LMFDB - Embedded newform 429.2.n.d.196.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.7
Character	$\chi$	$=$	429.196
Dual form			429.2.n.d.313.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.423381 - 1.30303i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.0993922 + 0.0722127i) q^{4} +(-1.34435 - 4.13749i) q^{5} +(0.423381 + 1.30303i) q^{6} +(0.830818 + 0.603625i) q^{7} +(2.35303 - 1.70957i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.423381 - 1.30303i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.0993922 + 0.0722127i) q^{4} +(-1.34435 - 4.13749i) q^{5} +(0.423381 + 1.30303i) q^{6} +(0.830818 + 0.603625i) q^{7} +(2.35303 - 1.70957i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.96045 q^{10} +(-3.22981 + 0.753873i) q^{11} -0.122856 q^{12} +(-0.309017 + 0.951057i) q^{13} +(1.13829 - 0.827020i) q^{14} +(3.51956 + 2.55711i) q^{15} +(-1.15547 - 3.55619i) q^{16} +(-1.73313 - 5.33402i) q^{17} +(-1.10843 - 0.805318i) q^{18} +(2.08959 - 1.51817i) q^{19} +(0.165161 - 0.508313i) q^{20} -1.02695 q^{21} +(-0.385119 + 4.52772i) q^{22} -2.03571 q^{23} +(-0.898776 + 2.76615i) q^{24} +(-11.2664 + 8.18555i) q^{25} +(1.10843 + 0.805318i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.0389875 + 0.119991i) q^{28} +(-0.357214 - 0.259531i) q^{29} +(4.82211 - 3.50347i) q^{30} +(2.54507 - 7.83291i) q^{31} +0.693972 q^{32} +(2.16986 - 2.50833i) q^{33} -7.68418 q^{34} +(1.38058 - 4.24898i) q^{35} +(0.0993922 - 0.0722127i) q^{36} +(0.270672 + 0.196655i) q^{37} +(-1.09354 - 3.36557i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-10.2366 - 7.43735i) q^{40} +(-0.848531 + 0.616494i) q^{41} +(-0.434790 + 1.33815i) q^{42} +7.90290 q^{43} +(-0.375457 - 0.158304i) q^{44} -4.35041 q^{45} +(-0.861880 + 2.65259i) q^{46} +(1.04772 - 0.761210i) q^{47} +(3.02507 + 2.19784i) q^{48} +(-1.83722 - 5.65439i) q^{49} +(5.89604 + 18.1461i) q^{50} +(4.53739 + 3.29661i) q^{51} +(-0.0993922 + 0.0722127i) q^{52} +(-2.37727 + 7.31650i) q^{53} +1.37009 q^{54} +(7.46114 + 12.3498i) q^{55} +2.98688 q^{56} +(-0.798151 + 2.45646i) q^{57} +(-0.489415 + 0.355581i) q^{58} +(8.85798 + 6.43570i) q^{59} +(0.165161 + 0.508313i) q^{60} +(2.20527 + 6.78712i) q^{61} +(-9.12900 - 6.63261i) q^{62} +(0.830818 - 0.603625i) q^{63} +(2.60476 - 8.01664i) q^{64} +4.35041 q^{65} +(-2.34976 - 3.88937i) q^{66} +6.39450 q^{67} +(0.212924 - 0.655314i) q^{68} +(1.64692 - 1.19656i) q^{69} +(-4.95205 - 3.59788i) q^{70} +(2.27464 + 7.00062i) q^{71} +(-0.898776 - 2.76615i) q^{72} +(10.0853 + 7.32736i) q^{73} +(0.370845 - 0.269434i) q^{74} +(4.30340 - 13.2445i) q^{75} +0.317320 q^{76} +(-3.13844 - 1.32326i) q^{77} -1.37009 q^{78} +(2.59339 - 7.98163i) q^{79} +(-13.1603 + 9.56153i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.444059 + 1.36667i) q^{82} +(3.06616 + 9.43668i) q^{83} +(-0.102071 - 0.0741586i) q^{84} +(-19.7395 + 14.3416i) q^{85} +(3.34594 - 10.2977i) q^{86} +0.441540 q^{87} +(-6.31103 + 7.29548i) q^{88} +12.9003 q^{89} +(-1.84188 + 5.66873i) q^{90} +(-0.830818 + 0.603625i) q^{91} +(-0.202334 - 0.147004i) q^{92} +(2.54507 + 7.83291i) q^{93} +(-0.548299 - 1.68749i) q^{94} +(-9.09057 - 6.60468i) q^{95} +(-0.561435 + 0.407906i) q^{96} +(3.31927 - 10.2157i) q^{97} -8.14570 q^{98} +(-0.281091 + 3.30469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.423381	−	1.30303i	0.299375	−	0.921383i	−0.682341	−	0.731034i	$-0.739038\pi$
$2$	0.423381	−	1.30303i	0.299375	−	0.921383i	0.981716	−	0.190349i	$-0.0609619\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.0993922	+	0.0722127i	0.0496961	+	0.0361063i
$5$	−1.34435	−	4.13749i	−0.601212	−	1.85034i	−0.520988	−	0.853564i	$-0.674436\pi$
$5$	−1.34435	−	4.13749i	−0.601212	−	1.85034i	−0.0802245	−	0.996777i	$-0.525564\pi$
$6$	0.423381	+	1.30303i	0.172845	+	0.531961i
$7$	0.830818	+	0.603625i	0.314020	+	0.228149i	0.733619	−	0.679561i	$-0.237830\pi$
$7$	0.830818	+	0.603625i	0.314020	+	0.228149i	−0.419600	+	0.907709i	$0.637830\pi$
$8$	2.35303	−	1.70957i	0.831921	−	0.604426i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−5.96045			−1.88486
$11$	−3.22981	+	0.753873i	−0.973824	+	0.227301i
$11$	−3.22981	+	0.753873i	−0.973824	+	0.227301i
$12$	−0.122856			−0.0354653
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	1.13829	−	0.827020i	0.304222	−	0.221030i
$15$	3.51956	+	2.55711i	0.908746	+	0.660243i
$16$	−1.15547	−	3.55619i	−0.288869	−	0.889047i
$17$	−1.73313	−	5.33402i	−0.420346	−	1.29369i	−0.907381	−	0.420308i	$-0.861922\pi$
$17$	−1.73313	−	5.33402i	−0.420346	−	1.29369i	0.487036	−	0.873382i	$-0.338078\pi$
$18$	−1.10843	−	0.805318i	−0.261258	−	0.189815i
$19$	2.08959	−	1.51817i	0.479384	−	0.348293i	−0.321703	−	0.946841i	$-0.604255\pi$
$19$	2.08959	−	1.51817i	0.479384	−	0.348293i	0.801087	+	0.598548i	$0.204255\pi$
$20$	0.165161	−	0.508313i	0.0369311	−	0.113662i
$21$	−1.02695			−0.224098
$22$	−0.385119	+	4.52772i	−0.0821077	+	0.965314i
$23$	−2.03571			−0.424475			−0.212237	−	0.977218i	$-0.568075\pi$
$23$	−2.03571			−0.424475			−0.212237	+	0.977218i	$0.568075\pi$
$24$	−0.898776	+	2.76615i	−0.183462	+	0.564638i
$25$	−11.2664	+	8.18555i	−2.25329	+	1.63711i
$26$	1.10843	+	0.805318i	0.217380	+	0.157936i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.0389875	+	0.119991i	0.00736794	+	0.0226762i
$29$	−0.357214	−	0.259531i	−0.0663329	−	0.0481937i	0.554125	−	0.832434i	$-0.313053\pi$
$29$	−0.357214	−	0.259531i	−0.0663329	−	0.0481937i	−0.620458	+	0.784240i	$0.713053\pi$
$30$	4.82211	−	3.50347i	0.880392	−	0.639643i
$31$	2.54507	−	7.83291i	0.457108	−	1.40683i	−0.411535	−	0.911394i	$-0.635007\pi$
$31$	2.54507	−	7.83291i	0.457108	−	1.40683i	0.868643	−	0.495439i	$-0.164993\pi$
$32$	0.693972			0.122678
$33$	2.16986	−	2.50833i	0.377723	−	0.436644i
$34$	−7.68418			−1.31783
$35$	1.38058	−	4.24898i	0.233360	−	0.718209i
$36$	0.0993922	−	0.0722127i	0.0165654	−	0.0120354i
$37$	0.270672	+	0.196655i	0.0444982	+	0.0323298i	0.609812	−	0.792546i	$-0.291245\pi$
$37$	0.270672	+	0.196655i	0.0444982	+	0.0323298i	−0.565314	+	0.824876i	$0.691245\pi$
$38$	−1.09354	−	3.36557i	−0.177395	−	0.545967i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−10.2366	−	7.43735i	−1.61855	−	1.17595i
$41$	−0.848531	+	0.616494i	−0.132518	+	0.0962801i	−0.652070	−	0.758159i	$-0.726099\pi$
$41$	−0.848531	+	0.616494i	−0.132518	+	0.0962801i	0.519551	+	0.854439i	$0.326099\pi$
$42$	−0.434790	+	1.33815i	−0.0670895	+	0.206480i
$43$	7.90290			1.20518			0.602590	−	0.798051i	$-0.294135\pi$
$43$	7.90290			1.20518			0.602590	+	0.798051i	$0.294135\pi$
$44$	−0.375457	−	0.158304i	−0.0566023	−	0.0238652i
$45$	−4.35041			−0.648521
$46$	−0.861880	+	2.65259i	−0.127077	+	0.391104i
$47$	1.04772	−	0.761210i	0.152825	−	0.111034i	−0.508745	−	0.860917i	$-0.669890\pi$
$47$	1.04772	−	0.761210i	0.152825	−	0.111034i	0.661570	+	0.749883i	$0.269890\pi$
$48$	3.02507	+	2.19784i	0.436632	+	0.317231i
