LMFDB - Embedded newform 220.2.r.d.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	220.151
Dual form			220.2.r.d.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 0.00460387i) q^{2} +(-2.09469 + 0.680607i) q^{3} +(1.99996 + 0.0130217i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.96546 - 0.952875i) q^{6} +(-0.548700 + 1.68872i) q^{7} +(-2.82829 - 0.0276229i) q^{8} +(1.49746 - 1.08797i) q^{9} +(1.14141 + 0.834974i) q^{10} +(0.218764 - 3.30940i) q^{11} +(-4.19816 + 1.33391i) q^{12} +(0.368242 + 0.506841i) q^{13} +(0.783749 - 2.38568i) q^{14} +(2.09469 + 0.680607i) q^{15} +(3.99966 + 0.0520855i) q^{16} +(4.68469 - 6.44792i) q^{17} +(-2.12273 + 1.53172i) q^{18} +(-1.50197 - 4.62260i) q^{19} +(-1.61035 - 1.18608i) q^{20} -3.91081i q^{21} +(-0.324613 + 4.67917i) q^{22} -4.01581i q^{23} +(5.94320 - 1.86709i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.518436 - 0.718473i) q^{26} +(1.48753 - 2.04741i) q^{27} +(-1.11937 + 3.37023i) q^{28} +(-0.923402 - 0.300032i) q^{29} +(-2.95919 - 0.972162i) q^{30} +(2.21616 + 3.05028i) q^{31} +(-5.65610 - 0.0920736i) q^{32} +(1.79416 + 7.08107i) q^{33} +(-6.65480 + 9.09711i) q^{34} +(1.43651 - 1.04369i) q^{35} +(3.00903 - 2.15639i) q^{36} +(1.35825 - 4.18026i) q^{37} +(2.10282 + 6.54423i) q^{38} +(-1.11631 - 0.811049i) q^{39} +(2.27190 + 1.68478i) q^{40} +(-7.91566 + 2.57195i) q^{41} +(-0.0180049 + 5.53069i) q^{42} -8.42797 q^{43} +(0.480613 - 6.61582i) q^{44} -1.85096 q^{45} +(-0.0184883 + 5.67919i) q^{46} +(7.43548 - 2.41593i) q^{47} +(-8.41351 + 2.61309i) q^{48} +(3.11240 + 2.26129i) q^{49} +(-0.432635 - 1.34641i) q^{50} +(-5.42448 + 16.6948i) q^{51} +(0.729868 + 1.01846i) q^{52} +(-7.51011 + 5.45641i) q^{53} +(-2.11310 + 2.88862i) q^{54} +(-2.12220 + 2.54878i) q^{55} +(1.59853 - 4.76105i) q^{56} +(6.29235 + 8.66068i) q^{57} +(1.30450 + 0.428558i) q^{58} +(2.45740 + 0.798458i) q^{59} +(4.18043 + 1.38846i) q^{60} +(5.77741 - 7.95192i) q^{61} +(-3.12006 - 4.32392i) q^{62} +(1.01562 + 3.12577i) q^{63} +(7.99847 + 0.156251i) q^{64} -0.626490i q^{65} +(-2.50471 - 10.0224i) q^{66} -7.43389i q^{67} +(9.45313 - 12.8346i) q^{68} +(2.73319 + 8.41190i) q^{69} +(-2.03633 + 1.46938i) q^{70} +(1.04793 - 1.44235i) q^{71} +(-4.26531 + 3.03573i) q^{72} +(-3.83520 - 1.24613i) q^{73} +(-1.94009 + 5.90550i) q^{74} +(-1.29459 - 1.78185i) q^{75} +(-2.94369 - 9.26457i) q^{76} +(5.46863 + 2.18530i) q^{77} +(1.57496 + 1.15213i) q^{78} +(-2.58308 + 1.87672i) q^{79} +(-3.20518 - 2.39308i) q^{80} +(-3.43838 + 10.5822i) q^{81} +(11.2062 - 3.60083i) q^{82} +(-6.14025 - 4.46116i) q^{83} +(0.0509252 - 7.82145i) q^{84} +(-7.57998 + 2.46288i) q^{85} +(11.9189 + 0.0388013i) q^{86} +2.13845 q^{87} +(-0.710144 + 9.35391i) q^{88} -6.28641 q^{89} +(2.61764 + 0.00852160i) q^{90} +(-1.05797 + 0.343755i) q^{91} +(0.0522925 - 8.03146i) q^{92} +(-6.71820 - 4.88106i) q^{93} +(-10.5264 + 3.38239i) q^{94} +(-1.50197 + 4.62260i) q^{95} +(11.9105 - 3.65672i) q^{96} +(4.44805 - 3.23170i) q^{97} +(-4.39117 - 3.21226i) q^{98} +(-3.27294 - 5.19371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) $ 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.41421	−	0.00460387i	−0.999995	−	0.00325543i
$2$	−1.41421	−	0.00460387i	−0.999995	−	0.00325543i
$3$	−2.09469	+	0.680607i	−1.20937	+	0.392949i	−0.843201	−	0.537599i	$-0.819331\pi$
$3$	−2.09469	+	0.680607i	−1.20937	+	0.392949i	−0.366171	+	0.930548i	$0.619331\pi$
$4$	1.99996	+	0.0130217i	0.999979	+	0.00651083i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	2.96546	−	0.952875i	1.21064	−	0.389009i
$7$	−0.548700	+	1.68872i	−0.207389	+	0.638278i	0.792218	+	0.610238i	$0.208926\pi$
$7$	−0.548700	+	1.68872i	−0.207389	+	0.638278i	−0.999607	+	0.0280392i	$0.991074\pi$
$8$	−2.82829	−	0.0276229i	−0.999952	−	0.00976615i
$9$	1.49746	−	1.08797i	0.499154	−	0.362656i
$10$	1.14141	+	0.834974i	0.360946	+	0.264042i
$11$	0.218764	−	3.30940i	0.0659598	−	0.997822i
$11$	0.218764	−	3.30940i	0.0659598	−	0.997822i
$12$	−4.19816	+	1.33391i	−1.21190	+	0.385066i
$13$	0.368242	+	0.506841i	0.102132	+	0.140572i	0.857024	−	0.515277i	$-0.172311\pi$
$13$	0.368242	+	0.506841i	0.102132	+	0.140572i	−0.754892	+	0.655849i	$0.772311\pi$
$14$	0.783749	−	2.38568i	0.209466	−	0.637599i
$15$	2.09469	+	0.680607i	0.540847	+	0.175732i
$16$	3.99966	+	0.0520855i	0.999915	+	0.0130214i
$17$	4.68469	−	6.44792i	1.13620	−	1.56385i	0.360490	−	0.932763i	$-0.382609\pi$
$17$	4.68469	−	6.44792i	1.13620	−	1.56385i	0.775713	−	0.631086i	$-0.217391\pi$
$18$	−2.12273	+	1.53172i	−0.500332	+	0.361029i
$19$	−1.50197	−	4.62260i	−0.344577	−	1.06050i	−0.961810	−	0.273718i	$-0.911747\pi$
$19$	−1.50197	−	4.62260i	−0.344577	−	1.06050i	0.617233	−	0.786780i	$-0.288253\pi$
$20$	−1.61035	−	1.18608i	−0.360084	−	0.265216i
$21$		−	3.91081i		−	0.853408i
$22$	−0.324613	+	4.67917i	−0.0692078	+	0.997602i
$23$		−	4.01581i		−	0.837355i	−0.908135	−	0.418677i	$-0.862494\pi$
$23$		−	4.01581i		−	0.837355i	0.908135	−	0.418677i	$-0.137506\pi$
$24$	5.94320	−	1.86709i	1.21315	−	0.381119i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.518436	−	0.718473i	−0.101674	−	0.140904i
$27$	1.48753	−	2.04741i	0.286276	−	0.394025i
$28$	−1.11937	+	3.37023i	−0.211540	+	0.636914i
$29$	−0.923402	−	0.300032i	−0.171472	−	0.0557145i	0.222023	−	0.975041i	$-0.428734\pi$
$29$	−0.923402	−	0.300032i	−0.171472	−	0.0557145i	−0.393495	+	0.919327i	$0.628734\pi$
$30$	−2.95919	−	0.972162i	−0.540272	−	0.177492i
$31$	2.21616	+	3.05028i	0.398033	+	0.547846i	0.960249	−	0.279145i	$-0.0900510\pi$
$31$	2.21616	+	3.05028i	0.398033	+	0.547846i	−0.562216	+	0.826991i	$0.690051\pi$
$32$	−5.65610	−	0.0920736i	−0.999868	−	0.0162765i
$33$	1.79416	+	7.08107i	0.312323	+	1.23266i
$34$	−6.65480	+	9.09711i	−1.14129	+	1.56014i
$35$	1.43651	−	1.04369i	0.242815	−	0.176416i
$36$	3.00903	−	2.15639i	0.501504	−	0.359399i
$37$	1.35825	−	4.18026i	0.223295	−	0.687231i	−0.775165	−	0.631759i	$-0.782333\pi$
$37$	1.35825	−	4.18026i	0.223295	−	0.687231i	0.998460	−	0.0554727i	$-0.0176666\pi$
$38$	2.10282	+	6.54423i	0.341122	+	1.06161i
$39$	−1.11631	−	0.811049i	−0.178753	−	0.129872i
$40$	2.27190	+	1.68478i	0.359219	+	0.266386i
$41$	−7.91566	+	2.57195i	−1.23622	+	0.401672i	−0.852963	−	0.521971i	$-0.825197\pi$
$41$	−7.91566	+	2.57195i	−1.23622	+	0.401672i	−0.383255	+	0.923642i	$0.625197\pi$
$42$	−0.0180049	+	5.53069i	−0.00277821	+	0.853403i
$43$	−8.42797			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$43$	−8.42797			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$44$	0.480613	−	6.61582i	0.0724551	−	0.997372i
$45$	−1.85096			−0.275925
$46$	−0.0184883	+	5.67919i	−0.00272595	+	0.837351i
$47$	7.43548	−	2.41593i	1.08458	−	0.352400i	0.288427	−	0.957502i	$-0.406868\pi$
$47$	7.43548	−	2.41593i	1.08458	−	0.352400i	0.796148	+	0.605102i	$0.206868\pi$
$48$	−8.41351	+	2.61309i	−1.21439	+	0.377168i
$49$	3.11240	+	2.26129i	0.444629	+	0.323042i
$50$	−0.432635	−	1.34641i	−0.0611839	−	0.190411i
$51$	−5.42448	+	16.6948i	−0.759579	+	2.33774i
$52$	0.729868	+	1.01846i	0.101214	+	0.141234i
$53$	−7.51011	+	5.45641i	−1.03159	+	0.749496i	−0.968627	−	0.248520i	$-0.920056\pi$
$53$	−7.51011	+	5.45641i	−1.03159	+	0.749496i	−0.0629660	+	0.998016i	$0.520056\pi$
$54$	−2.11310	+	2.88862i	−0.287557	+	0.393091i
$55$	−2.12220	+	2.54878i	−0.286158	+	0.343677i
$56$	1.59853	−	4.76105i	0.213613	−	0.636222i
$57$	6.29235	+	8.66068i	0.833442	+	1.14714i
$58$	1.30450	+	0.428558i	0.171289	+	0.0562724i
$59$	2.45740	+	0.798458i	0.319926	+	0.103950i	0.464578	−	0.885532i	$-0.346206\pi$
$59$	2.45740	+	0.798458i	0.319926	+	0.103950i	−0.144652	+	0.989483i	$0.546206\pi$
$60$	4.18043	+	1.38846i	0.539692	+	0.179250i
$61$	5.77741	−	7.95192i	0.739722	−	1.01814i	−0.258913	−	0.965901i	$-0.583364\pi$
$61$	5.77741	−	7.95192i	0.739722	−	1.01814i	0.998635	−	0.0522388i	$-0.0166357\pi$
$62$	−3.12006	−	4.32392i	−0.396248	−	0.549139i
$63$	1.01562	+	3.12577i	0.127956	+	0.393810i
$64$	7.99847	+	0.156251i	0.999809	+	0.0195314i
$65$		−	0.626490i		−	0.0777065i
$66$	−2.50471	−	10.0224i	−0.308308	−	1.23367i
$67$		−	7.43389i		−	0.908195i	−0.890952	−	0.454097i	$-0.849962\pi$
$67$		−	7.43389i		−	0.908195i	0.890952	−	0.454097i	$-0.150038\pi$
$68$	9.45313	−	12.8346i	1.14636	−	1.55642i
$69$	2.73319	+	8.41190i	0.329037	+	1.01267i
$70$	−2.03633	+	1.46938i	−0.243388	+	0.175624i
$71$	1.04793	−	1.44235i	0.124366	−	0.171176i	−0.742294	−	0.670075i	$-0.766262\pi$
$71$	1.04793	−	1.44235i	0.124366	−	0.171176i	0.866660	+	0.498899i	$0.166262\pi$
$72$	−4.26531	+	3.03573i	−0.502672	+	0.357764i
$73$	−3.83520	−	1.24613i	−0.448877	−	0.145849i	0.0758507	−	0.997119i	$-0.475833\pi$
$73$	−3.83520	−	1.24613i	−0.448877	−	0.145849i	−0.524727	+	0.851270i	$0.675833\pi$
$74$	−1.94009	+	5.90550i	−0.225531	+	0.686501i
$75$	−1.29459	−	1.78185i	−0.149487	−	0.205751i
$76$	−2.94369	−	9.26457i	−0.337665	−	1.06272i
$77$	5.46863	+	2.18530i	0.623208	+	0.249038i
$78$	1.57496	+	1.15213i	0.178329	+	0.130453i
$79$	−2.58308	+	1.87672i	−0.290619	+	0.211147i	−0.723536	−	0.690287i	$-0.757484\pi$
$79$	−2.58308	+	1.87672i	−0.290619	+	0.211147i	0.432917	+	0.901434i	$0.357484\pi$
