LMFDB - Embedded newform 380.2.n.a.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104103 + 1.41038i) q^{2} +(-0.481867 - 0.834618i) q^{3} +(-1.97833 - 0.293648i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.22729 - 0.592728i) q^{6} -1.00869i q^{7} +(0.620104 - 2.75961i) q^{8} +(1.03561 - 1.79373i) q^{9} +O(q^{10})$	\(q+(-0.104103 + 1.41038i) q^{2} +(-0.481867 - 0.834618i) q^{3} +(-1.97833 - 0.293648i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.22729 - 0.592728i) q^{6} -1.00869i q^{7} +(0.620104 - 2.75961i) q^{8} +(1.03561 - 1.79373i) q^{9} +(-1.27347 + 0.615033i) q^{10} +4.53449i q^{11} +(0.708205 + 1.79264i) q^{12} +(4.62223 + 2.66864i) q^{13} +(1.42263 + 0.105007i) q^{14} +(0.481867 - 0.834618i) q^{15} +(3.82754 + 1.16186i) q^{16} +(2.17215 + 3.76227i) q^{17} +(2.42202 + 1.64733i) q^{18} +(2.83968 - 3.30700i) q^{19} +(-0.734856 - 1.86010i) q^{20} +(-0.841868 + 0.486053i) q^{21} +(-6.39534 - 0.472053i) q^{22} +(-2.38107 - 1.37471i) q^{23} +(-2.60203 + 0.812217i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-4.24498 + 6.24127i) q^{26} -4.88730 q^{27} +(-0.296199 + 1.99551i) q^{28} +(3.30897 + 1.91044i) q^{29} +(1.12696 + 0.766500i) q^{30} +6.27901 q^{31} +(-2.03712 + 5.27732i) q^{32} +(3.78456 - 2.18502i) q^{33} +(-5.53234 + 2.67188i) q^{34} +(0.873549 - 0.504344i) q^{35} +(-2.57550 + 3.24447i) q^{36} +3.89849i q^{37} +(4.36849 + 4.34928i) q^{38} -5.14372i q^{39} +(2.69995 - 0.842781i) q^{40} +(-0.221296 + 0.127766i) q^{41} +(-0.597877 - 1.23795i) q^{42} +(-1.13112 + 0.653052i) q^{43} +(1.33155 - 8.97069i) q^{44} +2.07122 q^{45} +(2.18674 - 3.21510i) q^{46} +(-5.20027 - 3.00238i) q^{47} +(-0.874653 - 3.75440i) q^{48} +5.98255 q^{49} +(-1.16937 - 0.795344i) q^{50} +(2.09337 - 3.62583i) q^{51} +(-8.36063 - 6.63676i) q^{52} +(-8.70264 - 5.02447i) q^{53} +(0.508782 - 6.89294i) q^{54} +(-3.92698 + 2.26724i) q^{55} +(-2.78359 - 0.625491i) q^{56} +(-4.12842 - 0.776514i) q^{57} +(-3.03891 + 4.46801i) q^{58} +(4.64424 + 8.04406i) q^{59} +(-1.19837 + 1.50965i) q^{60} +(4.67339 - 8.09454i) q^{61} +(-0.653662 + 8.85577i) q^{62} +(-1.80931 - 1.04461i) q^{63} +(-7.23094 - 3.42250i) q^{64} +5.33729i q^{65} +(2.68772 + 5.56513i) q^{66} +(2.09151 - 3.62261i) q^{67} +(-3.19243 - 8.08084i) q^{68} +2.64972i q^{69} +(0.620376 + 1.28454i) q^{70} +(1.75626 + 3.04194i) q^{71} +(-4.30781 - 3.97018i) q^{72} +(-7.39818 - 12.8140i) q^{73} +(-5.49835 - 0.405844i) q^{74} +0.963733 q^{75} +(-6.58890 + 5.70845i) q^{76} +4.57388 q^{77} +(7.25459 + 0.535476i) q^{78} +(-5.03491 - 8.72072i) q^{79} +(0.907567 + 3.89568i) q^{80} +(-0.751799 - 1.30215i) q^{81} +(-0.157160 - 0.325412i) q^{82} +1.98884i q^{83} +(1.80822 - 0.714357i) q^{84} +(-2.17215 + 3.76227i) q^{85} +(-0.803297 - 1.66329i) q^{86} -3.68230i q^{87} +(12.5134 + 2.81185i) q^{88} +(-0.0672238 - 0.0388117i) q^{89} +(-0.215620 + 2.92120i) q^{90} +(2.69183 - 4.66238i) q^{91} +(4.30686 + 3.41883i) q^{92} +(-3.02564 - 5.24057i) q^{93} +(4.77585 - 7.02179i) q^{94} +(4.28378 + 0.805735i) q^{95} +(5.38617 - 0.842747i) q^{96} +(-14.0057 + 8.08620i) q^{97} +(-0.622800 + 8.43765i) q^{98} +(8.13364 + 4.69596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.104103	+	1.41038i	−0.0736118	+	0.997287i
$2$	−0.104103	+	1.41038i	−0.0736118	+	0.997287i
$3$	−0.481867	−	0.834618i	−0.278206	−	0.481867i	0.692733	−	0.721194i	$-0.256406\pi$
$3$	−0.481867	−	0.834618i	−0.278206	−	0.481867i	−0.970939	+	0.239327i	$0.923073\pi$
$4$	−1.97833	−	0.293648i	−0.989163	−	0.146824i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.22729	−	0.592728i	0.501039	−	0.241980i
$7$		−	1.00869i		−	0.381248i	−0.981663	−	0.190624i	$-0.938949\pi$
$7$		−	1.00869i		−	0.381248i	0.981663	−	0.190624i	$-0.0610511\pi$
$8$	0.620104	−	2.75961i	0.219240	−	0.975671i
$9$	1.03561	−	1.79373i	0.345203	−	0.597909i
$10$	−1.27347	+	0.615033i	−0.402708	+	0.194490i
$11$			4.53449i			1.36720i	0.729857	+	0.683600i	$0.239587\pi$
$11$			4.53449i			1.36720i	−0.729857	+	0.683600i	$0.760413\pi$
$12$	0.708205	+	1.79264i	0.204441	+	0.517492i
$13$	4.62223	+	2.66864i	1.28198	+	0.740149i	0.977209	−	0.212279i	$-0.0680884\pi$
$13$	4.62223	+	2.66864i	1.28198	+	0.740149i	0.304766	+	0.952427i	$0.401422\pi$
$14$	1.42263	+	0.105007i	0.380214	+	0.0280643i
$15$	0.481867	−	0.834618i	0.124417	−	0.215497i
$16$	3.82754	+	1.16186i	0.956885	+	0.290466i
$17$	2.17215	+	3.76227i	0.526823	+	0.912484i	0.999511	+	0.0312548i	$0.00995032\pi$
$17$	2.17215	+	3.76227i	0.526823	+	0.912484i	−0.472688	+	0.881230i	$0.656716\pi$
$18$	2.42202	+	1.64733i	0.570876	+	0.388280i
$19$	2.83968	−	3.30700i	0.651467	−	0.758677i
$19$	2.83968	−	3.30700i	0.651467	−	0.758677i
$20$	−0.734856	−	1.86010i	−0.164319	−	0.415932i
$21$	−0.841868	+	0.486053i	−0.183711	+	0.106065i
$22$	−6.39534	−	0.472053i	−1.36349	−	0.100642i
$23$	−2.38107	−	1.37471i	−0.496488	−	0.286648i	0.230774	−	0.973007i	$-0.425874\pi$
$23$	−2.38107	−	1.37471i	−0.496488	−	0.286648i	−0.727262	+	0.686360i	$0.759208\pi$
$24$	−2.60203	+	0.812217i	−0.531137	+	0.165793i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.24498	+	6.24127i	−0.832509	+	1.22401i
$27$	−4.88730			−0.940562
$28$	−0.296199	+	1.99551i	−0.0559764	+	0.377116i
$29$	3.30897	+	1.91044i	0.614461	+	0.354759i	0.774709	−	0.632318i	$-0.217896\pi$
$29$	3.30897	+	1.91044i	0.614461	+	0.354759i	−0.160249	+	0.987077i	$0.551230\pi$
$30$	1.12696	+	0.766500i	0.205754	+	0.139943i
$31$	6.27901			1.12774			0.563871	−	0.825863i	$-0.309311\pi$
$31$	6.27901			1.12774			0.563871	+	0.825863i	$0.309311\pi$
$32$	−2.03712	+	5.27732i	−0.360116	+	0.932908i
$33$	3.78456	−	2.18502i	0.658808	−	0.380363i
$34$	−5.53234	+	2.67188i	−0.948789	+	0.458224i
$35$	0.873549	−	0.504344i	0.147657	−	0.0852496i
$36$	−2.57550	+	3.24447i	−0.429249	+	0.540745i
$37$			3.89849i			0.640909i	0.947264	+	0.320454i	$0.103836\pi$
$37$			3.89849i			0.640909i	−0.947264	+	0.320454i	$0.896164\pi$
$38$	4.36849	+	4.34928i	0.708663	+	0.705547i
$39$		−	5.14372i		−	0.823655i
$40$	2.69995	−	0.842781i	0.426899	−	0.133255i
$41$	−0.221296	+	0.127766i	−0.0345607	+	0.0199536i	−0.517181	−	0.855876i	$-0.673019\pi$
$41$	−0.221296	+	0.127766i	−0.0345607	+	0.0199536i	0.482620	+	0.875830i	$0.339685\pi$
$42$	−0.597877	−	1.23795i	−0.0922544	−	0.191020i
$43$	−1.13112	+	0.653052i	−0.172494	+	0.0995895i	−0.583761	−	0.811925i	$-0.698420\pi$
$43$	−1.13112	+	0.653052i	−0.172494	+	0.0995895i	0.411267	+	0.911515i	$0.365086\pi$
$44$	1.33155	−	8.97069i	0.200738	−	1.35238i
$45$	2.07122			0.308759
$46$	2.18674	−	3.21510i	0.322417	−	0.474041i
$47$	−5.20027	−	3.00238i	−0.758538	−	0.437942i	0.0702326	−	0.997531i	$-0.477626\pi$
$47$	−5.20027	−	3.00238i	−0.758538	−	0.437942i	−0.828771	+	0.559589i	$0.810959\pi$
$48$	−0.874653	−	3.75440i	−0.126245	−	0.541901i
$49$	5.98255			0.854650
$50$	−1.16937	−	0.795344i	−0.165374	−	0.112479i
$51$	2.09337	−	3.62583i	0.293131	−	0.507717i
$52$	−8.36063	−	6.63676i	−1.15941	−	0.920352i
$53$	−8.70264	−	5.02447i	−1.19540	−	0.690165i	−0.235874	−	0.971784i	$-0.575795\pi$
$53$	−8.70264	−	5.02447i	−1.19540	−	0.690165i	−0.959526	+	0.281619i	$0.909129\pi$
$54$	0.508782	−	6.89294i	0.0692364	−	0.938010i
$55$	−3.92698	+	2.26724i	−0.529514	+	0.305715i
$56$	−2.78359	−	0.625491i	−0.371972	−	0.0835847i
$57$	−4.12842	−	0.776514i	−0.546823	−	0.102852i
$58$	−3.03891	+	4.46801i	−0.399028	+	0.586679i
$59$	4.64424	+	8.04406i	0.604629	+	1.04725i	0.992110	+	0.125370i	$0.0400117\pi$
$59$	4.64424	+	8.04406i	0.604629	+	1.04725i	−0.387482	+	0.921877i	$0.626655\pi$
$60$	−1.19837	+	1.50965i	−0.154709	+	0.194894i
$61$	4.67339	−	8.09454i	0.598366	−	1.03640i	−0.394696	−	0.918812i	$-0.629150\pi$
$61$	4.67339	−	8.09454i	0.598366	−	1.03640i	0.993062	−	0.117589i	$-0.0375164\pi$
$62$	−0.653662	+	8.85577i	−0.0830152	+	1.12468i
$63$	−1.80931	−	1.04461i	−0.227952	−	0.131608i
$64$	−7.23094	−	3.42250i	−0.903868	−	0.427812i
$65$			5.33729i			0.662009i
$66$	2.68772	+	5.56513i	0.330835	+	0.685020i
$67$	2.09151	−	3.62261i	0.255519	−	0.442572i	−0.709517	−	0.704688i	$-0.751087\pi$
$67$	2.09151	−	3.62261i	0.255519	−	0.442572i	0.965036	+	0.262116i	$0.0844204\pi$
$68$	−3.19243	−	8.08084i	−0.387139	−	0.979946i
$69$			2.64972i			0.318988i
$70$	0.620376	+	1.28454i	0.0741491	+	0.153531i
$71$	1.75626	+	3.04194i	0.208430	+	0.361012i	0.951220	−	0.308513i	$-0.0998312\pi$
$71$	1.75626	+	3.04194i	0.208430	+	0.361012i	−0.742790	+	0.669525i	$0.766498\pi$
$72$	−4.30781	−	3.97018i	−0.507680	−	0.467890i
$73$	−7.39818	−	12.8140i	−0.865892	−	1.49977i	−0.866159	−	0.499768i	$-0.833418\pi$
$73$	−7.39818	−	12.8140i	−0.865892	−	1.49977i	0.000267392	−	1.00000i	$-0.499915\pi$
$74$	−5.49835	−	0.405844i	−0.639170	−	0.0471784i
$75$	0.963733			0.111282
$76$	−6.58890	+	5.70845i	−0.755799	+	0.654804i
$77$	4.57388			0.521242
$78$	7.25459	+	0.535476i	0.821420	+	0.0606307i
$79$	−5.03491	−	8.72072i	−0.566472	−	0.981158i	−0.996911	−	0.0785384i	$-0.974975\pi$
