LMFDB - Embedded newform 700.2.bj.a.323.15

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			323.15
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22102 + 0.713522i) q^{2} +(1.38699 + 2.72212i) q^{3} +(0.981773 - 1.74245i) q^{4} +(-0.521836 + 2.17432i) q^{5} +(-3.63583 - 2.33411i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.0445120 + 2.82808i) q^{8} +(-3.72285 + 5.12406i) q^{9} +(-0.914257 - 3.02723i) q^{10} +(3.29096 + 4.52962i) q^{11} +(6.10486 + 0.255747i) q^{12} +(-0.466368 - 2.94453i) q^{13} +(1.36793 + 0.358854i) q^{14} +(-6.64256 + 1.59527i) q^{15} +(-2.07225 - 3.42137i) q^{16} +(-0.336967 - 0.171693i) q^{17} +(0.889536 - 8.91291i) q^{18} +(1.65135 + 5.08233i) q^{19} +(3.27632 + 3.04396i) q^{20} +(0.944080 - 2.90558i) q^{21} +(-7.25031 - 3.18258i) 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} +(-1.92631 + 0.537878i) q^{28} +(-4.85833 - 1.57857i) q^{29} +(6.97243 - 6.68746i) q^{30} +(3.80180 - 1.23528i) q^{31} +(4.97148 + 2.69897i) q^{32} +(-7.76564 + 15.2409i) q^{33} +(0.533950 - 0.0307927i) q^{34} +(1.90647 - 1.16849i) q^{35} +(5.27342 + 11.5175i) q^{36} +(-9.90352 + 1.56856i) q^{37} +(-5.64268 - 5.02734i) q^{38} +(7.36852 - 5.35354i) q^{39} +(-6.17238 - 1.37901i) q^{40} +(7.26889 + 5.28115i) q^{41} +(0.920456 + 4.22139i) q^{42} +(6.36022 - 6.36022i) q^{43} +(11.1236 - 1.28727i) q^{44} +(-9.19866 - 10.7686i) q^{45} +(1.32372 + 3.39506i) q^{46} +(-2.63896 + 1.34462i) q^{47} +(6.43921 - 10.3863i) q^{48} +1.00000i q^{49} +(7.05928 - 0.408173i) q^{50} -1.15540i q^{51} +(-5.58855 - 2.07824i) q^{52} +(4.35488 - 2.21892i) q^{53} +(13.4195 - 5.23221i) q^{54} +(-11.5662 + 4.79190i) q^{55} +(1.96828 - 2.03123i) q^{56} +(-11.5443 + 11.5443i) q^{57} +(7.05846 - 1.53907i) q^{58} +(-2.45814 - 1.78594i) q^{59} +(-3.74181 + 13.1405i) q^{60} +(11.3787 - 8.26713i) q^{61} +(-3.76067 + 4.22096i) q^{62} +(6.25571 - 0.990807i) q^{63} +(-7.99604 + 0.251767i) q^{64} +(6.64573 + 0.522527i) q^{65} +(-1.39275 - 24.1504i) q^{66} +(2.52751 - 4.96052i) q^{67} +(-0.629992 + 0.418584i) q^{68} +(7.48678 - 2.43260i) q^{69} +(-1.49410 + 2.78705i) q^{70} +(1.25440 + 0.407579i) q^{71} +(-14.6570 - 10.3004i) 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} +(-5.17723 + 11.7944i) q^{78} +(-4.91522 + 15.1275i) q^{79} +(8.52055 - 2.72034i) q^{80} +(-3.74360 - 11.5216i) q^{81} +(-12.6437 - 1.26188i) q^{82} +(4.71921 + 2.40456i) q^{83} +(-4.13595 - 4.49763i) q^{84} +(0.549158 - 0.643080i) q^{85} +(-3.22779 + 12.3041i) q^{86} +(-2.44141 - 15.4144i) q^{87} +(-12.6636 + 9.50871i) q^{88} +(-2.60270 - 3.58231i) q^{89} +(18.9154 + 6.58522i) q^{90} +(-1.75232 + 2.41187i) q^{91} +(-4.03873 - 3.20093i) q^{92} +(8.63563 + 8.63563i) q^{93} +(2.26280 - 3.52475i) q^{94} +(-11.9124 + 0.938426i) q^{95} +(-0.451533 + 17.2764i) q^{96} +(2.29520 + 4.50459i) q^{97} +(-0.713522 - 1.22102i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−1.22102	+	0.713522i	−0.863390	+	0.504536i
$2$	−1.22102	+	0.713522i	−0.863390	+	0.504536i
$3$	1.38699	+	2.72212i	0.800779	+	1.57162i	0.820386	+	0.571810i	$0.193759\pi$
$3$	1.38699	+	2.72212i	0.800779	+	1.57162i	−0.0196069	+	0.999808i	$0.506241\pi$
$4$	0.981773	−	1.74245i	0.490886	−	0.871224i
$5$	−0.521836	+	2.17432i	−0.233372	+	0.972388i
$5$	−0.521836	+	2.17432i	−0.233372	+	0.972388i
$6$	−3.63583	−	2.33411i	−1.48432	−	0.952898i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.0445120	+	2.82808i	0.0157374	+	0.999876i
$9$	−3.72285	+	5.12406i	−1.24095	+	1.70802i
$10$	−0.914257	−	3.02723i	−0.289113	−	0.957295i
$11$	3.29096	+	4.52962i	0.992262	+	1.36573i	0.929954	+	0.367675i	$0.119846\pi$
$11$	3.29096	+	4.52962i	0.992262	+	1.36573i	0.0623076	+	0.998057i	$0.480154\pi$
$12$	6.10486	+	0.255747i	1.76232	+	0.0738278i
$13$	−0.466368	−	2.94453i	−0.129347	−	0.816665i	−0.964003	−	0.265893i	$-0.914333\pi$
$13$	−0.466368	−	2.94453i	−0.129347	−	0.816665i	0.834655	−	0.550772i	$-0.185667\pi$
$14$	1.36793	+	0.358854i	0.365594	+	0.0959078i
$15$	−6.64256	+	1.59527i	−1.71510	+	0.411896i
$16$	−2.07225	−	3.42137i	−0.518061	−	0.855344i
$17$	−0.336967	−	0.171693i	−0.0817265	−	0.0416417i	0.412650	−	0.910890i	$-0.364603\pi$
$17$	−0.336967	−	0.171693i	−0.0817265	−	0.0416417i	−0.494376	+	0.869248i	$0.664603\pi$
$18$	0.889536	−	8.91291i	0.209666	−	2.10079i
$19$	1.65135	+	5.08233i	0.378845	+	1.16597i	0.940848	+	0.338830i	$0.110031\pi$
$19$	1.65135	+	5.08233i	0.378845	+	1.16597i	−0.562003	+	0.827135i	$0.689969\pi$
$20$	3.27632	+	3.04396i	0.732608	+	0.680651i
$21$	0.944080	−	2.90558i	0.206015	−	0.634050i
$22$	−7.25031	−	3.18258i	−1.54577	−	0.678527i
$23$	0.403083	−	2.54496i	0.0840486	−	0.530662i	−0.909358	−	0.416015i	$-0.863426\pi$
$23$	0.403083	−	2.54496i	0.0840486	−	0.530662i	0.993406	−	0.114647i	$-0.0365736\pi$
$24$	−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
$28$	−1.92631	+	0.537878i	−0.364039	+	0.101649i
$29$	−4.85833	−	1.57857i	−0.902170	−	0.293133i	−0.179038	−	0.983842i	$-0.557298\pi$
$29$	−4.85833	−	1.57857i	−0.902170	−	0.293133i	−0.723132	+	0.690709i	$0.757298\pi$
$30$	6.97243	−	6.68746i	1.27299	−	1.22096i
$31$	3.80180	−	1.23528i	0.682823	−	0.221863i	0.0529920	−	0.998595i	$-0.483124\pi$
$31$	3.80180	−	1.23528i	0.682823	−	0.221863i	0.629831	+	0.776732i	$0.283124\pi$
$32$	4.97148	+	2.69897i	0.878841	+	0.477115i
$33$	−7.76564	+	15.2409i	−1.35183	+	2.65311i
$34$	0.533950	−	0.0307927i	0.0915717	−	0.00528091i
$35$	1.90647	−	1.16849i	0.322253	−	0.197510i
$36$	5.27342	+	11.5175i	0.878903	+	1.91959i
$37$	−9.90352	+	1.56856i	−1.62813	+	0.257870i	−0.902651	−	0.430374i	$-0.858382\pi$
$37$	−9.90352	+	1.56856i	−1.62813	+	0.257870i	−0.725479	+	0.688245i	$0.758382\pi$
$38$	−5.64268	−	5.02734i	−0.915363	−	0.815542i
$39$	7.36852	−	5.35354i	1.17991	−	0.857253i
$40$	−6.17238	−	1.37901i	−0.975940	−	0.218040i
$41$	7.26889	+	5.28115i	1.13521	+	0.824778i	0.986445	−	0.164095i	$-0.0524703\pi$
$41$	7.26889	+	5.28115i	1.13521	+	0.824778i	0.148765	+	0.988873i	$0.452470\pi$
$42$	0.920456	+	4.22139i	0.142029	+	0.651375i
$43$	6.36022	−	6.36022i	0.969924	−	0.969924i	−0.0296368	−	0.999561i	$-0.509435\pi$
$43$	6.36022	−	6.36022i	0.969924	−	0.969924i	0.999561	+	0.0296368i	$0.00943506\pi$
$44$	11.1236	−	1.28727i	1.67695	−	0.194063i
$45$	−9.19866	−	10.7686i	−1.37125	−	1.60529i
$46$	1.32372	+	3.39506i	0.195171	+	0.500574i
$47$	−2.63896	+	1.34462i	−0.384931	+	0.196132i	−0.635738	−	0.771905i	$-0.719304\pi$
$47$	−2.63896	+	1.34462i	−0.384931	+	0.196132i	0.250807	+	0.968037i	$0.419304\pi$
$48$	6.43921	−	10.3863i	0.929420	−	1.49914i
$49$			1.00000i			0.142857i
$50$	7.05928	−	0.408173i	0.998333	−	0.0577244i
$51$		−	1.15540i		−	0.161789i
$52$	−5.58855	−	2.07824i	−0.774993	−	0.288200i
$53$	4.35488	−	2.21892i	0.598188	−	0.304792i	−0.128554	−	0.991703i	$-0.541034\pi$
$53$	4.35488	−	2.21892i	0.598188	−	0.304792i	0.726742	+	0.686910i	$0.241034\pi$
$54$	13.4195	−	5.23221i	1.82617	−	0.712013i
$55$	−11.5662	+	4.79190i	−1.55959	+	0.646140i
$56$	1.96828	−	2.03123i	0.263022	−	0.271434i
$57$	−11.5443	+	11.5443i	−1.52908	+	1.52908i
$58$	7.05846	−	1.53907i	0.926821	−	0.202089i
$59$	−2.45814	−	1.78594i	−0.320022	−	0.232510i	0.416163	−	0.909290i	$-0.363375\pi$
$59$	−2.45814	−	1.78594i	−0.320022	−	0.232510i	−0.736185	+	0.676780i	$0.763375\pi$
$60$	−3.74181	+	13.1405i	−0.483066	+	1.69643i
$61$	11.3787	−	8.26713i	1.45690	−	1.05850i	0.472739	−	0.881203i	$-0.343265\pi$
$61$	11.3787	−	8.26713i	1.45690	−	1.05850i	0.984158	−	0.177295i	$-0.0567346\pi$
$62$	−3.76067	+	4.22096i	−0.477605	+	0.536063i
$63$	6.25571	−	0.990807i	0.788145	−	0.124830i
$64$	−7.99604	+	0.251767i	−0.999505	+	0.0314708i
$65$	6.64573	+	0.522527i	0.824301	+	0.0648114i
$66$	−1.39275	−	24.1504i	−0.171435	−	2.97271i
$67$	2.52751	−	4.96052i	0.308785	−	0.606024i	−0.683508	−	0.729943i	$-0.739546\pi$
$67$	2.52751	−	4.96052i	0.308785	−	0.606024i	0.992292	+	0.123919i	$0.0395464\pi$
$68$	−0.629992	+	0.418584i	−0.0763977	+	0.0507607i
$69$	7.48678	−	2.43260i	0.901302	−	0.292851i
$70$	−1.49410	+	2.78705i	−0.178579	+	0.333117i
$71$	1.25440	+	0.407579i	0.148870	+	0.0483708i	0.382504	−	0.923954i	$-0.375062\pi$
$71$	1.25440	+	0.407579i	0.148870	+	0.0483708i	−0.233634	+	0.972325i	$0.575062\pi$
$72$	−14.6570	−	10.3004i	−1.72734	−	1.21392i
$73$	−8.73442	−	1.38340i	−1.02229	−	0.161914i	−0.377287	−	0.926097i	$-0.623143\pi$
$73$	−8.73442	−	1.38340i	−1.02229	−	0.161914i	−0.645000	+	0.764182i	$0.723143\pi$
$74$	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
$78$	−5.17723	+	11.7944i	−0.586206	+	1.33545i
$79$	−4.91522	+	15.1275i	−0.553006	+	1.70198i	0.148148	+	0.988965i	$0.452669\pi$
$79$	−4.91522	+	15.1275i	−0.553006	+	1.70198i	−0.701153	+	0.713011i	$0.747331\pi$
$80$	8.52055	−	2.72034i	0.952626	−	0.304143i