$49$	−1.83722	−	5.65439i	−0.262460	−	0.807770i
$50$	5.89604	+	18.1461i	0.833826	+	2.56625i
$51$	4.53739	+	3.29661i	0.635362	+	0.461617i
$52$	−0.0993922	+	0.0722127i	−0.0137832	+	0.0100141i
$53$	−2.37727	+	7.31650i	−0.326544	+	1.00500i	0.644195	+	0.764861i	$0.277192\pi$
$53$	−2.37727	+	7.31650i	−0.326544	+	1.00500i	−0.970739	+	0.240137i	$0.922808\pi$
$54$	1.37009			0.186446
$55$	7.46114	+	12.3498i	1.00606	+	1.66525i
$56$	2.98688			0.399138
$57$	−0.798151	+	2.45646i	−0.105718	+	0.325366i
$58$	−0.489415	+	0.355581i	−0.0642633	+	0.0466900i
$59$	8.85798	+	6.43570i	1.15321	+	0.837857i	0.988905	−	0.148552i	$-0.0474613\pi$
$59$	8.85798	+	6.43570i	1.15321	+	0.837857i	0.164307	+	0.986409i	$0.447461\pi$
$60$	0.165161	+	0.508313i	0.0213222	+	0.0656230i
$61$	2.20527	+	6.78712i	0.282356	+	0.869001i	0.987179	+	0.159618i	$0.0510263\pi$
$61$	2.20527	+	6.78712i	0.282356	+	0.869001i	−0.704823	+	0.709383i	$0.748974\pi$
$62$	−9.12900	−	6.63261i	−1.15938	−	0.842342i
$63$	0.830818	−	0.603625i	0.104673	−	0.0760496i
$64$	2.60476	−	8.01664i	0.325596	−	1.00208i
$65$	4.35041			0.539602
$66$	−2.34976	−	3.88937i	−0.289236	−	0.478749i
$67$	6.39450			0.781213			0.390606	−	0.920558i	$-0.372265\pi$
$67$	6.39450			0.781213			0.390606	+	0.920558i	$0.372265\pi$
$68$	0.212924	−	0.655314i	0.0258209	−	0.0794685i
$69$	1.64692	−	1.19656i	0.198266	−	0.144049i
$70$	−4.95205	−	3.59788i	−0.591883	−	0.430029i
$71$	2.27464	+	7.00062i	0.269950	+	0.830821i	0.990511	+	0.137430i	$0.0438842\pi$
$71$	2.27464	+	7.00062i	0.269950	+	0.830821i	−0.720561	+	0.693391i	$0.756116\pi$
$72$	−0.898776	−	2.76615i	−0.105922	−	0.325994i
$73$	10.0853	+	7.32736i	1.18039	+	0.857603i	0.992215	−	0.124533i	$-0.0397432\pi$
$73$	10.0853	+	7.32736i	1.18039	+	0.857603i	0.188174	+	0.982136i	$0.439743\pi$
$74$	0.370845	−	0.269434i	0.0431098	−	0.0313211i
$75$	4.30340	−	13.2445i	0.496914	−	1.52934i
$76$	0.317320			0.0363991
$77$	−3.13844	−	1.32326i	−0.357659	−	0.150800i
$78$	−1.37009			−0.155132
$79$	2.59339	−	7.98163i	0.291779	−	0.898003i	−0.692505	−	0.721413i	$-0.743493\pi$
$79$	2.59339	−	7.98163i	0.291779	−	0.898003i	0.984284	−	0.176591i	$-0.0565069\pi$
$80$	−13.1603	+	9.56153i	−1.47137	+	1.06901i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.444059	+	1.36667i	0.0490382	+	0.150924i
$83$	3.06616	+	9.43668i	0.336555	+	1.03581i	0.965951	+	0.258725i	$0.0833025\pi$
$83$	3.06616	+	9.43668i	0.336555	+	1.03581i	−0.629396	+	0.777085i	$0.716698\pi$
$84$	−0.102071	−	0.0741586i	−0.0111368	−	0.00809137i
$85$	−19.7395	+	14.3416i	−2.14105	+	1.55557i
$86$	3.34594	−	10.2977i	0.360801	−	1.11043i
$87$	0.441540			0.0473381
$88$	−6.31103	+	7.29548i	−0.672758	+	0.777701i
$89$	12.9003			1.36743			0.683714	−	0.729750i	$-0.260364\pi$
$89$	12.9003			1.36743			0.683714	+	0.729750i	$0.260364\pi$
$90$	−1.84188	+	5.66873i	−0.194151	+	0.597536i
$91$	−0.830818	+	0.603625i	−0.0870934	+	0.0632771i
$92$	−0.202334	−	0.147004i	−0.0210947	−	0.0153262i
$93$	2.54507	+	7.83291i	0.263911	+	0.812235i
$94$	−0.548299	−	1.68749i	−0.0565527	−	0.174051i
$95$	−9.09057	−	6.60468i	−0.932673	−	0.677626i
$96$	−0.561435	+	0.407906i	−0.0573012	+	0.0416318i
$97$	3.31927	−	10.2157i	0.337020	−	1.03724i	−0.628698	−	0.777650i	$-0.716412\pi$
$97$	3.31927	−	10.2157i	0.337020	−	1.03724i	0.965718	−	0.259593i	$-0.0835883\pi$
$98$	−8.14570			−0.822840
$99$	−0.281091	+	3.30469i	−0.0282507	+	0.332134i
$100$	−1.71090			−0.171090
$101$	3.43713	−	10.5784i	0.342008	−	1.05259i	−0.621159	−	0.783685i	$-0.713338\pi$
$101$	3.43713	−	10.5784i	0.342008	−	1.05259i	0.963166	−	0.268906i	$-0.0866622\pi$
$102$	6.21663	−	4.51665i	0.615538	−	0.447215i
$103$	−5.52980	−	4.01764i	−0.544868	−	0.395870i	0.281022	−	0.959701i	$-0.409327\pi$
$103$	−5.52980	−	4.01764i	−0.544868	−	0.395870i	−0.825890	+	0.563832i	$0.809327\pi$
$104$	0.898776	+	2.76615i	0.0881323	+	0.271243i
$105$	1.38058	+	4.24898i	0.134731	+	0.414658i
$106$	8.52714	+	6.19533i	0.828229	+	0.601744i
$107$	4.67282	−	3.39500i	0.451738	−	0.328207i	−0.338543	−	0.940951i	$-0.609934\pi$
$107$	4.67282	−	3.39500i	0.451738	−	0.328207i	0.790282	+	0.612744i	$0.209934\pi$
$108$	−0.0379644	+	0.116843i	−0.00365313	+	0.0112432i
$109$	−17.6727			−1.69274			−0.846368	−	0.532599i	$-0.821215\pi$
$109$	−17.6727			−1.69274			−0.846368	+	0.532599i	$0.821215\pi$
$110$	19.2511	−	4.49342i	1.83552	−	0.428431i
$111$	−0.334569			−0.0317559
$112$	1.18661	−	3.65202i	0.112124	−	0.345083i
$113$	−1.33346	+	0.968812i	−0.125441	+	0.0911382i	−0.648737	−	0.761013i	$-0.724702\pi$
$113$	−1.33346	+	0.968812i	−0.125441	+	0.0911382i	0.523296	+	0.852151i	$0.324702\pi$
$114$	2.86292	+	2.08003i	0.268137	+	0.194813i
$115$	2.73671	+	8.42272i	0.255199	+	0.785423i
$116$	−0.0167628	−	0.0515907i	−0.00155639	−	0.00479008i
$117$	0.809017	+	0.587785i	0.0747936	+	0.0543408i
$118$	12.1362	−	8.81749i	1.11723	−	0.811715i
$119$	1.77983	−	5.47776i	0.163157	−	0.502146i
$120$	12.6532			1.15507
$121$	9.86335	−	4.86973i	0.896668	−	0.442703i
$122$	9.77750			0.885213
$123$	0.324110	−	0.997507i	0.0292240	−	0.0899422i
$124$	0.818595	−	0.594744i	0.0735120	−	0.0534096i
$125$	31.4159	+	22.8250i	2.80992	+	2.04153i
$126$	−0.434790	−	1.33815i	−0.0387342	−	0.119212i
$127$	0.671907	+	2.06792i	0.0596221	+	0.183498i	0.976432	−	0.215827i	$-0.0692446\pi$
$127$	0.671907	+	2.06792i	0.0596221	+	0.183498i	−0.916810	+	0.399325i	$0.869245\pi$
$128$	−8.22026	−	5.97237i	−0.726576	−	0.527888i
$129$	−6.39358	+	4.64521i	−0.562923	+	0.408988i
$130$	1.84188	−	5.66873i	0.161544	−	0.497180i
$131$	−3.64102			−0.318117			−0.159059	−	0.987269i	$-0.550846\pi$
$131$	−3.64102			−0.318117			−0.159059	+	0.987269i	$0.550846\pi$
$132$	0.396800	−	0.0926175i	0.0345370	−	0.00806132i
$133$	2.65247			0.229999
$134$	2.70731	−	8.33224i	0.233876	−	0.719796i
$135$	3.51956	−	2.55711i	0.302915	−	0.220081i
$136$	−13.1970	−	9.58819i	−1.13163	−	0.822180i
$137$	3.46808	+	10.6737i	0.296298	+	0.911913i	0.982782	+	0.184768i	$0.0591533\pi$
$137$	3.46808	+	10.6737i	0.296298	+	0.911913i	−0.686484	+	0.727145i	$0.740847\pi$
$138$	−0.861880	−	2.65259i	−0.0733681	−	0.225804i
$139$	−10.6139	−	7.71148i	−0.900263	−	0.654080i	0.0382703	−	0.999267i	$-0.487815\pi$
$139$	−10.6139	−	7.71148i	−0.900263	−	0.654080i	−0.938534	+	0.345188i	$0.887815\pi$
$140$	0.444049	−	0.322621i	0.0375290	−	0.0272664i
$141$	−0.400192	+	1.23166i	−0.0337022	+	0.103725i
$142$	10.0851			0.846321
$143$	0.281091	−	3.30469i	0.0235060	−	0.276352i
$144$	−3.73920			−0.311600
$145$	−0.593585	+	1.82687i	−0.0492946	+	0.151713i
$146$	13.8177	−	10.0391i	1.14356	−	0.830845i
$147$	4.80991	+	3.49461i	0.396715	+	0.288230i
$148$	0.0127017	+	0.0390919i	0.00104408	+	0.00321333i
$149$	−5.03332	−	15.4910i	−0.412346	−	1.26907i	−0.914603	−	0.404352i	$-0.867497\pi$
$149$	−5.03332	−	15.4910i	−0.412346	−	1.26907i	0.502258	−	0.864718i	$-0.332503\pi$
$150$	−15.4360	−	11.2149i	−1.26035	−	0.915696i
$151$	4.96968	−	3.61068i	0.404427	−	0.293833i	−0.366915	−	0.930254i	$-0.619586\pi$
