.327527	+	0.944842i	$0.393785\pi$
$798$	−29.0205	+	6.17394i	−1.02731	+	0.218555i
$799$	2.99668	+	5.19040i	0.106015	+	0.183623i
$800$	−0.860196	−	4.92545i	−0.0304125	−	0.174141i
$801$	10.7875	+	10.0378i	0.381158	+	0.354670i
$802$	9.98203	+	5.76313i	0.352478	+	0.203503i
$803$	−5.62801	−	3.24933i	−0.198608	−	0.114667i
$804$	−5.03894	−	1.98176i	−0.177710	−	0.0698913i
$805$	−34.7528	−	4.00095i	−1.22487	−	0.141015i
$806$	7.82282	+	4.51651i	0.275547	+	0.159087i
$807$	16.5711	−	42.1346i	0.583329	−	1.48321i
$808$	−7.98647			−0.280963
$809$	−3.85053	−	2.22310i	−0.135377	−	0.0781602i	0.430782	−	0.902456i	$-0.358238\pi$
$809$	−3.85053	−	2.22310i	−0.135377	−	0.0781602i	−0.566159	+	0.824296i	$0.691571\pi$
$810$	−20.0172	−	2.07686i	−0.703331	−	0.0729735i
$811$		−	18.5713i		−	0.652126i	−0.945348	−	0.326063i	$-0.894278\pi$
$811$		−	18.5713i		−	0.652126i	0.945348	−	0.326063i	$-0.105722\pi$
$812$	−10.2368	+	20.5135i	−0.359242	+	0.719883i
$813$	−1.68177	+	1.33922i	−0.0589824	+	0.0469686i
$814$	0.580142			0.0203340
$815$	−12.3700	−	34.0727i	−0.433301	−	1.19352i
$816$	−9.73694	+	7.75367i	−0.340861	+	0.271433i
$817$	15.5091	−	26.8625i	0.542594	−	0.939801i
$818$			4.88381i			0.170758i
$819$	33.5554	+	5.59050i	1.17252	+	0.195348i
$820$	−4.36750	+	24.6516i	−0.152520	+	0.860870i
$821$	20.7624	+	11.9872i	0.724611	+	0.418354i	0.816448	−	0.577420i	$-0.195940\pi$
$821$	20.7624	+	11.9872i	0.724611	+	0.418354i	−0.0918363	+	0.995774i	$0.529274\pi$
$822$	−0.427941	+	1.08811i	−0.0149262	+	0.0379521i
$823$	−18.0054	+	10.3954i	−0.627629	+	0.362361i	−0.779833	−	0.625988i	$-0.784696\pi$
$823$	−18.0054	+	10.3954i	−0.627629	+	0.362361i	0.152205	+	0.988349i	$0.451363\pi$
$824$	−15.2058			−0.529718
$825$	2.03516	−	9.94732i	0.0708550	−	0.346321i
$826$	−0.496770	−	8.17019i	−0.0172849	−	0.284277i
$827$	−27.6796			−0.962513			−0.481257	−	0.876580i	$-0.659819\pi$
$827$	−27.6796			−0.962513			−0.481257	+	0.876580i	$0.659819\pi$
$828$	12.9867	+	12.0842i	0.451319	+	0.419954i
$829$	21.5900	+	12.4650i	0.749853	+	0.432928i	0.825641	−	0.564196i	$-0.190814\pi$
$829$	21.5900	+	12.4650i	0.749853	+	0.432928i	−0.0757878	+	0.997124i	$0.524147\pi$
$830$	−18.0186	−	3.19234i	−0.625435	−	0.110808i
$831$	−1.08824	−	7.25489i	−0.0377507	−	0.251669i
$832$	2.14293	−	3.71166i	0.0742927	−	0.128679i
$833$	46.2909	+	19.6885i	1.60388	+	0.682166i
$834$	29.8313	−	23.7551i	1.03297	−	0.822571i
$835$	−19.7554	+	23.5045i	−0.683663	+	0.813408i
