LMFDB - Embedded newform 84.2.n.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(11,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("84.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	84.11
Dual form			84.2.n.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32175 + 0.502962i) q^{2} +(-1.72058 - 0.199011i) q^{3} +(1.49406 - 1.32958i) q^{4} +(1.79791 - 1.03802i) q^{5} +(2.37428 - 0.602344i) q^{6} +(2.61347 + 0.412056i) q^{7} +(-1.30604 + 2.50883i) q^{8} +(2.92079 + 0.684828i) q^{9} +(-1.85431 + 2.27629i) q^{10} +(1.99399 - 3.45368i) q^{11} +(-2.83525 + 1.99032i) q^{12} -1.30998 q^{13} +(-3.66160 + 0.769840i) q^{14} +(-3.30003 + 1.42820i) q^{15} +(0.464417 - 3.97295i) q^{16} +(-2.54752 - 1.47081i) q^{17} +(-4.20500 + 0.563873i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(1.30604 - 3.94134i) q^{20} +(-4.41467 - 1.22908i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(3.75063 + 6.49627i) q^{23} +(2.74644 - 4.05673i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(1.73147 - 0.658872i) q^{26} +(-4.88916 - 1.75957i) q^{27} +(4.45253 - 2.85919i) q^{28} +0.865568i q^{29} +(3.64349 - 3.54752i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(1.38440 + 5.48484i) q^{32} +(-4.11813 + 5.54551i) q^{33} +(4.10695 + 0.662741i) q^{34} +(5.12651 - 1.97200i) q^{35} +(5.27436 - 2.86026i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(0.979678 - 1.20262i) q^{38} +(2.25393 + 0.260701i) q^{39} +(0.256080 + 5.86637i) q^{40} +7.01712i q^{41} +(6.45329 - 0.595872i) q^{42} +4.27597i q^{43} +(-1.61283 - 7.81117i) q^{44} +(5.96219 - 1.80059i) q^{45} +(-8.22478 - 6.70004i) q^{46} +(-3.75063 - 6.49627i) q^{47} +(-1.58973 + 6.74335i) q^{48} +(6.66042 + 2.15379i) q^{49} +(0.155459 - 0.963368i) q^{50} +(4.09050 + 3.03763i) q^{51} +(-1.95719 + 1.74173i) q^{52} +(-4.27909 - 2.47053i) q^{53} +(7.34726 - 0.133348i) q^{54} -8.27923i q^{55} +(-4.44708 + 6.01859i) q^{56} +(1.74349 - 0.754555i) q^{57} +(-0.435348 - 1.14407i) q^{58} +(-2.44458 + 4.23414i) q^{59} +(-3.03152 + 6.52148i) q^{60} +(-2.05347 - 3.55672i) q^{61} +(5.13856 + 0.829212i) q^{62} +(7.35120 + 2.99330i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(-2.35524 + 1.35980i) q^{65} +(2.65397 - 9.40106i) q^{66} +(2.09778 + 1.21116i) q^{67} +(-5.76170 + 1.18966i) q^{68} +(-5.16042 - 11.9238i) q^{69} +(-5.78413 + 5.18494i) q^{70} -0.901192 q^{71} +(-5.53280 + 6.43336i) q^{72} +(-6.50543 + 11.2677i) q^{73} +(4.57989 + 3.73085i) q^{74} +(0.712537 - 0.959509i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(6.63432 - 8.20446i) q^{77} +(-3.11026 + 0.789060i) q^{78} +(-8.97336 + 5.18077i) q^{79} +(-3.28904 - 7.62509i) q^{80} +(8.06202 + 4.00048i) q^{81} +(-3.52935 - 9.27489i) q^{82} -12.4386 q^{83} +(-8.22995 + 4.03336i) q^{84} -6.10695 q^{85} +(-2.15065 - 5.65178i) q^{86} +(0.172258 - 1.48928i) q^{87} +(6.06049 + 9.51324i) q^{88} +(7.38393 - 4.26311i) q^{89} +(-6.97491 + 5.37869i) q^{90} +(-3.42360 - 0.539786i) q^{91} +(14.2410 + 4.71904i) q^{92} +(5.11797 + 3.80064i) q^{93} +(8.22478 + 6.70004i) q^{94} +(-1.13854 + 1.97200i) q^{95} +(-1.29043 - 9.71261i) q^{96} +15.3909 q^{97} +(-9.88670 + 0.503167i) q^{98} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.32175	+	0.502962i	−0.934620	+	0.355648i
$2$	−1.32175	+	0.502962i	−0.934620	+	0.355648i
$3$	−1.72058	−	0.199011i	−0.993377	−	0.114899i
$3$	−1.72058	−	0.199011i	−0.993377	−	0.114899i
$4$	1.49406	−	1.32958i	0.747029	−	0.664792i
$5$	1.79791	−	1.03802i	0.804051	−	0.464219i	−0.0408349	−	0.999166i	$-0.513002\pi$
$5$	1.79791	−	1.03802i	0.804051	−	0.464219i	0.844886	+	0.534947i	$0.179668\pi$
$6$	2.37428	−	0.602344i	0.969294	−	0.245906i
$7$	2.61347	+	0.412056i	0.987798	+	0.155742i
$7$	2.61347	+	0.412056i	0.987798	+	0.155742i
$8$	−1.30604	+	2.50883i	−0.461756	+	0.887007i
$9$	2.92079	+	0.684828i	0.973596	+	0.228276i
$10$	−1.85431	+	2.27629i	−0.586383	+	0.719827i
$11$	1.99399	−	3.45368i	0.601209	−	1.04132i	−0.391429	−	0.920208i	$-0.628019\pi$
$11$	1.99399	−	3.45368i	0.601209	−	1.04132i	0.992638	−	0.121117i	$-0.0386475\pi$
$12$	−2.83525	+	1.99032i	−0.818465	+	0.574556i
$13$	−1.30998			−0.363324			−0.181662	−	0.983361i	$-0.558148\pi$
$13$	−1.30998			−0.363324			−0.181662	+	0.983361i	$0.558148\pi$
$14$	−3.66160	+	0.769840i	−0.978605	+	0.205748i
$15$	−3.30003	+	1.42820i	−0.852064	+	0.368760i
$16$	0.464417	−	3.97295i	0.116104	−	0.993237i
$17$	−2.54752	−	1.47081i	−0.617863	−	0.356724i	0.158173	−	0.987411i	$-0.449440\pi$
$17$	−2.54752	−	1.47081i	−0.617863	−	0.356724i	−0.776037	+	0.630688i	$0.782773\pi$
$18$	−4.20500	+	0.563873i	−0.991129	+	0.132906i
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	−0.604986	−	0.796236i	$-0.706821\pi$
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	0.387068	+	0.922051i	$0.373488\pi$
$20$	1.30604	−	3.94134i	0.292040	−	0.881311i
$21$	−4.41467	−	1.22908i	−0.963361	−	0.268208i
$22$	−0.898482	+	5.56781i	−0.191557	+	1.18706i
$23$	3.75063	+	6.49627i	0.782059	+	1.35457i	0.930740	+	0.365681i	$0.119164\pi$
$23$	3.75063	+	6.49627i	0.782059	+	1.35457i	−0.148681	+	0.988885i	$0.547503\pi$
$24$	2.74644	−	4.05673i	0.560614	−	0.828077i
$25$	−0.345008	+	0.597572i	−0.0690016	+	0.119514i
$26$	1.73147	−	0.658872i	0.339570	−	0.129216i
$27$	−4.88916	−	1.75957i	−0.940920	−	0.338630i
$28$	4.45253	−	2.85919i	0.841450	−	0.540336i
$29$			0.865568i			0.160732i	0.996765	+	0.0803660i	$0.0256089\pi$
$29$			0.865568i			0.160732i	−0.996765	+	0.0803660i	$0.974391\pi$
$30$	3.64349	−	3.54752i	0.665207	−	0.647685i
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	0.185661	−	0.982614i	$-0.440557\pi$
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	−0.758138	+	0.652094i	$0.773891\pi$
$32$	1.38440	+	5.48484i	0.244729	+	0.969591i
$33$	−4.11813	+	5.54551i	−0.716875	+	0.965350i
$34$	4.10695	+	0.662741i	0.704336	+	0.113659i
$35$	5.12651	−	1.97200i	0.866538	−	0.333330i
$36$	5.27436	−	2.86026i	0.879061	−	0.476710i
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	0.641705	−	0.766952i	$-0.278227\pi$
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	−0.985052	+	0.172257i	$0.944894\pi$
$38$	0.979678	−	1.20262i	0.158925	−	0.195091i
$39$	2.25393	+	0.260701i	0.360918	+	0.0417456i
$40$	0.256080	+	5.86637i	0.0404899	+	0.927554i
$41$			7.01712i			1.09589i	0.836514	+	0.547945i	$0.184590\pi$
$41$			7.01712i			1.09589i	−0.836514	+	0.547945i	$0.815410\pi$
$42$	6.45329	−	0.595872i	0.995764	−	0.0919450i
$43$			4.27597i			0.652080i	0.945356	+	0.326040i	$0.105714\pi$
$43$			4.27597i			0.652080i	−0.945356	+	0.326040i	$0.894286\pi$
$44$	−1.61283	−	7.81117i	−0.243143	−	1.17758i
$45$	5.96219	−	1.80059i	0.888791	−	0.268416i
$46$	−8.22478	−	6.70004i	−1.21268	−	0.987867i
$47$	−3.75063	−	6.49627i	−0.547085	−	0.947579i	−0.998473	−	0.0552509i	$-0.982404\pi$
$47$	−3.75063	−	6.49627i	−0.547085	−	0.947579i	0.451388	−	0.892328i	$-0.350929\pi$
$48$	−1.58973	+	6.74335i	−0.229457	+	0.973319i
$49$	6.66042	+	2.15379i	0.951489	+	0.307684i
$50$	0.155459	−	0.963368i	0.0219853	−	0.136241i
$51$	4.09050	+	3.03763i	0.572784	+	0.425353i
$52$	−1.95719	+	1.74173i	−0.271414	+	0.241535i
$53$	−4.27909	−	2.47053i	−0.587778	−	0.339354i	0.176440	−	0.984311i	$-0.443542\pi$
$53$	−4.27909	−	2.47053i	−0.587778	−	0.339354i	−0.764218	+	0.644957i	$0.776875\pi$
$54$	7.34726	−	0.133348i	0.999835	−	0.0181463i
$55$		−	8.27923i		−	1.11637i
$56$	−4.44708	+	6.01859i	−0.594266	+	0.804268i
$57$	1.74349	−	0.754555i	0.230931	−	0.0999432i
$58$	−0.435348	−	1.14407i	−0.0571640	−	0.150223i
$59$	−2.44458	+	4.23414i	−0.318257	+	0.551238i	−0.980125	−	0.198383i	$-0.936431\pi$
$59$	−2.44458	+	4.23414i	−0.318257	+	0.551238i	0.661867	+	0.749621i	$0.269764\pi$
$60$	−3.03152	+	6.52148i	−0.391368	+	0.841919i
$61$	−2.05347	−	3.55672i	−0.262920	−	0.455391i	0.704096	−	0.710104i	$-0.251352\pi$
$61$	−2.05347	−	3.55672i	−0.262920	−	0.455391i	−0.967017	+	0.254713i	$0.918019\pi$
$62$	5.13856	+	0.829212i	0.652597	+	0.105310i
$63$	7.35120	+	2.99330i	0.926164	+	0.377121i
$64$	−4.58850	−	6.55330i	−0.573562	−	0.819162i
$65$	−2.35524	+	1.35980i	−0.292131	+	0.168662i
$66$	2.65397	−	9.40106i	0.326681	−	1.15719i
$67$	2.09778	+	1.21116i	0.256285	+	0.147966i	0.622639	−	0.782509i	$-0.286061\pi$
$67$	2.09778	+	1.21116i	0.256285	+	0.147966i	−0.366354	+	0.930476i	$0.619394\pi$
$68$	−5.76170	+	1.18966i	−0.698709	+	0.144268i
$69$	−5.16042	−	11.9238i	−0.621242	−	1.43545i
$70$	−5.78413	+	5.18494i	−0.691336	+	0.619719i
$71$	−0.901192			−0.106952			−0.0534759	−	0.998569i	$-0.517030\pi$
$71$	−0.901192			−0.106952			−0.0534759	+	0.998569i	$0.517030\pi$
$72$	−5.53280	+	6.43336i	−0.652047	+	0.758179i
$73$	−6.50543	+	11.2677i	−0.761403	+	1.31879i	0.180725	+	0.983534i	$0.442156\pi$
$73$	−6.50543	+	11.2677i	−0.761403	+	1.31879i	−0.942128	+	0.335255i	$0.891178\pi$
$74$	4.57989	+	3.73085i	0.532401	+	0.433703i
$75$	0.712537	−	0.959509i	0.0822767	−	0.110795i
$76$	−0.690016	+	2.08231i	−0.0791503	+	0.238858i
$77$	6.63432	−	8.20446i	0.756051	−	0.934985i
$78$	−3.11026	+	0.789060i	−0.352168	+	0.0893435i
$79$	−8.97336	+	5.18077i	−1.00958	+	0.582882i	−0.911069	−	0.412254i	$-0.864742\pi$
$79$	−8.97336	+	5.18077i	−1.00958	+	0.582882i	−0.0985123	+	0.995136i	$0.531408\pi$