$81$	−3.74360	−	11.5216i	−0.415956	−	1.28018i
$82$	−12.6437	−	1.26188i	−1.39626	−	0.139351i
$83$	4.71921	+	2.40456i	0.518001	+	0.263935i	0.693387	−	0.720565i	$-0.256118\pi$
$83$	4.71921	+	2.40456i	0.518001	+	0.263935i	−0.175387	+	0.984500i	$0.556118\pi$
$84$	−4.13595	−	4.49763i	−0.451269	−	0.490732i
$85$	0.549158	−	0.643080i	0.0595646	−	0.0697518i
$86$	−3.22779	+	12.3041i	−0.348061	+	1.32678i
$87$	−2.44141	−	15.4144i	−0.261746	−	1.65260i
$88$	−12.6636	+	9.50871i	−1.34995	+	1.01363i
$89$	−2.60270	−	3.58231i	−0.275886	−	0.379724i	0.648480	−	0.761232i	$-0.275405\pi$
$89$	−2.60270	−	3.58231i	−0.275886	−	0.379724i	−0.924366	+	0.381508i	$0.875405\pi$
$90$	18.9154	+	6.58522i	1.99385	+	0.694143i
$91$	−1.75232	+	2.41187i	−0.183694	+	0.252832i
$92$	−4.03873	−	3.20093i	−0.421067	−	0.333720i
$93$	8.63563	+	8.63563i	0.895474	+	0.895474i
$94$	2.26280	−	3.52475i	0.233390	−	0.363551i
$95$	−11.9124	+	0.938426i	−1.22218	+	0.0962804i
$96$	−0.451533	+	17.2764i	−0.0460844	+	1.76327i
$97$	2.29520	+	4.50459i	0.233043	+	0.457372i	0.977681	−	0.210097i	$-0.0673778\pi$
$97$	2.29520	+	4.50459i	0.233043	+	0.457372i	−0.744638	+	0.667469i	$0.767378\pi$
$98$	−0.713522	−	1.22102i	−0.0720766	−	0.123341i
$99$	−35.4618			−3.56405
$100$	−8.32827	+	5.53534i	−0.832827	+	0.553534i
$101$	−3.28935			−0.327302			−0.163651	−	0.986518i	$-0.552327\pi$
$101$	−3.28935			−0.327302			−0.163651	+	0.986518i	$0.552327\pi$
$102$	0.824405	+	1.41077i	0.0816283	+	0.139687i
$103$	1.70666	+	3.34950i	0.168162	+	0.330036i	0.959673	−	0.281118i	$-0.0907054\pi$
$103$	1.70666	+	3.34950i	0.168162	+	0.330036i	−0.791511	+	0.611155i	$0.790705\pi$
$104$	8.30659	−	1.44999i	0.814529	−	0.142183i
$105$	5.82502	+	3.56897i	0.568464	+	0.348296i
$106$	−3.73414	+	5.81664i	−0.362691	+	0.564962i
$107$	−12.0604	−	12.0604i	−1.16592	−	1.16592i	−0.983157	−	0.182765i	$-0.941495\pi$
$107$	−12.0604	−	12.0604i	−1.16592	−	1.16592i	−0.182765	−	0.983157i	$-0.558505\pi$
$108$	−12.6522	+	15.9637i	−1.21746	+	1.53611i
$109$	−1.90988	+	2.62873i	−0.182934	+	0.251787i	−0.890629	−	0.454732i	$-0.849735\pi$
$109$	−1.90988	+	2.62873i	−0.182934	+	0.251787i	0.707695	+	0.706518i	$0.249735\pi$
$110$	10.7034	−	14.1037i	1.02053	−	1.34474i
$111$	−18.0059	−	24.7830i	−1.70905	−	2.35230i
$112$	−0.953978	+	3.88458i	−0.0901425	+	0.367058i
$113$	1.62558	+	10.2635i	0.152922	+	0.965511i	0.938131	+	0.346280i	$0.112555\pi$
$113$	1.62558	+	10.2635i	0.152922	+	0.965511i	−0.785209	+	0.619231i	$0.787445\pi$
$114$	5.85869	−	22.3329i	0.548717	−	2.09167i
$115$	5.32324	+	2.20449i	0.496394	+	0.205569i
$116$	−7.52035	+	6.91560i	−0.698247	+	0.642097i
$117$	16.8242	+	8.57234i	1.55539	+	0.792513i
$118$	4.27574	+	0.426732i	0.393614	+	0.0392839i
$119$	0.116866	+	0.359677i	0.0107131	+	0.0329716i
$120$	−4.80721	−	18.7147i	−0.438836	−	1.70841i
$121$	−6.28784	+	19.3520i	−0.571622	+	1.75927i
$122$	−7.99486	+	18.2133i	−0.723820	+	1.64895i
$123$	−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	$-0.120659\pi$
$127$	19.1378	+	3.03113i	1.69820	+	0.268969i	0.769192	+	0.639018i	$0.220659\pi$
$128$	9.58367	−	6.01276i	0.847085	−	0.531458i
$129$	26.1348	+	8.49173i	2.30104	+	0.747655i
$130$	−8.48739	+	4.10386i	−0.744393	+	0.359932i
$131$	9.06603	−	2.94573i	0.792103	−	0.257370i	0.115104	−	0.993353i	$-0.463280\pi$
$131$	9.06603	−	2.94573i	0.792103	−	0.257370i	0.676999	+	0.735984i	$0.263280\pi$
$132$	18.9324	+	28.4944i	1.64786	+	2.48012i
$133$	2.42607	−	4.76143i	0.210367	−	0.412868i
$134$	0.453302	+	7.86032i	0.0391593	+	0.679028i
$135$	8.71360	−	21.0410i	0.749947	−	1.81092i
$136$	0.470563	−	0.960611i	0.0403504	−	0.0823717i
$137$	7.95248	−	1.25955i	0.679426	−	0.107610i	0.192823	−	0.981234i	$-0.438236\pi$
$137$	7.95248	−	1.25955i	0.679426	−	0.107610i	0.486603	+	0.873623i	$0.338236\pi$
$138$	−7.40578	+	8.31223i	−0.630422	+	0.707584i
$139$	5.11855	−	3.71884i	0.434149	−	0.315428i	−0.349156	−	0.937064i	$-0.613532\pi$
$139$	5.11855	−	3.71884i	0.434149	−	0.315428i	0.783306	+	0.621636i	$0.213532\pi$
$140$	−0.164302	−	4.46912i	−0.0138860	−	0.377709i
$141$	−7.32042	−	5.31859i	−0.616490	−	0.447906i
$142$	−1.82246	+	0.397380i	−0.152938	+	0.0333474i
$143$	11.8028	−	11.8028i	0.986999	−	0.986999i
$144$	25.2460	+	2.11895i	2.10383	+	0.176579i
$145$	5.96757	−	9.73984i	0.495580	−	0.808850i
$146$	11.6520	−	4.54305i	0.964325	−	0.375986i
$147$	−2.72212	+	1.38699i	−0.224517	+	0.114397i
$148$	−6.98987	+	18.7963i	−0.574564	+	1.54505i
$149$			12.5613i			1.02906i	0.857472	+	0.514531i	$0.172034\pi$
$149$			12.5613i			1.02906i	−0.857472	+	0.514531i	$0.827966\pi$
$150$	10.9022	+	18.6501i	0.890165	+	1.52277i
$151$			10.8828i			0.885626i	0.896614	+	0.442813i	$0.146019\pi$
$151$			10.8828i			0.885626i	−0.896614	+	0.442813i	$0.853981\pi$
$152$	−14.2997	+	4.89636i	−1.15986	+	0.397147i
$153$	2.13424	−	1.08745i	0.172543	−	0.0879153i
$154$	2.87632	+	7.37716i	0.231781	+	0.594469i
$155$	0.701983	+	8.91095i	0.0563846	+	0.715745i
$156$	−2.09406	−	18.0952i	−0.167659	−	1.44878i
$157$	−2.47322	+	2.47322i	−0.197384	+	0.197384i	−0.798878	−	0.601493i	$-0.794573\pi$
$157$	−2.47322	+	2.47322i	−0.197384	+	0.197384i	0.601493	+	0.798878i	$0.294573\pi$
$158$	−4.79222	−	21.9781i	−0.381249	−	1.74848i
$159$	12.0803	+	8.77688i	0.958033	+	0.696052i
$160$	−8.46273	+	9.40118i	−0.669037	+	0.743229i
$161$	−2.08458	+	1.51454i	−0.164288	+	0.119362i
$162$	12.7919	+	11.3970i	1.00503	+	0.895430i
$163$	−5.55254	+	0.879435i	−0.434908	+	0.0688827i	−0.370050	−	0.929012i	$-0.620659\pi$
$163$	−5.55254	+	0.879435i	−0.434908	+	0.0688827i	−0.0648581	+	0.997894i	$0.520659\pi$
$164$	16.3385	−	7.48076i	1.27582	−	0.584149i
$165$	−29.0863	−	24.8383i	−2.26437	−	1.93366i
$166$	−7.47795	+	0.431251i	−0.580401	+	0.0334716i
$167$	−1.27379	+	2.49994i	−0.0985685	+	0.193451i	−0.935025	−	0.354582i	$-0.884623\pi$
$167$	−1.27379	+	2.49994i	−0.0985685	+	0.193451i	0.836457	+	0.548033i	$0.184623\pi$
$168$	8.25923	+	2.54060i	0.637213	+	0.196011i
$169$	3.91098	−	1.27076i	0.300845	−	0.0977505i
$170$	−0.211681	+	1.17705i	−0.0162352	+	0.0902756i
$171$	−32.1899	−	10.4591i	−2.46162	−	0.799829i
$172$	−4.83806	−	17.3266i	−0.368898	−	1.32114i
$173$	−4.76900	−	0.755335i	−0.362580	−	0.0574271i	−0.0275134	−	0.999621i	$-0.508759\pi$
$173$	−4.76900	−	0.755335i	−0.362580	−	0.0574271i	−0.335067	+	0.942194i	$0.608759\pi$
$174$	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
$178$	5.73400	+	2.51698i	0.429781	+	0.188656i
$179$	0.698547	−	2.14991i	0.0522119	−	0.160692i	−0.921551	−	0.388258i	$-0.873077\pi$
$179$	0.698547	−	2.14991i	0.0522119	−	0.160692i	0.973763	+	0.227566i	$0.0730769\pi$
$180$	−27.7947	+	5.45586i	−2.07170	+	0.406656i
$181$	−2.37134	−	7.29824i	−0.176260	−	0.542474i	0.823428	−	0.567420i	$-0.192058\pi$
$181$	−2.37134	−	7.29824i	−0.176260	−	0.542474i	−0.999689	+	0.0249464i	$0.992058\pi$
$182$	0.418700	−	4.19526i	0.0310361	−	0.310973i
$183$	38.2863	+	19.5079i	2.83021	+	1.44206i
$184$	7.21530	+	1.02667i	0.531919	+	0.0756870i
$185$	1.75745	−	22.3520i	0.129210	−	1.64335i
$186$	−16.7060	−	4.38255i	−1.22494	−	0.321344i
$187$	−0.331240	−	2.09137i	−0.0242227	−	0.152936i
$188$	−0.247934	+	5.91835i	−0.0180824	+	0.431640i
$189$	5.98646	+	8.23966i	0.435451	+	0.599347i
$190$	13.8756	−	9.64556i	1.00664	−	0.699763i
$191$	−6.30580	+	8.67919i	−0.456271	+	0.628004i	−0.973730	−	0.227704i	$-0.926878\pi$
$191$	−6.30580	+	8.67919i	−0.456271	+	0.628004i	0.517459	+	0.855708i	$0.326878\pi$
$192$	−11.7758	−	21.4170i	−0.849843	−	1.54564i
$193$	5.82770	+	5.82770i	0.419487	+	0.419487i	0.885027	−	0.465540i	$-0.154140\pi$
$193$	5.82770	+	5.82770i	0.419487	+	0.419487i	−0.465540	+	0.885027i	$0.654140\pi$
$194$	−6.01661	−	3.86251i	−0.431968	−	0.277312i
$195$	7.79518	+	18.8152i	0.558224	+	1.34739i
$196$	1.74245	+	0.981773i	0.124461	+	0.0701266i
$197$	10.9184	+	21.4286i	0.777906	+	1.52673i	0.848485	+	0.529220i	$0.177515\pi$
$197$	10.9184	+	21.4286i	0.777906	+	1.52673i	−0.0705790	+	0.997506i	$0.522485\pi$
$198$	43.2995	−	25.3028i	3.07716	−	1.79819i
$199$	0.459550			0.0325766			0.0162883	−	0.999867i	$-0.494815\pi$
$199$	0.459550			0.0325766			0.0162883	+	0.999867i	$0.494815\pi$
$200$	6.21938	−	12.7012i	0.439777	−	0.898107i
$201$	17.0088			1.19971
$202$	4.01635	−	2.34702i	0.282590	−	0.165136i
$203$	2.31914	+	4.55158i	0.162772	+	0.319458i
$204$	−2.01323	−	1.13434i	−0.140954	−	0.0794199i
$205$	−15.2761	+	13.0490i	−1.06693	+	0.911383i
$206$	−4.47380	−	2.87207i	−0.311705	−	0.200106i
$207$	11.5399	+	11.5399i	0.802081	+	0.802081i
$208$	−9.10791	+	7.69740i	−0.631520	+	0.533719i
$209$	−17.5865	+	24.2057i	−1.21648	+	1.67434i
$210$	−9.65900	−	0.201503i	−0.666534	−	0.0139050i
$211$	12.5564	+	17.2824i	0.864420	+	1.18977i	0.980497	+	0.196532i	$0.0629680\pi$
