LMFDB - Embedded newform 280.2.ba.b.19.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.18
Character	$\chi$	$=$	280.19
Dual form			280.2.ba.b.59.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326985 + 1.37589i) q^{2} +(-1.39824 - 2.42182i) q^{3} +(-1.78616 - 0.899793i) q^{4} +(0.326208 + 2.21215i) q^{5} +(3.78937 - 1.13193i) q^{6} +(-2.32367 - 1.26513i) q^{7} +(1.82207 - 2.16335i) q^{8} +(-2.41015 + 4.17451i) q^{9} +O(q^{10})$	\(q+(-0.326985 + 1.37589i) q^{2} +(-1.39824 - 2.42182i) q^{3} +(-1.78616 - 0.899793i) q^{4} +(0.326208 + 2.21215i) q^{5} +(3.78937 - 1.13193i) q^{6} +(-2.32367 - 1.26513i) q^{7} +(1.82207 - 2.16335i) q^{8} +(-2.41015 + 4.17451i) q^{9} +(-3.15034 - 0.274512i) q^{10} +(2.81429 + 4.87449i) q^{11} +(0.318344 + 5.58389i) q^{12} +3.09140i q^{13} +(2.50048 - 2.78345i) q^{14} +(4.90131 - 3.88313i) q^{15} +(2.38075 + 3.21435i) q^{16} +(1.34123 + 2.32308i) q^{17} +(-4.95559 - 4.68111i) q^{18} +(0.00896628 + 0.00517669i) q^{19} +(1.40781 - 4.24477i) q^{20} +(0.185144 + 7.39648i) q^{21} +(-7.62701 + 2.27827i) q^{22} +(-1.25202 + 2.16856i) q^{23} +(-7.78693 - 1.38784i) q^{24} +(-4.78718 + 1.44324i) q^{25} +(-4.25344 - 1.01084i) q^{26} +5.09045 q^{27} +(3.01211 + 4.35054i) q^{28} +7.20373i q^{29} +(3.74011 + 8.01340i) q^{30} +(-2.49620 - 4.32355i) q^{31} +(-5.20107 + 2.22461i) q^{32} +(7.87010 - 13.6314i) q^{33} +(-3.63486 + 1.08578i) q^{34} +(2.04064 - 5.55300i) q^{35} +(8.06111 - 5.28770i) q^{36} +(-0.224770 + 0.389313i) q^{37} +(-0.0100544 + 0.0106439i) q^{38} +(7.48684 - 4.32253i) q^{39} +(5.38001 + 3.32498i) q^{40} -10.6661i q^{41} +(-10.2373 - 2.16380i) q^{42} +9.44007i q^{43} +(-0.640742 - 11.2389i) q^{44} +(-10.0208 - 3.96985i) q^{45} +(-2.57431 - 2.43173i) q^{46} +(1.23879 + 0.715215i) q^{47} +(4.45573 - 10.2602i) q^{48} +(3.79892 + 5.87948i) q^{49} +(-0.420406 - 7.05856i) q^{50} +(3.75072 - 6.49644i) q^{51} +(2.78162 - 5.52175i) q^{52} +(-2.17123 - 3.76068i) q^{53} +(-1.66450 + 7.00391i) q^{54} +(-9.86504 + 7.81571i) q^{55} +(-6.97079 + 2.72177i) q^{56} -0.0289530i q^{57} +(-9.91155 - 2.35551i) q^{58} +(0.320832 - 0.185233i) q^{59} +(-12.2485 + 2.52573i) q^{60} +(2.24283 - 3.88469i) q^{61} +(6.76496 - 2.02077i) q^{62} +(10.8817 - 6.65104i) q^{63} +(-1.36015 - 7.88353i) q^{64} +(-6.83864 + 1.00844i) q^{65} +(16.1820 + 15.2857i) q^{66} +(4.32212 - 2.49538i) q^{67} +(-0.305364 - 5.35622i) q^{68} +7.00248 q^{69} +(6.97307 + 4.62345i) q^{70} +9.31593i q^{71} +(4.63945 + 12.8202i) q^{72} +(4.50169 + 7.79716i) q^{73} +(-0.462156 - 0.436559i) q^{74} +(10.1889 + 9.57570i) q^{75} +(-0.0113573 - 0.0173142i) q^{76} +(-0.372646 - 14.8872i) q^{77} +(3.49925 + 11.7145i) q^{78} +(-4.69042 - 2.70802i) q^{79} +(-6.33399 + 6.31510i) q^{80} +(0.112790 + 0.195358i) q^{81} +(14.6755 + 3.48767i) q^{82} -11.3308 q^{83} +(6.32460 - 13.3779i) q^{84} +(-4.70146 + 3.72480i) q^{85} +(-12.9885 - 3.08676i) q^{86} +(17.4462 - 10.0725i) q^{87} +(15.6730 + 2.79336i) q^{88} +(0.909465 + 0.525080i) q^{89} +(8.73875 - 12.4895i) q^{90} +(3.91101 - 7.18342i) q^{91} +(4.18755 - 2.74684i) q^{92} +(-6.98059 + 12.0907i) q^{93} +(-1.38912 + 1.47058i) q^{94} +(-0.00852671 + 0.0215234i) q^{95} +(12.6599 + 9.48554i) q^{96} -6.06940 q^{97} +(-9.33172 + 3.30440i) q^{98} -27.1315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) $ 80 * q + 6 * q^4 - 52 * q^9	$ 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) $ 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.326985	+	1.37589i	−0.231213	+	0.972903i
$2$	−0.326985	+	1.37589i	−0.231213	+	0.972903i
$3$	−1.39824	−	2.42182i	−0.807274	−	1.39824i	−0.914745	−	0.404032i	$-0.867608\pi$
$3$	−1.39824	−	2.42182i	−0.807274	−	1.39824i	0.107470	−	0.994208i	$-0.465725\pi$
$4$	−1.78616	−	0.899793i	−0.893081	−	0.449896i
$5$	0.326208	+	2.21215i	0.145885	+	0.989302i
$5$	0.326208	+	2.21215i	0.145885	+	0.989302i
$6$	3.78937	−	1.13193i	1.54700	−	0.462108i
$7$	−2.32367	−	1.26513i	−0.878266	−	0.478172i
$7$	−2.32367	−	1.26513i	−0.878266	−	0.478172i
$8$	1.82207	−	2.16335i	0.644198	−	0.764859i
$9$	−2.41015	+	4.17451i	−0.803384	+	1.39150i
$10$	−3.15034	−	0.274512i	−0.996225	−	0.0868082i
$11$	2.81429	+	4.87449i	0.848540	+	1.46971i	0.882511	+	0.470292i	$0.155851\pi$
$11$	2.81429	+	4.87449i	0.848540	+	1.46971i	−0.0339711	+	0.999423i	$0.510815\pi$
$12$	0.318344	+	5.58389i	0.0918980	+	1.61193i
$13$			3.09140i			0.857401i	0.903447	+	0.428701i	$0.141029\pi$
$13$			3.09140i			0.857401i	−0.903447	+	0.428701i	$0.858971\pi$
$14$	2.50048	−	2.78345i	0.668282	−	0.743908i
$15$	4.90131	−	3.88313i	1.26551	−	1.00262i
$16$	2.38075	+	3.21435i	0.595186	+	0.803588i
$17$	1.34123	+	2.32308i	0.325296	+	0.563429i	0.981572	−	0.191092i	$-0.0612028\pi$
$17$	1.34123	+	2.32308i	0.325296	+	0.563429i	−0.656276	+	0.754521i	$0.727869\pi$
$18$	−4.95559	−	4.68111i	−1.16804	−	1.10335i
$19$	0.00896628	+	0.00517669i	0.00205701	+	0.00118761i	0.501028	−	0.865431i	$-0.332955\pi$
$19$	0.00896628	+	0.00517669i	0.00205701	+	0.00118761i	−0.498971	+	0.866619i	$0.666289\pi$
$20$	1.40781	−	4.24477i	0.314797	−	0.949159i
$21$	0.185144	+	7.39648i	0.0404018	+	1.61404i
$22$	−7.62701	+	2.27827i	−1.62608	+	0.485730i
$23$	−1.25202	+	2.16856i	−0.261063	+	0.452175i	−0.966525	−	0.256573i	$-0.917407\pi$
$23$	−1.25202	+	2.16856i	−0.261063	+	0.452175i	0.705461	+	0.708748i	$0.250740\pi$
$24$	−7.78693	−	1.38784i	−1.58950	−	0.283292i
$25$	−4.78718	+	1.44324i	−0.957435	+	0.288648i
$26$	−4.25344	−	1.01084i	−0.834168	−	0.198243i
$27$	5.09045			0.979657
$28$	3.01211	+	4.35054i	0.569234	+	0.822175i
$29$			7.20373i			1.33770i	0.743398	+	0.668849i	$0.233213\pi$
$29$			7.20373i			1.33770i	−0.743398	+	0.668849i	$0.766787\pi$
$30$	3.74011	+	8.01340i	0.682848	+	1.46304i
$31$	−2.49620	−	4.32355i	−0.448331	−	0.776533i	0.549946	−	0.835200i	$-0.314648\pi$
$31$	−2.49620	−	4.32355i	−0.448331	−	0.776533i	−0.998278	+	0.0586673i	$0.981315\pi$
$32$	−5.20107	+	2.22461i	−0.919428	+	0.393259i
$33$	7.87010	−	13.6314i	1.37001	−	2.37293i
$34$	−3.63486	+	1.08578i	−0.623374	+	0.186209i
$35$	2.04064	−	5.55300i	0.344931	−	0.938628i
$36$	8.06111	−	5.28770i	1.34352	−	0.881284i
$37$	−0.224770	+	0.389313i	−0.0369519	+	0.0640026i	−0.883910	−	0.467657i	$-0.845098\pi$
$37$	−0.224770	+	0.389313i	−0.0369519	+	0.0640026i	0.846958	+	0.531660i	$0.178432\pi$
$38$	−0.0100544	+	0.0106439i	−0.00163104	+	0.00172668i
$39$	7.48684	−	4.32253i	1.19885	−	0.692158i
$40$	5.38001	+	3.32498i	0.850655	+	0.525725i
$41$		−	10.6661i		−	1.66577i	−0.553445	−	0.832886i	$-0.686687\pi$
$41$		−	10.6661i		−	1.66577i	0.553445	−	0.832886i	$-0.313313\pi$
$42$	−10.2373	−	2.16380i	−1.57965	−	0.333881i
$43$			9.44007i			1.43960i	0.694183	+	0.719798i	$0.255766\pi$
$43$			9.44007i			1.43960i	−0.694183	+	0.719798i	$0.744234\pi$
$44$	−0.640742	−	11.2389i	−0.0965956	−	1.69433i
$45$	−10.0208	−	3.96985i	−1.49382	−	0.591790i
$46$	−2.57431	−	2.43173i	−0.379561	−	0.358538i
$47$	1.23879	+	0.715215i	0.180696	+	0.104325i	0.587620	−	0.809137i	$-0.300065\pi$
$47$	1.23879	+	0.715215i	0.180696	+	0.104325i	−0.406924	+	0.913462i	$0.633398\pi$
$48$	4.45573	−	10.2602i	0.643130	−	1.48093i
$49$	3.79892	+	5.87948i	0.542702	+	0.839925i
$50$	−0.420406	−	7.05856i	−0.0594544	−	0.998231i
$51$	3.75072	−	6.49644i	0.525206	−	0.909683i
$52$	2.78162	−	5.52175i	0.385742	−	0.765729i
$53$	−2.17123	−	3.76068i	−0.298241	−	0.516569i	0.677493	−	0.735530i	$-0.263067\pi$
$53$	−2.17123	−	3.76068i	−0.298241	−	0.516569i	−0.975734	+	0.218961i	$0.929733\pi$
$54$	−1.66450	+	7.00391i	−0.226510	+	0.953111i
$55$	−9.86504	+	7.81571i	−1.33020	+	1.05387i
$56$	−6.97079	+	2.72177i	−0.931511	+	0.363712i
$57$		−	0.0289530i		−	0.00383492i
$58$	−9.91155	−	2.35551i	−1.30145	−	0.309294i
$59$	0.320832	−	0.185233i	0.0417688	−	0.0241152i	−0.478970	−	0.877831i	$-0.658990\pi$
$59$	0.320832	−	0.185233i	0.0417688	−	0.0241152i	0.520739	+	0.853716i	$0.325656\pi$
$60$	−12.2485	+	2.52573i	−1.58128	+	0.326071i
$61$	2.24283	−	3.88469i	0.287165	−	0.497384i	−0.685967	−	0.727633i	$-0.740621\pi$
$61$	2.24283	−	3.88469i	0.287165	−	0.497384i	0.973132	+	0.230249i	$0.0739540\pi$
$62$	6.76496	−	2.02077i	0.859151	−	0.256638i
$63$	10.8817	−	6.65104i	1.37096	−	0.837953i
$64$	−1.36015	−	7.88353i	−0.170018	−	0.985441i
$65$	−6.83864	+	1.00844i	−0.848229	+	0.125082i
$66$	16.1820	+	15.2857i	1.99186	+	1.88154i
$67$	4.32212	−	2.49538i	0.528031	−	0.304859i	−0.212183	−	0.977230i	$-0.568057\pi$
$67$	4.32212	−	2.49538i	0.528031	−	0.304859i	0.740214	+	0.672371i	$0.234724\pi$
$68$	−0.305364	−	5.35622i	−0.0370308	−	0.649537i
$69$	7.00248			0.843000
$70$	6.97307	+	4.62345i	0.833441	+	0.552608i
$71$			9.31593i			1.10560i	0.833315	+	0.552799i	$0.186440\pi$
$71$			9.31593i			1.10560i	−0.833315	+	0.552799i	$0.813560\pi$
$72$	4.63945	+	12.8202i	0.546765	+	1.51088i
$73$	4.50169	+	7.79716i	0.526883	+	0.912589i	0.999509	+	0.0313255i	$0.00997284\pi$
$73$	4.50169	+	7.79716i	0.526883	+	0.912589i	−0.472626	+	0.881263i	$0.656694\pi$
$74$	−0.462156	−	0.436559i	−0.0537246	−	0.0507489i
$75$	10.1889	+	9.57570i	1.17651	+	1.10571i
$76$	−0.0113573	−	0.0173142i	−0.00130277	−	0.00198607i
$77$	−0.372646	−	14.8872i	−0.0424670	−	1.69655i
$78$	3.49925	+	11.7145i	0.396212	+	1.32640i