$80$	−3.20518	−	2.39308i	−0.358350	−	0.267554i
$81$	−3.43838	+	10.5822i	−0.382042	+	1.17580i
$82$	11.2062	−	3.60083i	1.23752	−	0.397645i
$83$	−6.14025	−	4.46116i	−0.673980	−	0.489675i	0.197375	−	0.980328i	$-0.436758\pi$
$83$	−6.14025	−	4.46116i	−0.673980	−	0.489675i	−0.871355	+	0.490653i	$0.836758\pi$
$84$	0.0509252	−	7.82145i	0.00555639	−	0.853390i
$85$	−7.57998	+	2.46288i	−0.822164	+	0.267137i
$86$	11.9189	+	0.0388013i	1.28525	+	0.00418405i
$87$	2.13845			0.229266
$88$	−0.710144	+	9.35391i	−0.0757016	+	0.997131i
$89$	−6.28641			−0.666358			−0.333179	−	0.942864i	$-0.608121\pi$
$89$	−6.28641			−0.666358			−0.333179	+	0.942864i	$0.608121\pi$
$90$	2.61764	+	0.00852160i	0.275924	+	0.000898256i
$91$	−1.05797	+	0.343755i	−0.110905	+	0.0360353i
$92$	0.0522925	−	8.03146i	0.00545187	−	0.837337i
$93$	−6.71820	−	4.88106i	−0.696645	−	0.506142i
$94$	−10.5264	+	3.38239i	−1.08572	+	0.348867i
$95$	−1.50197	+	4.62260i	−0.154099	+	0.474269i
$96$	11.9105	−	3.65672i	1.21561	−	0.373212i
$97$	4.44805	−	3.23170i	0.451631	−	0.328129i	−0.338608	−	0.940927i	$-0.609956\pi$
$97$	4.44805	−	3.23170i	0.451631	−	0.328129i	0.790239	+	0.612798i	$0.209956\pi$
$98$	−4.39117	−	3.21226i	−0.443575	−	0.324488i
$99$	−3.27294	−	5.19371i	−0.328943	−	0.521987i
$100$	0.605637	+	1.90610i	0.0605637	+	0.190610i
$101$	−10.9785	−	15.1106i	−1.09240	−	1.50357i	−0.845086	−	0.534631i	$-0.820451\pi$
$101$	−10.9785	−	15.1106i	−1.09240	−	1.50357i	−0.247318	−	0.968934i	$-0.579549\pi$
$102$	7.74819	−	23.5850i	0.767185	−	2.33526i
$103$	18.5018	+	6.01159i	1.82303	+	0.592339i	0.999693	+	0.0247923i	$0.00789244\pi$
$103$	18.5018	+	6.01159i	1.82303	+	0.592339i	0.823341	+	0.567547i	$0.192108\pi$
$104$	−1.02749	−	1.44367i	−0.100754	−	0.141563i
$105$	−2.29871	+	3.16391i	−0.224332	+	0.308766i
$106$	10.6460	−	7.68192i	1.03403	−	0.746134i
$107$	0.626212	+	1.92728i	0.0605382	+	0.186317i	0.976752	−	0.214372i	$-0.0687706\pi$
$107$	0.626212	+	1.92728i	0.0605382	+	0.186317i	−0.916214	+	0.400690i	$0.868771\pi$
$108$	3.00166	−	4.07537i	0.288835	−	0.392153i
$109$		−	11.1024i		−	1.06342i	−0.846926	−	0.531710i	$-0.821549\pi$
$109$		−	11.1024i		−	1.06342i	0.846926	−	0.531710i	$-0.178451\pi$
$110$	3.01296	−	3.59472i	0.287275	−	0.342744i
$111$			9.68080i			0.918861i
$112$	−2.28257	+	6.72574i	−0.215683	+	0.635523i
$113$	2.09343	+	6.44293i	0.196934	+	0.606100i	0.999949	+	0.0101406i	$0.00322790\pi$
$113$	2.09343	+	6.44293i	0.196934	+	0.606100i	−0.803015	+	0.595959i	$0.796772\pi$
$114$	−8.85881	−	12.2770i	−0.829704	−	1.14984i
$115$	−2.36044	+	3.24886i	−0.220112	+	0.302958i
$116$	−1.84286	−	0.612075i	−0.171105	−	0.0568297i
$117$	1.10286	+	0.358339i	0.101959	+	0.0331285i
$118$	−3.47159	−	1.14050i	−0.319586	−	0.104991i
$119$	8.31826	+	11.4491i	0.762534	+	1.04954i
$120$	−5.90560	−	1.98282i	−0.539105	−	0.181006i
$121$	−10.9043	−	1.44796i	−0.991299	−	0.131632i
$122$	−8.20706	+	11.2191i	−0.743032	+	1.01573i
$123$	14.8304	−	10.7749i	1.33721	−	0.971541i
$124$	4.39250	+	6.12928i	0.394458	+	0.550426i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−1.42191	−	4.42515i	−0.126674	−	0.394224i
$127$	−3.57222	−	2.59537i	−0.316983	−	0.230302i	0.417904	−	0.908491i	$-0.362765\pi$
$127$	−3.57222	−	2.59537i	−0.316983	−	0.230302i	−0.734887	+	0.678189i	$0.762765\pi$
$128$	−11.3108	−	0.257795i	−0.999740	−	0.0227861i
$129$	17.6540	−	5.73614i	1.55435	−	0.505039i
$130$	−0.00288428	+	0.885986i	−0.000252968	+	0.0777061i
$131$	15.8380			1.38377			0.691885	−	0.722008i	$-0.256781\pi$
$131$	15.8380			1.38377			0.691885	+	0.722008i	$0.256781\pi$
$132$	3.49603	+	14.1852i	0.304291	+	1.23466i
$133$	8.63043			0.748353
$134$	−0.0342247	+	10.5131i	−0.00295656	+	0.908190i
$135$	−2.40688	+	0.782042i	−0.207151	+	0.0673075i
$136$	−13.4278	+	18.1072i	−1.15142	+	1.55268i
$137$	−10.5499	−	7.66498i	−0.901342	−	0.654863i	0.0374684	−	0.999298i	$-0.488071\pi$
$137$	−10.5499	−	7.66498i	−0.901342	−	0.654863i	−0.938810	+	0.344435i	$0.888071\pi$
$138$	−3.82657	−	11.9087i	−0.325739	−	1.01374i
$139$	−1.35598	+	4.17327i	−0.115013	+	0.353972i	−0.991950	−	0.126633i	$-0.959583\pi$
$139$	−1.35598	+	4.17327i	−0.115013	+	0.353972i	0.876937	+	0.480605i	$0.159583\pi$
$140$	2.88656	−	2.06863i	0.243959	−	0.174831i
$141$	−13.9307	+	10.1213i	−1.17318	+	0.852365i
$142$	−1.48863	+	2.03496i	−0.124923	+	0.170770i
$143$	1.75790	−	1.10778i	0.147003	−	0.0926373i
$144$	6.04600	−	4.27351i	0.503834	−	0.356126i
$145$	0.570694	+	0.785493i	0.0473936	+	0.0652316i
$146$	5.41803	+	1.77995i	0.448400	+	0.147309i
$147$	−8.05858	−	2.61839i	−0.664660	−	0.215961i
$148$	2.77088	−	8.34267i	0.227765	−	0.685763i
$149$	−6.62175	+	9.11405i	−0.542475	+	0.746652i	−0.988967	−	0.148135i	$-0.952673\pi$
$149$	−6.62175	+	9.11405i	−0.542475	+	0.746652i	0.446492	+	0.894787i	$0.352673\pi$
$150$	1.82262	+	2.52587i	0.148816	+	0.206236i
$151$	−2.29452	−	7.06179i	−0.186725	−	0.574681i	0.813249	−	0.581916i	$-0.197697\pi$
$151$	−2.29452	−	7.06179i	−0.186725	−	0.574681i	−0.999974	+	0.00723559i	$0.997697\pi$
$152$	4.12033	+	13.1156i	0.334203	+	1.06381i
$153$		−	14.7523i		−	1.19265i
$154$	−7.72371	−	3.11564i	−0.622394	−	0.251065i
$155$		−	3.77035i		−	0.302842i
$156$	−2.22202	−	1.63660i	−0.177904	−	0.131033i
$157$	4.74943	+	14.6172i	0.379046	+	1.16658i	0.940708	+	0.339216i	$0.110162\pi$
$157$	4.74943	+	14.6172i	0.379046	+	1.16658i	−0.561663	+	0.827366i	$0.689838\pi$
$158$	3.66165	−	2.64217i	0.291305	−	0.210200i
$159$	12.0177	−	16.5409i	0.953065	−	1.31178i
$160$	4.52177	+	3.39906i	0.357477	+	0.268720i
$161$	6.78160	+	2.20348i	0.534465	+	0.173658i
$162$	4.91129	−	14.9496i	0.385868	−	1.17455i
$163$	0.00497751	+	0.00685096i	0.000389869	+	0.000536609i	0.809212	−	0.587517i	$-0.199894\pi$
$163$	0.00497751	+	0.00685096i	0.000389869	+	0.000536609i	−0.808822	+	0.588054i	$0.799894\pi$
$164$	−15.8645	+	5.04072i	−1.23881	+	0.393614i
$165$	2.71065	−	6.78329i	0.211023	−	0.528078i
$166$	8.66304	+	6.33726i	0.672383	+	0.491867i
$167$	−6.48096	+	4.70870i	−0.501512	+	0.364370i	−0.809594	−	0.586990i	$-0.800313\pi$
$167$	−6.48096	+	4.70870i	−0.501512	+	0.364370i	0.308082	+	0.951360i	$0.400313\pi$
$168$	−0.108028	+	11.0609i	−0.00833451	+	0.853367i
$169$	3.89593	−	11.9905i	0.299687	−	0.922343i
$170$	10.7310	−	3.44813i	0.823030	−	0.264459i
$171$	−7.27840	−	5.28807i	−0.556593	−	0.404389i
$172$	−16.8556	−	0.109746i	−1.28523	−	0.00836806i
$173$	24.6276	−	8.00199i	1.87240	−	0.608380i	0.881795	−	0.471633i	$-0.156335\pi$
$173$	24.6276	−	8.00199i	1.87240	−	0.608380i	0.990606	−	0.136747i	$-0.0436648\pi$
$174$	−3.02421	−	0.00984514i	−0.229264	−	0.000746358i
$175$	−1.77563			−0.134225
$176$	1.04735	−	13.2251i	0.0789473	−	0.996879i
$177$	−5.69093			−0.427757
$178$	8.89028	+	0.0289418i	0.666355	+	0.00216928i
$179$	−19.6591	+	6.38763i	−1.46939	+	0.477434i	−0.930924	−	0.365212i	$-0.880996\pi$
$179$	−19.6591	+	6.38763i	−1.46939	+	0.477434i	−0.538467	+	0.842646i	$0.680996\pi$
$180$	−3.70185	−	0.0241026i	−0.275920	−	0.00179650i
$181$	1.48487	+	1.07882i	0.110370	+	0.0801881i	0.641601	−	0.767039i	$-0.278271\pi$
$181$	1.48487	+	1.07882i	0.110370	+	0.0801881i	−0.531231	+	0.847227i	$0.678271\pi$
$182$	1.49777	−	0.481269i	0.111022	−	0.0356741i
$183$	−6.68977	+	20.5890i	−0.494522	+	1.52198i
$184$	−0.110928	+	11.3579i	−0.00817774	+	0.837315i
$185$	−3.55595	+	2.58355i	−0.261438	+	0.189946i
$186$	9.47845	+	6.93375i	0.694994	+	0.508408i
$187$	−20.3139	−	16.9141i	−1.48550	−	1.23688i
$188$	14.9021	−	4.73494i	1.08685	−	0.345331i
$189$	2.64131	+	3.63545i	0.192127	+	0.264440i
$190$	2.14538	−	6.53040i	0.155643	−	0.473765i
$191$	14.4987	+	4.71091i	1.04909	+	0.340870i	0.782311	−	0.622888i	$-0.214041\pi$
$191$	14.4987	+	4.71091i	1.04909	+	0.340870i	0.266778	+	0.963758i	$0.414041\pi$
$192$	−16.8607	+	5.11652i	−1.21682	+	0.369253i
$193$	6.02034	−	8.28628i	0.433353	−	0.596460i	−0.535365	−	0.844620i	$-0.679826\pi$
$193$	6.02034	−	8.28628i	0.433353	−	0.596460i	0.968719	+	0.248161i	$0.0798261\pi$
$194$	−6.30534	+	4.54981i	−0.452697	+	0.326657i
$195$	0.426394	+	1.31230i	0.0305347	+	0.0939761i
$196$	6.19523	+	4.56302i	0.442516	+	0.325930i
$197$			22.4488i			1.59941i	0.600393	+	0.799705i	$0.295011\pi$
$197$			22.4488i			1.59941i	−0.600393	+	0.799705i	$0.704989\pi$
$198$	4.60470	+	7.36004i	0.327241	+	0.523055i
$199$		−	7.97659i		−	0.565445i	−0.959202	−	0.282723i	$-0.908762\pi$
$199$		−	7.97659i		−	0.565445i	0.959202	−	0.282723i	$-0.0912376\pi$
$200$	−0.847719	−	2.69840i	−0.0599428	−	0.190806i
$201$	5.05956	+	15.5717i	0.356874	+	1.09834i
$202$	15.4563	+	21.4201i	1.08750	+	1.50711i
$203$	1.01334	−	1.39474i	0.0711226	−	0.0978918i
$204$	−11.0661	+	33.3183i	−0.774784	+	2.33275i
$205$	7.91566	+	2.57195i	0.552854	+	0.179633i
$206$	−26.1376	−	8.58681i	−1.82110	−	0.598271i
$207$	−4.36908	−	6.01352i	−0.303672	−	0.417969i
$208$	1.44644	+	2.04637i	0.100293	+	0.141890i
$209$	−15.6266	+	3.95938i	−1.08092	+	0.273876i
$210$	3.26542	−	4.46384i	0.225336	−	0.308034i
$211$	−4.50029	+	3.26965i	−0.309813	+	0.225092i	−0.731816	−	0.681502i	$-0.761327\pi$
$211$	−4.50029	+	3.26965i	−0.309813	+	0.225092i	0.422004	+	0.906594i	$0.361327\pi$
