LMFDB - Embedded newform 630.2.r.b.59.17

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			59.17
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.08196 - 1.35254i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.96632 - 1.06470i) q^{5} +(-0.630353 - 1.61327i) q^{6} +(0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-0.658722 - 2.92679i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.08196 - 1.35254i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.96632 - 1.06470i) q^{5} +(-0.630353 - 1.61327i) q^{6} +(0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-0.658722 - 2.92679i) q^{9} +(0.0611015 - 2.23523i) q^{10} +1.30502i q^{11} +(-1.71231 - 0.260736i) q^{12} +(3.03357 - 5.25429i) q^{13} +(2.56820 + 0.635870i) q^{14} +(0.687431 - 3.81149i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.502991 - 0.290402i) q^{17} +(-2.86403 - 0.892924i) q^{18} +(-6.86424 + 3.96307i) q^{19} +(-1.90522 - 1.17053i) q^{20} +(4.23177 + 1.75843i) q^{21} +(1.13018 + 0.652510i) q^{22} +6.57244 q^{23} +(-1.08196 + 1.35254i) q^{24} +(2.73282 - 4.18708i) 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} +(-2.95713 - 2.50108i) q^{30} +(-1.19742 + 0.691334i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.76509 + 1.41198i) q^{33} +(-0.502991 + 0.290402i) q^{34} +(4.14868 + 4.21764i) q^{35} +(-2.20531 + 2.03386i) q^{36} +(2.02863 - 1.17123i) q^{37} +7.92614i q^{38} +(-3.82443 - 9.78795i) q^{39} +(-1.96632 + 1.06470i) q^{40} +(-3.16905 + 5.48896i) q^{41} +(3.63873 - 2.78561i) q^{42} +(-10.0713 + 5.81466i) q^{43} +(1.13018 - 0.652510i) q^{44} +(-4.41141 - 5.05366i) q^{45} +(3.28622 - 5.69190i) q^{46} +(4.69056 + 2.70810i) q^{47} +(0.630353 + 1.61327i) q^{48} +(-5.92418 + 3.72881i) q^{49} +(-2.25971 - 4.46024i) q^{50} +(-0.936996 + 0.366111i) q^{51} -6.06713 q^{52} +(-4.19068 + 7.25846i) q^{53} +(-4.30649 + 2.90761i) q^{54} +(1.38946 + 2.56609i) q^{55} +(-0.733422 - 2.54206i) q^{56} +(-2.06663 + 13.5720i) q^{57} +0.144970i q^{58} +(-1.54358 - 2.67356i) q^{59} +(-3.64456 + 1.31041i) q^{60} +(1.83643 + 1.06026i) q^{61} +1.38267i q^{62} +(6.95696 - 3.82108i) q^{63} +1.00000 q^{64} +(0.370711 - 13.5615i) q^{65} +(2.10536 - 0.822623i) q^{66} +(11.4291 - 6.59859i) q^{67} +0.580804i q^{68} +(7.11112 - 8.88948i) q^{69} +(5.72692 - 1.48404i) q^{70} +10.3545i q^{71} +(0.658722 + 2.92679i) q^{72} +(3.84599 - 6.66144i) q^{73} -2.34246i q^{74} +(-2.70639 - 8.22651i) q^{75} +(6.86424 + 3.96307i) q^{76} +(-3.31745 + 0.957131i) q^{77} +(-10.3888 - 1.58192i) q^{78} +(3.54596 - 6.14179i) q^{79} +(-0.0611015 + 2.23523i) q^{80} +(-8.13217 + 3.85588i) q^{81} +(3.16905 + 5.48896i) q^{82} +(-4.32983 + 2.49983i) q^{83} +(-0.593040 - 4.54404i) q^{84} +(-1.29823 - 0.0354880i) q^{85} +11.6293i q^{86} +(-0.0377989 + 0.248234i) q^{87} -1.30502i 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} +(-0.360511 + 2.36756i) q^{93} +(4.69056 - 2.70810i) q^{94} +(-9.27780 + 15.1010i) q^{95} +(1.71231 + 0.260736i) 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 + 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
$3$	1.08196	−	1.35254i	0.624670	−	0.780889i
$3$	1.08196	−	1.35254i	0.624670	−	0.780889i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.96632	−	1.06470i	0.879365	−	0.476149i
$5$	1.96632	−	1.06470i	0.879365	−	0.476149i
$6$	−0.630353	−	1.61327i	−0.257340	−	0.658617i
$7$	0.733422	+	2.54206i	0.277207	+	0.960810i
$7$	0.733422	+	2.54206i	0.277207	+	0.960810i
$8$	−1.00000			−0.353553
$9$	−0.658722	−	2.92679i	−0.219574	−	0.975596i
$10$	0.0611015	−	2.23523i	0.0193220	−	0.706843i
$11$			1.30502i			0.393478i	0.980456	+	0.196739i	$0.0630352\pi$
$11$			1.30502i			0.393478i	−0.980456	+	0.196739i	$0.936965\pi$
$12$	−1.71231	−	0.260736i	−0.494302	−	0.0752680i
$13$	3.03357	−	5.25429i	0.841360	−	1.45728i	−0.0473853	−	0.998877i	$-0.515089\pi$
$13$	3.03357	−	5.25429i	0.841360	−	1.45728i	0.888745	−	0.458402i	$-0.151578\pi$
$14$	2.56820	+	0.635870i	0.686381	+	0.169944i
$15$	0.687431	−	3.81149i	0.177494	−	0.984122i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.502991	−	0.290402i	−0.121993	−	0.0704328i	0.437762	−	0.899091i	$-0.355771\pi$
$17$	−0.502991	−	0.290402i	−0.121993	−	0.0704328i	−0.559755	+	0.828658i	$0.689105\pi$
$18$	−2.86403	−	0.892924i	−0.675059	−	0.210464i
$19$	−6.86424	+	3.96307i	−1.57476	+	0.909191i	−0.579193	+	0.815191i	$0.696632\pi$
$19$	−6.86424	+	3.96307i	−1.57476	+	0.909191i	−0.995572	+	0.0940001i	$0.970035\pi$
$20$	−1.90522	−	1.17053i	−0.426020	−	0.261739i
$21$	4.23177	+	1.75843i	0.923449	+	0.383721i
$22$	1.13018	+	0.652510i	0.240955	+	0.139116i
$23$	6.57244			1.37045			0.685224	−	0.728332i	$-0.259704\pi$
$23$	6.57244			1.37045			0.685224	+	0.728332i	$0.259704\pi$
$24$	−1.08196	+	1.35254i	−0.220854	+	0.276086i
$25$	2.73282	−	4.18708i	0.546565	−	0.837417i
$26$	−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	$0.337618\pi$
$30$	−2.95713	−	2.50108i	−0.539896	−	0.456632i
$31$	−1.19742	+	0.691334i	−0.215064	+	0.124167i	−0.603663	−	0.797240i	$-0.706293\pi$
$31$	−1.19742	+	0.691334i	−0.215064	+	0.124167i	0.388599	+	0.921407i	$0.372959\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.76509	+	1.41198i	0.307263	+	0.245794i
$34$	−0.502991	+	0.290402i	−0.0862622	+	0.0498035i
$35$	4.14868	+	4.21764i	0.701255	+	0.712911i
$36$	−2.20531	+	2.03386i	−0.367552	+	0.338977i
$37$	2.02863	−	1.17123i	0.333505	−	0.192549i	−0.323891	−	0.946094i	$-0.604991\pi$
$37$	2.02863	−	1.17123i	0.333505	−	0.192549i	0.657396	+	0.753545i	$0.271658\pi$
$38$			7.92614i			1.28579i
$39$	−3.82443	−	9.78795i	−0.612399	−	1.56733i
$40$	−1.96632	+	1.06470i	−0.310902	+	0.168344i
$41$	−3.16905	+	5.48896i	−0.494923	+	0.857232i	−0.999983	−	0.00585232i	$-0.998137\pi$
$41$	−3.16905	+	5.48896i	−0.494923	+	0.857232i	0.505060	+	0.863084i	$0.331470\pi$
$42$	3.63873	−	2.78561i	0.561469	−	0.429829i
$43$	−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
$45$	−4.41141	−	5.05366i	−0.657614	−	0.753355i
$46$	3.28622	−	5.69190i	0.484527	−	0.839225i
$47$	4.69056	+	2.70810i	0.684188	+	0.395016i	0.801431	−	0.598087i	$-0.204072\pi$
$47$	4.69056	+	2.70810i	0.684188	+	0.395016i	−0.117243	+	0.993103i	$0.537406\pi$
$48$	0.630353	+	1.61327i	0.0909835	+	0.232856i
$49$	−5.92418	+	3.72881i	−0.846312	+	0.532687i
$50$	−2.25971	−	4.46024i	−0.319571	−	0.630773i
$51$	−0.936996	+	0.366111i	−0.131206	+	0.0512658i
$52$	−6.06713			−0.841360
$53$	−4.19068	+	7.25846i	−0.575634	+	0.997027i	0.420339	+	0.907367i	$0.361911\pi$
$53$	−4.19068	+	7.25846i	−0.575634	+	0.997027i	−0.995972	+	0.0896594i	$0.971422\pi$
$54$	−4.30649	+	2.90761i	−0.586038	+	0.395675i
$55$	1.38946	+	2.56609i	0.187354	+	0.346011i
$56$	−0.733422	−	2.54206i	−0.0980076	−	0.339698i
$57$	−2.06663	+	13.5720i	−0.273732	+	1.79766i
$58$			0.144970i			0.0190355i
$59$	−1.54358	−	2.67356i	−0.200957	−	0.348067i	0.747880	−	0.663834i	$-0.231072\pi$
$59$	−1.54358	−	2.67356i	−0.200957	−	0.348067i	−0.948837	+	0.315766i	$0.897738\pi$
$60$	−3.64456	+	1.31041i	−0.470511	+	0.169173i
$61$	1.83643	+	1.06026i	0.235131	+	0.135753i	0.612937	−	0.790132i	$-0.289988\pi$
$61$	1.83643	+	1.06026i	0.235131	+	0.135753i	−0.377806	+	0.925885i	$0.623321\pi$
$62$			1.38267i			0.175599i
$63$	6.95696	−	3.82108i	0.876495	−	0.481411i
$64$	1.00000			0.125000
$65$	0.370711	−	13.5615i	0.0459810	−	1.68209i
$66$	2.10536	−	0.822623i	0.259151	−	0.101258i
$67$	11.4291	−	6.59859i	1.39629	−	0.806146i	0.402284	−	0.915515i	$-0.368216\pi$
$67$	11.4291	−	6.59859i	1.39629	−	0.806146i	0.994001	+	0.109369i	$0.0348830\pi$
$68$			0.580804i			0.0704328i
$69$	7.11112	−	8.88948i	0.856078	−	1.07017i
$70$	5.72692	−	1.48404i	0.684498	−	0.177377i
$71$			10.3545i			1.22885i	0.788975	+	0.614425i	$0.210612\pi$
$71$			10.3545i			1.22885i	−0.788975	+	0.614425i	$0.789388\pi$
$72$	0.658722	+	2.92679i	0.0776311	+	0.344925i
$73$	3.84599	−	6.66144i	0.450139	−	0.779663i	−0.548256	−	0.836311i	$-0.684708\pi$
$73$	3.84599	−	6.66144i	0.450139	−	0.779663i	0.998394	+	0.0566478i	$0.0180412\pi$
$74$		−	2.34246i		−	0.272306i
$75$	−2.70639	−	8.22651i	−0.312507	−	0.949916i
$76$	6.86424	+	3.96307i	0.787382	+	0.454595i
$77$	−3.31745	+	0.957131i	−0.378058	+	0.109075i
$78$	−10.3888	−	1.58192i	−1.17630	−	0.179117i
$79$	3.54596	−	6.14179i	0.398952	−	0.691005i	−0.594645	−	0.803988i	$-0.702707\pi$
$79$	3.54596	−	6.14179i	0.398952	−	0.691005i	0.993597	+	0.112983i	$0.0360407\pi$
$80$	−0.0611015	+	2.23523i	−0.00683135	+	0.249907i
$81$	−8.13217	+	3.85588i	−0.903575	+	0.428431i
$82$	3.16905	+	5.48896i	0.349964	+	0.606155i
