LMFDB - Embedded newform 350.2.m.b.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	350.29
Dual form			350.2.m.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.909805 + 1.25224i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02853 - 0.940783i) q^{5} +(1.25224 - 0.909805i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.186694 + 0.574585i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.909805 + 1.25224i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02853 - 0.940783i) q^{5} +(1.25224 - 0.909805i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.186694 + 0.574585i) q^{9} +(-2.21996 + 0.267888i) q^{10} +(1.82002 - 5.60146i) q^{11} +(-1.47209 + 0.478313i) q^{12} +(-1.64171 + 0.533424i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.667480 + 3.39613i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58734 + 2.18478i) q^{17} -0.604154i q^{18} +(1.09978 - 0.799037i) q^{19} +(2.19409 + 0.431230i) q^{20} +(1.25224 + 0.909805i) q^{21} +(-3.46189 + 4.76489i) q^{22} +(5.13918 + 1.66982i) q^{23} +1.54785 q^{24} +(3.22986 - 3.81681i) q^{25} +1.72620 q^{26} +(-5.30566 - 1.72391i) q^{27} +(0.587785 - 0.809017i) q^{28} +(5.28827 + 3.84215i) q^{29} +(1.68427 - 3.02365i) q^{30} +(6.10965 - 4.43892i) q^{31} -1.00000i q^{32} +(5.35850 + 7.37534i) q^{33} +(-0.834513 - 2.56837i) q^{34} +(-0.940783 - 2.02853i) q^{35} +(-0.186694 + 0.574585i) q^{36} +(0.163703 - 0.0531902i) q^{37} +(-1.29287 + 0.420078i) q^{38} +(0.825662 - 2.54113i) q^{39} +(-1.95345 - 1.08814i) q^{40} +(1.53687 + 4.72999i) q^{41} +(-0.909805 - 1.25224i) q^{42} +1.06470i q^{43} +(4.76489 - 3.46189i) q^{44} +(0.919274 + 0.989923i) q^{45} +(-4.37165 - 3.17619i) q^{46} +(-0.297434 + 0.409383i) q^{47} +(-1.47209 - 0.478313i) q^{48} -1.00000 q^{49} +(-4.25123 + 2.63192i) q^{50} -4.18004 q^{51} +(-1.64171 - 0.533424i) q^{52} +(-1.68331 + 2.31688i) q^{53} +(4.51326 + 3.27908i) q^{54} +(-1.57779 - 13.0750i) q^{55} +(-0.809017 + 0.587785i) q^{56} +2.10415i q^{57} +(-3.84215 - 5.28827i) q^{58} +(-0.0158173 - 0.0486806i) q^{59} +(-2.53620 + 2.35519i) q^{60} +(-0.778477 + 2.39591i) q^{61} +(-7.18233 + 2.33368i) q^{62} +(0.574585 - 0.186694i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.82842 + 2.62656i) q^{65} +(-2.81713 - 8.67023i) q^{66} +(-6.01707 - 8.28179i) q^{67} +2.70054i q^{68} +(-6.76667 + 4.91627i) q^{69} +(0.267888 + 2.21996i) q^{70} +(-8.91827 - 6.47950i) q^{71} +(0.355113 - 0.488771i) q^{72} +(-10.9934 - 3.57196i) q^{73} -0.172127 q^{74} +(1.84102 + 7.51710i) q^{75} +1.35940 q^{76} +(-5.60146 - 1.82002i) q^{77} +(-1.57050 + 2.16161i) q^{78} +(-0.646542 - 0.469740i) q^{79} +(1.52159 + 1.63853i) q^{80} +(5.51955 - 4.01019i) q^{81} -4.97340i q^{82} +(6.40364 + 8.81386i) q^{83} +(0.478313 + 1.47209i) q^{84} +(5.27537 + 2.93855i) q^{85} +(0.329010 - 1.01259i) q^{86} +(-9.62258 + 3.12657i) q^{87} +(-5.60146 + 1.82002i) q^{88} +(-4.47558 + 13.7744i) q^{89} +(-0.568378 - 1.22554i) q^{90} +(0.533424 + 1.64171i) q^{91} +(3.17619 + 4.37165i) q^{92} +11.6893i q^{93} +(0.409383 - 0.297434i) q^{94} +(1.47921 - 2.65552i) q^{95} +(1.25224 + 0.909805i) q^{96} +(-0.0557125 + 0.0766817i) q^{97} +(0.951057 + 0.309017i) q^{98} +3.55830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.909805	+	1.25224i	−0.525276	+	0.722980i	−0.986401	−	0.164355i	$-0.947446\pi$
$3$	−0.909805	+	1.25224i	−0.525276	+	0.722980i	0.461125	+	0.887335i	$0.347446\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.02853	−	0.940783i	0.907185	−	0.420731i
$5$	2.02853	−	0.940783i	0.907185	−	0.420731i
$6$	1.25224	−	0.909805i	0.511224	−	0.371426i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.186694	+	0.574585i	0.0622313	+	0.191528i
$10$	−2.21996	+	0.267888i	−0.702014	+	0.0847136i
$11$	1.82002	−	5.60146i	0.548758	−	1.68890i	−0.163125	−	0.986605i	$-0.552157\pi$
$11$	1.82002	−	5.60146i	0.548758	−	1.68890i	0.711883	−	0.702298i	$-0.247843\pi$
$12$	−1.47209	+	0.478313i	−0.424957	+	0.138077i
$13$	−1.64171	+	0.533424i	−0.455329	+	0.147945i	−0.527697	−	0.849433i	$-0.676944\pi$
$13$	−1.64171	+	0.533424i	−0.455329	+	0.147945i	0.0723682	+	0.997378i	$0.476944\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−0.667480	+	3.39613i	−0.172343	+	0.876877i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.58734	+	2.18478i	0.384986	+	0.529888i	0.956897	−	0.290428i	$-0.0937977\pi$
$17$	1.58734	+	2.18478i	0.384986	+	0.529888i	−0.571911	+	0.820316i	$0.693798\pi$
$18$		−	0.604154i		−	0.142401i
$19$	1.09978	−	0.799037i	0.252307	−	0.183312i	−0.454442	−	0.890776i	$-0.650161\pi$
$19$	1.09978	−	0.799037i	0.252307	−	0.183312i	0.706749	+	0.707465i	$0.250161\pi$
$20$	2.19409	+	0.431230i	0.490614	+	0.0964259i
$21$	1.25224	+	0.909805i	0.273261	+	0.198536i
$22$	−3.46189	+	4.76489i	−0.738078	+	1.01588i
$23$	5.13918	+	1.66982i	1.07159	+	0.348182i	0.791108	−	0.611676i	$-0.209505\pi$
$23$	5.13918	+	1.66982i	1.07159	+	0.348182i	0.280485	+	0.959858i	$0.409505\pi$
$24$	1.54785			0.315954
$25$	3.22986	−	3.81681i	0.645971	−	0.763362i
$26$	1.72620			0.338535
$27$	−5.30566	−	1.72391i	−1.02107	−	0.331767i
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	5.28827	+	3.84215i	0.982007	+	0.713470i	0.958156	−	0.286246i	$-0.0924074\pi$
$29$	5.28827	+	3.84215i	0.982007	+	0.713470i	0.0238505	+	0.999716i	$0.492407\pi$
$30$	1.68427	−	3.02365i	0.307505	−	0.552040i
$31$	6.10965	−	4.43892i	1.09733	−	0.797254i	0.116705	−	0.993167i	$-0.462767\pi$
$31$	6.10965	−	4.43892i	1.09733	−	0.797254i	0.980621	+	0.195913i	$0.0627669\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.35850	+	7.37534i	0.932794	+	1.28388i
$34$	−0.834513	−	2.56837i	−0.143118	−	0.440471i
$35$	−0.940783	−	2.02853i	−0.159021	−	0.342884i
$36$	−0.186694	+	0.574585i	−0.0311157	+	0.0957641i
$37$	0.163703	−	0.0531902i	0.0269125	−	0.00874442i	−0.295530	−	0.955334i	$-0.595496\pi$
$37$	0.163703	−	0.0531902i	0.0269125	−	0.00874442i	0.322442	+	0.946589i	$0.395496\pi$
$38$	−1.29287	+	0.420078i	−0.209731	+	0.0681457i
$39$	0.825662	−	2.54113i	0.132212	−	0.406906i
$40$	−1.95345	−	1.08814i	−0.308867	−	0.172049i
$41$	1.53687	+	4.72999i	0.240018	+	0.738700i	0.996416	+	0.0845880i	$0.0269574\pi$
$41$	1.53687	+	4.72999i	0.240018	+	0.738700i	−0.756398	+	0.654112i	$0.773043\pi$
$42$	−0.909805	−	1.25224i	−0.140386	−	0.193225i
$43$			1.06470i			0.162365i	0.996699	+	0.0811826i	$0.0258697\pi$
$43$			1.06470i			0.162365i	−0.996699	+	0.0811826i	$0.974130\pi$
$44$	4.76489	−	3.46189i	0.718334	−	0.521900i
$45$	0.919274	+	0.989923i	0.137037	+	0.147569i
$46$	−4.37165	−	3.17619i	−0.644565	−	0.468304i
$47$	−0.297434	+	0.409383i	−0.0433853	+	0.0597147i	−0.830158	−	0.557527i	$-0.811750\pi$
$47$	−0.297434	+	0.409383i	−0.0433853	+	0.0597147i	0.786773	+	0.617242i	$0.211750\pi$
$48$	−1.47209	−	0.478313i	−0.212479	−	0.0690385i
$49$	−1.00000			−0.142857
$50$	−4.25123	+	2.63192i	−0.601215	+	0.372210i
$51$	−4.18004			−0.585322
$52$	−1.64171	−	0.533424i	−0.227664	−	0.0739727i
$53$	−1.68331	+	2.31688i	−0.231220	+	0.318248i	−0.908824	−	0.417180i	$-0.863019\pi$
$53$	−1.68331	+	2.31688i	−0.231220	+	0.318248i	0.677604	+	0.735427i	$0.263019\pi$
$54$	4.51326	+	3.27908i	0.614177	+	0.446226i
$55$	−1.57779	−	13.0750i	−0.212749	−	1.76303i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$			2.10415i			0.278702i
$58$	−3.84215	−	5.28827i	−0.504499	−	0.694384i
$59$	−0.0158173	−	0.0486806i	−0.00205924	−	0.00633768i	0.950022	−	0.312184i	$-0.101061\pi$
$59$	−0.0158173	−	0.0486806i	−0.00205924	−	0.00633768i	−0.952081	+	0.305846i	$0.901061\pi$
$60$	−2.53620	+	2.35519i	−0.327422	+	0.304054i
$61$	−0.778477	+	2.39591i	−0.0996738	+	0.306764i	−0.988444	−	0.151590i	$-0.951561\pi$
$61$	−0.778477	+	2.39591i	−0.0996738	+	0.306764i	0.888770	+	0.458354i	$0.151561\pi$
$62$	−7.18233	+	2.33368i	−0.912156	+	0.296378i
$63$	0.574585	−	0.186694i	0.0723909	−	0.0235212i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.82842	+	2.62656i	−0.350823	+	0.325785i
$66$	−2.81713	−	8.67023i	−0.346765	−	1.06723i
$67$	−6.01707	−	8.28179i	−0.735103	−	1.01178i	−0.998885	−	0.0471999i	$-0.984970\pi$
$67$	−6.01707	−	8.28179i	−0.735103	−	1.01178i	0.263783	−	0.964582i	$-0.415030\pi$
$68$			2.70054i			0.327489i
$69$	−6.76667	+	4.91627i	−0.814611	+	0.591849i
$70$	0.267888	+	2.21996i	0.0320187	+	0.265336i
$71$	−8.91827	−	6.47950i	−1.05840	−	0.768976i	−0.0846115	−	0.996414i	$-0.526965\pi$
$71$	−8.91827	−	6.47950i	−1.05840	−	0.768976i	−0.973792	+	0.227439i	$0.926965\pi$
$72$	0.355113	−	0.488771i	0.0418505	−	0.0576022i
$73$	−10.9934	−	3.57196i	−1.28668	−	0.418066i	−0.415749	−	0.909479i	$-0.636481\pi$
$73$	−10.9934	−	3.57196i	−1.28668	−	0.418066i	−0.870927	+	0.491413i	$0.836481\pi$
$74$	−0.172127			−0.0200094
$75$	1.84102	+	7.51710i	0.212583	+	0.868000i
$76$	1.35940			0.155934
$77$	−5.60146	−	1.82002i	−0.638345	−	0.207411i
$78$	−1.57050	+	2.16161i	−0.177824	+	0.244754i
$79$	−0.646542	−	0.469740i	−0.0727416	−	0.0528499i	0.550820	−	0.834624i	$-0.314315\pi$
