LMFDB - Embedded newform 429.2.t.a.296.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(296,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.296");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.t (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			296.16
Character	$\chi$	$=$	429.296
Dual form			429.2.t.a.329.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09482 + 0.632095i) q^{2} +(0.177995 - 1.72288i) q^{3} +(-0.200911 + 0.347987i) q^{4} -4.13662 q^{5} +(0.894153 + 1.99876i) q^{6} +(0.620239 - 1.07429i) q^{7} -3.03636i q^{8} +(-2.93664 - 0.613327i) q^{9} +O(q^{10})$	\(q+(-1.09482 + 0.632095i) q^{2} +(0.177995 - 1.72288i) q^{3} +(-0.200911 + 0.347987i) q^{4} -4.13662 q^{5} +(0.894153 + 1.99876i) q^{6} +(0.620239 - 1.07429i) q^{7} -3.03636i q^{8} +(-2.93664 - 0.613327i) q^{9} +(4.52886 - 2.61474i) q^{10} +(3.29051 - 0.415381i) q^{11} +(0.563780 + 0.408085i) q^{12} +(2.90409 + 2.13688i) q^{13} +1.56820i q^{14} +(-0.736296 + 7.12691i) q^{15} +(1.51745 + 2.62830i) q^{16} +(-2.43465 + 4.21694i) q^{17} +(3.60277 - 1.18475i) q^{18} +(-1.67153 + 2.89518i) q^{19} +(0.831091 - 1.43949i) q^{20} +(-1.74047 - 1.25982i) q^{21} +(-3.33996 + 2.53468i) q^{22} +(-5.91424 + 3.41459i) q^{23} +(-5.23129 - 0.540456i) q^{24} +12.1116 q^{25} +(-4.53017 - 0.503840i) q^{26} +(-1.57939 + 4.95030i) q^{27} +(0.249225 + 0.431671i) q^{28} +(4.19202 + 7.26080i) q^{29} +(-3.69877 - 8.26810i) q^{30} -0.243427i q^{31} +(1.93646 + 1.11802i) q^{32} +(-0.129959 - 5.74309i) q^{33} -6.15573i q^{34} +(-2.56569 + 4.44391i) q^{35} +(0.803431 - 0.898689i) q^{36} +(-0.983279 + 0.567696i) q^{37} -4.22627i q^{38} +(4.19850 - 4.62305i) q^{39} +12.5603i q^{40} +(8.87337 - 5.12304i) q^{41} +(2.70182 + 0.279131i) q^{42} +(-3.46891 - 2.00277i) q^{43} +(-0.516551 + 1.22851i) q^{44} +(12.1478 + 2.53710i) q^{45} +(4.31669 - 7.47672i) q^{46} -0.186546 q^{47} +(4.79834 - 2.14656i) q^{48} +(2.73061 + 4.72955i) q^{49} +(-13.2601 + 7.65571i) q^{50} +(6.83194 + 4.94521i) q^{51} +(-1.32707 + 0.581265i) q^{52} -0.981050i q^{53} +(-1.39991 - 6.41803i) q^{54} +(-13.6116 + 1.71827i) q^{55} +(-3.26192 - 1.88327i) q^{56} +(4.69053 + 3.39518i) q^{57} +(-9.17904 - 5.29952i) q^{58} +(4.22819 - 7.32344i) q^{59} +(-2.33214 - 1.68809i) q^{60} +(0.321966 + 0.185887i) q^{61} +(0.153869 + 0.266509i) q^{62} +(-2.48030 + 2.77438i) q^{63} -8.89657 q^{64} +(-12.0131 - 8.83947i) q^{65} +(3.77246 + 6.20551i) q^{66} +(-7.80314 + 4.50514i) q^{67} +(-0.978296 - 1.69446i) q^{68} +(4.83022 + 10.7973i) q^{69} -6.48706i q^{70} +(-5.06007 + 8.76429i) q^{71} +(-1.86228 + 8.91669i) q^{72} -1.57753 q^{73} +(0.717676 - 1.24305i) q^{74} +(2.15581 - 20.8669i) q^{75} +(-0.671658 - 1.16334i) q^{76} +(1.59467 - 3.79258i) q^{77} +(-1.67440 + 7.71527i) q^{78} +7.03179i q^{79} +(-6.27711 - 10.8723i) q^{80} +(8.24766 + 3.60223i) q^{81} +(-6.47650 + 11.2176i) q^{82} -4.69182i q^{83} +(0.788078 - 0.352550i) q^{84} +(10.0712 - 17.4439i) q^{85} +5.06378 q^{86} +(13.2556 - 5.92998i) q^{87} +(-1.26125 - 9.99118i) q^{88} +(4.62316 + 8.00755i) q^{89} +(-14.9033 + 4.90087i) q^{90} +(4.09685 - 1.79445i) q^{91} -2.74411i q^{92} +(-0.419396 - 0.0433287i) q^{93} +(0.204234 - 0.117915i) q^{94} +(6.91450 - 11.9763i) q^{95} +(2.27089 - 3.13729i) q^{96} +(-5.14746 - 2.97189i) q^{97} +(-5.97905 - 3.45201i) q^{98} +(-9.91780 - 0.798335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) $ 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9	$ 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) $ 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9 - 4 * q^12 - 36 * q^15 - 44 * q^16 - 12 * q^22 + 64 * q^25 + 4 * q^27 + 12 * q^33 + 28 * q^36 - 12 * q^37 + 50 * q^42 - 66 * q^45 + 16 * q^48 - 24 * q^49 - 8 * q^55 - 24 * q^58 - 104 * q^64 - 60 * q^66 - 60 * q^67 - 42 * q^69 - 42 * q^75 + 16 * q^78 - 22 * q^81 - 16 * q^82 + 92 * q^88 - 84 * q^91 + 126 * q^93 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.09482	+	0.632095i	−0.774156	+	0.446959i	−0.834355	−	0.551227i	$-0.814160\pi$
$2$	−1.09482	+	0.632095i	−0.774156	+	0.446959i	0.0601994	+	0.998186i	$0.480826\pi$
$3$	0.177995	−	1.72288i	0.102765	−	0.994706i
$3$	0.177995	−	1.72288i	0.102765	−	0.994706i
$4$	−0.200911	+	0.347987i	−0.100455	+	0.173994i
$5$	−4.13662			−1.84995			−0.924977	−	0.380024i	$-0.875916\pi$
$5$	−4.13662			−1.84995			−0.924977	+	0.380024i	$0.875916\pi$
$6$	0.894153	+	1.99876i	0.365036	+	0.815989i
$7$	0.620239	−	1.07429i	0.234428	−	0.406042i	−0.724678	−	0.689088i	$-0.758012\pi$
$7$	0.620239	−	1.07429i	0.234428	−	0.406042i	0.959106	+	0.283046i	$0.0913448\pi$
$8$		−	3.03636i		−	1.07352i
$9$	−2.93664	−	0.613327i	−0.978879	−	0.204442i
$10$	4.52886	−	2.61474i	1.43215	−	0.826853i
$11$	3.29051	−	0.415381i	0.992126	−	0.125242i
$11$	3.29051	−	0.415381i	0.992126	−	0.125242i
$12$	0.563780	+	0.408085i	0.162749	+	0.117804i
$13$	2.90409	+	2.13688i	0.805450	+	0.592664i
$13$	2.90409	+	2.13688i	0.805450	+	0.592664i
$14$			1.56820i			0.419119i
$15$	−0.736296	+	7.12691i	−0.190111	+	1.84016i
$16$	1.51745	+	2.62830i	0.379362	+	0.657074i
$17$	−2.43465	+	4.21694i	−0.590490	+	1.02276i	0.403676	+	0.914902i	$0.367732\pi$
$17$	−2.43465	+	4.21694i	−0.590490	+	1.02276i	−0.994166	+	0.107857i	$0.965601\pi$
$18$	3.60277	−	1.18475i	0.849182	−	0.279248i
$19$	−1.67153	+	2.89518i	−0.383476	+	0.664200i	−0.991556	−	0.129676i	$-0.958606\pi$
$19$	−1.67153	+	2.89518i	−0.383476	+	0.664200i	0.608081	+	0.793875i	$0.291940\pi$
$20$	0.831091	−	1.43949i	0.185838	−	0.321880i
$21$	−1.74047	−	1.25982i	−0.379801	−	0.274914i
$22$	−3.33996	+	2.53468i	−0.712082	+	0.540397i
$23$	−5.91424	+	3.41459i	−1.23320	+	0.711990i	−0.967696	−	0.252119i	$-0.918873\pi$
$23$	−5.91424	+	3.41459i	−1.23320	+	0.711990i	−0.265507	+	0.964109i	$0.585539\pi$
$24$	−5.23129	−	0.540456i	−1.06783	−	0.110320i
$25$	12.1116			2.42233
$26$	−4.53017	−	0.503840i	−0.888440	−	0.0988111i
$27$	−1.57939	+	4.95030i	−0.303955	+	0.952687i
$28$	0.249225	+	0.431671i	0.0470992	+	0.0815781i
$29$	4.19202	+	7.26080i	0.778439	+	1.34830i	0.932841	+	0.360288i	$0.117322\pi$
$29$	4.19202	+	7.26080i	0.778439	+	1.34830i	−0.154402	+	0.988008i	$0.549345\pi$
$30$	−3.69877	−	8.26810i	−0.675300	−	1.50954i
$31$		−	0.243427i		−	0.0437208i	−0.999761	−	0.0218604i	$-0.993041\pi$
$31$		−	0.243427i		−	0.0437208i	0.999761	−	0.0218604i	$-0.00695893\pi$
$32$	1.93646	+	1.11802i	0.342321	+	0.197639i
$33$	−0.129959	−	5.74309i	−0.0226230	−	0.999744i
$34$		−	6.15573i		−	1.05570i
$35$	−2.56569	+	4.44391i	−0.433682	+	0.751159i
$36$	0.803431	−	0.898689i	0.133905	−	0.149781i
$37$	−0.983279	+	0.567696i	−0.161650	+	0.0933287i	−0.578643	−	0.815581i	$-0.696417\pi$
$37$	−0.983279	+	0.567696i	−0.161650	+	0.0933287i	0.416993	+	0.908910i	$0.363084\pi$
$38$		−	4.22627i		−	0.685592i
$39$	4.19850	−	4.62305i	0.672298	−	0.740280i
$40$			12.5603i			1.98595i
$41$	8.87337	−	5.12304i	1.38579	−	0.800085i	0.392950	−	0.919560i	$-0.371454\pi$
$41$	8.87337	−	5.12304i	1.38579	−	0.800085i	0.992837	+	0.119475i	$0.0381212\pi$
$42$	2.70182	+	0.279131i	0.416900	+	0.0430709i
$43$	−3.46891	−	2.00277i	−0.529003	−	0.305420i	0.211607	−	0.977355i	$-0.432130\pi$
$43$	−3.46891	−	2.00277i	−0.529003	−	0.305420i	−0.740610	+	0.671935i	$0.765464\pi$
$44$	−0.516551	+	1.22851i	−0.0778730	+	0.185205i
$45$	12.1478	+	2.53710i	1.81088	+	0.378209i
$46$	4.31669	−	7.47672i	0.636461	−	1.10238i
$47$	−0.186546			−0.0272105			−0.0136052	−	0.999907i	$-0.504331\pi$
$47$	−0.186546			−0.0272105			−0.0136052	+	0.999907i	$0.504331\pi$
$48$	4.79834	−	2.14656i	0.692581	−	0.309829i
$49$	2.73061	+	4.72955i	0.390087	+	0.675650i
$50$	−13.2601	+	7.65571i	−1.87526	+	1.08268i
$51$	6.83194	+	4.94521i	0.956663	+	0.692468i
$52$	−1.32707	+	0.581265i	−0.184032	+	0.0806070i
$53$		−	0.981050i		−	0.134758i	−0.997727	−	0.0673788i	$-0.978536\pi$
$53$		−	0.981050i		−	0.134758i	0.997727	−	0.0673788i	$-0.0214636\pi$
$54$	−1.39991	−	6.41803i	−0.190504	−	0.873383i
$55$	−13.6116	+	1.71827i	−1.83539	+	0.231692i
$56$	−3.26192	−	1.88327i	−0.435892	−	0.251663i
$57$	4.69053	+	3.39518i	0.621275	+	0.449702i
$58$	−9.17904	−	5.29952i	−1.20527	−	0.695861i
$59$	4.22819	−	7.32344i	0.550464	−	0.953431i	−0.447778	−	0.894145i	$-0.647784\pi$
$59$	4.22819	−	7.32344i	0.550464	−	0.953431i	0.998241	−	0.0592858i	$-0.0188823\pi$
$60$	−2.33214	−	1.68809i	−0.301079	−	0.217932i
$61$	0.321966	+	0.185887i	0.0412236	+	0.0238004i	0.520470	−	0.853880i	$-0.325757\pi$
$61$	0.321966	+	0.185887i	0.0412236	+	0.0238004i	−0.479247	+	0.877680i	$0.659090\pi$
$62$	0.153869	+	0.266509i	0.0195414	+	0.0338467i
$63$	−2.48030	+	2.77438i	−0.312489	+	0.349539i
$64$	−8.89657			−1.11207
$65$	−12.0131	−	8.83947i	−1.49004	−	1.09640i
$66$	3.77246	+	6.20551i	0.464358	+	0.763846i
$67$	−7.80314	+	4.50514i	−0.953305	+	0.550391i	−0.894106	−	0.447855i	$-0.852188\pi$
$67$	−7.80314	+	4.50514i	−0.953305	+	0.550391i	−0.0591991	+	0.998246i	$0.518855\pi$
$68$	−0.978296	−	1.69446i	−0.118636	−	0.205483i
$69$	4.83022	+	10.7973i	0.581490	+	1.29984i
$70$		−	6.48706i		−	0.775352i
$71$	−5.06007	+	8.76429i	−0.600520	+	1.04013i	0.392223	+	0.919870i	$0.371706\pi$