$83$	−4.32983	+	2.49983i	−0.475261	+	0.274392i	−0.718439	−	0.695589i	$-0.755143\pi$
$83$	−4.32983	+	2.49983i	−0.475261	+	0.274392i	0.243178	+	0.969982i	$0.421810\pi$
$84$	−0.593040	−	4.54404i	−0.0647060	−	0.495795i
$85$	−1.29823	−	0.0354880i	−0.140813	−	0.00384921i
$86$			11.6293i			1.25402i
$87$	−0.0377989	+	0.248234i	−0.00405247	+	0.0266135i
$88$		−	1.30502i		−	0.139116i
$89$	−1.35235	−	2.34234i	−0.143349	−	0.248288i	0.785407	−	0.618980i	$-0.212454\pi$
$89$	−1.35235	−	2.34234i	−0.143349	−	0.248288i	−0.928756	+	0.370692i	$0.879121\pi$
$90$	−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
$93$	−0.360511	+	2.36756i	−0.0373833	+	0.245504i
$94$	4.69056	−	2.70810i	0.483794	−	0.279319i
$95$	−9.27780	+	15.1010i	−0.951882	+	1.54933i
$96$	1.71231	+	0.260736i	0.174762	+	0.0266113i
$97$	−5.76032	−	9.97717i	−0.584872	−	1.01303i	−0.994891	−	0.100951i	$-0.967811\pi$
$97$	−5.76032	−	9.97717i	−0.584872	−	1.01303i	0.410019	−	0.912077i	$-0.365522\pi$
$98$	0.267153	+	6.99490i	0.0269865	+	0.706592i
$99$	3.81952	−	0.859646i	0.383876	−	0.0863976i
$100$	−4.99253	−	0.273152i	−0.499253	−	0.0273152i
$101$	14.3532			1.42819			0.714097	−	0.700047i	$-0.246838\pi$
$101$	14.3532			1.42819			0.714097	+	0.700047i	$0.246838\pi$
$102$	−0.151437	+	0.994518i	−0.0149945	+	0.0984720i
$103$	0.772004			0.0760678			0.0380339	−	0.999276i	$-0.487891\pi$
$103$	0.772004			0.0760678			0.0380339	+	0.999276i	$0.487891\pi$
$104$	−3.03357	+	5.25429i	−0.297466	+	0.515226i
$105$	10.1932	−	1.04793i	0.994757	−	0.102268i
$106$	4.19068	+	7.25846i	0.407034	+	0.705004i
$107$	8.60622	+	14.9064i	0.831995	+	1.44106i	0.896454	+	0.443137i	$0.146134\pi$
$107$	8.60622	+	14.9064i	0.831995	+	1.44106i	−0.0644590	+	0.997920i	$0.520532\pi$
$108$	0.364819	+	5.18333i	0.0351047	+	0.498766i
$109$	−6.30827	+	10.9262i	−0.604223	+	1.04654i	0.387951	+	0.921680i	$0.373183\pi$
$109$	−6.30827	+	10.9262i	−0.604223	+	1.04654i	−0.992174	+	0.124864i	$0.960150\pi$
$110$	2.91702	+	0.0797387i	0.278127	+	0.00760279i
$111$	0.610765	−	4.01103i	0.0579712	−	0.380710i
$112$	−2.56820	−	0.635870i	−0.242672	−	0.0600841i
$113$	−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	$0.974766\pi$
$114$	10.7204	+	8.57577i	1.00406	+	0.803195i
$115$	12.9235	−	6.99768i	1.20512	−	0.652537i
$116$	0.125548	+	0.0724850i	0.0116568	+	0.00673006i
$117$	−17.3765	−	5.41749i	−1.60646	−	0.500847i
$118$	−3.08716			−0.284196
$119$	0.369316	−	1.49162i	0.0338551	−	0.136737i
$120$	−0.687431	+	3.81149i	−0.0627536	+	0.347940i
$121$	9.29692			0.845175
$122$	1.83643	−	1.06026i	0.166263	−	0.0959918i
$123$	3.99524	+	10.2251i	0.360239	+	0.921967i
$124$	1.19742	+	0.691334i	0.107532	+	0.0620836i
$125$	0.915610	−	11.1428i	0.0818946	−	0.996641i
$126$	0.169326	−	7.93545i	0.0150847	−	0.706946i
$127$		−	14.7512i		−	1.30896i	−0.756079	−	0.654480i	$-0.772887\pi$
$127$		−	14.7512i		−	1.30896i	0.756079	−	0.654480i	$-0.227113\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.03219	+	19.9131i	−0.266969	+	1.75325i
$130$	−11.5592	−	7.10177i	−1.01381	−	0.622867i
$131$	15.6922			1.37103			0.685517	−	0.728057i	$-0.259576\pi$
$131$	15.6922			1.37103			0.685517	+	0.728057i	$0.259576\pi$
$132$	0.340266	−	2.23460i	0.0296164	−	0.194497i
$133$	−15.1088	−	14.5427i	−1.31010	−	1.26102i
$134$		−	13.1972i		−	1.14006i
$135$	−11.6082	+	0.498746i	−0.999078	+	0.0429253i
$136$	0.502991	+	0.290402i	0.0431311	+	0.0249018i
$137$	−8.85857			−0.756839			−0.378419	−	0.925634i	$-0.623532\pi$
$137$	−8.85857			−0.756839			−0.378419	+	0.925634i	$0.623532\pi$
$138$	−4.14295	−	10.6032i	−0.352672	−	0.902600i
$139$	1.39913	+	0.807790i	0.118673	+	0.0685158i	0.558161	−	0.829732i	$-0.311507\pi$
$139$	1.39913	+	0.807790i	0.118673	+	0.0685158i	−0.439489	+	0.898248i	$0.644840\pi$
$140$	1.57824	−	5.70168i	0.133386	−	0.481880i
$141$	8.73781	−	3.41411i	0.735856	−	0.287520i
$142$	8.96724	+	5.17724i	0.752514	+	0.434464i
$143$	6.85696	+	3.95887i	0.573408	+	0.331057i
$144$	2.86403	+	0.892924i	0.238669	+	0.0744103i
$145$	−0.169692	+	0.276199i	−0.0140922	+	0.0229371i
$146$	−3.84599	−	6.66144i	−0.318296	−	0.551305i
$147$	−1.36637	+	12.0471i	−0.112697	+	0.993629i
$148$	−2.02863	−	1.17123i	−0.166753	−	0.0962746i
$149$			9.59314i			0.785901i	0.919560	+	0.392950i	$0.128546\pi$
$149$			9.59314i			0.785901i	−0.919560	+	0.392950i	$0.871454\pi$
$150$	−8.47756	−	1.76946i	−0.692190	−	0.144475i
$151$	−17.3655			−1.41318			−0.706592	−	0.707621i	$-0.749768\pi$
$151$	−17.3655			−1.41318			−0.706592	+	0.707621i	$0.749768\pi$
$152$	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
$156$	−6.56440	+	8.20603i	−0.525573	+	0.657008i
$157$	1.69869	+	2.94222i	0.135570	+	0.234814i	0.925815	−	0.377977i	$-0.123380\pi$
$157$	1.69869	+	2.94222i	0.135570	+	0.234814i	−0.790245	+	0.612791i	$0.790047\pi$
$158$	−3.54596	−	6.14179i	−0.282102	−	0.488614i
$159$	5.28321	+	13.5214i	0.418985	+	1.07232i
$160$	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	$-0.596047\pi$
$163$	4.86586	−	2.80931i	0.381124	−	0.220042i	0.678307	+	0.734778i	$0.262714\pi$
$164$	6.33811			0.494923
$165$	4.97407	+	0.897111i	0.387231	+	0.0698400i
$166$			4.99966i			0.388049i
$167$	−5.55272	−	3.20586i	−0.429682	−	0.248077i	0.269529	−	0.962992i	$-0.413132\pi$
$167$	−5.55272	−	3.20586i	−0.429682	−	0.248077i	−0.699211	+	0.714915i	$0.746465\pi$
$168$	−4.23177	−	1.75843i	−0.326488	−	0.135666i
$169$	−11.9051	−	20.6202i	−0.915773	−	1.58617i
$170$	−0.679850	+	1.10656i	−0.0521421	+	0.0848691i
$171$	16.1207	+	17.4796i	1.23278	+	1.33670i
$172$	10.0713	+	5.81466i	0.767929	+	0.443364i
$173$	6.95118	+	4.01327i	0.528489	+	0.305123i	0.740401	−	0.672166i	$-0.234636\pi$
$173$	6.95118	+	4.01327i	0.528489	+	0.305123i	−0.211912	+	0.977289i	$0.567969\pi$
$174$	0.196078	+	0.156852i	0.0148646	+	0.0118909i
$175$	12.6482	+	3.87611i	0.956110	+	0.293007i
$176$	−1.13018	−	0.652510i	−0.0851906	−	0.0491848i
$177$	−5.28618	−	0.804933i	−0.397333	−	0.0605025i
$178$	−2.70471			−0.202726
$179$	14.3104	+	8.26209i	1.06961	+	0.617538i	0.928074	−	0.372396i	$-0.121464\pi$
$179$	14.3104	+	8.26209i	1.06961	+	0.617538i	0.141533	+	0.989934i	$0.454797\pi$
$180$	−2.17089	+	6.34722i	−0.161809	+	0.473094i
$181$			6.84621i			0.508875i	0.967089	+	0.254437i	$0.0818903\pi$
$181$			6.84621i			0.508875i	−0.967089	+	0.254437i	$0.918110\pi$
$182$	11.1319	−	11.5651i	0.825149	−	0.857265i
$183$	3.42099	−	1.33668i	0.252887	−	0.0988102i
$184$	−6.57244			−0.484527
$185$	2.74193	−	4.46290i	0.201590	−	0.328119i
$186$	1.87011	+	1.49599i	0.137123	+	0.109691i
$187$	0.378980	−	0.656413i	0.0277138	−	0.0480017i
$188$		−	5.41619i		−	0.395016i
$189$	2.35900	−	13.5438i	0.171592	−	0.985168i
$190$	8.43897	+	15.5853i	0.612227	+	1.13068i
$191$	−7.33287	−	4.23363i	−0.530588	−	0.306335i	0.210668	−	0.977558i	$-0.432436\pi$
$191$	−7.33287	−	4.23363i	−0.530588	−	0.306335i	−0.741256	+	0.671223i	$0.765769\pi$
$192$	1.08196	−	1.35254i	0.0780838	−	0.0976111i
$193$	1.96645	−	1.13533i	0.141548	−	0.0817227i	−0.427554	−	0.903990i	$-0.640624\pi$
$193$	1.96645	−	1.13533i	0.141548	−	0.0817227i	0.569101	+	0.822267i	$0.307291\pi$
$194$	−11.5206			−0.827134
$195$	−17.9413	−	15.1744i	−1.28480	−	1.08666i
$196$	6.19134	+	3.26609i	0.442238	+	0.233292i
$197$	−13.0144			−0.927240			−0.463620	−	0.886034i	$-0.653450\pi$
$197$	−13.0144			−0.927240			−0.463620	+	0.886034i	$0.653450\pi$
$198$	1.16528	−	3.73762i	0.0828131	−	0.265621i
$199$	−2.76888	−	1.59861i	−0.196280	−	0.113323i	0.398639	−	0.917108i	$-0.369483\pi$
$199$	−2.76888	−	1.59861i	−0.196280	−	0.113323i	−0.594919	+	0.803785i	$0.702816\pi$
$200$	−2.73282	+	4.18708i	−0.193240	+	0.296072i
$201$	3.44098	−	22.5977i	0.242708	−	1.59392i
$202$	7.17658	−	12.4302i	0.504943	−	0.874586i
$203$	−0.276341	−	0.265988i	−0.0193953	−	0.0186687i
$204$	0.785560	+	0.628407i	0.0550002	+	0.0439973i
$205$	−0.387268	+	14.1672i	−0.0270480	+	0.989477i
$206$	0.386002	−	0.668575i	0.0268940	−	0.0465818i
$207$	−4.32941	−	19.2361i	−0.300915	−	1.33700i
$208$	3.03357	+	5.25429i	0.210340	+	0.364320i
$209$	−5.17189	−	8.95797i	−0.357747	−	0.619636i
$210$	4.18907	−	9.35156i	0.289074	−	0.645319i
$211$	−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	$0.279761\pi$
$212$	8.38135			0.575634
$213$	14.0048	+	11.2031i	0.959595	+	0.767627i
$214$	17.2124			1.17662
$215$	−13.6125	+	22.1564i	−0.928365	+	1.51105i
$216$	4.67130	+	2.27572i	0.317842	+	0.154843i
$217$	−2.63563	−	2.53689i	−0.178918	−	0.172215i
$218$	6.30827	+	10.9262i	0.427250	+	0.740019i
$219$	−4.84865	−	12.4093i	−0.327642	−	0.838541i
