LMFDB - Embedded newform 370.2.ba.a.87.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(17,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("370.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$370 = 2 \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$ , degree $12$ , 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			87.4
Character	$\chi$	$=$	370.87
Dual form			370.2.ba.a.353.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.513008 + 0.732652i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.23092 - 0.151579i) q^{5} +(0.632438 + 0.632438i) q^{6} +(1.16632 + 0.102040i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.752459 + 2.06736i) q^{9} +(-0.536672 + 2.17071i) q^{10} +(2.99132 + 1.72704i) q^{11} +(0.732652 - 0.513008i) q^{12} +(5.00909 + 1.82316i) q^{13} +(0.303020 - 1.13089i) q^{14} +(1.25554 - 1.55673i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.75525 - 4.82251i) q^{17} +(2.16662 - 0.382034i) q^{18} +(1.31264 + 0.919118i) q^{19} +(2.04454 + 0.905459i) q^{20} +(-0.673094 + 0.802162i) q^{21} +(2.22024 - 2.64598i) q^{22} +(2.54869 + 4.41446i) q^{23} +(-0.377991 - 0.810604i) q^{24} +(4.95405 + 0.676323i) q^{25} +(2.66528 - 4.61640i) q^{26} +(-4.49246 - 1.20375i) q^{27} +(-1.06109 - 0.494793i) q^{28} +(2.28998 - 0.613599i) q^{29} +(-1.31506 - 1.50679i) q^{30} +(-3.84545 + 3.84545i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-2.79989 + 1.30561i) q^{33} +(-5.05404 + 0.891163i) q^{34} +(-2.58651 - 0.404434i) q^{35} -2.20004i q^{36} +(1.93519 + 5.76672i) q^{37} +(1.13309 - 1.13309i) q^{38} +(-3.90545 + 2.73462i) q^{39} +(1.24673 - 1.85625i) q^{40} +(-3.41259 + 9.37601i) q^{41} +(0.673094 + 0.802162i) q^{42} +7.74769 q^{43} +(-2.22024 - 2.64598i) q^{44} +(-1.36531 - 4.72619i) q^{45} +(4.78997 - 1.74341i) q^{46} +(3.48935 - 13.0224i) q^{47} +(-0.863927 + 0.231488i) q^{48} +(-5.54375 - 0.977513i) q^{49} +(1.52631 - 4.76134i) q^{50} +(4.43368 + 1.18800i) q^{51} +(-4.08345 - 3.42642i) q^{52} +(-13.8186 + 1.20897i) q^{53} +(-1.96557 + 4.21518i) q^{54} +(-6.41163 - 4.30632i) q^{55} +(-0.671532 + 0.959046i) q^{56} +(-1.34679 + 0.490190i) q^{57} +(-0.206626 - 2.36174i) q^{58} +(3.02914 - 0.265015i) q^{59} +(-1.71225 + 1.03343i) q^{60} +(4.57909 - 2.13526i) q^{61} +(3.11928 + 4.45479i) q^{62} +(0.666657 + 2.48800i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.8986 - 4.82661i) q^{65} +(0.799580 + 2.98407i) q^{66} +(0.504022 - 5.76100i) q^{67} +5.13201i q^{68} +(-4.54176 - 0.397352i) q^{69} +(-0.847433 + 2.47699i) q^{70} +(0.297044 + 1.68462i) q^{71} +(-2.16662 - 0.382034i) q^{72} +(-5.25053 - 5.25053i) q^{73} +(6.01515 - 0.904415i) q^{74} +(-3.03698 + 3.28263i) q^{75} +(-0.919118 - 1.31264i) q^{76} +(3.31263 + 2.31953i) q^{77} +(2.01490 + 4.32098i) q^{78} +(-0.639152 + 7.30554i) q^{79} +(-1.61155 - 1.55013i) q^{80} +(-1.86940 + 1.56861i) q^{81} +(8.64098 + 4.98887i) q^{82} +(6.36369 - 13.6470i) q^{83} +(0.906857 - 0.523574i) q^{84} +(3.18484 + 11.0247i) q^{85} +(1.34537 - 7.62998i) q^{86} +(-0.725226 + 1.99254i) q^{87} +(-2.99132 + 1.72704i) q^{88} +(0.479052 + 5.47559i) q^{89} +(-4.89147 + 0.523874i) q^{90} +(5.65619 + 2.63752i) q^{91} +(-0.885150 - 5.01994i) q^{92} +(-0.844629 - 4.79013i) q^{93} +(-12.2187 - 5.69767i) q^{94} +(-2.78907 - 2.24945i) q^{95} +(0.0779523 + 0.890999i) q^{96} +(8.83646 - 5.10173i) q^{97} +(-1.92533 + 5.28979i) q^{98} +(-1.31958 + 7.48368i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30}+ \cdots - 42 q^{99}+O(q^{100})$ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$ .

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.513008	+	0.732652i	−0.296186	+	0.422997i	−0.939470	−	0.342630i	$-0.888682\pi$
$3$	−0.513008	+	0.732652i	−0.296186	+	0.422997i	0.643285	+	0.765627i	$0.277571\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−2.23092	−	0.151579i	−0.997700	−	0.0677882i
$5$	−2.23092	−	0.151579i	−0.997700	−	0.0677882i
$6$	0.632438	+	0.632438i	0.258192	+	0.258192i
$7$	1.16632	+	0.102040i	0.440829	+	0.0385676i	0.305410	−	0.952221i	$-0.401206\pi$
$7$	1.16632	+	0.102040i	0.440829	+	0.0385676i	0.135419	+	0.990788i	$0.456762\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.752459	+	2.06736i	0.250820	+	0.689122i
$10$	−0.536672	+	2.17071i	−0.169711	+	0.686439i
$11$	2.99132	+	1.72704i	0.901918	+	0.520723i	0.877822	−	0.478987i	$-0.158996\pi$
$11$	2.99132	+	1.72704i	0.901918	+	0.520723i	0.0240959	+	0.999710i	$0.492329\pi$
$12$	0.732652	−	0.513008i	0.211498	−	0.148093i
$13$	5.00909	+	1.82316i	1.38927	+	0.505654i	0.924976	−	0.380026i	$-0.124085\pi$
$13$	5.00909	+	1.82316i	1.38927	+	0.505654i	0.464296	+	0.885680i	$0.346307\pi$
$14$	0.303020	−	1.13089i	0.0809855	−	0.302242i
$15$	1.25554	−	1.55673i	0.324178	−	0.401946i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.75525	−	4.82251i	−0.425711	−	1.16963i	−0.948392	−	0.317102i	$-0.897290\pi$
$17$	−1.75525	−	4.82251i	−0.425711	−	1.16963i	0.522681	−	0.852528i	$-0.324932\pi$
$18$	2.16662	−	0.382034i	0.510677	−	0.0900462i
$19$	1.31264	+	0.919118i	0.301139	+	0.210860i	0.714373	−	0.699765i	$-0.246712\pi$
$19$	1.31264	+	0.919118i	0.301139	+	0.210860i	−0.413234	+	0.910625i	$0.635601\pi$
$20$	2.04454	+	0.905459i	0.457173	+	0.202467i
$21$	−0.673094	+	0.802162i	−0.146881	+	0.175046i
$22$	2.22024	−	2.64598i	0.473357	−	0.564125i
$23$	2.54869	+	4.41446i	0.531438	+	0.920478i	0.999327	+	0.0366904i	$0.0116816\pi$
$23$	2.54869	+	4.41446i	0.531438	+	0.920478i	−0.467888	+	0.883788i	$0.654985\pi$
$24$	−0.377991	−	0.810604i	−0.0771571	−	0.165464i
$25$	4.95405	+	0.676323i	0.990810	+	0.135265i
$26$	2.66528	−	4.61640i	0.522705	−	0.905351i
$27$	−4.49246	−	1.20375i	−0.864574	−	0.231662i
$28$	−1.06109	−	0.494793i	−0.200527	−	0.0935071i
$29$	2.28998	−	0.613599i	0.425239	−	0.113942i	−0.0398514	−	0.999206i	$-0.512688\pi$
$29$	2.28998	−	0.613599i	0.425239	−	0.113942i	0.465091	+	0.885263i	$0.346022\pi$
$30$	−1.31506	−	1.50679i	−0.240096	−	0.275100i
$31$	−3.84545	+	3.84545i	−0.690664	+	0.690664i	−0.962378	−	0.271714i	$-0.912409\pi$
$31$	−3.84545	+	3.84545i	−0.690664	+	0.690664i	0.271714	+	0.962378i	$0.412409\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−2.79989	+	1.30561i	−0.487399	+	0.227278i
$34$	−5.05404	+	0.891163i	−0.866761	+	0.152833i
$35$	−2.58651	−	0.404434i	−0.437201	−	0.0683619i
$36$		−	2.20004i		−	0.366674i
$37$	1.93519	+	5.76672i	0.318144	+	0.948042i
$37$	1.93519	+	5.76672i	0.318144	+	0.948042i
$38$	1.13309	−	1.13309i	0.183812	−	0.183812i
$39$	−3.90545	+	2.73462i	−0.625372	+	0.437890i
$40$	1.24673	−	1.85625i	0.197126	−	0.293499i
$41$	−3.41259	+	9.37601i	−0.532957	+	1.46429i	0.322579	+	0.946543i	$0.395450\pi$
$41$	−3.41259	+	9.37601i	−0.532957	+	1.46429i	−0.855536	+	0.517744i	$0.826772\pi$
$42$	0.673094	+	0.802162i	0.103861	+	0.123776i
$43$	7.74769			1.18151			0.590756	−	0.806851i	$-0.298830\pi$
$43$	7.74769			1.18151			0.590756	+	0.806851i	$0.298830\pi$
$44$	−2.22024	−	2.64598i	−0.334714	−	0.398897i
$45$	−1.36531	−	4.72619i	−0.203528	−	0.704539i
$46$	4.78997	−	1.74341i	0.706242	−	0.257051i
$47$	3.48935	−	13.0224i	0.508974	−	1.89952i	0.0785038	−	0.996914i	$-0.474986\pi$
$47$	3.48935	−	13.0224i	0.508974	−	1.89952i	0.430471	−	0.902605i	$-0.358348\pi$
$48$	−0.863927	+	0.231488i	−0.124697	+	0.0334125i
$49$	−5.54375	−	0.977513i	−0.791965	−	0.139645i
$50$	1.52631	−	4.76134i	0.215853	−	0.673355i
$51$	4.43368	+	1.18800i	0.620839	+	0.166353i
$52$	−4.08345	−	3.42642i	−0.566272	−	0.475159i
$53$	−13.8186	+	1.20897i	−1.89813	+	0.166065i	−0.975555	−	0.219756i	$-0.929474\pi$
$53$	−13.8186	+	1.20897i	−1.89813	+	0.166065i	−0.922574	+	0.385821i	$0.873918\pi$
$54$	−1.96557	+	4.21518i	−0.267480	+	0.573613i
$55$	−6.41163	−	4.30632i	−0.864544	−	0.580664i
$56$	−0.671532	+	0.959046i	−0.0897372	+	0.128158i
$57$	−1.34679	+	0.490190i	−0.178386	+	0.0649273i
$58$	−0.206626	−	2.36174i	−0.0271313	−	0.310112i
$59$	3.02914	−	0.265015i	0.394360	−	0.0345021i	0.111749	−	0.993736i	$-0.464355\pi$
$59$	3.02914	−	0.265015i	0.394360	−	0.0345021i	0.282612	+	0.959234i	$0.408799\pi$
$60$	−1.71225	+	1.03343i	−0.221051	+	0.133415i
$61$	4.57909	−	2.13526i	0.586292	−	0.273392i	−0.106754	−	0.994285i	$-0.534046\pi$
$61$	4.57909	−	2.13526i	0.586292	−	0.273392i	0.693046	+	0.720893i	$0.256268\pi$
$62$	3.11928	+	4.45479i	0.396148	+	0.565759i
$63$	0.666657	+	2.48800i	0.0839909	+	0.313458i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−10.8986	−	4.82661i	−1.35180	−	0.598667i
$66$	0.799580	+	2.98407i	0.0984215	+	0.367314i
$67$	0.504022	−	5.76100i	0.0615761	−	0.703818i	−0.901180	−	0.433446i	$-0.857298\pi$
$67$	0.504022	−	5.76100i	0.0615761	−	0.703818i	0.962756	−	0.270372i	$-0.0871468\pi$
$68$			5.13201i			0.622347i
$69$	−4.54176	−	0.397352i	−0.546763	−	0.0478356i
$70$	−0.847433	+	2.47699i	−0.101288	+	0.296057i
$71$	0.297044	+	1.68462i	0.0352526	+	0.199927i	0.997347	−	0.0727876i	$-0.0231895\pi$
$71$	0.297044	+	1.68462i	0.0352526	+	0.199927i	−0.962095	+	0.272715i	$0.912078\pi$
