LMFDB - Embedded newform 60.2.e.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,2,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("60.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.7
Root			$1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	60.11
Dual form			60.2.e.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17915 - 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.44293 + 0.179147i) q^{6} +3.02045i q^{7} +(-0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})$	\(q+(1.17915 - 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.44293 + 0.179147i) q^{6} +3.02045i q^{7} +(-0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +(0.780776 + 1.17915i) q^{10} +1.32431 q^{11} +(-2.74070 + 2.11862i) q^{12} -5.12311 q^{13} +(2.35829 + 3.56155i) q^{14} +(0.848071 - 1.51022i) q^{15} +(-2.78078 - 2.87529i) q^{16} -2.00000i q^{17} +(3.84130 + 1.80122i) q^{18} -1.32431i q^{19} +(1.84130 + 0.780776i) q^{20} +(2.56155 - 4.56155i) q^{21} +(1.56155 - 1.03399i) q^{22} +0.371834 q^{23} +(-1.57752 + 4.63804i) q^{24} -1.00000 q^{25} +(-6.04090 + 4.00000i) q^{26} +(-0.185917 - 5.19283i) q^{27} +(5.56155 + 2.35829i) q^{28} -3.12311i q^{29} +(-0.179147 - 2.44293i) q^{30} +4.71659i q^{31} +(-5.52390 - 1.21922i) q^{32} +(-2.00000 - 1.12311i) q^{33} +(-1.56155 - 2.35829i) q^{34} -3.02045 q^{35} +(5.93581 - 0.875288i) q^{36} +5.12311 q^{37} +(-1.03399 - 1.56155i) q^{38} +(7.73704 + 4.34475i) q^{39} +(2.78078 - 0.516994i) q^{40} +1.12311i q^{41} +(-0.541105 - 7.37874i) q^{42} -7.73704i q^{43} +(1.03399 - 2.43845i) q^{44} +(-2.56155 + 1.56155i) q^{45} +(0.438447 - 0.290319i) q^{46} +3.02045 q^{47} +(1.76115 + 6.70062i) q^{48} -2.12311 q^{49} +(-1.17915 + 0.780776i) q^{50} +(-1.69614 + 3.02045i) q^{51} +(-4.00000 + 9.43318i) q^{52} +12.2462i q^{53} +(-4.27366 - 5.97795i) q^{54} +1.32431i q^{55} +(8.39919 - 1.56155i) q^{56} +(-1.12311 + 2.00000i) q^{57} +(-2.43845 - 3.68260i) q^{58} -14.1498 q^{59} +(-2.11862 - 2.74070i) q^{60} +3.12311 q^{61} +(3.68260 + 5.56155i) q^{62} +(-7.73704 + 4.71659i) q^{63} +(-7.46543 + 2.87529i) q^{64} -5.12311i q^{65} +(-3.23519 + 0.237246i) q^{66} +4.34475i q^{67} +(-3.68260 - 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} +(-3.56155 + 2.35829i) q^{70} +3.39228 q^{71} +(6.31579 - 5.66664i) q^{72} +8.24621 q^{73} +(6.04090 - 4.00000i) q^{74} +(1.51022 + 0.848071i) q^{75} +(-2.43845 - 1.03399i) q^{76} +4.00000i q^{77} +(12.5154 - 0.917790i) q^{78} -8.10887i q^{79} +(2.87529 - 2.78078i) q^{80} +(-4.12311 + 8.00000i) q^{81} +(0.876894 + 1.32431i) q^{82} +15.1022 q^{83} +(-6.39919 - 8.27814i) q^{84} +2.00000 q^{85} +(-6.04090 - 9.12311i) q^{86} +(-2.64861 + 4.71659i) q^{87} +(-0.684658 - 3.68260i) q^{88} -10.2462i q^{89} +(-1.80122 + 3.84130i) q^{90} -15.4741i q^{91} +(0.290319 - 0.684658i) q^{92} +(4.00000 - 7.12311i) q^{93} +(3.56155 - 2.35829i) q^{94} +1.32431 q^{95} +(7.30834 + 6.52596i) q^{96} -6.00000 q^{97} +(-2.50345 + 1.65767i) q^{98} +(2.06798 + 3.39228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{10} + 4 q^{12} - 8 q^{13} - 14 q^{16} + 16 q^{18} + 4 q^{21} - 4 q^{22} - 2 q^{24} - 8 q^{25} + 28 q^{28} + 8 q^{30} - 16 q^{33} + 4 q^{34} + 18 q^{36} + 8 q^{37} + 14 q^{40} - 12 q^{42} - 4 q^{45} + 20 q^{46} - 36 q^{48} + 16 q^{49} - 32 q^{52} - 10 q^{54} + 24 q^{57} - 36 q^{58} - 14 q^{60} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 12 q^{70} + 24 q^{72} - 36 q^{76} + 40 q^{78} + 40 q^{82} + 16 q^{84} + 16 q^{85} + 44 q^{88} + 18 q^{90} + 32 q^{93} + 12 q^{94} + 42 q^{96} - 48 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^10 + 4 * q^12 - 8 * q^13 - 14 * q^16 + 16 * q^18 + 4 * q^21 - 4 * q^22 - 2 * q^24 - 8 * q^25 + 28 * q^28 + 8 * q^30 - 16 * q^33 + 4 * q^34 + 18 * q^36 + 8 * q^37 + 14 * q^40 - 12 * q^42 - 4 * q^45 + 20 * q^46 - 36 * q^48 + 16 * q^49 - 32 * q^52 - 10 * q^54 + 24 * q^57 - 36 * q^58 - 14 * q^60 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 12 * q^70 + 24 * q^72 - 36 * q^76 + 40 * q^78 + 40 * q^82 + 16 * q^84 + 16 * q^85 + 44 * q^88 + 18 * q^90 + 32 * q^93 + 12 * q^94 + 42 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.17915	−	0.780776i	0.833783	−	0.552092i
$2$	1.17915	−	0.780776i	0.833783	−	0.552092i
$3$	−1.51022	−	0.848071i	−0.871928	−	0.489634i
$3$	−1.51022	−	0.848071i	−0.871928	−	0.489634i
$4$	0.780776	−	1.84130i	0.390388	−	0.920650i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.44293	+	0.179147i	−0.997322	+	0.0731366i
$7$			3.02045i			1.14162i	0.821081	+	0.570811i	$0.193371\pi$
$7$			3.02045i			1.14162i	−0.821081	+	0.570811i	$0.806629\pi$
$8$	−0.516994	−	2.78078i	−0.182785	−	0.983153i
$9$	1.56155	+	2.56155i	0.520518	+	0.853851i
$10$	0.780776	+	1.17915i	0.246903	+	0.372879i
$11$	1.32431			0.399294			0.199647	−	0.979868i	$-0.436021\pi$
$11$	1.32431			0.399294			0.199647	+	0.979868i	$0.436021\pi$
$12$	−2.74070	+	2.11862i	−0.791172	+	0.611594i
$13$	−5.12311			−1.42089			−0.710447	−	0.703751i	$-0.751507\pi$
$13$	−5.12311			−1.42089			−0.710447	+	0.703751i	$0.751507\pi$
$14$	2.35829	+	3.56155i	0.630281	+	0.951865i
$15$	0.848071	−	1.51022i	0.218971	−	0.389938i
$16$	−2.78078	−	2.87529i	−0.695194	−	0.718822i
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	3.84130	+	1.80122i	0.905403	+	0.424553i
$19$		−	1.32431i		−	0.303817i	−0.988395	−	0.151908i	$-0.951458\pi$
$19$		−	1.32431i		−	0.303817i	0.988395	−	0.151908i	$-0.0485419\pi$
$20$	1.84130	+	0.780776i	0.411727	+	0.174587i
$21$	2.56155	−	4.56155i	0.558977	−	0.995412i
$22$	1.56155	−	1.03399i	0.332924	−	0.220447i
$23$	0.371834			0.0775328			0.0387664	−	0.999248i	$-0.487657\pi$
$23$	0.371834			0.0775328			0.0387664	+	0.999248i	$0.487657\pi$
$24$	−1.57752	+	4.63804i	−0.322010	+	0.946736i
$25$	−1.00000			−0.200000
$26$	−6.04090	+	4.00000i	−1.18472	+	0.784465i
$27$	−0.185917	−	5.19283i	−0.0357798	−	0.999360i
$28$	5.56155	+	2.35829i	1.05103	+	0.445676i
$29$		−	3.12311i		−	0.579946i	−0.957035	−	0.289973i	$-0.906354\pi$
$29$		−	3.12311i		−	0.579946i	0.957035	−	0.289973i	$-0.0936464\pi$
$30$	−0.179147	−	2.44293i	−0.0327077	−	0.446016i
$31$			4.71659i			0.847124i	0.905867	+	0.423562i	$0.139220\pi$
$31$			4.71659i			0.847124i	−0.905867	+	0.423562i	$0.860780\pi$
$32$	−5.52390	−	1.21922i	−0.976497	−	0.215530i
$33$	−2.00000	−	1.12311i	−0.348155	−	0.195508i
$34$	−1.56155	−	2.35829i	−0.267804	−	0.404444i
$35$	−3.02045			−0.510549
$36$	5.93581	−	0.875288i	0.989302	−	0.145881i
$37$	5.12311			0.842233			0.421117	−	0.907006i	$-0.361638\pi$
$37$	5.12311			0.842233			0.421117	+	0.907006i	$0.361638\pi$
$38$	−1.03399	−	1.56155i	−0.167735	−	0.253317i
$39$	7.73704	+	4.34475i	1.23892	+	0.695718i
$40$	2.78078	−	0.516994i	0.439679	−	0.0817439i
$41$			1.12311i			0.175400i	0.996147	+	0.0876998i	$0.0279516\pi$
$41$			1.12311i			0.175400i	−0.996147	+	0.0876998i	$0.972048\pi$
$42$	−0.541105	−	7.37874i	−0.0834943	−	1.13856i
$43$		−	7.73704i		−	1.17989i	−0.807445	−	0.589944i	$-0.799150\pi$
$43$		−	7.73704i		−	1.17989i	0.807445	−	0.589944i	$-0.200850\pi$
$44$	1.03399	−	2.43845i	0.155879	−	0.367610i
$45$	−2.56155	+	1.56155i	−0.381854	+	0.232783i
$46$	0.438447	−	0.290319i	0.0646455	−	0.0428052i
$47$	3.02045			0.440578			0.220289	−	0.975435i	$-0.429300\pi$
$47$	3.02045			0.440578			0.220289	+	0.975435i	$0.429300\pi$
$48$	1.76115	+	6.70062i	0.254200	+	0.967152i
$49$	−2.12311			−0.303301
$50$	−1.17915	+	0.780776i	−0.166757	+	0.110418i
$51$	−1.69614	+	3.02045i	−0.237507	+	0.422947i
$52$	−4.00000	+	9.43318i	−0.554700	+	1.30815i
$53$			12.2462i			1.68215i	0.540921	+	0.841073i	$0.318076\pi$
$53$			12.2462i			1.68215i	−0.540921	+	0.841073i	$0.681924\pi$
$54$	−4.27366	−	5.97795i	−0.581571	−	0.813495i
$55$			1.32431i			0.178570i
$56$	8.39919	−	1.56155i	1.12239	−	0.208671i
$57$	−1.12311	+	2.00000i	−0.148759	+	0.264906i
$58$	−2.43845	−	3.68260i	−0.320184	−	0.483549i
$59$	−14.1498			−1.84214			−0.921071	−	0.389394i	$-0.872685\pi$
$59$	−14.1498			−1.84214			−0.921071	+	0.389394i	$0.872685\pi$
$60$	−2.11862	−	2.74070i	−0.273513	−	0.353823i
$61$	3.12311			0.399873			0.199936	−	0.979809i	$-0.435926\pi$
$61$	3.12311			0.399873			0.199936	+	0.979809i	$0.435926\pi$
$62$	3.68260	+	5.56155i	0.467691	+	0.706318i
$63$	−7.73704	+	4.71659i	−0.974775	+	0.594234i
$64$	−7.46543	+	2.87529i	−0.933179	+	0.359411i
$65$		−	5.12311i		−	0.635443i
$66$	−3.23519	+	0.237246i	−0.398224	+	0.0292030i
$67$			4.34475i			0.530796i	0.964139	+	0.265398i	$0.0855034\pi$