$220$	1.52757	−	2.48635i	0.102989	−	0.167630i
$221$	−3.05171	+	1.76191i	−0.205280	+	0.118519i
$222$	−3.16827	−	2.53445i	−0.212640	−	0.170101i
$223$	−1.58167	−	2.73954i	−0.105917	−	0.183453i	0.808196	−	0.588914i	$-0.200444\pi$
$223$	−1.58167	−	2.73954i	−0.105917	−	0.183453i	−0.914112	+	0.405461i	$0.867111\pi$
$224$	−1.83478	+	1.90619i	−0.122592	+	0.127363i
$225$	−14.0549	−	5.24027i	−0.936992	−	0.349351i
$226$	6.02741	+	10.4398i	0.400938	+	0.694444i
$227$		−	9.59332i		−	0.636731i	−0.947968	−	0.318365i	$-0.896866\pi$
$227$		−	9.59332i		−	0.636731i	0.947968	−	0.318365i	$-0.103134\pi$
$228$	12.7870	−	4.99626i	0.846843	−	0.330886i
$229$		−	3.59517i		−	0.237575i	−0.992920	−	0.118788i	$-0.962099\pi$
$229$		−	3.59517i		−	0.237575i	0.992920	−	0.118788i	$-0.0379008\pi$
$230$	0.401586	−	14.6909i	0.0264798	−	0.968691i
$231$	−2.29479	+	5.52255i	−0.150986	+	0.363357i
$232$	0.125548	−	0.0724850i	0.00824261	−	0.00475887i
$233$	2.91309	+	5.04563i	0.190843	+	0.330550i	0.945530	−	0.325535i	$-0.105544\pi$
$233$	2.91309	+	5.04563i	0.190843	+	0.330550i	−0.754687	+	0.656085i	$0.772211\pi$
$234$	−13.3799	+	12.3397i	−0.874673	+	0.806673i
$235$	12.1065	+	0.330937i	0.789738	+	0.0215880i
$236$	−1.54358	+	2.67356i	−0.100478	+	0.174034i
$237$	−4.47041	−	11.4412i	−0.290384	−	0.743187i
$238$	−1.10713	−	1.06565i	−0.0717643	−	0.0690757i
$239$	−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	$0.933954\pi$
$240$	2.95713	+	2.50108i	0.190882	+	0.161444i
$241$		−	6.84601i		−	0.440990i	−0.975388	−	0.220495i	$-0.929233\pi$
$241$		−	6.84601i		−	0.440990i	0.975388	−	0.220495i	$-0.0707673\pi$
$242$	4.64846	−	8.05137i	0.298814	−	0.517562i
$243$	−3.58346	+	15.1710i	−0.229879	+	0.973219i
$244$		−	2.12053i		−	0.135753i
$245$	−7.67877	+	13.6395i	−0.490579	+	0.871397i
$246$	10.8528	+	1.65257i	0.691951	+	0.105364i
$247$			48.0890i			3.05983i
$248$	1.19742	−	0.691334i	0.0760366	−	0.0438997i
$249$	−1.30359	+	8.56099i	−0.0826118	+	0.542531i
$250$	−9.19213	−	6.36433i	−0.581361	−	0.402516i
$251$	12.2160			0.771068			0.385534	−	0.922694i	$-0.374017\pi$
$251$	12.2160			0.771068			0.385534	+	0.922694i	$0.374017\pi$
$252$	−6.78764	−	4.11436i	−0.427581	−	0.259181i
$253$			8.57717i			0.539242i
$254$	−12.7749	−	7.37562i	−0.801571	−	0.462788i
$255$	−1.45263	+	1.71751i	−0.0909675	+	0.107555i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	26.3720i		−	1.64504i	−0.568737	−	0.822520i	$-0.692568\pi$
$257$		−	26.3720i		−	1.64504i	0.568737	−	0.822520i	$-0.307432\pi$
$258$	15.7291	+	12.5825i	0.979252	+	0.783351i
$259$	4.46519	+	4.29791i	0.277453	+	0.267059i
$260$	−11.9299	+	6.45968i	−0.739862	+	0.400613i
$261$	0.294849	+	0.319704i	0.0182507	+	0.0197892i
$262$	7.84610	−	13.5898i	0.484734	−	0.839583i
$263$	−20.6961			−1.27618			−0.638088	−	0.769963i	$-0.720274\pi$
$263$	−20.6961			−1.27618			−0.638088	+	0.769963i	$0.720274\pi$
$264$	−1.76509	−	1.41198i	−0.108634	−	0.0869014i
$265$	−0.512113	+	18.7343i	−0.0314589	+	1.15084i
$266$	−20.1488	+	5.81321i	−1.23540	+	0.356431i
$267$	−4.63130	−	0.705215i	−0.283431	−	0.0431584i
$268$	−11.4291	−	6.59859i	−0.698143	−	0.403073i
$269$	4.69521	−	8.13233i	0.286272	−	0.495837i	−0.686645	−	0.726993i	$-0.740917\pi$
$269$	4.69521	−	8.13233i	0.286272	−	0.495837i	0.972917	+	0.231156i	$0.0742507\pi$
$270$	−5.37219	+	10.3024i	−0.326941	+	0.626984i
$271$	−2.94143	+	1.69824i	−0.178679	+	0.103161i	−0.586672	−	0.809825i	$-0.699562\pi$
$271$	−2.94143	+	1.69824i	−0.178679	+	0.103161i	0.407993	+	0.912985i	$0.366229\pi$
$272$	0.502991	−	0.290402i	0.0304983	−	0.0176082i
$273$	22.0767	−	16.9007i	1.33614	−	1.02287i
$274$	−4.42929	+	7.67175i	−0.267583	+	0.463467i
$275$	5.46423	+	3.56639i	0.329506	+	0.215061i
$276$	−11.2541	−	1.71367i	−0.677416	−	0.103151i
$277$			20.9520i			1.25888i	0.777047	+	0.629442i	$0.216717\pi$
$277$			20.9520i			1.25888i	−0.777047	+	0.629442i	$0.783283\pi$
$278$	1.39913	−	0.807790i	0.0839144	−	0.0484480i
$279$	2.81216	+	3.04921i	0.168359	+	0.182552i
$280$	−4.14868	−	4.21764i	−0.247931	−	0.252052i
$281$	0.919808	−	0.531051i	0.0548712	−	0.0316799i	−0.472313	−	0.881431i	$-0.656581\pi$
$281$	0.919808	−	0.531051i	0.0548712	−	0.0316799i	0.527185	+	0.849751i	$0.323248\pi$
$282$	1.41220	−	9.27422i	0.0840951	−	0.552272i
$283$	−10.4824	−	18.1560i	−0.623113	−	1.07926i	−0.988903	−	0.148565i	$-0.952534\pi$
$283$	−10.4824	−	18.1560i	−0.623113	−	1.07926i	0.365790	−	0.930697i	$-0.380799\pi$
$284$	8.96724	−	5.17724i	0.532108	−	0.307213i
$285$	10.3865	+	28.8873i	0.615244	+	1.71114i
$286$	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
$290$	0.154350	+	0.285057i	0.00906373	+	0.0167391i
$291$	−19.7270	−	3.00385i	−1.15641	−	0.176089i
$292$	−7.69197			−0.450139
$293$	−19.5706	−	11.2991i	−1.14332	−	0.660099i	−0.196073	−	0.980589i	$-0.562819\pi$
$293$	−19.5706	−	11.2991i	−1.14332	−	0.660099i	−0.947252	+	0.320491i	$0.896152\pi$
$294$	9.74992	+	7.20687i	0.568627	+	0.420313i
$295$	−5.88170	−	3.61361i	−0.342446	−	0.210393i
$296$	−2.02863	+	1.17123i	−0.117912	+	0.0680764i
$297$	2.96986	−	6.09615i	0.172329	−	0.353734i
$298$	8.30790	+	4.79657i	0.481264	+	0.277858i
$299$	19.9379	−	34.5335i	1.15304	−	1.99712i
$300$	−5.77117	+	6.45705i	−0.333199	+	0.372798i
$301$	−22.1678	−	21.3373i	−1.27773	−	1.22986i
$302$	−8.68275	+	15.0390i	−0.499636	+	0.865395i
$303$	15.5296	−	19.4132i	0.892150	−	1.11526i
$304$		−	7.92614i		−	0.454595i
$305$	4.73987	+	0.129567i	0.271404	+	0.00741901i
$306$	1.18128	+	1.28085i	0.0675291	+	0.0732215i
$307$	−29.2086			−1.66702			−0.833512	−	0.552501i	$-0.813674\pi$
$307$	−29.2086			−1.66702			−0.833512	+	0.552501i	$0.813674\pi$
$308$	2.48762	+	2.39443i	0.141745	+	0.136435i
$309$	0.835278	−	1.04416i	0.0475173	−	0.0594005i
$310$	1.47213	+	2.71877i	0.0836112	+	0.154415i
$311$	−6.50531	−	11.2675i	−0.368882	−	0.638923i	0.620509	−	0.784199i	$-0.286926\pi$
$311$	−6.50531	−	11.2675i	−0.368882	−	0.638923i	−0.989391	+	0.145277i	$0.953593\pi$
$312$	3.82443	+	9.78795i	0.216516	+	0.554134i
$313$	3.62723	−	6.28255i	0.205023	−	0.355111i	−0.745117	−	0.666934i	$-0.767606\pi$
$313$	3.62723	−	6.28255i	0.205023	−	0.355111i	0.950140	+	0.311823i	$0.100940\pi$
$314$	3.39738			0.191725
$315$	9.61130	−	14.9206i	0.541535	−	0.840678i
$316$	−7.09192			−0.398952
$317$	14.2603	−	24.6996i	0.800939	−	1.38727i	−0.118059	−	0.993007i	$-0.537667\pi$
$317$	14.2603	−	24.6996i	0.800939	−	1.38727i	0.918999	−	0.394261i	$-0.128999\pi$
$318$	14.3515	+	2.18532i	0.804792	+	0.122547i
$319$	−0.0945944	−	0.163842i	−0.00529627	−	0.00917341i
$320$	1.96632	−	1.06470i	0.109921	−	0.0595186i
$321$	29.4731	+	4.48791i	1.64503	+	0.250490i
$322$	16.8794	+	4.17922i	0.940650	+	0.232899i
$323$	4.60353			0.256147
$324$	7.40537	+	5.11473i	0.411410	+	0.284152i
$325$	−13.7100	−	27.0608i	−0.760492	−	1.50107i
$326$		−	5.61862i		−	0.311186i
$327$	7.95287	+	20.3539i	0.439795	+	1.12558i
$328$	3.16905	−	5.48896i	0.174982	−	0.303077i
$329$	−3.44400	+	13.9099i	−0.189874	+	0.766877i
$330$	3.26396	−	3.85911i	0.179675	−	0.212437i
$331$	−12.3511	+	21.3927i	−0.678877	+	1.17585i	0.296443	+	0.955051i	$0.404200\pi$
$331$	−12.3511	+	21.3927i	−0.678877	+	1.17585i	−0.975319	+	0.220798i	$0.929134\pi$
$332$	4.32983	+	2.49983i	0.237631	+	0.137196i
$333$	−4.76425	−	5.16586i	−0.261079	−	0.283087i
$334$	−5.55272	+	3.20586i	−0.303831	+	0.175417i
$335$	15.4477	−	25.1435i	0.843999	−	1.37374i
$336$	−3.63873	+	2.78561i	−0.198509	+	0.151967i
$337$	−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	$0.728497\pi$
$338$	−23.8101			−1.29510
$339$	7.59879	+	19.4477i	0.412710	+	1.05626i
$340$	0.618383	+	1.14205i	0.0335365	+	0.0619361i
$341$	−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
$345$	4.51810	−	25.0508i	0.243246	−	1.34869i
$346$	6.95118	−	4.01327i	0.373698	−	0.215755i
$347$	3.87822	+	6.71728i	0.208194	+	0.360603i	0.951146	−	0.308743i	$-0.0999081\pi$
$347$	3.87822	+	6.71728i	0.208194	+	0.360603i	−0.742952	+	0.669345i	$0.766575\pi$
$348$	0.233876	−	0.0913822i	0.0125371	−	0.00489860i
$349$	8.89557	−	5.13586i	0.476169	−	0.274916i	−0.242650	−	0.970114i	$-0.578017\pi$
$349$	8.89557	−	5.13586i	0.476169	−	0.274916i	0.718819	+	0.695198i	$0.244683\pi$
$350$	9.68089	−	9.01556i	0.517465	−	0.481902i
$351$	−26.1280	+	17.6408i	−1.39461	+	0.941598i
$352$	−1.13018	+	0.652510i	−0.0602388	+	0.0347789i
$353$			21.0732i			1.12161i	0.827947	+	0.560807i	$0.189509\pi$
$353$			21.0732i			1.12161i	−0.827947	+	0.560807i	$0.810491\pi$
$354$	−3.34018	+	4.17550i	−0.177529	+	0.221925i
$355$	11.0244	+	20.3602i	0.585116	+	1.08061i