$211$	12.5564	+	17.2824i	0.864420	+	1.18977i	−0.116077	+	0.993240i	$0.537032\pi$
$212$	0.409147	−	9.76662i	0.0281003	−	0.670774i
$213$	0.630361	+	3.97994i	0.0431916	+	0.272701i
$214$	23.3313	+	6.12060i	1.59489	+	0.418396i
$215$	10.5102	+	17.1482i	0.716789	+	1.16950i
$216$	4.05807	−	28.5196i	0.276117	−	1.94052i
$217$	−3.56175	−	1.81480i	−0.241787	−	0.123197i
$218$	0.456347	−	4.57247i	0.0309077	−	0.309687i
$219$	−8.34879	−	25.6949i	−0.564159	−	1.73630i
$220$	−3.00575	+	24.8581i	−0.202648	+	1.67593i
$221$	−0.348405	+	1.07228i	−0.0234363	+	0.0721294i
$222$	39.6688	+	17.4129i	2.66239	+	1.16868i
$223$	−0.516020	+	3.25802i	−0.0345552	+	0.218173i	−0.998923	−	0.0463908i	$-0.985228\pi$
$223$	−0.516020	+	3.25802i	−0.0345552	+	0.218173i	0.964368	+	0.264564i	$0.0852281\pi$
$224$	−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	$-0.186811\pi$
$227$	21.8986	+	3.46840i	1.45346	+	0.230206i	0.620792	+	0.783975i	$0.286811\pi$
$228$	8.78146	+	31.4492i	0.581566	+	2.08278i
$229$	3.95138	+	1.28388i	0.261114	+	0.0848412i	0.436649	−	0.899632i	$-0.356165\pi$
$229$	3.95138	+	1.28388i	0.261114	+	0.0848412i	−0.175534	+	0.984473i	$0.556165\pi$
$230$	−8.07272	+	1.10653i	−0.532299	+	0.0729622i
$231$	16.2681	−	5.28583i	1.07036	−	0.347782i
$232$	4.24806	−	13.8100i	0.278899	−	0.906671i
$233$	−4.08828	+	8.02369i	−0.267832	+	0.525650i	−0.985277	−	0.170965i	$-0.945311\pi$
$233$	−4.08828	+	8.02369i	−0.267832	+	0.525650i	0.717445	+	0.696615i	$0.245311\pi$
$234$	−26.6592	+	1.53743i	−1.74276	+	0.100505i
$235$	−1.54653	−	6.43962i	−0.100884	−	0.420074i
$236$	−5.52524	+	2.52979i	−0.359662	+	0.164675i
$237$	−47.9962	+	7.60186i	−3.11769	+	0.493794i
$238$	−0.399333	−	0.355786i	−0.0258849	−	0.0230622i
$239$	3.45082	−	2.50717i	0.223215	−	0.162175i	−0.470558	−	0.882369i	$-0.655947\pi$
$239$	3.45082	−	2.50717i	0.223215	−	0.162175i	0.693773	+	0.720194i	$0.255947\pi$
$240$	19.2230	+	19.4209i	1.24084	+	1.25361i
$241$	−12.1689	−	8.84125i	−0.783870	−	0.569515i	0.122268	−	0.992497i	$-0.460983\pi$
$241$	−12.1689	−	8.84125i	−0.783870	−	0.569515i	−0.906138	+	0.422982i	$0.860983\pi$
$242$	−6.13050	−	28.1156i	−0.394083	−	1.80734i
$243$	4.56573	−	4.56573i	0.292892	−	0.292892i
$244$	−3.23371	−	27.9433i	−0.207017	−	1.78888i
$245$	−2.17432	−	0.521836i	−0.138913	−	0.0333389i
$246$	−14.1017	−	36.1678i	−0.899089	−	2.30598i
$247$	14.1949	−	7.23267i	0.903201	−	0.460204i
$248$	3.66269	+	10.6968i	0.232581	+	0.679247i
$249$			16.1814i			1.02545i
$250$	−2.79628	+	15.5622i	−0.176852	+	0.984237i
$251$			5.22621i			0.329876i	0.986304	+	0.164938i	$0.0527423\pi$
$251$			5.22621i			0.329876i	−0.986304	+	0.164938i	$0.947258\pi$
$252$	4.41526	−	11.8730i	0.278135	−	0.747928i
$253$	12.8543	−	6.54957i	0.808140	−	0.411768i
$254$	−25.5304	+	9.95417i	−1.60192	+	0.624580i
$255$	2.51222	+	0.602930i	0.157321	+	0.0377570i
$256$	−7.41160	+	14.1799i	−0.463225	+	0.886241i
$257$	−1.61866	+	1.61866i	−0.100969	+	0.100969i	−0.755787	−	0.654818i	$-0.772745\pi$
$257$	−1.61866	+	1.61866i	−0.100969	+	0.100969i	0.654818	+	0.755787i	$0.272745\pi$
$258$	−37.9702	+	8.27923i	−2.36392	+	0.515443i
$259$	8.11199	+	5.89371i	0.504055	+	0.366217i
$260$	7.43507	−	11.0668i	0.461103	−	0.686336i
$261$	26.1755	−	19.0176i	1.62022	−	1.17716i
$262$	−8.96795	+	10.0656i	−0.554042	+	0.621856i
$263$	8.31302	−	1.31665i	0.512603	−	0.0811883i	0.105226	−	0.994448i	$-0.466443\pi$
$263$	8.31302	−	1.31665i	0.512603	−	0.0811883i	0.407377	+	0.913260i	$0.366443\pi$
$264$	−43.4482	−	21.2834i	−2.67405	−	1.30990i
$265$	2.55212	+	10.6268i	0.156776	+	0.652801i
$266$	0.435109	+	7.54484i	0.0266782	+	0.462604i
$267$	6.14156	−	12.0535i	0.375857	−	0.737662i
$268$	−6.16200	−	9.27416i	−0.376404	−	0.566509i
$269$	25.2507	−	8.20445i	1.53956	−	0.500234i	0.588306	−	0.808638i	$-0.299795\pi$
$269$	25.2507	−	8.20445i	1.53956	−	0.500234i	0.951255	+	0.308404i	$0.0997950\pi$
$270$	4.37373	+	31.9087i	0.266177	+	1.94190i
$271$	−26.6318	−	8.65320i	−1.61777	−	0.525645i	−0.646354	−	0.763038i	$-0.723707\pi$
$271$	−26.6318	−	8.65320i	−1.61777	−	0.525645i	−0.971414	+	0.237393i	$0.923707\pi$
$272$	0.110851	+	1.50868i	0.00672135	+	0.0914772i
$273$	−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	−0.994823	−	0.101619i	$-0.967598\pi$
$277$	−0.287731	+	1.81666i	−0.0172881	+	0.109153i	0.977535	+	0.210772i	$0.0675977\pi$
$278$	−3.59637	+	8.19297i	−0.215696	+	0.491382i
$279$	−7.82387	+	24.0794i	−0.468403	+	1.44160i
$280$	3.38943	+	5.33964i	0.202557	+	0.319105i
$281$	5.99275	+	18.4438i	0.357498	+	1.10026i	0.954547	+	0.298060i	$0.0963395\pi$
$281$	5.99275	+	18.4438i	0.357498	+	1.10026i	−0.597050	+	0.802204i	$0.703660\pi$
$282$	12.7333	+	1.27082i	0.758257	+	0.0756764i
$283$	−23.3107	−	11.8774i	−1.38568	−	0.706038i	−0.407382	−	0.913258i	$-0.633558\pi$
$283$	−23.3107	−	11.8774i	−1.38568	−	0.706038i	−0.978294	+	0.207220i	$0.933558\pi$
$284$	1.94172	−	1.78558i	0.115220	−	0.105954i
$285$	−19.0768	−	31.1253i	−1.13001	−	1.84370i
$286$	−5.98988	+	22.8330i	−0.354189	+	1.35014i
$287$	−1.40554	−	8.87422i	−0.0829663	−	0.523829i
$288$	−32.3377	+	15.4263i	−1.90552	+	0.909003i
$289$	−9.90828	−	13.6376i	−0.582840	−	0.802211i
$290$	−0.336926	+	16.1505i	−0.0197850	+	0.948391i
$291$	−9.07862	+	12.4957i	−0.532198	+	0.732508i
$292$	−10.9857	+	13.8611i	−0.642890	+	0.811159i
$293$	−13.8932	−	13.8932i	−0.811647	−	0.811647i	0.173234	−	0.984881i	$-0.444578\pi$
$293$	−13.8932	−	13.8932i	−0.811647	−	0.811647i	−0.984881	+	0.173234i	$0.944578\pi$
$294$	2.33411	−	3.63583i	0.136128	−	0.212046i
$295$	5.16596	−	4.41282i	0.300774	−	0.256924i
$296$	−4.87684	−	27.9381i	−0.283461	−	1.62387i
$297$	−25.8882	−	50.8085i	−1.50219	−	2.94821i
$298$	−8.96277	−	15.3376i	−0.519199	−	0.888482i
$299$	−7.68171			−0.444245
$300$	−26.6191	−	14.9931i	−1.53685	−	0.865627i
$301$	−8.99470			−0.518446
$302$	−7.76509	−	13.2880i	−0.446831	−	0.764641i
$303$	−4.56229	−	8.95400i	−0.262097	−	0.514394i
$304$	13.9665	−	16.1817i	0.801036	−	0.928084i
$305$	12.0376	+	29.0551i	0.689271	+	1.66369i
$306$	−1.83003	+	2.85063i	−0.104616	+	0.162960i
$307$	19.8963	+	19.8963i	1.13554	+	1.13554i	0.989240	+	0.146303i	$0.0467374\pi$
$307$	19.8963	+	19.8963i	1.13554	+	1.13554i	0.146303	+	0.989240i	$0.453263\pi$
$308$	−8.77581	−	6.95533i	−0.500048	−	0.396317i
$309$	−6.75063	+	9.29145i	−0.384030	+	0.528572i
$310$	−7.21529	−	10.3796i	−0.409801	−	0.589519i
$311$	5.35015	+	7.36384i	0.303379	+	0.417565i	0.933302	−	0.359092i	$-0.116914\pi$
$311$	5.35015	+	7.36384i	0.303379	+	0.417565i	−0.629923	+	0.776657i	$0.716914\pi$
$312$	15.4682	+	20.6004i	0.875715	+	1.16627i
$313$	−2.24480	−	14.1731i	−0.126884	−	0.801111i	−0.966261	−	0.257563i	$-0.917080\pi$
$313$	−2.24480	−	14.1731i	−0.126884	−	0.801111i	0.839378	−	0.543548i	$-0.182920\pi$
$314$	1.25515	−	4.78454i	0.0708322	−	0.270007i
$315$	−1.11012	+	14.1190i	−0.0625481	+	0.795515i
$316$	21.5332	+	23.4163i	1.21134	+	1.31727i
$317$	−3.53672	−	1.80205i	−0.198642	−	0.101213i	0.351840	−	0.936060i	$-0.385556\pi$
$317$	−3.53672	−	1.80205i	−0.198642	−	0.101213i	−0.550482	+	0.834847i	$0.685556\pi$
$318$	−21.0128	−	2.09715i	−1.17834	−	0.117602i
$319$	−8.83827	−	27.2014i	−0.494848	−	1.52299i
$320$	3.62520	−	17.5174i	0.202655	−	0.979250i
$321$	16.1022	−	49.5575i	0.898737	−	2.76603i
$322$	1.46466	−	3.33668i	0.0816223	−	0.185946i
$323$	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
$328$	−14.6120	+	20.7920i	−0.806810	+	1.14805i
$329$	2.81681	+	0.915238i	0.155296	+	0.0504587i
$330$	53.2376	+	9.57427i	2.93064	+	0.527046i
$331$	21.1371	−	6.86786i	1.16180	−	0.377491i	0.336223	−	0.941782i	$-0.390850\pi$
$331$	21.1371	−	6.86786i	1.16180	−	0.377491i	0.825576	+	0.564291i	$0.190850\pi$
$332$	8.82301	−	5.86225i	0.484225	−	0.321733i
$333$	28.8319	−	56.5858i	1.57998	−	3.10088i
$334$	−0.228450	−	3.96135i	−0.0125002	−	0.216756i
$335$	9.46683	+	8.08421i	0.517228	+	0.441687i
$336$	−11.8974	+	2.79102i	−0.649059	+	0.152263i
$337$	−28.5306	+	4.51880i	−1.55416	+	0.246155i	−0.873639	−	0.486575i	$-0.838246\pi$
$337$	−28.5306	+	4.51880i	−1.55416	+	0.246155i	−0.680520	+	0.732729i	$0.738246\pi$
$338$	−3.86867	+	4.34219i	−0.210428	+	0.236184i
$339$	−25.6839	+	18.6604i	−1.39496	+	1.01350i
$340$	−0.581384	−	1.58824i	−0.0315300	−	0.0861343i
$341$	18.1069	+	13.1554i	0.980544	+	0.712407i
$342$	46.7672	−	10.1974i	2.52888	−	0.551412i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	18.2703	+	17.7041i	0.985068	+	0.954540i
$345$	1.38240	+	17.5481i	0.0744257	+	0.944758i
$346$	6.36198	−	2.48051i	0.342022	−	0.133353i
$347$	−26.7115	+	13.6102i	−1.43395	+	0.730632i	−0.986513	−	0.163685i	$-0.947662\pi$
$347$	−26.7115	+	13.6102i	−1.43395	+	0.730632i	−0.447434	+	0.894317i	$0.647662\pi$
$348$	−29.2557	−	10.8794i	−1.56827	−	0.583200i
