LMFDB - Embedded newform 966.2.l.c.47.20

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			47.20
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.784148 + 1.54438i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85941 + 3.22059i) q^{5} +(-1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} +1.00000i q^{8} +(-1.77022 - 2.42205i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.784148 + 1.54438i) 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} +(-1.77022 - 2.42205i) q^{9} +(-3.22059 + 1.85941i) q^{10} +(1.46962 - 0.848486i) q^{11} +(-1.72955 + 0.0930981i) 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} +(-0.322035 - 2.98267i) q^{18} +(-0.745335 - 0.430319i) q^{19} -3.71882 q^{20} +(-1.85305 - 4.19121i) q^{21} +1.69697 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.54438 - 0.784148i) 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} +(-0.346215 - 6.43188i) q^{30} +(3.96735 - 2.29055i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.157985 + 2.93499i) 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} +(0.496984 + 0.252340i) q^{39} +(-3.22059 - 1.85941i) q^{40} -0.635105 q^{41} +(0.490819 - 4.55622i) q^{42} -3.17857 q^{43} +(1.46962 + 0.848486i) q^{44} +(11.0920 - 1.19759i) 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} +(-11.2306 + 0.604519i) q^{51} +(0.278688 - 0.160901i) q^{52} +(6.29811 - 3.63622i) q^{53} +(4.85889 + 1.84151i) 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} +(2.91611 - 5.74328i) q^{60} +(-7.07196 - 4.08300i) q^{61} +4.58111 q^{62} +(7.92588 + 0.424720i) q^{63} -1.00000 q^{64} +(1.03639 + 0.598361i) q^{65} +(-1.33068 + 2.62077i) 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} +(2.42205 - 1.77022i) q^{72} +(-13.5743 + 7.83714i) q^{73} +(-2.81563 + 1.62560i) q^{74} +(15.2713 - 0.822022i) 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} +(-2.73262 + 8.57513i) q^{81} +(-0.550017 - 0.317552i) q^{82} +9.85134 q^{83} +(2.70317 - 3.70039i) q^{84} -24.1477 q^{85} +(-2.75272 - 1.58929i) q^{86} +(1.63837 + 0.831869i) 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} +(0.426492 + 7.92324i) q^{93} +(3.21084 - 1.85378i) q^{94} +(2.77177 - 1.60028i) q^{95} +(-0.0930981 - 1.72955i) 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
$3$	−0.784148	+	1.54438i	−0.452728	+	0.891649i
$3$	−0.784148	+	1.54438i	−0.452728	+	0.891649i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.85941	+	3.22059i	−0.831554	+	1.44029i	0.0652518	+	0.997869i	$0.479215\pi$
$5$	−1.85941	+	3.22059i	−0.831554	+	1.44029i	−0.896806	+	0.442425i	$0.854118\pi$
$6$	−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
$9$	−1.77022	−	2.42205i	−0.590074	−	0.807349i
$10$	−3.22059	+	1.85941i	−1.01844	+	0.587997i
$11$	1.46962	−	0.848486i	0.443108	−	0.255828i	−0.261807	−	0.965120i	$-0.584318\pi$
$11$	1.46962	−	0.848486i	0.443108	−	0.255828i	0.704915	+	0.709292i	$0.250985\pi$
$12$	−1.72955	+	0.0930981i	−0.499277	+	0.0268751i
$13$		−	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	$0.121925\pi$
$17$	3.24668	+	5.62342i	0.787436	+	1.36388i	−0.140098	+	0.990138i	$0.544742\pi$
$18$	−0.322035	−	2.98267i	−0.0759044	−	0.703021i
$19$	−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
$21$	−1.85305	−	4.19121i	−0.404368	−	0.914596i
$22$	1.69697			0.361796
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	−1.54438	−	0.784148i	−0.315245	−	0.160064i
$25$	−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	$-0.968596\pi$
$29$		−	1.06086i		−	0.196996i	0.995137	−	0.0984981i	$-0.0314038\pi$
$30$	−0.346215	−	6.43188i	−0.0632099	−	1.17429i
$31$	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
$33$	0.157985	+	2.93499i	0.0275016	+	0.510917i
$34$			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
$39$	0.496984	+	0.252340i	0.0795811	+	0.0404067i
$40$	−3.22059	−	1.85941i	−0.509221	−	0.293999i
$41$	−0.635105			−0.0991867			−0.0495933	−	0.998769i	$-0.515793\pi$
$41$	−0.635105			−0.0991867			−0.0495933	+	0.998769i	$0.515793\pi$
$42$	0.490819	−	4.55622i	0.0757351	−	0.703039i
$43$	−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
$45$	11.0920	−	1.19759i	1.65350	−	0.178526i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.85378	−	3.21084i	0.270402	−	0.468350i	−0.698563	−	0.715549i	$-0.746177\pi$
$47$	1.85378	−	3.21084i	0.270402	−	0.468350i	0.968965	+	0.247199i	$0.0795101\pi$
$48$	−0.945399	−	1.45128i	−0.136457	−	0.209475i
$49$	−1.40045	−	6.85848i	−0.200065	−	0.979783i
$50$		−	8.82964i		−	1.24870i
$51$	−11.2306	+	0.604519i	−1.57259	+	0.0846496i
$52$	0.278688	−	0.160901i	0.0386471	−	0.0223129i
$53$	6.29811	−	3.63622i	0.865112	−	0.499473i	−0.000608788	−	1.00000i	$-0.500194\pi$
$53$	6.29811	−	3.63622i	0.865112	−	0.499473i	0.865721	+	0.500527i	$0.166860\pi$
$54$	4.85889	+	1.84151i	0.661212	+	0.250597i
$55$			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	$0.107062\pi$
$59$	5.82082	+	10.0820i	0.757806	+	1.31256i	−0.186161	+	0.982519i	$0.559605\pi$
$60$	2.91611	−	5.74328i	0.376468	−	0.741454i
$61$	−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
$63$	7.92588	+	0.424720i	0.998567	+	0.0535097i
$64$	−1.00000			−0.125000
$65$	1.03639	+	0.598361i	0.128548	+	0.0742175i
$66$	−1.33068	+	2.62077i	−0.163795	+	0.322595i
$67$	−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	$-0.926706\pi$
$71$		−	3.84622i		−	0.456462i	0.973607	−	0.228231i	$-0.0732941\pi$
$72$	2.42205	−	1.77022i	0.285441	−	0.208623i
$73$	−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
$75$	15.2713	−	0.822022i	1.76337	−	0.0949189i
$76$		−	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