$67$			4.34475i			0.530796i	−0.964139	+	0.265398i	$0.914497\pi$
$68$	−3.68260	−	1.56155i	−0.446581	−	0.189366i
$69$	−0.561553	−	0.315342i	−0.0676030	−	0.0379627i
$70$	−3.56155	+	2.35829i	−0.425687	+	0.281870i
$71$	3.39228			0.402590			0.201295	−	0.979531i	$-0.435485\pi$
$71$	3.39228			0.402590			0.201295	+	0.979531i	$0.435485\pi$
$72$	6.31579	−	5.66664i	0.744323	−	0.667819i
$73$	8.24621			0.965146			0.482573	−	0.875856i	$-0.339702\pi$
$73$	8.24621			0.965146			0.482573	+	0.875856i	$0.339702\pi$
$74$	6.04090	−	4.00000i	0.702240	−	0.464991i
$75$	1.51022	+	0.848071i	0.174386	+	0.0979267i
$76$	−2.43845	−	1.03399i	−0.279709	−	0.118607i
$77$			4.00000i			0.455842i
$78$	12.5154	−	0.917790i	1.41709	−	0.103919i
$79$		−	8.10887i		−	0.912319i	−0.889898	−	0.456160i	$-0.849225\pi$
$79$		−	8.10887i		−	0.912319i	0.889898	−	0.456160i	$-0.150775\pi$
$80$	2.87529	−	2.78078i	0.321467	−	0.310900i
$81$	−4.12311	+	8.00000i	−0.458123	+	0.888889i
$82$	0.876894	+	1.32431i	0.0968368	+	0.146245i
$83$	15.1022			1.65769			0.828843	−	0.559481i	$-0.189000\pi$
$83$	15.1022			1.65769			0.828843	+	0.559481i	$0.189000\pi$
$84$	−6.39919	−	8.27814i	−0.698209	−	0.903219i
$85$	2.00000			0.216930
$86$	−6.04090	−	9.12311i	−0.651407	−	0.983770i
$87$	−2.64861	+	4.71659i	−0.283961	+	0.505671i
$88$	−0.684658	−	3.68260i	−0.0729848	−	0.392567i
$89$		−	10.2462i		−	1.08610i	−0.839702	−	0.543048i	$-0.817270\pi$
$89$		−	10.2462i		−	1.08610i	0.839702	−	0.543048i	$-0.182730\pi$
$90$	−1.80122	+	3.84130i	−0.189866	+	0.404909i
$91$		−	15.4741i		−	1.62212i
$92$	0.290319	−	0.684658i	0.0302679	−	0.0713806i
$93$	4.00000	−	7.12311i	0.414781	−	0.738632i
$94$	3.56155	−	2.35829i	0.367346	−	0.243240i
$95$	1.32431			0.135871
$96$	7.30834	+	6.52596i	0.745904	+	0.666053i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	−2.50345	+	1.65767i	−0.252887	+	0.167450i
$99$	2.06798	+	3.39228i	0.207839	+	0.340937i
$100$	−0.780776	+	1.84130i	−0.0780776	+	0.184130i
$101$			0.876894i			0.0872543i	0.999048	+	0.0436271i	$0.0138914\pi$
$101$			0.876894i			0.0872543i	−0.999048	+	0.0436271i	$0.986109\pi$
$102$	0.358294	+	4.88586i	0.0354764	+	0.483772i
$103$			9.80501i			0.966117i	0.875588	+	0.483058i	$0.160474\pi$
$103$			9.80501i			0.966117i	−0.875588	+	0.483058i	$0.839526\pi$
$104$	2.64861	+	14.2462i	0.259718	+	1.39696i
$105$	4.56155	+	2.56155i	0.445162	+	0.249982i
$106$	9.56155	+	14.4401i	0.928700	+	1.40255i
$107$	−3.02045			−0.291998			−0.145999	−	0.989285i	$-0.546640\pi$
$107$	−3.02045			−0.291998			−0.145999	+	0.989285i	$0.546640\pi$
$108$	−9.70671	−	3.71211i	−0.934029	−	0.357198i
$109$	−0.876894			−0.0839912			−0.0419956	−	0.999118i	$-0.513372\pi$
$109$	−0.876894			−0.0839912			−0.0419956	+	0.999118i	$0.513372\pi$
$110$	1.03399	+	1.56155i	0.0985868	+	0.148888i
$111$	−7.73704	−	4.34475i	−0.734367	−	0.412386i
$112$	8.68466	−	8.39919i	0.820623	−	0.793649i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	0.237246	+	3.23519i	0.0222201	+	0.303003i
$115$			0.371834i			0.0346737i
$116$	−5.75058	−	2.43845i	−0.533928	−	0.226404i
$117$	−8.00000	−	13.1231i	−0.739600	−	1.21323i
$118$	−16.6847	+	11.0478i	−1.53595	+	1.01703i
$119$	6.04090			0.553768
$120$	−4.63804	−	1.57752i	−0.423393	−	0.144007i
$121$	−9.24621			−0.840565
$122$	3.68260	−	2.43845i	0.333407	−	0.220767i
$123$	0.952473	−	1.69614i	0.0858816	−	0.152936i
$124$	8.68466	+	3.68260i	0.779905	+	0.330707i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.44050	+	11.6024i	−0.484679	+	1.03363i
$127$		−	15.1022i		−	1.34011i	−0.742313	−	0.670054i	$-0.766271\pi$
$127$		−	15.1022i		−	1.34011i	0.742313	−	0.670054i	$-0.233729\pi$
$128$	−6.55789	+	9.21922i	−0.579641	+	0.814872i
$129$	−6.56155	+	11.6847i	−0.577713	+	1.02878i
$130$	−4.00000	−	6.04090i	−0.350823	−	0.529822i
$131$	5.46026			0.477065			0.238532	−	0.971135i	$-0.423334\pi$
$131$	5.46026			0.477065			0.238532	+	0.971135i	$0.423334\pi$
$132$	−3.62953	+	2.80571i	−0.315910	+	0.244205i
$133$	4.00000			0.346844
$134$	3.39228	+	5.12311i	0.293049	+	0.442569i
$135$	5.19283	−	0.185917i	0.446927	−	0.0160012i
$136$	−5.56155	+	1.03399i	−0.476899	+	0.0886637i
$137$			8.24621i			0.704521i	0.935902	+	0.352261i	$0.114587\pi$
$137$			8.24621i			0.704521i	−0.935902	+	0.352261i	$0.885413\pi$
$138$	−0.908365	+	0.0666131i	−0.0773251	+	0.00567048i
$139$			17.5420i			1.48790i	0.668237	+	0.743949i	$0.267049\pi$
$139$			17.5420i			1.48790i	−0.668237	+	0.743949i	$0.732951\pi$
$140$	−2.35829	+	5.56155i	−0.199312	+	0.470037i
$141$	−4.56155	−	2.56155i	−0.384152	−	0.215722i
$142$	4.00000	−	2.64861i	0.335673	−	0.222267i
$143$	−6.78456			−0.567354
$144$	3.02287	−	11.6130i	0.251906	−	0.967752i
$145$	3.12311			0.259360
$146$	9.72350	−	6.43845i	0.804722	−	0.532850i
$147$	3.20636	+	1.80054i	0.264457	+	0.148506i
$148$	4.00000	−	9.43318i	0.328798	−	0.775402i
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$	2.44293	−	0.179147i	0.199464	−	0.0146273i
$151$			7.36520i			0.599372i	0.954038	+	0.299686i	$0.0968819\pi$
$151$			7.36520i			0.599372i	−0.954038	+	0.299686i	$0.903118\pi$
$152$	−3.68260	+	0.684658i	−0.298698	+	0.0555331i
$153$	5.12311	−	3.12311i	0.414179	−	0.252488i
$154$	3.12311	+	4.71659i	0.251667	+	0.380074i
$155$	−4.71659			−0.378846
$156$	14.0409	−	10.8539i	1.12417	−	0.869010i
$157$	−3.36932			−0.268901			−0.134450	−	0.990920i	$-0.542927\pi$
$157$	−3.36932			−0.268901			−0.134450	+	0.990920i	$0.542927\pi$
$158$	−6.33122	−	9.56155i	−0.503684	−	0.760676i
$159$	10.3857	−	18.4945i	0.823636	−	1.46671i
$160$	1.21922	−	5.52390i	0.0963881	−	0.436703i
$161$			1.12311i			0.0885131i
$162$	1.38446	+	12.6524i	0.108774	+	0.994067i
$163$			15.6829i			1.22838i	0.789159	+	0.614189i	$0.210517\pi$
$163$			15.6829i			1.22838i	−0.789159	+	0.614189i	$0.789483\pi$
$164$	2.06798	+	0.876894i	0.161482	+	0.0684739i
$165$	1.12311	−	2.00000i	0.0874337	−	0.155700i
$166$	17.8078	−	11.7915i	1.38215	−	0.915196i
$167$	−9.06134			−0.701188			−0.350594	−	0.936528i	$-0.614020\pi$
$167$	−9.06134			−0.701188			−0.350594	+	0.936528i	$0.614020\pi$
$168$	−14.0090	−	4.76481i	−1.08082	−	0.367613i
$169$	13.2462			1.01894
$170$	2.35829	−	1.56155i	0.180873	−	0.119766i
$171$	3.39228	−	2.06798i	0.259414	−	0.158142i
$172$	−14.2462	−	6.04090i	−1.08626	−	0.460614i
$173$		−	2.00000i		−	0.152057i	−0.997106	−	0.0760286i	$-0.975776\pi$
$173$		−	2.00000i		−	0.152057i	0.997106	−	0.0760286i	$-0.0242240\pi$
$174$	0.559496	+	7.62953i	0.0424153	+	0.578393i
$175$		−	3.02045i		−	0.228324i
$176$	−3.68260	−	3.80776i	−0.277587	−	0.287021i
$177$	21.3693	+	12.0000i	1.60622	+	0.901975i
$178$	−8.00000	−	12.0818i	−0.599625	−	0.905569i
$179$	−10.0138			−0.748468			−0.374234	−	0.927334i	$-0.622094\pi$
$179$	−10.0138			−0.748468			−0.374234	+	0.927334i	$0.622094\pi$
$180$	0.875288	+	5.93581i	0.0652401	+	0.442429i
$181$	−12.2462			−0.910254			−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462			−0.910254			−0.455127	+	0.890427i	$0.650406\pi$
$182$	−12.0818	−	18.2462i	−0.895562	−	1.35250i
$183$	−4.71659	−	2.64861i	−0.348660	−	0.195791i
$184$	−0.192236	−	1.03399i	−0.0141718	−	0.0762266i
$185$			5.12311i			0.376658i
$186$	−0.844964	−	11.5223i	−0.0619558	−	0.844856i
$187$		−	2.64861i		−	0.193686i
$188$	2.35829	−	5.56155i	0.171996	−	0.405618i
$189$	15.6847	−	0.561553i	1.14089	−	0.0408470i
$190$	1.56155	−	1.03399i	0.113287	−	0.0750133i
$191$	−24.9073			−1.80223			−0.901113	−	0.433585i	$-0.857248\pi$
$191$	−24.9073			−1.80223			−0.901113	+	0.433585i	$0.857248\pi$
$192$	13.7129	+	1.98889i	0.989645	+	0.143535i
$193$	−0.246211			−0.0177227			−0.00886134	−	0.999961i	$-0.502821\pi$
$193$	−0.246211			−0.0177227			−0.00886134	+	0.999961i	$0.502821\pi$
$194$	−7.07488	+	4.68466i	−0.507947	+	0.336339i
$195$	−4.34475	+	7.73704i	−0.311134	+	0.554061i
$196$	−1.65767	+	3.90928i	−0.118405	+	0.279234i
$197$		−	4.24621i		−	0.302530i	−0.988493	−	0.151265i	$-0.951665\pi$
$197$		−	4.24621i		−	0.302530i	0.988493	−	0.151265i	$-0.0483347\pi$
$198$	5.08706	+	2.38537i	0.361522	+	0.169521i
$199$		−	5.46026i		−	0.387067i	−0.981094	−	0.193534i	$-0.938005\pi$
$199$		−	5.46026i		−	0.387067i	0.981094	−	0.193534i	$-0.0619949\pi$
$200$	0.516994	+	2.78078i	0.0365570	+	0.196631i
$201$	3.68466	−	6.56155i	0.259896	−	0.462816i
$202$	0.684658	+	1.03399i	0.0481724	+	0.0727511i
$203$	9.43318			0.662079
$204$	4.23725	+	5.48140i	0.296667	+	0.383775i
$205$	−1.12311			−0.0784411
$206$	7.65552	+	11.5616i	0.533385	+	0.805532i