$72$	−2.16662	−	0.382034i	−0.255339	−	0.0450231i
$73$	−5.25053	−	5.25053i	−0.614528	−	0.614528i	0.329594	−	0.944123i	$-0.393088\pi$
$73$	−5.25053	−	5.25053i	−0.614528	−	0.614528i	−0.944123	+	0.329594i	$0.893088\pi$
$74$	6.01515	−	0.904415i	0.699247	−	0.105136i
$75$	−3.03698	+	3.28263i	−0.350680	+	0.379046i
$76$	−0.919118	−	1.31264i	−0.105430	−	0.150570i
$77$	3.31263	+	2.31953i	0.377509	+	0.264334i
$78$	2.01490	+	4.32098i	0.228143	+	0.489254i
$79$	−0.639152	+	7.30554i	−0.0719102	+	0.821937i	0.871519	+	0.490362i	$0.163136\pi$
$79$	−0.639152	+	7.30554i	−0.0719102	+	0.821937i	−0.943429	+	0.331575i	$0.892420\pi$
$80$	−1.61155	−	1.55013i	−0.180177	−	0.173309i
$81$	−1.86940	+	1.56861i	−0.207711	+	0.174290i
$82$	8.64098	+	4.98887i	0.954236	+	0.550929i
$83$	6.36369	−	13.6470i	0.698505	−	1.49795i	−0.161071	−	0.986943i	$-0.551495\pi$
$83$	6.36369	−	13.6470i	0.698505	−	1.49795i	0.859577	−	0.511007i	$-0.170727\pi$
$84$	0.906857	−	0.523574i	0.0989462	−	0.0571266i
$85$	3.18484	+	11.0247i	0.345444	+	1.19580i
$86$	1.34537	−	7.62998i	0.145075	−	0.822762i
$87$	−0.725226	+	1.99254i	−0.0777524	+	0.213623i
$88$	−2.99132	+	1.72704i	−0.318876	+	0.184103i
$89$	0.479052	+	5.47559i	0.0507794	+	0.580411i	0.978377	+	0.206830i	$0.0663147\pi$
$89$	0.479052	+	5.47559i	0.0507794	+	0.580411i	−0.927598	+	0.373581i	$0.878130\pi$
$90$	−4.89147	+	0.523874i	−0.515607	+	0.0552212i
$91$	5.65619	+	2.63752i	0.592930	+	0.276488i
$92$	−0.885150	−	5.01994i	−0.0922833	−	0.523364i
$93$	−0.844629	−	4.79013i	−0.0875839	−	0.496713i
$94$	−12.2187	−	5.69767i	−1.26026	−	0.587669i
$95$	−2.78907	−	2.24945i	−0.286153	−	0.230789i
$96$	0.0779523	+	0.890999i	0.00795598	+	0.0909372i
$97$	8.83646	−	5.10173i	0.897207	−	0.518002i	0.0209137	−	0.999781i	$-0.493342\pi$
$97$	8.83646	−	5.10173i	0.897207	−	0.518002i	0.876293	+	0.481779i	$0.160009\pi$
$98$	−1.92533	+	5.28979i	−0.194487	+	0.534349i
$99$	−1.31958	+	7.48368i	−0.132622	+	0.752139i
$100$	−4.42397	−	2.32992i	−0.442397	−	0.232992i
$101$	−8.27933	+	4.78007i	−0.823824	+	0.475635i	−0.851733	−	0.523975i	$-0.824448\pi$
$101$	−8.27933	+	4.78007i	−0.823824	+	0.475635i	0.0279094	+	0.999610i	$0.491115\pi$
$102$	1.93985	−	4.16003i	0.192074	−	0.411904i
$103$	4.95820	+	2.86262i	0.488546	+	0.282062i	0.723971	−	0.689830i	$-0.242315\pi$
$103$	4.95820	+	2.86262i	0.488546	+	0.282062i	−0.235425	+	0.971892i	$0.575648\pi$
$104$	−4.08345	+	3.42642i	−0.400415	+	0.335988i
$105$	1.62321	−	1.68754i	0.158409	−	0.164687i
$106$	−1.20897	+	13.8186i	−0.117425	+	1.34218i
$107$	−2.57200	−	5.51567i	−0.248645	−	0.533220i	0.741884	−	0.670529i	$-0.233933\pi$
$107$	−2.57200	−	5.51567i	−0.248645	−	0.533220i	−0.990528	+	0.137308i	$0.956155\pi$
$108$	3.80982	+	2.66767i	0.366600	+	0.256696i
$109$	4.34117	+	6.19983i	0.415808	+	0.593836i	0.971350	−	0.237653i	$-0.0763780\pi$
$109$	4.34117	+	6.19983i	0.415808	+	0.593836i	−0.555542	+	0.831489i	$0.687489\pi$
$110$	−5.35427	+	5.56644i	−0.510509	+	0.530739i
$111$	−5.21777	−	1.54055i	−0.495249	−	0.146223i
$112$	0.827866	+	0.827866i	0.0782260	+	0.0782260i
$113$	−5.41849	−	0.955426i	−0.509728	−	0.0898789i	−0.0871319	−	0.996197i	$-0.527770\pi$
$113$	−5.41849	−	0.955426i	−0.509728	−	0.0898789i	−0.422597	+	0.906318i	$0.638881\pi$
$114$	0.248876	+	1.41145i	0.0233094	+	0.132194i
$115$	−5.01679	−	10.2346i	−0.467818	−	0.954386i
$116$	−2.36174	−	0.206626i	−0.219282	−	0.0191847i
$117$			11.7275i			1.08421i
$118$	0.265015	−	3.02914i	0.0243966	−	0.278855i
$119$	−1.55510	−	5.80371i	−0.142556	−	0.532026i
$120$	0.720399	+	1.86569i	0.0657631	+	0.170314i
$121$	0.465343	+	0.805997i	0.0423039	+	0.0732725i
$122$	−1.30767	−	4.88030i	−0.118391	−	0.441842i
$123$	−5.11866	−	7.31021i	−0.461534	−	0.659140i
$124$	4.92877	−	2.29832i	0.442616	−	0.206395i
$125$	−10.9496	−	2.25975i	−0.979361	−	0.202119i
$126$	2.56596	−	0.224493i	0.228594	−	0.0199994i
$127$	−0.327777	−	3.74651i	−0.0290855	−	0.332449i	−0.996771	−	0.0802906i	$-0.974415\pi$
$127$	−0.327777	−	3.74651i	−0.0290855	−	0.332449i	0.967686	−	0.252158i	$-0.0811404\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−3.97463	+	5.67636i	−0.349946	+	0.499775i
$130$	−6.64579	+	9.89485i	−0.582875	+	0.867835i
$131$	7.79275	−	16.7116i	0.680856	−	1.46010i	−0.196621	−	0.980480i	$-0.562997\pi$
$131$	7.79275	−	16.7116i	0.680856	−	1.46010i	0.877476	−	0.479620i	$-0.159226\pi$
$132$	3.07759	−	0.269254i	0.267869	−	0.0234355i
$133$	1.43717	+	1.20593i	0.124619	+	0.104567i
$134$	−5.58595	−	1.49675i	−0.482553	−	0.129300i
$135$	9.83987	+	3.36644i	0.846881	+	0.289737i
$136$	5.05404	+	0.891163i	0.433380	+	0.0764166i
$137$	−11.1000	+	2.97424i	−0.948338	+	0.254106i	−0.699657	−	0.714479i	$-0.746664\pi$
$137$	−11.1000	+	2.97424i	−0.948338	+	0.254106i	−0.248681	+	0.968585i	$0.579997\pi$
$138$	−1.17998	+	4.40376i	−0.100447	+	0.374873i
$139$	21.4391	−	7.80321i	1.81844	−	0.661860i	0.822832	−	0.568285i	$-0.192393\pi$
$139$	21.4391	−	7.80321i	1.81844	−	0.661860i	0.995612	−	0.0935751i	$-0.0298295\pi$
$140$	2.29220	+	1.26468i	0.193727	+	0.106885i
$141$	7.75085	+	9.23710i	0.652739	+	0.777904i
$142$	1.71061			0.143551
$143$	11.8351	+	14.1046i	0.989704	+	1.17948i
$144$	−0.752459	+	2.06736i	−0.0627049	+	0.172280i
$145$	−5.20179	+	1.02178i	−0.431985	+	0.0848542i
$146$	−6.08251	+	4.25902i	−0.503392	+	0.352479i
$147$	3.56017	−	3.56017i	0.293638	−	0.293638i
$148$	0.153845	−	6.08082i	0.0126460	−	0.499840i
$149$		−	0.260119i		−	0.0213098i	−0.999943	−	0.0106549i	$-0.996608\pi$
$149$		−	0.260119i		−	0.0213098i	0.999943	−	0.0106549i	$-0.00339162\pi$
$150$	2.70540	+	3.56086i	0.220895	+	0.290743i
$151$	−21.3463	+	3.76393i	−1.73714	+	0.306304i	−0.950410	−	0.310999i	$-0.899337\pi$
$151$	−21.3463	+	3.76393i	−1.73714	+	0.306304i	−0.786726	+	0.617303i	$0.788225\pi$
$152$	−1.45230	+	0.677217i	−0.117797	+	0.0549296i
$153$	8.64913	−	7.25748i	0.699241	−	0.586733i
$154$	2.85952	−	2.85952i	0.230427	−	0.230427i
$155$	9.16181	−	7.99603i	0.735894	−	0.642256i
$156$	4.60522	−	1.23396i	0.368712	−	0.0987962i
$157$	−0.676256	−	0.315343i	−0.0539711	−	0.0251671i	0.395445	−	0.918490i	$-0.370590\pi$
$157$	−0.676256	−	0.315343i	−0.0539711	−	0.0251671i	−0.449416	+	0.893322i	$0.648368\pi$
$158$	7.08356	+	1.89804i	0.563538	+	0.151000i
$159$	6.20330	−	10.7444i	0.491953	−	0.852088i
$160$	−1.80642	+	1.31789i	−0.142810	+	0.104189i
$161$	2.52214	+	5.40876i	0.198773	+	0.426270i
$162$	1.22016	+	2.11338i	0.0958649	+	0.166043i
$163$	4.46566	−	5.32196i	0.349777	−	0.416848i	−0.562257	−	0.826963i	$-0.690067\pi$
$163$	4.46566	−	5.32196i	0.349777	−	0.416848i	0.912034	+	0.410114i	$0.134511\pi$
$164$	6.41357	−	7.64339i	0.500816	−	0.596849i
$165$	6.44425	−	2.48832i	0.501685	−	0.193715i
$166$	−12.3346	−	8.63678i	−0.957351	−	0.670344i
$167$	−8.14081	+	1.43544i	−0.629955	+	0.111078i	−0.479504	−	0.877540i	$-0.659183\pi$
$167$	−8.14081	+	1.43544i	−0.629955	+	0.111078i	−0.150450	+	0.988618i	$0.548072\pi$
$168$	−0.358146	−	0.983998i	−0.0276316	−	0.0759171i
$169$	11.8085	+	9.90851i	0.908347	+	0.762193i
$170$	11.4103	−	1.22203i	0.875127	−	0.0937256i
$171$	−0.912446	+	3.40530i	−0.0697765	+	0.260409i
$172$	−7.28044	−	2.64986i	−0.555129	−	0.202050i
$173$	8.85952	−	6.20350i	0.673577	−	0.471644i	−0.186067	−	0.982537i	$-0.559574\pi$
$173$	8.85952	−	6.20350i	0.673577	−	0.471644i	0.859644	+	0.510893i	$0.170685\pi$
$174$	1.83634	+	1.06021i	0.139212	+	0.0803743i
$175$	5.70901	+	1.29432i	0.431561	+	0.0978416i
$176$	1.18137	+	3.24578i	0.0890488	+	0.244660i
$177$	−1.35981	+	2.35526i	−0.102210	+	0.177032i
$178$	5.47559	+	0.479052i	0.410413	+	0.0359065i
$179$	−4.68500	−	4.68500i	−0.350174	−	0.350174i	0.510001	−	0.860174i	$-0.329645\pi$
$179$	−4.68500	−	4.68500i	−0.350174	−	0.350174i	−0.860174	+	0.510001i	$0.829645\pi$
$180$	−0.333480	+	4.90813i	−0.0248562	+	0.365830i
$181$	8.25482	+	3.00451i	0.613576	+	0.223323i	0.630067	−	0.776541i	$-0.283027\pi$
$181$	8.25482	+	3.00451i	0.613576	+	0.223323i	−0.0164913	+	0.999864i	$0.505250\pi$
$182$	3.57964	−	5.11226i	0.265341	−	0.378946i
$183$	−0.784705	+	4.45028i	−0.0580071	+	0.328974i
$184$	−5.09738			−0.375784
$185$	−3.44316	−	13.1584i	−0.253146	−	0.967428i
$186$	−4.86402			−0.356648
$187$	3.07815	−	17.4571i	0.225097	−	1.27659i
$188$	−7.73286	+	11.0437i	−0.563977	+	0.805442i
$189$	−5.11683	−	1.86237i	−0.372195	−	0.135468i
$190$	−2.69959	+	2.35609i	−0.195849	+	0.170929i
$191$	0.374690	+	0.374690i	0.0271117	+	0.0271117i	0.720533	−	0.693421i	$-0.243897\pi$
$191$	0.374690	+	0.374690i	0.0271117	+	0.0271117i	−0.693421	+	0.720533i	$0.743897\pi$
$192$	0.890999	+	0.0779523i	0.0643023	+	0.00562573i
$193$	3.01068	−	5.21465i	0.216714	−	0.375359i	−0.737088	−	0.675797i	$-0.763800\pi$
$193$	3.01068	−	5.21465i	0.216714	−	0.375359i	0.953801	+	0.300438i	$0.0971329\pi$
$194$	−3.48979	−	9.58812i	−0.250552	−	0.688387i
$195$	9.12727	−	5.50876i	0.653617	−	0.394490i
$196$	4.87510	+	2.81464i	0.348221	+	0.201046i
$197$	2.89101	−	2.02430i	0.205976	−	0.144226i	−0.466037	−	0.884765i	$-0.654319\pi$