$79$	−0.646542	−	0.469740i	−0.0727416	−	0.0528499i	−0.623562	+	0.781774i	$0.714315\pi$
$80$	1.52159	+	1.63853i	0.170119	+	0.183193i
$81$	5.51955	−	4.01019i	0.613283	−	0.445576i
$82$		−	4.97340i		−	0.549220i
$83$	6.40364	+	8.81386i	0.702891	+	0.967447i	0.999921	+	0.0125783i	$0.00400391\pi$
$83$	6.40364	+	8.81386i	0.702891	+	0.967447i	−0.297030	+	0.954868i	$0.595996\pi$
$84$	0.478313	+	1.47209i	0.0521882	+	0.160619i
$85$	5.27537	+	2.93855i	0.572194	+	0.318731i
$86$	0.329010	−	1.01259i	0.0354781	−	0.109190i
$87$	−9.62258	+	3.12657i	−1.03165	+	0.335203i
$88$	−5.60146	+	1.82002i	−0.597118	+	0.194015i
$89$	−4.47558	+	13.7744i	−0.474410	+	1.46009i	0.372341	+	0.928096i	$0.378555\pi$
$89$	−4.47558	+	13.7744i	−0.474410	+	1.46009i	−0.846751	+	0.531989i	$0.821445\pi$
$90$	−0.568378	−	1.22554i	−0.0599123	−	0.129184i
$91$	0.533424	+	1.64171i	0.0559181	+	0.172098i
$92$	3.17619	+	4.37165i	0.331141	+	0.455776i
$93$			11.6893i			1.21212i
$94$	0.409383	−	0.297434i	0.0422247	−	0.0306780i
$95$	1.47921	−	2.65552i	0.151764	−	0.272451i
$96$	1.25224	+	0.909805i	0.127806	+	0.0928565i
$97$	−0.0557125	+	0.0766817i	−0.00565675	+	0.00778585i	−0.811836	−	0.583886i	$-0.801532\pi$
$97$	−0.0557125	+	0.0766817i	−0.00565675	+	0.00778585i	0.806179	+	0.591671i	$0.201532\pi$
$98$	0.951057	+	0.309017i	0.0960712	+	0.0312154i
$99$	3.55830			0.357623
$100$	4.85647	−	1.18940i	0.485647	−	0.118940i
$101$	−3.75398			−0.373535			−0.186768	−	0.982404i	$-0.559801\pi$
$101$	−3.75398			−0.373535			−0.186768	+	0.982404i	$0.559801\pi$
$102$	3.97545	+	1.29170i	0.393628	+	0.127898i
$103$	−11.3582	+	15.6332i	−1.11915	+	1.54038i	−0.311961	+	0.950095i	$0.600986\pi$
$103$	−11.3582	+	15.6332i	−1.11915	+	1.54038i	−0.807193	+	0.590288i	$0.799014\pi$
$104$	1.39652	+	1.01463i	0.136940	+	0.0994930i
$105$	3.39613	+	0.667480i	0.331428	+	0.0651394i
$106$	2.31688	−	1.68331i	0.225035	−	0.163498i
$107$		−	12.4345i		−	1.20208i	−0.799217	−	0.601042i	$-0.794752\pi$
$107$		−	12.4345i		−	1.20208i	0.799217	−	0.601042i	$-0.205248\pi$
$108$	−3.27908	−	4.51326i	−0.315529	−	0.434289i
$109$	−4.08781	−	12.5810i	−0.391541	−	1.20504i	−0.931623	−	0.363427i	$-0.881607\pi$
$109$	−4.08781	−	12.5810i	−0.391541	−	1.20504i	0.540082	−	0.841613i	$-0.318393\pi$
$110$	−2.53982	+	12.9226i	−0.242163	+	1.23212i
$111$	−0.0823306	+	0.253387i	−0.00781447	+	0.0240505i
$112$	0.951057	−	0.309017i	0.0898664	−	0.0291994i
$113$	19.4278	−	6.31248i	1.82761	−	0.593828i	0.828171	−	0.560476i	$-0.189382\pi$
$113$	19.4278	−	6.31248i	1.82761	−	0.593828i	0.999444	−	0.0333523i	$-0.0106183\pi$
$114$	0.650219	−	2.00117i	0.0608986	−	0.187427i
$115$	11.9959	−	1.44757i	1.11862	−	0.134987i
$116$	2.01994	+	6.21673i	0.187547	+	0.577209i
$117$	−0.612995	−	0.843715i	−0.0566714	−	0.0780015i
$118$			0.0511858i			0.00471204i
$119$	2.18478	−	1.58734i	0.200279	−	0.145511i
$120$	3.13986	−	1.45619i	0.286629	−	0.132932i
$121$	−19.1647	−	13.9239i	−1.74224	−	1.26581i
$122$	1.48075	−	2.03808i	0.134061	−	0.184519i
$123$	−7.32132	−	2.37884i	−0.660141	−	0.214493i
$124$	7.55195			0.678185
$125$	2.96106	−	10.7811i	0.264846	−	0.964291i
$126$	−0.604154			−0.0538223
$127$	−7.85563	−	2.55245i	−0.697074	−	0.226493i	−0.0610189	−	0.998137i	$-0.519435\pi$
$127$	−7.85563	−	2.55245i	−0.697074	−	0.226493i	−0.636055	+	0.771643i	$0.719435\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−1.33326	−	0.968669i	−0.117387	−	0.0852865i
$130$	3.50164	−	1.62398i	0.307114	−	0.142432i
$131$	−14.8448	+	10.7854i	−1.29700	+	0.942326i	−0.999922	−	0.0125268i	$-0.996012\pi$
$131$	−14.8448	+	10.7854i	−1.29700	+	0.942326i	−0.297079	+	0.954853i	$0.596012\pi$
$132$			9.11642i			0.793482i
$133$	−0.799037	−	1.09978i	−0.0692853	−	0.0953630i
$134$	3.16336	+	9.73583i	0.273273	+	0.841048i
$135$	−12.3845	+	1.49447i	−1.06589	+	0.128623i
$136$	0.834513	−	2.56837i	0.0715589	−	0.220236i
$137$	14.6672	−	4.76567i	1.25311	−	0.407159i	0.394073	−	0.919079i	$-0.371066\pi$
$137$	14.6672	−	4.76567i	1.25311	−	0.407159i	0.859033	+	0.511921i	$0.171066\pi$
$138$	7.95469	−	2.58464i	0.677148	−	0.220019i
$139$	1.21791	−	3.74836i	0.103302	−	0.317931i	−0.886026	−	0.463635i	$-0.846545\pi$
$139$	1.21791	−	3.74836i	0.103302	−	0.317931i	0.989328	+	0.145704i	$0.0465447\pi$
$140$	0.431230	−	2.19409i	0.0364456	−	0.185435i
$141$	−0.242038	−	0.744918i	−0.0203833	−	0.0627334i
$142$	6.47950	+	8.91827i	0.543748	+	0.748405i
$143$			10.1668i			0.850193i
$144$	−0.488771	+	0.355113i	−0.0407309	+	0.0295927i
$145$	14.3420	+	2.81880i	1.19104	+	0.234089i
$146$	9.35152	+	6.79427i	0.773937	+	0.562298i
$147$	0.909805	−	1.25224i	0.0750394	−	0.103283i
$148$	0.163703	+	0.0531902i	0.0134563	+	0.00437221i
$149$	5.79740			0.474942			0.237471	−	0.971395i	$-0.423682\pi$
$149$	5.79740			0.474942			0.237471	+	0.971395i	$0.423682\pi$
$150$	0.571998	−	7.71809i	0.0467034	−	0.630180i
$151$	−17.9615			−1.46169			−0.730843	−	0.682545i	$-0.760873\pi$
$151$	−17.9615			−1.46169			−0.730843	+	0.682545i	$0.760873\pi$
$152$	−1.29287	−	0.420078i	−0.104865	−	0.0340729i
$153$	−0.958997	+	1.31995i	−0.0775303	+	0.106711i
$154$	4.76489	+	3.46189i	0.383965	+	0.278967i
$155$	8.21754	−	14.7523i	0.660049	−	1.18494i
$156$	2.16161	−	1.57050i	0.173067	−	0.125741i
$157$		−	11.1057i		−	0.886335i	−0.896439	−	0.443167i	$-0.853855\pi$
$157$		−	11.1057i		−	0.886335i	0.896439	−	0.443167i	$-0.146145\pi$
$158$	0.469740	+	0.646542i	0.0373705	+	0.0514361i
$159$	−1.36980	−	4.21581i	−0.108632	−	0.334336i
$160$	−0.940783	−	2.02853i	−0.0743754	−	0.160369i
$161$	1.66982	−	5.13918i	0.131600	−	0.405024i
$162$	−6.48862	+	2.10828i	−0.509794	+	0.165642i
$163$	15.3158	−	4.97640i	1.19963	−	0.389782i	0.360002	−	0.932951i	$-0.382776\pi$
$163$	15.3158	−	4.97640i	1.19963	−	0.389782i	0.839623	+	0.543170i	$0.182776\pi$
$164$	−1.53687	+	4.72999i	−0.120009	+	0.369350i
$165$	17.8085	+	9.91990i	1.38639	+	0.772263i
$166$	−3.36659	−	10.3613i	−0.261298	−	0.804194i
$167$	12.7730	+	17.5806i	0.988407	+	1.36043i	0.932175	+	0.362008i	$0.117909\pi$
$167$	12.7730	+	17.5806i	0.988407	+	1.36043i	0.0562318	+	0.998418i	$0.482091\pi$
$168$		−	1.54785i		−	0.119419i
$169$	−8.10655	+	5.88975i	−0.623580	+	0.453058i
$170$	−4.10911	−	4.42491i	−0.315154	−	0.339375i
$171$	0.664437	+	0.482741i	0.0508107	+	0.0369162i
$172$	−0.625815	+	0.861360i	−0.0477179	+	0.0656781i
$173$	−23.7644	−	7.72152i	−1.80677	−	0.587057i	−0.806781	−	0.590850i	$-0.798792\pi$
$173$	−23.7644	−	7.72152i	−1.80677	−	0.587057i	−0.999993	+	0.00379354i	$0.998792\pi$
$174$	10.1178			0.767027
$175$	−3.81681	−	3.22986i	−0.288524	−	0.244154i
$176$	5.88972			0.443955
$177$	0.0753504	+	0.0244828i	0.00566368	+	0.00184024i
$178$	8.51306	−	11.7172i	0.638081	−	0.878243i
$179$	−7.99861	−	5.81133i	−0.597844	−	0.434359i	0.247269	−	0.968947i	$-0.420467\pi$
$179$	−7.99861	−	5.81133i	−0.597844	−	0.434359i	−0.845113	+	0.534588i	$0.820467\pi$
$180$	0.161846	+	1.34120i	0.0120633	+	0.0999672i
$181$	2.54655	−	1.85018i	0.189283	−	0.137522i	−0.489108	−	0.872223i	$-0.662677\pi$
$181$	2.54655	−	1.85018i	0.189283	−	0.137522i	0.678391	+	0.734701i	$0.262677\pi$
$182$		−	1.72620i		−	0.127954i
$183$	−2.29198	−	3.15465i	−0.169428	−	0.233198i
$184$	−1.66982	−	5.13918i	−0.123101	−	0.378866i
$185$	0.282035	−	0.261906i	0.0207356	−	0.0192557i
$186$	3.61219	−	11.1172i	0.264859	−	0.815151i
$187$	15.1270	−	4.91505i	1.10619	−	0.359424i
$188$	−0.481259	+	0.156371i	−0.0350994	+	0.0114045i
$189$	−1.72391	+	5.30566i	−0.125396	+	0.385930i
$190$	−2.22742	+	2.06845i	−0.161594	+	0.150061i
$191$	3.86527	+	11.8961i	0.279681	+	0.860771i	0.987943	+	0.154820i	$0.0494799\pi$
$191$	3.86527	+	11.8961i	0.279681	+	0.860771i	−0.708261	+	0.705950i	$0.750520\pi$
$192$	−0.909805	−	1.25224i	−0.0656595	−	0.0903725i
$193$			18.1554i			1.30686i	0.756988	+	0.653429i	$0.226670\pi$
$193$			18.1554i			1.30686i	−0.756988	+	0.653429i	$0.773330\pi$
$194$	0.0766817	−	0.0557125i	0.00550542	−	0.00399992i
$195$	−0.715769	−	5.93152i	−0.0512573	−	0.424765i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	1.58924	−	2.18740i	0.113229	−	0.155846i	−0.748641	−	0.662975i	$-0.769293\pi$
$197$	1.58924	−	2.18740i	0.113229	−	0.155846i	0.861870	+	0.507129i	$0.169293\pi$
$198$	−3.38415	−	1.09958i	−0.240501	−	0.0781434i
$199$	4.61734			0.327314			0.163657	−	0.986517i	$-0.447671\pi$
$199$	4.61734			0.327314			0.163657	+	0.986517i	$0.447671\pi$
$200$	−4.98633	−	0.369543i	−0.352586	−	0.0261306i
$201$	15.8451			1.11763
$202$	3.57025	+	1.16004i	0.251202	+	0.0816205i
$203$	3.84215	−	5.28827i	0.269666	−	0.371164i
$204$	−3.38172	−	2.45696i	−0.236768	−	0.172022i
$205$	7.56747	+	8.14905i	0.528535	+	0.569155i
$206$	15.6332	−	11.3582i	1.08922	−	0.791361i
$207$			3.26464i			0.226908i
$208$	−1.01463	−	1.39652i	−0.0703522	−	0.0968315i
$209$	−2.47415	−	7.61464i	−0.171140	−	0.526715i
$210$	−3.02365	−	1.68427i	−0.208652	−	0.116226i
$211$	−7.70431	+	23.7114i	−0.530387	+	1.63236i	0.223024	+	0.974813i	$0.428407\pi$
$211$	−7.70431	+	23.7114i	−0.530387	+	1.63236i	−0.753411	+	0.657550i	$0.771593\pi$