$207$	0.580639	+	0.952473i	0.0403572	+	0.0662014i
$208$	14.2462	+	14.7304i	0.987797	+	1.02137i
$209$		−	1.75379i		−	0.121312i
$210$	7.37874	−	0.541105i	0.509182	−	0.0373398i
$211$			16.7984i			1.15645i	0.815878	+	0.578224i	$0.196254\pi$
$211$			16.7984i			1.15645i	−0.815878	+	0.578224i	$0.803746\pi$
$212$	22.5490	+	9.56155i	1.54867	+	0.656690i
$213$	−5.12311	−	2.87689i	−0.351029	−	0.197122i
$214$	−3.56155	+	2.35829i	−0.243463	+	0.161210i
$215$	7.73704			0.527662
$216$	−14.3440	+	3.20165i	−0.975983	+	0.217845i
$217$	−14.2462			−0.967096
$218$	−1.03399	+	0.684658i	−0.0700305	+	0.0463709i
$219$	−12.4536	−	6.99337i	−0.841538	−	0.472568i
$220$	2.43845	+	1.03399i	0.164400	+	0.0697114i
$221$			10.2462i			0.689235i
$222$	−12.5154	+	0.917790i	−0.839978	+	0.0615980i
$223$		−	8.31768i		−	0.556993i	−0.960437	−	0.278496i	$-0.910164\pi$
$223$		−	8.31768i		−	0.556993i	0.960437	−	0.278496i	$-0.0898360\pi$
$224$	3.68260	−	16.6847i	0.246054	−	1.11479i
$225$	−1.56155	−	2.56155i	−0.104104	−	0.170770i
$226$	−10.9309	−	16.5081i	−0.727111	−	1.09810i
$227$	21.8868			1.45268			0.726339	−	0.687337i	$-0.241220\pi$
$227$	21.8868			1.45268			0.726339	+	0.687337i	$0.241220\pi$
$228$	2.80571	+	3.62953i	0.185812	+	0.240371i
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$	0.290319	+	0.438447i	0.0191431	+	0.0289104i
$231$	3.39228	−	6.04090i	0.223196	−	0.397462i
$232$	−8.68466	+	1.61463i	−0.570176	+	0.106005i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	−19.6794	−	9.22786i	−1.28648	−	0.603244i
$235$			3.02045i			0.197032i
$236$	−11.0478	+	26.0540i	−0.719151	+	1.69597i
$237$	−6.87689	+	12.2462i	−0.446702	+	0.795477i
$238$	7.12311	−	4.71659i	0.461722	−	0.305731i
$239$	17.3790			1.12416			0.562078	−	0.827084i	$-0.310002\pi$
$239$	17.3790			1.12416			0.562078	+	0.827084i	$0.310002\pi$
$240$	−6.70062	+	1.76115i	−0.432523	+	0.113682i
$241$	13.3693			0.861193			0.430597	−	0.902544i	$-0.358303\pi$
$241$	13.3693			0.861193			0.430597	+	0.902544i	$0.358303\pi$
$242$	−10.9026	+	7.21922i	−0.700849	+	0.464069i
$243$	13.0114	−	8.58511i	0.834680	−	0.550735i
$244$	2.43845	−	5.75058i	0.156106	−	0.368143i
$245$		−	2.12311i		−	0.135640i
$246$	−0.201201	−	2.74367i	−0.0128281	−	0.174930i
$247$			6.78456i			0.431691i
$248$	13.1158	−	2.43845i	0.832853	−	0.154842i
$249$	−22.8078	−	12.8078i	−1.44538	−	0.811659i
$250$	−0.780776	−	1.17915i	−0.0493806	−	0.0745758i
$251$	18.7033			1.18054			0.590272	−	0.807205i	$-0.299021\pi$
$251$	18.7033			1.18054			0.590272	+	0.807205i	$0.299021\pi$
$252$	2.64376	+	17.9288i	0.166541	+	1.12941i
$253$	0.492423			0.0309583
$254$	−11.7915	−	17.8078i	−0.739863	−	1.11736i
$255$	−3.02045	−	1.69614i	−0.189148	−	0.106216i
$256$	−0.534565	+	15.9911i	−0.0334103	+	0.999442i
$257$		−	30.4924i		−	1.90207i	−0.309091	−	0.951033i	$-0.600025\pi$
$257$		−	30.4924i		−	1.90207i	0.309091	−	0.951033i	$-0.399975\pi$
$258$	1.38607	+	18.9010i	0.0862929	+	1.17673i
$259$			15.4741i			0.961512i
$260$	−9.43318	−	4.00000i	−0.585021	−	0.248069i
$261$	8.00000	−	4.87689i	0.495188	−	0.301872i
$262$	6.43845	−	4.26324i	0.397769	−	0.263384i
$263$	−23.7917			−1.46706			−0.733531	−	0.679656i	$-0.762129\pi$
$263$	−23.7917			−1.46706			−0.733531	+	0.679656i	$0.762129\pi$
$264$	−2.08912	+	6.14219i	−0.128576	+	0.378026i
$265$	−12.2462			−0.752279
$266$	4.71659	−	3.12311i	0.289193	−	0.191490i
$267$	−8.68951	+	15.4741i	−0.531789	+	0.946998i
$268$	8.00000	+	3.39228i	0.488678	+	0.207217i
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$	5.97795	−	4.27366i	0.363806	−	0.260087i
$271$		−	15.3110i		−	0.930080i	−0.885290	−	0.465040i	$-0.846040\pi$
$271$		−	15.3110i		−	0.930080i	0.885290	−	0.465040i	$-0.153960\pi$
$272$	−5.75058	+	5.56155i	−0.348680	+	0.337219i
$273$	−13.1231	+	23.3693i	−0.794246	+	1.41438i
$274$	6.43845	+	9.72350i	0.388961	+	0.587418i
$275$	−1.32431			−0.0798587
$276$	−1.01909	+	0.787776i	−0.0613418	+	0.0474186i
$277$	23.3693			1.40413			0.702063	−	0.712115i	$-0.252262\pi$
$277$	23.3693			1.40413			0.702063	+	0.712115i	$0.252262\pi$
$278$	13.6964	+	20.6847i	0.821457	+	1.24058i
$279$	−12.0818	+	7.36520i	−0.723318	+	0.440943i
$280$	1.56155	+	8.39919i	0.0933206	+	0.501948i
$281$		−	13.6155i		−	0.812234i	−0.913821	−	0.406117i	$-0.866882\pi$
$281$		−	13.6155i		−	0.812234i	0.913821	−	0.406117i	$-0.133118\pi$
$282$	−7.37874	+	0.541105i	−0.439398	+	0.0322223i
$283$		−	23.2111i		−	1.37976i	−0.723925	−	0.689879i	$-0.757664\pi$
$283$		−	23.2111i		−	1.37976i	0.723925	−	0.689879i	$-0.242336\pi$
$284$	2.64861	−	6.24621i	0.157166	−	0.370644i
$285$	−2.00000	−	1.12311i	−0.118470	−	0.0665270i
$286$	−8.00000	+	5.29723i	−0.473050	+	0.313232i
$287$	−3.39228			−0.200240
$288$	−5.50276	−	16.0536i	−0.324253	−	0.945970i
$289$	13.0000			0.764706
$290$	3.68260	−	2.43845i	0.216250	−	0.143191i
$291$	9.06134	+	5.08842i	0.531185	+	0.298289i
$292$	6.43845	−	15.1838i	0.376782	−	0.888562i
$293$		−	2.49242i		−	0.145609i	−0.997346	−	0.0728044i	$-0.976805\pi$
$293$		−	2.49242i		−	0.145609i	0.997346	−	0.0728044i	$-0.0231949\pi$
$294$	5.18660	−	0.380349i	0.302489	−	0.0221824i
$295$		−	14.1498i		−	0.823831i
$296$	−2.64861	−	14.2462i	−0.153948	−	0.828044i
$297$	−0.246211	−	6.87689i	−0.0142866	−	0.399038i
$298$	10.9309	+	16.5081i	0.633208	+	0.956286i
$299$	−1.90495			−0.110166
$300$	2.74070	−	2.11862i	0.158234	−	0.122319i
$301$	23.3693			1.34699
$302$	5.75058	+	8.68466i	0.330908	+	0.499746i
$303$	0.743668	−	1.32431i	0.0427226	−	0.0760794i
$304$	−3.80776	+	3.68260i	−0.218390	+	0.211212i
$305$			3.12311i			0.178829i
$306$	3.60245	−	7.68260i	0.205938	−	0.439185i
$307$		−	11.1293i		−	0.635184i	−0.948227	−	0.317592i	$-0.897126\pi$
$307$		−	11.1293i		−	0.635184i	0.948227	−	0.317592i	$-0.102874\pi$
$308$	7.36520	+	3.12311i	0.419671	+	0.177955i
$309$	8.31534	−	14.8078i	0.473043	−	0.842384i
$310$	−5.56155	+	3.68260i	−0.315875	+	0.209158i
$311$	20.7713			1.17783			0.588916	−	0.808194i	$-0.299555\pi$
$311$	20.7713			1.17783			0.588916	+	0.808194i	$0.299555\pi$
$312$	8.08179	−	23.7612i	0.457541	−	1.34521i
$313$	−22.4924			−1.27135			−0.635673	−	0.771958i	$-0.719278\pi$
$313$	−22.4924			−1.27135			−0.635673	+	0.771958i	$0.719278\pi$
$314$	−3.97292	+	2.63068i	−0.224205	+	0.148458i
$315$	−4.71659	−	7.73704i	−0.265750	−	0.435933i
$316$	−14.9309	−	6.33122i	−0.839927	−	0.356159i
$317$			16.7386i			0.940135i	0.882630	+	0.470068i	$0.155770\pi$
$317$			16.7386i			0.940135i	−0.882630	+	0.470068i	$0.844230\pi$
$318$	−2.19387	−	29.9166i	−0.123026	−	1.67764i
$319$		−	4.13595i		−	0.231569i
$320$	−2.87529	−	7.46543i	−0.160734	−	0.417330i
$321$	4.56155	+	2.56155i	0.254601	+	0.142972i
$322$	0.876894	+	1.32431i	0.0488674	+	0.0738007i
$323$	−2.64861			−0.147373
$324$	11.5112	+	13.8381i	0.639510	+	0.768783i
$325$	5.12311			0.284179
$326$	12.2448	+	18.4924i	0.678178	+	1.02420i
$327$	1.32431	+	0.743668i	0.0732343	+	0.0411249i
$328$	3.12311	−	0.580639i	0.172445	−	0.0320604i
$329$			9.12311i			0.502973i
$330$	−0.237246	−	3.23519i	−0.0130600	−	0.178091i
$331$			3.22925i			0.177496i	0.996054	+	0.0887479i	$0.0282865\pi$
$331$			3.22925i			0.177496i	−0.996054	+	0.0887479i	$0.971713\pi$
$332$	11.7915	−	27.8078i	0.647141	−	1.52615i
$333$	8.00000	+	13.1231i	0.438397	+	0.719142i
$334$	−10.6847	+	7.07488i	−0.584638	+	0.387120i
$335$	−4.34475			−0.237379
$336$	−20.2389	+	5.31946i	−1.10412	+	0.290200i
$337$	−1.50758			−0.0821230			−0.0410615	−	0.999157i	$-0.513074\pi$
$337$	−1.50758			−0.0821230			−0.0410615	+	0.999157i	$0.513074\pi$
$338$	15.6192	−	10.3423i	0.849574	−	0.562549i
$339$	−11.8730	+	21.1431i	−0.644852	+	1.14834i
$340$	1.56155	−	3.68260i	0.0846871	−	0.199717i
$341$			6.24621i			0.338251i
$342$	2.38537	−	5.08706i	0.128986	−	0.275077i
$343$			14.7304i			0.795367i
$344$	−21.5150	+	4.00000i	−1.16001	+	0.215666i
$345$	0.315342	−	0.561553i	0.0169774	−	0.0302330i
$346$	−1.56155	−	2.35829i	−0.0839496	−	0.126783i
$347$	−22.6305			−1.21487			−0.607434	−	0.794370i	$-0.707801\pi$
$347$	−22.6305			−1.21487			−0.607434	+	0.794370i	$0.707801\pi$
$348$	6.61668	+	8.55950i	0.354691	+	0.458837i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−2.35829	−	3.56155i	−0.126056	−	0.190373i
$351$	0.952473	+	26.6034i	0.0508392	+	1.41998i
$352$	−7.31534	−	1.61463i	−0.389909	−	0.0860599i
$353$			20.2462i			1.07760i	0.842435	+	0.538799i	$0.181122\pi$
$353$			20.2462i			1.07760i	−0.842435	+	0.538799i	$0.818878\pi$
$354$	34.5669	−	2.53489i	1.83721	−	0.134728i