$197$	2.89101	−	2.02430i	0.205976	−	0.144226i	0.672013	+	0.740539i	$0.265430\pi$
$198$	7.14085	+	2.59906i	0.507478	+	0.184707i
$199$	3.07806	−	11.4875i	0.218198	−	0.814326i	−0.766818	−	0.641864i	$-0.778161\pi$
$199$	3.07806	−	11.4875i	0.218198	−	0.814326i	0.985016	−	0.172462i	$-0.0551721\pi$
$200$	−3.06274	+	3.95217i	−0.216568	+	0.279461i
$201$	3.96224	+	3.32471i	0.279475	+	0.234507i
$202$	3.26976	+	8.98360i	0.230060	+	0.632084i
$203$	2.73347	−	0.481985i	0.191852	−	0.0338287i
$204$	−3.75997	−	2.63276i	−0.263251	−	0.184330i
$205$	9.03443	−	20.3999i	0.630992	−	1.42479i
$206$	3.68011	−	4.38578i	0.256405	−	0.305572i
$207$	−7.20851	+	8.59077i	−0.501026	+	0.597100i
$208$	2.66528	+	4.61640i	0.184804	+	0.320090i
$209$	2.33916	+	5.01635i	0.161803	+	0.346988i
$210$	−1.38003	−	1.89159i	−0.0952312	−	0.130532i
$211$	−1.25376	+	2.17158i	−0.0863125	+	0.149498i	−0.905950	−	0.423385i	$-0.860842\pi$
$211$	−1.25376	+	2.17158i	−0.0863125	+	0.149498i	0.819637	+	0.572883i	$0.194175\pi$
$212$	13.3987	+	3.59017i	0.920227	+	0.246574i
$213$	−1.38662	−	0.646593i	−0.0950099	−	0.0443038i
$214$	−5.87850	+	1.57514i	−0.401846	+	0.107674i
$215$	−17.2845	−	1.17439i	−1.17879	−	0.0800925i
$216$	3.28871	−	3.28871i	0.223768	−	0.223768i
$217$	−4.87744	+	4.09266i	−0.331102	+	0.277828i
$218$	6.85948	−	3.19863i	0.464582	−	0.216638i
$219$	6.54038	−	1.15324i	0.441958	−	0.0779291i
$220$	4.55212	+	6.23952i	0.306904	+	0.420669i
$221$		−	27.3565i		−	1.84020i
$222$	−2.42320	+	4.87098i	−0.162635	+	0.326919i
$223$	−11.9057	+	11.9057i	−0.797261	+	0.797261i	−0.982663	−	0.185401i	$-0.940641\pi$
$223$	−11.9057	+	11.9057i	−0.797261	+	0.797261i	0.185401	+	0.982663i	$0.440641\pi$
$224$	0.959046	−	0.671532i	0.0640790	−	0.0448686i
$225$	2.32951	+	10.7507i	0.155301	+	0.716715i
$226$	−1.88182	+	5.17026i	−0.125177	+	0.343921i
$227$	16.4996	+	19.6635i	1.09512	+	1.30511i	0.948801	+	0.315876i	$0.102298\pi$
$227$	16.4996	+	19.6635i	1.09512	+	1.30511i	0.146319	+	0.989237i	$0.453257\pi$
$228$	1.43322			0.0949173
$229$	−10.4237	−	12.4225i	−0.688819	−	0.820903i	0.302393	−	0.953183i	$-0.402215\pi$
$229$	−10.4237	−	12.4225i	−0.688819	−	0.820903i	−0.991212	+	0.132280i	$0.957770\pi$
$230$	−10.9503	+	3.16335i	−0.722043	+	0.208585i
$231$	−3.39881	+	1.23707i	−0.223625	+	0.0813929i
$232$	−0.613599	+	2.28998i	−0.0402848	+	0.150345i
$233$	6.02048	−	1.61318i	0.394415	−	0.105683i	−0.0561600	−	0.998422i	$-0.517886\pi$
$233$	6.02048	−	1.61318i	0.394415	−	0.105683i	0.450575	+	0.892739i	$0.351219\pi$
$234$	11.5493	+	2.03645i	0.755002	+	0.133127i
$235$	−9.75841	+	28.5232i	−0.636569	+	1.86065i
$236$	−2.93710	−	0.786994i	−0.191189	−	0.0512289i
$237$	−5.02453	−	4.21608i	−0.326378	−	0.273864i
$238$	−5.98558	+	0.523671i	−0.387988	+	0.0339445i
$239$	8.23595	−	17.6620i	0.532739	−	1.14246i	−0.437256	−	0.899337i	$-0.644050\pi$
$239$	8.23595	−	17.6620i	0.532739	−	1.14246i	0.969995	−	0.243126i	$-0.0781727\pi$
$240$	1.96244	−	0.385480i	0.126675	−	0.0248826i
$241$	−8.87184	+	12.6703i	−0.571485	+	0.816166i	−0.996009	−	0.0892511i	$-0.971553\pi$
$241$	−8.87184	+	12.6703i	−0.571485	+	0.816166i	0.424524	+	0.905417i	$0.360442\pi$
$242$	0.874558	−	0.318313i	0.0562187	−	0.0204619i
$243$	−1.40630	−	16.0740i	−0.0902139	−	1.03115i
$244$	−5.03324	+	0.440351i	−0.322220	+	0.0281906i
$245$	12.2195	+	3.02108i	0.780677	+	0.193009i
$246$	−8.08800	+	3.77150i	−0.515672	+	0.240462i
$247$	4.89941	+	6.99709i	0.311742	+	0.445214i
$248$	−1.40753	−	5.25299i	−0.0893785	−	0.333565i
$249$	6.73385	+	11.6634i	0.426741	+	0.739137i
$250$	−4.12680	+	10.3908i	−0.261002	+	0.657174i
$251$	−5.17794	−	19.3244i	−0.326829	−	1.21974i	−0.912460	−	0.409165i	$-0.865820\pi$
$251$	−5.17794	−	19.3244i	−0.326829	−	1.21974i	0.585631	−	0.810577i	$-0.300847\pi$
$252$	0.224493	−	2.56596i	0.0141417	−	0.161641i
$253$			17.6068i			1.10693i
$254$	−3.74651	−	0.327777i	−0.235077	−	0.0205666i
$255$	−9.71112	−	3.32239i	−0.608134	−	0.208056i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−15.3246	−	2.70214i	−0.955922	−	0.168555i	−0.326136	−	0.945323i	$-0.605747\pi$
$257$	−15.3246	−	2.70214i	−0.955922	−	0.168555i	−0.629787	+	0.776768i	$0.716858\pi$
$258$	4.89993	+	4.89993i	0.305057	+	0.305057i
$259$	1.66863	+	6.92333i	0.103684	+	0.430195i
$260$	8.59049	+	8.26305i	0.532760	+	0.512453i
$261$	2.99165	+	4.27252i	0.185179	+	0.264462i
$262$	−15.1045	−	10.5763i	−0.933160	−	0.653406i
$263$	9.10251	+	19.5204i	0.561285	+	1.20368i	0.958273	+	0.285855i	$0.0922777\pi$
$263$	9.10251	+	19.5204i	0.561285	+	1.20368i	−0.396988	+	0.917824i	$0.629945\pi$
$264$	0.269254	−	3.07759i	0.0165714	−	0.189412i
$265$	31.0115	−	0.602512i	1.90502	−	0.0370120i
$266$	1.43717	−	1.20593i	0.0881187	−	0.0739404i
$267$	−4.25746	−	2.45804i	−0.260552	−	0.150430i
$268$	−2.44400	+	5.24118i	−0.149291	+	0.320156i
$269$	−1.85742	+	1.07238i	−0.113249	+	0.0653844i	−0.555555	−	0.831480i	$-0.687494\pi$
$269$	−1.85742	+	1.07238i	−0.113249	+	0.0653844i	0.442306	+	0.896864i	$0.354161\pi$
$270$	5.02397	−	9.10580i	0.305749	−	0.554162i
$271$	0.0358887	−	0.203535i	0.00218009	−	0.0123639i	−0.983698	−	0.179827i	$-0.942446\pi$
$271$	0.0358887	−	0.203535i	0.00218009	−	0.0123639i	0.985878	+	0.167463i	$0.0535574\pi$
$272$	1.75525	−	4.82251i	0.106428	−	0.292408i
$273$	−4.83406	+	2.79095i	−0.292571	+	0.168916i
$274$	1.00156	+	11.4478i	0.0605062	+	0.691589i
$275$	13.6511	+	10.5789i	0.823194	+	0.637934i
$276$	4.13195	+	1.92676i	0.248714	+	0.115977i
$277$	0.621436	+	3.52434i	0.0373385	+	0.211757i	0.997769	−	0.0667632i	$-0.0212672\pi$
$277$	0.621436	+	3.52434i	0.0373385	+	0.211757i	−0.960430	+	0.278520i	$0.910156\pi$
$278$	−3.96179	−	22.4684i	−0.237613	−	1.34757i
$279$	−10.8435	−	5.05641i	−0.649183	−	0.302719i
$280$	1.64351	−	2.03777i	0.0982184	−	0.121780i
$281$	0.0944573	+	1.07965i	0.00563485	+	0.0644066i	0.998491	−	0.0549069i	$-0.0174862\pi$
$281$	0.0944573	+	1.07965i	0.00563485	+	0.0644066i	−0.992857	+	0.119314i	$0.961931\pi$
$282$	10.4427	−	6.02909i	0.621853	−	0.359027i
$283$	0.960587	−	2.63919i	0.0571009	−	0.156884i	−0.907862	−	0.419268i	$-0.862287\pi$
$283$	0.960587	−	2.63919i	0.0571009	−	0.156884i	0.964963	+	0.262385i	$0.0845089\pi$
$284$	0.297044	−	1.68462i	0.0176263	−	0.0999637i
$285$	3.07888	−	0.889433i	0.182377	−	0.0526854i
$286$	15.9454	−	9.20610i	0.942874	−	0.544368i
$287$	−4.93691	+	10.5872i	−0.291417	+	0.624945i
$288$	1.90529	+	1.10002i	0.112271	+	0.0648194i
$289$	−7.15293	+	6.00202i	−0.420761	+	0.353060i
$290$	0.102976	+	5.30019i	0.00604694	+	0.311238i
$291$	−0.795384	+	9.09128i	−0.0466262	+	0.532940i
$292$	3.13810	+	6.72967i	0.183643	+	0.393824i
$293$	−17.2652	−	12.0892i	−1.00864	−	0.706259i	−0.0523376	−	0.998629i	$-0.516667\pi$
$293$	−17.2652	−	12.0892i	−1.00864	−	0.706259i	−0.956305	+	0.292370i	$0.905556\pi$
$294$	−2.88787	−	4.12430i	−0.168424	−	0.240534i
$295$	−6.79795	+	0.132075i	−0.395792	+	0.00768972i
$296$	−5.96172	−	1.20743i	−0.346518	−	0.0701805i
$297$	−11.3595	−	11.3595i	−0.659143	−	0.659143i
$298$	−0.256167	−	0.0451691i	−0.0148394	−	0.00261658i
$299$	4.71835	+	26.7591i	0.272869	+	1.54752i
$300$	3.97655	−	2.04596i	0.229586	−	0.118123i
$301$	9.03632	+	0.790575i	0.520845	+	0.0455680i
$302$			21.6756i			1.24729i
$303$	0.745236	−	8.51808i	0.0428127	−	0.489351i
$304$	0.414740	+	1.54783i	0.0237870	+	0.0887742i
$305$	−10.5393	+	4.06952i	−0.603476	+	0.233020i
$306$	−5.64532	−	9.77798i	−0.322721	−	0.558970i
$307$	3.20027	+	11.9436i	0.182649	+	0.681656i	0.995122	+	0.0986565i	$0.0314545\pi$
$307$	3.20027	+	11.9436i	0.182649	+	0.681656i	−0.812472	+	0.583000i	$0.801879\pi$
$308$	−2.31953	−	3.31263i	−0.132167	−	0.188754i
$309$	−4.64090	+	2.16409i	−0.264012	+	0.123111i
$310$	−6.28362	−	10.4111i	−0.356885	−	0.591311i
$311$	−26.4432	+	2.31348i	−1.49945	+	0.131185i	−0.807118	−	0.590390i	$-0.798974\pi$
$311$	−26.4432	+	2.31348i	−1.49945	+	0.131185i	−0.692336	+	0.721575i	$0.743418\pi$
$312$	−0.415530	−	4.74953i	−0.0235247	−	0.268889i
$313$	−24.2153	+	8.81366i	−1.36873	+	0.498178i	−0.918743	−	0.394856i	$-0.870794\pi$
$313$	−24.2153	+	8.81366i	−1.36873	+	0.498178i	−0.449989	+	0.893034i	$0.648572\pi$
$314$	−0.427983	+	0.611223i	−0.0241525	+	0.0344933i
$315$	−1.11013	−	5.65159i	−0.0625489	−	0.318431i
$316$	3.09925	−	6.64636i	0.174346	−	0.373887i
$317$	16.9791	−	1.48548i	0.953643	−	0.0834329i	0.400298	−	0.916385i	$-0.368907\pi$
$317$	16.9791	−	1.48548i	0.953643	−	0.0834329i	0.553345	+	0.832952i	$0.313351\pi$
$318$	−9.50400	−	7.97480i	−0.532958	−	0.447205i
$319$	7.90979	+	2.11942i	0.442863	+	0.118665i
$320$	0.984191	+	2.00783i	0.0550179	+	0.112241i
$321$	5.36052	+	0.945205i	0.299195	+	0.0527562i
$322$	5.76455	−	1.54461i	0.321246	−	0.0860776i
$323$	2.12845	−	7.94348i	0.118430	−	0.441987i
$324$	2.29315	−	0.834640i	0.127397	−	0.0463689i
$325$	23.5822	+	12.4198i	1.30811	+	0.688926i
$326$	−4.46566	−	5.32196i	−0.247330	−	0.294756i
$327$	−6.76937			−0.374347
$328$	−6.41357	−	7.64339i	−0.354130	−	0.422036i
$329$	5.39853	−	14.8323i	0.297631	−	0.817733i
$330$	−1.33148	−	6.77844i	−0.0732956	−	0.373141i