$836$	−3.79540	+	6.57382i	−0.131267	+	0.227360i
$837$	6.18846	−	9.03548i	0.213905	−	0.312312i
$838$	15.6980	+	27.1897i	0.542278	+	0.939253i
$839$	−17.3808	−	30.1044i	−0.600051	−	1.03932i	−0.992813	−	0.119679i	$-0.961814\pi$
$839$	−17.3808	−	30.1044i	−0.600051	−	1.03932i	0.392761	−	0.919640i	$-0.371520\pi$
$840$	10.2409	−	0.351089i	0.353346	−	0.0121137i
$841$	23.0426	−	39.9109i	0.794572	−	1.37624i
$842$	19.1707			0.660667
$843$	−3.82416	+	3.04523i	−0.131711	+	0.104883i
$844$	9.13053			0.314286
$845$	−11.2839	+	4.09658i	−0.388179	+	0.140927i
$846$	−1.70439	+	1.83169i	−0.0585983	+	0.0629747i
$847$	1.54558	+	25.4196i	0.0531069	+	0.873428i
$848$	2.38948	+	4.13870i	0.0820550	+	0.142123i
$849$	−13.3296	−	16.7392i	−0.457472	−	0.574486i
$850$	35.3956	−	6.18160i	1.21406	−	0.212027i
$851$	2.53396	−	1.46298i	0.0868630	−	0.0501504i
$852$	2.32946	−	1.85499i	0.0798061	−	0.0635508i
$853$	14.3176	+	24.7989i	0.490226	+	0.849097i	0.999937	−	0.0112491i	$-0.00358076\pi$
$853$	14.3176	+	24.7989i	0.490226	+	0.849097i	−0.509710	+	0.860346i	$0.670247\pi$
$854$	−3.96077	−	5.98874i	−0.135535	−	0.204930i
$855$	−26.1472	−	34.6798i	−0.894217	−	1.18603i
$856$	−9.09652	−	15.7556i	−0.310913	−	0.538516i
$857$		−	13.6574i		−	0.466527i	−0.972414	−	0.233263i	$-0.925060\pi$
$857$		−	13.6574i		−	0.466527i	0.972414	−	0.233263i	$-0.0749404\pi$
$858$	6.80827	−	5.42153i	0.232431	−	0.185088i
$859$			17.4795i			0.596392i	0.954505	+	0.298196i	$0.0963850\pi$
$859$			17.4795i			0.596392i	−0.954505	+	0.298196i	$0.903615\pi$
$860$	−6.89261	+	8.20069i	−0.235036	+	0.279641i
$861$	−48.7991	−	15.8461i	−1.66307	−	0.540034i
$862$	0.601870	−	0.347490i	0.0204998	−	0.0118356i
$863$	1.59431	+	2.76142i	0.0542709	+	0.0940000i	0.891885	−	0.452263i	$-0.149383\pi$
$863$	1.59431	+	2.76142i	0.0542709	+	0.0940000i	−0.837614	+	0.546263i	$0.816050\pi$
$864$	−4.28703	−	2.93622i	−0.145848	−	0.0998921i
$865$	0.607412	−	0.722686i	0.0206526	−	0.0245720i
$866$	15.3923	−	26.6603i	0.523053	−	0.905955i
$867$	−37.3777	−	46.9383i	−1.26941	−	1.59411i
$868$	−2.48991	+	4.98950i	−0.0845130	+	0.169355i
$869$	−5.74680	−	3.31791i	−0.194947	−	0.112553i
$870$	−33.5483	−	0.887849i	−1.13739	−	0.0301009i
$871$			13.3982i			0.453981i
$872$	3.71187	−	6.42915i	0.125700	−	0.217719i
$873$	10.7819	+	10.0326i	0.364911	+	0.339551i
$874$			38.2844i			1.29499i
$875$	−26.4353	−	13.2730i	−0.893678	−	0.448710i