$79$	−4.69042	−	2.70802i	−0.527714	−	0.304676i	0.212371	−	0.977189i	$-0.431881\pi$
$79$	−4.69042	−	2.70802i	−0.527714	−	0.304676i	−0.740085	+	0.672513i	$0.765215\pi$
$80$	−6.33399	+	6.31510i	−0.708162	+	0.706050i
$81$	0.112790	+	0.195358i	0.0125322	+	0.0217065i
$82$	14.6755	+	3.48767i	1.62063	+	0.385149i
$83$	−11.3308			−1.24372			−0.621860	−	0.783129i	$-0.713623\pi$
$83$	−11.3308			−1.24372			−0.621860	+	0.783129i	$0.713623\pi$
$84$	6.32460	−	13.3779i	0.690070	−	1.45965i
$85$	−4.70146	+	3.72480i	−0.509945	+	0.404011i
$86$	−12.9885	−	3.08676i	−1.40059	−	0.332854i
$87$	17.4462	−	10.0725i	1.87042	−	1.07989i
$88$	15.6730	+	2.79336i	1.67075	+	0.297773i
$89$	0.909465	+	0.525080i	0.0964031	+	0.0556584i	0.547426	−	0.836854i	$-0.315608\pi$
$89$	0.909465	+	0.525080i	0.0964031	+	0.0556584i	−0.451023	+	0.892512i	$0.648941\pi$
$90$	8.73875	−	12.4895i	0.921145	−	1.31651i
$91$	3.91101	−	7.18342i	0.409986	−	0.753027i
$92$	4.18755	−	2.74684i	0.436583	−	0.286377i
$93$	−6.98059	+	12.0907i	−0.723853	+	1.25375i
$94$	−1.38912	+	1.47058i	−0.143277	+	0.151678i
$95$	−0.00852671	+	0.0215234i	−0.000874822	+	0.00220825i
$96$	12.6599	+	9.48554i	1.29210	+	0.968114i
$97$	−6.06940			−0.616254			−0.308127	−	0.951345i	$-0.599702\pi$
$97$	−6.06940			−0.616254			−0.308127	+	0.951345i	$0.599702\pi$
$98$	−9.33172	+	3.30440i	−0.942646	+	0.333795i
$99$	−27.1315			−2.72681
$100$	9.84929	+	1.72961i	0.984929	+	0.172961i
$101$	1.53154	+	2.65270i	0.152393	+	0.263953i	0.932107	−	0.362183i	$-0.117969\pi$
$101$	1.53154	+	2.65270i	0.152393	+	0.263953i	−0.779713	+	0.626137i	$0.784635\pi$
$102$	7.71197	+	7.28483i	0.763599	+	0.721305i
$103$	−0.926219	−	0.534753i	−0.0912631	−	0.0526908i	0.453674	−	0.891168i	$-0.350113\pi$
$103$	−0.926219	−	0.534753i	−0.0912631	−	0.0526908i	−0.544937	+	0.838477i	$0.683446\pi$
$104$	6.68778	+	5.63275i	0.655791	+	0.552336i
$105$	−16.3017	+	2.82235i	−1.59088	+	0.275434i
$106$	5.88425	−	1.75769i	0.571529	−	0.170722i
$107$	0.826678	+	0.477283i	0.0799180	+	0.0461407i	0.539426	−	0.842033i	$-0.318641\pi$
$107$	0.826678	+	0.477283i	0.0799180	+	0.0461407i	−0.459508	+	0.888173i	$0.651974\pi$
$108$	−9.09236	−	4.58035i	−0.874913	−	0.440744i
$109$	−0.742830	+	0.428873i	−0.0711502	+	0.0410786i	−0.535153	−	0.844755i	$-0.679746\pi$
$109$	−0.742830	+	0.428873i	−0.0711502	+	0.0410786i	0.464003	+	0.885834i	$0.346413\pi$
$110$	−7.52786	−	16.1289i	−0.717754	−	1.53783i
$111$	1.25713			0.119321
$112$	−1.46552	−	10.4810i	−0.138479	−	0.990365i
$113$		−	2.14152i		−	0.201457i	−0.994914	−	0.100729i	$-0.967883\pi$
$113$		−	2.14152i		−	0.201457i	0.994914	−	0.100729i	$-0.0321174\pi$
$114$	0.0398362	+	0.00946720i	0.00373100	+	0.000886685i
$115$	−5.20558	−	2.06224i	−0.485423	−	0.192305i
$116$	6.48186	−	12.8670i	0.601826	−	1.19467i
$117$	−12.9051	−	7.45076i	−1.19308	−	0.688823i
$118$	0.149953	+	0.501999i	0.0138043	+	0.0462128i
$119$	−0.177595	−	7.09489i	−0.0162801	−	0.650388i
$120$	0.529952	−	17.6786i	0.0483778	−	1.61382i
$121$	−10.3404	+	17.9102i	−0.940040	+	1.62820i
$122$	4.61155	+	4.35613i	0.417510	+	0.394385i
$123$	−25.8315	+	14.9138i	−2.32915	+	1.34473i
$124$	0.568322	+	9.96863i	0.0510369	+	0.895209i
$125$	−4.75427	−	10.1191i	−0.425235	−	0.905083i
$126$	5.59298	+	17.1468i	0.498262	+	1.52756i
$127$	−14.7459			−1.30849			−0.654244	−	0.756284i	$-0.727013\pi$
$127$	−14.7459			−1.30849			−0.654244	+	0.756284i	$0.727013\pi$
$128$	11.2916	+	0.706379i	0.998049	+	0.0624356i
$129$	22.8622	−	13.1995i	2.01290	−	1.16215i
$130$	0.848627	−	9.73898i	0.0744295	−	0.854165i
$131$	1.85181	+	1.06915i	0.161794	+	0.0934117i	0.578711	−	0.815533i	$-0.303556\pi$
$131$	1.85181	+	1.06915i	0.161794	+	0.0934117i	−0.416917	+	0.908945i	$0.636889\pi$
$132$	−26.3227	+	17.2665i	−2.29110	+	1.50285i
$133$	−0.0142856	−	0.0233724i	−0.00123871	−	0.00202664i
$134$	2.02010	+	6.76273i	0.174510	+	0.584211i
$135$	1.66054	+	11.2608i	0.142917	+	0.969176i
$136$	7.46943	+	1.33126i	0.640498	+	0.114154i
$137$	11.0212	−	6.36309i	0.941605	−	0.543636i	0.0511418	−	0.998691i	$-0.483714\pi$
$137$	11.0212	−	6.36309i	0.941605	−	0.543636i	0.890463	+	0.455056i	$0.150381\pi$
$138$	−2.28971	+	9.63466i	−0.194913	+	0.820157i
$139$			6.35401i			0.538940i	0.963009	+	0.269470i	$0.0868485\pi$
$139$			6.35401i			0.538940i	−0.963009	+	0.269470i	$0.913152\pi$
$140$	−8.64146	+	8.08240i	−0.730337	+	0.683087i
$141$		−	4.00017i		−	0.336875i
$142$	−12.8177	−	3.04617i	−1.07564	−	0.255629i
$143$	−15.0690	+	8.70011i	−1.26014	+	0.727539i
$144$	−19.1563	+	2.19136i	−1.59636	+	0.182614i
$145$	−15.9357	+	2.34991i	−1.32339	+	0.195150i
$146$	−12.2000	+	3.64429i	−1.00968	+	0.301604i
$147$	8.92725	−	17.4212i	0.736307	−	1.43688i
$148$	0.751776	−	0.493129i	0.0617956	−	0.0405350i
$149$	−6.88939	−	3.97759i	−0.564400	−	0.325857i	0.190509	−	0.981685i	$-0.438986\pi$
$149$	−6.88939	−	3.97759i	−0.564400	−	0.325857i	−0.754910	+	0.655829i	$0.772319\pi$
$150$	−16.5068	+	10.8877i	−1.34777	+	0.888978i
$151$	17.2792	−	9.97613i	1.40616	−	0.811846i	0.411143	−	0.911571i	$-0.365130\pi$
$151$	17.2792	−	9.97613i	1.40616	−	0.811846i	0.995015	+	0.0997254i	$0.0317964\pi$
$152$	0.0275361	−	0.00996492i	0.00223348	−	0.000808262i
$153$	−12.9303			−1.04535
$154$	20.6050	+	4.35516i	1.66040	+	0.350948i
$155$	8.75004	−	6.93234i	0.702820	−	0.556819i
$156$	−17.2621	+	0.984130i	−1.38207	+	0.0787935i
$157$	1.89627	−	1.09481i	0.151339	−	0.0873757i	−0.422418	−	0.906401i	$-0.638819\pi$
$157$	1.89627	−	1.09481i	0.151339	−	0.0873757i	0.573757	+	0.819025i	$0.305485\pi$
$158$	5.25964	−	5.56804i	0.418434	−	0.442969i
$159$	−6.07180	+	10.5167i	−0.481525	+	0.834025i
$160$	−6.61778	−	10.7798i	−0.523182	−	0.852221i
$161$	5.65277	−	3.45506i	0.445501	−	0.272297i
$162$	−0.305673	+	0.0913079i	−0.0240159	+	0.00717382i
$163$	12.7286	+	7.34887i	0.996982	+	0.575608i	0.907354	−	0.420368i	$-0.138099\pi$
$163$	12.7286	+	7.34887i	0.996982	+	0.575608i	0.0896280	+	0.995975i	$0.471432\pi$
$164$	−9.59731	+	19.0514i	−0.749424	+	1.48767i
$165$	32.7220	+	12.9631i	2.54740	+	1.00918i
$166$	3.70501	−	15.5900i	0.287565	−	1.21002i
$167$		−	10.2205i		−	0.790884i	−0.918491	−	0.395442i	$-0.870591\pi$
$167$		−	10.2205i		−	0.790884i	0.918491	−	0.395442i	$-0.129409\pi$
$168$	16.3385	+	13.0763i	1.26054	+	1.00886i
$169$	3.44322			0.264863
$170$	−3.58761	−	7.68666i	−0.275157	−	0.589540i
$171$	−0.0432202	+	0.0249532i	−0.00330513	+	0.00190822i
$172$	8.49410	−	16.8615i	0.647669	−	1.28568i
$173$	20.2375	+	11.6841i	1.53863	+	0.888326i	0.998920	+	0.0464719i	$0.0147978\pi$
$173$	20.2375	+	11.6841i	1.53863	+	0.888326i	0.539706	+	0.841854i	$0.318536\pi$
$174$	8.15410	+	27.2976i	0.618161	+	2.06943i
$175$	12.9497	+	2.70276i	0.978906	+	0.204310i
$176$	−8.96822	+	20.6510i	−0.676005	+	1.55663i
$177$	−0.897201	−	0.517999i	−0.0674378	−	0.0389352i
$178$	−1.01984	+	1.07963i	−0.0764399	+	0.0809219i
$179$	−10.2591	−	17.7693i	−0.766801	−	1.32814i	−0.939289	−	0.343127i	$-0.888514\pi$
$179$	−10.2591	−	17.7693i	−0.766801	−	1.32814i	0.172488	−	0.985012i	$-0.444819\pi$
$180$	14.3268	+	16.1075i	1.06785	+	1.20058i
$181$	10.1199			0.752204			0.376102	−	0.926578i	$-0.377264\pi$
$181$	10.1199			0.752204			0.376102	+	0.926578i	$0.377264\pi$
$182$	8.60477	+	7.73001i	0.637828	+	0.572986i
$183$	−12.5440			−0.927283
$184$	2.41008	+	6.65980i	0.177674	+	0.490967i
$185$	−0.934538	−	0.370227i	−0.0687086	−	0.0272196i
$186$	−14.3530	−	13.5580i	−1.05241	−	0.994123i
$187$	−7.54921	+	13.0756i	−0.552053	+	0.956184i
$188$	−1.56913	−	2.39214i	−0.114441	−	0.174465i
$189$	−11.8285	−	6.44005i	−0.860399	−	0.468445i
$190$	−0.0268258	−	0.0187697i	−0.00194615	−	0.00136169i
$191$	10.2933	+	5.94286i	0.744800	+	0.430010i	0.823812	−	0.566863i	$-0.191843\pi$
$191$	10.2933	+	5.94286i	0.744800	+	0.430010i	−0.0790121	+	0.996874i	$0.525177\pi$
$192$	−17.1907	+	14.3171i	−1.24063	+	1.03325i
$193$	−1.46075	+	0.843365i	−0.105147	+	0.0607067i	−0.551651	−	0.834075i	$-0.686002\pi$
$193$	−1.46075	+	0.843365i	−0.105147	+	0.0607067i	0.446504	+	0.894782i	$0.352669\pi$
$194$	1.98460	−	8.35084i	0.142486	−	0.599555i
$195$	12.0043	+	15.1519i	0.859647	+	1.08505i
$196$	−1.49517	−	13.9199i	−0.106798	−	0.994281i
$197$	12.2308			0.871407			0.435703	−	0.900090i	$-0.356500\pi$
$197$	12.2308			0.871407			0.435703	+	0.900090i	$0.356500\pi$
$198$	8.87158	−	37.3300i	0.630476	−	2.65293i
$199$	−5.79902	−	10.0442i	−0.411082	−	0.712014i	0.583927	−	0.811806i	$-0.301516\pi$
$199$	−5.79902	−	10.0442i	−0.411082	−	0.712014i	−0.995008	+	0.0997922i	$0.968182\pi$
$200$	−5.60033	+	12.9860i	−0.396003	+	0.918249i
$201$	−12.0867	−	6.97828i	−0.852533	−	0.492210i
$202$	−4.15062	+	1.23984i	−0.292036	+	0.0872345i
$203$	9.11362	−	16.7391i	0.639650	−	1.17486i
$204$	−12.5448	+	8.22882i	−0.878314	+	0.576132i
$205$	23.5951	−	3.47938i	1.64795	−	0.243010i
$206$	1.03862	−	1.09952i	0.0723642	−	0.0766073i
$207$	−6.03510	−	10.4531i	−0.419468	−	0.726541i
$208$	−9.93686	+	7.35985i	−0.688997	+	0.510314i
$209$			0.0582748i			0.00403095i
$210$	1.44715	−	23.3522i	0.0998629	−	1.61146i
$211$	−5.59881			−0.385438			−0.192719	−	0.981254i	$-0.561731\pi$
$211$	−5.59881			−0.385438			−0.192719	+	0.981254i	$0.561731\pi$
$212$	0.494334	+	8.67083i	0.0339510	+	0.595515i