$331$	10.6785	−	7.47719i	0.586945	−	0.410984i	−0.242030	−	0.970269i	$-0.577813\pi$
$331$	10.6785	−	7.47719i	0.586945	−	0.410984i	0.828975	+	0.559285i	$0.188924\pi$
$332$	−10.6474	+	10.6474i	−0.584355	+	0.584355i
$333$	−10.4658	+	8.33997i	−0.573520	+	0.457028i
$334$			8.26639i			0.452317i
$335$	−1.99768	+	12.7760i	−0.109145	+	0.698025i
$336$	−1.03124	+	0.181835i	−0.0562588	+	0.00991994i
$337$	−9.57519	+	4.46498i	−0.521594	+	0.243223i	−0.665540	−	0.746362i	$-0.731799\pi$
$337$	−9.57519	+	4.46498i	−0.521594	+	0.243223i	0.143946	+	0.989586i	$0.454021\pi$
$338$	11.8085	−	9.90851i	0.642298	−	0.538952i
$339$	3.47972	−	3.47972i	0.188993	−	0.188993i
$340$	0.777904	−	11.4491i	0.0421878	−	0.620916i
$341$	−18.1442	+	4.86174i	−0.982566	+	0.263278i
$342$	3.19512	+	1.48991i	0.172772	+	0.0805650i
$343$	−14.2823	−	3.82692i	−0.771170	−	0.206634i
$344$	−3.87384	+	6.70969i	−0.208864	+	0.361762i
$345$	10.0721	+	1.57490i	0.542263	+	0.0847897i
$346$	−4.57082	−	9.80215i	−0.245729	−	0.526967i
$347$	−2.93738	−	5.08768i	−0.157687	−	0.273121i	0.776347	−	0.630305i	$-0.217070\pi$
$347$	−2.93738	−	5.08768i	−0.157687	−	0.273121i	−0.934034	+	0.357184i	$0.883737\pi$
$348$	1.36298	−	1.62433i	0.0730633	−	0.0870735i
$349$	−12.3928	+	14.7692i	−0.663372	+	0.790576i	−0.987866	−	0.155312i	$-0.950362\pi$
$349$	−12.3928	+	14.7692i	−0.663372	+	0.790576i	0.324493	+	0.945888i	$0.394806\pi$
$350$	2.26602	−	5.39752i	0.121124	−	0.288510i
$351$	−20.3085	−	14.2202i	−1.08399	−	0.759016i
$352$	3.40161	−	0.599795i	0.181306	−	0.0319692i
$353$	−12.1352	−	33.3413i	−0.645894	−	1.77458i	−0.632364	−	0.774671i	$-0.717915\pi$
$353$	−12.1352	−	33.3413i	−0.645894	−	1.77458i	−0.0135298	−	0.999908i	$-0.504307\pi$
$354$	2.08335	+	1.74814i	0.110729	+	0.0929125i
$355$	−0.407329	−	3.80328i	−0.0216188	−	0.201857i
$356$	1.42260	−	5.30921i	0.0753976	−	0.281388i
$357$	5.04988	+	1.83801i	0.267268	+	0.0972776i
$358$	−5.42737	+	3.80028i	−0.286845	+	0.200851i
$359$	−11.2746	−	6.50942i	−0.595053	−	0.343554i	0.172040	−	0.985090i	$-0.444964\pi$
$359$	−11.2746	−	6.50942i	−0.595053	−	0.343554i	−0.767093	+	0.641536i	$0.778298\pi$
$360$	4.77566	+	1.18070i	0.251699	+	0.0622285i
$361$	−5.62015	−	15.4412i	−0.295797	−	0.812696i
$362$	4.39230	−	7.60768i	0.230854	−	0.399851i
$363$	−0.829240	−	0.0725491i	−0.0435238	−	0.00380784i
$364$	−4.41299	−	4.41299i	−0.231304	−	0.231304i
$365$	10.9177	+	12.5094i	0.571457	+	0.654772i
$366$	4.24641	+	1.54557i	0.221963	+	0.0807881i
$367$	−2.24821	+	3.21078i	−0.117356	+	0.167601i	−0.873532	−	0.486766i	$-0.838176\pi$
$367$	−2.24821	+	3.21078i	−0.117356	+	0.167601i	0.756176	+	0.654368i	$0.227065\pi$
$368$	−0.885150	+	5.01994i	−0.0461416	+	0.261682i
$369$	−21.9515			−1.14275
$370$	−13.5564	+	1.10591i	−0.704766	+	0.0574936i
$371$	−16.2403			−0.843155
$372$	−0.844629	+	4.79013i	−0.0437920	+	0.248357i
$373$	−11.4639	+	16.3722i	−0.593579	+	0.847719i	−0.997756	−	0.0669623i	$-0.978669\pi$
$373$	−11.4639	+	16.3722i	−0.593579	+	0.847719i	0.404176	+	0.914681i	$0.367558\pi$
$374$	−16.6573	−	6.06278i	−0.861331	−	0.313499i
$375$	7.27284	−	6.86296i	0.375568	−	0.354402i
$376$	9.53309	+	9.53309i	0.491632	+	0.491632i
$377$	12.5894	+	1.10143i	0.648388	+	0.0567266i
$378$	−2.72261	+	4.71570i	−0.140036	+	0.242549i
$379$	−0.482966	−	1.32694i	−0.0248083	−	0.0681602i	0.926670	−	0.375875i	$-0.122658\pi$
$379$	−0.482966	−	1.32694i	−0.0248083	−	0.0681602i	−0.951479	+	0.307715i	$0.900436\pi$
$380$	1.85151	+	3.06771i	0.0949807	+	0.157370i
$381$	2.91304	+	1.68184i	0.149240	+	0.0861635i
$382$	0.434062	−	0.303934i	0.0222086	−	0.0155506i
$383$	6.12203	+	2.22824i	0.312821	+	0.113858i	0.493660	−	0.869655i	$-0.335659\pi$
$383$	6.12203	+	2.22824i	0.312821	+	0.113858i	−0.180839	+	0.983513i	$0.557881\pi$
$384$	0.231488	−	0.863927i	0.0118131	−	0.0440871i
$385$	−7.03863	−	5.67681i	−0.358722	−	0.289317i
$386$	−4.61263	−	3.87046i	−0.234777	−	0.197001i
$387$	5.82982	+	16.0173i	0.296346	+	0.814205i
$388$	−10.0485	+	1.77181i	−0.510133	+	0.0899502i
$389$	4.76766	+	3.33835i	0.241730	+	0.169261i	0.688163	−	0.725556i	$-0.258417\pi$
$389$	4.76766	+	3.33835i	0.241730	+	0.169261i	−0.446434	+	0.894817i	$0.647306\pi$
$390$	−3.84013	−	9.94519i	−0.194453	−	0.503594i
$391$	16.8152	−	20.0395i	0.850380	−	1.01344i
$392$	3.61843	−	4.31228i	0.182758	−	0.217803i
$393$	8.24604	+	14.2826i	0.415958	+	0.720460i
$394$	−1.49153	−	3.19860i	−0.0751423	−	0.161143i
$395$	2.53327	−	16.2012i	0.127462	−	0.815172i
$396$	3.79957	−	6.58104i	0.190935	−	0.330710i
$397$	−29.4015	−	7.87811i	−1.47562	−	0.395391i	−0.570766	−	0.821113i	$-0.693354\pi$
$397$	−29.4015	−	7.87811i	−1.47562	−	0.395391i	−0.904854	+	0.425722i	$0.860020\pi$
$398$	−10.7785	−	5.02608i	−0.540275	−	0.251935i
$399$	−1.62081	+	0.434294i	−0.0811419	+	0.0217419i
$400$	3.36029	+	3.70249i	0.168014	+	0.185125i
$401$	22.9440	−	22.9440i	1.14577	−	1.14577i	0.158395	−	0.987376i	$-0.449368\pi$
$401$	22.9440	−	22.9440i	1.14577	−	1.14577i	0.987376	−	0.158395i	$-0.0506319\pi$
$402$	3.96224	−	3.32471i	0.197618	−	0.165822i
$403$	−26.2731	+	12.2513i	−1.30876	+	0.610283i
$404$	9.41491	−	1.66010i	0.468409	−	0.0825932i
$405$	4.40825	−	3.21609i	0.219048	−	0.159809i
$406$		−	2.77564i		−	0.137753i
$407$	−4.17056	+	20.5923i	−0.206727	+	1.02072i
$408$	−3.24568	+	3.24568i	−0.160685	+	0.160685i
$409$	30.9752	−	21.6890i	1.53162	−	1.07245i	0.562217	−	0.826990i	$-0.309948\pi$
$409$	30.9752	−	21.6890i	1.53162	−	1.07245i	0.969406	−	0.245464i	$-0.0789404\pi$
$410$	−18.5212	−	12.4396i	−0.914695	−	0.614347i
$411$	3.51532	−	9.65825i	0.173398	−	0.476406i
$412$	−3.68011	−	4.38578i	−0.181306	−	0.216072i
$413$	3.56000			0.175176
$414$	7.20851	+	8.59077i	0.354279	+	0.422213i
$415$	−16.2655	+	29.4808i	−0.798442	+	1.44715i
$416$	5.00909	−	1.82316i	0.245591	−	0.0893878i
$417$	−5.28142	+	19.7105i	−0.258632	+	0.965229i
$418$	5.34634	−	1.43255i	0.261498	−	0.0700681i
$419$	−7.21324	−	1.27189i	−0.352390	−	0.0621358i	−0.00534859	−	0.999986i	$-0.501703\pi$
$419$	−7.21324	−	1.27189i	−0.352390	−	0.0621358i	−0.347041	+	0.937850i	$0.612814\pi$
$420$	−2.10249	+	1.03059i	−0.102591	+	0.0502878i
$421$	−8.67970	−	2.32572i	−0.423023	−	0.113349i	0.0410265	−	0.999158i	$-0.486937\pi$
$421$	−8.67970	−	2.32572i	−0.423023	−	0.113349i	−0.464049	+	0.885809i	$0.653604\pi$
$422$	1.92087	+	1.61180i	0.0935067	+	0.0784614i
$423$	29.5477	−	2.58509i	1.43666	−	0.125691i
$424$	5.86229	−	12.5717i	0.284698	−	0.610537i
$425$	−5.43402	−	25.0780i	−0.263589	−	1.21646i
$426$	−0.877555	+	1.25328i	−0.0425177	+	0.0607215i
$427$	5.55858	−	2.02316i	0.268999	−	0.0979075i
$428$	0.530419	+	6.06271i	0.0256387	+	0.293052i
$429$	−16.4053	+	1.43527i	−0.792054	+	0.0692957i
$430$	−4.15797	+	16.8180i	−0.200515	+	0.811035i
$431$	14.3032	−	6.66969i	0.688960	−	0.321268i	−0.0464200	−	0.998922i	$-0.514781\pi$
$431$	14.3032	−	6.66969i	0.688960	−	0.321268i	0.735380	+	0.677654i	$0.237003\pi$
$432$	−2.66767	−	3.80982i	−0.128348	−	0.183300i
$433$	−0.967244	−	3.60980i	−0.0464828	−	0.173476i	0.938782	−	0.344511i	$-0.111955\pi$
$433$	−0.967244	−	3.60980i	−0.0464828	−	0.173476i	−0.985265	+	0.171035i	$0.945289\pi$
$434$	3.18352	+	5.51402i	0.152814	+	0.264681i
$435$	1.91995	−	4.33528i	0.0920546	−	0.207861i
$436$	−1.95890	−	7.31070i	−0.0938141	−	0.350119i
$437$	−0.711906	+	8.13712i	−0.0340551	+	0.389251i
$438$		−	6.64127i		−	0.317332i
$439$	17.6375	+	1.54308i	0.841792	+	0.0736473i	0.499891	−	0.866088i	$-0.333373\pi$
$439$	17.6375	+	1.54308i	0.841792	+	0.0736473i	0.341902	+	0.939736i	$0.388929\pi$
$440$	6.93520	−	3.39948i	0.330623	−	0.162064i
$441$	−2.15057	−	12.1965i	−0.102408	−	0.580786i
$442$	−26.9409	−	4.75040i	−1.28145	−	0.225954i
$443$	19.4656	+	19.4656i	0.924837	+	0.924837i	0.997366	−	0.0725290i	$-0.0231070\pi$
$443$	19.4656	+	19.4656i	0.924837	+	0.924837i	−0.0725290	+	0.997366i	$0.523107\pi$
$444$	4.37620	+	3.23222i	0.207685	+	0.153395i
$445$	−0.238744	−	12.2882i	−0.0113176	−	0.582518i
$446$	9.65738	+	13.7922i	0.457290	+	0.653078i
$447$	0.190576	+	0.133443i	0.00901396	+	0.00631164i
$448$	−0.494793	−	1.06109i	−0.0233768	−	0.0501316i
$449$	0.279385	−	3.19339i	0.0131850	−	0.150705i	−0.986748	−	0.162259i	$-0.948122\pi$
$449$	0.279385	−	3.19339i	0.0131850	−	0.150705i	0.999933	+	0.0115534i	$0.00367765\pi$
$450$	10.9919	−	0.427278i	0.518164	−	0.0201421i
$451$	−26.4009	+	22.1530i	−1.24317	+	1.04314i
$452$	4.76494	+	2.75104i	0.224124	+	0.129398i
$453$	8.19318	−	17.5703i	0.384949	−	0.825526i
$454$	22.2299	−	12.8344i	1.04330	−	0.602350i
$455$	−12.2187	−	6.74148i	−0.572823	−	0.316045i
$456$	0.248876	−	1.41145i	0.0116547	−	0.0660970i
$457$	1.01893	−	2.79949i	0.0476636	−	0.130955i	−0.913577	−	0.406666i	$-0.866691\pi$
$457$	1.01893	−	2.79949i	0.0476636	−	0.130955i	0.961240	+	0.275712i	$0.0889135\pi$
$458$	−14.0439	+	8.10822i	−0.656226	+	0.378872i
$459$	2.08029	+	23.7778i	0.0970995	+	1.10985i
$460$	1.21379	+	11.3333i	0.0565931	+	0.528416i
$461$	36.8478	+	17.1824i	1.71617	+	0.800265i	0.994102	+	0.108448i	$0.0345880\pi$