$355$			3.39228i			0.180044i
$356$	−18.8664	−	8.00000i	−0.999915	−	0.423999i
$357$	−9.12311	−	5.12311i	−0.482846	−	0.271144i
$358$	−11.8078	+	7.81855i	−0.624060	+	0.413223i
$359$	21.5150			1.13552			0.567758	−	0.823195i	$-0.307811\pi$
$359$	21.5150			1.13552			0.567758	+	0.823195i	$0.307811\pi$
$360$	5.66664	+	6.31579i	0.298658	+	0.332871i
$361$	17.2462			0.907695
$362$	−14.4401	+	9.56155i	−0.758954	+	0.502544i
$363$	13.9638	+	7.84144i	0.732912	+	0.411569i
$364$	−28.4924	−	12.0818i	−1.49341	−	0.633258i
$365$			8.24621i			0.431626i
$366$	−7.62953	+	0.559496i	−0.398802	+	0.0292453i
$367$			10.9663i			0.572436i	0.958165	+	0.286218i	$0.0923981\pi$
$367$			10.9663i			0.572436i	−0.958165	+	0.286218i	$0.907602\pi$
$368$	−1.03399	−	1.06913i	−0.0539003	−	0.0557323i
$369$	−2.87689	+	1.75379i	−0.149765	+	0.0912986i
$370$	4.00000	+	6.04090i	0.207950	+	0.314051i
$371$	−36.9890			−1.92038
$372$	−9.99267	−	12.9268i	−0.518096	−	0.670221i
$373$	−9.12311			−0.472377			−0.236188	−	0.971707i	$-0.575898\pi$
$373$	−9.12311			−0.472377			−0.236188	+	0.971707i	$0.575898\pi$
$374$	−2.06798	−	3.12311i	−0.106932	−	0.161492i
$375$	−0.848071	+	1.51022i	−0.0437942	+	0.0779876i
$376$	−1.56155	−	8.39919i	−0.0805309	−	0.433155i
$377$			16.0000i			0.824042i
$378$	18.0561	−	12.9084i	0.928704	−	0.663935i
$379$		−	18.7033i		−	0.960725i	−0.877070	−	0.480363i	$-0.840505\pi$
$379$		−	18.7033i		−	0.960725i	0.877070	−	0.480363i	$-0.159495\pi$
$380$	1.03399	−	2.43845i	0.0530424	−	0.125090i
$381$	−12.8078	+	22.8078i	−0.656162	+	1.16848i
$382$	−29.3693	+	19.4470i	−1.50266	+	0.994995i
$383$	−15.1022			−0.771688			−0.385844	−	0.922564i	$-0.626090\pi$
$383$	−15.1022			−0.771688			−0.385844	+	0.922564i	$0.626090\pi$
$384$	17.7224	−	8.36154i	0.904394	−	0.426698i
$385$	−4.00000			−0.203859
$386$	−0.290319	+	0.192236i	−0.0147769	+	0.00978455i
$387$	19.8188	−	12.0818i	1.00745	−	0.614152i
$388$	−4.68466	+	11.0478i	−0.237827	+	0.560867i
$389$			20.7386i			1.05149i	0.850642	+	0.525745i	$0.176213\pi$
$389$			20.7386i			1.05149i	−0.850642	+	0.525745i	$0.823787\pi$
$390$	0.917790	+	12.5154i	0.0464741	+	0.633741i
$391$		−	0.743668i		−	0.0376089i
$392$	1.09763	+	5.90388i	0.0554388	+	0.298191i
$393$	−8.24621	−	4.63068i	−0.415966	−	0.233587i
$394$	−3.31534	−	5.00691i	−0.167024	−	0.252244i
$395$	8.10887			0.408002
$396$	7.86084	−	1.15915i	0.395022	−	0.0582495i
$397$	14.8769			0.746650			0.373325	−	0.927701i	$-0.378218\pi$
$397$	14.8769			0.746650			0.373325	+	0.927701i	$0.378218\pi$
$398$	−4.26324	−	6.43845i	−0.213697	−	0.322730i
$399$	−6.04090	−	3.39228i	−0.302423	−	0.169827i
$400$	2.78078	+	2.87529i	0.139039	+	0.143764i
$401$		−	24.0000i		−	1.19850i	−0.800561	−	0.599251i	$-0.795465\pi$
$401$		−	24.0000i		−	1.19850i	0.800561	−	0.599251i	$-0.204535\pi$
$402$	−0.778351	−	10.6139i	−0.0388206	−	0.529375i
$403$		−	24.1636i		−	1.20367i
$404$	1.61463	+	0.684658i	0.0803307	+	0.0340630i
$405$	−8.00000	−	4.12311i	−0.397523	−	0.204879i
$406$	11.1231	−	7.36520i	0.552030	−	0.365529i
$407$	6.78456			0.336298
$408$	9.27608	+	3.15504i	0.459235	+	0.156198i
$409$	25.3693			1.25443			0.627216	−	0.778845i	$-0.284194\pi$
$409$	25.3693			1.25443			0.627216	+	0.778845i	$0.284194\pi$
$410$	−1.32431	+	0.876894i	−0.0654029	+	0.0433067i
$411$	6.99337	−	12.4536i	0.344957	−	0.614292i
$412$	18.0540	+	7.65552i	0.889456	+	0.377161i
$413$		−	42.7386i		−	2.10303i
$414$	1.42833	+	0.669757i	0.0701984	+	0.0329167i
$415$			15.1022i			0.741340i
$416$	28.2995	+	6.24621i	1.38750	+	0.306246i
$417$	14.8769	−	26.4924i	0.728525	−	1.29734i
$418$	−1.36932	−	2.06798i	−0.0669755	−	0.101148i
$419$	7.36520			0.359814			0.179907	−	0.983684i	$-0.442420\pi$
$419$	7.36520			0.359814			0.179907	+	0.983684i	$0.442420\pi$
$420$	8.27814	−	6.39919i	0.403932	−	0.312249i
$421$	−25.3693			−1.23642			−0.618212	−	0.786011i	$-0.712143\pi$
$421$	−25.3693			−1.23642			−0.618212	+	0.786011i	$0.712143\pi$
$422$	13.1158	+	19.8078i	0.638466	+	0.964227i
$423$	4.71659	+	7.73704i	0.229328	+	0.376188i
$424$	34.0540	−	6.33122i	1.65381	−	0.307471i
$425$			2.00000i			0.0970143i
$426$	−8.28711	+	0.607718i	−0.401512	+	0.0294440i
$427$			9.43318i			0.456503i
$428$	−2.35829	+	5.56155i	−0.113992	+	0.268828i
$429$	10.2462	+	5.75379i	0.494692	+	0.277796i
$430$	9.12311	−	6.04090i	0.439955	−	0.291318i
$431$	−16.6354			−0.801297			−0.400648	−	0.916232i	$-0.631215\pi$
$431$	−16.6354			−0.801297			−0.400648	+	0.916232i	$0.631215\pi$
$432$	−14.4139	+	14.9747i	−0.693488	+	0.720468i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$	−16.7984	+	11.1231i	−0.806348	+	0.533926i
$435$	−4.71659	−	2.64861i	−0.226143	−	0.126991i
$436$	−0.684658	+	1.61463i	−0.0327892	+	0.0773266i
$437$		−	0.492423i		−	0.0235558i
$438$	−20.1449	+	1.47729i	−0.962561	+	0.0705875i
$439$		−	9.27015i		−	0.442440i	−0.975224	−	0.221220i	$-0.928996\pi$
$439$		−	9.27015i		−	0.442440i	0.975224	−	0.221220i	$-0.0710039\pi$
$440$	3.68260	−	0.684658i	0.175561	−	0.0326398i
$441$	−3.31534	−	5.43845i	−0.157873	−	0.258974i
$442$	8.00000	+	12.0818i	0.380521	+	0.574672i
$443$	−16.5896			−0.788195			−0.394097	−	0.919069i	$-0.628943\pi$
$443$	−16.5896			−0.788195			−0.394097	+	0.919069i	$0.628943\pi$
$444$	−14.0409	+	10.8539i	−0.666351	+	0.515105i
$445$	10.2462			0.485717
$446$	−6.49424	−	9.80776i	−0.307511	−	0.464411i
$447$	11.8730	−	21.1431i	0.561573	−	1.00004i
$448$	−8.68466	−	22.5490i	−0.410312	−	1.06534i
$449$			27.3693i			1.29164i	0.763491	+	0.645819i	$0.223484\pi$
$449$			27.3693i			1.29164i	−0.763491	+	0.645819i	$0.776516\pi$
$450$	−3.84130	−	1.80122i	−0.181081	−	0.0849105i
$451$			1.48734i			0.0700359i
$452$	−25.7782	−	10.9309i	−1.21250	−	0.514145i
$453$	6.24621	−	11.1231i	0.293473	−	0.522609i
$454$	25.8078	−	17.0887i	1.21122	−	0.802012i
$455$	15.4741			0.725436
$456$	6.14219	+	2.08912i	0.287634	+	0.0978319i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	−19.1567	+	12.6847i	−0.895133	+	0.592715i
$459$	−10.3857	+	0.371834i	−0.484761	+	0.0173557i
$460$	0.684658	+	0.290319i	0.0319224	+	0.0135362i
$461$		−	41.8617i		−	1.94970i	−0.222872	−	0.974848i	$-0.571543\pi$
$461$		−	41.8617i		−	1.94970i	0.222872	−	0.974848i	$-0.428457\pi$
$462$	−0.716589	−	9.77172i	−0.0333387	−	0.454622i
$463$		−	3.02045i		−	0.140372i	−0.997534	−	0.0701861i	$-0.977641\pi$
$463$		−	3.02045i		−	0.140372i	0.997534	−	0.0701861i	$-0.0223593\pi$
$464$	−8.97983	+	8.68466i	−0.416878	+	0.403175i
$465$	7.12311	+	4.00000i	0.330326	+	0.185496i
$466$	7.80776	+	11.7915i	0.361688	+	0.546229i
$467$	2.27678			0.105357			0.0526784	−	0.998612i	$-0.483224\pi$
$467$	2.27678			0.105357			0.0526784	+	0.998612i	$0.483224\pi$
$468$	−30.4098	+	4.48419i	−1.40569	+	0.207282i
$469$	−13.1231			−0.605969
$470$	2.35829	+	3.56155i	0.108780	+	0.164282i
$471$	5.08842	+	2.85742i	0.234462	+	0.131663i
$472$	7.31534	+	39.3473i	0.336716	+	1.81111i
$473$		−	10.2462i		−	0.471121i
$474$	1.45268	+	19.8094i	0.0667239	+	0.909876i
$475$			1.32431i			0.0607634i
$476$	4.71659	−	11.1231i	0.216184	−	0.509827i
$477$	−31.3693	+	19.1231i	−1.43630	+	0.875587i
$478$	20.4924	−	13.5691i	0.937302	−	0.620637i
$479$	25.6509			1.17202			0.586010	−	0.810304i	$-0.300698\pi$
$479$	25.6509			1.17202			0.586010	+	0.810304i	$0.300698\pi$
$480$	−6.52596	+	7.30834i	−0.297868	+	0.333579i
$481$	−26.2462			−1.19672
$482$	15.7644	−	10.4384i	0.718048	−	0.475458i
$483$	0.952473	−	1.69614i	0.0433390	−	0.0771771i
$484$	−7.21922	+	17.0251i	−0.328147	+	0.773866i
$485$		−	6.00000i		−	0.272446i
$486$	8.63928	−	20.2821i	0.391886	−	0.920014i
$487$			25.2791i			1.14550i	0.819728	+	0.572752i	$0.194124\pi$
$487$			25.2791i			1.14550i	−0.819728	+	0.572752i	$0.805876\pi$
$488$	−1.61463	−	8.68466i	−0.0730907	−	0.393136i
$489$	13.3002	−	23.6847i	0.601455	−	1.07106i
$490$	−1.65767	−	2.50345i	−0.0748859	−	0.113095i
$491$	26.9752			1.21737			0.608687	−	0.793410i	$-0.291696\pi$
$491$	26.9752			1.21737			0.608687	+	0.793410i	$0.291696\pi$
$492$	−2.37944	−	3.07810i	−0.107273	−	0.138771i
$493$	−6.24621			−0.281315
$494$	5.29723	+	8.00000i	0.238334	+	0.359937i
$495$	−3.39228	+	2.06798i	−0.152472	+	0.0929486i
$496$	13.5616	−	13.1158i	0.608932	−	0.588916i
$497$			10.2462i			0.459605i
$498$	−36.8937	+	2.70552i	−1.65325	+	0.121237i
$499$		−	32.2725i		−	1.44471i	−0.691521	−	0.722357i	$-0.743059\pi$
$499$		−	32.2725i		−	1.44471i	0.691521	−	0.722357i	$-0.256941\pi$
$500$	−1.84130	−	0.780776i	−0.0823455	−	0.0349174i
