LMFDB - Embedded newform 462.2.n.f.65.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.11
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.43353 + 0.972102i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72427 - 2.15021i) q^{5} +(1.55863 - 0.755426i) q^{6} +(-2.62857 - 0.301041i) q^{7} -1.00000 q^{8} +(1.11004 + 2.78708i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.43353 + 0.972102i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72427 - 2.15021i) q^{5} +(1.55863 - 0.755426i) q^{6} +(-2.62857 - 0.301041i) q^{7} -1.00000 q^{8} +(1.11004 + 2.78708i) q^{9} +(-3.72427 + 2.15021i) q^{10} +(-0.167821 - 3.31238i) q^{11} +(0.125098 - 1.72753i) q^{12} -2.22468i q^{13} +(-1.57499 + 2.12589i) q^{14} +(-3.24864 - 6.70276i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.17622 - 3.76933i) q^{17} +(2.96870 + 0.432220i) q^{18} +(-1.35056 - 0.779747i) q^{19} +4.30042i q^{20} +(-3.47550 - 2.98679i) q^{21} +(-2.95251 - 1.51085i) q^{22} +(1.48946 + 0.859942i) q^{23} +(-1.43353 - 0.972102i) q^{24} +(6.74679 + 11.6858i) q^{25} +(-1.92663 - 1.11234i) q^{26} +(-1.11805 + 5.07444i) q^{27} +(1.05357 + 2.42693i) q^{28} -4.52500 q^{29} +(-7.42908 - 0.537973i) q^{30} +(-1.83135 - 3.17199i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.97939 - 4.91154i) q^{33} -4.35245 q^{34} +(9.14220 + 6.77313i) q^{35} +(1.85866 - 2.35486i) q^{36} +(3.36669 - 5.83129i) q^{37} +(-1.35056 + 0.779747i) q^{38} +(2.16262 - 3.18916i) q^{39} +(3.72427 + 2.15021i) q^{40} +10.0223 q^{41} +(-4.32438 + 1.51648i) q^{42} +4.66108i q^{43} +(-2.78469 + 1.80152i) q^{44} +(1.85873 - 12.7666i) q^{45} +(1.48946 - 0.859942i) q^{46} +(-3.24960 - 1.87616i) q^{47} +(-1.55863 + 0.755426i) q^{48} +(6.81875 + 1.58262i) q^{49} +13.4936 q^{50} +(0.544482 - 7.51897i) q^{51} +(-1.92663 + 1.11234i) q^{52} +(2.14220 - 1.23680i) q^{53} +(3.83557 + 3.50548i) q^{54} +(-6.49729 + 12.6970i) q^{55} +(2.62857 + 0.301041i) q^{56} +(-1.17808 - 2.43068i) q^{57} +(-2.26250 + 3.91876i) q^{58} +(3.19636 - 1.84542i) q^{59} +(-4.18044 + 6.16479i) q^{60} +(-4.02253 - 2.32241i) q^{61} -3.66270 q^{62} +(-2.07878 - 7.66020i) q^{63} +1.00000 q^{64} +(-4.78353 + 8.28532i) q^{65} +(-2.76382 - 5.03600i) q^{66} +(-2.08595 - 3.61297i) q^{67} +(-2.17622 + 3.76933i) q^{68} +(1.29925 + 2.68067i) q^{69} +(10.4368 - 4.53081i) q^{70} +7.07802i q^{71} +(-1.11004 - 2.78708i) q^{72} +(12.7024 - 7.33373i) q^{73} +(-3.36669 - 5.83129i) q^{74} +(-1.68802 + 23.3105i) q^{75} +1.55949i q^{76} +(-0.556035 + 8.75733i) q^{77} +(-1.68058 - 3.46746i) q^{78} +(8.48475 + 4.89868i) q^{79} +(3.72427 - 2.15021i) q^{80} +(-6.53564 + 6.18752i) q^{81} +(5.01114 - 8.67956i) q^{82} -17.6583 q^{83} +(-0.848886 + 4.50326i) q^{84} +18.7173i q^{85} +(4.03661 + 2.33054i) q^{86} +(-6.48674 - 4.39876i) q^{87} +(0.167821 + 3.31238i) q^{88} +(-10.8244 - 6.24946i) q^{89} +(-10.1269 - 7.99303i) q^{90} +(-0.669722 + 5.84773i) q^{91} -1.71988i q^{92} +(0.458196 - 6.32741i) q^{93} +(-3.24960 + 1.87616i) q^{94} +(3.35323 + 5.80797i) q^{95} +(-0.125098 + 1.72753i) q^{96} -0.541718 q^{97} +(4.77996 - 5.11390i) q^{98} +(9.04557 - 4.14459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	1.43353	+	0.972102i	0.827651	+	0.561243i
$3$	1.43353	+	0.972102i	0.827651	+	0.561243i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.72427	−	2.15021i	−1.66554	−	0.961602i	−0.969996	−	0.243123i	$-0.921828\pi$
$5$	−3.72427	−	2.15021i	−1.66554	−	0.961602i	−0.695548	−	0.718479i	$-0.744838\pi$
$6$	1.55863	−	0.755426i	0.636309	−	0.308401i
$7$	−2.62857	−	0.301041i	−0.993506	−	0.113783i
$7$	−2.62857	−	0.301041i	−0.993506	−	0.113783i
$8$	−1.00000			−0.353553
$9$	1.11004	+	2.78708i	0.370012	+	0.929027i
$10$	−3.72427	+	2.15021i	−1.17772	+	0.679955i
$11$	−0.167821	−	3.31238i	−0.0505998	−	0.998719i
$11$	−0.167821	−	3.31238i	−0.0505998	−	0.998719i
$12$	0.125098	−	1.72753i	0.0361127	−	0.498694i
$13$		−	2.22468i		−	0.617016i	−0.951222	−	0.308508i	$-0.900170\pi$
$13$		−	2.22468i		−	0.617016i	0.951222	−	0.308508i	$-0.0998297\pi$
$14$	−1.57499	+	2.12589i	−0.420935	+	0.568167i
$15$	−3.24864	−	6.70276i	−0.838796	−	1.73065i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.17622	−	3.76933i	−0.527812	−	0.914197i	−0.999474	−	0.0324176i	$-0.989679\pi$
$17$	−2.17622	−	3.76933i	−0.527812	−	0.914197i	0.471663	−	0.881779i	$-0.343654\pi$
$18$	2.96870	+	0.432220i	0.699730	+	0.101875i
$19$	−1.35056	−	0.779747i	−0.309840	−	0.178886i	0.337015	−	0.941499i	$-0.390583\pi$
$19$	−1.35056	−	0.779747i	−0.309840	−	0.178886i	−0.646855	+	0.762613i	$0.723916\pi$
$20$			4.30042i			0.961602i
$21$	−3.47550	−	2.98679i	−0.758416	−	0.651771i
$22$	−2.95251	−	1.51085i	−0.629478	−	0.322115i
$23$	1.48946	+	0.859942i	0.310575	+	0.179310i	0.647184	−	0.762334i	$-0.275947\pi$
$23$	1.48946	+	0.859942i	0.310575	+	0.179310i	−0.336609	+	0.941645i	$0.609280\pi$
$24$	−1.43353	−	0.972102i	−0.292619	−	0.198429i
$25$	6.74679	+	11.6858i	1.34936	+	2.33716i
$26$	−1.92663	−	1.11234i	−0.377844	−	0.218148i
$27$	−1.11805	+	5.07444i	−0.215169	+	0.976577i
$28$	1.05357	+	2.42693i	0.199107	+	0.458646i
$29$	−4.52500			−0.840271			−0.420136	−	0.907461i	$-0.638018\pi$
$29$	−4.52500			−0.840271			−0.420136	+	0.907461i	$0.638018\pi$
$30$	−7.42908	−	0.537973i	−1.35636	−	0.0982200i
$31$	−1.83135	−	3.17199i	−0.328920	−	0.569706i	0.653378	−	0.757032i	$-0.273351\pi$
$31$	−1.83135	−	3.17199i	−0.328920	−	0.569706i	−0.982298	+	0.187326i	$0.940018\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.97939	−	4.91154i	0.518645	−	0.854990i
$34$	−4.35245			−0.746438
$35$	9.14220	+	6.77313i	1.54531	+	1.14487i
$36$	1.85866	−	2.35486i	0.309777	−	0.392477i
$37$	3.36669	−	5.83129i	0.553481	−	0.958658i	−0.444539	−	0.895760i	$-0.646632\pi$
$37$	3.36669	−	5.83129i	0.553481	−	0.958658i	0.998020	−	0.0628979i	$-0.0200343\pi$
$38$	−1.35056	+	0.779747i	−0.219090	+	0.126492i
$39$	2.16262	−	3.18916i	0.346296	−	0.510674i
$40$	3.72427	+	2.15021i	0.588859	+	0.339978i
$41$	10.0223			1.56522			0.782609	−	0.622513i	$-0.213888\pi$
$41$	10.0223			1.56522			0.782609	+	0.622513i	$0.213888\pi$
$42$	−4.32438	+	1.51648i	−0.667267	+	0.233997i
$43$			4.66108i			0.710808i	0.934713	+	0.355404i	$0.115657\pi$
$43$			4.66108i			0.710808i	−0.934713	+	0.355404i	$0.884343\pi$
$44$	−2.78469	+	1.80152i	−0.419808	+	0.271590i
$45$	1.85873	−	12.7666i	0.277083	−	1.90314i
$46$	1.48946	−	0.859942i	0.219609	−	0.126792i
$47$	−3.24960	−	1.87616i	−0.474002	−	0.273665i	0.243911	−	0.969798i	$-0.421569\pi$
$47$	−3.24960	−	1.87616i	−0.474002	−	0.273665i	−0.717914	+	0.696132i	$0.754903\pi$
$48$	−1.55863	+	0.755426i	−0.224969	+	0.109036i
$49$	6.81875	+	1.58262i	0.974107	+	0.226088i
$50$	13.4936			1.90828
$51$	0.544482	−	7.51897i	0.0762428	−	1.05287i
$52$	−1.92663	+	1.11234i	−0.267176	+	0.154254i
$53$	2.14220	−	1.23680i	0.294254	−	0.169887i	−0.345605	−	0.938380i	$-0.612326\pi$
$53$	2.14220	−	1.23680i	0.294254	−	0.169887i	0.639859	+	0.768493i	$0.278993\pi$
$54$	3.83557	+	3.50548i	0.521955	+	0.477036i
$55$	−6.49729	+	12.6970i	−0.876094	+	1.71207i
$56$	2.62857	+	0.301041i	0.351257	+	0.0402283i
$57$	−1.17808	−	2.43068i	−0.156041	−	0.321951i
$58$	−2.26250	+	3.91876i	−0.297081	+	0.514559i
$59$	3.19636	−	1.84542i	0.416131	−	0.240253i	−0.277290	−	0.960786i	$-0.589436\pi$
$59$	3.19636	−	1.84542i	0.416131	−	0.240253i	0.693420	+	0.720533i	$0.256103\pi$
$60$	−4.18044	+	6.16479i	−0.539693	+	0.795871i
$61$	−4.02253	−	2.32241i	−0.515033	−	0.297354i	0.219867	−	0.975530i	$-0.429438\pi$
$61$	−4.02253	−	2.32241i	−0.515033	−	0.297354i	−0.734900	+	0.678176i	$0.762771\pi$
$62$	−3.66270			−0.465163
$63$	−2.07878	−	7.66020i	−0.261902	−	0.965095i
$64$	1.00000			0.125000
$65$	−4.78353	+	8.28532i	−0.593324	+	1.02767i
$66$	−2.76382	−	5.03600i	−0.340203	−	0.619888i
$67$	−2.08595	−	3.61297i	−0.254839	−	0.441394i	0.710013	−	0.704189i	$-0.248689\pi$
$67$	−2.08595	−	3.61297i	−0.254839	−	0.441394i	−0.964852	+	0.262795i	$0.915356\pi$
$68$	−2.17622	+	3.76933i	−0.263906	+	0.457098i
$69$	1.29925	+	2.68067i	0.156411	+	0.322714i
$70$	10.4368	−	4.53081i	1.24744	−	0.541535i
$71$			7.07802i			0.840006i	0.907523	+	0.420003i	$0.137971\pi$
$71$			7.07802i			0.840006i	−0.907523	+	0.420003i	$0.862029\pi$
$72$	−1.11004	−	2.78708i	−0.130819	−	0.328461i
$73$	12.7024	−	7.33373i	1.48670	−	0.858348i	0.486818	−	0.873504i	$-0.338158\pi$
$73$	12.7024	−	7.33373i	1.48670	−	0.858348i	0.999885	+	0.0151552i	$0.00482423\pi$
$74$	−3.36669	−	5.83129i	−0.391370	−	0.677873i
$75$	−1.68802	+	23.3105i	−0.194916	+	2.69167i
$76$			1.55949i			0.178886i
$77$	−0.556035	+	8.75733i	−0.0633660	+	0.997990i
$78$	−1.68058	−	3.46746i	−0.190289	−	0.392613i
$79$	8.48475	+	4.89868i	0.954609	+	0.551144i	0.894510	−	0.447048i	$-0.147525\pi$
$79$	8.48475	+	4.89868i	0.954609	+	0.551144i	0.0600997	+	0.998192i	$0.480858\pi$
$80$	3.72427	−	2.15021i	0.416386	−	0.240401i