$461$	36.8478	+	17.1824i	1.71617	+	0.800265i	0.722072	+	0.691818i	$0.243190\pi$
$462$	0.628075	+	3.56199i	0.0292207	+	0.165719i
$463$	−5.07509	−	28.7823i	−0.235859	−	1.33763i	−0.840796	−	0.541352i	$-0.817913\pi$
$463$	−5.07509	−	28.7823i	−0.235859	−	1.33763i	0.604937	−	0.796274i	$-0.293198\pi$
$464$	2.14864	+	1.00193i	0.0997482	+	0.0465134i
$465$	1.15822	+	10.8144i	0.0537112	+	0.501508i
$466$	−0.543230	−	6.20914i	−0.0251646	−	0.287633i
$467$	−30.7998	+	17.7822i	−1.42524	+	0.822864i	−0.996740	−	0.0806762i	$-0.974292\pi$
$467$	−30.7998	+	17.7822i	−1.42524	+	0.822864i	−0.428503	+	0.903541i	$0.640959\pi$
$468$	4.01103	−	11.0202i	0.185410	−	0.509410i
$469$	1.17571	−	6.66776i	0.0542891	−	0.307889i
$470$	26.3953	+	14.5632i	1.21752	+	0.671748i
$471$	0.577962	−	0.333686i	0.0266311	−	0.0153755i
$472$	−1.28506	+	2.75582i	−0.0591497	+	0.126847i
$473$	23.1758	+	13.3806i	1.06563	+	0.615239i
$474$	−5.02453	+	4.21608i	−0.230784	+	0.193651i
$475$	5.88124	+	5.44112i	0.269850	+	0.249656i
$476$	−0.523671	+	5.98558i	−0.0240024	+	0.274349i
$477$	−12.8973	−	27.6584i	−0.590527	−	1.26639i
$478$	−15.9636	−	11.1778i	−0.730156	−	0.511261i
$479$	7.16198	+	10.2284i	0.327239	+	0.467346i	0.948735	−	0.316071i	$-0.102364\pi$
$479$	7.16198	+	10.2284i	0.327239	+	0.467346i	−0.621496	+	0.783417i	$0.713475\pi$
$480$	−0.0388490	−	1.99957i	−0.00177321	−	0.0912674i
$481$	−0.820080	+	32.4142i	−0.0373924	+	1.47796i
$482$	10.9372	+	10.9372i	0.498177	+	0.498177i
$483$	−5.25662	−	0.926884i	−0.239184	−	0.0421747i
$484$	−0.161612	−	0.916546i	−0.00734599	−	0.0416612i
$485$	−20.4868	+	10.0422i	−0.930257	+	0.455991i
$486$	−16.0740	−	1.40630i	−0.729133	−	0.0637909i
$487$		−	3.23347i		−	0.146523i	−0.997313	−	0.0732613i	$-0.976659\pi$
$487$		−	3.23347i		−	0.146523i	0.997313	−	0.0732613i	$-0.0233407\pi$
$488$	−0.440351	+	5.03324i	−0.0199338	+	0.227844i
$489$	1.60823	+	6.00198i	0.0727265	+	0.271419i
$490$	5.09708	−	11.5093i	0.230262	−	0.519936i
$491$	18.5283	+	32.0919i	0.836169	+	1.44829i	0.893075	+	0.449908i	$0.148543\pi$
$491$	18.5283	+	32.0919i	0.836169	+	1.44829i	−0.0569057	+	0.998380i	$0.518123\pi$
$492$	2.30973	+	8.62004i	0.104131	+	0.388621i
$493$	−6.97858	−	9.96644i	−0.314299	−	0.448866i
$494$	7.74156	−	3.60995i	0.348309	−	0.162419i
$495$	4.07824	−	16.4955i	0.183303	−	0.741418i
$496$	−5.41760	+	0.473978i	−0.243257	+	0.0212823i
$497$	0.174550	+	1.99512i	0.00782966	+	0.0894934i
$498$	12.6555	−	4.60623i	0.567107	−	0.206410i
$499$	8.40655	−	12.0058i	0.376329	−	0.537453i	−0.585655	−	0.810561i	$-0.699163\pi$
$499$	8.40655	−	12.0058i	0.376329	−	0.537453i	0.961984	+	0.273107i	$0.0880515\pi$
$500$	9.51637	+	5.86845i	0.425585	+	0.262445i
$501$	3.12462	−	6.70077i	0.139598	−	0.299368i
$502$	−19.9299	+	1.74364i	−0.889516	+	0.0778225i
$503$	5.28343	+	4.43333i	0.235577	+	0.197672i	0.752932	−	0.658099i	$-0.228639\pi$
$503$	5.28343	+	4.43333i	0.235577	+	0.197672i	−0.517355	+	0.855771i	$0.673083\pi$
$504$	−2.48800	−	0.666657i	−0.110824	−	0.0296953i
$505$	19.1951	−	9.40901i	0.854171	−	0.418695i
$506$	17.3393	+	3.05738i	0.770825	+	0.135917i
$507$	−13.3174	+	3.56837i	−0.591444	+	0.158477i
$508$	−0.973372	+	3.63267i	−0.0431864	+	0.161174i
$509$	16.4350	−	5.98186i	0.728470	−	0.265141i	0.0489528	−	0.998801i	$-0.484412\pi$
$509$	16.4350	−	5.98186i	0.728470	−	0.265141i	0.679517	+	0.733660i	$0.262189\pi$
$510$	−4.95824	+	8.98666i	−0.219554	+	0.397936i
$511$	−5.58806	−	6.65959i	−0.247201	−	0.294603i
$512$	1.00000			0.0441942
$513$	−4.79057	−	5.70918i	−0.211509	−	0.252067i
$514$	−5.32218	+	14.6226i	−0.234751	+	0.644974i
$515$	−10.6275	−	7.13784i	−0.468302	−	0.314531i
$516$	5.67636	−	3.97463i	0.249888	−	0.174973i
$517$	32.9281	−	32.9281i	1.44818	−	1.44818i
$518$	7.10790	−	0.441054i	0.312303	−	0.0193788i
$519$			9.67340i			0.424615i
$520$	9.62924	−	7.02512i	0.422270	−	0.308072i
$521$	−30.7727	+	5.42606i	−1.34818	+	0.237720i	−0.800682	−	0.599089i	$-0.795530\pi$
$521$	−30.7727	+	5.42606i	−1.34818	+	0.237720i	−0.547495	+	0.836809i	$0.684418\pi$
$522$	4.72711	−	2.20429i	0.206900	−	0.0964790i
$523$	13.9758	−	11.7271i	0.611120	−	0.512790i	−0.283878	−	0.958860i	$-0.591621\pi$
$523$	13.9758	−	11.7271i	0.611120	−	0.512790i	0.894998	+	0.446070i	$0.147177\pi$
$524$	−13.0385	+	13.0385i	−0.569589	+	0.569589i
$525$	−3.87706	+	3.51872i	−0.169209	+	0.153570i
$526$	20.8045	−	5.57454i	0.907118	−	0.243062i
$527$	25.2945	+	11.7950i	1.10184	+	0.513798i
$528$	−2.98407	−	0.799580i	−0.129865	−	0.0347973i
$529$	−1.49162	+	2.58356i	−0.0648531	+	0.112329i
$530$	4.79173	−	30.6450i	0.208139	−	1.33113i
$531$	2.82719	+	6.06292i	0.122689	+	0.263108i
$532$	−0.938048	−	1.62475i	−0.0406695	−	0.0704417i
$533$	−34.1879	+	40.7436i	−1.48084	+	1.76480i
$534$	−3.16000	+	3.76594i	−0.136747	+	0.162968i
$535$	4.90188	+	12.6949i	0.211927	+	0.548849i
$536$	4.73716	+	3.31699i	0.204614	+	0.143272i
$537$	5.83592	−	1.02903i	0.251839	−	0.0444059i
$538$	0.733554	+	2.01542i	0.0316258	+	0.0868910i
$539$	−14.8950	−	12.4983i	−0.641571	−	0.538342i
$540$	−8.09506	−	6.52885i	−0.348356	−	0.280957i
$541$	−7.45630	+	27.8273i	−0.320572	+	1.19639i	0.598118	+	0.801408i	$0.295916\pi$
$541$	−7.45630	+	27.8273i	−0.320572	+	1.19639i	−0.918689	+	0.394981i	$0.870751\pi$
$542$	−0.194211	−	0.0706870i	−0.00834207	−	0.00303627i
$543$	−6.43605	+	4.50657i	−0.276197	+	0.193395i
$544$	−4.44445	−	2.56600i	−0.190554	−	0.110016i
$545$	−8.74505	−	14.4894i	−0.374597	−	0.620657i
$546$	1.90912	+	5.24526i	0.0817028	+	0.224477i
$547$	14.6036	−	25.2941i	0.624404	−	1.08150i	−0.364252	−	0.931300i	$-0.618675\pi$
$547$	14.6036	−	25.2941i	0.624404	−	1.08150i	0.988656	−	0.150199i	$-0.0479914\pi$
$548$	11.4478	+	1.00156i	0.489028	+	0.0427844i
$549$	7.85994	+	7.85994i	0.335454	+	0.335454i
$550$	12.7887	−	11.6067i	0.545313	−	0.494912i
$551$	3.56988	+	1.29933i	0.152082	+	0.0553534i
$552$	2.61500	−	3.73460i	0.111302	−	0.158955i
$553$	−1.49092	+	8.45541i	−0.0634002	+	0.359561i
$554$	3.57871			0.152045
$555$	11.4069	+	4.22775i	0.484197	+	0.179458i
$556$	−22.8151			−0.967574
$557$	−7.02954	+	39.8665i	−0.297851	+	1.68920i	0.357532	+	0.933901i	$0.383618\pi$
$557$	−7.02954	+	39.8665i	−0.297851	+	1.68920i	−0.655383	+	0.755297i	$0.727493\pi$
$558$	−6.86254	+	9.80073i	−0.290515	+	0.414898i
$559$	38.8089	+	14.1253i	1.64144	+	0.597435i
$560$	−1.72142	−	1.97239i	−0.0727433	−	0.0833489i
$561$	11.2108	+	11.2108i	0.473322	+	0.473322i
$562$	1.07965	+	0.0944573i	0.0455424	+	0.00398444i
$563$	−3.56369	+	6.17249i	−0.150191	+	0.260139i	−0.931298	−	0.364259i	$-0.881322\pi$
$563$	−3.56369	+	6.17249i	−0.150191	+	0.260139i	0.781106	+	0.624398i	$0.214656\pi$
$564$	−4.12414	−	11.3310i	−0.173658	−	0.477120i
$565$	11.9434	+	2.95281i	0.502463	+	0.124226i
$566$	−2.43229	−	1.40428i	−0.102237	−	0.0590264i
$567$	−2.34038	+	1.63875i	−0.0982869	+	0.0688212i
$568$	−1.60744	−	0.585062i	−0.0674468	−	0.0245486i
$569$	−5.87989	+	21.9440i	−0.246498	+	0.919942i	0.726127	+	0.687561i	$0.241318\pi$
$569$	−5.87989	+	21.9440i	−0.246498	+	0.919942i	−0.972625	+	0.232381i	$0.925348\pi$
$570$	−0.341278	−	3.18655i	−0.0142946	−	0.133470i
$571$	5.49650	+	4.61211i	0.230022	+	0.193011i	0.750513	−	0.660856i	$-0.229807\pi$
$571$	5.49650	+	4.61211i	0.230022	+	0.193011i	−0.520491	+	0.853867i	$0.674251\pi$
$572$	−6.29735	−	17.3018i	−0.263305	−	0.723425i
$573$	−0.466737	+	0.0822983i	−0.0194982	+	0.00343806i
$574$	9.56912	+	6.70037i	0.399407	+	0.279668i
$575$	9.64072	+	23.5932i	0.402046	+	0.983903i
$576$	1.41416	−	1.68533i	0.0589234	−	0.0702221i
$577$	16.4111	−	19.5580i	0.683204	−	0.814211i	−0.307312	−	0.951609i	$-0.599430\pi$
$577$	16.4111	−	19.5580i	0.683204	−	0.814211i	0.990516	+	0.137398i	$0.0438740\pi$
$578$	4.66874	+	8.08650i	0.194194	+	0.336354i
$579$	2.27602	+	4.88094i	0.0945882	+	0.202845i
$580$	5.23755	+	0.818957i	0.217477	+	0.0340053i
$581$	8.81466	−	15.2674i	0.365694	−	0.633400i
$582$	8.81505	+	2.36198i	0.365395	+	0.0979074i
$583$	−43.4238	−	20.2488i	−1.79843	−	0.838621i
$584$	7.17236	−	1.92183i	0.296794	−	0.0795258i
$585$	1.77764	−	26.1631i	0.0734963	−	1.08171i
$586$	−14.9036	+	14.9036i	−0.615663	+	0.615663i
$587$	−19.0110	+	15.9521i	−0.784666	+	0.658413i	−0.944419	−	0.328744i	$-0.893375\pi$
$587$	−19.0110	+	15.9521i	−0.784666	+	0.658413i	0.159753	+	0.987157i	$0.448930\pi$
$588$	−4.56311	+	2.12782i	−0.188180	+	0.0877496i
$589$	−8.58210	+	1.51326i	−0.353619	+	0.0623526i
$590$	−1.05038	+	6.71761i	−0.0432436	+	0.276560i
$591$			3.15659i			0.129845i
$592$	−2.22433	+	5.66148i	−0.0914193	+	0.232685i
$593$	6.85117	−	6.85117i	0.281344	−	0.281344i	−0.552301	−	0.833645i	$-0.686250\pi$
$593$	6.85117	−	6.85117i	0.281344	−	0.281344i	0.833645	+	0.552301i	$0.186250\pi$
$594$	−13.1594	+	9.21434i	−0.539938	+	0.378069i
$595$	2.58959	+	13.1834i	0.106163	+	0.540465i
$596$	−0.0889658	+	0.244432i	−0.00364418	+	0.0100123i
$597$	6.83725	+	8.14832i	0.279830	+	0.333489i
$598$	27.1719			1.11114
$599$	−13.2151	−	15.7491i	−0.539953	−	0.643491i	0.425224	−	0.905088i	$-0.360195\pi$