$501$	13.6847	+	7.68466i	0.611385	+	0.343325i
$502$	22.0540	−	14.6031i	0.984317	−	0.651769i
$503$	14.3586			0.640217			0.320109	−	0.947381i	$-0.396281\pi$
$503$	14.3586			0.640217			0.320109	+	0.947381i	$0.396281\pi$
$504$	17.1158	+	19.0765i	0.762397	+	0.849736i
$505$	−0.876894			−0.0390213
$506$	0.580639	−	0.384472i	0.0258125	−	0.0170919i
$507$	−20.0047	−	11.2337i	−0.888442	−	0.498907i
$508$	−27.8078	−	11.7915i	−1.23377	−	0.523162i
$509$		−	11.1231i		−	0.493023i	−0.969140	−	0.246511i	$-0.920716\pi$
$509$		−	11.1231i		−	0.493023i	0.969140	−	0.246511i	$-0.0792843\pi$
$510$	−4.88586	+	0.358294i	−0.216350	+	0.0158655i
$511$			24.9073i			1.10183i
$512$	11.8551	+	19.2732i	0.523927	+	0.851763i
$513$	−6.87689	+	0.246211i	−0.303622	+	0.0108705i
$514$	−23.8078	−	35.9551i	−1.05012	−	1.58591i
$515$	−9.80501			−0.432060
$516$	16.3919	+	21.2049i	0.721612	+	0.933494i
$517$	4.00000			0.175920
$518$	12.0818	+	18.2462i	0.530843	+	0.801692i
$519$	−1.69614	+	3.02045i	−0.0744523	+	0.132583i
$520$	−14.2462	+	2.64861i	−0.624738	+	0.116149i
$521$			38.2462i			1.67560i	0.545980	+	0.837798i	$0.316158\pi$
$521$			38.2462i			1.67560i	−0.545980	+	0.837798i	$0.683842\pi$
$522$	5.62541	−	11.9968i	0.246218	−	0.525085i
$523$			35.2929i			1.54325i	0.636077	+	0.771625i	$0.280556\pi$
$523$			35.2929i			1.54325i	−0.636077	+	0.771625i	$0.719444\pi$
$524$	4.26324	−	10.0540i	0.186241	−	0.439210i
$525$	−2.56155	+	4.56155i	−0.111795	+	0.199082i
$526$	−28.0540	+	18.5760i	−1.22321	+	0.809954i
$527$	9.43318			0.410916
$528$	2.33230	+	8.87368i	0.101500	+	0.386177i
$529$	−22.8617			−0.993989
$530$	−14.4401	+	9.56155i	−0.627237	+	0.415327i
$531$	−22.0956	−	36.2454i	−0.958868	−	1.57292i
$532$	3.12311	−	7.36520i	0.135404	−	0.319322i
$533$		−	5.75379i		−	0.249224i
$534$	1.83558	+	25.0308i	0.0794333	+	1.08319i
$535$		−	3.02045i		−	0.130585i
$536$	12.0818	−	2.24621i	0.521854	−	0.0970215i
$537$	15.1231	+	8.49242i	0.652610	+	0.366475i
$538$	−10.9309	−	16.5081i	−0.471263	−	0.711713i
$539$	−2.81164			−0.121106
$540$	3.71211	−	9.70671i	0.159744	−	0.417710i
$541$	−26.9848			−1.16017			−0.580085	−	0.814556i	$-0.696980\pi$
$541$	−26.9848			−1.16017			−0.580085	+	0.814556i	$0.696980\pi$
$542$	−11.9545	−	18.0540i	−0.513490	−	0.775485i
$543$	18.4945	+	10.3857i	0.793676	+	0.445691i
$544$	−2.43845	+	11.0478i	−0.104548	+	0.473671i
$545$		−	0.876894i		−	0.0375620i
$546$	2.77214	+	37.8021i	0.118637	+	1.61778i
$547$		−	5.83209i		−	0.249362i	−0.992197	−	0.124681i	$-0.960209\pi$
$547$		−	5.83209i		−	0.249362i	0.992197	−	0.124681i	$-0.0397908\pi$
$548$	15.1838	+	6.43845i	0.648618	+	0.275037i
$549$	4.87689	+	8.00000i	0.208141	+	0.341432i
$550$	−1.56155	+	1.03399i	−0.0665848	+	0.0440894i
$551$	−4.13595			−0.176197
$552$	−0.586575	+	1.72458i	−0.0249663	+	0.0734031i
$553$	24.4924			1.04152
$554$	27.5559	−	18.2462i	1.17074	−	0.775207i
$555$	4.34475	−	7.73704i	0.184425	−	0.328419i
$556$	32.3002	+	13.6964i	1.36983	+	0.580858i
$557$		−	36.2462i		−	1.53580i	−0.640569	−	0.767901i	$-0.721301\pi$
$557$		−	36.2462i		−	1.53580i	0.640569	−	0.767901i	$-0.278699\pi$
$558$	−8.49563	+	18.1178i	−0.359649	+	0.766989i
$559$			39.6377i			1.67649i
$560$	8.39919	+	8.68466i	0.354931	+	0.366994i
$561$	−2.24621	+	4.00000i	−0.0948351	+	0.168880i
$562$	−10.6307	−	16.0547i	−0.448428	−	0.677227i
$563$	−7.90007			−0.332948			−0.166474	−	0.986046i	$-0.553238\pi$
$563$	−7.90007			−0.332948			−0.166474	+	0.986046i	$0.553238\pi$
$564$	−8.27814	+	6.39919i	−0.348573	+	0.269455i
$565$	14.0000			0.588984
$566$	−18.1227	−	27.3693i	−0.761753	−	1.15042i
$567$	−24.1636	−	12.4536i	−1.01478	−	0.523003i
$568$	−1.75379	−	9.43318i	−0.0735873	−	0.395807i
$569$			13.1231i			0.550149i	0.961423	+	0.275075i	$0.0887026\pi$
$569$			13.1231i			0.550149i	−0.961423	+	0.275075i	$0.911297\pi$
$570$	−3.23519	+	0.237246i	−0.135507	+	0.00993714i
$571$		−	33.0161i		−	1.38168i	−0.723007	−	0.690841i	$-0.757241\pi$
$571$		−	33.0161i		−	1.38168i	0.723007	−	0.690841i	$-0.242759\pi$
$572$	−5.29723	+	12.4924i	−0.221488	+	0.522334i
$573$	37.6155	+	21.1231i	1.57141	+	0.882430i
$574$	−4.00000	+	2.64861i	−0.166957	+	0.110551i
$575$	−0.371834			−0.0155066
$576$	−19.0229	−	14.6332i	−0.792620	−	0.609716i
$577$	−32.2462			−1.34243			−0.671214	−	0.741264i	$-0.734227\pi$
$577$	−32.2462			−1.34243			−0.671214	+	0.741264i	$0.734227\pi$
$578$	15.3289	−	10.1501i	0.637599	−	0.422188i
$579$	0.371834	+	0.208805i	0.0154529	+	0.00867762i
$580$	2.43845	−	5.75058i	0.101251	−	0.238780i
$581$			45.6155i			1.89245i
$582$	14.6576	−	1.07488i	0.607576	−	0.0445554i
$583$			16.2177i			0.671670i
$584$	−4.26324	−	22.9309i	−0.176414	−	0.948886i
$585$	13.1231	−	8.00000i	0.542574	−	0.330759i
$586$	−1.94602	−	2.93893i	−0.0803895	−	0.121406i
$587$	1.85917			0.0767362			0.0383681	−	0.999264i	$-0.487784\pi$
$587$	1.85917			0.0767362			0.0383681	+	0.999264i	$0.487784\pi$
$588$	5.81880	−	4.49806i	0.239963	−	0.185497i
$589$	6.24621			0.257371
$590$	−11.0478	−	16.6847i	−0.454831	−	0.686897i
$591$	−3.60109	+	6.41273i	−0.148129	+	0.263784i
$592$	−14.2462	−	14.7304i	−0.585516	−	0.605416i
$593$		−	8.24621i		−	0.338631i	−0.985562	−	0.169316i	$-0.945844\pi$
$593$		−	8.24621i		−	0.338631i	0.985562	−	0.169316i	$-0.0541557\pi$
$594$	−5.65964	−	7.91664i	−0.232218	−	0.324823i
$595$			6.04090i			0.247653i
$596$	25.7782	+	10.9309i	1.05592	+	0.447746i
$597$	−4.63068	+	8.24621i	−0.189521	+	0.337495i
$598$	−2.24621	+	1.48734i	−0.0918544	+	0.0608217i
$599$	−44.1912			−1.80560			−0.902802	−	0.430056i	$-0.858494\pi$
$599$	−44.1912			−1.80560			−0.902802	+	0.430056i	$0.858494\pi$
$600$	1.57752	−	4.63804i	0.0644019	−	0.189347i
$601$	23.1231			0.943211			0.471606	−	0.881810i	$-0.343675\pi$
$601$	23.1231			0.943211			0.471606	+	0.881810i	$0.343675\pi$
$602$	27.5559	−	18.2462i	1.12309	−	0.743660i
$603$	−11.1293	+	6.78456i	−0.453221	+	0.276289i
$604$	13.5616	+	5.75058i	0.551812	+	0.233988i
$605$		−	9.24621i		−	0.375912i
$606$	−0.157093	−	2.14219i	−0.00638148	−	0.0870206i
$607$		−	4.50778i		−	0.182965i	−0.995807	−	0.0914827i	$-0.970839\pi$
$607$		−	4.50778i		−	0.182965i	0.995807	−	0.0914827i	$-0.0291606\pi$
$608$	−1.61463	+	7.31534i	−0.0654817	+	0.296676i
$609$	−14.2462	−	8.00000i	−0.577286	−	0.324176i
$610$	2.43845	+	3.68260i	0.0987298	+	0.149104i
$611$	−15.4741			−0.626014
$612$	−1.75058	−	11.8716i	−0.0707629	−	0.479882i
$613$	9.12311			0.368479			0.184239	−	0.982881i	$-0.441018\pi$
$613$	9.12311			0.368479			0.184239	+	0.982881i	$0.441018\pi$
$614$	−8.68951	−	13.1231i	−0.350680	−	0.529605i
$615$	1.69614	+	0.952473i	0.0683950	+	0.0384074i
$616$	11.1231	−	2.06798i	0.448163	−	0.0833211i
$617$			14.0000i			0.563619i	0.959470	+	0.281809i	$0.0909346\pi$
$617$			14.0000i			0.563619i	−0.959470	+	0.281809i	$0.909065\pi$
$618$	−1.75654	−	23.9530i	−0.0706584	−	0.963529i
$619$			28.1365i			1.13090i	0.824782	+	0.565451i	$0.191298\pi$
$619$			28.1365i			1.13090i	−0.824782	+	0.565451i	$0.808702\pi$
$620$	−3.68260	+	8.68466i	−0.147897	+	0.348784i
$621$	−0.0691303	−	1.93087i	−0.00277410	−	0.0774831i
$622$	24.4924	−	16.2177i	0.982057	−	0.650272i
$623$	30.9481			1.23991
$624$	−9.02255	−	34.3280i	−0.361191	−	1.37422i
$625$	1.00000			0.0400000
$626$	−26.5219	+	17.5616i	−1.06003	+	0.701901i
$627$	−1.48734	+	2.64861i	−0.0593985	+	0.105775i
$628$	−2.63068	+	6.20393i	−0.104976	+	0.247564i
$629$		−	10.2462i		−	0.408543i
$630$	−11.6024	−	5.44050i	−0.462253	−	0.216755i
$631$		−	39.8007i		−	1.58444i	−0.610235	−	0.792220i	$-0.708925\pi$
$631$		−	39.8007i		−	1.58444i	0.610235	−	0.792220i	$-0.291075\pi$
$632$	−22.5490	+	4.19224i	−0.896949	+	0.166758i
$633$	14.2462	−	25.3693i	0.566236	−	1.00834i
$634$	13.0691	+	19.7373i	0.519041	+	0.783869i
$635$	15.1022			0.599314
$636$	−25.9451	−	33.5632i	−1.02879	−	1.33087i
$637$	10.8769			0.430958
$638$	−3.22925	−	4.87689i	−0.127847	−	0.193078i
$639$	5.29723	+	8.68951i	0.209555	+	0.343752i
$640$	−9.21922	−	6.55789i	−0.364422	−	0.259223i
$641$			6.38447i			0.252171i	0.992019	+	0.126086i	$0.0402414\pi$
$641$			6.38447i			0.252171i	−0.992019	+	0.126086i	$0.959759\pi$
$642$	7.37874	−	0.541105i	0.291216	−	0.0213557i
$643$		−	3.60109i		−	0.142013i	−0.997476	−	0.0710065i	$-0.977379\pi$
$643$		−	3.60109i		−	0.142013i	0.997476	−	0.0710065i	$-0.0226211\pi$
$644$	2.06798	+	0.876894i	0.0814896	+	0.0345545i
$645$	−11.6847	−	6.56155i	−0.460083	−	0.258361i
$646$	−3.12311	+	2.06798i	−0.122877	+	0.0813634i