$213$	22.5615	−	13.0259i	1.54589	−	0.892521i
$214$	−0.927002	+	0.981356i	−0.0633685	+	0.0670841i
$215$	−20.8828	+	3.07942i	−1.42420	+	0.210015i
$216$	9.27513	−	11.0124i	0.631093	−	0.749299i
$217$	0.330528	+	13.2045i	0.0224377	+	0.896382i
$218$	−0.347189	−	1.16229i	−0.0235146	−	0.0787202i
$219$	12.5889	−	21.8046i	0.850679	−	1.47342i
$220$	24.6531	−	5.08363i	1.66211	−	0.342739i
$221$	−7.18157	+	4.14628i	−0.483085	+	0.278909i
$222$	−0.411062	+	1.72967i	−0.0275887	+	0.116088i
$223$		−	0.966855i		−	0.0647454i	−0.999476	−	0.0323727i	$-0.989694\pi$
$223$		−	0.966855i		−	0.0647454i	0.999476	−	0.0323727i	$-0.0103064\pi$
$224$	14.9000	+	1.41075i	0.995548	+	0.0942594i
$225$	5.51302	−	23.4625i	0.367534	−	1.56417i
$226$	2.94650	+	0.700245i	0.195998	+	0.0465796i
$227$	8.25091	+	14.2910i	0.547632	+	0.948526i	0.998436	+	0.0559034i	$0.0178039\pi$
$227$	8.25091	+	14.2910i	0.547632	+	0.948526i	−0.450804	+	0.892623i	$0.648863\pi$
$228$	−0.0260517	+	0.0517147i	−0.00172532	+	0.00342489i
$229$	−9.83500	+	17.0347i	−0.649915	+	1.12569i	0.333228	+	0.942846i	$0.391862\pi$
$229$	−9.83500	+	17.0347i	−0.649915	+	1.12569i	−0.983143	+	0.182839i	$0.941471\pi$
$230$	4.53957	−	6.48800i	0.299331	−	0.427806i
$231$	−35.5330	+	21.7183i	−2.33790	+	1.42896i
$232$	15.5842	+	13.1257i	1.02315	+	0.861742i
$233$	21.2525	+	12.2702i	1.39230	+	0.803845i	0.993570	−	0.113223i	$-0.0361174\pi$
$233$	21.2525	+	12.2702i	1.39230	+	0.803845i	0.398731	+	0.917068i	$0.369451\pi$
$234$	14.4712	−	15.3197i	0.946013	−	1.00148i
$235$	−1.17806	+	2.97369i	−0.0768480	+	0.193982i
$236$	−0.739729	+	0.0421728i	−0.0481523	+	0.00274521i
$237$			15.1458i			0.983827i
$238$	9.81988	+	2.07557i	0.636528	+	0.134539i
$239$		−	4.28437i		−	0.277133i	−0.990353	−	0.138567i	$-0.955751\pi$
$239$		−	4.28437i		−	0.277133i	0.990353	−	0.138567i	$-0.0442495\pi$
$240$	24.1505	+	6.50978i	1.55891	+	0.420205i
$241$	−6.54522	+	3.77888i	−0.421615	+	0.243419i	−0.695768	−	0.718267i	$-0.744936\pi$
$241$	−6.54522	+	3.77888i	−0.421615	+	0.243419i	0.274153	+	0.961686i	$0.411602\pi$
$242$	−21.2613	−	20.0837i	−1.36673	−	1.29103i
$243$	7.95108	−	13.7717i	0.510062	−	0.883454i
$244$	−7.50147	+	4.92061i	−0.480232	+	0.315010i
$245$	−11.7670	+	10.3217i	−0.751767	+	0.659428i
$246$	−12.0733	−	40.4180i	−0.769766	−	2.57696i
$247$	−0.0160032	+	0.0277184i	−0.00101826	+	0.00176368i
$248$	−13.9016	−	2.47764i	−0.882752	−	0.157330i
$249$	15.8432	+	27.4413i	1.00402	+	1.73902i
$250$	15.4774	−	3.23256i	0.978878	−	0.204445i
$251$			24.1608i			1.52502i	0.646978	+	0.762508i	$0.276032\pi$
$251$			24.1608i			1.52502i	−0.646978	+	0.762508i	$0.723968\pi$
$252$	−25.4210	+	2.08858i	−1.60137	+	0.131568i
$253$	−14.0941			−0.886091
$254$	4.82169	−	20.2888i	0.302540	−	1.27303i
$255$	15.5946	+	6.17795i	0.976570	+	0.386878i
$256$	−4.66410	+	15.3051i	−0.291506	+	0.956569i
$257$	5.36561	−	9.29351i	0.334697	−	0.579713i	−0.648729	−	0.761019i	$-0.724699\pi$
$257$	5.36561	−	9.29351i	0.334697	−	0.579713i	0.983427	+	0.181306i	$0.0580325\pi$
$258$	10.6855	+	35.7719i	0.665249	+	2.22706i
$259$	1.01482	−	0.620274i	0.0630579	−	0.0385419i
$260$	13.1223	+	4.35212i	0.813810	+	0.269907i
$261$	−30.0720	−	17.3621i	−1.86141	−	1.07469i
$262$	−2.07655	+	2.19830i	−0.128289	+	0.135812i
$263$	10.8614	+	18.8124i	0.669740	+	1.16002i	0.977977	+	0.208714i	$0.0669277\pi$
$263$	10.8614	+	18.8124i	0.669740	+	1.16002i	−0.308237	+	0.951310i	$0.599739\pi$
$264$	−15.1497	−	41.8631i	−0.932397	−	2.57650i
$265$	7.61089	−	6.02983i	0.467534	−	0.370410i
$266$	0.0368291	−	0.0120130i	0.00225814	−	0.000736562i
$267$		−	2.93675i		−	0.179726i
$268$	−9.96533	+	0.568135i	−0.608730	+	0.0347044i
$269$	−11.0937	−	19.2149i	−0.676396	−	1.17155i	−0.976059	−	0.217507i	$-0.930207\pi$
$269$	−11.0937	−	19.2149i	−0.676396	−	1.17155i	0.299663	−	0.954045i	$-0.403126\pi$
$270$	−16.0366	−	1.39739i	−0.975959	−	0.0850422i
$271$	1.07939	−	1.86956i	0.0655683	−	0.113568i	−0.831378	−	0.555708i	$-0.812447\pi$
$271$	1.07939	−	1.86956i	0.0655683	−	0.113568i	0.896946	+	0.442140i	$0.145781\pi$
$272$	−4.27406	+	9.84183i	−0.259153	+	0.596749i
$273$	−22.8655	+	0.572356i	−1.38388	+	0.0346405i
$274$	5.15117	+	17.2446i	0.311193	+	1.04179i
$275$	−20.5076	−	19.2734i	−1.23665	−	1.16223i
$276$	−12.5076	−	6.30078i	−0.752867	−	0.379262i
$277$	−4.02100	−	6.96457i	−0.241598	−	0.418460i	0.719571	−	0.694418i	$-0.244338\pi$
$277$	−4.02100	−	6.96457i	−0.241598	−	0.418460i	−0.961170	+	0.275958i	$0.911005\pi$
$278$	−8.74243	−	2.07767i	−0.524336	−	0.124610i
$279$	24.0649			1.44073
$280$	−8.29488	−	14.5325i	−0.495714	−	0.868486i
$281$	12.1508			0.724858			0.362429	−	0.932011i	$-0.381948\pi$
$281$	12.1508			0.724858			0.362429	+	0.932011i	$0.381948\pi$
$282$	5.50381	+	1.30800i	0.327747	+	0.0778900i
$283$	−7.59282	−	13.1511i	−0.451346	−	0.781755i	0.547124	−	0.837052i	$-0.315723\pi$
$283$	−7.59282	−	13.1511i	−0.451346	−	0.781755i	−0.998470	+	0.0552972i	$0.982389\pi$
$284$	8.38241	−	16.6398i	0.497404	−	0.987388i
$285$	0.0640483	−	0.00944470i	0.00379389	−	0.000559456i
$286$	−7.04307	−	23.5782i	−0.416465	−	1.39421i
$287$	−13.4940	+	24.7846i	−0.796526	+	1.46299i
$288$	3.24874	−	27.0735i	0.191434	−	1.59532i
$289$	4.90221	−	8.49088i	0.288365	−	0.499464i
$290$	1.97751	−	22.6942i	0.116123	−	1.33265i
$291$	8.48648	+	14.6990i	0.497486	+	0.861671i
$292$	−1.02492	−	17.9776i	−0.0599790	−	1.05206i
$293$		−	20.5769i		−	1.20212i	−0.799205	−	0.601058i	$-0.794746\pi$
$293$		−	20.5769i		−	1.20212i	0.799205	−	0.601058i	$-0.205254\pi$
$294$	21.0507	+	17.9794i	1.22770	+	1.04858i
$295$	0.514420	+	0.649303i	0.0299507	+	0.0378039i
$296$	0.432673	+	1.19561i	0.0251486	+	0.0694934i
$297$	14.3260	+	24.8133i	0.831278	+	1.43982i
$298$	7.72546	−	8.17844i	0.447524	−	0.473764i
$299$	−6.70389	−	3.87049i	−0.387696	−	0.223836i
$300$	−9.58286	−	26.2716i	−0.553267	−	1.51679i
$301$	11.9429	−	21.9356i	0.688375	−	1.26435i
$302$	8.07605	+	27.0363i	0.464725	+	1.55576i
$303$	4.28291	−	7.41821i	0.246047	−	0.426165i
$304$	0.00470676	+	0.0411451i	0.000269951	+	0.00235984i
$305$	9.32513	+	3.69425i	0.533956	+	0.211532i
$306$	4.22800	−	17.7906i	0.241699	−	1.01702i
$307$	5.13799			0.293241			0.146620	−	0.989193i	$-0.453160\pi$
$307$	5.13799			0.293241			0.146620	+	0.989193i	$0.453160\pi$
$308$	−12.7297	+	26.9262i	−0.725345	+	1.53426i
$309$			2.99085i			0.170144i
$310$	6.67703	+	14.3059i	0.379230	+	0.812520i
$311$	−10.7172	−	18.5628i	−0.607718	−	1.05260i	−0.991616	−	0.129222i	$-0.958752\pi$
$311$	−10.7172	−	18.5628i	−0.607718	−	1.05260i	0.383898	−	0.923376i	$-0.374581\pi$
$312$	4.29038	−	24.0726i	0.242895	−	1.36284i
$313$	0.582955	−	1.00971i	0.0329506	−	0.0570720i	−0.849080	−	0.528265i	$-0.822843\pi$
$313$	0.582955	−	1.00971i	0.0329506	−	0.0570720i	0.882030	+	0.471192i	$0.156176\pi$
$314$	0.886294	+	2.96706i	0.0500165	+	0.167441i
$315$	18.2628	+	21.9022i	1.02899	+	1.23405i
$316$	5.94120	+	9.05736i	0.334218	+	0.509516i
$317$	7.41747	−	12.8474i	0.416607	−	0.721584i	−0.578989	−	0.815335i	$-0.696553\pi$
$317$	7.41747	−	12.8474i	0.416607	−	0.721584i	0.995596	+	0.0937515i	$0.0298859\pi$
$318$	−12.4844	−	11.7929i	−0.700091	−	0.661315i
$319$	−35.1145	+	20.2734i	−1.96603	+	1.13509i
$320$	16.9958	−	5.58051i	0.950095	−	0.311960i
$321$		−	2.66942i		−	0.148993i
$322$	2.90542	+	8.90736i	0.161913	+	0.496388i
$323$			0.0277725i			0.00154530i
$324$	−0.0256795	−	0.450429i	−0.00142664	−	0.0250238i
$325$	−4.46163	−	14.7991i	−0.247487	−	0.820906i
$326$	−14.2733	+	15.1102i	−0.790526	+	0.836879i
$327$	2.07731	+	1.19934i	0.114875	+	0.0663234i
$328$	−23.0746	−	19.4344i	−1.27408	−	1.07309i
$329$	−1.97370	−	3.22915i	−0.108814	−	0.178029i
$330$	−28.5355	+	40.7832i	−1.57083	+	2.24504i
$331$	−7.74145	+	13.4086i	−0.425509	+	0.737003i	−0.996468	−	0.0839759i	$-0.973238\pi$
$331$	−7.74145	+	13.4086i	−0.425509	+	0.737003i	0.570959	+	0.820978i	$0.306571\pi$
$332$	20.2387	+	10.1954i	1.11074	+	0.559545i
$333$	−1.08346	−	1.87661i	−0.0593732	−	0.102837i
$334$	14.0623	+	3.34194i	0.769454	+	0.182863i
$335$	6.93005	+	8.74715i	0.378629	+	0.477908i
$336$	−23.3341	+	18.2042i	−1.27298	+	0.993123i
$337$		−	28.7826i		−	1.56789i	−0.620832	−	0.783944i	$-0.713205\pi$
$337$		−	28.7826i		−	1.56789i	0.620832	−	0.783944i	$-0.286795\pi$
$338$	−1.12588	+	4.73750i	−0.0612398	+	0.257686i
$339$	−5.18638	+	2.99436i	−0.281686	+	0.162631i
$340$	11.7491	−	2.42275i	0.637185	−	0.131392i
$341$	14.0501	−	24.3354i	0.760854	−	1.31784i
$342$	−0.0202006	−	0.0676257i	−0.00109232	−	0.00365678i
$343$	−1.38917	−	18.4681i	−0.0750080	−	0.997183i
$344$	20.4221	+	17.2004i	1.10109	+	0.927385i
$345$	2.28426	+	15.4905i	0.122981	+	0.833981i
$346$	−22.6934	+	24.0240i	−1.22001	+	1.29154i
$347$	4.40442	−	2.54289i	0.236442	−	0.136510i	−0.377099	−	0.926173i	$-0.623078\pi$
$347$	4.40442	−	2.54289i	0.236442	−	0.136510i	0.613540	+	0.789664i	$0.289745\pi$
$348$	−40.2248	+	2.29326i	−2.15628	+	0.122932i
$349$	13.7007			0.733381			0.366690	−	0.930343i	$-0.380491\pi$
$349$	13.7007			0.733381			0.366690	+	0.930343i	$0.380491\pi$
$350$	−7.95308	+	16.9337i	−0.425110	+	0.905142i
$351$			15.7366i			0.839959i
$352$	−25.4811	−	19.0919i	−1.35815	−	1.01760i
$353$	−0.825203	−	1.42929i	−0.0439211	−	0.0760736i	0.843229	−	0.537554i	$-0.180652\pi$