$599$	−13.2151	−	15.7491i	−0.539953	−	0.643491i	−0.965177	+	0.261597i	$0.915751\pi$
$600$	−1.32436	−	4.27142i	−0.0540666	−	0.174380i
$601$	25.9301	−	9.43778i	1.05771	−	0.384975i	0.246143	−	0.969234i	$-0.420837\pi$
$601$	25.9301	−	9.43778i	1.05771	−	0.384975i	0.811568	+	0.584258i	$0.198614\pi$
$602$	2.34770	−	8.76175i	0.0956853	−	0.357102i
$603$	12.2893	−	3.29292i	0.500461	−	0.134098i
$604$	21.3463	+	3.76393i	0.868568	+	0.153152i
$605$	−0.915972	−	1.86865i	−0.0372396	−	0.0759716i
$606$	−8.25927	−	2.21306i	−0.335510	−	0.0898996i
$607$	−29.9302	−	25.1145i	−1.21483	−	1.01936i	−0.999079	−	0.0429163i	$-0.986335\pi$
$607$	−29.9302	−	25.1145i	−1.21483	−	1.01936i	−0.215753	−	0.976448i	$-0.569220\pi$
$608$	1.59633	−	0.139661i	0.0647399	−	0.00566401i
$609$	−1.04917	+	2.24995i	−0.0425144	+	0.0911725i
$610$	2.17757	+	11.0858i	0.0881672	+	0.448851i
$611$	41.2205	−	58.8690i	1.66760	−	2.38158i
$612$	−10.6097	+	3.86163i	−0.428873	+	0.156097i
$613$	−2.34745	−	26.8315i	−0.0948126	−	1.08371i	−0.883346	−	0.468722i	$-0.844715\pi$
$613$	−2.34745	−	26.8315i	−0.0948126	−	1.08371i	0.788533	−	0.614992i	$-0.210841\pi$
$614$	12.3179	−	1.07767i	0.497108	−	0.0434913i
$615$	10.3113	+	17.0844i	0.415791	+	0.688910i
$616$	−3.66508	+	1.70906i	−0.147670	+	0.0688598i
$617$	21.0550	+	30.0696i	0.847642	+	1.21056i	0.975770	+	0.218800i	$0.0702143\pi$
$617$	21.0550	+	30.0696i	0.847642	+	1.21056i	−0.128128	+	0.991758i	$0.540897\pi$
$618$	1.32533	+	4.94618i	0.0533124	+	0.198965i
$619$	−15.9002	−	27.5400i	−0.639085	−	1.10693i	−0.985634	−	0.168895i	$-0.945980\pi$
$619$	−15.9002	−	27.5400i	−0.639085	−	1.10693i	0.346549	−	0.938032i	$-0.387353\pi$
$620$	−11.3441	+	4.38028i	−0.455589	+	0.175916i
$621$	−6.13597	−	22.8997i	−0.246228	−	0.918935i
$622$	−2.31348	+	26.4432i	−0.0927619	+	1.06027i
$623$			6.43519i			0.257821i
$624$	−4.74953	−	0.415530i	−0.190133	−	0.0166345i
$625$	24.0852	+	6.70107i	0.963407	+	0.268043i
$626$	4.47481	+	25.3779i	0.178850	+	1.01431i
$627$	−4.87525	−	0.859638i	−0.194699	−	0.0343307i
$628$	0.527619	+	0.527619i	0.0210543	+	0.0210543i
$629$	24.4133	−	19.4545i	0.973422	−	0.775702i
$630$	−5.75850	+	0.111880i	−0.229424	+	0.00445741i
$631$	−10.2512	−	14.6403i	−0.408096	−	0.582821i	0.561517	−	0.827465i	$-0.310218\pi$
$631$	−10.2512	−	14.6403i	−0.408096	−	0.582821i	−0.969613	+	0.244644i	$0.921329\pi$
$632$	−6.00721	−	4.20629i	−0.238954	−	0.167317i
$633$	−0.947821	−	2.03261i	−0.0376725	−	0.0807889i
$634$	1.48548	−	16.9791i	0.0589960	−	0.674327i
$635$	0.163354	+	8.40786i	0.00648250	+	0.333656i
$636$	−9.50400	+	7.97480i	−0.376858	+	0.316222i
$637$	−25.9870	−	15.0036i	−1.02964	−	0.594465i
$638$	3.46074	−	7.42159i	0.137012	−	0.293823i
$639$	−3.25921	+	1.88170i	−0.128932	+	0.0744390i
$640$	2.14823	−	0.620583i	0.0849161	−	0.0245307i
$641$	−1.76288	+	9.99782i	−0.0696298	+	0.394890i	0.929997	+	0.367567i	$0.119809\pi$
$641$	−1.76288	+	9.99782i	−0.0696298	+	0.394890i	−0.999627	+	0.0273227i	$0.991302\pi$
$642$	1.86169	−	5.11495i	0.0734751	−	0.201871i
$643$	7.59318	−	4.38393i	0.299446	−	0.172885i	−0.342748	−	0.939427i	$-0.611358\pi$
$643$	7.59318	−	4.38393i	0.299446	−	0.172885i	0.642194	+	0.766542i	$0.278024\pi$
$644$	−0.520137	−	5.94519i	−0.0204963	−	0.234273i
$645$	9.72751	−	12.0611i	0.383020	−	0.474904i
$646$	−7.45320	−	3.47548i	−0.293242	−	0.136741i
$647$	1.13329	+	6.42718i	0.0445540	+	0.252678i	0.998947	−	0.0458741i	$-0.0146073\pi$
$647$	1.13329	+	6.42718i	0.0445540	+	0.252678i	−0.954393	+	0.298553i	$0.903496\pi$
$648$	−0.423758	−	2.40325i	−0.0166468	−	0.0944085i
$649$	9.51883	+	4.43870i	0.373647	+	0.174234i
$650$	16.3261	−	21.0673i	0.640363	−	0.826327i
$651$	−0.496326	−	5.67303i	−0.0194525	−	0.222344i
$652$	−6.01656	+	3.47367i	−0.235627	+	0.136039i
$653$	−7.04390	+	19.3530i	−0.275649	+	0.757340i	0.722194	+	0.691691i	$0.243134\pi$
$653$	−7.04390	+	19.3530i	−0.275649	+	0.757340i	−0.997843	+	0.0656489i	$0.979088\pi$
$654$	−1.17549	+	6.66653i	−0.0459653	+	0.260682i
$655$	−19.9182	+	36.1011i	−0.778267	+	1.41059i
$656$	−8.64098	+	4.98887i	−0.337373	+	0.194783i
$657$	6.90395	−	14.8056i	0.269349	−	0.577620i
$658$	−13.6696	−	7.89212i	−0.532895	−	0.307667i
$659$	21.7689	−	18.2663i	0.847995	−	0.711553i	−0.111352	−	0.993781i	$-0.535518\pi$
$659$	21.7689	−	18.2663i	0.847995	−	0.711553i	0.959347	+	0.282228i	$0.0910736\pi$
$660$	−6.90667	+	0.134188i	−0.268842	+	0.00522325i
$661$	−0.274540	+	3.13800i	−0.0106784	+	0.122054i	−0.999663	−	0.0259650i	$-0.991734\pi$
$661$	−0.274540	+	3.13800i	−0.0106784	+	0.122054i	0.988984	+	0.148019i	$0.0472897\pi$
$662$	−5.50929	−	11.8147i	−0.214125	−	0.459191i
$663$	20.0428	+	14.0341i	0.778397	+	0.545040i
$664$	8.63678	+	12.3346i	0.335172	+	0.478675i
$665$	−3.02343	−	2.90819i	−0.117244	−	0.112775i
$666$	6.39591	+	11.7550i	0.247837	+	0.455496i
$667$	8.54516	+	8.54516i	0.330870	+	0.330870i
$668$	8.14081	+	1.43544i	0.314977	+	0.0555390i
$669$	−2.61500	−	14.8304i	−0.101102	−	0.573376i
$670$	12.2350	+	4.18585i	0.472678	+	0.161714i
$671$	17.3852	+	1.52101i	0.671149	+	0.0587179i
$672$			1.04715i			0.0403946i
$673$	1.21769	−	13.9183i	0.0469386	−	0.536511i	−0.935928	−	0.352192i	$-0.885436\pi$
$673$	1.21769	−	13.9183i	0.0469386	−	0.536511i	0.982866	−	0.184319i	$-0.0590080\pi$
$674$	2.73444	+	10.2051i	0.105327	+	0.393084i
$675$	−21.4417	−	9.00179i	−0.825292	−	0.346479i
$676$	−7.70746	−	13.3497i	−0.296441	−	0.513450i
$677$	−3.23473	−	12.0722i	−0.124321	−	0.463971i	0.875494	−	0.483229i	$-0.160536\pi$
$677$	−3.23473	−	12.0722i	−0.124321	−	0.463971i	−0.999815	+	0.0192580i	$0.993870\pi$
$678$	−2.82261	−	4.03111i	−0.108402	−	0.154814i
$679$	10.8268	−	5.04860i	0.415493	−	0.193748i
$680$	−11.1401	−	2.75420i	−0.427203	−	0.105619i
$681$	−22.8710	+	2.00095i	−0.876417	+	0.0766766i
$682$	1.63716	+	18.7128i	0.0626901	+	0.716551i
$683$	19.2489	−	7.00604i	0.736540	−	0.268079i	0.0536095	−	0.998562i	$-0.482927\pi$
$683$	19.2489	−	7.00604i	0.736540	−	0.268079i	0.682930	+	0.730483i	$0.260705\pi$
$684$	2.02210	−	2.88786i	0.0773169	−	0.110420i
$685$	25.2141	−	4.95277i	0.963382	−	0.189236i
$686$	−6.24887	+	13.4008i	−0.238583	+	0.511643i
$687$	14.4488	−	1.26411i	0.551258	−	0.0482288i
$688$	5.93507	+	4.98012i	0.226273	+	0.189865i
$689$	−71.4227	−	19.1377i	−2.72099	−	0.729087i
$690$	3.29997	−	9.64559i	0.125628	−	0.367201i
$691$	6.04707	+	1.06626i	0.230041	+	0.0405625i	0.287480	−	0.957786i	$-0.407182\pi$
$691$	6.04707	+	1.06626i	0.230041	+	0.0405625i	−0.0574390	+	0.998349i	$0.518293\pi$
$692$	−10.4470	+	2.79925i	−0.397134	+	0.106412i
$693$	−2.30269	+	8.59375i	−0.0874719	+	0.326450i
$694$	−5.52046	+	2.00928i	−0.209554	+	0.0762714i
$695$	−49.0119	+	14.1586i	−1.85913	+	0.537068i
$696$	−1.36298	−	1.62433i	−0.0516636	−	0.0615703i
$697$	51.2058			1.93956
$698$	12.3928	+	14.7692i	0.469075	+	0.559022i
$699$	−1.90666	+	5.23849i	−0.0721163	+	0.198138i
$700$	−4.92203	−	3.16886i	−0.186035	−	0.119772i
$701$	−20.1250	+	14.0917i	−0.760110	+	0.532235i	−0.888161	−	0.459533i	$-0.848017\pi$
$701$	−20.1250	+	14.0917i	−0.760110	+	0.532235i	0.128050	+	0.991768i	$0.459128\pi$
$702$	−17.5307	+	17.5307i	−0.661652	+	0.661652i
$703$	−2.76008	+	9.34827i	−0.104099	+	0.352577i
$704$		−	3.45408i		−	0.130181i
$705$	−15.8914	−	21.7821i	−0.598505	−	0.820363i
$706$	−34.9421	+	6.16123i	−1.31506	+	0.231881i
$707$	−10.1441	+	4.73029i	−0.381510	+	0.177901i
$708$	2.08335	−	1.74814i	0.0782971	−	0.0656991i
$709$	30.2981	−	30.2981i	1.13787	−	1.13787i	0.149038	−	0.988831i	$-0.452382\pi$
$709$	30.2981	−	30.2981i	1.13787	−	1.13787i	0.988831	−	0.149038i	$-0.0476177\pi$
$710$	−3.81623	−	0.259292i	−0.143221	−	0.00973105i
$711$	−15.5842	+	4.17576i	−0.584451	+	0.156603i
$712$	−4.98152	−	2.32292i	−0.186690	−	0.0870552i
$713$	−26.7764	−	7.17473i	−1.00279	−	0.268696i
$714$	2.68699	−	4.65400i	0.100558	−	0.174171i
$715$	−24.2653	−	33.2602i	−0.907472	−	1.24386i
$716$	2.80010	+	6.00483i	0.104645	+	0.224411i
$717$	8.71502	+	15.0949i	0.325468	+	0.563728i
$718$	−8.36835	+	9.97301i	−0.312304	+	0.372190i
$719$	−15.0594	+	17.9471i	−0.561620	+	0.669312i	−0.969888	−	0.243549i	$-0.921688\pi$
$719$	−15.0594	+	17.9471i	−0.561620	+	0.669312i	0.408269	+	0.912862i	$0.366133\pi$
$720$	1.99205	−	4.49808i	0.0742393	−	0.167633i
$721$	5.49077	+	3.84468i	0.204487	+	0.143183i
$722$	−16.1826	+	2.85342i	−0.602253	+	0.106193i
$723$	−4.73159	−	12.9999i	−0.175970	−	0.483473i
$724$	−6.72939	−	5.64663i	−0.250096	−	0.209855i
$725$	11.7597	−	1.49103i	0.436743	−	0.0553755i
$726$	−0.215443	+	0.804044i	−0.00799584	+	0.0298409i
$727$	9.19350	+	3.34616i	0.340968	+	0.124102i	0.506828	−	0.862047i	$-0.330818\pi$
$727$	9.19350	+	3.34616i	0.340968	+	0.124102i	−0.165860	+	0.986149i	$0.553040\pi$
$728$	−5.11226	+	3.57964i	−0.189473	+	0.132670i
$729$	6.15797	+	3.55530i	0.228073	+	0.131678i
$730$	14.2152	−	8.57957i	0.526128	−	0.317544i
$731$	−13.5991	−	37.3633i	−0.502982	−	1.38193i
$732$	2.25947	−	3.91351i	0.0835123	−	0.144648i
$733$	−17.4342	−	1.52530i	−0.643947	−	0.0563381i	−0.239496	−	0.970897i	$-0.576982\pi$