$80$	−3.28904	−	7.62509i	−0.367726	−	0.852511i
$81$	8.06202	+	4.00048i	0.895780	+	0.444498i
$82$	−3.52935	−	9.27489i	−0.389751	−	1.02424i
$83$	−12.4386			−1.36531			−0.682657	−	0.730739i	$-0.739176\pi$
$83$	−12.4386			−1.36531			−0.682657	+	0.730739i	$0.739176\pi$
$84$	−8.22995	+	4.03336i	−0.897961	+	0.440075i
$85$	−6.10695			−0.662391
$86$	−2.15065	−	5.65178i	−0.231911	−	0.609447i
$87$	0.172258	−	1.48928i	0.0184680	−	0.159668i
$88$	6.06049	+	9.51324i	0.646050	+	1.01411i
$89$	7.38393	−	4.26311i	0.782695	−	0.451889i	−0.0546896	−	0.998503i	$-0.517417\pi$
$89$	7.38393	−	4.26311i	0.782695	−	0.451889i	0.837385	+	0.546614i	$0.184084\pi$
$90$	−6.97491	+	5.37869i	−0.735220	+	0.566964i
$91$	−3.42360	−	0.539786i	−0.358891	−	0.0565850i
$92$	14.2410	+	4.71904i	1.48473	+	0.491994i
$93$	5.11797	+	3.80064i	0.530709	+	0.394108i
$94$	8.22478	+	6.70004i	0.848321	+	0.691056i
$95$	−1.13854	+	1.97200i	−0.116811	+	0.202323i
$96$	−1.29043	−	9.71261i	−0.131703	−	0.991289i
$97$	15.3909			1.56271			0.781354	−	0.624088i	$-0.214529\pi$
$97$	15.3909			1.56271			0.781354	+	0.624088i	$0.214529\pi$
$98$	−9.88670	+	0.503167i	−0.998707	+	0.0508275i
$99$	8.18919	−	8.72195i	0.823045	−	0.876588i
$100$	0.279059	+	1.35152i	0.0279059	+	0.135152i
$101$	5.28731	+	3.05263i	0.526107	+	0.303748i	0.739430	−	0.673234i	$-0.235095\pi$
$101$	5.28731	+	3.05263i	0.526107	+	0.303748i	−0.213322	+	0.976982i	$0.568428\pi$
$102$	−6.93444	−	1.95763i	−0.686612	−	0.193834i
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	−0.163805	−	0.986493i	$-0.552377\pi$
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	0.772425	+	0.635106i	$0.219044\pi$
$104$	1.71090	−	3.28653i	0.167767	−	0.322271i
$105$	−9.21302	+	2.37276i	−0.899098	+	0.231558i
$106$	6.89848	+	1.11321i	0.670040	+	0.108125i
$107$	1.20838	+	2.09297i	0.116818	+	0.202335i	0.918505	−	0.395409i	$-0.129397\pi$
$107$	1.20838	+	2.09297i	0.116818	+	0.202335i	−0.801687	+	0.597744i	$0.796064\pi$
$108$	−9.64419	+	3.87165i	−0.928012	+	0.372549i
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	0.981617	+	0.190864i	$0.0611288\pi$
$110$	4.16414	+	10.9431i	0.397035	+	1.04338i
$111$	2.87353	+	6.63963i	0.272743	+	0.630206i
$112$	2.85082	−	10.1918i	0.269377	−	0.963035i
$113$		−	3.16365i		−	0.297611i	−0.988867	−	0.148805i	$-0.952457\pi$
$113$		−	3.16365i		−	0.297611i	0.988867	−	0.148805i	$-0.0475428\pi$
$114$	−1.92495	+	1.87424i	−0.180288	+	0.175539i
$115$	13.4866	+	7.78649i	1.25763	+	0.726094i
$116$	1.15085	+	1.29321i	0.106853	+	0.120071i
$117$	−3.82619	−	0.897114i	−0.353731	−	0.0829382i
$118$	1.10152	−	6.82601i	0.101403	−	0.628386i
$119$	−6.05179	−	4.89363i	−0.554767	−	0.448598i
$120$	0.726865	−	10.1445i	0.0663534	−	0.926064i
$121$	−2.45196	−	4.24691i	−0.222905	−	0.386083i
$122$	4.50308	+	3.66828i	0.407690	+	0.332111i
$123$	1.39648	−	12.0735i	0.125917	−	1.08863i
$124$	−7.20896	+	1.48849i	−0.647384	+	0.133670i
$125$			11.8128i			1.05657i
$126$	−11.2220	−	0.259030i	−0.999734	−	0.0230762i
$127$		−	15.0889i		−	1.33892i	−0.742848	−	0.669460i	$-0.766526\pi$
$127$		−	15.0889i		−	1.33892i	0.742848	−	0.669460i	$-0.233474\pi$
$128$	9.36092	+	6.35399i	0.827396	+	0.561619i
$129$	0.850965	−	7.35715i	0.0749233	−	0.647761i
$130$	2.42911	−	2.98191i	0.213047	−	0.261531i
$131$	3.70488	+	6.41704i	0.323697	+	0.560660i	0.981248	−	0.192751i	$-0.0617408\pi$
$131$	3.70488	+	6.41704i	0.323697	+	0.560660i	−0.657551	+	0.753410i	$0.728407\pi$
$132$	1.22049	+	13.7607i	0.106230	+	1.19772i
$133$	−2.70847	+	1.04186i	−0.234854	+	0.0903407i
$134$	−3.38192	−	0.545742i	−0.292153	−	0.0471449i
$135$	−10.6168	+	1.91152i	−0.913745	+	0.164517i
$136$	7.01718	−	4.47035i	0.601719	−	0.383330i
$137$	−13.0764	−	7.54965i	−1.11719	−	0.645010i	−0.176508	−	0.984299i	$-0.556480\pi$
$137$	−13.0764	−	7.54965i	−1.11719	−	0.645010i	−0.940682	+	0.339290i	$0.889813\pi$
$138$	12.8180	+	13.1648i	1.09114	+	1.12066i
$139$			14.4761i			1.22785i	0.789364	+	0.613925i	$0.210410\pi$
$139$			14.4761i			1.22785i	−0.789364	+	0.613925i	$0.789590\pi$
$140$	5.03736	−	9.76241i	0.425734	−	0.825074i
$141$	5.16042	+	11.9238i	0.434586	+	1.00416i
$142$	1.19115	−	0.453266i	0.0999593	−	0.0380372i
$143$	−2.61209	+	4.52427i	−0.218434	+	0.378338i
$144$	4.07725	−	11.2861i	0.339771	−	0.940508i
$145$	0.898482	+	1.55622i	0.0746148	+	0.129237i
$146$	2.93132	−	18.1651i	0.242598	−	1.50336i
$147$	−11.0312	−	5.03126i	−0.909834	−	0.414971i
$148$	−7.92995	−	2.62775i	−0.651838	−	0.216000i
$149$	−9.86511	+	5.69562i	−0.808181	+	0.466604i	−0.846324	−	0.532669i	$-0.821189\pi$
$149$	−9.86511	+	5.69562i	−0.808181	+	0.466604i	0.0381428	+	0.999272i	$0.487856\pi$
$150$	−0.459201	+	1.62661i	−0.0374936	+	0.132812i
$151$	0.795186	+	0.459101i	0.0647113	+	0.0373611i	0.532007	−	0.846740i	$-0.321438\pi$
$151$	0.795186	+	0.459101i	0.0647113	+	0.0373611i	−0.467295	+	0.884101i	$0.654771\pi$
$152$	−0.135294	−	3.09935i	−0.0109738	−	0.251391i
$153$	−6.43351	−	6.04054i	−0.520118	−	0.488348i
$154$	−4.64240	+	14.1811i	−0.374095	+	1.14274i
$155$	−7.64093			−0.613734
$156$	3.71413	−	2.60729i	0.297368	−	0.208750i
$157$	4.36346	−	7.55773i	0.348242	−	0.603172i	−0.637695	−	0.770289i	$-0.720112\pi$
$157$	4.36346	−	7.55773i	0.348242	−	0.603172i	0.985937	+	0.167116i	$0.0534455\pi$
$158$	9.25482	−	11.3610i	0.736274	−	0.903829i
$159$	6.87085	+	5.10234i	0.544894	+	0.404642i
$160$	8.18242	+	8.42422i	0.646877	+	0.665993i
$161$	7.12531	+	18.5233i	0.561553	+	1.45984i
$162$	−12.6681	−	1.23275i	−0.995299	−	0.0968540i
$163$	7.78729	−	4.49599i	0.609948	−	0.352153i	−0.162997	−	0.986627i	$-0.552116\pi$
$163$	7.78729	−	4.49599i	0.609948	−	0.352153i	0.772945	+	0.634473i	$0.218783\pi$
$164$	9.32984	+	10.4840i	0.728538	+	0.818661i
$165$	−1.64766	+	14.2451i	−0.128270	+	1.10898i
$166$	16.4408	−	6.25615i	1.27605	−	0.485571i
$167$	16.1830			1.25228			0.626141	−	0.779710i	$-0.284633\pi$
$167$	16.1830			1.25228			0.626141	+	0.779710i	$0.284633\pi$
$168$	8.84933	−	9.47045i	0.682740	−	0.730661i
$169$	−11.2839			−0.867996
$170$	8.07187	−	3.07156i	0.619084	−	0.235578i
$171$	−3.14998	+	0.951298i	−0.240885	+	0.0727476i
$172$	5.68526	+	6.38855i	0.433497	+	0.487122i
$173$	−3.66216	+	2.11435i	−0.278429	+	0.160751i	−0.632712	−	0.774387i	$-0.718058\pi$
$173$	−3.66216	+	2.11435i	−0.278429	+	0.160751i	0.354283	+	0.935138i	$0.384725\pi$
$174$	0.521370	+	2.05510i	0.0395249	+	0.155797i
$175$	−1.14790	+	1.41957i	−0.0867731	+	0.107310i
$176$	−12.7953	−	9.52595i	−0.964479	−	0.718046i
$177$	5.04874	−	6.79868i	0.379486	−	0.511020i
$178$	−7.61554	+	9.34862i	−0.570809	+	0.700709i
$179$	−3.27593	+	5.67408i	−0.244855	+	0.424101i	−0.962091	−	0.272729i	$-0.912074\pi$
$179$	−3.27593	+	5.67408i	−0.244855	+	0.424101i	0.717236	+	0.696830i	$0.245407\pi$
$180$	6.51382	−	10.6174i	0.485512	−	0.791375i
$181$	−12.2839			−0.913058			−0.456529	−	0.889708i	$-0.650908\pi$
$181$	−12.2839			−0.913058			−0.456529	+	0.889708i	$0.650908\pi$
$182$	4.79664	−	1.00848i	0.355551	−	0.0747533i
$183$	2.82534	+	6.52828i	0.208855	+	0.482585i
$184$	−21.1966	+	0.925278i	−1.56263	+	0.0682124i
$185$	−7.50987	−	4.33583i	−0.552137	−	0.318776i
$186$	−8.67627	−	2.44935i	−0.636175	−	0.179595i
$187$	−10.1594	+	5.86554i	−0.742930	+	0.428931i
$188$	−14.2410	−	4.71904i	−1.03863	−	0.344171i
$189$	−12.0526	−	6.61319i	−0.876699	−	0.481039i
$190$	0.513020	−	3.17914i	0.0372184	−	0.230639i
$191$	−11.8662	−	20.5529i	−0.858611	−	1.48716i	−0.873254	−	0.487266i	$-0.837994\pi$
$191$	−11.8662	−	20.5529i	−0.858611	−	1.48716i	0.0146426	−	0.999893i	$-0.495339\pi$
$192$	6.59070	+	12.1886i	0.475643	+	0.879639i
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	−0.785609	−	0.618724i	$-0.787650\pi$
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	0.928635	+	0.370995i	$0.120983\pi$
$194$	−20.3429	+	7.74104i	−1.46054	+	0.555774i
$195$	4.32298	−	1.87092i	0.309575	−	0.133979i
$196$	12.8147	−	5.63770i	0.915335	−	0.402693i
$197$		−	19.7720i		−	1.40870i	−0.709853	−	0.704350i	$-0.751239\pi$
$197$		−	19.7720i		−	1.40870i	0.709853	−	0.704350i	$-0.248761\pi$
$198$	−6.43727	+	15.6471i	−0.457477	+	1.11199i
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	0.245859	−	0.969305i	$-0.420930\pi$
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	−0.716513	+	0.697573i	$0.754263\pi$
$200$	−1.04861	−	1.64602i	−0.0741481	−	0.116391i
$201$	−3.36837	−	2.50137i	−0.237587	−	0.176433i
$202$	−8.52388	−	1.37550i	−0.599738	−	0.0967801i
$203$	−0.356662	+	2.26213i	−0.0250328	+	0.158771i
$204$	10.1502	−	0.900265i	0.710657	−	0.0630311i
$205$	7.28394	+	12.6162i	0.508733	+	0.881151i
$206$	−6.37056	+	7.82032i	−0.443858	+	0.544868i
$207$	6.50595	+	21.5428i	0.452195	+	1.49733i
$208$	−0.608379	+	5.20450i	−0.0421835	+	0.360867i
$209$			4.37413i			0.302565i
$210$	10.9839	−	7.77000i	0.757962	−	0.536181i
$211$			11.7483i			0.808789i	0.914585	+	0.404395i	$0.132518\pi$
$211$			11.7483i			0.808789i	−0.914585	+	0.404395i	$0.867482\pi$
$212$	−9.67799	+	1.99829i	−0.664687	+	0.137243i
$213$	1.55057	+	0.179347i	0.106243	+	0.0122887i
$214$	−2.64986	−	2.15862i	−0.181141	−	0.147560i
$215$	4.43857	+	7.68782i	0.302708	+	0.524305i
$216$	10.7999	−	9.96802i	0.734842	−	0.678238i