$79$	−5.03491	−	8.72072i	−0.566472	−	0.981158i	0.430439	−	0.902620i	$-0.358359\pi$
$80$	0.907567	+	3.89568i	0.101469	+	0.435550i
$81$	−0.751799	−	1.30215i	−0.0835332	−	0.144684i
$82$	−0.157160	−	0.325412i	−0.0173554	−	0.0359357i
$83$			1.98884i			0.218304i	0.994025	+	0.109152i	$0.0348135\pi$
$83$			1.98884i			0.218304i	−0.994025	+	0.109152i	$0.965186\pi$
$84$	1.80822	−	0.714357i	0.197293	−	0.0779428i
$85$	−2.17215	+	3.76227i	−0.235602	+	0.408075i
$86$	−0.803297	−	1.66329i	−0.0866217	−	0.179357i
$87$		−	3.68230i		−	0.394784i
$88$	12.5134	+	2.81185i	1.33394	+	0.299745i
$89$	−0.0672238	−	0.0388117i	−0.00712571	−	0.00411403i	0.496433	−	0.868075i	$-0.334643\pi$
$89$	−0.0672238	−	0.0388117i	−0.00712571	−	0.00411403i	−0.503559	+	0.863961i	$0.667976\pi$
$90$	−0.215620	+	2.92120i	−0.0227283	+	0.307921i
$91$	2.69183	−	4.66238i	0.282180	−	0.488750i
$92$	4.30686	+	3.41883i	0.449021	+	0.356438i
$93$	−3.02564	−	5.24057i	−0.313745	−	0.543422i
$94$	4.77585	−	7.02179i	0.492591	−	0.724242i
$95$	4.28378	+	0.805735i	0.439507	+	0.0826667i
$96$	5.38617	−	0.842747i	0.549723	−	0.0860125i
$97$	−14.0057	+	8.08620i	−1.42206	+	0.821029i	−0.996475	−	0.0838873i	$-0.973266\pi$
$97$	−14.0057	+	8.08620i	−1.42206	+	0.821029i	−0.425589	+	0.904917i	$0.639933\pi$
$98$	−0.622800	+	8.43765i	−0.0629123	+	0.852331i
$99$	8.13364	+	4.69596i	0.817461	+	0.471962i
$100$	1.24347	−	1.56646i	0.124347	−	0.156646i
$101$	7.68692	−	13.3141i	0.764877	−	1.32481i	−0.175434	−	0.984491i	$-0.556133\pi$
$101$	7.68692	−	13.3141i	0.764877	−	1.32481i	0.940311	−	0.340315i	$-0.110534\pi$
$102$	4.89585	+	3.32990i	0.484762	+	0.329709i
$103$	−1.75581			−0.173005			−0.0865027	−	0.996252i	$-0.527569\pi$
$103$	−1.75581			−0.173005			−0.0865027	+	0.996252i	$0.527569\pi$
$104$	10.2307	−	11.1007i	1.00320	−	1.08852i
$105$	−0.841868	−	0.486053i	−0.0821579	−	0.0474339i
$106$	7.99237	−	11.7509i	0.776288	−	1.14135i
$107$	14.7127			1.42233			0.711167	−	0.703024i	$-0.248167\pi$
$107$	14.7127			1.42233			0.711167	+	0.703024i	$0.248167\pi$
$108$	9.66867	+	1.43515i	0.930368	+	0.138097i
$109$	−9.92633	+	5.73097i	−0.950770	+	0.548927i	−0.893320	−	0.449421i	$-0.851630\pi$
$109$	−9.92633	+	5.73097i	−0.950770	+	0.548927i	−0.0574500	+	0.998348i	$0.518297\pi$
$110$	−2.78886	−	5.77455i	−0.265907	−	0.550582i
$111$	3.25375	−	1.87855i	0.308832	−	0.178305i
$112$	1.17196	−	3.86079i	0.110740	−	0.364810i
$113$			4.64759i			0.437208i	0.975814	+	0.218604i	$0.0701503\pi$
$113$			4.64759i			0.437208i	−0.975814	+	0.218604i	$0.929850\pi$
$114$	1.52496	−	5.74180i	0.142825	−	0.537768i
$115$		−	2.74943i		−	0.256385i
$116$	−5.98523	−	4.75114i	−0.555714	−	0.441132i
$117$	9.57364	−	5.52734i	0.885083	−	0.511003i
$118$	−11.8286	+	5.71272i	−1.08891	+	0.525898i
$119$	3.79495	−	2.19102i	0.347883	−	0.200850i
$120$	−2.00442	−	1.84732i	−0.182977	−	0.168636i
$121$	−9.56159			−0.869236
$122$	10.9298	+	7.43390i	0.989542	+	0.673034i
$123$	0.213271	+	0.123132i	0.0192300	+	0.0111024i
$124$	−12.4219	−	1.84382i	−1.11552	−	0.165580i
$125$	−1.00000			−0.0894427
$126$	1.66164	−	2.44306i	0.148031	−	0.217645i
$127$	−4.93086	+	8.54050i	−0.437543	+	0.757847i	−0.997499	−	0.0706752i	$-0.977485\pi$
$127$	−4.93086	+	8.54050i	−0.437543	+	0.757847i	0.559956	+	0.828522i	$0.310818\pi$
$128$	5.57977	−	9.84206i	0.493187	−	0.869924i
$129$	1.09010	+	0.629368i	0.0959777	+	0.0554128i
$130$	−7.52759	−	0.555627i	−0.660213	−	0.0487317i
$131$	−19.2298	+	11.1024i	−1.68012	+	0.970017i	−0.718541	+	0.695485i	$0.755190\pi$
$131$	−19.2298	+	11.1024i	−1.68012	+	0.970017i	−0.961578	+	0.274532i	$0.911477\pi$
$132$	−8.12873	+	3.21135i	−0.707515	+	0.279512i
$133$	−3.33572	−	2.86435i	−0.289244	−	0.248370i
$134$	4.89151	+	3.32694i	0.422562	+	0.287404i
$135$	−2.44365	−	4.23253i	−0.210316	−	0.364278i
$136$	11.7294	−	3.66129i	1.00579	−	0.313953i
$137$	−5.46055	+	9.45794i	−0.466526	+	0.808046i	−0.999269	−	0.0382305i	$-0.987828\pi$
$137$	−5.46055	+	9.45794i	−0.466526	+	0.808046i	0.532743	+	0.846277i	$0.321161\pi$
$138$	−3.73710	−	0.275843i	−0.318123	−	0.0234813i
$139$	11.8455	+	6.83899i	1.00472	+	0.580076i	0.909642	−	0.415394i	$-0.136356\pi$
$139$	11.8455	+	6.83899i	1.00472	+	0.580076i	0.0950789	+	0.995470i	$0.469690\pi$
$140$	−1.87626	+	0.741239i	−0.158573	+	0.0626462i
$141$			5.78699i			0.487352i
$142$	−4.47311	+	2.16032i	−0.375375	+	0.181290i
$143$	−12.1009	+	20.9594i	−1.01193	+	1.75272i
$144$	6.04790	−	5.66233i	0.503992	−	0.471861i
$145$			3.82087i			0.317306i
$146$	18.8428	−	9.10025i	1.55944	−	0.753142i
$147$	−2.88279	−	4.99314i	−0.237769	−	0.411827i
$148$	1.14479	−	7.71249i	0.0941009	−	0.633963i
$149$	−6.04182	−	10.4647i	−0.494965	−	0.857305i	0.505018	−	0.863109i	$-0.331486\pi$
$149$	−6.04182	−	10.4647i	−0.494965	−	0.857305i	−0.999983	+	0.00580419i	$0.998152\pi$
$150$	−0.100327	+	1.35923i	−0.00819169	+	0.110980i
$151$	−19.2678			−1.56799			−0.783994	−	0.620768i	$-0.786821\pi$
$151$	−19.2678			−1.56799			−0.783994	+	0.620768i	$0.786821\pi$
$152$	−7.36514	−	9.88710i	−0.597392	−	0.801950i
$153$	8.99798			0.727444
$154$	−0.476154	+	6.45089i	−0.0383696	+	0.519828i
$155$	3.13950	+	5.43778i	0.252171	+	0.436773i
$156$	−1.51045	+	10.1760i	−0.120932	+	0.814729i
$157$	−0.937924	−	1.62453i	−0.0748545	−	0.129652i	0.826169	−	0.563423i	$-0.190516\pi$
$157$	−0.937924	−	1.62453i	−0.0748545	−	0.129652i	−0.901023	+	0.433771i	$0.857183\pi$
$158$	12.8237	−	6.19327i	1.02020	−	0.492710i
$159$			9.68451i			0.768031i
$160$	−5.58886	+	0.874461i	−0.441838	+	0.0691322i
$161$	−1.38666	+	2.40176i	−0.109284	+	0.189285i
$162$	1.91479	−	0.924762i	0.150440	−	0.0726561i
$163$		−	10.1371i		−	0.793995i	−0.917820	−	0.396998i	$-0.870052\pi$
$163$		−	10.1371i		−	0.793995i	0.917820	−	0.396998i	$-0.129948\pi$
$164$	0.475314	−	0.187778i	0.0371158	−	0.0146630i
$165$	3.78456	+	2.18502i	0.294628	+	0.170104i
$166$	−2.80502	−	0.207044i	−0.217712	−	0.0160698i
$167$	−9.36314	+	16.2174i	−0.724541	+	1.25494i	0.234621	+	0.972087i	$0.424615\pi$
$167$	−9.36314	+	16.2174i	−0.724541	+	1.25494i	−0.959163	+	0.282855i	$0.908718\pi$
$168$	0.819272	+	2.62463i	0.0632082	+	0.202495i
$169$	7.74332	+	13.4118i	0.595640	+	1.03168i
$170$	−5.08009	−	3.45521i	−0.389625	−	0.265002i
$171$	−2.99105	−	8.51836i	−0.228732	−	0.651416i
$172$	2.42949	−	0.959798i	0.185247	−	0.0731839i
$173$	4.54400	−	2.62348i	0.345474	−	0.199459i	−0.317216	−	0.948353i	$-0.602748\pi$
$173$	4.54400	−	2.62348i	0.345474	−	0.199459i	0.662690	+	0.748894i	$0.269415\pi$
$174$	5.19343	+	0.383338i	0.393713	+	0.0290608i
$175$	0.873549	+	0.504344i	0.0660341	+	0.0381248i
$176$	−5.26846	+	17.3559i	−0.397125	+	1.30825i
$177$	4.47581	−	7.75233i	0.336422	−	0.582701i
$178$	0.0617373	−	0.0907705i	0.00462741	−	0.00680354i
$179$	24.3278			1.81835			0.909173	−	0.416419i	$-0.136715\pi$
$179$	24.3278			1.81835			0.909173	+	0.416419i	$0.136715\pi$
$180$	−4.09754	−	0.608210i	−0.305413	−	0.0453333i
$181$	−15.3824	−	8.88101i	−1.14336	−	0.660120i	−0.196101	−	0.980584i	$-0.562828\pi$
$181$	−15.3824	−	8.88101i	−1.14336	−	0.660120i	−0.947261	+	0.320463i	$0.896161\pi$
$182$	6.29549	+	4.28186i	0.466653	+	0.317392i
$183$	−9.00780			−0.665876
$184$	−5.27019	+	5.71838i	−0.388524	+	0.421565i
$185$	−3.37620	+	1.94925i	−0.248223	+	0.143312i
$186$	7.70616	−	3.72174i	0.565043	−	0.272891i
$187$	−17.0600	+	9.84958i	−1.24755	+	0.720273i
$188$	9.40619	+	7.46674i	0.686017	+	0.544568i
$189$			4.92976i			0.358587i
$190$	−1.58234	+	5.95787i	−0.114795	+	0.432229i
$191$		−	2.43108i		−	0.175907i	−0.996125	−	0.0879535i	$-0.971967\pi$
$191$		−	2.43108i		−	0.175907i	0.996125	−	0.0879535i	$-0.0280327\pi$
$192$	0.627876	+	7.68426i	0.0453130	+	0.554564i
$193$	−1.71887	+	0.992391i	−0.123727	+	0.0714339i	−0.560586	−	0.828096i	$-0.689424\pi$
$193$	−1.71887	+	0.992391i	−0.123727	+	0.0714339i	0.436859	+	0.899530i	$0.356091\pi$
$194$	−9.94656	−	20.5951i	−0.714121	−	1.47864i
$195$	4.45459	−	2.57186i	0.319000	−	0.184175i
$196$	−11.8354	−	1.75677i	−0.845388	−	0.125483i
$197$	−15.4753			−1.10257			−0.551285	−	0.834317i	$-0.685862\pi$
$197$	−15.4753			−1.10257			−0.551285	+	0.834317i	$0.685862\pi$
$198$	−7.46980	+	10.9826i	−0.530856	+	0.780502i
$199$	−9.00340	−	5.19811i	−0.638234	−	0.368485i	0.145700	−	0.989329i	$-0.453457\pi$
$199$	−9.00340	−	5.19811i	−0.638234	−	0.368485i	−0.783934	+	0.620844i	$0.786790\pi$
$200$	2.07984	+	1.91683i	0.147067	+	0.135541i
$201$	−4.03132			−0.284347
$202$	17.9777	+	12.2275i	1.26491	+	0.860324i
$203$	1.92703	−	3.33772i	0.135251	−	0.234262i
$204$	−5.20609	+	6.55835i	−0.364499	+	0.459176i
$205$	−0.221296	−	0.127766i	−0.0154560	−	0.00892353i
$206$	0.182785	−	2.47636i	0.0127352	−	0.172536i
$207$	−4.93172	+	2.84733i	−0.342779	+	0.197903i
$208$	14.5912	+	15.5847i	1.01172	+	1.08061i
$209$	14.9955	+	12.8765i	1.03726	+	0.890686i
$210$	0.773158	−	1.13675i	0.0533530	−	0.0784433i
$211$	2.10807	+	3.65128i	0.145125	+	0.251365i	0.929420	−	0.369024i	$-0.120308\pi$