$212$	−15.0910	+	10.8148i	−1.03645	+	0.742764i
$213$	−1.21342	+	3.73451i	−0.0831420	+	0.255885i
$214$	−0.876720	−	2.72846i	−0.0599313	−	0.186514i
$215$	6.81837	+	4.95384i	0.465009	+	0.337849i
$216$	−4.26373	+	5.74959i	−0.290110	+	0.391210i
$217$	−6.36708	+	2.06879i	−0.432225	+	0.140439i
$218$	−0.0511142	+	15.7011i	−0.00346189	+	1.06342i
$219$	8.88170			0.600170
$220$	−4.27750	+	5.06981i	−0.288389	+	0.341807i
$221$	4.99317			0.335877
$222$	0.0445692	−	13.6907i	0.00299129	−	0.918856i
$223$	−17.3846	+	5.64858i	−1.16416	+	0.378257i	−0.826459	−	0.562998i	$-0.809648\pi$
$223$	−17.3846	+	5.64858i	−1.16416	+	0.378257i	−0.337697	+	0.941255i	$0.609648\pi$
$224$	3.25899	−	9.50108i	0.217750	−	0.634817i
$225$	1.49746	+	1.08797i	0.0998307	+	0.0725313i
$226$	−2.93088	−	9.12126i	−0.194960	−	0.606737i
$227$	−5.21694	+	16.0561i	−0.346261	+	1.06568i	0.614645	+	0.788804i	$0.289299\pi$
$227$	−5.21694	+	16.0561i	−0.346261	+	1.06568i	−0.960905	+	0.276877i	$0.910701\pi$
$228$	12.4717	+	17.4029i	0.825956	+	1.15254i
$229$	3.27049	−	2.37615i	0.216120	−	0.157020i	−0.474458	−	0.880278i	$-0.657356\pi$
$229$	3.27049	−	2.37615i	0.216120	−	0.157020i	0.690578	+	0.723258i	$0.257356\pi$
$230$	3.35310	−	4.58369i	0.221097	−	0.302240i
$231$	−12.9424	−	0.855544i	−0.851549	−	0.0562906i
$232$	2.60336	+	0.874084i	0.170919	+	0.0573864i
$233$	−5.49310	−	7.56060i	−0.359865	−	0.495311i	0.590246	−	0.807223i	$-0.299031\pi$
$233$	−5.49310	−	7.56060i	−0.359865	−	0.495311i	−0.950111	+	0.311912i	$0.899031\pi$
$234$	−1.55801	−	0.511843i	−0.101851	−	0.0334602i
$235$	−7.43548	−	2.41593i	−0.485037	−	0.157598i
$236$	4.90430	+	1.62888i	0.319243	+	0.106031i
$237$	4.13345	−	5.68921i	0.268496	−	0.369554i
$238$	−11.7110	−	16.2297i	−0.759113	−	1.05201i
$239$	1.10268	+	3.39372i	0.0713268	+	0.219521i	0.980365	−	0.197192i	$-0.0631821\pi$
$239$	1.10268	+	3.39372i	0.0713268	+	0.219521i	−0.909038	+	0.416713i	$0.863182\pi$
$240$	8.34261	+	2.83130i	0.538513	+	0.182760i
$241$			1.86526i			0.120152i	0.998194	+	0.0600758i	$0.0191343\pi$
$241$			1.86526i			0.120152i	−0.998194	+	0.0600758i	$0.980866\pi$
$242$	15.4142	+	2.09791i	0.990865	+	0.134859i
$243$		−	16.9145i		−	1.08507i
$244$	11.6581	−	15.8283i	0.746335	−	1.01330i
$245$	−1.18883	−	3.65885i	−0.0759517	−	0.233755i
$246$	−21.0228	+	15.1697i	−1.34037	+	0.967182i
$247$	1.78984	−	2.46350i	0.113885	−	0.156749i
$248$	−6.18368	−	8.68829i	−0.392664	−	0.551707i
$249$	15.8982	+	5.16565i	1.00751	+	0.327360i
$250$	−0.441392	+	1.34357i	−0.0279161	+	0.0849747i
$251$	−12.0949	−	16.6472i	−0.763425	−	1.05076i	−0.996921	−	0.0784068i	$-0.975017\pi$
$251$	−12.0949	−	16.6472i	−0.763425	−	1.05076i	0.233496	−	0.972358i	$-0.424983\pi$
$252$	1.99050	+	6.26462i	0.125390	+	0.394634i
$253$	−13.2899	−	0.878515i	−0.835531	−	0.0552318i
$254$	5.03991	+	3.68683i	0.316232	+	0.231333i
$255$	14.2015	−	10.3180i	0.889331	−	0.646137i
$256$	15.9946	+	0.416649i	0.999661	+	0.0260405i
$257$	9.43965	−	29.0522i	0.588829	−	1.81223i	0.00551129	−	0.999985i	$-0.498246\pi$
$257$	9.43965	−	29.0522i	0.588829	−	1.81223i	0.583318	−	0.812244i	$-0.301754\pi$
$258$	−24.9928	+	8.03080i	−1.55598	+	0.499976i
$259$	6.31404	+	4.58742i	0.392335	+	0.285048i
$260$	0.00815794	−	1.25295i	0.000505934	−	0.0777049i
$261$	−1.70918	+	0.555348i	−0.105796	+	0.0343752i
$262$	−22.3981	−	0.0729160i	−1.38376	−	0.00450476i
$263$	−2.53284			−0.156182			−0.0780908	−	0.996946i	$-0.524882\pi$
$263$	−2.53284			−0.156182			−0.0780908	+	0.996946i	$0.524882\pi$
$264$	−4.87881	−	20.0769i	−0.300270	−	1.23565i
$265$	9.28301			0.570250
$266$	−12.2052	−	0.0397334i	−0.748349	−	0.00243621i
$267$	13.1681	−	4.27858i	0.805875	−	0.261845i
$268$	0.0968016	−	14.8675i	0.00591310	−	0.908175i
$269$	23.3661	+	16.9764i	1.42465	+	1.03507i	0.990981	+	0.134002i	$0.0427828\pi$
$269$	23.3661	+	16.9764i	1.42465	+	1.03507i	0.433673	+	0.901070i	$0.357217\pi$
$270$	3.40742	−	1.09489i	0.207369	−	0.0666327i
$271$	5.35670	−	16.4862i	0.325396	−	1.00147i	−0.645865	−	0.763451i	$-0.723503\pi$
$271$	5.35670	−	16.4862i	0.325396	−	1.00147i	0.971261	−	0.238015i	$-0.0764967\pi$
$272$	19.0730	−	25.5455i	1.15647	−	1.54892i
$273$	1.98216	−	1.44012i	0.119966	−	0.0871601i
$274$	14.8845	+	10.8884i	0.899205	+	0.657794i
$275$	3.21503	−	0.814605i	0.193874	−	0.0491225i
$276$	5.35673	+	16.8590i	0.322437	+	1.01479i
$277$	14.1653	+	19.4969i	0.851112	+	1.17146i	0.983617	+	0.180273i	$0.0576982\pi$
$277$	14.1653	+	19.4969i	0.851112	+	1.17146i	−0.132504	+	0.991182i	$0.542302\pi$
$278$	1.93685	−	5.89562i	0.116164	−	0.353596i
$279$	6.63721	+	2.15656i	0.397359	+	0.129110i
$280$	−4.09171	+	2.91218i	−0.244527	+	0.174036i
$281$	−5.77593	+	7.94989i	−0.344563	+	0.474251i	−0.945767	−	0.324845i	$-0.894688\pi$
$281$	−5.77593	+	7.94989i	−0.344563	+	0.474251i	0.601204	+	0.799096i	$0.294688\pi$
$282$	19.7475	−	14.2494i	1.17595	−	0.848541i
$283$	−3.78494	−	11.6489i	−0.224992	−	0.692453i	−0.998292	−	0.0584137i	$-0.981396\pi$
$283$	−3.78494	−	11.6489i	−0.224992	−	0.692453i	0.773301	−	0.634039i	$-0.218604\pi$
$284$	2.11460	−	2.87100i	0.125478	−	0.170362i
$285$		−	10.7052i		−	0.634121i
$286$	−2.49113	+	1.55854i	−0.147304	+	0.0921583i
$287$		−	14.7786i		−	0.872353i
$288$	−8.56997	+	6.01579i	−0.504990	+	0.354484i
$289$	−14.3761	−	44.2449i	−0.845650	−	2.60264i
$290$	−0.803463	−	1.11348i	−0.0471809	−	0.0653856i
$291$	−7.11778	+	9.79678i	−0.417252	+	0.574298i
$292$	−7.65402	−	2.54215i	−0.447918	−	0.148768i
$293$	12.6735	+	4.11785i	0.740391	+	0.240568i	0.654841	−	0.755766i	$-0.272735\pi$
$293$	12.6735	+	4.11785i	0.740391	+	0.240568i	0.0855496	+	0.996334i	$0.472735\pi$
$294$	11.3844	+	3.74005i	0.663954	+	0.218124i
$295$	−1.51876	−	2.09039i	−0.0884255	−	0.121707i
$296$	−3.95700	+	11.7855i	−0.229996	+	0.685018i
$297$	−6.45029	−	5.37074i	−0.374284	−	0.311642i
$298$	9.40647	−	12.8587i	0.544902	−	0.744882i
$299$	2.03538	−	1.47879i	0.117709	−	0.0855206i
$300$	−2.56593	−	3.58049i	−0.148144	−	0.206719i
$301$	4.62442	−	14.2325i	0.266547	−	0.820348i
$302$	3.21241	+	9.99739i	0.184853	+	0.575285i
$303$	33.2810	+	24.1801i	1.91195	+	1.38911i
$304$	−5.76662	−	18.5671i	−0.330738	−	1.06489i
$305$	−9.34805	+	3.03736i	−0.535268	+	0.173919i
$306$	−0.0679177	+	20.8628i	−0.00388260	+	1.19265i
$307$	13.3026			0.759218			0.379609	−	0.925147i	$-0.376059\pi$
$307$	13.3026			0.759218			0.379609	+	0.925147i	$0.376059\pi$
$308$	10.9086	+	4.44172i	0.621574	+	0.253090i
$309$	−42.8471			−2.43748
$310$	−0.0173582	+	5.33205i	−0.000985880	+	0.302840i
$311$	−1.96539	+	0.638593i	−0.111447	+	0.0362113i	−0.364210	−	0.931317i	$-0.618661\pi$
$311$	−1.96539	+	0.638593i	−0.111447	+	0.0362113i	0.252763	+	0.967528i	$0.418661\pi$
$312$	3.13486	+	2.32472i	0.177476	+	0.131611i
$313$	−1.92812	−	1.40086i	−0.108984	−	0.0791813i	0.531959	−	0.846770i	$-0.321456\pi$
$313$	−1.92812	−	1.40086i	−0.108984	−	0.0791813i	−0.640942	+	0.767589i	$0.721456\pi$
$314$	−6.64937	−	20.6937i	−0.375246	−	1.16781i
$315$	1.01562	−	3.12577i	0.0572239	−	0.176117i
$316$	−5.19049	+	3.71972i	−0.291988	+	0.209250i
$317$	−0.147861	+	0.107427i	−0.00830471	+	0.00603372i	−0.591930	−	0.805989i	$-0.701634\pi$
$317$	−0.147861	+	0.107427i	−0.00830471	+	0.00603372i	0.583625	+	0.812023i	$0.301634\pi$
$318$	−17.0717	+	23.3370i	−0.957331	+	1.30867i
$319$	−1.19493	+	2.99027i	−0.0669034	+	0.167423i
$320$	−6.37906	−	4.82779i	−0.356600	−	0.269882i
$321$	−2.62344	−	3.61086i	−0.146426	−	0.201539i
$322$	−9.58043	−	3.14739i	−0.533897	−	0.175397i
$323$	−36.8424	−	11.9708i	−2.04997	−	0.666075i
$324$	−7.01441	+	21.1193i	−0.389689	+	1.17329i
$325$	−0.368242	+	0.506841i	−0.0204264	+	0.0281145i
$326$	−0.00700769	−	0.00971159i	−0.000388120	−	0.000537875i
$327$	7.55640	+	23.2562i	0.417870	+	1.28607i
$328$	22.4588	−	7.05559i	1.24008	−	0.389580i
$329$			13.8821i			0.765344i
$330$	−3.86464	+	9.58049i	−0.212741	+	0.527389i
$331$			25.9358i			1.42556i	0.701386	+	0.712781i	$0.252565\pi$
$331$			25.9358i			1.42556i	−0.701386	+	0.712781i	$0.747435\pi$
$332$	−12.2222	−	9.00208i	−0.670778	−	0.494053i
$333$	−2.51407	−	7.73752i	−0.137770	−	0.424013i
$334$	9.18710	−	6.62923i	0.502695	−	0.362735i
$335$	−4.36953	+	6.01415i	−0.238733	+	0.328588i
$336$	0.203696	−	15.6419i	0.0111125	−	0.853335i
$337$	−1.63673	−	0.531804i	−0.0891581	−	0.0289692i	0.264098	−	0.964496i	$-0.414926\pi$
$337$	−1.63673	−	0.531804i	−0.0891581	−	0.0289692i	−0.353256	+	0.935527i	$0.614926\pi$
$338$	−5.56486	+	16.9390i	−0.302688	+	0.921362i
$339$	−8.77020	−	12.0711i	−0.476332	−	0.655615i
$340$	−15.1917	+	4.82696i	−0.823886	+	0.261779i
$341$	10.5794	−	6.66686i	0.572907	−	0.361031i
$342$	10.2688	+	7.51192i	0.555274	+	0.406198i
$343$	−15.5821	+	11.3210i	−0.841353	+	0.611279i
$344$	23.8368	+	0.232805i	1.28519	+	0.0125520i
$345$	2.73319	−	8.41190i	0.147150	−	0.452881i
$346$	−34.8653	+	11.2031i	−1.87437	+	0.602281i
$347$	27.1588	+	19.7320i	1.45796	+	1.05927i	0.983889	+	0.178783i	$0.0572160\pi$
$347$	27.1588	+	19.7320i	1.45796	+	1.05927i	0.474071	+	0.880487i	$0.342784\pi$
$348$	4.27680	+	0.0278461i	0.229261	+	0.00149271i
$349$	11.3060	−	3.67353i	0.605194	−	0.196640i	0.00963854	−	0.999954i	$-0.496932\pi$