$71$	−5.06007	+	8.76429i	−0.600520	+	1.04013i	−0.992742	+	0.120260i	$0.961627\pi$
$72$	−1.86228	+	8.91669i	−0.219472	+	1.05084i
$73$	−1.57753			−0.184636			−0.0923182	−	0.995730i	$-0.529428\pi$
$73$	−1.57753			−0.184636			−0.0923182	+	0.995730i	$0.529428\pi$
$74$	0.717676	−	1.24305i	0.0834282	−	0.144502i
$75$	2.15581	−	20.8669i	0.248931	−	2.40950i
$76$	−0.671658	−	1.16334i	−0.0770444	−	0.133445i
$77$	1.59467	−	3.79258i	0.181729	−	0.432205i
$78$	−1.67440	+	7.71527i	−0.189589	+	0.873582i
$79$			7.03179i			0.791139i	0.918436	+	0.395569i	$0.129453\pi$
$79$			7.03179i			0.791139i	−0.918436	+	0.395569i	$0.870547\pi$
$80$	−6.27711	−	10.8723i	−0.701802	−	1.21556i
$81$	8.24766	+	3.60223i	0.916407	+	0.400248i
$82$	−6.47650	+	11.2176i	−0.715210	+	1.23878i
$83$		−	4.69182i		−	0.514994i	−0.966279	−	0.257497i	$-0.917102\pi$
$83$		−	4.69182i		−	0.514994i	0.966279	−	0.257497i	$-0.0828978\pi$
$84$	0.788078	−	0.352550i	0.0859864	−	0.0384664i
$85$	10.0712	−	17.4439i	1.09238	−	1.89206i
$86$	5.06378			0.546041
$87$	13.2556	−	5.92998i	1.42115	−	0.635760i
$88$	−1.26125	−	9.99118i	−0.134449	−	1.06506i
$89$	4.62316	+	8.00755i	0.490054	+	0.848799i	0.999934	−	0.0114464i	$-0.00364357\pi$
$89$	4.62316	+	8.00755i	0.490054	+	0.848799i	−0.509880	+	0.860245i	$0.670310\pi$
$90$	−14.9033	+	4.90087i	−1.57095	+	0.516597i
$91$	4.09685	−	1.79445i	0.429467	−	0.188109i
$92$		−	2.74411i		−	0.286093i
$93$	−0.419396	−	0.0433287i	−0.0434893	−	0.00449297i
$94$	0.204234	−	0.117915i	0.0210652	−	0.0121620i
$95$	6.91450	−	11.9763i	0.709413	−	1.22874i
$96$	2.27089	−	3.13729i	0.231772	−	0.320198i
$97$	−5.14746	−	2.97189i	−0.522645	−	0.301749i	0.215371	−	0.976532i	$-0.430904\pi$
$97$	−5.14746	−	2.97189i	−0.522645	−	0.301749i	−0.738016	+	0.674783i	$0.764237\pi$
$98$	−5.97905	−	3.45201i	−0.603976	−	0.348705i
$99$	−9.91780	−	0.798335i	−0.996776	−	0.0802357i
$100$	−2.43336	+	4.21470i	−0.243336	+	0.421470i
$101$	6.80761	+	11.7911i	0.677383	+	1.17326i	0.975766	+	0.218815i	$0.0702191\pi$
$101$	6.80761	+	11.7911i	0.677383	+	1.17326i	−0.298384	+	0.954446i	$0.596448\pi$
$102$	−10.6056	−	1.09569i	−1.05011	−	0.108489i
$103$	−2.45798			−0.242192			−0.121096	−	0.992641i	$-0.538641\pi$
$103$	−2.45798			−0.242192			−0.121096	+	0.992641i	$0.538641\pi$
$104$	6.48834	−	8.81787i	0.636234	−	0.864663i
$105$	7.19965	+	5.21138i	0.702614	+	0.508578i
$106$	0.620117	+	1.07407i	0.0602311	+	0.104323i
$107$	3.86753	+	6.69877i	0.373889	+	0.647594i	0.990160	−	0.139940i	$-0.0446909\pi$
$107$	3.86753	+	6.69877i	0.373889	+	0.647594i	−0.616271	+	0.787534i	$0.711358\pi$
$108$	−1.40533	−	1.54418i	−0.135228	−	0.148589i
$109$	−10.0251			−0.960234			−0.480117	−	0.877205i	$-0.659406\pi$
$109$	−10.0251			−0.960234			−0.480117	+	0.877205i	$0.659406\pi$
$110$	13.8162	−	10.4850i	1.31732	−	0.999709i
$111$	0.803055	+	1.79512i	0.0762226	+	0.170385i
$112$	3.76472			0.355733
$113$	3.12909	+	1.80658i	0.294360	+	0.169949i	0.639906	−	0.768453i	$-0.278973\pi$
$113$	3.12909	+	1.80658i	0.294360	+	0.169949i	−0.345546	+	0.938402i	$0.612306\pi$
$114$	−7.28136	−	0.752254i	−0.681962	−	0.0704550i
$115$	24.4650	−	14.1249i	2.28137	−	1.31715i
$116$	−3.36889			−0.312794
$117$	−7.21765	−	8.05640i	−0.667272	−	0.744814i
$118$			10.6905i			0.984139i
$119$	3.02014	+	5.23103i	0.276855	+	0.479528i
$120$	21.6399	+	2.23566i	1.97544	+	0.204087i
$121$	10.6549	−	2.73363i	0.968629	−	0.248512i
$122$	−0.469994			−0.0425513
$123$	−7.24698	−	16.1996i	−0.653438	−	1.46067i
$124$	0.0847095	+	0.0489071i	0.00760714	+	0.00439198i
$125$	−29.4182			−2.63124
$126$	0.961820	−	4.60524i	0.0856857	−	0.410267i
$127$	1.33931	−	0.773249i	0.118844	−	0.0686148i	−0.439399	−	0.898292i	$-0.644809\pi$
$127$	1.33931	−	0.773249i	0.118844	−	0.0686148i	0.558244	+	0.829677i	$0.311475\pi$
$128$	5.86723	−	3.38745i	0.518595	−	0.299411i
$129$	−4.06799	+	5.62003i	−0.358166	+	0.494816i
$130$	18.7396	+	2.08420i	1.64357	+	0.182796i
$131$	−21.6050			−1.88764			−0.943818	−	0.330465i	$-0.892794\pi$
$131$	−21.6050			−1.88764			−0.943818	+	0.330465i	$0.892794\pi$
$132$	2.02463	+	1.10862i	0.176222	+	0.0964934i
$133$	2.07350	+	3.59141i	0.179795	+	0.311415i
$134$	5.69536	−	9.86466i	0.492004	−	0.852177i
$135$	6.53336	−	20.4775i	0.562302	−	1.76243i
$136$	12.8042	+	7.39249i	1.09795	+	0.633901i
$137$	−2.24066	+	3.88094i	−0.191433	+	0.331571i	−0.945725	−	0.324967i	$-0.894647\pi$
$137$	−2.24066	+	3.88094i	−0.191433	+	0.331571i	0.754293	+	0.656538i	$0.227980\pi$
$138$	−12.1132	−	8.76796i	−1.03114	−	0.746378i
$139$	−0.617096	−	0.356281i	−0.0523414	−	0.0302193i	0.473601	−	0.880740i	$-0.342954\pi$
$139$	−0.617096	−	0.356281i	−0.0523414	−	0.0302193i	−0.525942	+	0.850520i	$0.676287\pi$
$140$	−1.03095	−	1.78566i	−0.0871313	−	0.150916i
$141$	−0.0332041	+	0.321396i	−0.00279629	+	0.0270664i
$142$		−	12.7938i		−	1.07363i
$143$	10.4436	+	5.82512i	0.873334	+	0.487121i
$144$	−2.84419	−	8.64905i	−0.237016	−	0.720754i
$145$	−17.3408	−	30.0352i	−1.44008	−	2.49429i
$146$	1.72712	−	0.997152i	0.142937	−	0.0825249i
$147$	8.63448	−	3.86268i	0.712160	−	0.318588i
$148$		−	0.456225i		−	0.0375014i
$149$	−3.66256	−	2.11458i	−0.300049	−	0.173233i	0.342416	−	0.939548i	$-0.388755\pi$
$149$	−3.66256	−	2.11458i	−0.300049	−	0.173233i	−0.642465	+	0.766315i	$0.722088\pi$
$150$	10.8297	+	24.2082i	0.884238	+	1.97659i
$151$	0.620315			0.0504805			0.0252403	−	0.999681i	$-0.491965\pi$
$151$	0.620315			0.0504805			0.0252403	+	0.999681i	$0.491965\pi$
$152$	8.79081	+	5.07538i	0.713029	+	0.411667i
$153$	9.73606	−	10.8904i	0.787114	−	0.880436i
$154$	0.651401	+	5.16018i	0.0524914	+	0.415819i
$155$			1.00697i			0.0808814i
$156$	0.765239	+	2.38985i	0.0612682	+	0.191341i
$157$	−18.6856			−1.49127			−0.745636	−	0.666354i	$-0.767854\pi$
$157$	−18.6856			−1.49127			−0.745636	+	0.666354i	$0.767854\pi$
$158$	−4.44477	−	7.69856i	−0.353607	−	0.612465i
$159$	−1.69023	−	0.174622i	−0.134044	−	0.0138484i
$160$	−8.01041	−	4.62481i	−0.633278	−	0.365623i
$161$			8.47144i			0.667643i
$162$	−11.3067	+	1.26950i	−0.888336	+	0.0997417i
$163$	0.0847175	+	0.0489117i	0.00663559	+	0.00383106i	0.503314	−	0.864104i	$-0.332114\pi$
$163$	0.0847175	+	0.0489117i	0.00663559	+	0.00383106i	−0.496679	+	0.867935i	$0.665447\pi$
$164$			4.11709i			0.321491i
$165$	0.537592	+	23.7570i	0.0418515	+	1.84948i
$166$	2.96568	+	5.13671i	0.230181	+	0.398686i
$167$	1.29557	−	0.747996i	0.100254	−	0.0578816i	−0.449035	−	0.893514i	$-0.648232\pi$
$167$	1.29557	−	0.747996i	0.100254	−	0.0578816i	0.549289	+	0.835633i	$0.314899\pi$
$168$	−3.82525	+	5.28469i	−0.295125	+	0.407722i
$169$	3.86748	+	12.4114i	0.297499	+	0.954722i
$170$			25.4639i			1.95300i
$171$	6.68437	−	7.47689i	0.511167	−	0.571772i
$172$	1.39388	−	0.804757i	0.106282	−	0.0613622i
$173$	−2.66933	+	4.62341i	−0.202945	+	0.351511i	−0.949476	−	0.313839i	$-0.898385\pi$
$173$	−2.66933	+	4.62341i	−0.202945	+	0.351511i	0.746531	+	0.665351i	$0.231718\pi$
$174$	−10.7643	+	14.8711i	−0.816036	+	1.12738i
$175$	7.51211	−	13.0114i	0.567862	−	0.983567i
$176$	6.08493	+	8.01812i	0.458669	+	0.604389i
$177$	−11.8648	−	8.58820i	−0.891815	−	0.645529i
$178$	−10.1231	−	5.84456i	−0.758757	−	0.438068i
$179$	−3.89062	+	2.24625i	−0.290799	+	0.167893i	−0.638302	−	0.769786i	$-0.720363\pi$
$179$	−3.89062	+	2.24625i	−0.290799	+	0.167893i	0.347503	+	0.937679i	$0.387030\pi$
$180$	−3.32349	+	3.71753i	−0.247718	+	0.277089i
$181$	−14.8734			−1.10553			−0.552767	−	0.833336i	$-0.686428\pi$
$181$	−14.8734			−1.10553			−0.552767	+	0.833336i	$0.686428\pi$
$182$	−3.35106	+	4.55420i	−0.248397	+	0.337580i
$183$	0.377570	−	0.521623i	0.0279108	−	0.0385595i
$184$	10.3679	+	17.9578i	0.764333	+	1.32386i
$185$	4.06745	−	2.34834i	0.299045	−	0.172654i
$186$	0.486551	−	0.217661i	0.0356757	−	0.0159597i
$187$	−6.25961	+	14.8872i	−0.457748	+	1.08866i
$188$	0.0374790	−	0.0649156i	0.00273344	−	0.00473446i
$189$	4.33844	+	4.76709i	0.315575	+	0.346755i
$190$			17.4825i			1.26831i
$191$	10.8325	+	6.25412i	0.783809	+	0.452532i	0.837778	−	0.546010i	$-0.183854\pi$
$191$	10.8325	+	6.25412i	0.783809	+	0.452532i	−0.0539697	+	0.998543i	$0.517187\pi$
$192$	−1.58354	+	15.3277i	−0.114282	+	1.10618i
$193$	12.2549	+	21.2262i	0.882130	+	1.52789i	0.848968	+	0.528445i	$0.177225\pi$
$193$	12.2549	+	21.2262i	0.882130	+	1.52789i	0.0331628	+	0.999450i	$0.489442\pi$
$194$	7.51407			0.539479
$195$	−17.3676	+	19.1238i	−1.24372	+	1.36948i
$196$	−2.19443			−0.156745
$197$	7.62514	−	4.40238i	0.543269	−	0.313656i	−0.203134	−	0.979151i	$-0.565113\pi$
$197$	7.62514	−	4.40238i	0.543269	−	0.313656i	0.746403	+	0.665495i	$0.231779\pi$
$198$	11.3628	−	5.39496i	0.807522	−	0.383403i
$199$	−0.745741	+	1.29166i	−0.0528642	+	0.0915635i	−0.891247	−	0.453519i	$-0.850168\pi$
$199$	−0.745741	+	1.29166i	−0.0528642	+	0.0915635i	0.838382	+	0.545083i	$0.183502\pi$
$200$		−	36.7753i		−	2.60041i
$201$	6.37291	+	14.2458i	0.449510	+	1.00482i
$202$	−14.9062	−	8.60612i	−1.04880	−	0.605524i
$203$	10.4002			0.729953
$204$	−3.09348	+	1.38388i	−0.216587	+	0.0968912i
$205$	−36.7058	+	21.1921i	−2.56364	+	1.48012i
$206$	2.69105	−	1.55368i	0.187494	−	0.108250i