$353$	−0.825203	−	1.42929i	−0.0439211	−	0.0760736i	−0.887150	+	0.461481i	$0.847318\pi$
$354$	1.00608	−	1.06507i	0.0534727	−	0.0566081i
$355$	−20.6082	+	3.03893i	−1.09377	+	0.161290i
$356$	−1.15199	−	1.75621i	−0.0610553	−	0.0930788i
$357$	−16.9343	+	10.3505i	−0.896256	+	0.547805i
$358$	27.8032	−	8.30513i	1.46944	−	0.438940i
$359$	29.4837	+	17.0224i	1.55609	+	0.898408i	0.997625	+	0.0688791i	$0.0219423\pi$
$359$	29.4837	+	17.0224i	1.55609	+	0.898408i	0.558464	+	0.829529i	$0.311391\pi$
$360$	−26.8468	+	14.4452i	−1.41495	+	0.761329i
$361$	−9.49995	−	16.4544i	−0.499997	−	0.866021i
$362$	−3.30905	+	13.9239i	−0.173920	+	0.731822i
$363$	57.8337			3.03548
$364$	−13.4493	+	9.31164i	−0.704934	+	0.488062i
$365$	−15.7800	+	12.5019i	−0.825961	+	0.654379i
$366$	4.10172	−	17.2593i	0.214400	−	0.902156i
$367$	9.86880	−	5.69776i	0.515147	−	0.297421i	−0.219800	−	0.975545i	$-0.570540\pi$
$367$	9.86880	−	5.69776i	0.515147	−	0.297421i	0.734947	+	0.678125i	$0.237207\pi$
$368$	−9.95123	+	1.13836i	−0.518744	+	0.0593412i
$369$	44.5259	+	25.7070i	2.31792	+	1.33825i
$370$	0.814972	−	1.16477i	0.0423684	−	0.0605533i
$371$	0.287497	+	11.4855i	0.0149261	+	0.596295i
$372$	23.3476	−	15.3149i	1.21052	−	0.794041i
$373$	−14.8647	+	25.7464i	−0.769664	+	1.33310i	0.168080	+	0.985773i	$0.446243\pi$
$373$	−14.8647	+	25.7464i	−0.769664	+	1.33310i	−0.937745	+	0.347325i	$0.887090\pi$
$374$	−15.5222	−	14.6624i	−0.802632	−	0.758176i
$375$	−17.8592	+	25.6630i	−0.922243	+	1.32523i
$376$	3.80442	−	1.37676i	0.196198	−	0.0710011i
$377$	−22.2696			−1.14694
$378$	12.7286	−	14.1690i	0.654687	−	0.728774i
$379$	−35.7110			−1.83435			−0.917176	−	0.398482i	$-0.869537\pi$
$379$	−35.7110			−1.83435			−0.917176	+	0.398482i	$0.869537\pi$
$380$	0.0345967	−	0.0307720i	0.00177477	−	0.00157857i
$381$	20.6183	+	35.7120i	1.05631	+	1.82958i
$382$	−11.5425	+	12.2193i	−0.590566	+	0.625194i
$383$	27.0665	+	15.6269i	1.38303	+	0.798495i	0.992518	−	0.122101i	$-0.0389631\pi$
$383$	27.0665	+	15.6269i	1.38303	+	0.798495i	0.390517	+	0.920596i	$0.372296\pi$
$384$	−14.0777	−	28.3340i	−0.718399	−	1.44592i
$385$	32.8110	−	5.68065i	1.67220	−	0.289513i
$386$	−0.682736	−	2.28560i	−0.0347503	−	0.116334i
$387$	−39.4076	−	22.7520i	−2.00320	−	1.15655i
$388$	10.8409	+	5.46120i	0.550365	+	0.277250i
$389$	12.5630	−	7.25326i	0.636970	−	0.367755i	−0.146476	−	0.989214i	$-0.546793\pi$
$389$	12.5630	−	7.25326i	0.636970	−	0.367755i	0.783446	+	0.621459i	$0.213460\pi$
$390$	−24.7727	+	11.5622i	−1.25441	+	0.585475i
$391$	−6.71696			−0.339691
$392$	19.6412	+	2.49442i	0.992032	+	0.125987i
$393$		−	5.97969i		−	0.301635i
$394$	−3.99928	+	16.8282i	−0.201481	+	0.847794i
$395$	4.46047	−	11.2593i	0.224431	−	0.566515i
$396$	48.4612	+	24.4127i	2.43527	+	1.22678i
$397$	29.3306	+	16.9340i	1.47206	+	0.849895i	0.999507	−	0.0314062i	$-0.00999855\pi$
$397$	29.3306	+	16.9340i	1.47206	+	0.849895i	0.472555	+	0.881301i	$0.343332\pi$
$398$	15.7159	−	4.69453i	0.787768	−	0.235315i
$399$	−0.0366292	+	0.0672773i	−0.00183375	+	0.00336808i
$400$	−16.0361	−	11.9517i	−0.801806	−	0.597584i
$401$	2.50564	−	4.33990i	0.125126	−	0.216724i	−0.796656	−	0.604433i	$-0.793400\pi$
$401$	2.50564	−	4.33990i	0.125126	−	0.216724i	0.921782	+	0.387708i	$0.126733\pi$
$402$	13.5535	−	14.3483i	0.675989	−	0.715626i
$403$	13.3658	−	7.71678i	0.665800	−	0.384400i
$404$	−0.348692	−	6.11621i	−0.0173481	−	0.304293i
$405$	−0.395368	+	0.313236i	−0.0196460	+	0.0155648i
$406$	20.0512	+	18.0128i	0.995124	+	0.893960i
$407$	−2.53027			−0.125421
$408$	−7.21999	−	19.9511i	−0.357443	−	0.987724i
$409$	−24.6325	+	14.2216i	−1.21800	+	0.703211i	−0.964489	−	0.264123i	$-0.914918\pi$
$409$	−24.6325	+	14.2216i	−1.21800	+	0.703211i	−0.253507	+	0.967333i	$0.581584\pi$
$410$	−2.92798	+	33.6020i	−0.144603	+	1.65948i
$411$	−30.8206	−	17.7943i	−1.52027	−	0.877727i
$412$	1.17321	+	1.78856i	0.0577999	+	0.0881160i
$413$	−0.979852	+	0.0245271i	−0.0482154	+	0.00120690i
$414$	16.3557	−	4.88564i	0.803840	−	0.240116i
$415$	−3.69620	−	25.0654i	−0.181440	−	1.23041i
$416$	−6.87716	−	16.0786i	−0.337180	−	0.788319i
$417$	15.3883	−	8.88443i	0.753567	−	0.435072i
$418$	−0.0801798	−	0.0190550i	−0.00392172	−	0.000932009i
$419$		−	11.6710i		−	0.570167i	−0.958503	−	0.285083i	$-0.907979\pi$
$419$		−	11.6710i		−	0.570167i	0.958503	−	0.285083i	$-0.0920213\pi$
$420$	31.6570	+	9.62696i	1.54470	+	0.469747i
$421$		−	11.0632i		−	0.539185i	−0.962974	−	0.269593i	$-0.913111\pi$
$421$		−	11.0632i		−	0.539185i	0.962974	−	0.269593i	$-0.0868890\pi$
$422$	1.83073	−	7.70337i	0.0891185	−	0.374994i
$423$	−5.97134	+	3.44755i	−0.290337	+	0.167626i
$424$	−12.0918	−	2.15508i	−0.587228	−	0.104660i
$425$	−9.77345	−	9.18526i	−0.474082	−	0.445551i
$426$	10.5450	+	35.3015i	0.510905	+	1.71036i
$427$	−10.1262	+	6.18930i	−0.490042	+	0.299521i
$428$	−1.04713	−	1.59634i	−0.0506147	−	0.0771622i
$429$	42.1402	+	24.3297i	2.03455	+	1.17465i
$430$	2.59141	−	29.7394i	0.124969	−	1.43416i
$431$	23.4715	−	13.5513i	1.13058	−	0.652741i	0.186500	−	0.982455i	$-0.440286\pi$
$431$	23.4715	−	13.5513i	1.13058	−	0.652741i	0.944081	+	0.329714i	$0.106952\pi$
$432$	12.1191	+	16.3625i	0.583078	+	0.787240i
$433$	−9.64178			−0.463354			−0.231677	−	0.972793i	$-0.574421\pi$
$433$	−9.64178			−0.463354			−0.231677	+	0.972793i	$0.574421\pi$
$434$	−18.2761	−	3.86291i	−0.877281	−	0.185426i
$435$	27.9730	+	35.3077i	1.34120	+	1.69287i
$436$	1.71271	−	0.0976435i	0.0820240	−	0.00467628i
$437$	−0.0224519	+	0.0129626i	−0.00107402	+	0.000620085i
$438$	25.8844	+	24.4508i	1.23681	+	1.16830i
$439$	12.9469	−	22.4247i	0.617922	−	1.07027i	−0.371942	−	0.928256i	$-0.621308\pi$
$439$	12.9469	−	22.4247i	0.617922	−	1.07027i	0.989864	−	0.142016i	$-0.0453586\pi$
$440$	−1.06665	+	35.5823i	−0.0508507	+	1.69632i
$441$	−33.6999	+	1.68817i	−1.60476	+	0.0803890i
$442$	−3.35657	−	11.2368i	−0.159656	−	0.534482i
$443$	−11.1960	−	6.46402i	−0.531938	−	0.307115i	0.209867	−	0.977730i	$-0.432697\pi$
$443$	−11.1960	−	6.46402i	−0.531938	−	0.307115i	−0.741805	+	0.670615i	$0.766030\pi$
$444$	−2.24544	−	1.13116i	−0.106564	−	0.0536823i
$445$	−0.864879	+	2.18315i	−0.0409992	+	0.103491i
$446$	1.33029	+	0.316147i	0.0629910	+	0.0149700i
$447$			22.2465i			1.05222i
$448$	−6.81311	+	20.0395i	−0.321889	+	0.946777i
$449$	4.43065			0.209095			0.104548	−	0.994520i	$-0.466661\pi$
$449$	4.43065			0.209095			0.104548	+	0.994520i	$0.466661\pi$
$450$	30.4792	+	15.2572i	1.43681	+	0.719232i
$451$	51.9920	−	30.0176i	2.44821	−	1.41347i
$452$	−1.92692	+	3.82510i	−0.0906349	+	0.179918i
$453$	−48.3208	−	27.8980i	−2.27031	−	1.31076i
$454$	−22.3608	+	6.67942i	−1.04944	+	0.313481i
$455$	17.1666	+	6.30845i	0.804781	+	0.295745i
$456$	−0.0626354	−	0.0527543i	−0.00293317	−	0.00247045i
$457$	−3.41299	−	1.97049i	−0.159653	−	0.0921756i	0.418045	−	0.908426i	$-0.362715\pi$
$457$	−3.41299	−	1.97049i	−0.159653	−	0.0921756i	−0.577698	+	0.816251i	$0.696049\pi$
$458$	−20.2220	−	19.1020i	−0.944914	−	0.892578i
$459$	6.82745	+	11.8255i	0.318678	+	0.551967i
$460$	7.44242	+	8.36744i	0.347004	+	0.390134i
$461$	−36.5212			−1.70096			−0.850481	−	0.526006i	$-0.823689\pi$
$461$	−36.5212			−1.70096			−0.850481	+	0.526006i	$0.823689\pi$
$462$	−18.2633	−	55.9912i	−0.849685	−	2.60494i
$463$	−12.7228			−0.591279			−0.295639	−	0.955300i	$-0.595533\pi$
$463$	−12.7228			−0.591279			−0.295639	+	0.955300i	$0.595533\pi$
$464$	−23.1553	+	17.1502i	−1.07496	+	0.796180i
$465$	−29.0236	−	11.4980i	−1.34594	−	0.533206i
$466$	−23.8317	+	25.2291i	−1.10398	+	1.16871i
$467$	−11.0255	+	19.0967i	−0.510198	+	0.883689i	0.489732	+	0.871873i	$0.337095\pi$
$467$	−11.0255	+	19.0967i	−0.510198	+	0.883689i	−0.999930	+	0.0118159i	$0.996239\pi$
$468$	16.3464	+	24.9202i	0.755614	+	1.15193i
$469$	−13.2002	+	0.330419i	−0.609527	+	0.0152573i
$470$	−3.70627	−	2.59323i	−0.170958	−	0.119617i
$471$	−5.30290	−	3.06163i	−0.244345	−	0.141072i
$472$	0.183855	−	1.03158i	0.00846262	−	0.0474822i
$473$	−46.0155	+	26.5671i	−2.11580	+	1.22156i
$474$	−20.8390	−	4.95246i	−0.957169	−	0.227474i
$475$	−0.0503944	−	0.0118412i	−0.00231225	−	0.000543313i
$476$	−6.06672	+	12.8324i	−0.278068	+	0.588173i
$477$	20.9320			0.958409
$478$	5.89484	+	1.40093i	0.269624	+	0.0640769i
$479$	19.2131	+	33.2781i	0.877870	+	1.52052i	0.853674	+	0.520808i	$0.174369\pi$
$479$	19.2131	+	33.2781i	0.877870	+	1.52052i	0.0241958	+	0.999707i	$0.492297\pi$
$480$	−16.8536	+	31.0999i	−0.769259	+	1.41951i
$481$	−1.20352	−	0.694855i	−0.0548760	−	0.0316826i
$482$	−3.05915	−	10.2412i	−0.139340	−	0.466472i
$483$	−16.2715	−	8.85901i	−0.740378	−	0.403099i
$484$	34.5851	−	22.6862i	1.57205	−	1.03119i
$485$	−1.97989	−	13.4264i	−0.0899019	−	0.609661i
$486$	16.3485	+	15.4430i	0.741582	+	0.700507i
$487$	3.89253	+	6.74205i	0.176387	+	0.305512i	0.940640	−	0.339405i	$-0.110226\pi$
$487$	3.89253	+	6.74205i	0.176387	+	0.305512i	−0.764253	+	0.644916i	$0.776892\pi$
$488$	−4.31736	−	11.9302i	−0.195438	−	0.540054i
$489$		−	41.1019i		−	1.85869i
$490$	−10.3539	−	19.5652i	−0.467741	−	0.883865i
$491$	4.73617			0.213740			0.106870	−	0.994273i	$-0.465917\pi$
$491$	4.73617			0.213740			0.106870	+	0.994273i	$0.465917\pi$
$492$	59.5586	−	3.39550i	2.68511	−	0.153081i
