LMFDB - Embedded newform 966.2.l.c.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.72955 - 0.0930981i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85941 - 3.22059i) q^{5} +(1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} -1.00000i q^{8} +(2.98267 + 0.322035i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72955 - 0.0930981i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85941 - 3.22059i) q^{5} +(1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} -1.00000i q^{8} +(2.98267 + 0.322035i) q^{9} +(-3.22059 + 1.85941i) q^{10} +(-1.46962 + 0.848486i) q^{11} +(-0.784148 - 1.54438i) q^{12} -0.321801i q^{13} +(2.47380 - 0.938245i) q^{14} +(-3.51577 + 5.39706i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24668 - 5.62342i) q^{17} +(-2.42205 - 1.77022i) q^{18} +(-0.745335 - 0.430319i) q^{19} +3.71882 q^{20} +(3.08477 - 3.38884i) q^{21} +1.69697 q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.0930981 + 1.72955i) q^{24} +(-4.41482 - 7.64669i) q^{25} +(-0.160901 + 0.278688i) q^{26} +(-5.12868 - 0.834655i) q^{27} +(-2.61150 - 0.424357i) q^{28} +1.06086i q^{29} +(5.74328 - 2.91611i) q^{30} +(3.96735 - 2.29055i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.62077 - 1.33068i) q^{33} +6.49336i q^{34} +(3.48917 + 9.19963i) q^{35} +(1.21244 + 2.74408i) q^{36} +(-1.62560 + 2.81563i) q^{37} +(0.430319 + 0.745335i) q^{38} +(-0.0299591 + 0.556570i) q^{39} +(-3.22059 - 1.85941i) q^{40} +0.635105 q^{41} +(-4.36591 + 1.39243i) q^{42} -3.17857 q^{43} +(-1.46962 - 0.848486i) q^{44} +(6.58314 - 9.00716i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.85378 + 3.21084i) q^{47} +(0.945399 - 1.45128i) q^{48} +(-1.40045 - 6.85848i) q^{49} +8.82964i q^{50} +(5.09176 + 10.0282i) q^{51} +(0.278688 - 0.160901i) q^{52} +(-6.29811 + 3.63622i) q^{53} +(4.02424 + 3.28717i) q^{54} +6.31074i q^{55} +(2.04945 + 1.67325i) q^{56} +(1.24903 + 0.813647i) q^{57} +(0.530428 - 0.918729i) q^{58} +(-5.82082 - 10.0820i) q^{59} +(-6.43188 - 0.346215i) q^{60} +(-7.07196 - 4.08300i) q^{61} -4.58111 q^{62} +(-5.65075 + 5.57396i) q^{63} -1.00000 q^{64} +(-1.03639 - 0.598361i) q^{65} +(-2.93499 - 0.157985i) q^{66} +(-1.79862 - 3.11530i) q^{67} +(3.24668 - 5.62342i) q^{68} +(-1.45128 - 0.945399i) q^{69} +(1.57811 - 9.71170i) q^{70} +3.84622i q^{71} +(0.322035 - 2.98267i) q^{72} +(-13.5743 + 7.83714i) q^{73} +(2.81563 - 1.62560i) q^{74} +(6.92374 + 13.6363i) q^{75} -0.860639i q^{76} +(0.720122 - 4.43164i) q^{77} +(0.304230 - 0.467024i) q^{78} +(-8.26120 + 14.3088i) q^{79} +(1.85941 + 3.22059i) q^{80} +(8.79259 + 1.92105i) q^{81} +(-0.550017 - 0.317552i) q^{82} -9.85134 q^{83} +(4.47720 + 0.977070i) q^{84} -24.1477 q^{85} +(2.75272 + 1.58929i) q^{86} +(0.0987637 - 1.83480i) q^{87} +(0.848486 + 1.46962i) q^{88} +(4.33024 - 7.50019i) q^{89} +(-10.2048 + 4.50886i) q^{90} +(0.659514 + 0.538455i) q^{91} +1.00000i q^{92} +(-7.07497 + 3.59227i) q^{93} +(3.21084 - 1.85378i) q^{94} +(-2.77177 + 1.60028i) q^{95} +(-1.54438 + 0.784148i) q^{96} +9.27603i q^{97} +(-2.21641 + 6.63984i) q^{98} +(-4.65663 + 2.05748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.72955	−	0.0930981i	−0.998554	−	0.0537502i
$3$	−1.72955	−	0.0930981i	−0.998554	−	0.0537502i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.85941	−	3.22059i	0.831554	−	1.44029i	−0.0652518	−	0.997869i	$-0.520785\pi$
$5$	1.85941	−	3.22059i	0.831554	−	1.44029i	0.896806	−	0.442425i	$-0.145882\pi$
$6$	1.45128	+	0.945399i	0.592484	+	0.385957i
$7$	−1.67325	+	2.04945i	−0.632430	+	0.774617i
$7$	−1.67325	+	2.04945i	−0.632430	+	0.774617i
$8$		−	1.00000i		−	0.353553i
$9$	2.98267	+	0.322035i	0.994222	+	0.107345i
$10$	−3.22059	+	1.85941i	−1.01844	+	0.587997i
$11$	−1.46962	+	0.848486i	−0.443108	+	0.255828i	−0.704915	−	0.709292i	$-0.749015\pi$
$11$	−1.46962	+	0.848486i	−0.443108	+	0.255828i	0.261807	+	0.965120i	$0.415682\pi$
$12$	−0.784148	−	1.54438i	−0.226364	−	0.445824i
$13$		−	0.321801i		−	0.0892516i	−0.999004	−	0.0446258i	$-0.985790\pi$
$13$		−	0.321801i		−	0.0892516i	0.999004	−	0.0446258i	$-0.0142096\pi$
$14$	2.47380	−	0.938245i	0.661151	−	0.250757i
$15$	−3.51577	+	5.39706i	−0.907768	+	1.39352i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.24668	−	5.62342i	−0.787436	−	1.36388i	−0.927533	−	0.373741i	$-0.878075\pi$
$17$	−3.24668	−	5.62342i	−0.787436	−	1.36388i	0.140098	−	0.990138i	$-0.455258\pi$
$18$	−2.42205	−	1.77022i	−0.570882	−	0.417246i
$19$	−0.745335	−	0.430319i	−0.170992	−	0.0987220i	0.412062	−	0.911156i	$-0.364809\pi$
$19$	−0.745335	−	0.430319i	−0.170992	−	0.0987220i	−0.583053	+	0.812434i	$0.698142\pi$
$20$	3.71882			0.831554
$21$	3.08477	−	3.38884i	0.673152	−	0.739504i
$22$	1.69697			0.361796
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	−0.0930981	+	1.72955i	−0.0190036	+	0.353042i
$25$	−4.41482	−	7.64669i	−0.882964	−	1.52934i
$26$	−0.160901	+	0.278688i	−0.0315552	+	0.0546552i
$27$	−5.12868	−	0.834655i	−0.987015	−	0.160629i
$28$	−2.61150	−	0.424357i	−0.493527	−	0.0801959i
$29$			1.06086i			0.196996i	0.995137	+	0.0984981i	$0.0314038\pi$
$29$			1.06086i			0.196996i	−0.995137	+	0.0984981i	$0.968596\pi$
$30$	5.74328	−	2.91611i	1.04857	−	0.532406i
$31$	3.96735	−	2.29055i	0.712558	−	0.411395i	−0.0994495	−	0.995043i	$-0.531708\pi$
$31$	3.96735	−	2.29055i	0.712558	−	0.411395i	0.812007	+	0.583647i	$0.198375\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.62077	−	1.33068i	0.456218	−	0.231641i
$34$			6.49336i			1.11360i
$35$	3.48917	+	9.19963i	0.589777	+	1.55502i
$36$	1.21244	+	2.74408i	0.202074	+	0.457347i
$37$	−1.62560	+	2.81563i	−0.267247	+	0.462886i	−0.968150	−	0.250371i	$-0.919447\pi$
$37$	−1.62560	+	2.81563i	−0.267247	+	0.462886i	0.700903	+	0.713257i	$0.252781\pi$
$38$	0.430319	+	0.745335i	0.0698070	+	0.120909i
$39$	−0.0299591	+	0.556570i	−0.00479729	+	0.0891226i
$40$	−3.22059	−	1.85941i	−0.509221	−	0.293999i
$41$	0.635105			0.0991867			0.0495933	−	0.998769i	$-0.484207\pi$
$41$	0.635105			0.0991867			0.0495933	+	0.998769i	$0.484207\pi$
$42$	−4.36591	+	1.39243i	−0.673674	+	0.214857i
$43$	−3.17857			−0.484728			−0.242364	−	0.970185i	$-0.577923\pi$
$43$	−3.17857			−0.484728			−0.242364	+	0.970185i	$0.577923\pi$
$44$	−1.46962	−	0.848486i	−0.221554	−	0.127914i
$45$	6.58314	−	9.00716i	0.981357	−	1.34271i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−1.85378	+	3.21084i	−0.270402	+	0.468350i	−0.968965	−	0.247199i	$-0.920490\pi$
$47$	−1.85378	+	3.21084i	−0.270402	+	0.468350i	0.698563	+	0.715549i	$0.253823\pi$
$48$	0.945399	−	1.45128i	0.136457	−	0.209475i
$49$	−1.40045	−	6.85848i	−0.200065	−	0.979783i
$50$			8.82964i			1.24870i
$51$	5.09176	+	10.0282i	0.712989	+	1.40423i
$52$	0.278688	−	0.160901i	0.0386471	−	0.0223129i
$53$	−6.29811	+	3.63622i	−0.865112	+	0.499473i	−0.865721	−	0.500527i	$-0.833140\pi$
$53$	−6.29811	+	3.63622i	−0.865112	+	0.499473i	0.000608788		1.00000i	$0.499806\pi$
$54$	4.02424	+	3.28717i	0.547630	+	0.447327i
$55$			6.31074i			0.850940i
$56$	2.04945	+	1.67325i	0.273869	+	0.223598i
$57$	1.24903	+	0.813647i	0.165438	+	0.107770i
$58$	0.530428	−	0.918729i	0.0696487	−	0.120635i
$59$	−5.82082	−	10.0820i	−0.757806	−	1.31256i	−0.943967	−	0.330040i	$-0.892938\pi$
$59$	−5.82082	−	10.0820i	−0.757806	−	1.31256i	0.186161	−	0.982519i	$-0.440395\pi$
$60$	−6.43188	−	0.346215i	−0.830352	−	0.0446962i
$61$	−7.07196	−	4.08300i	−0.905471	−	0.522774i	−0.0265001	−	0.999649i	$-0.508436\pi$
$61$	−7.07196	−	4.08300i	−0.905471	−	0.522774i	−0.878971	+	0.476875i	$0.841770\pi$
$62$	−4.58111			−0.581801
$63$	−5.65075	+	5.57396i	−0.711927	+	0.702253i
$64$	−1.00000			−0.125000
$65$	−1.03639	−	0.598361i	−0.128548	−	0.0742175i
$66$	−2.93499	−	0.157985i	−0.361273	−	0.0194466i
$67$	−1.79862	−	3.11530i	−0.219736	−	0.380594i	0.734991	−	0.678077i	$-0.237186\pi$
$67$	−1.79862	−	3.11530i	−0.219736	−	0.380594i	−0.954727	+	0.297483i	$0.903853\pi$
$68$	3.24668	−	5.62342i	0.393718	−	0.681939i
$69$	−1.45128	−	0.945399i	−0.174714	−	0.113813i
$70$	1.57811	−	9.71170i	0.188620	−	1.16077i
$71$			3.84622i			0.456462i	0.973607	+	0.228231i	$0.0732941\pi$
$71$			3.84622i			0.456462i	−0.973607	+	0.228231i	$0.926706\pi$
$72$	0.322035	−	2.98267i	0.0379522	−	0.351511i
$73$	−13.5743	+	7.83714i	−1.58875	+	0.917268i	−0.595242	+	0.803546i	$0.702944\pi$
$73$	−13.5743	+	7.83714i	−1.58875	+	0.917268i	−0.993513	+	0.113722i	$0.963723\pi$
$74$	2.81563	−	1.62560i	0.327310	−	0.188972i
$75$	6.92374	+	13.6363i	0.799485	+	1.57459i
$76$		−	0.860639i		−	0.0987220i
$77$	0.720122	−	4.43164i	0.0820655	−	0.505032i
$78$	0.304230	−	0.467024i	0.0344473	−	0.0528801i
$79$	−8.26120	+	14.3088i	−0.929457	+	1.60987i	−0.145226	+	0.989398i	$0.546391\pi$
$79$	−8.26120	+	14.3088i	−0.929457	+	1.60987i	−0.784231	+	0.620469i	$0.786942\pi$
$80$	1.85941	+	3.22059i	0.207888	+	0.360073i