$81$	−6.53564	+	6.18752i	−0.726182	+	0.687503i
$82$	5.01114	−	8.67956i	0.553388	−	0.958497i
$83$	−17.6583			−1.93825			−0.969126	−	0.246564i	$-0.920698\pi$
$83$	−17.6583			−1.93825			−0.969126	+	0.246564i	$0.920698\pi$
$84$	−0.848886	+	4.50326i	−0.0926210	+	0.491346i
$85$			18.7173i			2.03018i
$86$	4.03661	+	2.33054i	0.435279	+	0.251309i
$87$	−6.48674	−	4.39876i	−0.695451	−	0.471596i
$88$	0.167821	+	3.31238i	0.0178897	+	0.353100i
$89$	−10.8244	−	6.24946i	−1.14738	−	0.662441i	−0.199134	−	0.979972i	$-0.563813\pi$
$89$	−10.8244	−	6.24946i	−1.14738	−	0.662441i	−0.948248	+	0.317531i	$0.897146\pi$
$90$	−10.1269	−	7.99303i	−1.06747	−	0.842539i
$91$	−0.669722	+	5.84773i	−0.0702059	+	0.613009i
$92$		−	1.71988i		−	0.179310i
$93$	0.458196	−	6.32741i	0.0475127	−	0.656122i
$94$	−3.24960	+	1.87616i	−0.335170	+	0.193511i
$95$	3.35323	+	5.80797i	0.344035	+	0.595885i
$96$	−0.125098	+	1.72753i	−0.0127678	+	0.176315i
$97$	−0.541718			−0.0550031			−0.0275016	−	0.999622i	$-0.508755\pi$
$97$	−0.541718			−0.0550031			−0.0275016	+	0.999622i	$0.508755\pi$
$98$	4.77996	−	5.11390i	0.482849	−	0.516582i
$99$	9.04557	−	4.14459i	0.909114	−	0.416547i
$100$	6.74679	−	11.6858i	0.674679	−	1.16858i
$101$	−3.92520	−	6.79864i	−0.390572	−	0.676490i	0.601953	−	0.798531i	$-0.294389\pi$
$101$	−3.92520	−	6.79864i	−0.390572	−	0.676490i	−0.992525	+	0.122041i	$0.961056\pi$
$102$	−6.23938	−	4.23102i	−0.617791	−	0.418933i
$103$	4.84871	−	8.39821i	0.477758	−	0.827500i	−0.521917	−	0.852996i	$-0.674783\pi$
$103$	4.84871	−	8.39821i	0.477758	−	0.827500i	0.999675	+	0.0254957i	$0.00811641\pi$
$104$			2.22468i			0.218148i
$105$	6.52148	+	18.5966i	0.636431	+	1.81485i
$106$		−	2.47360i		−	0.240257i
$107$	1.75893	−	3.04655i	0.170042	−	0.294521i	−0.768392	−	0.639979i	$-0.778943\pi$
$107$	1.75893	−	3.04655i	0.170042	−	0.294521i	0.938434	+	0.345458i	$0.112276\pi$
$108$	4.95362	−	1.56896i	0.476662	−	0.150973i
$109$	2.06323	−	1.19121i	0.197622	−	0.114097i	−0.397924	−	0.917418i	$-0.630269\pi$
$109$	2.06323	−	1.19121i	0.197622	−	0.114097i	0.595546	+	0.803321i	$0.296936\pi$
$110$	7.74731	+	11.9753i	0.738677	+	1.14180i
$111$	10.4949	−	5.08657i	0.996129	−	0.482796i
$112$	1.57499	−	2.12589i	0.148823	−	0.200877i
$113$		−	10.4210i		−	0.980328i	−0.871630	−	0.490164i	$-0.836937\pi$
$113$		−	10.4210i		−	0.980328i	0.871630	−	0.490164i	$-0.163063\pi$
$114$	−2.69407	−	0.195089i	−0.252323	−	0.0182718i
$115$	−3.69811	−	6.40531i	−0.344850	−	0.597299i
$116$	2.26250	+	3.91876i	0.210068	+	0.363848i
$117$	6.20037	−	2.46948i	0.573225	−	0.228304i
$118$		−	3.69084i		−	0.339769i
$119$	4.58563	+	10.5631i	0.420364	+	0.968316i
$120$	3.24864	+	6.70276i	0.296559	+	0.611876i
$121$	−10.9437	+	1.11177i	−0.994879	+	0.101070i
$122$	−4.02253	+	2.32241i	−0.364183	+	0.210261i
$123$	14.3673	+	9.74268i	1.29545	+	0.878468i
$124$	−1.83135	+	3.17199i	−0.164460	+	0.284853i
$125$		−	36.5259i		−	3.26697i
$126$	−7.67332	−	2.02982i	−0.683594	−	0.180831i
$127$		−	2.29923i		−	0.204024i	−0.994783	−	0.102012i	$-0.967472\pi$
$127$		−	2.29923i		−	0.204024i	0.994783	−	0.102012i	$-0.0325280\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.53104	+	6.68181i	−0.398936	+	0.588301i
$130$	4.78353	+	8.28532i	0.419543	+	0.726671i
$131$	3.88858	−	6.73522i	0.339747	−	0.588459i	−0.644638	−	0.764488i	$-0.722992\pi$
$131$	3.88858	−	6.73522i	0.339747	−	0.588459i	0.984385	+	0.176029i	$0.0563253\pi$
$132$	−5.74321	−	0.124457i	−0.499883	−	0.0108326i
$133$	3.31531	+	2.45619i	0.287473	+	0.212979i
$134$	−4.17189			−0.360397
$135$	15.0750	−	16.4945i	1.29745	−	1.41962i
$136$	2.17622	+	3.76933i	0.186610	+	0.323217i
$137$	−8.00701	+	4.62285i	−0.684085	+	0.394957i	−0.801392	−	0.598139i	$-0.795907\pi$
$137$	−8.00701	+	4.62285i	−0.684085	+	0.394957i	0.117307	+	0.993096i	$0.462574\pi$
$138$	2.97115	+	0.215154i	0.252921	+	0.0183151i
$139$			17.9867i			1.52561i	0.646626	+	0.762807i	$0.276179\pi$
$139$			17.9867i			1.52561i	−0.646626	+	0.762807i	$0.723821\pi$
$140$	1.29460	−	11.3039i	0.109414	−	0.955357i
$141$	−2.83459	−	5.84847i	−0.238716	−	0.492530i
$142$	6.12975	+	3.53901i	0.514397	+	0.296987i
$143$	−7.36899	+	0.373348i	−0.616226	+	0.0312209i
$144$	−2.96870	−	0.432220i	−0.247392	−	0.0360184i
$145$	16.8523	+	9.72969i	1.39951	+	0.808007i
$146$		−	14.6675i		−	1.21389i
$147$	8.23644	+	8.89725i	0.679330	+	0.733833i
$148$	−6.73339			−0.553481
$149$	−2.47440	+	4.28578i	−0.202711	+	0.351105i	−0.949401	−	0.314067i	$-0.898308\pi$
$149$	−2.47440	+	4.28578i	−0.202711	+	0.351105i	0.746690	+	0.665172i	$0.231642\pi$
$150$	19.3435	+	13.1171i	1.57939	+	1.07101i
$151$	6.71375	−	3.87618i	0.546357	−	0.315439i	−0.201294	−	0.979531i	$-0.564515\pi$
$151$	6.71375	−	3.87618i	0.546357	−	0.315439i	0.747651	+	0.664091i	$0.231181\pi$
$152$	1.35056	+	0.779747i	0.109545	+	0.0632458i
$153$	8.08974	−	10.2494i	0.654016	−	0.828615i
$154$	7.30605	+	4.86020i	0.588739	+	0.391646i
$155$			15.7511i			1.26516i
$156$	−3.84320	−	0.278303i	−0.307702	−	0.0222821i
$157$	−7.06587	−	12.2385i	−0.563918	−	0.976735i	−0.997149	−	0.0754521i	$-0.975960\pi$
$157$	−7.06587	−	12.2385i	−0.563918	−	0.976735i	0.433231	−	0.901283i	$-0.357373\pi$
$158$	8.48475	−	4.89868i	0.675011	−	0.389718i
$159$	4.27321	+	0.309442i	0.338887	+	0.0245403i
$160$		−	4.30042i		−	0.339978i
$161$	−3.65628	−	2.70881i	−0.288155	−	0.213484i
$162$	2.09073	+	8.75379i	0.164264	+	0.687763i
$163$	8.63677	−	14.9593i	0.676484	−	1.17170i	−0.299549	−	0.954081i	$-0.596836\pi$
$163$	8.63677	−	14.9593i	0.676484	−	1.17170i	0.976033	−	0.217623i	$-0.0698304\pi$
$164$	−5.01114	−	8.67956i	−0.391305	−	0.677759i
$165$	−21.6569	+	11.8856i	−1.68599	+	0.925292i
$166$	−8.82916	+	15.2926i	−0.685276	+	1.18693i
$167$	14.3557			1.11088			0.555440	−	0.831556i	$-0.312550\pi$
$167$	14.3557			1.11088			0.555440	+	0.831556i	$0.312550\pi$
$168$	3.47550	+	2.98679i	0.268141	+	0.230436i
$169$	8.05078			0.619291
$170$	16.2097	+	9.35866i	1.24323	+	0.717777i
$171$	0.674045	−	4.62967i	0.0515455	−	0.354040i
$172$	4.03661	−	2.33054i	0.307789	−	0.177702i
$173$	−8.69404	+	15.0585i	−0.660996	+	1.14488i	0.319358	+	0.947634i	$0.396533\pi$
$173$	−8.69404	+	15.0585i	−0.660996	+	1.14488i	−0.980354	+	0.197244i	$0.936801\pi$
$174$	−7.05281	+	3.41830i	−0.534672	+	0.259141i
$175$	−14.2165	−	32.7479i	−1.07467	−	2.47551i
$176$	2.95251	+	1.51085i	0.222554	+	0.113885i
$177$	6.37602	+	0.461716i	0.479251	+	0.0347047i
$178$	−10.8244	+	6.24946i	−0.811321	+	0.468417i
$179$	12.6301	−	7.29196i	0.944014	−	0.545027i	0.0527980	−	0.998605i	$-0.483186\pi$
$179$	12.6301	−	7.29196i	0.944014	−	0.545027i	0.891216	+	0.453578i	$0.149853\pi$
$180$	−11.9856	+	4.77362i	−0.893354	+	0.355805i
$181$	−23.8500			−1.77275			−0.886377	−	0.462964i	$-0.846786\pi$
$181$	−23.8500			−1.77275			−0.886377	+	0.462964i	$0.846786\pi$
$182$	4.72943	+	3.50386i	0.350568	+	0.259724i
$183$	−3.50882	−	7.23957i	−0.259379	−	0.535164i
$184$	−1.48946	−	0.859942i	−0.109805	−	0.0633958i
$185$	−25.0770	+	14.4782i	−1.84369	+	1.06446i
$186$	−5.25060	−	3.56051i	−0.384993	−	0.261070i
$187$	−12.1202	+	7.84104i	−0.886318	+	0.573394i
$188$			3.75231i			0.273665i
$189$	4.46649	−	13.0019i	0.324889	−	0.945752i
$190$	6.70647			0.486538
$191$	−1.01941	−	0.588558i	−0.0737620	−	0.0425865i	0.462665	−	0.886533i	$-0.346893\pi$
$191$	−1.01941	−	0.588558i	−0.0737620	−	0.0425865i	−0.536427	+	0.843946i	$0.680226\pi$
$192$	1.43353	+	0.972102i	0.103456	+	0.0701554i
$193$	−1.67930	+	0.969543i	−0.120879	+	0.0697893i	−0.559220	−	0.829019i	$-0.688899\pi$
$193$	−1.67930	+	0.969543i	−0.120879	+	0.0697893i	0.438342	+	0.898808i	$0.355566\pi$
$194$	−0.270859	+	0.469142i	−0.0194465	+	0.0336824i
$195$	−14.9115	+	7.22720i	−1.06784	+	0.517551i
$196$	−2.03879	−	6.69652i	−0.145628	−	0.478323i
$197$	−1.04430			−0.0744031			−0.0372015	−	0.999308i	$-0.511844\pi$
$197$	−1.04430			−0.0744031			−0.0372015	+	0.999308i	$0.511844\pi$
$198$	0.933467	−	9.90599i	0.0663386	−	0.703988i
$199$	12.1261	+	21.0030i	0.859596	+	1.48886i	0.872315	+	0.488944i	$0.162618\pi$
$199$	12.1261	+	21.0030i	0.859596	+	1.48886i	−0.0127192	+	0.999919i	$0.504049\pi$
$200$	−6.74679	−	11.6858i	−0.477070	−	0.826309i
$201$	0.521895	−	7.20706i	0.0368117	−	0.508347i
$202$	−7.85039			−0.552352
$203$	11.8943	+	1.36221i	0.834814	+	0.0956085i
$204$	−6.78386	+	3.28795i	−0.474965	+	0.230203i
$205$	−37.3257	−	21.5500i	−2.60694	−	1.50512i
$206$	−4.84871	−	8.39821i	−0.337826	−	0.585131i
$207$	−0.743369	+	5.10582i	−0.0516677	+	0.354879i
$208$	1.92663	+	1.11234i	0.133588	+	0.0771270i
$209$	−2.35616	+	4.60442i	−0.162979	+	0.318495i
$210$	19.3659	+	3.65056i	1.33637	+	0.251913i
$211$		−	19.8659i		−	1.36762i	−0.729658	−	0.683812i	$-0.760321\pi$
$211$		−	19.8659i		−	1.36762i	0.729658	−	0.683812i	$-0.239679\pi$
$212$	−2.14220	−	1.23680i	−0.147127	−	0.0849437i
$213$	−6.88056	+	10.1466i	−0.471448	+	0.695232i