$151$	4.96968	−	3.61068i	0.404427	−	0.293833i	0.771342	+	0.636421i	$0.219586\pi$
$152$	2.32142	−	7.14461i	0.188292	−	0.579504i
$153$	−5.60852			−0.453422
$154$	−3.05301	+	3.52925i	−0.246018	+	0.284395i
$155$	−35.8300			−2.87794
$156$	0.0379644	−	0.116843i	0.00303959	−	0.00935489i
$157$	−3.22389	+	2.34229i	−0.257294	+	0.186935i	−0.708953	−	0.705255i	$-0.750832\pi$
$157$	−3.22389	+	2.34229i	−0.257294	+	0.186935i	0.451659	+	0.892191i	$0.350832\pi$
$158$	−9.30233	−	6.75854i	−0.740054	−	0.537680i
$159$	−2.37727	−	7.31650i	−0.188530	−	0.580236i
$160$	−0.932942	−	2.87130i	−0.0737555	−	0.226996i
$161$	−1.69130	−	1.22880i	−0.133293	−	0.0968433i
$162$	−1.10843	+	0.805318i	−0.0870861	+	0.0632718i
$163$	−6.49037	+	19.9753i	−0.508365	+	1.56459i	0.286674	+	0.958028i	$0.407450\pi$
$163$	−6.49037	+	19.9753i	−0.508365	+	1.56459i	−0.795039	+	0.606558i	$0.792550\pi$
$164$	−0.128856			−0.0100620
$165$	−13.2952	−	5.60568i	−1.03503	−	0.436401i
$166$	13.5945			1.05513
$167$	3.91662	−	12.0541i	0.303077	−	0.932776i	−0.677311	−	0.735697i	$-0.736855\pi$
$167$	3.91662	−	12.0541i	0.303077	−	0.932776i	0.980388	−	0.197078i	$-0.0631454\pi$
$168$	−2.41644	+	1.75564i	−0.186432	+	0.135451i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	10.3302	+	31.7932i	0.792293	+	2.43843i
$171$	−0.798151	−	2.45646i	−0.0610362	−	0.187850i
$172$	0.785486	+	0.570689i	0.0598928	+	0.0435147i
$173$	−16.6772	+	12.1167i	−1.26794	+	0.921214i	−0.999119	−	0.0419757i	$-0.986635\pi$
$173$	−16.6772	+	12.1167i	−1.26794	+	0.921214i	−0.268823	+	0.963189i	$0.586635\pi$
$174$	0.186940	−	0.575341i	0.0141719	−	0.0436165i
$175$	−14.3014			−1.08108
$176$	6.41288	+	10.6147i	0.483389	+	0.800115i
$177$	−10.9491			−0.822983
$178$	5.46174	−	16.8095i	0.409374	−	1.25993i
$179$	−4.93796	+	3.58764i	−0.369081	+	0.268153i	−0.756830	−	0.653612i	$-0.773253\pi$
$179$	−4.93796	+	3.58764i	−0.369081	+	0.268153i	0.387749	+	0.921765i	$0.373253\pi$
$180$	−0.432397	−	0.314155i	−0.0322290	−	0.0234157i
$181$	3.70105	+	11.3906i	0.275097	+	0.846660i	0.989194	+	0.146614i	$0.0468374\pi$
$181$	3.70105	+	11.3906i	0.275097	+	0.846660i	−0.714097	+	0.700046i	$0.753163\pi$
$182$	0.434790	+	1.33815i	0.0322288	+	0.0991900i
$183$	−5.77347	−	4.19467i	−0.426787	−	0.310079i
$184$	−4.79008	+	3.48020i	−0.353129	+	0.256563i
$185$	0.449778	−	1.38428i	0.0330684	−	0.101774i
$186$	11.2841			0.827388
$187$	9.61885	+	15.9213i	0.703400	+	1.16428i
$188$	0.159104			0.0116038
$189$	−0.317344	+	0.976685i	−0.0230834	+	0.0710434i
$190$	−12.4549	+	9.04901i	−0.903573	+	0.656484i
$191$	16.2842	+	11.8312i	1.17828	+	0.856073i	0.991977	−	0.126418i	$-0.0403481\pi$
$191$	16.2842	+	11.8312i	1.17828	+	0.856073i	0.186307	+	0.982492i	$0.440348\pi$
$192$	2.60476	+	8.01664i	0.187983	+	0.578551i
$193$	−7.50334	−	23.0929i	−0.540103	−	1.66226i	−0.732358	−	0.680920i	$-0.761580\pi$
$193$	−7.50334	−	23.0929i	−0.540103	−	1.66226i	0.192255	−	0.981345i	$-0.438420\pi$
$194$	−11.9060	−	8.65022i	−0.854802	−	0.621050i
$195$	−3.51956	+	2.55711i	−0.252041	+	0.183118i
$196$	0.225713	−	0.694673i	0.0161224	−	0.0496195i
$197$	−9.31810			−0.663887			−0.331943	−	0.943299i	$-0.607704\pi$
$197$	−9.31810			−0.663887			−0.331943	+	0.943299i	$0.607704\pi$
$198$	4.18711	+	1.76541i	0.297565	+	0.125462i
$199$	27.1176			1.92231			0.961157	−	0.276004i	$-0.0890102\pi$
$199$	27.1176			1.92231			0.961157	+	0.276004i	$0.0890102\pi$
$200$	−12.5164	+	38.5216i	−0.885046	+	2.72389i
$201$	−5.17326	+	3.75859i	−0.364894	+	0.265111i
$202$	−12.3288	−	8.95739i	−0.867451	−	0.630240i
$203$	−0.140120	−	0.431246i	−0.00983452	−	0.0302675i
$204$	0.212924	+	0.655314i	0.0149077	+	0.0458812i
$205$	3.69146	+	2.68200i	0.257823	+	0.187319i
$206$	−7.57632	+	5.50452i	−0.527868	+	0.383518i
$207$	−0.629069	+	1.93607i	−0.0437233	+	0.134566i
$208$	3.73920			0.259267
$209$	−5.60446	+	6.47870i	−0.387669	+	0.448141i
$210$	6.12107			0.422394
$211$	−3.40448	+	10.4779i	−0.234374	+	0.721328i	0.762830	+	0.646599i	$0.223809\pi$
$211$	−3.40448	+	10.4779i	−0.234374	+	0.721328i	−0.997204	+	0.0747293i	$0.976191\pi$
$212$	−0.764626	+	0.555534i	−0.0525147	+	0.0381542i
$213$	−5.95509	−	4.32662i	−0.408036	−	0.296455i
$214$	−2.44541	−	7.52621i	−0.167165	−	0.514481i
$215$	−10.6243	−	32.6981i	−0.724569	−	2.22999i
$216$	2.35303	+	1.70957i	0.160103	+	0.116322i
$217$	6.84263	−	4.97146i	0.464508	−	0.337485i
$218$	−7.48227	+	23.0281i	−0.506763	+	1.55966i
$219$	−12.4661			−0.842378
$220$	−0.150235	+	1.76627i	−0.0101288	+	0.119082i
$221$	5.60852			0.377270
$222$	−0.141650	+	0.435954i	−0.00950693	+	0.0292593i
$223$	−2.60562	+	1.89309i	−0.174485	+	0.126771i	−0.671600	−	0.740914i	$-0.734393\pi$
$223$	−2.60562	+	1.89309i	−0.174485	+	0.126771i	0.497115	+	0.867685i	$0.334393\pi$
$224$	0.576564	+	0.418898i	0.0385233	+	0.0279888i
$225$	4.30340	+	13.2445i	0.286893	+	0.882967i
$226$	0.697834	+	2.14771i	0.0464192	+	0.142864i
$227$	−7.82974	−	5.68864i	−0.519678	−	0.377568i	0.296805	−	0.954938i	$-0.404079\pi$
$227$	−7.82974	−	5.68864i	−0.519678	−	0.377568i	−0.816483	+	0.577370i	$0.804079\pi$
$228$	−0.256717	+	0.186516i	−0.0170015	+	0.0123523i
$229$	−0.973013	+	2.99462i	−0.0642985	+	0.197890i	−0.978045	−	0.208395i	$-0.933176\pi$
$229$	−0.973013	+	2.99462i	−0.0642985	+	0.197890i	0.913746	+	0.406285i	$0.133176\pi$
$230$	12.1337			0.800076
$231$	3.31685	−	0.774188i	0.218232	−	0.0509378i
$232$	−1.28422			−0.0843132
$233$	−3.62220	+	11.1480i	−0.237298	+	0.730328i	0.759510	+	0.650495i	$0.225439\pi$
$233$	−3.62220	+	11.1480i	−0.237298	+	0.730328i	−0.996808	+	0.0798329i	$0.974561\pi$
$234$	1.10843	−	0.805318i	0.0724600	−	0.0526453i
$235$	−4.55800	−	3.31158i	−0.297331	−	0.216024i
$236$	0.415675	+	1.27932i	0.0270582	+	0.0832765i
$237$	2.59339	+	7.98163i	0.168459	+	0.518463i
$238$	−6.38415	−	4.63836i	−0.413823	−	0.300660i
$239$	4.40860	−	3.20303i	0.285168	−	0.207187i	−0.436000	−	0.899947i	$-0.643605\pi$
$239$	4.40860	−	3.20303i	0.285168	−	0.207187i	0.721169	+	0.692760i	$0.243605\pi$
$240$	5.02679	−	15.4709i	0.324478	−	0.998641i
$241$	8.79776			0.566713			0.283357	−	0.959015i	$-0.408552\pi$
$241$	8.79776			0.566713			0.283357	+	0.959015i	$0.408552\pi$
$242$	−2.16947	−	14.9140i	−0.139459	−	0.958709i
$243$	1.00000			0.0641500
$244$	−0.270929	+	0.833835i	−0.0173445	+	0.0533808i
$245$	−20.9251	+	15.2030i	−1.33686	+	0.971283i
$246$	−1.16256	−	0.844651i	−0.0741223	−	0.0538530i
$247$	0.798151	+	2.45646i	0.0507852	+	0.156301i
$248$	−7.40233	−	22.7820i	−0.470049	−	1.44666i
$249$	−8.02732	−	5.83219i	−0.508711	−	0.369600i
$250$	43.0426	−	31.2723i	2.72225	−	1.97783i
$251$	4.67149	−	14.3774i	0.294862	−	0.907491i	−0.688406	−	0.725325i	$-0.741689\pi$
$251$	4.67149	−	14.3774i	0.294862	−	0.907491i	0.983268	−	0.182165i	$-0.0583106\pi$
$252$	0.126166			0.00794772
$253$	6.57495	−	1.53467i	0.413364	−	0.0964836i
$254$	2.97904			0.186921
$255$	7.53983	−	23.2052i	0.472162	−	1.45317i
