LMFDB - Embedded newform 700.2.bj.a.687.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(127,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1, 0]))

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

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

chi := DirichletCharacter("700.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$700 = 2^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$ , degree $8$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			687.68
Character	$\chi$	$=$	700.687
Dual form			700.2.bj.a.323.68

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.940767 - 1.05592i) q^{2} +(-1.38699 + 2.72212i) q^{3} +(-0.229914 - 1.98674i) q^{4} +(-0.521836 - 2.17432i) q^{5} +(1.56949 + 4.02543i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.31413 - 1.62629i) q^{8} +(-3.72285 - 5.12406i) q^{9} +(-2.78683 - 1.49452i) q^{10} +(-3.29096 + 4.52962i) q^{11} +(5.72704 + 2.12974i) q^{12} +(-0.466368 + 2.94453i) q^{13} +(-0.0814220 - 1.41187i) q^{14} +(6.64256 + 1.59527i) q^{15} +(-3.89428 + 0.913559i) q^{16} +(-0.336967 + 0.171693i) q^{17} +(-8.91291 - 0.889536i) q^{18} +(-1.65135 + 5.08233i) q^{19} +(-4.19984 + 1.53666i) q^{20} +(0.944080 + 2.90558i) q^{21} +(1.68687 + 7.73629i) q^{22} +(-0.403083 - 2.54496i) q^{23} +(7.63663 - 4.04368i) q^{24} +(-4.45537 + 2.26928i) q^{25} +(2.67043 + 3.26256i) q^{26} +(10.0594 - 1.59325i) q^{27} +(-1.56741 - 1.24226i) q^{28} +(-4.85833 + 1.57857i) q^{29} +(7.93357 - 5.51320i) q^{30} +(-3.80180 - 1.23528i) q^{31} +(-2.69897 + 4.97148i) q^{32} +(-7.76564 - 15.2409i) q^{33} +(-0.135714 + 0.517332i) q^{34} +(-1.90647 - 1.16849i) q^{35} +(-9.32425 + 8.57443i) q^{36} +(-9.90352 - 1.56856i) q^{37} +(3.81297 + 6.52497i) q^{38} +(-7.36852 - 5.35354i) q^{39} +(-2.32849 + 5.88032i) q^{40} +(7.26889 - 5.28115i) q^{41} +(3.95621 + 1.73661i) q^{42} +(-6.36022 - 6.36022i) q^{43} +(9.75582 + 5.49686i) q^{44} +(-9.19866 + 10.7686i) q^{45} +(-3.06647 - 1.96860i) q^{46} +(2.63896 + 1.34462i) q^{47} +(2.91451 - 11.8678i) q^{48} -1.00000i q^{49} +(-1.79530 + 6.83936i) q^{50} -1.15540i q^{51} +(5.95724 + 0.249563i) q^{52} +(4.35488 + 2.21892i) q^{53} +(7.78121 - 12.1207i) q^{54} +(11.5662 + 4.79190i) q^{55} +(-2.78630 + 0.486373i) q^{56} +(-11.5443 - 11.5443i) q^{57} +(-2.90373 + 6.61505i) q^{58} +(2.45814 - 1.78594i) q^{59} +(1.64216 - 13.5638i) q^{60} +(11.3787 + 8.26713i) q^{61} +(-4.88096 + 2.85227i) q^{62} +(-6.25571 - 0.990807i) q^{63} +(2.71036 + 7.52688i) q^{64} +(6.64573 - 0.522527i) q^{65} +(-23.3988 - 6.13831i) q^{66} +(-2.52751 - 4.96052i) q^{67} +(0.418584 + 0.629992i) q^{68} +(7.48678 + 2.43260i) q^{69} +(-3.02737 + 0.913801i) q^{70} +(-1.25440 + 0.407579i) q^{71} +(0.281925 + 17.9122i) q^{72} +(-8.73442 + 1.38340i) q^{73} +(-10.9732 + 8.98163i) q^{74} +(0.00230103 - 15.2755i) q^{75} +(10.4769 + 2.11230i) q^{76} +(0.875864 + 5.52999i) q^{77} +(-12.5849 + 2.74409i) q^{78} +(4.91522 + 15.1275i) q^{79} +(4.01855 + 7.99070i) q^{80} +(-3.74360 + 11.5216i) q^{81} +(1.26188 - 12.6437i) q^{82} +(-4.71921 + 2.40456i) q^{83} +(5.55558 - 2.54368i) q^{84} +(0.549158 + 0.643080i) q^{85} +(-12.6993 + 0.732367i) q^{86} +(2.44141 - 15.4144i) q^{87} +(14.9822 - 5.13005i) q^{88} +(-2.60270 + 3.58231i) q^{89} +(2.71694 + 19.8437i) q^{90} +(1.75232 + 2.41187i) q^{91} +(-4.96351 + 1.38594i) q^{92} +(8.63563 - 8.63563i) q^{93} +(3.90244 - 1.52154i) q^{94} +(11.9124 + 0.938426i) q^{95} +(-9.78952 - 14.2423i) q^{96} +(2.29520 - 4.50459i) q^{97} +(-1.05592 - 0.940767i) q^{98} +35.4618 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100})$ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$ .

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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

)

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

$2$	0.940767	−	1.05592i	0.665223	−	0.746645i
$2$	0.940767	−	1.05592i	0.665223	−	0.746645i
$3$	−1.38699	+	2.72212i	−0.800779	+	1.57162i	0.0196069	+	0.999808i	$0.493759\pi$
$3$	−1.38699	+	2.72212i	−0.800779	+	1.57162i	−0.820386	+	0.571810i	$0.806241\pi$
$4$	−0.229914	−	1.98674i	−0.114957	−	0.993370i
$5$	−0.521836	−	2.17432i	−0.233372	−	0.972388i
$5$	−0.521836	−	2.17432i	−0.233372	−	0.972388i
$6$	1.56949	+	4.02543i	0.640744	+	1.64337i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.31413	−	1.62629i	−0.818167	−	0.574981i
$9$	−3.72285	−	5.12406i	−1.24095	−	1.70802i
$10$	−2.78683	−	1.49452i	−0.881273	−	0.472608i
$11$	−3.29096	+	4.52962i	−0.992262	+	1.36573i	−0.0623076	+	0.998057i	$0.519846\pi$
$11$	−3.29096	+	4.52962i	−0.992262	+	1.36573i	−0.929954	+	0.367675i	$0.880154\pi$
$12$	5.72704	+	2.12974i	1.65325	+	0.614802i
$13$	−0.466368	+	2.94453i	−0.129347	+	0.816665i	0.834655	+	0.550772i	$0.185667\pi$
$13$	−0.466368	+	2.94453i	−0.129347	+	0.816665i	−0.964003	+	0.265893i	$0.914333\pi$
$14$	−0.0814220	−	1.41187i	−0.0217609	−	0.377338i
$15$	6.64256	+	1.59527i	1.71510	+	0.411896i
$16$	−3.89428	+	0.913559i	−0.973570	+	0.228390i
$17$	−0.336967	+	0.171693i	−0.0817265	+	0.0416417i	−0.494376	−	0.869248i	$-0.664603\pi$
$17$	−0.336967	+	0.171693i	−0.0817265	+	0.0416417i	0.412650	+	0.910890i	$0.364603\pi$
$18$	−8.91291	−	0.889536i	−2.10079	−	0.209666i
$19$	−1.65135	+	5.08233i	−0.378845	+	1.16597i	0.562003	+	0.827135i	$0.310031\pi$
$19$	−1.65135	+	5.08233i	−0.378845	+	1.16597i	−0.940848	+	0.338830i	$0.889969\pi$
$20$	−4.19984	+	1.53666i	−0.939113	+	0.343608i
$21$	0.944080	+	2.90558i	0.206015	+	0.634050i
$22$	1.68687	+	7.73629i	0.359641	+	1.64938i
$23$	−0.403083	−	2.54496i	−0.0840486	−	0.530662i	−0.993406	−	0.114647i	$-0.963426\pi$
$23$	−0.403083	−	2.54496i	−0.0840486	−	0.530662i	0.909358	−	0.416015i	$-0.136574\pi$
$24$	7.63663	−	4.04368i	1.55882	−	0.825413i
$25$	−4.45537	+	2.26928i	−0.891075	+	0.453856i
$26$	2.67043	+	3.26256i	0.523714	+	0.639841i
$27$	10.0594	−	1.59325i	1.93593	−	0.306621i
$28$	−1.56741	−	1.24226i	−0.296213	−	0.234766i
$29$	−4.85833	+	1.57857i	−0.902170	+	0.293133i	−0.723132	−	0.690709i	$-0.757298\pi$
$29$	−4.85833	+	1.57857i	−0.902170	+	0.293133i	−0.179038	+	0.983842i	$0.557298\pi$
$30$	7.93357	−	5.51320i	1.44846	−	1.00657i
$31$	−3.80180	−	1.23528i	−0.682823	−	0.221863i	−0.0529920	−	0.998595i	$-0.516876\pi$
$31$	−3.80180	−	1.23528i	−0.682823	−	0.221863i	−0.629831	+	0.776732i	$0.716876\pi$
$32$	−2.69897	+	4.97148i	−0.477115	+	0.878841i
$33$	−7.76564	−	15.2409i	−1.35183	−	2.65311i
$34$	−0.135714	+	0.517332i	−0.0232748	+	0.0887217i
$35$	−1.90647	−	1.16849i	−0.322253	−	0.197510i
$36$	−9.32425	+	8.57443i	−1.55404	+	1.42907i
$37$	−9.90352	−	1.56856i	−1.62813	−	0.257870i	−0.725479	−	0.688245i	$-0.758382\pi$
$37$	−9.90352	−	1.56856i	−1.62813	−	0.257870i	−0.902651	+	0.430374i	$0.858382\pi$
$38$	3.81297	+	6.52497i	0.618546	+	1.05849i
$39$	−7.36852	−	5.35354i	−1.17991	−	0.857253i
$40$	−2.32849	+	5.88032i	−0.368167	+	0.929760i
$41$	7.26889	−	5.28115i	1.13521	−	0.824778i	0.148765	−	0.988873i	$-0.452470\pi$
$41$	7.26889	−	5.28115i	1.13521	−	0.824778i	0.986445	+	0.164095i	$0.0524703\pi$
$42$	3.95621	+	1.73661i	0.610456	+	0.267964i
$43$	−6.36022	−	6.36022i	−0.969924	−	0.969924i	0.0296368	−	0.999561i	$-0.490565\pi$
$43$	−6.36022	−	6.36022i	−0.969924	−	0.969924i	−0.999561	+	0.0296368i	$0.990565\pi$
$44$	9.75582	+	5.49686i	1.47075	+	0.828683i
$45$	−9.19866	+	10.7686i	−1.37125	+	1.60529i
$46$	−3.06647	−	1.96860i	−0.452127	−	0.290254i
$47$	2.63896	+	1.34462i	0.384931	+	0.196132i	0.635738	−	0.771905i	$-0.280696\pi$
$47$	2.63896	+	1.34462i	0.384931	+	0.196132i	−0.250807	+	0.968037i	$0.580696\pi$
$48$	2.91451	−	11.8678i	0.420673	−	1.71297i
$49$		−	1.00000i		−	0.142857i
$50$	−1.79530	+	6.83936i	−0.253894	+	0.967232i
$51$		−	1.15540i		−	0.161789i
$52$	5.95724	+	0.249563i	0.826121	+	0.0346081i
$53$	4.35488	+	2.21892i	0.598188	+	0.304792i	0.726742	−	0.686910i	$-0.241034\pi$
$53$	4.35488	+	2.21892i	0.598188	+	0.304792i	−0.128554	+	0.991703i	$0.541034\pi$
$54$	7.78121	−	12.1207i	1.05889	−	1.64942i
$55$	11.5662	+	4.79190i	1.55959	+	0.646140i
$56$	−2.78630	+	0.486373i	−0.372334	+	0.0649943i
$57$	−11.5443	−	11.5443i	−1.52908	−	1.52908i
$58$	−2.90373	+	6.61505i	−0.381278	+	0.868599i
$59$	2.45814	−	1.78594i	0.320022	−	0.232510i	−0.416163	−	0.909290i	$-0.636625\pi$
$59$	2.45814	−	1.78594i	0.320022	−	0.232510i	0.736185	+	0.676780i	$0.236625\pi$
$60$	1.64216	−	13.5638i	0.212002	−	1.75108i
$61$	11.3787	+	8.26713i	1.45690	+	1.05850i	0.984158	+	0.177295i	$0.0567346\pi$
$61$	11.3787	+	8.26713i	1.45690	+	1.05850i	0.472739	+	0.881203i	$0.343265\pi$
$62$	−4.88096	+	2.85227i	−0.619882	+	0.362238i
$63$	−6.25571	−	0.990807i	−0.788145	−	0.124830i
$64$	2.71036	+	7.52688i	0.338794	+	0.940860i
$65$	6.64573	−	0.522527i	0.824301	−	0.0648114i
$66$	−23.3988	−	6.13831i	−2.88019	−	0.755574i
$67$	−2.52751	−	4.96052i	−0.308785	−	0.606024i	0.683508	−	0.729943i	$-0.260454\pi$
$67$	−2.52751	−	4.96052i	−0.308785	−	0.606024i	−0.992292	+	0.123919i	$0.960454\pi$