$214$	−1.75893	−	3.04655i	−0.120238	−	0.208258i
$215$	10.0223	−	17.3591i	0.683514	−	1.18388i
$216$	1.11805	−	5.07444i	0.0760737	−	0.345272i
$217$	3.85893	+	8.88910i	0.261961	+	0.603432i
$218$		−	2.38242i		−	0.161358i
$219$	25.3384	+	1.83487i	1.71221	+	0.123989i
$220$	14.2446	−	0.721698i	0.960370	−	0.0486569i
$221$	−8.38557	+	4.84141i	−0.564074	+	0.325668i
$222$	0.842333	−	11.6321i	0.0565337	−	0.780696i
$223$	−17.1150			−1.14611			−0.573053	−	0.819518i	$-0.694241\pi$
$223$	−17.1150			−1.14611			−0.573053	+	0.819518i	$0.694241\pi$
$224$	−1.05357	−	2.42693i	−0.0703949	−	0.162156i
$225$	−25.0800	+	31.7755i	−1.67200	+	2.11837i
$226$	−9.02487	−	5.21051i	−0.600326	−	0.346598i
$227$	9.55949	+	16.5575i	0.634486	+	1.09896i	0.986624	+	0.163013i	$0.0521214\pi$
$227$	9.55949	+	16.5575i	0.634486	+	1.09896i	−0.352138	+	0.935948i	$0.614545\pi$
$228$	−1.51599	+	2.23559i	−0.100399	+	0.148055i
$229$	6.76018	−	11.7090i	0.446725	−	0.773751i	−0.551445	−	0.834211i	$-0.685923\pi$
$229$	6.76018	−	11.7090i	0.446725	−	0.773751i	0.998171	+	0.0604599i	$0.0192567\pi$
$230$	−7.39622			−0.487692
$231$	−9.31011	+	12.0134i	−0.612560	+	0.790424i
$232$	4.52500			0.297081
$233$	−3.87397	+	6.70992i	−0.253792	+	0.439581i	−0.964567	−	0.263839i	$-0.915011\pi$
$233$	−3.87397	+	6.70992i	−0.253792	+	0.439581i	0.710774	+	0.703420i	$0.248345\pi$
$234$	0.961553	−	6.60442i	0.0628587	−	0.431744i
$235$	8.06825	+	13.9746i	0.526314	+	0.911603i
$236$	−3.19636	−	1.84542i	−0.208065	−	0.120127i
$237$	7.40117	+	15.2705i	0.480758	+	0.991923i
$238$	11.4407	+	1.31027i	0.741591	+	0.0849320i
$239$	−11.9552			−0.773319			−0.386659	−	0.922223i	$-0.626371\pi$
$239$	−11.9552			−0.773319			−0.386659	+	0.922223i	$0.626371\pi$
$240$	7.42908	+	0.537973i	0.479545	+	0.0347260i
$241$	−24.4654	+	14.1251i	−1.57595	+	0.909876i	−0.580536	+	0.814235i	$0.697157\pi$
$241$	−24.4654	+	14.1251i	−1.57595	+	0.909876i	−0.995416	+	0.0956417i	$0.969510\pi$
$242$	−4.50902	+	10.0334i	−0.289851	+	0.644970i
$243$	−15.3840	+	2.51672i	−0.986881	+	0.161448i
$244$			4.64482i			0.297354i
$245$	−21.9919	−	20.5558i	−1.40501	−	1.31326i
$246$	15.6211	−	7.57109i	0.995962	−	0.482715i
$247$	−1.73469	+	3.00457i	−0.110376	+	0.191176i
$248$	1.83135	+	3.17199i	0.116291	+	0.201421i
$249$	−25.3138	−	17.1657i	−1.60420	−	1.08783i
$250$	−31.6323	−	18.2629i	−2.00061	−	1.15505i
$251$			1.79928i			0.113569i	0.998386	+	0.0567847i	$0.0180849\pi$
$251$			1.79928i			0.113569i	−0.998386	+	0.0567847i	$0.981915\pi$
$252$	−5.59454	+	5.63038i	−0.352423	+	0.354680i
$253$	2.59849	−	5.07798i	0.163366	−	0.319250i
$254$	−1.99119	−	1.14962i	−0.124939	−	0.0721333i
$255$	−18.1951	+	26.8319i	−1.13942	+	1.68028i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.30536	+	1.90835i	0.206183	+	0.119040i	0.599536	−	0.800348i	$-0.295352\pi$
$257$	3.30536	+	1.90835i	0.206183	+	0.119040i	−0.393353	+	0.919387i	$0.628685\pi$
$258$	3.52110	+	7.26490i	0.219214	+	0.452293i
$259$	−10.6050	+	14.3144i	−0.658966	+	0.889455i
$260$	9.56706			0.593324
$261$	−5.02292	−	12.6115i	−0.310911	−	0.780635i
$262$	−3.88858	−	6.73522i	−0.240237	−	0.416103i
$263$	7.81378	+	13.5339i	0.481818	+	0.834533i	0.999782	−	0.0208689i	$-0.00664325\pi$
$263$	7.81378	+	13.5339i	0.481818	+	0.834533i	−0.517964	+	0.855402i	$0.673310\pi$
$264$	−2.97939	+	4.91154i	−0.183369	+	0.302284i
$265$	−10.6375			−0.653456
$266$	3.78478	−	1.64304i	0.232060	−	0.100741i
$267$	−9.44200	−	19.4812i	−0.577841	−	1.19223i
$268$	−2.08595	+	3.61297i	−0.127420	+	0.220697i
$269$	10.1509	−	5.86060i	0.618909	−	0.357327i	−0.157535	−	0.987513i	$-0.550355\pi$
$269$	10.1509	−	5.86060i	0.618909	−	0.357327i	0.776444	+	0.630186i	$0.217021\pi$
$270$	−6.74718	−	21.3026i	−0.410620	−	1.29644i
$271$	9.87548	+	5.70161i	0.599893	+	0.346348i	0.768999	−	0.639249i	$-0.220755\pi$
$271$	9.87548	+	5.70161i	0.599893	+	0.346348i	−0.169107	+	0.985598i	$0.554088\pi$
$272$	4.35245			0.263906
$273$	−6.64466	+	7.73188i	−0.402153	+	0.467955i
$274$			9.24570i			0.558553i
$275$	37.5754	−	24.3090i	2.26588	−	1.46589i
$276$	1.67190	−	2.46551i	0.100637	−	0.148406i
$277$	19.9310	−	11.5072i	1.19754	−	0.691398i	0.237531	−	0.971380i	$-0.423662\pi$
$277$	19.9310	−	11.5072i	1.19754	−	0.691398i	0.960005	+	0.279982i	$0.0903284\pi$
$278$	15.5770	+	8.99336i	0.934244	+	0.539386i
$279$	6.80772	−	8.62514i	0.407568	−	0.516374i
$280$	−9.14220	−	6.77313i	−0.546351	−	0.404772i
$281$	10.8023			0.644409			0.322205	−	0.946670i	$-0.395576\pi$
$281$	10.8023			0.644409			0.322205	+	0.946670i	$0.395576\pi$
$282$	−6.48222	−	0.469406i	−0.386010	−	0.0279527i
$283$	13.2070	−	7.62507i	0.785075	−	0.453263i	−0.0531507	−	0.998587i	$-0.516926\pi$
$283$	13.2070	−	7.62507i	0.785075	−	0.453263i	0.838226	+	0.545323i	$0.183593\pi$
$284$	6.12975	−	3.53901i	0.363733	−	0.210002i
$285$	−0.838965	+	11.5856i	−0.0496960	+	0.686272i
$286$	−3.36117	+	6.56841i	−0.198750	+	0.388398i
$287$	−26.3443	−	3.01712i	−1.55505	−	0.178095i
$288$	−1.85866	+	2.35486i	−0.109523	+	0.138761i
$289$	−0.971897	+	1.68337i	−0.0571704	+	0.0990220i
$290$	16.8523	−	9.72969i	0.989602	−	0.571347i
$291$	−0.776571	−	0.526605i	−0.0455234	−	0.0308701i
$292$	−12.7024	−	7.33373i	−0.743351	−	0.429174i
$293$	10.6037			0.619474			0.309737	−	0.950822i	$-0.399759\pi$
$293$	10.6037			0.619474			0.309737	+	0.950822i	$0.399759\pi$
$294$	11.8235	−	2.68434i	0.689558	−	0.156554i
$295$	−15.8721			−0.924112
$296$	−3.36669	+	5.83129i	−0.195685	+	0.338937i
$297$	16.9961	+	2.85181i	0.986213	+	0.165479i
$298$	2.47440	+	4.28578i	0.143338	+	0.248269i
$299$	1.91310	−	3.31359i	0.110637	−	0.191630i
$300$	21.0315	−	10.1934i	1.21425	−	0.588516i
$301$	1.40318	−	12.2520i	0.0808778	−	0.706192i
$302$		−	7.75237i		−	0.446099i
$303$	0.982068	−	13.5618i	0.0564183	−	0.779103i
$304$	1.35056	−	0.779747i	0.0774600	−	0.0447215i
$305$	9.98733	+	17.2986i	0.571873	+	0.990513i
$306$	−4.83138	−	12.1306i	−0.276191	−	0.693461i
$307$		−	6.44519i		−	0.367846i	−0.982941	−	0.183923i	$-0.941120\pi$
$307$		−	6.44519i		−	0.367846i	0.982941	−	0.183923i	$-0.0588797\pi$
$308$	7.86209	−	3.89712i	0.447984	−	0.222059i
$309$	15.1147	−	7.32568i	0.859845	−	0.416743i
$310$	13.6409	+	7.87556i	0.774749	+	0.447302i
$311$	8.01305	−	4.62634i	0.454378	−	0.262335i	−0.255299	−	0.966862i	$-0.582174\pi$
$311$	8.01305	−	4.62634i	0.454378	−	0.262335i	0.709678	+	0.704527i	$0.248841\pi$
$312$	−2.16262	+	3.18916i	−0.122434	+	0.180551i
$313$	−0.408129	+	0.706900i	−0.0230688	+	0.0399563i	−0.877329	−	0.479889i	$-0.840677\pi$
$313$	−0.408129	+	0.706900i	−0.0230688	+	0.0399563i	0.854261	+	0.519845i	$0.174010\pi$
$314$	−14.1317			−0.797501
$315$	−8.72908	+	32.9985i	−0.491828	+	1.85925i
$316$		−	9.79735i		−	0.551144i
$317$	−7.19272	−	4.15272i	−0.403983	−	0.233240i	0.284218	−	0.958760i	$-0.408266\pi$
$317$	−7.19272	−	4.15272i	−0.403983	−	0.233240i	−0.688201	+	0.725520i	$0.741599\pi$
$318$	2.40459	−	3.54598i	0.134843	−	0.198849i
$319$	0.759388	+	14.9885i	0.0425175	+	0.839195i
$320$	−3.72427	−	2.15021i	−0.208193	−	0.120200i
$321$	5.48304	−	2.65748i	0.306033	−	0.148326i
$322$	−4.17404	+	1.81203i	−0.232610	+	0.100980i
$323$			6.78761i			0.377673i
$324$	8.62637	+	2.56627i	0.479243	+	0.142570i
$325$	25.9972	−	15.0095i	1.44206	−	0.832575i
$326$	−8.63677	−	14.9593i	−0.478346	−	0.828520i
$327$	4.11569	+	0.298036i	0.227598	+	0.0164814i
$328$	−10.0223			−0.553388
$329$	7.97699	+	5.90987i	0.439785	+	0.325821i
$330$	−0.535217	+	24.6982i	−0.0294627	+	1.35959i
$331$	−11.4714	+	19.8690i	−0.630523	+	1.09210i	0.356922	+	0.934134i	$0.383826\pi$
$331$	−11.4714	+	19.8690i	−0.630523	+	1.09210i	−0.987445	+	0.157963i	$0.949507\pi$
$332$	8.82916	+	15.2926i	0.484563	+	0.839288i
$333$	19.9894	+	2.91031i	1.09541	+	0.159484i
$334$	7.17787	−	12.4324i	0.392756	−	0.680273i
$335$			17.9409i			0.980215i
$336$	4.32438	−	1.51648i	0.235915	−	0.0827305i
$337$		−	33.7202i		−	1.83686i	−0.395587	−	0.918429i	$-0.629459\pi$
$337$		−	33.7202i		−	1.83686i	0.395587	−	0.918429i	$-0.370541\pi$
$338$	4.02539	−	6.97218i	0.218952	−	0.379237i
$339$	10.1303	−	14.9389i	0.550202	−	0.811369i
$340$	16.2097	−	9.35866i	0.879093	−	0.507545i
$341$	−10.1995	+	6.59844i	−0.552333	+	0.357326i
$342$	−3.67239	−	2.89857i	−0.198580	−	0.156737i
$343$	−17.4471	−	6.21274i	−0.942056	−	0.335456i
$344$		−	4.66108i		−	0.251309i
$345$	0.925252	−	12.7772i	0.0498139	−	0.687900i
$346$	8.69404	+	15.0585i	0.467395	+	0.809551i
$347$	3.83938	+	6.65000i	0.206109	+	0.356991i	0.950485	−	0.310769i	$-0.100587\pi$
$347$	3.83938	+	6.65000i	0.206109	+	0.356991i	−0.744377	+	0.667760i	$0.767253\pi$
$348$	−0.566068	+	7.81706i	−0.0303444	+	0.419038i
$349$		−	3.88135i		−	0.207764i	−0.994590	−	0.103882i	$-0.966874\pi$
$349$		−	3.88135i		−	0.207764i	0.994590	−	0.103882i	$-0.0331265\pi$
$350$	−35.4688	−	4.06212i	−1.89589	−	0.217130i
$351$	11.2890	+	2.48731i	0.602564	+	0.132763i