$217$	−7.57192	−	6.12284i	−0.514016	−	0.415646i
$218$	−1.53134	+	9.48959i	−0.103716	+	0.642716i
$219$	13.4355	−	18.0924i	0.907888	−	1.22257i
$220$	−11.0079	−	12.3696i	−0.742154	−	0.833961i
$221$	3.33720	+	1.92674i	0.224485	+	0.129606i
$222$	−7.13758	−	7.33067i	−0.479043	−	0.492003i
$223$		−	14.5202i		−	0.972345i	−0.873863	−	0.486173i	$-0.838393\pi$
$223$		−	14.5202i		−	0.972345i	0.873863	−	0.486173i	$-0.161607\pi$
$224$	1.35802	+	14.9049i	0.0907366	+	0.995875i
$225$	−1.41693	+	1.50911i	−0.0944620	+	0.100607i
$226$	1.59119	+	4.18156i	0.105845	+	0.278153i
$227$	10.7314	−	18.5874i	0.712271	−	1.23369i	−0.251732	−	0.967797i	$-0.581000\pi$
$227$	10.7314	−	18.5874i	0.712271	−	1.23369i	0.964003	−	0.265892i	$-0.0856665\pi$
$228$	1.60163	−	3.44546i	0.106071	−	0.228181i
$229$	9.81541	+	17.0008i	0.648621	+	1.12344i	0.983453	+	0.181166i	$0.0579872\pi$
$229$	9.81541	+	17.0008i	0.648621	+	1.12344i	−0.334832	+	0.942278i	$0.608680\pi$
$230$	−21.7422	−	3.50856i	−1.43364	−	0.231348i
$231$	−13.0477	+	12.7961i	−0.858473	+	0.841923i
$232$	−2.17157	−	1.13047i	−0.142570	−	0.0742190i
$233$	12.3530	−	7.13202i	0.809273	−	0.467234i	−0.0374302	−	0.999299i	$-0.511917\pi$
$233$	12.3530	−	7.13202i	0.809273	−	0.467234i	0.846703	+	0.532065i	$0.178584\pi$
$234$	5.50848	−	0.738665i	0.360101	−	0.0482880i
$235$	−13.4866	−	7.78649i	−0.879768	−	0.507934i
$236$	1.97729	+	9.57632i	0.128711	+	0.623365i
$237$	16.4704	−	7.12813i	1.06987	−	0.463022i
$238$	10.4603	+	3.42434i	0.678040	+	0.221967i
$239$	15.2819			0.988501			0.494251	−	0.869320i	$-0.335443\pi$
$239$	15.2819			0.988501			0.494251	+	0.869320i	$0.335443\pi$
$240$	4.14158	+	13.7741i	0.267338	+	0.889116i
$241$	2.95196	−	5.11294i	0.190152	−	0.329353i	−0.755148	−	0.655554i	$-0.772435\pi$
$241$	2.95196	−	5.11294i	0.190152	−	0.329353i	0.945301	+	0.326201i	$0.105769\pi$
$242$	5.37691	+	4.38012i	0.345641	+	0.281565i
$243$	−13.0752	−	8.48757i	−0.838775	−	0.544478i
$244$	−7.79696	−	2.58368i	−0.499149	−	0.165403i
$245$	14.2105	−	3.04136i	0.907878	−	0.194305i
$246$	4.22672	+	16.6606i	0.269486	+	1.06224i
$247$	1.24433	−	0.718415i	0.0791749	−	0.0457116i
$248$	8.77981	−	5.59325i	0.557518	−	0.355171i
$249$	21.4016	+	2.47542i	1.35627	+	0.156873i
$250$	−5.94137	−	15.6135i	−0.375765	−	0.987487i
$251$	23.7400			1.49845			0.749226	−	0.662314i	$-0.230425\pi$
$251$	23.7400			1.49845			0.749226	+	0.662314i	$0.230425\pi$
$252$	14.9630	−	5.30186i	0.942578	−	0.333986i
$253$	29.9148			1.88073
$254$	7.58913	+	19.9437i	0.476184	+	1.25138i
$255$	10.5075	+	1.21535i	0.658004	+	0.0761081i
$256$	−15.5686	−	3.69021i	−0.973040	−	0.230638i
$257$	12.8177	−	7.40033i	0.799549	−	0.461620i	−0.0437643	−	0.999042i	$-0.513935\pi$
$257$	12.8177	−	7.40033i	0.799549	−	0.461620i	0.843314	+	0.537422i	$0.180602\pi$
$258$	2.57560	+	10.1523i	0.160350	+	0.632057i
$259$	−3.96766	−	10.3145i	−0.246538	−	0.640911i
$260$	−1.71090	+	5.16309i	−0.106105	+	0.320202i
$261$	−0.592766	+	2.52814i	−0.0366913	+	0.156488i
$262$	−8.12447	−	6.61833i	−0.501931	−	0.408881i
$263$	−6.95299	+	12.0429i	−0.428740	+	0.742599i	−0.996761	−	0.0804148i	$-0.974376\pi$
$263$	−6.95299	+	12.0429i	−0.428740	+	0.742599i	0.568022	+	0.823013i	$0.307709\pi$
$264$	−8.53431	−	17.5744i	−0.525251	−	1.08163i
$265$	−10.2579			−0.630138
$266$	3.05590	−	2.73934i	0.187369	−	0.167960i
$267$	−13.5530	+	5.86554i	−0.829433	+	0.358965i
$268$	4.74454	−	0.979641i	0.289819	−	0.0598411i
$269$	−7.15156	−	4.12896i	−0.436039	−	0.251747i	0.265877	−	0.964007i	$-0.414338\pi$
$269$	−7.15156	−	4.12896i	−0.436039	−	0.251747i	−0.701916	+	0.712260i	$0.747672\pi$
$270$	13.0713	−	7.86639i	0.795494	−	0.478733i
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	−0.353911	−	0.935279i	$-0.615148\pi$
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	0.633020	+	0.774135i	$0.281815\pi$
$272$	−7.02656	+	9.43808i	−0.426048	+	0.572268i
$273$	5.78315	+	1.61008i	0.350012	+	0.0974464i
$274$	21.0809	+	3.40184i	1.27354	+	0.205513i
$275$	1.37588	+	2.38310i	0.0829688	+	0.143706i
$276$	−23.5636	−	10.9536i	−1.41836	−	0.659329i
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	−0.990870	−	0.134824i	$-0.956953\pi$
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	0.612196	+	0.790706i	$0.290287\pi$
$278$	−7.28095	−	19.1339i	−0.436683	−	1.14757i
$279$	−8.04951	−	7.55783i	−0.481912	−	0.452476i
$280$	−1.74801	+	15.4371i	−0.104464	+	0.922542i
$281$			2.02977i			0.121086i	0.998166	+	0.0605428i	$0.0192832\pi$
$281$			2.02977i			0.121086i	−0.998166	+	0.0605428i	$0.980717\pi$
$282$	−12.8180	−	13.1648i	−0.763301	−	0.783951i
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	0.289181	−	0.957274i	$-0.406617\pi$
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	−0.684434	+	0.729075i	$0.739950\pi$
$284$	−1.34643	+	1.19821i	−0.0798961	+	0.0711006i
$285$	2.35139	−	3.16641i	0.139285	−	0.187562i
$286$	1.17700	−	7.29374i	0.0695972	−	0.431288i
$287$	−2.89144	+	18.3390i	−0.170676	+	1.08252i
$288$	0.287363	+	16.9681i	0.0169331	+	0.999857i
$289$	−4.17344	−	7.22861i	−0.245497	−	0.425212i
$290$	−1.97029	−	1.60503i	−0.115699	−	0.0942506i
$291$	−26.4813	−	3.06296i	−1.55236	−	0.179554i
$292$	5.26190	+	25.4842i	0.307929	+	1.49135i
$293$			1.55539i			0.0908671i	0.998967	+	0.0454336i	$0.0144669\pi$
$293$			1.55539i			0.0908671i	−0.998967	+	0.0454336i	$0.985533\pi$
$294$	17.1110	+	1.10182i	0.997933	+	0.0642596i
$295$			10.1501i			0.590964i
$296$	11.8031	−	0.515232i	0.686041	−	0.0299472i
$297$	−15.8259	+	13.3771i	−0.918313	+	0.776216i
$298$	10.1745	−	12.4900i	0.589395	−	0.723525i
$299$	−4.91326	−	8.51001i	−0.284141	−	0.492147i
$300$	−0.211175	−	2.38094i	−0.0121922	−	0.137464i
$301$	−1.76194	+	11.1751i	−0.101556	+	0.644123i
$302$	−1.28195	−	0.206869i	−0.0737679	−	0.0119040i
$303$	−8.48974	−	6.30453i	−0.487723	−	0.362186i
$304$	1.73768	+	4.02853i	0.0996629	+	0.231052i
$305$	−7.38393	−	4.26311i	−0.422803	−	0.244105i
$306$	11.5417	+	4.74828i	0.659793	+	0.271441i
$307$			31.5800i			1.80237i	0.433437	+	0.901184i	$0.357301\pi$
$307$			31.5800i			1.80237i	−0.433437	+	0.901184i	$0.642699\pi$
$308$	−0.996442	−	21.0788i	−0.0567775	−	1.20108i
$309$	−11.3374	+	4.90665i	−0.644963	+	0.279130i
$310$	10.0994	−	3.84310i	0.573608	−	0.218273i
$311$	9.13857	−	15.8285i	0.518201	−	0.897550i	−0.481575	−	0.876405i	$-0.659935\pi$
$311$	9.13857	−	15.8285i	0.518201	−	0.897550i	0.999776	−	0.0211458i	$-0.00673141\pi$
$312$	−3.59779	+	5.31425i	−0.203685	+	0.300860i
$313$	−14.8909	−	25.7918i	−0.841683	−	1.45784i	−0.888471	−	0.458933i	$-0.848232\pi$
$313$	−14.8909	−	25.7918i	−0.841683	−	1.45784i	0.0467882	−	0.998905i	$-0.485101\pi$
$314$	−1.96616	+	12.1841i	−0.110957	+	0.687589i
$315$	16.3239	−	2.24903i	0.919749	−	0.126719i
$316$	−6.51845	+	19.6712i	−0.366691	+	1.10659i
$317$	−15.3252	+	8.84800i	−0.860748	+	0.496953i	−0.864263	−	0.503041i	$-0.832215\pi$
$317$	−15.3252	+	8.84800i	−0.860748	+	0.496953i	0.00351474	+	0.999994i	$0.498881\pi$
$318$	−11.6478	−	3.28824i	−0.653179	−	0.184396i
$319$	2.98940	+	1.72593i	0.167374	+	0.0966336i
$320$	−15.0522	−	7.01927i	−0.841444	−	0.392389i
$321$	−1.66258	−	3.84160i	−0.0927964	−	0.214417i
$322$	−18.7344	−	20.8994i	−1.04403	−	1.16468i
$323$	3.22646			0.179525
$324$	17.3641	−	4.74218i	0.964672	−	0.263454i
$325$	0.451955	−	0.782809i	0.0250700	−	0.0434224i
$326$	−8.03155	+	9.85930i	−0.444827	+	0.546056i
$327$	−7.01881	+	9.45159i	−0.388141	+	0.522674i
$328$	−17.6048	−	9.16466i	−0.972062	−	0.506034i
$329$	−7.12531	−	18.5233i	−0.392831	−	1.02122i
$330$	−4.98694	−	19.6572i	−0.274522	−	1.08209i
$331$	30.3818	−	17.5410i	1.66994	−	0.964138i	0.702268	−	0.711913i	$-0.252171\pi$
$331$	30.3818	−	17.5410i	1.66994	−	0.964138i	0.967668	−	0.252225i	$-0.0811625\pi$
$332$	−18.5840	+	16.5382i	−1.01993	+	0.907649i
$333$	−3.62278	−	11.9959i	−0.198527	−	0.657370i
$334$	−21.3900	+	8.13946i	−1.17041	+	0.445372i
$335$	5.02884			0.274755
$336$	−6.93334	+	16.9685i	−0.378244	+	0.925706i
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	14.9146	−	5.67540i	0.811246	−	0.308701i
$339$	−0.629600	+	5.44330i	−0.0341952	+	0.295640i
$340$	−9.12413	+	8.11969i	−0.494826	+	0.440352i
$341$	−12.7113	+	7.33889i	−0.688357	+	0.397423i
$342$	3.68502	−	2.84170i	0.199263	−	0.153662i
$343$	16.5193	+	8.37332i	0.891959	+	0.452117i
$344$	−10.7277	−	5.58461i	−0.578399	−	0.301102i
$345$	−21.6552	−	16.0812i	−1.16587	−	0.865785i
$346$	3.77703	−	4.63658i	0.203055	−	0.249264i
$347$	−0.0976681	+	0.169166i	−0.00524310	+	0.00908131i	−0.868635	−	0.495452i	$-0.835002\pi$
$347$	−0.0976681	+	0.169166i	−0.00524310	+	0.00908131i	0.863392	+	0.504534i	$0.168336\pi$
$348$	−1.72276	−	2.45410i	−0.0923495	−	0.131554i
$349$	5.80782			0.310885			0.155443	−	0.987845i	$-0.450320\pi$
$349$	5.80782			0.310885			0.155443	+	0.987845i	$0.450320\pi$
$350$	0.803249	−	2.45367i	0.0429355	−	0.131154i
$351$	6.40472	+	2.30501i	0.341859	+	0.123032i
$352$	21.7034	+	6.15541i	1.15679	+	0.328085i
$353$	17.3154	+	9.99704i	0.921604	+	0.532089i	0.884147	−	0.467210i	$-0.154741\pi$
$353$	17.3154	+	9.99704i	0.921604	+	0.532089i	0.0374578	+	0.999298i	$0.488074\pi$
$354$	−3.25370	+	11.5255i	−0.172932	+	0.612573i
$355$	−1.62026	+	0.935460i	−0.0859947	+	0.0496490i