$207$	19.4622	−	6.40004i	1.35272	−	0.444833i
$208$	−1.20955	+	10.8754i	−0.0838672	+	0.754075i
$209$	−4.29759	+	10.2209i	−0.297271	+	0.706997i
$210$	−11.1764	−	1.15466i	−0.771247	−	0.0796792i
$211$	13.9078	−	8.02969i	0.957455	−	0.552787i	0.0620662	−	0.998072i	$-0.480231\pi$
$211$	13.9078	−	8.02969i	0.957455	−	0.552787i	0.895389	+	0.445285i	$0.146898\pi$
$212$	0.341393	+	0.197103i	0.0234470	+	0.0135371i
$213$	14.1992	+	10.2779i	0.972911	+	0.704229i
$214$	−8.46852	−	4.88930i	−0.578896	−	0.334226i
$215$	14.3496	+	8.28472i	0.978631	+	0.565013i
$216$	15.0309	+	4.79561i	1.02272	+	0.326300i
$217$	−0.261510	−	0.150983i	−0.0177525	−	0.0102494i
$218$	10.9757	−	6.33684i	0.743370	−	0.429185i
$219$	−0.280792	+	2.71790i	−0.0189742	+	0.183659i
$220$	2.13678	−	5.08188i	0.144061	−	0.342621i
$221$	−16.0816	+	7.04382i	−1.08176	+	0.473819i
$222$	−2.01389	−	1.45773i	−0.135163	−	0.0978362i
$223$	−10.6584	+	6.15361i	−0.713737	+	0.412076i	−0.812443	−	0.583040i	$-0.801863\pi$
$223$	−10.6584	+	6.15361i	−0.713737	+	0.412076i	0.0987062	+	0.995117i	$0.468530\pi$
$224$	2.40214	−	1.38687i	0.160500	−	0.0926645i
$225$	−35.5675	−	7.42839i	−2.37117	−	0.495226i
$226$	−4.56773			−0.303841
$227$	−4.40336	−	2.54228i	−0.292262	−	0.168737i	0.346700	−	0.937976i	$-0.387302\pi$
$227$	−4.40336	−	2.54228i	−0.292262	−	0.168737i	−0.638961	+	0.769239i	$0.720636\pi$
$228$	−2.12386	+	0.950117i	−0.140656	+	0.0629230i
$229$		−	7.54764i		−	0.498762i	−0.968405	−	0.249381i	$-0.919773\pi$
$229$		−	7.54764i		−	0.498762i	0.968405	−	0.249381i	$-0.0802272\pi$
$230$	−17.8565	+	30.9284i	−1.17742	+	2.03936i
$231$	−6.25033	−	3.42248i	−0.411241	−	0.225182i
$232$	22.0464	−	12.7285i	1.44742	−	0.835667i
$233$	18.0225			1.18070			0.590348	−	0.807149i	$-0.298991\pi$
$233$	18.0225			1.18070			0.590348	+	0.807149i	$0.298991\pi$
$234$	12.9945	+	4.25807i	0.849474	+	0.278359i
$235$	0.771669			0.0503382
$236$	1.69898	+	2.94271i	0.110594	+	0.191554i
$237$	12.1149	+	1.25162i	0.786950	+	0.0813015i
$238$	−6.61302	−	3.81803i	−0.428658	−	0.247486i
$239$			17.3654i			1.12327i	0.827384	+	0.561637i	$0.189828\pi$
$239$			17.3654i			1.12327i	−0.827384	+	0.561637i	$0.810172\pi$
$240$	−19.8489	+	8.87951i	−1.28124	+	0.573170i
$241$	7.23204	−	12.5263i	0.465856	−	0.806887i	−0.533383	−	0.845874i	$-0.679080\pi$
$241$	7.23204	−	12.5263i	0.465856	−	0.806887i	0.999240	+	0.0389866i	$0.0124130\pi$
$242$	−9.93732	+	9.72776i	−0.638795	+	0.625324i
$243$	7.67426	−	13.5686i	0.492304	−	0.870423i
$244$	−0.129373	+	0.0746935i	−0.00828225	+	0.00478176i
$245$	−11.2955	−	19.5644i	−0.721642	−	1.24992i
$246$	18.1739	+	13.1549i	1.15872	+	0.838727i
$247$	−11.0409	+	4.83600i	−0.702518	+	0.307707i
$248$	−0.739132			−0.0469349
$249$	−8.08345	−	0.835119i	−0.512268	−	0.0529235i
$250$	32.2076	−	18.5951i	2.03699	−	1.17606i
$251$	−17.1739	−	9.91535i	−1.08401	−	0.625851i	−0.152032	−	0.988376i	$-0.548582\pi$
$251$	−17.1739	−	9.91535i	−1.08401	−	0.625851i	−0.931974	+	0.362524i	$0.881915\pi$
$252$	−0.467129	−	1.42052i	−0.0294263	−	0.0894841i
$253$	−18.0425	+	13.6924i	−1.13432	+	0.860833i
$254$	−0.977535	+	1.69314i	−0.0613360	+	0.106237i
$255$	−28.2611	−	20.4565i	−1.76978	−	1.28103i
$256$	4.61419	−	7.99201i	0.288387	−	0.499500i
$257$	−13.7477	+	7.93724i	−0.857558	+	0.495112i	−0.863194	−	0.504873i	$-0.831539\pi$
$257$	−13.7477	+	7.93724i	−0.857558	+	0.495112i	0.00563556	+	0.999984i	$0.498206\pi$
$258$	0.901325	−	8.72428i	0.0561140	−	0.543150i
$259$			1.40843i			0.0875156i
$260$	5.48959	−	2.40447i	0.340450	−	0.149119i
$261$	−7.85721	−	23.8934i	−0.486349	−	1.47896i
$262$	23.6536	−	13.6564i	1.46132	−	0.843696i
$263$	−7.30094	−	12.6456i	−0.450195	−	0.779761i	0.548202	−	0.836346i	$-0.315312\pi$
$263$	−7.30094	−	12.6456i	−0.450195	−	0.779761i	−0.998398	+	0.0565844i	$0.981979\pi$
$264$	−17.4381	+	0.394603i	−1.07324	+	0.0242861i
$265$			4.05823i			0.249295i
$266$	−4.54023	−	2.62130i	−0.278379	−	0.160722i
$267$	14.6190	−	6.53986i	0.894666	−	0.400233i
$268$		−	3.62053i		−	0.221159i
$269$	15.5837	+	8.99726i	0.950155	+	0.548573i	0.893129	−	0.449800i	$-0.148505\pi$
$269$	15.5837	+	8.99726i	0.950155	+	0.548573i	0.0570263	+	0.998373i	$0.481838\pi$
$270$	5.79090	+	26.5490i	0.352423	+	1.61572i
$271$	−1.25223	−	2.16892i	−0.0760674	−	0.131753i	0.825483	−	0.564428i	$-0.190903\pi$
$271$	−1.25223	−	2.16892i	−0.0760674	−	0.131753i	−0.901550	+	0.432675i	$0.857570\pi$
$272$	−14.7778			−0.896039
$273$	−2.36240	−	7.37779i	−0.142979	−	0.446524i
$274$		−	5.66525i		−	0.342250i
$275$	39.8535	−	5.03095i	2.40326	−	0.303378i
$276$	−4.72777	−	0.488436i	−0.284578	−	0.0294004i
$277$	17.0065	+	9.81872i	1.02182	+	0.589950i	0.914631	−	0.404289i	$-0.132481\pi$
$277$	17.0065	+	9.81872i	1.02182	+	0.589950i	0.107191	+	0.994238i	$0.465814\pi$
$278$	0.900814			0.0540272
$279$	−0.149300	+	0.714856i	−0.00893837	+	0.0427973i
$280$	13.4933	+	7.79038i	0.806380	+	0.465564i
$281$		−	13.4868i		−	0.804555i	−0.915518	−	0.402278i	$-0.868219\pi$
$281$		−	13.4868i		−	0.804555i	0.915518	−	0.402278i	$-0.131781\pi$
$282$	−0.166800	−	0.372859i	−0.00993282	−	0.0222035i
$283$	25.4622	−	14.7006i	1.51357	−	0.873861i	0.513698	−	0.857971i	$-0.328275\pi$
$283$	25.4622	−	14.7006i	1.51357	−	0.873861i	0.999874	−	0.0158900i	$-0.00505816\pi$
$284$	−2.03324	−	3.52168i	−0.120651	−	0.208973i
$285$	−19.4029	−	14.0446i	−1.14933	−	0.831928i
$286$	−15.1159	+	0.223858i	−0.893820	+	0.0132370i
$287$		−	12.7100i		−	0.750250i
$288$	−5.00097	−	4.47089i	−0.294685	−	0.263450i
$289$	−3.35508	−	5.81117i	−0.197358	−	0.341833i
$290$	37.9702	+	21.9221i	2.22969	+	1.28731i
$291$	−6.03643	+	8.33948i	−0.353862	+	0.488869i
$292$	0.316943	−	0.548962i	0.0185477	−	0.0321256i
$293$	−6.41037	−	3.70103i	−0.374498	−	0.216216i	0.300924	−	0.953648i	$-0.402705\pi$
$293$	−6.41037	−	3.70103i	−0.374498	−	0.216216i	−0.675422	+	0.737432i	$0.736038\pi$
$294$	−7.01164	+	9.68676i	−0.408927	+	0.564943i
$295$	−17.4904	+	30.2943i	−1.01833	+	1.76380i
$296$	1.72373	+	2.98559i	0.100190	+	0.173534i
$297$	−3.14075	+	16.9451i	−0.182245	+	0.983253i
$298$	5.34647			0.309713
$299$	−24.4720	−	2.72175i	−1.41525	−	0.157403i
$300$	6.82830	+	4.94258i	0.394232	+	0.285360i
$301$	−4.30310	+	2.48440i	−0.248027	+	0.143198i
$302$	−0.679134	+	0.392098i	−0.0390798	+	0.0225627i
$303$	21.5264	−	9.62994i	1.23666	−	0.553226i
$304$	−10.1459			−0.581905
$305$	−1.33185	−	0.768946i	−0.0762617	−	0.0440297i
$306$	−3.77548	+	18.0772i	−0.215830	+	1.03340i
$307$	−13.9747			−0.797580			−0.398790	−	0.917042i	$-0.630570\pi$
$307$	−13.9747			−0.797580			−0.398790	+	0.917042i	$0.630570\pi$
$308$	0.999386	+	1.31689i	0.0569453	+	0.0750370i
$309$	−0.437507	+	4.23481i	−0.0248889	+	0.240910i
$310$	−0.636498	−	1.10245i	−0.0361507	−	0.0626148i
$311$			24.7334i			1.40250i	0.712916	+	0.701250i	$0.247374\pi$
$311$			24.7334i			1.40250i	−0.712916	+	0.701250i	$0.752626\pi$
$312$	−14.0372	−	12.7482i	−0.794702	−	0.721723i
$313$	7.09716			0.401155			0.200578	−	0.979678i	$-0.435718\pi$
$313$	7.09716			0.401155			0.200578	+	0.979678i	$0.435718\pi$
$314$	20.4574	−	11.8111i	1.15448	−	0.666537i
$315$	10.2601	−	11.4765i	0.578090	−	0.646630i
$316$	−2.44698	−	1.41276i	−0.137653	−	0.0794741i
$317$	−0.369289			−0.0207413			−0.0103707	−	0.999946i	$-0.503301\pi$
$317$	−0.369289			−0.0207413			−0.0103707	+	0.999946i	$0.503301\pi$
$318$	1.96088	−	0.877209i	0.109961	−	0.0491914i
$319$	16.8099	+	22.1504i	0.941174	+	1.24019i
$320$	36.8017			2.05728
$321$	12.2296	−	5.47096i	0.682588	−	0.305359i
$322$	−5.35476	−	9.27471i	−0.298409	−	0.516860i
$323$	−8.13921	−	14.0975i	−0.452878	−	0.784407i
$324$	−2.91058	+	2.14636i	−0.161699	+	0.119242i
$325$	35.1733	+	25.8811i	1.95106	+	1.43563i
$326$	−0.123667			−0.00684931
$327$	−1.78442	+	17.2721i	−0.0986786	+	0.955150i
$328$	−15.5554	−	26.9427i	−0.858903	−	1.48766i
$329$	−0.115703	+	0.200403i	−0.00637891	+	0.0110486i
$330$	−15.6053	−	25.6699i	−0.859041	−	1.41308i
$331$	4.03836	+	2.33155i	0.221968	+	0.128153i	0.606861	−	0.794808i	$-0.292428\pi$
$331$	4.03836	+	2.33155i	0.221968	+	0.128153i	−0.384893	+	0.922961i	$0.625762\pi$
$332$	1.63270	+	0.942637i	0.0896058	+	0.0517339i
$333$	3.23571	−	1.06405i	0.177316	−	0.0583093i
$334$	−0.945609	+	1.63784i	−0.0517414	+	0.0896188i
$335$	32.2786	−	18.6361i	1.76357	−	1.01820i
$336$	0.670100	−	6.48617i	0.0365570	−	0.353850i
$337$			14.0674i			0.766302i	0.923686	+	0.383151i	$0.125161\pi$
$337$			14.0674i			0.766302i	−0.923686	+	0.383151i	$0.874839\pi$
$338$	−12.0794	−	11.1436i	−0.657032	−	0.606134i
$339$	3.66948	−	5.06949i	0.199299	−	0.275337i
$340$	4.04684	+	7.00933i	0.219471	+	0.380134i
$341$	−0.101115	−	0.800999i	−0.00547568	−	0.0433765i
$342$	−2.59209	+	12.4110i	−0.140164	+	0.671111i
$343$	15.4579			0.834646
$344$	−6.08114	+	10.5328i	−0.327873	+	0.567893i
$345$	−19.9808	−	44.6644i	−1.07573	−	2.40465i
$346$		−	6.74908i		−	0.362833i
$347$	1.83858	−	3.18452i	0.0987004	−	0.170954i	−0.812447	−	0.583036i	$-0.801865\pi$
$347$	1.83858	−	3.18452i	0.0987004	−	0.170954i	0.911147	+	0.412082i	$0.135198\pi$
$348$	−0.599644	+	5.80419i	−0.0321443	+	0.311137i