$211$	2.10807	+	3.65128i	0.145125	+	0.251365i	−0.784294	+	0.620389i	$0.786975\pi$
$212$	15.7412	+	12.4956i	1.08111	+	0.858199i
$213$	1.69257	−	2.93162i	0.115973	−	0.200871i
$214$	−1.53164	+	20.7505i	−0.104700	+	1.41847i
$215$	−1.13112	−	0.653052i	−0.0771417	−	0.0445378i
$216$	−3.03064	+	13.4871i	−0.206209	+	0.917679i
$217$		−	6.33355i		−	0.429950i
$218$	−7.04947	−	14.5965i	−0.477450	−	0.988598i
$219$	−7.12987	+	12.3493i	−0.481792	+	0.834489i
$220$	8.43462	−	3.33220i	0.568662	−	0.224657i
$221$			23.1868i			1.55971i
$222$	2.31075	+	4.78458i	0.155087	+	0.321120i
$223$	−0.364242	−	0.630886i	−0.0243915	−	0.0422473i	0.853572	−	0.520975i	$-0.174431\pi$
$223$	−0.364242	−	0.630886i	−0.0243915	−	0.0422473i	−0.877963	+	0.478728i	$0.841098\pi$
$224$	5.32317	+	2.05482i	0.355669	+	0.137293i
$225$	1.03561	+	1.79373i	0.0690406	+	0.119582i
$226$	−6.55485	−	0.483827i	−0.436022	−	0.0321837i
$227$	19.0722			1.26587			0.632935	−	0.774205i	$-0.281850\pi$
$227$	19.0722			1.26587			0.632935	+	0.774205i	$0.281850\pi$
$228$	7.93934	+	2.74850i	0.525796	+	0.182024i
$229$	14.5393			0.960787			0.480393	−	0.877053i	$-0.340494\pi$
$229$	14.5393			0.960787			0.480393	+	0.877053i	$0.340494\pi$
$230$	3.87773	+	0.286223i	0.255690	+	0.0188730i
$231$	−2.20400	−	3.81744i	−0.145013	−	0.251169i
$232$	7.32397	−	7.94682i	0.480842	−	0.521734i
$233$	−13.2895	−	23.0181i	−0.870625	−	1.50797i	−0.861351	−	0.508010i	$-0.830381\pi$
$233$	−13.2895	−	23.0181i	−0.870625	−	1.50797i	−0.00927385	−	0.999957i	$-0.502952\pi$
$234$	6.79899	+	14.0779i	0.444464	+	0.920298i
$235$		−	6.00476i		−	0.391707i
$236$	−6.82569	−	17.2775i	−0.444315	−	1.12467i
$237$	−4.85231	+	8.40445i	−0.315192	+	0.545928i
$238$	2.69509	+	5.58040i	0.174697	+	0.361724i
$239$		−	16.1707i		−	1.04600i	−0.852333	−	0.522999i	$-0.824813\pi$
$239$		−	16.1707i		−	1.04600i	0.852333	−	0.522999i	$-0.175187\pi$
$240$	2.81408	−	2.63467i	0.181648	−	0.170067i
$241$	−12.6222	−	7.28741i	−0.813066	−	0.469424i	0.0349538	−	0.999389i	$-0.488872\pi$
$241$	−12.6222	−	7.28741i	−0.813066	−	0.469424i	−0.848019	+	0.529965i	$0.822205\pi$
$242$	0.995389	−	13.4854i	0.0639860	−	0.866878i
$243$	−8.05549	+	13.9525i	−0.516760	+	0.895054i
$244$	−11.6224	+	14.6413i	−0.744050	+	0.937314i
$245$	2.99128	+	5.18104i	0.191106	+	0.331005i
$246$	−0.195864	+	0.287974i	−0.0124879	+	0.0183605i
$247$	21.9508	−	7.70760i	1.39670	−	0.490423i
$248$	3.89364	−	17.3276i	0.247246	−	1.10031i
$249$	1.65992	−	0.958358i	0.105193	−	0.0607335i
$250$	0.104103	−	1.41038i	0.00658404	−	0.0892001i
$251$	4.30583	+	2.48597i	0.271782	+	0.156913i	0.629697	−	0.776841i	$-0.283179\pi$
$251$	4.30583	+	2.48597i	0.271782	+	0.156913i	−0.357915	+	0.933754i	$0.616512\pi$
$252$	3.27266	+	2.59787i	0.206158	+	0.163650i
$253$	6.23363	−	10.7970i	0.391905	−	0.678799i
$254$	−11.5320	−	7.84346i	−0.723583	−	0.492143i
$255$	4.18674			0.262184
$256$	13.3001	+	8.89416i	0.831259	+	0.555885i
$257$	2.97565	+	1.71799i	0.185616	+	0.107165i	0.589929	−	0.807455i	$-0.299156\pi$
$257$	2.97565	+	1.71799i	0.185616	+	0.107165i	−0.404313	+	0.914621i	$0.632489\pi$
$258$	−1.00113	+	1.47193i	−0.0623275	+	0.0916383i
$259$	3.93236			0.244345
$260$	1.56729	−	10.5589i	0.0971989	−	0.654835i
$261$	6.85360	−	3.95693i	0.424227	−	0.244928i
$262$	−13.6566	−	28.2771i	−0.843709	−	1.74697i
$263$	13.5155	−	7.80316i	0.833400	−	0.481164i	−0.0216155	−	0.999766i	$-0.506881\pi$
$263$	13.5155	−	7.80316i	0.833400	−	0.481164i	0.855015	+	0.518603i	$0.173548\pi$
$264$	−3.68299	−	11.7989i	−0.226672	−	0.726171i
$265$		−	10.0489i		−	0.617302i
$266$	4.38707	−	4.40644i	0.268988	−	0.270176i
$267$			0.0748083i			0.00457819i
$268$	−5.20146	+	6.55252i	−0.317730	+	0.400259i
$269$	−23.4209	+	13.5220i	−1.42800	+	0.824453i	−0.996963	−	0.0778831i	$-0.975184\pi$
$269$	−23.4209	+	13.5220i	−1.42800	+	0.824453i	−0.431033	+	0.902336i	$0.641851\pi$
$270$	6.22385	−	3.00585i	0.378771	−	0.182930i
$271$	−12.4510	+	7.18860i	−0.756346	+	0.436676i	−0.827982	−	0.560754i	$-0.810511\pi$
$271$	−12.4510	+	7.18860i	−0.756346	+	0.436676i	0.0716365	+	0.997431i	$0.477178\pi$
$272$	3.94274	+	16.9240i	0.239064	+	1.02617i
$273$	−5.18841			−0.314017
$274$	−12.7708	−	8.68602i	−0.771512	−	0.524742i
$275$	−3.92698	−	2.26724i	−0.236806	−	0.136720i
$276$	0.778084	−	5.24200i	0.0468352	−	0.315531i
$277$	27.7012			1.66440			0.832201	−	0.554474i	$-0.187080\pi$
$277$	27.7012			1.66440			0.832201	+	0.554474i	$0.187080\pi$
$278$	−10.8787	+	15.9946i	−0.652461	+	0.959294i
$279$	6.50260	−	11.2628i	0.389300	−	0.674288i
$280$	−0.850103	−	2.72340i	−0.0508034	−	0.162754i
$281$	15.5000	+	8.94894i	0.924654	+	0.533849i	0.885117	−	0.465369i	$-0.154078\pi$
$281$	15.5000	+	8.94894i	0.924654	+	0.533849i	0.0395370	+	0.999218i	$0.487412\pi$
$282$	−8.16183	−	0.602442i	−0.486030	−	0.0358749i
$283$	9.30913	−	5.37463i	0.553371	−	0.319489i	−0.197110	−	0.980381i	$-0.563156\pi$
$283$	9.30913	−	5.37463i	0.553371	−	0.319489i	0.750480	+	0.660893i	$0.229822\pi$
$284$	−2.58120	−	6.53367i	−0.153166	−	0.387702i
$285$	−1.39173	−	3.96358i	−0.0824390	−	0.234782i
$286$	−28.3010	−	19.2488i	−1.67347	−	1.13821i
$287$	0.128875	+	0.223219i	0.00760728	+	0.0131762i
$288$	7.35641	+	9.11929i	0.433481	+	0.537359i
$289$	−0.936449	+	1.62198i	−0.0550852	+	0.0954104i
$290$	−5.38887	−	0.397763i	−0.316445	−	0.0233575i
$291$	13.4978	+	7.79294i	0.791253	+	0.456830i
$292$	10.8732	+	27.5228i	0.636305	+	1.61065i
$293$		−	1.14249i		−	0.0667452i	−0.999443	−	0.0333726i	$-0.989375\pi$
$293$		−	1.14249i		−	0.0667452i	0.999443	−	0.0333726i	$-0.0106248\pi$
$294$	7.34232	−	3.54602i	0.428213	−	0.206808i
$295$	−4.64424	+	8.04406i	−0.270398	+	0.468343i
$296$	10.7583	+	2.41747i	0.625316	+	0.140513i
$297$		−	22.1614i		−	1.28594i
$298$	15.3882	−	7.43183i	0.891414	−	0.430514i
$299$	−7.33725	−	12.7085i	−0.424324	−	0.734950i
$300$	−1.90658	−	0.282999i	−0.110076	−	0.0163389i
$301$	0.658725	+	1.14095i	0.0379683	+	0.0657630i
$302$	2.00583	−	27.1748i	0.115422	−	1.56373i
$303$	−14.8163			−0.851174
$304$	14.7113	−	9.35835i	0.843749	−	0.536738i
$305$	9.34677			0.535195
$306$	−0.936715	+	12.6905i	−0.0535484	+	0.725470i
$307$	−5.61181	−	9.71994i	−0.320283	−	0.554746i	0.660263	−	0.751034i	$-0.270445\pi$
$307$	−5.61181	−	9.71994i	−0.320283	−	0.554746i	−0.980546	+	0.196288i	$0.937111\pi$
$308$	−9.04862	−	1.34311i	−0.515593	−	0.0765309i
$309$	0.846068	+	1.46543i	0.0481311	+	0.0833655i
$310$	−7.99615	+	3.86179i	−0.454151	+	0.219335i
$311$		−	17.6370i		−	1.00010i	−0.865996	−	0.500051i	$-0.833314\pi$
$311$		−	17.6370i		−	1.00010i	0.865996	−	0.500051i	$-0.166686\pi$
$312$	−14.1947	−	3.18964i	−0.803616	−	0.180578i
$313$	−0.570027	+	0.987315i	−0.0322198	+	0.0558063i	−0.881686	−	0.471837i	$-0.843591\pi$
$313$	−0.570027	+	0.987315i	−0.0322198	+	0.0558063i	0.849466	+	0.527644i	$0.176924\pi$
$314$	2.38884	−	1.15371i	0.134810	−	0.0651075i
$315$		−	2.08921i		−	0.117714i
$316$	7.39987	+	18.7309i	0.416275	+	1.05370i
$317$	−5.60077	−	3.23361i	−0.314571	−	0.181618i	0.334399	−	0.942432i	$-0.391467\pi$
$317$	−5.60077	−	3.23361i	−0.314571	−	0.181618i	−0.648970	+	0.760814i	$0.724800\pi$
$318$	−13.6588	−	1.00818i	−0.765948	−	0.0565362i
$319$	−8.66285	+	15.0045i	−0.485026	+	0.840090i
$320$	−0.651503	−	7.97343i	−0.0364201	−	0.445728i
$321$	−7.08957	−	12.2795i	−0.395701	−	0.685375i
$322$	−3.24303	−	2.20574i	−0.180727	−	0.122921i
$323$	18.6100	+	3.50035i	1.03549	+	0.194765i
$324$	1.10493	+	2.79685i	0.0613848	+	0.155380i
$325$	−4.62223	+	2.66864i	−0.256395	+	0.148030i
$326$	14.2971	+	1.05530i	0.791841	+	0.0584474i
$327$	9.56634	+	5.52313i	0.529020	+	0.305430i
$328$	0.215357	+	0.689920i	0.0118911	+	0.0380945i
$329$	−3.02846	+	5.24545i	−0.166964	+	0.289191i
$330$	−3.47568	+	5.11020i	−0.191330	+	0.281307i
$331$	17.3540			0.953863			0.476931	−	0.878940i	$-0.341749\pi$
$331$	17.3540			0.953863			0.476931	+	0.878940i	$0.341749\pi$
$332$	0.584021	−	3.93458i	0.0320523	−	0.215938i
$333$	6.99284	+	4.03732i	0.383205	+	0.221244i
$334$	−21.8980	−	14.8938i	−1.19820	−	0.814954i
$335$	4.18303			0.228543
$336$	−3.78701	+	0.882251i	−0.206598	+	0.0481307i
$337$	16.1344	−	9.31522i	0.878899	−	0.507432i	0.00860366	−	0.999963i	$-0.497261\pi$
$337$	16.1344	−	9.31522i	0.878899	−	0.507432i	0.870295	+	0.492531i	$0.163928\pi$
$338$	−19.7218	+	9.52479i	−1.07273	+	0.518081i
$339$	3.87896	−	2.23952i	0.210676	−	0.121634i
$340$	5.40200	−	6.80515i	0.292964	−	0.369061i
$341$			28.4721i			1.54185i
$342$	12.3255	−	3.33173i	0.666486	−	0.180159i
$343$		−	13.0953i		−	0.707081i
$344$	1.10076	+	3.52641i	0.0593490	+	0.190131i
$345$	−2.29472	+	1.32486i	−0.123544	+	0.0713279i
$346$	3.22705	+	6.68186i	0.173487	+	0.359219i
$347$	7.19175	−	4.15216i	0.386074	−	0.222900i	−0.294384	−	0.955687i	$-0.595114\pi$
$347$	7.19175	−	4.15216i	0.386074	−	0.222900i	0.680457	+	0.732788i	$0.261781\pi$
$348$	−1.08130	+	7.28479i	−0.0579638	+	0.390506i
$349$	−12.8450			−0.687579			−0.343789	−	0.939047i	$-0.611711\pi$