$647$	−36.6172			−1.43957			−0.719786	−	0.694197i	$-0.755760\pi$
$647$	−36.6172			−1.43957			−0.719786	+	0.694197i	$0.755760\pi$
$648$	24.3778	+	7.32948i	0.957652	+	0.287929i
$649$	−18.7386			−0.735556
$650$	6.04090	−	4.00000i	0.236943	−	0.156893i
$651$	21.5150	+	12.0818i	0.843238	+	0.473523i
$652$	28.8769	+	12.2448i	1.13091	+	0.479544i
$653$			38.9848i			1.52559i	0.646638	+	0.762797i	$0.276175\pi$
$653$			38.9848i			1.52559i	−0.646638	+	0.762797i	$0.723825\pi$
$654$	2.14219	−	0.157093i	0.0837663	−	0.00614283i
$655$			5.46026i			0.213350i
$656$	3.22925	−	3.12311i	0.126081	−	0.121937i
$657$	12.8769	+	21.1231i	0.502375	+	0.824091i
$658$	7.12311	+	10.7575i	0.277688	+	0.419370i
$659$	24.7442			0.963898			0.481949	−	0.876199i	$-0.339929\pi$
$659$	24.7442			0.963898			0.481949	+	0.876199i	$0.339929\pi$
$660$	−2.80571	−	3.62953i	−0.109212	−	0.141279i
$661$	28.1080			1.09327			0.546636	−	0.837370i	$-0.315908\pi$
$661$	28.1080			1.09327			0.546636	+	0.837370i	$0.315908\pi$
$662$	2.52132	+	3.80776i	0.0979940	+	0.147993i
$663$	8.68951	−	15.4741i	0.337473	−	0.600963i
$664$	−7.80776	−	41.9960i	−0.303000	−	1.62976i
$665$			4.00000i			0.155113i
$666$	19.6794	+	9.22786i	0.762561	+	0.357572i
$667$		−	1.16128i		−	0.0449648i
$668$	−7.07488	+	16.6847i	−0.273735	+	0.645549i
$669$	−7.05398	+	12.5616i	−0.272722	+	0.485658i
$670$	−5.12311	+	3.39228i	−0.197923	+	0.131055i
$671$	4.13595			0.159667
$672$	−19.7113	+	22.0745i	−0.760381	+	0.851541i
$673$	22.4924			0.867019			0.433510	−	0.901149i	$-0.357275\pi$
$673$	22.4924			0.867019			0.433510	+	0.901149i	$0.357275\pi$
$674$	−1.77766	+	1.17708i	−0.0684727	+	0.0453395i
$675$	0.185917	+	5.19283i	0.00715595	+	0.199872i
$676$	10.3423	−	24.3903i	0.397782	−	0.938087i
$677$		−	1.50758i		−	0.0579409i	−0.999580	−	0.0289705i	$-0.990777\pi$
$677$		−	1.50758i		−	0.0579409i	0.999580	−	0.0289705i	$-0.00922287\pi$
$678$	2.50806	+	34.2010i	0.0963215	+	1.31348i
$679$		−	18.1227i		−	0.695485i
$680$	−1.03399	−	5.56155i	−0.0396516	−	0.213276i
$681$	−33.0540	−	18.5616i	−1.26663	−	0.711280i
$682$	4.87689	+	7.36520i	0.186746	+	0.282028i
$683$	7.90007			0.302288			0.151144	−	0.988512i	$-0.451704\pi$
$683$	7.90007			0.302288			0.151144	+	0.988512i	$0.451704\pi$
$684$	−1.15915	−	7.86084i	−0.0443212	−	0.300567i
$685$	−8.24621			−0.315072
$686$	11.5012	+	17.3693i	0.439116	+	0.663164i
$687$	24.5354	+	13.7779i	0.936085	+	0.525661i
$688$	−22.2462	+	21.5150i	−0.848129	+	0.820251i
$689$		−	62.7386i		−	2.39015i
$690$	−0.0666131	−	0.908365i	−0.00253592	−	0.0345809i
$691$			18.2857i			0.695621i	0.937565	+	0.347811i	$0.113075\pi$
$691$			18.2857i			0.695621i	−0.937565	+	0.347811i	$0.886925\pi$
$692$	−3.68260	−	1.56155i	−0.139991	−	0.0593613i
$693$	−10.2462	+	6.24621i	−0.389221	+	0.237274i
$694$	−26.6847	+	17.6693i	−1.01294	+	0.670719i
$695$	−17.5420			−0.665408
$696$	14.4851	+	4.92676i	0.549056	+	0.186748i
$697$	2.24621			0.0850813
$698$	−16.5081	+	10.9309i	−0.624839	+	0.413740i
$699$	8.48071	−	15.1022i	0.320770	−	0.571219i
$700$	−5.56155	−	2.35829i	−0.210207	−	0.0891352i
$701$		−	17.5076i		−	0.661252i	−0.943762	−	0.330626i	$-0.892740\pi$
$701$		−	17.5076i		−	0.661252i	0.943762	−	0.330626i	$-0.107260\pi$
$702$	21.8944	+	30.6256i	0.826351	+	1.15589i
$703$		−	6.78456i		−	0.255885i
$704$	−9.88653	+	3.80776i	−0.372612	+	0.143511i
$705$	2.56155	−	4.56155i	0.0964737	−	0.171798i
$706$	15.8078	+	23.8733i	0.594933	+	0.898482i
$707$	−2.64861			−0.0996114
$708$	38.7803	−	29.9780i	1.45745	−	1.12664i
$709$	6.49242			0.243828			0.121914	−	0.992541i	$-0.461097\pi$
$709$	6.49242			0.243828			0.121914	+	0.992541i	$0.461097\pi$
$710$	2.64861	+	4.00000i	0.0994007	+	0.150117i
$711$	20.7713	−	12.6624i	0.778985	−	0.474878i
$712$	−28.4924	+	5.29723i	−1.06780	+	0.198522i
$713$			1.75379i			0.0656799i
$714$	−14.7575	+	1.08221i	−0.552285	+	0.0405007i
$715$		−	6.78456i		−	0.253728i
$716$	−7.81855	+	18.4384i	−0.292193	+	0.689077i
$717$	−26.2462	−	14.7386i	−0.980183	−	0.550424i
$718$	25.3693	−	16.7984i	0.946774	−	0.626910i
$719$	−30.9481			−1.15417			−0.577086	−	0.816684i	$-0.695810\pi$
$719$	−30.9481			−1.15417			−0.577086	+	0.816684i	$0.695810\pi$
$720$	11.6130	+	3.02287i	0.432792	+	0.112656i
$721$	−29.6155			−1.10294
$722$	20.3358	−	13.4654i	0.756821	−	0.501132i
$723$	−20.1907	−	11.3381i	−0.750899	−	0.421669i
$724$	−9.56155	+	22.5490i	−0.355352	+	0.838025i
$725$			3.12311i			0.115989i
$726$	22.5878	−	1.65643i	0.838314	−	0.0614760i
$727$		−	10.9663i		−	0.406717i	−0.979104	−	0.203359i	$-0.934814\pi$
$727$		−	10.9663i		−	0.406717i	0.979104	−	0.203359i	$-0.0651857\pi$
$728$	−43.0299	+	8.00000i	−1.59480	+	0.296500i
$729$	−26.9309	+	1.93087i	−0.997440	+	0.0715137i
$730$	6.43845	+	9.72350i	0.238298	+	0.359883i
$731$	−15.4741			−0.572329
$732$	−8.55950	+	6.61668i	−0.316368	+	0.244560i
$733$	−26.8769			−0.992721			−0.496360	−	0.868117i	$-0.665331\pi$
$733$	−26.8769			−0.992721			−0.496360	+	0.868117i	$0.665331\pi$
$734$	8.56222	+	12.9309i	0.316037	+	0.477287i
$735$	−1.80054	+	3.20636i	−0.0664140	+	0.118269i
$736$	−2.05398	−	0.453349i	−0.0757105	−	0.0167107i
$737$			5.75379i			0.211944i
$738$	−2.02297	+	4.31419i	−0.0744664	+	0.158807i
$739$		−	26.9752i		−	0.992300i	−0.868237	−	0.496150i	$-0.834747\pi$
$739$		−	26.9752i		−	0.992300i	0.868237	−	0.496150i	$-0.165253\pi$
$740$	9.43318	+	4.00000i	0.346771	+	0.147043i
$741$	5.75379	−	10.2462i	0.211371	−	0.376404i
$742$	−43.6155	+	28.8802i	−1.60118	+	1.06022i
$743$	−9.80501			−0.359711			−0.179856	−	0.983693i	$-0.557563\pi$
$743$	−9.80501			−0.359711			−0.179856	+	0.983693i	$0.557563\pi$
$744$	−21.8757	−	7.44050i	−0.802004	−	0.272782i
$745$	−14.0000			−0.512920
$746$	−10.7575	+	7.12311i	−0.393860	+	0.260795i
$747$	23.5829	+	38.6852i	0.862855	+	1.41542i
$748$	−4.87689	−	2.06798i	−0.178317	−	0.0756127i
$749$		−	9.12311i		−	0.333351i
$750$	0.179147	+	2.44293i	0.00654153	+	0.0892032i
$751$			11.5012i			0.419683i	0.977735	+	0.209842i	$0.0672948\pi$
$751$			11.5012i			0.419683i	−0.977735	+	0.209842i	$0.932705\pi$
$752$	−8.39919	−	8.68466i	−0.306287	−	0.316697i
$753$	−28.2462	−	15.8617i	−1.02935	−	0.578034i
$754$	12.4924	+	18.8664i	0.454947	+	0.687072i
$755$	−7.36520			−0.268047
$756$	11.2122	−	29.3186i	0.407785	−	1.06631i
$757$	10.8769			0.395327			0.197664	−	0.980270i	$-0.436665\pi$
$757$	10.8769			0.395327			0.197664	+	0.980270i	$0.436665\pi$
$758$	−14.6031	−	22.0540i	−0.530409	−	0.801036i
$759$	−0.743668	−	0.417609i	−0.0269934	−	0.0151582i
$760$	−0.684658	−	3.68260i	−0.0248352	−	0.133582i
$761$			31.2311i			1.13212i	0.824362	+	0.566062i	$0.191534\pi$
$761$			31.2311i			1.13212i	−0.824362	+	0.566062i	$0.808466\pi$
$762$	2.70552	+	36.8937i	0.0980108	+	1.33652i
$763$		−	2.64861i		−	0.0958863i
$764$	−19.4470	+	45.8617i	−0.703568	+	1.65922i
$765$	3.12311	+	5.12311i	0.112916	+	0.185226i
$766$	−17.8078	+	11.7915i	−0.643421	+	0.426043i
$767$	72.4908			2.61749
$768$	14.3689	−	23.6967i	0.518492	−	0.855083i
$769$	38.9848			1.40583			0.702915	−	0.711274i	$-0.251882\pi$
$769$	38.9848			1.40583			0.702915	+	0.711274i	$0.251882\pi$
$770$	−4.71659	+	3.12311i	−0.169974	+	0.112549i
$771$	−25.8597	+	46.0504i	−0.931315	+	1.65846i
$772$	−0.192236	+	0.453349i	−0.00691872	+	0.0163164i
$773$			0.246211i			0.00885560i	0.999990	+	0.00442780i	$0.00140942\pi$
$773$			0.246211i			0.00885560i	−0.999990	+	0.00442780i	$0.998591\pi$
$774$	13.9361	−	29.7203i	0.500924	−	1.06827i
$775$		−	4.71659i		−	0.169425i
$776$	3.10196	+	16.6847i	0.111354	+	0.598944i
$777$	13.1231	−	23.3693i	0.470789	−	0.838370i
$778$	16.1922	+	24.4539i	0.580520	+	0.876715i
$779$	1.48734			0.0532894
$780$	10.8539	+	14.0409i	0.388633	+	0.502745i
$781$	4.49242			0.160752
$782$	−0.580639	−	0.876894i	−0.0207636	−	0.0313577i
$783$	−16.2177	+	0.580639i	−0.579575	+	0.0207503i
$784$	5.90388	+	6.10454i	0.210853	+	0.218019i
$785$		−	3.36932i		−	0.120256i
$786$	−13.3390	+	0.978190i	−0.475787	+	0.0348909i
$787$		−	42.0775i		−	1.49990i	−0.661495	−	0.749950i	$-0.730078\pi$
$787$		−	42.0775i		−	1.49990i	0.661495	−	0.749950i	$-0.269922\pi$
$788$	−7.81855	−	3.31534i	−0.278524	−	0.118104i
$789$	35.9309	+	20.1771i	1.27917	+	0.718323i
$790$	9.56155	−	6.33122i	0.340185	−	0.225255i
$791$	42.2863			1.50353
$792$	8.36405	−	7.50437i	0.297203	−	0.266656i
$793$	−16.0000			−0.568177
$794$	17.5420	−	11.6155i	0.622544	−	0.412220i
$795$	18.4945	+	10.3857i	0.655933	+	0.368341i
$796$	−10.0540	−	4.26324i	−0.356354	−	0.151107i