$876$	9.49453	−	1.42419i	0.320790	−	0.0481189i
$877$		−	3.03519i		−	0.102491i	−0.998686	−	0.0512455i	$-0.983681\pi$
$877$		−	3.03519i		−	0.102491i	0.998686	−	0.0512455i	$-0.0163191\pi$
$878$	−25.5026	+	14.7240i	−0.860673	+	0.496910i
$879$	−13.6104	−	5.35281i	−0.459066	−	0.180546i
$880$	1.68677	−	2.00688i	0.0568609	−	0.0676518i
$881$	15.1683			0.511034			0.255517	−	0.966805i	$-0.417754\pi$
$881$	15.1683			0.511034			0.255517	+	0.966805i	$0.417754\pi$
$882$	−2.18760	+	20.8857i	−0.0736602	+	0.703260i
$883$			25.3528i			0.853190i	0.904443	+	0.426595i	$0.140287\pi$
$883$			25.3528i			0.853190i	−0.904443	+	0.426595i	$0.859713\pi$
$884$	26.6730	+	15.3997i	0.897110	+	0.517947i
$885$	10.5316	−	5.71439i	0.354016	−	0.192087i
$886$	−0.807475	−	1.39859i	−0.0271276	−	0.0469865i
$887$		−	10.1985i		−	0.342431i	−0.985234	−	0.171216i	$-0.945231\pi$
$887$		−	10.1985i		−	0.342431i	0.985234	−	0.171216i	$-0.0547694\pi$
$888$	−0.670461	+	0.533898i	−0.0224992	+	0.0179165i
$889$	−32.3039	+	1.96417i	−1.08344	+	0.0658761i
$890$	1.91602	−	10.8146i	0.0642251	−	0.362507i
$891$	−5.91925	−	8.73504i	−0.198302	−	0.292635i
$892$	−5.48740	+	9.50446i	−0.183732	+	0.318233i
$893$	−5.39976			−0.180696
$894$	16.8667	+	6.63349i	0.564107	+	0.221857i
$895$	31.0725	−	36.9694i	1.03864	−	1.23575i
$896$	2.36735	+	1.18138i	0.0790876	+	0.0394670i
$897$	16.0655	−	40.8491i	0.536412	−	1.36391i
$898$	−30.2287	−	17.4525i	−1.00874	−	0.582398i
$899$	9.13149	−	15.8162i	0.304552	−	0.527500i
$900$	6.80241	+	13.3689i	0.226747	+	0.445630i
$901$	−29.7418	+	17.1714i	−0.990843	+	0.572063i
$902$	−11.3679	+	6.56328i	−0.378511	+	0.218533i
$903$	−14.6932	−	16.3126i	−0.488959	−	0.542848i
$904$	−2.85988	+	4.95345i	−0.0951181	+	0.164749i
$905$	−31.2869	−	5.54308i	−1.04001	−	0.184258i
$906$	7.39726	−	18.8087i	0.245757	−	0.624877i
$907$		−	45.9845i		−	1.52689i	−0.645872	−	0.763445i	$-0.723506\pi$
$907$		−	45.9845i		−	1.52689i	0.645872	−	0.763445i	$-0.276494\pi$
$908$	6.60089	−	3.81103i	0.219058	−	0.126473i
$909$	22.9049	−	7.02970i	0.759709	−	0.233161i
$910$	−10.0831	−	23.2644i	−0.334253	−	0.771206i
$911$	−2.56228	+	1.47933i	−0.0848920	+	0.0490124i	−0.541845	−	0.840478i	$-0.682274\pi$
$911$	−2.56228	+	1.47933i	−0.0848920	+	0.0490124i	0.456953	+	0.889491i	$0.348941\pi$
$912$	−1.66353	−	11.0901i	−0.0550850	−	0.367230i
$913$	−4.79730	−	8.30918i	−0.158768	−	0.274994i
$914$	0.249715	−	0.144173i	0.00825984	−	0.00476882i