$81$	−2.73262	+	8.57513i	−0.303624	+	0.952792i
$82$	−0.550017	−	0.317552i	−0.0607392	−	0.0350678i
$83$	9.85134			1.08133			0.540663	−	0.841239i	$-0.318174\pi$
$83$	9.85134			1.08133			0.540663	+	0.841239i	$0.318174\pi$
$84$	2.70317	−	3.70039i	0.294940	−	0.403745i
$85$	−24.1477			−2.61918
$86$	−2.75272	−	1.58929i	−0.296834	−	0.171377i
$87$	1.63837	+	0.831869i	0.175651	+	0.0891857i
$88$	0.848486	+	1.46962i	0.0904490	+	0.156662i
$89$	−4.33024	+	7.50019i	−0.459004	+	0.795019i	−0.998909	−	0.0467077i	$-0.985127\pi$
$89$	−4.33024	+	7.50019i	−0.459004	+	0.795019i	0.539904	+	0.841726i	$0.318460\pi$
$90$	10.2048	+	4.50886i	1.07568	+	0.475275i
$91$	0.659514	+	0.538455i	0.0691358	+	0.0564454i
$92$		−	1.00000i		−	0.104257i
$93$	0.426492	+	7.92324i	0.0442252	+	0.821602i
$94$	3.21084	−	1.85378i	0.331173	−	0.191203i
$95$	2.77177	−	1.60028i	0.284377	−	0.164185i
$96$	−0.0930981	−	1.72955i	−0.00950178	−	0.176521i
$97$			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	$-0.920772\pi$
$101$	−7.01408	−	12.1488i	−0.697927	−	1.20885i	0.271256	−	0.962507i	$-0.412561\pi$
$102$	−10.0282	−	5.09176i	−0.992942	−	0.504159i
$103$	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
$105$	16.9438	+	1.82527i	1.65354	+	0.178128i
$106$	7.27243			0.706361
$107$	6.13504	+	3.54207i	0.593097	+	0.342424i	0.766321	−	0.642458i	$-0.222085\pi$
$107$	6.13504	+	3.54207i	0.593097	+	0.342424i	−0.173224	+	0.984882i	$0.555419\pi$
$108$	3.28717	+	4.02424i	0.316308	+	0.387233i
$109$	−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	$0.429221\pi$
$113$			20.7369i			1.95076i	−0.220531	+	0.975380i	$0.570779\pi$
$114$	1.48852	−	0.0801238i	0.139412	−	0.00750428i
$115$	3.22059	−	1.85941i	0.300322	−	0.173391i
$116$	0.918729	−	0.530428i	0.0853019	−	0.0492490i
$117$	−0.779417	+	0.569660i	−0.0720572	+	0.0526651i
$118$			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
$123$	0.498016	−	0.980843i	0.0449046	−	0.0884397i
$124$	3.96735	+	2.29055i	0.356279	+	0.205698i
$125$	14.2417			1.27382
$126$	6.65166	+	4.33076i	0.592577	+	0.385815i
$127$	−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
$129$	2.49247	−	4.90893i	0.219450	−	0.432207i
$130$	0.598361	+	1.03639i	0.0524797	+	0.0908975i
$131$	−3.65809	+	6.33599i	−0.319608	+	0.553578i	−0.980406	−	0.196986i	$-0.936885\pi$
$131$	−3.65809	+	6.33599i	−0.319608	+	0.553578i	0.660798	+	0.750564i	$0.270218\pi$
$132$	−2.46279	+	1.60432i	−0.214358	+	0.139638i
$133$	2.12905	−	0.807490i	0.184612	−	0.0700183i
$134$		−	3.59723i		−	0.310754i
$135$	−6.84824	+	18.0694i	−0.589402	+	1.55516i
$136$	−5.62342	+	3.24668i	−0.482204	+	0.278401i
$137$	19.4324	−	11.2193i	1.66022	−	0.958531i	0.687618	−	0.726072i	$-0.258656\pi$
$137$	19.4324	−	11.2193i	1.66022	−	0.958531i	0.972606	−	0.232459i	$-0.0746771\pi$
$138$	1.72955	−	0.0930981i	0.147229	−	0.00792503i
$139$			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
$144$	2.98267	−	0.322035i	0.248555	−	0.0268362i
$145$	3.41659	+	1.97257i	0.283732	+	0.163813i
$146$	−15.6743			−1.29721
$147$	11.6903	+	3.21523i	0.964197	+	0.265188i
$148$	−3.25120			−0.267247
$149$	−17.1479	−	9.90037i	−1.40481	−	0.811070i	−0.409933	−	0.912116i	$-0.634448\pi$
$149$	−17.1479	−	9.90037i	−1.40481	−	0.811070i	−0.994882	+	0.101046i	$0.967781\pi$
$150$	13.6363	+	6.92374i	1.11340	+	0.565321i
$151$	−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
$156$	0.0299591	+	0.556570i	0.00239865	+	0.0445613i
$157$	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
$159$	0.677049	+	12.5780i	0.0536935	+	0.997501i
$160$		−	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
$165$	−9.74618	−	4.94856i	−0.758739	−	0.385245i
$166$	8.53151	+	4.92567i	0.662174	+	0.382306i
$167$	−10.3254			−0.799001			−0.399501	−	0.916733i	$-0.630816\pi$
$167$	−10.3254			−0.799001			−0.399501	+	0.916733i	$0.630816\pi$
$168$	4.19121	−	1.85305i	0.323359	−	0.142966i
$169$	12.8964			0.992034
$170$	−20.9125	−	12.0738i	−1.60391	−	0.926020i
$171$	0.277156	+	2.56700i	0.0211946	+	0.196303i
$172$	−1.58929	−	2.75272i	−0.121182	−	0.209893i
$173$	−7.84102	+	13.5810i	−0.596142	+	1.03255i	0.397243	+	0.917714i	$0.369967\pi$
$173$	−7.84102	+	13.5810i	−0.596142	+	1.03255i	−0.993385	+	0.114834i	$0.963366\pi$
$174$	1.00293	+	1.53960i	0.0760321	+	0.116717i
$175$	23.0586	+	3.74691i	1.74306	+	0.283240i
$176$			1.69697i			0.127914i
$177$	−20.1348	+	1.08381i	−1.51342	+	0.0814645i
$178$	−7.50019	+	4.33024i	−0.562163	+	0.324565i
$179$	17.4328	−	10.0648i	1.30299	−	0.752279i	0.322071	−	0.946715i	$-0.395621\pi$
$179$	17.4328	−	10.0648i	1.30299	−	0.752279i	0.980915	+	0.194436i	$0.0622877\pi$
$180$	6.58314	+	9.00716i	0.490679	+	0.671354i
$181$		−	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
$186$	−3.59227	+	7.07497i	−0.263398	+	0.518762i
$187$	9.54278	+	5.50953i	0.697837	+	0.402897i
$188$	3.70756			0.270402
$189$	−6.87100	+	11.9075i	−0.499791	+	0.866146i
$190$	3.20056			0.232193
$191$	3.28393	+	1.89598i	0.237617	+	0.137188i	0.614081	−	0.789243i	$-0.289527\pi$
$191$	3.28393	+	1.89598i	0.237617	+	0.137188i	−0.376464	+	0.926431i	$0.622860\pi$
$192$	0.784148	−	1.54438i	0.0565910	−	0.111456i
$193$	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	$0.197670\pi$
$197$			16.3332i			1.16370i	−0.813298	+	0.581848i	$0.802330\pi$
$198$	−3.00402	−	4.11015i	−0.213486	−	0.292095i
$199$	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
$201$	6.22158	−	0.334895i	0.438837	−	0.0236217i
$202$		−	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
$207$	0.322035	+	2.98267i	0.0223830	+	0.207310i
$208$	0.278688	+	0.160901i	0.0193235	+	0.0111564i