$349$	−12.8450			−0.687579			−0.343789	+	0.939047i	$0.611711\pi$
$350$	−0.802253	+	1.17953i	−0.0428822	+	0.0630485i
$351$	−22.5902	−	13.0425i	−1.20578	−	0.696156i
$352$	−23.9300	−	9.23731i	−1.27547	−	0.492350i
$353$	−30.3460			−1.61516			−0.807578	−	0.589761i	$-0.799222\pi$
$353$	−30.3460			−1.61516			−0.807578	+	0.589761i	$0.799222\pi$
$354$	10.4678	+	7.11962i	0.556355	+	0.378403i
$355$	−1.75626	+	3.04194i	−0.0932128	+	0.161449i
$356$	0.121594	+	0.0965223i	0.00644445	+	0.00511567i
$357$	−3.65732	−	2.11156i	−0.193566	−	0.111755i
$358$	−2.53259	+	34.3114i	−0.133852	+	1.81341i
$359$	6.75492	−	3.89995i	0.356511	−	0.205832i	−0.311038	−	0.950397i	$-0.600677\pi$
$359$	6.75492	−	3.89995i	0.356511	−	0.205832i	0.667549	+	0.744566i	$0.267343\pi$
$360$	1.28437	−	5.71576i	0.0676923	−	0.301247i
$361$	−2.87245	−	18.7816i	−0.151182	−	0.988506i
$362$	14.1269	−	20.7704i	0.742494	−	1.09167i
$363$	4.60741	+	7.98027i	0.241827	+	0.418856i
$364$	−6.69441	+	8.43325i	−0.350882	+	0.442023i
$365$	7.39818	−	12.8140i	0.387239	−	0.670717i
$366$	0.937737	−	12.7044i	0.0490163	−	0.664069i
$367$	−13.2620	−	7.65685i	−0.692273	−	0.399684i	0.112190	−	0.993687i	$-0.464214\pi$
$367$	−13.2620	−	7.65685i	−0.692273	−	0.399684i	−0.804463	+	0.594003i	$0.797547\pi$
$368$	−7.51643	−	8.02826i	−0.391821	−	0.418502i
$369$			0.529260i			0.0275522i
$370$	−2.39770	−	4.96463i	−0.124651	−	0.258099i
$371$	−5.06812	+	8.77824i	−0.263124	+	0.455744i
$372$	4.44682	+	11.2560i	0.230557	+	0.583598i
$373$			5.42216i			0.280749i	0.990098	+	0.140374i	$0.0448306\pi$
$373$			5.42216i			0.280749i	−0.990098	+	0.140374i	$0.955169\pi$
$374$	−12.1156	−	25.0864i	−0.626484	−	1.29718i
$375$	0.481867	+	0.834618i	0.0248835	+	0.0430995i
$376$	−11.5101	+	12.4890i	−0.593589	+	0.644069i
$377$	10.1965	+	17.6609i	0.525149	+	0.909584i
$378$	−6.95282	−	0.513202i	−0.357614	−	0.0263962i
$379$	−23.0089			−1.18189			−0.590944	−	0.806712i	$-0.701245\pi$
$379$	−23.0089			−1.18189			−0.590944	+	0.806712i	$0.701245\pi$
$380$	−8.23811	−	2.85193i	−0.422606	−	0.146301i
$381$	9.50407			0.486908
$382$	3.42874	+	0.253083i	0.175430	+	0.0129488i
$383$	−1.24491	−	2.15624i	−0.0636118	−	0.110179i	0.832466	−	0.554077i	$-0.186929\pi$
$383$	−1.24491	−	2.15624i	−0.0636118	−	0.110179i	−0.896077	+	0.443898i	$0.853595\pi$
$384$	−10.9031	+	0.0855884i	−0.556395	+	0.00436766i
$385$	2.28694	+	3.96110i	0.116553	+	0.201876i
$386$	−1.22071	−	2.52757i	−0.0621323	−	0.128650i
$387$			2.70523i			0.137514i
$388$	30.0823	−	11.8844i	1.52720	−	0.603338i
$389$	−9.78547	+	16.9489i	−0.496143	+	0.859345i	−0.999990	−	0.00444775i	$-0.998584\pi$
$389$	−9.78547	+	16.9489i	−0.496143	+	0.859345i	0.503847	+	0.863793i	$0.331918\pi$
$390$	3.16356	+	6.55040i	0.160193	+	0.331692i
$391$		−	11.9443i		−	0.604051i
$392$	3.70980	−	16.5095i	0.187373	−	0.833857i
$393$	18.5324	+	10.6997i	0.934838	+	0.539729i
$394$	1.61102	−	21.8260i	0.0811621	−	1.09958i
$395$	5.03491	−	8.72072i	0.253334	−	0.438787i
$396$	−14.7120	−	11.6786i	−0.739307	−	0.586870i
$397$	−10.9519	−	18.9692i	−0.549659	−	0.952038i	−0.998298	−	0.0583246i	$-0.981424\pi$
$397$	−10.9519	−	18.9692i	−0.549659	−	0.952038i	0.448638	−	0.893713i	$-0.351909\pi$
$398$	8.26858	−	12.1570i	0.414466	−	0.609378i
$399$	−0.783260	+	4.16429i	−0.0392120	+	0.208475i
$400$	−2.91997	+	2.73382i	−0.145999	+	0.136691i
$401$	18.1750	−	10.4933i	0.907615	−	0.524012i	0.0279521	−	0.999609i	$-0.491101\pi$
$401$	18.1750	−	10.4933i	0.907615	−	0.524012i	0.879663	+	0.475597i	$0.157768\pi$
$402$	0.419672	−	5.68568i	0.0209313	−	0.283576i
$403$	29.0230	+	16.7564i	1.44574	+	0.834698i
$404$	−19.1169	+	24.0825i	−0.951102	+	1.19815i
$405$	0.751799	−	1.30215i	0.0373572	−	0.0647045i
$406$	4.50683	+	3.06531i	0.223670	+	0.152129i
$407$	−17.6777			−0.876250
$408$	−8.70777	−	8.02529i	−0.431099	−	0.397311i
$409$	21.9922	+	12.6972i	1.08744	+	0.627837i	0.932895	−	0.360148i	$-0.117274\pi$
$409$	21.9922	+	12.6972i	1.08744	+	0.627837i	0.154550	+	0.987985i	$0.450607\pi$
$410$	0.203235	−	0.298810i	0.0100371	−	0.0147572i
$411$	10.5250			0.519161
$412$	3.47357	+	0.515592i	0.171130	+	0.0254014i
$413$	8.11394	−	4.68458i	0.399261	−	0.230513i
$414$	−3.50241	−	7.25200i	−0.172134	−	0.356417i
$415$	−1.72239	+	0.994422i	−0.0845488	+	0.0488143i
$416$	−23.4993	+	18.9566i	−1.15215	+	0.929425i
$417$		−	13.1819i		−	0.645522i
$418$	−19.7218	+	19.8089i	−0.964624	+	0.968884i
$419$			8.85719i			0.432702i	0.976316	+	0.216351i	$0.0694155\pi$
$419$			8.85719i			0.432702i	−0.976316	+	0.216351i	$0.930584\pi$
$420$	1.52276	+	1.20878i	0.0743031	+	0.0589826i
$421$	5.08793	−	2.93752i	0.247971	−	0.143166i	−0.370864	−	0.928687i	$-0.620938\pi$
$421$	5.08793	−	2.93752i	0.247971	−	0.143166i	0.618835	+	0.785521i	$0.287605\pi$
$422$	−5.36914	+	2.59306i	−0.261365	+	0.126228i
$423$	−10.7709	+	6.21858i	−0.523699	+	0.302358i
$424$	−19.2622	+	20.9002i	−0.935453	+	1.01501i
$425$	−4.34429			−0.210729
$426$	3.95849	+	2.69235i	0.191789	+	0.130445i
$427$	−8.16486	−	4.71399i	−0.395125	−	0.228126i
$428$	−29.1066	−	4.32037i	−1.40692	−	0.208833i
$429$	23.3242			1.12610
$430$	1.03880	−	1.52732i	0.0500955	−	0.0736539i
$431$	−9.07042	+	15.7104i	−0.436907	+	0.756745i	−0.997449	−	0.0713810i	$-0.977259\pi$
$431$	−9.07042	+	15.7104i	−0.436907	+	0.756745i	0.560542	+	0.828126i	$0.310593\pi$
$432$	−18.7064	−	5.67838i	−0.900010	−	0.273201i
$433$	21.8342	+	12.6060i	1.04929	+	0.605805i	0.922449	−	0.386118i	$-0.126184\pi$
$433$	21.8342	+	12.6060i	1.04929	+	0.605805i	0.126837	+	0.991924i	$0.459518\pi$
$434$	8.93270	+	0.659340i	0.428783	+	0.0316494i
$435$	3.18897	−	1.84115i	0.152899	−	0.0882764i
$436$	21.3204	−	8.42287i	1.02106	−	0.403382i
$437$	−11.3077	+	3.97046i	−0.540919	+	0.189933i
$438$	−16.6749	−	11.3414i	−0.796759	−	0.541913i
$439$	−8.32200	−	14.4141i	−0.397187	−	0.687949i	0.596190	−	0.802843i	$-0.296680\pi$
$439$	−8.32200	−	14.4141i	−0.397187	−	0.687949i	−0.993378	+	0.114894i	$0.963347\pi$
$440$	3.82158	+	12.2429i	0.182187	+	0.583657i
$441$	6.19558	−	10.7311i	0.295028	−	0.511003i
$442$	−32.7021	−	2.41381i	−1.55548	−	0.114813i
$443$	−13.4967	−	7.79234i	−0.641249	−	0.370225i	0.143847	−	0.989600i	$-0.454053\pi$
$443$	−13.4967	−	7.79234i	−0.641249	−	0.370225i	−0.785095	+	0.619375i	$0.787386\pi$
$444$	−6.98861	+	2.76093i	−0.331665	+	0.131028i
$445$		−	0.0776234i		−	0.00367970i
$446$	0.927706	−	0.448042i	0.0439282	−	0.0212154i
$447$	−5.82270	+	10.0852i	−0.275404	+	0.477014i
$448$	−3.45223	+	7.29376i	−0.163102	+	0.344598i
$449$			2.53183i			0.119484i	0.998214	+	0.0597421i	$0.0190278\pi$
$449$			2.53183i			0.119484i	−0.998214	+	0.0597421i	$0.980972\pi$
$450$	−2.63764	+	1.27387i	−0.124340	+	0.0600507i
$451$	−0.579351	−	1.00347i	−0.0272806	−	0.0472514i
$452$	1.36476	−	9.19444i	0.0641927	−	0.432470i
$453$	9.28449	+	16.0812i	0.436224	+	0.755561i
$454$	−1.98547	+	26.8990i	−0.0931829	+	1.26243i
$455$	5.38365			0.252390
$456$	−4.70293	+	10.9113i	−0.220235	+	0.510970i
$457$	13.8954			0.650001			0.325001	−	0.945714i	$-0.394635\pi$
$457$	13.8954			0.650001			0.325001	+	0.945714i	$0.394635\pi$
$458$	−1.51359	+	20.5060i	−0.0707252	+	0.958180i
$459$	−10.6159	−	18.3873i	−0.495510	−	0.858248i
$460$	−0.807365	+	5.43926i	−0.0376436	+	0.253607i
$461$	−14.9800	−	25.9460i	−0.697686	−	1.20843i	−0.969267	−	0.246012i	$-0.920880\pi$
$461$	−14.9800	−	25.9460i	−0.697686	−	1.20843i	0.271581	−	0.962416i	$-0.412454\pi$
$462$	5.61347	−	2.71107i	0.261162	−	0.126130i
$463$		−	23.1722i		−	1.07690i	−0.842656	−	0.538452i	$-0.819009\pi$
$463$		−	23.1722i		−	1.07690i	0.842656	−	0.538452i	$-0.180991\pi$
$464$	10.4456	+	11.1568i	0.484923	+	0.517944i
$465$	3.02564	−	5.24057i	0.140311	−	0.243026i
$466$	33.8477	−	16.3470i	1.56796	−	0.757259i
$467$		−	21.0645i		−	0.974747i	−0.873194	−	0.487374i	$-0.837955\pi$
$467$		−	21.0645i		−	0.974747i	0.873194	−	0.487374i	$-0.162045\pi$
$468$	−20.5629	+	8.12360i	−0.950519	+	0.375514i
$469$	−3.65408	−	2.10968i	−0.168730	−	0.0974160i
$470$	8.46897	+	0.625112i	0.390645	+	0.0288343i
$471$	−0.903908	+	1.56562i	−0.0416499	+	0.0721397i
$472$	25.0784	−	7.82816i	1.15433	−	0.360320i
$473$	−2.96126	−	5.12905i	−0.136159	−	0.235834i
$474$	−11.3483	−	7.71852i	−0.521245	−	0.354523i
$475$	1.44410	+	4.11273i	0.0662600	+	0.188705i
$476$	−8.15104	+	3.22016i	−0.373602	+	0.147596i
$477$	−18.0251	+	10.4068i	−0.825311	+	0.476494i
$478$	22.8068	+	1.68342i	1.04316	+	0.0769978i
$479$	−7.97192	−	4.60259i	−0.364246	−	0.210298i	0.306695	−	0.951808i	$-0.400777\pi$
$479$	−7.97192	−	4.60259i	−0.364246	−	0.210298i	−0.670942	+	0.741510i	$0.734110\pi$
$480$	3.42292	+	4.24318i	0.156234	+	0.193674i
$481$	−10.4037	+	18.0197i	−0.474368	+	0.821629i
$482$	11.5920	−	17.0434i	0.528001	−	0.776305i
$483$	2.67273			0.121614
$484$	18.9159	+	2.80775i	0.859816	+	0.127625i
$485$	−14.0057	−	8.08620i	−0.635966	−	0.367175i
$486$	−18.8397	−	12.8138i	−0.854586	−	0.581244i