$356$	5.36385	−	16.1869i	0.284284	−	0.857903i
$357$	9.43871	+	9.62425i	0.499549	+	0.509370i
$358$	1.47612	−	9.14741i	0.0780155	−	0.483455i
$359$	−6.95299	−	12.0429i	−0.366965	−	0.635601i	0.622125	−	0.782918i	$-0.286270\pi$
$359$	−6.95299	−	12.0429i	−0.366965	−	0.635601i	−0.989089	+	0.147317i	$0.952936\pi$
$360$	−3.26950	+	17.3098i	−0.172318	+	0.912307i
$361$	−8.89848	+	15.4126i	−0.468341	+	0.811191i
$362$	16.2363	−	6.17836i	0.853363	−	0.324727i
$363$	3.37360	+	7.79511i	0.177068	+	0.409137i
$364$	−5.83275	+	3.74549i	−0.305719	+	0.196317i
$365$			27.0112i			1.41383i
$366$	−7.01788	−	7.20774i	−0.366830	−	0.376754i
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	0.0103306	−	0.999947i	$-0.496712\pi$
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	−0.860814	+	0.508920i	$0.830045\pi$
$368$	27.5512	−	11.8841i	1.43621	−	0.619499i
$369$	−4.80552	+	20.4955i	−0.250165	+	1.06695i
$370$	12.1069	+	1.95371i	0.629410	+	0.101568i
$371$	−10.1653	−	8.21988i	−0.527754	−	0.426755i
$372$	12.6998	−	1.12640i	0.658455	−	0.0584011i
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	0.780752	−	0.624841i	$-0.214836\pi$
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	−0.931504	+	0.363731i	$0.881503\pi$
$374$	10.4781	−	12.8626i	0.541809	−	0.665109i
$375$	2.35087	−	20.3248i	0.121398	−	1.04957i
$376$	21.1966	−	0.925278i	1.09313	−	0.0477176i
$377$		−	1.13388i		−	0.0583978i
$378$	19.2568	+	2.67898i	0.990461	+	0.137792i
$379$			12.0598i			0.619469i	0.950823	+	0.309735i	$0.100240\pi$
$379$			12.0598i			0.619469i	−0.950823	+	0.309735i	$0.899760\pi$
$380$	0.920903	+	4.46007i	0.0472413	+	0.228797i
$381$	−3.00285	+	25.9616i	−0.153841	+	1.33005i
$382$	26.0216	+	21.1976i	1.33138	+	1.08456i
$383$	6.07589	+	10.5237i	0.310463	+	0.537738i	0.978463	−	0.206423i	$-0.0661824\pi$
$383$	6.07589	+	10.5237i	0.310463	+	0.537738i	−0.667999	+	0.744162i	$0.732849\pi$
$384$	−14.8417	−	12.7955i	−0.757387	−	0.652966i
$385$	3.41150	−	21.6375i	0.173866	−	1.10275i
$386$	−0.895325	+	5.54825i	−0.0455708	+	0.282399i
$387$	−2.92831	+	12.4892i	−0.148854	+	0.634862i
$388$	22.9949	−	20.4635i	1.16739	−	1.03888i
$389$	−1.04831	−	0.605241i	−0.0531513	−	0.0306869i	0.473189	−	0.880961i	$-0.343103\pi$
$389$	−1.04831	−	0.605241i	−0.0531513	−	0.0306869i	−0.526340	+	0.850274i	$0.676436\pi$
$390$	−4.77291	+	4.64719i	−0.241686	+	0.235320i
$391$		−	22.0658i		−	1.11592i
$392$	−14.1023	+	13.8969i	−0.712274	+	0.701902i
$393$	−5.09748	−	11.7783i	−0.257134	−	0.594139i
$394$	9.94459	+	26.1337i	0.501001	+	1.31660i
$395$	−10.7555	+	18.6291i	−0.541170	+	0.937334i
$396$	0.638575	−	23.9193i	0.0320896	−	1.20199i
$397$	4.77851	+	8.27663i	0.239827	+	0.415392i	0.960664	−	0.277712i	$-0.0895760\pi$
$397$	4.77851	+	8.27663i	0.239827	+	0.415392i	−0.720838	+	0.693104i	$0.756243\pi$
$398$	10.7036	+	1.72725i	0.536524	+	0.0865792i
$399$	4.86747	−	1.25359i	0.243678	−	0.0627580i
$400$	2.21389	+	1.64822i	0.110695	+	0.0824111i
$401$	−9.73916	+	5.62291i	−0.486351	+	0.280795i	−0.723059	−	0.690786i	$-0.757265\pi$
$401$	−9.73916	+	5.62291i	−0.486351	+	0.280795i	0.236709	+	0.971581i	$0.423931\pi$
$402$	5.71025	+	1.61203i	0.284801	+	0.0804008i
$403$	4.17546	+	2.41071i	0.207995	+	0.120086i
$404$	11.9583	−	2.46911i	0.594947	−	0.122843i
$405$	18.6474	−	1.17607i	0.926597	−	0.0584393i
$406$	−0.666349	−	3.16937i	−0.0330704	−	0.157293i
$407$	−16.6577			−0.825693
$408$	−12.9633	+	6.29510i	−0.641778	+	0.311654i
$409$	7.78394	−	13.4822i	0.384891	−	0.666651i	−0.606863	−	0.794807i	$-0.707572\pi$
$409$	7.78394	−	13.4822i	0.384891	−	0.666651i	0.991754	+	0.128155i	$0.0409056\pi$
$410$	−15.9730	−	13.0119i	−0.788851	−	0.642611i
$411$	20.9965	+	15.5921i	1.03568	+	0.769102i
$412$	4.48698	−	13.5407i	0.221058	−	0.667101i
$413$	−8.13353	+	10.0585i	−0.400225	+	0.494945i
$414$	−19.4345	−	25.2020i	−0.955152	−	1.23861i
$415$	−22.3635	+	12.9116i	−1.09778	+	0.633805i
$416$	−1.81354	−	7.18505i	−0.0889161	−	0.352276i
$417$	2.88091	−	24.9074i	0.141079	−	1.21972i
$418$	−2.20002	−	5.78151i	−0.107607	−	0.282783i
$419$	−18.0336			−0.881000			−0.440500	−	0.897753i	$-0.645199\pi$
$419$	−18.0336			−0.881000			−0.440500	+	0.897753i	$0.645199\pi$
$420$	−10.6100	+	15.7945i	−0.517715	+	0.770693i
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	−5.90898	−	15.5284i	−0.287644	−	0.755911i
$423$	−6.50595	−	21.5428i	−0.316330	−	1.04745i
$424$	11.7868	−	7.50890i	0.572419	−	0.364664i
$425$	1.75783	−	1.01488i	0.0852672	−	0.0492290i
$426$	−2.13968	+	0.542827i	−0.103668	+	0.0263001i
$427$	−3.90112	−	10.1415i	−0.188788	−	0.490782i
$428$	4.58816	+	1.52038i	0.221777	+	0.0734903i
$429$	5.39468	−	7.26453i	0.260458	−	0.350735i
$430$	−9.73337	−	7.92897i	−0.469385	−	0.382369i
$431$	6.22304	−	10.7786i	0.299753	−	0.519188i	−0.676326	−	0.736602i	$-0.736429\pi$
$431$	6.22304	−	10.7786i	0.299753	−	0.519188i	0.976079	+	0.217415i	$0.0697624\pi$
$432$	−9.26130	+	18.6072i	−0.445584	+	0.895240i
$433$	−0.497837			−0.0239245			−0.0119623	−	0.999928i	$-0.503808\pi$
$433$	−0.497837			−0.0239245			−0.0119623	+	0.999928i	$0.503808\pi$
$434$	13.0878	+	4.28449i	0.628233	+	0.205662i
$435$	−1.23621	−	2.85640i	−0.0592715	−	0.136954i
$436$	−2.74885	−	13.3131i	−0.131646	−	0.637582i
$437$	−7.12531	−	4.11380i	−0.340850	−	0.196790i
$438$	−8.65863	+	30.6712i	−0.413725	+	1.46553i
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	−0.593206	−	0.805051i	$-0.702138\pi$
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	0.400592	+	0.916257i	$0.368805\pi$
$440$	20.7712	+	10.8130i	0.990228	+	0.515491i
$441$	17.9787	+	10.8520i	0.856129	+	0.516762i
$442$	−5.38003	−	0.868179i	−0.255902	−	0.0412951i
$443$	11.0349	+	19.1130i	0.524283	+	0.908086i	0.999600	+	0.0282709i	$0.00900011\pi$
$443$	11.0349	+	19.1130i	0.524283	+	0.908086i	−0.475317	+	0.879815i	$0.657667\pi$
$444$	13.1212	+	6.09940i	0.622703	+	0.289465i
$445$	8.85044	−	15.3294i	0.419551	−	0.726684i
$446$	7.30312	+	19.1921i	0.345813	+	0.908773i
$447$	18.1072	−	7.83651i	0.856441	−	0.370654i
$448$	−9.29157	−	19.0175i	−0.438985	−	0.898494i
$449$		−	6.02866i		−	0.284510i	−0.989830	−	0.142255i	$-0.954565\pi$
$449$		−	6.02866i		−	0.284510i	0.989830	−	0.142255i	$-0.0454353\pi$
$450$	1.11381	−	2.70733i	0.0525053	−	0.127625i
$451$	24.2349	+	13.9920i	1.14118	+	0.658859i
$452$	−4.20633	−	4.72667i	−0.197849	−	0.222324i
$453$	−1.27681	−	0.948170i	−0.0599900	−	0.0445489i
$454$	−4.83554	+	29.9654i	−0.226943	+	1.40635i
$455$	−6.71564	+	2.58329i	−0.314834	+	0.121107i
$456$	−0.384021	+	5.35961i	−0.0179834	+	0.250987i
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.833926	+	0.551877i	$0.186088\pi$
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.0609766	+	0.998139i	$0.480578\pi$
$458$	−21.5243	−	17.5341i	−1.00576	−	0.819312i
$459$	9.86723	+	11.6736i	0.460563	+	0.544875i
$460$	30.5025	−	6.29808i	1.42219	−	0.293650i
$461$		−	12.4563i		−	0.580148i	−0.957004	−	0.290074i	$-0.906320\pi$
$461$		−	12.4563i		−	0.580148i	0.957004	−	0.290074i	$-0.0936799\pi$
$462$	10.8098	−	23.4758i	0.502918	−	1.09219i
$463$		−	28.0609i		−	1.30410i	−0.758176	−	0.652050i	$-0.773909\pi$
$463$		−	28.0609i		−	1.30410i	0.758176	−	0.652050i	$-0.226091\pi$
$464$	3.43886	+	0.401985i	0.159645	+	0.0186617i
$465$	13.1468	+	1.52063i	0.609669	+	0.0705174i
$466$	−12.7405	+	15.6399i	−0.590192	+	0.724503i
$467$	−8.54830	−	14.8061i	−0.395568	−	0.685144i	0.597605	−	0.801790i	$-0.296119\pi$
$467$	−8.54830	−	14.8061i	−0.395568	−	0.685144i	−0.993174	+	0.116646i	$0.962786\pi$
$468$	−6.90933	+	3.74689i	−0.319384	+	0.173200i
$469$	4.98342	+	4.02972i	0.230113	+	0.186075i
$470$	21.7422	+	3.50856i	1.00289	+	0.161838i
$471$	−9.01175	+	12.1353i	−0.415239	+	0.559165i
$472$	−7.43002	−	11.6630i	−0.341994	−	0.536834i
$473$	14.7679	+	8.52623i	0.679027	+	0.392036i
$474$	−18.1846	+	17.7056i	−0.835247	+	0.813246i
$475$		−	0.756831i		−	0.0347258i
$476$	−15.5482	+	0.734998i	−0.712651	+	0.0336886i
$477$	−10.8064	−	10.1464i	−0.494792	−	0.464569i
$478$	−20.1988	+	7.68620i	−0.923873	+	0.351558i
$479$	−8.21329	+	14.2258i	−0.375275	+	0.649995i	−0.990368	−	0.138459i	$-0.955785\pi$
$479$	−8.21329	+	14.2258i	−0.375275	+	0.649995i	0.615093	+	0.788454i	$0.289118\pi$
$480$	−12.4020	−	16.1229i	−0.566071	−	0.735908i
$481$	2.73590	+	4.73871i	0.124746	+	0.216067i
$482$	−1.33014	+	8.24276i	−0.0605862	+	0.375447i
$483$	−8.57333	−	33.2888i	−0.390100	−	1.51469i
$484$	−9.30998	−	3.08505i	−0.423181	−	0.140230i
$485$	27.6715	−	15.9761i	1.25650	−	0.725439i
$486$	21.5511	+	4.64213i	0.977578	+	0.210571i
$487$	27.7018	+	15.9937i	1.25529	+	0.724742i	0.972155	−	0.234339i	$-0.0752924\pi$
$487$	27.7018	+	15.9937i	1.25529	+	0.724742i	0.283134	+	0.959080i	$0.408626\pi$
$488$	11.6051	−	0.506591i	0.525340	−	0.0229323i
$489$	−14.2934	+	6.18596i	−0.646370	+	0.279739i
$490$	−17.2531	+	11.1673i	−0.779416	+	0.504487i
$491$	−2.03844			−0.0919935			−0.0459968	−	0.998942i	$-0.514646\pi$
$491$	−2.03844			−0.0919935			−0.0459968	+	0.998942i	$0.514646\pi$
$492$	−13.9663	−	19.8953i	−0.629650	−	0.896948i
$493$	1.27309	−	2.20505i	0.0573369	−	0.0993104i
$494$	−1.28336	+	1.57542i	−0.0577412	+	0.0708814i
$495$	5.66985	−	24.1819i	0.254841	−	1.08689i
$496$	−8.79153	+	11.8088i	−0.394752	+	0.530231i