$349$	11.3060	−	3.67353i	0.605194	−	0.196640i	0.595556	+	0.803314i	$0.296932\pi$
$350$	2.51111	+	0.00817477i	0.134224	+	0.000436960i
$351$	1.58548			0.0846269
$352$	−1.54206	+	18.6982i	−0.0821921	+	0.996617i
$353$	17.7555			0.945030			0.472515	−	0.881323i	$-0.343346\pi$
$353$	17.7555			0.945030			0.472515	+	0.881323i	$0.343346\pi$
$354$	8.04815	+	0.0262003i	0.427755	+	0.00139253i
$355$	−1.69559	+	0.550930i	−0.0899924	+	0.0292403i
$356$	−12.5726	−	0.0818595i	−0.666344	−	0.00433854i
$357$	−25.2165	−	18.3209i	−1.33460	−	0.969645i
$358$	27.8315	−	8.94292i	1.47094	−	0.472648i
$359$	2.53193	−	7.79249i	0.133630	−	0.411272i	−0.861744	−	0.507343i	$-0.830628\pi$
$359$	2.53193	−	7.79249i	0.133630	−	0.411272i	0.995374	+	0.0960712i	$0.0306276\pi$
$360$	5.23507	+	0.0511289i	0.275912	+	0.00269473i
$361$	−3.74121	+	2.71815i	−0.196906	+	0.143060i
$362$	−2.09495	−	1.53251i	−0.110108	−	0.0805470i
$363$	23.8266	−	4.38851i	1.25057	−	0.230337i
$364$	−2.12037	+	0.673719i	−0.111138	+	0.0353125i
$365$	2.37029	+	3.26242i	0.124066	+	0.170763i
$366$	9.55550	−	29.0863i	0.499474	−	1.52036i
$367$	22.3003	+	7.24580i	1.16406	+	0.378228i	0.826424	−	0.563048i	$-0.190371\pi$
$367$	22.3003	+	7.24580i	1.16406	+	0.378228i	0.337640	+	0.941275i	$0.390371\pi$
$368$	0.209166	−	16.0619i	0.0109035	−	0.837284i
$369$	−9.05519	+	12.4634i	−0.471394	+	0.648818i
$370$	5.04073	−	3.63729i	0.262055	−	0.189094i
$371$	−5.09358	−	15.6764i	−0.264446	−	0.813880i
$372$	−13.3726	−	9.84940i	−0.693335	−	0.510667i
$373$			3.19283i			0.165318i	0.996578	+	0.0826592i	$0.0263413\pi$
$373$			3.19283i			0.165318i	−0.996578	+	0.0826592i	$0.973659\pi$
$374$	28.6502	+	24.0135i	1.48147	+	1.24171i
$375$			2.20249i			0.113736i
$376$	−21.0964	+	6.62757i	−1.08797	+	0.341791i
$377$	−0.187967	−	0.578502i	−0.00968078	−	0.0297944i
$378$	−3.71861	−	5.15343i	−0.191265	−	0.265064i
$379$	4.67731	−	6.43776i	0.240257	−	0.330686i	−0.671812	−	0.740721i	$-0.734484\pi$
$379$	4.67731	−	6.43776i	0.240257	−	0.330686i	0.912069	+	0.410036i	$0.134484\pi$
$380$	−3.06408	+	9.22545i	−0.157184	+	0.473256i
$381$	9.24913	+	3.00523i	0.473847	+	0.153962i
$382$	−20.4825	−	6.72895i	−1.04797	−	0.344283i
$383$	6.68453	+	9.20047i	0.341564	+	0.470122i	0.944897	−	0.327367i	$-0.106161\pi$
$383$	6.68453	+	9.20047i	0.341564	+	0.470122i	−0.603334	+	0.797489i	$0.706161\pi$
$384$	23.8680	−	7.15819i	1.21801	−	0.365290i
$385$	−3.13973	−	4.98232i	−0.160015	−	0.253923i
$386$	−8.55215	+	11.6908i	−0.435293	+	0.595046i
$387$	−12.6206	+	9.16937i	−0.641539	+	0.466105i
$388$	8.93799	−	6.40534i	0.453758	−	0.325182i
$389$	−4.66431	+	14.3553i	−0.236490	+	0.727841i	0.760431	+	0.649419i	$0.224988\pi$
$389$	−4.66431	+	14.3553i	−0.236490	+	0.727841i	−0.996920	+	0.0784214i	$0.975012\pi$
$390$	−0.596967	−	1.85783i	−0.0302286	−	0.0940750i
$391$	−25.8936	−	18.8128i	−1.30950	−	0.951405i
$392$	−8.74032	−	6.48157i	−0.441453	−	0.327369i
$393$	−33.1757	+	10.7794i	−1.67349	+	0.543750i
$394$	0.103351	−	31.7472i	0.00520677	−	1.59940i
$395$	3.19286			0.160650
$396$	−6.47810	−	10.4298i	−0.325537	−	0.524118i
$397$	−23.1986			−1.16430			−0.582151	−	0.813081i	$-0.697789\pi$
$397$	−23.1986			−1.16430			−0.582151	+	0.813081i	$0.697789\pi$
$398$	−0.0367232	+	11.2805i	−0.00184077	+	0.565442i
$399$	−18.0781	+	5.87393i	−0.905037	+	0.294064i
$400$	1.18643	+	3.82000i	0.0593213	+	0.191000i
$401$	21.4646	+	15.5949i	1.07189	+	0.778773i	0.976251	−	0.216643i	$-0.0695108\pi$
$401$	21.4646	+	15.5949i	1.07189	+	0.778773i	0.0956383	+	0.995416i	$0.469511\pi$
$402$	−7.08357	−	22.0449i	−0.353296	−	1.09950i
$403$	−0.729925	+	2.24648i	−0.0363601	+	0.111905i
$404$	−21.7598	−	30.3636i	−1.08259	−	1.51065i
$405$	9.00179	−	6.54018i	0.447303	−	0.324984i
$406$	−1.43949	+	1.96779i	−0.0714409	+	0.0976598i
$407$	−13.5370	−	5.40949i	−0.671006	−	0.268138i
$408$	15.8032	−	47.0680i	0.782374	−	2.33021i
$409$	3.20486	+	4.41111i	0.158470	+	0.218116i	0.880868	−	0.473362i	$-0.156960\pi$
$409$	3.20486	+	4.41111i	0.158470	+	0.218116i	−0.722398	+	0.691478i	$0.756960\pi$
$410$	−11.1825	−	3.67372i	−0.552266	−	0.181432i
$411$	27.3157	+	8.87541i	1.34738	+	0.437792i
$412$	36.9245	+	12.2638i	1.81914	+	0.604196i
$413$	−2.69675	+	3.71176i	−0.132698	+	0.182644i
$414$	6.15110	+	8.52448i	0.302310	+	0.418955i
$415$	2.34537	+	7.21830i	0.115130	+	0.354332i
$416$	−2.03615	−	2.90065i	−0.0998303	−	0.142216i
$417$		−	9.66461i		−	0.473278i
$418$	22.1175	−	5.52744i	1.08180	−	0.270356i
$419$			27.6169i			1.34918i	0.738195	+	0.674588i	$0.235679\pi$
$419$			27.6169i			1.34918i	−0.738195	+	0.674588i	$0.764321\pi$
$420$	−4.63853	+	6.29775i	−0.226337	+	0.307299i
$421$	1.71563	+	5.28017i	0.0836147	+	0.257340i	0.984120	−	0.177506i	$-0.0568029\pi$
$421$	1.71563	+	5.28017i	0.0836147	+	0.257340i	−0.900505	+	0.434846i	$0.856803\pi$
$422$	6.37939	−	4.60324i	0.310544	−	0.224082i
$423$	8.50587	−	11.7073i	0.413570	−	0.569230i
$424$	21.3915	−	15.2249i	1.03886	−	0.739386i
$425$	7.57998	+	2.46288i	0.367683	+	0.119467i
$426$	1.73322	−	5.27579i	0.0839746	−	0.255613i
$427$	10.2585	+	14.1197i	0.496445	+	0.683299i
$428$	1.22730	+	3.86264i	0.0593238	+	0.186708i
$429$	−2.92830	+	3.51690i	−0.141379	+	0.169798i
$430$	−9.61978	−	7.03714i	−0.463907	−	0.339361i
$431$	16.7905	−	12.1990i	0.808771	−	0.587607i	−0.104703	−	0.994504i	$-0.533389\pi$
$431$	16.7905	−	12.1990i	0.808771	−	0.587607i	0.913474	+	0.406897i	$0.133389\pi$
$432$	6.05627	−	8.11148i	0.291382	−	0.390264i
$433$	−2.41689	+	7.43843i	−0.116148	+	0.357468i	−0.992185	−	0.124777i	$-0.960178\pi$
$433$	−2.41689	+	7.43843i	−0.116148	+	0.357468i	0.876036	+	0.482245i	$0.160178\pi$
$434$	9.01388	−	2.89638i	0.432680	−	0.139031i
$435$	−1.73004	−	1.25695i	−0.0829491	−	0.0602660i
$436$	0.144572	−	22.2044i	0.00692375	−	1.06340i
$437$	−18.5635	+	6.03165i	−0.888013	+	0.288533i
$438$	−12.5606	−	0.0408902i	−0.600167	−	0.00195381i
$439$	−12.4565			−0.594515			−0.297258	−	0.954797i	$-0.596072\pi$
$439$	−12.4565			−0.594515			−0.297258	+	0.954797i	$0.596072\pi$
$440$	6.07261	−	7.15006i	0.289500	−	0.340866i
$441$	7.12092			0.339091
$442$	−7.06136	−	0.0229879i	−0.335875	−	0.00109342i
$443$	−15.3505	+	4.98766i	−0.729322	+	0.236971i	−0.650060	−	0.759883i	$-0.725256\pi$
$443$	−15.3505	+	4.98766i	−0.729322	+	0.236971i	−0.0792619	+	0.996854i	$0.525256\pi$
$444$	−0.126060	+	19.3612i	−0.00598255	+	0.918842i
$445$	5.08581	+	3.69506i	0.241091	+	0.175163i
$446$	24.6113	−	7.90823i	1.16538	−	0.374465i
$447$	7.66744	−	23.5979i	0.362657	−	1.11614i
$448$	−4.65262	+	13.4215i	−0.219816	+	0.634105i
$449$	−29.6817	+	21.5650i	−1.40077	+	1.01772i	−0.406180	+	0.913793i	$0.633139\pi$
$449$	−29.6817	+	21.5650i	−1.40077	+	1.01772i	−0.994585	+	0.103923i	$0.966861\pi$
$450$	−2.11271	−	1.54551i	−0.0995941	−	0.0728559i
$451$	6.77997	+	26.7588i	0.319256	+	1.26002i
$452$	4.10288	+	12.9128i	0.192983	+	0.607369i
$453$	9.61261	+	13.2306i	0.451640	+	0.621629i
$454$	7.45176	−	22.6826i	0.349728	−	1.06455i
$455$	1.05797	+	0.343755i	0.0495983	+	0.0161155i
$456$	−17.5574	−	24.6687i	−0.822200	−	1.15522i
$457$	−13.6114	+	18.7345i	−0.636717	+	0.876365i	−0.998435	−	0.0559221i	$-0.982190\pi$
$457$	−13.6114	+	18.7345i	−0.636717	+	0.876365i	0.361719	+	0.932287i	$0.382190\pi$
$458$	−4.63608	+	3.34531i	−0.216630	+	0.156316i
$459$	−6.23292	−	19.1830i	−0.290928	−	0.895384i
$460$	−4.76308	+	6.46685i	−0.222080	+	0.301518i
$461$			7.69778i			0.358521i	0.983802	+	0.179261i	$0.0573705\pi$
$461$			7.69778i			0.358521i	−0.983802	+	0.179261i	$0.942629\pi$
$462$	18.2993	+	1.26950i	0.851362	+	0.0590625i
$463$		−	36.9280i		−	1.71619i	−0.513492	−	0.858095i	$-0.671648\pi$
$463$		−	36.9280i		−	1.71619i	0.513492	−	0.858095i	$-0.328352\pi$
$464$	−3.67767	−	1.24812i	−0.170731	−	0.0579425i
$465$	2.56613	+	7.89772i	0.119001	+	0.366248i
$466$	7.73357	+	10.7175i	0.358251	+	0.496480i
$467$	−12.0908	+	16.6415i	−0.559494	+	0.770077i	−0.991262	−	0.131907i	$-0.957890\pi$
$467$	−12.0908	+	16.6415i	−0.559494	+	0.770077i	0.431768	+	0.901985i	$0.357890\pi$
$468$	2.20100	+	0.731024i	0.101741	+	0.0337916i
$469$	12.5538	+	4.07897i	0.579680	+	0.188350i
$470$	10.5042	+	3.45086i	0.484521	+	0.159176i
$471$	−19.8972	−	27.3861i	−0.916814	−	1.26189i
$472$	−6.92819	−	2.32615i	−0.318896	−	0.107070i
$473$	−1.84374	+	27.8915i	−0.0847751	+	1.28245i
$474$	−5.87174	+	8.02668i	−0.269698	+	0.368678i
$475$	3.93222	−	2.85693i	0.180423	−	0.131085i
$476$	16.4871	+	23.0060i	0.755684	+	1.05448i
$477$	−5.30969	+	16.3415i	−0.243114	+	0.748227i
$478$	−1.54380	−	4.80449i	−0.0706117	−	0.219752i
$479$	15.6396	+	11.3629i	0.714593	+	0.519182i	0.884652	−	0.466252i	$-0.154396\pi$
$479$	15.6396	+	11.3629i	0.714593	+	0.519182i	−0.170059	+	0.985434i	$0.554396\pi$
$480$	−11.7851	−	4.04245i	−0.537915	−	0.184512i
$481$	2.61889	−	0.850930i	0.119411	−	0.0387991i
$482$	0.00858740	−	2.63786i	0.000391145	−	0.120151i
$483$	−15.7051			−0.714605
$484$	−21.7893	−	3.03784i	−0.990421	−	0.138084i
$485$	−5.49809			−0.249655
$486$	−0.0778722	+	23.9206i	−0.00353236	+	1.08506i
$487$	−16.9147	+	5.49593i	−0.766479	+	0.249044i	−0.666057	−	0.745901i	$-0.732019\pi$