$356$	−1.35235	+	2.34234i	−0.0716746	+	0.124144i
$357$	−1.61789	−	2.11339i	−0.0856279	−	0.111853i
$358$	14.3104	−	8.26209i	0.756326	−	0.436665i
$359$	−15.0004	+	8.66050i	−0.791692	+	0.457084i	−0.840558	−	0.541722i	$-0.817773\pi$
$359$	−15.0004	+	8.66050i	−0.791692	+	0.457084i	0.0488656	+	0.998805i	$0.484439\pi$
$360$	4.41141	+	5.05366i	0.232502	+	0.266351i
$361$	21.9119	−	37.9525i	1.15326	−	1.99750i
$362$	5.92899	+	3.42310i	0.311621	+	0.179914i
$363$	10.0589	−	12.5744i	0.527956	−	0.659987i
$364$	−4.44977	−	15.4230i	−0.233231	−	0.808387i
$365$	0.469991	−	17.1934i	0.0246005	−	0.899941i
$366$	0.552898	−	3.63101i	0.0289004	−	0.189796i
$367$	6.99660			0.365220			0.182610	−	0.983185i	$-0.441546\pi$
$367$	6.99660			0.365220			0.182610	+	0.983185i	$0.441546\pi$
$368$	−3.28622	+	5.69190i	−0.171306	+	0.296711i
$369$	18.1526	+	5.65945i	0.944984	+	0.294619i
$370$	−2.49402	−	4.60603i	−0.129658	−	0.239456i
$371$	−21.5250	−	5.32945i	−1.11752	−	0.276691i
$372$	2.23062	−	0.871568i	0.115652	−	0.0451887i
$373$		−	14.9568i		−	0.774432i	−0.921989	−	0.387216i	$-0.873437\pi$
$373$		−	14.9568i		−	0.774432i	0.921989	−	0.387216i	$-0.126563\pi$
$374$	−0.378980	−	0.656413i	−0.0195966	−	0.0339423i
$375$	−14.0804	−	13.2945i	−0.727108	−	0.686523i
$376$	−4.69056	−	2.70810i	−0.241897	−	0.139659i
$377$			0.879552i			0.0452992i
$378$	−10.5498	−	8.81486i	−0.542623	−	0.453388i
$379$	1.81688			0.0933268			0.0466634	−	0.998911i	$-0.485141\pi$
$379$	1.81688			0.0933268			0.0466634	+	0.998911i	$0.485141\pi$
$380$	17.7168	+	0.484299i	0.908851	+	0.0248440i
$381$	−19.9516	−	15.9603i	−1.02215	−	0.817669i
$382$	−7.33287	+	4.23363i	−0.375182	+	0.216611i
$383$		−	4.60201i		−	0.235152i	−0.993064	−	0.117576i	$-0.962488\pi$
$383$		−	4.60201i		−	0.235152i	0.993064	−	0.117576i	$-0.0375123\pi$
$384$	−0.630353	−	1.61327i	−0.0321675	−	0.0823271i
$385$	−5.50410	+	5.41411i	−0.280515	+	0.275929i
$386$		−	2.27066i		−	0.115573i
$387$	23.6525	+	25.6463i	1.20232	+	1.30367i
$388$	−5.76032	+	9.97717i	−0.292436	+	0.506514i
$389$			17.1177i			0.867902i	0.900936	+	0.433951i	$0.142881\pi$
$389$			17.1177i			0.867902i	−0.900936	+	0.433951i	$0.857119\pi$
$390$	−22.1120	+	7.95044i	−1.11969	+	0.402586i
$391$	−3.30588	−	1.90865i	−0.167185	−	0.0965245i
$392$	5.92418	−	3.72881i	0.299217	−	0.188333i
$393$	16.9783	−	21.2243i	0.856444	−	1.07062i
$394$	−6.50721	+	11.2708i	−0.327829	+	0.567816i
$395$	0.433327	−	15.8521i	0.0218031	−	0.797606i
$396$	−2.65423	−	2.87798i	−0.133380	−	0.144624i
$397$	7.42358	+	12.8580i	0.372579	+	0.645325i	0.989961	−	0.141338i	$-0.0451403\pi$
$397$	7.42358	+	12.8580i	0.372579	+	0.645325i	−0.617383	+	0.786663i	$0.711807\pi$
$398$	−2.76888	+	1.59861i	−0.138791	+	0.0801312i
$399$	−36.0167	+	4.70052i	−1.80309	+	0.235320i
$400$	2.25971	+	4.46024i	0.112985	+	0.223012i
$401$		−	9.57306i		−	0.478056i	−0.971013	−	0.239028i	$-0.923171\pi$
$401$		−	9.57306i		−	0.478056i	0.971013	−	0.239028i	$-0.0768287\pi$
$402$	−17.8497	−	14.2788i	−0.890262	−	0.712163i
$403$			8.38883i			0.417877i
$404$	−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
$408$	0.936996	−	0.366111i	0.0463882	−	0.0181252i
$409$	−33.4503	+	19.3125i	−1.65401	+	0.954944i	−0.678612	+	0.734497i	$0.737418\pi$
$409$	−33.4503	+	19.3125i	−1.65401	+	0.954944i	−0.975399	+	0.220446i	$0.929249\pi$
$410$	12.0755	+	7.41896i	0.596365	+	0.366396i
$411$	−9.58463	+	11.9816i	−0.472775	+	0.591007i
$412$	−0.386002	−	0.668575i	−0.0190169	−	0.0329383i
$413$	5.66426	−	5.88472i	0.278720	−	0.289568i
$414$	−18.8237	−	5.86869i	−0.925134	−	0.288430i
$415$	−5.85226	+	9.52544i	−0.287276	+	0.467586i
$416$	6.06713			0.297466
$417$	2.60637	−	1.01838i	0.127635	−	0.0498705i
$418$	−10.3438			−0.505931
$419$	6.88512	−	11.9254i	0.336360	−	0.582593i	−0.647385	−	0.762163i	$-0.724137\pi$
$419$	6.88512	−	11.9254i	0.336360	−	0.582593i	0.983745	+	0.179570i	$0.0574707\pi$
$420$	−6.00415	−	8.30362i	−0.292973	−	0.405175i
$421$	−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
$423$	4.83625	−	15.5122i	0.235146	−	0.754227i
$424$	4.19068	−	7.25846i	0.203517	−	0.352502i
$425$	−2.59052	+	1.31245i	−0.125659	+	0.0636631i
$426$	16.7046	−	6.52697i	0.809342	−	0.316233i
$427$	−1.34838	+	5.44595i	−0.0652527	+	0.263548i
$428$	8.60622	−	14.9064i	0.415997	−	0.720529i
$429$	12.7735	−	4.99096i	0.616709	−	0.240966i
$430$	12.3818	+	22.8670i	0.597101	+	1.10274i
$431$	29.2156	+	16.8676i	1.40726	+	0.812485i	0.995124	−	0.0986352i	$-0.0314477\pi$
$431$	29.2156	+	16.8676i	1.40726	+	0.812485i	0.412141	+	0.911120i	$0.364781\pi$
$432$	4.30649	−	2.90761i	0.207196	−	0.139892i
$433$	−7.29213			−0.350437			−0.175219	−	0.984530i	$-0.556063\pi$
$433$	−7.29213			−0.350437			−0.175219	+	0.984530i	$0.556063\pi$
$434$	−3.51483	+	1.01408i	−0.168717	+	0.0486773i
$435$	0.189970	+	0.528352i	0.00910838	+	0.0253325i
$436$	12.6165			0.604223
$437$	−45.1148	+	26.0470i	−2.15813	+	1.24600i
$438$	−13.1711	−	2.00558i	−0.629338	−	0.0958301i
$439$	2.29308	+	1.32391i	0.109443	+	0.0631868i	0.553722	−	0.832701i	$-0.313207\pi$
$439$	2.29308	+	1.32391i	0.109443	+	0.0631868i	−0.444279	+	0.895888i	$0.646540\pi$
$440$	−1.38946	−	2.56609i	−0.0662397	−	0.122333i
$441$	14.8158	+	14.8826i	0.705516	+	0.708694i
$442$			3.52381i			0.167611i
$443$	−12.9543	+	22.4376i	−0.615480	+	1.06604i	0.374821	+	0.927097i	$0.377704\pi$
$443$	−12.9543	+	22.4376i	−0.615480	+	1.06604i	−0.990300	+	0.138945i	$0.955629\pi$
$444$	−3.77904	+	1.47658i	−0.179345	+	0.0700752i
$445$	−5.15305	−	3.16594i	−0.244278	−	0.150080i
$446$	−3.16334			−0.149789
$447$	12.9751	+	10.3794i	0.613701	+	0.490929i
$448$	0.733422	+	2.54206i	0.0346509	+	0.120101i
$449$		−	11.3781i		−	0.536965i	−0.963285	−	0.268482i	$-0.913478\pi$
$449$		−	11.3781i		−	0.536965i	0.963285	−	0.268482i	$-0.0865221\pi$
$450$	−11.5656	+	9.55175i	−0.545210	+	0.450274i
$451$	−7.16321	−	4.13568i	−0.337302	−	0.194742i
$452$	12.0548			0.567011
$453$	−18.7888	+	23.4875i	−0.882774	+	1.10354i
$454$	−8.30806	−	4.79666i	−0.389916	−	0.225118i
$455$	34.7460	−	9.00390i	1.62892	−	0.422109i
$456$	2.06663	−	13.5720i	0.0967789	−	0.635569i
$457$	−9.95317	−	5.74647i	−0.465590	−	0.268808i	0.248802	−	0.968554i	$-0.419963\pi$
$457$	−9.95317	−	5.74647i	−0.465590	−	0.268808i	−0.714392	+	0.699746i	$0.753296\pi$
$458$	−3.11351	−	1.79758i	−0.145485	−	0.0839956i
$459$	1.68875	+	2.50122i	0.0788241	+	0.116747i
$460$	−12.5219	−	7.69325i	−0.583838	−	0.358700i
$461$	0.576578	+	0.998663i	0.0268539	+	0.0465124i	0.879140	−	0.476564i	$-0.158118\pi$
$461$	0.576578	+	0.998663i	0.0268539	+	0.0465124i	−0.852286	+	0.523076i	$0.824784\pi$
$462$	3.63528	+	4.74862i	0.169128	+	0.220926i
$463$	−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	$0.801149\pi$
$464$		−	0.144970i		−	0.00673006i
$465$	1.81186	+	5.03921i	0.0840231	+	0.233688i
$466$	5.82619			0.269893
$467$	16.2441	−	9.37851i	0.751685	−	0.433986i	−0.0746173	−	0.997212i	$-0.523774\pi$
$467$	16.2441	−	9.37851i	0.751685	−	0.433986i	0.826302	+	0.563227i	$0.190440\pi$
$468$	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
$471$	5.81737	+	0.885819i	0.268050	+	0.0408164i
$472$	1.54358	+	2.67356i	0.0710489	+	0.123060i
$473$	−7.58826	−	13.1432i	−0.348908	−	0.604327i
$474$	−12.1436	−	1.84912i	−0.557774	−	0.0849329i
$475$	−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
$479$	−0.124194			−0.00567456			−0.00283728	−	0.999996i	$-0.500903\pi$
$479$	−0.124194			−0.00567456			−0.00283728	+	0.999996i	$0.500903\pi$
$480$	3.64456	−	1.31041i	0.166351	−	0.0598118i
$481$		−	14.2120i		−	0.648013i
$482$	−5.92882	−	3.42300i	−0.270050	−	0.155914i
$483$	27.8131	+	11.5572i	1.26554	+	0.525870i
$484$	−4.64846	−	8.05137i	−0.211294	−	0.365971i
$485$	−21.9493	−	13.4853i	−0.996668	−	0.612335i
$486$	11.3467	+	10.6889i	0.514698	+	0.484857i
$487$	−22.4789	−	12.9782i	−1.01862	−	0.588099i	−0.104914	−	0.994481i	$-0.533457\pi$
$487$	−22.4789	−	12.9782i	−1.01862	−	0.588099i	−0.913703	+	0.406382i	$0.866790\pi$
$488$	−1.83643	−	1.06026i	−0.0831313	−	0.0479959i
$489$	1.46498	−	9.62083i	0.0662485	−	0.435069i
$490$	7.97279	+	13.4698i	0.360174	+	0.608502i
$491$	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	$0.516073\pi$
$492$	6.85759	−	8.57254i	0.309164	−	0.386480i
$493$	0.0841991			0.00379214
$494$	41.6463	+	24.0445i	1.87375	+	1.08181i
$495$	6.59513	−	5.75698i	0.296429	−	0.258757i
$496$		−	1.38267i		−	0.0620836i
$497$	−26.3218	+	7.59420i	−1.18069	+	0.340646i
$498$	6.76224	+	5.40944i	0.303023	+	0.242403i
$499$	−7.61998			−0.341117			−0.170559	−	0.985348i	$-0.554557\pi$