$493$	−16.7348	+	9.66184i	−0.753698	+	0.435148i
$494$	−0.0329047	−	0.0310822i	−0.00148045	−	0.00139846i
$495$	−8.85049	−	60.0187i	−0.397800	−	2.69764i
$496$	7.95458	−	18.3170i	0.357171	−	0.822455i
$497$	11.7858	−	21.6472i	0.528666	−	0.971009i
$498$	−42.9367	+	12.8257i	−1.92404	+	0.574733i
$499$	−9.26180	+	16.0419i	−0.414615	+	0.718134i	−0.995388	−	0.0959313i	$-0.969417\pi$
$499$	−9.26180	+	16.0419i	−0.414615	+	0.718134i	0.580773	+	0.814066i	$0.302750\pi$
$500$	−0.613235	+	22.3523i	−0.0274247	+	0.999624i
$501$	−24.7522	+	14.2907i	−1.10585	+	0.638461i
$502$	−33.2427	−	7.90022i	−1.48369	−	0.352604i
$503$			8.37050i			0.373222i	0.982434	+	0.186611i	$0.0597504\pi$
$503$			8.37050i			0.373222i	−0.982434	+	0.186611i	$0.940250\pi$
$504$	5.43862	−	35.6595i	0.242255	−	1.58840i
$505$	−5.36855	+	4.25331i	−0.238897	+	0.189270i
$506$	4.60857	−	19.3920i	0.204876	−	0.862081i
$507$	−4.81444	−	8.33886i	−0.213817	−	0.370342i
$508$	26.3386	+	13.2683i	1.16859	+	0.588684i
$509$	−17.2908	+	29.9486i	−0.766402	+	1.32745i	0.173101	+	0.984904i	$0.444621\pi$
$509$	−17.2908	+	29.9486i	−0.766402	+	1.32745i	−0.939502	+	0.342543i	$0.888712\pi$
$510$	−13.5994	+	19.4364i	−0.602191	+	0.860657i
$511$	−0.596079	−	23.8133i	−0.0263690	−	1.05344i
$512$	−19.5331	−	11.4218i	−0.863249	−	0.504779i
$513$	0.0456424	+	0.0263516i	0.00201516	+	0.00116345i
$514$	11.0324	+	10.4213i	0.486618	+	0.459666i
$515$	0.880811	−	2.22337i	0.0388132	−	0.0979735i
$516$	−52.7123	+	3.00519i	−2.32053	+	0.132296i
$517$			8.05129i			0.354095i
$518$	0.521599	+	1.59911i	0.0229177	+	0.0702607i
$519$		−	65.3487i		−	2.86849i
$520$	−10.2788	+	16.6318i	−0.450757	+	0.729353i
$521$	−19.8789	+	11.4771i	−0.870912	+	0.502821i	−0.867651	−	0.497174i	$-0.834371\pi$
$521$	−19.8789	+	11.4771i	−0.870912	+	0.502821i	−0.00326053	+	0.999995i	$0.501038\pi$
$522$	33.7214	−	35.6987i	1.47595	−	1.56249i
$523$	10.7152	−	18.5593i	0.468543	−	0.811541i	−0.530810	−	0.847491i	$-0.678112\pi$
$523$	10.7152	−	18.5593i	0.468543	−	0.811541i	0.999354	+	0.0359497i	$0.0114456\pi$
$524$	−2.34563	−	3.57592i	−0.102469	−	0.156215i
$525$	−11.5612	−	35.1410i	−0.504572	−	1.53368i
$526$	−29.4354	+	8.79268i	−1.28344	+	0.383379i
$527$	6.69596	−	11.5977i	0.291681	−	0.505206i
$528$	62.5529	−	7.15568i	2.72226	−	0.311411i
$529$	8.36491	+	14.4884i	0.363692	+	0.629933i
$530$	5.80776	+	12.4434i	0.252273	+	0.540508i
$531$			1.78576i			0.0774952i
$532$	0.00448600	+	0.0546009i	0.000194493	+	0.00236725i
$533$	32.9734			1.42823
$534$	4.04066	+	0.960274i	0.174856	+	0.0415551i
$535$	−0.786150	+	1.98443i	−0.0339882	+	0.0857942i
$536$	2.47682	−	13.8970i	0.106982	−	0.600259i
$537$	−28.6894	+	49.6914i	−1.23804	+	2.14434i
$538$	30.0651	−	8.98079i	1.29620	−	0.387189i
$539$	−17.9682	+	35.0643i	−0.773945	+	1.51033i
$540$	7.16639	−	21.6078i	0.308393	−	0.929850i
$541$	8.22241	+	4.74721i	0.353509	+	0.204099i	0.666230	−	0.745747i	$-0.267907\pi$
$541$	8.22241	+	4.74721i	0.353509	+	0.204099i	−0.312721	+	0.949845i	$0.601240\pi$
$542$	2.21937	+	2.09644i	0.0953300	+	0.0900499i
$543$	−14.1500	−	24.5085i	−0.607235	−	1.05176i
$544$	−12.1438	−	9.09877i	−0.520659	−	0.390107i
$545$	−1.19105	−	1.50335i	−0.0510188	−	0.0643963i
$546$	6.68918	−	31.6476i	0.286270	−	1.35439i
$547$			39.4155i			1.68528i	0.538474	+	0.842642i	$0.319001\pi$
$547$			39.4155i			1.68528i	−0.538474	+	0.842642i	$0.680999\pi$
$548$	−25.4111	+	1.44872i	−1.08551	+	0.0618861i
$549$	10.8111	+	18.7254i	0.461407	+	0.799180i
$550$	33.2237	−	21.9141i	1.41667	−	0.934420i
$551$	−0.0372914	+	0.0645906i	−0.00158867	+	0.00275165i
$552$	12.7590	−	15.1488i	0.543058	−	0.644776i
$553$	7.47303	+	12.2265i	0.317785	+	0.519924i
$554$	10.8973	−	3.25515i	0.462982	−	0.138298i
$555$	0.410085	+	2.78095i	0.0174072	+	0.118045i
$556$	5.71729	−	11.3493i	0.242467	−	0.481317i
$557$	6.09239	+	10.5523i	0.258143	+	0.447116i	0.965744	−	0.259495i	$-0.0835562\pi$
$557$	6.09239	+	10.5523i	0.258143	+	0.447116i	−0.707602	+	0.706612i	$0.750223\pi$
$558$	−7.86887	+	33.1107i	−0.333116	+	1.40169i
$559$	−29.1831			−1.23431
$560$	22.7075	−	6.66094i	0.959568	−	0.281476i
$561$	42.2224			1.78263
$562$	−3.97314	+	16.7182i	−0.167597	+	0.705217i
$563$	13.1210	+	22.7262i	0.552983	+	0.957795i	0.998057	+	0.0623013i	$0.0198440\pi$
$563$	13.1210	+	22.7262i	0.552983	+	0.957795i	−0.445074	+	0.895494i	$0.646823\pi$
$564$	−3.59933	+	7.14495i	−0.151559	+	0.300857i
$565$	4.73735	−	0.698580i	0.199302	−	0.0293895i
$566$	20.5773	−	6.14667i	0.864929	−	0.258364i
$567$	−0.0149348	−	0.596642i	−0.000627203	−	0.0250566i
$568$	20.1536	+	16.9742i	0.845626	+	0.712223i
$569$	2.65884	−	4.60525i	0.111465	−	0.193062i	−0.804896	−	0.593415i	$-0.797779\pi$
$569$	2.65884	−	4.60525i	0.111465	−	0.193062i	0.916361	+	0.400353i	$0.131113\pi$
$570$	−0.00794794	+	0.0912118i	−0.000332902	+	0.00382044i
$571$	−22.7432	−	39.3924i	−0.951774	−	1.64852i	−0.741583	−	0.670861i	$-0.765925\pi$
$571$	−22.7432	−	39.3924i	−0.951774	−	1.64852i	−0.210191	−	0.977660i	$-0.567409\pi$
$572$	34.7440	−	1.98079i	1.45272	−	0.0828212i
$573$		−	33.2382i		−	1.38855i
$574$	−29.6886	−	26.6705i	−1.23918	−	1.11321i
$575$	2.86388	−	12.1882i	0.119432	−	0.508284i
$576$	36.1880	+	13.3226i	1.50783	+	0.555106i
$577$	−11.2954	−	19.5642i	−0.470234	−	0.814469i	0.529187	−	0.848505i	$-0.322497\pi$
$577$	−11.2954	−	19.5642i	−0.470234	−	0.814469i	−0.999421	+	0.0340364i	$0.989164\pi$
$578$	10.0796	+	9.52131i	0.419256	+	0.396034i
$579$	4.08496	+	2.35845i	0.169765	+	0.0980140i
$580$	30.5782	+	10.1415i	1.26969	+	0.421103i
$581$	26.3291	+	14.3349i	1.09232	+	0.594712i
$582$	−22.9992	+	6.87013i	−0.953348	+	0.284776i
$583$	12.2209	−	21.1673i	0.506139	−	0.876658i
$584$	25.0704	+	4.46822i	1.03742	+	0.184896i
$585$	12.2724	−	30.9784i	0.507402	−	1.28080i
$586$	28.3116	+	6.72835i	1.16954	+	0.277945i
$587$	−1.24935			−0.0515660			−0.0257830	−	0.999668i	$-0.508208\pi$
$587$	−1.24935			−0.0515660			−0.0257830	+	0.999668i	$0.508208\pi$
$588$	−31.6210	+	23.0844i	−1.30403	+	0.951986i
$589$		−	0.0516882i		−	0.00212978i
$590$	−1.06158	+	0.495474i	−0.0437045	+	0.0203983i
$591$	−17.1016	−	29.6208i	−0.703464	−	1.21844i
$592$	−1.78651	+	0.204366i	−0.0734250	+	0.00839938i
$593$	0.393538	−	0.681629i	0.0161607	−	0.0279911i	−0.857832	−	0.513930i	$-0.828189\pi$
$593$	0.393538	−	0.681629i	0.0161607	−	0.0279911i	0.873993	+	0.485939i	$0.161522\pi$
$594$	−38.8249	+	11.5974i	−1.59300	+	0.475848i
$595$	15.6370	−	2.70728i	0.641055	−	0.110987i
$596$	8.72655	+	13.3036i	0.357453	+	0.544938i
$597$	−16.2168	+	28.0884i	−0.663711	+	1.14958i
$598$	7.51745	−	7.95823i	0.307411	−	0.325436i
$599$	31.1544	−	17.9870i	1.27293	−	0.734929i	0.297395	−	0.954755i	$-0.403882\pi$
$599$	31.1544	−	17.9870i	1.27293	−	0.734929i	0.975539	+	0.219826i	$0.0705489\pi$
$600$	39.2804	−	4.59455i	1.60362	−	0.187572i
$601$			29.9875i			1.22322i	0.791161	+	0.611608i	$0.209477\pi$
$601$			29.9875i			1.22322i	−0.791161	+	0.611608i	$0.790523\pi$
$602$	26.2759	+	23.6047i	1.07093	+	0.962057i
$603$			24.0570i			0.979676i
$604$	−39.8398	+	2.27131i	−1.62106	+	0.0924184i
$605$	−42.9930	−	17.0321i	−1.74792	−	0.692454i
$606$	8.80622	+	8.31847i	0.357728	+	0.337915i
$607$	−12.3990	−	7.15859i	−0.503262	−	0.290558i	0.226798	−	0.973942i	$-0.427174\pi$
$607$	−12.3990	−	7.15859i	−0.503262	−	0.290558i	−0.730060	+	0.683384i	$0.760508\pi$
$608$	−0.0581503	−	0.00697785i	−0.00235831	−	0.000282989i
$609$	−53.2822	+	1.33373i	−2.15910	+	0.0540454i
$610$	−8.13206	+	11.6224i	−0.329258	+	0.470578i
$611$	−2.21102	+	3.82960i	−0.0894483	+	0.154929i
$612$	23.0955	+	11.6346i	0.933582	+	0.470299i
$613$	0.332888	+	0.576579i	0.0134452	+	0.0232878i	0.872670	−	0.488311i	$-0.162387\pi$
$613$	0.332888	+	0.576579i	0.0134452	+	0.0232878i	−0.859225	+	0.511599i	$0.829053\pi$
$614$	−1.68005	+	7.06933i	−0.0678012	+	0.285295i
$615$	−41.4180	−	52.2780i	−1.67013	−	2.10805i
$616$	−32.8851	−	26.3192i	−1.32498	−	1.06043i
$617$			10.1780i			0.409753i	0.978788	+	0.204876i	$0.0656792\pi$
$617$			10.1780i			0.409753i	−0.978788	+	0.204876i	$0.934321\pi$
$618$	−4.11509	−	0.977964i	−0.165533	−	0.0393395i
$619$	4.94937	−	2.85752i	0.198932	−	0.114853i	−0.397225	−	0.917721i	$-0.630027\pi$
$619$	4.94937	−	2.85752i	0.198932	−	0.114853i	0.596157	+	0.802868i	$0.296693\pi$
$620$	−21.8667	+	4.50906i	−0.878186	+	0.181088i
$621$	−6.37332	+	11.0389i	−0.255753	+	0.442976i
$622$	29.0447	−	8.67599i	1.16459	−	0.347876i
$623$	−1.44901	−	2.37070i	−0.0580533	−	0.0949802i
$624$	31.7184	+	13.7745i	1.26975	+	0.551420i
$625$	20.8341	−	13.8181i	0.833365	−	0.552723i
$626$	1.19863	+	1.13224i	0.0479069	+	0.0452535i
$627$	0.141131	−	0.0814821i	0.00563624	−	0.00325408i
$628$	−4.37216	+	0.249262i	−0.174468	+	0.00994662i
$629$	−1.20587			−0.0480812
$630$	−36.1068	+	17.9659i	−1.43853	+	0.715779i
$631$			49.0996i			1.95463i	0.211800	+	0.977313i	$0.432067\pi$
$631$			49.0996i			1.95463i	−0.211800	+	0.977313i	$0.567933\pi$
$632$	−14.4046	+	5.21283i	−0.572986	+	0.207355i
$633$	7.82849	+	13.5593i	0.311154	+	0.538935i
$634$	15.2513	+	14.4066i	0.605706	+	0.572158i
$635$	−4.81023	−	32.6201i	−0.190888	−	1.29449i
$636$	20.3080	−	13.3211i	0.805266	−	0.528216i
$637$	−18.1758	+	11.7440i	−0.720153	+	0.465314i