$68$	0.418584	+	0.629992i	0.0507607	+	0.0763977i
$69$	7.48678	+	2.43260i	0.901302	+	0.292851i
$70$	−3.02737	+	0.913801i	−0.361840	+	0.109220i
$71$	−1.25440	+	0.407579i	−0.148870	+	0.0483708i	−0.382504	−	0.923954i	$-0.624938\pi$
$71$	−1.25440	+	0.407579i	−0.148870	+	0.0483708i	0.233634	+	0.972325i	$0.424938\pi$
$72$	0.281925	+	17.9122i	0.0332252	+	2.11097i
$73$	−8.73442	+	1.38340i	−1.02229	+	0.161914i	−0.645000	−	0.764182i	$-0.723143\pi$
$73$	−8.73442	+	1.38340i	−1.02229	+	0.161914i	−0.377287	+	0.926097i	$0.623143\pi$
$74$	−10.9732	+	8.98163i	−1.27561	+	1.04409i
$75$	0.00230103	−	15.2755i	0.000265700	−	1.76387i
$76$	10.4769	+	2.11230i	1.20179	+	0.242298i
$77$	0.875864	+	5.52999i	0.0998139	+	0.630200i
$78$	−12.5849	+	2.74409i	−1.42496	+	0.310707i
$79$	4.91522	+	15.1275i	0.553006	+	1.70198i	0.701153	+	0.713011i	$0.252669\pi$
$79$	4.91522	+	15.1275i	0.553006	+	1.70198i	−0.148148	+	0.988965i	$0.547331\pi$
$80$	4.01855	+	7.99070i	0.449288	+	0.893387i
$81$	−3.74360	+	11.5216i	−0.415956	+	1.28018i
$82$	1.26188	−	12.6437i	0.139351	−	1.39626i
$83$	−4.71921	+	2.40456i	−0.518001	+	0.263935i	−0.693387	−	0.720565i	$-0.743882\pi$
$83$	−4.71921	+	2.40456i	−0.518001	+	0.263935i	0.175387	+	0.984500i	$0.443882\pi$
$84$	5.55558	−	2.54368i	0.606163	−	0.277538i
$85$	0.549158	+	0.643080i	0.0595646	+	0.0697518i
$86$	−12.6993	+	0.732367i	−1.36940	+	0.0789731i
$87$	2.44141	−	15.4144i	0.261746	−	1.65260i
$88$	14.9822	−	5.13005i	1.59711	−	0.546865i
$89$	−2.60270	+	3.58231i	−0.275886	+	0.379724i	−0.924366	−	0.381508i	$-0.875405\pi$
$89$	−2.60270	+	3.58231i	−0.275886	+	0.379724i	0.648480	+	0.761232i	$0.275405\pi$
$90$	2.71694	+	19.8437i	0.286390	+	2.09171i
$91$	1.75232	+	2.41187i	0.183694	+	0.252832i
$92$	−4.96351	+	1.38594i	−0.517482	+	0.144495i
$93$	8.63563	−	8.63563i	0.895474	−	0.895474i
$94$	3.90244	−	1.52154i	0.402506	−	0.156935i
$95$	11.9124	+	0.938426i	1.22218	+	0.0962804i
$96$	−9.78952	−	14.2423i	−0.999139	−	1.45360i
$97$	2.29520	−	4.50459i	0.233043	−	0.457372i	−0.744638	−	0.667469i	$-0.767378\pi$
$97$	2.29520	−	4.50459i	0.233043	−	0.457372i	0.977681	+	0.210097i	$0.0673778\pi$
$98$	−1.05592	−	0.940767i	−0.106664	−	0.0950318i
$99$	35.4618			3.56405
$100$	5.53283	+	8.32994i	0.553283	+	0.832994i
$101$	−3.28935			−0.327302			−0.163651	−	0.986518i	$-0.552327\pi$
$101$	−3.28935			−0.327302			−0.163651	+	0.986518i	$0.552327\pi$
$102$	−1.22001	−	1.08696i	−0.120799	−	0.107626i
$103$	−1.70666	+	3.34950i	−0.168162	+	0.330036i	−0.959673	−	0.281118i	$-0.909295\pi$
$103$	−1.70666	+	3.34950i	−0.168162	+	0.330036i	0.791511	+	0.611155i	$0.209295\pi$
$104$	5.86789	−	6.05556i	0.575394	−	0.593797i
$105$	5.82502	−	3.56897i	0.568464	−	0.348296i
$106$	6.43992	−	2.51089i	0.625500	−	0.243879i
$107$	12.0604	−	12.0604i	1.16592	−	1.16592i	0.182765	−	0.983157i	$-0.441495\pi$
$107$	12.0604	−	12.0604i	1.16592	−	1.16592i	0.983157	−	0.182765i	$-0.0585046\pi$
$108$	−5.47817	−	19.6191i	−0.527137	−	1.88785i
$109$	−1.90988	−	2.62873i	−0.182934	−	0.251787i	0.707695	−	0.706518i	$-0.249735\pi$
$109$	−1.90988	−	2.62873i	−0.182934	−	0.251787i	−0.890629	+	0.454732i	$0.849735\pi$
$110$	15.9409	−	7.70487i	1.51991	−	0.734631i
$111$	18.0059	−	24.7830i	1.70905	−	2.35230i
$112$	−2.10769	+	3.39966i	−0.199158	+	0.321237i
$113$	1.62558	−	10.2635i	0.152922	−	0.965511i	−0.785209	−	0.619231i	$-0.787445\pi$
$113$	1.62558	−	10.2635i	0.152922	−	0.965511i	0.938131	−	0.346280i	$-0.112555\pi$
$114$	−23.0503	+	1.32930i	−2.15886	+	0.124501i
$115$	−5.32324	+	2.20449i	−0.496394	+	0.205569i
$116$	4.25321	+	9.28932i	0.394900	+	0.862491i
$117$	16.8242	−	8.57234i	1.55539	−	0.792513i
$118$	0.426732	−	4.27574i	0.0392839	−	0.393614i
$119$	−0.116866	+	0.359677i	−0.0107131	+	0.0329716i
$120$	−12.7773	−	14.4944i	−1.16641	−	1.32315i
$121$	−6.28784	−	19.3520i	−0.571622	−	1.75927i
$122$	19.4341	−	4.23753i	1.75948	−	0.383648i
$123$	4.29407	+	27.1117i	0.387183	+	2.44458i
$124$	−1.58009	+	7.83719i	−0.141896	+	0.703801i
$125$	7.25913	+	8.50324i	0.649276	+	0.760553i
$126$	−6.93138	+	5.67338i	−0.617496	+	0.505425i
$127$	−19.1378	+	3.03113i	−1.69820	+	0.268969i	−0.929012	−	0.370049i	$-0.879341\pi$
$127$	−19.1378	+	3.03113i	−1.69820	+	0.268969i	−0.769192	+	0.639018i	$0.779341\pi$
$128$	10.4976	+	4.21914i	0.927862	+	0.372923i
$129$	26.1348	−	8.49173i	2.30104	−	0.747655i
$130$	5.70034	−	7.50890i	0.499953	−	0.658574i
$131$	−9.06603	−	2.94573i	−0.792103	−	0.257370i	−0.115104	−	0.993353i	$-0.536720\pi$
$131$	−9.06603	−	2.94573i	−0.792103	−	0.257370i	−0.676999	+	0.735984i	$0.736720\pi$
$132$	−28.4944	+	18.9324i	−2.48012	+	1.64786i
$133$	2.42607	+	4.76143i	0.210367	+	0.412868i
$134$	−7.61569	−	1.99786i	−0.657895	−	0.172589i
$135$	−8.71360	−	21.0410i	−0.749947	−	1.81092i
$136$	1.05901	+	0.150687i	0.0908091	+	0.0129213i
$137$	7.95248	+	1.25955i	0.679426	+	0.107610i	0.486603	−	0.873623i	$-0.338236\pi$
$137$	7.95248	+	1.25955i	0.679426	+	0.107610i	0.192823	+	0.981234i	$0.438236\pi$
$138$	9.61193	−	5.61689i	0.818222	−	0.478141i
$139$	−5.11855	−	3.71884i	−0.434149	−	0.315428i	0.349156	−	0.937064i	$-0.386468\pi$
$139$	−5.11855	−	3.71884i	−0.434149	−	0.315428i	−0.783306	+	0.621636i	$0.786468\pi$
$140$	−1.88315	+	4.05632i	−0.159156	+	0.342822i
$141$	−7.32042	+	5.31859i	−0.616490	+	0.447906i
$142$	−0.749730	+	1.70798i	−0.0629159	+	0.143330i
$143$	−11.8028	−	11.8028i	−0.986999	−	0.986999i
$144$	19.1789	+	16.5535i	1.59825	+	1.37946i
$145$	5.96757	+	9.73984i	0.495580	+	0.808850i
$146$	−6.75631	+	10.5243i	−0.559156	+	0.870995i
$147$	2.72212	+	1.38699i	0.224517	+	0.114397i
$148$	−0.839371	+	20.0364i	−0.0689958	+	1.64698i
$149$		−	12.5613i		−	1.02906i	−0.857472	−	0.514531i	$-0.827966\pi$
$149$		−	12.5613i		−	1.02906i	0.857472	−	0.514531i	$-0.172034\pi$
$150$	−16.1275	−	14.3732i	−1.31681	−	1.17356i
$151$			10.8828i			0.885626i	0.896614	+	0.442813i	$0.146019\pi$
$151$			10.8828i			0.885626i	−0.896614	+	0.442813i	$0.853981\pi$
$152$	12.0868	−	9.07557i	0.980366	−	0.736126i
$153$	2.13424	+	1.08745i	0.172543	+	0.0879153i
$154$	6.66318	+	4.27759i	0.536934	+	0.344698i
$155$	−0.701983	+	8.91095i	−0.0563846	+	0.715745i
$156$	−8.94197	+	15.8702i	−0.715931	+	1.27063i
$157$	−2.47322	−	2.47322i	−0.197384	−	0.197384i	0.601493	−	0.798878i	$-0.294573\pi$
$157$	−2.47322	−	2.47322i	−0.197384	−	0.197384i	−0.798878	+	0.601493i	$0.794573\pi$
$158$	20.5974	+	9.04139i	1.63864	+	0.719295i
$159$	−12.0803	+	8.77688i	−0.958033	+	0.696052i
$160$	12.2180	+	3.27414i	0.965919	+	0.258843i
$161$	−2.08458	−	1.51454i	−0.164288	−	0.119362i
$162$	8.64400	+	14.7921i	0.679137	+	1.16218i
$163$	5.55254	+	0.879435i	0.434908	+	0.0688827i	0.370050	−	0.929012i	$-0.379341\pi$
$163$	5.55254	+	0.879435i	0.434908	+	0.0688827i	0.0648581	+	0.997894i	$0.479341\pi$
$164$	−12.1635	−	13.2272i	−0.949810	−	1.03287i
$165$	−29.0863	+	24.8383i	−2.26437	+	1.93366i
$166$	−1.90067	+	7.24522i	−0.147521	+	0.562338i
$167$	1.27379	+	2.49994i	0.0985685	+	0.193451i	0.935025	−	0.354582i	$-0.115377\pi$
$167$	1.27379	+	2.49994i	0.0985685	+	0.193451i	−0.836457	+	0.548033i	$0.815377\pi$
$168$	2.54060	−	8.25923i	0.196011	−	0.637213i
$169$	3.91098	+	1.27076i	0.300845	+	0.0977505i
$170$	1.19567	+	0.0251238i	0.0917036	+	0.00192691i
$171$	32.1899	−	10.4591i	2.46162	−	0.799829i
$172$	−11.1738	+	14.0984i	−0.851994	+	1.07499i
$173$	−4.76900	+	0.755335i	−0.362580	+	0.0574271i	−0.335067	−	0.942194i	$-0.608759\pi$
$173$	−4.76900	+	0.755335i	−0.362580	+	0.0574271i	−0.0275134	+	0.999621i	$0.508759\pi$
$174$	−13.9795	−	17.0793i	−1.05979	−	1.29478i
$175$	−1.54580	+	4.75505i	−0.116852	+	0.359448i
$176$	8.67784	−	20.6461i	0.654117	−	1.55626i
$177$	1.45214	+	9.16843i	0.109149	+	0.689141i
$178$	1.33408	+	6.11835i	0.0999935	+	0.458589i
$179$	−0.698547	−	2.14991i	−0.0522119	−	0.160692i	0.921551	−	0.388258i	$-0.126923\pi$
$179$	−0.698547	−	2.14991i	−0.0522119	−	0.160692i	−0.973763	+	0.227566i	$0.926923\pi$
$180$	23.5093	+	15.7995i	1.75228	+	1.17762i
$181$	−2.37134	+	7.29824i	−0.176260	+	0.542474i	−0.999689	−	0.0249464i	$-0.992058\pi$
$181$	−2.37134	+	7.29824i	−0.176260	+	0.542474i	0.823428	+	0.567420i	$0.192058\pi$
$182$	4.19526	+	0.418700i	0.310973	+	0.0310361i
$183$	−38.2863	+	19.5079i	−2.83021	+	1.44206i
$184$	−3.20607	+	6.54490i	−0.236355	+	0.482496i
$185$	1.75745	+	22.3520i	0.129210	+	1.64335i
$186$	−0.994376	−	17.2426i	−0.0729112	−	1.26429i
$187$	0.331240	−	2.09137i	0.0242227	−	0.152936i
$188$	2.06467	−	5.55207i	0.150582	−	0.404926i
$189$	5.98646	−	8.23966i	0.435451	−	0.599347i
$190$	12.1977	−	11.6956i	0.884911	−	0.848488i
$191$	6.30580	+	8.67919i	0.456271	+	0.628004i	0.973730	−	0.227704i	$-0.0731219\pi$
$191$	6.30580	+	8.67919i	0.456271	+	0.628004i	−0.517459	+	0.855708i	$0.673122\pi$
$192$	−24.2483	−	3.06180i	−1.74997	−	0.220966i
$193$	5.82770	−	5.82770i	0.419487	−	0.419487i	−0.465540	−	0.885027i	$-0.654140\pi$
$193$	5.82770	−	5.82770i	0.419487	−	0.419487i	0.885027	+	0.465540i	$0.154140\pi$
$194$	−2.59721	−	6.66131i	−0.186469	−	0.478254i