$487$	−16.9147	+	5.49593i	−0.766479	+	0.249044i	−0.100422	+	0.994945i	$0.532019\pi$
$488$	−16.5599	+	22.3308i	−0.749630	+	1.01087i
$489$	−0.0150892	−	0.0109629i	−0.000682356	−	0.000495761i
$490$	1.66441	+	5.17984i	0.0751903	+	0.234001i
$491$	6.03134	−	18.5626i	0.272191	−	0.837716i	−0.717758	−	0.696292i	$-0.754832\pi$
$491$	6.03134	−	18.5626i	0.272191	−	0.837716i	0.989949	−	0.141424i	$-0.0451682\pi$
$492$	29.8005	−	21.3562i	1.34351	−	0.962814i
$493$	−6.26043	+	4.54847i	−0.281955	+	0.204853i
$494$	−2.54254	+	3.47565i	−0.114394	+	0.156377i
$495$	−0.404924	+	6.12558i	−0.0182000	+	0.275324i
$496$	8.70499	+	12.3155i	0.390866	+	0.552982i
$497$	1.86074	+	2.56108i	0.0834654	+	0.114880i
$498$	−22.4596	−	7.37849i	−1.00644	−	0.330638i
$499$	0.443782	+	0.144194i	0.0198664	+	0.00645499i	0.318933	−	0.947777i	$-0.396675\pi$
$499$	0.443782	+	0.144194i	0.0198664	+	0.00645499i	−0.299067	+	0.954232i	$0.596675\pi$
$500$	0.630405	−	1.89805i	0.0281926	−	0.0848833i
$501$	10.3709	−	14.2743i	0.463336	−	0.637727i
$502$	17.0281	+	23.5983i	0.760000	+	1.05324i
$503$	11.7242	+	36.0834i	0.522756	+	1.60888i	0.768711	+	0.639596i	$0.220898\pi$
$503$	11.7242	+	36.0834i	0.522756	+	1.60888i	−0.245955	+	0.969281i	$0.579102\pi$
$504$	−2.78614	−	8.86863i	−0.124104	−	0.395040i
$505$			18.6778i			0.831150i
$506$	18.7907	+	1.30359i	0.835347	+	0.0579515i
$507$			27.7679i			1.23322i
$508$	−7.11049	−	5.23715i	−0.315477	−	0.232361i
$509$	0.0861708	+	0.265207i	0.00381945	+	0.0117551i	0.952948	−	0.303134i	$-0.0980328\pi$
$509$	0.0861708	+	0.265207i	0.00381945	+	0.0117551i	−0.949129	+	0.314889i	$0.898033\pi$
$510$	−20.1313	+	14.5264i	−0.891429	+	0.643238i
$511$	4.20875	−	5.79285i	0.186184	−	0.256261i
$512$	−22.6177	−	0.662864i	−0.999571	−	0.0292947i
$513$	−11.6986	−	3.80111i	−0.516506	−	0.167823i
$514$	−13.4834	+	41.0424i	−0.594725	+	1.81030i
$515$	−11.4347	−	15.7385i	−0.503874	−	0.693523i
$516$	35.3820	−	11.2421i	1.55760	−	0.494908i
$517$	−6.36868	−	25.1355i	−0.280094	−	1.10546i
$518$	−8.90823	−	6.51662i	−0.391405	−	0.286324i
$519$	−46.1410	+	33.5234i	−2.02537	+	1.47151i
$520$	−0.0173054	+	1.77190i	−0.000758894	+	0.0777028i
$521$	8.78567	−	27.0395i	0.384907	−	1.18462i	−0.551640	−	0.834082i	$-0.685998\pi$
$521$	8.78567	−	27.0395i	0.384907	−	1.18462i	0.936548	−	0.350540i	$-0.114002\pi$
$522$	2.41970	−	0.777507i	0.105907	−	0.0340306i
$523$	9.73848	+	7.07542i	0.425834	+	0.309386i	0.779981	−	0.625803i	$-0.215229\pi$
$523$	9.73848	+	7.07542i	0.425834	+	0.309386i	−0.354147	+	0.935190i	$0.615229\pi$
$524$	31.6753	+	0.206236i	1.38374	+	0.00900948i
$525$	3.71940	−	1.20851i	0.162328	−	0.0527435i
$526$	3.58196	+	0.0116609i	0.156181	+	0.000508439i
$527$	30.0499			1.30899
$528$	6.80721	+	28.4153i	0.296246	+	1.23662i
$529$	6.87324			0.298837
$530$	−13.1281	−	0.0427378i	−0.570247	−	0.00185641i
$531$	4.54856	−	1.47792i	0.197391	−	0.0641361i
$532$	17.2605	+	0.112382i	0.748338	+	0.00487240i
$533$	−4.21845	−	3.06488i	−0.182721	−	0.132755i
$534$	−18.6421	+	5.99016i	−0.806723	+	0.259220i
$535$	0.626212	−	1.92728i	0.0270735	−	0.0833237i
$536$	−0.205345	+	21.0252i	−0.00886957	+	0.908151i
$537$	36.8323	−	26.7603i	1.58943	−	1.15479i
$538$	−32.9663	−	24.1158i	−1.42128	−	1.03970i
$539$	8.16441	−	9.80550i	0.351666	−	0.422353i
$540$	−4.82384	+	1.53271i	−0.207585	+	0.0659573i
$541$	−16.6335	−	22.8940i	−0.715128	−	0.984290i	−0.999672	−	0.0256266i	$-0.991842\pi$
$541$	−16.6335	−	22.8940i	−0.715128	−	0.984290i	0.284543	−	0.958663i	$-0.408158\pi$
$542$	−7.65137	+	23.2902i	−0.328655	+	1.00040i
$543$	−3.84460	−	1.24919i	−0.164988	−	0.0536077i
$544$	−27.0908	+	36.0388i	−1.16151	+	1.54515i
$545$	−6.52585	+	8.98206i	−0.279537	+	0.384749i
$546$	−2.80981	+	2.02750i	−0.120249	+	0.0867691i
$547$	6.72560	+	20.6993i	0.287566	+	0.885037i	0.985618	+	0.168990i	$0.0540504\pi$
$547$	6.72560	+	20.6993i	0.287566	+	0.885037i	−0.698052	+	0.716047i	$0.745950\pi$
$548$	−20.9996	−	15.4670i	−0.897059	−	0.660718i
$549$		−	18.1933i		−	0.776473i
$550$	−4.55047	+	1.13722i	−0.194033	+	0.0484911i
$551$			4.71916i			0.201043i
$552$	−7.49790	−	23.8668i	−0.319132	−	1.01584i
$553$	−1.75192	−	5.39186i	−0.0744993	−	0.229285i
$554$	−19.9429	−	27.6379i	−0.847294	−	1.17422i
$555$	5.69023	−	7.83194i	0.241537	−	0.332447i
$556$	−2.76624	+	8.32871i	−0.117315	+	0.353216i
$557$	−6.62309	−	2.15197i	−0.280629	−	0.0911820i	0.165321	−	0.986240i	$-0.447134\pi$
$557$	−6.62309	−	2.15197i	−0.280629	−	0.0911820i	−0.445950	+	0.895058i	$0.647134\pi$
$558$	−9.37646	−	3.08038i	−0.396937	−	0.130403i
$559$	−3.10353	−	4.27164i	−0.131265	−	0.180671i
$560$	5.79993	−	4.09958i	0.245092	−	0.173239i
$561$	54.0632	+	21.6040i	2.28255	+	0.912122i
$562$	8.20496	−	11.2162i	0.346105	−	0.473126i
$563$	12.0051	−	8.72223i	0.505955	−	0.367598i	−0.305332	−	0.952246i	$-0.598767\pi$
$563$	12.0051	−	8.72223i	0.505955	−	0.367598i	0.811287	+	0.584648i	$0.198767\pi$
$564$	−27.9927	+	20.0607i	−1.17870	+	0.844708i
$565$	2.09343	−	6.44293i	0.0880714	−	0.271056i
$566$	5.29906	+	16.4913i	0.222736	+	0.693182i
$567$	−15.9838	−	11.6129i	−0.671258	−	0.487698i
$568$	−3.00370	+	4.05045i	−0.126032	+	0.169953i
$569$	0.884380	−	0.287353i	0.0370752	−	0.0120464i	−0.290421	−	0.956899i	$-0.593795\pi$
$569$	0.884380	−	0.287353i	0.0370752	−	0.0120464i	0.327496	+	0.944853i	$0.393795\pi$
$570$	−0.0492853	+	15.1393i	−0.00206434	+	0.634117i
$571$	36.9918			1.54806			0.774030	−	0.633148i	$-0.218238\pi$
$571$	36.9918			1.54806			0.774030	+	0.633148i	$0.218238\pi$
$572$	3.53015	−	2.19262i	0.147603	−	0.0916782i
$573$	−33.5766			−1.40268
$574$	−0.0680388	+	20.9000i	−0.00283988	+	0.872348i
$575$	3.81927	−	1.24095i	0.159274	−	0.0517514i
$576$	12.1474	−	8.46811i	0.506142	−	0.352838i
$577$	−15.4877	−	11.2525i	−0.644760	−	0.468446i	0.216722	−	0.976233i	$-0.430463\pi$
$577$	−15.4877	−	11.2525i	−0.644760	−	0.468446i	−0.861482	+	0.507788i	$0.830463\pi$
$578$	20.1270	+	62.6377i	0.837173	+	2.60538i
$579$	−6.97106	+	21.4547i	−0.289707	+	0.891627i
$580$	1.13114	+	1.57838i	0.0469678	+	0.0655388i
$581$	10.9028	−	7.92136i	0.452325	−	0.328633i
$582$	10.1111	−	13.8219i	0.419119	−	0.572936i
$583$	16.4145	+	26.0476i	0.679820	+	1.07878i
$584$	10.8127	+	3.63037i	0.447431	+	0.150226i
$585$	−0.681602	−	0.938145i	−0.0281808	−	0.0387875i
$586$	−17.9039	−	5.88184i	−0.739604	−	0.242977i
$587$	−44.4346	−	14.4377i	−1.83401	−	0.595907i	−0.998953	−	0.0457498i	$-0.985432\pi$
$587$	−44.4346	−	14.4377i	−1.83401	−	0.595907i	−0.835061	−	0.550157i	$-0.814568\pi$
$588$	−16.0827	−	5.34161i	−0.663240	−	0.220284i
$589$	10.7716	−	14.8258i	0.443836	−	0.610888i
$590$	2.13821	+	2.96323i	0.0880288	+	0.121994i
$591$	−15.2788	−	47.0233i	−0.628486	−	1.93428i
$592$	5.65027	−	16.6489i	0.232225	−	0.684265i
$593$		−	20.9247i		−	0.859274i	−0.903002	−	0.429637i	$-0.858642\pi$
$593$		−	20.9247i		−	0.859274i	0.903002	−	0.429637i	$-0.141358\pi$
$594$	9.09732	+	7.62503i	0.373268	+	0.312859i
$595$		−	14.1519i		−	0.580170i
$596$	−13.3619	+	18.1415i	−0.547324	+	0.743105i
$597$	5.42892	+	16.7085i	0.222191	+	0.683833i
$598$	−2.88525	+	2.08194i	−0.117987	+	0.0851370i
$599$	1.09400	−	1.50577i	0.0446997	−	0.0615239i	−0.786082	−	0.618122i	$-0.787894\pi$
$599$	1.09400	−	1.50577i	0.0446997	−	0.0615239i	0.830782	+	0.556598i	$0.187894\pi$
$600$	3.61226	+	5.07536i	0.147470	+	0.207201i
$601$	18.3967	+	5.97743i	0.750415	+	0.243825i	0.659160	−	0.752003i	$-0.270912\pi$
$601$	18.3967	+	5.97743i	0.750415	+	0.243825i	0.0912553	+	0.995828i	$0.470912\pi$
$602$	−6.60541	+	20.1064i	−0.269217	+	0.819476i
$603$	−8.08785	−	11.1320i	−0.329363	−	0.453329i
$604$	−4.49698	−	14.1532i	−0.182979	−	0.575884i
$605$	7.97066	+	7.58080i	0.324054	+	0.308203i
$606$	−46.9549	−	34.3489i	−1.90741	−	1.39533i
$607$	−21.9574	+	15.9530i	−0.891222	+	0.647511i	−0.936196	−	0.351477i	$-0.885679\pi$
$607$	−21.9574	+	15.9530i	−0.891222	+	0.647511i	0.0449744	+	0.998988i	$0.485679\pi$
$608$	8.06971	+	26.2842i	0.327270	+	1.06597i
$609$	−1.17337	+	3.61125i	−0.0475472	+	0.146335i
$610$	13.2340	−	4.25242i	0.535831	−	0.172176i
$611$	3.96255	+	2.87896i	0.160307	+	0.116470i
$612$	0.192099	−	29.5040i	0.00776515	−	1.19263i
$613$	−5.71658	+	1.85743i	−0.230891	+	0.0750209i	−0.422177	−	0.906513i	$-0.638734\pi$
$613$	−5.71658	+	1.85743i	−0.230891	+	0.0750209i	0.191287	+	0.981534i	$0.438734\pi$
$614$	−18.8126	−	0.0612434i	−0.759214	−	0.00247158i
$615$	−18.3314			−0.739192
$616$	−15.4065	−	6.33172i	−0.620746	−	0.255112i
$617$	20.2958			0.817079			0.408540	−	0.912741i	$-0.366038\pi$
$617$	20.2958			0.817079			0.408540	+	0.912741i	$0.366038\pi$
$618$	60.5946	+	0.197262i	2.43747	+	0.00793506i
$619$	36.7403	−	11.9376i	1.47672	−	0.479814i	0.543586	−	0.839353i	$-0.317066\pi$
$619$	36.7403	−	11.9376i	1.47672	−	0.479814i	0.933130	+	0.359539i	$0.117066\pi$
$620$	0.0490962	−	7.54054i	0.00197175	−	0.302835i
$621$	−8.22203	−	5.97365i	−0.329939	−	0.239714i
$622$	2.78240	−	0.894053i	0.111564	−	0.0358483i
$623$	3.44935	−	10.6160i	0.138195	−	0.425322i
$624$	−4.42263	−	3.30206i	−0.177047	−	0.132188i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	2.72031	+	1.98998i	0.108725	+	0.0795357i