$209$	−1.46048			−0.101024
$210$	13.7611	+	10.0526i	0.949605	+	0.693696i
$211$	−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
$213$	5.94002	+	3.01600i	0.407004	+	0.206653i
$214$	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
$219$	−1.45925	−	27.1094i	−0.0986067	−	1.83188i
$220$	−5.46526	+	3.15537i	−0.368468	+	0.212735i
$221$	1.80962	−	1.04479i	0.121728	−	0.0702799i
$222$	−0.302681	−	5.62311i	−0.0203146	−	0.377398i
$223$		−	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	$0.0210094\pi$
$227$	8.37744	+	14.5101i	0.556030	+	0.963072i	−0.441793	+	0.897117i	$0.645657\pi$
$228$	1.32915	+	0.674868i	0.0880254	+	0.0446942i
$229$	−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
$231$	−6.27946	−	4.58721i	−0.413158	−	0.301816i
$232$	1.06086			0.0696487
$233$	−15.7202	−	9.07605i	−1.02986	−	0.594592i	−0.112917	−	0.993604i	$-0.536020\pi$
$233$	−15.7202	−	9.07605i	−1.02986	−	0.594592i	−0.916945	+	0.399013i	$0.869353\pi$
$234$	−0.959825	+	0.103631i	−0.0627457	+	0.00677459i
$235$	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	$0.290860\pi$
$239$			24.4821i			1.58362i	−0.610770	+	0.791808i	$0.709140\pi$
$240$	6.43188	−	0.346215i	0.415176	−	0.0223481i
$241$	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
$243$	−11.1005	−	10.9444i	−0.712096	−	0.702082i
$244$		−	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
$249$	−7.72491	+	15.2142i	−0.489547	+	0.964162i
$250$	12.3337	+	7.12087i	0.780052	+	0.450363i
$251$	16.7672			1.05833			0.529167	−	0.848518i	$-0.322505\pi$
$251$	16.7672			1.05833			0.529167	+	0.848518i	$0.322505\pi$
$252$	3.59512	+	7.07638i	0.226471	+	0.445770i
$253$	−1.69697			−0.106688
$254$	−2.42807	−	1.40185i	−0.152351	−	0.0879597i
$255$	18.9353	−	37.2932i	1.18578	−	2.33539i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.4161	+	21.5053i	−0.774495	+	1.34147i	0.160582	+	0.987022i	$0.448663\pi$
$257$	−12.4161	+	21.5053i	−0.774495	+	1.34147i	−0.935078	+	0.354443i	$0.884671\pi$
$258$	4.61301	−	3.00502i	0.287193	−	0.187084i
$259$	−3.05043	−	8.04283i	−0.189544	−	0.499757i
$260$			1.19672i			0.0742175i
$261$	−2.56944	+	1.87795i	−0.159045	+	0.116242i
$262$	−6.33599	+	3.65809i	−0.391439	+	0.225997i
$263$	16.0389	−	9.26008i	0.989003	−	0.571001i	0.0840266	−	0.996464i	$-0.473222\pi$
$263$	16.0389	−	9.26008i	0.989003	−	0.571001i	0.904976	+	0.425463i	$0.139889\pi$
$264$	−2.93499	+	0.157985i	−0.180636	+	0.00972330i
$265$			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	0.853571	−	0.520977i	$-0.174432\pi$
$269$	−0.400087	−	0.692971i	−0.0243938	−	0.0422512i	−0.877965	+	0.478726i	$0.841099\pi$
$270$	−14.9654	+	12.2244i	−0.910767	+	0.743954i
$271$	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
$273$	−1.34874	+	0.596312i	−0.0816292	+	0.0360905i
$274$	22.4386			1.35557
$275$	−12.9762	−	7.49183i	−0.782496	−	0.451774i
$276$	1.54438	+	0.784148i	0.0929608	+	0.0472002i
$277$	−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	$0.136738\pi$
$281$			13.9631i			0.832967i	−0.909143	+	0.416484i	$0.863262\pi$
$282$	0.345167	+	6.41240i	0.0205544	+	0.381853i
$283$	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
$285$	0.297966	+	5.53552i	0.0176500	+	0.327896i
$286$		−	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
$291$	−14.3257	−	7.27378i	−0.839789	−	0.426397i
$292$	−13.5743	−	7.83714i	−0.794377	−	0.458634i
$293$	−6.31967			−0.369199			−0.184600	−	0.982814i	$-0.559099\pi$
$293$	−6.31967			−0.369199			−0.184600	+	0.982814i	$0.559099\pi$
$294$	8.51645	+	8.62961i	0.496689	+	0.503289i
$295$	−43.2932			−2.52063
$296$	−2.81563	−	1.62560i	−0.163655	−	0.0944862i
$297$	6.82902	−	5.57824i	0.396260	−	0.323682i
$298$	−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
$303$	24.2624	−	1.30600i	1.39384	−	0.0750275i
$304$	0.745335	−	0.430319i	0.0427479	−	0.0246805i
$305$	26.2994	−	15.1839i	1.50590	−	0.869430i
$306$	15.7272	−	11.4947i	0.899065	−	0.657108i
$307$		−	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	0.724904	−	0.688850i	$-0.241884\pi$
$311$	−4.12858	−	7.15090i	−0.234110	−	0.405491i	−0.959014	+	0.283360i	$0.908551\pi$
$312$	−0.252340	+	0.496984i	−0.0142859	+	0.0281362i
$313$	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
$315$	−16.1053	+	24.7363i	−0.907432	+	1.39373i
$316$	−16.5224			−0.929457
$317$	26.8815	+	15.5200i	1.50982	+	0.871692i	0.999934	+	0.0114476i	$0.00364398\pi$
$317$	26.8815	+	15.5200i	1.50982	+	0.871692i	0.509881	+	0.860245i	$0.329689\pi$
$318$	−5.70266	+	11.2314i	−0.319790	+	0.629826i
$319$	−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
$324$	−8.79259	+	1.92105i	−0.488477	+	0.106725i
$325$	−2.46071	+	1.42069i	−0.136496	+	0.0788059i
$326$	21.2893	−	12.2914i	1.17910	−	0.680756i
$327$	6.70688	−	0.361018i	0.370892	−	0.0199644i
$328$		−	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
$333$	9.69725	−	1.04700i	0.531406	−	0.0573753i
$334$	−8.94203	−	5.16268i	−0.489286	−	0.282490i
$335$	13.3775			0.730889
$336$	4.55622	+	0.490819i	0.248562	+	0.0267764i
$337$	−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
$339$	−32.0256	−	16.2608i	−1.73939	−	0.883164i
$340$	−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
$345$	0.346215	+	6.43188i	0.0186396	+	0.346281i
$346$	−13.5810	+	7.84102i	−0.730122	+	0.421536i
$347$	2.54549	−	1.46964i	0.136649	−	0.0788943i	−0.430117	−	0.902773i	$-0.641528\pi$
$347$	2.54549	−	1.46964i	0.136649	−	0.0788943i	0.566766	+	0.823879i	$0.308194\pi$
$348$	0.0987637	+	1.83480i	0.00529429	+	0.0983557i
$349$			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	0.502353	−	0.864663i	$-0.332468\pi$