$915$	5.49421	−	8.96012i	0.181633	−	0.296213i
$916$	−10.8475	+	6.26278i	−0.358410	+	0.206928i
$917$	−1.42396	−	23.4193i	−0.0470233	−	0.773374i
$918$	21.1004	−	30.8078i	0.696418	−	1.01681i
$919$	−9.74310	−	16.8755i	−0.321395	−	0.556673i	0.659381	−	0.751809i	$-0.270818\pi$
$919$	−9.74310	−	16.8755i	−0.321395	−	0.556673i	−0.980776	+	0.195136i	$0.937485\pi$
$920$	2.30662	−	13.0193i	0.0760471	−	0.429234i
$921$	−18.1287	+	2.71932i	−0.597359	+	0.0896046i
$922$	−15.2228			−0.501338
$923$	−6.38124	−	3.68421i	−0.210041	−	0.121267i
$924$	3.59573	+	3.99202i	0.118291	+	0.131328i
$925$	2.43725	−	0.425650i	0.0801364	−	0.0139953i
$926$	−19.2284	+	11.1015i	−0.631884	+	0.364818i
$927$	43.6097	−	13.3842i	1.43233	−	0.439593i
$928$	−7.50426	−	4.33259i	−0.246339	−	0.142224i
$929$	13.8243	−	23.9443i	0.453560	−	0.785588i	−0.545045	−	0.838407i	$-0.683487\pi$
$929$	13.8243	−	23.9443i	0.453560	−	0.785588i	0.998604	+	0.0528188i	$0.0168206\pi$
$930$	−8.15996	−	0.215952i	−0.267576	−	0.00708134i
$931$	−36.2150	+	27.2493i	−1.18690	+	0.893059i
$932$	−10.0310	+	17.3742i	−0.328576	+	0.569111i
$933$	−22.7976	−	28.6289i	−0.746361	−	0.937269i
$934$			26.4125i			0.864243i
$935$	14.4220	+	12.1216i	0.471649	+	0.396417i
$936$	−2.87884	+	12.5311i	−0.0940979	+	0.409593i
$937$	−50.1495			−1.63831			−0.819156	−	0.573570i	$-0.805558\pi$
$937$	−50.1495			−1.63831			−0.819156	+	0.573570i	$0.805558\pi$
$938$	−8.25574	+	0.501973i	−0.269560	+	0.0163900i
$939$	−5.17985	+	13.1706i	−0.169038	+	0.429806i
$940$	1.83629	+	0.325334i	0.0598931	+	0.0106112i
$941$	−9.02956	−	15.6397i	−0.294355	−	0.509838i	0.680480	−	0.732767i	$-0.261772\pi$
$941$	−9.02956	−	15.6397i	−0.294355	−	0.509838i	−0.974835	+	0.222929i	$0.928438\pi$
$942$	−40.1284	+	6.01930i	−1.30745	+	0.196119i
$943$	−33.1021	+	57.3345i	−1.07795	+	1.86707i
$944$	3.09374			0.100693
$945$	−29.0617	+	10.0210i	−0.945376	+	0.325983i
$946$	−5.61680			−0.182618
$947$	−8.69967	+	15.0683i	−0.282701	+	0.489653i	−0.972049	−	0.234777i	$-0.924564\pi$
$947$	−8.69967	+	15.0683i	−0.282701	+	0.489653i	0.689348	+	0.724430i	$0.257897\pi$
$948$	9.69492	−	1.45425i	0.314876	−	0.0472318i
$949$	−11.8783	−	20.5737i	−0.385584	−	0.667852i
$950$	−11.1217	+	30.4021i	−0.360837	+	0.986376i
$951$	−19.9662	+	50.7672i	−0.647447	+	1.64624i
$952$	−8.48969	+	17.0124i	−0.275153	+	0.551376i
$953$	1.90844			0.0618206			0.0309103	−	0.999522i	$-0.490159\pi$
$953$	1.90844			0.0618206			0.0309103	+	0.999522i	$0.490159\pi$