$212$	−2.72365	+	0.884968i	−0.187061	+	0.0607799i
$213$	16.2278	−	5.27272i	1.11191	−	0.361281i
$214$	−3.84246	+	11.8259i	−0.262665	+	0.808400i
$215$	1.00165	+	2.15977i	0.0683121	+	0.147295i
$216$	1.72391	+	5.30566i	0.117297	+	0.361004i
$217$	−4.43892	−	6.10965i	−0.301334	−	0.414750i
$218$			13.2284i			0.895942i
$219$	14.4748	−	10.5165i	0.978114	−	0.710641i
$220$	6.40882	−	11.5053i	0.432082	−	0.775685i
$221$	−3.77137	−	2.74006i	−0.253690	−	0.184316i
$222$	0.156602	−	0.215544i	0.0105104	−	0.0144664i
$223$	−16.3215	−	5.30319i	−1.09297	−	0.355128i	−0.293578	−	0.955935i	$-0.594846\pi$
$223$	−16.3215	−	5.30319i	−1.09297	−	0.355128i	−0.799394	+	0.600807i	$0.794846\pi$
$224$	−1.00000			−0.0668153
$225$	2.79608	+	1.14325i	0.186405	+	0.0762167i
$226$	−20.4276			−1.35882
$227$	−2.91399	−	0.946813i	−0.193408	−	0.0628422i	0.210711	−	0.977548i	$-0.432422\pi$
$227$	−2.91399	−	0.946813i	−0.193408	−	0.0628422i	−0.404120	+	0.914706i	$0.632422\pi$
$228$	−1.23679	+	1.70230i	−0.0819085	+	0.112737i
$229$	10.6142	+	7.71168i	0.701407	+	0.509602i	0.880390	−	0.474250i	$-0.157281\pi$
$229$	10.6142	+	7.71168i	0.701407	+	0.509602i	−0.178983	+	0.983852i	$0.557281\pi$
$230$	−11.8561	−	2.33022i	−0.781769	−	0.153650i
$231$	7.37534	−	5.35850i	0.485262	−	0.352563i
$232$		−	6.53666i		−	0.429153i
$233$	−2.81174	−	3.87003i	−0.184203	−	0.253534i	0.706922	−	0.707292i	$-0.250083\pi$
$233$	−2.81174	−	3.87003i	−0.184203	−	0.253534i	−0.891125	+	0.453758i	$0.850083\pi$
$234$	0.322271	+	0.991847i	0.0210675	+	0.0648391i
$235$	−0.218213	+	1.11027i	−0.0142347	+	0.0724258i
$236$	0.0158173	−	0.0486806i	0.00102962	−	0.00316884i
$237$	1.17645	−	0.382253i	0.0764189	−	0.0248300i
$238$	−2.56837	+	0.834513i	−0.166482	+	0.0540934i
$239$	−6.47416	+	19.9254i	−0.418779	+	1.28887i	0.490048	+	0.871695i	$0.336979\pi$
$239$	−6.47416	+	19.9254i	−0.418779	+	1.28887i	−0.908827	+	0.417173i	$0.863021\pi$
$240$	−3.43617	+	0.414651i	−0.221804	+	0.0267656i
$241$	9.21283	+	28.3542i	0.593450	+	1.82645i	0.562294	+	0.826938i	$0.309919\pi$
$241$	9.21283	+	28.3542i	0.593450	+	1.82645i	0.0311567	+	0.999515i	$0.490081\pi$
$242$	13.9239	+	19.1647i	0.895065	+	1.23195i
$243$		−	6.17582i		−	0.396179i
$244$	−2.03808	+	1.48075i	−0.130475	+	0.0947954i
$245$	−2.02853	+	0.940783i	−0.129598	+	0.0601044i
$246$	6.22789	+	4.52482i	0.397075	+	0.288492i
$247$	−1.37930	+	1.89844i	−0.0877625	+	0.120795i
$248$	−7.18233	−	2.33368i	−0.456078	−	0.148189i
$249$	−16.8631			−1.06866
$250$	−6.14768	+	9.33842i	−0.388814	+	0.590613i
$251$	21.4284			1.35255			0.676275	−	0.736649i	$-0.263593\pi$
$251$	21.4284			1.35255			0.676275	+	0.736649i	$0.263593\pi$
$252$	0.574585	+	0.186694i	0.0361954	+	0.0117606i
$253$	18.7069	−	25.7478i	1.17609	−	1.61875i
$254$	6.68240	+	4.85504i	0.419291	+	0.304633i
$255$	−8.47932	+	3.93251i	−0.530996	+	0.246263i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			6.88046i			0.429192i	0.976703	+	0.214596i	$0.0688434\pi$
$257$			6.88046i			0.429192i	−0.976703	+	0.214596i	$0.931157\pi$
$258$	0.968669	+	1.33326i	0.0603067	+	0.0830050i
$259$	−0.0531902	−	0.163703i	−0.00330508	−	0.0101720i
$260$	−3.83209	+	0.462428i	−0.237656	+	0.0286785i
$261$	−1.22035	+	3.75586i	−0.0755380	+	0.232482i
$262$	17.4512	−	5.67023i	1.07814	−	0.350308i
$263$	−18.2068	+	5.91575i	−1.12268	+	0.364781i	−0.810790	−	0.585337i	$-0.800962\pi$
$263$	−18.2068	+	5.91575i	−1.12268	+	0.364781i	−0.311890	+	0.950118i	$0.600962\pi$
$264$	2.81713	−	8.67023i	0.173382	−	0.533616i
$265$	−1.23496	+	6.28348i	−0.0758632	+	0.385991i
$266$	0.420078	+	1.29287i	0.0257567	+	0.0792709i
$267$	−13.1770	−	18.1365i	−0.806416	−	1.10994i
$268$		−	10.2369i		−	0.625316i
$269$	−20.8174	+	15.1247i	−1.26926	+	0.922171i	−0.999173	−	0.0406649i	$-0.987052\pi$
$269$	−20.8174	+	15.1247i	−1.26926	+	0.922171i	−0.270087	+	0.962836i	$0.587052\pi$
$270$	12.2402	+	2.40570i	0.744913	+	0.146406i
$271$	−3.59299	−	2.61046i	−0.218259	−	0.158574i	0.473284	−	0.880910i	$-0.343069\pi$
$271$	−3.59299	−	2.61046i	−0.218259	−	0.158574i	−0.691542	+	0.722336i	$0.743069\pi$
$272$	−1.58734	+	2.18478i	−0.0962465	+	0.132472i
$273$	−2.54113	−	0.825662i	−0.153796	−	0.0499713i
$274$	−15.4220			−0.931679
$275$	−15.5013	−	25.0386i	−0.934763	−	1.50988i
$276$	−8.36406			−0.503457
$277$	−1.14528	−	0.372123i	−0.0688130	−	0.0223587i	0.274408	−	0.961613i	$-0.411518\pi$
$277$	−1.14528	−	0.372123i	−0.0688130	−	0.0223587i	−0.343221	+	0.939255i	$0.611518\pi$
$278$	−2.31661	+	3.18854i	−0.138941	+	0.191236i
$279$	3.69117	+	2.68179i	0.220985	+	0.160555i
$280$	−1.08814	+	1.95345i	−0.0650285	+	0.116741i
$281$	−9.98823	+	7.25688i	−0.595848	+	0.432909i	−0.844403	−	0.535709i	$-0.820044\pi$
$281$	−9.98823	+	7.25688i	−0.595848	+	0.432909i	0.248555	+	0.968618i	$0.420044\pi$
$282$			0.783253i			0.0466420i
$283$	−0.835507	−	1.14998i	−0.0496657	−	0.0683590i	0.783462	−	0.621440i	$-0.213452\pi$
$283$	−0.835507	−	1.14998i	−0.0496657	−	0.0683590i	−0.833128	+	0.553081i	$0.813452\pi$
$284$	−3.40648	−	10.4841i	−0.202137	−	0.622114i
$285$	1.97955	+	4.26834i	0.117259	+	0.252834i
$286$	3.14172	−	9.66922i	0.185774	−	0.571753i
$287$	4.72999	−	1.53687i	0.279202	−	0.0907183i
$288$	0.574585	−	0.186694i	0.0338577	−	0.0110010i
$289$	2.99965	−	9.23198i	0.176450	−	0.543058i
$290$	−12.7690	−	7.11277i	−0.749823	−	0.417676i
$291$	−0.0453363	−	0.139531i	−0.00265766	−	0.00817943i
$292$	−6.79427	−	9.35152i	−0.397605	−	0.547256i
$293$		−	11.6637i		−	0.681400i	−0.940172	−	0.340700i	$-0.889336\pi$
$293$		−	11.6637i		−	0.681400i	0.940172	−	0.340700i	$-0.110664\pi$
$294$	−1.25224	+	0.909805i	−0.0730320	+	0.0530609i
$295$	−0.0778837	−	0.0838694i	−0.00453457	−	0.00488307i
$296$	−0.139254	−	0.101174i	−0.00809396	−	0.00588061i
$297$	−19.3128	+	26.5819i	−1.12065	+	1.54244i
$298$	−5.51366	−	1.79150i	−0.319398	−	0.103779i
$299$	−9.32778			−0.539439
$300$	−2.92902	+	7.16359i	−0.169107	+	0.413590i
$301$	1.06470			0.0613683
$302$	17.0824	+	5.55041i	0.982982	+	0.319390i
$303$	3.41539	−	4.70088i	0.196209	−	0.270059i
$304$	1.09978	+	0.799037i	0.0630767	+	0.0458279i
$305$	0.674865	+	5.59254i	0.0386426	+	0.320228i
$306$	1.31995	−	0.958997i	0.0754563	−	0.0548222i
$307$			17.5958i			1.00425i	0.864796	+	0.502123i	$0.167447\pi$
$307$			17.5958i			1.00425i	−0.864796	+	0.502123i	$0.832553\pi$
$308$	−3.46189	−	4.76489i	−0.197260	−	0.271505i
$309$	−9.24276	−	28.4463i	−0.525802	−	1.61825i
$310$	−12.3741	+	11.4909i	−0.702800	+	0.652642i
$311$	−1.48936	+	4.58377i	−0.0844538	+	0.259922i	−0.984362	−	0.176157i	$-0.943633\pi$
$311$	−1.48936	+	4.58377i	−0.0844538	+	0.259922i	0.899908	+	0.436079i	$0.143633\pi$
$312$	−2.54113	+	0.825662i	−0.143863	+	0.0467439i
$313$	4.44712	−	1.44496i	0.251366	−	0.0816737i	−0.180624	−	0.983552i	$-0.557812\pi$
$313$	4.44712	−	1.44496i	0.251366	−	0.0816737i	0.431990	+	0.901879i	$0.357812\pi$
$314$	−3.43186	+	10.5622i	−0.193671	+	0.596059i
$315$	0.989923	−	0.919274i	0.0557759	−	0.0517952i
$316$	−0.246957	−	0.760056i	−0.0138924	−	0.0427565i
$317$	13.6156	+	18.7403i	0.764730	+	1.05256i	0.996806	+	0.0798631i	$0.0254483\pi$
$317$	13.6156	+	18.7403i	0.764730	+	1.05256i	−0.232076	+	0.972698i	$0.574552\pi$
$318$			4.43277i			0.248577i
$319$	31.1464	−	22.6292i	1.74387	−	1.26699i
$320$	0.267888	+	2.21996i	0.0149754	+	0.124100i
$321$	15.5709	+	11.3129i	0.869083	+	0.631426i
$322$	−3.17619	+	4.37165i	−0.177002	+	0.243622i
$323$	3.49144	+	1.13444i	0.194269	+	0.0631219i
$324$	6.82253			0.379030
$325$	−3.26651	+	7.98898i	−0.181193	+	0.443149i
$326$	−16.1040			−0.891917
$327$	19.4735	+	6.32732i	1.07689	+	0.349902i
$328$	2.92329	−	4.02357i	0.161412	−	0.222164i
$329$	0.409383	+	0.297434i	0.0225700	+	0.0163981i
$330$	−13.8714	−	14.9375i	−0.763597	−	0.822282i
$331$	−24.6014	+	17.8739i	−1.35221	+	0.982441i	−0.353316	+	0.935504i	$0.614946\pi$
$331$	−24.6014	+	17.8739i	−1.35221	+	0.982441i	−0.998898	+	0.0469364i	$0.985054\pi$
$332$			10.8945i			0.597915i
$333$	0.0611246	+	0.0841308i	0.00334961	+	0.00461034i
$334$	−6.71518	−	20.6672i	−0.367438	−	1.13086i
$335$	−19.9972	−	11.1391i	−1.09256	−	0.608594i
$336$	−0.478313	+	1.47209i	−0.0260941	+	0.0803093i
$337$	−1.42354	+	0.462537i	−0.0775453	+	0.0251960i	−0.347533	−	0.937668i	$-0.612980\pi$
$337$	−1.42354	+	0.462537i	−0.0775453	+	0.0251960i	0.269987	+	0.962864i	$0.412980\pi$
$338$	9.52982	−	3.09643i	0.518354	−	0.168423i
$339$	−9.77078	+	30.0714i	−0.530676	+	1.63325i
$340$	2.54062	+	5.47812i	0.137785	+	0.297093i
$341$	−13.7447	−	42.3019i	−0.744319	−	2.29078i
$342$	−0.482741	−	0.664437i	−0.0261037	−	0.0359286i
$343$			1.00000i			0.0539949i
$344$	0.861360	−	0.625815i	0.0464414	−	0.0337417i
$345$	−9.10123	+	16.3388i	−0.489994	+	0.879649i
$346$	20.2152	+	14.6872i	1.08678	+	0.789589i
$347$	13.2139	−	18.1874i	0.709361	−	0.976351i	−0.290450	−	0.956890i	$-0.593805\pi$
$347$	13.2139	−	18.1874i	0.709361	−	0.976351i	0.999811	−	0.0194612i	$-0.00619507\pi$
$348$	−9.62258	−	3.12657i	−0.515824	−	0.167602i
$349$	−21.5056			−1.15117			−0.575585	−	0.817742i	$-0.695225\pi$