$352$	2.78469	−	1.80152i	0.148425	−	0.0960216i
$353$	2.97893	−	1.71988i	0.158552	−	0.0915402i	−0.418625	−	0.908159i	$-0.637488\pi$
$353$	2.97893	−	1.71988i	0.158552	−	0.0915402i	0.577177	+	0.816619i	$0.304154\pi$
$354$	3.58787	−	5.29094i	0.190693	−	0.281210i
$355$	15.2192	−	26.3605i	0.807752	−	1.39907i
$356$			12.4989i			0.662441i
$357$	−3.69473	+	19.6002i	−0.195546	+	1.03735i
$358$		−	14.5839i		−	0.770785i
$359$	−11.0163	+	19.0808i	−0.581419	+	1.00705i	0.413893	+	0.910326i	$0.364169\pi$
$359$	−11.0163	+	19.0808i	−0.581419	+	1.00705i	−0.995312	+	0.0967211i	$0.969165\pi$
$360$	−1.85873	+	12.7666i	−0.0979635	+	0.672861i
$361$	−8.28399	−	14.3483i	−0.435999	−	0.755173i
$362$	−11.9250	+	20.6547i	−0.626763	+	1.08559i
$363$	−16.7689	−	9.04460i	−0.880138	−	0.474719i
$364$	5.39915	−	2.34387i	0.282992	−	0.122852i
$365$	−63.0762			−3.30156
$366$	−8.02406	−	0.581058i	−0.419424	−	0.0303724i
$367$	5.41730	+	9.38303i	0.282781	+	0.489790i	0.972069	−	0.234697i	$-0.0754099\pi$
$367$	5.41730	+	9.38303i	0.282781	+	0.489790i	−0.689288	+	0.724487i	$0.742077\pi$
$368$	−1.48946	+	0.859942i	−0.0776437	+	0.0448276i
$369$	11.1251	+	27.9329i	0.579150	+	1.45413i
$370$			28.9564i			1.50537i
$371$	−6.00324	+	2.60612i	−0.311673	+	0.135303i
$372$	−5.70879	+	2.76690i	−0.295987	+	0.143457i
$373$	−5.25214	−	3.03232i	−0.271945	−	0.157008i	0.357826	−	0.933788i	$-0.383518\pi$
$373$	−5.25214	−	3.03232i	−0.271945	−	0.157008i	−0.629771	+	0.776781i	$0.716851\pi$
$374$	0.730430	+	14.4169i	0.0377696	+	0.745482i
$375$	35.5069	−	52.3611i	1.83357	−	2.70391i
$376$	3.24960	+	1.87616i	0.167585	+	0.0967553i
$377$			10.0667i			0.518461i
$378$	−9.02677	−	10.3691i	−0.464287	−	0.533327i
$379$	−1.95715			−0.100532			−0.0502659	−	0.998736i	$-0.516007\pi$
$379$	−1.95715			−0.100532			−0.0502659	+	0.998736i	$0.516007\pi$
$380$	3.35323	−	5.80797i	0.172017	−	0.297943i
$381$	2.23509	−	3.29602i	0.114507	−	0.168860i
$382$	−1.01941	+	0.588558i	−0.0521576	+	0.0301132i
$383$	−9.20867	−	5.31663i	−0.470541	−	0.271667i	0.245925	−	0.969289i	$-0.420908\pi$
$383$	−9.20867	−	5.31663i	−0.470541	−	0.271667i	−0.716466	+	0.697622i	$0.754242\pi$
$384$	1.55863	−	0.755426i	0.0795386	−	0.0385502i
$385$	20.9009	−	31.4191i	1.06521	−	1.60126i
$386$			1.93909i			0.0986969i
$387$	−12.9908	+	5.17397i	−0.660360	+	0.263008i
$388$	0.270859	+	0.469142i	0.0137508	+	0.0238171i
$389$	17.3287	−	10.0047i	0.878601	−	0.507261i	0.00840444	−	0.999965i	$-0.497325\pi$
$389$	17.3287	−	10.0047i	0.878601	−	0.507261i	0.870197	+	0.492704i	$0.163991\pi$
$390$	−1.19682	+	16.5274i	−0.0606033	+	0.836896i
$391$		−	7.48571i		−	0.378568i
$392$	−6.81875	−	1.58262i	−0.344399	−	0.0799342i
$393$	12.1217	−	5.87507i	0.611460	−	0.296358i
$394$	−0.522149	+	0.904388i	−0.0263055	+	0.0455624i
$395$	−21.0663	−	36.4880i	−1.05996	−	1.83591i
$396$	−8.11211	−	5.76140i	−0.407649	−	0.289521i
$397$	8.09039	−	14.0130i	0.406045	−	0.703291i	−0.588397	−	0.808572i	$-0.700241\pi$
$397$	8.09039	−	14.0130i	0.406045	−	0.703291i	0.994443	+	0.105281i	$0.0335742\pi$
$398$	24.2522			1.21565
$399$	2.36493	+	6.74385i	0.118395	+	0.337615i
$400$	−13.4936			−0.674679
$401$	20.3865	+	11.7702i	1.01805	+	0.587774i	0.913540	−	0.406750i	$-0.133338\pi$
$401$	20.3865	+	11.7702i	1.01805	+	0.587774i	0.104514	+	0.994523i	$0.466671\pi$
$402$	−5.98055	−	4.05551i	−0.298283	−	0.202270i
$403$	−7.05667	+	4.07417i	−0.351518	+	0.202949i
$404$	−3.92520	+	6.79864i	−0.195286	+	0.338245i
$405$	37.6449	−	8.99103i	1.87059	−	0.446768i
$406$	7.12685	−	9.61964i	0.353699	−	0.477415i
$407$	−19.8804	−	10.1731i	−0.985436	−	0.504264i
$408$	−0.544482	+	7.51897i	−0.0269559	+	0.372245i
$409$	−29.6972	+	17.1457i	−1.46843	+	0.847800i	−0.999374	−	0.0353664i	$-0.988740\pi$
$409$	−29.6972	+	17.1457i	−1.46843	+	0.847800i	−0.469059	+	0.883167i	$0.655407\pi$
$410$	−37.3257	+	21.5500i	−1.84338	+	1.06428i
$411$	−15.9722	−	1.15662i	−0.787851	−	0.0570518i
$412$	−9.69742			−0.477758
$413$	−8.95740	+	3.88857i	−0.440765	+	0.191344i
$414$	4.05009	+	3.19669i	0.199051	+	0.157109i
$415$	65.7643	+	37.9691i	3.22824	+	1.86383i
$416$	1.92663	−	1.11234i	0.0944609	−	0.0545370i
$417$	−17.4849	+	25.7846i	−0.856240	+	1.26268i
$418$	2.80947	+	4.34271i	0.137415	+	0.212409i
$419$			23.8983i			1.16751i	0.811930	+	0.583755i	$0.198417\pi$
$419$			23.8983i			1.16751i	−0.811930	+	0.583755i	$0.801583\pi$
$420$	12.8444	−	14.9461i	0.626744	−	0.729294i
$421$	21.3778			1.04189			0.520944	−	0.853591i	$-0.325580\pi$
$421$	21.3778			1.04189			0.520944	+	0.853591i	$0.325580\pi$
$422$	−17.2044	−	9.93294i	−0.837495	−	0.483528i
$423$	1.62182	−	11.1395i	0.0788558	−	0.541620i
$424$	−2.14220	+	1.23680i	−0.104034	+	0.0600643i
$425$	29.3650	−	50.8617i	1.42441	−	2.46716i
$426$	5.34692	+	11.0320i	0.259059	+	0.534503i
$427$	9.87437	+	7.31557i	0.477854	+	0.354025i
$428$	−3.51786			−0.170042
$429$	−10.9266	−	6.62820i	−0.527542	−	0.320013i
$430$	−10.0223	−	17.3591i	−0.483318	−	0.837131i
$431$	1.14236	+	1.97863i	0.0550256	+	0.0953071i	0.892226	−	0.451589i	$-0.149143\pi$
$431$	1.14236	+	1.97863i	0.0550256	+	0.0953071i	−0.837201	+	0.546896i	$0.815809\pi$
$432$	−3.83557	−	3.50548i	−0.184539	−	0.168658i
$433$	−10.0236			−0.481702			−0.240851	−	0.970562i	$-0.577427\pi$
$433$	−10.0236			−0.481702			−0.240851	+	0.970562i	$0.577427\pi$
$434$	9.62765	+	1.10262i	0.462142	+	0.0529276i
$435$	14.7001	+	30.3300i	0.704816	+	1.45421i
$436$	−2.06323	−	1.19121i	−0.0988110	−	0.0570486i
$437$	−1.34107	−	2.32281i	−0.0641523	−	0.111115i
$438$	14.2583	−	21.0263i	0.681286	−	1.00468i
$439$	−5.95435	−	3.43774i	−0.284185	−	0.164075i	0.351131	−	0.936326i	$-0.385797\pi$
$439$	−5.95435	−	3.43774i	−0.284185	−	0.164075i	−0.635317	+	0.772252i	$0.719130\pi$
$440$	6.49729	−	12.6970i	0.309746	−	0.605307i
$441$	3.15818	+	20.7612i	0.150390	+	0.988627i
$442$			9.68282i			0.460565i
$443$	−18.4525	−	10.6536i	−0.876706	−	0.506166i	−0.00713504	−	0.999975i	$-0.502271\pi$
$443$	−18.4525	−	10.6536i	−0.876706	−	0.506166i	−0.869571	+	0.493808i	$0.835605\pi$
$444$	−9.65254	−	6.54554i	−0.458089	−	0.310638i
$445$	26.8753	+	46.5493i	1.27401	+	2.20665i
$446$	−8.55750	+	14.8220i	−0.405210	+	0.701844i
$447$	−7.71335	+	3.73845i	−0.364829	+	0.176823i
$448$	−2.62857	−	0.301041i	−0.124188	−	0.0142229i
$449$			11.3648i			0.536340i	0.963372	+	0.268170i	$0.0864189\pi$
$449$			11.3648i			0.536340i	−0.963372	+	0.268170i	$0.913581\pi$
$450$	14.9784	+	37.6077i	0.706087	+	1.77284i
$451$	−1.68195	−	33.1976i	−0.0791997	−	1.56321i
$452$	−9.02487	+	5.21051i	−0.424494	+	0.245082i
$453$	13.3924	+	0.969805i	0.629231	+	0.0455654i
$454$	19.1190			0.897298
$455$	15.0681	−	20.3385i	0.706402	−	0.953483i
$456$	1.17808	+	2.43068i	0.0551687	+	0.113827i
$457$	0.879305	+	0.507667i	0.0411321	+	0.0237476i	0.520425	−	0.853907i	$-0.325774\pi$
$457$	0.879305	+	0.507667i	0.0411321	+	0.0237476i	−0.479293	+	0.877655i	$0.659107\pi$
$458$	−6.76018	−	11.7090i	−0.315883	−	0.547125i
$459$	21.5604	−	6.82882i	1.00635	−	0.318742i
$460$	−3.69811	+	6.40531i	−0.172425	+	0.298649i
$461$	29.8887			1.39206			0.696029	−	0.718014i	$-0.254949\pi$
$461$	29.8887			1.39206			0.696029	+	0.718014i	$0.254949\pi$
$462$	5.74886	+	14.0695i	0.267461	+	0.654572i
$463$	−8.61123			−0.400198			−0.200099	−	0.979776i	$-0.564126\pi$
$463$	−8.61123			−0.400198			−0.200099	+	0.979776i	$0.564126\pi$
$464$	2.26250	−	3.91876i	0.105034	−	0.181924i
$465$	−15.3117	+	22.5798i	−0.710062	+	1.04711i
$466$	3.87397	+	6.70992i	0.179458	+	0.310831i
$467$	31.5910	+	18.2391i	1.46186	+	0.844003i	0.999097	−	0.0424805i	$-0.0135260\pi$
$467$	31.5910	+	18.2391i	1.46186	+	0.844003i	0.462759	+	0.886484i	$0.346859\pi$
$468$	−5.23882	−	4.13494i	−0.242164	−	0.191138i
$469$	4.39540	+	10.1249i	0.202961	+	0.467524i
$470$	16.1365			0.744321
$471$	1.76785	−	24.4130i	0.0814584	−	1.12489i
$472$	−3.19636	+	1.84542i	−0.147124	+	0.0849423i
$473$	15.4392	−	0.782225i	0.709897	−	0.0359667i
$474$	16.9252	+	1.22563i	0.777400	+	0.0562950i
$475$		−	21.0431i		−	0.965525i
$476$	6.85508	−	9.25281i	0.314202	−	0.424102i
$477$	5.82498	+	4.59759i	0.266707	+	0.210509i
$478$	−5.97761	+	10.3535i	−0.273410	+	0.473559i
$479$	2.94400	+	5.09916i	0.134515	+	0.232987i	0.925412	−	0.378962i	$-0.123719\pi$
$479$	2.94400	+	5.09916i	0.134515	+	0.232987i	−0.790897	+	0.611949i	$0.790386\pi$
$480$	4.18044	−	6.16479i	0.190810	−	0.281383i
$481$	−12.9728	−	7.48983i	−0.591507	−	0.341507i
$482$			28.2502i			1.28676i
$483$	−2.60816	−	7.43744i	−0.118676	−	0.338415i
$484$	6.43466	+	8.92161i	0.292484	+	0.405528i
$485$	2.01750	+	1.16481i	0.0916101	+	0.0528911i
$486$	−5.51243	+	14.5813i	−0.250049	+	0.661419i
$487$	13.0643	+	22.6280i	0.592000	+	1.02537i	0.993963	+	0.109718i	$0.0349948\pi$
$487$	13.0643	+	22.6280i	0.592000	+	1.02537i	−0.401963	+	0.915656i	$0.631672\pi$
$488$	4.02253	+	2.32241i	0.182092	+	0.105131i
$489$	26.9231	−	13.0489i	1.21750	−	0.590090i