$954$	−10.4958	−	9.76643i	−0.339815	−	0.316200i
$955$	10.6696	−	12.6945i	0.345260	−	0.410783i
$956$		−	12.4972i		−	0.404187i
$957$	−10.9613	−	13.7650i	−0.354327	−	0.444959i
$958$	19.7412	−	34.1927i	0.637808	−	1.10472i
$959$	0.108396	+	1.78275i	0.00350029	+	0.0575679i
$960$	−0.102462	+	3.87163i	−0.00330694	+	0.124956i
$961$	−13.2789	+	22.9998i	−0.428353	+	0.741929i
$962$	1.83664	+	1.06038i	0.0592156	+	0.0341881i
$963$	39.9567	+	37.1799i	1.28759	+	1.19810i
$964$	−14.7942	+	8.54144i	−0.476489	+	0.275101i
$965$	13.3345	+	36.7296i	0.429254	+	1.18237i
$966$	25.7725	+	8.36886i	0.829215	+	0.269264i
$967$	−31.9191	−	18.4285i	−1.02645	−	0.592620i	−0.110483	−	0.993878i	$-0.535240\pi$
$967$	−31.9191	−	18.4285i	−1.02645	−	0.592620i	−0.915965	+	0.401258i	$0.868573\pi$
$968$	−9.62545			−0.309374
$969$	79.6966	−	11.9546i	2.56022	−	0.384036i
$970$	1.91501	−	10.8090i	0.0614874	−	0.347054i
$971$	−22.1728	−	38.4045i	−0.711560	−	1.23246i	−0.964271	−	0.264917i	$-0.914655\pi$
$971$	−22.1728	−	38.4045i	−0.711560	−	1.23246i	0.252711	−	0.967542i	$-0.418678\pi$
$972$	14.8795	+	4.64753i	0.477261	+	0.149069i
$973$	26.0100	−	52.1213i	0.833844	−	1.67093i
$974$	−21.3058	+	12.3009i	−0.682682	+	0.394147i
$975$	24.6247	−	27.7718i	0.788620	−	0.889408i
$976$	2.35021	−	1.35690i	0.0752285	−	0.0434332i
$977$	−16.3304	−	28.2851i	−0.522457	−	0.904921i	−0.999659	−	0.0261277i	$-0.991682\pi$
$977$	−16.3304	−	28.2851i	−0.522457	−	0.904921i	0.477202	−	0.878794i	$-0.341651\pi$
$978$	4.16515	+	27.7675i	0.133187	+	0.887906i
$979$	4.98710	−	2.87930i	0.159388	−	0.0920230i
$980$	13.9573	−	7.08468i	0.445851	−	0.226312i
$981$	−4.98658	+	21.7058i	−0.159209	+	0.693013i
$982$	−13.3649	+	7.71621i	−0.426490	+	0.246234i
$983$			42.4513i			1.35399i	0.735989	+	0.676994i	$0.236718\pi$
$983$			42.4513i			1.35399i	−0.735989	+	0.676994i	$0.763282\pi$
$984$	7.09763	−	18.0468i	0.226264	−	0.575312i
$985$	7.35320	−	41.5038i	0.234292	−	1.32242i
$986$	31.1351	−	53.9276i	0.991544	−	1.71741i
$987$	−1.18037	+	3.63503i	−0.0375717	+	0.115704i
$988$	−24.0312	+	13.8744i	−0.764535	+	0.441404i
$989$	−24.5332	+	14.1642i	−0.780110	+	0.450397i
$990$	−3.07113	+	7.24036i	−0.0976070	+	0.230114i
$991$	8.15778	−	14.1297i	0.259140	−	0.448844i	−0.706872	−	0.707342i	$-0.749894\pi$
$991$	8.15778	−	14.1297i	0.259140	−	0.448844i	0.966012	+	0.258498i	$0.0832274\pi$
$992$	−1.82526	−	1.05382i	−0.0579521	−	0.0334587i