$81$	8.79259	+	1.92105i	0.976954	+	0.213449i
$82$	−0.550017	−	0.317552i	−0.0607392	−	0.0350678i
$83$	−9.85134			−1.08133			−0.540663	−	0.841239i	$-0.681826\pi$
$83$	−9.85134			−1.08133			−0.540663	+	0.841239i	$0.681826\pi$
$84$	4.47720	+	0.977070i	0.488503	+	0.106607i
$85$	−24.1477			−2.61918
$86$	2.75272	+	1.58929i	0.296834	+	0.171377i
$87$	0.0987637	−	1.83480i	0.0105886	−	0.196711i
$88$	0.848486	+	1.46962i	0.0904490	+	0.156662i
$89$	4.33024	−	7.50019i	0.459004	−	0.795019i	−0.539904	−	0.841726i	$-0.681540\pi$
$89$	4.33024	−	7.50019i	0.459004	−	0.795019i	0.998909	+	0.0467077i	$0.0148729\pi$
$90$	−10.2048	+	4.50886i	−1.07568	+	0.475275i
$91$	0.659514	+	0.538455i	0.0691358	+	0.0564454i
$92$			1.00000i			0.104257i
$93$	−7.07497	+	3.59227i	−0.733640	+	0.372501i
$94$	3.21084	−	1.85378i	0.331173	−	0.191203i
$95$	−2.77177	+	1.60028i	−0.284377	+	0.164185i
$96$	−1.54438	+	0.784148i	−0.157623	+	0.0800318i
$97$			9.27603i			0.941838i	0.882176	+	0.470919i	$0.156078\pi$
$97$			9.27603i			0.941838i	−0.882176	+	0.470919i	$0.843922\pi$
$98$	−2.21641	+	6.63984i	−0.223891	+	0.670725i
$99$	−4.65663	+	2.05748i	−0.468009	+	0.206785i
$100$	4.41482	−	7.64669i	0.441482	−	0.764669i
$101$	7.01408	+	12.1488i	0.697927	+	1.20885i	0.969184	+	0.246339i	$0.0792275\pi$
$101$	7.01408	+	12.1488i	0.697927	+	1.20885i	−0.271256	+	0.962507i	$0.587439\pi$
$102$	0.604519	−	11.2306i	0.0598563	−	1.11199i
$103$	0.0113596	+	0.00655847i	0.00111930	+	0.000646226i	0.500560	−	0.865702i	$-0.333128\pi$
$103$	0.0113596	+	0.00655847i	0.00111930	+	0.000646226i	−0.499440	+	0.866348i	$0.666461\pi$
$104$	−0.321801			−0.0315552
$105$	−5.17821	−	16.2360i	−0.505342	−	1.58447i
$106$	7.27243			0.706361
$107$	−6.13504	−	3.54207i	−0.593097	−	0.342424i	0.173224	−	0.984882i	$-0.444581\pi$
$107$	−6.13504	−	3.54207i	−0.593097	−	0.342424i	−0.766321	+	0.642458i	$0.777915\pi$
$108$	−1.84151	−	4.85889i	−0.177199	−	0.467547i
$109$	−1.93891	−	3.35830i	−0.185714	−	0.321667i	0.758103	−	0.652135i	$-0.226127\pi$
$109$	−1.93891	−	3.35830i	−0.185714	−	0.321667i	−0.943817	+	0.330469i	$0.892793\pi$
$110$	3.15537	−	5.46526i	0.300853	−	0.521092i
$111$	3.07368	−	4.71842i	0.291741	−	0.447852i
$112$	−0.938245	−	2.47380i	−0.0886559	−	0.233752i
$113$		−	20.7369i		−	1.95076i	−0.220531	−	0.975380i	$-0.570779\pi$
$113$		−	20.7369i		−	1.95076i	0.220531	−	0.975380i	$-0.429221\pi$
$114$	−0.674868	−	1.32915i	−0.0632072	−	0.124487i
$115$	3.22059	−	1.85941i	0.300322	−	0.173391i
$116$	−0.918729	+	0.530428i	−0.0853019	+	0.0492490i
$117$	0.103631	−	0.959825i	0.00958071	−	0.0887359i
$118$			11.6416i			1.07170i
$119$	16.9574	+	2.75550i	1.55448	+	0.252596i
$120$	5.39706	+	3.51577i	0.492682	+	0.320944i
$121$	−4.06014	+	7.03237i	−0.369104	+	0.639306i
$122$	4.08300	+	7.07196i	0.369657	+	0.640265i
$123$	−1.09844	−	0.0591270i	−0.0990433	−	0.00533130i
$124$	3.96735	+	2.29055i	0.356279	+	0.205698i
$125$	−14.2417			−1.27382
$126$	7.68067	−	2.00182i	0.684249	−	0.178336i
$127$	−2.80369			−0.248788			−0.124394	−	0.992233i	$-0.539699\pi$
$127$	−2.80369			−0.248788			−0.124394	+	0.992233i	$0.539699\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	5.49749	+	0.295919i	0.484027	+	0.0260542i
$130$	0.598361	+	1.03639i	0.0524797	+	0.0908975i
$131$	3.65809	−	6.33599i	0.319608	−	0.553578i	−0.660798	−	0.750564i	$-0.729782\pi$
$131$	3.65809	−	6.33599i	0.319608	−	0.553578i	0.980406	+	0.196986i	$0.0631153\pi$
$132$	2.46279	+	1.60432i	0.214358	+	0.139638i
$133$	2.12905	−	0.807490i	0.184612	−	0.0700183i
$134$			3.59723i			0.310754i
$135$	−12.2244	+	14.9654i	−1.05211	+	1.28802i
$136$	−5.62342	+	3.24668i	−0.482204	+	0.278401i
$137$	−19.4324	+	11.2193i	−1.66022	+	0.958531i	−0.687618	+	0.726072i	$0.741344\pi$
$137$	−19.4324	+	11.2193i	−1.66022	+	0.958531i	−0.972606	+	0.232459i	$0.925323\pi$
$138$	0.784148	+	1.54438i	0.0667511	+	0.131466i
$139$			7.14230i			0.605802i	0.953022	+	0.302901i	$0.0979552\pi$
$139$			7.14230i			0.605802i	−0.953022	+	0.302901i	$0.902045\pi$
$140$	−6.22253	+	7.62152i	−0.525900	+	0.644136i
$141$	3.50512	−	5.38072i	0.295185	−	0.453138i
$142$	1.92311	−	3.33092i	0.161384	−	0.279525i
$143$	0.273044	+	0.472926i	0.0228331	+	0.0395481i
$144$	−1.77022	+	2.42205i	−0.147519	+	0.201837i
$145$	3.41659	+	1.97257i	0.283732	+	0.163813i
$146$	15.6743			1.29721
$147$	1.78364	+	11.9924i	0.147112	+	0.989120i
$148$	−3.25120			−0.267247
$149$	17.1479	+	9.90037i	1.40481	+	0.811070i	0.994882	−	0.101046i	$-0.0322188\pi$
$149$	17.1479	+	9.90037i	1.40481	+	0.811070i	0.409933	+	0.912116i	$0.365552\pi$
$150$	0.822022	−	15.2713i	0.0671178	−	1.24689i
$151$	−6.59105	−	11.4160i	−0.536372	−	0.929023i	−0.999096	−	0.0425205i	$-0.986461\pi$
$151$	−6.59105	−	11.4160i	−0.536372	−	0.929023i	0.462724	−	0.886502i	$-0.346872\pi$
$152$	−0.430319	+	0.745335i	−0.0349035	+	0.0604547i
$153$	−7.87283	−	17.8183i	−0.636480	−	1.44053i
$154$	−2.83946	+	3.47785i	−0.228811	+	0.280253i
$155$		−	17.0363i		−	1.36839i
$156$	−0.496984	+	0.252340i	−0.0397905	+	0.0202034i
$157$	2.62308	−	1.51444i	0.209345	−	0.120865i	−0.391662	−	0.920109i	$-0.628100\pi$
$157$	2.62308	−	1.51444i	0.209345	−	0.120865i	0.601007	+	0.799244i	$0.294766\pi$
$158$	14.3088	−	8.26120i	1.13835	−	0.657226i
$159$	11.2314	−	5.70266i	0.890708	−	0.452251i
$160$		−	3.71882i		−	0.293999i
$161$	−2.47380	+	0.938245i	−0.194963	+	0.0739441i
$162$	−6.65408	−	6.05997i	−0.522794	−	0.476116i
$163$	12.2914	−	21.2893i	0.962734	−	1.66750i	0.247150	−	0.968977i	$-0.420506\pi$
$163$	12.2914	−	21.2893i	0.962734	−	1.66750i	0.715584	−	0.698527i	$-0.246161\pi$
$164$	0.317552	+	0.550017i	0.0247967	+	0.0429491i
$165$	0.587518	−	10.9147i	0.0457382	−	0.849710i
$166$	8.53151	+	4.92567i	0.662174	+	0.382306i
$167$	10.3254			0.799001			0.399501	−	0.916733i	$-0.369184\pi$
$167$	10.3254			0.799001			0.399501	+	0.916733i	$0.369184\pi$
$168$	−3.38884	−	3.08477i	−0.261454	−	0.237995i
$169$	12.8964			0.992034
$170$	20.9125	+	12.0738i	1.60391	+	0.926020i
$171$	−2.08451	−	1.52352i	−0.159406	−	0.116507i
$172$	−1.58929	−	2.75272i	−0.121182	−	0.209893i
$173$	7.84102	−	13.5810i	0.596142	−	1.03255i	−0.397243	−	0.917714i	$-0.630033\pi$
$173$	7.84102	−	13.5810i	0.596142	−	1.03255i	0.993385	−	0.114834i	$-0.0366338\pi$
$174$	−1.00293	+	1.53960i	−0.0760321	+	0.116717i
$175$	23.0586	+	3.74691i	1.74306	+	0.283240i
$176$		−	1.69697i		−	0.127914i
$177$	9.12877	+	17.9791i	0.686160	+	1.35139i
$178$	−7.50019	+	4.33024i	−0.562163	+	0.324565i
$179$	−17.4328	+	10.0648i	−1.30299	+	0.752279i	−0.980915	−	0.194436i	$-0.937712\pi$
$179$	−17.4328	+	10.0648i	−1.30299	+	0.752279i	−0.322071	+	0.946715i	$0.604379\pi$
$180$	11.0920	+	1.19759i	0.826749	+	0.0892631i
$181$		−	1.17617i		−	0.0874243i	−0.999044	−	0.0437122i	$-0.986082\pi$
$181$		−	1.17617i		−	0.0874243i	0.999044	−	0.0437122i	$-0.0139184\pi$
$182$	−0.301928	−	0.796072i	−0.0223804	−	0.0590088i
$183$	11.8512	+	7.72012i	0.876063	+	0.570688i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	6.04532	+	10.4708i	0.444461	+	0.769829i
$186$	7.92324	+	0.426492i	0.580960	+	0.0312719i
$187$	9.54278	+	5.50953i	0.697837	+	0.402897i
$188$	−3.70756			−0.270402
$189$	10.2922	−	9.11436i	0.748644	−	0.662972i
$190$	3.20056			0.232193
$191$	−3.28393	−	1.89598i	−0.237617	−	0.137188i	0.376464	−	0.926431i	$-0.377140\pi$
$191$	−3.28393	−	1.89598i	−0.237617	−	0.137188i	−0.614081	+	0.789243i	$0.710473\pi$
$192$	1.72955	+	0.0930981i	0.124819	+	0.00671877i
$193$	10.8831	+	18.8501i	0.783383	+	1.35686i	0.929960	+	0.367660i	$0.119841\pi$
$193$	10.8831	+	18.8501i	0.783383	+	1.35686i	−0.146577	+	0.989199i	$0.546826\pi$
$194$	4.63802	−	8.03328i	0.332990	−	0.576756i
$195$	1.73678	+	1.13138i	0.124373	+	0.0810197i
$196$	5.23939	−	4.64207i	0.374242	−	0.331576i
$197$		−	16.3332i		−	1.16370i	−0.813298	−	0.581848i	$-0.802330\pi$
$197$		−	16.3332i		−	1.16370i	0.813298	−	0.581848i	$-0.197670\pi$
$198$	5.06150	+	0.546485i	0.359705	+	0.0388370i
$199$	2.58227	−	1.49087i	0.183052	−	0.105685i	−0.405674	−	0.914018i	$-0.632963\pi$
$199$	2.58227	−	1.49087i	0.183052	−	0.105685i	0.588726	+	0.808333i	$0.299630\pi$
$200$	−7.64669	+	4.41482i	−0.540703	+	0.312175i
$201$	2.82076	+	5.55550i	0.198961	+	0.391855i
$202$		−	14.0282i		−	0.987018i
$203$	−2.17417	−	1.77508i	−0.152597	−	0.124586i
$204$	−6.13882	+	9.42370i	−0.429803	+	0.659791i
$205$	1.18092	−	2.04541i	0.0824791	−	0.142858i
$206$	−0.00655847	−	0.0113596i	−0.000456950	−	0.000791461i
$207$	2.42205	+	1.77022i	0.168344	+	0.123039i
$208$	0.278688	+	0.160901i	0.0193235	+	0.0111564i
$209$	1.46048			0.101024
$210$	−3.63355	+	16.6499i	−0.250739	+	1.14895i
$211$	−0.429035			−0.0295360			−0.0147680	−	0.999891i	$-0.504701\pi$
$211$	−0.429035			−0.0295360			−0.0147680	+	0.999891i	$0.504701\pi$
$212$	−6.29811	−	3.63622i	−0.432556	−	0.249736i
$213$	0.358075	−	6.65221i	0.0245349	−	0.455802i