$195$	−7.79518	+	18.8152i	−0.558224	+	1.34739i
$196$	−1.98674	+	0.229914i	−0.141910	+	0.0164224i
$197$	10.9184	−	21.4286i	0.777906	−	1.52673i	−0.0705790	−	0.997506i	$-0.522485\pi$
$197$	10.9184	−	21.4286i	0.777906	−	1.52673i	0.848485	−	0.529220i	$-0.177515\pi$
$198$	33.3613	−	37.4447i	2.37088	−	2.66108i
$199$	−0.459550			−0.0325766			−0.0162883	−	0.999867i	$-0.505185\pi$
$199$	−0.459550			−0.0325766			−0.0162883	+	0.999867i	$0.505185\pi$
$200$	14.0008	+	1.99433i	0.990007	+	0.141021i
$201$	17.0088			1.19971
$202$	−3.09451	+	3.47327i	−0.217729	+	0.244379i
$203$	−2.31914	+	4.55158i	−0.162772	+	0.319458i
$204$	−2.29549	+	0.265643i	−0.160716	+	0.0185987i
$205$	−15.2761	−	13.0490i	−1.06693	−	0.911383i
$206$	1.93122	+	4.95319i	0.134555	+	0.345105i
$207$	−11.5399	+	11.5399i	−0.802081	+	0.802081i
$208$	−0.873837	−	11.8929i	−0.0605897	−	0.824622i
$209$	−17.5865	−	24.2057i	−1.21648	−	1.67434i
$210$	1.71145	−	9.50830i	0.118102	−	0.656135i
$211$	−12.5564	+	17.2824i	−0.864420	+	1.18977i	0.116077	+	0.993240i	$0.462968\pi$
$211$	−12.5564	+	17.2824i	−0.864420	+	1.18977i	−0.980497	+	0.196532i	$0.937032\pi$
$212$	3.40717	−	9.16217i	0.234006	−	0.629260i
$213$	0.630361	−	3.97994i	0.0431916	−	0.272701i
$214$	−1.38873	−	24.0808i	−0.0949316	−	1.64613i
$215$	−10.5102	+	17.1482i	−0.716789	+	1.16950i
$216$	−25.8698	−	12.6725i	−1.76022	−	0.862255i
$217$	−3.56175	+	1.81480i	−0.241787	+	0.123197i
$218$	−4.57247	−	0.456347i	−0.309687	−	0.0309077i
$219$	8.34879	−	25.6949i	0.564159	−	1.73630i
$220$	6.86103	−	24.0808i	0.462570	−	1.62353i
$221$	−0.348405	−	1.07228i	−0.0234363	−	0.0721294i
$222$	−9.22939	−	42.3278i	−0.619436	−	2.84085i
$223$	0.516020	+	3.25802i	0.0345552	+	0.218173i	0.998923	−	0.0463908i	$-0.0147719\pi$
$223$	0.516020	+	3.25802i	0.0345552	+	0.218173i	−0.964368	+	0.264564i	$0.914772\pi$
$224$	1.60691	+	5.42382i	0.107366	+	0.362394i
$225$	28.2146	+	14.3814i	1.88097	+	0.958762i
$226$	−9.30811	−	11.3721i	−0.619167	−	0.756458i
$227$	−21.8986	+	3.46840i	−1.45346	+	0.230206i	−0.832670	−	0.553770i	$-0.813189\pi$
$227$	−21.8986	+	3.46840i	−1.45346	+	0.230206i	−0.620792	+	0.783975i	$0.713189\pi$
$228$	−20.2813	+	25.5897i	−1.34316	+	1.69472i
$229$	3.95138	−	1.28388i	0.261114	−	0.0848412i	−0.175534	−	0.984473i	$-0.556165\pi$
$229$	3.95138	−	1.28388i	0.261114	−	0.0848412i	0.436649	+	0.899632i	$0.356165\pi$
$230$	−2.68017	+	7.69480i	−0.176725	+	0.507380i
$231$	−16.2681	−	5.28583i	−1.07036	−	0.347782i
$232$	13.8100	+	4.24806i	0.906671	+	0.278899i
$233$	−4.08828	−	8.02369i	−0.267832	−	0.525650i	0.717445	−	0.696615i	$-0.245311\pi$
$233$	−4.08828	−	8.02369i	−0.267832	−	0.525650i	−0.985277	+	0.170965i	$0.945311\pi$
$234$	6.77596	−	25.8295i	0.442958	−	1.68852i
$235$	1.54653	−	6.43962i	0.100884	−	0.420074i
$236$	−4.11336	−	4.47307i	−0.267757	−	0.291172i
$237$	−47.9962	−	7.60186i	−3.11769	−	0.493794i
$238$	0.269845	+	0.461773i	0.0174914	+	0.0299323i
$239$	−3.45082	−	2.50717i	−0.223215	−	0.162175i	0.470558	−	0.882369i	$-0.344053\pi$
$239$	−3.45082	−	2.50717i	−0.223215	−	0.162175i	−0.693773	+	0.720194i	$0.744053\pi$
$240$	−27.3253	−	0.144040i	−1.76384	−	0.00929773i
$241$	−12.1689	+	8.84125i	−0.783870	+	0.569515i	−0.906138	−	0.422982i	$-0.860983\pi$
$241$	−12.1689	+	8.84125i	−0.783870	+	0.569515i	0.122268	+	0.992497i	$0.460983\pi$
$242$	−26.3494	−	11.5663i	−1.69381	−	0.743509i
$243$	−4.56573	−	4.56573i	−0.292892	−	0.292892i
$244$	13.8085	−	24.5073i	0.883999	−	1.56892i
$245$	−2.17432	+	0.521836i	−0.138913	+	0.0333389i
$246$	32.6674	+	20.9716i	2.08280	+	1.33710i
$247$	−14.1949	−	7.23267i	−0.903201	−	0.460204i
$248$	6.78891	+	9.04142i	0.431096	+	0.574131i
$249$		−	16.1814i		−	1.02545i
$250$	15.8078	+	0.334542i	0.999776	+	0.0211583i
$251$			5.22621i			0.329876i	0.986304	+	0.164938i	$0.0527423\pi$
$251$			5.22621i			0.329876i	−0.986304	+	0.164938i	$0.947258\pi$
$252$	−0.530201	+	12.6563i	−0.0333995	+	0.797271i
$253$	12.8543	+	6.54957i	0.808140	+	0.411768i
$254$	−14.8036	+	23.0595i	−0.928860	+	1.44688i
$255$	−2.51222	+	0.602930i	−0.157321	+	0.0377570i
$256$	14.3308	−	7.11531i	0.895676	−	0.444707i
$257$	−1.61866	−	1.61866i	−0.100969	−	0.100969i	0.654818	−	0.755787i	$-0.272745\pi$
$257$	−1.61866	−	1.61866i	−0.100969	−	0.100969i	−0.755787	+	0.654818i	$0.772745\pi$
$258$	15.6203	−	35.5849i	0.972475	−	2.21542i
$259$	−8.11199	+	5.89371i	−0.504055	+	0.366217i
$260$	−2.56607	−	13.0832i	−0.159141	−	0.811386i
$261$	26.1755	+	19.0176i	1.62022	+	1.17716i
$262$	−11.6395	+	6.80172i	−0.719089	+	0.420211i
$263$	−8.31302	−	1.31665i	−0.512603	−	0.0811883i	−0.105226	−	0.994448i	$-0.533557\pi$
$263$	−8.31302	−	1.31665i	−0.512603	−	0.0811883i	−0.407377	+	0.913260i	$0.633557\pi$
$264$	−6.81552	+	47.8986i	−0.419466	+	2.94796i
$265$	2.55212	−	10.6268i	0.156776	−	0.652801i
$266$	7.31003	+	1.91767i	0.448207	+	0.117580i
$267$	−6.14156	−	12.0535i	−0.375857	−	0.737662i
$268$	−9.27416	+	6.16200i	−0.566509	+	0.376404i
$269$	25.2507	+	8.20445i	1.53956	+	0.500234i	0.951255	−	0.308404i	$-0.0997950\pi$
$269$	25.2507	+	8.20445i	1.53956	+	0.500234i	0.588306	+	0.808638i	$0.299795\pi$
$270$	−30.4149	−	10.5938i	−1.85099	−	0.644720i
$271$	26.6318	−	8.65320i	1.61777	−	0.525645i	0.646354	−	0.763038i	$-0.276293\pi$
$271$	26.6318	−	8.65320i	1.61777	−	0.525645i	0.971414	+	0.237393i	$0.0762929\pi$
$272$	1.15539	−	0.976461i	0.0700559	−	0.0592066i
$273$	−8.99585	+	1.42480i	−0.544454	+	0.0862330i
$274$	8.81141	−	7.21220i	0.532316	−	0.435705i
$275$	4.38348	−	27.6493i	0.264334	−	1.66731i
$276$	3.11163	−	15.4336i	0.187298	−	0.928992i
$277$	−0.287731	−	1.81666i	−0.0172881	−	0.109153i	0.977535	−	0.210772i	$-0.0675977\pi$
$277$	−0.287731	−	1.81666i	−0.0172881	−	0.109153i	−0.994823	+	0.101619i	$0.967598\pi$
$278$	−8.74214	+	1.90619i	−0.524319	+	0.114326i
$279$	7.82387	+	24.0794i	0.468403	+	1.44160i
$280$	2.51152	+	5.80450i	0.150092	+	0.346885i
$281$	5.99275	−	18.4438i	0.357498	−	1.10026i	−0.597050	−	0.802204i	$-0.703660\pi$
$281$	5.99275	−	18.4438i	0.357498	−	1.10026i	0.954547	−	0.298060i	$-0.0963395\pi$
$282$	−1.27082	+	12.7333i	−0.0756764	+	0.758257i
$283$	23.3107	−	11.8774i	1.38568	−	0.706038i	0.407382	−	0.913258i	$-0.366442\pi$
$283$	23.3107	−	11.8774i	1.38568	−	0.706038i	0.978294	+	0.207220i	$0.0664416\pi$
$284$	1.09816	+	2.39846i	0.0651638	+	0.142322i
$285$	−19.0768	+	31.1253i	−1.13001	+	1.84370i
$286$	−23.5664	+	1.35907i	−1.39351	+	0.0803634i
$287$	1.40554	−	8.87422i	0.0829663	−	0.523829i
$288$	35.5220	−	4.67837i	2.09315	−	0.275676i
$289$	−9.90828	+	13.6376i	−0.582840	+	0.802211i
$290$	15.8985	+	2.86167i	0.933595	+	0.168043i
$291$	9.07862	+	12.4957i	0.532198	+	0.732508i
$292$	4.75662	+	17.0350i	0.278360	+	0.996897i
$293$	−13.8932	+	13.8932i	−0.811647	+	0.811647i	−0.984881	−	0.173234i	$-0.944578\pi$
$293$	−13.8932	+	13.8932i	−0.811647	+	0.811647i	0.173234	+	0.984881i	$0.444578\pi$
$294$	4.02543	−	1.56949i	0.234768	−	0.0915348i
$295$	−5.16596	−	4.41282i	−0.300774	−	0.256924i
$296$	20.3671	+	19.7359i	1.18381	+	1.14712i
$297$	−25.8882	+	50.8085i	−1.50219	+	2.94821i
$298$	−13.2637	−	11.8173i	−0.768344	−	0.684556i
$299$	7.68171			0.444245
$300$	−30.3491	+	3.50749i	−1.75220	+	0.202505i
$301$	−8.99470			−0.518446
$302$	11.4913	+	10.2381i	0.661248	+	0.589139i
$303$	4.56229	−	8.95400i	0.262097	−	0.514394i
$304$	1.78780	−	21.3006i	0.102537	−	1.22167i
$305$	12.0376	−	29.0551i	0.689271	−	1.66369i
$306$	3.15608	−	1.23054i	0.180421	−	0.0703454i
$307$	−19.8963	+	19.8963i	−1.13554	+	1.13554i	−0.146303	+	0.989240i	$0.546737\pi$
$307$	−19.8963	+	19.8963i	−1.13554	+	1.13554i	−0.989240	+	0.146303i	$0.953263\pi$
$308$	10.7853	−	3.01154i	0.614548	−	0.171598i
$309$	−6.75063	−	9.29145i	−0.384030	−	0.528572i
$310$	8.74881	+	9.12437i	0.496899	+	0.518229i
$311$	−5.35015	+	7.36384i	−0.303379	+	0.417565i	−0.933302	−	0.359092i	$-0.883086\pi$
$311$	−5.35015	+	7.36384i	−0.303379	+	0.417565i	0.629923	+	0.776657i	$0.283086\pi$
$312$	8.34526	+	24.3721i	0.472457	+	1.37980i
$313$	−2.24480	+	14.1731i	−0.126884	+	0.801111i	0.839378	+	0.543548i	$0.182920\pi$
$313$	−2.24480	+	14.1731i	−0.126884	+	0.801111i	−0.966261	+	0.257563i	$0.917080\pi$
$314$	−4.93823	+	0.284786i	−0.278680	+	0.0160714i
$315$	1.11012	+	14.1190i	0.0625481	+	0.795515i
$316$	28.9243	−	13.2433i	1.62712	−	0.744993i
$317$	−3.53672	+	1.80205i	−0.198642	+	0.101213i	−0.550482	−	0.834847i	$-0.685556\pi$
$317$	−3.53672	+	1.80205i	−0.198642	+	0.101213i	0.351840	+	0.936060i	$0.385556\pi$
$318$	−2.09715	+	21.0128i	−0.117602	+	1.17834i
$319$	8.83827	−	27.2014i	0.494848	−	1.52299i
$320$	14.9515	−	9.82099i	0.835816	−	0.549010i
$321$	16.1022	+	49.5575i	0.898737	+	2.76603i
$322$	−3.56033	+	0.776316i	−0.198410	+	0.0432624i
$323$	−0.316151	−	1.99610i	−0.0175911	−	0.111066i
$324$	23.7512	+	4.78858i	1.31951	+	0.266032i
$325$	−4.60412	−	14.1773i	−0.255391	−	0.786415i
$326$	6.15225	−	5.03566i	0.340742	−	0.278900i
$327$	9.80471	−	1.55291i	0.542202	−	0.0858763i
$328$	−25.4098	+	0.399933i	−1.40302	+	0.0220826i