$349$	−2.56390	−	4.44080i	−0.137242	−	0.237710i	0.789210	−	0.614124i	$-0.210491\pi$
$349$	−2.56390	−	4.44080i	−0.137242	−	0.237710i	−0.926452	+	0.376414i	$0.877157\pi$
$350$			18.9935i			1.01524i
$351$	−15.1649	+	11.0012i	−0.809443	+	0.587198i
$352$	6.83635	+	2.87447i	0.364378	+	0.153210i
$353$	−4.45460	−	7.71560i	−0.237095	−	0.410660i	0.722785	−	0.691073i	$-0.242862\pi$
$353$	−4.45460	−	7.71560i	−0.237095	−	0.410660i	−0.959879	+	0.280413i	$0.909528\pi$
$354$	18.4184	+	1.90285i	0.978928	+	0.101135i
$355$	20.9316	−	36.2546i	1.11093	−	1.92419i
$356$	−3.71537			−0.196914
$357$	9.55001	−	4.27224i	0.505440	−	0.226111i
$358$	2.83969	−	4.91849i	0.150082	−	0.259950i
$359$			24.6971i			1.30347i	0.758449	+	0.651733i	$0.225958\pi$
$359$			24.6971i			1.30347i	−0.758449	+	0.651733i	$0.774042\pi$
$360$	7.70355	−	36.8850i	0.406013	−	1.94401i
$361$	3.91196	+	6.77571i	0.205892	+	0.356616i
$362$	16.2837	−	9.40142i	0.855855	−	0.494128i
$363$	−2.81320	−	18.8437i	−0.147655	−	0.989039i
$364$	−0.198656	+	1.78618i	−0.0104124	+	0.0936211i
$365$	6.52566			0.341569
$366$	−0.0836564	+	0.809744i	−0.00437279	+	0.0423260i
$367$	−4.66517	−	8.08031i	−0.243520	−	0.421789i	0.718195	−	0.695842i	$-0.244969\pi$
$367$	−4.66517	−	8.08031i	−0.243520	−	0.421789i	−0.961714	+	0.274054i	$0.911635\pi$
$368$	−17.9491	−	10.3629i	−0.935661	−	0.540204i
$369$	−29.2000	+	9.60223i	−1.52009	+	0.499872i
$370$	−2.96876	+	5.14204i	−0.154338	+	0.267322i
$371$	−1.05393	−	0.608486i	−0.0547172	−	0.0315910i
$372$	0.0993389	−	0.137239i	0.00515048	−	0.00711552i
$373$	5.98152	+	3.45343i	0.309712	+	0.178812i	0.646797	−	0.762662i	$-0.276108\pi$
$373$	5.98152	+	3.45343i	0.309712	+	0.178812i	−0.337086	+	0.941474i	$0.609441\pi$
$374$	−2.55698	−	20.2555i	−0.132218	−	1.04739i
$375$	−5.23627	+	50.6840i	−0.270400	+	2.61731i
$376$			0.566420i			0.0292109i
$377$	−3.34144	+	30.0439i	−0.172093	+	1.54734i
$378$	−7.76307	−	2.47681i	−0.399289	−	0.127393i
$379$	−4.47075	+	2.58119i	−0.229647	+	0.132587i	−0.610409	−	0.792086i	$-0.708995\pi$
$379$	−4.47075	+	2.58119i	−0.229647	+	0.132587i	0.380762	+	0.924673i	$0.375662\pi$
$380$	2.77839	+	4.81232i	0.142529	+	0.246867i
$381$	−1.09383	−	2.44510i	−0.0560384	−	0.125266i
$382$	−15.8128			−0.809053
$383$	14.3171	−	24.7979i	0.731569	−	1.26712i	−0.224643	−	0.974441i	$-0.572122\pi$
$383$	14.3171	−	24.7979i	0.731569	−	1.26712i	0.956212	−	0.292674i	$-0.0945452\pi$
$384$	−4.79183	−	10.7115i	−0.244532	−	0.546618i
$385$	−6.59653	+	15.6885i	−0.336190	+	0.799559i
$386$	−26.8340	−	15.4926i	−1.36581	−	0.788552i
$387$	8.95856	+	8.00899i	0.455389	+	0.407120i
$388$	2.06836	−	1.19417i	0.105005	−	0.0606247i
$389$		−	19.7794i		−	1.00285i	−0.865200	−	0.501427i	$-0.832809\pi$
$389$		−	19.7794i		−	1.00285i	0.865200	−	0.501427i	$-0.167191\pi$
$390$	6.92637	−	31.9151i	0.350730	−	1.61609i
$391$		−	33.2533i		−	1.68169i
$392$	14.3606	−	8.29111i	0.725321	−	0.418764i
$393$	−3.84557	+	37.2228i	−0.193983	+	1.87764i
$394$	−5.56544	+	9.63963i	−0.280383	+	0.485638i
$395$		−	29.0879i		−	1.46357i
$396$	2.27040	−	3.29087i	0.114092	−	0.165373i
$397$	−14.7727	−	8.52902i	−0.741421	−	0.428059i	0.0811649	−	0.996701i	$-0.474136\pi$
$397$	−14.7727	−	8.52902i	−0.741421	−	0.428059i	−0.822586	+	0.568641i	$0.807469\pi$
$398$		−	1.88552i		−	0.0945125i
$399$	6.55664	−	2.93314i	0.328243	−	0.146841i
$400$	18.3788	+	31.8330i	0.918940	+	1.59165i
$401$	1.38119	+	2.39229i	0.0689733	+	0.119465i	0.898450	−	0.439077i	$-0.144694\pi$
$401$	1.38119	+	2.39229i	0.0689733	+	0.119465i	−0.829476	+	0.558542i	$0.811361\pi$
$402$	−15.9819	−	11.5683i	−0.797104	−	0.576974i
$403$	0.520174	−	0.706934i	0.0259117	−	0.0352149i
$404$	−5.47089			−0.272187
$405$	−34.1175	−	14.9011i	−1.69531	−	0.740441i
$406$	−11.3864	+	6.57394i	−0.565097	+	0.326259i
$407$	−2.99968	+	2.27645i	−0.148689	+	0.112839i
$408$	15.0154	−	20.7442i	0.743375	−	1.02699i
$409$	−0.528451	+	0.915303i	−0.0261302	+	0.0452588i	−0.878795	−	0.477200i	$-0.841652\pi$
$409$	−0.528451	+	0.915303i	−0.0261302	+	0.0452588i	0.852665	+	0.522459i	$0.174985\pi$
$410$	26.7908	−	46.4031i	1.32311	−	2.29169i
$411$	6.28757	+	4.55118i	0.310143	+	0.224493i
$412$	0.493834	−	0.855346i	0.0243295	−	0.0421399i
$413$	−5.24498	−	9.08457i	−0.258089	−	0.447022i
$414$	−17.2622	+	19.3089i	−0.848392	+	0.948979i
$415$			19.4083i			0.952716i
$416$	3.23459	+	7.38480i	0.158589	+	0.362070i
$417$	−0.723669	+	0.999767i	−0.0354382	+	0.0489588i
$418$	−1.75551	−	13.9066i	−0.0858650	−	0.680194i
$419$	31.6187	−	18.2551i	1.54467	−	0.891818i	0.546140	−	0.837694i	$-0.316097\pi$
$419$	31.6187	−	18.2551i	1.54467	−	0.891818i	0.998534	−	0.0541246i	$-0.0172368\pi$
$420$	−3.25998	+	1.45837i	−0.159071	+	0.0711611i
$421$			26.4552i			1.28935i	0.764458	+	0.644674i	$0.223007\pi$
$421$			26.4552i			1.28935i	−0.764458	+	0.644674i	$0.776993\pi$
$422$	−10.1511	+	17.5822i	−0.494146	+	0.855886i
$423$	0.547817	+	0.114414i	0.0266358	+	0.00556298i
$424$	−2.97882			−0.144664
$425$	−29.4877	+	51.0741i	−1.43036	+	2.47746i
$426$	−22.0422	−	2.27722i	−1.06795	−	0.110332i
$427$	0.399392	−	0.230589i	0.0193279	−	0.0111590i
$428$	−3.10812			−0.150236
$429$	11.8949	−	16.9562i	0.574291	−	0.818652i
$430$	−20.9469			−1.01015
$431$	−27.8225	+	16.0633i	−1.34016	+	0.773744i	−0.986831	−	0.161754i	$-0.948285\pi$
$431$	−27.8225	+	16.0633i	−1.34016	+	0.773744i	−0.353333	+	0.935498i	$0.614952\pi$
$432$	−15.4075	+	3.36071i	−0.741295	+	0.161692i
$433$	15.6033	−	27.0258i	0.749849	−	1.29878i	−0.198046	−	0.980193i	$-0.563460\pi$
$433$	15.6033	−	27.0258i	0.749849	−	1.29878i	0.947895	−	0.318583i	$-0.103207\pi$
$434$	0.381742			0.0183242
$435$	−54.8336	+	24.5301i	−2.62907	+	1.17613i
$436$	2.01416	−	3.48862i	0.0964606	−	0.167075i
$437$		−	22.8304i		−	1.09212i
$438$	−1.41056	−	3.15311i	−0.0673990	−	0.150661i
$439$	−3.80990	+	2.19965i	−0.181837	+	0.104983i	−0.588155	−	0.808748i	$-0.700146\pi$
$439$	−3.80990	+	2.19965i	−0.181837	+	0.104983i	0.406319	+	0.913731i	$0.366812\pi$
$440$	5.21730	+	41.3297i	0.248725	+	1.97032i
$441$	−5.11804	−	15.5637i	−0.243716	−	0.741129i
$442$	13.1541	−	17.8768i	0.625675	−	0.850313i
$443$		−	21.2390i		−	1.00910i	−0.863383	−	0.504548i	$-0.831659\pi$
$443$		−	21.2390i		−	1.00910i	0.863383	−	0.504548i	$-0.168341\pi$
$444$	−0.786021	−	0.0812055i	−0.0373029	−	0.00385384i
$445$	−19.1243	−	33.1242i	−0.906578	−	1.57024i
$446$	7.77934	−	13.4742i	0.368362	−	0.638022i
$447$	−4.29509	+	5.93377i	−0.203151	+	0.280658i
$448$	−5.51800	+	9.55745i	−0.260701	+	0.451547i
$449$	−18.3562	+	31.7939i	−0.866284	+	1.50045i	−0.000516632		1.00000i	$0.500164\pi$
$449$	−18.3562	+	31.7939i	−0.866284	+	1.50045i	−0.865767	+	0.500447i	$0.833169\pi$
$450$	43.6355	−	14.3493i	2.05700	−	0.676431i
$451$	27.0699	−	20.5433i	1.27467	−	0.967344i
$452$	−1.25733	+	0.725923i	−0.0591401	+	0.0341445i
$453$	0.110413	−	1.06873i	0.00518764	−	0.0502133i
$454$	6.42786			0.301675
$455$	−16.9471	+	7.42295i	−0.794493	+	0.347993i
$456$	10.3090	−	14.2421i	0.482762	−	0.666949i
$457$	−1.32900	−	2.30189i	−0.0621678	−	0.107678i	0.833266	−	0.552872i	$-0.186468\pi$
$457$	−1.32900	−	2.30189i	−0.0621678	−	0.107678i	−0.895434	+	0.445194i	$0.853135\pi$
$458$	4.77083	+	8.26332i	0.222926	+	0.386120i
$459$	−17.0299	−	18.7125i	−0.794887	−	0.873425i
$460$			11.3513i			0.529259i
$461$	22.1383	+	12.7816i	1.03109	+	0.595297i	0.917295	−	0.398208i	$-0.130368\pi$
$461$	22.1383	+	12.7816i	1.03109	+	0.595297i	0.113790	+	0.993505i	$0.463701\pi$
$462$	9.00633	−	0.203802i	0.419012	−	0.00948174i
$463$			10.4527i			0.485777i	0.970054	+	0.242889i	$0.0780950\pi$
$463$			10.4527i			0.485777i	−0.970054	+	0.242889i	$0.921905\pi$
$464$	−12.7224	+	22.0358i	−0.590621	+	1.02299i
$465$	1.73488	+	0.179234i	0.0804532	+	0.00831179i
$466$	−19.7315	+	11.3920i	−0.914042	+	0.527722i
$467$		−	30.2230i		−	1.39855i	−0.714851	−	0.699276i	$-0.753506\pi$
$467$		−	30.2230i		−	1.39855i	0.714851	−	0.699276i	$-0.246494\pi$
$468$	4.25363	−	0.893036i	0.196624	−	0.0412806i
$469$			11.1771i			0.516109i
$470$	−0.844840	+	0.487769i	−0.0389696	+	0.0224991i
$471$	−3.32593	+	32.1930i	−0.153251	+	1.48338i
$472$	−22.2366	−	12.8383i	−1.02352	−	0.590931i
$473$	−12.2464	−	5.14923i	−0.563089	−	0.236762i
$474$	−14.0548	+	6.28750i	−0.645560	+	0.288794i
$475$	−20.2450	+	35.0654i	−0.928905	+	1.60891i
$476$	−2.42711			−0.111246
$477$	−0.601704	+	2.88099i	−0.0275501	+	0.131911i
$478$	−10.9766	−	19.0120i	−0.502057	−	0.869588i
$479$	14.1161	−	8.14992i	0.644980	−	0.372379i	−0.141551	−	0.989931i	$-0.545209\pi$
$479$	14.1161	−	8.14992i	0.644980	−	0.372379i	0.786530	+	0.617552i	$0.211875\pi$
$480$	−9.39380	+	12.9778i	−0.428767	+	0.592352i
$481$	−4.06863	−	0.452508i	−0.185514	−	0.0206326i
$482$			18.2854i			0.832875i
$483$	14.5953	+	1.50787i	0.664108	+	0.0686105i
$484$	−1.18942	+	4.25699i	−0.0540644	+	0.193500i
$485$	21.2931	+	12.2936i	0.966870	+	0.558223i
$486$	0.174679	+	19.7060i	0.00792359	+	0.893883i
$487$	21.0507	+	12.1536i	0.953898	+	0.550733i	0.894290	−	0.447489i	$-0.147682\pi$
$487$	21.0507	+	12.1536i	0.953898	+	0.550733i	0.0596081	+	0.998222i	$0.481015\pi$
$488$	0.564421	−	0.977606i	0.0255501	−	0.0442541i