$627$	30.0382	−	18.9293i	1.19961	−	0.755963i
$628$	9.30831	+	29.2957i	0.371442	+	1.16903i
$629$	−20.5910	−	28.3411i	−0.821018	−	1.13003i
$630$	−1.45069	+	4.41580i	−0.0577969	+	0.175930i
$631$	41.1179	+	13.3600i	1.63688	+	0.531854i	0.975838	−	0.218497i	$-0.0701153\pi$
$631$	41.1179	+	13.3600i	1.63688	+	0.531854i	0.661040	+	0.750351i	$0.270115\pi$
$632$	7.35754	−	5.23655i	0.292667	−	0.208299i
$633$	7.20137	−	9.91184i	0.286229	−	0.393960i
$634$	0.209601	−	0.151244i	0.00832431	−	0.00600666i
$635$	1.36447	+	4.19940i	0.0541472	+	0.166648i
$636$	24.2503	−	32.9247i	0.961586	−	1.30555i
$637$			2.41020i			0.0954954i
$638$	1.70365	−	4.22336i	0.0674480	−	0.167204i
$639$		−	3.29998i		−	0.130545i
$640$	8.99908	+	6.85686i	0.355720	+	0.271041i
$641$	−3.88178	−	11.9469i	−0.153321	−	0.471873i	0.844666	−	0.535294i	$-0.179799\pi$
$641$	−3.88178	−	11.9469i	−0.153321	−	0.471873i	−0.997987	+	0.0634204i	$0.979799\pi$
$642$	3.69347	+	5.11858i	0.145769	+	0.202014i
$643$	2.67991	−	3.68858i	0.105685	−	0.145463i	−0.752898	−	0.658137i	$-0.771345\pi$
$643$	2.67991	−	3.68858i	0.105685	−	0.145463i	0.858584	+	0.512673i	$0.171345\pi$
$644$	13.5342	+	4.49516i	0.533323	+	0.177134i
$645$	−17.6540	−	5.73614i	−0.695126	−	0.225860i
$646$	52.0477	+	17.0988i	2.04779	+	0.672745i
$647$	−22.6602	−	31.1891i	−0.890864	−	1.22617i	−0.973292	−	0.229573i	$-0.926267\pi$
$647$	−22.6602	−	31.1891i	−0.890864	−	1.22617i	0.0824272	−	0.996597i	$-0.473733\pi$
$648$	10.0170	−	29.8347i	0.393507	−	1.17202i
$649$	3.18001	−	7.95785i	0.124826	−	0.312373i
$650$	0.523103	−	0.715082i	0.0205178	−	0.0280478i
$651$	11.9290	−	8.66695i	0.467536	−	0.339685i
$652$	0.00986561	+	0.0137664i	0.000386367	+	0.000539136i
$653$	−0.605436	+	1.86334i	−0.0236925	+	0.0729181i	−0.962204	−	0.272331i	$-0.912205\pi$
$653$	−0.605436	+	1.86334i	−0.0236925	+	0.0729181i	0.938511	+	0.345249i	$0.112205\pi$
$654$	−10.5792	−	32.9238i	−0.413681	−	1.28742i
$655$	−12.8132	−	9.30932i	−0.500652	−	0.363745i
$656$	−31.7939	+	9.87465i	−1.24134	+	0.385540i
$657$	−7.09882	+	2.30655i	−0.276952	+	0.0899870i
$658$	0.0639114	−	19.6321i	0.00249152	−	0.765340i
$659$	6.26307			0.243974			0.121987	−	0.992532i	$-0.461073\pi$
$659$	6.26307			0.243974			0.121987	+	0.992532i	$0.461073\pi$
$660$	5.50951	−	13.5310i	0.214457	−	0.526693i
$661$	14.1110			0.548853			0.274427	−	0.961608i	$-0.411512\pi$
$661$	14.1110			0.548853			0.274427	+	0.961608i	$0.411512\pi$
$662$	0.119405	−	36.6786i	0.00464082	−	1.42556i
$663$	−10.4591	+	3.39838i	−0.406200	+	0.131982i
$664$	17.2432	+	12.7871i	0.669166	+	0.496234i
$665$	−6.98217	−	5.07284i	−0.270757	−	0.196716i
$666$	3.51979	+	10.9540i	0.136389	+	0.424460i
$667$	−1.20487	+	3.70821i	−0.0466528	+	0.143583i
$668$	−13.0230	+	9.33280i	−0.503874	+	0.361097i
$669$	32.5708	−	23.6641i	1.25926	−	0.914907i
$670$	6.20711	−	8.48513i	0.239802	−	0.327809i
$671$	−25.0522	−	20.8594i	−0.967130	−	0.805267i
$672$	−0.360082	+	22.1199i	−0.0138905	+	0.853295i
$673$	10.4569	+	14.3926i	0.403082	+	0.554795i	0.961514	−	0.274755i	$-0.0885969\pi$
$673$	10.4569	+	14.3926i	0.403082	+	0.554795i	−0.558432	+	0.829550i	$0.688597\pi$
$674$	2.31222	+	0.759616i	0.0890633	+	0.0292593i
$675$	2.40688	+	0.782042i	0.0926408	+	0.0301008i
$676$	7.94784	−	23.9297i	0.305686	−	0.920372i
$677$	21.2842	−	29.2952i	0.818020	−	1.12591i	−0.172016	−	0.985094i	$-0.555028\pi$
$677$	21.2842	−	29.2952i	0.818020	−	1.12591i	0.990036	−	0.140814i	$-0.0449718\pi$
$678$	12.3473	+	17.1115i	0.474195	+	0.657162i
$679$	3.01680	+	9.28476i	0.115774	+	0.356316i
$680$	21.5064	−	6.75638i	0.824734	−	0.259095i
$681$		−	37.1833i		−	1.42487i
$682$	−14.9922	+	9.37960i	−0.574079	+	0.359164i
$683$		−	35.3702i		−	1.35340i	−0.736257	−	0.676702i	$-0.763409\pi$
$683$		−	35.3702i		−	1.35340i	0.736257	−	0.676702i	$-0.236591\pi$
$684$	−14.4876	−	10.6707i	−0.553948	−	0.408004i
$685$	4.02972	+	12.4022i	0.153968	+	0.473863i
$686$	22.0884	−	15.9385i	0.843338	−	0.608536i
$687$	−5.23344	+	7.20321i	−0.199668	+	0.274820i
$688$	−33.7090	−	0.438975i	−1.28514	−	0.0167358i
$689$	−5.53107	−	1.79715i	−0.210717	−	0.0684661i
$690$	−3.90402	+	11.8836i	−0.148624	+	0.452400i
$691$	−8.42589	−	11.5972i	−0.320536	−	0.441180i	0.618095	−	0.786104i	$-0.287905\pi$
$691$	−8.42589	−	11.5972i	−0.320536	−	0.441180i	−0.938631	+	0.344924i	$0.887905\pi$
$692$	49.3583	−	15.6829i	1.87632	−	0.596176i
$693$	10.5666	−	2.67730i	0.401392	−	0.101702i
$694$	−38.3173	−	28.0302i	−1.45450	−	1.06401i
$695$	3.55000	−	2.57922i	0.134659	−	0.0978355i
$696$	−6.04816	−	0.0590700i	−0.229255	−	0.00223904i
$697$	−20.4986	+	63.0883i	−0.776441	+	2.38964i
$698$	−16.0059	+	5.14308i	−0.605831	+	0.194668i
$699$	16.6522	+	12.0985i	0.629842	+	0.457607i
$700$	−3.55118	−	0.0231216i	−0.134222	−	0.000873915i
$701$	35.1338	−	11.4156i	1.32698	−	0.431163i	0.442096	−	0.896968i	$-0.354235\pi$
$701$	35.1338	−	11.4156i	1.32698	−	0.431163i	0.884888	+	0.465805i	$0.154235\pi$
$702$	−2.24220	−	0.00729937i	−0.0846265	−	0.000275497i
$703$	−21.3638			−0.805750
$704$	2.26688	−	26.4360i	0.0854361	−	0.996344i
$705$	17.2193			0.648518
$706$	−25.1099	−	0.0817441i	−0.945025	−	0.00307648i
$707$	31.5416	−	10.2485i	1.18624	−	0.385434i
$708$	−11.3816	−	0.0741054i	−0.427748	−	0.00278505i
$709$	−4.18365	−	3.03960i	−0.157120	−	0.114155i	0.506447	−	0.862271i	$-0.330958\pi$
$709$	−4.18365	−	3.03960i	−0.157120	−	0.114155i	−0.663568	+	0.748116i	$0.730958\pi$
$710$	2.40045	−	0.771322i	0.0900871	−	0.0289472i
$711$	−1.82625	+	5.62062i	−0.0684897	+	0.210790i
$712$	17.7798	+	0.173649i	0.666327	+	0.00650776i
$713$	12.2493	−	8.89967i	0.458741	−	0.333295i
$714$	35.5770	+	26.0256i	1.33144	+	0.973984i
$715$	−2.07331	−	0.137053i	−0.0775373	−	0.00512551i
$716$	−39.4006	+	12.5190i	−1.47247	+	0.467857i
$717$	−4.61957	−	6.35830i	−0.172521	−	0.237455i
$718$	−3.61655	+	11.0085i	−0.134969	+	0.410835i
$719$	−20.8501	−	6.77462i	−0.777579	−	0.252651i	−0.106773	−	0.994283i	$-0.534052\pi$
$719$	−20.8501	−	6.77462i	−0.777579	−	0.252651i	−0.670806	+	0.741633i	$0.734052\pi$
$720$	−7.40323	−	0.0964084i	−0.275902	−	0.00359293i
$721$	−20.3038	+	27.9458i	−0.756154	+	1.04076i
$722$	5.30336	−	3.82680i	0.197371	−	0.142419i
$723$	−1.26951	−	3.90714i	−0.0472134	−	0.145308i
$724$	2.95563	+	2.17693i	0.109845	+	0.0809050i
$725$		−	0.970923i		−	0.0360592i
$726$	−33.7159	+	6.09656i	−1.25132	+	0.226265i
$727$			6.31816i			0.234327i	0.993113	+	0.117164i	$0.0373802\pi$
$727$			6.31816i			0.234327i	−0.993113	+	0.117164i	$0.962620\pi$
$728$	3.00174	−	0.943015i	0.111252	−	0.0349505i
$729$	1.19699	+	3.68396i	0.0443330	+	0.136443i
$730$	−3.33705	−	4.62465i	−0.123510	−	0.171166i
$731$	−39.4824	+	54.3428i	−1.46031	+	2.00994i
$732$	−13.6474	+	41.0900i	−0.504421	+	1.51873i
$733$	−22.1201	−	7.18727i	−0.817026	−	0.265468i	−0.129455	−	0.991585i	$-0.541323\pi$
$733$	−22.1201	−	7.18727i	−0.817026	−	0.265468i	−0.687571	+	0.726118i	$0.741323\pi$
$734$	−31.5038	−	10.3497i	−1.16283	−	0.382015i
$735$	4.98048	+	6.85504i	0.183708	+	0.252852i
$736$	−0.369750	+	22.7139i	−0.0136292	+	0.837244i
$737$	−24.6017	−	1.62627i	−0.906217	−	0.0599044i
$738$	12.8633	−	17.5841i	0.473504	−	0.647280i
$739$	−7.52553	+	5.46762i	−0.276831	+	0.201130i	−0.717534	−	0.696523i	$-0.754729\pi$
$739$	−7.52553	+	5.46762i	−0.276831	+	0.201130i	0.440703	+	0.897653i	$0.354729\pi$
$740$	−7.14538	+	5.12068i	−0.262669	+	0.188240i
$741$	−2.07248	+	6.37845i	−0.0761346	+	0.234318i
$742$	7.13120	+	22.1932i	0.261795	+	0.814736i
$743$	−27.3431	−	19.8659i	−1.00312	−	0.728810i	−0.0403653	−	0.999185i	$-0.512852\pi$
$743$	−27.3431	−	19.8659i	−1.00312	−	0.728810i	−0.962755	+	0.270375i	$0.912852\pi$
$744$	18.8662	+	13.9906i	0.691669	+	0.512922i
$745$	10.7142	−	3.48126i	0.392538	−	0.127543i
$746$	0.0146994	−	4.51532i	0.000538183	−	0.165318i
$747$	−14.0484			−0.514004
$748$	−40.4067	−	34.0920i	−1.47742	−	1.24653i
$749$	−3.59825			−0.131477
$750$	0.0101400	−	3.11478i	0.000370260	−	0.113736i
$751$	−9.51233	+	3.09074i	−0.347110	+	0.112783i	−0.477383	−	0.878695i	$-0.658415\pi$
$751$	−9.51233	+	3.09074i	−0.347110	+	0.112783i	0.130273	+	0.991478i	$0.458415\pi$
$752$	29.8652	−	9.27563i	1.08907	−	0.338247i
$753$	36.6654	+	26.6390i	1.33616	+	0.970778i
$754$	0.263160	+	0.818987i	0.00958374	+	0.0298257i
$755$	−2.29452	+	7.06179i	−0.0835060	+	0.257005i
$756$	5.23516	+	7.30513i	0.190401	+	0.265685i
$757$	12.1952	−	8.86034i	0.443242	−	0.322034i	−0.343680	−	0.939087i	$-0.611673\pi$
$757$	12.1952	−	8.86034i	0.443242	−	0.322034i	0.786922	+	0.617053i	$0.211673\pi$
$758$	−6.64431	+	9.08279i	−0.241332	+	0.329902i
$759$	28.4363	−	7.20501i	1.03217	−	0.261525i
$760$	4.37571	−	13.0326i	0.158724	−	0.472742i
$761$	−5.13551	−	7.06842i	−0.186162	−	0.256230i	0.705727	−	0.708483i	$-0.250620\pi$
$761$	−5.13551	−	7.06842i	−0.186162	−	0.256230i	−0.891890	+	0.452253i	$0.850620\pi$
$762$	−13.0663	−	4.29259i	−0.473344	−	0.155504i
$763$	18.7490	+	6.09190i	0.678758	+	0.220542i
$764$	28.9354	+	9.61042i	1.04685	+	0.347693i
$765$	−8.67118	+	11.9349i	−0.313507	+	0.431506i
$766$	−9.41095	−	13.0421i	−0.340031	−	0.471232i
$767$	0.500226	+	1.53954i	0.0180621	+	0.0555895i