$256$	2.37623	−	1.72643i	0.148514	−	0.107902i
$257$	−12.3084	−	8.94256i	−0.767775	−	0.557821i	0.133510	−	0.991047i	$-0.457375\pi$
$257$	−12.3084	−	8.94256i	−0.767775	−	0.557821i	−0.901285	+	0.433226i	$0.857375\pi$
$258$	3.34594	+	10.2977i	0.208309	+	0.641109i
$259$	0.106174	+	0.326769i	0.00659730	+	0.0203044i
$260$	0.432397	+	0.314155i	0.0268161	+	0.0194831i
$261$	−0.357214	+	0.259531i	−0.0221110	+	0.0160646i
$262$	−1.54154	+	4.74436i	−0.0952364	+	0.293108i
$263$	−27.1806			−1.67603			−0.838013	−	0.545650i	$-0.816283\pi$
$263$	−27.1806			−1.67603			−0.838013	+	0.545650i	$0.816283\pi$
$264$	0.817552	−	9.61170i	0.0503169	−	0.591559i
$265$	33.4678			2.05591
$266$	1.12301	−	3.45626i	0.0688560	−	0.211917i
$267$	−10.4366	+	7.58260i	−0.638707	+	0.464048i
$268$	0.635564	+	0.461764i	0.0388232	+	0.0282067i
$269$	−7.08941	−	21.8189i	−0.432249	−	1.33032i	−0.895880	−	0.444296i	$-0.853454\pi$
$269$	−7.08941	−	21.8189i	−0.432249	−	1.33032i	0.463631	−	0.886028i	$-0.346546\pi$
$270$	−1.84188	−	5.66873i	−0.112093	−	0.344988i
$271$	−9.02100	−	6.55414i	−0.547987	−	0.398136i	0.279056	−	0.960275i	$-0.409979\pi$
$271$	−9.02100	−	6.55414i	−0.547987	−	0.398136i	−0.827043	+	0.562139i	$0.809979\pi$
$272$	−16.9662	+	12.3267i	−1.02873	+	0.747413i
$273$	0.317344	−	0.976685i	0.0192065	−	0.0591117i
$274$	15.3765			0.928925
$275$	30.2176	−	34.9312i	1.82219	−	2.10643i
$276$	0.250098			0.0150541
$277$	−3.95531	+	12.1732i	−0.237651	+	0.731416i	0.759107	+	0.650966i	$0.225636\pi$
$277$	−3.95531	+	12.1732i	−0.237651	+	0.731416i	−0.996759	+	0.0804503i	$0.974364\pi$
$278$	−14.5421	+	10.5654i	−0.872174	+	0.633672i
$279$	−6.66307	−	4.84101i	−0.398908	−	0.289823i
$280$	−4.01541	−	12.3582i	−0.239967	−	0.738542i
$281$	4.67883	+	14.3999i	0.279115	+	0.859029i	0.988101	+	0.153806i	$0.0491531\pi$
$281$	4.67883	+	14.3999i	0.279115	+	0.859029i	−0.708986	+	0.705223i	$0.750847\pi$
$282$	1.43546	+	1.04293i	0.0854807	+	0.0621054i
$283$	−12.6838	+	9.21531i	−0.753973	+	0.547794i	−0.897056	−	0.441917i	$-0.854299\pi$
$283$	−12.6838	+	9.21531i	−0.753973	+	0.547794i	0.143083	+	0.989711i	$0.454299\pi$
$284$	−0.279452	+	0.860065i	−0.0165824	+	0.0510355i
$285$	11.2366			0.665596
$286$	−4.18711	−	1.76541i	−0.247589	−	0.104391i
$287$	−1.07711			−0.0635795
$288$	0.214449	−	0.660006i	0.0126365	−	0.0388912i
$289$	−11.6948	+	8.49675i	−0.687928	+	0.499809i
$290$	2.12916	+	1.54692i	0.125028	+	0.0908384i
$291$	3.31927	+	10.2157i	0.194579	+	0.598852i
$292$	0.473267	+	1.45657i	0.0276958	+	0.0852391i
$293$	14.7899	+	10.7455i	0.864036	+	0.627759i	0.928980	−	0.370130i	$-0.120687\pi$
$293$	14.7899	+	10.7455i	0.864036	+	0.627759i	−0.0649438	+	0.997889i	$0.520687\pi$
$294$	6.59001	−	4.78792i	0.384337	−	0.279237i
$295$	14.7194	−	45.3016i	0.856997	−	2.63756i
$296$	0.973094			0.0565600
$297$	−1.71504	−	2.83877i	−0.0995168	−	0.164722i
$298$	−22.3163			−1.29275
$299$	0.629069	−	1.93607i	0.0363800	−	0.111966i
$300$	1.38414	−	1.00564i	0.0799136	−	0.0580607i
$301$	6.56587	+	4.77038i	0.378450	+	0.274960i
$302$	−2.60077	−	8.00434i	−0.149657	−	0.460598i
$303$	3.43713	+	10.5784i	0.197458	+	0.607714i
$304$	−7.81338	−	5.67675i	−0.448128	−	0.325584i
$305$	25.1170	−	18.2485i	1.43819	−	1.04491i
$306$	−2.37454	+	7.30809i	−0.135743	+	0.417776i
$307$	−12.9495			−0.739068			−0.369534	−	0.929217i	$-0.620483\pi$
$307$	−12.9495			−0.739068			−0.369534	+	0.929217i	$0.620483\pi$
$308$	−0.216380	−	0.358157i	−0.0123294	−	0.0204079i
$309$	6.83521			0.388842
$310$	−15.1698	+	46.6877i	−0.861584	+	2.65168i
$311$	10.6136	−	7.71121i	0.601841	−	0.437263i	−0.244691	−	0.969601i	$-0.578687\pi$
$311$	10.6136	−	7.71121i	0.601841	−	0.437263i	0.846532	+	0.532338i	$0.178687\pi$
$312$	−2.35303	−	1.70957i	−0.133214	−	0.0967856i
$313$	8.23236	+	25.3366i	0.465321	+	1.43211i	0.858579	+	0.512681i	$0.171348\pi$
$313$	8.23236	+	25.3366i	0.465321	+	1.43211i	−0.393258	+	0.919428i	$0.628652\pi$
$314$	1.68715	+	5.19251i	0.0952113	+	0.293030i
$315$	−3.61440	−	2.62602i	−0.203648	−	0.147959i
$316$	0.834137	−	0.606036i	0.0469239	−	0.0340922i
$317$	−3.09275	+	9.51850i	−0.173706	+	0.534612i	−0.999572	−	0.0292544i	$-0.990687\pi$
$317$	−3.09275	+	9.51850i	−0.173706	+	0.534612i	0.825866	+	0.563866i	$0.190687\pi$
$318$	−10.5401			−0.591061
$319$	1.34939	+	0.568942i	0.0755511	+	0.0318546i
$320$	−36.6705			−2.04994
$321$	−1.78486	+	5.49323i	−0.0996210	+	0.306602i
$322$	−2.31724	+	1.68357i	−0.129135	+	0.0938217i
$323$	−11.7195	−	8.51472i	−0.652090	−	0.473771i
$324$	−0.0379644	−	0.116843i	−0.00210914	−	0.00649125i
$325$	−4.30340	−	13.2445i	−0.238710	−	0.734673i
$326$	23.2806	+	16.9143i	1.28939	+	0.936798i
$327$	14.2975	−	10.3877i	0.790653	−	0.574443i
$328$	−0.942674	+	2.90125i	−0.0520505	+	0.160195i
$329$	1.32995			0.0733224
$330$	−12.9333	+	14.9508i	−0.711956	+	0.823014i
$331$	35.0412			1.92604			0.963020	−	0.269431i	$-0.0868356\pi$
$331$	35.0412			1.92604			0.963020	+	0.269431i	$0.0868356\pi$
$332$	−0.376695	+	1.15935i	−0.0206738	+	0.0636275i
$333$	0.270672	−	0.196655i	0.0148327	−	0.0107766i
$334$	−14.0487	−	10.2070i	−0.768710	−	0.558500i
$335$	−8.59646	−	26.4572i	−0.469675	−	1.44551i
$336$	1.18661	+	3.65202i	0.0647350	+	0.199234i
$337$	−9.15271	−	6.64983i	−0.498580	−	0.362240i	0.309894	−	0.950771i	$-0.399706\pi$
$337$	−9.15271	−	6.64983i	−0.498580	−	0.362240i	−0.808474	+	0.588531i	$0.799706\pi$
$338$	−1.10843	+	0.805318i	−0.0602904	+	0.0438035i
$339$	0.509335	−	1.56757i	0.0276633	−	0.0851388i
$340$	−2.99760			−0.162568
$341$	−2.31506	+	27.2175i	−0.125368	+	1.47391i
$342$	−3.53877			−0.191355
$343$	4.10814	−	12.6436i	0.221819	−	0.682688i
$344$	18.5957	−	13.5106i	1.00261	−	0.728442i
$345$	−7.16479	−	5.20553i	−0.385740	−	0.280256i
$346$	8.72762	+	26.8609i	0.469200	+	1.44405i
$347$	0.332210	+	1.02244i	0.0178340	+	0.0548873i	0.959577	−	0.281445i	$-0.0908136\pi$
$347$	0.332210	+	1.02244i	0.0178340	+	0.0548873i	−0.941743	+	0.336332i	$0.890814\pi$
$348$	0.0438857	+	0.0318848i	0.00235252	+	0.00170921i
$349$	10.7503	−	7.81059i	0.575453	−	0.418091i	−0.261629	−	0.965169i	$-0.584260\pi$
$349$	10.7503	−	7.81059i	0.575453	−	0.418091i	0.837082	+	0.547077i	$0.184260\pi$
$350$	−6.05492	+	18.6351i	−0.323649	+	0.996090i
$351$	−1.00000			−0.0533761
$352$	−2.24140	+	0.523166i	−0.119467	+	0.0278849i
$353$	19.2759			1.02595			0.512976	−	0.858403i	$-0.328543\pi$
$353$	19.2759			1.02595			0.512976	+	0.858403i	$0.328543\pi$
$354$	−4.63563	+	14.2670i	−0.246381	+	0.758282i
$355$	25.9071	−	18.8226i	1.37501	−	0.999000i
$356$	1.28219	+	0.931565i	0.0679559	+	0.0493728i
$357$	1.77983	+	5.47776i	0.0941987	+	0.289914i
$358$	2.58417	+	7.95326i	0.136578	+	0.420343i
$359$	−16.5737	−	12.0415i	−0.874725	−	0.635525i	0.0571256	−	0.998367i	$-0.481806\pi$
$359$	−16.5737	−	12.0415i	−0.874725	−	0.635525i	−0.931851	+	0.362842i	$0.881806\pi$
$360$	−10.2366	+	7.43735i	−0.539518	+	0.391983i
$361$	−3.80980	+	11.7254i	−0.200516	+	0.617124i