$214$	3.54207	+	6.13504i	0.242131	+	0.419383i
$215$	−5.91027	+	10.2369i	−0.403077	+	0.698150i
$216$	−0.834655	+	5.12868i	−0.0567911	+	0.348962i
$217$	−1.94402	+	11.9635i	−0.131969	+	0.812139i
$218$			3.87783i			0.262640i
$219$	24.2071	−	12.2910i	1.63576	−	0.830546i
$220$	−5.46526	+	3.15537i	−0.368468	+	0.212735i
$221$	−1.80962	+	1.04479i	−0.121728	+	0.0702799i
$222$	−5.02110	+	2.54943i	−0.336994	+	0.171106i
$223$		−	4.77976i		−	0.320076i	−0.987111	−	0.160038i	$-0.948838\pi$
$223$		−	4.77976i		−	0.320076i	0.987111	−	0.160038i	$-0.0511618\pi$
$224$	−0.424357	+	2.61150i	−0.0283535	+	0.174488i
$225$	−10.7054	−	24.2292i	−0.713695	−	1.61528i
$226$	−10.3684	+	17.9586i	−0.689698	+	1.19459i
$227$	−8.37744	−	14.5101i	−0.556030	−	0.963072i	−0.997823	−	0.0659551i	$-0.978991\pi$
$227$	−8.37744	−	14.5101i	−0.556030	−	0.963072i	0.441793	−	0.897117i	$-0.354343\pi$
$228$	−0.0801238	+	1.48852i	−0.00530633	+	0.0985793i
$229$	−15.4243	−	8.90523i	−1.01927	−	0.588474i	−0.105376	−	0.994432i	$-0.533605\pi$
$229$	−15.4243	−	8.90523i	−1.01927	−	0.588474i	−0.913892	+	0.405958i	$0.866938\pi$
$230$	−3.71882			−0.245212
$231$	−1.65806	+	7.59769i	−0.109092	+	0.499891i
$232$	1.06086			0.0696487
$233$	15.7202	+	9.07605i	1.02986	+	0.594592i	0.916945	−	0.399013i	$-0.130647\pi$
$233$	15.7202	+	9.07605i	1.02986	+	0.594592i	0.112917	+	0.993604i	$0.463980\pi$
$234$	−0.569660	+	0.779417i	−0.0372398	+	0.0509521i
$235$	6.89388	+	11.9406i	0.449707	+	0.778916i
$236$	5.82082	−	10.0820i	0.378903	−	0.656279i
$237$	15.6203	−	23.9787i	1.01464	−	1.55758i
$238$	−13.3078	−	10.8650i	−0.862616	−	0.704275i
$239$		−	24.4821i		−	1.58362i	−0.610770	−	0.791808i	$-0.709140\pi$
$239$		−	24.4821i		−	1.58362i	0.610770	−	0.791808i	$-0.290860\pi$
$240$	−2.91611	−	5.74328i	−0.188234	−	0.370727i
$241$	2.34741	−	1.35528i	0.151210	−	0.0873012i	−0.422486	−	0.906369i	$-0.638842\pi$
$241$	2.34741	−	1.35528i	0.151210	−	0.0873012i	0.573696	+	0.819068i	$0.305509\pi$
$242$	7.03237	−	4.06014i	0.452058	−	0.260996i
$243$	−15.0283	−	4.14111i	−0.964069	−	0.265652i
$244$		−	8.16599i		−	0.522774i
$245$	−24.6924	−	8.24244i	−1.57754	−	0.526590i
$246$	0.921716	+	0.600427i	0.0587665	+	0.0382818i
$247$	−0.138477	+	0.239850i	−0.00881110	+	0.0152613i
$248$	−2.29055	−	3.96735i	−0.145450	−	0.251927i
$249$	17.0384	+	0.917141i	1.07976	+	0.0581215i
$250$	12.3337	+	7.12087i	0.780052	+	0.450363i
$251$	−16.7672			−1.05833			−0.529167	−	0.848518i	$-0.677495\pi$
$251$	−16.7672			−1.05833			−0.529167	+	0.848518i	$0.677495\pi$
$252$	−7.65257	−	2.10671i	−0.482066	−	0.132710i
$253$	−1.69697			−0.106688
$254$	2.42807	+	1.40185i	0.152351	+	0.0879597i
$255$	41.7645	+	2.24810i	2.61539	+	0.140781i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.4161	−	21.5053i	0.774495	−	1.34147i	−0.160582	−	0.987022i	$-0.551337\pi$
$257$	12.4161	−	21.5053i	0.774495	−	1.34147i	0.935078	−	0.354443i	$-0.115329\pi$
$258$	−4.61301	−	3.00502i	−0.287193	−	0.187084i
$259$	−3.05043	−	8.04283i	−0.189544	−	0.499757i
$260$		−	1.19672i		−	0.0742175i
$261$	−0.341633	+	3.16418i	−0.0211466	+	0.195858i
$262$	−6.33599	+	3.65809i	−0.391439	+	0.225997i
$263$	−16.0389	+	9.26008i	−0.989003	+	0.571001i	−0.904976	−	0.425463i	$-0.860111\pi$
$263$	−16.0389	+	9.26008i	−0.989003	+	0.571001i	−0.0840266	+	0.996464i	$0.526778\pi$
$264$	−1.33068	−	2.62077i	−0.0818976	−	0.161297i
$265$			27.0449i			1.66135i
$266$	−2.24756	−	0.365218i	−0.137807	−	0.0223929i
$267$	−8.18760	+	12.5688i	−0.501073	+	0.769198i
$268$	1.79862	−	3.11530i	0.109868	−	0.190297i
$269$	0.400087	+	0.692971i	0.0243938	+	0.0422512i	0.877965	−	0.478726i	$-0.158901\pi$
$269$	0.400087	+	0.692971i	0.0243938	+	0.0422512i	−0.853571	+	0.520977i	$0.825568\pi$
$270$	18.0694	−	6.84824i	1.09967	−	0.416770i
$271$	17.9972	+	10.3907i	1.09325	+	0.631189i	0.934440	−	0.356120i	$-0.115901\pi$
$271$	17.9972	+	10.3907i	1.09325	+	0.631189i	0.158811	+	0.987309i	$0.449234\pi$
$272$	6.49336			0.393718
$273$	−1.09053	−	0.992682i	−0.0660020	−	0.0600799i
$274$	22.4386			1.35557
$275$	12.9762	+	7.49183i	0.782496	+	0.451774i
$276$	0.0930981	−	1.72955i	0.00560384	−	0.104106i
$277$	−14.8338	−	25.6928i	−0.891275	−	1.54373i	−0.838348	−	0.545135i	$-0.816478\pi$
$277$	−14.8338	−	25.6928i	−0.891275	−	1.54373i	−0.0529265	−	0.998598i	$-0.516855\pi$
$278$	3.57115	−	6.18542i	0.214183	−	0.370977i
$279$	12.5709	−	5.55433i	0.752602	−	0.332529i
$280$	9.19963	−	3.48917i	0.549783	−	0.208518i
$281$		−	13.9631i		−	0.832967i	−0.909143	−	0.416484i	$-0.863262\pi$
$281$		−	13.9631i		−	0.832967i	0.909143	−	0.416484i	$-0.136738\pi$
$282$	−5.72589	+	2.90728i	−0.340972	+	0.173126i
$283$	7.65703	−	4.42079i	0.455163	−	0.262789i	−0.254845	−	0.966982i	$-0.582024\pi$
$283$	7.65703	−	4.42079i	0.455163	−	0.262789i	0.710008	+	0.704193i	$0.248691\pi$
$284$	−3.33092	+	1.92311i	−0.197654	+	0.114115i
$285$	4.94289	−	2.50972i	0.292791	−	0.148663i
$286$		−	0.546088i		−	0.0322909i
$287$	−1.06269	+	1.30161i	−0.0627286	+	0.0768317i
$288$	2.74408	−	1.21244i	0.161697	−	0.0714438i
$289$	−12.5819	+	21.7924i	−0.740110	+	1.28191i
$290$	−1.97257	−	3.41659i	−0.115833	−	0.200629i
$291$	0.863581	−	16.0433i	0.0506240	−	0.940477i
$292$	−13.5743	−	7.83714i	−0.794377	−	0.458634i
$293$	6.31967			0.369199			0.184600	−	0.982814i	$-0.440901\pi$
$293$	6.31967			0.369199			0.184600	+	0.982814i	$0.440901\pi$
$294$	4.45155	−	11.2776i	0.259619	−	0.657722i
$295$	−43.2932			−2.52063
$296$	2.81563	+	1.62560i	0.163655	+	0.0944862i
$297$	8.24541	−	3.12499i	0.478447	−	0.181330i
$298$	−9.90037	−	17.1479i	−0.573513	−	0.993354i
$299$	0.160901	−	0.278688i	0.00930512	−	0.0161169i
$300$	−8.34753	+	12.8143i	−0.481945	+	0.739834i
$301$	5.31856	−	6.51431i	0.306556	−	0.375479i
$302$			13.1821i			0.758544i
$303$	−11.0002	−	21.6648i	−0.631943	−	1.24461i
$304$	0.745335	−	0.430319i	0.0427479	−	0.0246805i
$305$	−26.2994	+	15.1839i	−1.50590	+	0.869430i
$306$	−2.09109	+	19.3675i	−0.119540	+	1.10717i
$307$		−	23.9301i		−	1.36577i	−0.730528	−	0.682883i	$-0.760726\pi$
$307$		−	23.9301i		−	1.36577i	0.730528	−	0.682883i	$-0.239274\pi$
$308$	4.19797	−	1.59218i	0.239202	−	0.0907227i
$309$	−0.0190364	−	0.0124007i	−0.00108294	−	0.000705454i
$310$	−8.51816	+	14.7539i	−0.483799	+	0.837964i
$311$	4.12858	+	7.15090i	0.234110	+	0.405491i	0.959014	−	0.283360i	$-0.0914491\pi$
$311$	4.12858	+	7.15090i	0.234110	+	0.405491i	−0.724904	+	0.688850i	$0.758116\pi$
$312$	0.556570	+	0.0299591i	0.0315096	+	0.00169610i
$313$	21.5320	+	12.4315i	1.21706	+	0.702670i	0.964288	−	0.264856i	$-0.0853245\pi$
$313$	21.5320	+	12.4315i	1.21706	+	0.702670i	0.252772	+	0.967526i	$0.418658\pi$
$314$	−3.02887			−0.170929
$315$	7.44442	+	28.5630i	0.419445	+	1.60935i
$316$	−16.5224			−0.929457
$317$	−26.8815	−	15.5200i	−1.50982	−	0.871692i	−0.999934	−	0.0114476i	$-0.996356\pi$
$317$	−26.8815	−	15.5200i	−1.50982	−	0.871692i	−0.509881	−	0.860245i	$-0.670311\pi$
$318$	−12.5780	−	0.677049i	−0.705340	−	0.0379670i
$319$	−0.900123	−	1.55906i	−0.0503972	−	0.0872905i
$320$	−1.85941	+	3.22059i	−0.103944	+	0.180037i
$321$	10.2811	+	6.69733i	0.573834	+	0.373809i
$322$	2.61150	+	0.424357i	0.145533	+	0.0236485i
$323$			5.58844i			0.310949i
$324$	2.73262	+	8.57513i	0.151812	+	0.476396i
$325$	−2.46071	+	1.42069i	−0.136496	+	0.0788059i
$326$	−21.2893	+	12.2914i	−1.17910	+	0.680756i
$327$	3.04079	+	5.98884i	0.168156	+	0.331184i
$328$		−	0.635105i		−	0.0350678i
$329$	−3.47860	−	9.17177i	−0.191782	−	0.505656i
$330$	−5.96617	+	9.15867i	−0.328427	+	0.504168i
$331$	9.15196	−	15.8517i	0.503037	−	0.871286i	−0.496957	−	0.867775i	$-0.665549\pi$
$331$	9.15196	−	15.8517i	0.503037	−	0.871286i	0.999994	−	0.00351036i	$-0.00111738\pi$
$332$	−4.92567	−	8.53151i	−0.270331	−	0.468228i
$333$	−5.75536	+	7.87457i	−0.315392	+	0.431524i
$334$	−8.94203	−	5.16268i	−0.489286	−	0.282490i
$335$	−13.3775			−0.730889
$336$	1.39243	+	4.36591i	0.0759635	+	0.238180i
$337$	−6.18537			−0.336939			−0.168469	−	0.985707i	$-0.553882\pi$
$337$	−6.18537			−0.336939			−0.168469	+	0.985707i	$0.553882\pi$
$338$	−11.1686	−	6.44822i	−0.607494	−	0.350737i
$339$	−1.93056	+	35.8654i	−0.104854	+	1.94794i
$340$	−12.0738	−	20.9125i	−0.654795	−	1.13414i
$341$	−3.88701	+	6.73249i	−0.210493	+	0.364585i
$342$	1.04347	+	2.36166i	0.0564247	+	0.127704i
$343$	16.3994	+	8.60582i	0.885484	+	0.464671i
$344$			3.17857i			0.171377i
$345$	−5.74328	+	2.91611i	−0.309208	+	0.156998i
$346$	−13.5810	+	7.84102i	−0.730122	+	0.421536i
$347$	−2.54549	+	1.46964i	−0.136649	+	0.0788943i	−0.566766	−	0.823879i	$-0.691806\pi$
$347$	−2.54549	+	1.46964i	−0.136649	+	0.0788943i	0.430117	+	0.902773i	$0.358472\pi$
$348$	1.63837	−	0.831869i	0.0878257	−	0.0445929i
$349$			7.71294i			0.412864i	0.978461	+	0.206432i	$0.0661852\pi$
$349$			7.71294i			0.412864i	−0.978461	+	0.206432i	$0.933815\pi$
$350$	−18.0959	−	14.7742i	−0.967264	−	0.789715i