$733$	−17.4342	−	1.52530i	−0.643947	−	0.0563381i	−0.404452	+	0.914559i	$0.632538\pi$
$734$	2.77160	+	2.77160i	0.102302	+	0.102302i
$735$	−8.48212	+	7.40282i	−0.312868	+	0.273057i
$736$	4.78997	+	1.74341i	0.176561	+	0.0642628i
$737$	11.4572	−	16.3625i	0.422030	−	0.602722i
$738$	−3.81183	+	21.6180i	−0.140315	+	0.795769i
$739$	−24.8534			−0.914246			−0.457123	−	0.889404i	$-0.651120\pi$
$739$	−24.8534			−0.914246			−0.457123	+	0.889404i	$0.651120\pi$
$740$	−1.26494	+	13.5425i	−0.0465001	+	0.497833i
$741$	−7.63987			−0.280658
$742$	−2.82010	+	15.9936i	−0.103529	+	0.587143i
$743$	−8.91872	+	12.7373i	−0.327196	+	0.467285i	−0.948723	−	0.316108i	$-0.897624\pi$
$743$	−8.91872	+	12.7373i	−0.327196	+	0.467285i	0.621527	+	0.783393i	$0.286513\pi$
$744$	4.57069	+	1.66359i	0.167570	+	0.0609903i
$745$	−0.0394285	+	0.580305i	−0.00144455	+	0.0212607i
$746$	14.1328	+	14.1328i	0.517437	+	0.517437i
$747$	33.0017	+	2.88727i	1.20747	+	0.105640i
$748$	−8.86319	+	15.3515i	−0.324070	+	0.561306i
$749$	−2.43697	−	6.69551i	−0.0890448	−	0.244649i
$750$	−5.49578	−	8.35409i	−0.200678	−	0.305048i
$751$	17.0265	+	9.83026i	0.621306	+	0.358711i	0.777377	−	0.629034i	$-0.216550\pi$
$751$	17.0265	+	9.83026i	0.621306	+	0.358711i	−0.156071	+	0.987746i	$0.549883\pi$
$752$	11.0437	−	7.73286i	0.402721	−	0.281988i
$753$	16.8144	+	6.11992i	0.612749	+	0.223022i
$754$	3.27083	−	12.2069i	0.119117	−	0.444549i
$755$	48.1925	−	5.16139i	1.75390	−	0.187842i
$756$	4.17128	+	3.50012i	0.151708	+	0.127298i
$757$	−16.1822	−	44.4603i	−0.588153	−	1.61594i	−0.773877	−	0.633336i	$-0.781685\pi$
$757$	−16.1822	−	44.4603i	−0.588153	−	1.61594i	0.185723	−	0.982602i	$-0.440537\pi$
$758$	−1.39064	+	0.245208i	−0.0505105	+	0.00890636i
$759$	−12.8996	−	9.03241i	−0.468227	−	0.327856i
$760$	3.34262	−	1.29068i	0.121249	−	0.0468180i
$761$	24.4006	−	29.0795i	0.884522	−	1.05413i	−0.113639	−	0.993522i	$-0.536251\pi$
$761$	24.4006	−	29.0795i	0.884522	−	1.05413i	0.998161	−	0.0606107i	$-0.0193048\pi$
$762$	2.16214	−	2.57673i	0.0783260	−	0.0933453i
$763$	4.43058	+	7.67399i	0.160398	+	0.277817i
$764$	−0.223942	−	0.480246i	−0.00810194	−	0.0173747i
$765$	−20.3956	+	14.8799i	−0.737406	+	0.537983i
$766$	3.25746	−	5.64209i	0.117697	−	0.203857i
$767$	15.6564	+	4.19512i	0.565320	+	0.151477i
$768$	−0.810604	−	0.377991i	−0.0292502	−	0.0136396i
$769$	−0.908670	+	0.243477i	−0.0327675	+	0.00878002i	−0.275166	−	0.961397i	$-0.588733\pi$
$769$	−0.908670	+	0.243477i	−0.0327675	+	0.00878002i	0.242398	+	0.970177i	$0.422066\pi$
$770$	−6.81281	+	5.94593i	−0.245517	+	0.214276i
$771$	9.84138	−	9.84138i	0.354429	−	0.354429i
$772$	−4.61263	+	3.87046i	−0.166012	+	0.139301i
$773$	43.9567	−	20.4974i	1.58101	−	0.737239i	0.583804	−	0.811895i	$-0.301564\pi$
$773$	43.9567	−	20.4974i	1.58101	−	0.737239i	0.997209	+	0.0746559i	$0.0237858\pi$
$774$	16.7863	−	2.95988i	0.603371	−	0.106391i
$775$	−21.6513	+	16.4498i	−0.777739	+	0.590894i
$776$			10.2035i			0.366283i
$777$	−5.92841	−	2.32920i	−0.212681	−	0.0835597i
$778$	4.11553	−	4.11553i	0.147549	−	0.147549i
$779$	−13.0971	+	9.17072i	−0.469254	+	0.328575i
$780$	−10.4609	+	2.05483i	−0.374562	+	0.0735746i
$781$	−2.02085	+	5.55224i	−0.0723117	+	0.198675i
$782$	−16.8152	−	20.0395i	−0.601309	−	0.716613i
$783$	−11.0263			−0.394047
$784$	−3.61843	−	4.31228i	−0.129230	−	0.154010i
$785$	1.46088	+	0.806013i	0.0521409	+	0.0287678i
$786$	15.4975	−	5.64063i	0.552777	−	0.201194i
$787$	1.12880	−	4.21275i	0.0402375	−	0.150168i	−0.942884	−	0.333120i	$-0.891899\pi$
$787$	1.12880	−	4.21275i	0.0402375	−	0.150168i	0.983122	+	0.182952i	$0.0585652\pi$
$788$	−3.40901	+	0.913442i	−0.121441	+	0.0325400i
$789$	−18.9713	−	3.34516i	−0.675397	−	0.119091i
$790$	−15.5152	−	5.30809i	−0.552006	−	0.188853i
$791$	−6.22222	−	1.66724i	−0.221237	−	0.0592802i
$792$	−5.82127	−	4.88463i	−0.206850	−	0.173568i
$793$	26.8300	−	2.34732i	0.952761	−	0.0833558i
$794$	−12.8639	+	27.5868i	−0.456525	+	0.979020i
$795$	−15.4677	+	23.0297i	−0.548583	+	0.816780i
$796$	−6.82138	+	9.74194i	−0.241777	+	0.345294i
$797$	−4.63673	+	1.68763i	−0.164241	+	0.0597789i	−0.422832	−	0.906208i	$-0.638964\pi$
$797$	−4.63673	+	1.68763i	−0.164241	+	0.0597789i	0.258591	+	0.965987i	$0.416742\pi$
$798$	0.146246	+	1.67160i	0.00517705	+	0.0591740i
$799$	−68.9255	+	6.03020i	−2.43841	+	0.213333i
$800$	4.22975	−	2.66631i	0.149544	−	0.0942682i
$801$	−10.9596	+	5.11053i	−0.387237	+	0.180572i
$802$	−18.6113	−	26.5797i	−0.657187	−	0.938561i
$803$	−6.63815	−	24.7739i	−0.234255	−	0.874252i
$804$	−2.58617	−	4.47937i	−0.0912071	−	0.157975i
$805$	−4.80686	−	12.4488i	−0.169420	−	0.438764i
$806$	7.50295	+	28.0014i	0.264280	+	0.986307i
$807$	0.167190	−	1.91099i	0.00588536	−	0.0672699i
$808$		−	9.56015i		−	0.336325i
$809$	−29.4152	−	2.57350i	−1.03418	−	0.0904793i	−0.442597	−	0.896721i	$-0.645943\pi$
$809$	−29.4152	−	2.57350i	−1.03418	−	0.0904793i	−0.591587	+	0.806241i	$0.701498\pi$
$810$	−2.40174	−	4.89975i	−0.0843887	−	0.172160i
$811$	−6.46851	−	36.6847i	−0.227140	−	1.28817i	−0.858552	−	0.512727i	$-0.828635\pi$
$811$	−6.46851	−	36.6847i	−0.227140	−	1.28817i	0.631412	−	0.775448i	$-0.282476\pi$
$812$	−2.73347	−	0.481985i	−0.0959261	−	0.0169144i
$813$	0.130709	+	0.130709i	0.00458417	+	0.00458417i
$814$	19.5552	+	7.68301i	0.685410	+	0.269290i
$815$	−10.7692	+	11.1960i	−0.377230	+	0.392179i
$816$	2.63276	+	3.75997i	0.0921651	+	0.131625i
$817$	10.1699	+	7.12103i	0.355799	+	0.249133i
$818$	−15.9808	−	34.2708i	−0.558754	−	1.19825i
$819$	−1.19667	+	13.6780i	−0.0418151	+	0.477949i
$820$	−15.4668	+	16.0797i	−0.540123	+	0.561526i
$821$	20.9339	−	17.5656i	0.730598	−	0.613044i	−0.199697	−	0.979858i	$-0.563996\pi$
$821$	20.9339	−	17.5656i	0.730598	−	0.613044i	0.930294	+	0.366814i	$0.119551\pi$
$822$	−8.90109	−	5.13905i	−0.310461	−	0.179245i
$823$	−4.98420	+	10.6886i	−0.173738	+	0.372583i	−0.973824	−	0.227303i	$-0.927009\pi$
$823$	−4.98420	+	10.6886i	−0.173738	+	0.372583i	0.800086	+	0.599885i	$0.204787\pi$
$824$	−4.95820	+	2.86262i	−0.172727	+	0.0997240i
$825$	−14.7538	+	4.57443i	−0.513662	+	0.159261i
$826$	0.618188	−	3.50592i	0.0215095	−	0.121986i
$827$	−12.1956	+	33.5070i	−0.424081	+	1.16515i	0.525269	+	0.850936i	$0.323965\pi$
$827$	−12.1956	+	33.5070i	−0.424081	+	1.16515i	−0.949351	+	0.314218i	$0.898258\pi$
$828$	9.71200	−	5.60722i	0.337515	−	0.194865i
$829$	−0.0241173	−	0.275663i	−0.000837630	−	0.00957416i	0.995764	−	0.0919418i	$-0.0293074\pi$
$829$	−0.0241173	−	0.275663i	−0.000837630	−	0.00957416i	−0.996602	+	0.0823677i	$0.973752\pi$
$830$	26.2084	+	21.1377i	0.909707	+	0.733699i
$831$	−2.90091	−	1.35272i	−0.100632	−	0.0469253i
$832$	−0.925643	−	5.24958i	−0.0320909	−	0.181996i
$833$	5.01660	+	28.4506i	0.173815	+	0.985754i
$834$	18.4940	+	8.62389i	0.640394	+	0.298621i
$835$	18.3791	−	1.96839i	0.636035	−	0.0681190i
$836$	−0.482401	−	5.51387i	−0.0166842	−	0.190701i
$837$	21.9045	−	12.6466i	0.757130	−	0.437129i
$838$	−2.50513	+	6.88279i	−0.0865384	+	0.237762i
$839$	−4.27477	+	24.2434i	−0.147582	+	0.836976i	0.817677	+	0.575678i	$0.195262\pi$
$839$	−4.27477	+	24.2434i	−0.147582	+	0.836976i	−0.965258	+	0.261298i	$0.915849\pi$
$840$	0.649843	+	2.24951i	0.0224217	+	0.0776155i
$841$	−20.2472	+	11.6897i	−0.698180	+	0.403094i
$842$	−3.79760	+	8.14398i	−0.130874	+	0.280660i
$843$	−0.839466	−	0.484666i	−0.0289128	−	0.0166928i
$844$	1.92087	−	1.61180i	0.0661192	−	0.0554806i
$845$	−24.8420	−	23.8951i	−0.854590	−	0.822015i
$846$	2.58509	−	29.5477i	0.0888773	−	1.01587i
$847$	0.460496	+	0.987538i	0.0158228	+	0.0339322i
$848$	−11.3628	−	7.95629i	−0.390199	−	0.273220i
$849$	1.44082	+	2.05770i	0.0494488	+	0.0706202i
$850$	−25.6407	+	0.996705i	−0.879468	+	0.0341867i
$851$	−20.5247	+	23.2404i	−0.703578	+	0.796671i
$852$	1.08185	+	1.08185i	0.0370637	+	0.0370637i
$853$	−16.0985	−	2.83860i	−0.551202	−	0.0971918i	−0.108891	−	0.994054i	$-0.534730\pi$
$853$	−16.0985	−	2.83860i	−0.551202	−	0.0971918i	−0.442311	+	0.896862i	$0.645841\pi$
$854$	−1.02718	−	5.82545i	−0.0351495	−	0.199343i
$855$	2.55177	−	7.45865i	0.0872687	−	0.255080i
$856$	6.06271	+	0.530419i	0.207219	+	0.0181293i
$857$		−	31.9987i		−	1.09305i	−0.837441	−	0.546527i	$-0.815950\pi$
$857$		−	31.9987i		−	1.09305i	0.837441	−	0.546527i	$-0.184050\pi$
$858$	−1.43527	+	16.4053i	−0.0489995	+	0.560066i
$859$	7.16489	+	26.7397i	0.244463	+	0.912348i	0.973653	+	0.228037i	$0.0732306\pi$
$859$	7.16489	+	26.7397i	0.244463	+	0.912348i	−0.729190	+	0.684312i	$0.760103\pi$
$860$	15.8405	+	7.01521i	0.540155	+	0.239217i
$861$	−5.22409	−	9.04839i	−0.178036	−	0.308368i
$862$	−4.08464	−	15.2441i	−0.139123	−	0.519215i
$863$	8.14619	+	11.6340i	0.277300	+	0.396025i	0.933509	−	0.358554i	$-0.116730\pi$
$863$	8.14619	+	11.6340i	0.277300	+	0.396025i	−0.656209	+	0.754579i	$0.727841\pi$
$864$	−4.21518	+	1.96557i	−0.143403	+	0.0668700i
$865$	−20.7052	+	12.4966i	−0.704000	+	0.424898i
$866$	−3.72292	+	0.325714i	−0.126510	+	0.0110682i
$867$	−0.727879	−	8.31969i	−0.0247201	−	0.282552i
$868$	5.98306	−	2.17766i	0.203078	−	0.0739145i