$349$	−21.5056			−1.15117			−0.575585	+	0.817742i	$0.695225\pi$
$350$	2.63192	+	4.25123i	0.140682	+	0.227238i
$351$	9.62993			0.514008
$352$	−5.60146	−	1.82002i	−0.298559	−	0.0970076i
$353$	12.2163	−	16.8143i	0.650207	−	0.894933i	−0.348901	−	0.937159i	$-0.613445\pi$
$353$	12.2163	−	16.8143i	0.650207	−	0.894933i	0.999108	+	0.0422268i	$0.0134452\pi$
$354$	−0.0640969	−	0.0465691i	−0.00340671	−	0.00247512i
$355$	−24.1868	−	4.75370i	−1.28370	−	0.252300i
$356$	−11.7172	+	8.51306i	−0.621011	+	0.451191i
$357$			4.18004i			0.221231i
$358$	5.81133	+	7.99861i	0.307138	+	0.422740i
$359$	−8.94809	−	27.5394i	−0.472262	−	1.45347i	−0.849615	−	0.527404i	$-0.823165\pi$
$359$	−8.94809	−	27.5394i	−0.472262	−	1.45347i	0.377353	−	0.926070i	$-0.376835\pi$
$360$	0.260529	−	1.32557i	0.0137311	−	0.0698637i
$361$	−5.30027	+	16.3125i	−0.278961	+	0.858555i
$362$	−2.99365	+	0.972695i	−0.157343	+	0.0511237i
$363$	34.8722	−	11.3307i	1.83032	−	0.594706i
$364$	−0.533424	+	1.64171i	−0.0279590	+	0.0860491i
$365$	−25.6608	+	3.09655i	−1.34315	+	0.162081i
$366$	1.20497	+	3.70851i	0.0629846	+	0.193847i
$367$	−14.2775	−	19.6512i	−0.745277	−	1.02579i	−0.998298	−	0.0583253i	$-0.981424\pi$
$367$	−14.2775	−	19.6512i	−0.745277	−	1.02579i	0.253020	−	0.967461i	$-0.418576\pi$
$368$			5.40366i			0.281685i
$369$	−2.43085	+	1.76612i	−0.126545	+	0.0919405i
$370$	−0.349165	+	0.161934i	−0.0181522	+	0.00841856i
$371$	2.31688	+	1.68331i	0.120286	+	0.0873931i
$372$	−6.87079	+	9.45684i	−0.356234	+	0.490314i
$373$	3.86978	+	1.25737i	0.200370	+	0.0651041i	0.407483	−	0.913213i	$-0.366407\pi$
$373$	3.86978	+	1.25737i	0.200370	+	0.0651041i	−0.207113	+	0.978317i	$0.566407\pi$
$374$	−15.9054			−0.822450
$375$	10.8065	+	13.5167i	0.558046	+	0.697997i
$376$	0.506026			0.0260963
$377$	−10.7313	−	3.48681i	−0.552690	−	0.179580i
$378$	3.27908	−	4.51326i	0.168657	−	0.232137i
$379$	21.4787	+	15.6052i	1.10329	+	0.801585i	0.981593	−	0.190983i	$-0.0611676\pi$
$379$	21.4787	+	15.6052i	1.10329	+	0.801585i	0.121693	+	0.992568i	$0.461168\pi$
$380$	2.75759	−	1.27890i	0.141461	−	0.0656063i
$381$	10.3434	−	7.51489i	0.529906	−	0.385000i
$382$		−	12.5083i		−	0.639980i
$383$	−0.979215	−	1.34777i	−0.0500356	−	0.0688680i	0.783266	−	0.621687i	$-0.213552\pi$
$383$	−0.979215	−	1.34777i	−0.0500356	−	0.0688680i	−0.833302	+	0.552819i	$0.813552\pi$
$384$	0.478313	+	1.47209i	0.0244088	+	0.0751225i
$385$	−13.0750	+	1.57779i	−0.666362	+	0.0804114i
$386$	5.61034	−	17.2669i	0.285559	−	0.878860i
$387$	−0.611760	+	0.198773i	−0.0310975	+	0.0101042i
$388$	−0.0901447	+	0.0292898i	−0.00457640	+	0.00148696i
$389$	6.70973	−	20.6504i	0.340197	−	1.04702i	−0.623909	−	0.781497i	$-0.714456\pi$
$389$	6.70973	−	20.6504i	0.340197	−	1.04702i	0.964105	−	0.265520i	$-0.0855437\pi$
$390$	−1.15220	+	5.86239i	−0.0583440	+	0.296854i
$391$	4.50942	+	13.8786i	0.228051	+	0.701869i
$392$	0.587785	+	0.809017i	0.0296876	+	0.0408615i
$393$		−	28.4019i		−	1.43269i
$394$	−2.18740	+	1.58924i	−0.110200	+	0.0800648i
$395$	−1.75345	−	0.344626i	−0.0882257	−	0.0173400i
$396$	2.87873	+	2.09152i	0.144661	+	0.105103i
$397$	17.7500	−	24.4307i	0.890845	−	1.22614i	−0.0824519	−	0.996595i	$-0.526275\pi$
$397$	17.7500	−	24.4307i	0.890845	−	1.22614i	0.973297	−	0.229548i	$-0.0737249\pi$
$398$	−4.39135	−	1.42684i	−0.220119	−	0.0715208i
$399$	2.10415			0.105339
$400$	4.62808	+	1.89232i	0.231404	+	0.0946158i
$401$	28.2131			1.40890			0.704448	−	0.709756i	$-0.251195\pi$
$401$	28.2131			1.40890			0.704448	+	0.709756i	$0.251195\pi$
$402$	−15.0696	−	4.89642i	−0.751605	−	0.244211i
$403$	−7.66246	+	10.5465i	−0.381694	+	0.525357i
$404$	−3.03704	−	2.20654i	−0.151098	−	0.109779i
$405$	7.42384	−	13.3275i	0.368894	−	0.662247i
$406$	−5.28827	+	3.84215i	−0.262452	+	0.190683i
$407$		−	1.01378i		−	0.0502513i
$408$	2.45696	+	3.38172i	0.121638	+	0.167420i
$409$	4.35127	+	13.3918i	0.215156	+	0.662183i	0.999142	+	0.0414049i	$0.0131834\pi$
$409$	4.35127	+	13.3918i	0.215156	+	0.662183i	−0.783986	+	0.620778i	$0.786817\pi$
$410$	−4.67889	−	10.0887i	−0.231074	−	0.498245i
$411$	−7.37655	+	22.7027i	−0.363858	+	1.11984i
$412$	−18.3779	+	5.97134i	−0.905414	+	0.294187i
$413$	−0.0486806	+	0.0158173i	−0.00239542	+	0.000778318i
$414$	1.00883	−	3.10486i	0.0495813	−	0.152595i
$415$	21.2819	+	11.8547i	1.04469	+	0.581925i
$416$	0.533424	+	1.64171i	0.0261533	+	0.0804915i
$417$	3.58577	+	4.93539i	0.175596	+	0.241687i
$418$			8.00650i			0.391611i
$419$	7.95267	−	5.77795i	0.388513	−	0.282271i	−0.376333	−	0.926485i	$-0.622815\pi$
$419$	7.95267	−	5.77795i	0.388513	−	0.282271i	0.764846	+	0.644213i	$0.222815\pi$
$420$	2.35519	+	2.53620i	0.114922	+	0.123754i
$421$	−11.6072	−	8.43309i	−0.565698	−	0.411004i	0.267842	−	0.963463i	$-0.413690\pi$
$421$	−11.6072	−	8.43309i	−0.565698	−	0.411004i	−0.833540	+	0.552459i	$0.813690\pi$
$422$	14.6545	−	20.1702i	0.713369	−	0.981868i
$423$	−0.290755	−	0.0944719i	−0.0141370	−	0.00459338i
$424$	2.86382			0.139079
$425$	13.4658	+	0.997966i	0.653186	+	0.0484085i
$426$	−17.0629			−0.826699
$427$	2.39591	+	0.778477i	0.115946	+	0.0376731i
$428$	7.30879	−	10.0597i	0.353284	−	0.486253i
$429$	−12.7313	−	9.24982i	−0.614672	−	0.446586i
$430$	−0.285220	−	2.36359i	−0.0137545	−	0.113983i
$431$	24.0923	−	17.5041i	1.16049	−	0.843142i	0.170647	−	0.985332i	$-0.445414\pi$
$431$	24.0923	−	17.5041i	1.16049	−	0.843142i	0.989839	+	0.142190i	$0.0454143\pi$
$432$		−	5.57870i		−	0.268405i
$433$	8.26317	+	11.3733i	0.397102	+	0.546565i	0.960014	−	0.279953i	$-0.0903188\pi$
$433$	8.26317	+	11.3733i	0.397102	+	0.546565i	−0.562911	+	0.826517i	$0.690319\pi$
$434$	2.33368	+	7.18233i	0.112020	+	0.344763i
$435$	−16.5783	+	15.3951i	−0.794867	+	0.738138i
$436$	4.08781	−	12.5810i	0.195771	−	0.602520i
$437$	6.98622	−	2.26996i	0.334196	−	0.108587i
$438$	−17.0161	+	5.52887i	−0.813061	+	0.264179i
$439$	2.01681	−	6.20712i	0.0962573	−	0.296249i	−0.891322	−	0.453371i	$-0.850221\pi$
$439$	2.01681	−	6.20712i	0.0962573	−	0.296249i	0.987579	+	0.157121i	$0.0502214\pi$
$440$	−9.65047	+	8.96173i	−0.460068	+	0.427234i
$441$	−0.186694	−	0.574585i	−0.00889019	−	0.0273612i
$442$	2.74006	+	3.77137i	0.130331	+	0.179386i
$443$			37.8514i			1.79837i	0.437565	+	0.899187i	$0.355841\pi$
$443$			37.8514i			1.79837i	−0.437565	+	0.899187i	$0.644159\pi$
$444$	−0.215544	+	0.156602i	−0.0102293	+	0.00743200i
$445$	3.87990	+	32.1523i	0.183925	+	1.52417i
$446$	13.8839	+	10.0873i	0.657423	+	0.477646i
$447$	−5.27450	+	7.25973i	−0.249475	+	0.343373i
$448$	0.951057	+	0.309017i	0.0449332	+	0.0145997i
$449$	9.08806			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$449$	9.08806			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$450$	−2.30594	−	1.95133i	−0.108703	−	0.0919866i
$451$	29.2920			1.37930
$452$	19.4278	+	6.31248i	0.913807	+	0.296914i
$453$	16.3415	−	22.4921i	0.767789	−	1.05677i
$454$	2.47879	+	1.80095i	0.116335	+	0.0845226i
$455$	2.62656	+	2.82842i	0.123135	+	0.132598i
$456$	1.70230	−	1.23679i	0.0797173	−	0.0579180i
$457$			17.9428i			0.839328i	0.907680	+	0.419664i	$0.137852\pi$
$457$			17.9428i			0.839328i	−0.907680	+	0.419664i	$0.862148\pi$
$458$	−7.71168	−	10.6142i	−0.360343	−	0.495970i
$459$	−4.65549	−	14.3281i	−0.217300	−	0.668780i
$460$	10.5558	+	5.87991i	0.492165	+	0.274152i
$461$	6.38006	−	19.6358i	0.297149	−	0.914531i	−0.685342	−	0.728221i	$-0.740347\pi$
$461$	6.38006	−	19.6358i	0.297149	−	0.914531i	0.982491	−	0.186310i	$-0.0596528\pi$
$462$	−8.67023	+	2.81713i	−0.403376	+	0.131065i
$463$	−28.5549	+	9.27806i	−1.32706	+	0.431188i	−0.884914	−	0.465754i	$-0.845783\pi$
$463$	−28.5549	+	9.27806i	−1.32706	+	0.431188i	−0.442147	+	0.896943i	$0.645783\pi$
$464$	−2.01994	+	6.21673i	−0.0937733	+	0.288605i
$465$	10.9971	+	23.7121i	0.509978	+	1.09962i
$466$	1.47822	+	4.54949i	0.0684772	+	0.210751i
$467$	−9.15701	−	12.6035i	−0.423736	−	0.583222i	0.542765	−	0.839884i	$-0.317377\pi$
$467$	−9.15701	−	12.6035i	−0.423736	−	0.583222i	−0.966501	+	0.256662i	$0.917377\pi$
$468$		−	1.04289i		−	0.0482076i
$469$	−8.28179	+	6.01707i	−0.382418	+	0.277843i
$470$	0.550625	−	0.988495i	0.0253984	−	0.0455959i
$471$	13.9070	+	10.1041i	0.640802	+	0.465570i
$472$	−0.0300863	+	0.0414102i	−0.00138483	+	0.00190606i
$473$	5.96387	+	1.93778i	0.274219	+	0.0890992i
$474$	−1.23700			−0.0568171
$475$	0.502358	−	6.77842i	0.0230498	−	0.311015i
$476$	2.70054			0.123779
$477$	−1.64551	−	0.534657i	−0.0753426	−	0.0244803i
$478$	12.3146	−	16.9496i	0.563256	−	0.775256i
$479$	7.72923	+	5.61562i	0.353158	+	0.256584i	0.750193	−	0.661219i	$-0.229961\pi$
$479$	7.72923	+	5.61562i	0.353158	+	0.256584i	−0.397035	+	0.917804i	$0.629961\pi$
$480$	3.39613	+	0.667480i	0.155011	+	0.0304661i
$481$	−0.240379	+	0.174646i	−0.0109604	+	0.00796317i
$482$		−	29.8133i		−	1.35796i
$483$	4.91627	+	6.76667i	0.223698	+	0.307894i
$484$	−7.32025	−	22.5294i	−0.332739	−	1.02406i
$485$	−0.0408736	+	0.207964i	−0.00185597	+	0.00944317i
$486$	−1.90843	+	5.87355i	−0.0865683	+	0.266430i