$349$		−	22.7165i		−	1.21599i	−0.793941	−	0.607994i	$-0.791974\pi$
$349$		−	22.7165i		−	1.21599i	0.793941	−	0.607994i	$-0.208026\pi$
$350$	−5.28028	−	4.70304i	−0.282243	−	0.251388i
$351$			30.3632i			1.62067i
$352$	4.13563	+	31.4011i	0.220430	+	1.67368i
$353$	9.79833	−	4.99250i	0.521513	−	0.265724i	−0.173358	−	0.984859i	$-0.555462\pi$
$353$	9.79833	−	4.99250i	0.521513	−	0.265724i	0.694870	+	0.719135i	$0.255462\pi$
$354$	4.76879	+	12.2310i	0.253458	+	0.650068i
$355$	−1.54080	+	2.51478i	−0.0817773	+	0.133471i
$356$	−8.79724	+	1.01805i	−0.466253	+	0.0539568i
$357$	−0.816993	+	0.816993i	−0.0432398	+	0.0432398i
$358$	0.681067	+	3.12351i	0.0359955	+	0.165082i
$359$	19.7173	+	14.3255i	1.04064	+	0.756069i	0.970410	−	0.241461i	$-0.0776267\pi$
$359$	19.7173	+	14.3255i	1.04064	+	0.756069i	0.0702298	+	0.997531i	$0.477627\pi$
$360$	30.0450	−	26.4938i	1.58351	−	1.39635i
$361$	−7.73176	+	5.61745i	−0.406935	+	0.295655i
$362$	8.10291	+	7.21928i	0.425879	+	0.379437i
$363$	−61.3996	+	9.72474i	−3.22264	+	0.510417i
$364$	2.48217	+	5.42124i	0.130101	+	0.284150i
$365$	7.56589	−	18.2696i	0.396017	−	0.956273i
$366$	−60.6676	+	3.49868i	−3.17115	+	0.182879i
$367$	13.4170	−	26.3324i	0.700364	−	1.37454i	−0.216873	−	0.976200i	$-0.569586\pi$
$367$	13.4170	−	26.3324i	0.700364	−	1.37454i	0.917237	−	0.398342i	$-0.130414\pi$
$368$	−9.54256	+	3.89469i	−0.497440	+	0.203025i
$369$	−54.1219	+	17.5853i	−2.81747	+	0.915453i
$370$	13.8028	+	28.5462i	0.717572	+	1.48405i
$371$	−4.64838	−	1.51035i	−0.241332	−	0.0784134i
$372$	23.5254	−	6.56891i	1.21973	−	0.340582i
$373$	−0.892883	−	0.141419i	−0.0462317	−	0.00732239i	0.133276	−	0.991079i	$-0.457450\pi$
$373$	−0.892883	−	0.141419i	−0.0462317	−	0.00732239i	−0.179507	+	0.983757i	$0.557450\pi$
$374$	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
$378$	−13.1888	−	5.78931i	−0.678357	−	0.297770i
$379$	5.99747	−	18.4583i	0.308069	−	0.948139i	−0.670445	−	0.741959i	$-0.733897\pi$
$379$	5.99747	−	18.4583i	0.308069	−	0.948139i	0.978514	−	0.206180i	$-0.0661033\pi$
$380$	−10.0601	+	21.6780i	−0.516071	+	1.11206i
$381$	18.2928	+	56.2995i	0.937170	+	2.88431i
$382$	1.50671	−	15.0968i	0.0770898	−	0.772418i
$383$	13.2339	+	6.74300i	0.676220	+	0.344551i	0.758144	−	0.652087i	$-0.226106\pi$
$383$	13.2339	+	6.74300i	0.676220	+	0.344551i	−0.0819239	+	0.996639i	$0.526106\pi$
$384$	29.6599	+	17.7483i	1.51358	+	0.905713i
$385$	11.5669	+	4.79016i	0.589505	+	0.244129i
$386$	−11.2739	−	2.95754i	−0.573827	−	0.150535i
$387$	8.91202	+	56.2683i	0.453023	+	2.86028i
$388$	10.1024	+	0.423213i	0.512871	+	0.0214854i
$389$	−15.0466	−	20.7099i	−0.762894	−	1.05003i	−0.996968	−	0.0778150i	$-0.975206\pi$
$389$	−15.0466	−	20.7099i	−0.762894	−	1.05003i	0.234074	−	0.972219i	$-0.424794\pi$
$390$	−22.9431	−	17.4117i	−1.16177	−	0.881676i
$391$	−0.572779	+	0.788363i	−0.0289667	+	0.0398692i
$392$	−2.82808	+	0.0445120i	−0.142839	+	0.00224819i
$393$	20.5931	+	20.5931i	1.03879	+	1.03879i
$394$	−28.6214	−	18.3742i	−1.44193	−	0.925679i
$395$	−30.3271	−	18.5814i	−1.52592	−	0.934929i
$396$	−34.8154	+	61.7903i	−1.74954	+	3.10508i
$397$	−6.66232	−	13.0755i	−0.334372	−	0.656243i	0.661203	−	0.750207i	$-0.270046\pi$
$397$	−6.66232	−	13.0755i	−0.334372	−	0.656243i	−0.995576	+	0.0939641i	$0.970046\pi$
$398$	−0.561119	+	0.327899i	−0.0281264	+	0.0164361i
$399$	16.3261			0.817328
$400$	1.46857	+	19.9460i	0.0734284	+	0.997300i
$401$	−29.8137			−1.48883			−0.744413	−	0.667719i	$-0.767271\pi$
$401$	−29.8137			−1.48883			−0.744413	+	0.667719i	$0.767271\pi$
$402$	−20.7680	+	12.1361i	−1.03581	+	0.605295i
$403$	−5.41035	−	10.6184i	−0.269509	−	0.528940i
$404$	−3.22939	+	5.73151i	−0.160668	+	0.285153i
$405$	27.0053	−	2.12741i	1.34190	−	0.105712i
$406$	−6.07937	−	3.90280i	−0.301714	−	0.193693i
$407$	−39.6971	−	39.6971i	−1.96771	−	1.96771i
$408$	3.26757	−	0.0514292i	0.161769	−	0.00254613i
$409$	10.6126	−	14.6070i	0.524761	−	0.722272i	−0.461560	−	0.887109i	$-0.652710\pi$
$409$	10.6126	−	14.6070i	0.524761	−	0.722272i	0.986321	+	0.164837i	$0.0527099\pi$
$410$	9.34165	−	26.8329i	0.461351	−	1.32518i
$411$	14.4587	+	19.9006i	0.713193	+	0.981626i
$412$	7.51188	+	0.314690i	0.370084	+	0.0155037i
$413$	0.475314	+	3.00102i	0.0233887	+	0.147670i
$414$	−22.3245	−	5.85648i	−1.09719	−	0.287830i
$415$	−7.69094	+	9.00631i	−0.377534	+	0.442102i
$416$	5.62866	−	15.8974i	0.275968	−	0.779432i
$417$	17.2225	+	8.77531i	0.843390	+	0.429729i
$418$	4.20211	−	42.1040i	0.205532	−	2.05937i
$419$	1.11371	+	3.42766i	0.0544085	+	0.167452i	0.974568	−	0.224091i	$-0.0719413\pi$
$419$	1.11371	+	3.42766i	0.0544085	+	0.167452i	−0.920160	+	0.391543i	$0.871941\pi$
$420$	11.9376	−	6.64587i	0.582495	−	0.324285i
$421$	7.43037	−	22.8683i	0.362134	−	1.11453i	−0.589622	−	0.807679i	$-0.700723\pi$
$421$	7.43037	−	22.8683i	0.362134	−	1.11453i	0.951756	−	0.306855i	$-0.0992766\pi$
$422$	−27.6630	−	12.1429i	−1.34662	−	0.591107i
$423$	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
$428$	−32.8551	+	9.17403i	−1.58811	+	0.443443i
$429$	48.4990	+	15.7583i	2.34155	+	0.760817i
$430$	−25.0687	−	13.4390i	−1.20892	−	0.648085i
$431$	7.83962	−	2.54725i	0.377621	−	0.122697i	−0.114056	−	0.993474i	$-0.536384\pi$
$431$	7.83962	−	2.54725i	0.377621	−	0.122697i	0.491677	+	0.870778i	$0.336384\pi$
$432$	15.3944	+	37.7185i	0.740664	+	1.81473i
$433$	9.84759	−	19.3270i	0.473245	−	0.928796i	−0.523790	−	0.851847i	$-0.675482\pi$
$433$	9.84759	−	19.3270i	0.473245	−	0.928796i	0.997035	−	0.0769484i	$-0.0245177\pi$
$434$	5.64386	−	0.325480i	0.270914	−	0.0156235i
$435$	34.7900	+	2.73540i	1.66805	+	0.131152i
$436$	2.70535	+	5.90869i	0.129563	+	0.282975i
$437$	13.6000	−	2.15402i	0.650575	−	0.103041i
$438$	28.5279	+	25.4169i	1.36312	+	1.21447i
$439$	24.4982	−	17.7990i	1.16924	−	0.849501i	0.178320	−	0.983973i	$-0.442934\pi$
$439$	24.4982	−	17.7990i	1.16924	−	0.849501i	0.990917	+	0.134472i	$0.0429337\pi$
$440$	−14.0667	−	32.4968i	−0.670603	−	1.54923i
$441$	−5.12406	−	3.72285i	−0.244003	−	0.177279i
$442$	−0.339687	−	1.55787i	−0.0161573	−	0.0741003i
$443$	−10.1059	+	10.1059i	−0.480144	+	0.480144i	−0.905178	−	0.425033i	$-0.860262\pi$
$443$	−10.1059	+	10.1059i	−0.480144	+	0.480144i	0.425033	+	0.905178i	$0.360262\pi$
$444$	−60.8608	+	7.04307i	−2.88833	+	0.334249i
$445$	9.14728	−	3.78974i	0.433623	−	0.179651i
$446$	−1.69460	−	4.34630i	−0.0802416	−	0.205803i
$447$	−34.1934	+	17.4224i	−1.61729	+	0.824051i
$448$	5.83208	+	5.47603i	0.275540	+	0.258718i
$449$		−	25.8281i		−	1.21890i	−0.792824	−	0.609451i	$-0.791390\pi$
$449$		−	25.8281i		−	1.21890i	0.792824	−	0.609451i	$-0.208610\pi$
$450$	−24.1891	+	37.6917i	−1.14029	+	1.77681i
$451$			50.3054i			2.36879i
$452$	19.4796	+	7.24395i	0.916243	+	0.340727i
$453$	−29.6242	+	15.0943i	−1.39187	+	0.709191i
$454$	−29.2134	+	11.3902i	−1.37105	+	0.534567i
$455$	−4.32976	−	5.06872i	−0.202982	−	0.237625i
$456$	−33.1620	−	32.1343i	−1.55295	−	1.50483i
$457$	−10.1735	+	10.1735i	−0.475897	+	0.475897i	−0.903817	−	0.427920i	$-0.859247\pi$
$457$	−10.1735	+	10.1735i	−0.475897	+	0.475897i	0.427920	+	0.903817i	$0.359247\pi$
$458$	−5.74078	+	1.25175i	−0.268249	+	0.0584906i
$459$	3.11613	+	2.26400i	0.145449	+	0.105675i
$460$	9.06741	−	7.11115i	0.422770	−	0.331559i
$461$	7.94901	−	5.77529i	0.370222	−	0.268982i	−0.387081	−	0.922046i	$-0.626517\pi$
$461$	7.94901	−	5.77529i	0.370222	−	0.268982i	0.757303	+	0.653064i	$0.226517\pi$
$462$	−16.0921	+	18.0617i	−0.748673	+	0.840309i
$463$	−18.1709	+	2.87799i	−0.844474	+	0.133752i	−0.563656	−	0.826009i	$-0.690606\pi$
$463$	−18.1709	+	2.87799i	−0.844474	+	0.133752i	−0.280818	+	0.959761i	$0.590606\pi$
$464$	4.66679	+	19.8934i	0.216650	+	0.923526i
$465$	−23.2831	+	14.2703i	−1.07973	+	0.661769i
$466$	−0.733221	−	12.7142i	−0.0339658	−	0.588972i
$467$	3.68668	−	7.23553i	0.170599	−	0.334820i	−0.789838	−	0.613315i	$-0.789836\pi$
$467$	3.68668	−	7.23553i	0.170599	−	0.334820i	0.960438	+	0.278495i	$0.0898356\pi$
$468$	31.4544	−	20.8991i	1.45398	−	0.966063i
$469$	−5.29484	+	1.72040i	−0.244493	+	0.0794405i
$470$	6.48315	+	6.75941i	0.299045	+	0.311788i
$471$	−10.1627	−	3.30207i	−0.468274	−	0.152151i
$472$	4.94136	−	7.03130i	0.227445	−	0.323642i
$473$	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
$478$	−2.42460	+	5.52353i	−0.110898	+	0.252640i
$479$	5.99252	−	18.4431i	0.273805	−	0.842685i	−0.715728	−	0.698379i	$-0.753905\pi$
$479$	5.99252	−	18.4431i	0.273805	−	0.842685i	0.989533	−	0.144306i	$-0.0460950\pi$
$480$	−37.3289	−	9.99723i	−1.70382	−	0.456309i
$481$	9.23736	+	28.4297i	0.421188	+	1.29628i
$482$	21.1669	+	2.11253i	0.964127	+	0.0962229i
$483$	−7.01406	−	3.57384i	−0.319151	−	0.162615i
$484$	27.5466	+	29.9555i	1.25212	+	1.36161i
$485$	−10.9922	+	2.63986i	−0.499128	+	0.119870i
$486$	−2.31709	+	8.83259i	−0.105105	+	0.400654i