$499$	−7.61998			−0.341117			−0.170559	+	0.985348i	$0.554557\pi$
$500$	−10.1077	+	4.77845i	−0.452032	+	0.213699i
$501$	−10.3439	+	4.04165i	−0.462130	+	0.180568i
$502$	6.10801	−	10.5794i	0.272614	−	0.472181i
$503$		−	20.5824i		−	0.917723i	−0.888508	−	0.458861i	$-0.848257\pi$
$503$		−	20.5824i		−	0.917723i	0.888508	−	0.458861i	$-0.151743\pi$
$504$	−6.95696	+	3.82108i	−0.309888	+	0.170205i
$505$	28.2229	−	15.2818i	1.25590	−	0.680032i
$506$	7.42805	+	4.28858i	0.330217	+	0.190651i
$507$	−40.7704	−	6.20815i	−1.81067	−	0.275714i
$508$	−12.7749	+	7.37562i	−0.566797	+	0.327240i
$509$	2.57903			0.114313			0.0571567	−	0.998365i	$-0.481797\pi$
$509$	2.57903			0.114313			0.0571567	+	0.998365i	$0.481797\pi$
$510$	0.761092	+	2.11678i	0.0337017	+	0.0937324i
$511$	19.7546	+	4.89110i	0.873890	+	0.216369i
$512$	−1.00000			−0.0441942
$513$	41.0838	−	2.89161i	1.81389	−	0.127668i
$514$	−22.8388	−	13.1860i	−1.00738	−	0.581609i
$515$	1.51801	−	0.821953i	0.0668913	−	0.0362196i
$516$	18.7613	−	7.33058i	0.825920	−	0.322711i
$517$	−3.53412	+	6.12128i	−0.155430	+	0.269213i
$518$	5.95469	−	1.71801i	0.261634	−	0.0754852i
$519$	12.9490	−	5.05955i	0.568398	−	0.222089i
$520$	−0.370711	+	13.5615i	−0.0162567	+	0.594709i
$521$	16.7954	−	29.0904i	0.735818	−	1.27447i	−0.218545	−	0.975827i	$-0.570131\pi$
$521$	16.7954	−	29.0904i	0.735818	−	1.27447i	0.954363	−	0.298648i	$-0.0965357\pi$
$522$	0.424296	−	0.0954949i	0.0185709	−	0.00417970i
$523$	−1.28600	−	2.22742i	−0.0562330	−	0.0973984i	0.836539	−	0.547908i	$-0.184576\pi$
$523$	−1.28600	−	2.22742i	−0.0562330	−	0.0973984i	−0.892772	+	0.450510i	$0.851242\pi$
$524$	−7.84610	−	13.5898i	−0.342758	−	0.593675i
$525$	18.9274	−	12.9133i	0.826059	−	0.563583i
$526$	−10.3480	+	17.9233i	−0.451196	+	0.781495i
$527$	0.803058			0.0349818
$528$	−2.10536	+	0.822623i	−0.0916239	+	0.0358001i
$529$	20.1970			0.878129
$530$	15.9683	+	9.81064i	0.693619	+	0.426147i
$531$	−6.80814	+	6.27885i	−0.295448	+	0.272479i
$532$	−5.04000	+	20.3559i	−0.218512	+	0.882542i
$533$	19.2271	+	33.3023i	0.832817	+	1.44248i
$534$	−2.92639	+	3.65822i	−0.126637	+	0.158307i
$535$	32.7935	+	20.1477i	1.41778	+	0.871062i
$536$	−11.4291	+	6.59859i	−0.493661	+	0.285016i
$537$	26.6580	−	10.4161i	1.15038	−	0.449486i
$538$	−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	−0.977559	−	0.210662i	$-0.932438\pi$
$541$	−15.6121	−	27.0410i	−0.671218	−	1.16258i	0.306341	−	0.951922i	$-0.400895\pi$
$542$			3.39647i			0.145891i
$543$	9.25976	+	7.40733i	0.397374	+	0.317879i
$544$		−	0.580804i		−	0.0249018i
$545$	−0.770889	+	28.2009i	−0.0330213	+	1.20799i
$546$	−3.59805	−	27.5693i	−0.153982	−	1.17986i
$547$	−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
$549$	1.89347	−	6.07326i	0.0808113	−	0.259200i
$550$	5.82070	−	2.94897i	0.248195	−	0.125744i
$551$	0.574526	−	0.995109i	0.0244756	−	0.0423931i
$552$	−7.11112	+	8.88948i	−0.302669	+	0.378361i
$553$	18.2135	+	4.50954i	0.774517	+	0.191765i
$554$	18.1450	+	10.4760i	0.770906	+	0.445083i
$555$	−3.06959	−	8.53725i	−0.130297	−	0.362386i
$556$		−	1.61558i		−	0.0685158i
$557$	6.54619	−	11.3383i	0.277371	−	0.480421i	−0.693360	−	0.720592i	$-0.743870\pi$
$557$	6.54619	−	11.3383i	0.277371	−	0.480421i	0.970731	+	0.240171i	$0.0772035\pi$
$558$	4.04677	−	0.910793i	0.171314	−	0.0385569i
$559$			70.5567i			2.98423i
$560$	−5.72692	+	1.48404i	−0.242007	+	0.0627123i
$561$	−0.477783	−	1.22280i	−0.0201720	−	0.0516266i
$562$		−	1.06210i		−	0.0448021i
$563$	−4.96871	+	2.86869i	−0.209406	+	0.120901i	−0.601035	−	0.799222i	$-0.705245\pi$
$563$	−4.96871	+	2.86869i	−0.209406	+	0.120901i	0.391629	+	0.920123i	$0.371912\pi$
$564$	−7.32561	−	5.86011i	−0.308464	−	0.246755i
$565$	−0.736568	+	26.9453i	−0.0309876	+	1.13360i
$566$	−20.9648			−0.881214
$567$	−15.7662	−	17.8445i	−0.662118	−	0.749399i
$568$		−	10.3545i		−	0.434464i
$569$	36.9166	+	21.3138i	1.54762	+	0.893521i	0.998323	+	0.0578969i	$0.0184395\pi$
$569$	36.9166	+	21.3138i	1.54762	+	0.893521i	0.549301	+	0.835624i	$0.314894\pi$
$570$	30.2104	+	5.44867i	1.26537	+	0.228220i
$571$	16.9274	+	29.3191i	0.708390	+	1.22697i	0.965454	+	0.260573i	$0.0839116\pi$
$571$	16.9274	+	29.3191i	0.708390	+	1.22697i	−0.257064	+	0.966394i	$0.582755\pi$
$572$		−	7.91773i		−	0.331057i
$573$	−13.6600	+	5.33736i	−0.570656	+	0.222971i
$574$	−11.6290	+	12.0817i	−0.485387	+	0.504279i
$575$	17.9613	−	27.5194i	0.749039	−	1.14764i
$576$	−0.658722	−	2.92679i	−0.0274467	−	0.121949i
$577$	6.51191	−	11.2790i	0.271095	−	0.469549i	−0.698048	−	0.716051i	$-0.745948\pi$
$577$	6.51191	−	11.2790i	0.271095	−	0.469549i	0.969142	+	0.246502i	$0.0792811\pi$
$578$	−16.6627			−0.693076
$579$	0.592042	−	3.88807i	0.0246044	−	0.161583i
$580$	0.324042	+	0.00885788i	0.0134551	+	0.000367804i
$581$	−9.53033	−	9.17329i	−0.395385	−	0.380572i
$582$	−12.4649	+	15.5821i	−0.516686	+	0.645900i
$583$	−9.47244	−	5.46892i	−0.392309	−	0.226499i
$584$	−3.84599	+	6.66144i	−0.159148	+	0.275653i
$585$	−39.9357	+	7.84824i	−1.65114	+	0.324485i
$586$	−19.5706	+	11.2991i	−0.808452	+	0.466760i
$587$	33.7149	−	19.4653i	1.39156	−	0.803419i	0.398075	−	0.917353i	$-0.369678\pi$
$587$	33.7149	−	19.4653i	1.39156	−	0.803419i	0.993488	+	0.113934i	$0.0363451\pi$
$588$	11.1163	−	4.84024i	0.458428	−	0.199608i
$589$	5.47961	−	9.49096i	0.225783	−	0.391068i
$590$	−6.07033	+	3.28690i	−0.249912	+	0.135319i
$591$	−14.0811	+	17.6025i	−0.579219	+	0.724071i
$592$			2.34246i			0.0962746i
$593$	−22.4867	+	12.9827i	−0.923419	+	0.533136i	−0.884724	−	0.466115i	$-0.845653\pi$
$593$	−22.4867	+	12.9827i	−0.923419	+	0.533136i	−0.0386950	+	0.999251i	$0.512320\pi$
$594$	−3.79449	−	5.62005i	−0.155690	−	0.230594i
$595$	−0.861939	−	3.32622i	−0.0353361	−	0.136362i
$596$	8.30790	−	4.79657i	0.340305	−	0.196475i
$597$	−5.15800	+	2.01538i	−0.211103	+	0.0824839i
$598$	−19.9379	−	34.5335i	−0.815323	−	1.41218i
$599$	−22.1583	+	12.7931i	−0.905364	+	0.522712i	−0.878937	−	0.476938i	$-0.841747\pi$
$599$	−22.1583	+	12.7931i	−0.905364	+	0.522712i	−0.0264277	+	0.999651i	$0.508413\pi$
$600$	2.70639	+	8.22651i	0.110488	+	0.335846i
$601$	−29.1769	+	16.8453i	−1.19015	+	0.687133i	−0.958340	−	0.285629i	$-0.907798\pi$
$601$	−29.1769	+	16.8453i	−1.19015	+	0.687133i	−0.231809	+	0.972761i	$0.574464\pi$
$602$	−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
$605$	18.2807	−	9.89844i	0.743217	−	0.402429i
$606$	−9.04755	−	23.1556i	−0.367532	−	0.940632i
$607$	27.8164			1.12903			0.564517	−	0.825422i	$-0.309063\pi$
$607$	27.8164			1.12903			0.564517	+	0.825422i	$0.309063\pi$
$608$	−6.86424	−	3.96307i	−0.278382	−	0.160724i
$609$	−0.658750	+	0.0859730i	−0.0266939	+	0.00348380i
$610$	2.48214	−	4.04007i	0.100499	−	0.163577i
$611$	28.4582	−	16.4304i	1.15130	−	0.664702i
$612$	1.69989	−	0.382588i	0.0687140	−	0.0154652i
$613$	24.9598	+	14.4106i	1.00812	+	0.582037i	0.910640	−	0.413201i	$-0.135589\pi$
$613$	24.9598	+	14.4106i	1.00812	+	0.582037i	0.0974774	+	0.995238i	$0.468923\pi$
$614$	−14.6043	+	25.2954i	−0.589382	+	1.02084i
$615$	18.7426	+	15.8521i	0.755775	+	0.639218i
$616$	3.31745	−	0.957131i	0.133664	−	0.0385639i
$617$	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	$0.0980627\pi$
$618$	−0.486634	−	1.24545i	−0.0195753	−	0.0500995i
$619$			34.6381i			1.39222i	0.717934	+	0.696111i	$0.245088\pi$
$619$			34.6381i			1.39222i	−0.717934	+	0.696111i	$0.754912\pi$
$620$	3.09058	+	0.0844830i	0.124121	+	0.00339292i
$621$	−30.7019	−	14.9570i	−1.23202	−	0.600206i
$622$	−13.0106			−0.521678
$623$	4.96254	−	5.15569i	0.198820	−	0.206559i
$624$	10.3888	+	1.58192i	0.415886	+	0.0633275i
$625$	−10.0634	−	22.8851i	−0.402534	−	0.915405i
$626$	−3.62723	−	6.28255i	−0.144973	−	0.251101i
$627$	−17.7118	−	2.69700i	−0.707341	−	0.107708i
$628$	1.69869	−	2.94222i	0.0677851	−	0.117407i
$629$	−1.36051			−0.0542471
$630$	−8.11593	−	15.7839i	−0.323346	−	0.628846i
$631$	−17.6726			−0.703534			−0.351767	−	0.936088i	$-0.614419\pi$
$631$	−17.6726			−0.703534			−0.351767	+	0.936088i	$0.614419\pi$
$632$	−3.54596	+	6.14179i	−0.141051	+	0.244307i
$633$	6.37046	+	16.3040i	0.253203	+	0.648028i
$634$	−14.2603	−	24.6996i	−0.566350	−	0.980946i
$635$	−15.7057	−	29.0056i	−0.623260	−	1.15105i
$636$	9.06829	−	11.3361i	0.359581	−	0.449506i
$637$	1.62085	+	42.4390i	0.0642205	+	1.68149i
$638$	−0.189189			−0.00749006
$639$	30.3054	−	6.82072i	1.19886	−	0.269824i
$640$	0.0611015	−	2.23523i	0.00241525	−	0.0883553i
$641$		−	13.7317i		−	0.542369i	−0.962527	−	0.271185i	$-0.912585\pi$
$641$		−	13.7317i		−	0.542369i	0.962527	−	0.271185i	$-0.0874154\pi$
$642$	18.6232	−	23.2805i	0.734999	−	0.918808i