$487$	38.1741	−	12.4035i	1.72983	−	0.562057i	0.736407	−	0.676539i	$-0.236521\pi$
$487$	38.1741	−	12.4035i	1.72983	−	0.562057i	0.993425	+	0.114482i	$0.0365208\pi$
$488$	2.39591	−	0.778477i	0.108458	−	0.0352400i
$489$	−7.70273	+	23.7066i	−0.348330	+	1.07205i
$490$	2.21996	−	0.267888i	0.100288	−	0.0121019i
$491$	−2.48259	−	7.64063i	−0.112038	−	0.344817i	0.879280	−	0.476305i	$-0.158024\pi$
$491$	−2.48259	−	7.64063i	−0.112038	−	0.344817i	−0.991318	+	0.131489i	$0.958024\pi$
$492$	−4.52482	−	6.22789i	−0.203995	−	0.280775i
$493$			17.6525i			0.795029i
$494$	1.89844	−	1.37930i	0.0854147	−	0.0620574i
$495$	7.21811	−	3.34759i	0.324430	−	0.150463i
$496$	6.10965	+	4.43892i	0.274331	+	0.199314i
$497$	−6.47950	+	8.91827i	−0.290645	+	0.400039i
$498$	16.0378	+	5.21099i	0.718670	+	0.233510i
$499$	−15.0653			−0.674414			−0.337207	−	0.941431i	$-0.609482\pi$
$499$	−15.0653			−0.674414			−0.337207	+	0.941431i	$0.609482\pi$
$500$	8.73252	−	6.98162i	0.390530	−	0.312228i
$501$	−33.6360			−1.50275
$502$	−20.3796	−	6.62174i	−0.909588	−	0.295543i
$503$	−2.72805	+	3.75484i	−0.121638	+	0.167420i	−0.865493	−	0.500920i	$-0.832995\pi$
$503$	−2.72805	+	3.75484i	−0.121638	+	0.167420i	0.743856	+	0.668340i	$0.232995\pi$
$504$	−0.488771	−	0.355113i	−0.0217716	−	0.0158180i
$505$	−7.61506	+	3.53168i	−0.338866	+	0.157158i
$506$	−25.7478	+	18.7069i	−1.14463	+	0.831622i
$507$		−	15.5099i		−	0.688817i
$508$	−4.85504	−	6.68240i	−0.215408	−	0.296483i
$509$	−8.16840	−	25.1398i	−0.362058	−	1.11430i	−0.951803	−	0.306711i	$-0.900772\pi$
$509$	−8.16840	−	25.1398i	−0.362058	−	1.11430i	0.589745	−	0.807590i	$-0.299228\pi$
$510$	9.27953	−	1.11978i	0.410904	−	0.0495848i
$511$	−3.57196	+	10.9934i	−0.158014	+	0.486318i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−7.21252	+	2.34349i	−0.318441	+	0.103468i
$514$	2.12618	−	6.54371i	0.0937818	−	0.288631i
$515$	−8.33294	+	42.3979i	−0.367193	+	1.86828i
$516$	−0.509259	−	1.56734i	−0.0224189	−	0.0689982i
$517$	1.75181	+	2.41115i	0.0770444	+	0.106042i
$518$			0.172127i			0.00756283i
$519$	31.2902	−	22.7336i	1.37349	−	0.997895i
$520$	3.78744	+	0.744388i	0.166090	+	0.0326436i
$521$	−5.16811	−	3.75485i	−0.226419	−	0.164503i	0.468792	−	0.883308i	$-0.344689\pi$
$521$	−5.16811	−	3.75485i	−0.226419	−	0.164503i	−0.695211	+	0.718805i	$0.744689\pi$
$522$	2.32125	−	3.19493i	0.101598	−	0.139838i
$523$	−13.9641	−	4.53720i	−0.610606	−	0.198398i	−0.0126410	−	0.999920i	$-0.504024\pi$
$523$	−13.9641	−	4.53720i	−0.610606	−	0.198398i	−0.597965	+	0.801522i	$0.704024\pi$
$524$	−18.3492			−0.801590
$525$	7.51710	−	1.84102i	0.328073	−	0.0803487i
$526$	19.1438			0.834708
$527$	19.3962	+	6.30220i	0.844910	+	0.274528i
$528$	−5.35850	+	7.37534i	−0.233199	+	0.320970i
$529$	5.01550	+	3.64397i	0.218065	+	0.158434i
$530$	3.11622	−	5.59432i	0.135360	−	0.243002i
$531$	0.0250182	−	0.0181768i	0.00108570	−	0.000788804i
$532$		−	1.35940i		−	0.0589376i
$533$	−5.04618	−	6.94547i	−0.218574	−	0.300842i
$534$	6.92753	+	21.3208i	0.299784	+	0.922639i
$535$	−11.6981	−	25.2236i	−0.505754	−	1.09051i
$536$	−3.16336	+	9.73583i	−0.136636	+	0.420524i
$537$	14.5543	−	4.72899i	0.628066	−	0.204071i
$538$	24.4723	−	7.95154i	1.05508	−	0.342815i
$539$	−1.82002	+	5.60146i	−0.0783940	+	0.241272i
$540$	−10.8977	−	6.07038i	−0.468962	−	0.261228i
$541$	0.747791	+	2.30146i	0.0321500	+	0.0989476i	0.965844	−	0.259125i	$-0.0834341\pi$
$541$	0.747791	+	2.30146i	0.0321500	+	0.0989476i	−0.933694	+	0.358072i	$0.883434\pi$
$542$	2.61046	+	3.59299i	0.112129	+	0.154332i
$543$			4.87218i			0.209085i
$544$	2.18478	−	1.58734i	0.0936718	−	0.0680565i
$545$	−20.1282	−	21.6751i	−0.862198	−	0.928461i
$546$	2.16161	+	1.57050i	0.0925084	+	0.0672113i
$547$	1.84443	−	2.53864i	0.0788620	−	0.108544i	−0.767764	−	0.640733i	$-0.778630\pi$
$547$	1.84443	−	2.53864i	0.0788620	−	0.108544i	0.846626	+	0.532189i	$0.178630\pi$
$548$	14.6672	+	4.76567i	0.626553	+	0.203579i
$549$	−1.52199			−0.0649569
$550$	7.00525	+	28.6033i	0.298705	+	1.21965i
$551$	8.88595			0.378554
$552$	7.95469	+	2.58464i	0.338574	+	0.110009i
$553$	−0.469740	+	0.646542i	−0.0199754	+	0.0274938i
$554$	0.974231	+	0.707820i	0.0413911	+	0.0300724i
$555$	0.0713727	+	0.591459i	0.00302960	+	0.0251060i
$556$	3.18854	−	2.31661i	0.135224	−	0.0982462i
$557$		−	2.62814i		−	0.111358i	−0.998449	−	0.0556789i	$-0.982268\pi$
$557$		−	2.62814i		−	0.111358i	0.998449	−	0.0556789i	$-0.0177323\pi$
$558$	−2.68179	−	3.69117i	−0.113529	−	0.156260i
$559$	−0.567937	−	1.74793i	−0.0240212	−	0.0739295i
$560$	1.63853	−	1.52159i	0.0692404	−	0.0642988i
$561$	−7.60777	+	23.4143i	−0.321200	+	0.988553i
$562$	11.7419	−	3.81517i	0.495301	−	0.160933i
$563$	26.6951	−	8.67377i	1.12507	−	0.365556i	0.313367	−	0.949632i	$-0.398543\pi$
$563$	26.6951	−	8.67377i	1.12507	−	0.365556i	0.811699	+	0.584076i	$0.198543\pi$
$564$	0.242038	−	0.744918i	0.0101917	−	0.0313667i
$565$	33.4712	−	31.0824i	1.40814	−	1.30765i
$566$	0.439252	+	1.35188i	0.0184631	+	0.0568237i
$567$	−4.01019	−	5.51955i	−0.168412	−	0.231799i
$568$			11.0236i			0.462540i
$569$	−22.4666	+	16.3229i	−0.941848	+	0.684293i	−0.948865	−	0.315683i	$-0.897767\pi$
$569$	−22.4666	+	16.3229i	−0.941848	+	0.684293i	0.00701656	+	0.999975i	$0.497767\pi$
$570$	−0.563677	−	4.67114i	−0.0236099	−	0.195653i
$571$	−4.56707	−	3.31817i	−0.191126	−	0.138861i	0.488107	−	0.872784i	$-0.337688\pi$
$571$	−4.56707	−	3.31817i	−0.191126	−	0.138861i	−0.679233	+	0.733922i	$0.737688\pi$
$572$	−5.97591	+	8.22513i	−0.249865	+	0.343910i
$573$	−18.4134	−	5.98287i	−0.769230	−	0.249938i
$574$	−4.97340			−0.207586
$575$	22.9722	−	14.2220i	0.958007	−	0.593098i
$576$	−0.604154			−0.0251731
$577$	−6.64792	−	2.16004i	−0.276757	−	0.0899237i	0.167350	−	0.985898i	$-0.446479\pi$
$577$	−6.64792	−	2.16004i	−0.276757	−	0.0899237i	−0.444107	+	0.895974i	$0.646479\pi$
$578$	−5.70568	+	7.85320i	−0.237325	+	0.326650i
$579$	−22.7349	−	16.5179i	−0.944832	−	0.686461i
$580$	9.94610	+	10.7105i	0.412989	+	0.444729i
$581$	8.81386	−	6.40364i	0.365660	−	0.265668i
$582$			0.146711i			0.00608138i
$583$	9.91423	+	13.6458i	0.410605	+	0.565150i
$584$	3.57196	+	10.9934i	0.147809	+	0.454909i
$585$	−2.03723	−	1.13481i	−0.0842291	−	0.0469184i
$586$	−3.60428	+	11.0928i	−0.148891	+	0.458241i
$587$	−10.2348	+	3.32550i	−0.422437	+	0.137258i	−0.512518	−	0.858676i	$-0.671287\pi$
$587$	−10.2348	+	3.32550i	−0.422437	+	0.137258i	0.0900811	+	0.995934i	$0.471287\pi$
$588$	1.47209	−	0.478313i	0.0607082	−	0.0197253i
$589$	3.17241	−	9.76367i	0.130717	−	0.402305i
$590$	0.0481548	+	0.103832i	0.00198250	+	0.00427469i
$591$	1.29325	+	3.98022i	0.0531973	+	0.163724i
$592$	0.101174	+	0.139254i	0.00415822	+	0.00572329i
$593$			31.8286i			1.30704i	0.756907	+	0.653522i	$0.226709\pi$
$593$			31.8286i			1.30704i	−0.756907	+	0.653522i	$0.773291\pi$
$594$	26.5819	−	19.3128i	1.09067	−	0.792416i
$595$	2.93855	−	5.27537i	0.120469	−	0.216269i
$596$	4.69020	+	3.40763i	0.192118	+	0.139582i
$597$	−4.20088	+	5.78201i	−0.171930	+	0.236642i
$598$	8.87124	+	2.88244i	0.362772	+	0.117872i
$599$	−21.4371			−0.875897			−0.437949	−	0.899000i	$-0.644295\pi$
$599$	−21.4371			−0.875897			−0.437949	+	0.899000i	$0.644295\pi$
$600$	4.99934	−	5.90786i	0.204097	−	0.241187i
$601$	−29.7150			−1.21210			−0.606050	−	0.795427i	$-0.707247\pi$
$601$	−29.7150			−1.21210			−0.606050	+	0.795427i	$0.707247\pi$
$602$	−1.01259	−	0.329010i	−0.0412701	−	0.0134095i
$603$	3.63524	−	5.00348i	0.148038	−	0.203757i
$604$	−14.5312	−	10.5575i	−0.591265	−	0.429579i
$605$	−51.9755	−	10.2153i	−2.11310	−	0.415312i
$606$	−4.70088	+	3.41539i	−0.190960	+	0.138741i
$607$			14.9591i			0.607172i	0.952804	+	0.303586i	$0.0981840\pi$
$607$			14.9591i			0.607172i	−0.952804	+	0.303586i	$0.901816\pi$
$608$	−0.799037	−	1.09978i	−0.0324052	−	0.0446020i
$609$	3.12657	+	9.62258i	0.126695	+	0.389927i
$610$	1.08636	−	5.52737i	0.0439853	−	0.223797i
$611$	0.269926	−	0.830748i	0.0109201	−	0.0336085i
$612$	−1.55169	+	0.504174i	−0.0627233	+	0.0203800i
$613$	−1.67063	+	0.542821i	−0.0674761	+	0.0219243i	−0.342561	−	0.939496i	$-0.611294\pi$
$613$	−1.67063	+	0.542821i	−0.0674761	+	0.0219243i	0.275084	+	0.961420i	$0.411294\pi$
$614$	5.43740	−	16.7346i	0.219436	−	0.675354i
$615$	−17.0895	+	2.06223i	−0.689114	+	0.0831570i
$616$	1.82002	+	5.60146i	0.0733309	+	0.225689i
$617$	13.0660	+	17.9838i	0.526017	+	0.724001i	0.986517	−	0.163659i	$-0.0523298\pi$
$617$	13.0660	+	17.9838i	0.526017	+	0.724001i	−0.460500	+	0.887660i	$0.652330\pi$
$618$			29.9102i			1.20316i
$619$	35.6300	−	25.8867i	1.43209	−	1.04047i	0.442466	−	0.896785i	$-0.354104\pi$
$619$	35.6300	−	25.8867i	1.43209	−	1.04047i	0.989623	−	0.143688i	$-0.0458962\pi$
$620$	15.3193	−	7.10474i	0.615239	−	0.285333i
$621$	−24.3881	−	17.7190i	−0.978661	−	0.711039i
$622$	2.83293	−	3.89919i	0.113590	−	0.156343i
$623$	13.7744	+	4.47558i	0.551860	+	0.179310i
$624$	2.67190			0.106962
$625$	−4.13607	−	24.6555i	−0.165443	−	0.986219i
$626$	−4.67597			−0.186889
$627$	11.7863	+	3.82961i	0.470701	+	0.152940i
$628$	6.52779	−	8.98473i	0.260487	−	0.358530i