$487$	36.9569			1.67468			0.837338	−	0.546685i	$-0.184110\pi$
$487$	36.9569			1.67468			0.837338	+	0.546685i	$0.184110\pi$
$488$	−19.4398	−	17.9162i	−0.880000	−	0.811028i
$489$	−8.46056	+	4.88471i	−0.382600	+	0.220894i
$490$	−7.61862	+	3.67946i	−0.344174	+	0.166221i
$491$	24.8736	−	14.3608i	1.12253	−	0.648094i	0.180486	−	0.983578i	$-0.442233\pi$
$491$	24.8736	−	14.3608i	1.12253	−	0.648094i	0.942046	+	0.335483i	$0.108900\pi$
$492$	−0.385761	−	0.306222i	−0.0173915	−	0.0138055i
$493$			16.5990i			0.747581i
$494$	8.58548	+	31.7613i	0.386279	+	1.42901i
$495$			9.39192i			0.422135i
$496$	24.0332	+	7.29535i	1.07912	+	0.327571i
$497$	3.06836	−	1.77152i	0.137635	−	0.0794636i
$498$	1.17884	+	2.44089i	0.0528252	+	0.109379i
$499$	16.6731	−	9.62623i	0.746391	−	0.430929i	−0.0779972	−	0.996954i	$-0.524853\pi$
$499$	16.6731	−	9.62623i	0.746391	−	0.430929i	0.824389	+	0.566024i	$0.191519\pi$
$500$	1.97833	+	0.293648i	0.0884734	+	0.0131324i
$501$	18.0471			0.806287
$502$	−3.95441	+	5.81405i	−0.176494	+	0.259494i
$503$	−37.3664	−	21.5735i	−1.66609	−	0.961915i	−0.969717	−	0.244230i	$-0.921465\pi$
$503$	−37.3664	−	21.5735i	−1.66609	−	0.961915i	−0.696368	−	0.717685i	$-0.745202\pi$
$504$	−4.00467	+	4.34523i	−0.178382	+	0.193552i
$505$	15.3738			0.684127
$506$	14.5788	+	9.91575i	0.648108	+	0.440809i
$507$	7.46250	−	12.9254i	0.331421	−	0.574038i
$508$	12.2627	−	15.4480i	0.544072	−	0.685392i
$509$	12.8383	+	7.41220i	0.569048	+	0.328540i	0.756769	−	0.653682i	$-0.226777\pi$
$509$	12.8383	+	7.41220i	0.569048	+	0.328540i	−0.187721	+	0.982222i	$0.560110\pi$
$510$	−0.435852	+	5.90488i	−0.0192998	+	0.261473i
$511$	−12.9253	+	7.46245i	−0.571783	+	0.330119i
$512$	−13.9287	+	17.8323i	−0.615567	+	0.788084i
$513$	−13.8784	+	16.1623i	−0.612745	+	0.713583i
$514$	−2.73279	+	4.01794i	−0.120538	+	0.177224i
$515$	−0.877907	−	1.52058i	−0.0386852	−	0.0670047i
$516$	−1.97175	−	1.56520i	−0.0868016	−	0.0689041i
$517$	13.6143	−	23.5806i	0.598754	−	1.03707i
$518$	−0.409370	+	5.54611i	−0.0179867	+	0.243682i
$519$	−4.37920	−	2.52833i	−0.192226	−	0.110982i
$520$	14.7289	+	3.30967i	0.645903	+	0.145139i
$521$			28.3724i			1.24302i	0.783407	+	0.621509i	$0.213480\pi$
$521$			28.3724i			1.24302i	−0.783407	+	0.621509i	$0.786520\pi$
$522$	4.86728	+	10.0781i	0.213035	+	0.441106i
$523$	−17.5072	+	30.3233i	−0.765535	+	1.32595i	0.174428	+	0.984670i	$0.444193\pi$
$523$	−17.5072	+	30.3233i	−0.765535	+	1.32595i	−0.939963	+	0.341276i	$0.889141\pi$
$524$	41.3031	−	16.3173i	1.80433	−	0.712823i
$525$		−	0.972105i		−	0.0424262i
$526$	9.59840	+	19.8742i	0.418510	+	0.866558i
$527$	13.6389	+	23.6233i	0.594121	+	1.02905i
$528$	17.0243	−	3.96610i	0.740886	−	0.172603i
$529$	−7.72032	−	13.3720i	−0.335666	−	0.581391i
$530$	14.1728	+	1.04612i	0.615627	+	0.0454407i
$531$	19.2385			0.834878
$532$	5.75804	+	6.64614i	0.249643	+	0.288147i
$533$	−1.36384			−0.0590746
$534$	−0.105508	−	0.00778775i	−0.00456577	−	0.000337009i
$535$	7.35636	+	12.7416i	0.318043	+	0.550867i
$536$	−8.70004	−	8.01816i	−0.375785	−	0.346332i
$537$	−11.7228	−	20.3044i	−0.505874	−	0.876200i
$538$	−16.6330	−	34.4399i	−0.717099	−	1.48481i
$539$			27.1278i			1.16848i
$540$	3.59146	+	9.09089i	0.154552	+	0.391210i
$541$	−3.01267	+	5.21810i	−0.129525	+	0.224344i	−0.923493	−	0.383616i	$-0.874679\pi$
$541$	−3.01267	+	5.21810i	−0.129525	+	0.224344i	0.793968	+	0.607960i	$0.208012\pi$
$542$	−8.84245	−	18.3090i	−0.379816	−	0.786438i
$543$			17.1179i			0.734597i
$544$	−24.2796	+	3.79891i	−1.04098	+	0.162877i
$545$	−9.92633	−	5.73097i	−0.425197	−	0.245488i
$546$	0.540128	−	7.31761i	0.0231153	−	0.313165i
$547$	12.2390	−	21.1985i	0.523300	−	0.906383i	−0.476332	−	0.879266i	$-0.658034\pi$
$547$	12.2390	−	21.1985i	0.523300	−	0.906383i	0.999632	−	0.0271173i	$-0.00863278\pi$
$548$	13.5800	−	17.1074i	0.580111	−	0.730792i
$549$	−9.67960	−	16.7656i	−0.413115	−	0.715537i
$550$	3.60648	−	5.30250i	0.153781	−	0.226099i
$551$	15.7142	−	5.51774i	0.669448	−	0.235063i
$552$	7.31219	+	1.64310i	0.311228	+	0.0699349i
$553$	−8.79648	+	5.07865i	−0.374064	+	0.215966i
$554$	−2.88377	+	39.0691i	−0.122520	+	1.65989i
$555$	3.25375	+	1.87855i	0.138114	+	0.0797402i
$556$	−21.4260	−	17.0082i	−0.908663	−	0.721306i
$557$	−7.08447	+	12.2707i	−0.300179	+	0.519925i	−0.976176	−	0.216979i	$-0.930380\pi$
$557$	−7.08447	+	12.2707i	−0.300179	+	0.519925i	0.675998	+	0.736904i	$0.263713\pi$
$558$	15.2079	+	10.3436i	0.643801	+	0.437880i
$559$	−6.97105			−0.294844
$560$	3.92952	−	0.915451i	0.166053	−	0.0386849i
$561$	16.4413	+	9.49237i	0.694151	+	0.400768i
$562$	−14.2350	+	20.9293i	−0.600466	+	0.882848i
$563$	22.0923			0.931080			0.465540	−	0.885027i	$-0.345860\pi$
$563$	22.0923			0.931080			0.465540	+	0.885027i	$0.345860\pi$
$564$	1.69934	−	11.4485i	0.0715551	−	0.482071i
$565$	−4.02493	+	2.32379i	−0.169330	+	0.0977627i
$566$	6.61115	+	13.6889i	0.277887	+	0.575387i
$567$	−1.31347	+	0.758330i	−0.0551604	+	0.0318468i
$568$	9.48365	−	2.96029i	0.397925	−	0.124211i
$569$		−	23.5107i		−	0.985620i	−0.870137	−	0.492810i	$-0.835970\pi$
$569$		−	23.5107i		−	0.985620i	0.870137	−	0.492810i	$-0.164030\pi$
$570$	5.73502	−	1.55025i	0.240214	−	0.0649327i
$571$			40.7278i			1.70441i	0.523212	+	0.852203i	$0.324734\pi$
$571$			40.7278i			1.70441i	−0.523212	+	0.852203i	$0.675266\pi$
$572$	30.0943	−	37.9112i	1.25831	−	1.58515i
$573$	−2.02902	+	1.17146i	−0.0847637	+	0.0489384i
$574$	−0.328239	+	0.158525i	−0.0137004	+	0.00661671i
$575$	2.38107	−	1.37471i	0.0992977	−	0.0573295i
$576$	−13.6275	+	9.42597i	−0.567810	+	0.392749i
$577$	30.0075			1.24923			0.624614	−	0.780934i	$-0.285256\pi$
$577$	30.0075			1.24923			0.624614	+	0.780934i	$0.285256\pi$
$578$	−2.19011	−	1.48960i	−0.0910967	−	0.0619591i
$579$	1.65653	+	0.956401i	0.0688432	+	0.0397467i
$580$	1.12199	−	7.55893i	0.0465882	−	0.313867i
$581$	2.00612			0.0832280
$582$	−12.3961	+	18.2257i	−0.513836	+	0.755479i
$583$	22.7834	−	39.4621i	0.943593	−	1.63435i
$584$	−39.9494	+	12.4701i	−1.65312	+	0.516016i
$585$	9.57364	+	5.52734i	0.395821	+	0.228528i
$586$	1.61135	+	0.118937i	0.0665641	+	0.00491323i
$587$	−21.9009	+	12.6445i	−0.903948	+	0.521894i	−0.878479	−	0.477781i	$-0.841441\pi$
$587$	−21.9009	+	12.6445i	−0.903948	+	0.521894i	−0.0254687	+	0.999676i	$0.508108\pi$
$588$	4.23687	+	10.7246i	0.174726	+	0.442274i
$589$	17.8304	−	20.7647i	0.734687	−	0.855593i
$590$	−10.8617	−	7.38754i	−0.447168	−	0.304140i
$591$	7.45703	+	12.9160i	0.306741	+	0.531291i
$592$	−4.52952	+	14.9216i	−0.186162	+	0.613276i
$593$	−11.2576	+	19.4988i	−0.462296	+	0.800720i	−0.999075	−	0.0430031i	$-0.986307\pi$
$593$	−11.2576	+	19.4988i	−0.462296	+	0.800720i	0.536779	+	0.843723i	$0.319641\pi$
$594$	31.2560	+	2.30707i	1.28245	+	0.0946600i
$595$	3.79495	+	2.19102i	0.155578	+	0.0898229i
$596$	8.87973	+	22.4768i	0.363728	+	0.920686i
$597$			10.0192i			0.410058i
$598$	18.6876	−	9.02529i	0.764192	−	0.369072i
$599$	2.25652	−	3.90841i	0.0921991	−	0.159693i	−0.816237	−	0.577717i	$-0.803944\pi$
$599$	2.25652	−	3.90841i	0.0921991	−	0.159693i	0.908436	+	0.418024i	$0.137277\pi$
$600$	0.597615	−	2.65953i	0.0243975	−	0.108575i
$601$			16.0409i			0.654322i	0.944969	+	0.327161i	$0.106092\pi$
$601$			16.0409i			0.654322i	−0.944969	+	0.327161i	$0.893908\pi$
$602$	−1.67774	+	0.810275i	−0.0683795	+	0.0330243i
$603$	−4.33198	−	7.50321i	−0.176412	−	0.305554i
$604$	38.1179	+	5.65795i	1.55100	+	0.230219i
$605$	−4.78080	−	8.28058i	−0.194367	−	0.336654i
$606$	1.54242	−	20.8966i	0.0626564	−	0.848864i
$607$	−28.7296			−1.16610			−0.583049	−	0.812437i	$-0.698141\pi$
$607$	−28.7296			−1.16610			−0.583049	+	0.812437i	$0.698141\pi$
$608$	11.6673	+	21.7227i	0.473172	+	0.880970i
$609$	−3.71429			−0.150511
$610$	−0.973025	+	13.1825i	−0.0393966	+	0.533743i
$611$	−16.0246	−	27.7554i	−0.648285	−	1.12286i
$612$	−17.8009	−	2.64224i	−0.719560	−	0.106806i
$613$	11.6457	+	20.1709i	0.470364	+	0.814694i	0.999426	−	0.0338894i	$-0.0107894\pi$
$613$	11.6457	+	20.1709i	0.470364	+	0.814694i	−0.529062	+	0.848583i	$0.677456\pi$
$614$	14.2930	−	6.90289i	0.576818	−	0.278578i
$615$			0.246264i			0.00993031i
$616$	2.83628	−	12.6221i	0.114277	−	0.508561i
$617$	−4.21133	+	7.29423i	−0.169542	+	0.293655i	−0.938259	−	0.345934i	$-0.887562\pi$
$617$	−4.21133	+	7.29423i	−0.169542	+	0.293655i	0.768717	+	0.639589i	$0.220895\pi$
$618$	−2.15489	+	1.04072i	−0.0866824	+	0.0418639i
$619$			6.04220i			0.242856i	0.992600	+	0.121428i	$0.0387474\pi$
$619$			6.04220i			0.242856i	−0.992600	+	0.121428i	$0.961253\pi$
$620$	−4.61416	−	11.6796i	−0.185309	−	0.469064i
$621$	11.6370	+	6.71864i	0.466978	+	0.269610i
$622$	24.8748	+	1.83606i	0.997389	+	0.0736193i
$623$	−0.0391489	+	0.0678078i	−0.00156847	+	0.00271666i
$624$	5.97631	−	19.6878i	0.239244	−	0.788143i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.33314	−	0.906734i	−0.0532832	−	0.0362404i
$627$	3.52109	−	18.7203i	0.140619	−	0.747617i
$628$	1.37848	+	3.48927i	0.0550072	+	0.139237i