$497$	−2.35524	−	0.371341i	−0.105647	−	0.0166569i
$498$	−29.5327	+	7.49231i	−1.32339	+	0.335739i
$499$	−3.71805	+	2.14662i	−0.166443	+	0.0960957i	−0.580907	−	0.813970i	$-0.697302\pi$
$499$	−3.71805	+	2.14662i	−0.166443	+	0.0960957i	0.414465	+	0.910065i	$0.363969\pi$
$500$	15.7060	+	17.6489i	0.702396	+	0.789285i
$501$	−27.8442	−	3.22060i	−1.24399	−	0.143886i
$502$	−31.3783	+	11.9403i	−1.40048	+	0.532922i
$503$	−26.3039			−1.17283			−0.586415	−	0.810010i	$-0.699461\pi$
$503$	−26.3039			−1.17283			−0.586415	+	0.810010i	$0.699461\pi$
$504$	−17.1107	+	14.5336i	−0.762171	+	0.647376i
$505$	12.6748			0.564023
$506$	−39.5399	+	15.0460i	−1.75776	+	0.668876i
$507$	19.4149	+	2.24563i	0.862247	+	0.0997318i
$508$	−20.0619	−	22.5436i	−0.890103	−	1.00021i
$509$	35.3140	−	20.3886i	1.56527	−	0.903707i	0.568557	−	0.822644i	$-0.307502\pi$
$509$	35.3140	−	20.3886i	1.56527	−	0.903707i	0.996709	−	0.0810631i	$-0.0258315\pi$
$510$	−14.4996	+	3.67848i	−0.642052	+	0.162886i
$511$	−21.6447	+	26.7673i	−0.957503	+	1.18411i
$512$	22.4339	−	2.95289i	0.991448	−	0.130500i
$513$	5.60911	−	1.00990i	0.247648	−	0.0445884i
$514$	−13.2198	+	16.2282i	−0.583100	+	0.715797i
$515$	7.40358	−	12.8234i	0.326241	−	0.565066i
$516$	−8.51055	−	12.1234i	−0.374656	−	0.533705i
$517$	−29.9148			−1.31565
$518$	10.4321	+	11.6376i	0.458358	+	0.511328i
$519$	6.72182	−	2.90910i	0.295055	−	0.127695i
$520$	−0.335461	−	7.68485i	−0.0147109	−	0.337003i
$521$	−6.01740	−	3.47415i	−0.263627	−	0.152205i	0.362361	−	0.932038i	$-0.381971\pi$
$521$	−6.01740	−	3.47415i	−0.263627	−	0.152205i	−0.625988	+	0.779833i	$0.715304\pi$
$522$	−0.488071	−	3.63972i	−0.0213623	−	0.159306i
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	−0.636183	−	0.771538i	$-0.719488\pi$
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	0.350080	+	0.936720i	$0.386154\pi$
$524$	14.0673	+	4.66149i	0.614533	+	0.203638i
$525$	2.25756	−	2.21404i	0.0985282	−	0.0966287i
$526$	3.13299	−	19.4149i	0.136605	−	0.846528i
$527$	5.41333	+	9.37617i	0.235808	+	0.408432i
$528$	20.1195	+	18.9366i	0.875589	+	0.824108i
$529$	−16.6344	+	28.8116i	−0.723234	+	1.25268i
$530$	13.5584	−	5.15934i	0.588939	−	0.224107i
$531$	−10.0398	+	10.6929i	−0.435689	+	0.464033i
$532$	−2.66136	+	5.15773i	−0.115385	+	0.223616i
$533$		−	9.19231i		−	0.398163i
$534$	14.9636	−	14.5695i	0.647539	−	0.630482i
$535$	4.34511	+	2.50865i	0.187855	+	0.108458i
$536$	−5.77839	+	3.68117i	−0.249588	+	0.159002i
$537$	6.76571	−	9.11077i	0.291962	−	0.393159i
$538$	11.5293	+	1.86049i	0.497064	+	0.0802115i
$539$	20.7193	−	18.7084i	0.892443	−	0.805826i
$540$	−13.3205	+	16.9718i	−0.573224	+	0.730349i
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	0.720922	−	0.693016i	$-0.243719\pi$
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	−0.960631	+	0.277829i	$0.910385\pi$
$542$	−4.73884	+	5.81726i	−0.203551	+	0.249873i
$543$	21.1355	+	2.44464i	0.907011	+	0.104910i
$544$	4.54037	−	16.0089i	0.194667	−	0.686376i
$545$		−	14.1108i		−	0.604442i
$546$	−8.45370	+	0.780582i	−0.361785	+	0.0334058i
$547$		−	39.2870i		−	1.67979i	−0.542748	−	0.839896i	$-0.682616\pi$
$547$		−	39.2870i		−	1.67979i	0.542748	−	0.839896i	$-0.317384\pi$
$548$	−29.5747	+	6.10651i	−1.26337	+	0.260857i
$549$	−3.56202	−	11.7947i	−0.152023	−	0.503386i
$550$	−3.01718	−	2.45785i	−0.128653	−	0.104803i
$551$	−0.474691	−	0.822189i	−0.0202225	−	0.0350264i
$552$	36.6545	+	2.62633i	1.56012	+	0.111784i
$553$	−25.5863	+	9.84225i	−1.08804	+	0.418535i
$554$	2.83983	−	17.5982i	0.120653	−	0.747676i
$555$	12.0585	+	8.95468i	0.511853	+	0.380105i
$556$	19.2472	+	21.6282i	0.816264	+	0.917240i
$557$	25.5152	+	14.7312i	1.08112	+	0.624182i	0.931197	−	0.364516i	$-0.118766\pi$
$557$	25.5152	+	14.7312i	1.08112	+	0.624182i	0.149919	+	0.988698i	$0.452099\pi$
$558$	14.4408	+	5.94098i	0.611327	+	0.251502i
$559$		−	5.60145i		−	0.236916i
$560$	−5.45383	−	21.2832i	−0.230466	−	0.899379i
$561$	18.6474	−	8.07030i	0.787294	−	0.340728i
$562$	−1.02090	−	2.68285i	−0.0430639	−	0.113169i
$563$	−20.3385	+	35.2274i	−0.857167	+	1.48466i	0.0174537	+	0.999848i	$0.494444\pi$
$563$	−20.3385	+	35.2274i	−0.857167	+	1.48466i	−0.874620	+	0.484808i	$0.838889\pi$
$564$	23.5636	+	10.9536i	0.992207	+	0.461230i
$565$	−3.28394	−	5.68796i	−0.138157	−	0.239294i
$566$	10.7194	+	1.72980i	0.450570	+	0.0727087i
$567$	19.4214	+	13.7771i	0.815622	+	0.578585i
$568$	1.17700	−	2.26094i	0.0493857	−	0.0948670i
$569$	−4.30534	+	2.48569i	−0.180489	+	0.104206i	−0.587523	−	0.809208i	$-0.699897\pi$
$569$	−4.30534	+	2.48569i	−0.180489	+	0.104206i	0.407033	+	0.913413i	$0.366563\pi$
$570$	−1.51538	+	5.36787i	−0.0634721	+	0.224835i
$571$	−30.2952	−	17.4909i	−1.26781	−	0.731973i	−0.293240	−	0.956039i	$-0.594734\pi$
$571$	−30.2952	−	17.4909i	−1.26781	−	0.731973i	−0.974574	+	0.224066i	$0.928067\pi$
$572$	2.11278	+	10.2325i	0.0883398	+	0.427843i
$573$	16.3266	+	37.7245i	0.682052	+	1.57596i
$574$	−5.40206	−	25.6939i	−0.225478	−	1.07244i
$575$	−5.17599			−0.215854
$576$	−8.91415	−	22.2831i	−0.371423	−	0.928464i
$577$	7.33386	−	12.7026i	0.305313	−	0.528817i	−0.672018	−	0.740535i	$-0.734572\pi$
$577$	7.33386	−	12.7026i	0.305313	−	0.528817i	0.977331	+	0.211718i	$0.0679057\pi$
$578$	9.15197	+	7.45535i	0.380672	+	0.310102i
$579$	−4.10366	+	5.52603i	−0.170542	+	0.229654i
$580$	3.41150	+	1.13047i	0.141655	+	0.0469402i
$581$	−32.5079	−	5.12540i	−1.34865	−	0.212637i
$582$	36.5422	−	9.27060i	1.51472	−	0.384279i
$583$	−17.0649	+	9.85242i	−0.706755	+	0.408045i
$584$	−19.7725	−	31.0372i	−0.818192	−	1.28433i
$585$	−7.81037	+	2.35874i	−0.322919	+	0.0975221i
$586$	−0.782305	−	2.05585i	−0.0323167	−	0.0849262i
$587$	−18.7469			−0.773769			−0.386885	−	0.922128i	$-0.626449\pi$
$587$	−18.7469			−0.773769			−0.386885	+	0.922128i	$0.626449\pi$
$588$	−23.1707	+	7.14985i	−0.955542	+	0.294855i
$589$	4.03690			0.166337
$590$	−5.10514	−	13.4160i	−0.210175	−	0.552327i
$591$	−3.93485	+	34.0194i	−0.161858	+	1.39937i
$592$	−15.3416	+	6.61752i	−0.630537	+	0.271978i
$593$	−38.8836	+	22.4494i	−1.59676	+	0.921888i	−0.604651	+	0.796491i	$0.706687\pi$
$593$	−38.8836	+	22.4494i	−1.59676	+	0.921888i	−0.992107	+	0.125398i	$0.959979\pi$
$594$	14.1898	−	25.6410i	0.582214	−	1.05206i
$595$	−15.9603	−	2.51640i	−0.654309	−	0.103162i
$596$	−7.16624	+	21.6261i	−0.293541	+	0.885838i
$597$	10.6607	+	7.91673i	0.436315	+	0.324010i
$598$	10.7743	+	8.77694i	0.440595	+	0.358916i
$599$	−0.596454	+	1.03309i	−0.0243704	+	0.0422108i	−0.877953	−	0.478746i	$-0.841091\pi$
$599$	−0.596454	+	1.03309i	−0.0243704	+	0.0422108i	0.853583	+	0.520957i	$0.174425\pi$
$600$	1.47664	+	3.04080i	0.0602838	+	0.124140i
$601$	37.4089			1.52594			0.762970	−	0.646434i	$-0.223741\pi$
$601$	37.4089			1.52594			0.762970	+	0.646434i	$0.223741\pi$
$602$	−3.29181	−	15.6569i	−0.134164	−	0.638128i
$603$	5.29775	+	4.97415i	0.215741	+	0.202563i
$604$	1.79847	−	0.371343i	0.0731786	−	0.0151097i
$605$	−8.81680	−	5.09038i	−0.358454	−	0.206953i
$606$	14.3923	+	4.06301i	0.584646	+	0.165048i
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	−0.0735982	−	0.997288i	$-0.523448\pi$
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	0.826878	+	0.562382i	$0.190115\pi$
$608$	−4.32298	−	4.45073i	−0.175320	−	0.180501i
$609$	1.06386	−	3.82120i	0.0431096	−	0.154843i
$610$	11.9039	+	1.92094i	0.481975	+	0.0777766i
$611$	4.91326	+	8.51001i	0.198769	+	0.344278i
$612$	−17.6434	−	0.471028i	−0.713193	−	0.0190402i
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	−0.0881290	−	0.996109i	$-0.528089\pi$
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	0.906720	−	0.421733i	$-0.138578\pi$
$614$	−15.8836	−	41.7410i	−0.641009	−	1.68453i
$615$	−10.0219	−	23.1567i	−0.404120	−	0.933768i
$616$	11.9189	+	27.3598i	0.480226	+	1.10236i
$617$			46.2548i			1.86215i	0.364830	+	0.931074i	$0.381127\pi$
$617$			46.2548i			1.86215i	−0.364830	+	0.931074i	$0.618873\pi$
$618$	12.5174	−	12.1877i	0.503523	−	0.490260i
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.0214035	−	0.999771i	$-0.506813\pi$
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.876529	+	0.481349i	$0.840147\pi$
$620$	−11.4160	+	10.1592i	−0.458477	+	0.408005i
$621$	−6.90676	−	38.3608i	−0.277159	−	1.53937i
$622$	−4.11780	+	25.5177i	−0.165109	+	1.02317i
$623$	21.0543	−	8.09892i	0.843523	−	0.324476i
$624$	2.08252	−	8.83368i	0.0833674	−	0.353630i
$625$	10.5369	+	18.2504i	0.421476	+	0.730018i
$626$	32.6544	+	26.6008i	1.30513	+	1.06318i
$627$	0.870499	−	7.52603i	0.0347644	−	0.300561i
$628$	−3.52937	−	17.0933i	−0.140837	−	0.682095i
$629$			12.2871i			0.489920i
$630$	−20.4450	+	11.1830i	−0.814549	+	0.445541i
$631$			26.5913i			1.05858i	0.848440	+	0.529291i	$0.177542\pi$
$631$			26.5913i			1.05858i	−0.848440	+	0.529291i	$0.822458\pi$
$632$	−1.27809	−	29.2790i	−0.0508398	−	1.16466i
$633$	2.33805	−	20.2140i	0.0929291	−	0.803433i
$634$	15.8059	−	19.4028i	0.627732	−	0.770586i
$635$	−15.6626	−	27.1284i	−0.621552	−	1.07656i
$636$	17.0494	−	1.51218i	0.676054	−	0.0599620i
$637$	−8.72504	−	2.82143i	−0.345699	−	0.111789i
$638$	−4.81932	−	0.777697i	−0.190799	−	0.0307893i
$639$	−2.63219	−	0.617162i	−0.104128	−	0.0244145i
$640$	23.4257	+	1.70705i	0.925982	+	0.0674771i