$993$	−5.86867	+	14.9220i	−0.186236	+	0.473536i
$994$	2.03107	−	4.07005i	0.0644217	−	0.129094i
$995$	9.23889	−	10.9922i	0.292893	−	0.348477i
$996$	13.1910	+	5.18788i	0.417973	+	0.164384i
$997$	−36.5310			−1.15695			−0.578475	−	0.815700i	$-0.696352\pi$
$997$	−36.5310			−1.15695			−0.578475	+	0.815700i	$0.696352\pi$
$998$	5.34955	−	9.26568i	0.169337	−	0.293300i
$999$	1.45292	−	2.12135i	0.0459685	−	0.0671164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.59.1	yes	48
3.2	odd	2		1890.2.r.a.1529.11		48
5.4	even	2		630.2.r.a.59.24	✓	48
7.5	odd	6		630.2.bi.a.509.9	yes	48
9.2	odd	6		630.2.bi.b.479.16	yes	48
9.7	even	3		1890.2.bi.a.899.19		48
15.14	odd	2		1890.2.r.b.1529.11		48
21.5	even	6		1890.2.bi.b.719.3		48
35.19	odd	6		630.2.bi.b.509.16	yes	48
45.29	odd	6		630.2.bi.a.479.9	yes	48
45.34	even	6		1890.2.bi.b.899.3		48
63.47	even	6		630.2.r.a.299.24	yes	48
63.61	odd	6		1890.2.r.b.89.11		48
105.89	even	6		1890.2.bi.a.719.19		48
315.124	odd	6		1890.2.r.a.89.11		48
315.299	even	6	inner	630.2.r.b.299.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.24	✓	48	5.4	even	2
630.2.r.a.299.24	yes	48	63.47	even	6
630.2.r.b.59.1	yes	48	1.1	even	1	trivial
630.2.r.b.299.1	yes	48	315.299	even	6	inner
630.2.bi.a.479.9	yes	48	45.29	odd	6
630.2.bi.a.509.9	yes	48	7.5	odd	6
630.2.bi.b.479.16	yes	48	9.2	odd	6
630.2.bi.b.509.16	yes	48	35.19	odd	6
1890.2.r.a.89.11		48	315.124	odd	6
1890.2.r.a.1529.11		48	3.2	odd	2
1890.2.r.b.89.11		48	63.61	odd	6
1890.2.r.b.1529.11		48	15.14	odd	2
1890.2.bi.a.719.19		48	105.89	even	6
1890.2.bi.a.899.19		48	9.7	even	3
1890.2.bi.b.719.3		48	21.5	even	6
1890.2.bi.b.899.3		48	45.34	even	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71289 + 0.256935i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.390088 - 2.20178i) q^{5} +(-0.633932 + 1.61187i) q^{6} +(0.160573 + 2.64087i) q^{7} -1.00000 q^{8} +(2.86797 - 0.880202i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.71289 + 0.256935i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.390088 - 2.20178i) q^{5} +(-0.633932 + 1.61187i) q^{6} +(0.160573 + 2.64087i) q^{7} -1.00000 q^{8} +(2.86797 - 0.880202i) q^{9} +(-1.71175 - 1.43872i) q^{10} -1.17241i q^{11} +(1.07896 + 1.35494i) q^{12} +(2.14293 - 3.71166i) q^{13} +(2.36735 + 1.18138i) q^{14} +(-0.102462 + 3.87163i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.22349 - 3.59313i) q^{17} +(0.671707 - 2.92383i) q^{18} +(5.60709 - 3.23726i) q^{19} +(-2.10184 + 0.763064i) q^{20} +(-0.953576 - 4.48226i) q^{21} +(-1.01534 - 0.586205i) q^{22} -5.91309 q^{23} +(1.71289 - 0.256935i) q^{24} +(-4.69566 - 1.71777i) q^{25} +(-2.14293 - 3.71166i) q^{26} +(-4.68635 + 2.24457i) q^{27} +(2.20678 - 1.45950i) q^{28} +(-7.50426 + 4.33259i) q^{29} +(3.30170 + 2.02455i) q^{30} +(-1.82526 + 1.05382i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.301234 + 2.00821i) q^{33} +(-6.22349 + 3.59313i) q^{34} +(5.87726 + 0.676627i) q^{35} +(-2.19626 - 2.04363i) q^{36} +(-0.428534 + 0.247414i) q^{37} -6.47451i q^{38} +(-2.71694 + 6.90826i) q^{39} +(-0.390088 + 2.20178i) q^{40} +(5.59810 - 9.69620i) q^{41} +(-4.35854 - 1.41531i) q^{42} +(4.14896 - 2.39541i) q^{43} +(-1.01534 + 0.586205i) q^{44} +(-0.819251 - 6.65799i) q^{45} +(-2.95654 + 5.12089i) q^{46} +(-0.722267 - 0.417001i) q^{47} +(0.633932 - 1.61187i) q^{48} +(-6.94843 + 0.848104i) q^{49} +(-3.83547 + 3.20768i) q^{50} +(11.5833 + 4.55560i) q^{51} -4.28586 q^{52} +(2.38948 - 4.13870i) q^{53} +(-0.399323 + 5.18079i) q^{54} +(-2.58139 - 0.457343i) q^{55} +(-0.160573 - 2.64087i) q^{56} +(-8.77256 + 6.98572i) q^{57} +8.66517i q^{58} +(-1.54687 - 2.67926i) q^{59} +(3.40416 - 1.84708i) q^{60} +(-2.35021 - 1.35690i) q^{61} +2.10763i q^{62} +(2.78502 + 7.43261i) q^{63} +1.00000 q^{64} +(-7.33633 - 6.16613i) q^{65} +(1.88978 + 0.743228i) q^{66} +(-2.70732 + 1.56307i) q^{67} +7.18627i q^{68} +(10.1285 - 1.51928i) q^{69} +(3.52461 - 4.75154i) q^{70} -1.71924i q^{71} +(-2.86797 + 0.880202i) q^{72} +(2.77150 - 4.80038i) q^{73} +0.494829i q^{74} +(8.48450 + 1.73587i) q^{75} +(-5.60709 - 3.23726i) q^{76} +(3.09619 - 0.188257i) q^{77} +(4.62425 + 5.80707i) q^{78} +(2.82999 - 4.90169i) q^{79} +(1.71175 + 1.43872i) q^{80} +(7.45049 - 5.04878i) q^{81} +(-5.59810 - 9.69620i) q^{82} +(7.08726 - 4.09183i) q^{83} +(-3.40497 + 3.06695i) q^{84} +(-10.3390 + 12.3011i) q^{85} -4.79081i q^{86} +(11.7408 - 9.34934i) q^{87} +1.17241i q^{88} +(2.45588 + 4.25371i) q^{89} +(-6.17561 - 2.61950i) q^{90} +(10.1461 + 5.06322i) q^{91} +(2.95654 + 5.12089i) q^{92} +(2.85571 - 2.27404i) q^{93} +(-0.722267 + 0.417001i) q^{94} +(-4.94047 - 13.6084i) q^{95} +(-1.07896 - 1.35494i) q^{96} +(2.45459 + 4.25148i) q^{97} +(-2.73974 + 6.44157i) q^{98} +(-1.03196 - 3.36244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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