$362$	16.4093			0.862455
$363$	−5.11726	+	9.73723i	−0.268587	+	0.511072i
$364$	−0.126166			−0.00661291
$365$	16.7588	−	51.5782i	0.877194	−	2.69972i
$366$	−7.91016	+	5.74707i	−0.413471	+	0.300404i
$367$	6.63156	+	4.81811i	0.346164	+	0.251503i	0.747258	−	0.664534i	$-0.231370\pi$
$367$	6.63156	+	4.81811i	0.346164	+	0.251503i	−0.401094	+	0.916037i	$0.631370\pi$
$368$	2.35221	+	7.23936i	0.122617	+	0.377378i
$369$	0.324110	+	0.997507i	0.0168725	+	0.0519282i
$370$	−1.61333	−	1.17215i	−0.0838729	−	0.0609372i
$371$	−6.39150	+	4.64370i	−0.331830	+	0.241089i
$372$	−0.312676	+	0.962316i	−0.0162115	+	0.0498938i
$373$	3.26807			0.169214			0.0846071	−	0.996414i	$-0.473036\pi$
$373$	3.26807			0.169214			0.0846071	+	0.996414i	$0.473036\pi$
$374$	24.8184	−	5.79289i	1.28333	−	0.299543i
$375$	−38.8322			−2.00528
$376$	1.16396	−	3.58230i	0.0600266	−	0.184743i
$377$	0.357214	−	0.259531i	0.0183974	−	0.0133665i
$378$	1.13829	+	0.827020i	0.0585476	+	0.0425373i
$379$	3.08672	+	9.49995i	0.158554	+	0.487980i	0.998504	−	0.0546850i	$-0.0174155\pi$
$379$	3.08672	+	9.49995i	0.158554	+	0.487980i	−0.839949	+	0.542665i	$0.817415\pi$
$380$	−0.426590	−	1.31291i	−0.0218836	−	0.0673508i
$381$	−1.75908	−	1.27804i	−0.0901202	−	0.0654762i
$382$	22.3108	−	16.2098i	1.14152	−	0.829363i
$383$	0.166126	−	0.511283i	0.00848864	−	0.0261253i	−0.946722	−	0.322051i	$-0.895628\pi$
$383$	0.166126	−	0.511283i	0.00848864	−	0.0261253i	0.955211	+	0.295925i	$0.0956279\pi$
$384$	10.1608			0.518516
$385$	−1.25581	+	14.7642i	−0.0640022	+	0.752453i
$386$	−33.2676			−1.69328
$387$	2.44213	−	7.51610i	0.124140	−	0.382065i
$388$	1.06761	−	0.775663i	0.0541996	−	0.0393783i
$389$	−3.39061	−	2.46342i	−0.171911	−	0.124901i	0.498503	−	0.866888i	$-0.333883\pi$
$389$	−3.39061	−	2.46342i	−0.171911	−	0.124901i	−0.670414	+	0.741988i	$0.733883\pi$
$390$	1.84188	+	5.66873i	0.0932673	+	0.287047i
$391$	3.52815	+	10.8585i	0.178426	+	0.549139i
$392$	−13.9896	−	10.1641i	−0.706583	−	0.513363i
$393$	2.94564	−	2.14014i	0.148588	−	0.107956i
$394$	−3.94510	+	12.1418i	−0.198751	+	0.611694i
$395$	−36.5103			−1.83703
$396$	−0.266579	+	0.308162i	−0.0133961	+	0.0154857i
$397$	−0.899302			−0.0451347			−0.0225673	−	0.999745i	$-0.507184\pi$
$397$	−0.899302			−0.0451347			−0.0225673	+	0.999745i	$0.507184\pi$
$398$	11.4811	−	35.3351i	0.575493	−	1.77119i
$399$	−2.14590	+	1.55909i	−0.107429	+	0.0780519i
$400$	42.1274	+	30.6074i	2.10637	+	1.53037i
$401$	−5.10592	−	15.7144i	−0.254978	−	0.784741i	−0.993834	−	0.110878i	$-0.964634\pi$
$401$	−5.10592	−	15.7144i	−0.254978	−	0.784741i	0.738856	−	0.673863i	$-0.235366\pi$
$402$	2.70731	+	8.33224i	0.135028	+	0.415575i
$403$	6.66307	+	4.84101i	0.331911	+	0.241148i
$404$	1.10552	−	0.803207i	0.0550017	−	0.0399610i
$405$	−1.34435	+	4.13749i	−0.0668014	+	0.205593i
$406$	−0.621252			−0.0308322
$407$	−1.02247	−	0.431105i	−0.0506820	−	0.0213691i
$408$	16.3124			0.807584
$409$	−9.11103	+	28.0409i	−0.450511	+	1.38653i	0.425813	+	0.904811i	$0.359988\pi$
$409$	−9.11103	+	28.0409i	−0.450511	+	1.38653i	−0.876325	+	0.481721i	$0.840012\pi$
$410$	5.05763	−	3.67458i	0.249778	−	0.181475i
$411$	−9.07956	−	6.59669i	−0.447862	−	0.325391i
$412$	−0.259495	−	0.798644i	−0.0127844	−	0.0393464i
$413$	3.47462	+	10.6938i	0.170975	+	0.526207i
$414$	2.25643	+	1.63939i	0.110898	+	0.0805718i
$415$	34.9222	−	25.3724i	1.71426	−	1.24548i
$416$	−0.214449	+	0.660006i	−0.0105142	+	0.0323595i
$417$	13.1196			0.642468
$418$	6.06913	+	10.0458i	0.296851	+	0.491354i
$419$	11.0311			0.538906			0.269453	−	0.963013i	$-0.413157\pi$
$419$	11.0311			0.538906			0.269453	+	0.963013i	$0.413157\pi$
$420$	−0.169612	+	0.522011i	−0.00827620	+	0.0254715i
$421$	28.8576	−	20.9663i	1.40643	−	1.02183i	0.412603	−	0.910911i	$-0.364620\pi$
$421$	28.8576	−	20.9663i	1.40643	−	1.02183i	0.993829	−	0.110922i	$-0.0353804\pi$
$422$	12.2117	+	8.87228i	0.594454	+	0.431896i
$423$	−0.400192	−	1.23166i	−0.0194580	−	0.0598856i
$424$	6.91430	+	21.2800i	0.335788	+	1.03345i
$425$	63.1881	+	45.9088i	3.06507	+	2.22691i
$426$	−8.15900	+	5.92786i	−0.395305	+	0.287206i
$427$	−2.26469	+	6.97001i	−0.109596	+	0.337303i
$428$	0.709604			0.0343000
$429$	1.71504	+	2.83877i	0.0828030	+	0.137057i
$430$	−47.1048			−2.27160
$431$	2.31798	−	7.13401i	0.111653	−	0.343633i	−0.879581	−	0.475749i	$-0.842177\pi$
$431$	2.31798	−	7.13401i	0.111653	−	0.343633i	0.991234	+	0.132116i	$0.0421771\pi$
$432$	3.02507	−	2.19784i	0.145544	−	0.105744i
$433$	−14.1041	−	10.2472i	−0.677800	−	0.492450i	0.194827	−	0.980838i	$-0.437585\pi$
$433$	−14.1041	−	10.2472i	−0.677800	−	0.492450i	−0.872627	+	0.488387i	$0.837585\pi$
$434$	−3.58093	−	11.0210i	−0.171890	−	0.529024i
$435$	−0.593585	−	1.82687i	−0.0284602	−	0.0875916i
$436$	−1.75653	−	1.27619i	−0.0841224	−	0.0611185i
$437$	−4.25379	+	3.09056i	−0.203486	+	0.147842i
$438$	−5.27789	+	16.2437i	−0.252187	+	0.776153i
$439$	5.39218			0.257355			0.128677	−	0.991687i	$-0.458927\pi$
$439$	5.39218			0.257355			0.128677	+	0.991687i	$0.458927\pi$
$440$	38.6692	+	16.3041i	1.84348	+	0.777268i
$441$	−5.94538			−0.283113
$442$	2.37454	−	7.30809i	0.112945	−	0.347610i
$443$	−28.4233	+	20.6508i	−1.35043	+	0.981147i	−0.351444	+	0.936209i	$0.614309\pi$
$443$	−28.4233	+	20.6508i	−1.35043	+	0.981147i	−0.998990	+	0.0449384i	$0.985691\pi$
$444$	−0.0332536	−	0.0241601i	−0.00157814	−	0.00114659i
$445$	−17.3425	−	53.3748i	−0.822115	−	2.53021i
$446$	1.36359	+	4.19670i	0.0645679	+	0.198720i
$447$	13.1774	+	9.57395i	0.623270	+	0.452832i
$448$	7.00313	−	5.08807i	0.330867	−	0.240389i
$449$	2.82937	−	8.70792i	0.133526	−	0.410952i	−0.861831	−	0.507195i	$-0.830682\pi$
$449$	2.82937	−	8.70792i	0.133526	−	0.410952i	0.995358	+	0.0962427i	$0.0306825\pi$
$450$	19.0800			0.899439
$451$	2.27584	−	2.63084i	0.107165	−	0.123881i
$452$	−0.202496			−0.00952459
$453$	−1.89825	+	5.84220i	−0.0891874	+	0.274491i
$454$	−10.7274	+	7.79394i	−0.503464	+	0.365788i
$455$	3.61440	+	2.62602i	0.169446	+	0.123110i
$456$	2.32142	+	7.14461i	0.108711	+	0.334577i
$457$	9.05144	+	27.8575i	0.423409	+	1.30312i	0.904510	+	0.426453i	$0.140237\pi$
$457$	9.05144	+	27.8575i	0.423409	+	1.30312i	−0.481101	+	0.876665i	$0.659763\pi$
$458$	3.49014	+	2.53573i	0.163083	+	0.118487i
$459$	4.53739	−	3.29661i	0.211787	−	0.153872i
$460$	−0.336220	+	1.03478i	−0.0156763	+	0.0482468i
$461$	−5.79396			−0.269852			−0.134926	−	0.990856i	$-0.543080\pi$
$461$	−5.79396			−0.269852			−0.134926	+	0.990856i	$0.543080\pi$
$462$	0.395497	−	4.64973i	0.0184002	−	0.216325i
$463$	−15.1326			−0.703271			−0.351635	−	0.936137i	$-0.614374\pi$
$463$	−15.1326			−0.703271			−0.351635	+	0.936137i	$0.614374\pi$
$464$	−0.510189	+	1.57020i	−0.0236849	+	0.0728947i
$465$	28.9871	−	21.0604i	1.34425	−	0.976651i
$466$	12.9926	+	9.43968i	0.601871	+	0.437285i
$467$	13.0425	+	40.1408i	0.603537	+	1.85750i	0.506550	+	0.862210i	$0.330920\pi$
$467$	13.0425	+	40.1408i	0.603537	+	1.85750i	0.0969868	+	0.995286i	$0.469080\pi$