$797$		−	12.7386i		−	0.451226i	−0.974217	−	0.225613i	$-0.927562\pi$
$797$		−	12.7386i		−	0.451226i	0.974217	−	0.225613i	$-0.0724384\pi$
$798$	−9.77172	+	0.716589i	−0.345915	+	0.0253670i
$799$		−	6.04090i		−	0.213712i
$800$	5.52390	+	1.21922i	0.195299	+	0.0431061i
$801$	26.2462	−	16.0000i	0.927364	−	0.565332i
$802$	−18.7386	−	28.2995i	−0.661684	−	0.999291i
$803$	10.9205			0.385377
$804$	−9.20490	−	11.9077i	−0.324632	−	0.419951i
$805$	−1.12311			−0.0395843
$806$	−18.8664	−	28.4924i	−0.664539	−	1.00360i
$807$	−11.8730	+	21.1431i	−0.417949	+	0.744274i
$808$	2.43845	−	0.453349i	0.0857843	−	0.0159488i
$809$			29.7538i			1.04609i	0.852306	+	0.523044i	$0.175204\pi$
$809$			29.7538i			1.04609i	−0.852306	+	0.523044i	$0.824796\pi$
$810$	−12.6524	+	1.38446i	−0.444560	+	0.0486451i
$811$			46.2592i			1.62438i	0.583393	+	0.812190i	$0.301725\pi$
$811$			46.2592i			1.62438i	−0.583393	+	0.812190i	$0.698275\pi$
$812$	7.36520	−	17.3693i	0.258468	−	0.609544i
$813$	−12.9848	+	23.1231i	−0.455398	+	0.810963i
$814$	8.00000	−	5.29723i	0.280400	−	0.185668i
$815$	−15.6829			−0.549347
$816$	13.4012	−	3.52230i	0.469137	−	0.123305i
$817$	−10.2462			−0.358470
$818$	29.9142	−	19.8078i	1.04592	−	0.692562i
$819$	39.6377	−	24.1636i	1.38505	−	0.844344i
$820$	−0.876894	+	2.06798i	−0.0306225	+	0.0722168i
$821$		−	53.2311i		−	1.85778i	−0.370360	−	0.928888i	$-0.620766\pi$
$821$		−	53.2311i		−	1.85778i	0.370360	−	0.928888i	$-0.379234\pi$
$822$	−1.47729	−	20.1449i	−0.0515263	−	0.702635i
$823$		−	48.2814i		−	1.68298i	−0.540270	−	0.841492i	$-0.681678\pi$
$823$		−	48.2814i		−	1.68298i	0.540270	−	0.841492i	$-0.318322\pi$
$824$	27.2655	−	5.06913i	0.949840	−	0.176592i
$825$	2.00000	+	1.12311i	0.0696311	+	0.0391015i
$826$	−33.3693	−	50.3951i	−1.16107	−	1.75347i
$827$	−17.7509			−0.617258			−0.308629	−	0.951183i	$-0.599870\pi$
$827$	−17.7509			−0.617258			−0.308629	+	0.951183i	$0.599870\pi$
$828$	2.20714	−	0.325462i	0.0767033	−	0.0113106i
$829$	−8.87689			−0.308307			−0.154154	−	0.988047i	$-0.549265\pi$
$829$	−8.87689			−0.308307			−0.154154	+	0.988047i	$0.549265\pi$
$830$	11.7915	+	17.8078i	0.409288	+	0.618117i
$831$	−35.2929	−	19.8188i	−1.22430	−	0.687508i
$832$	38.2462	−	14.7304i	1.32595	−	0.510685i
$833$			4.24621i			0.147122i
$834$	−3.14261	−	42.8540i	−0.108820	−	1.48391i
$835$		−	9.06134i		−	0.313581i
$836$	−3.22925	−	1.36932i	−0.111686	−	0.0473588i
$837$	24.4924	−	0.876894i	0.846582	−	0.0303099i
$838$	8.68466	−	5.75058i	0.300007	−	0.198650i
$839$	−17.7051			−0.611247			−0.305624	−	0.952152i	$-0.598865\pi$
$839$	−17.7051			−0.611247			−0.305624	+	0.952152i	$0.598865\pi$
$840$	4.76481	−	14.0090i	0.164402	−	0.483355i
$841$	19.2462			0.663662
$842$	−29.9142	+	19.8078i	−1.03091	+	0.682621i
$843$	−11.5469	+	20.5625i	−0.397697	+	0.708210i
$844$	30.9309	+	13.1158i	1.06468	+	0.451464i
$845$			13.2462i			0.455684i
$846$	11.6024	+	5.44050i	0.398900	+	0.187048i
$847$		−	27.9277i		−	0.959607i
$848$	35.2114	−	34.0540i	1.20916	−	1.16942i
$849$	−19.6847	+	35.0540i	−0.675576	+	1.20305i
$850$	1.56155	+	2.35829i	0.0535608	+	0.0808888i
$851$	1.90495			0.0653007
$852$	−9.29723	+	7.18697i	−0.318518	+	0.246221i
$853$	−7.86174			−0.269181			−0.134590	−	0.990901i	$-0.542972\pi$
$853$	−7.86174			−0.269181			−0.134590	+	0.990901i	$0.542972\pi$
$854$	7.36520	+	11.1231i	0.252032	+	0.380625i
$855$	2.06798	+	3.39228i	0.0707233	+	0.116014i
$856$	1.56155	+	8.39919i	0.0533728	+	0.287078i
$857$			20.7386i			0.708418i	0.935166	+	0.354209i	$0.115250\pi$
$857$			20.7386i			0.708418i	−0.935166	+	0.354209i	$0.884750\pi$
$858$	16.5742	−	1.21544i	0.565834	−	0.0414943i
$859$			33.4337i			1.14074i	0.821386	+	0.570372i	$0.193201\pi$
$859$			33.4337i			1.14074i	−0.821386	+	0.570372i	$0.806799\pi$
$860$	6.04090	−	14.2462i	0.205993	−	0.485792i
$861$	5.12311	+	2.87689i	0.174595	+	0.0980443i
$862$	−19.6155	+	12.9885i	−0.668108	+	0.442390i
$863$	10.5487			0.359081			0.179541	−	0.983751i	$-0.442539\pi$
$863$	10.5487			0.359081			0.179541	+	0.983751i	$0.442539\pi$
$864$	−5.30423	+	28.9113i	−0.180453	+	0.983584i
$865$	2.00000			0.0680020
$866$	21.2247	−	14.0540i	0.721243	−	0.477574i
$867$	−19.6329	−	11.0249i	−0.666769	−	0.374426i
$868$	−11.1231	+	26.2316i	−0.377543	+	0.890357i
$869$		−	10.7386i		−	0.364283i
$870$	−7.62953	+	0.559496i	−0.258665	+	0.0189687i
$871$		−	22.2586i		−	0.754205i
$872$	0.453349	+	2.43845i	0.0153523	+	0.0825762i
$873$	−9.36932	−	15.3693i	−0.317103	−	0.520173i
$874$	−0.384472	−	0.580639i	−0.0130050	−	0.0196404i
$875$	3.02045			0.102110
$876$	−22.6004	+	17.4706i	−0.763596	+	0.590277i
$877$	37.6155			1.27019			0.635093	−	0.772436i	$-0.280962\pi$
$877$	37.6155			1.27019			0.635093	+	0.772436i	$0.280962\pi$
$878$	−7.23791	−	10.9309i	−0.244268	−	0.368899i
$879$	−2.11375	+	3.76412i	−0.0712950	+	0.126960i
$880$	3.80776	−	3.68260i	0.128360	−	0.124140i
$881$		−	0.630683i		−	0.0212483i	−0.999944	−	0.0106241i	$-0.996618\pi$
$881$		−	0.630683i		−	0.0212483i	0.999944	−	0.0106241i	$-0.00338183\pi$
$882$	−8.15549	−	3.82419i	−0.274610	−	0.128767i
$883$			22.4674i			0.756090i	0.925787	+	0.378045i	$0.123403\pi$
$883$			22.4674i			0.756090i	−0.925787	+	0.378045i	$0.876597\pi$
$884$	18.8664	+	8.00000i	0.634544	+	0.269069i
$885$	−12.0000	+	21.3693i	−0.403376	+	0.718322i
$886$	−19.5616	+	12.9527i	−0.657183	+	0.435156i
$887$	−51.6737			−1.73503			−0.867516	−	0.497409i	$-0.834285\pi$
$887$	−51.6737			−1.73503			−0.867516	+	0.497409i	$0.834285\pi$
$888$	−8.08179	+	23.7612i	−0.271207	+	0.797373i
$889$	45.6155			1.52990
$890$	12.0818	−	8.00000i	0.404983	−	0.268161i
$891$	−5.46026	+	10.5945i	−0.182925	+	0.354928i
$892$	−15.3153	−	6.49424i	−0.512796	−	0.217443i
$893$		−	4.00000i		−	0.133855i
$894$	−2.50806	−	34.2010i	−0.0838821	−	1.14385i
$895$		−	10.0138i		−	0.334725i
$896$	−27.8462	−	19.8078i	−0.930276	−	0.661731i
$897$	2.87689	+	1.61553i	0.0960567	+	0.0539409i
$898$	21.3693	+	32.2725i	0.713103	+	1.07695i
$899$	14.7304			0.491287
$900$	−5.93581	+	0.875288i	−0.197860	+	0.0291763i
$901$	24.4924			0.815961
$902$	1.16128	+	1.75379i	0.0386663	+	0.0583948i
$903$	−35.2929	−	19.8188i	−1.17447	−	0.659529i
$904$	−38.9309	+	7.23791i	−1.29482	+	0.240729i
$905$		−	12.2462i		−	0.407078i
$906$	−1.31946	−	17.9927i	−0.0438360	−	0.597767i
$907$			46.2134i			1.53449i	0.641353	+	0.767246i	$0.278373\pi$
$907$			46.2134i			1.53449i	−0.641353	+	0.767246i	$0.721627\pi$
$908$	17.0887	−	40.3002i	0.567108	−	1.33741i
$909$	−2.24621	+	1.36932i	−0.0745021	+	0.0454174i
$910$	18.2462	−	12.0818i	0.604856	−	0.400507i
$911$	−14.3128			−0.474204			−0.237102	−	0.971485i	$-0.576198\pi$
$911$	−14.3128			−0.474204			−0.237102	+	0.971485i	$0.576198\pi$
$912$	8.87368	−	2.33230i	0.293837	−	0.0772302i
$913$	20.0000			0.661903
$914$	−11.7915	+	7.80776i	−0.390027	+	0.258258i
$915$	2.64861	−	4.71659i	0.0875605	−	0.155926i
$916$	−12.6847	+	29.9142i	−0.419113	+	0.988392i
$917$			16.4924i			0.544628i
$918$	−11.9559	+	8.54732i	−0.394603	+	0.282104i
$919$			49.9775i			1.64861i	0.566148	+	0.824303i	$0.308433\pi$
$919$			49.9775i			1.64861i	−0.566148	+	0.824303i	$0.691567\pi$
$920$	1.03399	−	0.192236i	0.0340896	−	0.00633783i
$921$	−9.43845	+	16.8078i	−0.311007	+	0.553835i
$922$	−32.6847	−	49.3612i	−1.07641	−	1.62562i
$923$	−17.3790			−0.572037
$924$	−8.47449	−	10.9628i	−0.278790	−	0.360650i
$925$	−5.12311			−0.168447
$926$	−2.35829	−	3.56155i	−0.0774984	−	0.117040i
$927$	−25.1161	+	15.3110i	−0.824920	+	0.502881i
$928$	−3.80776	+	17.2517i	−0.124996	+	0.566316i
$929$			33.1231i			1.08673i	0.839495	+	0.543367i	$0.182851\pi$
$929$			33.1231i			1.08673i	−0.839495	+	0.543367i	$0.817149\pi$
$930$	11.5223	−	0.844964i	0.377831	−	0.0277075i
$931$			2.81164i			0.0921479i
$932$	18.4130	+	7.80776i	0.603138	+	0.255752i
$933$	−31.3693	−	17.6155i	−1.02699	−	0.576707i
$934$	2.68466	−	1.77766i	0.0878447	−	0.0581667i
$935$	2.64861			0.0866189
$936$	−32.3565	+	29.0308i	−1.05760	+	0.948901i
$937$	−22.4924			−0.734795			−0.367398	−	0.930064i	$-0.619751\pi$
$937$	−22.4924			−0.734795			−0.367398	+	0.930064i	$0.619751\pi$
$938$	−15.4741	+	10.2462i	−0.505246	+	0.334551i
$939$	33.9686	+	19.0752i	1.10852	+	0.622494i
$940$	5.56155	+	2.35829i	0.181398	+	0.0769191i
$941$		−	0.876894i		−	0.0285859i	−0.999898	−	0.0142930i	$-0.995450\pi$
$941$		−	0.876894i		−	0.0285859i	0.999898	−	0.0142930i	$-0.00454975\pi$
$942$	8.23100	−	0.603604i	0.268181	−	0.0196665i
$943$			0.417609i			0.0135992i
$944$	39.3473	+	40.6847i	1.28065	+	1.32417i