$351$	−0.268593	+	1.65042i	−0.0143364	+	0.0880926i
$352$	−0.848486	+	1.46962i	−0.0452245	+	0.0783311i
$353$	9.34988	+	16.1945i	0.497644	+	0.861944i	0.999996	−	0.00271865i	$-0.000865376\pi$
$353$	9.34988	+	16.1945i	0.497644	+	0.861944i	−0.502353	+	0.864663i	$0.667532\pi$
$354$	1.08381	−	20.1348i	0.0576041	−	1.07015i
$355$	12.3871	+	7.15170i	0.657439	+	0.379573i
$356$	8.66047			0.459004
$357$	−29.0721	−	6.34447i	−1.53866	−	0.335785i
$358$	20.1296			1.06388
$359$	8.95230	+	5.16861i	0.472484	+	0.272789i	0.717279	−	0.696786i	$-0.245387\pi$
$359$	8.95230	+	5.16861i	0.472484	+	0.272789i	−0.244795	+	0.969575i	$0.578721\pi$
$360$	−9.00716	−	6.58314i	−0.474719	−	0.346962i
$361$	−9.12965	−	15.8130i	−0.480508	−	0.832264i
$362$	−0.588087	+	1.01860i	−0.0309092	+	0.0535362i
$363$	7.67691	−	11.7848i	0.402933	−	0.618543i
$364$	−0.136558	+	0.840383i	−0.00715761	+	0.0440480i
$365$			58.2899i			3.05103i
$366$	−6.40335	−	12.6114i	−0.334708	−	0.659209i
$367$	22.6414	−	13.0720i	1.18187	−	0.682352i	0.225423	−	0.974261i	$-0.427624\pi$
$367$	22.6414	−	13.0720i	1.18187	−	0.682352i	0.956446	+	0.291909i	$0.0942903\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	1.89430	+	0.204526i	0.0986136	+	0.0106472i
$370$		−	12.0906i		−	0.628563i
$371$	3.08610	−	18.9919i	0.160223	−	0.986012i
$372$	−6.64848	−	4.33097i	−0.344708	−	0.224550i
$373$	−12.7902	+	22.1533i	−0.662252	+	1.14705i	0.317770	+	0.948168i	$0.397066\pi$
$373$	−12.7902	+	22.1533i	−0.662252	+	1.14705i	−0.980022	+	0.198887i	$0.936267\pi$
$374$	−5.50953	−	9.54278i	−0.284891	−	0.493446i
$375$	24.6318	+	1.32588i	1.27198	+	0.0684680i
$376$	3.21084	+	1.85378i	0.165587	+	0.0956014i
$377$	0.341385			0.0175822
$378$	−13.4704	+	2.74719i	−0.692845	+	0.141300i
$379$	8.15992			0.419147			0.209574	−	0.977793i	$-0.432792\pi$
$379$	8.15992			0.419147			0.209574	+	0.977793i	$0.432792\pi$
$380$	−2.77177	−	1.60028i	−0.142189	−	0.0820927i
$381$	4.84912	+	0.261019i	0.248428	+	0.0133724i
$382$	1.89598	+	3.28393i	0.0970066	+	0.168020i
$383$	−4.94652	+	8.56762i	−0.252755	+	0.437785i	−0.964283	−	0.264873i	$-0.914670\pi$
$383$	−4.94652	+	8.56762i	−0.252755	+	0.437785i	0.711528	+	0.702658i	$0.248003\pi$
$384$	−1.45128	−	0.945399i	−0.0740605	−	0.0482447i
$385$	−12.9335	−	10.5595i	−0.659153	−	0.538160i
$386$		−	21.7662i		−	1.10787i
$387$	−9.48062	−	1.02361i	−0.481927	−	0.0520331i
$388$	−8.03328	+	4.63802i	−0.407828	+	0.235460i
$389$	25.6876	−	14.8308i	1.30241	−	0.751949i	0.321597	−	0.946877i	$-0.395781\pi$
$389$	25.6876	−	14.8308i	1.30241	−	0.751949i	0.980818	+	0.194928i	$0.0624472\pi$
$390$	−0.938407	−	1.84819i	−0.0475181	−	0.0935869i
$391$		−	6.49336i		−	0.328383i
$392$	−6.85848	+	1.40045i	−0.346406	+	0.0707335i
$393$	−6.91670	+	10.6178i	−0.348901	+	0.535599i
$394$	−8.16662	+	14.1450i	−0.411429	+	0.712615i
$395$	30.7219	+	53.2119i	1.54579	+	2.67738i
$396$	−4.11015	−	3.00402i	−0.206543	−	0.150958i
$397$	−15.5089	−	8.95410i	−0.778372	−	0.449393i	0.0574811	−	0.998347i	$-0.481693\pi$
$397$	−15.5089	−	8.95410i	−0.778372	−	0.449393i	−0.835853	+	0.548953i	$0.815026\pi$
$398$	−2.98175			−0.149462
$399$	−3.75747	+	1.19838i	−0.188109	+	0.0599941i
$400$	8.82964			0.441482
$401$	10.5185	+	6.07284i	0.525267	+	0.303263i	0.739087	−	0.673610i	$-0.235257\pi$
$401$	10.5185	+	6.07284i	0.525267	+	0.303263i	−0.213820	+	0.976873i	$0.568590\pi$
$402$	0.334895	−	6.22158i	0.0167031	−	0.310304i
$403$	−0.737103	−	1.27670i	−0.0367177	−	0.0635969i
$404$	−7.01408	+	12.1488i	−0.348964	+	0.604423i
$405$	22.5359	−	24.7453i	1.11982	−	1.22961i
$406$	0.995344	+	2.62435i	0.0493981	+	0.130244i
$407$		−	5.51721i		−	0.273478i
$408$	10.0282	−	5.09176i	0.496471	−	0.252080i
$409$	−13.4437	+	7.76171i	−0.664747	+	0.383792i	−0.794083	−	0.607809i	$-0.792049\pi$
$409$	−13.4437	+	7.76171i	−0.664747	+	0.383792i	0.129337	+	0.991601i	$0.458715\pi$
$410$	−2.04541	+	1.18092i	−0.101016	+	0.0583215i
$411$	34.6538	−	17.5952i	1.70935	−	0.867908i
$412$			0.0131169i			0.000646226i
$413$	30.4021	+	4.94021i	1.49599	+	0.243092i
$414$	−1.21244	−	2.74408i	−0.0595883	−	0.134864i
$415$	−18.3177	+	31.7272i	−0.899180	+	1.55743i
$416$	−0.160901	−	0.278688i	−0.00788880	−	0.0136638i
$417$	0.664935	−	12.3529i	0.0325620	−	0.604926i
$418$	−1.26481	−	0.730240i	−0.0618640	−	0.0357172i
$419$	36.5547			1.78581			0.892907	−	0.450241i	$-0.148662\pi$
$419$	36.5547			1.78581			0.892907	+	0.450241i	$0.148662\pi$
$420$	11.4717	−	12.6025i	0.559762	−	0.614938i
$421$	23.4202			1.14143			0.570716	−	0.821148i	$-0.306666\pi$
$421$	23.4202			1.14143			0.570716	+	0.821148i	$0.306666\pi$
$422$	0.371555	+	0.214518i	0.0180870	+	0.0104425i
$423$	−6.56321	+	8.97989i	−0.319114	+	0.436617i
$424$	3.63622	+	6.29811i	0.176590	+	0.305863i
$425$	−28.6670	+	49.6527i	−1.39055	+	2.40851i
$426$	−3.63621	+	5.58195i	−0.176175	+	0.270446i
$427$	20.2010	−	7.66171i	0.977597	−	0.370776i
$428$		−	7.08413i		−	0.342424i
$429$	−0.428214	−	0.843368i	−0.0206744	−	0.0407182i
$430$	10.2369	−	5.91027i	0.493667	−	0.285019i
$431$	−28.0412	+	16.1896i	−1.35070	+	0.779825i	−0.988347	−	0.152217i	$-0.951359\pi$
$431$	−28.0412	+	16.1896i	−1.35070	+	0.779825i	−0.362350	+	0.932042i	$0.618025\pi$
$432$	3.28717	−	4.02424i	0.158154	−	0.193616i
$433$			8.23533i			0.395765i	0.980226	+	0.197882i	$0.0634064\pi$
$433$			8.23533i			0.395765i	−0.980226	+	0.197882i	$0.936594\pi$
$434$	7.66535	−	9.38873i	0.367948	−	0.450673i
$435$	−5.72551	−	3.72973i	−0.274517	−	0.178827i
$436$	1.93891	−	3.35830i	0.0928571	−	0.160833i
$437$	−0.430319	−	0.745335i	−0.0205850	−	0.0356542i
$438$	−27.1094	−	1.45925i	−1.29534	−	0.0697254i
$439$	32.8679	+	18.9763i	1.56870	+	0.905690i	0.996321	+	0.0857013i	$0.0273131\pi$
$439$	32.8679	+	18.9763i	1.56870	+	0.905690i	0.572380	+	0.819989i	$0.306020\pi$
$440$	6.31074			0.300853
$441$	−1.96841	−	20.9075i	−0.0937338	−	0.995597i
$442$	2.08957			0.0993908
$443$	−10.9312	−	6.31113i	−0.519357	−	0.299851i	0.217315	−	0.976102i	$-0.430270\pi$
$443$	−10.9312	−	6.31113i	−0.519357	−	0.299851i	−0.736671	+	0.676251i	$0.763604\pi$
$444$	5.62311	+	0.302681i	0.266861	+	0.0143646i
$445$	−16.1034	−	27.8919i	−0.763374	−	1.32220i
$446$	−2.38988	+	4.13939i	−0.113164	+	0.196006i
$447$	−28.7365	−	18.7196i	−1.35919	−	0.885407i
$448$	1.67325	−	2.04945i	0.0790538	−	0.0968272i
$449$		−	2.14091i		−	0.101036i	−0.998723	−	0.0505180i	$-0.983913\pi$
$449$		−	2.14091i		−	0.101036i	0.998723	−	0.0505180i	$-0.0160872\pi$
$450$	−2.84345	+	26.3359i	−0.134042	+	1.24148i
$451$	−0.933363	+	0.538878i	−0.0439504	+	0.0253748i
$452$	17.9586	−	10.3684i	0.844704	−	0.487690i
$453$	10.3367	+	20.3582i	0.485661	+	0.956510i
$454$			16.7549i			0.786345i
$455$	2.96045	−	1.12282i	0.138788	−	0.0526385i
$456$	0.813647	−	1.24903i	0.0381025	−	0.0584912i
$457$	8.39792	−	14.5456i	0.392838	−	0.680415i	−0.599985	−	0.800012i	$-0.704827\pi$
$457$	8.39792	−	14.5456i	0.392838	−	0.680415i	0.992823	+	0.119596i	$0.0381600\pi$
$458$	8.90523	+	15.4243i	0.416114	+	0.720731i
$459$	11.9576	+	31.5506i	0.558132	+	1.47265i
$460$	3.22059	+	1.85941i	0.150161	+	0.0866955i
$461$	−7.14089			−0.332584			−0.166292	−	0.986077i	$-0.553179\pi$
$461$	−7.14089			−0.332584			−0.166292	+	0.986077i	$0.553179\pi$
$462$	5.23477	−	5.75076i	0.243543	−	0.267550i
$463$	−27.9179			−1.29745			−0.648727	−	0.761021i	$-0.724698\pi$
$463$	−27.9179			−1.29745			−0.648727	+	0.761021i	$0.724698\pi$
$464$	−0.918729	−	0.530428i	−0.0426509	−	0.0246245i
$465$	−1.58605	+	29.4651i	−0.0735512	+	1.36641i
$466$	−9.07605	−	15.7202i	−0.420440	−	0.728223i
$467$	0.0969170	−	0.167865i	0.00448479	−	0.00776788i	−0.863774	−	0.503879i	$-0.831906\pi$
$467$	0.0969170	−	0.167865i	0.00448479	−	0.00776788i	0.868259	+	0.496111i	$0.165239\pi$
$468$	0.883049	−	0.390165i	0.0408189	−	0.0180354i
$469$	9.39417	+	1.52651i	0.433782	+	0.0704877i
$470$		−	13.7878i		−	0.635982i
$471$	−4.67773	+	2.37508i	−0.215538	+	0.109438i
$472$	−10.0820	+	5.82082i	−0.464060	+	0.267925i
$473$	4.67130	−	2.69698i	0.214787	−	0.124007i
$474$	−25.5169	+	12.9560i	−1.17203	+	0.595089i
$475$			7.59913i			0.348672i
$476$	6.09237	+	16.0633i	0.279243	+	0.736260i
$477$	−19.9561	+	8.81740i	−0.913729	+	0.403721i
$478$	−12.2411	+	21.2021i	−0.559893	+	0.969763i
$479$	−16.3490	−	28.3172i	−0.747003	−	1.29385i	−0.949253	−	0.314514i	$-0.898159\pi$
$479$	−16.3490	−	28.3172i	−0.747003	−	1.29385i	0.202250	−	0.979334i	$-0.435175\pi$
$480$	−0.346215	+	6.43188i	−0.0158025	+	0.293574i
$481$	0.906072	+	0.523121i	0.0413133	+	0.0238523i
$482$	−2.71056			−0.123462
$483$	4.36591	−	1.39243i	0.198656	−	0.0633579i
$484$	−8.12028			−0.369104
$485$	29.8743	+	17.2480i	1.35652	+	0.783189i
$486$	10.9444	+	11.1005i	0.496447	+	0.503528i
$487$	11.2148	+	19.4246i	0.508191	+	0.880212i	0.999955	+	0.00948366i	$0.00301879\pi$
$487$	11.2148	+	19.4246i	0.508191	+	0.880212i	−0.491764	+	0.870728i	$0.663648\pi$