$468$	0.0379644	+	0.116843i	0.00175491	+	0.00540105i
$469$	5.31267	+	3.85988i	0.245316	+	0.178233i
$470$	−6.24486	+	4.53716i	−0.288054	+	0.209284i
$471$	1.23141	−	3.78990i	0.0567406	−	0.174630i
$472$	31.8454			1.46580
$473$	−25.5249	+	5.95778i	−1.17363	+	0.273939i
$474$	11.4983			0.528135
$475$	−11.1151	+	34.2088i	−0.509997	+	1.56961i
$476$	0.572465	−	0.415920i	0.0262389	−	0.0190637i
$477$	6.22378	+	4.52184i	0.284967	+	0.207041i
$478$	−2.30714	−	7.10065i	−0.105526	−	0.324776i
$479$	−7.84249	−	24.1367i	−0.358333	−	1.10283i	−0.954052	−	0.299642i	$-0.903133\pi$
$479$	−7.84249	−	24.1367i	−0.358333	−	1.10283i	0.595719	−	0.803193i	$-0.296867\pi$
$480$	2.44247	+	1.77456i	0.111483	+	0.0809972i
$481$	−0.270672	+	0.196655i	−0.0123416	+	0.00896668i
$482$	3.72480	−	11.4638i	0.169660	−	0.522160i
$483$	2.09057			0.0951241
$484$	1.33200	+	0.228245i	0.0605453	+	0.0103748i
$485$	−46.7294			−2.12187
$486$	0.423381	−	1.30303i	0.0192049	−	0.0591067i
$487$	−6.86610	+	4.98852i	−0.311133	+	0.226051i	−0.732382	−	0.680894i	$-0.761592\pi$
$487$	−6.86610	+	4.98852i	−0.311133	+	0.226051i	0.421250	+	0.906945i	$0.361592\pi$
$488$	16.7921	+	12.2002i	0.760144	+	0.552277i
$489$	−6.49037	−	19.9753i	−0.293505	−	0.903314i
$490$	10.9507	+	33.7027i	0.494701	+	1.52253i
$491$	16.9685	+	12.3283i	0.765776	+	0.556369i	0.900676	−	0.434490i	$-0.143072\pi$
$491$	16.9685	+	12.3283i	0.765776	+	0.556369i	−0.134901	+	0.990859i	$0.543072\pi$
$492$	0.104247	−	0.0757396i	0.00469980	−	0.00341461i
$493$	−0.765246	+	2.35519i	−0.0344650	+	0.106072i
$494$	3.53877			0.159217
$495$	14.0510	−	3.27966i	0.631546	−	0.147410i
$496$	−30.7961			−1.38278
$497$	−2.33594	+	7.18927i	−0.104781	+	0.322483i
$498$	−10.9981	+	7.99062i	−0.492839	+	0.358068i
$499$	−27.6698	−	20.1033i	−1.23867	−	0.899948i	−0.241163	−	0.970485i	$-0.577529\pi$
$499$	−27.6698	−	20.1033i	−1.23867	−	0.899948i	−0.997509	+	0.0705368i	$0.977529\pi$
$500$	1.47424	+	4.53725i	0.0659301	+	0.202912i
$501$	3.91662	+	12.0541i	0.174982	+	0.538538i
$502$	−16.7563	−	12.1742i	−0.747872	−	0.543361i
$503$	8.04106	−	5.84217i	0.358533	−	0.260490i	−0.393907	−	0.919150i	$-0.628877\pi$
$503$	8.04106	−	5.84217i	0.358533	−	0.260490i	0.752440	+	0.658661i	$0.228877\pi$
$504$	0.922996	−	2.84069i	0.0411135	−	0.126534i
$505$	−48.3888			−2.15327
$506$	0.783990	−	9.21712i	0.0348526	−	0.409751i
$507$	1.00000			0.0444116
$508$	−0.0825475	+	0.254055i	−0.00366245	+	0.0112719i
$509$	−31.8201	+	23.1186i	−1.41040	+	1.02472i	−0.417137	+	0.908844i	$0.636966\pi$
$509$	−31.8201	+	23.1186i	−1.41040	+	1.02472i	−0.993264	+	0.115872i	$0.963034\pi$
$510$	−27.0449	−	19.6493i	−1.19757	−	0.870084i
$511$	3.95603	+	12.1754i	0.175005	+	0.538608i
$512$	−7.52327	−	23.1542i	−0.332485	−	1.02328i
$513$	2.08959	+	1.51817i	0.0922575	+	0.0670290i
$514$	−16.8636	+	12.2521i	−0.743820	+	0.540417i
$515$	−9.18893	+	28.2806i	−0.404913	+	1.24619i
$516$	−0.970915			−0.0427421
$517$	−2.81007	+	3.24841i	−0.123587	+	0.142865i
$518$	0.470742			0.0206832
$519$	6.37011	−	19.6052i	0.279617	−	0.860572i
$520$	10.2366	−	7.43735i	0.448906	−	0.326150i
$521$	−14.7295	−	10.7016i	−0.645310	−	0.468845i	0.216361	−	0.976314i	$-0.430581\pi$
$521$	−14.7295	−	10.7016i	−0.645310	−	0.468845i	−0.861670	+	0.507469i	$0.830581\pi$
$522$	0.186940	+	0.575341i	0.00818213	+	0.0251820i
$523$	−2.36406	−	7.27582i	−0.103373	−	0.318149i	0.885972	−	0.463738i	$-0.153492\pi$
$523$	−2.36406	−	7.27582i	−0.103373	−	0.318149i	−0.989345	+	0.145589i	$0.953492\pi$
$524$	−0.361889	−	0.262927i	−0.0158092	−	0.0114860i
$525$	11.5700	−	8.40613i	0.504958	−	0.366874i
$526$	−11.5077	+	35.4172i	−0.501761	+	1.54426i
$527$	−46.1919			−2.01215
$528$	−11.4273	−	4.81810i	−0.497310	−	0.209681i
$529$	−18.8559			−0.819821
$530$	14.1696	−	43.6096i	0.615489	−	1.89428i
$531$	8.85798	−	6.43570i	0.384404	−	0.279286i
$532$	0.263635	+	0.191542i	0.0114300	+	0.00830441i
$533$	−0.324110	−	0.997507i	−0.0140388	−	0.0432068i
$534$	5.46174	+	16.8095i	0.236352	+	0.727418i
$535$	−20.3287	−	14.7697i	−0.878886	−	0.638548i
$536$	15.0464	−	10.9319i	0.649907	−	0.472185i
$537$	1.88613	−	5.80492i	0.0813927	−	0.250501i
$538$	−31.4323			−1.35514
$539$	10.1966	+	16.8776i	0.439198	+	0.726969i
$540$	0.534472			0.0230000
$541$	12.3855	−	38.1188i	0.532496	−	1.63885i	−0.216502	−	0.976282i	$-0.569465\pi$
$541$	12.3855	−	38.1188i	0.532496	−	1.63885i	0.748998	−	0.662572i	$-0.230535\pi$
$542$	−12.3596	+	8.97976i	−0.530889	+	0.385714i
$543$	−9.68946	−	7.03981i	−0.415815	−	0.302107i
$544$	−1.20274	−	3.70166i	−0.0515671	−	0.158707i
$545$	23.7583	+	73.1205i	1.01769	+	3.13214i
$546$	−1.13829	−	0.827020i	−0.0487145	−	0.0353932i
$547$	−3.19049	+	2.31803i	−0.136416	+	0.0991118i	−0.653900	−	0.756581i	$-0.726868\pi$
$547$	−3.19049	+	2.31803i	−0.136416	+	0.0991118i	0.517485	+	0.855692i	$0.326868\pi$
$548$	−0.426073	+	1.31132i	−0.0182010	+	0.0560168i
$549$	7.13640			0.304574
$550$	−32.7230	−	54.1637i	−1.39531	−	2.30955i
$551$	−1.14044			−0.0485845
$552$	1.82965	−	5.63107i	0.0778749	−	0.239674i
$553$	6.97254	−	5.06585i	0.296503	−	0.215422i
$554$	14.1875	+	10.3078i	0.602767	+	0.437936i
$555$	0.449778	+	1.38428i	0.0190920	+	0.0587592i
$556$	−0.498077	−	1.53292i	−0.0211232	−	0.0650104i
$557$	30.4369	+	22.1137i	1.28965	+	0.936989i	0.999798	−	0.0200817i	$-0.00639264\pi$
$557$	30.4369	+	22.1137i	1.28965	+	0.936989i	0.289856	+	0.957070i	$0.406393\pi$
$558$	−9.12900	+	6.63261i	−0.386462	+	0.280781i
$559$	−2.44213	+	7.51610i	−0.103291	+	0.317897i
$560$	−16.7054			−0.705932
$561$	−17.1401	−	7.22680i	−0.723657	−	0.305116i
$562$	20.7445			0.875055
$563$	10.5515	−	32.4741i	0.444691	−	1.36862i	−0.438131	−	0.898911i	$-0.644359\pi$
$563$	10.5515	−	32.4741i	0.444691	−	1.36862i	0.882822	−	0.469707i	$-0.155641\pi$
$564$	−0.128718	+	0.0935189i	−0.00542000	+	0.00393786i
$565$	5.80108	+	4.21473i	0.244053	+	0.177315i
$566$	6.63778	+	20.4290i	0.279007	+	0.858694i
$567$	−0.317344	−	0.976685i	−0.0133272	−	0.0410169i
$568$	17.3204	+	12.5840i	0.726747	+	0.528013i
$569$	−2.04247	+	1.48394i	−0.0856247	+	0.0622100i	−0.629774	−	0.776778i	$-0.716853\pi$
$569$	−2.04247	+	1.48394i	−0.0856247	+	0.0622100i	0.544149	+	0.838988i	$0.316853\pi$
$570$	4.75734	−	14.6416i	0.199263	−	0.613269i
$571$	27.3411			1.14419			0.572095	−	0.820188i	$-0.306131\pi$
$571$	27.3411			1.14419			0.572095	+	0.820188i	$0.306131\pi$
$572$	0.266579	−	0.308162i	0.0111462	−	0.0128849i
$573$	−20.1284			−0.840876
$574$	−0.456026	+	1.40350i	−0.0190341	+	0.0585811i
$575$	22.9352	−	16.6634i	0.956464	−	0.694912i
$576$	−6.81936	−	4.95456i	−0.284140	−	0.206440i
$577$	−5.68447	−	17.4950i	−0.236648	−	0.728326i	−0.996899	−	0.0786968i	$-0.974924\pi$
$577$	−5.68447	−	17.4950i	−0.236648	−	0.728326i	0.760251	−	0.649629i	$-0.225076\pi$
$578$	6.12020	+	18.8360i	0.254567	+	0.783475i
$579$	19.6440	+	14.2722i	0.816377	+	0.593133i
$580$	−0.190921	+	0.138712i	−0.00792756	+	0.00575971i