$768$	−33.7873	+	10.0133i	−1.21919	+	0.361323i
$769$		−	1.85468i		−	0.0668816i	−0.999441	−	0.0334408i	$-0.989353\pi$
$769$		−	1.85468i		−	0.0668816i	0.999441	−	0.0334408i	$-0.0106465\pi$
$770$	4.41728	+	7.06049i	0.159188	+	0.254442i
$771$			67.2802i			2.42304i
$772$	12.1483	−	16.4938i	0.437228	−	0.593626i
$773$	−1.68039	−	5.17172i	−0.0604395	−	0.186014i	0.916278	−	0.400543i	$-0.131178\pi$
$773$	−1.68039	−	5.17172i	−0.0604395	−	0.186014i	−0.976718	+	0.214529i	$0.931178\pi$
$774$	17.8903	−	12.9093i	0.643053	−	0.464014i
$775$	−2.21616	+	3.05028i	−0.0796066	+	0.109569i
$776$	−12.6697	+	9.01731i	−0.454814	+	0.323703i
$777$	−16.3482	−	5.31185i	−0.586489	−	0.190562i
$778$	6.66238	−	20.2798i	0.238858	−	0.727067i
$779$	23.7782	+	32.7280i	0.851944	+	1.17260i
$780$	0.835681	+	2.63011i	0.0299222	+	0.0941729i
$781$	−4.54408	−	3.78356i	−0.162600	−	0.135386i
$782$	36.5323	+	26.7244i	1.30639	+	0.955663i
$783$	−1.98788	+	1.44428i	−0.0710410	+	0.0516143i
$784$	12.3308	+	9.20652i	0.440385	+	0.328804i
$785$	4.74943	−	14.6172i	0.169514	−	0.521712i
$786$	46.9669	−	15.0916i	1.67525	−	0.538299i
$787$	−15.2205	−	11.0583i	−0.542551	−	0.394186i	0.282481	−	0.959273i	$-0.408843\pi$
$787$	−15.2205	−	11.0583i	−0.542551	−	0.394186i	−0.825032	+	0.565087i	$0.808843\pi$
$788$	−0.292320	+	44.8966i	−0.0104135	+	1.59938i
$789$	5.30552	−	1.72387i	0.188882	−	0.0613714i
$790$	−4.51536	−	0.0146995i	−0.160649	−	0.000522986i
$791$	−12.0290			−0.427702
$792$	9.11336	+	14.7797i	0.323829	+	0.525175i
$793$	6.15785			0.218671
$794$	32.8075	+	0.106803i	1.16430	+	0.00379030i
$795$	−19.4450	+	6.31808i	−0.689645	+	0.224079i
$796$	0.103868	−	15.9528i	0.00368152	−	0.565433i
$797$	12.6490	+	9.19002i	0.448050	+	0.325527i	0.788825	−	0.614617i	$-0.210690\pi$
$797$	12.6490	+	9.19002i	0.448050	+	0.325527i	−0.340776	+	0.940145i	$0.610690\pi$
$798$	25.5932	−	8.22372i	0.905990	−	0.291117i
$799$	19.2551	−	59.2612i	0.681198	−	2.09651i
$800$	−1.66027	−	5.40773i	−0.0586992	−	0.191192i
$801$	−9.41366	+	6.83942i	−0.332615	+	0.241659i
$802$	−30.2835	−	22.1532i	−1.06935	−	0.782258i
$803$	−4.96296	+	12.4196i	−0.175139	+	0.438279i
$804$	9.91613	+	31.2087i	0.349715	+	1.10064i
$805$	−4.19126	−	5.76877i	−0.147722	−	0.203323i
$806$	1.04261	−	3.17362i	0.0367242	−	0.111786i
$807$	−60.4990	−	19.6573i	−2.12967	−	0.691971i
$808$	30.6331	+	43.0406i	1.07767	+	1.51416i
$809$	8.39109	−	11.5493i	0.295015	−	0.406053i	−0.635620	−	0.772002i	$-0.719255\pi$
$809$	8.39109	−	11.5493i	0.295015	−	0.406053i	0.930635	+	0.365949i	$0.119255\pi$
$810$	−12.7605	+	9.20772i	−0.448358	+	0.323526i
$811$	4.04772	+	12.4576i	0.142135	+	0.437446i	0.996631	−	0.0820110i	$-0.0261343\pi$
$811$	4.04772	+	12.4576i	0.142135	+	0.437446i	−0.854497	+	0.519457i	$0.826134\pi$
$812$	2.04480	−	2.77623i	0.0717584	−	0.0974267i
$813$			38.1794i			1.33901i
$814$	19.1193	+	7.71245i	0.670130	+	0.270321i
$815$		−	0.00846825i		−	0.000296630i
$816$	−22.5656	+	66.4911i	−0.789955	+	2.32766i
$817$	12.6586	+	38.9592i	0.442868	+	1.36301i
$818$	−4.51203	−	6.25298i	−0.157759	−	0.218630i
$819$	−1.21027	+	1.66580i	−0.0422903	+	0.0582077i
$820$	15.7975	+	5.24687i	0.551672	+	0.183229i
$821$	−32.1971	−	10.4615i	−1.12369	−	0.365107i	−0.312512	−	0.949914i	$-0.601171\pi$
$821$	−32.1971	−	10.4615i	−1.12369	−	0.365107i	−0.811173	+	0.584806i	$0.801171\pi$
$822$	−38.5892	−	12.6774i	−1.34595	−	0.442176i
$823$	17.7092	+	24.3746i	0.617304	+	0.849645i	0.997153	−	0.0754028i	$-0.0240243\pi$
$823$	17.7092	+	24.3746i	0.617304	+	0.849645i	−0.379850	+	0.925048i	$0.624024\pi$
$824$	−52.1624	−	17.5136i	−1.81716	−	0.610115i
$825$	−6.18008	+	3.89452i	−0.215163	+	0.135590i
$826$	3.83085	−	5.23677i	0.133292	−	0.182211i
$827$	−6.83918	+	4.96896i	−0.237822	+	0.172788i	−0.700312	−	0.713837i	$-0.746956\pi$
$827$	−6.83918	+	4.96896i	−0.237822	+	0.172788i	0.462491	+	0.886624i	$0.346956\pi$
$828$	−8.65967	−	12.0837i	−0.300944	−	0.419937i
$829$	−12.5127	+	38.5102i	−0.434585	+	1.33751i	0.458926	+	0.888474i	$0.348234\pi$
$829$	−12.5127	+	38.5102i	−0.434585	+	1.33751i	−0.893511	+	0.449041i	$0.851766\pi$
$830$	−3.28360	−	10.2190i	−0.113975	−	0.354705i
$831$	−42.9418	−	31.1990i	−1.48963	−	1.08228i
$832$	2.86618	+	4.11149i	0.0993668	+	0.142540i
$833$	29.1613	−	9.47506i	1.01038	−	0.328292i
$834$	−0.0444946	+	13.6678i	−0.00154072	+	0.473276i
$835$	8.01091			0.277229
$836$	−31.3042	+	7.71511i	−1.08268	+	0.266833i
$837$	9.54178			0.329812
$838$	0.127145	−	39.0560i	0.00439215	−	1.34917i
$839$	50.2337	−	16.3219i	1.73426	−	0.563495i	0.740206	−	0.672380i	$-0.234728\pi$
$839$	50.2337	−	16.3219i	1.73426	−	0.563495i	0.994054	+	0.108885i	$0.0347281\pi$
$840$	6.58883	−	8.88496i	0.227336	−	0.306560i
$841$	−22.6988	−	16.4917i	−0.782719	−	0.568678i
$842$	−2.40194	−	7.47514i	−0.0827765	−	0.257610i
$843$	6.68805	−	20.5837i	0.230349	−	0.708941i
$844$	−9.04296	+	6.48056i	−0.311271	+	0.223070i
$845$	−10.1997	+	7.41051i	−0.350880	+	0.254929i
$846$	−12.0830	+	16.5174i	−0.415421	+	0.567881i
$847$	8.42837	−	17.6198i	0.289602	−	0.605425i
$848$	−30.3221	+	21.4326i	−1.04126	+	0.736000i
$849$	15.8566	+	21.8247i	0.544197	+	0.749023i
$850$	−10.7083	−	3.51792i	−0.367292	−	0.120664i
$851$	−16.7872	−	5.45448i	−0.575457	−	0.186977i
$852$	−2.47541	+	7.45307i	−0.0848062	+	0.255338i
$853$	−0.362979	+	0.499597i	−0.0124281	+	0.0171059i	−0.815186	−	0.579199i	$-0.803365\pi$
$853$	−0.362979	+	0.499597i	−0.0124281	+	0.0171059i	0.802758	+	0.596305i	$0.203365\pi$
$854$	−14.4427	−	20.0153i	−0.494218	−	0.684911i
$855$	2.78010	+	8.55627i	0.0950774	+	0.292618i
$856$	−1.71787	−	5.46822i	−0.0587157	−	0.186900i
$857$		−	24.2305i		−	0.827697i	−0.910346	−	0.413848i	$-0.864184\pi$
$857$		−	24.2305i		−	0.827697i	0.910346	−	0.413848i	$-0.135816\pi$
$858$	4.15740	−	4.96014i	0.141931	−	0.169336i
$859$		−	21.5150i		−	0.734083i	−0.930205	−	0.367041i	$-0.880371\pi$
$859$		−	21.5150i		−	0.734083i	0.930205	−	0.367041i	$-0.119629\pi$
$860$	13.5719	+	9.99625i	0.462800	+	0.340869i
$861$	10.0584	+	30.9566i	0.342790	+	1.05500i
$862$	−23.8014	+	17.1746i	−0.810680	+	0.584971i
$863$	−13.2618	+	18.2532i	−0.451436	+	0.621348i	−0.972705	−	0.232044i	$-0.925459\pi$
$863$	−13.2618	+	18.2532i	−0.451436	+	0.621348i	0.521270	+	0.853392i	$0.325459\pi$
$864$	−8.60215	+	11.4434i	−0.292651	+	0.389313i
$865$	−24.6276	−	8.00199i	−0.837363	−	0.272076i
$866$	3.45223	−	10.5083i	0.117311	−	0.357088i
$867$	60.2268	+	82.8951i	2.04541	+	2.81527i
$868$	−12.7608	+	4.05458i	−0.433131	+	0.137621i
$869$	5.64573	+	8.95901i	0.191518	+	0.303913i
$870$	2.44085	+	1.78555i	0.0827525	+	0.0605358i
$871$	3.76780	−	2.73747i	0.127667	−	0.0927556i
$872$	−0.306681	+	31.4009i	−0.0103855	+	1.06337i
$873$	3.14479	−	9.67868i	0.106435	−	0.327574i
$874$	26.2804	−	8.44453i	0.888948	−	0.285641i
$875$	1.43651	+	1.04369i	0.0485630	+	0.0352831i
$876$	17.7630	+	0.115654i	0.600157	+	0.00390760i
$877$	6.24044	−	2.02764i	0.210725	−	0.0684686i	−0.201752	−	0.979437i	$-0.564664\pi$
$877$	6.24044	−	2.02764i	0.210725	−	0.0684686i	0.412477	+	0.910968i	$0.364664\pi$
$878$	17.6160	+	0.0573481i	0.594512	+	0.00193540i
$879$	−29.3496			−0.989938
$880$	−8.62084	+	10.0837i	−0.290608	+	0.339922i
$881$	−13.2814			−0.447461			−0.223731	−	0.974651i	$-0.571824\pi$
$881$	−13.2814			−0.447461			−0.223731	+	0.974651i	$0.571824\pi$
$882$	−10.0704	−	0.0327838i	−0.339090	−	0.00110389i
$883$	8.21990	−	2.67081i	0.276622	−	0.0898798i	−0.167421	−	0.985886i	$-0.553544\pi$
$883$	8.21990	−	2.67081i	0.276622	−	0.0898798i	0.444043	+	0.896006i	$0.353544\pi$
$884$	9.98612	+	0.0650193i	0.335870	+	0.00218683i
$885$	4.60406	+	3.34505i	0.154764	+	0.112443i
$886$	21.7317	−	6.98291i	0.730090	−	0.234596i
$887$	9.20731	−	28.3372i	0.309151	−	0.951470i	−0.668944	−	0.743313i	$-0.733253\pi$
$887$	9.20731	−	28.3372i	0.309151	−	0.951470i	0.978095	−	0.208157i	$-0.0667465\pi$
$888$	0.267411	−	27.3801i	0.00897374	−	0.918818i
$889$	6.34294	−	4.60842i	0.212735	−	0.154561i
$890$	−7.17538	−	5.24899i	−0.240519	−	0.175947i
$891$	34.2687	+	13.6940i	1.14804	+	0.458766i
$892$	−34.8419	+	11.0706i	−1.16659	+	0.370670i
$893$	−22.3358	−	30.7426i	−0.747439	−	1.02876i
$894$	−10.9520	+	33.3371i	−0.366289	+	1.11496i
$895$	19.6591	+	6.38763i	0.657132	+	0.213515i
$896$	6.64156	−	18.9593i	0.221879	−	0.633386i
$897$	−3.25702	+	4.48290i	−0.108749	+	0.149680i
$898$	42.0753	−	30.3607i	1.40407	−	1.01315i
$899$	−1.13122	−	3.48155i	−0.0377284	−	0.116116i
$900$	2.98069	+	2.19539i	0.0993564	+	0.0731797i
$901$			73.9861i			2.46484i
$902$	−9.46508	−	37.8736i	−0.315153	−	1.26105i
$903$			32.9602i			1.09685i
$904$	−5.74287	−	18.2803i	−0.191005	−	0.607994i
$905$	−0.567170	−	1.74557i	−0.0188534	−	0.0580247i
$906$	−13.5333	−	18.7551i	−0.449614	−	0.623096i
$907$	14.0223	−	19.3001i	0.465604	−	0.640849i	−0.510055	−	0.860142i	$-0.670375\pi$
$907$	14.0223	−	19.3001i	0.465604	−	0.640849i	0.975659	+	0.219293i	$0.0703750\pi$
$908$	−10.6427	+	32.0436i	−0.353192	+	1.06340i
$909$	−32.8798	−	10.6833i	−1.09055	−	0.354343i
$910$	−1.49460	−	0.491011i	−0.0495456	−	0.0162769i
$911$	8.81657	+	12.1350i	0.292106	+	0.402049i	0.929697	−	0.368326i	$-0.120069\pi$