$329$	2.81681	−	0.915238i	0.155296	−	0.0504587i
$330$	−1.13634	+	54.0798i	−0.0625536	+	2.97699i
$331$	−21.1371	−	6.86786i	−1.16180	−	0.377491i	−0.336223	−	0.941782i	$-0.609150\pi$
$331$	−21.1371	−	6.86786i	−1.16180	−	0.377491i	−0.825576	+	0.564291i	$0.809150\pi$
$332$	5.86225	+	8.82301i	0.321733	+	0.484225i
$333$	28.8319	+	56.5858i	1.57998	+	3.10088i
$334$	3.83806	+	1.00686i	0.210010	+	0.0550927i
$335$	−9.46683	+	8.08421i	−0.517228	+	0.441687i
$336$	−6.33093	−	10.4527i	−0.345381	−	0.570240i
$337$	−28.5306	−	4.51880i	−1.55416	−	0.246155i	−0.680520	−	0.732729i	$-0.738246\pi$
$337$	−28.5306	−	4.51880i	−1.55416	−	0.246155i	−0.873639	+	0.486575i	$0.838246\pi$
$338$	5.02114	−	2.93418i	0.273114	−	0.159599i
$339$	25.6839	+	18.6604i	1.39496	+	1.01350i
$340$	1.15137	−	1.23889i	0.0624420	−	0.0671882i
$341$	18.1069	−	13.1554i	0.980544	−	0.712407i
$342$	19.2392	−	43.8294i	1.04034	−	2.37002i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	4.37478	+	25.0619i	0.235872	+	1.35125i
$345$	1.38240	−	17.5481i	0.0744257	−	0.944758i
$346$	−3.68895	+	5.74625i	−0.198319	+	0.308920i
$347$	26.7115	+	13.6102i	1.43395	+	0.730632i	0.986513	−	0.163685i	$-0.0523380\pi$
$347$	26.7115	+	13.6102i	1.43395	+	0.730632i	0.447434	+	0.894317i	$0.352338\pi$
$348$	−31.1858	−	1.30645i	−1.67173	−	0.0700329i
$349$			22.7165i			1.21599i	0.793941	+	0.607994i	$0.208026\pi$
$349$			22.7165i			1.21599i	−0.793941	+	0.607994i	$0.791974\pi$
$350$	3.56669	+	6.10563i	0.190648	+	0.326360i
$351$			30.3632i			1.62067i
$352$	−13.6367	−	28.5862i	−0.726838	−	1.52365i
$353$	9.79833	+	4.99250i	0.521513	+	0.265724i	0.694870	−	0.719135i	$-0.255462\pi$
$353$	9.79833	+	4.99250i	0.521513	+	0.265724i	−0.173358	+	0.984859i	$0.555462\pi$
$354$	11.0472	+	7.09203i	0.587152	+	0.376937i
$355$	1.54080	+	2.51478i	0.0817773	+	0.133471i
$356$	7.71551	+	4.34727i	0.408921	+	0.230405i
$357$	−0.816993	−	0.816993i	−0.0432398	−	0.0432398i
$358$	−2.92729	−	1.28496i	−0.154712	−	0.0679120i
$359$	−19.7173	+	14.3255i	−1.04064	+	0.756069i	−0.970410	−	0.241461i	$-0.922373\pi$
$359$	−19.7173	+	14.3255i	−1.04064	+	0.756069i	−0.0702298	+	0.997531i	$0.522373\pi$
$360$	38.7997	−	9.96020i	2.04493	−	0.524949i
$361$	−7.73176	−	5.61745i	−0.406935	−	0.295655i
$362$	5.47544	+	9.36988i	0.287783	+	0.492470i
$363$	61.3996	+	9.72474i	3.22264	+	0.510417i
$364$	4.38887	−	4.03594i	0.230039	−	0.211541i
$365$	7.56589	+	18.2696i	0.396017	+	0.956273i
$366$	−15.4199	+	58.7794i	−0.806010	+	3.07245i
$367$	−13.4170	−	26.3324i	−0.700364	−	1.37454i	−0.917237	−	0.398342i	$-0.869586\pi$
$367$	−13.4170	−	26.3324i	−0.700364	−	1.37454i	0.216873	−	0.976200i	$-0.430414\pi$
$368$	3.89469	+	9.54256i	0.203025	+	0.497440i
$369$	−54.1219	−	17.5853i	−2.81747	−	0.915453i
$370$	25.2552	+	19.1723i	1.31295	+	0.996721i
$371$	4.64838	−	1.51035i	0.241332	−	0.0784134i
$372$	−19.1422	−	15.1713i	−0.992478	−	0.786596i
$373$	−0.892883	+	0.141419i	−0.0462317	+	0.00732239i	−0.179507	−	0.983757i	$-0.557450\pi$
$373$	−0.892883	+	0.141419i	−0.0462317	+	0.00732239i	0.133276	+	0.991079i	$0.457450\pi$
$374$	−1.89669	−	2.31725i	−0.0980754	−	0.119822i
$375$	−33.2152	+	7.96632i	−1.71522	+	0.411379i
$376$	−3.92014	−	7.40332i	−0.202166	−	0.381797i
$377$	−2.38237	−	15.0417i	−0.122698	−	0.774687i
$378$	−3.06851	−	14.0728i	−0.157827	−	0.723827i
$379$	−5.99747	−	18.4583i	−0.308069	−	0.948139i	−0.978514	−	0.206180i	$-0.933897\pi$
$379$	−5.99747	−	18.4583i	−0.308069	−	0.948139i	0.670445	−	0.741959i	$-0.266103\pi$
$380$	−0.874410	−	23.8825i	−0.0448563	−	1.22515i
$381$	18.2928	−	56.2995i	0.937170	−	2.88431i
$382$	15.0968	+	1.50671i	0.772418	+	0.0770898i
$383$	−13.2339	+	6.74300i	−0.676220	+	0.344551i	−0.758144	−	0.652087i	$-0.773894\pi$
$383$	−13.2339	+	6.74300i	−0.676220	+	0.344551i	0.0819239	+	0.996639i	$0.473894\pi$
$384$	−26.0450	+	22.7237i	−1.32910	+	1.15962i
$385$	11.5669	−	4.79016i	0.589505	−	0.244129i
$386$	−0.671048	−	11.6361i	−0.0341555	−	0.592260i
$387$	−8.91202	+	56.2683i	−0.453023	+	2.86028i
$388$	−9.47716	−	3.52431i	−0.481130	−	0.178920i
$389$	−15.0466	+	20.7099i	−0.762894	+	1.05003i	0.234074	+	0.972219i	$0.424794\pi$
$389$	−15.0466	+	20.7099i	−0.762894	+	1.05003i	−0.996968	+	0.0778150i	$0.975206\pi$
$390$	12.5338	+	25.9318i	0.634675	+	1.31311i
$391$	0.572779	+	0.788363i	0.0289667	+	0.0398692i
$392$	−1.62629	+	2.31413i	−0.0821401	+	0.116881i
$393$	20.5931	−	20.5931i	1.03879	−	1.03879i
$394$	−12.3551	−	31.6883i	−0.622441	−	1.59643i
$395$	30.3271	−	18.5814i	1.52592	−	0.934929i
$396$	−8.15317	−	70.4534i	−0.409712	−	3.54042i
$397$	−6.66232	+	13.0755i	−0.334372	+	0.656243i	−0.995576	−	0.0939641i	$-0.970046\pi$
$397$	−6.66232	+	13.0755i	−0.334372	+	0.656243i	0.661203	+	0.750207i	$0.270046\pi$
$398$	−0.432330	+	0.485246i	−0.0216707	+	0.0243232i
$399$	−16.3261			−0.817328
$400$	15.2773	−	12.9075i	0.763867	−	0.645373i
$401$	−29.8137			−1.48883			−0.744413	−	0.667719i	$-0.767271\pi$
$401$	−29.8137			−1.48883			−0.744413	+	0.667719i	$0.767271\pi$
$402$	16.0013	−	17.9598i	0.798072	−	0.895754i
$403$	5.41035	−	10.6184i	0.269509	−	0.528940i
$404$	0.756267	+	6.53508i	0.0376257	+	0.325132i
$405$	27.0053	+	2.12741i	1.34190	+	0.105712i
$406$	2.62430	+	6.73079i	0.130242	+	0.334044i
$407$	39.6971	−	39.6971i	1.96771	−	1.96771i
$408$	−1.87902	+	2.67375i	−0.0930254	+	0.132370i
$409$	10.6126	+	14.6070i	0.524761	+	0.722272i	0.986321	−	0.164837i	$-0.0527099\pi$
$409$	10.6126	+	14.6070i	0.524761	+	0.722272i	−0.461560	+	0.887109i	$0.652710\pi$
$410$	−28.1499	+	3.85419i	−1.39023	+	0.190345i
$411$	−14.4587	+	19.9006i	−0.713193	+	0.981626i
$412$	7.04698	+	2.62059i	0.347180	+	0.129107i
$413$	0.475314	−	3.00102i	0.0233887	−	0.147670i
$414$	1.32880	+	23.0416i	0.0653070	+	1.13243i
$415$	7.69094	+	9.00631i	0.377534	+	0.442102i
$416$	−13.3799	−	10.2657i	−0.656006	−	0.503319i
$417$	17.2225	−	8.77531i	0.843390	−	0.429729i
$418$	−42.1040	−	4.20211i	−2.05937	−	0.205532i
$419$	−1.11371	+	3.42766i	−0.0544085	+	0.167452i	−0.974568	−	0.224091i	$-0.928059\pi$
$419$	−1.11371	+	3.42766i	−0.0544085	+	0.167452i	0.920160	+	0.391543i	$0.128059\pi$
$420$	−8.42988	−	10.7523i	−0.411336	−	0.524656i
$421$	7.43037	+	22.8683i	0.362134	+	1.11453i	0.951756	+	0.306855i	$0.0992766\pi$
$421$	7.43037	+	22.8683i	0.362134	+	1.11453i	−0.589622	+	0.807679i	$0.700723\pi$
$422$	6.43612	+	29.5173i	0.313305	+	1.43688i
$423$	−2.93454	−	18.5280i	−0.142682	−	0.900861i
$424$	−6.46912	−	12.2172i	−0.314168	−	0.593317i
$425$	1.11169	−	1.52963i	0.0539251	−	0.0741980i
$426$	−3.60946	−	4.40980i	−0.174879	−	0.213656i
$427$	13.8917	−	2.20023i	0.672267	−	0.106477i
$428$	−26.7337	−	21.1880i	−1.29222	−	1.02416i
$429$	48.4990	−	15.7583i	2.34155	−	0.760817i
$430$	8.21937	+	27.2303i	0.396373	+	1.31316i
$431$	−7.83962	−	2.54725i	−0.377621	−	0.122697i	0.114056	−	0.993474i	$-0.463616\pi$
$431$	−7.83962	−	2.54725i	−0.377621	−	0.122697i	−0.491677	+	0.870778i	$0.663616\pi$
$432$	−37.7185	+	15.3944i	−1.81473	+	0.740664i
$433$	9.84759	+	19.3270i	0.473245	+	0.928796i	0.997035	+	0.0769484i	$0.0245177\pi$
$433$	9.84759	+	19.3270i	0.473245	+	0.928796i	−0.523790	+	0.851847i	$0.675482\pi$
$434$	−1.43450	+	5.46821i	−0.0688582	+	0.262483i
$435$	−34.7900	+	2.73540i	−1.66805	+	0.131152i
$436$	−4.78349	+	4.39883i	−0.229088	+	0.210666i
$437$	13.6000	+	2.15402i	0.650575	+	0.103041i
$438$	−19.2774	−	32.9886i	−0.921110	−	1.57625i
$439$	−24.4982	−	17.7990i	−1.16924	−	0.849501i	−0.178320	−	0.983973i	$-0.557066\pi$
$439$	−24.4982	−	17.7990i	−1.16924	−	0.849501i	−0.990917	+	0.134472i	$0.957066\pi$
$440$	−18.9726	−	29.8991i	−0.904485	−	1.42538i
$441$	−5.12406	+	3.72285i	−0.244003	+	0.177279i
$442$	−1.46001	−	0.640881i	−0.0694454	−	0.0304836i
$443$	10.1059	+	10.1059i	0.480144	+	0.480144i	0.905178	−	0.425033i	$-0.139738\pi$
$443$	10.1059	+	10.1059i	0.480144	+	0.480144i	−0.425033	+	0.905178i	$0.639738\pi$
$444$	−53.3772	−	30.0751i	−2.53317	−	1.42730i
$445$	9.14728	+	3.78974i	0.433623	+	0.179651i
$446$	3.92565	+	2.52017i	0.185885	+	0.119333i
$447$	34.1934	+	17.4224i	1.61729	+	0.824051i
$448$	7.23882	+	3.40580i	0.342002	+	0.160909i
$449$			25.8281i			1.21890i	0.792824	+	0.609451i	$0.208610\pi$
$449$			25.8281i			1.21890i	−0.792824	+	0.609451i	$0.791390\pi$
$450$	41.7290	−	16.2627i	1.96712	−	0.766630i
$451$			50.3054i			2.36879i
$452$	−20.7647	−	0.869882i	−0.976689	−	0.0409158i
$453$	−29.6242	−	15.0943i	−1.39187	−	0.709191i
$454$	−16.9392	+	26.3860i	−0.794994	+	1.23836i
$455$	4.32976	−	5.06872i	0.202982	−	0.237625i
$456$	7.94057	+	45.4894i	0.371851	+	2.13023i
$457$	−10.1735	−	10.1735i	−0.475897	−	0.475897i	0.427920	−	0.903817i	$-0.359247\pi$
$457$	−10.1735	−	10.1735i	−0.475897	−	0.475897i	−0.903817	+	0.427920i	$0.859247\pi$
$458$	2.36166	−	5.38015i	0.110353	−	0.251398i
$459$	−3.11613	+	2.26400i	−0.145449	+	0.105675i
$460$	5.60363	+	10.0690i	0.261271	+	0.469472i
$461$	7.94901	+	5.77529i	0.370222	+	0.268982i	0.757303	−	0.653064i	$-0.226517\pi$
$461$	7.94901	+	5.77529i	0.370222	+	0.268982i	−0.387081	+	0.922046i	$0.626517\pi$