$353$	−9.34988	−	16.1945i	−0.497644	−	0.861944i	−0.999996	+	0.00271865i	$0.999135\pi$
$354$	−17.9791	−	9.12877i	−0.955580	−	0.485189i
$355$	12.3871	+	7.15170i	0.657439	+	0.379573i
$356$	−8.66047			−0.459004
$357$	17.5527	−	24.0280i	0.928985	−	1.27169i
$358$	20.1296			1.06388
$359$	−8.95230	−	5.16861i	−0.472484	−	0.272789i	0.244795	−	0.969575i	$-0.421279\pi$
$359$	−8.95230	−	5.16861i	−0.472484	−	0.272789i	−0.717279	+	0.696786i	$0.754613\pi$
$360$	1.19759	+	11.0920i	0.0631186	+	0.584600i
$361$	−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
$366$	14.1235	−	0.760238i	0.738246	−	0.0397383i
$367$	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
$369$	1.12428	+	1.53825i	0.0585275	+	0.0800783i
$370$		−	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
$375$	−11.1676	+	21.9947i	−0.576694	+	1.13580i
$376$	3.21084	+	1.85378i	0.165587	+	0.0956014i
$377$	−0.341385			−0.0175822
$378$	−11.9042	+	6.87673i	−0.612287	+	0.353701i
$379$	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
$381$	2.19851	−	4.32997i	0.112633	−	0.221831i
$382$	1.89598	+	3.28393i	0.0970066	+	0.168020i
$383$	4.94652	−	8.56762i	0.252755	−	0.437785i	−0.711528	−	0.702658i	$-0.751997\pi$
$383$	4.94652	−	8.56762i	0.252755	−	0.437785i	0.964283	+	0.264873i	$0.0853299\pi$
$384$	1.45128	−	0.945399i	0.0740605	−	0.0482447i
$385$	−12.9335	−	10.5595i	−0.659153	−	0.538160i
$386$			21.7662i			1.10787i
$387$	5.62678	+	7.69865i	0.286025	+	0.391344i
$388$	−8.03328	+	4.63802i	−0.407828	+	0.235460i
$389$	−25.6876	+	14.8308i	−1.30241	+	0.751949i	−0.980818	−	0.194928i	$-0.937553\pi$
$389$	−25.6876	+	14.8308i	−1.30241	+	0.751949i	−0.321597	+	0.946877i	$0.604219\pi$
$390$	−2.06979	+	0.111412i	−0.104808	+	0.00564159i
$391$		−	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
$396$	−0.546485	−	5.06150i	−0.0274619	−	0.254350i
$397$	−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
$399$	−0.422418	+	3.92126i	−0.0211474	+	0.196308i
$400$	8.82964			0.441482
$401$	−10.5185	−	6.07284i	−0.525267	−	0.303263i	0.213820	−	0.976873i	$-0.431410\pi$
$401$	−10.5185	−	6.07284i	−0.525267	−	0.303263i	−0.739087	+	0.673610i	$0.764743\pi$
$402$	5.55550	+	2.82076i	0.277083	+	0.140687i
$403$	−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
$408$	−0.604519	−	11.2306i	−0.0299282	−	0.555996i
$409$	−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
$411$	2.08899	+	38.8087i	0.103042	+	1.91429i
$412$			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
$417$	−11.0304	−	5.60062i	−0.540163	−	0.274264i
$418$	−1.26481	−	0.730240i	−0.0618640	−	0.0357172i
$419$	−36.5547			−1.78581			−0.892907	−	0.450241i	$-0.851338\pi$
$419$	−36.5547			−1.78581			−0.892907	+	0.450241i	$0.851338\pi$
$420$	6.89115	+	15.5864i	0.336254	+	0.760536i
$421$	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
$423$	−11.0584	+	1.19396i	−0.537679	+	0.0580525i
$424$	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
$429$	0.944485	−	0.0508397i	0.0456002	−	0.00245457i
$430$	10.2369	−	5.91027i	0.493667	−	0.285019i
$431$	28.0412	−	16.1896i	1.35070	−	0.779825i	0.362350	−	0.932042i	$-0.381975\pi$
$431$	28.0412	−	16.1896i	1.35070	−	0.779825i	0.988347	+	0.152217i	$0.0486413\pi$
$432$	−1.84151	+	4.85889i	−0.0885996	+	0.233774i
$433$			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
$438$	12.2910	−	24.2071i	0.587285	−	1.15666i
$439$	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
$441$	−14.1324	+	15.5330i	−0.672974	+	0.739667i
$442$	2.08957			0.0993908
$443$	10.9312	+	6.31113i	0.519357	+	0.299851i	0.736671	−	0.676251i	$-0.236396\pi$
$443$	10.9312	+	6.31113i	0.519357	+	0.299851i	−0.217315	+	0.976102i	$0.569730\pi$
$444$	2.54943	−	5.02110i	0.120990	−	0.238291i
$445$	−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	$0.0160872\pi$
$449$			2.14091i			0.101036i	−0.998723	+	0.0505180i	$0.983913\pi$
$450$	−21.3858	+	15.6304i	−1.00814	+	0.736825i
$451$	−0.933363	+	0.538878i	−0.0439504	+	0.0253748i
$452$	−17.9586	+	10.3684i	−0.844704	+	0.487690i
$453$	22.7990	−	1.22723i	1.07119	−	0.0576602i
$454$			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
$459$	21.3448	+	26.1308i	0.996290	+	1.21968i
$460$	3.22059	+	1.85941i	0.150161	+	0.0866955i
$461$	7.14089			0.332584			0.166292	−	0.986077i	$-0.446821\pi$
$461$	7.14089			0.332584			0.166292	+	0.986077i	$0.446821\pi$
$462$	−3.14457	−	7.11237i	−0.146299	−	0.330897i
$463$	−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
$465$	−26.3106	−	13.3590i	−1.22012	−	0.619509i
$466$	−9.07605	−	15.7202i	−0.420440	−	0.728223i
$467$	−0.0969170	+	0.167865i	−0.00448479	+	0.00776788i	−0.868259	−	0.496111i	$-0.834761\pi$
$467$	−0.0969170	+	0.167865i	−0.00448479	+	0.00776788i	0.863774	+	0.503879i	$0.168094\pi$
$468$	−0.883049	−	0.390165i	−0.0408189	−	0.0180354i
$469$	9.39417	+	1.52651i	0.433782	+	0.0704877i
$470$			13.7878i			0.635982i
$471$	0.281982	+	5.23858i	0.0129931	+	0.241381i
$472$	−10.0820	+	5.82082i	−0.464060	+	0.267925i
$473$	−4.67130	+	2.69698i	−0.214787	+	0.124007i
$474$	−1.53820	−	28.5763i	−0.0706520	−	1.31255i
$475$			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	$0.101841\pi$
$479$	16.3490	+	28.3172i	0.747003	+	1.29385i	−0.202250	+	0.979334i	$0.564825\pi$
$480$	5.74328	+	2.91611i	0.262144	+	0.133101i
$481$	0.906072	+	0.523121i	0.0413133	+	0.0238523i
$482$	2.71056			0.123462
$483$	−0.490819	+	4.55622i	−0.0223330	+	0.207315i
$484$	−8.12028			−0.369104
$485$	−29.8743	−	17.2480i	−1.35652	−	0.783189i
$486$	−4.14111	−	15.0283i	−0.187845	−	0.681700i
$487$	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	$-0.883871\pi$
$491$		−	15.8118i		−	0.713579i	0.934185	−	0.356789i	$-0.116129\pi$