$629$	−14.6672	+	8.46810i	−0.584819	+	0.337645i
$630$	2.94657	+	0.217493i	0.117394	+	0.00866511i
$631$	22.5945	+	13.0450i	0.899475	+	0.519312i	0.877030	−	0.480436i	$-0.159522\pi$
$631$	22.5945	+	13.0450i	0.899475	+	0.519312i	0.0224449	+	0.999748i	$0.492855\pi$
$632$	−27.1880	+	8.48666i	−1.08148	+	0.337581i
$633$	2.03162	−	3.51886i	0.0807495	−	0.139862i
$634$	5.14366	−	7.56257i	0.204281	−	0.300348i
$635$	−9.86172			−0.391350
$636$	2.84384	−	19.1591i	0.112766	−	0.759708i
$637$	27.6527	+	15.9653i	1.09564	+	0.632568i
$638$	−20.2602	−	13.7799i	−0.802108	−	0.545551i
$639$	7.27521			0.287803
$640$	11.3134	−	0.0888092i	0.447200	−	0.00351049i
$641$	−5.43450	+	3.13761i	−0.214650	+	0.123928i	−0.603471	−	0.797385i	$-0.706216\pi$
$641$	−5.43450	+	3.13761i	−0.214650	+	0.123928i	0.388821	+	0.921313i	$0.372883\pi$
$642$	18.0568	−	8.72064i	0.712644	−	0.344176i
$643$	−38.3371	+	22.1339i	−1.51187	+	0.872877i	−0.511964	+	0.859007i	$0.671082\pi$
$643$	−38.3371	+	22.1339i	−1.51187	+	0.872877i	−0.999904	+	0.0138708i	$0.995585\pi$
$644$	3.44853	−	4.34427i	0.135891	−	0.171188i
$645$			1.25874i			0.0495627i
$646$	−6.87417	+	25.8827i	−0.270461	+	1.01834i
$647$			34.2770i			1.34757i	0.738929	+	0.673784i	$0.235332\pi$
$647$			34.2770i			1.34757i	−0.738929	+	0.673784i	$0.764668\pi$
$648$	−4.05963	+	1.26720i	−0.159478	+	0.0497805i
$649$	−36.4757	+	21.0593i	−1.43180	+	0.826648i
$650$	−3.28261	−	6.79690i	−0.128754	−	0.266596i
$651$	−5.28609	+	3.05193i	−0.207178	+	0.119614i
$652$	−2.97673	+	20.0544i	−0.116578	+	0.785391i
$653$	5.02590			0.196679			0.0983393	−	0.995153i	$-0.468647\pi$
$653$	5.02590			0.196679			0.0983393	+	0.995153i	$0.468647\pi$
$654$	−8.78557	+	12.9172i	−0.343543	+	0.505101i
$655$	−19.2298	−	11.1024i	−0.751372	−	0.433805i
$656$	−0.995467	+	0.231912i	−0.0388665	+	0.00905463i
$657$	−30.6465			−1.19563
$658$	−7.08279	−	4.81734i	−0.276116	−	0.187799i
$659$	−5.42515	+	9.39664i	−0.211334	+	0.366041i	−0.952132	−	0.305686i	$-0.901114\pi$
$659$	−5.42515	+	9.39664i	−0.211334	+	0.366041i	0.740798	+	0.671728i	$0.234447\pi$
$660$	−6.84547	−	5.43401i	−0.266460	−	0.211519i
$661$	−30.9602	−	17.8749i	−1.20421	−	0.695253i	−0.242724	−	0.970095i	$-0.578041\pi$
$661$	−30.9602	−	17.8749i	−1.20421	−	0.695253i	−0.961489	+	0.274843i	$0.911374\pi$
$662$	−1.80660	+	24.4757i	−0.0702156	+	0.951275i
$663$	19.3521	−	11.1729i	0.751572	−	0.433920i
$664$	5.48844	+	1.23329i	0.212993	+	0.0478609i
$665$	0.812735	−	4.32100i	0.0315165	−	0.167561i
$666$	−6.42211	+	9.44224i	−0.248852	+	0.365879i
$667$	−5.25261	−	9.09778i	−0.203382	−	0.352267i
$668$	23.2856	−	29.3339i	0.900945	−	1.13496i
$669$	−0.351033	+	0.608006i	−0.0135717	+	0.0235069i
$670$	−0.435465	+	5.89964i	−0.0168235	+	0.227923i
$671$	36.7046	+	21.1914i	1.41697	+	0.818086i
$672$	−0.850068	−	5.43296i	−0.0327921	−	0.209581i
$673$		−	10.8331i		−	0.417585i	−0.977960	−	0.208793i	$-0.933047\pi$
$673$		−	10.8331i		−	0.417585i	0.977960	−	0.208793i	$-0.0669534\pi$
$674$	11.4583	+	23.7254i	0.441358	+	0.913867i
$675$	2.44365	−	4.23253i	0.0940562	−	0.162910i
$676$	−11.3805	−	28.8068i	−0.437710	−	1.10795i
$677$		−	29.7794i		−	1.14452i	−0.820074	−	0.572258i	$-0.806068\pi$
$677$		−	29.7794i		−	1.14452i	0.820074	−	0.572258i	$-0.193932\pi$
$678$	2.75475	+	5.70393i	0.105796	+	0.219058i
$679$	8.15645	+	14.1274i	0.313016	+	0.542159i
$680$	9.03546	+	8.32729i	0.346494	+	0.319337i
$681$	−9.19028	−	15.9180i	−0.352172	−	0.609980i
$682$	−40.1564	−	2.96402i	−1.53767	−	0.113498i
$683$	−15.6920			−0.600439			−0.300219	−	0.953870i	$-0.597060\pi$
$683$	−15.6920			−0.600439			−0.300219	+	0.953870i	$0.597060\pi$
$684$	3.41587	+	17.7304i	0.130609	+	0.677939i
$685$	−10.9211			−0.417273
$686$	18.4693	+	1.36326i	0.705163	+	0.0520495i
$687$	−7.00602	−	12.1348i	−0.267297	−	0.462971i
$688$	−5.08816	+	1.18538i	−0.193984	+	0.0451921i
$689$	−26.8171	−	46.4485i	−1.02165	−	1.76955i
$690$	−1.62966	−	3.37434i	−0.0620402	−	0.128459i
$691$		−	12.5889i		−	0.478903i	−0.970908	−	0.239452i	$-0.923032\pi$
$691$		−	12.5889i		−	0.478903i	0.970908	−	0.239452i	$-0.0769677\pi$
$692$	−9.75989	+	3.85576i	−0.371015	+	0.146574i
$693$	4.73675	−	8.20429i	0.179934	−	0.311655i
$694$	5.10743	+	10.5753i	0.193875	+	0.401434i
$695$			13.6780i			0.518835i
$696$	−10.1617	−	2.28341i	−0.385179	−	0.0865524i
$697$	−0.961377	−	0.555051i	−0.0364147	−	0.0210241i
$698$	1.33720	−	18.1163i	0.0506139	−	0.685713i
$699$	−12.8075	+	22.1833i	−0.484426	+	0.839050i
$700$	−1.58006	−	1.25427i	−0.0597208	−	0.0474070i
$701$	12.9813	+	22.4842i	0.490295	+	0.849216i	0.999938	−	0.0111701i	$-0.00355562\pi$
$701$	12.9813	+	22.4842i	0.490295	+	0.849216i	−0.509642	+	0.860386i	$0.670222\pi$
$702$	20.7465	−	30.5030i	0.783026	−	1.15126i
$703$	12.8923	+	11.0705i	0.486243	+	0.417531i
$704$	15.5193	−	32.7886i	0.584904	−	1.23577i
$705$	−5.01168	+	2.89349i	−0.188751	+	0.108975i
$706$	3.15910	−	42.7993i	0.118894	−	1.61077i
$707$	−13.4298	−	7.75370i	−0.505080	−	0.291608i
$708$	−11.1311	+	14.0223i	−0.418331	+	0.526991i
$709$	−13.2447	+	22.9405i	−0.497416	+	0.861550i	−0.999996	−	0.00298099i	$-0.999051\pi$
$709$	−13.2447	+	22.9405i	−0.497416	+	0.861550i	0.502579	+	0.864531i	$0.332384\pi$
$710$	−4.10745	−	2.79367i	−0.154150	−	0.104845i
$711$	−20.8568			−0.782191
$712$	−0.148791	+	0.161445i	−0.00557618	+	0.00605039i
$713$	−14.9508	−	8.63184i	−0.559911	−	0.323265i
$714$	3.35883	−	4.93838i	0.125701	−	0.184814i
$715$	−24.2019			−0.905099
$716$	−48.1283	−	7.14382i	−1.79864	−	0.266977i
$717$	−13.4964	+	7.79214i	−0.504032	+	0.291003i
$718$	4.79720	+	9.93297i	0.179030	+	0.370695i
$719$	−20.7553	+	11.9831i	−0.774043	+	0.446894i	−0.834315	−	0.551288i	$-0.814136\pi$
$719$	−20.7553	+	11.9831i	−0.774043	+	0.446894i	0.0602721	+	0.998182i	$0.480803\pi$
$720$	7.92767	+	2.40647i	0.295447	+	0.0896839i
$721$			1.77107i			0.0659579i
$722$	26.7882	−	2.09602i	0.996953	−	0.0780060i
$723$			14.0462i			0.522386i
$724$	27.8234	+	22.0865i	1.03405	+	0.820839i
$725$	−3.30897	+	1.91044i	−0.122892	+	0.0709518i
$726$	−11.7348	+	5.66742i	−0.435521	+	0.210338i
$727$	32.2300	−	18.6080i	1.19534	−	0.690132i	0.235830	−	0.971794i	$-0.424219\pi$
$727$	32.2300	−	18.6080i	1.19534	−	0.690132i	0.959514	+	0.281662i	$0.0908857\pi$
$728$	−11.1972	−	10.3196i	−0.414994	−	0.382468i
$729$	11.0159			0.407996
$730$	17.3024	+	11.7682i	0.640392	+	0.435561i
$731$	−4.91392	−	2.83705i	−0.181748	−	0.104932i
$732$	17.8204	+	2.64512i	0.658659	+	0.0977666i
$733$	−26.0537			−0.962317			−0.481158	−	0.876634i	$-0.659784\pi$
$733$	−26.0537			−0.962317			−0.481158	+	0.876634i	$0.659784\pi$
$734$	12.1797	−	17.9074i	0.449559	−	0.660974i
$735$	2.88279	−	4.99314i	0.106333	−	0.184175i
$736$	12.1054	−	9.76524i	0.446209	−	0.359951i
$737$	16.4267	+	9.48394i	0.605084	+	0.349345i
$738$	−0.746457	−	0.0550975i	−0.0274774	−	0.00202817i
$739$	−43.5142	+	25.1229i	−1.60069	+	0.924161i	−0.609346	+	0.792905i	$0.708568\pi$
$739$	−43.5142	+	25.1229i	−1.60069	+	0.924161i	−0.991348	+	0.131257i	$0.958099\pi$
$740$	7.25161	−	2.86483i	0.266574	−	0.105313i
$741$	−17.0103	−	14.6065i	−0.624888	−	0.536584i
$742$	−11.8530	−	8.06180i	−0.435138	−	0.295958i
$743$	−4.12806	−	7.15000i	−0.151444	−	0.262308i	0.780315	−	0.625387i	$-0.215059\pi$
$743$	−4.12806	−	7.15000i	−0.151444	−	0.262308i	−0.931758	+	0.363079i	$0.881726\pi$
$744$	−16.3382	+	5.09991i	−0.598986	+	0.186972i
$745$	6.04182	−	10.4647i	0.221355	−	0.383398i
$746$	−7.64729	−	0.564462i	−0.279987	−	0.0206664i
$747$	3.56744	+	2.05967i	0.130526	+	0.0753592i
$748$	36.6425	−	14.4760i	1.33978	−	0.529296i
$749$		−	14.8405i		−	0.542261i
$750$	−1.22729	+	0.592728i	−0.0448143	+	0.0216434i
$751$	11.7578	−	20.3651i	0.429048	−	0.743133i	−0.567741	−	0.823207i	$-0.692182\pi$
$751$	11.7578	−	20.3651i	0.429048	−	0.743133i	0.996789	+	0.0800745i	$0.0255158\pi$
$752$	−16.4159	−	17.5337i	−0.598627	−	0.639390i
$753$		−	4.79163i		−	0.174617i
$754$	−25.9701	+	12.5424i	−0.945774	+	0.456768i
$755$	−9.63388	−	16.6864i	−0.350613	−	0.607279i
$756$	1.44762	−	9.75267i	0.0526493	−	0.354701i
$757$	4.10392	+	7.10820i	0.149160	+	0.258352i	0.930917	−	0.365231i	$-0.119010\pi$
$757$	4.10392	+	7.10820i	0.149160	+	0.258352i	−0.781757	+	0.623583i	$0.785677\pi$
$758$	2.39529	−	32.4512i	0.0870010	−	1.17868i
$759$	−12.0151			−0.436121
$760$	4.87991	−	11.3219i	0.177013	−	0.410690i
$761$	−7.55979			−0.274042			−0.137021	−	0.990568i	$-0.543753\pi$
$761$	−7.55979			−0.274042			−0.137021	+	0.990568i	$0.543753\pi$
$762$	−0.989400	+	13.4043i	−0.0358422	+	0.485587i
$763$	5.78075	+	10.0126i	0.209277	+	0.362479i
$764$	−0.713883	+	4.80947i	−0.0258274	+	0.174001i
$765$	4.49899	+	7.79248i	0.162661	+	0.281738i
$766$	3.17071	−	1.53132i	0.114562	−	0.0553287i
$767$			49.5753i			1.79006i
$768$	1.01433	−	15.3863i	0.0366014	−	0.555207i
$769$	18.0628	−	31.2857i	0.651361	−	1.12819i	−0.331432	−	0.943479i	$-0.607532\pi$
$769$	18.0628	−	31.2857i	0.651361	−	1.12819i	0.982793	−	0.184711i	$-0.0591348\pi$