$911$	8.81657	+	12.1350i	0.292106	+	0.402049i	−0.637591	+	0.770375i	$0.720069\pi$
$912$	24.7162	+	34.9675i	0.818434	+	1.15789i
$913$	−16.1070	+	19.3446i	−0.533065	+	0.640214i
$914$	19.3356	−	26.4318i	0.639566	−	0.874288i
$915$	17.5140	−	12.7247i	0.578996	−	0.420665i
$916$	6.57178	−	4.70961i	0.217138	−	0.155610i
$917$	−8.69028	+	26.7459i	−0.286978	+	0.883229i
$918$	8.72632	+	27.1574i	0.288012	+	0.896327i
$919$	−17.6334	−	12.8114i	−0.581671	−	0.422609i	0.257655	−	0.966237i	$-0.417050\pi$
$919$	−17.6334	−	12.8114i	−0.581671	−	0.422609i	−0.839326	+	0.543628i	$0.817050\pi$
$920$	6.76575	−	9.12353i	0.223060	−	0.300794i
$921$	−27.8648	+	9.05382i	−0.918177	+	0.298334i
$922$	0.0354396	−	10.8862i	0.00116714	−	0.358519i
$923$	1.11694			0.0367644
$924$	−25.8732	−	1.87958i	−0.851165	−	0.0618337i
$925$	4.39539			0.144520
$926$	−0.170012	+	52.2238i	−0.00558693	+	1.71618i
$927$	34.2461	−	11.1272i	1.12479	−	0.365466i
$928$	5.19524	+	1.78203i	0.170542	+	0.0584980i
$929$	−33.0403	−	24.0052i	−1.08402	−	0.787584i	−0.105638	−	0.994405i	$-0.533688\pi$
$929$	−33.0403	−	24.0052i	−1.08402	−	0.787584i	−0.978379	+	0.206820i	$0.933688\pi$
$930$	−3.59267	−	11.1808i	−0.117808	−	0.366634i
$931$	5.77831	−	17.7838i	0.189376	−	0.582841i
$932$	−10.8875	−	15.1924i	−0.356632	−	0.497644i
$933$	3.68225	−	2.67531i	0.120551	−	0.0875857i
$934$	17.1754	−	23.4789i	0.561998	−	0.768252i
$935$	6.49245	+	25.6240i	0.212326	+	0.837994i
$936$	−3.10930	−	1.04395i	−0.101631	−	0.0341226i
$937$	−0.230716	−	0.317553i	−0.00753716	−	0.0103740i	0.805232	−	0.592960i	$-0.202041\pi$
$937$	−0.230716	−	0.317553i	−0.00753716	−	0.0103740i	−0.812769	+	0.582586i	$0.802041\pi$
$938$	−17.7349	−	5.82631i	−0.579064	−	0.190236i
$939$	4.99225	+	1.62208i	0.162916	+	0.0529346i
$940$	−14.8392	−	4.92858i	−0.484001	−	0.160753i
$941$	−16.4167	+	22.5956i	−0.535168	+	0.736596i	−0.987907	−	0.155047i	$-0.950447\pi$
$941$	−16.4167	+	22.5956i	−0.535168	+	0.736596i	0.452739	+	0.891643i	$0.350447\pi$
$942$	28.0126	+	38.8212i	0.912701	+	1.26486i
$943$	10.3285	+	31.7878i	0.336342	+	1.03515i
$944$	9.78718	+	3.32156i	0.318546	+	0.108107i
$945$		−	4.49366i		−	0.146179i
$946$	2.73583	−	39.4359i	0.0889496	−	1.28217i
$947$		−	22.0585i		−	0.716804i	−0.933567	−	0.358402i	$-0.883322\pi$
$947$		−	22.0585i		−	0.716804i	0.933567	−	0.358402i	$-0.116678\pi$
$948$	8.34081	−	11.3243i	0.270897	−	0.367798i
$949$	−0.780690	−	2.40272i	−0.0253423	−	0.0779955i
$950$	−5.57412	+	4.02218i	−0.180848	+	0.130497i
$951$	0.236608	−	0.325663i	0.00767253	−	0.0105603i
$952$	−23.2102	−	32.6112i	−0.752248	−	1.05693i
$953$	−27.8259	−	9.04118i	−0.901369	−	0.292872i	−0.178567	−	0.983928i	$-0.557146\pi$
$953$	−27.8259	−	9.04118i	−0.901369	−	0.292872i	−0.722802	+	0.691055i	$0.757146\pi$
$954$	7.58422	−	23.0859i	0.245548	−	0.747432i
$955$	−8.96069	−	12.3333i	−0.289961	−	0.399097i
$956$	2.16113	+	6.80165i	0.0698960	+	0.219981i
$957$	0.467815	−	7.07698i	0.0151223	−	0.228766i
$958$	−22.0653	−	16.1414i	−0.712899	−	0.521505i
$959$	18.7328	−	13.6102i	0.604913	−	0.439495i
$960$	16.6480	+	5.77111i	0.537312	+	0.186262i
$961$	5.18669	−	15.9630i	0.167313	−	0.514935i
$962$	−3.70757	+	1.19133i	−0.119537	+	0.0384101i
$963$	3.03455	+	2.20473i	0.0977871	+	0.0710465i
$964$	−0.0242887	+	3.73043i	−0.000782287	+	0.120149i
$965$	−9.74111	+	3.16508i	−0.313577	+	0.101887i
$966$	22.2102	+	0.0723041i	0.714602	+	0.00232635i
$967$	−24.8984			−0.800680			−0.400340	−	0.916367i	$-0.631108\pi$
$967$	−24.8984			−0.800680			−0.400340	+	0.916367i	$0.631108\pi$
$968$	30.8005	+	4.39645i	0.989966	+	0.141307i
$969$	85.3210			2.74091
$970$	7.77543	+	0.0253125i	0.249654	+	0.000812736i
$971$	13.6557	−	4.43702i	0.438233	−	0.142391i	−0.0815870	−	0.996666i	$-0.525999\pi$
$971$	13.6557	−	4.43702i	0.438233	−	0.142391i	0.519820	+	0.854276i	$0.325999\pi$
$972$	0.220255	−	33.8283i	0.00706467	−	1.08504i
$973$	−6.30348	−	4.57975i	−0.202080	−	0.146820i
$974$	23.9462	−	7.69450i	0.767286	−	0.246548i
$975$	0.426394	−	1.31230i	0.0136555	−	0.0420274i
$976$	23.5219	−	31.5041i	0.752916	−	1.00842i
$977$	−15.4697	+	11.2394i	−0.494918	+	0.359579i	−0.807073	−	0.590452i	$-0.798949\pi$
$977$	−15.4697	+	11.2394i	−0.494918	+	0.359579i	0.312154	+	0.950031i	$0.398949\pi$
$978$	0.0212887	+	0.0155733i	0.000680738	+	0.000497979i
$979$	−1.37524	+	20.8043i	−0.0439529	+	0.664907i
$980$	−2.32997	−	7.33302i	−0.0744281	−	0.234245i
$981$	−12.0791	−	16.6255i	−0.385656	−	0.530810i
$982$	−8.61502	+	26.2235i	−0.274916	+	0.836826i
$983$	−15.1340	−	4.91733i	−0.482699	−	0.156839i	0.0575515	−	0.998343i	$-0.481671\pi$
$983$	−15.1340	−	4.91733i	−0.482699	−	0.156839i	−0.540251	+	0.841504i	$0.681671\pi$
$984$	−42.2423	+	30.0649i	−1.34664	+	0.958435i
$985$	13.1951	−	18.1615i	0.420430	−	0.578672i
$986$	8.87448	−	6.40365i	0.282621	−	0.203934i
$987$	−9.44824	−	29.0787i	−0.300741	−	0.925585i
$988$	3.61167	−	4.90358i	0.114903	−	0.156004i
$989$			33.8452i			1.07621i
$990$	0.600848	−	8.66097i	0.0190962	−	0.275264i
$991$		−	31.6644i		−	1.00585i	−0.864329	−	0.502926i	$-0.832257\pi$
$991$		−	31.6644i		−	1.00585i	0.864329	−	0.502926i	$-0.167743\pi$
$992$	−12.2540	−	17.4567i	−0.389063	−	0.554252i
$993$	−17.6521	−	54.3276i	−0.560173	−	1.72403i
$994$	−2.61967	−	3.63047i	−0.0830910	−	0.115151i
$995$	−4.68852	+	6.45320i	−0.148636	+	0.204580i
$996$	31.7285	+	10.5381i	1.00536	+	0.333913i
$997$	44.3546	+	14.4117i	1.40473	+	0.456423i	0.910716	−	0.413033i	$-0.135531\pi$
$997$	44.3546	+	14.4117i	1.40473	+	0.456423i	0.494010	+	0.869456i	$0.335531\pi$
$998$	−0.626936	−	0.205963i	−0.0198453	−	0.00651963i
$999$	−6.53829	−	8.99918i	−0.206862	−	0.284721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.d.151.1	yes	48
4.3	odd	2	inner	220.2.r.d.151.8	yes	48
11.7	odd	10	inner	220.2.r.d.51.8	yes	48
44.7	even	10	inner	220.2.r.d.51.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.d.51.1	✓	48	44.7	even	10	inner
220.2.r.d.51.8	yes	48	11.7	odd	10	inner
220.2.r.d.151.1	yes	48	1.1	even	1	trivial
220.2.r.d.151.8	yes	48	4.3	odd	2	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 0.00460387i) q^{2} +(-2.09469 + 0.680607i) q^{3} +(1.99996 + 0.0130217i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.96546 - 0.952875i) q^{6} +(-0.548700 + 1.68872i) q^{7} +(-2.82829 - 0.0276229i) q^{8} +(1.49746 - 1.08797i) q^{9} +(1.14141 + 0.834974i) q^{10} +(0.218764 - 3.30940i) q^{11} +(-4.19816 + 1.33391i) q^{12} +(0.368242 + 0.506841i) q^{13} +(0.783749 - 2.38568i) q^{14} +(2.09469 + 0.680607i) q^{15} +(3.99966 + 0.0520855i) q^{16} +(4.68469 - 6.44792i) q^{17} +(-2.12273 + 1.53172i) q^{18} +(-1.50197 - 4.62260i) q^{19} +(-1.61035 - 1.18608i) q^{20} -3.91081i q^{21} +(-0.324613 + 4.67917i) q^{22} -4.01581i q^{23} +(5.94320 - 1.86709i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.518436 - 0.718473i) q^{26} +(1.48753 - 2.04741i) q^{27} +(-1.11937 + 3.37023i) q^{28} +(-0.923402 - 0.300032i) q^{29} +(-2.95919 - 0.972162i) q^{30} +(2.21616 + 3.05028i) q^{31} +(-5.65610 - 0.0920736i) q^{32} +(1.79416 + 7.08107i) q^{33} +(-6.65480 + 9.09711i) q^{34} +(1.43651 - 1.04369i) q^{35} +(3.00903 - 2.15639i) q^{36} +(1.35825 - 4.18026i) q^{37} +(2.10282 + 6.54423i) q^{38} +(-1.11631 - 0.811049i) q^{39} +(2.27190 + 1.68478i) q^{40} +(-7.91566 + 2.57195i) q^{41} +(-0.0180049 + 5.53069i) q^{42} -8.42797 q^{43} +(0.480613 - 6.61582i) q^{44} -1.85096 q^{45} +(-0.0184883 + 5.67919i) q^{46} +(7.43548 - 2.41593i) q^{47} +(-8.41351 + 2.61309i) q^{48} +(3.11240 + 2.26129i) q^{49} +(-0.432635 - 1.34641i) q^{50} +(-5.42448 + 16.6948i) q^{51} +(0.729868 + 1.01846i) q^{52} +(-7.51011 + 5.45641i) q^{53} +(-2.11310 + 2.88862i) q^{54} +(-2.12220 + 2.54878i) q^{55} +(1.59853 - 4.76105i) q^{56} +(6.29235 + 8.66068i) q^{57} +(1.30450 + 0.428558i) q^{58} +(2.45740 + 0.798458i) q^{59} +(4.18043 + 1.38846i) q^{60} +(5.77741 - 7.95192i) q^{61} +(-3.12006 - 4.32392i) q^{62} +(1.01562 + 3.12577i) q^{63} +(7.99847 + 0.156251i) q^{64} -0.626490i q^{65} +(-2.50471 - 10.0224i) q^{66} -7.43389i q^{67} +(9.45313 - 12.8346i) q^{68} +(2.73319 + 8.41190i) q^{69} +(-2.03633 + 1.46938i) q^{70} +(1.04793 - 1.44235i) q^{71} +(-4.26531 + 3.03573i) q^{72} +(-3.83520 - 1.24613i) q^{73} +(-1.94009 + 5.90550i) q^{74} +(-1.29459 - 1.78185i) q^{75} +(-2.94369 - 9.26457i) q^{76} +(5.46863 + 2.18530i) q^{77} +(1.57496 + 1.15213i) q^{78} +(-2.58308 + 1.87672i) q^{79} +(-3.20518 - 2.39308i) q^{80} +(-3.43838 + 10.5822i) q^{81} +(11.2062 - 3.60083i) q^{82} +(-6.14025 - 4.46116i) q^{83} +(0.0509252 - 7.82145i) q^{84} +(-7.57998 + 2.46288i) q^{85} +(11.9189 + 0.0388013i) q^{86} +2.13845 q^{87} +(-0.710144 + 9.35391i) q^{88} -6.28641 q^{89} +(2.61764 + 0.00852160i) q^{90} +(-1.05797 + 0.343755i) q^{91} +(0.0522925 - 8.03146i) q^{92} +(-6.71820 - 4.88106i) q^{93} +(-10.5264 + 3.38239i) q^{94} +(-1.50197 + 4.62260i) q^{95} +(11.9105 - 3.65672i) q^{96} +(4.44805 - 3.23170i) q^{97} +(-4.39117 - 3.21226i) q^{98} +(-3.27294 - 5.19371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) \) 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

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