$488$	−4.08300	+	7.07196i	−0.184829	+	0.320132i
$489$	−23.2405	+	35.6765i	−1.05097	+	1.61335i
$490$	17.2630	+	19.4844i	0.779864	+	0.880214i
$491$			15.8118i			0.713579i	0.934185	+	0.356789i	$0.116129\pi$
$491$			15.8118i			0.713579i	−0.934185	+	0.356789i	$0.883871\pi$
$492$	−0.498016	−	0.980843i	−0.0224523	−	0.0442198i
$493$	5.96564	−	3.44426i	0.268679	−	0.155122i
$494$	0.239850	−	0.138477i	0.0107913	−	0.00623039i
$495$	−2.03228	+	18.8228i	−0.0913441	+	0.846023i
$496$			4.58111i			0.205698i
$497$	−7.88261	−	6.43569i	−0.353583	−	0.288680i
$498$	−14.2971	−	9.31345i	−0.640668	−	0.417346i
$499$	0.534922	−	0.926511i	0.0239464	−	0.0414763i	−0.853804	−	0.520595i	$-0.825710\pi$
$499$	0.534922	−	0.926511i	0.0239464	−	0.0414763i	0.877750	+	0.479118i	$0.159044\pi$
$500$	−7.12087	−	12.3337i	−0.318455	−	0.551580i
$501$	−17.8582	−	0.961272i	−0.797846	−	0.0429465i
$502$	14.5208	+	8.38358i	0.648094	+	0.374177i
$503$	−12.8209			−0.571656			−0.285828	−	0.958281i	$-0.592269\pi$
$503$	−12.8209			−0.571656			−0.285828	+	0.958281i	$0.592269\pi$
$504$	5.57396	+	5.65075i	0.248284	+	0.251704i
$505$	52.1683			2.32146
$506$	1.46962	+	0.848486i	0.0653327	+	0.0377198i
$507$	−22.3050	−	1.20063i	−0.990600	−	0.0533220i
$508$	−1.40185	−	2.42807i	−0.0621969	−	0.107728i
$509$	9.36597	−	16.2223i	0.415139	−	0.719042i	−0.580304	−	0.814400i	$-0.697066\pi$
$509$	9.36597	−	16.2223i	0.415139	−	0.719042i	0.995443	+	0.0953578i	$0.0303995\pi$
$510$	−35.0451	−	22.8292i	−1.55182	−	1.01089i
$511$	6.65149	−	40.9334i	0.294244	−	1.81079i
$512$			1.00000i			0.0441942i
$513$	3.46342	+	2.82907i	0.152914	+	0.124906i
$514$	−21.5053	+	12.4161i	−0.948559	+	0.547651i
$515$	0.0422444	−	0.0243898i	0.00186151	−	0.00107474i
$516$	2.49247	+	4.90893i	0.109725	+	0.216103i
$517$		−	6.29163i		−	0.276706i
$518$	−1.37967	+	8.49051i	−0.0606192	+	0.373052i
$519$	−14.8258	+	22.7591i	−0.650780	+	0.999013i
$520$	−0.598361	+	1.03639i	−0.0262399	+	0.0454488i
$521$	−6.99473	−	12.1152i	−0.306444	−	0.530777i	0.671137	−	0.741333i	$-0.265806\pi$
$521$	−6.99473	−	12.1152i	−0.306444	−	0.530777i	−0.977582	+	0.210556i	$0.932473\pi$
$522$	1.87795	−	2.56944i	0.0821958	−	0.112462i
$523$	22.2317	+	12.8355i	0.972124	+	0.561256i	0.899883	−	0.436131i	$-0.143652\pi$
$523$	22.2317	+	12.8355i	0.972124	+	0.561256i	0.0722409	+	0.997387i	$0.476985\pi$
$524$	7.31617			0.319608
$525$	−39.5321	−	8.62717i	−1.72532	−	0.376521i
$526$	18.5202			0.807517
$527$	−25.7615	−	14.8734i	−1.12219	−	0.647895i
$528$	−0.157985	+	2.93499i	−0.00687541	+	0.127729i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	13.5224	−	23.4216i	0.587377	−	1.01737i
$531$	−14.1148	−	31.9456i	−0.612531	−	1.38632i
$532$	1.76383	+	1.44007i	0.0764718	+	0.0624348i
$533$		−	0.204377i		−	0.00885257i
$534$	13.3751	−	6.79110i	0.578796	−	0.293879i
$535$	−22.8151	+	13.1723i	−0.986383	+	0.569489i
$536$	−3.11530	+	1.79862i	−0.134560	+	0.0776884i
$537$	31.0878	−	15.7846i	1.34154	−	0.681156i
$538$		−	0.800175i		−	0.0344980i
$539$	7.87746	+	8.89110i	0.339306	+	0.382967i
$540$	−19.0726	−	3.10393i	−0.820756	−	0.133572i
$541$	19.1183	−	33.1138i	0.821959	−	1.42367i	−0.0822631	−	0.996611i	$-0.526215\pi$
$541$	19.1183	−	33.1138i	0.821959	−	1.42367i	0.904222	−	0.427063i	$-0.140452\pi$
$542$	−10.3907	−	17.9972i	−0.446318	−	0.773045i
$543$	−0.109500	+	2.03425i	−0.00469907	+	0.0872979i
$544$	−5.62342	−	3.24668i	−0.241102	−	0.139200i
$545$	−14.4209			−0.617726
$546$	0.448087	+	1.40495i	0.0191763	+	0.0601265i
$547$	−28.9076			−1.23600			−0.618000	−	0.786178i	$-0.712057\pi$
$547$	−28.9076			−1.23600			−0.618000	+	0.786178i	$0.712057\pi$
$548$	−19.4324	−	11.2193i	−0.830112	−	0.479266i
$549$	−19.7784	−	14.4556i	−0.844122	−	0.616951i
$550$	−7.49183	−	12.9762i	−0.319453	−	0.553308i
$551$	0.456507	−	0.790694i	0.0194479	−	0.0336847i
$552$	−0.945399	+	1.45128i	−0.0402388	+	0.0617707i
$553$	−15.5021	−	40.8731i	−0.659215	−	1.73810i
$554$			29.6675i			1.26045i
$555$	−9.48086	−	18.6726i	−0.402440	−	0.792606i
$556$	−6.18542	+	3.57115i	−0.262320	+	0.151451i
$557$	−3.99845	+	2.30851i	−0.169420	+	0.0978146i	−0.582312	−	0.812965i	$-0.697852\pi$
$557$	−3.99845	+	2.30851i	−0.169420	+	0.0978146i	0.412892	+	0.910780i	$0.364519\pi$
$558$	−13.6639	−	1.47528i	−0.578439	−	0.0624534i
$559$			1.02287i			0.0432627i
$560$	−9.71170	−	1.57811i	−0.410394	−	0.0666872i
$561$	−15.9918	−	10.4174i	−0.675173	−	0.439823i
$562$	−6.98154	+	12.0924i	−0.294498	+	0.510086i
$563$	−5.47511	−	9.48317i	−0.230748	−	0.399668i	0.727280	−	0.686341i	$-0.240784\pi$
$563$	−5.47511	−	9.48317i	−0.230748	−	0.399668i	−0.958029	+	0.286673i	$0.907451\pi$
$564$	6.41240	+	0.345167i	0.270011	+	0.0145341i
$565$	−66.7850	−	38.5583i	−2.80967	−	1.62216i
$566$	−8.84158			−0.371639
$567$	−18.6493	+	14.8055i	−0.783197	+	0.621774i
$568$	3.84622			0.161384
$569$	−27.1792	−	15.6919i	−1.13941	−	0.657839i	−0.193126	−	0.981174i	$-0.561862\pi$
$569$	−27.1792	−	15.6919i	−1.13941	−	0.657839i	−0.946284	+	0.323335i	$0.895196\pi$
$570$	−5.53552	−	0.297966i	−0.231858	−	0.0124804i
$571$	11.0196	+	19.0866i	0.461158	+	0.798748i	0.999019	−	0.0442849i	$-0.0141009\pi$
$571$	11.0196	+	19.0866i	0.461158	+	0.798748i	−0.537861	+	0.843033i	$0.680768\pi$
$572$	−0.273044	+	0.472926i	−0.0114165	+	0.0197740i
$573$	5.50320	+	3.58491i	0.229899	+	0.149762i
$574$	1.57112	−	0.595884i	0.0655774	−	0.0248717i
$575$		−	8.82964i		−	0.368221i
$576$	−2.98267	−	0.322035i	−0.124278	−	0.0134181i
$577$	−17.0343	+	9.83473i	−0.709145	+	0.409425i	−0.810744	−	0.585400i	$-0.800937\pi$
$577$	−17.0343	+	9.83473i	−0.709145	+	0.409425i	0.101599	+	0.994825i	$0.467604\pi$
$578$	21.7924	−	12.5819i	0.906446	−	0.523337i
$579$	−17.0679	−	33.6153i	−0.709319	−	1.39701i
$580$			3.94514i			0.163813i
$581$	16.4838	−	20.1898i	0.683863	−	0.837614i
$582$	−8.76955	+	13.4621i	−0.363509	+	0.558024i
$583$	6.17056	−	10.6877i	0.255558	−	0.442640i
$584$	7.83714	+	13.5743i	0.324303	+	0.561710i
$585$	−2.89851	−	2.11846i	−0.119839	−	0.0875877i
$586$	−5.47300	−	3.15984i	−0.226087	−	0.130532i
$587$	16.6830			0.688583			0.344291	−	0.938863i	$-0.388119\pi$
$587$	16.6830			0.688583			0.344291	+	0.938863i	$0.388119\pi$
$588$	−9.49394	+	7.54089i	−0.391524	+	0.310981i
$589$	−3.94268			−0.162455
$590$	37.4930	+	21.6466i	1.54356	+	0.891176i
$591$	−1.52059	+	28.2491i	−0.0625489	+	1.16201i
$592$	−1.62560	−	2.81563i	−0.0668118	−	0.115721i
$593$	1.40969	−	2.44165i	0.0578890	−	0.100267i	−0.835629	−	0.549295i	$-0.814896\pi$
$593$	1.40969	−	2.44165i	0.0578890	−	0.100267i	0.893518	+	0.449028i	$0.148230\pi$
$594$	−8.70323	−	1.41639i	−0.357098	−	0.0581151i
$595$	40.4051	−	49.4893i	1.65645	−	2.02886i
$596$			19.8007i			0.811070i
$597$	−4.60495	+	2.33813i	−0.188468	+	0.0956934i
$598$	−0.278688	+	0.160901i	−0.0113964	+	0.00657971i
$599$	14.5195	−	8.38281i	0.593249	−	0.342512i	−0.173132	−	0.984899i	$-0.555389\pi$
$599$	14.5195	−	8.38281i	0.593249	−	0.342512i	0.766381	+	0.642386i	$0.222055\pi$
$600$	13.6363	−	6.92374i	0.556700	−	0.282661i
$601$		−	28.5332i		−	1.16389i	−0.813227	−	0.581947i	$-0.802291\pi$
$601$		−	28.5332i		−	1.16389i	0.813227	−	0.581947i	$-0.197709\pi$
$602$	−7.86316	+	2.98228i	−0.320478	+	0.121549i
$603$	−4.36144	−	9.87110i	−0.177611	−	0.401982i
$604$	6.59105	−	11.4160i	0.268186	−	0.464511i
$605$	15.0989	+	26.1521i	0.613859	+	1.06324i
$606$	−1.30600	+	24.2624i	−0.0530524	+	0.985592i
$607$	−33.3901	−	19.2778i	−1.35526	−	0.782461i	−0.366282	−	0.930504i	$-0.619369\pi$
$607$	−33.3901	−	19.2778i	−1.35526	−	0.782461i	−0.988981	+	0.148043i	$0.952703\pi$
$608$	−0.860639			−0.0349035
$609$	3.59507	+	3.27250i	0.145680	+	0.132608i
$610$	30.3679			1.22956
$611$	1.03325	+	0.596549i	0.0418009	+	0.0241338i
$612$	11.4947	−	15.7272i	0.464646	−	0.635735i
$613$	19.9449	+	34.5457i	0.805569	+	1.39529i	0.915906	+	0.401392i	$0.131474\pi$
$613$	19.9449	+	34.5457i	0.805569	+	1.39529i	−0.110337	+	0.993894i	$0.535193\pi$
$614$	−11.9651	+	20.7241i	−0.482871	+	0.836357i
$615$	−2.23288	+	3.42770i	−0.0900385	+	0.138218i
$616$	−4.43164	−	0.720122i	−0.178556	−	0.0290145i
$617$			0.810004i			0.0326095i	0.999867	+	0.0163048i	$0.00519020\pi$
$617$			0.810004i			0.0326095i	−0.999867	+	0.0163048i	$0.994810\pi$
$618$	0.0102856	+	0.0202576i	0.000413749	+	0.000814878i
$619$	−30.8338	+	17.8019i	−1.23931	+	0.715519i	−0.968954	−	0.247240i	$-0.920476\pi$
$619$	−30.8338	+	17.8019i	−1.23931	+	0.715519i	−0.270361	+	0.962759i	$0.587143\pi$
$620$	14.7539	−	8.51816i	0.592530	−	0.342098i
$621$	−4.02424	−	3.28717i	−0.161487	−	0.131910i
$622$		−	8.25715i		−	0.331082i
$623$	8.12565	+	21.4243i	0.325547	+	0.858346i
$624$	−0.467024	−	0.304230i	−0.0186959	−	0.0121790i
$625$	−4.40715	+	7.63341i	−0.176286	+	0.305336i
$626$	−12.4315	−	21.5320i	−0.496863	−	0.860591i
$627$	−2.52597	−	0.135968i	−0.100878	−	0.00543004i