$490$	−28.7978	+	8.76764i	−1.30095	+	0.396081i
$491$	3.67030			0.165639			0.0828193	−	0.996565i	$-0.473608\pi$
$491$	3.67030			0.165639			0.0828193	+	0.996565i	$0.473608\pi$
$492$	1.25377	−	17.3138i	0.0565242	−	0.780565i
$493$	9.84741	+	17.0562i	0.443505	+	0.768173i
$494$	1.73469	+	3.00457i	0.0780474	+	0.135182i
$495$	−42.5999	−	4.01430i	−1.91472	−	0.180429i
$496$	3.66270			0.164460
$497$	2.13078	−	18.6051i	0.0955784	−	0.834551i
$498$	−27.5228	+	13.3396i	−1.23333	+	0.597760i
$499$	0.575545	−	0.996873i	0.0257649	−	0.0446262i	−0.852855	−	0.522147i	$-0.825131\pi$
$499$	0.575545	−	0.996873i	0.0257649	−	0.0446262i	0.878620	+	0.477521i	$0.158465\pi$
$500$	−31.6323	+	18.2629i	−1.41464	+	0.816744i
$501$	20.5794	+	13.9552i	0.919421	+	0.623474i
$502$	1.55822	+	0.899639i	0.0695468	+	0.0401528i
$503$	10.1687			0.453401			0.226701	−	0.973965i	$-0.427206\pi$
$503$	10.1687			0.453401			0.226701	+	0.973965i	$0.427206\pi$
$504$	2.07878	+	7.66020i	0.0925963	+	0.341212i
$505$			33.7599i			1.50230i
$506$	−3.09842	−	4.78935i	−0.137741	−	0.212913i
$507$	11.5411	+	7.82618i	0.512557	+	0.347573i
$508$	−1.99119	+	1.14962i	−0.0883449	+	0.0510059i
$509$	0.280452	+	0.161919i	0.0124308	+	0.00717692i	0.506203	−	0.862415i	$-0.331049\pi$
$509$	0.280452	+	0.161919i	0.0124308	+	0.00717692i	−0.493772	+	0.869592i	$0.664382\pi$
$510$	14.1396	+	29.1734i	0.626110	+	1.29182i
$511$	−35.5969	+	15.4533i	−1.57471	+	0.683612i
$512$	−1.00000			−0.0441942
$513$	5.46677	−	5.98155i	0.241364	−	0.264092i
$514$	3.30536	−	1.90835i	0.145793	−	0.0841738i
$515$	−36.1158	+	20.8515i	−1.59145	+	0.918825i
$516$	8.05214	+	0.583091i	0.354476	+	0.0256692i
$517$	−5.66918	+	11.0787i	−0.249330	+	0.487243i
$518$	7.09413	+	16.3415i	0.311698	+	0.718002i
$519$	−27.1016	+	13.1354i	−1.18963	+	0.576580i
$520$	4.78353	−	8.28532i	0.209772	−	0.363335i
$521$	30.0787	−	17.3659i	1.31777	−	0.760815i	0.334400	−	0.942431i	$-0.391466\pi$
$521$	30.0787	−	17.3659i	1.31777	−	0.760815i	0.983369	+	0.181616i	$0.0581329\pi$
$522$	−13.4334	−	1.95580i	−0.587963	−	0.0856029i
$523$	−0.209525	−	0.120969i	−0.00916189	−	0.00528962i	0.495412	−	0.868658i	$-0.335017\pi$
$523$	−0.209525	−	0.120969i	−0.00916189	−	0.00528962i	−0.504574	+	0.863368i	$0.668350\pi$
$524$	−7.77716			−0.339747
$525$	11.4545	−	60.7651i	0.499915	−	2.65201i
$526$	15.6276			0.681394
$527$	−7.97085	+	13.8059i	−0.347216	+	0.601395i
$528$	2.76382	+	5.03600i	0.120280	+	0.219164i
$529$	−10.0210	−	17.3569i	−0.435696	−	0.754647i
$530$	−5.31875	+	9.21234i	−0.231032	+	0.400159i
$531$	8.69141	+	6.86003i	0.377175	+	0.297700i
$532$	0.469472	−	4.09924i	0.0203542	−	0.177724i
$533$		−	22.2964i		−	0.965765i
$534$	−21.5922	−	1.56359i	−0.934387	−	0.0676631i
$535$	−13.1014	+	7.56412i	−0.566425	+	0.327025i
$536$	2.08595	+	3.61297i	0.0900992	+	0.156056i
$537$	25.1941	+	1.82442i	1.08721	+	0.0787295i
$538$		−	11.7212i		−	0.505337i
$539$	4.09789	−	22.8519i	0.176509	−	0.984299i
$540$	−21.8222	−	4.80808i	−0.939078	−	0.206907i
$541$	26.1669	+	15.1074i	1.12500	+	0.649520i	0.942673	−	0.333718i	$-0.108303\pi$
$541$	26.1669	+	15.1074i	1.12500	+	0.649520i	0.182328	+	0.983238i	$0.441637\pi$
$542$	9.87548	−	5.70161i	0.424188	−	0.244905i
$543$	−34.1897	−	23.1846i	−1.46722	−	0.994946i
$544$	2.17622	−	3.76933i	0.0933048	−	0.161609i
$545$	−10.2454			−0.438864
$546$	3.37368	+	9.62039i	0.144380	+	0.411715i
$547$		−	6.15235i		−	0.263056i	−0.991312	−	0.131528i	$-0.958012\pi$
$547$		−	6.15235i		−	0.263056i	0.991312	−	0.131528i	$-0.0419883\pi$
$548$	8.00701	+	4.62285i	0.342043	+	0.197478i
$549$	2.00759	−	13.7891i	0.0856817	−	0.588504i
$550$	−2.26450	−	44.6958i	−0.0965585	−	1.90583i
$551$	6.11129	+	3.52835i	0.260350	+	0.150313i
$552$	−1.29925	−	2.68067i	−0.0552995	−	0.114097i
$553$	−20.8281	−	15.4308i	−0.885699	−	0.656183i
$554$		−	23.0143i		−	0.977785i
$555$	−50.0229	−	3.62238i	−2.12335	−	0.153762i
$556$	15.5770	−	8.99336i	0.660610	−	0.381403i
$557$	−2.94874	−	5.10737i	−0.124942	−	0.216406i	0.796768	−	0.604285i	$-0.206541\pi$
$557$	−2.94874	−	5.10737i	−0.124942	−	0.216406i	−0.921710	+	0.387879i	$0.873208\pi$
$558$	−4.06573	−	10.2082i	−0.172116	−	0.432149i
$559$	10.3694			0.438580
$560$	−10.4368	+	4.53081i	−0.441035	+	0.191462i
$561$	−24.9970	−	0.541692i	−1.05538	−	0.0228703i
$562$	5.40113	−	9.35504i	0.227833	−	0.394619i
$563$	11.6358	+	20.1537i	0.490389	+	0.849378i	0.999939	−	0.0110627i	$-0.00352143\pi$
$563$	11.6358	+	20.1537i	0.490389	+	0.849378i	−0.509550	+	0.860441i	$0.670188\pi$
$564$	−3.64763	+	5.37906i	−0.153593	+	0.226499i
$565$	−22.4074	+	38.8107i	−0.942685	+	1.63278i
$566$		−	15.2501i		−	0.641011i
$567$	19.0421	−	14.2968i	0.799692	−	0.600411i
$568$		−	7.07802i		−	0.296987i
$569$	−19.2703	+	33.3771i	−0.807853	+	1.39924i	0.106496	+	0.994313i	$0.466037\pi$
$569$	−19.2703	+	33.3771i	−0.807853	+	1.39924i	−0.914348	+	0.404929i	$0.867296\pi$
$570$	9.61395	+	6.51937i	0.402684	+	0.273066i
$571$	11.4730	−	6.62396i	0.480131	−	0.277204i	−0.240340	−	0.970689i	$-0.577259\pi$
$571$	11.4730	−	6.62396i	0.480131	−	0.277204i	0.720471	+	0.693485i	$0.243926\pi$
$572$	4.00782	+	6.19506i	0.167575	+	0.259028i
$573$	−0.889223	−	1.83469i	−0.0371478	−	0.0766452i
$574$	−15.7850	+	21.3062i	−0.658855	+	0.889306i
$575$			23.2074i			0.967815i
$576$	1.11004	+	2.78708i	0.0462515	+	0.116128i
$577$	−11.6105	−	20.1099i	−0.483351	−	0.837188i	0.516466	−	0.856307i	$-0.327247\pi$
$577$	−11.6105	−	20.1099i	−0.483351	−	0.837188i	−0.999817	+	0.0191193i	$0.993914\pi$
$578$	0.971897	+	1.68337i	0.0404256	+	0.0700191i
$579$	−3.34983	−	0.242576i	−0.139214	−	0.0100811i
$580$		−	19.4594i		−	0.808007i
$581$	46.4161	+	5.31589i	1.92567	+	0.220540i
$582$	−0.844339	+	0.409228i	−0.0349990	+	0.0169630i
$583$	−4.45625	−	6.88821i	−0.184559	−	0.285280i
$584$	−12.7024	+	7.33373i	−0.525629	+	0.303472i
$585$	−28.4018	−	4.13508i	−1.17427	−	0.170964i
$586$	5.30185	−	9.18307i	0.219017	−	0.379349i
$587$		−	26.3040i		−	1.08568i	−0.839836	−	0.542841i	$-0.817349\pi$
$587$		−	26.3040i		−	1.08568i	0.839836	−	0.542841i	$-0.182651\pi$
$588$	3.58702	−	11.5816i	0.147926	−	0.477617i
$589$			5.71195i			0.235357i
$590$	−7.93607	+	13.7457i	−0.326723	+	0.565900i
$591$	−1.49704	−	1.01516i	−0.0615798	−	0.0417582i
$592$	3.36669	+	5.83129i	0.138370	+	0.239664i
$593$	15.9757	−	27.6707i	0.656043	−	1.13630i	−0.325588	−	0.945512i	$-0.605562\pi$
$593$	15.9757	−	27.6707i	0.656043	−	1.13630i	0.981631	−	0.190788i	$-0.0611044\pi$
$594$	10.9678	−	13.2931i	0.450014	−	0.545424i
$595$	5.63469	−	49.1998i	0.231000	−	2.01699i
$596$	4.94880			0.202711
$597$	−3.03390	+	41.8963i	−0.124169	+	1.71470i
$598$	−1.91310	−	3.31359i	−0.0782325	−	0.135503i
$599$	−23.9985	+	13.8555i	−0.980552	+	0.566122i	−0.902437	−	0.430822i	$-0.858224\pi$
$599$	−23.9985	+	13.8555i	−0.980552	+	0.566122i	−0.0781155	+	0.996944i	$0.524890\pi$
$600$	1.68802	−	23.3105i	0.0689131	−	0.951648i
$601$			4.24301i			0.173076i	0.996249	+	0.0865380i	$0.0275804\pi$
$601$			4.24301i			0.173076i	−0.996249	+	0.0865380i	$0.972420\pi$
$602$	−9.90893	−	7.34117i	−0.403858	−	0.299204i
$603$	7.75415	−	9.82423i	0.315773	−	0.400074i
$604$	−6.71375	−	3.87618i	−0.273179	−	0.157720i
$605$	43.1477	+	19.3906i	1.75420	+	0.788342i
$606$	−11.2538	−	7.63138i	−0.457154	−	0.310004i
$607$	8.07423	+	4.66166i	0.327723	+	0.189211i	0.654830	−	0.755776i	$-0.272740\pi$
$607$	8.07423	+	4.66166i	0.327723	+	0.189211i	−0.327107	+	0.944987i	$0.606074\pi$
$608$		−	1.55949i		−	0.0632458i
$609$	15.7266	+	13.5152i	0.637275	+	0.547664i
$610$	19.9747			0.808751
$611$	−4.17385	+	7.22932i	−0.168856	+	0.292467i
$612$	−12.9211	−	1.88122i	−0.522305	−	0.0760436i
$613$	−34.3925	+	19.8565i	−1.38910	+	0.801996i	−0.993214	−	0.116304i	$-0.962895\pi$
$613$	−34.3925	+	19.8565i	−1.38910	+	0.801996i	−0.395885	+	0.918300i	$0.629562\pi$
$614$	−5.58170	−	3.22259i	−0.225259	−	0.130053i
$615$	−32.5588	−	67.1770i	−1.31290	−	2.70884i
$616$	0.556035	−	8.75733i	0.0224033	−	0.352843i
$617$		−	16.5103i		−	0.664679i	−0.943160	−	0.332339i	$-0.892162\pi$
$617$		−	16.5103i		−	0.664679i	0.943160	−	0.332339i	$-0.107838\pi$
$618$	1.21313	−	16.7526i	0.0487991	−	0.673887i
$619$	7.63994	+	13.2328i	0.307075	+	0.531870i	0.977721	−	0.209908i	$-0.0673163\pi$
$619$	7.63994	+	13.2328i	0.307075	+	0.531870i	−0.670646	+	0.741778i	$0.733983\pi$
$620$	13.6409	−	7.87556i	0.547830	−	0.316290i
$621$	−6.02902	+	6.59674i	−0.241936	+	0.264718i
$622$		−	9.25267i		−	0.370998i
$623$	26.5713	+	19.6857i	1.06456	+	0.788692i
$624$	1.68058	+	3.46746i	0.0672772	+	0.138810i
$625$	−44.8043	+	77.6034i	−1.79217	+	3.10413i
$626$	0.408129	+	0.706900i	0.0163121	+	0.0282534i
$627$	−7.85360	+	4.31017i	−0.313643	+	0.172131i
$628$	−7.06587	+	12.2385i	−0.281959	+	0.488367i
$629$	−29.3067			−1.16854
$630$	24.2130	+	24.0588i	0.964668	+	0.958527i
$631$	31.1076			1.23837			0.619187	−	0.785244i	$-0.287462\pi$