$489$	0.0993483	−	0.137252i	0.00449268	−	0.00620676i
$490$	24.7331	+	14.2797i	1.11733	+	0.645089i
$491$	−8.25522	−	14.2985i	−0.372553	−	0.645280i	0.617405	−	0.786646i	$-0.288184\pi$
$491$	−8.25522	−	14.2985i	−0.372553	−	0.645280i	−0.989957	+	0.141365i	$0.954851\pi$
$492$	7.09326	+	0.732820i	0.319789	+	0.0330381i
$493$	−40.8245			−1.83864
$494$	9.03104	−	12.2735i	0.406326	−	0.552210i
$495$	41.0262	+	3.30241i	1.84399	+	0.148432i
$496$	0.639799	−	0.369388i	0.0287278	−	0.0165860i
$497$	6.27690	+	10.8719i	0.281558	+	0.487672i
$498$	9.37781	−	4.19521i	0.420230	−	0.187992i
$499$		−	29.0297i		−	1.29955i	−0.760128	−	0.649774i	$-0.774864\pi$
$499$		−	29.0297i		−	1.29955i	0.760128	−	0.649774i	$-0.225136\pi$
$500$	5.91042	−	10.2372i	0.264322	−	0.457819i
$501$	−1.05810	−	2.36525i	−0.0472726	−	0.105671i
$502$	25.0698			1.11892
$503$	1.49478	−	2.58903i	0.0666487	−	0.115439i	−0.830775	−	0.556608i	$-0.812103\pi$
$503$	1.49478	−	2.58903i	0.0666487	−	0.115439i	0.897424	+	0.441169i	$0.145436\pi$
$504$	8.42401	+	7.53110i	0.375235	+	0.335462i
$505$	−28.1605	−	48.7754i	−1.25313	−	2.17048i
$506$	11.0984	−	26.3953i	0.493385	−	1.17341i
$507$	22.0717	−	4.45406i	0.980240	−	0.197812i
$508$			0.621416i			0.0275709i
$509$	−2.64652	−	4.58390i	−0.117305	−	0.203178i	0.801394	−	0.598137i	$-0.204092\pi$
$509$	−2.64652	−	4.58390i	−0.117305	−	0.203178i	−0.918699	+	0.394959i	$0.870759\pi$
$510$	43.8713	+	4.53244i	1.94266	+	0.200700i
$511$	−0.978448	+	1.69472i	−0.0432840	+	0.0749701i
$512$			25.2162i			1.11441i
$513$	−11.6920	−	12.8472i	−0.516215	−	0.567219i
$514$	10.0342	−	17.3797i	0.442589	−	0.766587i
$515$	10.1677			0.448044
$516$	−1.13840	−	2.54473i	−0.0501152	−	0.112026i
$517$	−0.613831	+	0.0774876i	−0.0269962	+	0.00340790i
$518$	−0.890262	−	1.54198i	−0.0391159	−	0.0677507i
$519$	7.49046	+	5.42187i	0.328794	+	0.237994i
$520$	−26.8398	+	36.4762i	−1.17700	+	1.59959i
$521$		−	18.1143i		−	0.793601i	−0.917905	−	0.396801i	$-0.870120\pi$
$521$		−	18.1143i		−	0.793601i	0.917905	−	0.396801i	$-0.129880\pi$
$522$	23.7052	+	21.1925i	1.03755	+	0.927571i
$523$	−20.7433	+	11.9761i	−0.907040	+	0.523680i	−0.879477	−	0.475941i	$-0.842108\pi$
$523$	−20.7433	+	11.9761i	−0.907040	+	0.523680i	−0.0275622	+	0.999620i	$0.508774\pi$
$524$	4.34067	−	7.51826i	0.189623	−	0.328437i
$525$	−21.0799	−	15.2584i	−0.920003	−	0.665932i
$526$	15.9865	+	9.22978i	0.697043	+	0.402438i
$527$	1.02652	+	0.592660i	0.0447158	+	0.0258167i
$528$	14.8974	−	9.05642i	0.648324	−	0.394130i
$529$	11.8188	−	20.4707i	0.513861	−	0.890033i
$530$	−2.56519	−	4.44304i	−0.111425	−	0.192993i
$531$	−16.9083	+	18.9130i	−0.733759	+	0.820755i
$532$	−1.66635			−0.0722456
$533$	36.7164	+	4.08355i	1.59036	+	0.176878i
$534$	−11.8713	+	16.4006i	−0.513723	+	0.709721i
$535$	−15.9985	−	27.7103i	−0.691677	−	1.19802i
$536$	13.6792	+	23.6931i	0.590853	+	1.02339i
$537$	3.17751	+	7.10290i	0.137120	+	0.306513i
$538$	−22.7485			−0.980758
$539$	10.9497	+	14.4284i	0.471635	+	0.621475i
$540$	5.81331	+	6.38768i	0.250165	+	0.274882i
$541$	17.1999			0.739482			0.369741	−	0.929135i	$-0.379446\pi$
$541$	17.1999			0.739482			0.369741	+	0.929135i	$0.379446\pi$
$542$	2.74193	+	1.58305i	0.117776	+	0.0679980i
$543$	−2.64739	+	25.6251i	−0.113610	+	1.09968i
$544$	−9.42922	+	5.44396i	−0.404275	+	0.233408i
$545$	41.4702			1.77639
$546$	7.24987	+	6.58410i	0.310266	+	0.281773i
$547$		−	13.6790i		−	0.584872i	−0.956285	−	0.292436i	$-0.905534\pi$
$547$		−	13.6790i		−	0.584872i	0.956285	−	0.292436i	$-0.0944658\pi$
$548$	−0.900345	−	1.55944i	−0.0384608	−	0.0666161i
$549$	−0.831488	−	0.743354i	−0.0354871	−	0.0317256i
$550$	−40.4524	+	30.6992i	−1.72490	+	1.30902i
$551$	−28.0284			−1.19405
$552$	32.7845	−	14.6663i	1.39540	−	0.624239i
$553$	7.55416	+	4.36139i	0.321235	+	0.185465i
$554$	−24.8255			−1.05473
$555$	−3.32193	−	7.42573i	−0.141008	−	0.315205i
$556$	0.247962	−	0.143161i	0.0105160	−	0.00607139i
$557$	−19.9531	+	11.5200i	−0.845442	+	0.488116i	−0.859110	−	0.511790i	$-0.828982\pi$
$557$	−19.9531	+	11.5200i	−0.845442	+	0.488116i	0.0136683	+	0.999907i	$0.495649\pi$
$558$	−0.288400	−	0.877012i	−0.0122090	−	0.0371269i
$559$	−5.79433	−	13.2289i	−0.245074	−	0.559522i
$560$	−15.5732			−0.658089
$561$	24.5347	+	13.4344i	1.03586	+	0.567201i
$562$	8.52495	+	14.7656i	0.359603	+	0.622851i
$563$	−21.1955	+	36.7116i	−0.893282	+	1.54721i	−0.0573654	+	0.998353i	$0.518270\pi$
$563$	−21.1955	+	36.7116i	−0.893282	+	1.54721i	−0.835917	+	0.548857i	$0.815063\pi$
$564$	−0.105171	−	0.0761265i	−0.00442849	−	0.00320550i
$565$	−12.9439	−	7.47314i	−0.544552	−	0.314397i
$566$	−18.5844	+	32.1891i	−0.781160	+	1.35301i
$567$	8.98535	−	6.62610i	0.377349	−	0.278270i
$568$	26.6116	+	15.3642i	1.11660	+	0.644667i
$569$	−3.72486	−	6.45165i	−0.156154	−	0.270467i	0.777324	−	0.629100i	$-0.216576\pi$
$569$	−3.72486	−	6.45165i	−0.156154	−	0.270467i	−0.933479	+	0.358633i	$0.883243\pi$
$570$	30.1203	+	3.11179i	1.26160	+	0.130339i
$571$			28.7506i			1.20318i	0.798806	+	0.601588i	$0.205465\pi$
$571$			28.7506i			1.20318i	−0.798806	+	0.601588i	$0.794535\pi$
$572$	−4.12529	+	2.46390i	−0.172487	+	0.103021i
$573$	12.7032	−	17.5498i	0.530685	−	0.733154i
$574$	8.03396	+	13.9152i	0.335331	+	0.580810i
$575$	−71.6311	+	41.3562i	−2.98722	+	1.72467i
$576$	26.1260	+	5.45650i	1.08858	+	0.227354i
$577$			22.5576i			0.939085i	0.882910	+	0.469542i	$0.155581\pi$
$577$			22.5576i			0.939085i	−0.882910	+	0.469542i	$0.844419\pi$
$578$	7.34643	+	4.24146i	0.305571	+	0.176422i
$579$	38.7515	−	17.3357i	1.61046	−	0.720446i
$580$	13.9358			0.578654
$581$	−5.04036	−	2.91005i	−0.209109	−	0.120729i
$582$	1.33746	−	12.9458i	0.0554396	−	0.536622i
$583$	−0.407510	−	3.22816i	−0.0168773	−	0.133697i
$584$			4.78996i			0.198210i
$585$	29.8567	+	33.3263i	1.23442	+	1.37787i
$586$	9.35761			0.386559
$587$	−18.8884	−	32.7156i	−0.779606	−	1.35032i	−0.932169	−	0.362023i	$-0.882086\pi$
$587$	−18.8884	−	32.7156i	−0.779606	−	1.35032i	0.152563	−	0.988294i	$-0.451247\pi$
$588$	−0.390597	+	3.78074i	−0.0161079	+	0.155915i
$589$	0.704765	+	0.406896i	0.0290393	+	0.0167659i
$590$		−	44.2225i		−	1.82061i
$591$	−6.22754	−	13.9208i	−0.256167	−	0.572625i
$592$	−2.98415	−	1.72290i	−0.122648	−	0.0708107i
$593$		−	11.8238i		−	0.485547i	−0.970083	−	0.242773i	$-0.921943\pi$
$593$		−	11.8238i		−	0.485547i	0.970083	−	0.242773i	$-0.0780572\pi$
$594$	−7.27235	−	20.5371i	−0.298388	−	0.842647i
$595$	−12.4932	−	21.6388i	−0.512170	−	0.887104i
$596$	1.47170	−	0.849684i	0.0602830	−	0.0348044i
$597$	2.09264	+	1.51473i	0.0856461	+	0.0619939i
$598$	28.5129	−	12.4888i	1.16598	−	0.510706i
$599$			27.2805i			1.11465i	0.830294	+	0.557325i	$0.188172\pi$
$599$			27.2805i			1.11465i	−0.830294	+	0.557325i	$0.811828\pi$
$600$	−63.3595	−	6.54581i	−2.58664	−	0.267231i
$601$	17.7218	−	10.2317i	0.722889	−	0.417360i	−0.0929263	−	0.995673i	$-0.529622\pi$
$601$	17.7218	−	10.2317i	0.722889	−	0.417360i	0.815815	+	0.578313i	$0.196289\pi$
$602$	3.14075	−	5.43994i	0.128008	−	0.221716i
$603$	25.6781	−	8.44409i	1.04569	−	0.343870i
$604$	−0.124628	+	0.215862i	−0.00507104	+	0.00878330i
$605$	−44.0754	+	11.3080i	−1.79192	+	0.459736i
$606$	−17.4805	+	24.1498i	−0.710099	+	0.981020i
$607$	−8.75317	−	5.05365i	−0.355280	−	0.205121i	0.311728	−	0.950171i	$-0.399092\pi$
$607$	−8.75317	−	5.05365i	−0.355280	−	0.205121i	−0.667008	+	0.745050i	$0.732426\pi$
$608$	−6.47371	+	3.73760i	−0.262544	+	0.151580i
$609$	1.85118	−	17.9184i	0.0750138	−	0.726088i
$610$	1.94419			0.0787179
$611$	−0.541746	−	0.398626i	−0.0219167	−	0.0161267i
$612$	1.83364	+	5.57602i	0.0741206	+	0.225397i
$613$	−10.5185	−	18.2186i	−0.424839	−	0.735843i	0.571566	−	0.820556i	$-0.306336\pi$
$613$	−10.5185	−	18.2186i	−0.424839	−	0.735843i	−0.996405	+	0.0847131i	$0.973003\pi$
$614$	15.2998	−	8.83336i	0.617451	−	0.356485i
$615$	29.9780	+	67.0117i	1.20883	+	2.70217i
$616$	−11.5157	−	4.84198i	−0.463979	−	0.195089i
$617$	13.6536	−	23.6488i	0.549674	−	0.952063i	−0.448623	−	0.893721i	$-0.648085\pi$
$617$	13.6536	−	23.6488i	0.549674	−	0.952063i	0.998297	−	0.0583419i	$-0.0185813\pi$
$618$	−2.19781	−	4.91290i	−0.0884089	−	0.197626i
$619$			2.36601i			0.0950981i	0.998869	+	0.0475491i	$0.0151410\pi$
$619$			2.36601i			0.0950981i	−0.998869	+	0.0475491i	$0.984859\pi$
$620$	−0.350411	−	0.202310i	−0.0140729	−	0.00812497i
$621$	−7.56233	−	34.6702i	−0.303466	−	1.39127i
$622$	−15.6338	−	27.0786i	−0.626860	−	1.08575i
$623$	11.4699			0.459531
$624$	18.5218	+	4.01968i	0.741464	+	0.160916i
$625$	61.1336			2.44535
$626$	−7.77012	+	4.48608i	−0.310557	+	0.179300i
$627$	16.8445	+	9.22351i	0.672705	+	0.368352i
$628$	3.75413	−	6.50235i	0.149806	−	0.259472i
$629$		−	5.52857i		−	0.220439i
$630$	−3.97869	+	19.0501i	−0.158515	+	0.758975i
$631$	−12.7129	−	7.33977i	−0.506091	−	0.292192i	0.225135	−	0.974328i	$-0.427718\pi$
$631$	−12.7129	−	7.33977i	−0.506091	−	0.292192i	−0.731225	+	0.682136i	$0.761051\pi$
$632$	21.3511			0.849300
$633$	−11.3587	−	25.3908i	−0.451467	−	1.00919i
$634$	0.404306	−	0.233426i	0.0160570	−	0.00927053i
$635$	−5.54021	+	3.19864i	−0.219856	+	0.126934i