$628$	2.62308	+	1.51444i	0.104672	+	0.0604326i
$629$	21.1112			0.841760
$630$	7.83447	−	28.4585i	0.312133	−	1.13382i
$631$	−19.4422			−0.773980			−0.386990	−	0.922084i	$-0.626485\pi$
$631$	−19.4422			−0.773980			−0.386990	+	0.922084i	$0.626485\pi$
$632$	14.3088	+	8.26120i	0.569174	+	0.328613i
$633$	0.742036	+	0.0399423i	0.0294933	+	0.00158756i
$634$	15.5200	+	26.8815i	0.616380	+	1.06760i
$635$	−5.21322	+	9.02956i	−0.206880	+	0.358327i
$636$	10.5544	+	6.87535i	0.418507	+	0.272625i
$637$	−2.20707	+	0.450667i	−0.0874472	+	0.0178561i
$638$			1.80025i			0.0712724i
$639$	−1.23862	+	11.4720i	−0.0489989	+	0.453824i
$640$	3.22059	−	1.85941i	0.127305	−	0.0734997i
$641$	−2.60088	+	1.50162i	−0.102728	+	0.0593103i	−0.550484	−	0.834846i	$-0.685557\pi$
$641$	−2.60088	+	1.50162i	−0.102728	+	0.0593103i	0.447756	+	0.894156i	$0.352223\pi$
$642$	−5.55501	−	10.9406i	−0.219239	−	0.431791i
$643$		−	24.5418i		−	0.967833i	−0.875114	−	0.483917i	$-0.839214\pi$
$643$		−	24.5418i		−	0.967833i	0.875114	−	0.483917i	$-0.160786\pi$
$644$	−2.04945	−	1.67325i	−0.0807595	−	0.0659354i
$645$	11.1751	−	17.1550i	0.440020	−	0.675476i
$646$	2.79422	−	4.83973i	0.109937	−	0.190417i
$647$	−13.4747	−	23.3388i	−0.529744	−	0.917544i	−0.999398	−	0.0346930i	$-0.988955\pi$
$647$	−13.4747	−	23.3388i	−0.529744	−	0.917544i	0.469654	−	0.882851i	$-0.344379\pi$
$648$	1.92105	−	8.79259i	0.0754658	−	0.345405i
$649$	17.1088	+	9.87777i	0.671579	+	0.387737i
$650$	2.84139			0.111448
$651$	4.47606	−	20.5105i	0.175431	−	0.803871i
$652$	24.5827			0.962734
$653$	−5.57020	−	3.21596i	−0.217979	−	0.125850i	0.387035	−	0.922065i	$-0.373499\pi$
$653$	−5.57020	−	3.21596i	−0.217979	−	0.125850i	−0.605014	+	0.796215i	$0.706833\pi$
$654$	0.361018	−	6.70688i	0.0141169	−	0.262260i
$655$	−13.6038	−	23.5624i	−0.531543	−	0.920660i
$656$	−0.317552	+	0.550017i	−0.0123983	+	0.0214745i
$657$	−43.0115	+	19.0042i	−1.67804	+	0.741423i
$658$	−1.57333	+	9.68229i	−0.0613347	+	0.377455i
$659$			37.0418i			1.44294i	0.692444	+	0.721471i	$0.256534\pi$
$659$			37.0418i			1.44294i	−0.692444	+	0.721471i	$0.743466\pi$
$660$	9.74618	−	4.94856i	0.379370	−	0.192622i
$661$	6.86798	−	3.96523i	0.267134	−	0.154230i	−0.360451	−	0.932778i	$-0.617377\pi$
$661$	6.86798	−	3.96523i	0.267134	−	0.154230i	0.627584	+	0.778549i	$0.284044\pi$
$662$	−15.8517	+	9.15196i	−0.616092	+	0.355701i
$663$	3.22709	−	1.63853i	0.125330	−	0.0636354i
$664$			9.85134i			0.382306i
$665$	1.35818	−	8.35826i	0.0526679	−	0.324119i
$666$	8.92157	−	3.94190i	0.345704	−	0.152745i
$667$	−0.530428	+	0.918729i	−0.0205383	+	0.0355733i
$668$	5.16268	+	8.94203i	0.199750	+	0.345978i
$669$	−0.444987	+	8.26682i	−0.0172042	+	0.319614i
$670$	11.5852	+	6.68874i	0.447576	+	0.258408i
$671$	13.8575			0.534962
$672$	0.977070	−	4.47720i	0.0376913	−	0.172712i
$673$	25.3535			0.977306			0.488653	−	0.872478i	$-0.337488\pi$
$673$	25.3535			0.977306			0.488653	+	0.872478i	$0.337488\pi$
$674$	5.35669	+	3.09269i	0.206332	+	0.119126i
$675$	16.2598	+	42.9023i	0.625842	+	1.65131i
$676$	6.44822	+	11.1686i	0.248009	+	0.429563i
$677$	0.966051	−	1.67325i	0.0371283	−	0.0643082i	−0.846864	−	0.531809i	$-0.821512\pi$
$677$	0.966051	−	1.67325i	0.0371283	−	0.0643082i	0.883992	+	0.467501i	$0.154846\pi$
$678$	19.6046	−	30.0950i	0.752910	−	1.15579i
$679$	−19.0107	−	15.5211i	−0.729564	−	0.595647i
$680$			24.1477i			0.926020i
$681$	13.1383	+	25.8759i	0.503461	+	0.991567i
$682$	6.73249	−	3.88701i	0.257800	−	0.148841i
$683$	10.4798	−	6.05052i	0.400999	−	0.231517i	−0.285916	−	0.958255i	$-0.592298\pi$
$683$	10.4798	−	6.05052i	0.400999	−	0.231517i	0.686915	+	0.726738i	$0.258964\pi$
$684$	0.277156	−	2.56700i	0.0105973	−	0.0981516i
$685$			83.4453i			3.18828i
$686$	−9.89938	−	15.6526i	−0.377960	−	0.597617i
$687$	25.8480	+	16.8380i	0.986163	+	0.642409i
$688$	1.58929	−	2.75272i	0.0605910	−	0.104947i
$689$	1.17014	+	2.02674i	0.0445787	+	0.0772126i
$690$	6.43188	+	0.346215i	0.244857	+	0.0131802i
$691$	−13.9242	−	8.03916i	−0.529703	−	0.305824i	0.211193	−	0.977444i	$-0.432265\pi$
$691$	−13.9242	−	8.03916i	−0.529703	−	0.305824i	−0.740895	+	0.671620i	$0.765599\pi$
$692$	15.6820			0.596142
$693$	3.57503	−	12.9862i	0.135804	−	0.493305i
$694$	2.93928			0.111573
$695$	23.0025	+	13.2805i	0.872533	+	0.503757i
$696$	−1.83480	−	0.0987637i	−0.0695480	−	0.00374363i
$697$	−2.06198	−	3.57146i	−0.0781031	−	0.135279i
$698$	3.85647	−	6.67960i	0.145970	−	0.252827i
$699$	−26.3438	−	17.1610i	−0.996415	−	0.649087i
$700$	8.28437	+	21.8428i	0.313120	+	0.825579i
$701$		−	9.02681i		−	0.340938i	−0.985363	−	0.170469i	$-0.945472\pi$
$701$		−	9.02681i		−	0.340938i	0.985363	−	0.170469i	$-0.0545283\pi$
$702$	1.05782	−	1.29500i	0.0399247	−	0.0488768i
$703$	2.42324	−	1.39906i	0.0913941	−	0.0527664i
$704$	1.46962	−	0.848486i	0.0553884	−	0.0319785i
$705$	−10.8116	−	21.2936i	−0.407190	−	0.801962i
$706$		−	18.6998i		−	0.703775i
$707$	−36.6345	−	5.95295i	−1.37778	−	0.223884i
$708$	−11.0060	+	16.8953i	−0.413631	+	0.634965i
$709$	19.1428	−	33.1564i	0.718925	−	1.24521i	−0.242501	−	0.970151i	$-0.577968\pi$
$709$	19.1428	−	33.1564i	0.718925	−	1.24521i	0.961426	−	0.275063i	$-0.0886987\pi$
$710$	−7.15170	−	12.3871i	−0.268398	−	0.464880i
$711$	−29.2483	+	40.0180i	−1.09690	+	1.50079i
$712$	−7.50019	−	4.33024i	−0.281082	−	0.162283i
$713$	4.58111			0.171564
$714$	22.0049	+	20.0305i	0.823514	+	0.749623i
$715$	2.03080			0.0759478
$716$	−17.4328	−	10.0648i	−0.651493	−	0.376140i
$717$	−2.27924	+	42.3430i	−0.0851197	+	1.58133i
$718$	−5.16861	−	8.95230i	−0.192891	−	0.334097i
$719$	15.1744	−	26.2829i	0.565911	−	0.980186i	−0.431053	−	0.902326i	$-0.641858\pi$
$719$	15.1744	−	26.2829i	0.565911	−	0.980186i	0.996964	−	0.0778600i	$-0.0248087\pi$
$720$	4.50886	+	10.2048i	0.168035	+	0.380309i
$721$	−0.0324487	+	0.0123069i	−0.00120845	+	0.000458333i
$722$			18.2593i			0.679541i
$723$	−4.18613	+	2.12548i	−0.155684	+	0.0790474i
$724$	1.01860	−	0.588087i	0.0378558	−	0.0218561i
$725$	8.11204	−	4.68349i	0.301274	−	0.173940i
$726$	−12.5408	+	6.36751i	−0.465433	+	0.236320i
$727$			13.4004i			0.496994i	0.968633	+	0.248497i	$0.0799366\pi$
$727$			13.4004i			0.496994i	−0.968633	+	0.248497i	$0.920063\pi$
$728$	0.538455	−	0.659514i	0.0199565	−	0.0244432i
$729$	25.6067	+	8.56135i	0.948396	+	0.317087i
$730$	29.1449	−	50.4805i	1.07870	−	1.86837i
$731$	10.3198	+	17.8744i	0.381692	+	0.661110i
$732$	−0.760238	+	14.1235i	−0.0280992	+	0.522018i
$733$	6.44759	+	3.72252i	0.238147	+	0.137494i	0.614325	−	0.789053i	$-0.289428\pi$
$733$	6.44759	+	3.72252i	0.238147	+	0.137494i	−0.376178	+	0.926548i	$0.622762\pi$
$734$	−26.1440			−0.964992
$735$	41.9393	+	16.5545i	1.54695	+	0.610622i
$736$	1.00000			0.0368605
$737$	5.28657	+	3.05220i	0.194733	+	0.112429i
$738$	−1.53825	−	1.12428i	−0.0566239	−	0.0413852i
$739$	8.51929	+	14.7558i	0.313387	+	0.542802i	0.979093	−	0.203412i	$-0.0652029\pi$
$739$	8.51929	+	14.7558i	0.313387	+	0.542802i	−0.665706	+	0.746214i	$0.731870\pi$
$740$	−6.04532	+	10.4708i	−0.222231	+	0.384915i
$741$	0.261833	−	0.401939i	0.00961866	−	0.0147656i
$742$	−12.1686	+	14.9045i	−0.446724	+	0.547160i
$743$			10.8575i			0.398322i	0.979967	+	0.199161i	$0.0638216\pi$
$743$			10.8575i			0.398322i	−0.979967	+	0.199161i	$0.936178\pi$
$744$	3.59227	+	7.07497i	0.131699	+	0.259381i
$745$	63.7702	−	36.8177i	2.33636	−	1.34890i
$746$	22.1533	−	12.7902i	0.811090	−	0.468283i
$747$	−29.3833	−	3.17248i	−1.07508	−	0.116075i
$748$			11.0191i			0.402897i
$749$	17.5247	−	6.64665i	0.640340	−	0.242863i
$750$	−20.6688	−	13.4641i	−0.754717	−	0.491640i
$751$	−15.2654	+	26.4405i	−0.557043	+	0.964827i	0.440698	+	0.897655i	$0.354731\pi$
$751$	−15.2654	+	26.4405i	−0.557043	+	0.964827i	−0.997741	+	0.0671716i	$0.978603\pi$
$752$	−1.85378	−	3.21084i	−0.0676004	−	0.117087i
$753$	28.9996	+	1.56099i	1.05680	+	0.0568856i
$754$	−0.295648	−	0.170693i	−0.0107669	−	0.00621625i
$755$	−49.0218			−1.78409
$756$	13.0393	+	4.35609i	0.474236	+	0.158429i
$757$	42.4375			1.54242			0.771209	−	0.636582i	$-0.219652\pi$
$757$	42.4375			1.54242			0.771209	+	0.636582i	$0.219652\pi$
$758$	−7.06670	−	4.07996i	−0.256674	−	0.148191i
$759$	2.93499	+	0.157985i	0.106534	+	0.00573449i
$760$	1.60028	+	2.77177i	0.0580483	+	0.100543i
$761$	9.43081	−	16.3346i	0.341866	−	0.592130i	−0.642913	−	0.765939i	$-0.722274\pi$
$761$	9.43081	−	16.3346i	0.341866	−	0.592130i	0.984779	+	0.173809i	$0.0556076\pi$
$762$	−4.06895	−	2.65061i	−0.147403	−	0.0960215i
$763$	10.1269	+	1.64558i	0.366620	+	0.0595741i
$764$		−	3.79195i		−	0.137188i
$765$	−72.0244	−	7.77639i	−2.60405	−	0.281156i
$766$	8.56762	−	4.94652i	0.309561	−	0.178725i
$767$	−3.24439	+	1.87315i	−0.117148	+	0.0676354i
$768$	0.784148	+	1.54438i	0.0282955	+	0.0557280i
$769$			34.7688i			1.25379i	0.779102	+	0.626897i	$0.215675\pi$