$629$	0.376060	+	0.273224i	0.0149945	+	0.0108941i
$630$	−1.22554	+	0.568378i	−0.0488268	+	0.0226447i
$631$	19.8285	−	14.4063i	0.789362	−	0.573505i	−0.118412	−	0.992965i	$-0.537780\pi$
$631$	19.8285	−	14.4063i	0.789362	−	0.573505i	0.907774	+	0.419460i	$0.137780\pi$
$632$			0.799170i			0.0317893i
$633$	−22.6830	−	31.2204i	−0.901567	−	1.24090i
$634$	−7.15816	−	22.0306i	−0.284287	−	0.874945i
$635$	−18.3367	+	2.21273i	−0.727668	+	0.0878094i
$636$	1.36980	−	4.21581i	0.0543161	−	0.167168i
$637$	1.64171	−	0.533424i	0.0650470	−	0.0211350i
$638$	−36.6148	+	11.8969i	−1.44959	+	0.471002i
$639$	2.05804	−	6.33399i	0.0814147	−	0.250569i
$640$	0.431230	−	2.19409i	0.0170459	−	0.0867291i
$641$	−15.1636	−	46.6687i	−0.598926	−	1.84330i	−0.534124	−	0.845406i	$-0.679359\pi$
$641$	−15.1636	−	46.6687i	−0.598926	−	1.84330i	−0.0648015	−	0.997898i	$-0.520641\pi$
$642$	−11.3129	−	15.5709i	−0.446485	−	0.614534i
$643$		−	15.1507i		−	0.597484i	−0.954334	−	0.298742i	$-0.903433\pi$
$643$		−	15.1507i		−	0.597484i	0.954334	−	0.298742i	$-0.0965669\pi$
$644$	4.37165	−	3.17619i	0.172267	−	0.125159i
$645$	−3.61586	−	0.710666i	−0.142374	−	0.0279824i
$646$	−2.97000	−	2.15783i	−0.116853	−	0.0848987i
$647$	−12.5830	+	17.3190i	−0.494687	+	0.680879i	−0.981244	−	0.192770i	$-0.938253\pi$
$647$	−12.5830	+	17.3190i	−0.494687	+	0.680879i	0.486557	+	0.873649i	$0.338253\pi$
$648$	−6.48862	−	2.10828i	−0.254897	−	0.0828210i
$649$	−0.301470			−0.0118337
$650$	5.57537	−	6.58857i	0.218684	−	0.258425i
$651$	11.6893			0.458140
$652$	15.3158	+	4.97640i	0.599813	+	0.194891i
$653$	−2.06490	+	2.84208i	−0.0808056	+	0.111219i	−0.847506	−	0.530785i	$-0.821897\pi$
$653$	−2.06490	+	2.84208i	−0.0808056	+	0.111219i	0.766701	+	0.642005i	$0.221897\pi$
$654$	−16.5651	−	12.0353i	−0.647749	−	0.470617i
$655$	−19.9665	+	35.8443i	−0.780154	+	1.40055i
$656$	−4.02357	+	2.92329i	−0.157094	+	0.114135i
$657$		−	6.98349i		−	0.272452i
$658$	−0.297434	−	0.409383i	−0.0115952	−	0.0159594i
$659$	9.48942	+	29.2054i	0.369655	+	1.13768i	0.947014	+	0.321192i	$0.104083\pi$
$659$	9.48942	+	29.2054i	0.369655	+	1.13768i	−0.577359	+	0.816491i	$0.695917\pi$
$660$	8.57657	+	18.4929i	0.333843	+	0.719836i
$661$	−1.44977	+	4.46192i	−0.0563893	+	0.173549i	−0.975284	−	0.220954i	$-0.929083\pi$
$661$	−1.44977	+	4.46192i	−0.0563893	+	0.173549i	0.918895	+	0.394502i	$0.129083\pi$
$662$	28.9206	−	9.39689i	1.12403	−	0.365220i
$663$	6.86241	−	2.22973i	0.266514	−	0.0865957i
$664$	3.36659	−	10.3613i	0.130649	−	0.402097i
$665$	−2.65552	−	1.47921i	−0.102977	−	0.0573615i
$666$	−0.0321351	−	0.0989016i	−0.00124521	−	0.00383236i
$667$	20.7617	+	28.5760i	0.803895	+	1.10647i
$668$			21.7308i			0.840789i
$669$	21.4903	−	15.6136i	0.830862	−	0.603657i
$670$	15.5763	+	16.7734i	0.601764	+	0.648012i
$671$	12.0037	+	8.72121i	0.463399	+	0.336679i
$672$	0.909805	−	1.25224i	0.0350965	−	0.0483062i
$673$	−23.4225	−	7.61043i	−0.902870	−	0.293360i	−0.179449	−	0.983767i	$-0.557432\pi$
$673$	−23.4225	−	7.61043i	−0.902870	−	0.293360i	−0.723421	+	0.690407i	$0.757432\pi$
$674$	1.49680			0.0576547
$675$	−23.7163	+	14.6827i	−0.912843	+	0.565137i
$676$	−10.0202			−0.385394
$677$	24.9335	+	8.10137i	0.958271	+	0.311361i	0.746072	−	0.665866i	$-0.231938\pi$
$677$	24.9335	+	8.10137i	0.958271	+	0.311361i	0.212199	+	0.977227i	$0.431938\pi$
$678$	18.5851	−	25.5802i	0.713758	−	0.982403i
$679$	0.0766817	+	0.0557125i	0.00294277	+	0.00213805i
$680$	−0.723442	−	5.99510i	−0.0277427	−	0.229902i
$681$	3.83680	−	2.78760i	0.147026	−	0.106821i
$682$			44.4789i			1.70318i
$683$	7.18673	+	9.89168i	0.274992	+	0.378495i	0.924067	−	0.382230i	$-0.124844\pi$
$683$	7.18673	+	9.89168i	0.274992	+	0.378495i	−0.649075	+	0.760725i	$0.724844\pi$
$684$	0.253792	+	0.781092i	0.00970399	+	0.0298658i
$685$	25.2694	−	23.4660i	0.965495	−	0.896589i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−19.3137	+	6.27541i	−0.736864	+	0.239422i
$688$	−1.01259	+	0.329010i	−0.0386046	+	0.0125434i
$689$	1.52763	−	4.70156i	0.0581981	−	0.179115i
$690$	13.7047	−	12.7266i	0.521730	−	0.484495i
$691$	−1.63903	−	5.04440i	−0.0623515	−	0.191898i	0.915028	−	0.403389i	$-0.132168\pi$
$691$	−1.63903	−	5.04440i	−0.0623515	−	0.191898i	−0.977380	+	0.211491i	$0.932168\pi$
$692$	−14.6872	−	20.2152i	−0.558324	−	0.768467i
$693$		−	3.55830i		−	0.135169i
$694$	−18.1874	+	13.2139i	−0.690385	+	0.501594i
$695$	−1.05581	−	8.74944i	−0.0400493	−	0.331885i
$696$	8.18546	+	5.94708i	0.310269	+	0.225424i
$697$	−7.89447	+	10.8658i	−0.299024	+	0.411572i
$698$	20.4531	+	6.64560i	0.774160	+	0.251540i
$699$	7.40433			0.280058
$700$	−1.18940	−	4.85647i	−0.0449552	−	0.183557i
$701$	23.0262			0.869689			0.434844	−	0.900506i	$-0.356803\pi$
$701$	23.0262			0.869689			0.434844	+	0.900506i	$0.356803\pi$
$702$	−9.15861	−	2.97581i	−0.345669	−	0.112315i
$703$	0.137536	−	0.189302i	0.00518726	−	0.00713966i
$704$	4.76489	+	3.46189i	0.179583	+	0.130475i
$705$	−1.19179	−	1.28338i	−0.0448853	−	0.0483349i
$706$	−16.8143	+	12.2163i	−0.632813	+	0.459766i
$707$			3.75398i			0.141183i
$708$	0.0465691	+	0.0640969i	0.00175017	+	0.00240891i
$709$	6.54337	+	20.1384i	0.245741	+	0.756314i	0.995514	+	0.0946183i	$0.0301630\pi$
$709$	6.54337	+	20.1384i	0.245741	+	0.756314i	−0.749772	+	0.661696i	$0.769837\pi$
$710$	21.5340	+	11.9952i	0.808157	+	0.450170i
$711$	0.149200	−	0.459191i	0.00559544	−	0.0172210i
$712$	13.7744	−	4.47558i	0.516218	−	0.167729i
$713$	38.8108	−	12.6104i	1.45348	−	0.472263i
$714$	1.29170	−	3.97545i	0.0483407	−	0.148778i
$715$	9.56477	+	20.6237i	0.357702	+	0.771282i
$716$	−3.05520	−	9.40293i	−0.114178	−	0.351404i
$717$	−19.0612	−	26.2354i	−0.711852	−	0.979781i
$718$			28.9566i			1.08065i
$719$	−40.9359	+	29.7417i	−1.52665	+	1.10918i	−0.568590	+	0.822621i	$0.692511\pi$
$719$	−40.9359	+	29.7417i	−1.52665	+	1.10918i	−0.958063	+	0.286557i	$0.907489\pi$
$720$	−0.657402	+	1.18018i	−0.0244999	+	0.0439829i
$721$	15.6332	+	11.3582i	0.582210	+	0.423000i
$722$	10.0817	−	13.8763i	0.375202	−	0.516422i
$723$	−43.8880	−	14.2601i	−1.63221	−	0.530338i
$724$	3.14771			0.116984
$725$	31.7451	−	7.77472i	1.17898	−	0.288746i
$726$	−36.6668			−1.36083
$727$	−28.4973	−	9.25932i	−1.05691	−	0.343409i	−0.271530	−	0.962430i	$-0.587530\pi$
$727$	−28.4973	−	9.25932i	−1.05691	−	0.343409i	−0.785375	+	0.619021i	$0.787530\pi$
$728$	1.01463	−	1.39652i	0.0376048	−	0.0517586i
$729$	24.2922	+	17.6493i	0.899712	+	0.653679i
$730$	25.3618	+	4.98463i	0.938681	+	0.184489i
$731$	−2.32614	+	1.69004i	−0.0860353	+	0.0625083i
$732$		−	3.89936i		−	0.144124i
$733$	−11.9257	−	16.4144i	−0.440487	−	0.606278i	0.529833	−	0.848102i	$-0.322254\pi$
$733$	−11.9257	−	16.4144i	−0.440487	−	0.606278i	−0.970320	+	0.241824i	$0.922254\pi$
$734$	7.50610	+	23.1014i	0.277055	+	0.852689i
$735$	0.667480	−	3.39613i	0.0246204	−	0.125268i
$736$	1.66982	−	5.13918i	0.0615504	−	0.189433i
$737$	−57.3413	+	18.6313i	−2.11220	+	0.686294i
$738$	2.85764	−	0.928504i	0.105191	−	0.0341787i
$739$	−1.23309	+	3.79507i	−0.0453601	+	0.139604i	−0.971172	−	0.238382i	$-0.923383\pi$
$739$	−1.23309	+	3.79507i	−0.0453601	+	0.139604i	0.925811	+	0.377986i	$0.123383\pi$
$740$	0.382116	−	0.0461108i	0.0140469	−	0.00169507i
$741$	−1.12241	−	3.45441i	−0.0412326	−	0.126901i
$742$	−1.68331	−	2.31688i	−0.0617963	−	0.0850553i
$743$			3.48218i			0.127749i	0.997958	+	0.0638744i	$0.0203457\pi$
$743$			3.48218i			0.127749i	−0.997958	+	0.0638744i	$0.979654\pi$
$744$	9.45684	−	6.87079i	0.346704	−	0.251896i
$745$	11.7602	−	5.45410i	0.430860	−	0.199823i
$746$	−3.29183	−	2.39166i	−0.120523	−	0.0875648i
$747$	−3.86879	+	5.32493i	−0.141552	+	0.194829i
$748$	15.1270	+	4.91505i	0.553097	+	0.179712i
$749$	−12.4345			−0.454345
$750$	−6.10074	−	16.1945i	−0.222767	−	0.591339i
$751$	41.6278			1.51902			0.759509	−	0.650497i	$-0.225439\pi$
$751$	41.6278			1.51902			0.759509	+	0.650497i	$0.225439\pi$
$752$	−0.481259	−	0.156371i	−0.0175497	−	0.00570225i
$753$	−19.4957	+	26.8335i	−0.710462	+	0.977867i
$754$	9.12859	+	6.63231i	0.332444	+	0.241535i
$755$	−36.4354	+	16.8979i	−1.32602	+	0.614977i
$756$	−4.51326	+	3.27908i	−0.164146	+	0.119259i
$757$			21.1457i			0.768555i	0.923218	+	0.384277i	$0.125549\pi$
$757$			21.1457i			0.768555i	−0.923218	+	0.384277i	$0.874451\pi$
$758$	−15.6052	−	21.4787i	−0.566806	−	0.780141i
$759$	15.2228	+	46.8509i	0.552552	+	1.70058i
$760$	−3.01782	+	0.364168i	−0.109468	+	0.0132097i
$761$	16.9406	−	52.1377i	0.614095	−	1.88999i	0.199840	−	0.979829i	$-0.435958\pi$
$761$	16.9406	−	52.1377i	0.614095	−	1.88999i	0.414255	−	0.910161i	$-0.364042\pi$
$762$	−12.1593	+	3.95081i	−0.440487	+	0.143123i
$763$	−12.5810	+	4.08781i	−0.455462	+	0.147989i
$764$	−3.86527	+	11.8961i	−0.139841	+	0.430385i
$765$	−0.703570	+	3.57976i	−0.0254376	+	0.129426i
$766$	0.514804	+	1.58440i	0.0186006	+	0.0572468i
$767$	0.0519349	+	0.0714822i	0.00187526	+	0.00258107i
$768$		−	1.54785i		−	0.0558533i
$769$	−26.9874	+	19.6075i	−0.973192	+	0.707065i	−0.956177	−	0.292790i	$-0.905416\pi$