$631$	31.1076			1.23837			0.619187	+	0.785244i	$0.287462\pi$
$632$	−8.48475	−	4.89868i	−0.337505	−	0.194859i
$633$	19.3117	−	28.4784i	0.767569	−	1.13192i
$634$	−7.19272	+	4.15272i	−0.285659	+	0.164925i
$635$	−4.94382	+	8.56295i	−0.196190	+	0.339810i
$636$	−1.86862	−	3.85543i	−0.0740956	−	0.152878i
$637$	3.52082	−	15.1696i	0.139500	−	0.601040i
$638$	13.3601	+	6.83660i	0.528932	+	0.270664i
$639$	−19.7270	+	7.85686i	−0.780389	+	0.310813i
$640$	−3.72427	+	2.15021i	−0.147215	+	0.0849944i
$641$	1.86879	−	1.07895i	0.0738129	−	0.0426159i	−0.462639	−	0.886547i	$-0.653098\pi$
$641$	1.86879	−	1.07895i	0.0738129	−	0.0426159i	0.536452	+	0.843931i	$0.319764\pi$
$642$	0.440076	−	6.07719i	0.0173684	−	0.239848i
$643$	36.5368			1.44087			0.720435	−	0.693522i	$-0.243942\pi$
$643$	36.5368			1.44087			0.720435	+	0.693522i	$0.243942\pi$
$644$	−0.517756	+	4.52084i	−0.0204025	+	0.178146i
$645$	31.2421	−	15.1422i	1.23016	−	0.596223i
$646$	5.87824	+	3.39381i	0.231276	+	0.133528i
$647$	7.86424	−	4.54042i	0.309175	−	0.178502i	−0.337382	−	0.941368i	$-0.609541\pi$
$647$	7.86424	−	4.54042i	0.309175	−	0.178502i	0.646557	+	0.762865i	$0.276208\pi$
$648$	6.53564	−	6.18752i	0.256744	−	0.243069i
$649$	−6.64914	−	10.2778i	−0.261001	−	0.403441i
$650$		−	30.0189i		−	1.17744i
$651$	−3.10921	+	16.4941i	−0.121860	+	0.646454i
$652$	−17.2735			−0.676484
$653$	−11.3768	−	6.56840i	−0.445209	−	0.257041i	0.260596	−	0.965448i	$-0.416081\pi$
$653$	−11.3768	−	6.56840i	−0.445209	−	0.257041i	−0.705805	+	0.708407i	$0.749414\pi$
$654$	2.31595	−	3.41528i	0.0905609	−	0.133548i
$655$	−28.9642	+	16.7225i	−1.13173	+	0.653403i
$656$	−5.01114	+	8.67956i	−0.195652	+	0.338880i
$657$	34.5398	+	27.2619i	1.34753	+	1.06359i
$658$	9.10659	−	3.95334i	0.355012	−	0.154117i
$659$	40.4232			1.57466			0.787332	−	0.616530i	$-0.211462\pi$
$659$	40.4232			1.57466			0.787332	+	0.616530i	$0.211462\pi$
$660$	21.1217	+	12.8126i	0.822160	+	0.498730i
$661$	0.305691	+	0.529473i	0.0118900	+	0.0205941i	0.871909	−	0.489668i	$-0.162882\pi$
$661$	0.305691	+	0.529473i	0.0118900	+	0.0205941i	−0.860019	+	0.510262i	$0.829549\pi$
$662$	11.4714	+	19.8690i	0.445847	+	0.772230i
$663$	−16.7273	−	1.21130i	−0.649636	−	0.0470430i
$664$	17.6583			0.685276
$665$	−7.06577	−	16.2761i	−0.273999	−	0.631161i
$666$	12.5151	−	15.8562i	0.484951	−	0.614415i
$667$	−6.73982	−	3.89124i	−0.260967	−	0.150669i
$668$	−7.17787	−	12.4324i	−0.277720	−	0.481025i
$669$	−24.5349	−	16.6375i	−0.948575	−	0.643244i
$670$	15.5373	+	8.97044i	0.600257	+	0.346558i
$671$	−7.01764	+	13.7139i	−0.270913	+	0.529419i
$672$	0.848886	−	4.50326i	0.0327465	−	0.173717i
$673$		−	24.7930i		−	0.955700i	−0.878441	−	0.477850i	$-0.841416\pi$
$673$		−	24.7930i		−	0.955700i	0.878441	−	0.477850i	$-0.158584\pi$
$674$	−29.2026	−	16.8601i	−1.12484	−	0.649427i
$675$	−66.8420	+	21.1709i	−2.57275	+	0.814868i
$676$	−4.02539	−	6.97218i	−0.154823	−	0.268161i
$677$	13.3012	−	23.0383i	0.511206	−	0.885435i	−0.488709	−	0.872447i	$-0.662532\pi$
$677$	13.3012	−	23.0383i	0.511206	−	0.885435i	0.999916	−	0.0129885i	$-0.00413448\pi$
$678$	−7.87231	−	16.2425i	−0.302334	−	0.623791i
$679$	1.42394	+	0.163080i	0.0546459	+	0.00625842i
$680$		−	18.7173i		−	0.717777i
$681$	−2.39175	+	33.0286i	−0.0916519	+	1.26566i
$682$	0.614676	+	12.1322i	0.0235371	+	0.464567i
$683$	20.7868	−	12.0013i	0.795386	−	0.459216i	−0.0464694	−	0.998920i	$-0.514797\pi$
$683$	20.7868	−	12.0013i	0.795386	−	0.459216i	0.841855	+	0.539704i	$0.181464\pi$
$684$	−4.34643	+	1.73109i	−0.166190	+	0.0661901i
$685$	39.7604			1.51917
$686$	−14.1039	+	12.0033i	−0.538491	+	0.458287i
$687$	21.0733	−	10.2136i	0.803995	−	0.389674i
$688$	−4.03661	−	2.33054i	−0.153894	−	0.0888510i
$689$	−2.75149	−	4.76571i	−0.104823	−	0.181559i
$690$	−10.6027	−	7.18988i	−0.403639	−	0.273714i
$691$	1.78912	−	3.09884i	0.0680612	−	0.117886i	−0.829987	−	0.557783i	$-0.811652\pi$
$691$	1.78912	−	3.09884i	0.0680612	−	0.117886i	0.898048	+	0.439898i	$0.144985\pi$
$692$	17.3881			0.660996
$693$	−25.0246	+	8.17125i	−0.950606	+	0.310400i
$694$	7.67876			0.291482
$695$	38.6752	−	66.9874i	1.46703	−	2.54098i
$696$	6.48674	+	4.39876i	0.245879	+	0.166735i
$697$	−21.8107	−	37.7773i	−0.826141	−	1.43092i
$698$	−3.36135	−	1.94068i	−0.127229	−	0.0734557i
$699$	−12.0762	+	5.85299i	−0.456763	+	0.221381i
$700$	−21.2523	+	28.6858i	−0.803261	+	1.08422i
$701$	9.33214			0.352470			0.176235	−	0.984348i	$-0.443608\pi$
$701$	9.33214			0.352470			0.176235	+	0.984348i	$0.443608\pi$
$702$	7.79859	−	8.53293i	0.294339	−	0.322055i
$703$	−9.09385	+	5.25034i	−0.342981	+	0.198020i
$704$	−0.167821	−	3.31238i	−0.00632497	−	0.124840i
$705$	−2.01864	+	27.8762i	−0.0760265	+	1.04988i
$706$		−	3.43977i		−	0.129457i
$707$	8.27098	+	19.0523i	0.311062	+	0.716537i
$708$	−2.78815	−	5.75266i	−0.104785	−	0.216198i
$709$	8.01982	−	13.8907i	0.301191	−	0.521677i	−0.675215	−	0.737621i	$-0.735949\pi$
$709$	8.01982	−	13.8907i	0.301191	−	0.521677i	0.976406	+	0.215943i	$0.0692826\pi$
$710$	−15.2192	−	26.3605i	−0.571167	−	0.989290i
$711$	−4.23461	+	29.0854i	−0.158810	+	1.09079i
$712$	10.8244	+	6.24946i	0.405661	+	0.234208i
$713$		−	6.29942i		−	0.235915i
$714$	15.1269	+	12.9998i	0.566111	+	0.486507i
$715$	28.2469	+	14.4544i	1.05637	+	0.540564i
$716$	−12.6301	−	7.29196i	−0.472007	−	0.272514i
$717$	−17.1382	−	11.6217i	−0.640038	−	0.434020i
$718$	11.0163	+	19.0808i	0.411125	+	0.712090i
$719$	24.4747	+	14.1305i	0.912753	+	0.526978i	0.881316	−	0.472528i	$-0.156658\pi$
$719$	24.4747	+	14.1305i	0.912753	+	0.526978i	0.0314371	+	0.999506i	$0.489992\pi$
$720$	10.1269	+	7.99303i	0.377406	+	0.297883i
$721$	−15.2734	+	20.6156i	−0.568810	+	0.767766i
$722$	−16.5680			−0.616596
$723$	−48.8029	−	3.53404i	−1.81500	−	0.131432i
$724$	11.9250	+	20.6547i	0.443189	+	0.767625i
$725$	−30.5292	−	52.8781i	−1.13383	−	1.96384i
$726$	−16.2173	+	9.99997i	−0.601880	+	0.371134i
$727$	5.45714			0.202394			0.101197	−	0.994866i	$-0.467733\pi$
$727$	5.45714			0.202394			0.101197	+	0.994866i	$0.467733\pi$
$728$	0.669722	−	5.84773i	0.0248215	−	0.216731i
$729$	−24.4999	−	11.3470i	−0.907405	−	0.420258i
$730$	−31.5381	+	54.6256i	−1.16728	+	2.02178i
$731$	17.5691	−	10.1435i	0.649818	−	0.375173i
$732$	−4.51524	+	6.65851i	−0.166888	+	0.246106i
$733$	−23.3511	−	13.4818i	−0.862494	−	0.497961i	0.00235259	−	0.999997i	$-0.499251\pi$
$733$	−23.3511	−	13.4818i	−0.862494	−	0.497961i	−0.864847	+	0.502036i	$0.832584\pi$
$734$	10.8346			0.399912
$735$	−11.5438	−	50.8458i	−0.425799	−	1.87548i
$736$			1.71988i			0.0633958i
$737$	−11.6174	+	7.51577i	−0.427934	+	0.276847i
$738$	29.7532	+	4.33184i	1.09523	+	0.159457i
$739$	−28.7950	+	16.6248i	−1.05924	+	0.611553i	−0.925222	−	0.379426i	$-0.876121\pi$
$739$	−28.7950	+	16.6248i	−1.05924	+	0.611553i	−0.134018	+	0.990979i	$0.542788\pi$
$740$	25.0770	+	14.4782i	0.921847	+	0.532229i
$741$	−5.40748	+	2.62086i	−0.198649	+	0.0962796i
$742$	−0.744655	+	6.50202i	−0.0273372	+	0.238697i
$743$	6.13190			0.224958			0.112479	−	0.993654i	$-0.464121\pi$
$743$	6.13190			0.224958			0.112479	+	0.993654i	$0.464121\pi$
$744$	−0.458196	+	6.32741i	−0.0167983	+	0.231974i
$745$	18.4306	−	10.6409i	0.675247	−	0.389854i
$746$	−5.25214	+	3.03232i	−0.192294	+	0.111021i
$747$	−19.6014	−	49.2152i	−0.717177	−	1.80069i
$748$	12.8507	+	6.57590i	0.469866	+	0.240439i
$749$	−5.54060	+	7.47856i	−0.202449	+	0.273261i
$750$	−27.5926	−	56.9304i	−1.00754	−	2.07880i
$751$	4.62693	−	8.01408i	0.168839	−	0.292438i	−0.769173	−	0.639041i	$-0.779331\pi$
$751$	4.62693	−	8.01408i	0.168839	−	0.292438i	0.938012	+	0.346603i	$0.112665\pi$
$752$	3.24960	−	1.87616i	0.118501	−	0.0684163i
$753$	−1.74908	+	2.57932i	−0.0637400	+	0.0939958i
$754$	8.71801	+	5.03335i	0.317491	+	0.183304i
$755$	−33.3384			−1.21331
$756$	−13.4933	+	2.63288i	−0.490745	+	0.0957568i
$757$	−33.0544			−1.20138			−0.600691	−	0.799481i	$-0.705108\pi$
$757$	−33.0544			−1.20138			−0.600691	+	0.799481i	$0.705108\pi$
$758$	−0.978573	+	1.69494i	−0.0355434	+	0.0615629i
$759$	8.66134	−	4.75346i	0.314387	−	0.172540i
$760$	−3.35323	−	5.80797i	−0.121635	−	0.210677i
$761$	3.66311	−	6.34470i	0.132788	−	0.229995i	−0.791962	−	0.610570i	$-0.790940\pi$
$761$	3.66311	−	6.34470i	0.132788	−	0.229995i	0.924750	+	0.380575i	$0.124274\pi$
$762$	−1.73690	−	3.58365i	−0.0629212	−	0.129822i
$763$	−5.78196	+	2.51006i	−0.209321	+	0.0908701i
$764$			1.17712i			0.0425865i
$765$	−52.1667	+	20.7769i	−1.88609	+	0.751191i
$766$	−9.20867	+	5.31663i	−0.332723	+	0.192098i
$767$	−4.10547	−	7.11089i	−0.148240	−	0.256759i
$768$	0.125098	−	1.72753i	0.00451408	−	0.0623368i
$769$			44.3335i			1.59871i	0.600861	+	0.799353i	$0.294824\pi$
$769$			44.3335i			1.59871i	−0.600861	+	0.799353i	$0.705176\pi$
$770$	−16.7593	−	33.8102i	−0.603962	−	1.21844i
$771$	2.88324	+	5.94884i	0.103837	+	0.214242i
$772$	1.67930	+	0.969543i	0.0604393	+	0.0348946i