$643$	7.15031	−	12.3847i	0.281981	−	0.488405i	−0.689892	−	0.723912i	$-0.742342\pi$
$643$	7.15031	−	12.3847i	0.281981	−	0.488405i	0.971872	+	0.235508i	$0.0756753\pi$
$644$	12.0590	−	12.5283i	0.475191	−	0.493686i
$645$	15.2392	+	42.3838i	0.600043	+	1.66886i
$646$	2.30177	−	3.98678i	0.0905618	−	0.156858i
$647$	18.0964	+	10.4480i	0.711443	+	0.410752i	0.811595	−	0.584220i	$-0.198600\pi$
$647$	18.0964	+	10.4480i	0.711443	+	0.410752i	−0.100152	+	0.994972i	$0.531933\pi$
$648$	8.13217	−	3.85588i	0.319462	−	0.151473i
$649$	3.48904	−	2.01440i	0.136957	−	0.0790721i
$650$	−30.2904	−	1.65725i	−1.18809	−	0.0650027i
$651$	−6.28290	+	0.819977i	−0.246246	+	0.0321374i
$652$	−4.86586	−	2.80931i	−0.190562	−	0.110021i
$653$	−1.28292			−0.0502046			−0.0251023	−	0.999685i	$-0.507991\pi$
$653$	−1.28292			−0.0502046			−0.0251023	+	0.999685i	$0.507991\pi$
$654$	21.6035	+	3.28959i	0.844762	+	0.128633i
$655$	30.8559	−	16.7075i	1.20564	−	0.652816i
$656$	−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	$0.364390\pi$
$660$	−1.71011	−	4.75623i	−0.0665661	−	0.185136i
$661$	−8.66549	+	5.00302i	−0.337049	+	0.194595i	−0.658966	−	0.752173i	$-0.729006\pi$
$661$	−8.66549	+	5.00302i	−0.337049	+	0.194595i	0.321918	+	0.946768i	$0.395673\pi$
$662$	12.3511	+	21.3927i	0.480038	+	0.831451i
$663$	−0.918786	+	6.03387i	−0.0356827	+	0.234336i
$664$	4.32983	−	2.49983i	0.168030	−	0.0970123i
$665$	−45.1923	−	12.5094i	−1.75248	−	0.485092i
$666$	−6.85589	+	1.54303i	−0.265660	+	0.0597912i
$667$	−0.825155	+	0.476403i	−0.0319501	+	0.0184464i
$668$			6.41173i			0.248077i
$669$	−5.41663	−	0.824798i	−0.209419	−	0.0318885i
$670$	−14.0510	−	25.9499i	−0.542839	−	1.00253i
$671$	−1.38367	+	2.39658i	−0.0534158	+	0.0925189i
$672$	0.593040	+	4.54404i	0.0228770	+	0.175290i
$673$	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
$675$	−22.2945	+	13.3400i	−0.858115	+	0.513457i
$676$	−11.9051	+	20.6202i	−0.457887	+	0.793083i
$677$	7.77071	+	4.48642i	0.298653	+	0.172427i	0.641838	−	0.766841i	$-0.278172\pi$
$677$	7.77071	+	4.48642i	0.298653	+	0.172427i	−0.343185	+	0.939268i	$0.611506\pi$
$678$	20.6416	+	3.14313i	0.792737	+	0.120711i
$679$	21.1379	−	21.9606i	0.811197	−	0.842770i
$680$	1.29823	+	0.0354880i	0.0497849	+	0.00136090i
$681$	−12.9753	−	10.3796i	−0.497216	−	0.397747i
$682$	−1.80441			−0.0690944
$683$	0.499734	−	0.865564i	0.0191218	−	0.0331199i	−0.856306	−	0.516469i	$-0.827246\pi$
$683$	0.499734	−	0.865564i	0.0191218	−	0.0331199i	0.875428	+	0.483349i	$0.160580\pi$
$684$	7.07744	−	22.7007i	0.270613	−	0.867984i
$685$	−17.4188	+	9.43173i	−0.665537	+	0.360368i
$686$	−17.5856	+	5.80933i	−0.671420	+	0.221801i
$687$	−4.86260	−	3.88983i	−0.185520	−	0.148406i
$688$		−	11.6293i		−	0.443364i
$689$	25.4254	+	44.0381i	0.968630	+	1.67772i
$690$	−19.4356	−	16.4382i	−0.739899	−	0.625791i
$691$	−14.7899	−	8.53893i	−0.562633	−	0.324836i	0.191569	−	0.981479i	$-0.438643\pi$
$691$	−14.7899	−	8.53893i	−0.562633	−	0.324836i	−0.754202	+	0.656643i	$0.771976\pi$
$692$		−	8.02653i		−	0.305123i
$693$	4.98659	+	9.07898i	0.189425	+	0.344882i
$694$	7.75645			0.294431
$695$	3.61120	+	0.0987143i	0.136981	+	0.00374445i
$696$	0.0377989	−	0.248234i	0.00143276	−	0.00940929i
$697$	3.18801	−	1.84060i	0.120755	−	0.0697177i
$698$		−	10.2717i		−	0.388790i
$699$	9.97626	+	1.51910i	0.377337	+	0.0574575i
$700$	−2.96726	−	12.8917i	−0.112152	−	0.487260i
$701$			10.9031i			0.411803i	0.978573	+	0.205902i	$0.0660127\pi$
$701$			10.9031i			0.411803i	−0.978573	+	0.205902i	$0.933987\pi$
$702$	2.21341	+	31.4480i	0.0835396	+	1.18693i
$703$	−9.28334	+	16.0792i	−0.350128	+	0.606439i
$704$			1.30502i			0.0491848i
$705$	13.5463	−	16.0164i	0.510184	−	0.603212i
$706$	18.2499	+	10.5366i	0.686845	+	0.396550i
$707$	10.5269	+	36.4867i	0.395906	+	1.37222i
$708$	1.94600	+	4.98043i	0.0731350	+	0.187176i
$709$	23.2624	−	40.2917i	0.873638	−	1.51318i	0.0154309	−	0.999881i	$-0.495088\pi$
$709$	23.2624	−	40.2917i	0.873638	−	1.51318i	0.858207	−	0.513304i	$-0.171579\pi$
$710$	23.1447	+	0.632674i	0.868604	+	0.0237438i
$711$	−20.3115	−	6.33255i	−0.761741	−	0.237489i
$712$	1.35235	+	2.34234i	0.0506816	+	0.0877830i
$713$	−7.87000	+	4.54375i	−0.294734	+	0.170165i
$714$	−2.63920	+	0.344440i	−0.0987694	+	0.0128903i
$715$	17.6980	+	0.483785i	0.661867	+	0.0180925i
$716$		−	16.5242i		−	0.617538i
$717$	−37.1340	+	14.5093i	−1.38679	+	0.541860i
$718$			17.3210i			0.646414i
$719$	8.48584	+	14.6979i	0.316468	+	0.548139i	0.979749	−	0.200232i	$-0.0641696\pi$
$719$	8.48584	+	14.6979i	0.316468	+	0.548139i	−0.663280	+	0.748371i	$0.730836\pi$
$720$	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
$723$	−9.25949	−	7.40711i	−0.344364	−	0.275473i
$724$	5.92899	−	3.42310i	0.220349	−	0.127219i
$725$	−0.0395989	+	0.723768i	−0.00147066	+	0.0268801i
$726$	−5.86034	−	14.9985i	−0.217498	−	0.556646i
$727$	19.9409	+	34.5386i	0.739567	+	1.28097i	0.952691	+	0.303942i	$0.0983029\pi$
$727$	19.9409	+	34.5386i	0.739567	+	1.28097i	−0.213124	+	0.977025i	$0.568364\pi$
$728$	−15.5816	−	3.85791i	−0.577494	−	0.142984i
$729$	16.6422	+	21.2612i	0.616377	+	0.787451i
$730$	−14.6549	−	9.00370i	−0.542402	−	0.333242i
$731$	6.75436			0.249819
$732$	−2.86810	−	2.29433i	−0.106008	−	0.0848008i
$733$	14.2054			0.524689			0.262345	−	0.964974i	$-0.415504\pi$
$733$	14.2054			0.524689			0.262345	+	0.964974i	$0.415504\pi$
$734$	3.49830	−	6.05923i	0.129125	−	0.223650i
$735$	10.1399	+	25.1433i	0.374014	+	0.927423i
$736$	3.28622	+	5.69190i	0.121132	+	0.209806i
$737$	8.61129	+	14.9152i	0.317201	+	0.549408i
$738$	13.9775	−	12.8909i	0.514519	−	0.474519i
$739$	15.4922	−	26.8333i	0.569891	−	0.987080i	−0.426685	−	0.904400i	$-0.640319\pi$
$739$	15.4922	−	26.8333i	0.569891	−	0.987080i	0.996576	−	0.0826801i	$-0.0263480\pi$
$740$	−5.23595	−	0.143128i	−0.192477	−	0.00526149i
$741$	65.0422	+	52.0304i	2.38938	+	1.91138i
$742$	−15.3779	+	15.9765i	−0.564542	+	0.586515i
$743$	−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	$0.793300\pi$
$744$	0.360511	−	2.36756i	0.0132170	−	0.0867989i
$745$	10.2138	+	18.8632i	0.374206	+	0.691093i
$746$	−12.9529	−	7.47838i	−0.474241	−	0.273803i
$747$	10.1686	+	11.0258i	0.372051	+	0.403413i
$748$	−0.757961			−0.0277138
$749$	−31.5811	+	32.8103i	−1.15395	+	1.19886i
$750$	−18.5535	+	5.54675i	−0.677479	+	0.202539i
$751$	27.9926			1.02146			0.510732	−	0.859740i	$-0.329375\pi$
$751$	27.9926			1.02146			0.510732	+	0.859740i	$0.329375\pi$
$752$	−4.69056	+	2.70810i	−0.171047	+	0.0987541i
$753$	13.2173	−	16.5226i	0.481663	−	0.602118i
$754$	0.761715	+	0.439776i	0.0277400	+	0.0160157i
$755$	−34.1461	+	18.4891i	−1.24270	+	0.672886i
$756$	−12.9088	+	4.72896i	−0.469488	+	0.171991i
$757$			17.6703i			0.642238i	0.947039	+	0.321119i	$0.104059\pi$
$757$			17.6703i			0.642238i	−0.947039	+	0.321119i	$0.895941\pi$
$758$	0.908439	−	1.57346i	0.0329960	−	0.0571507i
$759$	11.6010	+	9.28016i	0.421088	+	0.336848i
$760$	9.27780	−	15.1010i	0.336541	−	0.547772i
$761$	2.05727			0.0745758			0.0372879	−	0.999305i	$-0.488128\pi$
$761$	2.05727			0.0745758			0.0372879	+	0.999305i	$0.488128\pi$
$762$	−23.7978	+	9.29848i	−0.862103	+	0.336848i
$763$	−32.4018	−	8.02248i	−1.17303	−	0.290433i
$764$			8.46726i			0.306335i
$765$	0.751308	+	3.82303i	0.0271636	+	0.138222i
$766$	−3.98546	−	2.30101i	−0.144000	−	0.0831387i
$767$	−18.7302			−0.676308
$768$	−1.71231	−	0.260736i	−0.0617878	−	0.00940850i
$769$	−12.1169	−	6.99571i	−0.436947	−	0.252272i	0.265355	−	0.964151i	$-0.414511\pi$
$769$	−12.1169	−	6.99571i	−0.436947	−	0.252272i	−0.702302	+	0.711879i	$0.747844\pi$
$770$	1.93671	+	7.47375i	0.0697941	+	0.269335i
$771$	−35.6691	−	28.5335i	−1.28459	−	1.02761i
$772$	−1.96645	−	1.13533i	−0.0707739	−	0.0408613i
$773$	36.5855	+	21.1226i	1.31589	+	0.759728i	0.983064	−	0.183261i	$-0.0586652\pi$
$773$	36.5855	+	21.1226i	1.31589	+	0.759728i	0.332824	+	0.942989i	$0.391999\pi$
$774$	34.0366	−	7.66049i	1.22342	−	0.275351i
$775$	−0.377678	+	6.90301i	−0.0135666	+	0.247963i
$776$	5.76032	+	9.97717i	0.206784	+	0.358160i
$777$	10.6442	−	1.38917i	0.381860	−	0.0498363i
$778$	14.8244	+	8.55885i	0.531479	+	0.306850i
$779$		−	50.2368i		−	1.79992i
$780$	−4.17073	+	23.1248i	−0.149336	+	0.828001i
$781$	−13.5128			−0.483526
$782$	−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
$786$	−9.89162	−	25.3158i	−0.352822	−	0.902986i
$787$	−22.4107	−	38.8164i	−0.798854	−	1.38366i	−0.920363	−	0.391065i	$-0.872107\pi$
$787$	−22.4107	−	38.8164i	−0.798854	−	1.38366i	0.121509	−	0.992590i	$-0.461227\pi$
$788$	6.50721	+	11.2708i	0.231810	+	0.401507i