$636$	0.400352	−	0.553096i	0.0158750	−	0.0219317i
$637$	−2.17655	+	19.5700i	−0.0862381	+	0.775392i
$638$	−32.4050	−	13.6253i	−1.28293	−	0.539432i
$639$	20.2350	−	22.6341i	0.800482	−	0.895390i
$640$	−24.2705	+	14.0126i	−0.959376	+	0.553896i
$641$	−13.4694	−	7.77658i	−0.532010	−	0.307156i	0.209824	−	0.977739i	$-0.432711\pi$
$641$	−13.4694	−	7.77658i	−0.532010	−	0.307156i	−0.741835	+	0.670583i	$0.766044\pi$
$642$	−9.93103	+	13.7200i	−0.391947	+	0.541484i
$643$	0.116777	+	0.0674214i	0.00460525	+	0.00265884i	0.502301	−	0.864693i	$-0.332487\pi$
$643$	0.116777	+	0.0674214i	0.00460525	+	0.00265884i	−0.497696	+	0.867352i	$0.665820\pi$
$644$	−2.94795	−	1.70200i	−0.116166	−	0.0670683i
$645$	16.8277	−	23.2479i	0.662591	−	0.915386i
$646$	17.8220	+	10.2895i	0.701196	+	0.404835i
$647$	−16.4081	+	9.47325i	−0.645071	+	0.372432i	−0.786565	−	0.617507i	$-0.788143\pi$
$647$	−16.4081	+	9.47325i	−0.645071	+	0.372432i	0.141494	+	0.989939i	$0.454809\pi$
$648$	10.9377	−	25.0429i	0.429673	−	0.983777i
$649$	10.8709	−	25.8542i	0.426720	−	1.01486i
$650$	−54.8678	−	6.10233i	−2.15209	−	0.239353i
$651$	−0.306673	+	0.423677i	−0.0120195	+	0.0166052i
$652$	−0.0340413	+	0.0196538i	−0.00133316	+	0.000769701i
$653$	−15.8414	+	9.14605i	−0.619923	+	0.357913i	−0.776839	−	0.629699i	$-0.783178\pi$
$653$	−15.8414	+	9.14605i	−0.619923	+	0.357913i	0.156916	+	0.987612i	$0.449845\pi$
$654$	−8.96400	−	20.0378i	−0.350520	−	0.783540i
$655$	89.3716			3.49204
$656$	26.9298	+	15.5479i	1.05143	+	0.607044i
$657$	4.63264	+	0.967544i	0.180737	+	0.0377475i
$658$		−	0.292541i		−	0.0114044i
$659$	22.9370	−	39.7281i	0.893499	−	1.54759i	0.0578482	−	0.998325i	$-0.481576\pi$
$659$	22.9370	−	39.7281i	0.893499	−	1.54759i	0.835651	−	0.549261i	$-0.185091\pi$
$660$	−8.37515	−	4.58596i	−0.326002	−	0.178508i
$661$	−21.6055	+	12.4739i	−0.840355	+	0.485179i	−0.857385	−	0.514676i	$-0.827912\pi$
$661$	−21.6055	+	12.4739i	−0.840355	+	0.485179i	0.0170300	+	0.999855i	$0.494579\pi$
$662$	−5.89504			−0.229117
$663$	9.27324	+	28.9604i	0.360143	+	1.12473i
$664$	−14.2461			−0.552855
$665$	−8.57729	−	14.8563i	−0.332613	−	0.576102i
$666$	−2.86995	+	3.21022i	−0.111208	+	0.124394i
$667$	−49.5852	−	28.6281i	−1.91995	−	1.10848i
$668$			0.601121i			0.0232581i
$669$	8.70481	+	19.4584i	0.336547	+	0.752305i
$670$	−23.5596	+	40.8064i	−0.910185	+	1.57649i
$671$	1.13665	+	0.477926i	0.0438798	+	0.0184501i
$672$	−1.96185	−	4.38545i	−0.0756801	−	0.169172i
$673$	25.9850	−	15.0025i	1.00165	−	0.578303i	0.0929139	−	0.995674i	$-0.470382\pi$
$673$	25.9850	−	15.0025i	1.00165	−	0.578303i	0.908736	+	0.417371i	$0.137049\pi$
$674$	−8.89196	−	15.4013i	−0.342506	−	0.593237i
$675$	−19.1291	+	59.9563i	−0.736278	+	2.30772i
$676$	−5.09603	−	1.14774i	−0.196001	−	0.0441440i
$677$	−3.90531			−0.150093			−0.0750467	−	0.997180i	$-0.523911\pi$
$677$	−3.90531			−0.150093			−0.0750467	+	0.997180i	$0.523911\pi$
$678$	−0.813030	+	7.86965i	−0.0312242	+	0.302232i
$679$	−6.38531	+	3.68656i	−0.245046	+	0.141477i
$680$	−52.9660	−	30.5799i	−2.03115	−	1.17269i
$681$	−5.16383	+	7.13396i	−0.197878	+	0.273374i
$682$	0.617011	+	0.813036i	0.0236266	+	0.0311328i
$683$	3.02787	−	5.24443i	0.115858	−	0.200672i	−0.802264	−	0.596969i	$-0.796371\pi$
$683$	3.02787	−	5.24443i	0.115858	−	0.200672i	0.918123	+	0.396297i	$0.129705\pi$
$684$	1.25890	+	3.82827i	0.0481354	+	0.146377i
$685$	9.26876	−	16.0540i	0.354141	−	0.613391i
$686$	−16.9236	+	9.77085i	−0.646146	+	0.373053i
$687$	−13.0037	−	1.34344i	−0.496122	−	0.0512554i
$688$		−	12.1564i		−	0.463459i
$689$	2.09639	−	2.84906i	0.0798660	−	0.108540i
$690$	50.1075	+	36.2697i	1.90756	+	1.38076i
$691$	−1.34003	+	0.773665i	−0.0509771	+	0.0294316i	−0.525272	−	0.850934i	$-0.676036\pi$
$691$	−1.34003	+	0.773665i	−0.0509771	+	0.0294316i	0.474295	+	0.880366i	$0.342703\pi$
$692$	−1.07259	−	1.85778i	−0.0407738	−	0.0706223i
$693$	−7.00904	+	10.1594i	−0.266252	+	0.385923i
$694$			4.64864i			0.176460i
$695$	2.55269	+	1.47380i	0.0968292	+	0.0559044i
$696$	−18.0055	−	40.2489i	−0.682498	−	1.52563i
$697$			49.8913i			1.88977i
$698$	5.61402	+	3.24125i	0.212494	+	0.122683i
$699$	3.20791	−	31.0507i	0.121334	−	1.17444i
$700$	3.01853	+	5.22824i	0.114090	+	0.197609i
$701$	−22.5407			−0.851350			−0.425675	−	0.904876i	$-0.639963\pi$
$701$	−22.5407			−0.851350			−0.425675	+	0.904876i	$0.639963\pi$
$702$	9.64909	−	21.6300i	0.364181	−	0.816371i
$703$		−	3.79569i		−	0.143157i
$704$	−29.2742	+	3.69547i	−1.10331	+	0.139278i
$705$	0.137353	−	1.32949i	0.00517301	−	0.0500716i
$706$	9.75399	+	5.63147i	0.367096	+	0.211943i
$707$	16.8894			0.635191
$708$	5.37236	−	2.40335i	0.201905	−	0.0903233i
$709$	26.8935	+	15.5270i	1.01001	+	0.583127i	0.911193	−	0.411979i	$-0.135162\pi$
$709$	26.8935	+	15.5270i	1.01001	+	0.583127i	0.0988125	+	0.995106i	$0.468496\pi$
$710$			52.9230i			1.98617i
$711$	4.31279	−	20.6498i	0.161742	−	0.774429i
$712$	24.3138	−	14.0376i	0.911199	−	0.526081i
$713$	0.831202	+	1.43968i	0.0311288	+	0.0539166i
$714$	−7.75509	+	10.7139i	−0.290227	+	0.400956i
$715$	−43.2011	−	24.0963i	−1.61563	−	0.901152i
$716$		−	1.80518i		−	0.0674629i
$717$	29.9185	+	3.09094i	1.11733	+	0.115433i
$718$	−15.6109	−	27.0390i	−0.582595	−	1.00908i
$719$	29.1335	+	16.8202i	1.08650	+	0.627289i	0.932641	−	0.360805i	$-0.117498\pi$
$719$	29.1335	+	16.8202i	1.08650	+	0.627289i	0.153855	+	0.988094i	$0.450831\pi$
$720$	11.7653	+	35.7778i	0.438468	+	1.33336i
$721$	−1.52454	+	2.64057i	−0.0567767	+	0.0983401i
$722$	−8.56579	−	4.94546i	−0.318786	−	0.184051i
$723$	−20.2940	−	14.6895i	−0.754741	−	0.546310i
$724$	2.98823	−	5.17577i	0.111057	−	0.192356i
$725$	50.7723	+	87.9402i	1.88564	+	3.26602i
$726$	14.9910	+	18.8523i	0.556368	+	0.699674i
$727$	28.3059			1.04981			0.524904	−	0.851162i	$-0.324101\pi$
$727$	28.3059			1.04981			0.524904	+	0.851162i	$0.324101\pi$
$728$	−5.44859	−	12.4395i	−0.201938	−	0.461039i
$729$	−22.0110	−	15.6370i	−0.815223	−	0.579147i
$730$	−7.14443	+	4.12484i	−0.264427	+	0.152667i
$731$	16.8912	−	9.75212i	0.624743	−	0.360695i
$732$	0.105660	+	0.236189i	0.00390532	+	0.00872980i
$733$	2.55702			0.0944459			0.0472229	−	0.998884i	$-0.484963\pi$
$733$	2.55702			0.0944459			0.0472229	+	0.998884i	$0.484963\pi$
$734$	10.2151	+	5.89766i	0.377044	+	0.217687i
$735$	−35.7176	+	15.9784i	−1.31746	+	0.589373i
$736$	−15.2702			−0.562869
$737$	−23.8050	+	18.0655i	−0.876867	+	0.665451i
$738$	25.8992	−	28.9699i	0.953363	−	1.06640i
$739$	−5.02824	−	8.70917i	−0.184967	−	0.320372i	0.758598	−	0.651558i	$-0.225884\pi$
$739$	−5.02824	−	8.70917i	−0.184967	−	0.320372i	−0.943565	+	0.331186i	$0.892551\pi$
$740$			1.88723i			0.0693759i
$741$	6.36662	+	19.8830i	0.233884	+	0.730420i
$742$	1.53848			0.0564795
$743$	1.15594	−	0.667382i	0.0424073	−	0.0244839i	−0.478646	−	0.878008i	$-0.658872\pi$
$743$	1.15594	−	0.667382i	0.0424073	−	0.0244839i	0.521054	+	0.853524i	$0.325539\pi$
$744$	−0.131561	+	1.27344i	−0.00482328	+	0.0466864i
$745$	15.1506	+	8.74722i	0.555076	+	0.320473i
$746$	−8.73160			−0.319687
$747$	−2.87762	+	13.7782i	−0.105287	+	0.504117i
$748$	−3.92294	−	5.16927i	−0.143437	−	0.189007i
$749$	9.59519			0.350600
$750$	−26.3043	−	58.7998i	−0.960499	−	2.14706i
$751$	26.3536	+	45.6458i	0.961657	+	1.66564i	0.718340	+	0.695692i	$0.244902\pi$
$751$	26.3536	+	45.6458i	0.961657	+	1.66564i	0.243316	+	0.969947i	$0.421765\pi$
$752$	−0.283074	−	0.490298i	−0.0103226	−	0.0178793i
$753$	−20.1398	+	27.8237i	−0.733936	+	1.01395i
$754$	−15.3323	−	35.0048i	−0.558370	−	1.27480i
$755$	−2.56601			−0.0933867
$756$	−2.53053	+	0.551963i	−0.0920344	+	0.0200747i
$757$	20.1608	+	34.9196i	0.732759	+	1.26918i	0.955700	+	0.294343i	$0.0951009\pi$
$757$	20.1608	+	34.9196i	0.732759	+	1.26918i	−0.222941	+	0.974832i	$0.571566\pi$
$758$	3.26312	−	5.65189i	0.118522	−	0.205286i
$759$	20.3789	+	33.5222i	0.739707	+	1.21678i
$760$	−36.3643	−	20.9949i	−1.31907	−	0.761566i
$761$	−27.7586	−	16.0265i	−1.00625	−	0.580959i	−0.0961585	−	0.995366i	$-0.530656\pi$
$761$	−27.7586	−	16.0265i	−1.00625	−	0.580959i	−0.910092	+	0.414407i	$0.863989\pi$
$762$	2.74308	+	1.98555i	0.0993714	+	0.0719287i
$763$	−6.21798	+	10.7699i	−0.225106	+	0.389895i
$764$	−4.35271	+	2.51304i	−0.157476	+	0.0909185i
$765$	−40.2744	+	45.0494i	−1.45612	+	1.62877i
$766$			36.1991i			1.30793i
$767$	27.9284	−	12.2328i	1.00843	−	0.441701i
$768$	−12.9480	−	9.37223i	−0.467220	−	0.338191i
$769$	8.80597	+	15.2524i	0.317551	+	0.550015i	0.979977	−	0.199113i	$-0.0638061\pi$
$769$	8.80597	+	15.2524i	0.317551	+	0.550015i	−0.662425	+	0.749128i	$0.730473\pi$
$770$	−2.69460	−	21.3457i	−0.0971067	−	0.769247i
$771$	11.2279	+	25.0984i	0.404363	+	0.903898i
$772$	−9.84860			−0.354459
$773$	−3.49632	+	6.05581i	−0.125754	+	0.217812i	−0.922027	−	0.387125i	$-0.873468\pi$
$773$	−3.49632	+	6.05581i	−0.125754	+	0.217812i	0.796273	+	0.604937i	$0.206802\pi$
$774$	−14.8705	−	3.10575i	−0.534508	−	0.111634i
$775$		−	2.94830i		−	0.105906i
$776$	−9.02372	+	15.6295i	−0.323933	+	0.561068i
$777$	2.42656	+	0.250693i	0.0870522	+	0.00899355i
$778$	12.5024	+	21.6549i	0.448234	+	0.776365i
$779$			34.2533i			1.22725i
$780$	−3.16550	−	9.88589i	−0.113343	−	0.353972i