$945$	0.561553	+	15.6847i	0.0182673	+	0.510222i
$946$	−8.00000	−	12.0818i	−0.260102	−	0.392813i
$947$	32.4813			1.05550			0.527750	−	0.849400i	$-0.323036\pi$
$947$	32.4813			1.05550			0.527750	+	0.849400i	$0.323036\pi$
$948$	17.1796	+	22.2240i	0.557969	+	0.721801i
$949$	−42.2462			−1.37137
$950$	1.03399	+	1.56155i	0.0335470	+	0.0506635i
$951$	14.1955	−	25.2791i	0.460322	−	0.819731i
$952$	−3.12311	−	16.7984i	−0.101220	−	0.544439i
$953$			22.4924i			0.728601i	0.931281	+	0.364301i	$0.118692\pi$
$953$			22.4924i			0.728601i	−0.931281	+	0.364301i	$0.881308\pi$
$954$	−22.0582	+	47.0414i	−0.714160	+	1.52302i
$955$		−	24.9073i		−	0.805980i
$956$	13.5691	−	32.0000i	0.438857	−	1.03495i
$957$	−3.50758	+	6.24621i	−0.113384	+	0.201911i
$958$	30.2462	−	20.0276i	0.977211	−	0.647063i
$959$	−24.9073			−0.804297
$960$	−1.98889	+	13.7129i	−0.0641910	+	0.442583i
$961$	8.75379			0.282380
$962$	−30.9481	+	20.4924i	−0.997808	+	0.660702i
$963$	−4.71659	−	7.73704i	−0.151990	−	0.249323i
$964$	10.4384	−	24.6169i	0.336200	−	0.792858i
$965$		−	0.246211i		−	0.00792582i
$966$	−0.201201	−	2.74367i	−0.00647354	−	0.0882761i
$967$		−	26.4404i		−	0.850265i	−0.905131	−	0.425132i	$-0.860228\pi$
$967$		−	26.4404i		−	0.850265i	0.905131	−	0.425132i	$-0.139772\pi$
$968$	4.78023	+	25.7116i	0.153643	+	0.826404i
$969$	4.00000	+	2.24621i	0.128499	+	0.0721587i
$970$	−4.68466	−	7.07488i	−0.150415	−	0.227161i
$971$	52.6261			1.68885			0.844427	−	0.535671i	$-0.179941\pi$
$971$	52.6261			1.68885			0.844427	+	0.535671i	$0.179941\pi$
$972$	−5.64879	−	30.6609i	−0.181185	−	0.983449i
$973$	−52.9848			−1.69862
$974$	19.7373	+	29.8078i	0.632424	+	0.955102i
$975$	−7.73704	−	4.34475i	−0.247783	−	0.139144i
$976$	−8.68466	−	8.97983i	−0.277989	−	0.287437i
$977$		−	31.7538i		−	1.01589i	−0.861388	−	0.507947i	$-0.830405\pi$
$977$		−	31.7538i		−	1.01589i	0.861388	−	0.507947i	$-0.169595\pi$
$978$	−2.80954	−	38.3122i	−0.0898393	−	1.22509i
$979$		−	13.5691i		−	0.433671i
$980$	−3.90928	−	1.65767i	−0.124877	−	0.0529524i
$981$	−1.36932	−	2.24621i	−0.0437189	−	0.0717160i
$982$	31.8078	−	21.0616i	1.01503	−	0.672103i
$983$	40.0095			1.27610			0.638052	−	0.769993i	$-0.279740\pi$
$983$	40.0095			1.27610			0.638052	+	0.769993i	$0.279740\pi$
$984$	−5.20901	−	1.77172i	−0.166057	−	0.0564804i
$985$	4.24621			0.135296
$986$	−7.36520	+	4.87689i	−0.234556	+	0.155312i
$987$	7.73704	−	13.7779i	0.246273	−	0.438556i
$988$	12.4924	+	5.29723i	0.397437	+	0.168527i
$989$		−	2.87689i		−	0.0914799i
$990$	−2.38537	+	5.08706i	−0.0758122	+	0.161677i
$991$			33.0161i			1.04879i	0.851475	+	0.524396i	$0.175709\pi$
$991$			33.0161i			1.04879i	−0.851475	+	0.524396i	$0.824291\pi$
$992$	5.75058	−	26.0540i	0.182581	−	0.827215i
$993$	2.73863	−	4.87689i	0.0869079	−	0.154764i
$994$	8.00000	+	12.0818i	0.253745	+	0.383211i
$995$	5.46026			0.173102
$996$	−41.3907	+	31.9960i	−1.31151	+	1.01383i
$997$	−33.6155			−1.06461			−0.532307	−	0.846551i	$-0.678675\pi$
$997$	−33.6155			−1.06461			−0.532307	+	0.846551i	$0.678675\pi$
$998$	−25.1976	−	38.0540i	−0.797615	−	1.20458i
$999$	−0.952473	−	26.6034i	−0.0301349	−	0.841694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.2.e.a.11.7	yes	8
3.2	odd	2	inner	60.2.e.a.11.2	yes	8
4.3	odd	2	inner	60.2.e.a.11.1	✓	8
5.2	odd	4		300.2.h.a.299.7		8
5.3	odd	4		300.2.h.b.299.2		8
5.4	even	2		300.2.e.c.251.2		8
8.3	odd	2		960.2.h.g.191.1		8
8.5	even	2		960.2.h.g.191.8		8
12.11	even	2	inner	60.2.e.a.11.8	yes	8
15.2	even	4		300.2.h.b.299.1		8
15.8	even	4		300.2.h.a.299.8		8
15.14	odd	2		300.2.e.c.251.7		8
20.3	even	4		300.2.h.b.299.3		8
20.7	even	4		300.2.h.a.299.6		8
20.19	odd	2		300.2.e.c.251.8		8
24.5	odd	2		960.2.h.g.191.2		8
24.11	even	2		960.2.h.g.191.7		8
60.23	odd	4		300.2.h.a.299.5		8
60.47	odd	4		300.2.h.b.299.4		8
60.59	even	2		300.2.e.c.251.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.1	✓	8	4.3	odd	2	inner
60.2.e.a.11.2	yes	8	3.2	odd	2	inner
60.2.e.a.11.7	yes	8	1.1	even	1	trivial
60.2.e.a.11.8	yes	8	12.11	even	2	inner
300.2.e.c.251.1		8	60.59	even	2
300.2.e.c.251.2		8	5.4	even	2
300.2.e.c.251.7		8	15.14	odd	2
300.2.e.c.251.8		8	20.19	odd	2
300.2.h.a.299.5		8	60.23	odd	4
300.2.h.a.299.6		8	20.7	even	4
300.2.h.a.299.7		8	5.2	odd	4
300.2.h.a.299.8		8	15.8	even	4
300.2.h.b.299.1		8	15.2	even	4
300.2.h.b.299.2		8	5.3	odd	4
300.2.h.b.299.3		8	20.3	even	4
300.2.h.b.299.4		8	60.47	odd	4
960.2.h.g.191.1		8	8.3	odd	2
960.2.h.g.191.2		8	24.5	odd	2
960.2.h.g.191.7		8	24.11	even	2
960.2.h.g.191.8		8	8.5	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17915 - 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.44293 + 0.179147i) q^{6} +3.02045i q^{7} +(-0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})\)	\(q+(1.17915 - 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.44293 + 0.179147i) q^{6} +3.02045i q^{7} +(-0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +(0.780776 + 1.17915i) q^{10} +1.32431 q^{11} +(-2.74070 + 2.11862i) q^{12} -5.12311 q^{13} +(2.35829 + 3.56155i) q^{14} +(0.848071 - 1.51022i) q^{15} +(-2.78078 - 2.87529i) q^{16} -2.00000i q^{17} +(3.84130 + 1.80122i) q^{18} -1.32431i q^{19} +(1.84130 + 0.780776i) q^{20} +(2.56155 - 4.56155i) q^{21} +(1.56155 - 1.03399i) q^{22} +0.371834 q^{23} +(-1.57752 + 4.63804i) q^{24} -1.00000 q^{25} +(-6.04090 + 4.00000i) q^{26} +(-0.185917 - 5.19283i) q^{27} +(5.56155 + 2.35829i) q^{28} -3.12311i q^{29} +(-0.179147 - 2.44293i) q^{30} +4.71659i q^{31} +(-5.52390 - 1.21922i) q^{32} +(-2.00000 - 1.12311i) q^{33} +(-1.56155 - 2.35829i) q^{34} -3.02045 q^{35} +(5.93581 - 0.875288i) q^{36} +5.12311 q^{37} +(-1.03399 - 1.56155i) q^{38} +(7.73704 + 4.34475i) q^{39} +(2.78078 - 0.516994i) q^{40} +1.12311i q^{41} +(-0.541105 - 7.37874i) q^{42} -7.73704i q^{43} +(1.03399 - 2.43845i) q^{44} +(-2.56155 + 1.56155i) q^{45} +(0.438447 - 0.290319i) q^{46} +3.02045 q^{47} +(1.76115 + 6.70062i) q^{48} -2.12311 q^{49} +(-1.17915 + 0.780776i) q^{50} +(-1.69614 + 3.02045i) q^{51} +(-4.00000 + 9.43318i) q^{52} +12.2462i q^{53} +(-4.27366 - 5.97795i) q^{54} +1.32431i q^{55} +(8.39919 - 1.56155i) q^{56} +(-1.12311 + 2.00000i) q^{57} +(-2.43845 - 3.68260i) q^{58} -14.1498 q^{59} +(-2.11862 - 2.74070i) q^{60} +3.12311 q^{61} +(3.68260 + 5.56155i) q^{62} +(-7.73704 + 4.71659i) q^{63} +(-7.46543 + 2.87529i) q^{64} -5.12311i q^{65} +(-3.23519 + 0.237246i) q^{66} +4.34475i q^{67} +(-3.68260 - 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} +(-3.56155 + 2.35829i) q^{70} +3.39228 q^{71} +(6.31579 - 5.66664i) q^{72} +8.24621 q^{73} +(6.04090 - 4.00000i) q^{74} +(1.51022 + 0.848071i) q^{75} +(-2.43845 - 1.03399i) q^{76} +4.00000i q^{77} +(12.5154 - 0.917790i) q^{78} -8.10887i q^{79} +(2.87529 - 2.78078i) q^{80} +(-4.12311 + 8.00000i) q^{81} +(0.876894 + 1.32431i) q^{82} +15.1022 q^{83} +(-6.39919 - 8.27814i) q^{84} +2.00000 q^{85} +(-6.04090 - 9.12311i) q^{86} +(-2.64861 + 4.71659i) q^{87} +(-0.684658 - 3.68260i) q^{88} -10.2462i q^{89} +(-1.80122 + 3.84130i) q^{90} -15.4741i q^{91} +(0.290319 - 0.684658i) q^{92} +(4.00000 - 7.12311i) q^{93} +(3.56155 - 2.35829i) q^{94} +1.32431 q^{95} +(7.30834 + 6.52596i) q^{96} -6.00000 q^{97} +(-2.50345 + 1.65767i) q^{98} +(2.06798 + 3.39228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{10} + 4 q^{12} - 8 q^{13} - 14 q^{16} + 16 q^{18} + 4 q^{21} - 4 q^{22} - 2 q^{24} - 8 q^{25} + 28 q^{28} + 8 q^{30} - 16 q^{33} + 4 q^{34} + 18 q^{36} + 8 q^{37} + 14 q^{40} - 12 q^{42} - 4 q^{45} + 20 q^{46} - 36 q^{48} + 16 q^{49} - 32 q^{52} - 10 q^{54} + 24 q^{57} - 36 q^{58} - 14 q^{60} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 12 q^{70} + 24 q^{72} - 36 q^{76} + 40 q^{78} + 40 q^{82} + 16 q^{84} + 16 q^{85} + 44 q^{88} + 18 q^{90} + 32 q^{93} + 12 q^{94} + 42 q^{96} - 48 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^10 + 4 * q^12 - 8 * q^13 - 14 * q^16 + 16 * q^18 + 4 * q^21 - 4 * q^22 - 2 * q^24 - 8 * q^25 + 28 * q^28 + 8 * q^30 - 16 * q^33 + 4 * q^34 + 18 * q^36 + 8 * q^37 + 14 * q^40 - 12 * q^42 - 4 * q^45 + 20 * q^46 - 36 * q^48 + 16 * q^49 - 32 * q^52 - 10 * q^54 + 24 * q^57 - 36 * q^58 - 14 * q^60 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 12 * q^70 + 24 * q^72 - 36 * q^76 + 40 * q^78 + 40 * q^82 + 16 * q^84 + 16 * q^85 + 44 * q^88 + 18 * q^90 + 32 * q^93 + 12 * q^94 + 42 * q^96 - 48 * q^97

Introduction

L-functions

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