$789$	−22.3924	+	27.9923i	−0.797189	+	0.996551i
$790$	−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
$794$	14.8472			0.526906
$795$	24.7847	+	20.9624i	0.879024	+	0.743460i
$796$			3.19722i			0.113323i
$797$	33.4229	+	19.2967i	1.18390	+	0.683524i	0.956913	−	0.290374i	$-0.0937796\pi$
$797$	33.4229	+	19.2967i	1.18390	+	0.683524i	0.226986	+	0.973898i	$0.427113\pi$
$798$	−13.9376	+	33.5416i	−0.493385	+	1.18736i
$799$	−1.57287	−	2.72430i	−0.0556442	−	0.0963786i
$800$	4.99253	+	0.273152i	0.176513	+	0.00965739i
$801$	−5.96472	+	5.50100i	−0.210753	+	0.194368i
$802$	−8.29051	−	4.78653i	−0.292748	−	0.169018i
$803$	8.69332	+	5.01909i	0.306781	+	0.177120i
$804$	−21.2907	+	8.31887i	−0.750864	+	0.293384i
$805$	27.2669	+	27.7202i	0.961034	+	0.977007i
$806$	7.26494	+	4.19441i	0.255896	+	0.147742i
$807$	−5.91927	−	15.1493i	−0.208368	−	0.533281i
$808$	−14.3532			−0.504943
$809$	−12.0653	−	6.96590i	−0.424193	−	0.244908i	0.272677	−	0.962106i	$-0.412091\pi$
$809$	−12.0653	−	6.96590i	−0.424193	−	0.244908i	−0.696870	+	0.717198i	$0.745424\pi$
$810$	8.12190	+	18.4129i	0.285374	+	0.646963i
$811$		−	50.7243i		−	1.78117i	−0.454815	−	0.890586i	$-0.650295\pi$
$811$		−	50.7243i		−	1.78117i	0.454815	−	0.890586i	$-0.349705\pi$
$812$	−0.0921821	+	0.372312i	−0.00323496	+	0.0130656i
$813$	−0.885584	+	5.81583i	−0.0310588	+	0.203970i
$814$	3.05696			0.107146
$815$	6.57677	−	10.7047i	0.230374	−	0.374969i
$816$	0.151437	−	0.994518i	0.00530134	−	0.0348151i
$817$	46.0879	−	79.8265i	1.61241	−	2.79278i
$818$			38.6251i			1.35049i
$819$	1.02732	−	48.1454i	0.0358975	−	1.68234i
$820$	12.4627	−	6.74819i	0.435218	−	0.235657i
$821$	−21.4858	−	12.4048i	−0.749860	−	0.432932i	0.0757835	−	0.997124i	$-0.475854\pi$
$821$	−21.4858	−	12.4048i	−0.749860	−	0.432932i	−0.825643	+	0.564193i	$0.809188\pi$
$822$	5.58402	+	14.2913i	0.194765	+	0.498467i
$823$	8.62872	−	4.98179i	0.300778	−	0.173654i	−0.342014	−	0.939695i	$-0.611109\pi$
$823$	8.62872	−	4.98179i	0.300778	−	0.173654i	0.642792	+	0.766040i	$0.277776\pi$
$824$	−0.772004			−0.0268940
$825$	10.7358	−	3.53189i	0.373771	−	0.122965i
$826$	−2.26419	−	7.84775i	−0.0787812	−	0.273058i
$827$	36.2819			1.26165			0.630823	−	0.775926i	$-0.282717\pi$
$827$	36.2819			1.26165			0.630823	+	0.775926i	$0.282717\pi$
$828$	−14.4943	+	13.3674i	−0.503711	+	0.464551i
$829$	−16.8402	−	9.72267i	−0.584883	−	0.337682i	0.178189	−	0.983996i	$-0.442976\pi$
$829$	−16.8402	−	9.72267i	−0.584883	−	0.337682i	−0.763071	+	0.646314i	$0.776310\pi$
$830$	5.32315	+	9.83093i	0.184769	+	0.341237i
$831$	28.3384	+	22.6693i	0.983049	+	0.786388i
$832$	3.03357	−	5.25429i	0.105170	−	0.182160i
$833$	4.06267	−	0.155163i	0.140763	−	0.00537610i
$834$	0.421240	−	2.76638i	0.0145863	−	0.0957919i
$835$	−14.3317	−	0.391766i	−0.495969	−	0.0135576i
$836$	−5.17189	+	8.95797i	−0.178874	+	0.309818i
$837$	7.16682	−	0.504423i	0.247722	−	0.0174354i
$838$	−6.88512	−	11.9254i	−0.237843	−	0.411956i
$839$	−21.1582	−	36.6471i	−0.730463	−	1.26520i	−0.956686	−	0.291123i	$-0.905971\pi$
$839$	−21.1582	−	36.6471i	−0.730463	−	1.26520i	0.226223	−	0.974075i	$-0.427362\pi$
$840$	−10.1932	+	1.04793i	−0.351700	+	0.0361572i
$841$	−14.4895	+	25.0965i	−0.499638	+	0.865398i
$842$	−18.8952			−0.651170
$843$	0.276929	−	1.81865i	0.00953793	−	0.0626377i
$844$	10.1062			0.347869
$845$	−45.3634	−	27.8705i	−1.56055	−	0.958774i
$846$	−11.0158	−	11.9444i	−0.378731	−	0.410657i
$847$	6.81857	+	23.6334i	0.234289	+	0.812052i
$848$	−4.19068	−	7.25846i	−0.143908	−	0.249257i
$849$	−35.8982	−	5.46627i	−1.23202	−	0.187602i
$850$	−0.158648	+	2.89968i	−0.00544158	+	0.0994583i
$851$	13.3331	−	7.69785i	0.457051	−	0.263879i
$852$	2.69979	−	17.7301i	0.0924932	−	0.607424i
$853$	4.70765	+	8.15389i	0.161187	+	0.279184i	0.935295	−	0.353870i	$-0.115134\pi$
$853$	4.70765	+	8.15389i	0.161187	+	0.279184i	−0.774108	+	0.633054i	$0.781801\pi$
$854$	4.04214	+	3.89070i	0.138319	+	0.133137i
$855$	50.3090	+	17.2068i	1.72053	+	0.588459i
$856$	−8.60622	−	14.9064i	−0.294155	−	0.509491i
$857$		−	36.5321i		−	1.24791i	−0.781459	−	0.623956i	$-0.785524\pi$
$857$		−	36.5321i		−	1.24791i	0.781459	−	0.623956i	$-0.214476\pi$
$858$	2.06444	−	13.5576i	0.0704788	−	0.462850i
$859$			25.9238i			0.884509i	0.896890	+	0.442254i	$0.145821\pi$
$859$			25.9238i			0.884509i	−0.896890	+	0.442254i	$0.854179\pi$
$860$	25.9943	+	0.710569i	0.886397	+	0.0242302i
$861$	−23.0627	+	17.6555i	−0.785975	+	0.601697i
$862$	29.2156	−	16.8676i	0.995087	−	0.574513i
$863$	−11.4281	−	19.7941i	−0.389018	−	0.673800i	0.603299	−	0.797515i	$-0.293852\pi$
$863$	−11.4281	−	19.7941i	−0.389018	−	0.673800i	−0.992318	+	0.123715i	$0.960519\pi$
$864$	−0.364819	−	5.18333i	−0.0124114	−	0.176340i
$865$	17.9412	+	0.490433i	0.610018	+	0.0166752i
$866$	−3.64607	+	6.31517i	−0.123898	+	0.214598i
$867$	−28.5317	−	4.34456i	−0.968988	−	0.147549i
$868$	−0.879197	+	3.55097i	−0.0298419	+	0.120528i
$869$	8.01516	+	4.62755i	0.271896	+	0.156979i
$870$	0.552551	+	0.0996569i	0.0187332	+	0.00337868i
$871$		−	80.0690i		−	2.71304i
$872$	6.30827	−	10.9262i	0.213625	−	0.370009i
$873$	−25.4066	+	23.4314i	−0.859884	+	0.793034i
$874$			52.0941i			1.76211i
$875$	28.9972	−	5.84482i	0.980285	−	0.197591i
$876$	−8.32241	+	10.4037i	−0.281188	+	0.351508i
$877$			4.90352i			0.165580i	0.996567	+	0.0827901i	$0.0263831\pi$
$877$			4.90352i			0.165580i	−0.996567	+	0.0827901i	$0.973617\pi$
$878$	2.29308	−	1.32391i	0.0773877	−	0.0446798i
$879$	−36.4570	+	14.2448i	−1.22966	+	0.480465i
$880$	−2.91702	−	0.0797387i	−0.0983329	−	0.00268799i
$881$	−42.9169			−1.44591			−0.722953	−	0.690897i	$-0.757216\pi$
$881$	−42.9169			−1.44591			−0.722953	+	0.690897i	$0.757216\pi$
$882$	20.2966	−	5.38959i	0.683422	−	0.181477i
$883$		−	39.4640i		−	1.32807i	−0.747701	−	0.664035i	$-0.768843\pi$
$883$		−	39.4640i		−	1.32807i	0.747701	−	0.664035i	$-0.231157\pi$
$884$	3.05171	+	1.76191i	0.102640	+	0.0592594i
$885$	−11.2513	+	4.04544i	−0.378209	+	0.135986i
$886$	12.9543	+	22.4376i	0.435210	+	0.753805i
$887$		−	27.7389i		−	0.931380i	−0.884948	−	0.465690i	$-0.845806\pi$
$887$		−	27.7389i		−	0.931380i	0.884948	−	0.465690i	$-0.154194\pi$
$888$	−0.610765	+	4.01103i	−0.0204959	+	0.134601i
$889$	37.4986	−	10.8189i	1.25766	−	0.362854i
$890$	−5.31832	+	2.87970i	−0.178270	+	0.0965279i
$891$	−5.03200	−	10.6126i	−0.168578	−	0.355537i
$892$	−1.58167	+	2.73954i	−0.0529583	+	0.0917264i
$893$	−42.9295			−1.43658
$894$	15.4764	−	6.04706i	0.517607	−	0.202244i
$895$	36.9354	+	1.00965i	1.23461	+	0.0337489i
$896$	2.56820	+	0.635870i	0.0857977	+	0.0212429i
$897$	−25.1359	−	64.3307i	−0.839262	−	2.14794i
$898$	−9.85371	−	5.68904i	−0.328822	−	0.189846i
$899$	0.100223	−	0.173591i	0.00334261	−	0.00578957i
$900$	2.48923	+	14.7920i	0.0829744	+	0.493067i
$901$	4.21574	−	2.43396i	0.140447	−	0.0810870i
$902$	−7.16321	+	4.13568i	−0.238509	+	0.137703i
$903$	−52.8441	+	6.89666i	−1.75854	+	0.229506i
$904$	6.02741	−	10.4398i	0.200469	−	0.347222i
$905$	7.28916	+	13.4618i	0.242300	+	0.447486i
$906$	10.9464	+	28.0153i	0.363669	+	0.930746i
$907$		−	44.6436i		−	1.48237i	−0.671303	−	0.741183i	$-0.734265\pi$
$907$		−	44.6436i		−	1.48237i	0.671303	−	0.741183i	$-0.265735\pi$
$908$	−8.30806	+	4.79666i	−0.275713	+	0.159183i
$909$	−9.45474	−	42.0087i	−0.313594	−	1.39334i
$910$	9.57539	−	34.5929i	0.317421	−	1.14674i
$911$	−14.1534	+	8.17148i	−0.468924	+	0.270733i	−0.715789	−	0.698317i	$-0.753933\pi$
$911$	−14.1534	+	8.17148i	−0.468924	+	0.270733i	0.246865	+	0.969050i	$0.420599\pi$
$912$	−10.7204	−	8.57577i	−0.354988	−	0.283972i
$913$	−3.26233	−	5.65052i	−0.107967	−	0.187005i
$914$	−9.95317	+	5.74647i	−0.329222	+	0.190076i
$915$	5.30360	−	6.27067i	0.175332	−	0.207302i
$916$	−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	0.987402	+	0.158234i	$0.0505801\pi$
$919$	19.1208	+	33.1181i	0.630736	+	1.09247i	−0.356666	+	0.934232i	$0.616087\pi$
$920$	−12.9235	+	6.99768i	−0.426076	+	0.230707i
$921$	−31.6026	+	39.5058i	−1.04134	+	1.30176i
$922$	1.15316			0.0379772
$923$	54.4054	+	31.4110i	1.79078	+	1.03391i
$924$	5.93007	−	0.773929i	0.195085	−	0.0254604i
$925$	0.639849	−	11.6948i	0.0210381	−	0.384523i
$926$	−15.2816	+	8.82285i	−0.502185	+	0.289937i
$927$	−0.508536	−	2.25949i	−0.0167025	−	0.0742114i
$928$	−0.125548	−	0.0724850i	−0.00412131	−	0.00237944i
$929$	−1.29878	+	2.24955i	−0.0426115	+	0.0738053i	−0.886545	−	0.462643i	$-0.846901\pi$
$929$	−1.29878	+	2.24955i	−0.0426115	+	0.0738053i	0.843933	+	0.536449i	$0.180234\pi$
$930$	5.27002	+	0.950488i	0.172811	+	0.0311677i
$931$	25.8875	−	49.0734i	0.848428	−	1.60832i