$769$	−26.9874	+	19.6075i	−0.973192	+	0.707065i	−0.0170152	+	0.999855i	$0.505416\pi$
$770$	12.9226	+	2.53982i	0.465698	+	0.0915289i
$771$	−8.61598	−	6.25988i	−0.310297	−	0.225444i
$772$	−10.6715	+	14.6881i	−0.384076	+	0.528635i
$773$	−10.2798	−	3.34011i	−0.369738	−	0.120135i	0.118254	−	0.992983i	$-0.462270\pi$
$773$	−10.2798	−	3.34011i	−0.369738	−	0.120135i	−0.487992	+	0.872848i	$0.662270\pi$
$774$	0.643243			0.0231209
$775$	2.79077	−	37.6565i	0.100247	−	1.35266i
$776$	0.0947838			0.00340254
$777$	0.253387	+	0.0823306i	0.00909022	+	0.00295359i
$778$	−12.7627	+	17.5663i	−0.457563	+	0.629782i
$779$	5.46965	+	3.97393i	0.195970	+	0.142381i
$780$	2.90739	−	5.21942i	0.104101	−	0.186885i
$781$	−52.5261	+	38.1625i	−1.87953	+	1.36556i
$782$		−	14.5928i		−	0.521837i
$783$	−21.4342	−	29.5016i	−0.765996	−	1.05430i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−10.4481	−	22.5283i	−0.372908	−	0.804070i
$786$	−8.77667	+	27.0118i	−0.313054	+	0.963480i
$787$	11.0995	−	3.60646i	0.395656	−	0.128556i	−0.104430	−	0.994532i	$-0.533302\pi$
$787$	11.0995	−	3.60646i	0.395656	−	0.128556i	0.500086	+	0.865976i	$0.333302\pi$
$788$	2.57145	−	0.835514i	0.0916040	−	0.0297639i
$789$	9.15671	−	28.1815i	0.325987	−	1.00329i
$790$	1.56114	+	0.869605i	0.0555428	+	0.0309392i
$791$	−6.31248	−	19.4278i	−0.224446	−	0.690773i
$792$	−2.09152	−	2.87873i	−0.0743188	−	0.102291i
$793$		−	4.34864i		−	0.154425i
$794$	−24.4307	+	17.7500i	−0.867014	+	0.629923i
$795$	−6.74484	−	7.26321i	−0.239215	−	0.257599i
$796$	3.73551	+	2.71400i	0.132401	+	0.0961953i
$797$	15.2257	−	20.9564i	0.539323	−	0.742315i	−0.449192	−	0.893435i	$-0.648288\pi$
$797$	15.2257	−	20.9564i	0.539323	−	0.742315i	0.988515	+	0.151120i	$0.0482881\pi$
$798$	−2.00117	−	0.650219i	−0.0708406	−	0.0230175i
$799$	−1.36654			−0.0483448
$800$	−3.81681	−	3.22986i	−0.134945	−	0.114193i
$801$	−8.75014			−0.309171
$802$	−26.8323	−	8.71833i	−0.947481	−	0.307855i
$803$	−40.0164	+	55.0778i	−1.41215	+	1.94365i
$804$	12.8190	+	9.31354i	0.452091	+	0.328463i
$805$	−1.44757	−	11.9959i	−0.0510203	−	0.422800i
$806$	10.5465	−	7.66246i	0.371483	−	0.269899i
$807$		−	39.8289i		−	1.40204i
$808$	2.20654	+	3.03704i	0.0776257	+	0.106843i
$809$	12.5801	+	38.7176i	0.442293	+	1.36124i	0.885425	+	0.464782i	$0.153867\pi$
$809$	12.5801	+	38.7176i	0.442293	+	1.36124i	−0.443132	+	0.896456i	$0.646133\pi$
$810$	−11.1789	+	10.3811i	−0.392787	+	0.364754i
$811$	11.3323	−	34.8773i	0.397931	−	1.22471i	−0.528723	−	0.848794i	$-0.677329\pi$
$811$	11.3323	−	34.8773i	0.397931	−	1.22471i	0.926655	−	0.375913i	$-0.122671\pi$
$812$	6.21673	−	2.01994i	0.218165	−	0.0708859i
$813$	6.53784	−	2.12427i	0.229292	−	0.0745015i
$814$	−0.313276	+	0.964163i	−0.0109803	+	0.0337939i
$815$	26.3868	−	24.5036i	0.924289	−	0.858324i
$816$	−1.29170	−	3.97545i	−0.0452186	−	0.139169i
$817$	0.850734	+	1.17094i	0.0297634	+	0.0409658i
$818$		−	14.0810i		−	0.492331i
$819$	−0.843715	+	0.612995i	−0.0294818	+	0.0214198i
$820$	1.33231	+	11.0408i	0.0465264	+	0.385560i
$821$	−35.7170	−	25.9499i	−1.24653	−	0.905659i	−0.248518	−	0.968627i	$-0.579943\pi$
$821$	−35.7170	−	25.9499i	−1.24653	−	0.905659i	−0.998016	+	0.0629681i	$0.979943\pi$
$822$	14.0310	−	19.3121i	0.489389	−	0.673586i
$823$	−21.1683	−	6.87800i	−0.737881	−	0.239752i	−0.0841227	−	0.996455i	$-0.526809\pi$
$823$	−21.1683	−	6.87800i	−0.737881	−	0.239752i	−0.653759	+	0.756703i	$0.726809\pi$
$824$	19.3237			0.673172
$825$	45.4574	+	3.36891i	1.58262	+	0.117290i
$826$	0.0511858			0.00178098
$827$	−46.8367	−	15.2182i	−1.62867	−	0.529188i	−0.654706	−	0.755883i	$-0.727208\pi$
$827$	−46.8367	−	15.2182i	−1.62867	−	0.529188i	−0.973966	+	0.226696i	$0.927208\pi$
$828$	−1.91891	+	2.64115i	−0.0666867	+	0.0917863i
$829$	−4.33032	−	3.14616i	−0.150398	−	0.109271i	0.510041	−	0.860150i	$-0.329630\pi$
$829$	−4.33032	−	3.14616i	−0.150398	−	0.109271i	−0.660440	+	0.750879i	$0.729630\pi$
$830$	−16.5770	−	17.8510i	−0.575395	−	0.619617i
$831$	1.50796	−	1.09560i	0.0523107	−	0.0380060i
$832$		−	1.72620i		−	0.0598451i
$833$	−1.58734	−	2.18478i	−0.0549980	−	0.0756982i
$834$	−1.88515	−	5.80190i	−0.0652775	−	0.200903i
$835$	42.4500	+	23.6460i	1.46904	+	0.818305i
$836$	2.47415	−	7.61464i	0.0855701	−	0.263358i
$837$	−40.0680	+	13.0189i	−1.38495	+	0.449999i
$838$	−9.34892	+	3.03765i	−0.322953	+	0.104934i
$839$	−10.3092	+	31.7283i	−0.355912	+	1.09538i	0.599567	+	0.800324i	$0.295339\pi$
$839$	−10.3092	+	31.7283i	−0.355912	+	1.09538i	−0.955479	+	0.295059i	$0.904661\pi$
$840$	−1.45619	−	3.13986i	−0.0502434	−	0.108336i
$841$	4.24215	+	13.0560i	0.146281	+	0.450207i
$842$	8.43309	+	11.6072i	0.290624	+	0.400009i
$843$		−	19.1100i		−	0.658183i
$844$	−20.1702	+	14.6545i	−0.694285	+	0.504428i
$845$	−10.9034	+	19.5740i	−0.375088	+	0.673367i
$846$	0.247331	+	0.179696i	0.00850341	+	0.00617809i
$847$	−13.9239	+	19.1647i	−0.478432	+	0.658506i
$848$	−2.72365	−	0.884968i	−0.0935306	−	0.0303899i
$849$	2.20019			0.0755105
$850$	−12.4983	−	5.11027i	−0.428689	−	0.175281i
$851$	0.930116			0.0318840
$852$	16.2278	+	5.27272i	0.555954	+	0.180640i
$853$	−5.39078	+	7.41977i	−0.184577	+	0.254048i	−0.891271	−	0.453471i	$-0.850186\pi$
$853$	−5.39078	+	7.41977i	−0.184577	+	0.254048i	0.706694	+	0.707519i	$0.250186\pi$
$854$	−2.03808	−	1.48075i	−0.0697416	−	0.0506703i
$855$	1.80198	+	0.354164i	0.0616265	+	0.0121122i
$856$	−10.0597	+	7.30879i	−0.343833	+	0.249809i
$857$			15.3815i			0.525423i	0.964874	+	0.262712i	$0.0846168\pi$
$857$			15.3815i			0.525423i	−0.964874	+	0.262712i	$0.915383\pi$
$858$	9.24982	+	12.7313i	0.315784	+	0.434639i
$859$	7.81869	+	24.0635i	0.266770	+	0.821035i	0.991280	+	0.131770i	$0.0420661\pi$
$859$	7.81869	+	24.0635i	0.266770	+	0.821035i	−0.724510	+	0.689264i	$0.757934\pi$
$860$	−0.459130	+	2.33605i	−0.0156562	+	0.0796586i
$861$	−2.37884	+	7.32132i	−0.0810707	+	0.249510i
$862$	−28.3222	+	9.20245i	−0.964659	+	0.313437i
$863$	−20.5848	+	6.68840i	−0.700714	+	0.227676i	−0.637642	−	0.770333i	$-0.720090\pi$
$863$	−20.5848	+	6.68840i	−0.700714	+	0.227676i	−0.0630725	+	0.998009i	$0.520090\pi$
$864$	−1.72391	+	5.30566i	−0.0586487	+	0.180502i
$865$	−55.4710	+	6.69382i	−1.88607	+	0.227597i
$866$	−4.34420	−	13.3701i	−0.147622	−	0.454334i
$867$	8.83155	+	12.1556i	0.299935	+	0.412825i
$868$		−	7.55195i		−	0.256330i
$869$	−3.80795	+	2.76664i	−0.129176	+	0.0938518i
$870$	20.5242	−	9.51863i	0.695836	−	0.322712i
$871$	14.2960	+	10.3867i	0.484402	+	0.351939i
$872$	−7.77548	+	10.7020i	−0.263311	+	0.362416i
$873$	−0.0544613	−	0.0176956i	−0.00184324	−	0.000598904i
$874$	−7.34574			−0.248473
$875$	−10.7811	−	2.96106i	−0.364468	−	0.100102i
$876$	17.8918			0.604508
$877$	23.1234	+	7.51325i	0.780822	+	0.253704i	0.672191	−	0.740378i	$-0.265353\pi$
$877$	23.1234	+	7.51325i	0.780822	+	0.253704i	0.108631	+	0.994082i	$0.465353\pi$
$878$	−3.83621	+	5.28009i	−0.129466	+	0.178194i
$879$	14.6057	+	10.6117i	0.492639	+	0.357923i
$880$	11.9475	−	5.54095i	0.402749	−	0.186785i
$881$	24.6115	−	17.8813i	0.829184	−	0.602438i	−0.0901442	−	0.995929i	$-0.528733\pi$
$881$	24.6115	−	17.8813i	0.829184	−	0.602438i	0.919328	+	0.393491i	$0.128733\pi$
$882$			0.604154i			0.0203429i
$883$	−3.57725	−	4.92366i	−0.120384	−	0.165695i	0.744572	−	0.667542i	$-0.232654\pi$
$883$	−3.57725	−	4.92366i	−0.120384	−	0.165695i	−0.864956	+	0.501848i	$0.832654\pi$
$884$	−1.44053	−	4.43351i	−0.0484504	−	0.149115i
$885$	0.175883	−	0.0212243i	0.00591226	−	0.000713446i
$886$	11.6967	−	35.9988i	0.392959	−	1.20940i
$887$	3.57807	−	1.16259i	0.120140	−	0.0390358i	−0.248330	−	0.968675i	$-0.579882\pi$
$887$	3.57807	−	1.16259i	0.120140	−	0.0390358i	0.368470	+	0.929640i	$0.379882\pi$
$888$	0.253387	−	0.0823306i	0.00850312	−	0.00276283i
$889$	−2.55245	+	7.85563i	−0.0856064	+	0.263469i
$890$	6.24562	−	31.7777i	0.209354	−	1.06519i
$891$	−12.4172	−	38.2161i	−0.415991	−	1.28029i
$892$	−10.0873	−	13.8839i	−0.337747	−	0.464868i
$893$			0.687893i			0.0230194i
$894$	7.25973	−	5.27450i	0.242802	−	0.176406i
$895$	−21.6926	−	4.26349i	−0.725104	−	0.142513i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	8.48645	−	11.6806i	0.283354	−	0.390004i
$898$	−8.64326	−	2.80837i	−0.288429	−	0.0937164i
$899$	49.3645			1.64640
$900$	1.59009	+	2.56840i	0.0530029	+	0.0856134i
$901$	−7.73386			−0.257652
$902$	−27.8583	−	9.05171i	−0.927580	−	0.301389i
$903$	−0.968669	+	1.33326i	−0.0322353	+	0.0443680i
$904$	−16.5263	−	12.0070i	−0.549656	−	0.399348i
$905$	3.42513	−	6.14888i	0.113855	−	0.204396i
$906$	−22.4921	+	16.3415i	−0.747250	+	0.542909i
$907$		−	5.95778i		−	0.197825i	−0.995096	−	0.0989123i	$-0.968464\pi$
$907$		−	5.95778i		−	0.197825i	0.995096	−	0.0989123i	$-0.0315363\pi$
$908$	−1.80095	−	2.47879i	−0.0597665	−	0.0822615i
$909$	−0.700846	−	2.15698i	−0.0232456	−	0.0715426i
$910$	−1.62398	−	3.50164i	−0.0538343	−	0.116078i
$911$	−10.6924	+	32.9078i	−0.354254	+	1.09028i	0.602186	+	0.798356i	$0.294296\pi$
$911$	−10.6924	+	32.9078i	−0.354254	+	1.09028i	−0.956441	+	0.291927i	$0.905704\pi$
$912$	−2.00117	+	0.650219i	−0.0662653	+	0.0215309i