$641$	5.24154	+	3.02620i	0.207028	+	0.119528i	0.599930	−	0.800053i	$-0.295195\pi$
$641$	5.24154	+	3.02620i	0.207028	+	0.119528i	−0.392901	+	0.919581i	$0.628529\pi$
$642$	4.12970	+	4.24143i	0.162986	+	0.167396i
$643$			9.95426i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$643$			9.95426i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$644$	35.2738	+	18.2011i	1.38998	+	0.717225i
$645$	−6.10695	−	14.1108i	−0.240461	−	0.555614i
$646$	−4.26458	+	1.62279i	−0.167787	+	0.0638477i
$647$	15.4951	−	26.8383i	0.609175	−	1.05512i	−0.382201	−	0.924079i	$-0.624834\pi$
$647$	15.4951	−	26.8383i	0.609175	−	1.05512i	0.991377	−	0.131044i	$-0.0418328\pi$
$648$	−20.5659	+	15.0015i	−0.807905	+	0.589313i
$649$	9.74892	+	16.8856i	0.382679	+	0.662819i
$650$	−0.203649	+	1.26200i	−0.00798778	+	0.0494996i
$651$	11.8096	+	12.0417i	0.462854	+	0.471953i
$652$	5.65686	−	17.0711i	0.221540	−	0.668557i
$653$	7.01889	−	4.05236i	0.274670	−	0.158581i	−0.356338	−	0.934357i	$-0.615975\pi$
$653$	7.01889	−	4.05236i	0.274670	−	0.158581i	0.631008	+	0.775776i	$0.282641\pi$
$654$	4.52333	−	16.0229i	0.176876	−	0.626543i
$655$	13.3221	+	7.69152i	0.520538	+	0.300533i
$656$	27.8786	+	3.25887i	1.08848	+	0.127238i
$657$	−26.7174	+	28.4556i	−1.04235	+	1.11016i
$658$	18.7344	+	20.8994i	0.730343	+	0.814744i
$659$	38.3085			1.49229			0.746143	−	0.665785i	$-0.231903\pi$
$659$	38.3085			1.49229			0.746143	+	0.665785i	$0.231903\pi$
$660$	16.4783	+	23.4737i	0.641417	+	0.913711i
$661$	−3.32843	+	5.76501i	−0.129461	+	0.224233i	−0.923468	−	0.383676i	$-0.874658\pi$
$661$	−3.32843	+	5.76501i	−0.129461	+	0.224233i	0.794007	+	0.607909i	$0.207991\pi$
$662$	−31.3348	+	38.4657i	−1.21786	+	1.49501i
$663$	−5.35848	−	3.97924i	−0.208106	−	0.154541i
$664$	16.2454	−	31.2064i	0.630442	−	1.21104i
$665$	−3.78811	+	4.68463i	−0.146896	+	0.181662i
$666$	10.8219	+	14.0335i	0.419340	+	0.543786i
$667$	−5.62297	+	3.24642i	−0.217722	+	0.125702i
$668$	24.1784	−	21.5167i	0.935491	−	0.832506i
$669$	−2.88968	+	24.9832i	−0.111722	+	0.965905i
$670$	−6.64688	+	2.52932i	−0.256791	+	0.0977160i
$671$	−16.3784			−0.632280
$672$	0.629652	−	25.9153i	0.0242894	−	0.999705i
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	0.175776	−	0.0668876i	0.00677065	−	0.00257642i
$675$	2.73827	−	2.31456i	0.105396	−	0.0890874i
$676$	−16.8589	+	15.0029i	−0.648418	+	0.577036i
$677$	−39.0358	+	22.5373i	−1.50027	+	0.866180i	−0.500267	+	0.865871i	$0.666765\pi$
$677$	−39.0358	+	22.5373i	−1.50027	+	0.866180i	−1.00000		0.000308342i	$0.999902\pi$
$678$	−1.90560	−	7.51136i	−0.0731842	−	0.288472i
$679$	40.2236	+	6.34190i	1.54364	+	0.243380i
$680$	7.97594	−	15.3213i	0.305863	−	0.587546i
$681$	−22.1634	+	29.8454i	−0.849303	+	1.14368i
$682$	13.1100	−	16.0935i	0.502009	−	0.616252i
$683$	7.80843	−	13.5246i	0.298781	−	0.517505i	−0.677076	−	0.735913i	$-0.736753\pi$
$683$	7.80843	−	13.5246i	0.298781	−	0.517505i	0.975857	+	0.218408i	$0.0700865\pi$
$684$	−3.44142	+	5.60945i	−0.131586	+	0.214483i
$685$	−31.3469			−1.19770
$686$	−26.0459	−	2.75886i	−0.994437	−	0.105334i
$687$	−13.5049	−	31.2046i	−0.515242	−	1.19053i
$688$	16.9882	+	1.98584i	0.647670	+	0.0757093i
$689$	5.60554	+	3.23636i	0.213554	+	0.123295i
$690$	36.7110	+	10.3637i	1.39756	+	0.394539i
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.288718	−	0.957414i	$-0.406771\pi$
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.973504	+	0.228670i	$0.0734376\pi$
$692$	−2.66028	+	8.02811i	−0.101129	+	0.305183i
$693$	24.9961	−	19.4201i	0.949524	−	0.737709i
$694$	0.0440088	−	0.272719i	0.00167055	−	0.0103523i
$695$	15.0266	+	26.0268i	0.569991	+	0.987254i
$696$	3.51138	+	2.37723i	0.133098	+	0.0901087i
$697$	10.3208	−	17.8762i	0.390930	−	0.677110i
$698$	−7.67650	+	2.92111i	−0.290560	+	0.110566i
$699$	−22.6737	+	9.81282i	−0.857598	+	0.371155i
$700$	0.172409	+	3.64715i	0.00651644	+	0.137849i
$701$		−	36.6488i		−	1.38420i	−0.721799	−	0.692102i	$-0.756685\pi$
$701$		−	36.6488i		−	1.38420i	0.721799	−	0.692102i	$-0.243315\pi$
$702$	−9.62479	+	0.174683i	−0.363264	+	0.00659300i
$703$	3.96766	+	2.29073i	0.149643	+	0.0863964i
$704$	−31.7824	+	2.78005i	−1.19784	+	0.104777i
$705$	21.6552	+	16.0812i	0.815580	+	0.605655i
$706$	−27.9148	−	4.50462i	−1.05059	−	0.169534i
$707$	12.5604	+	10.1566i	0.472381	+	0.381979i
$708$	−1.49630	−	16.8703i	−0.0562344	−	0.634026i
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	−0.973107	−	0.230353i	$-0.926012\pi$
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	0.287062	−	0.957912i	$-0.407322\pi$
$710$	1.67109	−	2.05138i	0.0627147	−	0.0769868i
$711$	−29.7572	+	8.98673i	−1.11598	+	0.337029i
$712$	1.05171	+	24.0929i	0.0394144	+	0.902918i
$713$		−	27.6084i		−	1.03394i
$714$	−17.3163	−	7.97356i	−0.648045	−	0.298403i
$715$			10.8457i			0.405604i
$716$	2.64973	+	12.8330i	0.0990251	+	0.479593i
$717$	−26.2937	−	3.04126i	−0.981954	−	0.113578i
$718$	15.2473	+	12.4207i	0.569023	+	0.463535i
$719$	12.2687	+	21.2499i	0.457543	+	0.792488i	0.998830	−	0.0483494i	$-0.0153961\pi$
$719$	12.2687	+	21.2499i	0.457543	+	0.792488i	−0.541287	+	0.840838i	$0.682063\pi$
$720$	−4.38471	−	24.5237i	−0.163408	−	0.913944i
$721$	17.6124	−	6.77492i	0.655919	−	0.252311i
$722$	4.00962	−	24.8473i	0.149223	−	0.924720i
$723$	−6.09660	+	8.20974i	−0.226735	+	0.305324i
$724$	−18.3529	+	16.3325i	−0.682081	+	0.606993i
$725$	−0.517239	−	0.298628i	−0.0192098	−	0.0110908i
$726$	−8.37972	−	8.60641i	−0.311000	−	0.319414i
$727$			7.89691i			0.292880i	0.989220	+	0.146440i	$0.0467816\pi$
$727$			7.89691i			0.292880i	−0.989220	+	0.146440i	$0.953218\pi$
$728$	5.82560	−	7.88426i	0.215911	−	0.292210i
$729$	20.8078	+	17.2057i	0.770660	+	0.637247i
$730$	−13.5856	−	35.7021i	−0.502826	−	1.32139i
$731$	6.28914	−	10.8931i	0.232612	−	0.402896i
$732$	12.9011	+	5.99711i	0.476839	+	0.221660i
$733$	−2.92236	−	5.06167i	−0.107940	−	0.186957i	0.806996	−	0.590557i	$-0.201092\pi$
$733$	−2.92236	−	5.06167i	−0.107940	−	0.186957i	−0.914935	+	0.403600i	$0.867759\pi$
$734$	26.2664	+	4.23863i	0.969511	+	0.156451i
$735$	−25.0556	+	2.40485i	−0.924191	+	0.0887044i
$736$	−30.4386	+	29.5650i	−1.12198	+	1.08978i
$737$	8.36590	−	4.83005i	0.308162	−	0.177917i
$738$	−3.95677	−	29.5070i	−0.145651	−	1.08617i
$739$	−1.22939	−	0.709786i	−0.0452237	−	0.0261099i	0.477218	−	0.878785i	$-0.341645\pi$
$739$	−1.22939	−	0.709786i	−0.0452237	−	0.0261099i	−0.522441	+	0.852675i	$0.674979\pi$
$740$	−16.9850	+	3.50702i	−0.624382	+	0.128921i
$741$	−2.28394	+	0.988455i	−0.0839027	+	0.0363118i
$742$	17.5702	+	5.75190i	0.645024	+	0.211159i
$743$	1.70600			0.0625872			0.0312936	−	0.999510i	$-0.490037\pi$
$743$	1.70600			0.0625872			0.0312936	+	0.999510i	$0.490037\pi$
$744$	−16.2195	+	7.87635i	−0.594635	+	0.288761i
$745$	−11.8244	+	20.4805i	−0.433212	+	0.750346i
$746$	6.38466	+	5.20105i	0.233759	+	0.190424i
$747$	−36.3305	−	8.51831i	−1.32926	−	0.311669i
$748$	−7.38003	+	22.2713i	−0.269841	+	0.814318i
$749$	2.29563	+	5.96782i	0.0838805	+	0.218059i
$750$	7.11534	+	28.0467i	0.259815	+	1.02412i
$751$	−23.1969	+	13.3927i	−0.846466	+	0.488707i	−0.859457	−	0.511208i	$-0.829198\pi$
$751$	−23.1969	+	13.3927i	−0.846466	+	0.488707i	0.0129912	+	0.999916i	$0.495865\pi$
$752$	−27.5512	+	11.8841i	−1.00469	+	0.433367i
$753$	−40.8465	−	4.72451i	−1.48853	−	0.172171i
$754$	0.570299	+	1.49871i	0.0207691	+	0.0545798i
$755$	1.90623			0.0693749
$756$	−26.8001	+	6.14448i	−0.974710	+	0.223473i
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	−6.06562	−	15.9400i	−0.220313	−	0.578969i
$759$	−51.4707	−	5.95337i	−1.86827	−	0.216094i
$760$	−3.46045	−	5.43193i	−0.125524	−	0.197037i
$761$	13.0696	−	7.54576i	0.473774	−	0.273533i	−0.244044	−	0.969764i	$-0.578474\pi$
$761$	13.0696	−	7.54576i	0.473774	−	0.273533i	0.717818	+	0.696231i	$0.245141\pi$
$762$	−9.08868	−	35.8251i	−0.329248	−	1.29781i
$763$	11.3073	−	13.9834i	0.409352	−	0.506233i
$764$	−45.0557	−	14.9301i	−1.63006	−	0.540153i
$765$	−17.8371	−	4.18221i	−0.644902	−	0.151208i
$766$	−13.3239	−	10.8538i	−0.481411	−	0.392165i
$767$	3.20236	−	5.54665i	0.115631	−	0.200278i
$768$	26.0527	+	9.44763i	0.940095	+	0.340912i
$769$	12.6792			0.457222			0.228611	−	0.973518i	$-0.426582\pi$
$769$	12.6792			0.457222			0.228611	+	0.973518i	$0.426582\pi$
$770$	6.37368	+	30.3153i	0.229691	+	1.09249i
$771$	−23.5267	+	10.1820i	−0.847294	+	0.366695i
$772$	−1.60716	−	7.78373i	−0.0578431	−	0.280143i
$773$	33.5367	+	19.3624i	1.20623	+	0.696417i	0.961934	−	0.273283i	$-0.0881097\pi$
$773$	33.5367	+	19.3624i	1.20623	+	0.696417i	0.244296	+	0.969701i	$0.421443\pi$
$774$	−2.41111	−	17.9805i	−0.0866655	−	0.646295i
$775$	2.19937	−	1.26981i	0.0790037	−	0.0456128i
$776$	−20.1012	+	38.6132i	−0.721590	+	1.38613i
$777$	4.77397	+	18.5365i	0.171265	+	0.664994i
$778$	1.69002	+	0.272719i	0.0605900	+	0.00977745i
$779$	−3.84829	−	6.66544i	−0.137879	−	0.238814i
$780$	3.97125	−	8.54303i	0.142193	−	0.305889i
$781$	−1.79696	+	3.11243i	−0.0643004	+	0.111372i
$782$	11.0983	+	29.1655i	0.396873	+	1.04296i
$783$	1.52303	−	4.23190i	0.0544286	−	0.151236i
$784$	11.6501	−	25.4612i	0.416075	−	0.909330i
$785$		−	18.1175i		−	0.646642i
$786$	12.6617	+	13.0042i	0.451627	+	0.463845i