$492$	1.09844	−	0.0591270i	0.0495216	−	0.00266565i
$493$	5.96564	−	3.44426i	0.268679	−	0.155122i
$494$	−0.239850	+	0.138477i	−0.0107913	+	0.00623039i
$495$	15.2849	−	11.1714i	0.687005	−	0.502118i
$496$			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
$501$	8.09662	−	15.9463i	0.361730	−	0.712428i
$502$	14.5208	+	8.38358i	0.648094	+	0.374177i
$503$	12.8209			0.571656			0.285828	−	0.958281i	$-0.407731\pi$
$503$	12.8209			0.571656			0.285828	+	0.958281i	$0.407731\pi$
$504$	−0.424720	+	7.92588i	−0.0189185	+	0.353047i
$505$	52.1683			2.32146
$506$	−1.46962	−	0.848486i	−0.0653327	−	0.0377198i
$507$	−10.1127	+	19.9170i	−0.449122	+	0.884546i
$508$	−1.40185	−	2.42807i	−0.0621969	−	0.107728i
$509$	−9.36597	+	16.2223i	−0.415139	+	0.719042i	−0.995443	−	0.0953578i	$-0.969600\pi$
$509$	−9.36597	+	16.2223i	−0.415139	+	0.719042i	0.580304	+	0.814400i	$0.302934\pi$
$510$	35.0451	−	22.8292i	1.55182	−	1.01089i
$511$	6.65149	−	40.9334i	0.294244	−	1.81079i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.18175	−	1.58487i	−0.184629	−	0.0699738i
$514$	−21.5053	+	12.4161i	−0.948559	+	0.547651i
$515$	−0.0422444	+	0.0243898i	−0.00186151	+	0.00107474i
$516$	5.49749	−	0.295919i	0.242014	−	0.0130271i
$517$		−	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	0.977582	−	0.210556i	$-0.0675273\pi$
$521$	6.99473	+	12.1152i	0.306444	+	0.530777i	−0.671137	+	0.741333i	$0.734194\pi$
$522$	−3.16418	+	0.341633i	−0.138492	+	0.0149529i
$523$	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
$525$	−23.8680	+	32.6731i	−1.04169	+	1.42597i
$526$	18.5202			0.807517
$527$	25.7615	+	14.8734i	1.12219	+	0.647895i
$528$	−2.62077	−	1.33068i	−0.114054	−	0.0579103i
$529$	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
$534$	−0.806273	−	14.9787i	−0.0348909	−	0.648192i
$535$	−22.8151	+	13.1723i	−0.986383	+	0.569489i
$536$	3.11530	−	1.79862i	0.134560	−	0.0776884i
$537$	1.87403	+	34.8151i	0.0808703	+	1.50238i
$538$		−	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
$543$	1.81646	+	0.922295i	0.0779518	+	0.0395795i
$544$	−5.62342	−	3.24668i	−0.241102	−	0.139200i
$545$	14.4209			0.617726
$546$	−1.46620	−	0.157946i	−0.0627474	−	0.00675947i
$547$	−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
$549$	2.62974	+	24.3564i	0.112234	+	1.03951i
$550$	−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
$555$	20.9113	−	1.12562i	0.887637	−	0.0477797i
$556$	−6.18542	+	3.57115i	−0.262320	+	0.151451i
$557$	3.99845	−	2.30851i	0.169420	−	0.0978146i	−0.412892	−	0.910780i	$-0.635481\pi$
$557$	3.99845	−	2.30851i	0.169420	−	0.0978146i	0.582312	+	0.812965i	$0.302148\pi$
$558$	−8.10958	−	11.0957i	−0.343306	−	0.469716i
$559$			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	0.958029	−	0.286673i	$-0.0925492\pi$
$563$	5.47511	+	9.48317i	0.230748	+	0.399668i	−0.727280	+	0.686341i	$0.759216\pi$
$564$	−2.90728	+	5.72589i	−0.122418	+	0.241103i
$565$	−66.7850	−	38.5583i	−2.80967	−	1.62216i
$566$	8.84158			0.371639
$567$	−13.0019	−	19.9487i	−0.546028	−	0.837767i
$568$	3.84622			0.161384
$569$	27.1792	+	15.6919i	1.13941	+	0.657839i	0.946284	−	0.323335i	$-0.104804\pi$
$569$	27.1792	+	15.6919i	1.13941	+	0.657839i	0.193126	+	0.981174i	$0.438138\pi$
$570$	−2.50972	+	4.94289i	−0.105120	+	0.207035i
$571$	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
$576$	1.77022	+	2.42205i	0.0737593	+	0.100919i
$577$	−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
$579$	−37.6457	+	2.02639i	−1.56450	+	0.0842140i
$580$			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
$585$	−0.385386	−	3.56942i	−0.0159338	−	0.147577i
$586$	−5.47300	−	3.15984i	−0.226087	−	0.130532i
$587$	−16.6830			−0.688583			−0.344291	−	0.938863i	$-0.611881\pi$
$587$	−16.6830			−0.688583			−0.344291	+	0.938863i	$0.611881\pi$
$588$	3.06066	+	11.7317i	0.126219	+	0.483806i
$589$	−3.94268			−0.162455
$590$	−37.4930	−	21.6466i	−1.54356	−	0.891176i
$591$	−25.2248	−	12.8077i	−1.03761	−	0.526838i
$592$	−1.62560	−	2.81563i	−0.0668118	−	0.115721i
$593$	−1.40969	+	2.44165i	−0.0578890	+	0.100267i	−0.893518	−	0.449028i	$-0.851770\pi$
$593$	−1.40969	+	2.44165i	−0.0578890	+	0.100267i	0.835629	+	0.549295i	$0.185104\pi$
$594$	8.70323	−	1.41639i	0.357098	−	0.0581151i
$595$	40.4051	−	49.4893i	1.65645	−	2.02886i
$596$		−	19.8007i		−	0.811070i
$597$	0.277595	+	5.15707i	0.0113612	+	0.211065i
$598$	−0.278688	+	0.160901i	−0.0113964	+	0.00657971i
$599$	−14.5195	+	8.38281i	−0.593249	+	0.342512i	−0.766381	−	0.642386i	$-0.777945\pi$
$599$	−14.5195	+	8.38281i	−0.593249	+	0.342512i	0.173132	+	0.984899i	$0.444611\pi$
$600$	0.822022	+	15.2713i	0.0335589	+	0.623447i
$601$		−	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
$606$	21.6648	+	11.0002i	0.880074	+	0.446851i
$607$	−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
$609$	−4.44627	+	1.96582i	−0.180172	+	0.0796589i
$610$	30.3679			1.22956
$611$	−1.03325	−	0.596549i	−0.0418009	−	0.0241338i
$612$	19.3675	−	2.09109i	0.782886	−	0.0845273i
$613$	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	$-0.994810\pi$
$617$		−	0.810004i		−	0.0326095i	0.999867	−	0.0163048i	$-0.00519020\pi$
$618$	−0.0226864	+	0.00122116i	−0.000912580	+	4.91224e-5i
$619$	−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
$621$	−4.85889	−	1.84151i	−0.194981	−	0.0738971i
$622$		−	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
$627$	1.14523	−	2.25554i	0.0457362	−	0.0900775i
$628$	2.62308	+	1.51444i	0.104672	+	0.0604326i
$629$	−21.1112			−0.841760
$630$	−26.3158	+	13.3696i	−1.04845	+	0.532658i
$631$	−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