$769$			34.7688i			1.25379i	−0.779102	+	0.626897i	$0.784325\pi$
$770$	5.92102	+	15.6115i	0.213379	+	0.562600i
$771$	−23.4763	+	36.0386i	−0.845480	+	1.29790i
$772$	−10.8831	+	18.8501i	−0.391692	+	0.678430i
$773$	13.2551	+	22.9586i	0.476754	+	0.825762i	0.999645	−	0.0266376i	$-0.00848000\pi$
$773$	13.2551	+	22.9586i	0.476754	+	0.825762i	−0.522891	+	0.852399i	$0.675147\pi$
$774$	7.69865	+	5.62678i	0.276722	+	0.202251i
$775$	−35.0303	−	20.2248i	−1.25833	−	0.726495i
$776$	9.27603			0.332990
$777$	4.52708	+	14.1944i	0.162408	+	0.509223i
$778$	−29.6615			−1.06342
$779$	−0.473366	−	0.273298i	−0.0169601	−	0.00979191i
$780$	−0.111412	+	2.06979i	−0.00398921	+	0.0741102i
$781$	−3.26346	−	5.65248i	−0.116776	−	0.202262i
$782$	−3.24668	+	5.62342i	−0.116101	+	0.201093i
$783$	0.885449	−	5.44079i	0.0316434	−	0.194438i
$784$	6.63984	+	2.21641i	0.237137	+	0.0791576i
$785$		−	11.2638i		−	0.402024i
$786$	11.2990	−	5.73696i	0.403020	−	0.204631i
$787$	−13.8063	+	7.97107i	−0.492141	+	0.284138i	−0.725462	−	0.688262i	$-0.758374\pi$
$787$	−13.8063	+	7.97107i	−0.492141	+	0.284138i	0.233321	+	0.972400i	$0.425041\pi$
$788$	14.1450	−	8.16662i	0.503895	−	0.290924i
$789$	28.6022	−	14.5225i	1.01826	−	0.517016i
$790$		−	61.4438i		−	2.18607i
$791$	42.4991	+	34.6980i	1.51109	+	1.23372i
$792$	2.05748	+	4.65663i	0.0731094	+	0.165466i
$793$	−1.31391	+	2.27576i	−0.0466584	+	0.0808148i
$794$	8.95410	+	15.5089i	0.317769	+	0.550392i
$795$	2.51783	−	46.7754i	0.0892981	−	1.65895i
$796$	2.58227	+	1.49087i	0.0915261	+	0.0528426i
$797$	25.4808			0.902576			0.451288	−	0.892378i	$-0.350965\pi$
$797$	25.4808			0.902576			0.451288	+	0.892378i	$0.350965\pi$
$798$	3.85325	+	0.840904i	0.136404	+	0.0297677i
$799$	24.0745			0.851696
$800$	−7.64669	−	4.41482i	−0.270351	−	0.156087i
$801$	15.3310	−	20.9761i	0.541693	−	0.741153i
$802$	−6.07284	−	10.5185i	−0.214440	−	0.371420i
$803$	13.2994	−	23.0353i	0.469326	−	0.812897i
$804$	−3.40082	+	5.22060i	−0.119938	+	0.184116i
$805$	−1.57811	+	9.71170i	−0.0556209	+	0.342292i
$806$			1.47421i			0.0519267i
$807$	−0.627455	−	1.23577i	−0.0220875	−	0.0435013i
$808$	12.1488	−	7.01408i	0.427392	−	0.246755i
$809$	4.77000	−	2.75396i	0.167704	−	0.0968242i	−0.413799	−	0.910368i	$-0.635798\pi$
$809$	4.77000	−	2.75396i	0.167704	−	0.0968242i	0.581503	+	0.813544i	$0.302465\pi$
$810$	−31.8894	+	10.1621i	−1.12048	+	0.357061i
$811$		−	29.2584i		−	1.02740i	−0.857969	−	0.513701i	$-0.828274\pi$
$811$		−	29.2584i		−	1.02740i	0.857969	−	0.513701i	$-0.171726\pi$
$812$	0.450182	−	2.77043i	0.0157983	−	0.0972229i
$813$	−30.1596	−	19.6467i	−1.05774	−	0.689039i
$814$	−2.75860	+	4.77804i	−0.0966890	+	0.167470i
$815$	−45.7094	−	79.1710i	−1.60113	−	2.77324i
$816$	−11.2306	−	0.604519i	−0.393149	−	0.0211624i
$817$	2.36910	+	1.36780i	0.0828844	+	0.0478533i
$818$	15.5234			0.542763
$819$	1.79371	+	1.81842i	0.0626772	+	0.0635406i
$820$	2.36184			0.0824791
$821$	10.9846	+	6.34199i	0.383367	+	0.221337i	0.679282	−	0.733877i	$-0.262291\pi$
$821$	10.9846	+	6.34199i	0.383367	+	0.221337i	−0.295915	+	0.955214i	$0.595625\pi$
$822$	−38.8087	−	2.08899i	−1.35361	−	0.0728620i
$823$	21.5000	+	37.2391i	0.749442	+	1.29807i	0.948090	+	0.318001i	$0.103012\pi$
$823$	21.5000	+	37.2391i	0.749442	+	1.29807i	−0.198648	+	0.980071i	$0.563655\pi$
$824$	0.00655847	−	0.0113596i	0.000228475	−	0.000395731i
$825$	−21.7455	−	14.1655i	−0.757082	−	0.493180i
$826$	−23.8589	−	19.4794i	−0.830157	−	0.677775i
$827$			8.94164i			0.310931i	0.987841	+	0.155466i	$0.0496878\pi$
$827$			8.94164i			0.310931i	−0.987841	+	0.155466i	$0.950312\pi$
$828$	−0.322035	+	2.98267i	−0.0111915	+	0.103655i
$829$	−14.7662	+	8.52524i	−0.512850	+	0.296094i	−0.734004	−	0.679145i	$-0.762351\pi$
$829$	−14.7662	+	8.52524i	−0.512850	+	0.296094i	0.221155	+	0.975239i	$0.429017\pi$
$830$	31.7272	−	18.3177i	1.10127	−	0.635817i
$831$	23.2637	+	45.8180i	0.807010	+	1.58941i
$832$			0.321801i			0.0111564i
$833$	−34.0213	+	30.1426i	−1.17877	+	1.04438i
$834$	−6.75232	+	10.3655i	−0.233814	+	0.358928i
$835$	19.1991	−	33.2538i	0.664412	−	1.15080i
$836$	0.730240	+	1.26481i	0.0252559	+	0.0437445i
$837$	−22.2591	+	8.43614i	−0.769387	+	0.291596i
$838$	−31.6573	−	18.2774i	−1.09358	−	0.631381i
$839$	−21.7261			−0.750068			−0.375034	−	0.927011i	$-0.622369\pi$
$839$	−21.7261			−0.750068			−0.375034	+	0.927011i	$0.622369\pi$
$840$	−16.2360	+	5.17821i	−0.560196	+	0.178665i
$841$	27.8746			0.961193
$842$	−20.2825	−	11.7101i	−0.698981	−	0.403557i
$843$	−1.29994	+	24.1498i	−0.0447721	+	0.831763i
$844$	−0.214518	−	0.371555i	−0.00738400	−	0.0127895i
$845$	23.9798	−	41.5342i	0.824930	−	1.42882i
$846$	10.1739	−	4.49520i	0.349784	−	0.154548i
$847$	−7.61882	−	20.0880i	−0.261786	−	0.690231i
$848$		−	7.27243i		−	0.249736i
$849$	−13.6548	+	6.93311i	−0.468630	+	0.237944i
$850$	49.6527	−	28.6670i	1.70307	−	0.983270i
$851$	−2.81563	+	1.62560i	−0.0965184	+	0.0557249i
$852$	5.94002	−	3.01600i	0.203502	−	0.103327i
$853$			47.7456i			1.63478i	0.576087	+	0.817389i	$0.304579\pi$
$853$			47.7456i			1.63478i	−0.576087	+	0.817389i	$0.695421\pi$
$854$	−21.3255	−	3.46529i	−0.729743	−	0.118580i
$855$	−8.78260	+	3.88050i	−0.300359	+	0.132710i
$856$	−3.54207	+	6.13504i	−0.121065	+	0.209691i
$857$	−20.5028	−	35.5118i	−0.700361	−	1.21306i	−0.968340	−	0.249636i	$-0.919689\pi$
$857$	−20.5028	−	35.5118i	−0.700361	−	1.21306i	0.267979	−	0.963425i	$-0.413644\pi$
$858$	−0.0508397	+	0.944485i	−0.00173564	+	0.0322442i
$859$	34.5178	+	19.9289i	1.17773	+	0.679965i	0.955489	−	0.295026i	$-0.0953285\pi$
$859$	34.5178	+	19.9289i	1.17773	+	0.679965i	0.222244	+	0.974991i	$0.428662\pi$
$860$	−11.8205			−0.403077
$861$	1.95915	−	2.15226i	0.0667677	−	0.0733490i
$862$	32.3792			1.10284
$863$	−4.23946	−	2.44766i	−0.144313	−	0.0833191i	0.426105	−	0.904674i	$-0.359885\pi$
$863$	−4.23946	−	2.44766i	−0.144313	−	0.0833191i	−0.570418	+	0.821355i	$0.693219\pi$
$864$	−4.85889	+	1.84151i	−0.165303	+	0.0626493i
$865$	−29.1594	−	50.5055i	−0.991448	−	1.71724i
$866$	4.11766	−	7.13200i	0.139924	−	0.242355i
$867$	23.7898	−	36.5197i	0.807943	−	1.24027i
$868$	−11.3327	+	4.29820i	−0.384659	+	0.145890i
$869$		−	28.0381i		−	0.951126i
$870$	3.09357	+	6.09279i	0.104882	+	0.206565i
$871$	−1.00251	+	0.578797i	−0.0339686	+	0.0196118i
$872$	−3.35830	+	1.93891i	−0.113726	+	0.0656599i
$873$	−2.98721	+	27.6673i	−0.101102	+	0.936396i
$874$			0.860639i			0.0291115i
$875$	23.8300	−	29.1877i	0.805602	−	0.986723i
$876$	22.7478	+	14.8184i	0.768577	+	0.500669i
$877$	7.10336	−	12.3034i	0.239863	−	0.415455i	−0.720812	−	0.693131i	$-0.756231\pi$
$877$	7.10336	−	12.3034i	0.239863	−	0.415455i	0.960675	+	0.277676i	$0.0895641\pi$
$878$	−18.9763	−	32.8679i	−0.640419	−	1.10924i
$879$	−10.9302	−	0.588349i	−0.368665	−	0.0198445i
$880$	−5.46526	−	3.15537i	−0.184234	−	0.106368i
$881$	−43.0998			−1.45207			−0.726035	−	0.687658i	$-0.758639\pi$
$881$	−43.0998			−1.45207			−0.726035	+	0.687658i	$0.758639\pi$
$882$	−8.74908	+	19.0907i	−0.294597	+	0.642816i
$883$	51.5871			1.73604			0.868022	−	0.496526i	$-0.165391\pi$
$883$	51.5871			1.73604			0.868022	+	0.496526i	$0.165391\pi$
$884$	−1.80962	−	1.04479i	−0.0608642	−	0.0351399i
$885$	74.8776	+	4.03051i	2.51698	+	0.135484i
$886$	6.31113	+	10.9312i	0.212027	+	0.367241i
$887$	−13.6369	+	23.6199i	−0.457884	+	0.793078i	−0.998849	−	0.0479673i	$-0.984726\pi$
$887$	−13.6369	+	23.6199i	−0.457884	+	0.793078i	0.540965	+	0.841045i	$0.318059\pi$
$888$	−4.71842	−	3.07368i	−0.158340	−	0.103146i
$889$	4.69129	−	5.74602i	0.157341	−	0.192715i
$890$			32.2068i			1.07957i
$891$	−14.5518	+	4.63718i	−0.487502	+	0.155351i
$892$	4.13939	−	2.38988i	0.138597	−	0.0800191i
$893$	2.76338	−	1.59544i	0.0924728	−	0.0533892i
$894$	15.5267	+	30.5799i	0.519291	+	1.02274i
$895$			74.8585i			2.50224i
$896$	−2.47380	+	0.938245i	−0.0826439	+	0.0313446i
$897$	−0.304230	+	0.467024i	−0.0101580	+	0.0155935i
$898$	−1.07046	+	1.85409i	−0.0357216	+	0.0618717i
$899$	2.42995	+	4.20880i	0.0810433	+	0.140371i
$900$	15.6304	−	21.3858i	0.521014	−	0.712860i
$901$	40.8959	+	23.6113i	1.36244	+	0.786605i
$902$	1.07776			0.0358853
$903$	−9.80516	+	10.7717i	−0.326295	+	0.358458i
$904$	−20.7369			−0.689698
$905$	−3.78798	−	2.18699i	−0.125917	−	0.0726980i
$906$	1.22723	−	22.7990i	0.0407719	−	0.757448i
$907$	−3.47967	−	6.02696i	−0.115540	−	0.200122i	0.802455	−	0.596712i	$-0.203527\pi$
$907$	−3.47967	−	6.02696i	−0.115540	−	0.200122i	−0.917996	+	0.396590i	$0.870193\pi$
$908$	8.37744	−	14.5101i	0.278015	−	0.481536i
$909$	17.0083	+	38.4944i	0.564131	+	1.27678i
$910$	−3.12524	−	0.507837i	−0.103601	−	0.0168346i
$911$		−	41.3796i		−	1.37097i	−0.728089	−	0.685483i	$-0.759591\pi$
$911$		−	41.3796i		−	1.37097i	0.728089	−	0.685483i	$-0.240409\pi$
$912$	−1.32915	+	0.674868i	−0.0440127	+	0.0223471i
$913$	14.4777	−	8.35873i	0.479144	−	0.276634i
$914$	−14.5456	+	8.39792i	−0.481126	+	0.277778i