$773$	−11.7168	+	6.76468i	−0.421423	+	0.243309i	−0.695686	−	0.718346i	$-0.744899\pi$
$773$	−11.7168	+	6.76468i	−0.421423	+	0.243309i	0.274263	+	0.961655i	$0.411566\pi$
$774$	−2.01461	+	13.8373i	−0.0724138	+	0.497373i
$775$	24.7114	−	42.8015i	0.887661	−	1.53747i
$776$	0.541718			0.0194465
$777$	−29.1178	+	10.2110i	−1.04459	+	0.366318i
$778$		−	20.0095i		−	0.717375i
$779$	−13.5357	−	7.81484i	−0.484967	−	0.279996i
$780$	13.7147	+	9.30016i	0.491065	+	0.332999i
$781$	23.4451	−	1.18784i	0.838930	−	0.0425042i
$782$	−6.48281	−	3.74285i	−0.231825	−	0.133844i
$783$	5.05918	−	22.9618i	0.180800	−	0.820589i
$784$	−4.77996	+	5.11390i	−0.170713	+	0.182639i
$785$			60.7724i			2.16906i
$786$	0.972907	−	13.4353i	0.0347024	−	0.479220i
$787$	24.1825	−	13.9618i	0.862013	−	0.497683i	−0.00267284	−	0.999996i	$-0.500851\pi$
$787$	24.1825	−	13.9618i	0.862013	−	0.497683i	0.864686	+	0.502313i	$0.167517\pi$
$788$	0.522149	+	0.904388i	0.0186008	+	0.0322175i
$789$	−1.95497	+	26.9970i	−0.0695990	+	0.961120i
$790$	−42.1327			−1.49901
$791$	−3.13716	+	27.3924i	−0.111545	+	0.973961i
$792$	−9.04557	+	4.14459i	−0.321420	+	0.147272i
$793$	−5.16663	+	8.94887i	−0.183472	+	0.317784i
$794$	−8.09039	−	14.0130i	−0.287117	−	0.497302i
$795$	−15.2492	−	10.3407i	−0.540834	−	0.366748i
$796$	12.1261	−	21.0030i	0.429798	−	0.744432i
$797$		−	18.8457i		−	0.667549i	−0.942653	−	0.333774i	$-0.891678\pi$
$797$		−	18.8457i		−	0.667549i	0.942653	−	0.333774i	$-0.108322\pi$
$798$	7.02281	+	1.32383i	0.248605	+	0.0468631i
$799$			16.3317i			0.577775i
$800$	−6.74679	+	11.6858i	−0.238535	+	0.413155i
$801$	5.40228	−	37.1055i	0.190880	−	1.31106i
$802$	20.3865	−	11.7702i	0.719873	−	0.415619i
$803$	−26.4238	−	40.8444i	−0.932476	−	1.44137i
$804$	−6.50245	+	3.15156i	−0.229324	+	0.111147i
$805$	7.79247	+	17.9501i	0.274649	+	0.632658i
$806$			8.14834i			0.287013i
$807$	20.2487	+	1.46630i	0.712788	+	0.0516162i
$808$	3.92520	+	6.79864i	0.138088	+	0.239175i
$809$	−21.4556	−	37.1622i	−0.754339	−	1.30655i	−0.945702	−	0.325034i	$-0.894624\pi$
$809$	−21.4556	−	37.1622i	−0.754339	−	1.30655i	0.191363	−	0.981519i	$-0.438709\pi$
$810$	11.0360	−	37.0970i	0.387766	−	1.30346i
$811$			7.13276i			0.250465i	0.992127	+	0.125233i	$0.0399677\pi$
$811$			7.13276i			0.250465i	−0.992127	+	0.125233i	$0.960032\pi$
$812$	−4.76743	−	10.9818i	−0.167304	−	0.385387i
$813$	8.61429	+	17.7734i	0.302116	+	0.623341i
$814$	−18.7504	+	12.1304i	−0.657202	+	0.425169i
$815$	−64.3313	+	37.1417i	−2.25343	+	1.30102i
$816$	6.23938	+	4.23102i	0.218422	+	0.148115i
$817$	3.63446	−	6.29507i	0.127154	−	0.220237i
$818$			34.2914i			1.19897i
$819$	−17.0415	+	4.62463i	−0.595479	+	0.161598i
$820$			43.1000i			1.50512i
$821$	−12.3220	+	21.3424i	−0.430041	+	0.744854i	−0.996876	−	0.0789778i	$-0.974834\pi$
$821$	−12.3220	+	21.3424i	−0.430041	+	0.744854i	0.566835	+	0.823831i	$0.308168\pi$
$822$	−8.98776	+	13.2540i	−0.313484	+	0.462287i
$823$	6.36507	+	11.0246i	0.221872	+	0.384294i	0.955376	−	0.295391i	$-0.0954499\pi$
$823$	6.36507	+	11.0246i	0.221872	+	0.384294i	−0.733504	+	0.679685i	$0.762117\pi$
$824$	−4.84871	+	8.39821i	−0.168913	+	0.292566i
$825$	77.4965	+	1.67937i	2.69808	+	0.0584681i
$826$	−1.11109	+	9.70162i	−0.0386599	+	0.337563i
$827$	−13.6994			−0.476376			−0.238188	−	0.971219i	$-0.576553\pi$
$827$	−13.6994			−0.476376			−0.238188	+	0.971219i	$0.576553\pi$
$828$	4.79346	−	1.90914i	0.166584	−	0.0663470i
$829$	18.7070	+	32.4015i	0.649722	+	1.12535i	0.983189	+	0.182590i	$0.0584481\pi$
$829$	18.7070	+	32.4015i	0.649722	+	1.12535i	−0.333467	+	0.942762i	$0.608219\pi$
$830$	65.7643	−	37.9691i	2.28271	−	1.31793i
$831$	39.7579	+	2.87904i	1.37918	+	0.0998729i
$832$		−	2.22468i		−	0.0771270i
$833$	−8.87372	−	29.1462i	−0.307456	−	1.00986i
$834$	13.5876	+	28.0347i	0.470501	+	0.970761i
$835$	−53.4646	−	30.8678i	−1.85022	−	1.06823i
$836$	5.16563	−	0.261715i	0.178657	−	0.00905160i
$837$	18.1436	−	5.74663i	0.627135	−	0.198633i
$838$	20.6966	+	11.9492i	0.714951	+	0.412777i
$839$			41.6482i			1.43786i	0.695085	+	0.718928i	$0.255367\pi$
$839$			41.6482i			1.43786i	−0.695085	+	0.718928i	$0.744633\pi$
$840$	−6.52148	−	18.5966i	−0.225012	−	0.641645i
$841$	−8.52438			−0.293944
$842$	10.6889	−	18.5137i	0.368363	−	0.638024i
$843$	15.4854	+	10.5009i	0.533346	+	0.361670i
$844$	−17.2044	+	9.93294i	−0.592198	+	0.341906i
$845$	−29.9833	−	17.3109i	−1.03146	−	0.595512i
$846$	−8.83617	−	6.97428i	−0.303794	−	0.239781i
$847$	29.1009	+	0.372136i	0.999918	+	0.0127867i
$848$			2.47360i			0.0849437i
$849$	26.3450	+	1.90776i	0.904159	+	0.0654742i
$850$	−29.3650	−	50.8617i	−1.00721	−	1.74454i
$851$	10.0291	−	5.79033i	0.343795	−	0.198490i
$852$	12.2275	+	0.885446i	0.418906	+	0.0303349i
$853$		−	20.2141i		−	0.692117i	−0.938213	−	0.346059i	$-0.887520\pi$
$853$		−	20.2141i		−	0.692117i	0.938213	−	0.346059i	$-0.112480\pi$
$854$	11.2727	−	4.89367i	0.385742	−	0.167458i
$855$	−12.4651	+	15.7928i	−0.426297	+	0.540102i
$856$	−1.75893	+	3.04655i	−0.0601189	+	0.104129i
$857$	−11.5198	−	19.9529i	−0.393510	−	0.681579i	0.599400	−	0.800450i	$-0.295406\pi$
$857$	−11.5198	−	19.9529i	−0.393510	−	0.681579i	−0.992910	+	0.118871i	$0.962073\pi$
$858$	−11.2035	+	6.14863i	−0.382481	+	0.209911i
$859$	−3.17916	+	5.50647i	−0.108472	+	0.187878i	−0.915151	−	0.403111i	$-0.867929\pi$
$859$	−3.17916	+	5.50647i	−0.108472	+	0.187878i	0.806680	+	0.590989i	$0.201262\pi$
$860$	−20.0446			−0.683514
$861$	−34.8324	−	29.9345i	−1.18709	−	1.02016i
$862$	2.28472			0.0778180
$863$	−43.7656	−	25.2681i	−1.48980	−	0.860135i	−0.489866	−	0.871798i	$-0.662954\pi$
$863$	−43.7656	−	25.2681i	−1.48980	−	0.860135i	−0.999932	+	0.0116621i	$0.996288\pi$
$864$	−4.95362	+	1.56896i	−0.168526	+	0.0533771i
$865$	64.7579	−	37.3880i	2.20184	−	1.27123i
$866$	−5.01179	+	8.68067i	−0.170307	+	0.294981i
$867$	−3.02966	+	1.46839i	−0.102893	+	0.0498692i
$868$	5.76873	−	7.78648i	0.195803	−	0.264290i
$869$	14.8023	−	28.9268i	0.502135	−	0.981274i
$870$	33.6166	+	2.43433i	1.13971	+	0.0825314i
$871$	−8.03771	+	4.64057i	−0.272347	+	0.157240i
$872$	−2.06323	+	1.19121i	−0.0698699	+	0.0403394i
$873$	−0.601327	−	1.50981i	−0.0203518	−	0.0510994i
$874$	−2.68215			−0.0907250
$875$	−10.9958	+	96.0108i	−0.371726	+	3.24576i
$876$	−11.0802	−	22.8612i	−0.374365	−	0.772407i
$877$	44.1014	+	25.4620i	1.48920	+	0.859789i	0.999924	−	0.0123404i	$-0.00392816\pi$
$877$	44.1014	+	25.4620i	1.48920	+	0.859789i	0.489275	+	0.872130i	$0.337261\pi$
$878$	−5.95435	+	3.43774i	−0.200949	+	0.116018i
$879$	15.2007	+	10.3079i	0.512708	+	0.347676i
$880$	−7.74731	−	11.9753i	−0.261162	−	0.403688i
$881$			43.9018i			1.47909i	0.673107	+	0.739545i	$0.264959\pi$
$881$			43.9018i			1.47909i	−0.673107	+	0.739545i	$0.735041\pi$
$882$	19.5588	+	7.64551i	0.658579	+	0.257438i
$883$	−22.1919			−0.746816			−0.373408	−	0.927667i	$-0.621811\pi$
$883$	−22.1919			−0.746816			−0.373408	+	0.927667i	$0.621811\pi$
$884$	8.38557	+	4.84141i	0.282037	+	0.162834i
$885$	−22.7532	−	15.4293i	−0.764842	−	0.518651i
$886$	−18.4525	+	10.6536i	−0.619925	+	0.357914i
$887$	−19.9074	+	34.4807i	−0.668426	+	1.15775i	0.309919	+	0.950763i	$0.399698\pi$
$887$	−19.9074	+	34.4807i	−0.668426	+	1.15775i	−0.978344	+	0.206984i	$0.933635\pi$
$888$	−10.4949	+	5.08657i	−0.352185	+	0.170694i
$889$	−0.692164	+	6.04369i	−0.0232144	+	0.202699i
$890$	53.7505			1.80172
$891$	21.5922	+	20.6101i	0.723367	+	0.690464i
$892$	8.55750	+	14.8220i	0.286526	+	0.496278i
$893$	2.92585	+	5.06772i	0.0979099	+	0.169585i
$894$	−0.619084	+	8.54918i	−0.0207053	+	0.285927i
$895$	−62.7170			−2.09640
$896$	−1.57499	+	2.12589i	−0.0526169	+	0.0710209i
$897$	5.96363	−	2.89041i	0.199120	−	0.0965080i
$898$	9.84224	+	5.68242i	0.328440	+	0.189625i
$899$	8.28685	+	14.3532i	0.276382	+	0.478708i
$900$	40.0584	+	5.83219i	1.33528	+	0.194406i
$901$	−9.32380	−	5.38310i	−0.310621	−	0.179337i
$902$	−29.5909	−	15.1422i	−0.985270	−	0.504180i
$903$	13.9217	−	16.1996i	0.463284	−	0.539088i
$904$			10.4210i			0.346598i
$905$	88.8237	+	51.2824i	2.95260	+	1.70468i
$906$	7.53609	−	11.1133i	0.250370	−	0.369214i
$907$	−18.2837	−	31.6682i	−0.607099	−	1.05153i	−0.991716	−	0.128450i	$-0.959000\pi$
$907$	−18.2837	−	31.6682i	−0.607099	−	1.05153i	0.384617	−	0.923076i	$-0.374333\pi$
$908$	9.55949	−	16.5575i	0.317243	−	0.549481i
$909$	14.5912	−	18.4866i	0.483961	−	0.613161i
$910$	−10.0796	−	23.2186i	−0.334136	−	0.769688i
$911$			55.8387i			1.85002i	0.379944	+	0.925010i	$0.375943\pi$
$911$			55.8387i			1.85002i	−0.379944	+	0.925010i	$0.624057\pi$
$912$	2.69407	+	0.195089i	0.0892095	+	0.00646006i
$913$	2.96343	+	58.4910i	0.0980752	+	1.93577i
$914$	0.879305	−	0.507667i	0.0290848	−	0.0167921i
$915$	−2.49879	+	34.5068i	−0.0826074	+	1.14076i
$916$	−13.5204			−0.446725
$917$	−12.2490	+	16.5334i	−0.404497	+	0.545980i
$918$	4.86626	−	22.0862i	0.160610	−	0.728955i