$581$	−3.14879	+	9.69098i	−0.130634	+	0.402049i
$582$	14.7166			0.610024
$583$	2.16244	−	25.4231i	0.0895589	−	1.05292i
$584$	36.2575			1.50035
$585$	1.34435	−	4.13749i	0.0555821	−	0.171064i
$586$	20.2635	−	14.7223i	0.837078	−	0.608173i
$587$	24.1437	+	17.5414i	0.996518	+	0.724012i	0.961339	−	0.275369i	$-0.0887999\pi$
$587$	24.1437	+	17.5414i	0.996518	+	0.724012i	0.0351789	+	0.999381i	$0.488800\pi$
$588$	0.225713	+	0.694673i	0.00930825	+	0.0286478i
$589$	−6.57358	−	20.2314i	−0.270860	−	0.833621i
$590$	−52.7976	−	38.3597i	−2.17364	−	1.57924i
$591$	7.53850	−	5.47704i	0.310092	−	0.225295i
$592$	0.386586	−	1.18979i	0.0158886	−	0.0489000i
$593$	−7.27702			−0.298831			−0.149416	−	0.988774i	$-0.547739\pi$
$593$	−7.27702			−0.298831			−0.149416	+	0.988774i	$0.547739\pi$
$594$	−4.42513	+	1.03287i	−0.181565	+	0.0423793i
$595$	−25.0569			−1.02723
$596$	0.618372	−	1.90315i	0.0253295	−	0.0779561i
$597$	−21.9386	+	15.9393i	−0.897886	+	0.652352i
$598$	−2.25643	−	1.63939i	−0.0922723	−	0.0670398i
$599$	12.5457	+	38.6118i	0.512605	+	1.57763i	0.787599	+	0.616189i	$0.211324\pi$
$599$	12.5457	+	38.6118i	0.512605	+	1.57763i	−0.274994	+	0.961446i	$0.588676\pi$
$600$	−12.5164	−	38.5216i	−0.510982	−	1.57264i
$601$	−30.8207	−	22.3926i	−1.25720	−	0.913412i	−0.258587	−	0.965988i	$-0.583257\pi$
$601$	−30.8207	−	22.3926i	−1.25720	−	0.913412i	−0.998617	+	0.0525762i	$0.983257\pi$
$602$	8.99583	−	6.53585i	0.366643	−	0.266381i
$603$	1.97601	−	6.08153i	0.0804694	−	0.247659i
$604$	0.754684			0.0307077
$605$	−33.4083	−	34.2629i	−1.35824	−	1.39298i
$606$	15.2392			0.619051
$607$	−9.25856	+	28.4949i	−0.375793	+	1.15657i	0.567148	+	0.823616i	$0.308047\pi$
$607$	−9.25856	+	28.4949i	−0.375793	+	1.15657i	−0.942942	+	0.332957i	$0.891953\pi$
$608$	1.45011	−	1.05357i	0.0588099	−	0.0427279i
$609$	0.366840	+	0.266525i	0.0148651	+	0.0108001i
$610$	−13.1444	−	40.4543i	−0.532201	−	1.63795i
$611$	0.400192	+	1.23166i	0.0161900	+	0.0498278i
$612$	−0.557444	−	0.405006i	−0.0225333	−	0.0163714i
$613$	7.59036	−	5.51472i	0.306572	−	0.222737i	−0.423852	−	0.905731i	$-0.639322\pi$
$613$	7.59036	−	5.51472i	0.306572	−	0.222737i	0.730424	+	0.682994i	$0.239322\pi$
$614$	−5.48258	+	16.8736i	−0.221259	+	0.680965i
$615$	−4.56289			−0.183994
$616$	−9.64705	+	2.25173i	−0.388691	+	0.0907247i
$617$	19.3560			0.779242			0.389621	−	0.920975i	$-0.372606\pi$
$617$	19.3560			0.779242			0.389621	+	0.920975i	$0.372606\pi$
$618$	2.89390	−	8.90650i	0.116410	−	0.358272i
$619$	−12.4232	+	9.02597i	−0.499330	+	0.362784i	−0.808761	−	0.588138i	$-0.799861\pi$
$619$	−12.4232	+	9.02597i	−0.499330	+	0.362784i	0.309431	+	0.950922i	$0.399861\pi$
$620$	−3.56123	−	2.58738i	−0.143022	−	0.103912i
$621$	−0.629069	−	1.93607i	−0.0252437	−	0.0776920i
$622$	−5.55438	−	17.0946i	−0.222710	−	0.685431i
$623$	10.7178	+	7.78693i	0.429399	+	0.311977i
$624$	−3.02507	+	2.19784i	−0.121100	+	0.0879842i
$625$	30.6871	−	94.4452i	1.22748	−	3.77781i
$626$	36.4998			1.45883
$627$	0.726021	−	8.53560i	0.0289945	−	0.340879i
$628$	−0.489572			−0.0195361
$629$	0.579851	−	1.78460i	0.0231202	−	0.0711566i
$630$	−4.95205	+	3.59788i	−0.197294	+	0.143343i
$631$	−5.97008	−	4.33751i	−0.237665	−	0.172674i	0.462577	−	0.886579i	$-0.346925\pi$
$631$	−5.97008	−	4.33751i	−0.237665	−	0.172674i	−0.700242	+	0.713905i	$0.746925\pi$
$632$	−7.54287	−	23.2146i	−0.300039	−	0.923426i
$633$	−3.40448	−	10.4779i	−0.135316	−	0.416459i
$634$	11.0935	+	8.05990i	0.440579	+	0.320099i
$635$	7.65271	−	5.56002i	0.303688	−	0.220643i
$636$	0.292061	−	0.898872i	0.0115810	−	0.0356426i
$637$	5.94538			0.235564
$638$	1.31265	−	1.51741i	0.0519685	−	0.0600750i
$639$	7.36089			0.291192
$640$	−13.6597	+	42.0402i	−0.539947	+	1.66179i
$641$	8.09850	−	5.88390i	0.319871	−	0.232400i	−0.416249	−	0.909251i	$-0.636656\pi$
$641$	8.09850	−	5.88390i	0.319871	−	0.232400i	0.736121	+	0.676850i	$0.236656\pi$
$642$	6.40218	+	4.65145i	0.252674	+	0.183578i
$643$	1.75638	+	5.40557i	0.0692647	+	0.213175i	0.979697	−	0.200483i	$-0.0642511\pi$
$643$	1.75638	+	5.40557i	0.0692647	+	0.213175i	−0.910433	+	0.413658i	$0.864251\pi$
$644$	−0.0793672	−	0.244267i	−0.00312751	−	0.00962547i
$645$	27.8147	+	20.2086i	1.09520	+	0.795711i
$646$	−16.0568	+	11.6659i	−0.631745	+	0.458989i
$647$	−6.07944	+	18.7106i	−0.239008	+	0.735590i	0.757557	+	0.652769i	$0.226393\pi$
$647$	−6.07944	+	18.7106i	−0.239008	+	0.735590i	−0.996564	+	0.0828207i	$0.973607\pi$
$648$	−2.90850			−0.114257
$649$	−33.4613	−	14.1083i	−1.31347	−	0.553799i
$650$	−19.0800			−0.748379
$651$	−2.61365	+	8.04399i	−0.102437	+	0.315269i
$652$	−2.08756	+	1.51670i	−0.0817552	+	0.0593987i
$653$	−12.7446	−	9.25953i	−0.498737	−	0.362353i	0.309798	−	0.950803i	$-0.399739\pi$
$653$	−12.7446	−	9.25953i	−0.498737	−	0.362353i	−0.808534	+	0.588449i	$0.799739\pi$
$654$	−7.48227	−	23.0281i	−0.292580	−	0.900469i
$655$	4.89480	+	15.0647i	0.191256	+	0.588625i
$656$	3.17282	+	2.30519i	0.123878	+	0.0900025i
$657$	10.0853	−	7.32736i	0.393463	−	0.285868i
$658$	0.563074	−	1.73296i	0.0219509	−	0.0675580i
$659$	35.0390			1.36493			0.682463	−	0.730920i	$-0.260909\pi$
$659$	35.0390			1.36493			0.682463	+	0.730920i	$0.260909\pi$
$660$	−0.916642	−	1.51725i	−0.0356803	−	0.0590587i
$661$	−12.8812			−0.501020			−0.250510	−	0.968114i	$-0.580598\pi$
$661$	−12.8812			−0.501020			−0.250510	+	0.968114i	$0.580598\pi$
$662$	14.8358	−	45.6598i	0.576609	−	1.77462i
$663$	−4.53739	+	3.29661i	−0.176218	+	0.128030i
$664$	23.3475	+	16.9629i	0.906058	+	0.658289i
$665$	−3.56586	−	10.9746i	−0.138278	−	0.425576i
$666$	−0.141650	−	0.435954i	−0.00548883	−	0.0168929i
$667$	0.727183	+	0.528329i	0.0281566	+	0.0204570i
$668$	1.25974	−	0.915256i	0.0487409	−	0.0354123i
$669$	0.995258	−	3.06309i	0.0384789	−	0.118426i
$670$	−38.1141			−1.47248
$671$	−12.2392	−	20.2586i	−0.472490	−	0.782075i
$672$	−0.712672			−0.0274919
$673$	−12.4887	+	38.4363i	−0.481404	+	1.48161i	0.355719	+	0.934593i	$0.384236\pi$
$673$	−12.4887	+	38.4363i	−0.481404	+	1.48161i	−0.837122	+	0.547015i	$0.815764\pi$
$674$	−12.5400	+	9.11087i	−0.483024	+	0.350937i
$675$	−11.2664	−	8.18555i	−0.433646	−	0.315062i
$676$	−0.0379644	−	0.116843i	−0.00146017	−	0.00449394i
$677$	−12.6853	−	39.0414i	−0.487536	−	1.50048i	−0.828274	−	0.560323i	$-0.810677\pi$
$677$	−12.6853	−	39.0414i	−0.487536	−	1.50048i	0.340738	−	0.940158i	$-0.389323\pi$
$678$	−1.82695	−	1.32736i	−0.0701637	−	0.0509769i
$679$	8.92413	−	6.48376i	0.342477	−	0.248824i
$680$	−21.9296	+	67.4924i	−0.840962	+	2.58821i
$681$	9.67809			0.370865
$682$	34.4851	+	14.5400i	1.32050	+	0.556764i
$683$	33.3631			1.27660			0.638302	−	0.769786i	$-0.279637\pi$
$683$	33.3631			1.27660			0.638302	+	0.769786i	$0.279637\pi$
$684$	0.0980573	−	0.301789i	0.00374932	−	0.0115392i
$685$	39.4998	−	28.6983i	1.50921	−	1.09651i
$686$	−14.7357	−	10.7061i	−0.562610	−	0.408760i
$687$	−0.973013	−	2.99462i	−0.0371227	−	0.114252i
$688$	−9.13160	−	28.1042i	−0.348139	−	1.07146i