$915$	46.8996	−	23.8129i	1.55045	−	0.787231i
$916$		−	17.8105i		−	0.588474i
$917$	6.86436	+	18.0988i	0.226681	+	0.597674i
$918$	5.41972	−	33.3024i	0.178877	−	1.09914i
$919$	−23.8946	+	41.3866i	−0.788210	+	1.36522i	0.138853	+	0.990313i	$0.455658\pi$
$919$	−23.8946	+	41.3866i	−0.788210	+	1.36522i	−0.927063	+	0.374906i	$0.877675\pi$
$920$	−1.85941	−	3.22059i	−0.0613030	−	0.106180i
$921$	−2.22785	+	41.3883i	−0.0734102	+	1.36379i
$922$	6.18419	+	3.57044i	0.203666	+	0.117586i
$923$	1.23772			0.0407399
$924$	−7.40882	+	2.36292i	−0.243732	+	0.0777344i
$925$	28.7070			0.943879
$926$	24.1776	+	13.9589i	0.794525	+	0.458719i
$927$	0.0317699	+	0.0232199i	0.00104346	+	0.000762642i
$928$	0.530428	+	0.918729i	0.0174122	+	0.0301588i
$929$	−8.20947	+	14.2192i	−0.269344	+	0.466517i	−0.968693	−	0.248263i	$-0.920140\pi$
$929$	−8.20947	+	14.2192i	−0.269344	+	0.466517i	0.699349	+	0.714781i	$0.253474\pi$
$930$	16.1061	−	24.7245i	0.528140	−	0.810749i
$931$	−1.90753	+	5.71451i	−0.0625168	+	0.187285i
$932$			18.1521i			0.594592i
$933$	−6.47483	−	12.7522i	−0.211976	−	0.417488i
$934$	−0.167865	+	0.0969170i	−0.00549272	+	0.00317122i
$935$	35.4879	−	20.4890i	1.16058	−	0.670061i
$936$	−0.959825	−	0.103631i	−0.0313729	−	0.00338729i
$937$		−	7.18711i		−	0.234793i	−0.993085	−	0.117396i	$-0.962545\pi$
$937$		−	7.18711i		−	0.234793i	0.993085	−	0.117396i	$-0.0374548\pi$
$938$	−7.37233	−	6.01908i	−0.240715	−	0.196530i
$939$	−36.0832	−	23.5054i	−1.17753	−	0.767071i
$940$	−6.89388	+	11.9406i	−0.224854	+	0.389458i
$941$	−26.3922	−	45.7127i	−0.860362	−	1.49019i	−0.871580	−	0.490254i	$-0.836904\pi$
$941$	−26.3922	−	45.7127i	−0.860362	−	1.49019i	0.0112176	−	0.999937i	$-0.496429\pi$
$942$	5.23858	+	0.281982i	0.170682	+	0.00918747i
$943$	0.550017	+	0.317552i	0.0179110	+	0.0103409i
$944$	11.6416			0.378903
$945$	−10.2163	−	50.0942i	−0.332336	−	1.62956i
$946$	−5.39395			−0.175373
$947$	9.65050	+	5.57172i	0.313599	+	0.181056i	0.648536	−	0.761184i	$-0.275382\pi$
$947$	9.65050	+	5.57172i	0.313599	+	0.181056i	−0.334937	+	0.942241i	$0.608715\pi$
$948$	28.5763	+	1.53820i	0.928114	+	0.0499585i
$949$	2.52200	+	4.36823i	0.0818676	+	0.141799i
$950$	3.79956	−	6.58104i	0.123274	−	0.213517i
$951$	45.0479	+	29.3453i	1.46078	+	0.951585i
$952$	2.75550	−	16.9574i	0.0893063	−	0.549592i
$953$		−	5.01854i		−	0.162566i	−0.996691	−	0.0812832i	$-0.974098\pi$
$953$		−	5.01854i		−	0.162566i	0.996691	−	0.0812832i	$-0.0259018\pi$
$954$	21.6912	+	2.34198i	0.702280	+	0.0758243i
$955$	−12.2123	+	7.05080i	−0.395182	+	0.228159i
$956$	21.2021	−	12.2411i	0.685726	−	0.395904i
$957$	1.41166	+	2.78026i	0.0456325	+	0.0898732i
$958$			32.6979i			1.05642i
$959$	9.52198	−	58.5985i	0.307481	−	1.89224i
$960$	3.51577	−	5.39706i	0.113471	−	0.174189i
$961$	−5.00673	+	8.67192i	−0.161508	+	0.279739i
$962$	−0.523121	−	0.906072i	−0.0168661	−	0.0292129i
$963$	−17.1581	−	12.5405i	−0.552912	−	0.404112i
$964$	2.34741	+	1.35528i	0.0756050	+	0.0436506i
$965$	80.9447			2.60570
$966$	−4.47720	−	0.977070i	−0.144052	−	0.0314367i
$967$	26.5549			0.853948			0.426974	−	0.904264i	$-0.359580\pi$
$967$	26.5549			0.853948			0.426974	+	0.904264i	$0.359580\pi$
$968$	7.03237	+	4.06014i	0.226029	+	0.130498i
$969$	0.520273	−	9.66547i	0.0167136	−	0.310499i
$970$	−17.2480	−	29.8743i	−0.553798	−	0.959207i
$971$	6.70238	−	11.6089i	0.215090	−	0.372546i	−0.738211	−	0.674570i	$-0.764329\pi$
$971$	6.70238	−	11.6089i	0.215090	−	0.372546i	0.953300	+	0.302024i	$0.0976623\pi$
$972$	−3.92787	−	15.0855i	−0.125986	−	0.483867i
$973$	−14.6378	−	11.9509i	−0.469265	−	0.383128i
$974$		−	22.4296i		−	0.718690i
$975$	4.38818	−	2.22807i	0.140534	−	0.0713553i
$976$	7.07196	−	4.08300i	0.226368	−	0.130694i
$977$	−11.0601	+	6.38556i	−0.353844	+	0.204292i	−0.666377	−	0.745615i	$-0.732156\pi$
$977$	−11.0601	+	6.38556i	−0.353844	+	0.204292i	0.312533	+	0.949907i	$0.398823\pi$
$978$	37.9651	−	19.2765i	1.21399	−	0.616395i
$979$			14.6966i			0.469705i
$980$	−5.20803	−	25.5055i	−0.166364	−	0.814742i
$981$	−4.70164	−	10.6411i	−0.150112	−	0.339743i
$982$	7.90592	−	13.6935i	0.252288	−	0.436976i
$983$	−16.1971	−	28.0543i	−0.516608	−	0.894792i	−0.999814	−	0.0192850i	$-0.993861\pi$
$983$	−16.1971	−	28.0543i	−0.516608	−	0.894792i	0.483206	−	0.875507i	$-0.339472\pi$
$984$	−0.0591270	+	1.09844i	−0.00188490	+	0.0350171i
$985$	−52.6028	−	30.3702i	−1.67606	−	0.967676i
$986$	−6.88853			−0.219375
$987$	5.16253	+	16.1869i	0.164325	+	0.515234i
$988$	−0.276955			−0.00881110
$989$	−2.75272	−	1.58929i	−0.0875316	−	0.0505364i
$990$	11.1714	−	15.2849i	0.355051	−	0.485786i
$991$	−6.04032	−	10.4621i	−0.191877	−	0.332341i	0.753995	−	0.656880i	$-0.228124\pi$
$991$	−6.04032	−	10.4621i	−0.191877	−	0.332341i	−0.945872	+	0.324539i	$0.894791\pi$
$992$	2.29055	−	3.96735i	0.0727251	−	0.125964i
$993$	−17.3045	+	26.5641i	−0.549142	+	0.842988i
$994$	3.60869	+	9.51478i	0.114461	+	0.301790i
$995$		−	11.0886i		−	0.351532i
$996$	7.72491	+	15.2142i	0.244773	+	0.482081i
$997$	−18.4131	+	10.6308i	−0.583150	+	0.336682i	−0.762384	−	0.647125i	$-0.775971\pi$
$997$	−18.4131	+	10.6308i	−0.583150	+	0.336682i	0.179235	+	0.983806i	$0.442638\pi$
$998$	−0.926511	+	0.534922i	−0.0293282	+	0.0169326i
$999$	10.6873	−	13.0836i	0.338130	−	0.413948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.1	✓	56
3.2	odd	2	inner	966.2.l.c.47.20	yes	56
7.3	odd	6	inner	966.2.l.c.185.20	yes	56
21.17	even	6	inner	966.2.l.c.185.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.1	✓	56	1.1	even	1	trivial
966.2.l.c.47.20	yes	56	3.2	odd	2	inner
966.2.l.c.185.1	yes	56	21.17	even	6	inner
966.2.l.c.185.20	yes	56	7.3	odd	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72955 - 0.0930981i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85941 - 3.22059i) q^{5} +(1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} -1.00000i q^{8} +(2.98267 + 0.322035i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72955 - 0.0930981i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85941 - 3.22059i) q^{5} +(1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} -1.00000i q^{8} +(2.98267 + 0.322035i) q^{9} +(-3.22059 + 1.85941i) q^{10} +(-1.46962 + 0.848486i) q^{11} +(-0.784148 - 1.54438i) q^{12} -0.321801i q^{13} +(2.47380 - 0.938245i) q^{14} +(-3.51577 + 5.39706i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.24668 - 5.62342i) q^{17} +(-2.42205 - 1.77022i) q^{18} +(-0.745335 - 0.430319i) q^{19} +3.71882 q^{20} +(3.08477 - 3.38884i) q^{21} +1.69697 q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.0930981 + 1.72955i) q^{24} +(-4.41482 - 7.64669i) q^{25} +(-0.160901 + 0.278688i) q^{26} +(-5.12868 - 0.834655i) q^{27} +(-2.61150 - 0.424357i) q^{28} +1.06086i q^{29} +(5.74328 - 2.91611i) q^{30} +(3.96735 - 2.29055i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.62077 - 1.33068i) q^{33} +6.49336i q^{34} +(3.48917 + 9.19963i) q^{35} +(1.21244 + 2.74408i) q^{36} +(-1.62560 + 2.81563i) q^{37} +(0.430319 + 0.745335i) q^{38} +(-0.0299591 + 0.556570i) q^{39} +(-3.22059 - 1.85941i) q^{40} +0.635105 q^{41} +(-4.36591 + 1.39243i) q^{42} -3.17857 q^{43} +(-1.46962 - 0.848486i) q^{44} +(6.58314 - 9.00716i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.85378 + 3.21084i) q^{47} +(0.945399 - 1.45128i) q^{48} +(-1.40045 - 6.85848i) q^{49} +8.82964i q^{50} +(5.09176 + 10.0282i) q^{51} +(0.278688 - 0.160901i) q^{52} +(-6.29811 + 3.63622i) q^{53} +(4.02424 + 3.28717i) q^{54} +6.31074i q^{55} +(2.04945 + 1.67325i) q^{56} +(1.24903 + 0.813647i) q^{57} +(0.530428 - 0.918729i) q^{58} +(-5.82082 - 10.0820i) q^{59} +(-6.43188 - 0.346215i) q^{60} +(-7.07196 - 4.08300i) q^{61} -4.58111 q^{62} +(-5.65075 + 5.57396i) q^{63} -1.00000 q^{64} +(-1.03639 - 0.598361i) q^{65} +(-2.93499 - 0.157985i) q^{66} +(-1.79862 - 3.11530i) q^{67} +(3.24668 - 5.62342i) q^{68} +(-1.45128 - 0.945399i) q^{69} +(1.57811 - 9.71170i) q^{70} +3.84622i q^{71} +(0.322035 - 2.98267i) q^{72} +(-13.5743 + 7.83714i) q^{73} +(2.81563 - 1.62560i) q^{74} +(6.92374 + 13.6363i) q^{75} -0.860639i q^{76} +(0.720122 - 4.43164i) q^{77} +(0.304230 - 0.467024i) q^{78} +(-8.26120 + 14.3088i) q^{79} +(1.85941 + 3.22059i) q^{80} +(8.79259 + 1.92105i) q^{81} +(-0.550017 - 0.317552i) q^{82} -9.85134 q^{83} +(4.47720 + 0.977070i) q^{84} -24.1477 q^{85} +(2.75272 + 1.58929i) q^{86} +(0.0987637 - 1.83480i) q^{87} +(0.848486 + 1.46962i) q^{88} +(4.33024 - 7.50019i) q^{89} +(-10.2048 + 4.50886i) q^{90} +(0.659514 + 0.538455i) q^{91} +1.00000i q^{92} +(-7.07497 + 3.59227i) q^{93} +(3.21084 - 1.85378i) q^{94} +(-2.77177 + 1.60028i) q^{95} +(-1.54438 + 0.784148i) q^{96} +9.27603i q^{97} +(-2.21641 + 6.63984i) q^{98} +(-4.65663 + 2.05748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

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