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	0.780456	−	0.625211i	$-0.214987\pi$
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	−0.151221	+	0.988500i	$0.548320\pi$
$788$	−26.2886	−	29.5406i	−0.936492	−	1.05234i
$789$	14.3598	−	19.3371i	0.511224	−	0.688419i
$790$	4.84640	−	30.0327i	0.172427	−	1.06852i
$791$	1.30360	−	8.26808i	0.0463506	−	0.293979i
$792$	11.1865	+	31.9366i	0.397494	+	1.13482i
$793$	2.69002	+	4.65925i	0.0955253	+	0.165455i
$794$	−10.4788	−	8.53624i	−0.371880	−	0.302940i
$795$	17.6495	+	2.04143i	0.625965	+	0.0724022i
$796$	−15.0163	+	3.10052i	−0.532237	+	0.109895i
$797$		−	27.9005i		−	0.988287i	−0.869380	−	0.494143i	$-0.835482\pi$
$797$		−	27.9005i		−	0.988287i	0.869380	−	0.494143i	$-0.164518\pi$
$798$	−5.80308	+	4.10509i	−0.205427	+	0.145319i
$799$			22.0658i			0.780632i
$800$	−3.75521	−	1.06504i	−0.132767	−	0.0376547i
$801$	24.4864	−	7.39493i	0.865184	−	0.261287i
$802$	10.0447	−	12.3305i	0.354689	−	0.435406i
$803$	25.9435	+	44.9354i	0.915525	+	1.58574i
$804$	−8.35832	+	0.741334i	−0.294775	+	0.0261448i
$805$	32.0383	+	25.9069i	1.12920	+	0.913100i
$806$	−6.73142	−	1.08625i	−0.237104	−	0.0382617i
$807$	11.4831	+	8.52744i	0.404225	+	0.300180i
$808$	−14.5640	+	9.27812i	−0.512360	+	0.326403i
$809$	−12.3530	−	7.13202i	−0.434309	−	0.250748i	0.266872	−	0.963732i	$-0.414010\pi$
$809$	−12.3530	−	7.13202i	−0.434309	−	0.250748i	−0.701181	+	0.712984i	$0.747343\pi$
$810$	−24.0557	+	10.9334i	−0.845232	+	0.384161i
$811$		−	38.4069i		−	1.34865i	−0.738435	−	0.674325i	$-0.764435\pi$
$811$		−	38.4069i		−	1.34865i	0.738435	−	0.674325i	$-0.235565\pi$
$812$	2.47482	+	3.85397i	0.0868492	+	0.135248i
$813$	−8.43351	+	3.64989i	−0.295776	+	0.128007i
$814$	22.0174	−	8.37821i	0.771710	−	0.293656i
$815$	9.33391	−	16.1668i	0.326953	−	0.566299i
$816$	13.9680	−	14.8406i	0.488979	−	0.519525i
$817$	−2.34501	−	4.06167i	−0.0820415	−	0.142100i
$818$	−3.50741	+	21.7351i	−0.122634	+	0.759951i
$819$	−9.62995	−	3.92118i	−0.336498	−	0.137017i
$820$	27.6569	+	9.16466i	0.965820	+	0.320044i
$821$	45.7169	−	26.3947i	1.59553	−	0.921181i	0.603198	−	0.797591i	$-0.293893\pi$
$821$	45.7169	−	26.3947i	1.59553	−	0.921181i	0.992333	−	0.123589i	$-0.0394406\pi$
$822$	−35.5944	−	10.0485i	−1.24150	−	0.350481i
$823$	4.96238	+	2.86503i	0.172978	+	0.0998687i	0.583989	−	0.811761i	$-0.301491\pi$
$823$	4.96238	+	2.86503i	0.172978	+	0.0998687i	−0.411012	+	0.911630i	$0.634824\pi$
$824$	0.879777	+	20.1542i	0.0306485	+	0.702105i
$825$	−1.89305	−	4.37413i	−0.0659077	−	0.152288i
$826$	5.69148	−	17.3857i	0.198032	−	0.604925i
$827$	−44.5253			−1.54830			−0.774149	−	0.633003i	$-0.781822\pi$
$827$	−44.5253			−1.54830			−0.774149	+	0.633003i	$0.781822\pi$
$828$	38.3632	+	23.5360i	1.33321	+	0.817931i
$829$	−13.0293	+	22.5674i	−0.452526	+	0.783799i	−0.998542	−	0.0539760i	$-0.982811\pi$
$829$	−13.0293	+	22.5674i	−0.452526	+	0.783799i	0.546016	+	0.837775i	$0.316144\pi$
$830$	23.0650	−	28.3139i	0.800597	−	0.982790i
$831$	13.0162	−	17.5277i	0.451526	−	0.608030i
$832$	6.01086	+	8.58471i	0.208389	+	0.297621i
$833$	−13.7997	−	15.2830i	−0.478132	−	0.529525i
$834$	8.71961	+	34.3703i	0.301935	+	1.19015i
$835$	29.0957	−	16.7984i	1.00690	−	0.581333i
$836$	5.81577	+	6.53520i	0.201142	+	0.226025i
$837$	12.3457	+	14.6058i	0.426731	+	0.504850i
$838$	23.8360	−	9.07023i	0.823400	−	0.313326i
$839$	46.0533			1.58994			0.794968	−	0.606652i	$-0.207488\pi$
$839$	46.0533			1.58994			0.794968	+	0.606652i	$0.207488\pi$
$840$	6.07974	−	26.2129i	0.209771	−	0.904430i
$841$	28.2508			0.974165
$842$	16.5190	−	6.28594i	0.569284	−	0.216628i
$843$	0.403945	−	3.49237i	0.0139126	−	0.120284i
$844$	15.6204	+	17.5527i	0.537676	+	0.604189i
$845$	−20.2875	+	11.7130i	−0.697912	+	0.402940i
$846$	19.4345	+	25.2020i	0.668171	+	0.866462i
$847$	−4.65814	−	12.1095i	−0.160056	−	0.416087i
$848$	−11.8026	+	15.8532i	−0.405302	+	0.544403i
$849$	10.6765	+	7.92840i	0.366415	+	0.272102i
$850$	−1.81297	+	2.22554i	−0.0621842	+	0.0763355i
$851$	15.6663	−	27.1349i	0.537035	−	0.930173i
$852$	2.55510	−	1.79366i	0.0875363	−	0.0614498i
$853$	46.3274			1.58622			0.793109	−	0.609079i	$-0.208461\pi$
$853$	46.3274			1.58622			0.793109	+	0.609079i	$0.208461\pi$
$854$	10.2571	+	11.4425i	0.350991	+	0.391553i
$855$	−4.67591	+	4.98011i	−0.159913	+	0.170316i
$856$	−6.82910	+	0.298106i	−0.233414	+	0.0101890i
$857$	35.6333	+	20.5729i	1.21721	+	0.702756i	0.964320	−	0.264739i	$-0.0852857\pi$
$857$	35.6333	+	20.5729i	1.21721	+	0.702756i	0.252890	+	0.967495i	$0.418619\pi$
$858$	−3.47665	+	12.3152i	−0.118691	+	0.420435i
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.747277	+	0.664512i	$0.768639\pi$
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.949123	+	0.314905i	$0.898027\pi$
$860$	16.8531	+	5.58461i	0.574685	+	0.190434i
$861$	8.62462	−	30.9783i	0.293926	−	1.05574i
$862$	−2.80407	+	17.3766i	−0.0955072	+	0.591850i
$863$	−12.7433	−	22.0721i	−0.433788	−	0.751343i	0.563408	−	0.826179i	$-0.309490\pi$
$863$	−12.7433	−	22.0721i	−0.433788	−	0.751343i	−0.997196	+	0.0748356i	$0.976157\pi$
$864$	2.88241	−	29.2522i	0.0980616	−	0.995180i
$865$	−4.38950	+	7.60283i	−0.149247	+	0.258504i
$866$	0.658017	−	0.250393i	0.0223603	−	0.00850871i
$867$	5.74216	+	13.2680i	0.195014	+	0.450604i
$868$	−19.4537	+	0.919620i	−0.660302	+	0.0312139i
$869$			41.3215i			1.40174i
$870$	3.07062	+	3.15369i	0.104104	+	0.106920i
$871$	−2.74806	−	1.58659i	−0.0931145	−	0.0537597i
$872$	10.3293	+	16.2140i	0.349794	+	0.549077i
$873$	44.9535	+	10.5401i	1.52145	+	0.356729i
$874$	11.4870	+	1.85366i	0.388553	+	0.0627010i
$875$	−4.86751	+	30.8723i	−0.164552	+	1.04367i
$876$	−3.98189	−	44.8947i	−0.134536	−	1.51685i
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	−0.966038	−	0.258402i	$-0.916804\pi$
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	0.259236	−	0.965814i	$-0.416529\pi$
$878$	4.16230	−	5.10952i	0.140471	−	0.172438i
$879$	0.309541	−	2.67618i	0.0104405	−	0.0902653i
$880$	−32.8929	−	3.84502i	−1.10882	−	0.129616i
$881$		−	38.5556i		−	1.29897i	−0.760373	−	0.649486i	$-0.774984\pi$
$881$		−	38.5556i		−	1.29897i	0.760373	−	0.649486i	$-0.225016\pi$
$882$	−29.2215	−	5.30105i	−0.983941	−	0.178496i
$883$		−	4.56420i		−	0.153597i	−0.997047	−	0.0767987i	$-0.975530\pi$
$883$		−	4.56420i		−	0.153597i	0.997047	−	0.0767987i	$-0.0244699\pi$
$884$	7.54773	−	1.55844i	0.253858	−	0.0524159i
$885$	2.01999	−	17.4641i	0.0679012	−	0.587050i
$886$	−24.1985	−	19.7125i	−0.812965	−	0.662255i
$887$	−20.2446	−	35.0647i	−0.679747	−	1.17736i	−0.975057	−	0.221955i	$-0.928756\pi$
$887$	−20.2446	−	35.0647i	−0.679747	−	1.17736i	0.295310	−	0.955401i	$-0.404577\pi$
$888$	−20.4107	−	1.46245i	−0.684938	−	0.0490765i
$889$	6.21745	−	39.4342i	0.208527	−	1.32258i
$890$	−3.98797	+	24.7131i	−0.133677	+	0.828385i
$891$	29.8919	−	19.8668i	1.00142	−	0.665562i
$892$	−19.3058	−	21.6940i	−0.646407	−	0.726370i
$893$	7.12531	+	4.11380i	0.238439	+	0.137663i
$894$	−19.9918	+	19.4652i	−0.668624	+	0.651012i
$895$			13.6020i			0.454665i
$896$	21.8463	+	20.4632i	0.729832	+	0.683626i
$897$	6.76007	+	15.6199i	0.225712	+	0.521535i
$898$	3.03219	+	7.96840i	0.101185	+	0.265909i
$899$	1.59287	−	2.75893i	0.0531251	−	0.0920154i
$900$	−0.110489	+	4.13862i	−0.00368297	+	0.137954i
$901$	7.26737	+	12.5874i	0.242111	+	0.419349i
$902$	−39.0700	−	6.30475i	−1.30089	−	0.209925i
$903$	5.25553	−	18.8770i	0.174893	−	0.628188i
$904$	7.93706	+	4.13186i	0.263983	+	0.137424i
$905$	−22.0854	+	12.7510i	−0.734145	+	0.423859i
$906$	2.16453	+	0.611056i	0.0719116	+	0.0203010i
$907$	2.36697	+	1.36657i	0.0785940	+	0.0453763i	0.538782	−	0.842445i	$-0.318885\pi$
$907$	2.36697	+	1.36657i	0.0785940	+	0.0453763i	−0.460188	+	0.887822i	$0.652218\pi$
$908$	−8.68010	−	42.0390i	−0.288059	−	1.39511i
$909$	13.3526	+	12.5370i	0.442878	+	0.415826i
$910$	7.57711	−	6.79219i	0.251179	−	0.225159i
$911$	5.16105			0.170993			0.0854966	−	0.996338i	$-0.472752\pi$
$911$	5.16105			0.170993			0.0854966	+	0.996338i	$0.472752\pi$
$912$	−2.18810	−	7.27722i	−0.0724552	−	0.240973i
$913$	−24.8024	+	42.9590i	−0.820839	+	1.42174i
$914$	−41.9521	−	34.1749i	−1.38765	−	1.13041i
$915$	11.8562	+	8.80451i	0.391955	+	0.291068i
$916$	37.2688	+	12.3498i	1.23139	+	0.408048i
$917$	7.03841	+	18.2973i	0.232429	+	0.604232i
$918$	−18.9134	−	10.4667i	−0.624235	−	0.345453i
$919$	34.5011	−	19.9192i	1.13809	−	0.657074i	0.192130	−	0.981370i	$-0.438461\pi$
$919$	34.5011	−	19.9192i	1.13809	−	0.657074i	0.945956	+	0.324296i	$0.105127\pi$
$920$	−37.1491	+	23.6661i	−1.22477	+	0.780249i
$921$	6.28477	−	54.3360i	0.207090	−	1.79043i
$922$	6.26505	+	16.4641i	0.206328	+	0.542218i
$923$	1.18055			0.0388582
$924$	−2.48046	+	36.4661i	−0.0816011	+	1.19965i
$925$	2.88220			0.0947660
$926$	14.1136	+	37.0895i	0.463801	+	1.21884i
$927$	20.4834	−	6.18602i	0.672763	−	0.203176i
$928$	−4.74750	+	1.19829i	−0.155844	+	0.0393358i
$929$	−22.2777	+	12.8621i	−0.730909	+	0.421990i	−0.818754	−	0.574144i	$-0.805335\pi$
$929$	−22.2777	+	12.8621i	−0.730909	+	0.421990i	0.0878459	+	0.996134i	$0.472002\pi$
$930$	−18.1417	+	4.60246i	−0.594889	+	0.150921i
$931$	−7.50779	+	1.60683i	−0.246058	+	0.0526617i
$932$	8.97351	−	27.0800i	0.293937	−	0.887035i
$933$	−18.8737	+	25.4155i	−0.617897	+	0.832065i