$462$	−20.8859	+	12.2050i	−0.971700	+	0.567828i
$463$	18.1709	+	2.87799i	0.844474	+	0.133752i	0.563656	−	0.826009i	$-0.309394\pi$
$463$	18.1709	+	2.87799i	0.844474	+	0.133752i	0.280818	+	0.959761i	$0.409394\pi$
$464$	17.4776	−	10.5858i	0.811377	−	0.491432i
$465$	−23.2831	−	14.2703i	−1.07973	−	0.661769i
$466$	−12.3185	−	3.23155i	−0.570641	−	0.149699i
$467$	−3.68668	−	7.23553i	−0.170599	−	0.334820i	0.789838	−	0.613315i	$-0.210164\pi$
$467$	−3.68668	−	7.23553i	−0.170599	−	0.334820i	−0.960438	+	0.278495i	$0.910164\pi$
$468$	−20.8991	−	31.4544i	−0.966063	−	1.45398i
$469$	−5.29484	−	1.72040i	−0.244493	−	0.0794405i
$470$	−5.34477	−	7.69118i	−0.246536	−	0.354768i
$471$	10.1627	−	3.30207i	0.468274	−	0.152151i
$472$	−8.59290	+	0.135246i	−0.395520	+	0.00622521i
$473$	49.7406	−	7.87814i	2.28707	−	0.362237i
$474$	−53.1802	+	43.5284i	−2.44265	+	1.99932i
$475$	−4.17585	−	26.3910i	−0.191601	−	1.21090i
$476$	0.741455	+	0.149488i	0.0339845	+	0.00685177i
$477$	−4.84266	−	30.5754i	−0.221730	−	1.39995i
$478$	−5.89377	+	1.28511i	−0.269575	+	0.0587797i
$479$	−5.99252	−	18.4431i	−0.273805	−	0.842685i	−0.989533	−	0.144306i	$-0.953905\pi$
$479$	−5.99252	−	18.4431i	−0.273805	−	0.842685i	0.715728	−	0.698379i	$-0.246095\pi$
$480$	−25.8589	+	28.7177i	−1.18029	+	1.31078i
$481$	9.23736	−	28.4297i	0.421188	−	1.29628i
$482$	−2.11253	+	21.1669i	−0.0962229	+	0.964127i
$483$	7.01406	−	3.57384i	0.319151	−	0.162615i
$484$	−37.0017	+	16.9416i	−1.68190	+	0.770073i
$485$	−10.9922	−	2.63986i	−0.499128	−	0.119870i
$486$	−9.11631	+	0.525735i	−0.413524	+	0.0238478i
$487$	1.92674	−	12.1649i	0.0873089	−	0.551246i	−0.904797	−	0.425843i	$-0.859978\pi$
$487$	1.92674	−	12.1649i	0.0873089	−	0.551246i	0.992106	−	0.125403i	$-0.0400225\pi$
$488$	−12.8870	−	37.6363i	−0.583369	−	1.70371i
$489$	−10.0952	+	13.8949i	−0.456523	+	0.628350i
$490$	−1.49452	+	2.78683i	−0.0675155	+	0.125896i
$491$	0.181400	+	0.249675i	0.00818645	+	0.0112677i	0.813091	−	0.582137i	$-0.197783\pi$
$491$	0.181400	+	0.249675i	0.00818645	+	0.0112677i	−0.804904	+	0.593405i	$0.797783\pi$
$492$	52.8767	−	14.7646i	2.38386	−	0.665638i
$493$	1.36607	−	1.36607i	0.0615247	−	0.0615247i
$494$	−20.9912	+	8.18437i	−0.944439	+	0.368232i
$495$	−18.5052	−	77.1055i	−0.831749	−	3.46563i
$496$	15.9338	+	1.33735i	0.715447	+	0.0600489i
$497$	−0.598793	+	1.17520i	−0.0268595	+	0.0527148i
$498$	−17.0861	−	15.2229i	−0.765649	−	0.682154i
$499$	−9.37954			−0.419886			−0.209943	−	0.977714i	$-0.567328\pi$
$499$	−9.37954			−0.419886			−0.209943	+	0.977714i	$0.567328\pi$
$500$	15.2248	−	16.3770i	0.680872	−	0.732403i
$501$	−8.57188			−0.382963
$502$	5.51844	+	4.91665i	0.246300	+	0.219441i
$503$	−1.06972	+	2.09944i	−0.0476963	+	0.0936093i	−0.913625	−	0.406559i	$-0.866729\pi$
$503$	−1.06972	+	2.09944i	−0.0476963	+	0.0936093i	0.865928	+	0.500168i	$0.166729\pi$
$504$	12.8652	+	12.4665i	0.573060	+	0.555300i
$505$	1.71650	+	7.15211i	0.0763832	+	0.318265i
$506$	19.0086	−	7.41138i	0.845037	−	0.329476i
$507$	−8.88365	+	8.88365i	−0.394537	+	0.394537i
$508$	10.4221	+	37.3249i	0.462406	+	1.65603i
$509$	14.1673	+	19.4996i	0.627953	+	0.864303i	0.997902	−	0.0647493i	$-0.0206248\pi$
$509$	14.1673	+	19.4996i	0.627953	+	0.864303i	−0.369949	+	0.929052i	$0.620625\pi$
$510$	−1.72677	+	3.21991i	−0.0764627	+	0.142580i
$511$	−5.19796	+	7.15438i	−0.229944	+	0.316491i
$512$	5.96880	−	21.8260i	0.263786	−	0.964581i
$513$	−8.51413	+	53.7561i	−0.375908	+	2.37339i
$514$	−3.23195	+	0.186385i	−0.142555	+	0.00822110i
$515$	8.17350	+	1.96293i	0.360167	+	0.0864972i
$516$	−22.8796	−	49.9708i	−1.00722	−	2.19984i
$517$	−14.7753	+	7.52839i	−0.649817	+	0.331098i
$518$	−1.40824	+	14.1102i	−0.0618745	+	0.619966i
$519$	4.55844	−	14.0294i	0.200093	−	0.615824i
$520$	−16.2288	−	9.59870i	−0.711681	−	0.420931i
$521$	4.56843	+	14.0602i	0.200147	+	0.615988i	0.999878	+	0.0156297i	$0.00497529\pi$
$521$	4.56843	+	14.0602i	0.200147	+	0.615988i	−0.799731	+	0.600358i	$0.795025\pi$
$522$	44.7061	−	9.74797i	1.95673	−	0.426657i
$523$	−1.47896	−	9.33781i	−0.0646706	−	0.408314i	−0.998693	−	0.0511009i	$-0.983727\pi$
$523$	−1.47896	−	9.33781i	−0.0646706	−	0.408314i	0.934023	−	0.357213i	$-0.116273\pi$
$524$	−3.76800	+	18.6891i	−0.164606	+	0.816438i
$525$	−10.7998	−	10.8031i	−0.471342	−	0.471485i
$526$	−9.21090	+	7.53918i	−0.401614	+	0.328724i
$527$	1.49317	−	0.236495i	0.0650435	−	0.0103019i
$528$	44.1651	+	52.2581i	1.92204	+	2.27424i
$529$	15.5599	−	5.05573i	0.676519	−	0.219814i
$530$	−8.82007	−	12.6922i	−0.383120	−	0.551314i
$531$	−18.3025	−	5.94686i	−0.794263	−	0.258072i
$532$	8.90193	−	5.91469i	0.385948	−	0.256434i
$533$	12.1605	+	23.8664i	0.526731	+	1.03377i
$534$	−18.5052	−	4.85456i	−0.800800	−	0.210077i
$535$	−32.5167	−	19.9296i	−1.40582	−	0.861634i
$536$	−2.21827	+	15.5897i	−0.0958147	+	0.673374i
$537$	6.82119	+	1.08037i	0.294356	+	0.0466214i
$538$	32.4182	−	18.9441i	1.39765	−	0.816739i
$539$	4.52962	+	3.29096i	0.195105	+	0.141752i
$540$	−39.7996	+	22.1493i	−1.71270	+	0.953153i
$541$	1.23475	−	0.897100i	0.0530861	−	0.0385693i	−0.560926	−	0.827866i	$-0.689555\pi$
$541$	1.23475	−	0.897100i	0.0530861	−	0.0385693i	0.614012	+	0.789297i	$0.289555\pi$
$542$	15.9173	−	36.2616i	0.683706	−	1.55757i
$543$	−16.5777	−	16.5777i	−0.711416	−	0.711416i
$544$	0.0558945	−	2.13862i	0.00239646	−	0.0916925i
$545$	−4.71906	+	5.52447i	−0.202143	+	0.236642i
$546$	−6.95853	+	10.8393i	−0.297798	+	0.463878i
$547$	−31.7224	−	16.1634i	−1.35635	−	0.691095i	−0.383720	−	0.923450i	$-0.625357\pi$
$547$	−31.7224	−	16.1634i	−1.35635	−	0.691095i	−0.972631	+	0.232354i	$0.925357\pi$
$548$	0.674010	−	16.0891i	0.0287923	−	0.687292i
$549$		−	89.0826i		−	3.80195i
$550$	−25.0714	−	30.6401i	−1.06905	−	1.30650i
$551$		−	27.2984i		−	1.16295i
$552$	−13.3692	−	17.8050i	−0.569032	−	0.757832i
$553$	14.1723	+	7.22117i	0.602669	+	0.307075i
$554$	−2.18893	−	1.40524i	−0.0929987	−	0.0597028i
$555$	−63.2824	−	26.2180i	−2.68619	−	1.11289i
$556$	−6.21155	+	11.0242i	−0.263428	+	0.467532i
$557$	5.08957	+	5.08957i	0.215652	+	0.215652i	0.806663	−	0.591011i	$-0.201271\pi$
$557$	5.08957	+	5.08957i	0.215652	+	0.215652i	−0.591011	+	0.806663i	$0.701271\pi$
$558$	32.7862	+	14.3918i	1.38795	+	0.609252i
$559$	21.6940	−	15.7616i	0.917560	−	0.666646i
$560$	8.49182	+	2.80873i	0.358845	+	0.118691i
$561$	5.23353	+	3.80238i	0.220960	+	0.160537i
$562$	−13.8373	−	23.6791i	−0.583691	−	0.998845i
$563$	−1.22815	−	0.194520i	−0.0517603	−	0.00819803i	0.130501	−	0.991448i	$-0.458342\pi$
$563$	−1.22815	−	0.194520i	−0.0517603	−	0.00819803i	−0.182261	+	0.983250i	$0.558342\pi$
$564$	12.2497	+	13.3209i	0.515807	+	0.560913i
$565$	−23.1645	+	1.82133i	−0.974538	+	0.0766240i
$566$	9.38842	−	35.7880i	0.394625	−	1.50428i
$567$	5.49989	+	10.7941i	0.230974	+	0.453311i
$568$	3.56568	+	1.09683i	0.149613	+	0.0460220i
$569$	16.2846	+	5.29120i	0.682687	+	0.221818i	0.629771	−	0.776781i	$-0.283149\pi$
$569$	16.2846	+	5.29120i	0.682687	+	0.221818i	0.0529156	+	0.998599i	$0.483149\pi$
$570$	14.9188	+	49.4252i	0.624881	+	2.07019i
$571$	−17.0898	+	5.55283i	−0.715187	+	0.232378i	−0.643935	−	0.765080i	$-0.722699\pi$
$571$	−17.0898	+	5.55283i	−0.715187	+	0.232378i	−0.0712521	+	0.997458i	$0.522699\pi$
$572$	−20.7355	+	26.1627i	−0.866994	+	1.09392i
$573$	−32.3719	+	5.12720i	−1.35235	+	0.214192i
$574$	−8.04814	−	9.83270i	−0.335923	−	0.410409i
$575$	7.57113	+	10.4241i	0.315738	+	0.434713i
$576$	28.4780	−	41.9095i	1.18658	−	1.74623i
$577$	5.22513	+	32.9902i	0.217525	+	1.37340i	0.818673	+	0.574260i	$0.194710\pi$
$577$	5.22513	+	32.9902i	0.217525	+	1.37340i	−0.601148	+	0.799138i	$0.705290\pi$
$578$	5.07874	+	23.2921i	0.211248	+	0.968823i
$579$	7.78074	+	23.9467i	0.323357	+	0.995190i
$580$	17.9785	−	14.0953i	0.746517	−	0.585278i
$581$	−1.63671	+	5.03726i	−0.0679020	+	0.208981i
$582$	21.7352	+	2.16924i	0.900954	+	0.0899180i
$583$	−24.3826	+	12.4235i	−1.00982	+	0.514531i
$584$	22.4624	+	11.0034i	0.929499	+	0.455322i
$585$	−27.4185	−	32.1078i	−1.13362	−	1.32750i
$586$	1.59977	+	27.7402i	0.0660859	+	1.14594i
$587$	4.10199	−	25.8989i	0.169307	−	1.06896i	−0.745923	−	0.666032i	$-0.767991\pi$
$587$	4.10199	−	25.8989i	0.169307	−	1.06896i	0.915230	−	0.402931i	$-0.132009\pi$
$588$	2.12974	−	5.72704i	0.0878288	−	0.236179i
$589$	12.5562	−	17.2821i	0.517368	−	0.712096i
$590$	−9.51953	+	1.30338i	−0.391913	+	0.0536593i
$591$	43.1876	+	59.4426i	1.77650	+	2.44514i
$592$	40.0001	−	2.93903i	1.64399	−	0.120793i
$593$	15.9612	−	15.9612i	0.655449	−	0.655449i	−0.298851	−	0.954300i	$-0.596603\pi$
$593$	15.9612	−	15.9612i	0.655449	−	0.655449i	0.954300	+	0.298851i	$0.0966034\pi$
$594$	29.2947	+	75.1348i	1.20198	+	3.08282i
$595$	0.843040	+	0.0664126i	0.0345613	+	0.00272265i
$596$	−24.9561	+	2.88802i	−1.02224	+	0.118298i
$597$	0.637392	−	1.25095i	0.0260867	−	0.0511980i
$598$	7.22670	−	8.11123i	0.295522	−	0.331693i
$599$	37.8626			1.54702			0.773512	−	0.633781i	$-0.218498\pi$