$487$	−1.92674	−	12.1649i	−0.0873089	−	0.551246i	−0.992106	−	0.125403i	$-0.959978\pi$
$487$	−1.92674	−	12.1649i	−0.0873089	−	0.551246i	0.904797	−	0.425843i	$-0.140022\pi$
$488$	23.8866	+	31.8119i	1.08129	+	1.44006i
$489$	−10.0952	−	13.8949i	−0.456523	−	0.628350i
$490$	3.02723	−	0.914257i	0.136756	−	0.0413019i
$491$	−0.181400	+	0.249675i	−0.00818645	+	0.0112677i	−0.813091	−	0.582137i	$-0.802217\pi$
$491$	−0.181400	+	0.249675i	−0.00818645	+	0.0112677i	0.804904	+	0.593405i	$0.202217\pi$
$492$	43.0249	+	34.0997i	1.93971	+	1.53733i
$493$	1.36607	+	1.36607i	0.0615247	+	0.0615247i
$494$	−12.1716	+	18.9596i	−0.547626	+	0.853033i
$495$	18.5052	−	77.1055i	0.831749	−	3.46563i
$496$	−12.1046	−	10.4476i	−0.543513	−	0.469110i
$497$	−0.598793	−	1.17520i	−0.0268595	−	0.0527148i
$498$	−11.5458	−	19.7577i	−0.517378	−	0.885366i
$499$	9.37954			0.419886			0.209943	−	0.977714i	$-0.432672\pi$
$499$	9.37954			0.419886			0.209943	+	0.977714i	$0.432672\pi$
$500$	−7.68963	−	20.9969i	−0.343891	−	0.939010i
$501$	−8.57188			−0.382963
$502$	−3.72902	−	6.38130i	−0.166434	−	0.284811i
$503$	1.06972	+	2.09944i	0.0476963	+	0.0936093i	0.913625	−	0.406559i	$-0.133271\pi$
$503$	1.06972	+	2.09944i	0.0476963	+	0.0936093i	−0.865928	+	0.500168i	$0.833271\pi$
$504$	3.08053	+	17.6475i	0.137218	+	0.786083i
$505$	1.71650	−	7.15211i	0.0763832	−	0.318265i
$506$	−11.0220	+	17.1689i	−0.489988	+	0.763252i
$507$	8.88365	+	8.88365i	0.394537	+	0.394537i
$508$	24.0705	−	30.3707i	1.06796	−	1.34748i
$509$	14.1673	−	19.4996i	0.627953	−	0.864303i	−0.369949	−	0.929052i	$-0.620625\pi$
$509$	14.1673	−	19.4996i	0.627953	−	0.864303i	0.997902	+	0.0647493i	$0.0206248\pi$
$510$	−3.49767	+	1.05633i	−0.154879	+	0.0467753i
$511$	5.19796	+	7.15438i	0.229944	+	0.316491i
$512$	−1.06793	−	22.6022i	−0.0471965	−	0.998886i
$513$	−8.51413	−	53.7561i	−0.375908	−	2.37339i
$514$	0.821463	−	3.13136i	0.0362332	−	0.138118i
$515$	−8.17350	+	1.96293i	−0.360167	+	0.0864972i
$516$	40.4549	−	37.2016i	1.78093	−	1.63771i
$517$	−14.7753	−	7.52839i	−0.649817	−	0.331098i
$518$	−14.1102	−	1.40824i	−0.619966	−	0.0618745i
$519$	−4.55844	−	14.0294i	−0.200093	−	0.615824i
$520$	−1.18193	+	18.8179i	−0.0518311	+	0.825219i
$521$	4.56843	−	14.0602i	0.200147	−	0.615988i	−0.799731	−	0.600358i	$-0.795025\pi$
$521$	4.56843	−	14.0602i	0.200147	−	0.615988i	0.999878	−	0.0156297i	$-0.00497529\pi$
$522$	−18.3913	+	41.8977i	−0.804965	+	1.83381i
$523$	1.47896	−	9.33781i	0.0646706	−	0.408314i	−0.934023	−	0.357213i	$-0.883727\pi$
$523$	1.47896	−	9.33781i	0.0646706	−	0.408314i	0.998693	−	0.0511009i	$-0.0162730\pi$
$524$	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
$528$	68.2373	−	5.01378i	2.96965	−	0.218197i
$529$	15.5599	+	5.05573i	0.676519	+	0.219814i
$530$	−10.6987	−	11.1546i	−0.464720	−	0.484523i
$531$	18.3025	−	5.94686i	0.794263	−	0.258072i
$532$	−5.91469	−	8.90193i	−0.256434	−	0.385948i
$533$	12.1605	−	23.8664i	0.526731	−	1.03377i
$534$	1.10147	+	19.0997i	0.0476654	+	0.826524i
$535$	32.5167	−	19.9296i	1.40582	−	0.861634i
$536$	14.1412	+	6.92719i	0.610808	+	0.299209i
$537$	6.82119	−	1.08037i	0.294356	−	0.0466214i
$538$	−24.9775	+	28.0347i	−1.07686	+	1.20866i
$539$	−4.52962	+	3.29096i	−0.195105	+	0.141752i
$540$	−28.1080	−	35.8404i	−1.20958	−	1.54233i
$541$	1.23475	+	0.897100i	0.0530861	+	0.0385693i	0.614012	−	0.789297i	$-0.289555\pi$
$541$	1.23475	+	0.897100i	0.0530861	+	0.0385693i	−0.560926	+	0.827866i	$0.689555\pi$
$542$	38.6922	−	8.43667i	1.66197	−	0.362386i
$543$	16.5777	−	16.5777i	0.711416	−	0.711416i
$544$	−1.21183	−	1.76303i	−0.0519567	−	0.0755894i
$545$	−4.71906	−	5.52447i	−0.202143	−	0.236642i
$546$	12.0007	−	4.67903i	0.513584	−	0.200244i
$547$	31.7224	−	16.1634i	1.35635	−	0.691095i	0.383720	−	0.923450i	$-0.374643\pi$
$547$	31.7224	−	16.1634i	1.35635	−	0.691095i	0.972631	+	0.232354i	$0.0746429\pi$
$548$	5.61283	−	15.0934i	0.239768	−	0.644756i
$549$			89.0826i			3.80195i
$550$	25.0807	+	30.6326i	1.06944	+	1.30618i
$551$		−	27.2984i		−	1.16295i
$552$	7.21283	+	21.0649i	0.306999	+	0.896582i
$553$	14.1723	−	7.22117i	0.602669	−	0.307075i
$554$	−0.944904	−	2.42348i	−0.0401451	−	0.102964i
$555$	63.2824	−	26.2180i	2.68619	−	1.11289i
$556$	−1.45464	−	12.5699i	−0.0616904	−	0.533081i
$557$	5.08957	−	5.08957i	0.215652	−	0.215652i	−0.591011	−	0.806663i	$-0.701271\pi$
$557$	5.08957	−	5.08957i	0.215652	−	0.215652i	0.806663	+	0.591011i	$0.201271\pi$
$558$	−7.62809	−	34.9839i	−0.322923	−	1.48099i
$559$	−21.6940	−	15.7616i	−0.917560	−	0.666646i
$560$	−7.94851	−	4.10137i	−0.335886	−	0.173314i
$561$	5.23353	−	3.80238i	0.220960	−	0.160537i
$562$	−20.4773	−	18.2442i	−0.863783	−	0.769587i
$563$	1.22815	−	0.194520i	0.0517603	−	0.00819803i	−0.130501	−	0.991448i	$-0.541658\pi$
$563$	1.22815	−	0.194520i	0.0517603	−	0.00819803i	0.182261	+	0.983250i	$0.441658\pi$
$564$	−16.4544	+	7.53379i	−0.692853	+	0.317230i
$565$	−23.1645	−	1.82133i	−0.974538	−	0.0766240i
$566$	36.9376	−	2.13018i	1.55260	−	0.0895381i
$567$	−5.49989	+	10.7941i	−0.230974	+	0.453311i
$568$	−1.09683	+	3.56568i	−0.0460220	+	0.149613i
$569$	16.2846	−	5.29120i	0.682687	−	0.221818i	0.0529156	−	0.998599i	$-0.483149\pi$
$569$	16.2846	−	5.29120i	0.682687	−	0.221818i	0.629771	+	0.776781i	$0.283149\pi$
$570$	45.5018	+	24.3928i	1.90586	+	1.02170i
$571$	17.0898	+	5.55283i	0.715187	+	0.232378i	0.643935	−	0.765080i	$-0.277301\pi$
$571$	17.0898	+	5.55283i	0.715187	+	0.232378i	0.0712521	+	0.997458i	$0.477301\pi$
$572$	−8.97809	−	32.1534i	−0.375393	−	1.34440i
$573$	−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	−0.601148	−	0.799138i	$-0.705290\pi$
$577$	5.22513	−	32.9902i	0.217525	−	1.37340i	0.818673	−	0.574260i	$-0.194710\pi$
$578$	21.8289	+	9.58196i	0.907963	+	0.398557i
$579$	−7.78074	+	23.9467i	−0.323357	+	0.995190i
$580$	−11.1124	−	19.9605i	−0.461416	−	0.828814i
$581$	−1.63671	−	5.03726i	−0.0679020	−	0.208981i
$582$	2.16924	−	21.7352i	0.0899180	−	0.900954i
$583$	24.3826	+	12.4235i	1.00982	+	0.514531i
$584$	3.52357	−	24.7632i	0.145806	−	1.02471i
$585$	−27.4185	+	32.1078i	−1.13362	+	1.32750i
$586$	26.8769	+	7.05073i	1.11027	+	0.291263i
$587$	−4.10199	−	25.8989i	−0.169307	−	1.06896i	−0.915230	−	0.402931i	$-0.867991\pi$
$587$	−4.10199	−	25.8989i	−0.169307	−	1.06896i	0.745923	−	0.666032i	$-0.232009\pi$
$588$	−0.255747	+	6.10486i	−0.0105468	+	0.251760i
$589$	12.5562	+	17.2821i	0.517368	+	0.712096i
$590$	−3.15909	+	9.07416i	−0.130058	+	0.373577i
$591$	−43.1876	+	59.4426i	−1.77650	+	2.44514i
$592$	25.8892	+	30.6332i	1.06404	+	1.25902i
$593$	15.9612	+	15.9612i	0.655449	+	0.655449i	0.954300	−	0.298851i	$-0.0966034\pi$
$593$	15.9612	+	15.9612i	0.655449	+	0.655449i	−0.298851	+	0.954300i	$0.596603\pi$
$594$	67.8630	+	43.5663i	2.78445	+	1.78755i
$595$	−0.843040	+	0.0664126i	−0.0345613	+	0.00272265i
$596$	21.8874	+	12.3323i	0.896543	+	0.505152i
$597$	0.637392	+	1.25095i	0.0260867	+	0.0511980i
$598$	9.37951	−	5.48107i	0.383557	−	0.224137i
$599$	−37.8626			−1.54702			−0.773512	−	0.633781i	$-0.781502\pi$
$599$	−37.8626			−1.54702			−0.773512	+	0.633781i	$0.781502\pi$
$600$	43.2003	−	0.686452i	1.76365	−	0.0280243i
$601$	−38.4991			−1.57041			−0.785206	−	0.619235i	$-0.787443\pi$
$601$	−38.4991			−1.57041			−0.785206	+	0.619235i	$0.787443\pi$
$602$	10.9827	−	6.41792i	0.447621	−	0.261575i
$603$	16.0085	+	31.4184i	0.651915	+	1.27946i
$604$	18.9626	+	10.6844i	0.771579	+	0.434742i
$605$	−38.7963	−	23.7704i	−1.57729	−	0.966403i
$606$	11.9595	+	7.67771i	0.485822	+	0.311886i
$607$	11.0930	+	11.0930i	0.450251	+	0.450251i	0.895438	−	0.445187i	$-0.146863\pi$
$607$	11.0930	+	11.0930i	0.450251	+	0.450251i	−0.445187	+	0.895438i	$0.646863\pi$
$608$	−5.50740	+	29.7236i	−0.223355	+	1.20545i
$609$	−9.17332	+	12.6260i	−0.371722	+	0.511631i
$610$	−35.4296	−	26.8878i	−1.43450	−	1.08865i
$611$	5.18998	+	7.14340i	0.209964	+	0.288991i
$612$	0.200515	−	4.78644i	0.00810535	−	0.193480i
$613$	−3.66796	−	23.1586i	−0.148148	−	0.935367i	−0.944017	−	0.329898i	$-0.892986\pi$
$613$	−3.66796	−	23.1586i	−0.148148	−	0.935367i	0.795869	−	0.605469i	$-0.207014\pi$
$614$	−38.4902	−	10.0973i	−1.55334	−	0.407494i
$615$	−56.7088	−	23.4846i	−2.28672	−	0.946989i
$616$	15.6782	+	2.23086i	0.631693	+	0.0898839i
$617$	10.3842	+	5.29103i	0.418054	+	0.213009i	0.650348	−	0.759637i	$-0.274623\pi$
$617$	10.3842	+	5.29103i	0.418054	+	0.213009i	−0.232294	+	0.972646i	$0.574623\pi$
$618$	1.61299	−	16.1618i	0.0648842	−	0.650121i
$619$	7.80479	+	24.0207i	0.313701	+	0.965472i	0.976286	+	0.216485i	$0.0694593\pi$
$619$	7.80479	+	24.0207i	0.313701	+	0.965472i	−0.662585	+	0.748987i	$0.730541\pi$
$620$	16.2161	+	7.52536i	0.651252	+	0.302226i
$621$	−8.10953	+	24.9586i	−0.325424	+	1.00155i
$622$	−11.7869	−	5.17394i	−0.472611	−	0.207456i