$934$	18.7456	+	15.2705i	0.613376	+	0.499666i
$935$	−12.1772	+	21.0915i	−0.398236	+	0.689765i
$936$	7.24788	−	8.42760i	0.236904	−	0.275465i
$937$	20.2068			0.660127			0.330063	−	0.943959i	$-0.392930\pi$
$937$	20.2068			0.660127			0.330063	+	0.943959i	$0.392930\pi$
$938$	−8.61365	−	2.81982i	−0.281246	−	0.0920702i
$939$	20.4881	+	47.3403i	0.668604	+	1.54489i
$940$	−30.5025	+	6.29808i	−0.994883	+	0.205421i
$941$	−41.4712	−	23.9434i	−1.35192	−	0.780533i	−0.363403	−	0.931632i	$-0.618385\pi$
$941$	−41.4712	−	23.9434i	−1.35192	−	0.780533i	−0.988519	+	0.151099i	$0.951719\pi$
$942$	5.80770	−	20.5724i	0.189225	−	0.670286i
$943$	−45.5851	+	26.3186i	−1.48446	+	0.857051i
$944$	15.6867	+	11.6786i	0.510559	+	0.380106i
$945$	−28.5342	+	0.620996i	−0.928218	+	0.0202010i
$946$	−23.8078	−	3.84188i	−0.774059	−	0.124910i
$947$	3.16035	+	5.47389i	0.102698	+	0.177878i	0.912795	−	0.408418i	$-0.133919\pi$
$947$	3.16035	+	5.47389i	0.102698	+	0.177878i	−0.810098	+	0.586295i	$0.800586\pi$
$948$	15.1303	−	32.5486i	0.491409	−	1.05713i
$949$	8.52200	−	14.7605i	0.276636	−	0.479148i
$950$	0.380657	+	1.00034i	0.0123502	+	0.0324554i
$951$	28.1290	−	12.1738i	0.912147	−	0.394763i
$952$	20.1812	−	8.79165i	0.654077	−	0.284939i
$953$		−	3.70027i		−	0.119863i	−0.998202	−	0.0599317i	$-0.980912\pi$
$953$		−	3.70027i		−	0.119863i	0.998202	−	0.0599317i	$-0.0190883\pi$
$954$	19.3867	+	7.97573i	0.627666	+	0.258224i
$955$	−42.6689	−	24.6349i	−1.38073	−	0.797167i
$956$	22.8320	−	20.3185i	0.738439	−	0.657147i
$957$	−4.80002	−	3.56452i	−0.155163	−	0.115225i
$958$	3.70087	−	22.9340i	0.119570	−	0.740964i
$959$	−31.0638	−	25.1189i	−1.00310	−	0.811133i
$960$	24.5016	+	15.0728i	0.790786	+	0.486472i
$961$	−8.72691	−	15.1155i	−0.281513	−	0.487595i
$962$	−5.99957	−	4.88735i	−0.193434	−	0.157575i
$963$	2.09609	+	6.94065i	0.0675455	+	0.223659i
$964$	−2.38768	−	11.5639i	−0.0769021	−	0.372448i
$965$		−	8.25014i		−	0.265581i
$966$	28.0748	+	39.6874i	0.903292	+	1.27692i
$967$			14.5970i			0.469409i	0.972067	+	0.234705i	$0.0754123\pi$
$967$			14.5970i			0.469409i	−0.972067	+	0.234705i	$0.924588\pi$
$968$	13.8572	−	0.604896i	0.445386	−	0.0194421i
$969$	−5.55138	−	0.642100i	−0.178336	−	0.0206272i
$970$	−28.5394	+	35.0342i	−0.916346	+	1.12488i
$971$	4.10729	+	7.11403i	0.131809	+	0.228300i	0.924374	−	0.381488i	$-0.124588\pi$
$971$	4.10729	+	7.11403i	0.131809	+	0.228300i	−0.792565	+	0.609788i	$0.791255\pi$
$972$	−30.8201	+	4.70365i	−0.988554	+	0.150870i
$973$	−5.96498	+	37.8329i	−0.191228	+	1.21287i
$974$	−44.6592	−	7.20668i	−1.43097	−	0.230917i
$975$	−0.933412	+	1.25694i	−0.0298931	+	0.0402543i
$976$	−15.0843	+	6.50654i	−0.482838	+	0.208269i
$977$	30.8426	+	17.8070i	0.986744	+	0.569697i	0.904299	−	0.426899i	$-0.140394\pi$
$977$	30.8426	+	17.8070i	0.986744	+	0.569697i	0.0824443	+	0.996596i	$0.473727\pi$
$978$	15.7810	−	15.3654i	0.504622	−	0.491330i
$979$		−	34.0023i		−	1.08672i
$980$	17.1876	−	23.4381i	0.549038	−	0.748701i
$981$	13.9574	−	14.8654i	0.445625	−	0.474615i
$982$	2.69431	−	1.02526i	0.0859790	−	0.0327173i
$983$	−15.5749	+	26.9764i	−0.496761	+	0.860415i	−0.999993	−	0.00373618i	$-0.998811\pi$
$983$	−15.5749	+	26.9764i	−0.496761	+	0.860415i	0.503232	+	0.864151i	$0.332144\pi$
$984$	28.4666	+	19.2721i	0.907481	+	0.614371i
$985$	−20.5239	−	35.5484i	−0.653945	−	1.13267i
$986$	−0.573647	+	3.55484i	−0.0182687	+	0.113209i
$987$	8.57333	+	33.2888i	0.272892	+	1.05959i
$988$	0.903910	−	2.72779i	0.0287572	−	0.0867827i
$989$	−27.7779	+	16.0376i	−0.883285	+	0.509965i
$990$	4.66844	+	34.8142i	0.148373	+	1.10647i
$991$	−30.1606	−	17.4132i	−0.958083	−	0.553149i	−0.0625004	−	0.998045i	$-0.519907\pi$
$991$	−30.1606	−	17.4132i	−0.958083	−	0.553149i	−0.895582	+	0.444896i	$0.853241\pi$
$992$	5.68085	−	20.0301i	0.180367	−	0.635957i
$993$	−55.7652	+	24.1343i	−1.76966	+	0.765879i
$994$	3.29981	−	0.693774i	0.104664	−	0.0220052i
$995$	−15.9161			−0.504573
$996$	35.2665	−	24.7568i	1.11746	−	0.784449i
$997$	−4.22860	+	7.32414i	−0.133921	+	0.231958i	−0.925185	−	0.379517i	$-0.876090\pi$
$997$	−4.22860	+	7.32414i	−0.133921	+	0.231958i	0.791264	+	0.611475i	$0.209424\pi$
$998$	3.83467	−	4.70733i	0.121384	−	0.149008i
$999$	3.84596	+	21.3608i	0.121681	+	0.675827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.11.1	✓	24
3.2	odd	2	inner	84.2.n.a.11.12	yes	24
4.3	odd	2	inner	84.2.n.a.11.3	yes	24
7.2	even	3	inner	84.2.n.a.23.10	yes	24
7.3	odd	6		588.2.e.d.491.7		12
7.4	even	3		588.2.e.e.491.7		12
7.5	odd	6		588.2.n.e.275.10		24
7.6	odd	2		588.2.n.e.263.1		24
12.11	even	2	inner	84.2.n.a.11.10	yes	24
21.2	odd	6	inner	84.2.n.a.23.3	yes	24
21.5	even	6		588.2.n.e.275.3		24
21.11	odd	6		588.2.e.e.491.6		12
21.17	even	6		588.2.e.d.491.6		12
21.20	even	2		588.2.n.e.263.12		24
28.3	even	6		588.2.e.d.491.5		12
28.11	odd	6		588.2.e.e.491.5		12
28.19	even	6		588.2.n.e.275.12		24
28.23	odd	6	inner	84.2.n.a.23.12	yes	24
28.27	even	2		588.2.n.e.263.3		24
84.11	even	6		588.2.e.e.491.8		12
84.23	even	6	inner	84.2.n.a.23.1	yes	24
84.47	odd	6		588.2.n.e.275.1		24
84.59	odd	6		588.2.e.d.491.8		12
84.83	odd	2		588.2.n.e.263.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	1.1	even	1	trivial
84.2.n.a.11.3	yes	24	4.3	odd	2	inner
84.2.n.a.11.10	yes	24	12.11	even	2	inner
84.2.n.a.11.12	yes	24	3.2	odd	2	inner
84.2.n.a.23.1	yes	24	84.23	even	6	inner
84.2.n.a.23.3	yes	24	21.2	odd	6	inner
84.2.n.a.23.10	yes	24	7.2	even	3	inner
84.2.n.a.23.12	yes	24	28.23	odd	6	inner
588.2.e.d.491.5		12	28.3	even	6
588.2.e.d.491.6		12	21.17	even	6
588.2.e.d.491.7		12	7.3	odd	6
588.2.e.d.491.8		12	84.59	odd	6
588.2.e.e.491.5		12	28.11	odd	6
588.2.e.e.491.6		12	21.11	odd	6
588.2.e.e.491.7		12	7.4	even	3
588.2.e.e.491.8		12	84.11	even	6
588.2.n.e.263.1		24	7.6	odd	2
588.2.n.e.263.3		24	28.27	even	2
588.2.n.e.263.10		24	84.83	odd	2
588.2.n.e.263.12		24	21.20	even	2
588.2.n.e.275.1		24	84.47	odd	6
588.2.n.e.275.3		24	21.5	even	6
588.2.n.e.275.10		24	7.5	odd	6
588.2.n.e.275.12		24	28.19	even	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32175 + 0.502962i) q^{2} +(-1.72058 - 0.199011i) q^{3} +(1.49406 - 1.32958i) q^{4} +(1.79791 - 1.03802i) q^{5} +(2.37428 - 0.602344i) q^{6} +(2.61347 + 0.412056i) q^{7} +(-1.30604 + 2.50883i) q^{8} +(2.92079 + 0.684828i) q^{9} +(-1.85431 + 2.27629i) q^{10} +(1.99399 - 3.45368i) q^{11} +(-2.83525 + 1.99032i) q^{12} -1.30998 q^{13} +(-3.66160 + 0.769840i) q^{14} +(-3.30003 + 1.42820i) q^{15} +(0.464417 - 3.97295i) q^{16} +(-2.54752 - 1.47081i) q^{17} +(-4.20500 + 0.563873i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(1.30604 - 3.94134i) q^{20} +(-4.41467 - 1.22908i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(3.75063 + 6.49627i) q^{23} +(2.74644 - 4.05673i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(1.73147 - 0.658872i) q^{26} +(-4.88916 - 1.75957i) q^{27} +(4.45253 - 2.85919i) q^{28} +0.865568i q^{29} +(3.64349 - 3.54752i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(1.38440 + 5.48484i) q^{32} +(-4.11813 + 5.54551i) q^{33} +(4.10695 + 0.662741i) q^{34} +(5.12651 - 1.97200i) q^{35} +(5.27436 - 2.86026i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(0.979678 - 1.20262i) q^{38} +(2.25393 + 0.260701i) q^{39} +(0.256080 + 5.86637i) q^{40} +7.01712i q^{41} +(6.45329 - 0.595872i) q^{42} +4.27597i q^{43} +(-1.61283 - 7.81117i) q^{44} +(5.96219 - 1.80059i) q^{45} +(-8.22478 - 6.70004i) q^{46} +(-3.75063 - 6.49627i) q^{47} +(-1.58973 + 6.74335i) q^{48} +(6.66042 + 2.15379i) q^{49} +(0.155459 - 0.963368i) q^{50} +(4.09050 + 3.03763i) q^{51} +(-1.95719 + 1.74173i) q^{52} +(-4.27909 - 2.47053i) q^{53} +(7.34726 - 0.133348i) q^{54} -8.27923i q^{55} +(-4.44708 + 6.01859i) q^{56} +(1.74349 - 0.754555i) q^{57} +(-0.435348 - 1.14407i) q^{58} +(-2.44458 + 4.23414i) q^{59} +(-3.03152 + 6.52148i) q^{60} +(-2.05347 - 3.55672i) q^{61} +(5.13856 + 0.829212i) q^{62} +(7.35120 + 2.99330i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(-2.35524 + 1.35980i) q^{65} +(2.65397 - 9.40106i) q^{66} +(2.09778 + 1.21116i) q^{67} +(-5.76170 + 1.18966i) q^{68} +(-5.16042 - 11.9238i) q^{69} +(-5.78413 + 5.18494i) q^{70} -0.901192 q^{71} +(-5.53280 + 6.43336i) q^{72} +(-6.50543 + 11.2677i) q^{73} +(4.57989 + 3.73085i) q^{74} +(0.712537 - 0.959509i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(6.63432 - 8.20446i) q^{77} +(-3.11026 + 0.789060i) q^{78} +(-8.97336 + 5.18077i) q^{79} +(-3.28904 - 7.62509i) q^{80} +(8.06202 + 4.00048i) q^{81} +(-3.52935 - 9.27489i) q^{82} -12.4386 q^{83} +(-8.22995 + 4.03336i) q^{84} -6.10695 q^{85} +(-2.15065 - 5.65178i) q^{86} +(0.172258 - 1.48928i) q^{87} +(6.06049 + 9.51324i) q^{88} +(7.38393 - 4.26311i) q^{89} +(-6.97491 + 5.37869i) q^{90} +(-3.42360 - 0.539786i) q^{91} +(14.2410 + 4.71904i) q^{92} +(5.11797 + 3.80064i) q^{93} +(8.22478 + 6.70004i) q^{94} +(-1.13854 + 1.97200i) q^{95} +(-1.29043 - 9.71261i) q^{96} +15.3909 q^{97} +(-9.88670 + 0.503167i) q^{98} +(8.18919 - 8.72195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37}+ \cdots + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Introduction

L-functions

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