$633$	0.336427	−	0.662593i	0.0133718	−	0.0263357i
$634$	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
$639$	−9.31571	+	6.80866i	−0.368524	+	0.269346i
$640$	3.22059	−	1.85941i	0.127305	−	0.0734997i
$641$	2.60088	−	1.50162i	0.102728	−	0.0593103i	−0.447756	−	0.894156i	$-0.647777\pi$
$641$	2.60088	−	1.50162i	0.102728	−	0.0593103i	0.550484	+	0.834846i	$0.314443\pi$
$642$	−12.2523	+	0.659519i	−0.483561	+	0.0260291i
$643$		−	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	$0.0110453\pi$
$647$	13.4747	+	23.3388i	0.529744	+	0.917544i	−0.469654	+	0.882851i	$0.655621\pi$
$648$	−8.57513	−	2.73262i	−0.336863	−	0.107347i
$649$	17.1088	+	9.87777i	0.671579	+	0.387737i
$650$	−2.84139			−0.111448
$651$	−16.9519	−	12.3835i	−0.664396	−	0.485348i
$652$	24.5827			0.962734
$653$	5.57020	+	3.21596i	0.217979	+	0.125850i	0.605014	−	0.796215i	$-0.293167\pi$
$653$	5.57020	+	3.21596i	0.217979	+	0.125850i	−0.387035	+	0.922065i	$0.626501\pi$
$654$	5.98884	+	3.04079i	0.234182	+	0.118904i
$655$	−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	$-0.743466\pi$
$659$		−	37.0418i		−	1.44294i	0.692444	−	0.721471i	$-0.256534\pi$
$660$	−0.587518	−	10.9147i	−0.0228691	−	0.424855i
$661$	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
$663$	0.194535	+	3.61401i	0.00755511	+	0.140357i
$664$			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
$669$	7.38177	+	3.74804i	0.285396	+	0.144908i
$670$	11.5852	+	6.68874i	0.447576	+	0.258408i
$671$	−13.8575			−0.534962
$672$	3.70039	+	2.70317i	0.142746	+	0.104277i
$673$	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
$675$	−29.0245	−	35.5326i	−1.11715	−	1.36765i
$676$	6.44822	+	11.1686i	0.248009	+	0.429563i
$677$	−0.966051	+	1.67325i	−0.0371283	+	0.0643082i	−0.883992	−	0.467501i	$-0.845154\pi$
$677$	−0.966051	+	1.67325i	−0.0371283	+	0.0643082i	0.846864	+	0.531809i	$0.178488\pi$
$678$	−19.6046	−	30.0950i	−0.752910	−	1.15579i
$679$	−19.0107	−	15.5211i	−0.729564	−	0.595647i
$680$		−	24.1477i		−	0.926020i
$681$	−28.9783	+	1.55985i	−1.11045	+	0.0597734i
$682$	6.73249	−	3.88701i	0.257800	−	0.148841i
$683$	−10.4798	+	6.05052i	−0.400999	+	0.231517i	−0.686915	−	0.726738i	$-0.741036\pi$
$683$	−10.4798	+	6.05052i	−0.400999	+	0.231517i	0.285916	+	0.958255i	$0.407702\pi$
$684$	−2.08451	+	1.52352i	−0.0797031	+	0.0582533i
$685$			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
$690$	−2.91611	+	5.74328i	−0.111014	+	0.218643i
$691$	−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
$693$	12.0084	−	6.10083i	0.456162	−	0.231751i
$694$	2.93928			0.111573
$695$	−23.0025	−	13.2805i	−0.872533	−	0.503757i
$696$	−0.831869	+	1.63837i	−0.0315319	+	0.0621021i
$697$	−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	$0.0545283\pi$
$701$			9.02681i			0.340938i	−0.985363	+	0.170469i	$0.945472\pi$
$702$	0.592599	−	1.56360i	0.0223662	−	0.0590142i
$703$	2.42324	−	1.39906i	0.0913941	−	0.0527664i
$704$	−1.46962	+	0.848486i	−0.0553884	+	0.0319785i
$705$	−23.8466	+	1.28361i	−0.898114	+	0.0483437i
$706$		−	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
$711$	49.2808	−	5.32079i	1.84817	−	0.199545i
$712$	−7.50019	−	4.33024i	−0.281082	−	0.162283i
$713$	−4.58111			−0.171564
$714$	27.2150	−	12.0325i	1.01850	−	0.450305i
$715$	2.03080			0.0759478
$716$	17.4328	+	10.0648i	0.651493	+	0.376140i
$717$	−37.8097	−	19.1976i	−1.41203	−	0.716948i
$718$	−5.16861	−	8.95230i	−0.192891	−	0.334097i
$719$	−15.1744	+	26.2829i	−0.565911	+	0.980186i	0.431053	+	0.902326i	$0.358142\pi$
$719$	−15.1744	+	26.2829i	−0.565911	+	0.980186i	−0.996964	+	0.0778600i	$0.975191\pi$
$720$	−4.50886	+	10.2048i	−0.168035	+	0.380309i
$721$	−0.0324487	+	0.0123069i	−0.00120845	+	0.000458333i
$722$		−	18.2593i		−	0.679541i
$723$	0.252348	+	4.68804i	0.00938491	+	0.174350i
$724$	1.01860	−	0.588087i	0.0378558	−	0.0218561i
$725$	−8.11204	+	4.68349i	−0.301274	+	0.173940i
$726$	−0.755983	−	14.0444i	−0.0280571	−	0.521237i
$727$			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
$732$	12.6114	+	6.40335i	0.466131	+	0.236675i
$733$	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
$735$	−32.0920	+	31.6712i	−1.18373	+	1.16821i
$736$	1.00000			0.0368605
$737$	−5.28657	−	3.05220i	−0.194733	−	0.112429i
$738$	0.204526	+	1.89430i	0.00752870	+	0.0697303i
$739$	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	$-0.936178\pi$
$743$		−	10.8575i		−	0.398322i	0.979967	−	0.199161i	$-0.0638216\pi$
$744$	−7.92324	+	0.426492i	−0.290480	+	0.0156360i
$745$	63.7702	−	36.8177i	2.33636	−	1.34890i
$746$	−22.1533	+	12.7902i	−0.811090	+	0.468283i
$747$	−17.4391	−	23.8604i	−0.638063	−	0.873007i
$748$			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
$753$	−13.1479	+	25.8949i	−0.479137	+	0.943661i
$754$	−0.295648	−	0.170693i	−0.0107669	−	0.00621625i
$755$	49.0218			1.78409
$756$	−13.7477	+	0.00331081i	−0.500000	+	0.000120413i
$757$	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
$759$	1.33068	−	2.62077i	0.0483006	−	0.0951280i
$760$	1.60028	+	2.77177i	0.0580483	+	0.100543i
$761$	−9.43081	+	16.3346i	−0.341866	+	0.592130i	−0.984779	−	0.173809i	$-0.944392\pi$
$761$	−9.43081	+	16.3346i	−0.341866	+	0.592130i	0.642913	+	0.765939i	$0.277726\pi$
$762$	4.06895	−	2.65061i	0.147403	−	0.0960215i
$763$	10.1269	+	1.64558i	0.366620	+	0.0595741i
$764$			3.79195i			0.137188i
$765$	42.7467	+	58.4867i	1.54551	+	2.11459i
$766$	8.56762	−	4.94652i	0.309561	−	0.178725i
$767$	3.24439	−	1.87315i	0.117148	−	0.0676354i
$768$	1.72955	−	0.0930981i	0.0624097	−	0.00335939i
$769$			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	0.522891	−	0.852399i	$-0.324853\pi$