$623$	−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
$628$	1.88131	+	6.73759i	0.0750726	+	0.268859i
$629$	3.60647	+	1.17181i	0.143800	+	0.0467233i
$630$	−8.71873	−	18.0316i	−0.347363	−	0.718398i
$631$	12.6378	−	4.10627i	0.503103	−	0.163468i	−0.0464601	−	0.998920i	$-0.514794\pi$
$631$	12.6378	−	4.10627i	0.503103	−	0.163468i	0.549564	+	0.835452i	$0.314794\pi$
$632$	−43.0005	−	13.2273i	−1.71047	−	0.526152i
$633$	−29.6293	+	58.1507i	−1.17766	+	2.31128i
$634$	5.60420	−	0.323193i	0.222571	−	0.0128356i
$635$	−16.5774	+	40.0300i	−0.657856	+	1.58854i
$636$	27.1534	−	12.4325i	1.07670	−	0.492979i
$637$	2.94453	−	0.466368i	0.116666	−	0.0184782i
$638$	30.2005	+	26.9071i	1.19565	+	1.06526i
$639$	−6.75841	+	4.91027i	−0.267358	+	0.194247i
$640$	8.07259	+	23.9757i	0.319097	+	0.947722i
$641$	−27.6451	−	20.0854i	−1.09192	−	0.793324i	−0.112195	−	0.993686i	$-0.535788\pi$
$641$	−27.6451	−	20.0854i	−1.09192	−	0.793324i	−0.979722	+	0.200362i	$0.935788\pi$
$642$	15.6993	+	71.9999i	0.619600	+	2.84161i
$643$	11.6757	−	11.6757i	0.460444	−	0.460444i	−0.438357	−	0.898801i	$-0.644439\pi$
$643$	11.6757	−	11.6757i	0.460444	−	0.460444i	0.898801	+	0.438357i	$0.144439\pi$
$644$	0.592417	+	5.11921i	0.0233445	+	0.201725i
$645$	−32.1019	+	52.3943i	−1.26401	+	2.06303i
$646$	1.03824	+	2.66286i	0.0408488	+	0.104769i
$647$	−9.64560	+	4.91468i	−0.379208	+	0.193216i	−0.633196	−	0.773991i	$-0.718257\pi$
$647$	−9.64560	+	4.91468i	−0.379208	+	0.193216i	0.253989	+	0.967207i	$0.418257\pi$
$648$	32.4174	−	11.1000i	1.27348	−	0.436051i
$649$		−	17.0119i		−	0.667775i
$650$	−4.49410	−	20.5959i	−0.176273	−	0.807837i
$651$		−	12.2126i		−	0.478651i
$652$	−3.91896	+	10.5384i	−0.153478	+	0.412716i
$653$	10.7160	−	5.46008i	0.419350	−	0.213669i	−0.231566	−	0.972819i	$-0.574385\pi$
$653$	10.7160	−	5.46008i	0.419350	−	0.213669i	0.650916	+	0.759150i	$0.274385\pi$
$654$	13.0798	−	5.09974i	0.511460	−	0.199416i
$655$	1.67400	+	21.2497i	0.0654085	+	0.830294i
$656$	3.00589	−	35.8134i	0.117360	−	1.39828i
$657$	39.6056	−	39.6056i	1.54516	−	1.54516i
$658$	−4.09242	+	0.892335i	−0.159539	+	0.0347868i
$659$	−27.8904	−	20.2636i	−1.08646	−	0.789356i	−0.107658	−	0.994188i	$-0.534335\pi$
$659$	−27.8904	−	20.2636i	−1.08646	−	0.789356i	−0.978797	+	0.204832i	$0.934335\pi$
$660$	−71.8356	+	26.2959i	−2.79620	+	1.02357i
$661$	−18.6280	+	13.5340i	−0.724544	+	0.526412i	−0.887833	−	0.460166i	$-0.847790\pi$
$661$	−18.6280	+	13.5340i	−0.724544	+	0.526412i	0.163289	+	0.986578i	$0.447790\pi$
$662$	−20.9084	+	23.4676i	−0.812628	+	0.912092i
$663$	−3.40212	+	0.538842i	−0.132127	+	0.0209269i
$664$	−6.59021	+	13.4533i	−0.255750	+	0.522090i
$665$	9.08688	+	7.75974i	0.352374	+	0.300910i
$666$	5.17092	+	89.6645i	0.200369	+	3.47443i
$667$	−5.97571	+	11.7280i	−0.231380	+	0.454110i
$668$	3.10545	+	4.67388i	0.120154	+	0.180838i
$669$	−9.58445	+	3.11418i	−0.370556	+	0.120401i
$670$	−17.3274	−	3.11617i	−0.669417	−	0.120388i
$671$	74.8939	+	24.3345i	2.89125	+	0.939423i
$672$	12.5355	−	11.8970i	0.483569	−	0.458936i
$673$	−24.8676	−	3.93864i	−0.958576	−	0.151823i	−0.342506	−	0.939516i	$-0.611276\pi$
$673$	−24.8676	−	3.93864i	−0.958576	−	0.151823i	−0.616069	+	0.787692i	$0.711276\pi$
$674$	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	0.131097	+	0.991370i	$0.458150\pi$
$677$	−7.80404	+	49.2728i	−0.299934	+	1.89371i	−0.431030	+	0.902337i	$0.641850\pi$
$678$	18.0459	−	41.1108i	0.693047	−	1.57885i
$679$	1.56227	−	4.80818i	0.0599545	−	0.184521i
$680$	1.84312	+	1.52444i	0.0706806	+	0.0584595i
$681$	20.9318	+	64.4213i	0.802107	+	2.46863i
$682$	−31.4956	−	3.14336i	−1.20603	−	0.120365i
$683$	7.91703	+	4.03393i	0.302937	+	0.154354i	0.598851	−	0.800861i	$-0.295624\pi$
$683$	7.91703	+	4.03393i	0.302937	+	0.154354i	−0.295914	+	0.955215i	$0.595624\pi$
$684$	−49.8276	+	45.8207i	−1.90521	+	1.75200i
$685$	−1.41122	+	17.9485i	−0.0539200	+	0.685779i
$686$	−0.358854	+	1.36793i	−0.0137011	+	0.0522277i
$687$	1.98564	+	12.5369i	0.0757570	+	0.478311i
$688$	−34.9406	−	8.58075i	−1.33210	−	0.327138i
$689$	−8.56465	−	11.7882i	−0.326287	−	0.449096i
$690$	−14.2089	−	20.4402i	−0.540923	−	0.778145i
$691$	14.2571	−	19.6233i	0.542367	−	0.746505i	−0.446584	−	0.894741i	$-0.647360\pi$
$691$	14.2571	−	19.6233i	0.542367	−	0.746505i	0.988952	+	0.148237i	$0.0473598\pi$
$692$	−5.99820	+	7.56816i	−0.228017	+	0.287698i
$693$	25.0753	+	25.0753i	0.952531	+	0.952531i
$694$	22.9040	−	35.6775i	0.869425	−	1.35430i
$695$	5.41493	+	13.0700i	0.205400	+	0.495774i
$696$	43.4845	−	7.59061i	1.64828	−	0.287721i
$697$	−1.54264	−	3.02759i	−0.0584315	−	0.114678i
$698$	16.2088	+	27.7373i	0.613510	+	1.04987i
$699$	−27.5119			−1.04059
$700$	9.80305	+	1.97490i	0.370520	+	0.0746442i
$701$	5.83965			0.220560			0.110280	−	0.993901i	$-0.464825\pi$
$701$	5.83965			0.220560			0.110280	+	0.993901i	$0.464825\pi$
$702$	−21.6648	−	37.0740i	−0.817686	−	1.39927i
$703$	−24.3261	−	47.7427i	−0.917477	−	1.80065i
$704$	−27.4551	−	35.3905i	−1.03475	−	1.33383i
$705$	15.3844	−	13.1415i	0.579410	−	0.494939i
$706$	−8.40169	+	13.0873i	−0.316202	+	0.492546i
$707$	2.32592	+	2.32592i	0.0874752	+	0.0874752i
$708$	−14.5498	−	11.5316i	−0.546816	−	0.433384i
$709$	10.3211	−	14.2058i	0.387617	−	0.533509i	−0.569966	−	0.821669i	$-0.693043\pi$
$709$	10.3211	−	14.2058i	0.387617	−	0.533509i	0.957582	+	0.288160i	$0.0930435\pi$
$710$	0.0869929	−	4.16999i	0.00326479	−	0.156497i
$711$	−59.2156	−	81.5033i	−2.22076	−	3.05661i
$712$	10.0152	−	7.52009i	0.375335	−	0.281827i
$713$	−1.61130	−	10.1734i	−0.0603437	−	0.380995i
$714$	0.414621	−	1.58051i	0.0155168	−	0.0591489i
$715$	19.5040	+	31.8222i	0.729408	+	1.19008i
$716$	−3.06029	−	3.32790i	−0.114368	−	0.124370i
$717$	11.6111	+	5.91613i	0.433623	+	0.220942i
$718$	−34.2967	−	3.42292i	−1.27994	−	0.127742i
$719$	10.0291	+	30.8663i	0.374021	+	1.15112i	0.944137	+	0.329553i	$0.106898\pi$
$719$	10.0291	+	30.8663i	0.374021	+	1.15112i	−0.570116	+	0.821564i	$0.693102\pi$
$720$	−17.7815	+	53.7872i	−0.662679	+	2.00453i
$721$	1.16167	−	3.57524i	0.0432627	−	0.133149i
$722$	5.43244	−	12.3758i	0.202175	−	0.460579i
$723$	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	$-0.653697\pi$
$727$	−31.8050	−	5.03742i	−1.17958	−	0.186827i	−0.715273	+	0.698846i	$0.753697\pi$
$728$	−6.89895	−	4.84835i	−0.255692	−	0.179692i
$729$	−15.8038	−	5.13496i	−0.585325	−	0.190184i
$730$	3.79765	+	27.7059i	0.140557	+	1.02544i
$731$	−3.23519	+	1.05118i	−0.119658	+	0.0388792i
$732$	71.5799	−	47.5596i	2.64567	−	1.75785i
$733$	9.36102	−	18.3720i	0.345757	−	0.678587i	−0.650998	−	0.759079i	$-0.725649\pi$
$733$	9.36102	−	18.3720i	0.345757	−	0.678587i	0.996755	+	0.0804928i	$0.0256494\pi$
$734$	2.40631	+	41.7257i	0.0888185	+	1.54013i
$735$	−1.59527	−	6.64256i	−0.0588423	−	0.245014i
$736$	8.87270	−	11.5643i	0.327052	−	0.426267i
$737$	30.7872	−	4.87621i	1.13406	−	0.179618i
$738$	53.5364	−	60.0891i	1.97070	−	2.21191i
$739$	−20.0121	+	14.5396i	−0.736156	+	0.534849i	−0.891505	−	0.453011i	$-0.850350\pi$
$739$	−20.0121	+	14.5396i	−0.736156	+	0.534849i	0.155349	+	0.987860i	$0.450350\pi$
$740$	−37.2218	−	25.0068i	−1.36830	−	0.919270i
$741$	39.3764	+	28.6086i	1.44653	+	1.05096i
$742$	6.75342	−	1.47255i	0.247926	−	0.0540592i
$743$	−14.9753	+	14.9753i	−0.549391	+	0.549391i	−0.926265	−	0.376873i	$-0.876999\pi$
$743$	−14.9753	+	14.9753i	−0.549391	+	0.549391i	0.376873	+	0.926265i	$0.376999\pi$
$744$	−24.0378	+	24.8066i	−0.881270	+	0.909455i
$745$	−27.3123	−	6.55494i	−1.00065	−	0.240154i
$746$	1.19113	−	0.464417i	0.0436104	−	0.0170035i
$747$	−29.8900	+	15.2297i	−1.09362	+	0.557226i
$748$	−3.96930	−	1.47608i	−0.145132	−	0.0539708i
$749$			17.0560i			0.623211i
$750$	−46.2405	+	13.9727i	−1.68846	+	0.510212i
$751$			3.84504i			0.140308i	0.997536	+	0.0701538i	$0.0223490\pi$
$751$			3.84504i			0.140308i	−0.997536	+	0.0701538i	$0.977651\pi$
$752$	10.0690	+	6.24249i	0.367179	+	0.227640i
$753$	−14.2264	+	7.24870i	−0.518438	+	0.264157i
$754$	−7.82366	−	20.0661i	−0.284921	−	0.730763i
$755$	−23.6626	−	5.67901i	−0.861172	−	0.206680i
$756$	20.2345	−	2.34162i	0.735922	−	0.0851641i
$757$	−16.8459	+	16.8459i	−0.612276	+	0.612276i	−0.943539	−	0.331263i	$-0.892525\pi$
$757$	−16.8459	+	16.8459i	−0.612276	+	0.612276i	0.331263	+	0.943539i	$0.392525\pi$
$758$	5.84739	+	26.8173i	0.212387	+	0.974047i
$759$	35.6574	+	25.9066i	1.29428	+	0.940352i
$760$	−3.18418	−	33.6473i	−0.115502	−	1.22052i
$761$	6.11744	−	4.44458i	0.221757	−	0.161116i	−0.471360	−	0.881941i	$-0.656237\pi$
$761$	6.11744	−	4.44458i	0.221757	−	0.161116i	0.693117	+	0.720825i	$0.256237\pi$
$762$	−62.5068	−	55.6904i	−2.26438	−	2.01745i
$763$	3.20928	−	0.508301i	0.116184	−	0.0184017i
$764$	8.93216	+	19.5085i	0.323154	+	0.705793i
$765$	1.25075	+	5.20801i	0.0452209	+	0.188296i