$638$	−16.4121	−	54.9429i	−0.649760	−	2.17521i
$639$	−38.8894	−	22.4528i	−1.53844	−	0.888219i
$640$	2.12081	+	25.2092i	0.0838323	+	0.996480i
$641$	2.06139	+	3.57044i	0.0814201	+	0.141024i	0.903860	−	0.427828i	$-0.140721\pi$
$641$	2.06139	+	3.57044i	0.0814201	+	0.141024i	−0.822440	+	0.568852i	$0.807388\pi$
$642$	3.67284	+	0.872862i	0.144956	+	0.0344491i
$643$	−23.6589			−0.933017			−0.466509	−	0.884517i	$-0.654488\pi$
$643$	−23.6589			−0.933017			−0.466509	+	0.884517i	$0.654488\pi$
$644$	−13.2056	+	1.08497i	−0.520374	+	0.0427538i
$645$	36.6570	+	46.2687i	1.44337	+	1.82183i
$646$	−0.0382119	−	0.00908118i	−0.00150343	−	0.000357294i
$647$	−17.0060	+	9.81839i	−0.668573	+	0.386001i	−0.795536	−	0.605907i	$-0.792811\pi$
$647$	−17.0060	+	9.81839i	−0.668573	+	0.386001i	0.126963	+	0.991908i	$0.459477\pi$
$648$	0.628139	+	0.111951i	0.0246756	+	0.00439787i
$649$	1.80583	+	1.04260i	0.0708850	+	0.0409255i
$650$	21.8209	−	1.29964i	0.855885	−	0.0509763i
$651$	31.5169	−	19.2636i	1.23524	−	0.755000i
$652$	−16.1229	−	24.5794i	−0.631422	−	0.962603i
$653$	6.03366	−	10.4506i	0.236115	−	0.408964i	−0.723481	−	0.690344i	$-0.757459\pi$
$653$	6.03366	−	10.4506i	0.236115	−	0.408964i	0.959596	+	0.281381i	$0.0907923\pi$
$654$	−2.32941	+	2.46599i	−0.0910870	+	0.0964278i
$655$	−1.76103	+	4.44525i	−0.0688091	+	0.173690i
$656$	34.2847	−	25.3934i	1.33859	−	0.991444i
$657$	−43.3991			−1.69316
$658$	5.08834	−	1.65972i	0.198364	−	0.0647027i
$659$	39.2192			1.52776			0.763881	−	0.645357i	$-0.223291\pi$
$659$	39.2192			1.52776			0.763881	+	0.645357i	$0.223291\pi$
$660$	−46.7826	−	52.5973i	−1.82101	−	2.04735i
$661$	21.5274	+	37.2866i	0.837319	+	1.45028i	0.892128	+	0.451783i	$0.149212\pi$
$661$	21.5274	+	37.2866i	0.837319	+	1.45028i	−0.0548084	+	0.998497i	$0.517455\pi$
$662$	−15.9174	−	15.0358i	−0.618649	−	0.584384i
$663$	20.0831	+	11.5950i	0.779964	+	0.450312i
$664$	−20.6455	+	24.5125i	−0.801201	+	0.951270i
$665$	0.0470431	−	0.0392260i	0.00182425	−	0.00152112i
$666$	2.93628	−	0.877101i	0.113779	−	0.0339870i
$667$	−15.6217	−	9.01918i	−0.604874	−	0.349224i
$668$	−9.19631	+	18.2554i	−0.355816	+	0.706324i
$669$	−2.34155	+	1.35190i	−0.0905297	+	0.0522673i
$670$	−14.3012	+	6.67482i	−0.552502	+	0.257871i
$671$	25.2479			0.974683
$672$	−17.4172	−	38.0577i	−0.671883	−	1.46811i
$673$		−	9.18260i		−	0.353963i	−0.984214	−	0.176982i	$-0.943367\pi$
$673$		−	9.18260i		−	0.353963i	0.984214	−	0.176982i	$-0.0566333\pi$
$674$	39.6017	+	9.41147i	1.52540	+	0.362516i
$675$	−24.3689	+	7.34673i	−0.937958	+	0.282776i
$676$	−6.15014	−	3.09818i	−0.236544	−	0.119161i
$677$	−28.6670	−	16.5509i	−1.10176	−	0.636102i	−0.165078	−	0.986280i	$-0.552788\pi$
$677$	−28.6670	−	16.5509i	−1.10176	−	0.636102i	−0.936683	+	0.350178i	$0.886121\pi$
$678$	−2.42405	−	8.11501i	−0.0930950	−	0.311655i
$679$	14.1033	+	7.67855i	0.541235	+	0.294676i
$680$	−0.508344	+	16.9577i	−0.0194941	+	0.650299i
$681$	23.0735	−	39.9645i	0.884178	−	1.53144i
$682$	28.8888	+	27.2887i	1.10621	+	1.04494i
$683$	−6.48677	+	3.74514i	−0.248209	+	0.143304i	−0.618944	−	0.785435i	$-0.712439\pi$
$683$	−6.48677	+	3.74514i	−0.248209	+	0.143304i	0.370735	+	0.928739i	$0.379106\pi$
$684$	0.0996510	−	0.00568121i	0.00381025	−	0.000217227i
$685$	17.6713	+	22.3048i	0.675185	+	0.852223i
$686$	25.8643	+	4.12744i	0.987505	+	0.157586i
$687$	55.0068			2.09864
$688$	−30.3437	+	22.4744i	−1.15684	+	0.856828i
$689$	11.6258	−	6.71214i	0.442907	−	0.255712i
$690$	−22.0602	−	1.92226i	−0.839817	−	0.0731793i
$691$	33.9093	+	19.5776i	1.28997	+	0.744766i	0.978649	−	0.205538i	$-0.0658945\pi$
$691$	33.9093	+	19.5776i	1.28997	+	0.744766i	0.311323	+	0.950304i	$0.399228\pi$
$692$	−25.6341	−	39.0792i	−0.974462	−	1.48557i
$693$	63.0446	+	34.3247i	2.39487	+	1.30389i
$694$	2.05857	+	6.89150i	0.0781422	+	0.261598i
$695$	−14.0560	+	2.07273i	−0.533174	+	0.0786230i
$696$	9.99764	−	56.0949i	0.378960	−	2.12627i
$697$	24.7783	−	14.3057i	0.938543	−	0.541868i
$698$	−4.47992	+	18.8507i	−0.169567	+	0.713508i
$699$		−	68.6265i		−	2.59569i
$700$	−20.6984	−	16.4796i	−0.782324	−	0.622871i
$701$		−	27.0282i		−	1.02084i	−0.859925	−	0.510420i	$-0.829490\pi$
$701$		−	27.0282i		−	1.02084i	0.859925	−	0.510420i	$-0.170510\pi$
$702$	−21.6519	−	5.14564i	−0.817199	−	0.194210i
$703$	−0.00403070	+	0.00232713i	−0.000152021	+	8.77692e-5i
$704$	34.6003	−	28.8165i	1.30405	−	1.08606i
$705$	8.84896	−	1.30489i	0.333271	−	0.0491449i
$706$	2.23638	−	0.668033i	0.0841674	−	0.0251418i
$707$	−0.202794	−	8.10158i	−0.00762686	−	0.304691i
$708$	1.13645	+	1.73253i	0.0427106	+	0.0651123i
$709$	−21.4335	−	12.3746i	−0.804952	−	0.464739i	0.0402480	−	0.999190i	$-0.487185\pi$
$709$	−21.4335	−	12.3746i	−0.804952	−	0.464739i	−0.845200	+	0.534451i	$0.820519\pi$
$710$	2.55733	−	29.3483i	0.0959749	−	1.10142i
$711$	22.6093	−	13.0535i	0.847913	−	0.489543i
$712$	2.79304	−	1.01076i	0.104673	−	0.0378798i
$713$	12.5012			0.468172
$714$	−8.70389	−	26.6842i	−0.325735	−	0.998630i
$715$	−24.1615	−	30.4968i	−0.903590	−	1.14052i
$716$	2.33574	+	40.9699i	0.0872906	+	1.53112i
$717$	−10.3760	+	5.99058i	−0.387499	+	0.223722i
$718$	−33.0617	+	35.0003i	−1.23385	+	1.30620i
$719$	−9.45728	+	16.3805i	−0.352697	+	0.610889i	−0.986721	−	0.162424i	$-0.948069\pi$
$719$	−9.45728	+	16.3805i	−0.352697	+	0.610889i	0.634024	+	0.773313i	$0.281402\pi$
$720$	−11.0965	−	41.6617i	−0.413544	−	1.55264i
$721$	1.47570	+	2.41437i	0.0549580	+	0.0899160i
$722$	25.7458	−	7.69057i	0.958160	−	0.286213i
$723$	18.3036	+	10.5676i	0.680717	+	0.393012i
$724$	−18.0757	−	9.10579i	−0.671779	−	0.338414i
$725$	−10.3967	−	34.4855i	−0.386124	−	1.28076i
$726$	−18.9108	+	79.5730i	−0.701844	+	2.95323i
$727$			36.7341i			1.36239i	0.732100	+	0.681197i	$0.238540\pi$
$727$			36.7341i			1.36239i	−0.732100	+	0.681197i	$0.761460\pi$
$728$	−8.41410	−	21.5495i	−0.311847	−	0.798679i
$729$	−43.7934			−1.62198
$730$	−12.0415	−	25.7995i	−0.445674	−	0.954881i
$731$	−21.9300	+	12.6613i	−0.811110	+	0.468295i
$732$	22.4057	+	11.2870i	0.828138	+	0.417181i
$733$	−29.6150	−	17.0982i	−1.09386	−	0.631538i	−0.159256	−	0.987237i	$-0.550909\pi$
$733$	−29.6150	−	17.0982i	−1.09386	−	0.631538i	−0.934600	+	0.355699i	$0.884243\pi$
$734$	4.61255	+	15.4415i	0.170252	+	0.569956i
$735$	41.4504	+	14.0654i	1.52892	+	0.518812i
$736$	1.68764	−	14.0641i	0.0622073	−	0.518408i
$737$	24.3274	+	14.0454i	0.896112	+	0.517370i
$738$	−49.9294	+	52.8570i	−1.83793	+	1.94569i
$739$	4.15465	+	7.19607i	0.152831	+	0.264712i	0.932267	−	0.361770i	$-0.117828\pi$
$739$	4.15465	+	7.19607i	0.152831	+	0.264712i	−0.779436	+	0.626482i	$0.784494\pi$
$740$	1.33611	+	1.50218i	0.0491163	+	0.0552211i
$741$	0.0895055			0.00328807
$742$	−15.8968	−	3.36001i	−0.583589	−	0.123350i
$743$	35.6106			1.30642			0.653212	−	0.757175i	$-0.273421\pi$
$743$	35.6106			1.30642			0.653212	+	0.757175i	$0.273421\pi$
$744$	13.4374	+	37.1315i	0.492638	+	1.36131i
$745$	6.55163	−	16.5378i	0.240033	−	0.605900i
$746$	−30.5637	−	28.8709i	−1.11902	−	1.05704i
$747$	27.3090	−	47.3006i	0.999185	−	1.73064i
$748$	25.2494	−	16.5624i	0.923211	−	0.605583i
$749$	−1.31711	−	2.15490i	−0.0481261	−	0.0787384i
$750$	−29.4698	−	32.9637i	−1.07609	−	1.20366i
$751$	2.56757	+	1.48238i	0.0936918	+	0.0540930i	0.546114	−	0.837711i	$-0.316107\pi$
$751$	2.56757	+	1.48238i	0.0936918	+	0.0540930i	−0.452422	+	0.891804i	$0.649440\pi$
$752$	0.650290	+	5.68465i	0.0237136	+	0.207298i
$753$	58.5132	−	33.7826i	2.13234	−	1.23111i
$754$	7.28184	−	30.6406i	0.265189	−	1.11587i
$755$	27.7052	+	34.9697i	1.00830	+	1.27268i
$756$	15.3330	+	22.1462i	0.557654	+	0.805449i
$757$	−50.4876			−1.83500			−0.917502	−	0.397732i	$-0.869797\pi$
$757$	−50.4876			−1.83500			−0.917502	+	0.397732i	$0.869797\pi$
$758$	11.6770	−	49.1345i	0.424127	−	1.78465i
$759$	19.7070	+	34.1335i	0.715319	+	1.23897i
$760$	0.0310264	+	0.0576633i	0.00112544	+	0.00209167i
$761$	34.8961	+	20.1473i	1.26498	+	0.730339i	0.974035	−	0.226399i	$-0.0726955\pi$
$761$	34.8961	+	20.1473i	1.26498	+	0.730339i	0.290950	+	0.956738i	$0.406029\pi$
$762$	−55.8777	+	16.6913i	−2.02424	+	0.604663i
$763$	2.26867	−	0.0567881i	0.0821314	−	0.00205587i
$764$	−13.0382	−	19.8768i	−0.471706	−	0.719117i
$765$	−4.21795	−	28.6036i	−0.152500	−	1.03417i
$766$	−30.3512	+	32.1309i	−1.09663	+	1.16094i
$767$	0.572629	+	0.991823i	0.0206764	+	0.0358126i
$768$	43.5878	−	10.1046i	1.57284	−	0.364618i
$769$		−	19.4159i		−	0.700154i	−0.936721	−	0.350077i	$-0.886155\pi$
$769$		−	19.4159i		−	0.700154i	0.936721	−	0.350077i	$-0.113845\pi$
$770$	−2.91273	+	47.0019i	−0.104968	+	1.69383i
$771$	−30.0096			−1.08077
$772$	3.36799	−	0.192013i	0.121217	−	0.00691069i
$773$	−3.26975	+	1.88779i	−0.117605	+	0.0678992i	−0.557649	−	0.830077i	$-0.688296\pi$
$773$	−3.26975	+	1.88779i	−0.117605	+	0.0678992i	0.440044	+	0.897976i	$0.354963\pi$
$774$	44.1900	−	46.7811i	1.58838	−	1.68151i
$775$	18.1897	+	17.0950i	0.653393	+	0.614070i
$776$	−11.0588	+	13.1302i	−0.396989	+	0.471347i
$777$	−2.92116	−	1.59043i	−0.104796	−	0.0570562i
$778$	5.87179	+	19.6571i	0.210514	+	0.704740i
$779$	0.0552152	−	0.0956356i	0.00197829	−	0.00342650i
$780$	−7.80806	−	37.8652i	−0.279574	−	1.35579i
$781$	−45.4104	+	26.2177i	−1.62491	+	0.938144i