$869$	−14.5289	+	20.7494i	−0.492858	+	0.703875i
$870$	−3.93602	−	2.64360i	−0.133444	−	0.0896263i
$871$	13.0279	−	27.9385i	0.441434	−	0.946658i
$872$	−7.53979	+	0.659647i	−0.255330	+	0.0223385i
$873$	17.1962	+	14.4293i	0.582004	+	0.488359i
$874$	7.88988	+	2.11409i	0.266879	+	0.0715100i
$875$	−12.5402	−	3.75290i	−0.423936	−	0.126871i
$876$	−6.54038	−	1.15324i	−0.220979	−	0.0389645i
$877$	15.6680	−	4.19823i	0.529070	−	0.141764i	0.0156114	−	0.999878i	$-0.495031\pi$
$877$	15.6680	−	4.19823i	0.529070	−	0.141764i	0.513459	+	0.858114i	$0.328364\pi$
$878$	4.58236	−	17.1016i	0.154647	−	0.577151i
$879$	17.7144	−	6.44750i	0.597491	−	0.217469i
$880$	−2.14355	−	7.42015i	−0.0722589	−	0.250133i
$881$	18.9409	+	22.5729i	0.638137	+	0.760502i	0.984075	−	0.177756i	$-0.0568837\pi$
$881$	18.9409	+	22.5729i	0.638137	+	0.760502i	−0.345938	+	0.938257i	$0.612439\pi$
$882$	−12.3847			−0.417013
$883$	26.3609	+	31.4157i	0.887115	+	1.05722i	0.997989	+	0.0633885i	$0.0201907\pi$
$883$	26.3609	+	31.4157i	0.887115	+	1.05722i	−0.110873	+	0.993835i	$0.535365\pi$
$884$	−9.35647	+	25.7067i	−0.314692	+	0.864609i
$885$	3.39064	−	5.04829i	0.113975	−	0.169696i
$886$	22.5500	−	15.7897i	0.757582	−	0.530465i
$887$	18.5278	−	18.5278i	0.622102	−	0.622102i	−0.323966	−	0.946069i	$-0.605016\pi$
$887$	18.5278	−	18.5278i	0.622102	−	0.622102i	0.946069	+	0.323966i	$0.105016\pi$
$888$	3.94304	−	3.74844i	0.132320	−	0.125790i
$889$		−	4.40309i		−	0.147675i
$890$	−12.1430	−	1.89871i	−0.407035	−	0.0636450i
$891$	−8.30102	+	1.46369i	−0.278095	+	0.0490356i
$892$	15.2596	−	7.11568i	0.510930	−	0.238251i
$893$	16.5494	−	13.8866i	0.553805	−	0.464697i
$894$	0.164509	−	0.164509i	0.00550201	−	0.00550201i
$895$	9.74174	+	11.1620i	0.325630	+	0.373106i
$896$	−1.13089	+	0.303020i	−0.0377803	+	0.0101232i
$897$	−22.0256	−	10.2707i	−0.735415	−	0.342930i
$898$	−3.09636	−	0.829667i	−0.103327	−	0.0276863i
$899$	−6.44646	+	11.1656i	−0.215001	+	0.372393i
$900$	1.48794	−	10.8991i	0.0495980	−	0.363304i
$901$	30.0853	+	64.5182i	1.00229	+	2.14941i
$902$	17.2320	+	29.8466i	0.573762	+	0.993785i
$903$	−5.21492	+	6.21490i	−0.173542	+	0.206819i
$904$	3.53667	−	4.21484i	0.117628	−	0.140183i
$905$	−17.9605	−	7.95409i	−0.597026	−	0.264403i
$906$	−15.8807	−	11.1198i	−0.527600	−	0.369429i
$907$	10.5192	−	1.85482i	0.349285	−	0.0615884i	0.00374660	−	0.999993i	$-0.498807\pi$
$907$	10.5192	−	1.85482i	0.349285	−	0.0615884i	0.345538	+	0.938405i	$0.387696\pi$
$908$	−8.77928	−	24.1209i	−0.291351	−	0.800479i
$909$	−16.1120	−	13.5196i	−0.534402	−	0.448416i
$910$	−8.76082	+	10.8625i	−0.290418	+	0.360087i
$911$	−5.75134	+	21.4643i	−0.190550	+	0.711144i	0.802823	+	0.596217i	$0.203330\pi$
$911$	−5.75134	+	21.4643i	−0.190550	+	0.711144i	−0.993374	+	0.114927i	$0.963337\pi$
$912$	−1.34679	−	0.490190i	−0.0445966	−	0.0162318i
$913$	42.6047	−	29.8322i	1.41001	−	0.987300i
$914$	−2.58002	−	1.48958i	−0.0853396	−	0.0492708i
$915$	2.42519	−	9.80930i	0.0801742	−	0.324286i
$916$	5.54635	+	15.2385i	0.183257	+	0.503493i
$917$	10.7941	−	18.6960i	0.356454	−	0.617396i
$918$	23.7778	+	2.08029i	0.784784	+	0.0686597i
$919$	−25.2896	−	25.2896i	−0.834228	−	0.834228i	0.153864	−	0.988092i	$-0.450828\pi$
$919$	−25.2896	−	25.2896i	−0.834228	−	0.834228i	−0.988092	+	0.153864i	$0.950828\pi$
$920$	11.3719	+	0.772655i	0.374919	+	0.0254737i
$921$	−10.3923	−	3.78247i	−0.342436	−	0.124637i
$922$	23.3199	−	33.3043i	0.768001	−	1.09682i
$923$	−1.58341	+	8.97996i	−0.0521186	+	0.295579i
$924$	3.61694			0.118988
$925$	5.68689	+	29.8774i	0.186984	+	0.982363i
$926$	−29.2263			−0.960435
$927$	−2.18723	+	12.4044i	−0.0718381	+	0.407414i
$928$	1.35981	−	1.94202i	0.0446381	−	0.0637498i
$929$	33.8228	+	12.3105i	1.10969	+	0.403895i	0.830880	−	0.556451i	$-0.187837\pi$
$929$	33.8228	+	12.3105i	1.10969	+	0.403895i	0.278811	+	0.960346i	$0.410060\pi$
$930$	10.8513	+	0.737284i	0.355827	+	0.0241765i
$931$	−6.37848	−	6.37848i	−0.209046	−	0.209046i
$932$	−6.20914	−	0.543230i	−0.203387	−	0.0177941i
$933$	11.8706	−	20.5605i	0.388626	−	0.673119i
$934$	12.1638	+	33.4197i	0.398011	+	1.09353i
$935$	−9.51325	+	38.4788i	−0.311117	+	1.25839i
$936$	−10.1563	−	5.86374i	−0.331969	−	0.191662i
$937$	−5.23200	+	3.66349i	−0.170922	+	0.119681i	−0.655907	−	0.754841i	$-0.727714\pi$
$937$	−5.23200	+	3.66349i	−0.170922	+	0.119681i	0.484985	+	0.874522i	$0.338825\pi$
$938$	−6.36230	−	2.31569i	−0.207737	−	0.0756099i
$939$	5.96533	−	22.2629i	0.194671	−	0.726522i
$940$	18.9254	−	23.4654i	0.617279	−	0.765358i
$941$	−22.4797	−	18.8627i	−0.732819	−	0.614908i	0.198080	−	0.980186i	$-0.436529\pi$
$941$	−22.4797	−	18.8627i	−0.732819	−	0.614908i	−0.930898	+	0.365278i	$0.880974\pi$
$942$	−0.228255	−	0.627125i	−0.00743694	−	0.0204328i
$943$	−50.0876	+	8.83180i	−1.63108	+	0.287603i
$944$	2.49080	+	1.74408i	0.0810688	+	0.0567650i
$945$	11.1330	+	4.93042i	0.362155	+	0.160387i
$946$	17.2017	−	20.5002i	0.559277	−	0.666520i
$947$	29.8378	−	35.5593i	0.969599	−	1.15552i	−0.0182070	−	0.999834i	$-0.505796\pi$
$947$	29.8378	−	35.5593i	0.969599	−	1.15552i	0.987806	−	0.155689i	$-0.0497598\pi$
$948$	3.27953	+	5.68031i	0.106514	+	0.184488i
$949$	−16.7278	−	35.8729i	−0.543008	−	1.16449i
$950$	6.37972	−	4.84705i	0.206985	−	0.157259i
$951$	−7.62209	+	13.2019i	−0.247163	+	0.428100i
$952$	5.80371	+	1.55510i	0.188099	+	0.0504011i
$953$	23.9420	+	11.1643i	0.775557	+	0.361648i	0.769759	−	0.638335i	$-0.220376\pi$
$953$	23.9420	+	11.1643i	0.775557	+	0.361648i	0.00579853	+	0.999983i	$0.498154\pi$
$954$	−29.4778	+	7.89854i	−0.954378	+	0.255725i
$955$	−0.779111	−	0.892701i	−0.0252114	−	0.0288871i
$956$	−13.7800	+	13.7800i	−0.445678	+	0.445678i
$957$	−5.61059	+	4.70784i	−0.181364	+	0.152183i
$958$	11.3166	−	5.27703i	0.365624	−	0.170493i
$959$	−13.2497	+	2.33628i	−0.427855	+	0.0754424i
$960$	−1.97594	−	0.308963i	−0.0637731	−	0.00997172i
$961$			1.42498i			0.0459670i
$962$	31.7793	+	6.43628i	1.02461	+	0.207514i
$963$	9.46758	−	9.46758i	0.305089	−	0.305089i
$964$	12.6703	−	8.87184i	0.408083	−	0.285743i
$965$	−7.50703	+	11.1771i	−0.241660	+	0.359805i
$966$	−1.82560	+	5.01581i	−0.0587379	+	0.161381i
$967$	15.6146	+	18.6088i	0.502132	+	0.598417i	0.956260	−	0.292519i	$-0.0944936\pi$
$967$	15.6146	+	18.6088i	0.502132	+	0.598417i	−0.454128	+	0.890936i	$0.650049\pi$
$968$	−0.930685			−0.0299134
$969$	4.72789	+	5.63448i	0.151882	+	0.181006i
$970$	6.33210	+	21.9194i	0.203312	+	0.703788i
$971$	−54.2436	+	19.7430i	−1.74076	+	0.633584i	−0.999300	−	0.0374135i	$-0.988088\pi$
$971$	−54.2436	+	19.7430i	−1.74076	+	0.633584i	−0.741459	+	0.670998i	$0.765866\pi$
$972$	−4.17616	+	15.5856i	−0.133950	+	0.499909i
$973$	25.8012	−	6.91342i	0.827150	−	0.221634i
$974$	−3.18435	−	0.561487i	−0.102033	−	0.0179912i
$975$	−21.1973	+	10.9061i	−0.678856	+	0.349275i
$976$	4.88030	+	1.30767i	0.156215	+	0.0418576i
$977$	8.36681	+	7.02059i	0.267678	+	0.224609i	0.766740	−	0.641958i	$-0.221878\pi$
$977$	8.36681	+	7.02059i	0.267678	+	0.224609i	−0.499062	+	0.866566i	$0.666322\pi$
$978$	6.19007	−	0.541561i	0.197936	−	0.0173172i
$979$	−8.02357	+	17.2066i	−0.256434	+	0.549925i
$980$	−10.4493	−	7.01821i	−0.333792	−	0.224188i
$981$	−9.55076	+	13.6399i	−0.304932	+	0.435488i
$982$	34.8218	−	12.6741i	1.11121	−	0.404446i
$983$	2.53293	+	28.9515i	0.0807878	+	0.923409i	0.923136	+	0.384475i	$0.125617\pi$
$983$	2.53293	+	28.9515i	0.0807878	+	0.923409i	−0.842348	+	0.538934i	$0.818827\pi$
$984$	8.89016	−	0.777788i	0.283408	−	0.0247950i
$985$	−6.75646	+	4.07785i	−0.215279	+	0.129931i
$986$	−11.0268	+	5.14190i	−0.351166	+	0.163752i
$987$	8.09745	+	11.5644i	0.257745	+	0.368097i
$988$	−2.21080	−	8.25081i	−0.0703349	−	0.262493i
$989$	19.7464	+	34.2018i	0.627900	+	1.08755i
$990$	−15.5367	−	6.88070i	−0.493790	−	0.218683i
$991$	3.54139	+	13.2167i	0.112496	+	0.419841i	0.999087	−	0.0427125i	$-0.0135999\pi$
$991$	3.54139	+	13.2167i	0.112496	+	0.419841i	−0.886591	+	0.462554i	$0.846933\pi$
$992$	−0.473978	+	5.41760i	−0.0150488	+	0.172009i
$993$			11.6595i			0.370003i
$994$	1.99512	+	0.174550i	0.0632814	+	0.00553640i
$995$	−8.60818	+	25.1611i	−0.272898	+	0.797662i
$996$	−2.33864	−	13.2631i	−0.0741027	−	0.420258i
$997$	−16.4750	−	2.90498i	−0.521767	−	0.0920017i	−0.0934393	−	0.995625i	$-0.529786\pi$
$997$	−16.4750	−	2.90498i	−0.521767	−	0.0920017i	−0.428328	+	0.903623i	$0.640897\pi$
$998$	−10.3636	−	10.3636i	−0.328055	−	0.328055i
$999$	−1.75209	−	28.2362i	−0.0554338	−	0.893354i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.87.4	✓	108
5.3	odd	4		370.2.bd.a.13.4	yes	108
37.20	odd	36		370.2.bd.a.57.4	yes	108
185.168	even	36	inner	370.2.ba.a.353.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.87.4	✓	108	1.1	even	1	trivial
370.2.ba.a.353.4	yes	108	185.168	even	36	inner
370.2.bd.a.13.4	yes	108	5.3	odd	4
370.2.bd.a.57.4	yes	108	37.20	odd	36

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	370.2.ba.a.87.4

Level	$370$
Weight	$2$
Character	370.87
Analytic conductor	$2.954$
Analytic rank	$0$
Dimension	$108$
Inner twists	$2$