$781$	−13.0097	+	30.9409i	−0.465523	+	1.10715i
$782$	21.0193	+	36.4065i	0.751648	+	1.30189i
$783$	−42.5640	+	9.28413i	−1.52111	+	0.331788i
$784$	−8.28711	+	14.3537i	−0.295968	+	0.512632i
$785$	77.2952			2.75878
$786$	−19.3182	−	43.1831i	−0.689056	−	1.54029i
$787$	−4.74047	+	8.21073i	−0.168979	+	0.292681i	−0.938061	−	0.346469i	$-0.887380\pi$
$787$	−4.74047	+	8.21073i	−0.168979	+	0.292681i	0.769082	+	0.639150i	$0.220714\pi$
$788$			3.53794i			0.126034i
$789$	−23.0864	+	10.3278i	−0.821897	+	0.367680i
$790$	18.3863	+	31.8460i	0.654156	+	1.13303i
$791$	3.88157	−	2.24102i	0.138013	−	0.0796816i
$792$	−2.42403	+	30.1140i	−0.0861343	+	1.07005i
$793$	0.537800	+	1.22784i	0.0190979	+	0.0436018i
$794$	21.5646			0.765300
$795$	6.99185	+	0.722343i	0.247975	+	0.0256189i
$796$	−0.299655	−	0.519017i	−0.0106210	−	0.0183961i
$797$	−32.1913	−	18.5857i	−1.14027	−	0.658338i	−0.193776	−	0.981046i	$-0.562073\pi$
$797$	−32.1913	−	18.5857i	−1.14027	−	0.658338i	−0.946499	+	0.322708i	$0.895407\pi$
$798$	−5.32432	+	7.35569i	−0.188479	+	0.260389i
$799$	0.454174	−	0.786653i	0.0160675	−	0.0278298i
$800$	23.4537	+	13.5410i	0.829214	+	0.478747i
$801$	−8.66530	−	26.3508i	−0.306173	−	0.931059i
$802$	−3.02431	−	1.74609i	−0.106792	−	0.0616564i
$803$	−5.19089	+	0.655278i	−0.183183	+	0.0231243i
$804$	−6.23773	−	0.644434i	−0.219988	−	0.0227274i
$805$		−	35.0431i		−	1.23511i
$806$	−0.122648	+	1.10277i	−0.00432010	+	0.0388433i
$807$	18.2750	−	25.2474i	0.643311	−	0.888751i
$808$	35.8021	−	20.6704i	1.25951	−	0.727181i
$809$	−14.5736	−	25.2421i	−0.512379	−	0.887467i	−0.999897	−	0.0143535i	$-0.995431\pi$
$809$	−14.5736	−	25.2421i	−0.512379	−	0.887467i	0.487518	−	0.873113i	$-0.337902\pi$
$810$	46.7714	−	5.25146i	1.64338	−	0.184518i
$811$	38.5706			1.35440			0.677199	−	0.735800i	$-0.263194\pi$
$811$	38.5706			1.35440			0.677199	+	0.735800i	$0.263194\pi$
$812$	−2.08952	+	3.61915i	−0.0733277	+	0.127007i
$813$	−3.95968	+	1.77138i	−0.138872	+	0.0621251i
$814$	1.84518	−	4.38838i	0.0646736	−	0.153813i
$815$	−0.350444	−	0.202329i	−0.0122755	−	0.00708728i
$816$	−2.63038	+	25.4605i	−0.0920816	+	0.891295i
$817$	11.5968	−	6.69540i	0.405720	−	0.234243i
$818$		−	1.33613i		−	0.0467165i
$819$	−13.1315	+	2.75693i	−0.458853	+	0.0963348i
$820$		−	17.0309i		−	0.594744i
$821$	40.9400	−	23.6367i	1.42882	−	0.824928i	0.431790	−	0.901974i	$-0.357882\pi$
$821$	40.9400	−	23.6367i	1.42882	−	0.824928i	0.997028	+	0.0770461i	$0.0245488\pi$
$822$	−9.76054	−	1.00838i	−0.340438	−	0.0351714i
$823$	9.28339	−	16.0793i	0.323599	−	0.560489i	−0.657629	−	0.753342i	$-0.728441\pi$
$823$	9.28339	−	16.0793i	0.323599	−	0.560489i	0.981228	+	0.192853i	$0.0617739\pi$
$824$			7.46331i			0.259997i
$825$	−1.57402	−	69.5583i	−0.0548003	−	2.42171i
$826$	11.4846	+	6.63065i	0.399601	+	0.230710i
$827$		−	4.75897i		−	0.165486i	−0.996571	−	0.0827428i	$-0.973632\pi$
$827$		−	4.75897i		−	0.165486i	0.996571	−	0.0827428i	$-0.0263680\pi$
$828$	−1.68303	+	8.05844i	−0.0584895	+	0.280050i
$829$	−7.80515	−	13.5189i	−0.271084	−	0.469532i	0.698056	−	0.716044i	$-0.254049\pi$
$829$	−7.80515	−	13.5189i	−0.271084	−	0.469532i	−0.969140	+	0.246512i	$0.920715\pi$
$830$	−12.2679	−	21.2486i	−0.425825	−	0.737550i
$831$	19.9436	−	27.5525i	0.691834	−	0.955787i
$832$	−25.8364	−	19.0109i	−0.895717	−	0.659084i
$833$	−26.5923			−0.921370
$834$	0.160340	−	1.55199i	0.00555212	−	0.0537412i
$835$	−5.35927	+	3.09417i	−0.185465	+	0.107078i
$836$	−2.69333	−	3.54900i	−0.0931507	−	0.122745i
$837$	1.20504	+	0.384467i	0.0416522	+	0.0132891i
$838$	−23.0779	+	39.9721i	−0.797212	+	1.38081i
$839$	20.5657	−	35.6208i	0.710006	−	1.22977i	−0.254848	−	0.966981i	$-0.582026\pi$
$839$	20.5657	−	35.6208i	0.710006	−	1.22977i	0.964854	−	0.262785i	$-0.0846411\pi$
$840$	15.8236	−	21.8607i	0.545967	−	0.754267i
$841$	−20.6461	+	35.7602i	−0.711936	+	1.23311i
$842$	−16.7222	−	28.9637i	−0.576285	−	0.998155i
$843$	−23.2362	−	2.40058i	−0.800296	−	0.0826803i
$844$			6.45300i			0.222122i
$845$	−15.9983	−	51.3412i	−0.550359	−	1.76619i
$846$	−0.672082	+	0.221010i	−0.0231067	+	0.00759849i
$847$	3.67189	−	13.1419i	0.126168	−	0.451562i
$848$	2.57849	−	1.48869i	0.0885458	−	0.0511219i
$849$	−20.7953	−	46.4850i	−0.713692	−	1.59536i
$850$		−	74.5561i		−	2.55725i
$851$	3.87689	−	6.71498i	0.132898	−	0.230186i
$852$	−6.42934	+	2.87620i	−0.220266	+	0.0985368i
$853$	−40.1240			−1.37382			−0.686910	−	0.726742i	$-0.741034\pi$
$853$	−40.1240			−1.37382			−0.686910	+	0.726742i	$0.741034\pi$
$854$	−0.291509	+	0.504908i	−0.00997523	+	0.0172776i
$855$	−27.6507	+	30.9291i	−0.945635	+	1.05775i
$856$	20.3399	−	11.7432i	0.695202	−	0.401375i
$857$	36.7938			1.25685			0.628425	−	0.777870i	$-0.283700\pi$
$857$	36.7938			1.25685			0.628425	+	0.777870i	$0.283700\pi$
$858$	−2.30486	+	26.0827i	−0.0786867	+	0.890448i
$859$	2.24175			0.0764874			0.0382437	−	0.999268i	$-0.487824\pi$
$859$	2.24175			0.0764874			0.0382437	+	0.999268i	$0.487824\pi$
$860$	−5.76596	+	3.32898i	−0.196617	+	0.113517i
$861$	−21.8979	−	2.26232i	−0.746278	−	0.0770996i
$862$	20.3071	−	35.1730i	0.691664	−	1.19800i
$863$	−13.8565			−0.471681			−0.235841	−	0.971792i	$-0.575784\pi$
$863$	−13.8565			−0.471681			−0.235841	+	0.971792i	$0.575784\pi$
$864$	−8.59295	+	7.82028i	−0.292338	+	0.266051i
$865$	11.0420	−	19.1253i	0.375439	−	0.650279i
$866$			39.4512i			1.34061i
$867$	−10.6091	+	4.74605i	−0.360305	+	0.161184i
$868$	0.105080	−	0.0606682i	0.00356666	−	0.00205921i
$869$	2.92087	+	23.1382i	0.0990839	+	0.784909i
$870$	44.5277	−	61.5161i	1.50963	−	2.08559i
$871$	−32.2880	−	3.59103i	−1.09404	−	0.121677i
$872$			30.4399i			1.03083i
$873$	13.2935	+	11.8844i	0.449916	+	0.402227i
$874$	14.4310	+	24.9952i	0.488135	+	0.845474i
$875$	−18.2463	+	31.6035i	−0.616838	+	1.06839i
$876$	−0.889382	−	0.643768i	−0.0300494	−	0.0217509i
$877$	8.79547	−	15.2342i	0.297002	−	0.514423i	−0.678447	−	0.734650i	$-0.737347\pi$
$877$	8.79547	−	15.2342i	0.297002	−	0.514423i	0.975449	+	0.220227i	$0.0706798\pi$
$878$	2.78077	−	4.81644i	0.0938466	−	0.162547i
$879$	−7.51744	+	10.3855i	−0.253557	+	0.350295i
$880$	−25.1710	−	33.1679i	−0.848515	−	1.11809i
$881$	−15.4359	+	8.91191i	−0.520048	+	0.300250i	−0.736954	−	0.675943i	$-0.763737\pi$
$881$	−15.4359	+	8.91191i	−0.520048	+	0.300250i	0.216906	+	0.976192i	$0.430403\pi$
$882$	15.4411	+	13.8044i	0.519929	+	0.464819i
$883$	−13.5495			−0.455978			−0.227989	−	0.973664i	$-0.573215\pi$
$883$	−13.5495			−0.455978			−0.227989	+	0.973664i	$0.573215\pi$
$884$	0.779794	−	7.01136i	0.0262273	−	0.235818i
$885$	49.0803	+	35.5261i	1.64982	+	1.19420i
$886$	13.4251	+	23.2529i	0.451025	+	0.781198i
$887$	−25.9762	−	44.9921i	−0.872195	−	1.51069i	−0.859721	−	0.510764i	$-0.829363\pi$
$887$	−25.9762	−	44.9921i	−0.872195	−	1.51069i	−0.0124736	−	0.999922i	$-0.503971\pi$
$888$	5.45063	−	2.43836i	0.182911	−	0.0818261i
$889$		−	1.91840i		−	0.0643410i
$890$	41.8753	+	24.1767i	1.40366	+	0.810406i
$891$	28.6353	+	8.42727i	0.959319	+	0.282324i
$892$		−	4.94530i		−	0.165581i
$893$	0.311817	−	0.540083i	0.0104346	−	0.0180732i
$894$	0.951642	−	9.21133i	0.0318277	−	0.308073i
$895$	16.0940	−	9.29189i	0.537964	−	0.310594i
$896$		−	8.40411i		−	0.280762i
$897$	−9.04514	+	41.6779i	−0.302008	+	1.39159i
$898$		−	46.4115i		−	1.54877i
$899$	1.76747	−	1.02045i	0.0589486	−	0.0340340i
$900$	9.73087	−	10.8846i	0.324362	−	0.362820i
$901$	4.13703	+	2.38852i	0.137825	+	0.0795730i
$902$	−16.6514	+	39.6020i	−0.554431	+	1.31860i
$903$	3.51439	+	7.85594i	0.116952	+	0.261429i
$904$	5.48543	−	9.50104i	0.182443	−	0.316000i
$905$	61.5257			2.04518
$906$	0.554657	+	1.23986i	0.0184272	+	0.0411916i
$907$	−17.3670	−	30.0805i	−0.576662	−	0.998808i	−0.995859	−	0.0909127i	$-0.971022\pi$
$907$	−17.3670	−	30.0805i	−0.576662	−	0.998808i	0.419197	−	0.907895i	$-0.362312\pi$
$908$	1.76937	−	1.02154i	0.0587185	−	0.0339011i
$909$	−12.7597	−	38.8015i	−0.423211	−	1.28697i
$910$	13.8621	−	18.8390i	0.459523	−	0.624507i
$911$		−	8.73289i		−	0.289334i	−0.989480	−	0.144667i	$-0.953789\pi$
$911$		−	8.73289i		−	0.289334i	0.989480	−	0.144667i	$-0.0462110\pi$
$912$	−1.80591	+	17.4801i	−0.0597996	+	0.578824i
$913$	−1.94889	−	15.4385i	−0.0644990	−	0.510940i
$914$	2.91002	+	1.68010i	0.0962551	+	0.0555729i
$915$	−1.56186	+	2.15776i	−0.0516336	+	0.0713332i
$916$	2.62649	+	1.51640i	0.0867815	+	0.0501033i
$917$	−13.4003	+	23.2099i	−0.442515	+	0.766459i
$918$	30.4728	+	9.72233i	1.00575	+	0.320885i
$919$	15.0596	+	8.69464i	0.496769	+	0.286810i	0.727378	−	0.686237i	$-0.240739\pi$
$919$	15.0596	+	8.69464i	0.496769	+	0.286810i	−0.230609	+	0.973046i	$0.574072\pi$
$920$	−42.8881	−	74.2844i	−1.41398	−	2.44909i
$921$	−2.48743	+	24.0768i	−0.0819634	+	0.793357i
$922$	−32.3167			−1.06429
$923$	−33.4231	+	14.6395i	−1.10014	+	0.481867i
$924$	2.44674	−	1.48742i	0.0804917	−	0.0489326i
$925$	−11.9091	+	6.87573i	−0.391569	+	0.226073i
$926$	−6.60709	−	11.4438i	−0.217123	−	0.376067i
$927$	7.21819	+	1.50754i	0.237076	+	0.0495143i
$928$			18.7470i			0.615401i
$929$	−13.3006	+	23.0372i	−0.436377	+	0.755828i	−0.997407	−	0.0719681i	$-0.977072\pi$