$782$	2.19635	−	9.24182i	0.0785412	−	0.330487i
$783$			36.6702i			1.31049i
$784$	−9.85444	+	26.2086i	−0.351944	+	0.936021i
$785$	3.04047	+	3.83770i	0.108519	+	0.136973i
$786$	8.22741	+	1.95527i	0.293462	+	0.0697422i
$787$	14.3939	+	24.9309i	0.513086	+	0.888691i	0.999885	+	0.0151767i	$0.00483108\pi$
$787$	14.3939	+	24.9309i	0.513086	+	0.888691i	−0.486799	+	0.873514i	$0.661836\pi$
$788$	−21.8461	−	11.0052i	−0.778236	−	0.392043i
$789$	30.3736	−	52.6086i	1.08133	−	1.87291i
$790$	14.0330	+	9.81875i	0.499273	+	0.349335i
$791$	−2.70929	+	4.97619i	−0.0963313	+	0.176933i
$792$	−49.4353	+	58.6948i	−1.75661	+	2.08563i
$793$	12.0092	+	6.93349i	0.426458	+	0.246215i
$794$	−32.8901	+	34.8186i	−1.16723	+	1.23567i
$795$	−25.2451	−	10.0011i	−0.895350	−	0.354702i
$796$	1.32029	+	23.1585i	0.0467964	+	0.820830i
$797$			34.9190i			1.23690i	0.785826	+	0.618448i	$0.212238\pi$
$797$			34.9190i			1.23690i	−0.785826	+	0.618448i	$0.787762\pi$
$798$	−0.0805892	−	0.0723965i	−0.00285283	−	0.00256281i
$799$			3.83707i			0.135746i
$800$	21.6878	−	18.1560i	0.766780	−	0.641910i
$801$	−4.38390	+	2.53105i	−0.154897	+	0.0894301i
$802$	5.15193	+	4.86658i	0.181921	+	0.171845i
$803$	−25.3381	+	43.8869i	−0.894163	+	1.54874i
$804$	15.3099	+	23.3399i	0.539937	+	0.823134i
$805$	9.48707	+	11.3777i	0.334375	+	0.401011i
$806$	6.24702	+	20.9132i	0.220042	+	0.736638i
$807$	−31.0234	+	53.7341i	−1.09207	+	1.89153i
$808$	8.52926	+	1.52015i	0.300058	+	0.0534786i
$809$	−1.15788	−	2.00552i	−0.0407091	−	0.0705102i	0.844953	−	0.534841i	$-0.179628\pi$
$809$	−1.15788	−	2.00552i	−0.0407091	−	0.0705102i	−0.885662	+	0.464330i	$0.846295\pi$
$810$	−0.301699	−	0.646407i	−0.0106006	−	0.0227124i
$811$			22.2021i			0.779621i	0.920895	+	0.389811i	$0.127460\pi$
$811$			22.2021i			0.779621i	−0.920895	+	0.389811i	$0.872540\pi$
$812$	−31.3401	+	21.6984i	−1.09982	+	0.761464i
$813$	−6.03699			−0.211726
$814$	0.827360	−	3.48138i	0.0289990	−	0.122022i
$815$	−12.1046	+	30.5548i	−0.424005	+	1.07029i
$816$	29.8113	−	3.41024i	1.04361	−	0.119382i
$817$	−0.0488683	+	0.0846423i	−0.00170968	+	0.00296126i
$818$	−11.5129	−	38.5419i	−0.402539	−	1.34758i
$819$	20.5611	+	33.6397i	0.718462	+	1.17547i
$820$	−45.2753	−	15.0159i	−1.58108	−	0.524379i
$821$	15.9612	+	9.21522i	0.557051	+	0.321613i	0.751961	−	0.659208i	$-0.229108\pi$
$821$	15.9612	+	9.21522i	0.557051	+	0.321613i	−0.194910	+	0.980821i	$0.562442\pi$
$822$	34.5609	−	36.5873i	1.20545	−	1.27613i
$823$	−15.6153	−	27.0465i	−0.544316	−	0.942782i	−0.998650	−	0.0519509i	$-0.983456\pi$
$823$	−15.6153	−	27.0465i	−0.544316	−	0.942782i	0.454334	−	0.890831i	$-0.349877\pi$
$824$	−2.84449	+	1.02938i	−0.0990925	+	0.0358601i
$825$	−18.0022	+	76.6145i	−0.626756	+	2.66737i
$826$	0.286650	−	1.35619i	0.00997384	−	0.0471879i
$827$			20.9134i			0.727229i	0.931550	+	0.363614i	$0.118457\pi$
$827$			20.9134i			0.727229i	−0.931550	+	0.363614i	$0.881543\pi$
$828$	1.37404	+	24.1013i	0.0477512	+	0.837577i
$829$	−14.1218	−	24.4596i	−0.490469	−	0.849517i	0.509471	−	0.860488i	$-0.329841\pi$
$829$	−14.1218	−	24.4596i	−0.490469	−	0.849517i	−0.999940	+	0.0109709i	$0.996508\pi$
$830$	35.6960	+	3.11044i	1.23902	+	0.107965i
$831$	−11.2446	+	19.4763i	−0.390072	+	0.675625i
$832$	24.3712	−	4.20477i	0.844918	−	0.145774i
$833$	−8.56325	+	16.7109i	−0.296699	+	0.578998i
$834$	7.19228	+	24.0777i	0.249048	+	0.833743i
$835$	22.6092	−	3.33400i	0.782423	−	0.115378i
$836$	0.0524352	−	0.104088i	0.00181351	−	0.00359996i
$837$	−12.7068	−	22.0088i	−0.439211	−	0.760736i
$838$	16.0581	+	3.81625i	0.554717	+	0.131830i
$839$	−21.4964			−0.742139			−0.371069	−	0.928605i	$-0.621009\pi$
$839$	−21.4964			−0.742139			−0.371069	+	0.928605i	$0.621009\pi$
$840$	−23.5970	+	40.4087i	−0.814175	+	1.39423i
$841$	−22.8937			−0.789437
$842$	15.2217	+	3.61749i	0.524575	+	0.124667i
$843$	−16.9898	−	29.4272i	−0.585159	−	1.01353i
$844$	10.0004	+	5.03777i	0.344228	+	0.173407i
$845$	1.12320	+	7.61690i	0.0386394	+	0.262029i
$846$	−2.79093	−	9.34322i	−0.0959540	−	0.321227i
$847$	46.6864	−	28.5354i	1.60416	−	0.980489i
$848$	6.91899	−	15.9323i	0.237599	−	0.547118i
$849$	−21.2332	+	36.7769i	−0.728720	+	1.26218i
$850$	15.8337	−	10.4438i	0.543092	−	0.358219i
$851$	−0.562831	−	0.974852i	−0.0192936	−	0.0334175i
$852$	−52.0192	+	2.96567i	−1.78215	+	0.101602i
$853$			5.60517i			0.191917i	0.995385	+	0.0959586i	$0.0305917\pi$
$853$			5.60517i			0.191917i	−0.995385	+	0.0959586i	$0.969408\pi$
$854$	−5.20469	−	15.9564i	−0.178101	−	0.546017i
$855$	−0.0692989	−	0.0874695i	−0.00236997	−	0.00299139i
$856$	2.53879	−	0.918751i	0.0867741	−	0.0314023i
$857$	−24.7908	−	42.9388i	−0.846836	−	1.46676i	−0.884017	−	0.467455i	$-0.845171\pi$
$857$	−24.7908	−	42.9388i	−0.846836	−	1.46676i	0.0371811	−	0.999309i	$-0.488162\pi$
$858$	−47.2543	+	50.0250i	−1.61323	+	1.70783i
$859$	31.5937	+	18.2406i	1.07796	+	0.622362i	0.930346	−	0.366683i	$-0.119507\pi$
$859$	31.5937	+	18.2406i	1.07796	+	0.622362i	0.147616	+	0.989045i	$0.452840\pi$
$860$	40.0709	+	13.2898i	1.36641	+	0.453180i
$861$	78.8918	−	1.97477i	2.68863	−	0.0673001i
$862$	10.9703	+	36.7253i	0.373648	+	1.25087i
$863$	17.0602	−	29.5491i	0.580736	−	1.00586i	−0.414656	−	0.909978i	$-0.636098\pi$
$863$	17.0602	−	29.5491i	0.580736	−	1.00586i	0.995392	−	0.0958862i	$-0.0305685\pi$
$864$	−26.4758	+	11.3242i	−0.900724	+	0.385258i
$865$	−19.2453	+	48.5796i	−0.654360	+	1.65176i
$866$	3.15272	−	13.2661i	0.107134	−	0.450799i
$867$	−27.4179			−0.931160
$868$	11.2910	−	23.8828i	0.383240	−	0.810636i
$869$		−	30.4846i		−	1.03412i
$870$	−57.7263	+	26.9428i	−1.95711	+	0.913445i
$871$	7.71423	+	13.3614i	0.261387	+	0.452735i
$872$	−0.425684	+	2.38843i	−0.0144155	+	0.0808826i
$873$	14.6282	−	25.3367i	0.495089	−	0.857519i
$874$	−0.0104937	−	0.0351299i	−0.000354955	−	0.00118829i
$875$	−1.75461	+	29.5283i	−0.0593166	+	0.998239i
$876$	−42.1054	+	27.6192i	−1.42261	+	0.933165i
$877$	14.2689	−	24.7144i	0.481825	−	0.834546i	−0.517957	−	0.855407i	$-0.673307\pi$
$877$	14.2689	−	24.7144i	0.481825	−	0.834546i	0.999782	+	0.0208608i	$0.00664067\pi$
$878$	26.6205	+	25.1461i	0.898399	+	0.848639i
$879$	−49.8337	+	28.7715i	−1.68085	+	0.970438i
$880$	−48.6086	−	13.1025i	−1.63860	−	0.441684i
$881$		−	26.4655i		−	0.891646i	−0.895121	−	0.445823i	$-0.852911\pi$
$881$		−	26.4655i		−	0.891646i	0.895121	−	0.445823i	$-0.147089\pi$
$882$	8.69662	−	46.9194i	0.292830	−	1.57986i
$883$		−	23.3339i		−	0.785249i	−0.919699	−	0.392625i	$-0.871567\pi$
$883$		−	23.3339i		−	0.785249i	0.919699	−	0.392625i	$-0.128433\pi$
$884$	16.5582	−	0.944003i	0.556914	−	0.0317503i
$885$	0.853216	−	2.15372i	0.0286805	−	0.0723964i
$886$	12.5547	−	13.2909i	0.421784	−	0.446515i
$887$	−5.91785	−	3.41667i	−0.198702	−	0.114721i	0.397348	−	0.917668i	$-0.369931\pi$
$887$	−5.91785	−	3.41667i	−0.198702	−	0.114721i	−0.596050	+	0.802947i	$0.703264\pi$
$888$	2.29057	−	2.71961i	0.0768666	−	0.0912641i
$889$	34.2647	+	18.6554i	1.14920	+	0.625683i
$890$	−2.72098	−	1.90384i	−0.0912076	−	0.0638168i
$891$	−0.634848	+	1.09959i	−0.0212682	+	0.0368376i
$892$	−0.869969	+	1.72696i	−0.0291287	+	0.0578229i
$893$	0.00740489	+	0.0128256i	0.000247795	+	0.000429194i
$894$	−30.6088	−	7.27427i	−1.02371	−	0.243288i
$895$	35.9616	−	28.4911i	1.20206	−	0.952352i
$896$	−25.3444	−	15.9267i	−0.846697	−	0.532075i
$897$			21.6475i			0.722789i
$898$	−1.44876	+	6.09610i	−0.0483457	+	0.203430i
$899$	31.1457	−	17.9820i	1.03877	−	0.599732i
$900$	−30.9585	+	36.9473i	−1.03195	+	1.23158i
$901$	5.82423	−	10.0879i	0.194033	−	0.336075i
$902$	24.3004	+	81.3507i	0.809114	+	2.70868i
$903$	−69.8232	+	1.74777i	−2.32357	+	0.0581623i
$904$	−4.63285	−	3.90199i	−0.154086	−	0.129778i
$905$	3.30118	+	22.3866i	0.109735	+	0.744157i
$906$	54.1849	−	57.3620i	1.80017	−	1.90573i
$907$	21.3186	−	12.3083i	0.707871	−	0.408690i	−0.102401	−	0.994743i	$-0.532653\pi$
$907$	21.3186	−	12.3083i	0.707871	−	0.408690i	0.810272	+	0.586054i	$0.199319\pi$
$908$	−1.87852	−	32.9501i	−0.0623410	−	1.09349i
$909$	−14.7649			−0.489722
$910$	−14.2930	+	21.5566i	−0.473807	+	0.714594i
$911$			17.5189i			0.580427i	0.956962	+	0.290214i	$0.0937264\pi$
$911$			17.5189i			0.580427i	−0.956962	+	0.290214i	$0.906274\pi$
$912$	0.0930651	−	0.0689297i	0.00308169	−	0.00228249i
$913$	−31.8882	−	55.2320i	−1.05535	−	1.82791i
$914$	3.82718	−	4.05159i	0.126592	−	0.134015i
$915$	−4.09197	−	27.7493i	−0.135276	−	0.917362i
$916$	32.8946	−	21.5773i	1.08687	−	0.712934i
$917$	−2.95041	−	4.82712i	−0.0974311	−	0.159406i
$918$	−18.5031	+	5.52708i	−0.610693	+	0.182421i
$919$	−4.72276	−	2.72669i	−0.155790	−	0.0899452i	0.420079	−	0.907488i	$-0.362003\pi$
$919$	−4.72276	−	2.72669i	−0.155790	−	0.0899452i	−0.575868	+	0.817543i	$0.695336\pi$
$920$	−13.9463	+	7.50394i	−0.459795	+	0.247397i
$921$	−7.18415	−	12.4433i	−0.236726	−	0.410021i
$922$	11.9419	−	50.2493i	0.393285	−	1.65487i
$923$	−28.7993			−0.947941
$924$	83.0097	−	6.82005i	2.73082	−	0.224363i
$925$	0.514142	−	2.18811i	0.0169049	−	0.0719445i
$926$	4.16017	−	17.5052i	0.136712	−	0.575257i
$927$	4.46466	−	2.57767i	0.146639	−	0.0846618i
$928$	−16.0255	−	37.4671i	−0.526061	−	1.22992i
$929$	−4.26168	−	2.46048i	−0.139821	−	0.0807258i	0.428458	−	0.903562i	$-0.359057\pi$