$766$	−20.9701	+	1.20934i	−0.757680	+	0.0436952i
$767$	−4.11236	+	8.07096i	−0.148489	+	0.291425i
$768$	−48.8791	−	0.507963i	−1.76377	−	0.0183295i
$769$	−0.160415	+	0.0521219i	−0.00578471	+	0.00187957i	−0.311908	−	0.950112i	$-0.600968\pi$
$769$	−0.160415	+	0.0521219i	−0.00578471	+	0.00187957i	0.306123	+	0.951992i	$0.400968\pi$
$770$	−17.5413	+	2.40439i	−0.632145	+	0.0866481i
$771$	−6.65125	−	2.16112i	−0.239539	−	0.0778309i
$772$	15.8759	−	4.43298i	0.571387	−	0.159547i
$773$	−13.8945	−	2.20067i	−0.499750	−	0.0791525i	−0.0985293	−	0.995134i	$-0.531414\pi$
$773$	−13.8945	−	2.20067i	−0.499750	−	0.0791525i	−0.401220	+	0.915982i	$0.631414\pi$
$774$	−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
$778$	33.1492	+	14.5511i	1.18846	+	0.521681i
$779$	−14.8371	+	45.6639i	−0.531594	+	1.63608i
$780$	40.4376	+	4.88958i	1.44790	+	0.175075i
$781$	2.28200	+	7.02329i	0.0816565	+	0.251313i
$782$	0.136860	−	1.37130i	0.00489409	−	0.0490374i
$783$	46.3568	+	23.6200i	1.65666	+	0.844109i
$784$	3.42137	−	2.07225i	0.122192	−	0.0740088i
$785$	−4.08696	−	6.66819i	−0.145870	−	0.237998i
$786$	−39.8383	−	10.4510i	−1.42098	−	0.372773i
$787$	−5.74297	−	36.2597i	−0.204715	−	1.29252i	−0.849269	−	0.527960i	$-0.822957\pi$
$787$	−5.74297	−	36.2597i	−0.204715	−	1.29252i	0.644555	−	0.764558i	$-0.277043\pi$
$788$	48.0577	+	2.01325i	1.71198	+	0.0717190i
$789$	15.1142	+	20.8029i	0.538079	+	0.740602i
$790$	50.2882	+	1.04909i	1.78917	+	0.0373251i
$791$	6.10795	−	8.40687i	0.217174	−	0.298914i
$792$	−1.57847	−	100.289i	−0.0560887	−	3.56360i
$793$	−29.6495	−	29.6495i	−1.05288	−	1.05288i
$794$	17.4645	+	11.2118i	0.619792	+	0.397891i
$795$	−25.3877	+	21.6865i	−0.900410	+	0.769140i
$796$	0.451174	−	0.800742i	0.0159914	−	0.0283815i
$797$	−5.98796	−	11.7520i	−0.212104	−	0.416278i	0.760303	−	0.649569i	$-0.225051\pi$
$797$	−5.98796	−	11.7520i	−0.212104	−	0.416278i	−0.972407	+	0.233291i	$0.925051\pi$
$798$	−19.9345	+	11.6490i	−0.705673	+	0.412372i
$799$	1.12010			0.0396264
$800$	−16.0251	−	23.3066i	−0.566572	−	0.824012i
$801$	28.0454			0.990936
$802$	36.4031	−	21.2728i	1.28544	−	0.751167i
$803$	−22.4784	−	44.1163i	−0.793245	−	1.55683i
$804$	16.6987	−	29.6369i	0.588919	−	1.04521i
$805$	−2.20529	−	5.32290i	−0.0777262	−	0.187608i
$806$	14.1826	+	9.10487i	0.499561	+	0.320705i
$807$	57.3560	+	57.3560i	2.01903	+	2.01903i
$808$	−0.146415	−	9.30253i	−0.00515087	−	0.327262i
$809$	−20.0269	+	27.5646i	−0.704107	+	0.969121i	0.295796	+	0.955251i	$0.404415\pi$
$809$	−20.0269	+	27.5646i	−0.704107	+	0.969121i	−0.999904	+	0.0138696i	$0.995585\pi$
$810$	−31.4560	+	21.8665i	−1.10525	+	0.768310i
$811$	21.3365	+	29.3672i	0.749226	+	1.03122i	0.998034	+	0.0626679i	$0.0199609\pi$
$811$	21.3365	+	29.3672i	0.749226	+	1.03122i	−0.248809	+	0.968553i	$0.580039\pi$
$812$	10.2078	+	0.427627i	0.358222	+	0.0150068i
$813$	−13.3830	−	84.4970i	−0.469362	−	2.96344i
$814$	76.7957	+	20.1461i	2.69169	+	0.706122i
$815$	0.985335	−	12.5319i	0.0345148	−	0.438975i
$816$	−3.95306	+	2.39428i	−0.138385	+	0.0838165i
$817$	42.8276	+	21.8218i	1.49835	+	0.763447i
$818$	−2.53578	+	25.4078i	−0.0886615	+	0.888364i
$819$	−5.83492	−	17.9580i	−0.203889	−	0.627505i
$820$	7.73956	+	39.4290i	0.270277	+	1.37692i
$821$	−11.3722	+	35.0001i	−0.396893	+	1.22151i	0.530584	+	0.847632i	$0.321973\pi$
$821$	−11.3722	+	35.0001i	−0.396893	+	1.22151i	−0.927477	+	0.373880i	$0.878027\pi$
$822$	−31.8538	−	13.9825i	−1.11103	−	0.487695i
$823$	−3.87781	+	24.4835i	−0.135172	+	0.853442i	0.823165	+	0.567802i	$0.192206\pi$
$823$	−3.87781	+	24.4835i	−0.135172	+	0.853442i	−0.958337	+	0.285640i	$0.907794\pi$
$824$	−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	$-0.390043\pi$
$827$	10.6371	+	1.68475i	0.369889	+	0.0585846i	0.0312769	+	0.999511i	$0.490043\pi$
$828$	31.4373	−	8.77814i	1.09252	−	0.305061i
$829$	14.5747	+	4.73561i	0.506201	+	0.164475i	0.550974	−	0.834523i	$-0.314256\pi$
$829$	14.5747	+	4.73561i	0.506201	+	0.164475i	−0.0447730	+	0.998997i	$0.514256\pi$
$830$	2.96458	−	16.4845i	0.102902	−	0.572186i
$831$	−5.34426	+	1.73645i	−0.185390	+	0.0602369i
$832$	4.47043	+	23.4271i	0.154984	+	0.812190i
$833$	0.171693	−	0.336967i	0.00594882	−	0.0116752i
$834$	−27.2904	+	1.57383i	−0.944989	+	0.0544972i
$835$	−4.77098	−	4.07418i	−0.165107	−	0.140993i
$836$	24.9113	+	54.4080i	0.861574	+	1.88174i
$837$	−40.2119	+	6.36893i	−1.38993	+	0.220143i
$838$	−3.80558	−	3.39058i	−0.131461	−	0.117126i
$839$	−0.527551	+	0.383288i	−0.0182131	+	0.0132326i	−0.596855	−	0.802349i	$-0.703583\pi$
$839$	−0.527551	+	0.383288i	−0.0182131	+	0.0132326i	0.578641	+	0.815582i	$0.303583\pi$
$840$	−9.83405	+	16.6325i	−0.339307	+	0.573875i
$841$	−2.34996	−	1.70735i	−0.0810332	−	0.0588740i
$842$	7.24444	+	33.2244i	0.249660	+	1.14499i
$843$	−41.8944	+	41.8944i	−1.44292	+	1.44292i
$844$	42.4413	−	4.91149i	1.46089	−	0.169060i
$845$	0.722144	+	9.16688i	0.0248425	+	0.315350i
$846$	9.63699	+	24.7169i	0.331327	+	0.849783i
$847$	18.1301	−	9.23774i	0.622957	−	0.317413i
$848$	−16.6161	−	10.3015i	−0.570600	−	0.353755i
$849$		−	79.9284i		−	2.74313i
$850$	−2.44882	−	1.07449i	−0.0839940	−	0.0368547i
$851$			25.8364i			0.885660i
$852$	7.55371	+	2.80903i	0.258786	+	0.0962356i
$853$	−14.7227	+	7.50160i	−0.504096	+	0.256850i	−0.687495	−	0.726189i	$-0.741290\pi$
$853$	−14.7227	+	7.50160i	−0.504096	+	0.256850i	0.183399	+	0.983039i	$0.441290\pi$
$854$	18.5320	−	7.22552i	0.634151	−	0.247252i
$855$	39.5394	−	64.5333i	1.35222	−	2.20699i
$856$	33.5709	−	34.6445i	1.14743	−	1.18413i
$857$	13.6502	−	13.6502i	0.466281	−	0.466281i	−0.434426	−	0.900707i	$-0.643049\pi$
$857$	13.6502	−	13.6502i	0.466281	−	0.466281i	0.900707	+	0.434426i	$0.143049\pi$
$858$	−70.4621	+	15.3640i	−2.40554	+	0.524517i
$859$	−24.0915	−	17.5035i	−0.821993	−	0.597213i	0.0952898	−	0.995450i	$-0.469622\pi$
$859$	−24.0915	−	17.5035i	−0.821993	−	0.597213i	−0.917283	+	0.398237i	$0.869622\pi$
$860$	40.1984	−	1.47785i	1.37075	−	0.0503941i
$861$	22.2072	−	16.1345i	0.756821	−	0.549862i
$862$	−7.75480	+	8.70397i	−0.264130	+	0.296459i
$863$	−30.4259	+	4.81899i	−1.03571	+	0.164040i	−0.651064	−	0.759023i	$-0.725677\pi$
$863$	−30.4259	+	4.81899i	−1.03571	+	0.164040i	−0.384647	+	0.923064i	$0.625677\pi$
$864$	−45.7099	−	35.0708i	−1.55508	−	1.19313i
$865$	4.13098	−	9.97519i	0.140457	−	0.339167i
$866$	1.76614	+	30.6251i	0.0600159	+	1.04068i
$867$	23.3805	−	45.8867i	0.794042	−	1.55840i
$868$	−6.65903	+	4.42444i	−0.226022	+	0.150175i
$869$	−84.6976	+	27.5199i	−2.87317	+	0.933549i
$870$	−44.4310	+	21.4835i	−1.50635	+	0.728358i
$871$	−15.7851	−	5.12890i	−0.534859	−	0.173786i
$872$	−7.51926	−	5.28429i	−0.254634	−	0.178949i
$873$	−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	−0.979259	−	0.202611i	$-0.935057\pi$
$877$	0.434792	−	2.74517i	0.0146819	−	0.0926978i	0.993941	+	0.109913i	$0.0350573\pi$
$878$	−17.2128	+	39.2130i	−0.580905	+	1.32337i
$879$	18.5492	−	57.0886i	0.625649	−	1.92555i
$880$	40.3629	+	29.6423i	1.36063	+	0.999242i
$881$	−8.47893	−	26.0955i	−0.285662	−	0.879179i	−0.986199	−	0.165562i	$-0.947056\pi$
$881$	−8.47893	−	26.0955i	−0.285662	−	0.879179i	0.700537	−	0.713616i	$-0.252944\pi$
$882$	8.91291	+	0.889536i	0.300113	+	0.0299523i
$883$	3.24114	+	1.65144i	0.109073	+	0.0555754i	0.507676	−	0.861548i	$-0.330505\pi$
$883$	3.24114	+	1.65144i	0.109073	+	0.0555754i	−0.398603	+	0.917124i	$0.630505\pi$
$884$	1.52634	+	1.65981i	0.0513363	+	0.0558256i
$885$	19.1774	+	7.94183i	0.644640	+	0.266962i
$886$	5.12869	−	19.5502i	0.172302	−	0.656802i
$887$	7.77216	+	49.0715i	0.260963	+	1.64766i	0.675306	+	0.737538i	$0.264012\pi$
$887$	7.77216	+	49.0715i	0.260963	+	1.64766i	−0.414343	+	0.910121i	$0.635988\pi$
$888$	69.2868	−	52.0252i	2.32511	−	1.74585i
$889$	−11.3891	−	15.6758i	−0.381979	−	0.525749i
$890$	−8.46494	+	11.1541i	−0.283745	+	0.373887i
$891$	39.8685	−	54.8743i	1.33565	−	1.83836i
$892$	5.17032	+	4.09777i	0.173115	+	0.137204i
$893$	−11.1916	−	11.1916i	−0.374513	−	0.374513i
$894$	29.3195	−	45.6708i	0.980591	−	1.52746i
$895$	4.31007	+	2.64077i	0.144070	+	0.0882711i
$896$	−11.0283	−	2.52501i	−0.368431	−	0.0843548i
$897$	−10.6545	−	20.9105i	−0.355742	−	0.698183i
$898$	18.4289	+	31.5366i	0.614981	+	1.05239i
$899$	−20.4204			−0.681057
$900$	2.64147	−	63.2818i	0.0880491	−	2.10939i
$901$	−1.84842			−0.0615799
$902$	−35.8940	−	61.4238i	−1.19514	−	2.04519i
$903$	−12.4756	−	24.4847i	−0.415161	−	0.814799i
$904$	−28.9537	+	5.05412i	−0.962985	+	0.168098i
$905$	17.1062	−	1.34758i	0.568629	−	0.0447952i
$906$	25.4016	−	39.5679i	0.843911	−	1.31456i
$907$	−9.85827	−	9.85827i	−0.327338	−	0.327338i	0.524235	−	0.851574i	$-0.324351\pi$
$907$	−9.85827	−	9.85827i	−0.327338	−	0.327338i	−0.851574	+	0.524235i	$0.824351\pi$