$932$	2.91309	−	5.04563i	0.0954215	−	0.165275i
$933$	−22.2783	−	3.39234i	−0.729357	−	0.111060i
$934$		−	18.7570i		−	0.613748i
$935$	0.0463125	−	1.69422i	0.00151458	−	0.0554069i
$936$	17.3765	+	5.41749i	0.567968	+	0.177076i
$937$	55.8623			1.82494			0.912472	−	0.409140i	$-0.134171\pi$
$937$	55.8623			1.82494			0.912472	+	0.409140i	$0.134171\pi$
$938$	33.5481	−	9.67910i	1.09538	−	0.316034i
$939$	−4.57287	−	11.7034i	−0.149230	−	0.381928i
$940$	−5.76663	−	10.6500i	−0.188087	−	0.347363i
$941$	−10.7190	−	18.5659i	−0.349430	−	0.605231i	0.636718	−	0.771097i	$-0.280291\pi$
$941$	−10.7190	−	18.5659i	−0.349430	−	0.605231i	−0.986148	+	0.165866i	$0.946958\pi$
$942$	3.67583	−	4.59508i	0.119765	−	0.149716i
$943$	−20.8284	+	36.0759i	−0.678267	+	1.17479i
$944$	3.08716			0.100478
$945$	−9.78158	−	29.1431i	−0.318195	−	0.948025i
$946$	−15.1765			−0.493431
$947$	10.2729	−	17.7933i	0.333826	−	0.578203i	−0.649433	−	0.760419i	$-0.724994\pi$
$947$	10.2729	−	17.7933i	0.333826	−	0.578203i	0.983259	+	0.182216i	$0.0583269\pi$
$948$	−7.67318	+	9.59210i	−0.249213	+	0.311537i
$949$	−23.3341	−	40.4159i	−0.757457	−	1.31195i
$950$	33.1874	+	21.6607i	1.07674	+	0.702767i
$951$	−17.9781	−	46.0116i	−0.582978	−	1.49203i
$952$	−0.369316	+	1.49162i	−0.0119696	+	0.0483438i
$953$	47.6780			1.54444			0.772220	−	0.635355i	$-0.219146\pi$
$953$	47.6780			1.54444			0.772220	+	0.635355i	$0.219146\pi$
$954$	18.4835	−	17.0465i	0.598425	−	0.551902i
$955$	−18.9263	−	0.517362i	−0.612441	−	0.0167415i
$956$			23.0178i			0.744448i
$957$	−0.323951	−	0.0493284i	−0.0104718	−	0.00159456i
$958$	−0.0620969	+	0.107555i	−0.00200626	+	0.00347495i
$959$	−6.49707	−	22.5191i	−0.209801	−	0.727178i
$960$	0.687431	−	3.81149i	0.0221867	−	0.123015i
$961$	−14.5441	+	25.1911i	−0.469165	+	0.812618i
$962$	−12.3080	−	7.10601i	−0.396825	−	0.229107i
$963$	37.9588	−	35.0078i	1.22321	−	1.12811i
$964$	−5.92882	+	3.42300i	−0.190954	+	0.110248i
$965$	2.65787	−	4.32609i	0.0855600	−	0.139262i
$966$	23.9154	−	18.3082i	0.769464	−	0.589058i
$967$	−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	$0.717383\pi$
$968$	−9.29692			−0.298814
$969$	4.98084	−	6.22646i	0.160008	−	0.200023i
$970$	−22.6533	+	12.2660i	−0.727353	+	0.393839i
$971$	−25.6986	−	44.5114i	−0.824709	−	1.42844i	−0.902142	−	0.431440i	$-0.858006\pi$
$971$	−25.6986	−	44.5114i	−0.824709	−	1.42844i	0.0774332	−	0.996998i	$-0.475328\pi$
$972$	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
$975$	−51.4345	−	10.7355i	−1.64722	−	0.343812i
$976$	−1.83643	+	1.06026i	−0.0587827	+	0.0339382i
$977$	−5.62485	−	9.74253i	−0.179955	−	0.311691i	0.761910	−	0.647683i	$-0.224262\pi$
$977$	−5.62485	−	9.74253i	−0.179955	−	0.311691i	−0.941865	+	0.335992i	$0.890929\pi$
$978$	−7.59939	−	6.07912i	−0.243002	−	0.194389i
$979$	3.05681	−	1.76485i	0.0976960	−	0.0564048i
$980$	15.6516	−	0.169750i	0.499971	−	0.00542247i
$981$	36.1342	+	11.2656i	1.15368	+	0.359683i
$982$	17.4877	−	10.0965i	0.558056	−	0.322194i
$983$		−	47.4181i		−	1.51240i	−0.654338	−	0.756202i	$-0.727053\pi$
$983$		−	47.4181i		−	1.51240i	0.654338	−	0.756202i	$-0.272947\pi$
$984$	−3.99524	−	10.2251i	−0.127364	−	0.325965i
$985$	−25.5905	+	13.8565i	−0.815382	+	0.441504i
$986$	0.0420996	−	0.0729186i	0.00134072	−	0.00232220i
$987$	15.0874	+	19.7081i	0.480237	+	0.627315i
$988$	41.6463	−	24.0445i	1.32494	−	0.764957i
$989$	−66.1930	+	38.2165i	−2.10481	+	1.21522i
$990$	−1.68813	−	8.59004i	−0.0536523	−	0.273009i
$991$	16.8939	−	29.2611i	0.536653	−	0.929511i	−0.462428	−	0.886657i	$-0.653022\pi$
$991$	16.8939	−	29.2611i	0.536653	−	0.929511i	0.999081	−	0.0428538i	$-0.0136450\pi$
$992$	−1.19742	−	0.691334i	−0.0380183	−	0.0219499i
$993$	15.5711	+	39.8514i	0.494133	+	1.26464i
$994$	−6.58411	+	26.5924i	−0.208835	+	0.843460i
$995$	−7.14654	−	0.195355i	−0.226561	−	0.00619317i
$996$	8.06583	−	3.15155i	0.255576	−	0.0998607i
$997$	−16.7948			−0.531898			−0.265949	−	0.963987i	$-0.585685\pi$
$997$	−16.7948			−0.531898			−0.265949	+	0.963987i	$0.585685\pi$
$998$	−3.80999	+	6.59910i	−0.120603	+	0.208891i
$999$	−12.1418	+	0.854575i	−0.384148	+	0.0270376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.59.17	yes	48
3.2	odd	2		1890.2.r.a.1529.5		48
5.4	even	2		630.2.r.a.59.8	✓	48
7.5	odd	6		630.2.bi.a.509.10	yes	48
9.2	odd	6		630.2.bi.b.479.15	yes	48
9.7	even	3		1890.2.bi.a.899.13		48
15.14	odd	2		1890.2.r.b.1529.5		48
21.5	even	6		1890.2.bi.b.719.5		48
35.19	odd	6		630.2.bi.b.509.15	yes	48
45.29	odd	6		630.2.bi.a.479.10	yes	48
45.34	even	6		1890.2.bi.b.899.5		48
63.47	even	6		630.2.r.a.299.8	yes	48
63.61	odd	6		1890.2.r.b.89.5		48
105.89	even	6		1890.2.bi.a.719.13		48
315.124	odd	6		1890.2.r.a.89.5		48
315.299	even	6	inner	630.2.r.b.299.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.8	✓	48	5.4	even	2
630.2.r.a.299.8	yes	48	63.47	even	6
630.2.r.b.59.17	yes	48	1.1	even	1	trivial
630.2.r.b.299.17	yes	48	315.299	even	6	inner
630.2.bi.a.479.10	yes	48	45.29	odd	6
630.2.bi.a.509.10	yes	48	7.5	odd	6
630.2.bi.b.479.15	yes	48	9.2	odd	6
630.2.bi.b.509.15	yes	48	35.19	odd	6
1890.2.r.a.89.5		48	315.124	odd	6
1890.2.r.a.1529.5		48	3.2	odd	2
1890.2.r.b.89.5		48	63.61	odd	6
1890.2.r.b.1529.5		48	15.14	odd	2
1890.2.bi.a.719.13		48	105.89	even	6
1890.2.bi.a.899.13		48	9.7	even	3
1890.2.bi.b.719.5		48	21.5	even	6
1890.2.bi.b.899.5		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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.08196 - 1.35254i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.96632 - 1.06470i) q^{5} +(-0.630353 - 1.61327i) q^{6} +(0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-0.658722 - 2.92679i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.08196 - 1.35254i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.96632 - 1.06470i) q^{5} +(-0.630353 - 1.61327i) q^{6} +(0.733422 + 2.54206i) q^{7} -1.00000 q^{8} +(-0.658722 - 2.92679i) q^{9} +(0.0611015 - 2.23523i) q^{10} +1.30502i q^{11} +(-1.71231 - 0.260736i) q^{12} +(3.03357 - 5.25429i) q^{13} +(2.56820 + 0.635870i) q^{14} +(0.687431 - 3.81149i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.502991 - 0.290402i) q^{17} +(-2.86403 - 0.892924i) q^{18} +(-6.86424 + 3.96307i) q^{19} +(-1.90522 - 1.17053i) q^{20} +(4.23177 + 1.75843i) q^{21} +(1.13018 + 0.652510i) q^{22} +6.57244 q^{23} +(-1.08196 + 1.35254i) q^{24} +(2.73282 - 4.18708i) 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} +(-2.95713 - 2.50108i) q^{30} +(-1.19742 + 0.691334i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.76509 + 1.41198i) q^{33} +(-0.502991 + 0.290402i) q^{34} +(4.14868 + 4.21764i) q^{35} +(-2.20531 + 2.03386i) q^{36} +(2.02863 - 1.17123i) q^{37} +7.92614i q^{38} +(-3.82443 - 9.78795i) q^{39} +(-1.96632 + 1.06470i) q^{40} +(-3.16905 + 5.48896i) q^{41} +(3.63873 - 2.78561i) q^{42} +(-10.0713 + 5.81466i) q^{43} +(1.13018 - 0.652510i) q^{44} +(-4.41141 - 5.05366i) q^{45} +(3.28622 - 5.69190i) q^{46} +(4.69056 + 2.70810i) q^{47} +(0.630353 + 1.61327i) q^{48} +(-5.92418 + 3.72881i) q^{49} +(-2.25971 - 4.46024i) q^{50} +(-0.936996 + 0.366111i) q^{51} -6.06713 q^{52} +(-4.19068 + 7.25846i) q^{53} +(-4.30649 + 2.90761i) q^{54} +(1.38946 + 2.56609i) q^{55} +(-0.733422 - 2.54206i) q^{56} +(-2.06663 + 13.5720i) q^{57} +0.144970i q^{58} +(-1.54358 - 2.67356i) q^{59} +(-3.64456 + 1.31041i) q^{60} +(1.83643 + 1.06026i) q^{61} +1.38267i q^{62} +(6.95696 - 3.82108i) q^{63} +1.00000 q^{64} +(0.370711 - 13.5615i) q^{65} +(2.10536 - 0.822623i) q^{66} +(11.4291 - 6.59859i) q^{67} +0.580804i q^{68} +(7.11112 - 8.88948i) q^{69} +(5.72692 - 1.48404i) q^{70} +10.3545i q^{71} +(0.658722 + 2.92679i) q^{72} +(3.84599 - 6.66144i) q^{73} -2.34246i q^{74} +(-2.70639 - 8.22651i) q^{75} +(6.86424 + 3.96307i) q^{76} +(-3.31745 + 0.957131i) q^{77} +(-10.3888 - 1.58192i) q^{78} +(3.54596 - 6.14179i) q^{79} +(-0.0611015 + 2.23523i) q^{80} +(-8.13217 + 3.85588i) q^{81} +(3.16905 + 5.48896i) q^{82} +(-4.32983 + 2.49983i) q^{83} +(-0.593040 - 4.54404i) q^{84} +(-1.29823 - 0.0354880i) q^{85} +11.6293i q^{86} +(-0.0377989 + 0.248234i) q^{87} -1.30502i 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} +(-0.360511 + 2.36756i) q^{93} +(4.69056 - 2.70810i) q^{94} +(-9.27780 + 15.1010i) q^{95} +(1.71231 + 0.260736i) q^{96} +(-5.76032 - 9.97717i) q^{97} +(0.267153 + 6.99490i) q^{98} +(3.81952 - 0.859646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 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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