$929$	−4.26168	−	2.46048i	−0.139821	−	0.0807258i	−0.568279	+	0.822836i	$0.692390\pi$
$930$	25.3103	−	36.1737i	0.829956	−	1.18618i
$931$	0.00362596	+	0.0723828i	0.000118836	+	0.00237225i
$932$	−26.9199	−	41.0394i	−0.881790	−	1.34429i
$933$	−29.9705	+	51.9104i	−0.981190	+	1.69947i
$934$	−22.6698	−	21.4142i	−0.741779	−	0.700694i
$935$	−31.3878	−	12.4346i	−1.02649	−	0.406654i
$936$	−39.6325	+	14.3424i	−1.29543	+	0.468797i
$937$	27.1974			0.888501			0.444251	−	0.895903i	$-0.353470\pi$
$937$	27.1974			0.888501			0.444251	+	0.895903i	$0.353470\pi$
$938$	3.86164	−	18.2701i	0.126087	−	0.596539i
$939$	−3.26044			−0.106401
$940$	4.77991	−	4.25148i	0.155903	−	0.138668i
$941$	−24.9798	−	43.2663i	−0.814319	−	1.41044i	−0.909816	−	0.415012i	$-0.863777\pi$
$941$	−24.9798	−	43.2663i	−0.814319	−	1.41044i	0.0954967	−	0.995430i	$-0.469556\pi$
$942$	5.94644	−	6.29511i	0.193745	−	0.205106i
$943$	23.1301	+	13.3542i	0.753220	+	0.434872i
$944$	1.35922	+	0.590276i	0.0442389	+	0.0192118i
$945$	10.3878	−	28.2672i	0.337914	−	0.919533i
$946$	−21.5071	−	71.9995i	−0.699255	−	2.34090i
$947$	17.0454	+	9.84119i	0.553902	+	0.319796i	0.750694	−	0.660650i	$-0.229719\pi$
$947$	17.0454	+	9.84119i	0.553902	+	0.319796i	−0.196792	+	0.980445i	$0.563052\pi$
$948$	13.6281	−	27.0529i	0.442620	−	0.878637i
$949$	−24.1042	+	13.9166i	−0.782455	+	0.451750i
$950$	0.0327705	−	0.0654653i	0.00106321	−	0.00212398i
$951$	−41.4856			−1.34526
$952$	−15.6723	−	12.5432i	−0.507942	−	0.406526i
$953$		−	13.8715i		−	0.449340i	−0.974435	−	0.224670i	$-0.927870\pi$
$953$		−	13.8715i		−	0.449340i	0.974435	−	0.224670i	$-0.0721305\pi$
$954$	−6.84444	+	28.8001i	−0.221597	+	0.932439i
$955$	−9.78871	+	24.7090i	−0.316755	+	0.799564i
$956$	−3.85505	+	7.65258i	−0.124681	+	0.247502i
$957$	98.1970	+	56.6941i	3.17426	+	1.83266i
$958$	−52.0695	+	15.5537i	−1.68229	+	0.502519i
$959$	−33.6598	+	0.842552i	−1.08693	+	0.0272074i
$960$	−37.2793	−	33.3580i	−1.20318	−	1.07662i
$961$	3.03794	−	5.26186i	0.0979979	−	0.169737i
$962$	1.34958	−	1.42871i	0.0435122	−	0.0460635i
$963$	−3.98484	+	2.30065i	−0.128410	+	0.0741374i
$964$	15.0910	−	0.860356i	0.486049	−	0.0277102i
$965$	−2.34215	−	2.95628i	−0.0753966	−	0.0951661i
$966$	17.5096	−	19.4910i	0.563362	−	0.627114i
$967$	14.3492			0.461441			0.230720	−	0.973020i	$-0.425892\pi$
$967$	14.3492			0.461441			0.230720	+	0.973020i	$0.425892\pi$
$968$	19.9050	+	55.0035i	0.639770	+	1.76788i
$969$	0.0672600	−	0.0388326i	0.00216070	−	0.00124748i
$970$	19.1207	+	1.66612i	0.613928	+	0.0534959i
$971$	−19.5133	−	11.2660i	−0.626212	−	0.361544i	0.153072	−	0.988215i	$-0.451083\pi$
$971$	−19.5133	−	11.2660i	−0.626212	−	0.361544i	−0.779284	+	0.626671i	$0.784417\pi$
$972$	−26.5936	+	17.4441i	−0.852989	+	0.559520i
$973$	8.03861	−	14.7646i	0.257706	−	0.473332i
$974$	−10.5491	+	3.15115i	−0.338016	+	0.100969i
$975$	−29.6024	+	31.4980i	−0.948035	+	1.00874i
$976$	17.8264	−	2.03923i	0.570608	−	0.0652741i
$977$	−47.6801	+	27.5281i	−1.52542	+	0.880703i	−0.525877	+	0.850561i	$0.676263\pi$
$977$	−47.6801	+	27.5281i	−1.52542	+	0.880703i	−0.999546	+	0.0301422i	$0.990404\pi$
$978$	56.5519	+	13.4397i	1.80833	+	0.429755i
$979$			5.91091i			0.188913i
$980$	30.3052	−	7.84832i	0.968063	−	0.250705i
$981$		−	4.13460i		−	0.132008i
$982$	−1.54866	+	6.51646i	−0.0494196	+	0.207949i
$983$	−20.7276	+	11.9671i	−0.661108	+	0.381691i	−0.792699	−	0.609613i	$-0.791325\pi$
$983$	−20.7276	+	11.9671i	−0.661108	+	0.381691i	0.131591	+	0.991304i	$0.457991\pi$
$984$	−14.8029	+	83.0565i	−0.471900	+	2.64774i
$985$	3.98977	+	27.0563i	0.127125	+	0.862084i
$986$	−7.82163	−	26.1846i	−0.249091	−	0.833887i
$987$	−5.06072	+	9.29509i	−0.161084	+	0.295866i
$988$	0.0535252	−	0.0351100i	0.00170286	−	0.00111700i
$989$	−20.4713	−	11.8191i	−0.650950	−	0.375826i
$990$	85.4733	+	7.44790i	2.71652	+	0.236710i
$991$	5.73341	−	3.31019i	0.182128	−	0.105152i	−0.406164	−	0.913800i	$-0.633134\pi$
$991$	5.73341	−	3.31019i	0.182128	−	0.105152i	0.588292	+	0.808649i	$0.299801\pi$
$992$	22.6011	+	16.9340i	0.717587	+	0.537656i
$993$	43.2976			1.37401
$994$	25.9304	+	23.2943i	0.822463	+	0.738851i
$995$	20.3275	−	16.1048i	0.644426	−	0.510556i
$996$	−3.60710	−	63.2701i	−0.114295	−	2.00479i
$997$	45.2960	−	26.1517i	1.43454	−	0.828232i	0.437077	−	0.899424i	$-0.356014\pi$
$997$	45.2960	−	26.1517i	1.43454	−	0.828232i	0.997463	+	0.0711927i	$0.0226805\pi$
$998$	−19.0435	−	17.9887i	−0.602811	−	0.569422i
$999$	−1.14418	+	1.98178i	−0.0362002	+	0.0627006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.b.19.18	yes	80
4.3	odd	2		1120.2.bq.b.719.35		80
5.4	even	2	inner	280.2.ba.b.19.23	yes	80
7.3	odd	6	inner	280.2.ba.b.59.11	yes	80
8.3	odd	2	inner	280.2.ba.b.19.30	yes	80
8.5	even	2		1120.2.bq.b.719.36		80
20.19	odd	2		1120.2.bq.b.719.5		80
28.3	even	6		1120.2.bq.b.1039.6		80
35.24	odd	6	inner	280.2.ba.b.59.30	yes	80
40.19	odd	2	inner	280.2.ba.b.19.11	✓	80
40.29	even	2		1120.2.bq.b.719.6		80
56.3	even	6	inner	280.2.ba.b.59.23	yes	80
56.45	odd	6		1120.2.bq.b.1039.5		80
140.59	even	6		1120.2.bq.b.1039.36		80
280.59	even	6	inner	280.2.ba.b.59.18	yes	80
280.269	odd	6		1120.2.bq.b.1039.35		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.11	✓	80	40.19	odd	2	inner
280.2.ba.b.19.18	yes	80	1.1	even	1	trivial
280.2.ba.b.19.23	yes	80	5.4	even	2	inner
280.2.ba.b.19.30	yes	80	8.3	odd	2	inner
280.2.ba.b.59.11	yes	80	7.3	odd	6	inner
280.2.ba.b.59.18	yes	80	280.59	even	6	inner
280.2.ba.b.59.23	yes	80	56.3	even	6	inner
280.2.ba.b.59.30	yes	80	35.24	odd	6	inner
1120.2.bq.b.719.5		80	20.19	odd	2
1120.2.bq.b.719.6		80	40.29	even	2
1120.2.bq.b.719.35		80	4.3	odd	2
1120.2.bq.b.719.36		80	8.5	even	2
1120.2.bq.b.1039.5		80	56.45	odd	6
1120.2.bq.b.1039.6		80	28.3	even	6
1120.2.bq.b.1039.35		80	280.269	odd	6
1120.2.bq.b.1039.36		80	140.59	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.326985 + 1.37589i) q^{2} +(-1.39824 - 2.42182i) q^{3} +(-1.78616 - 0.899793i) q^{4} +(0.326208 + 2.21215i) q^{5} +(3.78937 - 1.13193i) q^{6} +(-2.32367 - 1.26513i) q^{7} +(1.82207 - 2.16335i) q^{8} +(-2.41015 + 4.17451i) q^{9} +O(q^{10})\)	\(q+(-0.326985 + 1.37589i) q^{2} +(-1.39824 - 2.42182i) q^{3} +(-1.78616 - 0.899793i) q^{4} +(0.326208 + 2.21215i) q^{5} +(3.78937 - 1.13193i) q^{6} +(-2.32367 - 1.26513i) q^{7} +(1.82207 - 2.16335i) q^{8} +(-2.41015 + 4.17451i) q^{9} +(-3.15034 - 0.274512i) q^{10} +(2.81429 + 4.87449i) q^{11} +(0.318344 + 5.58389i) q^{12} +3.09140i q^{13} +(2.50048 - 2.78345i) q^{14} +(4.90131 - 3.88313i) q^{15} +(2.38075 + 3.21435i) q^{16} +(1.34123 + 2.32308i) q^{17} +(-4.95559 - 4.68111i) q^{18} +(0.00896628 + 0.00517669i) q^{19} +(1.40781 - 4.24477i) q^{20} +(0.185144 + 7.39648i) q^{21} +(-7.62701 + 2.27827i) q^{22} +(-1.25202 + 2.16856i) q^{23} +(-7.78693 - 1.38784i) q^{24} +(-4.78718 + 1.44324i) q^{25} +(-4.25344 - 1.01084i) q^{26} +5.09045 q^{27} +(3.01211 + 4.35054i) q^{28} +7.20373i q^{29} +(3.74011 + 8.01340i) q^{30} +(-2.49620 - 4.32355i) q^{31} +(-5.20107 + 2.22461i) q^{32} +(7.87010 - 13.6314i) q^{33} +(-3.63486 + 1.08578i) q^{34} +(2.04064 - 5.55300i) q^{35} +(8.06111 - 5.28770i) q^{36} +(-0.224770 + 0.389313i) q^{37} +(-0.0100544 + 0.0106439i) q^{38} +(7.48684 - 4.32253i) q^{39} +(5.38001 + 3.32498i) q^{40} -10.6661i q^{41} +(-10.2373 - 2.16380i) q^{42} +9.44007i q^{43} +(-0.640742 - 11.2389i) q^{44} +(-10.0208 - 3.96985i) q^{45} +(-2.57431 - 2.43173i) q^{46} +(1.23879 + 0.715215i) q^{47} +(4.45573 - 10.2602i) q^{48} +(3.79892 + 5.87948i) q^{49} +(-0.420406 - 7.05856i) q^{50} +(3.75072 - 6.49644i) q^{51} +(2.78162 - 5.52175i) q^{52} +(-2.17123 - 3.76068i) q^{53} +(-1.66450 + 7.00391i) q^{54} +(-9.86504 + 7.81571i) q^{55} +(-6.97079 + 2.72177i) q^{56} -0.0289530i q^{57} +(-9.91155 - 2.35551i) q^{58} +(0.320832 - 0.185233i) q^{59} +(-12.2485 + 2.52573i) q^{60} +(2.24283 - 3.88469i) q^{61} +(6.76496 - 2.02077i) q^{62} +(10.8817 - 6.65104i) q^{63} +(-1.36015 - 7.88353i) q^{64} +(-6.83864 + 1.00844i) q^{65} +(16.1820 + 15.2857i) q^{66} +(4.32212 - 2.49538i) q^{67} +(-0.305364 - 5.35622i) q^{68} +7.00248 q^{69} +(6.97307 + 4.62345i) q^{70} +9.31593i q^{71} +(4.63945 + 12.8202i) q^{72} +(4.50169 + 7.79716i) q^{73} +(-0.462156 - 0.436559i) q^{74} +(10.1889 + 9.57570i) q^{75} +(-0.0113573 - 0.0173142i) q^{76} +(-0.372646 - 14.8872i) q^{77} +(3.49925 + 11.7145i) q^{78} +(-4.69042 - 2.70802i) q^{79} +(-6.33399 + 6.31510i) q^{80} +(0.112790 + 0.195358i) q^{81} +(14.6755 + 3.48767i) q^{82} -11.3308 q^{83} +(6.32460 - 13.3779i) q^{84} +(-4.70146 + 3.72480i) q^{85} +(-12.9885 - 3.08676i) q^{86} +(17.4462 - 10.0725i) q^{87} +(15.6730 + 2.79336i) q^{88} +(0.909465 + 0.525080i) q^{89} +(8.73875 - 12.4895i) q^{90} +(3.91101 - 7.18342i) q^{91} +(4.18755 - 2.74684i) q^{92} +(-6.98059 + 12.0907i) q^{93} +(-1.38912 + 1.47058i) q^{94} +(-0.00852671 + 0.0215234i) q^{95} +(12.6599 + 9.48554i) q^{96} -6.06940 q^{97} +(-9.33172 + 3.30440i) q^{98} -27.1315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) \) 80 * q + 6 * q^4 - 52 * q^9	\( 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) \) 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

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