$770$	−5.82472	+	2.81309i	−0.209908	+	0.101377i
$771$		−	3.31137i		−	0.119256i
$772$	3.69190	−	1.45853i	0.132874	−	0.0524936i
$773$	2.17075	+	1.25329i	0.0780766	+	0.0450775i	0.538530	−	0.842606i	$-0.318980\pi$
$773$	2.17075	+	1.25329i	0.0780766	+	0.0450775i	−0.460453	+	0.887684i	$0.652313\pi$
$774$	−3.81539	−	0.281622i	−0.137141	−	0.0101227i
$775$	−3.13950	+	5.43778i	−0.112774	+	0.195331i
$776$	13.6298	+	43.6646i	0.489281	+	1.56747i
$777$	−1.89487	−	3.28202i	−0.0679782	−	0.117742i
$778$	−22.8857	−	15.5656i	−0.820492	−	0.558055i
$779$	−0.205890	+	1.09464i	−0.00737679	+	0.0392195i
$780$	−9.56786	+	3.77989i	−0.342584	+	0.135342i
$781$	−13.7936	+	7.96376i	−0.493575	+	0.284966i
$782$	16.8460	+	1.24344i	0.602412	+	0.0444652i
$783$	−16.1719	−	9.33688i	−0.577938	−	0.333673i
$784$	22.8985	+	6.95091i	0.817802	+	0.248247i
$785$	0.937924	−	1.62453i	0.0334759	−	0.0579820i
$786$	−17.0199	+	25.0239i	−0.607080	+	0.892571i
$787$	−3.65973			−0.130455			−0.0652276	−	0.997870i	$-0.520777\pi$
$787$	−3.65973			−0.130455			−0.0652276	+	0.997870i	$0.520777\pi$
$788$	30.6152	+	4.54430i	1.09062	+	0.161884i
$789$	−13.0253	−	7.52017i	−0.463713	−	0.267725i
$790$	11.7754	+	8.00897i	0.418948	+	0.284946i
$791$	4.68796			0.166685
$792$	18.0027	−	19.5337i	0.639699	−	0.694101i
$793$	43.2029	−	24.9432i	1.53418	−	0.885760i
$794$	27.8939	−	13.4715i	0.989917	−	0.478087i
$795$	−8.38703	+	4.84225i	−0.297457	+	0.171737i
$796$	16.2852	+	12.9274i	0.577215	+	0.458199i
$797$			3.15574i			0.111782i	0.998437	+	0.0558910i	$0.0177999\pi$
$797$			3.15574i			0.111782i	−0.998437	+	0.0558910i	$0.982200\pi$
$798$	−5.79168	−	1.53820i	−0.205023	−	0.0544519i
$799$		−	26.0864i		−	0.922872i
$800$	−3.55173	−	4.40286i	−0.125573	−	0.155665i
$801$	−0.139235	+	0.0803875i	−0.00491963	+	0.00284035i
$802$	12.9075	+	26.7260i	0.455779	+	0.943726i
$803$	58.1051	−	33.5470i	2.05048	−	1.18385i
$804$	7.97526	+	1.18379i	0.281266	+	0.0417491i
$805$	−2.77331			−0.0977464
$806$	−26.6543	+	39.1890i	−0.938856	+	1.38037i
$807$	22.5715	+	13.0316i	0.794553	+	0.458736i
$808$	−31.9752	−	29.4691i	−1.12488	−	1.03672i
$809$	−21.1873			−0.744904			−0.372452	−	0.928051i	$-0.621483\pi$
$809$	−21.1873			−0.744904			−0.372452	+	0.928051i	$0.621483\pi$
$810$	1.75826	+	1.19588i	0.0617791	+	0.0420188i
$811$	−28.1871	+	48.8214i	−0.989781	+	1.71435i	−0.371402	+	0.928472i	$0.621123\pi$
$811$	−28.1871	+	48.8214i	−0.989781	+	1.71435i	−0.618380	+	0.785880i	$0.712211\pi$
$812$	−4.79241	+	6.03722i	−0.168181	+	0.211865i
$813$	11.9995	+	6.92789i	0.420840	+	0.242972i
$814$	1.84030	−	24.9322i	0.0645023	−	0.873873i
$815$	8.77895	−	5.06853i	0.307513	−	0.177543i
$816$	12.2252	−	11.4458i	0.427967	−	0.400683i
$817$	−1.05237	+	5.59506i	−0.0368179	+	0.195747i
$818$	−20.1973	+	29.6955i	−0.706182	+	1.03828i
$819$	−5.57536	−	9.65681i	−0.194819	−	0.337436i
$820$	0.400278	+	0.317745i	0.0139783	+	0.0110961i
$821$	1.74584	−	3.02388i	0.0609301	−	0.105534i	−0.833951	−	0.551838i	$-0.813927\pi$
$821$	1.74584	−	3.02388i	0.0609301	−	0.105534i	0.894881	+	0.446304i	$0.147260\pi$
$822$	−1.09568	+	14.8442i	−0.0382164	+	0.517752i
$823$	8.68895	+	5.01657i	0.302878	+	0.174867i	0.643735	−	0.765248i	$-0.277384\pi$
$823$	8.68895	+	5.01657i	0.302878	+	0.174867i	−0.340857	+	0.940115i	$0.610717\pi$
$824$	−1.08879	+	4.84537i	−0.0379297	+	0.168796i
$825$			4.37004i			0.152145i
$826$	5.76235	+	11.9314i	0.200498	+	0.415146i
$827$	−13.4025	+	23.2138i	−0.466050	+	0.807222i	−0.999248	−	0.0387680i	$-0.987657\pi$
$827$	−13.4025	+	23.2138i	−0.466050	+	0.807222i	0.533198	+	0.845990i	$0.320990\pi$
$828$	10.5927	−	4.18476i	0.368121	−	0.145430i
$829$		−	50.0760i		−	1.73921i	−0.493745	−	0.869606i	$-0.664373\pi$
$829$		−	50.0760i		−	1.73921i	0.493745	−	0.869606i	$-0.335627\pi$
$830$	−1.22320	−	2.53274i	−0.0424580	−	0.0879127i
$831$	−13.3483	−	23.1199i	−0.463047	−	0.802020i
$832$	−24.2896	−	35.1164i	−0.842092	−	1.21744i
$833$	12.9950	+	22.5080i	0.450249	+	0.779855i
$834$	18.5915	+	1.37228i	0.643770	+	0.0475180i
$835$	−18.7263			−0.648049
$836$	−25.8849	−	29.8773i	−0.895248	−	1.03333i
$837$	−30.6874			−1.06071
$838$	−12.4920	−	0.922058i	−0.431528	−	0.0318520i
$839$	1.32567	+	2.29613i	0.0457672	+	0.0792712i	0.888002	−	0.459840i	$-0.152093\pi$
$839$	1.32567	+	2.29613i	0.0457672	+	0.0792712i	−0.842234	+	0.539112i	$0.818760\pi$
$840$	−1.86336	+	2.02183i	−0.0642922	+	0.0697597i
$841$	−7.20047	−	12.4716i	−0.248292	−	0.430055i
$842$	3.61334	+	7.48171i	0.124524	+	0.257837i
$843$		−	17.2488i		−	0.594080i
$844$	−3.09825	−	7.84245i	−0.106646	−	0.269948i
$845$	−7.74332	+	13.4118i	−0.266378	+	0.461381i
$846$	−7.64926	−	15.8384i	−0.262987	−	0.544535i
$847$			9.64466i			0.331394i
$848$	−27.4720	−	29.3427i	−0.943392	−	1.00763i
$849$	−8.97152	−	5.17971i	−0.307902	−	0.177767i
$850$	0.452253	−	6.12709i	0.0155122	−	0.210158i
$851$	5.35932	−	9.28261i	0.183715	−	0.318204i
$852$	−4.20932	+	5.30267i	−0.144209	+	0.181667i
$853$	14.3723	+	24.8935i	0.492097	+	0.852337i	0.999959	−	0.00910167i	$-0.00289719\pi$
$853$	14.3723	+	24.8935i	0.492097	+	0.852337i	−0.507862	+	0.861439i	$0.669564\pi$
$854$	7.49848	−	11.0248i	0.256593	−	0.377261i
$855$	5.88159	−	6.84951i	0.201146	−	0.234248i
$856$	9.12342	−	40.6015i	0.311832	−	1.38773i
$857$	−21.2610	+	12.2751i	−0.726263	+	0.419308i	−0.817053	−	0.576562i	$-0.804394\pi$
$857$	−21.2610	+	12.2751i	−0.726263	+	0.419308i	0.0907905	+	0.995870i	$0.471061\pi$
$858$	−2.42811	+	32.8959i	−0.0828943	+	1.12305i
$859$	30.5828	+	17.6570i	1.04347	+	0.602448i	0.920814	−	0.390002i	$-0.127526\pi$
$859$	30.5828	+	17.6570i	1.04347	+	0.602448i	0.122656	+	0.992449i	$0.460859\pi$
$860$	2.04595	+	1.62410i	0.0697664	+	0.0553814i
$861$	0.124202	−	0.215123i	0.00423278	−	0.00733139i
$862$	−21.2134	−	14.4282i	−0.722530	−	0.491427i
$863$	38.1816			1.29972			0.649858	−	0.760056i	$-0.274828\pi$
$863$	38.1816			1.29972			0.649858	+	0.760056i	$0.274828\pi$
$864$	9.95604	−	25.7919i	0.338711	−	0.877457i
$865$	4.54400	+	2.62348i	0.154501	+	0.0892010i
$866$	−20.0522	+	29.4822i	−0.681402	+	1.00184i
$867$	1.80497			0.0613002
$868$	−1.85984	+	12.5298i	−0.0631270	+	0.425290i
$869$	39.5440	−	22.8308i	1.34144	−	0.774480i
$870$	2.26474	+	4.68931i	0.0767817	+	0.158983i
$871$	19.3349	−	11.1630i	0.655138	−	0.378244i
$872$	9.65991	+	30.9466i	0.327126	+	1.04799i
$873$			33.4966i			1.13369i
$874$	−4.42269	−	16.3614i	−0.149600	−	0.553433i
$875$			1.00869i			0.0340998i
$876$	17.7316	−	22.3373i	0.599094	−	0.754706i
$877$	−42.9384	+	24.7905i	−1.44993	+	0.837116i	−0.998476	−	0.0551800i	$-0.982427\pi$
$877$	−42.9384	+	24.7905i	−1.44993	+	0.837116i	−0.451451	+	0.892296i	$0.649093\pi$
$878$	21.1957	−	10.2366i	0.715320	−	0.345469i
$879$	−0.953546	+	0.550530i	−0.0321623	+	0.0185689i
$880$	−17.6649	+	4.11535i	−0.595484	+	0.138729i
$881$	−22.4530			−0.756462			−0.378231	−	0.925711i	$-0.623468\pi$
$881$	−22.4530			−0.756462			−0.378231	+	0.925711i	$0.623468\pi$
$882$	14.4899	+	9.85524i	0.487899	+	0.331843i
$883$	10.6070	+	6.12393i	0.356953	+	0.206087i	0.667743	−	0.744392i	$-0.267260\pi$
$883$	10.6070	+	6.12393i	0.356953	+	0.206087i	−0.310791	+	0.950478i	$0.600594\pi$
$884$	6.80875	−	45.8709i	0.229003	−	1.54281i
$885$	8.95162			0.300905
$886$	12.3952	−	18.2243i	0.416424	−	0.612256i
$887$	−6.49545	+	11.2505i	−0.218096	+	0.377753i	−0.954226	−	0.299087i	$-0.903318\pi$
$887$	−6.49545	+	11.2505i	−0.218096	+	0.377753i	0.736130	+	0.676840i	$0.236651\pi$
$888$	−3.16642	−	10.1440i	−0.106258	−	0.340410i
$889$	8.61469	+	4.97370i	0.288928	+	0.166812i
$890$	0.109478	+	0.00808081i	0.00366972	+	0.000270869i
$891$	5.90460	−	3.40902i	0.197812	−	0.114207i
$892$	0.535331	+	1.35506i	0.0179242	+	0.0453707i
$893$	−24.6960	+	8.67150i	−0.826419	+	0.290181i
$894$	−13.6178	−	9.26210i	−0.455447	−	0.309771i
$895$	12.1639	+	21.0685i	0.406594	+	0.704242i
$896$	−9.92756	−	5.62824i	−0.331656	−	0.188026i
$897$	−7.07115	+	12.2476i	−0.236099	+	0.408935i
$898$	−3.57083	−	0.263570i	−0.119160	−	0.00879545i
$899$	20.7771	+	11.9956i	0.692954	+	0.400077i
$900$	−1.52205	−	3.85268i	−0.0507349	−	0.128423i
$901$		−	43.6556i		−	1.45438i
$902$	1.47558	−	0.712640i	0.0491313	−	0.0237283i
$903$	0.634835	−	1.09957i	0.0211260	−	0.0365913i
$904$	12.8255	+	2.88199i	0.426571	+	0.0958535i
$905$		−	17.7620i		−	0.590430i
$906$	−23.6471	+	11.4205i	−0.785623	+	0.379422i
$907$	5.91433	+	10.2439i	0.196382	+	0.340144i	0.947353	−	0.320192i	$-0.103747\pi$
$907$	5.91433	+	10.2439i	0.196382	+	0.340144i	−0.750971	+	0.660336i	$0.770414\pi$
$908$	−37.7311	−	5.60053i	−1.25215	−	0.185860i
$909$	−15.9213	−	27.5765i	−0.528076	−	0.914654i
$910$	−0.560453	+	7.59298i	−0.0185788	+	0.251705i
$911$	−34.5732			−1.14546			−0.572731	−	0.819743i	$-0.694116\pi$
$911$	−34.5732			−1.14546			−0.572731	+	0.819743i	$0.694116\pi$
$912$	−14.8995	−	7.76881i	−0.493372	−	0.257251i
$913$	−9.01839			−0.298465