$599$	37.8626			1.54702			0.773512	+	0.633781i	$0.218498\pi$
$600$	−24.8478	+	35.3458i	−1.01441	+	1.44299i
$601$	−38.4991			−1.57041			−0.785206	−	0.619235i	$-0.787443\pi$
$601$	−38.4991			−1.57041			−0.785206	+	0.619235i	$0.787443\pi$
$602$	−8.46192	+	9.49765i	−0.344882	+	0.387095i
$603$	−16.0085	+	31.4184i	−0.651915	+	1.27946i
$604$	21.6212	−	2.50210i	0.879755	−	0.101809i
$605$	−38.7963	+	23.7704i	−1.57729	+	0.966403i
$606$	−5.16261	−	13.2410i	−0.209717	−	0.537880i
$607$	−11.0930	+	11.0930i	−0.450251	+	0.450251i	−0.895438	−	0.445187i	$-0.853137\pi$
$607$	−11.0930	+	11.0930i	−0.450251	+	0.450251i	0.445187	+	0.895438i	$0.353137\pi$
$608$	−20.8097	−	21.9267i	−0.843946	−	0.889244i
$609$	−9.17332	−	12.6260i	−0.371722	−	0.511631i
$610$	−19.3552	−	40.0448i	−0.783668	−	1.62137i
$611$	−5.18998	+	7.14340i	−0.209964	+	0.288991i
$612$	1.66979	−	4.49021i	0.0674974	−	0.181506i
$613$	−3.66796	+	23.1586i	−0.148148	+	0.935367i	0.795869	+	0.605469i	$0.207014\pi$
$613$	−3.66796	+	23.1586i	−0.148148	+	0.935367i	−0.944017	+	0.329898i	$0.892986\pi$
$614$	2.29102	+	39.7266i	0.0924581	+	1.60324i
$615$	56.7088	−	23.4846i	2.28672	−	0.946989i
$616$	6.96651	−	14.2215i	0.280689	−	0.573000i
$617$	10.3842	−	5.29103i	0.418054	−	0.213009i	−0.232294	−	0.972646i	$-0.574623\pi$
$617$	10.3842	−	5.29103i	0.418054	−	0.213009i	0.650348	+	0.759637i	$0.274623\pi$
$618$	−16.1618	−	1.61299i	−0.650121	−	0.0648842i
$619$	−7.80479	+	24.0207i	−0.313701	+	0.965472i	0.662585	+	0.748987i	$0.269459\pi$
$619$	−7.80479	+	24.0207i	−0.313701	+	0.965472i	−0.976286	+	0.216485i	$0.930541\pi$
$620$	17.8652	−	0.654096i	0.717482	−	0.0262691i
$621$	−8.10953	−	24.9586i	−0.325424	−	1.00155i
$622$	2.74235	+	12.5770i	0.109958	+	0.504290i
$623$	0.692688	+	4.37346i	0.0277520	+	0.175219i
$624$	33.5858	+	14.1166i	1.34451	+	0.565116i
$625$	14.7007	−	20.2210i	0.588029	−	0.808840i
$626$	12.8538	+	15.7039i	0.513740	+	0.627655i
$627$	90.2832	−	14.2994i	3.60556	−	0.571065i
$628$	−4.34501	+	5.48227i	−0.173385	+	0.218766i
$629$	3.60647	−	1.17181i	0.143800	−	0.0467233i
$630$	15.9528	+	12.1105i	0.635575	+	0.482493i
$631$	−12.6378	−	4.10627i	−0.503103	−	0.163468i	0.0464601	−	0.998920i	$-0.485206\pi$
$631$	−12.6378	−	4.10627i	−0.503103	−	0.163468i	−0.549564	+	0.835452i	$0.685206\pi$
$632$	13.2273	−	43.0005i	0.526152	−	1.71047i
$633$	−29.6293	−	58.1507i	−1.17766	−	2.31128i
$634$	−1.42442	+	5.42979i	−0.0565709	+	0.215644i
$635$	16.5774	+	40.0300i	0.657856	+	1.58854i
$636$	20.2148	+	21.9826i	0.801570	+	0.871666i
$637$	2.94453	+	0.466368i	0.116666	+	0.0184782i
$638$	−20.4076	−	34.9227i	−0.807946	−	1.38260i
$639$	6.75841	+	4.91027i	0.267358	+	0.194247i
$640$	3.69577	−	25.0268i	0.146088	−	0.989272i
$641$	−27.6451	+	20.0854i	−1.09192	+	0.793324i	−0.979722	−	0.200362i	$-0.935788\pi$
$641$	−27.6451	+	20.0854i	−1.09192	+	0.793324i	−0.112195	+	0.993686i	$0.535788\pi$
$642$	67.4769	+	29.6195i	2.66310	+	1.16899i
$643$	−11.6757	−	11.6757i	−0.460444	−	0.460444i	0.438357	−	0.898801i	$-0.355561\pi$
$643$	−11.6757	−	11.6757i	−0.460444	−	0.460444i	−0.898801	+	0.438357i	$0.855561\pi$
$644$	−2.52972	+	4.48974i	−0.0996850	+	0.176921i
$645$	−32.1019	−	52.3943i	−1.26401	−	2.06303i
$646$	−2.40514	−	1.54404i	−0.0946289	−	0.0607494i
$647$	9.64560	+	4.91468i	0.379208	+	0.193216i	0.633196	−	0.773991i	$-0.281743\pi$
$647$	9.64560	+	4.91468i	0.379208	+	0.193216i	−0.253989	+	0.967207i	$0.581743\pi$
$648$	27.4007	−	20.5743i	1.07640	−	0.808235i
$649$			17.0119i			0.667775i
$650$	−19.3014	−	8.47597i	−0.757064	−	0.332455i
$651$		−	12.2126i		−	0.478651i
$652$	0.470604	−	11.2336i	0.0184303	−	0.439943i
$653$	10.7160	+	5.46008i	0.419350	+	0.213669i	0.650916	−	0.759150i	$-0.274385\pi$
$653$	10.7160	+	5.46008i	0.419350	+	0.213669i	−0.231566	+	0.972819i	$0.574385\pi$
$654$	7.58421	−	11.8139i	0.296566	−	0.461959i
$655$	−1.67400	+	21.2497i	−0.0654085	+	0.830294i
$656$	−23.4824	+	27.2068i	−0.916834	+	1.06225i
$657$	39.6056	+	39.6056i	1.54516	+	1.54516i
$658$	1.68355	−	3.83534i	0.0656316	−	0.149517i
$659$	27.8904	−	20.2636i	1.08646	−	0.789356i	0.107658	−	0.994188i	$-0.465665\pi$
$659$	27.8904	−	20.2636i	1.08646	−	0.789356i	0.978797	+	0.204832i	$0.0656648\pi$
$660$	56.0346	+	52.0764i	2.18114	+	2.02707i
$661$	−18.6280	−	13.5340i	−0.724544	−	0.526412i	0.163289	−	0.986578i	$-0.447790\pi$
$661$	−18.6280	−	13.5340i	−0.724544	−	0.526412i	−0.887833	+	0.460166i	$0.847790\pi$
$662$	−27.1369	+	15.8579i	−1.05471	+	0.616335i
$663$	3.40212	+	0.538842i	0.132127	+	0.0209269i
$664$	14.8314	+	2.11036i	0.575568	+	0.0818979i
$665$	9.08688	−	7.75974i	0.352374	−	0.300910i
$666$	86.8739	+	22.7900i	3.36630	+	0.883095i
$667$	5.97571	+	11.7280i	0.231380	+	0.454110i
$668$	4.67388	−	3.10545i	0.180838	−	0.120154i
$669$	−9.58445	−	3.11418i	−0.370556	−	0.120401i
$670$	−0.369849	+	17.6015i	−0.0142885	+	0.680006i
$671$	−74.8939	+	24.3345i	−2.89125	+	0.939423i
$672$	−16.9931	−	3.14860i	−0.655522	−	0.121460i
$673$	−24.8676	+	3.93864i	−0.958576	+	0.151823i	−0.616069	−	0.787692i	$-0.711276\pi$
$673$	−24.8676	+	3.93864i	−0.958576	+	0.151823i	−0.342506	+	0.939516i	$0.611276\pi$
$674$	−31.6121	+	25.8747i	−1.21765	+	0.996657i
$675$	−41.2028	+	29.9261i	−1.58590	+	1.15186i
$676$	1.62547	−	8.06228i	0.0625182	−	0.310088i
$677$	−7.80404	−	49.2728i	−0.299934	−	1.89371i	−0.431030	−	0.902337i	$-0.641850\pi$
$677$	−7.80404	−	49.2728i	−0.299934	−	1.89371i	0.131097	−	0.991370i	$-0.458150\pi$
$678$	43.8664	−	9.56488i	1.68468	−	0.367337i
$679$	−1.56227	−	4.80818i	−0.0599545	−	0.184521i
$680$	−0.224987	−	2.38126i	−0.00862784	−	0.0913171i
$681$	20.9318	−	64.4213i	0.802107	−	2.46863i
$682$	3.14336	−	31.4956i	0.120365	−	1.20603i
$683$	−7.91703	+	4.03393i	−0.302937	+	0.154354i	−0.598851	−	0.800861i	$-0.704376\pi$
$683$	−7.91703	+	4.03393i	−0.302937	+	0.154354i	0.295914	+	0.955215i	$0.404376\pi$
$684$	−28.1805	−	61.5482i	−1.07751	−	2.35336i
$685$	−1.41122	−	17.9485i	−0.0539200	−	0.685779i
$686$	−1.41187	+	0.0814220i	−0.0539054	+	0.00310871i
$687$	−1.98564	+	12.5369i	−0.0757570	+	0.478311i
$688$	30.5789	+	18.9580i	1.16581	+	0.722768i
$689$	−8.56465	+	11.7882i	−0.326287	+	0.449096i
$690$	−17.2288	−	17.9684i	−0.655889	−	0.684044i
$691$	−14.2571	−	19.6233i	−0.542367	−	0.746505i	0.446584	−	0.894741i	$-0.352640\pi$
$691$	−14.2571	−	19.6233i	−0.542367	−	0.746505i	−0.988952	+	0.148237i	$0.952640\pi$
$692$	2.59711	+	9.30110i	0.0987275	+	0.353575i
$693$	25.0753	−	25.0753i	0.952531	−	0.952531i
$694$	39.5005	−	15.4010i	1.49942	−	0.584615i
$695$	−5.41493	+	13.0700i	−0.205400	+	0.495774i
$696$	−30.7181	+	31.7005i	−1.16437	+	1.20160i
$697$	−1.54264	+	3.02759i	−0.0584315	+	0.114678i
$698$	23.9867	+	21.3710i	0.907912	+	0.808903i
$699$	27.5119			1.04059
$700$	9.80245	+	1.97785i	0.370498	+	0.0747558i
$701$	5.83965			0.220560			0.110280	−	0.993901i	$-0.464825\pi$
$701$	5.83965			0.220560			0.110280	+	0.993901i	$0.464825\pi$
$702$	32.0610	+	28.5647i	1.21006	+	1.07811i
$703$	24.3261	−	47.7427i	0.917477	−	1.80065i
$704$	−43.0136	−	12.4938i	−1.62114	−	0.470878i
$705$	15.3844	+	13.1415i	0.579410	+	0.494939i
$706$	14.4896	−	5.64943i	0.545324	−	0.212619i
$707$	−2.32592	+	2.32592i	−0.0874752	+	0.0874752i
$708$	17.8814	−	4.99297i	0.672025	−	0.187647i
$709$	10.3211	+	14.2058i	0.387617	+	0.533509i	0.957582	−	0.288160i	$-0.0930435\pi$
$709$	10.3211	+	14.2058i	0.387617	+	0.533509i	−0.569966	+	0.821669i	$0.693043\pi$
$710$	4.10493	+	0.738871i	0.154055	+	0.0277293i
$711$	59.2156	−	81.5033i	2.22076	−	3.05661i
$712$	11.8488	−	4.05716i	0.444054	−	0.152049i
$713$	−1.61130	+	10.1734i	−0.0603437	+	0.380995i
$714$	−1.63128	+	0.0940751i	−0.0610489	+	0.00352067i
$715$	−19.5040	+	31.8222i	−0.729408	+	1.19008i
$716$	−4.11070	+	1.88213i	−0.153624	+	0.0703384i
$717$	11.6111	−	5.91613i	0.433623	−	0.220942i
$718$	−3.42292	+	34.2967i	−0.127742	+	1.27994i
$719$	−10.0291	+	30.8663i	−0.374021	+	1.15112i	0.570116	+	0.821564i	$0.306898\pi$
$719$	−10.0291	+	30.8663i	−0.374021	+	1.15112i	−0.944137	+	0.329553i	$0.893102\pi$
$720$	25.9844	−	50.3395i	0.968381	−	1.87604i
$721$	1.16167	+	3.57524i	0.0432627	+	0.133149i
$722$	−13.2053	+	2.87937i	−0.491452	+	0.107159i
$723$	−7.18876	−	45.3880i	−0.267353	−	1.68800i
$724$	15.0449	+	3.03327i	0.559140	+	0.112731i
$725$	18.0635	−	18.0580i	0.670861	−	0.670659i
$726$	68.0313	−	55.6841i	2.52488	−	2.06663i
$727$	31.8050	−	5.03742i	1.17958	−	0.186827i	0.464309	−	0.885673i	$-0.346303\pi$
$727$	31.8050	−	5.03742i	1.17958	−	0.186827i	0.715273	+	0.698846i	$0.246303\pi$
$728$	−0.132701	−	8.43115i	−0.00491821	−	0.312479i
$729$	−15.8038	+	5.13496i	−0.585325	+	0.190184i
$730$	26.4089	+	9.19847i	0.977436	+	0.340451i
$731$	3.23519	+	1.05118i	0.119658	+	0.0388792i
$732$	47.5596	+	71.5799i	1.75785	+	2.64567i
$733$	9.36102	+	18.3720i	0.345757	+	0.678587i	0.996755	−	0.0804928i	$-0.0256494\pi$
$733$	9.36102	+	18.3720i	0.345757	+	0.678587i	−0.650998	+	0.759079i	$0.725649\pi$
$734$	−40.4271	−	10.6054i	−1.49219	−	0.391453i
$735$	1.59527	−	6.64256i	0.0588423	−	0.245014i