$929$	−13.3006	+	23.0372i	−0.436377	+	0.755828i	0.561030	+	0.827796i	$0.310405\pi$
$930$	−2.01268	+	0.900381i	−0.0659983	+	0.0295246i
$931$	−18.2572			−0.598355
$932$	−3.62092	+	6.27162i	−0.118607	+	0.205434i
$933$	42.6126	+	4.40240i	1.39507	+	0.144128i
$934$	19.1038	+	33.0888i	0.625096	+	1.08270i
$935$	25.8937	−	61.5828i	0.846813	−	2.01397i
$936$	−24.4621	+	21.9154i	−0.799570	+	0.716327i
$937$			42.2335i			1.37971i	0.723948	+	0.689854i	$0.242326\pi$
$937$			42.2335i			1.37971i	−0.723948	+	0.689854i	$0.757674\pi$
$938$	−7.06497	−	12.2369i	−0.230680	−	0.399549i
$939$	1.26326	−	12.2276i	0.0412248	−	0.399031i
$940$	−0.155037	+	0.268531i	−0.00505674	+	0.00875852i
$941$		−	15.9049i		−	0.518483i	−0.965812	−	0.259242i	$-0.916527\pi$
$941$		−	15.9049i		−	0.518483i	0.965812	−	0.259242i	$-0.0834726\pi$
$942$	−16.7078	−	37.3479i	−0.544368	−	1.21686i
$943$	−34.9861	+	60.5978i	−1.13931	+	1.97333i
$944$	25.6642			0.835300
$945$	−17.9465	−	19.7197i	−0.583799	−	0.641481i
$946$	16.6624	−	2.10340i	0.541742	−	0.0683874i
$947$	15.6897	+	27.1754i	0.509848	+	0.883082i	0.999935	+	0.0114088i	$0.00363162\pi$
$947$	15.6897	+	27.1754i	0.509848	+	0.883082i	−0.490087	+	0.871673i	$0.663035\pi$
$948$	−2.86957	+	3.96438i	−0.0931993	+	0.128757i
$949$	−4.58130	−	3.37100i	−0.148715	−	0.109427i
$950$		−	51.1871i		−	1.66073i
$951$	−0.0657314	+	0.636241i	−0.00213149	+	0.0206315i
$952$	15.8833	−	9.17022i	0.514780	−	0.297209i
$953$	−17.8965	+	30.9977i	−0.579726	+	1.00411i	0.415785	+	0.909463i	$0.363507\pi$
$953$	−17.8965	+	30.9977i	−0.579726	+	1.00411i	−0.995510	+	0.0946514i	$0.969826\pi$
$954$	−1.16230	−	3.53450i	−0.0376308	−	0.114434i
$955$	−44.8098	−	25.8709i	−1.45001	−	0.837163i
$956$	−6.04294	−	3.48889i	−0.195442	−	0.112839i
$957$	41.1546	−	25.0188i	1.33034	−	0.808743i
$958$	−10.3031	+	17.8454i	−0.332876	+	0.576559i
$959$	2.77949	+	4.81422i	0.0897544	+	0.155459i
$960$	6.55051	−	63.4050i	0.211417	−	2.04639i
$961$	30.9407			0.998088
$962$	4.74045	−	2.07635i	0.152838	−	0.0669441i
$963$	−7.24901	−	22.0439i	−0.233596	−	0.710355i
$964$	2.90599	+	5.03332i	0.0935955	+	0.162112i
$965$	−50.6941	−	87.8047i	−1.63190	−	2.82653i
$966$	−16.9323	+	7.57476i	−0.544789	+	0.243714i
$967$	17.9153			0.576117			0.288058	−	0.957613i	$-0.406990\pi$
$967$	17.9153			0.576117			0.288058	+	0.957613i	$0.406990\pi$
$968$	−8.30029	−	32.3522i	−0.266782	−	1.03984i
$969$	−25.7371	+	11.5136i	−0.826794	+	0.369870i
$970$	−31.0829			−0.998010
$971$	14.0000	+	8.08290i	0.449281	+	0.259393i	0.707527	−	0.706687i	$-0.249811\pi$
$971$	14.0000	+	8.08290i	0.449281	+	0.259393i	−0.258245	+	0.966079i	$0.583144\pi$
$972$	3.17985	+	5.39661i	0.101994	+	0.173096i
$973$	−0.765495	+	0.441959i	−0.0245406	+	0.0141685i
$974$	−30.7290			−0.984620
$975$	50.8508	−	55.9927i	1.62853	−	1.79320i
$976$			1.12830i			0.0361159i
$977$	12.3134	+	21.3274i	0.393939	+	0.682323i	0.992965	−	0.118407i	$-0.0377786\pi$
$977$	12.3134	+	21.3274i	0.393939	+	0.682323i	−0.599026	+	0.800730i	$0.704445\pi$
$978$	−0.0220121	+	0.213064i	−0.000703870	+	0.00681304i
$979$	18.5388	+	24.4286i	0.592501	+	0.780740i
$980$	9.07754			0.289971
$981$	29.4402	+	6.14868i	0.939952	+	0.196312i
$982$	18.0760	+	10.4362i	0.576828	+	0.333032i
$983$	−45.2956			−1.44471			−0.722353	−	0.691524i	$-0.756939\pi$
$983$	−45.2956			−1.44471			−0.722353	+	0.691524i	$0.756939\pi$
$984$	−49.1879	+	22.0044i	−1.56805	+	0.701476i
$985$	−31.5423	+	18.2110i	−1.00502	+	0.580250i
$986$	44.6956	−	25.8050i	1.42340	−	0.821798i
$987$	0.324677	+	0.235013i	0.0103346	+	0.00748055i
$988$	0.535375	−	4.81371i	0.0170325	−	0.153145i
$989$	27.3546			0.869825
$990$	−47.0038	+	22.3169i	−1.49388	+	0.709278i
$991$	−12.3767	−	21.4371i	−0.393159	−	0.680971i	0.599706	−	0.800221i	$-0.295284\pi$
$991$	−12.3767	−	21.4371i	−0.393159	−	0.680971i	−0.992864	+	0.119250i	$0.961951\pi$
$992$	0.272155	−	0.471387i	0.00864094	−	0.0149665i
$993$	4.73578	−	6.54260i	0.150285	−	0.207623i
$994$	−13.7442	−	7.93521i	−0.435939	−	0.251689i
$995$	3.08485	−	5.34312i	0.0977963	−	0.169388i
$996$	1.91466	−	2.64516i	0.0606684	−	0.0838150i
$997$	−7.55715	−	4.36312i	−0.239337	−	0.138181i	0.375535	−	0.926808i	$-0.377459\pi$
$997$	−7.55715	−	4.36312i	−0.239337	−	0.138181i	−0.614872	+	0.788627i	$0.710792\pi$
$998$	18.3495	+	31.7823i	0.580844	+	1.00605i
$999$	−1.25728	−	5.76414i	−0.0397787	−	0.182369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.t.a.296.16	yes	104
3.2	odd	2	inner	429.2.t.a.296.37	yes	104
11.10	odd	2	inner	429.2.t.a.296.38	yes	104
13.4	even	6	inner	429.2.t.a.329.15	yes	104
33.32	even	2	inner	429.2.t.a.296.15	✓	104
39.17	odd	6	inner	429.2.t.a.329.38	yes	104
143.43	odd	6	inner	429.2.t.a.329.37	yes	104
429.329	even	6	inner	429.2.t.a.329.16	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.t.a.296.15	✓	104	33.32	even	2	inner
429.2.t.a.296.16	yes	104	1.1	even	1	trivial
429.2.t.a.296.37	yes	104	3.2	odd	2	inner
429.2.t.a.296.38	yes	104	11.10	odd	2	inner
429.2.t.a.329.15	yes	104	13.4	even	6	inner
429.2.t.a.329.16	yes	104	429.329	even	6	inner
429.2.t.a.329.37	yes	104	143.43	odd	6	inner
429.2.t.a.329.38	yes	104	39.17	odd	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09482 + 0.632095i) q^{2} +(0.177995 - 1.72288i) q^{3} +(-0.200911 + 0.347987i) q^{4} -4.13662 q^{5} +(0.894153 + 1.99876i) q^{6} +(0.620239 - 1.07429i) q^{7} -3.03636i q^{8} +(-2.93664 - 0.613327i) q^{9} +O(q^{10})\)	\(q+(-1.09482 + 0.632095i) q^{2} +(0.177995 - 1.72288i) q^{3} +(-0.200911 + 0.347987i) q^{4} -4.13662 q^{5} +(0.894153 + 1.99876i) q^{6} +(0.620239 - 1.07429i) q^{7} -3.03636i q^{8} +(-2.93664 - 0.613327i) q^{9} +(4.52886 - 2.61474i) q^{10} +(3.29051 - 0.415381i) q^{11} +(0.563780 + 0.408085i) q^{12} +(2.90409 + 2.13688i) q^{13} +1.56820i q^{14} +(-0.736296 + 7.12691i) q^{15} +(1.51745 + 2.62830i) q^{16} +(-2.43465 + 4.21694i) q^{17} +(3.60277 - 1.18475i) q^{18} +(-1.67153 + 2.89518i) q^{19} +(0.831091 - 1.43949i) q^{20} +(-1.74047 - 1.25982i) q^{21} +(-3.33996 + 2.53468i) q^{22} +(-5.91424 + 3.41459i) q^{23} +(-5.23129 - 0.540456i) q^{24} +12.1116 q^{25} +(-4.53017 - 0.503840i) q^{26} +(-1.57939 + 4.95030i) q^{27} +(0.249225 + 0.431671i) q^{28} +(4.19202 + 7.26080i) q^{29} +(-3.69877 - 8.26810i) q^{30} -0.243427i q^{31} +(1.93646 + 1.11802i) q^{32} +(-0.129959 - 5.74309i) q^{33} -6.15573i q^{34} +(-2.56569 + 4.44391i) q^{35} +(0.803431 - 0.898689i) q^{36} +(-0.983279 + 0.567696i) q^{37} -4.22627i q^{38} +(4.19850 - 4.62305i) q^{39} +12.5603i q^{40} +(8.87337 - 5.12304i) q^{41} +(2.70182 + 0.279131i) q^{42} +(-3.46891 - 2.00277i) q^{43} +(-0.516551 + 1.22851i) q^{44} +(12.1478 + 2.53710i) q^{45} +(4.31669 - 7.47672i) q^{46} -0.186546 q^{47} +(4.79834 - 2.14656i) q^{48} +(2.73061 + 4.72955i) q^{49} +(-13.2601 + 7.65571i) q^{50} +(6.83194 + 4.94521i) q^{51} +(-1.32707 + 0.581265i) q^{52} -0.981050i q^{53} +(-1.39991 - 6.41803i) q^{54} +(-13.6116 + 1.71827i) q^{55} +(-3.26192 - 1.88327i) q^{56} +(4.69053 + 3.39518i) q^{57} +(-9.17904 - 5.29952i) q^{58} +(4.22819 - 7.32344i) q^{59} +(-2.33214 - 1.68809i) q^{60} +(0.321966 + 0.185887i) q^{61} +(0.153869 + 0.266509i) q^{62} +(-2.48030 + 2.77438i) q^{63} -8.89657 q^{64} +(-12.0131 - 8.83947i) q^{65} +(3.77246 + 6.20551i) q^{66} +(-7.80314 + 4.50514i) q^{67} +(-0.978296 - 1.69446i) q^{68} +(4.83022 + 10.7973i) q^{69} -6.48706i q^{70} +(-5.06007 + 8.76429i) q^{71} +(-1.86228 + 8.91669i) q^{72} -1.57753 q^{73} +(0.717676 - 1.24305i) q^{74} +(2.15581 - 20.8669i) q^{75} +(-0.671658 - 1.16334i) q^{76} +(1.59467 - 3.79258i) q^{77} +(-1.67440 + 7.71527i) q^{78} +7.03179i q^{79} +(-6.27711 - 10.8723i) q^{80} +(8.24766 + 3.60223i) q^{81} +(-6.47650 + 11.2176i) q^{82} -4.69182i q^{83} +(0.788078 - 0.352550i) q^{84} +(10.0712 - 17.4439i) q^{85} +5.06378 q^{86} +(13.2556 - 5.92998i) q^{87} +(-1.26125 - 9.99118i) q^{88} +(4.62316 + 8.00755i) q^{89} +(-14.9033 + 4.90087i) q^{90} +(4.09685 - 1.79445i) q^{91} -2.74411i q^{92} +(-0.419396 - 0.0433287i) q^{93} +(0.204234 - 0.117915i) q^{94} +(6.91450 - 11.9763i) q^{95} +(2.27089 - 3.13729i) q^{96} +(-5.14746 - 2.97189i) q^{97} +(-5.97905 - 3.45201i) q^{98} +(-9.91780 - 0.798335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9}+O(q^{10}) \) 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9	\( 104 q - 2 q^{3} + 44 q^{4} - 6 q^{9} - 4 q^{12} - 36 q^{15} - 44 q^{16} - 12 q^{22} + 64 q^{25} + 4 q^{27} + 12 q^{33} + 28 q^{36} - 12 q^{37} + 50 q^{42} - 66 q^{45} + 16 q^{48} - 24 q^{49} - 8 q^{55} - 24 q^{58} - 104 q^{64} - 60 q^{66} - 60 q^{67} - 42 q^{69} - 42 q^{75} + 16 q^{78} - 22 q^{81} - 16 q^{82} + 92 q^{88} - 84 q^{91} + 126 q^{93} + 36 q^{97}+O(q^{100}) \) 104 * q - 2 * q^3 + 44 * q^4 - 6 * q^9 - 4 * q^12 - 36 * q^15 - 44 * q^16 - 12 * q^22 + 64 * q^25 + 4 * q^27 + 12 * q^33 + 28 * q^36 - 12 * q^37 + 50 * q^42 - 66 * q^45 + 16 * q^48 - 24 * q^49 - 8 * q^55 - 24 * q^58 - 104 * q^64 - 60 * q^66 - 60 * q^67 - 42 * q^69 - 42 * q^75 + 16 * q^78 - 22 * q^81 - 16 * q^82 + 92 * q^88 - 84 * q^91 + 126 * q^93 + 36 * q^97

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