$914$	−1.44655	+	19.5978i	−0.0478478	+	0.648238i
$915$	−4.50390	−	7.80098i	−0.148894	−	0.257893i
$916$	−28.7635	−	4.26945i	−0.950374	−	0.141067i
$917$	11.1988	+	19.3969i	0.369817	+	0.640542i
$918$	27.0382	−	13.0583i	0.892395	−	0.430988i
$919$		−	49.2850i		−	1.62576i	−0.582431	−	0.812880i	$-0.697898\pi$
$919$		−	49.2850i		−	1.62576i	0.582431	−	0.812880i	$-0.302102\pi$
$920$	−7.58736	−	1.70493i	−0.250148	−	0.0562099i
$921$	−5.40829	+	9.36743i	−0.178209	+	0.308667i
$922$	38.1531	−	18.4263i	1.25651	−	0.606839i
$923$			18.7474i			0.617078i
$924$	3.23925	+	8.19934i	0.106563	+	0.269739i
$925$	−3.37620	−	1.94925i	−0.111009	−	0.0640909i
$926$	32.6816	+	2.41229i	1.07398	+	0.0792729i
$927$	−1.81834	+	3.14945i	−0.0597220	+	0.103442i
$928$	−16.8228	+	13.5707i	−0.552234	+	0.445481i
$929$	13.7364	+	23.7921i	0.450676	+	0.780594i	0.998428	−	0.0560468i	$-0.0178496\pi$
$929$	13.7364	+	23.7921i	0.450676	+	0.780594i	−0.547752	+	0.836641i	$0.684516\pi$
$930$	7.07620	+	4.81286i	0.232038	+	0.157820i
$931$	16.9885	−	19.7843i	0.556776	−	0.648403i
$932$	19.5318	+	49.4398i	0.639784	+	1.61945i
$933$	−14.7202	+	8.49868i	−0.481916	+	0.278234i
$934$	29.7088	+	2.19287i	0.972103	+	0.0717529i
$935$	−17.0600	−	9.84958i	−0.557921	−	0.322116i
$936$	−9.31669	−	29.8471i	−0.304525	−	0.975582i
$937$	−16.7870	+	29.0759i	−0.548407	+	0.949869i	0.449977	+	0.893040i	$0.351432\pi$
$937$	−16.7870	+	29.0759i	−0.548407	+	0.949869i	−0.998384	+	0.0568288i	$0.981901\pi$
$938$	3.35585	−	4.93400i	0.109572	−	0.161101i
$939$	1.09871			0.0358550
$940$	−1.76329	+	11.8794i	−0.0575121	+	0.387462i
$941$	25.6191	+	14.7912i	0.835160	+	0.482180i	0.855616	−	0.517611i	$-0.173178\pi$
$941$	25.6191	+	14.7912i	0.835160	+	0.482180i	−0.0204560	+	0.999791i	$0.506512\pi$
$942$	−2.11401	−	1.43784i	−0.0688781	−	0.0468472i
$943$	0.702564			0.0228786
$944$	8.42992	+	36.1849i	0.274371	+	1.17772i
$945$	−4.26930	+	2.46488i	−0.138880	+	0.0801825i
$946$	7.54216	−	3.64254i	0.245217	−	0.118429i
$947$	42.9690	−	24.8082i	1.39630	−	0.806157i	0.402302	−	0.915507i	$-0.368210\pi$
$947$	42.9690	−	24.8082i	1.39630	−	0.806157i	0.994003	+	0.109350i	$0.0348770\pi$
$948$	12.0674	−	15.2019i	0.391931	−	0.493734i
$949$		−	78.9725i		−	2.56355i
$950$	−5.95084	+	1.60858i	−0.193071	+	0.0521894i
$951$			6.23267i			0.202108i
$952$	−3.69310	−	11.8313i	−0.119694	−	0.383453i
$953$	−25.3558	+	14.6392i	−0.821354	+	0.474209i	−0.850883	−	0.525355i	$-0.823932\pi$
$953$	−25.3558	+	14.6392i	−0.821354	+	0.474209i	0.0295294	+	0.999564i	$0.490599\pi$
$954$	−12.8010	−	26.5055i	−0.414448	−	0.858148i
$955$	2.10538	−	1.21554i	0.0681285	−	0.0393340i
$956$	−4.74851	+	31.9910i	−0.153578	+	1.03466i
$957$	16.6974			0.539749
$958$	7.32129	−	10.7643i	0.236540	−	0.347778i
$959$	9.54010	+	5.50798i	0.308066	+	0.177862i
$960$	−6.34083	+	4.38589i	−0.204649	+	0.141554i
$961$	8.42593			0.271804
$962$	−24.3316	−	16.5490i	−0.784481	−	0.533562i
$963$	15.2366	−	26.3906i	0.490994	−	0.850426i
$964$	22.8308	+	18.1234i	0.735331	+	0.583714i
$965$	−1.71887	−	0.992391i	−0.0553325	−	0.0319462i
$966$	−0.278239	+	3.76956i	−0.00895219	+	0.121284i
$967$	4.85881	−	2.80524i	0.156249	−	0.0902103i	−0.419837	−	0.907600i	$-0.637913\pi$
$967$	4.85881	−	2.80524i	0.156249	−	0.0902103i	0.576086	+	0.817389i	$0.304579\pi$
$968$	−5.92918	+	26.3863i	−0.190571	+	0.848088i
$969$	−6.04609	−	17.2189i	−0.194228	−	0.553152i
$970$	12.8626	−	18.9115i	0.412994	−	0.607213i
$971$	−27.2047	−	47.1198i	−0.873039	−	1.51215i	−0.858837	−	0.512248i	$-0.828813\pi$
$971$	−27.2047	−	47.1198i	−0.873039	−	1.51215i	−0.0142015	−	0.999899i	$-0.504521\pi$
$972$	20.0335	−	25.2371i	0.642575	−	0.809481i
$973$	6.89840	−	11.9484i	0.221153	−	0.383048i
$974$	−3.84732	+	52.1231i	−0.123276	+	1.67013i
$975$	4.45459	+	2.57186i	0.142661	+	0.0823655i
$976$	27.2923	−	25.5524i	0.873607	−	0.817911i
$977$		−	25.8357i		−	0.826557i	−0.910605	−	0.413279i	$-0.864384\pi$
$977$		−	25.8357i		−	0.826557i	0.910605	−	0.413279i	$-0.135616\pi$
$978$	−6.00851	−	12.4411i	−0.192131	−	0.397822i
$979$	0.175991	−	0.304826i	0.00562471	−	0.00974228i
$980$	−4.39631	−	11.1282i	−0.140435	−	0.355476i
$981$			23.7402i			0.757965i
$982$	17.6647	+	36.5762i	0.563704	+	1.16719i
$983$	6.87368	+	11.9056i	0.219236	+	0.379729i	0.954575	−	0.297972i	$-0.0963100\pi$
$983$	6.87368	+	11.9056i	0.219236	+	0.379729i	−0.735338	+	0.677700i	$0.762977\pi$
$984$	0.472047	−	0.512190i	0.0150483	−	0.0163280i
$985$	−7.73765	−	13.4020i	−0.246542	−	0.427023i
$986$	−23.4108	−	1.72800i	−0.745553	−	0.0550308i
$987$	5.83726			0.185802
$988$	−45.6892	+	8.80231i	−1.45357	+	0.280039i
$989$	3.59104			0.114188
$990$	−13.2461	−	0.977725i	−0.420990	−	0.0310741i
$991$	−13.5525	−	23.4737i	−0.430510	−	0.745665i	0.566407	−	0.824126i	$-0.308333\pi$
$991$	−13.5525	−	23.4737i	−0.430510	−	0.745665i	−0.996917	+	0.0784603i	$0.975000\pi$
$992$	−12.7911	+	33.1363i	−0.406118	+	1.05208i
$993$	−8.36232	−	14.4840i	−0.265370	−	0.459635i
$994$	2.17909	+	4.51197i	0.0691164	+	0.143111i
$995$		−	10.3962i		−	0.329583i
$996$	−3.56529	+	1.40851i	−0.112971	+	0.0446303i
$997$	6.04421	−	10.4689i	0.191422	−	0.331553i	−0.754300	−	0.656530i	$-0.772023\pi$
$997$	6.04421	−	10.4689i	0.191422	−	0.331553i	0.945722	+	0.324977i	$0.105357\pi$
$998$	11.8409	+	24.5175i	0.374817	+	0.776088i
$999$		−	19.0531i		−	0.602814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.11	yes	40
4.3	odd	2	inner	380.2.n.a.31.4	✓	40
19.8	odd	6	inner	380.2.n.a.331.4	yes	40
76.27	even	6	inner	380.2.n.a.331.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.4	✓	40	4.3	odd	2	inner
380.2.n.a.31.11	yes	40	1.1	even	1	trivial
380.2.n.a.331.4	yes	40	19.8	odd	6	inner
380.2.n.a.331.11	yes	40	76.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104103 + 1.41038i) q^{2} +(-0.481867 - 0.834618i) q^{3} +(-1.97833 - 0.293648i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.22729 - 0.592728i) q^{6} -1.00869i q^{7} +(0.620104 - 2.75961i) q^{8} +(1.03561 - 1.79373i) q^{9} +O(q^{10})\)	\(q+(-0.104103 + 1.41038i) q^{2} +(-0.481867 - 0.834618i) q^{3} +(-1.97833 - 0.293648i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.22729 - 0.592728i) q^{6} -1.00869i q^{7} +(0.620104 - 2.75961i) q^{8} +(1.03561 - 1.79373i) q^{9} +(-1.27347 + 0.615033i) q^{10} +4.53449i q^{11} +(0.708205 + 1.79264i) q^{12} +(4.62223 + 2.66864i) q^{13} +(1.42263 + 0.105007i) q^{14} +(0.481867 - 0.834618i) q^{15} +(3.82754 + 1.16186i) q^{16} +(2.17215 + 3.76227i) q^{17} +(2.42202 + 1.64733i) q^{18} +(2.83968 - 3.30700i) q^{19} +(-0.734856 - 1.86010i) q^{20} +(-0.841868 + 0.486053i) q^{21} +(-6.39534 - 0.472053i) q^{22} +(-2.38107 - 1.37471i) q^{23} +(-2.60203 + 0.812217i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-4.24498 + 6.24127i) q^{26} -4.88730 q^{27} +(-0.296199 + 1.99551i) q^{28} +(3.30897 + 1.91044i) q^{29} +(1.12696 + 0.766500i) q^{30} +6.27901 q^{31} +(-2.03712 + 5.27732i) q^{32} +(3.78456 - 2.18502i) q^{33} +(-5.53234 + 2.67188i) q^{34} +(0.873549 - 0.504344i) q^{35} +(-2.57550 + 3.24447i) q^{36} +3.89849i q^{37} +(4.36849 + 4.34928i) q^{38} -5.14372i q^{39} +(2.69995 - 0.842781i) q^{40} +(-0.221296 + 0.127766i) q^{41} +(-0.597877 - 1.23795i) q^{42} +(-1.13112 + 0.653052i) q^{43} +(1.33155 - 8.97069i) q^{44} +2.07122 q^{45} +(2.18674 - 3.21510i) q^{46} +(-5.20027 - 3.00238i) q^{47} +(-0.874653 - 3.75440i) q^{48} +5.98255 q^{49} +(-1.16937 - 0.795344i) q^{50} +(2.09337 - 3.62583i) q^{51} +(-8.36063 - 6.63676i) q^{52} +(-8.70264 - 5.02447i) q^{53} +(0.508782 - 6.89294i) q^{54} +(-3.92698 + 2.26724i) q^{55} +(-2.78359 - 0.625491i) q^{56} +(-4.12842 - 0.776514i) q^{57} +(-3.03891 + 4.46801i) q^{58} +(4.64424 + 8.04406i) q^{59} +(-1.19837 + 1.50965i) q^{60} +(4.67339 - 8.09454i) q^{61} +(-0.653662 + 8.85577i) q^{62} +(-1.80931 - 1.04461i) q^{63} +(-7.23094 - 3.42250i) q^{64} +5.33729i q^{65} +(2.68772 + 5.56513i) q^{66} +(2.09151 - 3.62261i) q^{67} +(-3.19243 - 8.08084i) q^{68} +2.64972i q^{69} +(0.620376 + 1.28454i) q^{70} +(1.75626 + 3.04194i) q^{71} +(-4.30781 - 3.97018i) q^{72} +(-7.39818 - 12.8140i) q^{73} +(-5.49835 - 0.405844i) q^{74} +0.963733 q^{75} +(-6.58890 + 5.70845i) q^{76} +4.57388 q^{77} +(7.25459 + 0.535476i) q^{78} +(-5.03491 - 8.72072i) q^{79} +(0.907567 + 3.89568i) q^{80} +(-0.751799 - 1.30215i) q^{81} +(-0.157160 - 0.325412i) q^{82} +1.98884i q^{83} +(1.80822 - 0.714357i) q^{84} +(-2.17215 + 3.76227i) q^{85} +(-0.803297 - 1.66329i) q^{86} -3.68230i q^{87} +(12.5134 + 2.81185i) q^{88} +(-0.0672238 - 0.0388117i) q^{89} +(-0.215620 + 2.92120i) q^{90} +(2.69183 - 4.66238i) q^{91} +(4.30686 + 3.41883i) q^{92} +(-3.02564 - 5.24057i) q^{93} +(4.77585 - 7.02179i) q^{94} +(4.28378 + 0.805735i) q^{95} +(5.38617 - 0.842747i) q^{96} +(-14.0057 + 8.08620i) q^{97} +(-0.622800 + 8.43765i) q^{98} +(8.13364 + 4.69596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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