$736$	13.7401	+	4.86486i	0.506468	+	0.179321i
$737$	30.7872	+	4.87621i	1.13406	+	0.179618i
$738$	−69.4847	+	40.6045i	−2.55777	+	1.49467i
$739$	20.0121	+	14.5396i	0.736156	+	0.534849i	0.891505	−	0.453011i	$-0.149650\pi$
$739$	20.0121	+	14.5396i	0.736156	+	0.534849i	−0.155349	+	0.987860i	$0.549650\pi$
$740$	44.0036	−	8.63063i	1.61760	−	0.317268i
$741$	39.3764	−	28.6086i	1.44653	−	1.05096i
$742$	2.77824	−	6.32918i	0.101992	−	0.232351i
$743$	14.9753	+	14.9753i	0.549391	+	0.549391i	0.926265	−	0.376873i	$-0.123001\pi$
$743$	14.9753	+	14.9753i	0.549391	+	0.549391i	−0.376873	+	0.926265i	$0.623001\pi$
$744$	−34.0280	+	5.93989i	−1.24753	+	0.217767i
$745$	−27.3123	+	6.55494i	−1.00065	+	0.240154i
$746$	−0.690669	+	1.07585i	−0.0252872	+	0.0393897i
$747$	29.8900	+	15.2297i	1.09362	+	0.557226i
$748$	−4.23116	−	0.177253i	−0.154707	−	0.00648103i
$749$		−	17.0560i		−	0.623211i
$750$	−22.8360	+	42.5669i	−0.833853	+	1.55432i
$751$			3.84504i			0.140308i	0.997536	+	0.0701538i	$0.0223490\pi$
$751$			3.84504i			0.140308i	−0.997536	+	0.0701538i	$0.977651\pi$
$752$	−11.5052	−	2.82546i	−0.419552	−	0.103034i
$753$	−14.2264	−	7.24870i	−0.518438	−	0.264157i
$754$	−18.1240	−	11.6352i	−0.660038	−	0.423727i
$755$	23.6626	−	5.67901i	0.861172	−	0.206680i
$756$	−17.7464	−	9.99914i	−0.645432	−	0.363665i
$757$	−16.8459	−	16.8459i	−0.612276	−	0.612276i	0.331263	−	0.943539i	$-0.392525\pi$
$757$	−16.8459	−	16.8459i	−0.612276	−	0.612276i	−0.943539	+	0.331263i	$0.892525\pi$
$758$	−25.1326	−	11.0322i	−0.912858	−	0.400706i
$759$	−35.6574	+	25.9066i	−1.29428	+	0.940352i
$760$	−26.0405	−	21.5446i	−0.944590	−	0.781505i
$761$	6.11744	+	4.44458i	0.221757	+	0.161116i	0.693117	−	0.720825i	$-0.256237\pi$
$761$	6.11744	+	4.44458i	0.221757	+	0.161116i	−0.471360	+	0.881941i	$0.656237\pi$
$762$	−42.2382	−	72.2804i	−1.53013	−	2.61844i
$763$	−3.20928	−	0.508301i	−0.116184	−	0.0184017i
$764$	15.7935	−	14.5235i	0.571389	−	0.525440i
$765$	1.25075	−	5.20801i	0.0452209	−	0.188296i
$766$	−5.32997	+	20.3175i	−0.192580	+	0.734100i
$767$	4.11236	+	8.07096i	0.148489	+	0.291425i
$768$	−0.507963	+	48.8791i	−0.0183295	+	1.76377i
$769$	−0.160415	−	0.0521219i	−0.00578471	−	0.00187957i	0.306123	−	0.951992i	$-0.400968\pi$
$769$	−0.160415	−	0.0521219i	−0.00578471	−	0.00187957i	−0.311908	+	0.950112i	$0.600968\pi$
$770$	5.82379	−	16.7201i	0.209875	−	0.602551i
$771$	6.65125	−	2.16112i	0.239539	−	0.0778309i
$772$	−12.9180	−	10.2383i	−0.464929	−	0.368483i
$773$	−13.8945	+	2.20067i	−0.499750	+	0.0791525i	−0.401220	−	0.915982i	$-0.631414\pi$
$773$	−13.8945	+	2.20067i	−0.499750	+	0.0791525i	−0.0985293	+	0.995134i	$0.531414\pi$
$774$	51.0304	+	62.3457i	1.83425	+	2.24097i
$775$	19.7416	−	3.12372i	0.709140	−	0.112207i
$776$	−12.6372	+	6.69152i	−0.453648	+	0.240212i
$777$	−4.79213	−	30.2563i	−0.171917	−	1.08544i
$778$	7.71253	+	35.3712i	0.276508	+	1.26812i
$779$	14.8371	+	45.6639i	0.531594	+	1.63608i
$780$	39.1732	+	11.1611i	1.40263	+	0.399632i
$781$	2.28200	−	7.02329i	0.0816565	−	0.251313i
$782$	1.37130	+	0.136860i	0.0490374	+	0.00489409i
$783$	−46.3568	+	23.6200i	−1.65666	+	0.844109i
$784$	0.913559	+	3.89428i	0.0326271	+	0.139081i
$785$	−4.08696	+	6.66819i	−0.145870	+	0.237998i
$786$	−2.37126	−	41.1180i	−0.0845801	−	1.46663i
$787$	5.74297	−	36.2597i	0.204715	−	1.29252i	−0.644555	−	0.764558i	$-0.722957\pi$
$787$	5.74297	−	36.2597i	0.204715	−	1.29252i	0.849269	−	0.527960i	$-0.177043\pi$
$788$	−45.0834	−	16.7653i	−1.60603	−	0.597241i
$789$	15.1142	−	20.8029i	0.538079	−	0.740602i
$790$	8.91044	−	49.5036i	0.317019	−	1.76126i
$791$	−6.10795	−	8.40687i	−0.217174	−	0.298914i
$792$	−82.0631	−	57.6712i	−2.91598	−	2.04926i
$793$	−29.6495	+	29.6495i	−1.05288	+	1.05288i
$794$	7.53897	+	19.3359i	0.267548	+	0.686205i
$795$	25.3877	+	21.6865i	0.900410	+	0.769140i
$796$	0.105657	+	0.913007i	0.00374491	+	0.0323607i
$797$	−5.98796	+	11.7520i	−0.212104	+	0.416278i	−0.972407	−	0.233291i	$-0.925051\pi$
$797$	−5.98796	+	11.7520i	−0.212104	+	0.416278i	0.760303	+	0.649569i	$0.225051\pi$
$798$	−15.3591	+	17.2390i	−0.543705	+	0.610254i
$799$	−1.12010			−0.0396264
$800$	0.743239	−	28.2745i	0.0262775	−	0.999655i
$801$	28.0454			0.990936
$802$	−28.0478	+	31.4808i	−0.990402	+	1.11162i
$803$	22.4784	−	44.1163i	0.793245	−	1.55683i
$804$	−3.91056	−	33.7920i	−0.137915	−	1.19175i
$805$	−2.20529	+	5.32290i	−0.0777262	+	0.187608i
$806$	−6.12226	−	15.7023i	−0.215647	−	0.553091i
$807$	−57.3560	+	57.3560i	−2.01903	+	2.01903i
$808$	7.61196	+	5.34943i	0.267788	+	0.188192i
$809$	−20.0269	−	27.5646i	−0.704107	−	0.969121i	−0.999904	−	0.0138696i	$-0.995585\pi$
$809$	−20.0269	−	27.5646i	−0.704107	−	0.969121i	0.295796	−	0.955251i	$-0.404415\pi$
$810$	27.6521	−	26.5139i	0.971594	−	0.931603i
$811$	−21.3365	+	29.3672i	−0.749226	+	1.03122i	0.248809	+	0.968553i	$0.419961\pi$
$811$	−21.3365	+	29.3672i	−0.749226	+	1.03122i	−0.998034	+	0.0626679i	$0.980039\pi$
$812$	9.57601	+	3.56107i	0.336052	+	0.124969i
$813$	−13.3830	+	84.4970i	−0.469362	+	2.96344i
$814$	−4.57104	−	79.2625i	−0.160215	−	2.77815i
$815$	−0.985335	−	12.5319i	−0.0345148	−	0.438975i
$816$	1.05553	+	4.49946i	0.0369509	+	0.157513i
$817$	42.8276	−	21.8218i	1.49835	−	0.763447i
$818$	25.4078	+	2.53578i	0.888364	+	0.0886615i
$819$	5.83492	−	17.9580i	0.203889	−	0.627505i
$820$	−22.4128	+	33.3498i	−0.782690	+	1.16463i
$821$	−11.3722	−	35.0001i	−0.396893	−	1.22151i	−0.927477	−	0.373880i	$-0.878027\pi$
$821$	−11.3722	−	35.0001i	−0.396893	−	1.22151i	0.530584	−	0.847632i	$-0.321973\pi$
$822$	7.41115	+	33.9890i	0.258494	+	1.18550i
$823$	3.87781	+	24.4835i	0.135172	+	0.853442i	0.958337	+	0.285640i	$0.0922061\pi$
$823$	3.87781	+	24.4835i	0.135172	+	0.853442i	−0.823165	+	0.567802i	$0.807794\pi$
$824$	9.39668	−	4.97565i	0.327349	−	0.173335i
$825$	69.1848	+	50.2816i	2.40871	+	1.75058i
$826$	−2.72166	−	3.32515i	−0.0946986	−	0.115697i
$827$	−10.6371	+	1.68475i	−0.369889	+	0.0585846i	−0.338612	−	0.940926i	$-0.609957\pi$
$827$	−10.6371	+	1.68475i	−0.369889	+	0.0585846i	−0.0312769	+	0.999511i	$0.509957\pi$
$828$	25.5801	+	20.2737i	0.888969	+	0.704559i
$829$	14.5747	−	4.73561i	0.506201	−	0.164475i	−0.0447730	−	0.998997i	$-0.514256\pi$
$829$	14.5747	−	4.73561i	0.506201	−	0.164475i	0.550974	+	0.834523i	$0.314256\pi$
$830$	16.7453	+	0.351858i	0.581237	+	0.0122132i
$831$	5.34426	+	1.73645i	0.185390	+	0.0602369i
$832$	−23.4271	+	4.47043i	−0.812190	+	0.154984i
$833$	0.171693	+	0.336967i	0.00594882	+	0.0116752i
$834$	6.93639	−	26.4410i	0.240188	−	0.915578i
$835$	4.77098	−	4.07418i	0.165107	−	0.140993i
$836$	−44.0471	+	40.5050i	−1.52340	+	1.40090i
$837$	−40.2119	−	6.36893i	−1.38993	−	0.220143i
$838$	2.57157	+	4.40062i	0.0888335	+	0.152017i
$839$	0.527551	+	0.383288i	0.0182131	+	0.0132326i	0.596855	−	0.802349i	$-0.296417\pi$
$839$	0.527551	+	0.383288i	0.0182131	+	0.0132326i	−0.578641	+	0.815582i	$0.696417\pi$
$840$	−19.2840	−	1.21412i	−0.665362	−	0.0418913i
$841$	−2.34996	+	1.70735i	−0.0810332	+	0.0588740i
$842$	31.1373	+	13.6679i	1.07306	+	0.471028i
$843$	41.8944	+	41.8944i	1.44292	+	1.44292i
$844$	37.2226	+	20.9729i	1.28126	+	0.721917i
$845$	0.722144	−	9.16688i	0.0248425	−	0.315350i
$846$	−22.3247	−	14.3319i	−0.767539	−	0.492740i
$847$	−18.1301	−	9.23774i	−0.622957	−	0.317413i
$848$	−18.9862	−	4.66266i	−0.651989	−	0.160116i
$849$			79.9284i			2.74313i
$850$	−0.569315	−	2.61288i	−0.0195274	−	0.0896211i
$851$			25.8364i			0.885660i
$852$	−8.05204	−	0.337319i	−0.275858	−	0.0115564i
$853$	−14.7227	−	7.50160i	−0.504096	−	0.256850i	0.183399	−	0.983039i	$-0.441290\pi$
$853$	−14.7227	−	7.50160i	−0.504096	−	0.256850i	−0.687495	+	0.726189i	$0.741290\pi$
$854$	10.7456	−	16.7384i	0.367707	−	0.572776i
$855$	−39.5394	−	64.5333i	−1.35222	−	2.20699i
$856$	−47.5229	+	8.29555i	−1.62430	+	0.283536i
$857$	13.6502	+	13.6502i	0.466281	+	0.466281i	0.900707	−	0.434426i	$-0.143049\pi$
$857$	13.6502	+	13.6502i	0.466281	+	0.466281i	−0.434426	+	0.900707i	$0.643049\pi$
$858$	28.9869	−	66.0357i	0.989595	−	2.25442i
$859$	24.0915	−	17.5035i	0.821993	−	0.597213i	−0.0952898	−	0.995450i	$-0.530378\pi$
$859$	24.0915	−	17.5035i	0.821993	−	0.597213i	0.917283	+	0.398237i	$0.130378\pi$
$860$	36.4854	+	16.9384i	1.24414	+	0.577595i
$861$	22.2072	+	16.1345i	0.756821	+	0.549862i
$862$	−10.0649	+	5.88161i	−0.342813	+	0.200328i
$863$	30.4259	+	4.81899i	1.03571	+	0.164040i	0.651064	−	0.759023i	$-0.274323\pi$
$863$	30.4259	+	4.81899i	1.03571	+	0.164040i	0.384647	+	0.923064i	$0.374323\pi$
$864$	−19.2292	+	54.3101i	−0.654190	+	1.84767i
$865$	4.13098	+	9.97519i	0.140457	+	0.339167i
$866$	29.6720	+	7.78397i	1.00829	+	0.264510i
$867$	−23.3805	−	45.8867i	−0.794042	−	1.55840i
$868$	4.42444	+	6.65903i	0.150175	+	0.226022i
$869$	−84.6976	−	27.5199i	−2.87317	−	0.933549i
$870$	−29.8409	+	39.3087i	−1.01170	+	1.33269i
$871$	15.7851	−	5.12890i	0.534859	−	0.173786i
$872$	0.144632	+	9.18924i	0.00489787	+	0.311187i
$873$	−31.6265	+	5.00915i	−1.07040	+	0.169534i