$773$	−13.2551	−	22.9586i	−0.476754	−	0.825762i	−0.999645	+	0.0266376i	$0.991520\pi$
$774$	1.02361	+	9.48062i	0.0367930	+	0.340774i
$775$	−35.0303	−	20.2248i	−1.25833	−	0.726495i
$776$	−9.27603			−0.332990
$777$	14.8132	+	1.59575i	0.531420	+	0.0572473i
$778$	−29.6615			−1.06342
$779$	0.473366	+	0.273298i	0.0169601	+	0.00979191i
$780$	−1.84819	−	0.938407i	−0.0661759	−	0.0336004i
$781$	−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
$786$	−0.681121	−	12.6537i	−0.0242948	−	0.451341i
$787$	−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
$789$	1.72419	+	32.0315i	0.0613828	+	1.14035i
$790$		−	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
$795$	−41.7676	−	21.2072i	−1.48134	−	0.752142i
$796$	2.58227	+	1.49087i	0.0915261	+	0.0528426i
$797$	−25.4808			−0.902576			−0.451288	−	0.892378i	$-0.649035\pi$
$797$	−25.4808			−0.902576			−0.451288	+	0.892378i	$0.649035\pi$
$798$	−2.32645	+	3.18470i	−0.0823555	+	0.112737i
$799$	24.0745			0.851696
$800$	7.64669	+	4.41482i	0.270351	+	0.156087i
$801$	25.8313	−	2.78898i	0.912704	−	0.0985436i
$802$	−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
$807$	1.38394	−	0.0744947i	0.0487170	−	0.00262234i
$808$	12.1488	−	7.01408i	0.427392	−	0.246755i
$809$	−4.77000	+	2.75396i	−0.167704	+	0.0968242i	−0.581503	−	0.813544i	$-0.697535\pi$
$809$	−4.77000	+	2.75396i	−0.167704	+	0.0968242i	0.413799	+	0.910368i	$0.364202\pi$
$810$	−7.14402	−	32.6981i	−0.251015	−	1.14889i
$811$		−	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
$816$	5.09176	−	10.0282i	0.178247	−	0.351058i
$817$	2.36910	+	1.36780i	0.0828844	+	0.0478533i
$818$	−15.5234			−0.542763
$819$	0.136675	−	2.55056i	0.00477583	−	0.0891237i
$820$	2.36184			0.0824791
$821$	−10.9846	−	6.34199i	−0.383367	−	0.221337i	0.295915	−	0.955214i	$-0.404375\pi$
$821$	−10.9846	−	6.34199i	−0.383367	−	0.221337i	−0.679282	+	0.733877i	$0.737709\pi$
$822$	−17.5952	+	34.6538i	−0.613704	+	1.20869i
$823$	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	$-0.950312\pi$
$827$		−	8.94164i		−	0.310931i	0.987841	−	0.155466i	$-0.0496878\pi$
$828$	−2.42205	+	1.77022i	−0.0841719	+	0.0615195i
$829$	−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
$831$	51.3114	−	2.76199i	1.77997	−	0.0958124i
$832$			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
$837$	18.4355	−	15.0589i	0.637223	−	0.520511i
$838$	−31.6573	−	18.2774i	−1.09358	−	0.631381i
$839$	21.7261			0.750068			0.375034	−	0.927011i	$-0.377631\pi$
$839$	21.7261			0.750068			0.375034	+	0.927011i	$0.377631\pi$
$840$	−1.82527	+	16.9438i	−0.0629778	+	0.584615i
$841$	27.8746			0.961193
$842$	20.2825	+	11.7101i	0.698981	+	0.403557i
$843$	−21.5643	−	10.9491i	−0.742714	−	0.377108i
$844$	−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
$849$	0.823134	+	15.2919i	0.0282499	+	0.524818i
$850$	49.6527	−	28.6670i	1.70307	−	0.983270i
$851$	2.81563	−	1.62560i	0.0965184	−	0.0557249i
$852$	0.358075	+	6.65221i	0.0122675	+	0.227901i
$853$			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	$0.0803109\pi$
$857$	20.5028	+	35.5118i	0.700361	+	1.21306i	−0.267979	+	0.963425i	$0.586356\pi$
$858$	0.843368	+	0.428214i	0.0287921	+	0.0146190i
$859$	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
$861$	1.17688	+	2.66186i	0.0401079	+	0.0907158i
$862$	32.3792			1.10284
$863$	4.23946	+	2.44766i	0.144313	+	0.0833191i	0.570418	−	0.821355i	$-0.306781\pi$
$863$	4.23946	+	2.44766i	0.144313	+	0.0833191i	−0.426105	+	0.904674i	$0.640115\pi$
$864$	−4.02424	+	3.28717i	−0.136907	+	0.111832i
$865$	−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
$870$	−6.82330	+	0.367285i	−0.231332	+	0.0124521i
$871$	−1.00251	+	0.578797i	−0.0339686	+	0.0196118i
$872$	3.35830	−	1.93891i	0.113726	−	0.0656599i
$873$	22.4670	−	16.4206i	0.760392	−	0.555755i
$874$			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
$879$	4.95556	−	9.75998i	0.167147	−	0.329196i
$880$	−5.46526	−	3.15537i	−0.184234	−	0.106368i
$881$	43.0998			1.45207			0.726035	−	0.687658i	$-0.241361\pi$
$881$	43.0998			1.45207			0.726035	+	0.687658i	$0.241361\pi$
$882$	−20.0056	+	6.38575i	−0.673622	+	0.215019i
$883$	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
$885$	33.9483	−	66.8612i	1.14116	−	2.24751i
$886$	6.31113	+	10.9312i	0.212027	+	0.367241i
$887$	13.6369	−	23.6199i	0.457884	−	0.793078i	−0.540965	−	0.841045i	$-0.681941\pi$
$887$	13.6369	−	23.6199i	0.457884	−	0.793078i	0.998849	+	0.0479673i	$0.0152743\pi$
$888$	4.71842	−	3.07368i	0.158340	−	0.103146i
$889$	4.69129	−	5.74602i	0.157341	−	0.192715i
$890$		−	32.2068i		−	1.07957i
$891$	3.25996	+	14.9208i	0.109213	+	0.499865i
$892$	4.13939	−	2.38988i	0.138597	−	0.0800191i
$893$	−2.76338	+	1.59544i	−0.0924728	+	0.0533892i
$894$	34.2463	−	1.84341i	1.14537	−	0.0616529i
$895$			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
$900$	−26.3359	+	2.84345i	−0.877862	+	0.0947817i
$901$	40.8959	+	23.6113i	1.36244	+	0.786605i
$902$	−1.07776			−0.0358853
$903$	5.89004	+	13.3221i	0.196008	+	0.443330i
$904$	−20.7369			−0.689698
$905$	3.78798	+	2.18699i	0.125917	+	0.0726980i
$906$	20.3582	+	10.3367i	0.676355	+	0.343414i
$907$	−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	$0.240409\pi$
$911$			41.3796i			1.37097i	−0.728089	+	0.685483i	$0.759591\pi$
$912$	0.0801238	+	1.48852i	0.00265316	+	0.0492897i
$913$	14.4777	−	8.35873i	0.479144	−	0.276634i
$914$	14.5456	−	8.39792i	0.481126	−	0.277778i
$915$	2.82719	+	52.5227i	0.0934640	+	1.73635i
$916$		−	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
$921$	36.9573	+	18.7648i	1.21778	+	0.618321i
$922$	6.18419	+	3.57044i	0.203666	+	0.117586i
$923$	−1.23772			−0.0407399