$908$	27.5430	−	34.7520i	0.914045	−	1.15329i
$909$	12.2457	−	16.8548i	0.406166	−	0.559039i
$910$	8.90336	+	3.09963i	0.295143	+	0.102752i
$911$	−16.2149	−	22.3179i	−0.537224	−	0.739425i	0.450986	−	0.892531i	$-0.351072\pi$
$911$	−16.2149	−	22.3179i	−0.537224	−	0.739425i	−0.988210	+	0.153106i	$0.951072\pi$
$912$	63.4200	+	15.5748i	2.10005	+	0.515732i
$913$	4.63901	+	29.2895i	0.153529	+	0.969342i
$914$	5.16302	−	19.6811i	0.170778	−	0.650992i
$915$	−62.3956	+	73.0670i	−2.06273	+	2.41552i
$916$	6.11644	−	5.62459i	0.202093	−	0.185842i
$917$	−8.49360	−	4.32771i	−0.280483	−	0.142913i
$918$	−5.42027	−	0.540960i	−0.178896	−	0.0178543i
$919$	−17.0836	−	52.5779i	−0.563536	−	1.73439i	−0.672261	−	0.740314i	$-0.734677\pi$
$919$	−17.0836	−	52.5779i	−0.563536	−	1.73439i	0.108725	−	0.994072i	$-0.465323\pi$
$920$	−5.99751	+	15.1526i	−0.197732	+	0.499568i
$921$	−26.5642	+	81.7562i	−0.875320	+	2.69396i
$922$	−5.58509	+	12.7235i	−0.183935	+	0.419027i
$923$	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
$928$	−19.8926	−	20.9603i	−0.653006	−	0.688056i
$929$	−1.13019	−	0.367221i	−0.0370803	−	0.0120481i	0.290418	−	0.956900i	$-0.406206\pi$
$929$	−1.13019	−	0.367221i	−0.0370803	−	0.0120481i	−0.327498	+	0.944852i	$0.606206\pi$
$930$	18.2469	−	34.0373i	0.598339	−	1.11613i
$931$	−5.08233	+	1.65135i	−0.166566	+	0.0541207i
$932$	9.96710	+	15.0010i	0.326483	+	0.491376i
$933$	−12.6247	+	24.7773i	−0.413313	+	0.811173i
$934$	0.661197	+	11.4652i	0.0216350	+	0.375154i
$935$	4.72017	+	0.371127i	0.154366	+	0.0121372i
$936$	−23.4944	+	47.9616i	−0.767937	+	1.56767i
$937$	43.0017	−	6.81080i	1.40481	−	0.222499i	0.592424	−	0.805626i	$-0.298171\pi$
$937$	43.0017	−	6.81080i	1.40481	−	0.222499i	0.812381	+	0.583127i	$0.198171\pi$
$938$	5.23755	−	5.87862i	0.171012	−	0.191944i
$939$	35.4674	−	25.7686i	1.15744	−	0.840926i
$940$	−12.7390	−	3.62750i	−0.415501	−	0.118316i
$941$	27.8992	+	20.2699i	0.909486	+	0.660780i	0.940885	−	0.338726i	$-0.109996\pi$
$941$	27.8992	+	20.2699i	0.909486	+	0.660780i	−0.0313986	+	0.999507i	$0.509996\pi$
$942$	14.7650	−	3.21944i	0.481069	−	0.104895i
$943$	16.3703	−	16.3703i	0.533091	−	0.533091i
$944$	−1.01651	+	12.1111i	−0.0330846	+	0.394183i
$945$	−21.0397	+	8.71677i	−0.684420	+	0.283556i
$946$	−66.3554	+	25.8717i	−2.15740	+	0.841160i
$947$	52.4559	−	26.7276i	1.70459	−	0.868531i	0.719929	−	0.694048i	$-0.244175\pi$
$947$	52.4559	−	26.7276i	1.70459	−	0.868531i	0.984660	−	0.174483i	$-0.0558255\pi$
$948$	−33.8756	+	91.0942i	−1.10023	+	2.95860i
$949$			26.3639i			0.855810i
$950$	13.7318	+	35.2035i	0.445518	+	1.14215i
$951$		−	12.1268i		−	0.393239i
$952$	−1.01199	+	0.346517i	−0.0327989	+	0.0112307i
$953$	−12.8718	+	6.55853i	−0.416960	+	0.212452i	−0.649868	−	0.760047i	$-0.725176\pi$
$953$	−12.8718	+	6.55853i	−0.416960	+	0.212452i	0.232908	+	0.972499i	$0.425176\pi$
$954$	−15.9032	−	40.7884i	−0.514885	−	1.32057i
$955$	−15.5808	−	18.2400i	−0.504182	−	0.590231i
$956$	−0.980686	−	8.47434i	−0.0317177	−	0.274080i
$957$	61.7870	−	61.7870i	1.99729	−	1.99729i
$958$	5.84256	+	26.7951i	0.188765	+	0.865711i
$959$	−6.51389	−	4.73261i	−0.210344	−	0.152824i
$960$	52.7125	−	14.4282i	1.70129	−	0.465668i
$961$	−12.1518	+	8.82879i	−0.391993	+	0.284800i
$962$	−31.5642	−	28.1221i	−1.01767	−	0.906693i
$963$	106.697	−	16.8992i	3.43827	−	0.544568i
$964$	−27.3525	+	12.5236i	−0.880966	+	0.403359i
$965$	−15.7124	+	9.63021i	−0.505800	+	0.310007i
$966$	11.1143	−	0.640959i	0.357597	−	0.0206225i
$967$	−4.84598	+	9.51076i	−0.155836	+	0.305846i	−0.955703	−	0.294331i	$-0.904903\pi$
$967$	−4.84598	+	9.51076i	−0.155836	+	0.305846i	0.799867	+	0.600177i	$0.204903\pi$
$968$	−55.0088	−	16.9211i	−1.76805	−	0.543865i
$969$	5.87213	−	1.90797i	0.188640	−	0.0612929i
$970$	11.5380	−	11.0665i	0.370464	−	0.355323i
$971$	−15.9646	−	5.18721i	−0.512328	−	0.166465i	0.0414328	−	0.999141i	$-0.486808\pi$
$971$	−15.9646	−	5.18721i	−0.512328	−	0.166465i	−0.553761	+	0.832676i	$0.686808\pi$
$972$	−3.47303	−	12.4380i	−0.111398	−	0.398951i
$973$	−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	−0.929519	−	0.368775i	$-0.879777\pi$
$977$	2.13998	−	13.5113i	0.0684639	−	0.432264i	0.997983	−	0.0634888i	$-0.0202227\pi$
$978$	22.2408	+	9.76276i	0.711182	+	0.312179i
$979$	7.66111	−	23.5785i	0.244850	−	0.753571i
$980$	−3.04396	+	3.27632i	−0.0972359	+	0.104658i
$981$	−6.35956	−	19.5727i	−0.203045	−	0.624909i
$982$	0.0433436	−	0.434291i	0.00138315	−	0.0138588i
$983$	17.3886	+	8.85995i	0.554611	+	0.282588i	0.708749	−	0.705461i	$-0.249260\pi$
$983$	17.3886	+	8.85995i	0.554611	+	0.282588i	−0.154138	+	0.988049i	$0.549260\pi$
$984$	−76.8651	−	10.9372i	−2.45037	−	0.348664i
$985$	−52.2904	+	12.5580i	−1.66611	+	0.400131i
$986$	−2.64272	−	0.693275i	−0.0841612	−	0.0220784i
$987$	1.41550	+	8.93713i	0.0450559	+	0.284472i
$988$	1.33363	−	31.8347i	0.0424285	−	1.01280i
$989$	−13.6228	−	18.7502i	−0.433181	−	0.596222i
$990$	32.4212	+	107.351i	1.03041	+	3.41184i
$991$	−17.6031	+	24.2285i	−0.559180	+	0.769645i	−0.991222	−	0.132209i	$-0.957793\pi$
$991$	−17.6031	+	24.2285i	−0.559180	+	0.769645i	0.432042	+	0.901853i	$0.357793\pi$
$992$	22.2345	+	4.11977i	0.705947	+	0.130803i
$993$	48.0121	+	48.0121i	1.52362	+	1.52362i
$994$	1.56967	+	1.00769i	0.0497868	+	0.0319619i
$995$	−0.239810	+	0.999211i	−0.00760248	+	0.0316771i
$996$	28.1952	+	15.8864i	0.893398	+	0.503380i
$997$	−25.2660	−	49.5872i	−0.800181	−	1.57044i	−0.821184	−	0.570664i	$-0.806686\pi$
$997$	−25.2660	−	49.5872i	−0.800181	−	1.57044i	0.0210032	−	0.999779i	$-0.493314\pi$
$998$	−11.4526	+	6.69251i	−0.362525	+	0.211848i
$999$	102.123			3.23101

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.15	✓	720	1.1	even	1	trivial
700.2.bj.a.323.68	yes	720	4.3	odd	2	inner
700.2.bj.a.687.15	yes	720	100.87	even	20	inner
700.2.bj.a.687.68	yes	720	25.12	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22102 + 0.713522i) q^{2} +(1.38699 + 2.72212i) q^{3} +(0.981773 - 1.74245i) q^{4} +(-0.521836 + 2.17432i) q^{5} +(-3.63583 - 2.33411i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.0445120 + 2.82808i) q^{8} +(-3.72285 + 5.12406i) q^{9} +(-0.914257 - 3.02723i) q^{10} +(3.29096 + 4.52962i) q^{11} +(6.10486 + 0.255747i) q^{12} +(-0.466368 - 2.94453i) q^{13} +(1.36793 + 0.358854i) q^{14} +(-6.64256 + 1.59527i) q^{15} +(-2.07225 - 3.42137i) q^{16} +(-0.336967 - 0.171693i) q^{17} +(0.889536 - 8.91291i) q^{18} +(1.65135 + 5.08233i) q^{19} +(3.27632 + 3.04396i) q^{20} +(0.944080 - 2.90558i) q^{21} +(-7.25031 - 3.18258i) 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} +(-1.92631 + 0.537878i) q^{28} +(-4.85833 - 1.57857i) q^{29} +(6.97243 - 6.68746i) q^{30} +(3.80180 - 1.23528i) q^{31} +(4.97148 + 2.69897i) q^{32} +(-7.76564 + 15.2409i) q^{33} +(0.533950 - 0.0307927i) q^{34} +(1.90647 - 1.16849i) q^{35} +(5.27342 + 11.5175i) q^{36} +(-9.90352 + 1.56856i) q^{37} +(-5.64268 - 5.02734i) q^{38} +(7.36852 - 5.35354i) q^{39} +(-6.17238 - 1.37901i) q^{40} +(7.26889 + 5.28115i) q^{41} +(0.920456 + 4.22139i) q^{42} +(6.36022 - 6.36022i) q^{43} +(11.1236 - 1.28727i) q^{44} +(-9.19866 - 10.7686i) q^{45} +(1.32372 + 3.39506i) q^{46} +(-2.63896 + 1.34462i) q^{47} +(6.43921 - 10.3863i) q^{48} +1.00000i q^{49} +(7.05928 - 0.408173i) q^{50} -1.15540i q^{51} +(-5.58855 - 2.07824i) q^{52} +(4.35488 - 2.21892i) q^{53} +(13.4195 - 5.23221i) q^{54} +(-11.5662 + 4.79190i) q^{55} +(1.96828 - 2.03123i) q^{56} +(-11.5443 + 11.5443i) q^{57} +(7.05846 - 1.53907i) q^{58} +(-2.45814 - 1.78594i) q^{59} +(-3.74181 + 13.1405i) q^{60} +(11.3787 - 8.26713i) q^{61} +(-3.76067 + 4.22096i) q^{62} +(6.25571 - 0.990807i) q^{63} +(-7.99604 + 0.251767i) q^{64} +(6.64573 + 0.522527i) q^{65} +(-1.39275 - 24.1504i) q^{66} +(2.52751 - 4.96052i) q^{67} +(-0.629992 + 0.418584i) q^{68} +(7.48678 - 2.43260i) q^{69} +(-1.49410 + 2.78705i) q^{70} +(1.25440 + 0.407579i) q^{71} +(-14.6570 - 10.3004i) 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} +(-5.17723 + 11.7944i) q^{78} +(-4.91522 + 15.1275i) q^{79} +(8.52055 - 2.72034i) q^{80} +(-3.74360 - 11.5216i) q^{81} +(-12.6437 - 1.26188i) q^{82} +(4.71921 + 2.40456i) q^{83} +(-4.13595 - 4.49763i) q^{84} +(0.549158 - 0.643080i) q^{85} +(-3.22779 + 12.3041i) q^{86} +(-2.44141 - 15.4144i) q^{87} +(-12.6636 + 9.50871i) q^{88} +(-2.60270 - 3.58231i) q^{89} +(18.9154 + 6.58522i) q^{90} +(-1.75232 + 2.41187i) q^{91} +(-4.03873 - 3.20093i) q^{92} +(8.63563 + 8.63563i) q^{93} +(2.26280 - 3.52475i) q^{94} +(-11.9124 + 0.938426i) q^{95} +(-0.451533 + 17.2764i) q^{96} +(2.29520 + 4.50459i) q^{97} +(-0.713522 - 1.22102i) 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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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