$874$	15.0689	−	12.3340i	0.509712	−	0.417203i
$875$	11.1457	+	0.879718i	0.376793	+	0.0297399i
$876$	−52.9687	−	10.6793i	−1.78965	−	0.360818i
$877$	0.434792	+	2.74517i	0.0146819	+	0.0926978i	0.993941	−	0.109913i	$-0.0350573\pi$
$877$	0.434792	+	2.74517i	0.0146819	+	0.0926978i	−0.979259	+	0.202611i	$0.935057\pi$
$878$	−41.8414	+	9.12334i	−1.41208	+	0.307898i
$879$	−18.5492	−	57.0886i	−0.625649	−	1.92555i
$880$	−49.4197	−	8.09458i	−1.66594	−	0.272868i
$881$	−8.47893	+	26.0955i	−0.285662	+	0.879179i	0.700537	+	0.713616i	$0.252944\pi$
$881$	−8.47893	+	26.0955i	−0.285662	+	0.879179i	−0.986199	+	0.165562i	$0.947056\pi$
$882$	−0.889536	+	8.91291i	−0.0299523	+	0.300113i
$883$	−3.24114	+	1.65144i	−0.109073	+	0.0555754i	−0.507676	−	0.861548i	$-0.669495\pi$
$883$	−3.24114	+	1.65144i	−0.109073	+	0.0555754i	0.398603	+	0.917124i	$0.369495\pi$
$884$	−2.05024	+	0.938724i	−0.0689571	+	0.0315727i
$885$	19.1774	−	7.94183i	0.644640	−	0.266962i
$886$	20.1782	−	1.16367i	0.677900	−	0.0390943i
$887$	−7.77216	+	49.0715i	−0.260963	+	1.64766i	0.414343	+	0.910121i	$0.364012\pi$
$887$	−7.77216	+	49.0715i	−0.260963	+	1.64766i	−0.675306	+	0.737538i	$0.735988\pi$
$888$	−81.9723	+	28.0682i	−2.75081	+	0.941906i
$889$	−11.3891	+	15.6758i	−0.381979	+	0.525749i
$890$	12.6071	−	6.09350i	0.422591	−	0.204254i
$891$	−39.8685	−	54.8743i	−1.33565	−	1.83836i
$892$	6.35420	−	1.77426i	0.212754	−	0.0594067i
$893$	−11.1916	+	11.1916i	−0.374513	+	0.374513i
$894$	50.5646	−	19.7149i	1.69113	−	0.659365i
$895$	−4.31007	+	2.64077i	−0.144070	+	0.0882711i
$896$	10.4063	−	4.43952i	0.347649	−	0.148314i
$897$	−10.6545	+	20.9105i	−0.355742	+	0.698183i
$898$	27.2723	+	24.2982i	0.910087	+	0.810842i
$899$	20.4204			0.681057
$900$	22.0852	−	59.3616i	0.736174	−	1.97872i
$901$	−1.84842			−0.0615799
$902$	53.1182	+	47.3256i	1.76864	+	1.57577i
$903$	12.4756	−	24.4847i	0.415161	−	0.814799i
$904$	−20.4533	+	21.1074i	−0.680266	+	0.702022i
$905$	17.1062	+	1.34758i	0.568629	+	0.0447952i
$906$	−43.8078	+	17.0804i	−1.45542	+	0.567459i
$907$	9.85827	−	9.85827i	0.327338	−	0.327338i	−0.524235	−	0.851574i	$-0.675649\pi$
$907$	9.85827	−	9.85827i	0.327338	−	0.327338i	0.851574	+	0.524235i	$0.175649\pi$
$908$	11.9256	+	42.7094i	0.395765	+	1.41736i
$909$	12.2457	+	16.8548i	0.406166	+	0.559039i
$910$	−1.27885	−	9.34034i	−0.0423934	−	0.309629i
$911$	16.2149	−	22.3179i	0.537224	−	0.739425i	−0.450986	−	0.892531i	$-0.648928\pi$
$911$	16.2149	−	22.3179i	0.537224	−	0.739425i	0.988210	+	0.153106i	$0.0489276\pi$
$912$	55.5032	+	34.4103i	1.83789	+	1.13944i
$913$	4.63901	−	29.2895i	0.153529	−	0.969342i
$914$	−20.3133	+	1.17146i	−0.671904	+	0.0387485i
$915$	62.3956	+	73.0670i	2.06273	+	2.41552i
$916$	−3.45921	−	7.55518i	−0.114296	−	0.249630i
$917$	−8.49360	+	4.32771i	−0.280483	+	0.142913i
$918$	−0.540960	+	5.42027i	−0.0178543	+	0.178896i
$919$	17.0836	−	52.5779i	0.563536	−	1.73439i	−0.108725	−	0.994072i	$-0.534677\pi$
$919$	17.0836	−	52.5779i	0.563536	−	1.73439i	0.672261	−	0.740314i	$-0.265323\pi$
$920$	15.9038	+	3.55567i	0.524332	+	0.117227i
$921$	−26.5642	−	81.7562i	−0.875320	−	2.69396i
$922$	13.5764	−	2.96027i	0.447115	−	0.0974914i
$923$	−0.615118	−	3.88370i	−0.0202468	−	0.127834i
$924$	−6.76131	+	33.5358i	−0.222431	+	1.10325i
$925$	47.6834	−	15.4853i	1.56782	−	0.509155i
$926$	20.1335	−	16.4794i	0.661629	−	0.541548i
$927$	23.5167	−	3.72468i	0.772389	−	0.122334i
$928$	5.26468	−	28.4136i	0.172821	−	0.932722i
$929$	−1.13019	+	0.367221i	−0.0370803	+	0.0120481i	−0.327498	−	0.944852i	$-0.606206\pi$
$929$	−1.13019	+	0.367221i	−0.0370803	+	0.0120481i	0.290418	+	0.956900i	$0.406206\pi$
$930$	−36.9721	+	11.1599i	−1.21236	+	0.365948i
$931$	5.08233	+	1.65135i	0.166566	+	0.0541207i
$932$	−15.0010	+	9.96710i	−0.491376	+	0.326483i
$933$	−12.6247	−	24.7773i	−0.413313	−	0.811173i
$934$	−11.1084	−	2.91412i	−0.363478	−	0.0953529i
$935$	−4.72017	+	0.371127i	−0.154366	+	0.0121372i
$936$	−52.8743	−	7.52351i	−1.72825	−	0.245914i
$937$	43.0017	+	6.81080i	1.40481	+	0.222499i	0.812381	−	0.583127i	$-0.198171\pi$
$937$	43.0017	+	6.81080i	1.40481	+	0.222499i	0.592424	+	0.805626i	$0.298171\pi$
$938$	−6.79780	+	3.97241i	−0.221956	+	0.129704i
$939$	−35.4674	−	25.7686i	−1.15744	−	0.840926i
$940$	−13.1494	−	1.59199i	−0.428887	−	0.0519251i
$941$	27.8992	−	20.2699i	0.909486	−	0.660780i	−0.0313986	−	0.999507i	$-0.509996\pi$
$941$	27.8992	−	20.2699i	0.909486	−	0.660780i	0.940885	+	0.338726i	$0.109996\pi$
$942$	6.07405	−	13.8375i	0.197903	−	0.450849i
$943$	−16.3703	−	16.3703i	−0.533091	−	0.533091i
$944$	−7.94111	+	9.20061i	−0.258461	+	0.299454i
$945$	−21.0397	−	8.71677i	−0.684420	−	0.283556i
$946$	38.4757	−	59.9333i	1.25095	−	1.94860i
$947$	−52.4559	−	26.7276i	−1.70459	−	0.868531i	−0.984660	−	0.174483i	$-0.944175\pi$
$947$	−52.4559	−	26.7276i	−1.70459	−	0.868531i	−0.719929	−	0.694048i	$-0.755825\pi$
$948$	−4.06791	+	97.1039i	−0.132120	+	3.15379i
$949$		−	26.3639i		−	0.855810i
$950$	−31.7952	−	20.4185i	−1.03157	−	0.662463i
$951$		−	12.1268i		−	0.393239i
$952$	0.855383	−	0.642280i	0.0277231	−	0.0208164i
$953$	−12.8718	−	6.55853i	−0.416960	−	0.212452i	0.232908	−	0.972499i	$-0.425176\pi$
$953$	−12.8718	−	6.55853i	−0.416960	−	0.212452i	−0.649868	+	0.760047i	$0.725176\pi$
$954$	−36.8408	−	23.6509i	−1.19276	−	0.765725i
$955$	15.5808	−	18.2400i	0.504182	−	0.590231i
$956$	−4.18770	+	7.43232i	−0.135440	+	0.240378i
$957$	61.7870	+	61.7870i	1.99729	+	1.99729i
$958$	−25.1119	−	11.0230i	−0.811328	−	0.356138i
$959$	6.51389	−	4.73261i	0.210344	−	0.152824i
$960$	5.99631	+	54.3215i	0.193530	+	1.75322i
$961$	−12.1518	−	8.82879i	−0.391993	−	0.284800i
$962$	−21.3291	−	36.4996i	−0.687679	−	1.17679i
$963$	−106.697	−	16.8992i	−3.43827	−	0.544568i
$964$	20.3631	+	22.1438i	0.655851	+	0.713204i
$965$	−15.7124	−	9.63021i	−0.505800	−	0.310007i
$966$	2.82492	−	10.7684i	0.0908904	−	0.346468i
$967$	4.84598	+	9.51076i	0.155836	+	0.305846i	0.955703	−	0.294331i	$-0.0950969\pi$
$967$	4.84598	+	9.51076i	0.155836	+	0.305846i	−0.799867	+	0.600177i	$0.795097\pi$
$968$	−16.9211	+	55.0088i	−0.543865	+	1.76805i
$969$	5.87213	+	1.90797i	0.188640	+	0.0612929i
$970$	−13.1285	+	9.12330i	−0.421532	+	0.292932i
$971$	15.9646	−	5.18721i	0.512328	−	0.166465i	−0.0414328	−	0.999141i	$-0.513192\pi$
$971$	15.9646	−	5.18721i	0.512328	−	0.166465i	0.553761	+	0.832676i	$0.313192\pi$
$972$	−8.02119	+	10.1206i	−0.257280	+	0.324620i
$973$	−6.24898	+	0.989741i	−0.200333	+	0.0317296i
$974$	−11.0325	−	13.4789i	−0.353505	−	0.431890i
$975$	44.9782	+	7.13079i	1.44046	+	0.228368i
$976$	−51.8644	−	21.7994i	−1.66014	−	0.697781i
$977$	2.13998	+	13.5113i	0.0684639	+	0.432264i	0.997983	+	0.0634888i	$0.0202227\pi$
$977$	2.13998	+	13.5113i	0.0684639	+	0.432264i	−0.929519	+	0.368775i	$0.879777\pi$
$978$	5.17457	+	23.7316i	0.165465	+	0.758853i
$979$	−7.66111	−	23.5785i	−0.244850	−	0.753571i
$980$	1.53666	+	4.19984i	0.0490868	+	0.134159i
$981$	−6.35956	+	19.5727i	−0.203045	+	0.624909i
$982$	0.434291	+	0.0433436i	0.0138588	+	0.00138315i
$983$	−17.3886	+	8.85995i	−0.554611	+	0.282588i	−0.708749	−	0.705461i	$-0.750740\pi$
$983$	−17.3886	+	8.85995i	−0.554611	+	0.282588i	0.154138	+	0.988049i	$0.450740\pi$
$984$	34.1545	−	69.7233i	1.08881	−	2.22270i
$985$	−52.2904	−	12.5580i	−1.66611	−	0.400131i
$986$	−0.157300	−	2.72761i	−0.00500946	−	0.0868647i
$987$	−1.41550	+	8.93713i	−0.0450559	+	0.284472i
$988$	−11.1058	+	29.8645i	−0.353324	+	0.950117i
$989$	−13.6228	+	18.7502i	−0.433181	+	0.596222i
$990$	−98.8260	−	52.9983i	−3.14090	−	1.68440i
$991$	17.6031	+	24.2285i	0.559180	+	0.769645i	0.991222	−	0.132209i	$-0.0422069\pi$
$991$	17.6031	+	24.2285i	0.559180	+	0.769645i	−0.432042	+	0.901853i	$0.642207\pi$
$992$	16.4021	−	15.5666i	0.520767	−	0.494239i
$993$	48.0121	−	48.0121i	1.52362	−	1.52362i
$994$	0.677584	+	1.73786i	0.0214917	+	0.0551216i
$995$	0.239810	+	0.999211i	0.00760248	+	0.0316771i
$996$	−32.1482	+	3.72032i	−1.01865	+	0.117883i
$997$	−25.2660	+	49.5872i	−0.800181	+	1.57044i	0.0210032	+	0.999779i	$0.493314\pi$
$997$	−25.2660	+	49.5872i	−0.800181	+	1.57044i	−0.821184	+	0.570664i	$0.806686\pi$
$998$	−8.82396	+	9.90400i	−0.279318	+	0.313506i
$999$	−102.123			−3.23101

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instead) (See

a_n

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a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.687.68	yes	720
4.3	odd	2	inner	700.2.bj.a.687.15	yes	720
25.23	odd	20	inner	700.2.bj.a.323.15	✓	720
100.23	even	20	inner	700.2.bj.a.323.68	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.15	✓	720	25.23	odd	20	inner
700.2.bj.a.323.68	yes	720	100.23	even	20	inner
700.2.bj.a.687.15	yes	720	4.3	odd	2	inner
700.2.bj.a.687.68	yes	720	1.1	even	1	trivial

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Hilbert	Bianchi

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	700.2.bj.a.687.68

Level	$700$
Weight	$2$
Character	700.687
Analytic conductor	$5.590$
Analytic rank	$0$
Dimension	$720$
Inner twists	$4$