$924$	0.832907	−	7.73177i	0.0274006	−	0.254357i
$925$	28.7070			0.943879
$926$	−24.1776	−	13.9589i	−0.794525	−	0.458719i
$927$	−0.00422411	−	0.0391235i	−0.000138738	−	0.00128498i
$928$	0.530428	+	0.918729i	0.0174122	+	0.0301588i
$929$	8.20947	−	14.2192i	0.269344	−	0.466517i	−0.699349	−	0.714781i	$-0.746526\pi$
$929$	8.20947	−	14.2192i	0.269344	−	0.466517i	0.968693	+	0.248263i	$0.0798598\pi$
$930$	−16.1061	−	24.7245i	−0.528140	−	0.810749i
$931$	−1.90753	+	5.71451i	−0.0625168	+	0.187285i
$932$		−	18.1521i		−	0.594592i
$933$	14.2811	−	0.768725i	0.467543	−	0.0251669i
$934$	−0.167865	+	0.0969170i	−0.00549272	+	0.00317122i
$935$	−35.4879	+	20.4890i	−1.16058	+	0.670061i
$936$	−0.569660	−	0.779417i	−0.0186199	−	0.0254761i
$937$		−	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	$0.163096\pi$
$941$	26.3922	+	45.7127i	0.860362	+	1.49019i	−0.0112176	+	0.999937i	$0.503571\pi$
$942$	−2.37508	+	4.67773i	−0.0773844	+	0.152409i
$943$	0.550017	+	0.317552i	0.0179110	+	0.0103409i
$944$	−11.6416			−0.378903
$945$	−25.5733	−	44.2697i	−0.831901	−	1.44009i
$946$	−5.39395			−0.175373
$947$	−9.65050	−	5.57172i	−0.313599	−	0.181056i	0.334937	−	0.942241i	$-0.391285\pi$
$947$	−9.65050	−	5.57172i	−0.313599	−	0.181056i	−0.648536	+	0.761184i	$0.724618\pi$
$948$	12.9560	−	25.5169i	0.420792	−	0.828749i
$949$	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	$0.0259018\pi$
$953$			5.01854i			0.162566i	−0.996691	+	0.0812832i	$0.974098\pi$
$954$	−12.8738	−	17.6142i	−0.416806	−	0.570280i
$955$	−12.2123	+	7.05080i	−0.395182	+	0.228159i
$956$	−21.2021	+	12.2411i	−0.685726	+	0.395904i
$957$	3.11361	−	0.167599i	0.100649	−	0.00541772i
$958$			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
$963$	−2.28134	−	21.1296i	−0.0735151	−	0.680892i
$964$	2.34741	+	1.35528i	0.0756050	+	0.0436506i
$965$	−80.9447			−2.60570
$966$	−2.70317	+	3.70039i	−0.0869731	+	0.119058i
$967$	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
$969$	8.63068	+	4.38216i	0.277257	+	0.140775i
$970$	−17.2480	−	29.8743i	−0.553798	−	0.959207i
$971$	−6.70238	+	11.6089i	−0.215090	+	0.372546i	−0.953300	−	0.302024i	$-0.902338\pi$
$971$	−6.70238	+	11.6089i	−0.215090	+	0.372546i	0.738211	+	0.674570i	$0.235671\pi$
$972$	3.92787	−	15.0855i	0.125986	−	0.483867i
$973$	−14.6378	−	11.9509i	−0.469265	−	0.383128i
$974$			22.4296i			0.718690i
$975$	−0.264528	−	4.91431i	−0.00847167	−	0.157384i
$976$	7.07196	−	4.08300i	0.226368	−	0.130694i
$977$	11.0601	−	6.38556i	0.353844	−	0.204292i	−0.312533	−	0.949907i	$-0.601177\pi$
$977$	11.0601	−	6.38556i	0.353844	−	0.204292i	0.666377	+	0.745615i	$0.267844\pi$
$978$	2.28860	+	42.5170i	0.0731815	+	1.35954i
$979$			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	$0.00613900\pi$
$983$	16.1971	+	28.0543i	0.516608	+	0.894792i	−0.483206	+	0.875507i	$0.660528\pi$
$984$	0.980843	+	0.498016i	0.0312681	+	0.0158762i
$985$	−52.6028	−	30.3702i	−1.67606	−	0.967676i
$986$	6.88853			0.219375
$987$	−16.8924	−	1.81974i	−0.537693	−	0.0579230i
$988$	−0.276955			−0.00881110
$989$	2.75272	+	1.58929i	0.0875316	+	0.0505364i
$990$	18.8228	−	2.03228i	0.598229	−	0.0645901i
$991$	−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
$996$	−17.0384	+	0.917141i	−0.539881	+	0.0290607i
$997$	−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
$999$	−5.98712	+	15.7973i	−0.189424	+	0.499803i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.784148 + 1.54438i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.85941 + 3.22059i) q^{5} +(-1.45128 + 0.945399i) q^{6} +(-1.67325 + 2.04945i) q^{7} +1.00000i q^{8} +(-1.77022 - 2.42205i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.784148 + 1.54438i) 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} +(-1.77022 - 2.42205i) q^{9} +(-3.22059 + 1.85941i) q^{10} +(1.46962 - 0.848486i) q^{11} +(-1.72955 + 0.0930981i) 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} +(-0.322035 - 2.98267i) q^{18} +(-0.745335 - 0.430319i) q^{19} -3.71882 q^{20} +(-1.85305 - 4.19121i) q^{21} +1.69697 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.54438 - 0.784148i) 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} +(-0.346215 - 6.43188i) q^{30} +(3.96735 - 2.29055i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.157985 + 2.93499i) 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} +(0.496984 + 0.252340i) q^{39} +(-3.22059 - 1.85941i) q^{40} -0.635105 q^{41} +(0.490819 - 4.55622i) q^{42} -3.17857 q^{43} +(1.46962 + 0.848486i) q^{44} +(11.0920 - 1.19759i) 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} +(-11.2306 + 0.604519i) q^{51} +(0.278688 - 0.160901i) q^{52} +(6.29811 - 3.63622i) q^{53} +(4.85889 + 1.84151i) 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} +(2.91611 - 5.74328i) q^{60} +(-7.07196 - 4.08300i) q^{61} +4.58111 q^{62} +(7.92588 + 0.424720i) q^{63} -1.00000 q^{64} +(1.03639 + 0.598361i) q^{65} +(-1.33068 + 2.62077i) 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} +(2.42205 - 1.77022i) q^{72} +(-13.5743 + 7.83714i) q^{73} +(-2.81563 + 1.62560i) q^{74} +(15.2713 - 0.822022i) 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} +(-2.73262 + 8.57513i) q^{81} +(-0.550017 - 0.317552i) q^{82} +9.85134 q^{83} +(2.70317 - 3.70039i) q^{84} -24.1477 q^{85} +(-2.75272 - 1.58929i) q^{86} +(1.63837 + 0.831869i) 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} +(0.426492 + 7.92324i) q^{93} +(3.21084 - 1.85378i) q^{94} +(2.77177 - 1.60028i) q^{95} +(-0.0930981 - 1.72955i) 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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