$913$	61.0252	−	19.8283i	2.01964	−	0.656221i
$914$	5.54462	−	17.0646i	0.183400	−	0.564447i
$915$	−7.61719	−	4.24303i	−0.251817	−	0.140270i
$916$	4.05427	+	12.4778i	0.133957	+	0.412277i
$917$	10.7854	+	14.8448i	0.356166	+	0.490220i
$918$			15.0655i			0.497235i
$919$	32.6252	−	23.7036i	1.07621	−	0.781909i	0.0991885	−	0.995069i	$-0.468375\pi$
$919$	32.6252	−	23.7036i	1.07621	−	0.781909i	0.977017	+	0.213159i	$0.0683753\pi$
$920$	−8.22213	−	8.85404i	−0.271076	−	0.291909i
$921$	−22.0341	−	16.0087i	−0.726050	−	0.527506i
$922$	−12.1356	+	16.7032i	−0.399665	+	0.550091i
$923$	18.0976	+	5.88025i	0.595688	+	0.193551i
$924$	9.11642			0.299908
$925$	0.325719	−	0.796618i	0.0107096	−	0.0261926i
$926$	30.0244			0.986665
$927$	−11.1031	−	3.60761i	−0.364673	−	0.118490i
$928$	3.84215	−	5.28827i	0.126125	−	0.173596i
$929$	10.5338	+	7.65324i	0.345602	+	0.251095i	0.747022	−	0.664800i	$-0.231483\pi$
$929$	10.5338	+	7.65324i	0.345602	+	0.251095i	−0.401419	+	0.915894i	$0.631483\pi$
$930$	−3.13142	−	25.9498i	−0.102683	−	0.850928i
$931$	−1.09978	+	0.799037i	−0.0360438	+	0.0261874i
$932$		−	4.78362i		−	0.156693i
$933$	−4.38495	−	6.03537i	−0.143557	−	0.197589i
$934$	4.81413	+	14.8164i	0.157523	+	0.484806i
$935$	26.0615	−	24.2015i	0.852302	−	0.791474i
$936$	−0.322271	+	0.991847i	−0.0105337	+	0.0324195i
$937$	−41.9193	+	13.6204i	−1.36944	+	0.444959i	−0.899185	−	0.437569i	$-0.855840\pi$
$937$	−41.9193	+	13.6204i	−1.36944	+	0.444959i	−0.470259	+	0.882528i	$0.655840\pi$
$938$	9.73583	−	3.16336i	0.317886	−	0.103287i
$939$	−2.23658	+	6.88348i	−0.0729879	+	0.224634i
$940$	−0.829137	+	0.769962i	−0.0270435	+	0.0251134i
$941$	−11.3110	−	34.8117i	−0.368728	−	1.13483i	−0.947614	−	0.319419i	$-0.896512\pi$
$941$	−11.3110	−	34.8117i	−0.368728	−	1.13483i	0.578886	−	0.815409i	$-0.303488\pi$
$942$	−10.1041	−	13.9070i	−0.329208	−	0.453116i
$943$			26.8746i			0.875156i
$944$	0.0414102	−	0.0300863i	0.00134779	−	0.000979225i
$945$	1.49447	+	12.3845i	0.0486150	+	0.402868i
$946$	−5.07317	−	3.68588i	−0.164943	−	0.119838i
$947$	15.9944	−	22.0145i	0.519749	−	0.715374i	−0.465776	−	0.884903i	$-0.654225\pi$
$947$	15.9944	−	22.0145i	0.519749	−	0.715374i	0.985525	+	0.169529i	$0.0542247\pi$
$948$	1.17645	+	0.382253i	0.0382094	+	0.0124150i
$949$	19.9533			0.647712
$950$	−2.57242	+	6.29143i	−0.0834603	+	0.204121i
$951$	−35.8549			−1.16268
$952$	−2.56837	−	0.834513i	−0.0832412	−	0.0270467i
$953$	22.0196	−	30.3074i	0.713284	−	0.981752i	−0.286436	−	0.958099i	$-0.592471\pi$
$953$	22.0196	−	30.3074i	0.713284	−	0.981752i	0.999720	−	0.0236522i	$-0.00752943\pi$
$954$	1.39975	+	1.01698i	0.0453186	+	0.0329259i
$955$	19.0325	+	20.4952i	0.615876	+	0.663208i
$956$	−16.9496	+	12.3146i	−0.548189	+	0.398282i
$957$			59.5909i			1.92630i
$958$	−5.61562	−	7.72923i	−0.181432	−	0.249720i
$959$	−4.76567	−	14.6672i	−0.153892	−	0.473629i
$960$	−3.02365	−	1.68427i	−0.0975879	−	0.0543597i
$961$	8.04430	−	24.7578i	0.259493	−	0.798639i
$962$	0.282583	−	0.0918168i	0.00911084	−	0.00296029i
$963$	7.14465	−	2.32144i	0.230233	−	0.0748073i
$964$	−9.21283	+	28.3542i	−0.296725	+	0.913226i
$965$	17.0803	+	36.8288i	0.549835	+	1.18556i
$966$	−2.58464	−	7.95469i	−0.0831593	−	0.255938i
$967$	−9.57012	−	13.1721i	−0.307754	−	0.423587i	0.626925	−	0.779080i	$-0.284313\pi$
$967$	−9.57012	−	13.1721i	−0.307754	−	0.423587i	−0.934679	+	0.355492i	$0.884313\pi$
$968$			23.6888i			0.761388i
$969$	−4.59712	+	3.34000i	−0.147681	+	0.107296i
$970$	0.103138	−	0.185155i	0.00331155	−	0.00594498i
$971$	9.53458	+	6.92728i	0.305979	+	0.222307i	0.730169	−	0.683266i	$-0.239441\pi$
$971$	9.53458	+	6.92728i	0.305979	+	0.222307i	−0.424190	+	0.905573i	$0.639441\pi$
$972$	3.63005	−	4.99634i	0.116434	−	0.160258i
$973$	−3.74836	−	1.21791i	−0.120167	−	0.0390446i
$974$	−40.1386			−1.28612
$975$	−7.03223	−	11.3589i	−0.225212	−	0.363775i
$976$	−2.51920			−0.0806378
$977$	39.0235	+	12.6795i	1.24847	+	0.405653i	0.857373	−	0.514695i	$-0.172095\pi$
$977$	39.0235	+	12.6795i	1.24847	+	0.405653i	0.391099	+	0.920349i	$0.372095\pi$
$978$	14.6515	−	20.1660i	0.468502	−	0.644838i
$979$	69.0112	+	50.1396i	2.20561	+	1.60247i
$980$	−2.19409	−	0.431230i	−0.0700877	−	0.0137751i
$981$	6.46567	−	4.69759i	0.206433	−	0.149982i
$982$			8.03383i			0.256370i
$983$	−4.33326	−	5.96423i	−0.138210	−	0.190229i	0.734301	−	0.678823i	$-0.237510\pi$
$983$	−4.33326	−	5.96423i	−0.138210	−	0.190229i	−0.872511	+	0.488594i	$0.837510\pi$
$984$	2.37884	+	7.32132i	0.0758347	+	0.233395i
$985$	1.16595	−	5.93234i	0.0371502	−	0.189020i
$986$	5.45492	−	16.7885i	0.173720	−	0.534656i
$987$	−0.744918	+	0.242038i	−0.0237110	+	0.00770417i
$988$	−2.23175	+	0.725138i	−0.0710013	+	0.0230697i
$989$	−1.77786	+	5.47169i	−0.0565326	+	0.173989i
$990$	−7.89930	+	0.953226i	−0.251056	+	0.0302955i
$991$	6.84224	+	21.0582i	0.217351	+	0.668937i	0.998978	+	0.0451915i	$0.0143898\pi$
$991$	6.84224	+	21.0582i	0.217351	+	0.668937i	−0.781628	+	0.623745i	$0.785610\pi$
$992$	−4.43892	−	6.10965i	−0.140936	−	0.193982i
$993$		−	47.0686i		−	1.49368i
$994$	8.91827	−	6.47950i	0.282870	−	0.205517i
$995$	9.36640	−	4.34391i	0.296935	−	0.137711i
$996$	−13.6425	−	9.91189i	−0.432281	−	0.314070i
$997$	−3.05502	+	4.20487i	−0.0967535	+	0.133170i	−0.854649	−	0.519206i	$-0.826228\pi$
$997$	−3.05502	+	4.20487i	−0.0967535	+	0.133170i	0.757896	+	0.652376i	$0.226228\pi$
$998$	14.3279	+	4.65542i	0.453542	+	0.147365i
$999$	−0.960245			−0.0303808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.29.2	✓	40
25.12	odd	20		8750.2.a.bf.1.5		20
25.13	odd	20		8750.2.a.be.1.16		20
25.19	even	10	inner	350.2.m.b.169.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.2	✓	40	1.1	even	1	trivial
350.2.m.b.169.2	yes	40	25.19	even	10	inner
8750.2.a.be.1.16		20	25.13	odd	20
8750.2.a.bf.1.5		20	25.12	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.909805 + 1.25224i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02853 - 0.940783i) q^{5} +(1.25224 - 0.909805i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.186694 + 0.574585i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.909805 + 1.25224i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02853 - 0.940783i) q^{5} +(1.25224 - 0.909805i) q^{6} -1.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.186694 + 0.574585i) q^{9} +(-2.21996 + 0.267888i) q^{10} +(1.82002 - 5.60146i) q^{11} +(-1.47209 + 0.478313i) q^{12} +(-1.64171 + 0.533424i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-0.667480 + 3.39613i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58734 + 2.18478i) q^{17} -0.604154i q^{18} +(1.09978 - 0.799037i) q^{19} +(2.19409 + 0.431230i) q^{20} +(1.25224 + 0.909805i) q^{21} +(-3.46189 + 4.76489i) q^{22} +(5.13918 + 1.66982i) q^{23} +1.54785 q^{24} +(3.22986 - 3.81681i) q^{25} +1.72620 q^{26} +(-5.30566 - 1.72391i) q^{27} +(0.587785 - 0.809017i) q^{28} +(5.28827 + 3.84215i) q^{29} +(1.68427 - 3.02365i) q^{30} +(6.10965 - 4.43892i) q^{31} -1.00000i q^{32} +(5.35850 + 7.37534i) q^{33} +(-0.834513 - 2.56837i) q^{34} +(-0.940783 - 2.02853i) q^{35} +(-0.186694 + 0.574585i) q^{36} +(0.163703 - 0.0531902i) q^{37} +(-1.29287 + 0.420078i) q^{38} +(0.825662 - 2.54113i) q^{39} +(-1.95345 - 1.08814i) q^{40} +(1.53687 + 4.72999i) q^{41} +(-0.909805 - 1.25224i) q^{42} +1.06470i q^{43} +(4.76489 - 3.46189i) q^{44} +(0.919274 + 0.989923i) q^{45} +(-4.37165 - 3.17619i) q^{46} +(-0.297434 + 0.409383i) q^{47} +(-1.47209 - 0.478313i) q^{48} -1.00000 q^{49} +(-4.25123 + 2.63192i) q^{50} -4.18004 q^{51} +(-1.64171 - 0.533424i) q^{52} +(-1.68331 + 2.31688i) q^{53} +(4.51326 + 3.27908i) q^{54} +(-1.57779 - 13.0750i) q^{55} +(-0.809017 + 0.587785i) q^{56} +2.10415i q^{57} +(-3.84215 - 5.28827i) q^{58} +(-0.0158173 - 0.0486806i) q^{59} +(-2.53620 + 2.35519i) q^{60} +(-0.778477 + 2.39591i) q^{61} +(-7.18233 + 2.33368i) q^{62} +(0.574585 - 0.186694i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.82842 + 2.62656i) q^{65} +(-2.81713 - 8.67023i) q^{66} +(-6.01707 - 8.28179i) q^{67} +2.70054i q^{68} +(-6.76667 + 4.91627i) q^{69} +(0.267888 + 2.21996i) q^{70} +(-8.91827 - 6.47950i) q^{71} +(0.355113 - 0.488771i) q^{72} +(-10.9934 - 3.57196i) q^{73} -0.172127 q^{74} +(1.84102 + 7.51710i) q^{75} +1.35940 q^{76} +(-5.60146 - 1.82002i) q^{77} +(-1.57050 + 2.16161i) q^{78} +(-0.646542 - 0.469740i) q^{79} +(1.52159 + 1.63853i) q^{80} +(5.51955 - 4.01019i) q^{81} -4.97340i q^{82} +(6.40364 + 8.81386i) q^{83} +(0.478313 + 1.47209i) q^{84} +(5.27537 + 2.93855i) q^{85} +(0.329010 - 1.01259i) q^{86} +(-9.62258 + 3.12657i) q^{87} +(-5.60146 + 1.82002i) q^{88} +(-4.47558 + 13.7744i) q^{89} +(-0.568378 - 1.22554i) q^{90} +(0.533424 + 1.64171i) q^{91} +(3.17619 + 4.37165i) q^{92} +11.6893i q^{93} +(0.409383 - 0.297434i) q^{94} +(1.47921 - 2.65552i) q^{95} +(1.25224 + 0.909805i) q^{96} +(-0.0557125 + 0.0766817i) q^{97} +(0.951057 + 0.309017i) q^{98} +3.55830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more