$919$	45.8037	+	26.4448i	1.51092	+	0.872332i	0.999919	+	0.0127539i	$0.00405981\pi$
$919$	45.8037	+	26.4448i	1.51092	+	0.872332i	0.511005	+	0.859578i	$0.329274\pi$
$920$	3.69811	+	6.40531i	0.121923	+	0.211177i
$921$	6.26538	−	9.23939i	0.206451	−	0.304448i
$922$	14.9444	−	25.8844i	0.492167	−	0.852458i
$923$	15.7464			0.518298
$924$	15.0590	+	2.05609i	0.495404	+	0.0676404i
$925$	90.8575			2.98738
$926$	−4.30562	+	7.45755i	−0.141491	+	0.245070i
$927$	28.7887	+	4.19142i	0.945546	+	0.137664i
$928$	−2.26250	−	3.91876i	−0.0742702	−	0.128640i
$929$	−0.312131	−	0.180209i	−0.0102407	−	0.00591247i	0.494871	−	0.868967i	$-0.335215\pi$
$929$	−0.312131	−	0.180209i	−0.0102407	−	0.00591247i	−0.505112	+	0.863054i	$0.668549\pi$
$930$	11.8988	+	24.5502i	0.390177	+	0.805032i
$931$	−7.97509	−	7.45432i	−0.261373	−	0.244305i
$932$	7.74794			0.253792
$933$	15.9842	+	1.15749i	0.523301	+	0.0378945i
$934$	31.5910	−	18.2391i	1.03369	−	0.596801i
$935$	61.9988	−	3.14115i	2.02758	−	0.102727i
$936$	−6.20037	+	2.46948i	−0.202666	+	0.0807175i
$937$			23.8255i			0.778346i	0.921165	+	0.389173i	$0.127239\pi$
$937$			23.8255i			0.778346i	−0.921165	+	0.389173i	$0.872761\pi$
$938$	10.9661	+	1.25591i	0.358056	+	0.0410070i
$939$	−1.27224	+	0.616622i	−0.0415181	+	0.0201227i
$940$	8.06825	−	13.9746i	0.263157	−	0.455802i
$941$	−7.01514	−	12.1506i	−0.228687	−	0.396098i	0.728732	−	0.684799i	$-0.240110\pi$
$941$	−7.01514	−	12.1506i	−0.228687	−	0.396098i	−0.957419	+	0.288701i	$0.906777\pi$
$942$	−20.2583	−	13.7375i	−0.660052	−	0.447592i
$943$	14.9278	+	8.61859i	0.486117	+	0.280660i
$944$			3.69084i			0.120127i
$945$	−44.5913	+	38.8188i	−1.45055	+	1.26278i
$946$	7.04220	−	13.7619i	0.228962	−	0.447438i
$947$	−42.2760	−	24.4081i	−1.37379	−	0.793156i	−0.382384	−	0.924003i	$-0.624897\pi$
$947$	−42.2760	−	24.4081i	−1.37379	−	0.793156i	−0.991403	+	0.130847i	$0.958230\pi$
$948$	9.52402	−	14.0448i	0.309326	−	0.456155i
$949$	−16.3152	−	28.2588i	−0.529615	−	0.917320i
$950$	−18.2239	−	10.5216i	−0.591261	−	0.341365i
$951$	−6.27414	−	12.9451i	−0.203453	−	0.419774i
$952$	−4.58563	−	10.5631i	−0.148621	−	0.342351i
$953$	1.92134			0.0622385			0.0311192	−	0.999516i	$-0.490093\pi$
$953$	1.92134			0.0622385			0.0311192	+	0.999516i	$0.490093\pi$
$954$	6.89412	−	2.74578i	0.223205	−	0.0888980i
$955$	2.53104	+	4.38389i	0.0819026	+	0.141859i
$956$	5.97761	+	10.3535i	0.193330	+	0.334857i
$957$	−13.4817	+	22.2247i	−0.435803	+	0.718423i
$958$	5.88801			0.190233
$959$	22.4387	−	9.74104i	0.724582	−	0.314555i
$960$	−3.24864	−	6.70276i	−0.104850	−	0.216331i
$961$	8.79233	−	15.2288i	0.283623	−	0.491250i
$962$	−12.9728	+	7.48983i	−0.418259	+	0.241482i
$963$	10.4435	+	1.52049i	0.336536	+	0.0489970i
$964$	24.4654	+	14.1251i	0.787976	+	0.454938i
$965$	8.33888			0.268438
$966$	−7.74510	−	1.45999i	−0.249194	−	0.0469743i
$967$			1.76597i			0.0567899i	0.999597	+	0.0283949i	$0.00903960\pi$
$967$			1.76597i			0.0567899i	−0.999597	+	0.0283949i	$0.990960\pi$
$968$	10.9437	−	1.11177i	0.351743	−	0.0357336i
$969$	−6.59825	+	9.73027i	−0.211966	+	0.312581i
$970$	2.01750	−	1.16481i	0.0647782	−	0.0373997i
$971$	−21.2217	−	12.2523i	−0.681036	−	0.393197i	0.119209	−	0.992869i	$-0.461964\pi$
$971$	−21.2217	−	12.2523i	−0.681036	−	0.393197i	−0.800245	+	0.599673i	$0.795297\pi$
$972$	9.87152	+	12.0645i	0.316629	+	0.386970i
$973$	5.41475	−	47.2793i	0.173589	−	1.51571i
$974$	26.1286			0.837214
$975$	51.8585	+	3.75531i	1.66080	+	0.120266i
$976$	4.02253	−	2.32241i	0.128758	−	0.0743386i
$977$	26.1114	−	15.0755i	0.835379	−	0.482306i	−0.0203117	−	0.999794i	$-0.506466\pi$
$977$	26.1114	−	15.0755i	0.835379	−	0.482306i	0.855691	+	0.517487i	$0.173133\pi$
$978$	2.16088	−	29.8405i	0.0690974	−	0.954194i
$979$	−18.8840	+	36.9032i	−0.603535	+	1.17943i
$980$	−6.80591	+	29.3234i	−0.217407	+	0.936703i
$981$	5.61026	+	4.42811i	0.179122	+	0.141379i
$982$	1.83515	−	3.17858i	0.0585621	−	0.101432i
$983$	−30.3289	+	17.5104i	−0.967341	+	0.558494i	−0.898425	−	0.439128i	$-0.855287\pi$
$983$	−30.3289	+	17.5104i	−0.967341	+	0.558494i	−0.0689163	+	0.997622i	$0.521954\pi$
$984$	−14.3673	−	9.74268i	−0.458012	−	0.310585i
$985$	3.88924	+	2.24546i	0.123922	+	0.0715462i
$986$	19.6948			0.627211
$987$	5.69029	+	16.2264i	0.181124	+	0.516493i
$988$	3.46938			0.110376
$989$	−4.00826	+	6.94251i	−0.127455	+	0.220759i
$990$	−24.7764	+	34.8854i	−0.787446	+	1.10873i
$991$	2.32827	+	4.03268i	0.0739599	+	0.128102i	0.900633	−	0.434579i	$-0.143103\pi$
$991$	2.32827	+	4.03268i	0.0739599	+	0.128102i	−0.826674	+	0.562682i	$0.809770\pi$
$992$	1.83135	−	3.17199i	0.0581454	−	0.100711i
$993$	−35.7592	+	17.3315i	−1.13479	+	0.549999i
$994$	−15.0471	−	11.1478i	−0.477264	−	0.353588i
$995$		−	104.294i		−	3.30636i
$996$	−2.20902	+	30.5052i	−0.0699955	+	0.966595i
$997$	−8.75466	+	5.05450i	−0.277263	+	0.160078i	−0.632184	−	0.774819i	$-0.717841\pi$
$997$	−8.75466	+	5.05450i	−0.277263	+	0.160078i	0.354921	+	0.934896i	$0.384508\pi$
$998$	−0.575545	−	0.996873i	−0.0182186	−	0.0315555i
$999$	25.8264	+	23.6038i	0.817111	+	0.746790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.f.65.11	yes	24
3.2	odd	2		462.2.n.e.65.6	✓	24
7.4	even	3	inner	462.2.n.f.263.6	yes	24
11.10	odd	2		462.2.n.e.65.11	yes	24
21.11	odd	6		462.2.n.e.263.11	yes	24
33.32	even	2	inner	462.2.n.f.65.6	yes	24
77.32	odd	6		462.2.n.e.263.6	yes	24
231.32	even	6	inner	462.2.n.f.263.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.6	✓	24	3.2	odd	2
462.2.n.e.65.11	yes	24	11.10	odd	2
462.2.n.e.263.6	yes	24	77.32	odd	6
462.2.n.e.263.11	yes	24	21.11	odd	6
462.2.n.f.65.6	yes	24	33.32	even	2	inner
462.2.n.f.65.11	yes	24	1.1	even	1	trivial
462.2.n.f.263.6	yes	24	7.4	even	3	inner
462.2.n.f.263.11	yes	24	231.32	even	6	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.43353 + 0.972102i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72427 - 2.15021i) q^{5} +(1.55863 - 0.755426i) q^{6} +(-2.62857 - 0.301041i) q^{7} -1.00000 q^{8} +(1.11004 + 2.78708i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.43353 + 0.972102i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.72427 - 2.15021i) q^{5} +(1.55863 - 0.755426i) q^{6} +(-2.62857 - 0.301041i) q^{7} -1.00000 q^{8} +(1.11004 + 2.78708i) q^{9} +(-3.72427 + 2.15021i) q^{10} +(-0.167821 - 3.31238i) q^{11} +(0.125098 - 1.72753i) q^{12} -2.22468i q^{13} +(-1.57499 + 2.12589i) q^{14} +(-3.24864 - 6.70276i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.17622 - 3.76933i) q^{17} +(2.96870 + 0.432220i) q^{18} +(-1.35056 - 0.779747i) q^{19} +4.30042i q^{20} +(-3.47550 - 2.98679i) q^{21} +(-2.95251 - 1.51085i) q^{22} +(1.48946 + 0.859942i) q^{23} +(-1.43353 - 0.972102i) q^{24} +(6.74679 + 11.6858i) q^{25} +(-1.92663 - 1.11234i) q^{26} +(-1.11805 + 5.07444i) q^{27} +(1.05357 + 2.42693i) q^{28} -4.52500 q^{29} +(-7.42908 - 0.537973i) q^{30} +(-1.83135 - 3.17199i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.97939 - 4.91154i) q^{33} -4.35245 q^{34} +(9.14220 + 6.77313i) q^{35} +(1.85866 - 2.35486i) q^{36} +(3.36669 - 5.83129i) q^{37} +(-1.35056 + 0.779747i) q^{38} +(2.16262 - 3.18916i) q^{39} +(3.72427 + 2.15021i) q^{40} +10.0223 q^{41} +(-4.32438 + 1.51648i) q^{42} +4.66108i q^{43} +(-2.78469 + 1.80152i) q^{44} +(1.85873 - 12.7666i) q^{45} +(1.48946 - 0.859942i) q^{46} +(-3.24960 - 1.87616i) q^{47} +(-1.55863 + 0.755426i) q^{48} +(6.81875 + 1.58262i) q^{49} +13.4936 q^{50} +(0.544482 - 7.51897i) q^{51} +(-1.92663 + 1.11234i) q^{52} +(2.14220 - 1.23680i) q^{53} +(3.83557 + 3.50548i) q^{54} +(-6.49729 + 12.6970i) q^{55} +(2.62857 + 0.301041i) q^{56} +(-1.17808 - 2.43068i) q^{57} +(-2.26250 + 3.91876i) q^{58} +(3.19636 - 1.84542i) q^{59} +(-4.18044 + 6.16479i) q^{60} +(-4.02253 - 2.32241i) q^{61} -3.66270 q^{62} +(-2.07878 - 7.66020i) q^{63} +1.00000 q^{64} +(-4.78353 + 8.28532i) q^{65} +(-2.76382 - 5.03600i) q^{66} +(-2.08595 - 3.61297i) q^{67} +(-2.17622 + 3.76933i) q^{68} +(1.29925 + 2.68067i) q^{69} +(10.4368 - 4.53081i) q^{70} +7.07802i q^{71} +(-1.11004 - 2.78708i) q^{72} +(12.7024 - 7.33373i) q^{73} +(-3.36669 - 5.83129i) q^{74} +(-1.68802 + 23.3105i) q^{75} +1.55949i q^{76} +(-0.556035 + 8.75733i) q^{77} +(-1.68058 - 3.46746i) q^{78} +(8.48475 + 4.89868i) q^{79} +(3.72427 - 2.15021i) q^{80} +(-6.53564 + 6.18752i) q^{81} +(5.01114 - 8.67956i) q^{82} -17.6583 q^{83} +(-0.848886 + 4.50326i) q^{84} +18.7173i q^{85} +(4.03661 + 2.33054i) q^{86} +(-6.48674 - 4.39876i) q^{87} +(0.167821 + 3.31238i) q^{88} +(-10.8244 - 6.24946i) q^{89} +(-10.1269 - 7.99303i) q^{90} +(-0.669722 + 5.84773i) q^{91} -1.71988i q^{92} +(0.458196 - 6.32741i) q^{93} +(-3.24960 + 1.87616i) q^{94} +(3.35323 + 5.80797i) q^{95} +(-0.125098 + 1.72753i) q^{96} -0.541718 q^{97} +(4.77996 - 5.11390i) q^{98} +(9.04557 - 4.14459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

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