$689$	−6.22378	−	4.52184i	−0.237107	−	0.172269i
$690$	−9.81641	+	7.13204i	−0.373704	+	0.271512i
$691$	5.57968	−	17.1725i	0.212261	−	0.653273i	−0.787076	−	0.616857i	$-0.788406\pi$
$691$	5.57968	−	17.1725i	0.212261	−	0.653273i	0.999337	−	0.0364160i	$-0.0115941\pi$
$692$	−2.53256			−0.0962734
$693$	−2.22833	+	2.57592i	−0.0846472	+	0.0978513i
$694$	1.47292			0.0559113
$695$	−17.6373	+	54.2820i	−0.669021	+	2.05903i
$696$	1.03896	−	0.754846i	0.0393815	−	0.0286124i
$697$	4.75900	+	3.45762i	0.180260	+	0.130967i
$698$	−5.62595	−	17.3149i	−0.212945	−	0.655379i
$699$	−3.62220	−	11.1480i	−0.137004	−	0.421655i
$700$	−1.42144	−	1.03274i	−0.0537255	−	0.0390339i
$701$	−10.8864	+	7.90945i	−0.411175	+	0.298736i	−0.774077	−	0.633091i	$-0.781786\pi$
$701$	−10.8864	+	7.90945i	−0.411175	+	0.298736i	0.362903	+	0.931827i	$0.381786\pi$
$702$	−0.423381	+	1.30303i	−0.0159795	+	0.0491798i
$703$	0.864149			0.0325920
$704$	−2.36937	+	27.8559i	−0.0892989	+	1.04986i
$705$	5.63400			0.212189
$706$	8.16105	−	25.1171i	0.307145	−	0.945296i
$707$	9.24102	−	6.71400i	0.347544	−	0.252506i
$708$	−1.08825	−	0.790662i	−0.0408990	−	0.0297149i
$709$	1.57026	+	4.83275i	0.0589722	+	0.181498i	0.976203	−	0.216858i	$-0.0695809\pi$
$709$	1.57026	+	4.83275i	0.0589722	+	0.181498i	−0.917231	+	0.398356i	$0.869581\pi$
$710$	−13.5579	−	41.7269i	−0.508819	−	1.56598i
$711$	−6.78958	−	4.93292i	−0.254629	−	0.184999i
$712$	30.3547	−	22.0540i	1.13759	−	0.826509i
$713$	−5.18102	+	15.9455i	−0.194031	+	0.597165i
$714$	7.89125			0.295323
$715$	−14.0510	+	3.27966i	−0.525478	+	0.122652i
$716$	−0.749868			−0.0280239
$717$	−1.68393	+	5.18262i	−0.0628877	+	0.193548i
$718$	−22.7074	+	16.4979i	−0.847433	+	0.615696i
$719$	10.6522	+	7.73928i	0.397260	+	0.288626i	0.768424	−	0.639941i	$-0.221041\pi$
$719$	10.6522	+	7.73928i	0.397260	+	0.288626i	−0.371164	+	0.928567i	$0.621041\pi$
$720$	5.02679	+	15.4709i	0.187338	+	0.576566i
$721$	−2.16912	−	6.67585i	−0.0807821	−	0.248622i
$722$	13.6655	+	9.92858i	0.508578	+	0.369504i
$723$	−7.11754	+	5.17119i	−0.264704	+	0.192319i
$724$	−0.454694	+	1.39940i	−0.0168986	+	0.0520084i
$725$	6.14893			0.228366
$726$	10.5214	+	10.7905i	0.390485	+	0.400474i
$727$	38.0475			1.41110			0.705551	−	0.708659i	$-0.250699\pi$
$727$	38.0475			1.41110			0.705551	+	0.708659i	$0.250699\pi$
$728$	−0.922996	+	2.84069i	−0.0342085	+	0.105283i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−60.1127	−	43.6744i	−2.22487	−	1.61646i
$731$	−13.6967	−	42.1542i	−0.506592	−	1.55913i
$732$	−0.270929	−	0.833835i	−0.0100138	−	0.0308194i
$733$	21.8725	+	15.8913i	0.807879	+	0.586959i	0.913215	−	0.407478i	$-0.133592\pi$
$733$	21.8725	+	15.8913i	0.807879	+	0.586959i	−0.105336	+	0.994437i	$0.533592\pi$
$734$	9.08583	−	6.60124i	0.335364	−	0.243656i
$735$	7.99268	−	24.5989i	0.294814	−	0.907345i
$736$	−1.41272			−0.0520737
$737$	−20.6530	+	4.82064i	−0.760764	+	0.177571i
$738$	1.43701			0.0528969
$739$	−12.0927	+	37.2175i	−0.444837	+	1.36907i	0.437826	+	0.899060i	$0.355749\pi$
$739$	−12.0927	+	37.2175i	−0.444837	+	1.36907i	−0.882663	+	0.470007i	$0.844251\pi$
$740$	0.144667	−	0.105106i	0.00531805	−	0.00386379i
$741$	−2.08959	−	1.51817i	−0.0767629	−	0.0557715i
$742$	3.34485	+	10.2944i	0.122793	+	0.377919i
$743$	−1.04229	−	3.20783i	−0.0382378	−	0.117684i	0.930116	−	0.367267i	$-0.119706\pi$
$743$	−1.04229	−	3.20783i	−0.0382378	−	0.117684i	−0.968353	+	0.249583i	$0.919706\pi$
$744$	19.3796	+	14.0801i	0.710489	+	0.516200i
$745$	−57.3272	+	41.6506i	−2.10031	+	1.52596i
$746$	1.38364	−	4.25840i	0.0506586	−	0.155911i
$747$	9.92231			0.363038
$748$	−0.193682	+	2.27706i	−0.00708172	+	0.0832575i
$749$	5.93157			0.216735
$750$	−16.4408	+	50.5996i	−0.600333	+	1.84764i
$751$	−15.0059	+	10.9024i	−0.547573	+	0.397835i	−0.826890	−	0.562364i	$-0.809892\pi$
$751$	−15.0059	+	10.9024i	−0.547573	+	0.397835i	0.279317	+	0.960199i	$0.409892\pi$
$752$	−3.91762	−	2.84631i	−0.142861	−	0.103794i
$753$	4.67149	+	14.3774i	0.170238	+	0.523940i
$754$	−0.186940	−	0.575341i	−0.00680794	−	0.0209527i
$755$	−21.6201	−	15.7080i	−0.786838	−	0.571671i
$756$	−0.102071	+	0.0741586i	−0.00371227	+	0.00269712i
$757$	−12.2923	+	37.8318i	−0.446771	+	1.37502i	0.433759	+	0.901029i	$0.357187\pi$
$757$	−12.2923	+	37.8318i	−0.446771	+	1.37502i	−0.880530	+	0.473990i	$0.842813\pi$
$758$	13.6856			0.497083
$759$	−4.41719	+	5.10623i	−0.160334	+	0.185344i
$760$	−32.6816			−1.18548
$761$	6.72507	−	20.6976i	0.243784	−	0.750289i	−0.752050	−	0.659106i	$-0.770935\pi$
$761$	6.72507	−	20.6976i	0.243784	−	0.750289i	0.995834	−	0.0911835i	$-0.0290650\pi$
$762$	−2.41009	+	1.75103i	−0.0873084	+	0.0634333i
$763$	−14.6828	−	10.6677i	−0.531552	−	0.386195i
$764$	0.764163	+	2.35185i	0.0276465	+	0.0850870i
$765$	7.53983	+	23.2052i	0.272603	+	0.838986i
$766$	−0.595884	−	0.432935i	−0.0215302	−	0.0156426i
$767$	−8.85798	+	6.43570i	−0.319843	+	0.232380i
$768$	−0.907638	+	2.79342i	−0.0327516	+	0.100799i
$769$	−22.8546			−0.824158			−0.412079	−	0.911148i	$-0.635197\pi$
$769$	−22.8546			−0.824158			−0.412079	+	0.911148i	$0.635197\pi$
$770$	18.7065	+	7.88724i	0.674137	+	0.284236i
$771$	15.2140			0.547918
$772$	0.921827	−	2.83709i	0.0331773	−	0.102109i
$773$	13.7142	−	9.96391i	0.493264	−	0.358377i	−0.313174	−	0.949696i	$-0.601392\pi$
$773$	13.7142	−	9.96391i	0.493264	−	0.358377i	0.806438	+	0.591319i	$0.201392\pi$
$774$	−8.75977	−	6.36435i	−0.314864	−	0.228762i
$775$	35.4428	+	109.082i	1.27314	+	3.91833i
$776$	−9.65409	−	29.7122i	−0.346562	−	1.06661i
$777$	−0.277966	−	0.201954i	−0.00997197	−	0.00724506i
$778$	−4.64544	+	3.37511i	−0.166547	+	0.121004i
$779$	−0.837134	+	2.57643i	−0.0299934	+	0.0923103i
$780$	−0.534472			−0.0191372
$781$	−12.6242	−	20.8959i	−0.451731	−	0.747714i
$782$	15.6427			0.559383
$783$	0.136443	−	0.419930i	0.00487609	−	0.0150071i
$784$	−17.9852	+	13.0670i	−0.642329	+	0.466679i
$785$	14.0252	+	10.1899i	0.500582	+	0.363694i
$786$	−1.54154	−	4.74436i	−0.0549848	−	0.169226i
$787$	7.39412	+	22.7568i	0.263572	+	0.811191i	0.992019	+	0.126089i	$0.0402425\pi$
$787$	7.39412	+	22.7568i	0.263572	+	0.811191i	−0.728447	+	0.685102i	$0.759758\pi$
$788$	−0.926146	−	0.672885i	−0.0329926	−	0.0239705i
$789$	21.9896	−	15.9763i	0.782849	−	0.568773i
$790$	−15.4578	+	47.5741i	−0.549963	+	1.69261i
$791$	−1.69266			−0.0601840
$792$	4.98820	+	8.25657i	0.177248	+	0.293385i
$793$	−7.13640			−0.253421
$794$	−0.380747	+	1.17182i	−0.0135122	+	0.0415863i
$795$	−27.0760	+	19.6719i	−0.960288	+	0.697690i
$796$	2.69527	+	1.95823i	0.0955315	+	0.0694077i
$797$	−5.16432	−	15.8941i	−0.182930	−	0.562999i	0.816977	−	0.576670i	$-0.195648\pi$
$797$	−5.16432	−	15.8941i	−0.182930	−	0.562999i	−0.999907	+	0.0136709i	$0.995648\pi$
$798$	1.12301	+	3.45626i	0.0397540	+	0.122350i
$799$	−5.87614	−	4.26927i	−0.207883	−	0.151036i
$800$	−7.81859	+	5.68054i	−0.276429	+	0.200837i
$801$	3.98641	−	12.2689i	0.140853	−	0.433501i
$802$	−22.6381			−0.799381
$803$	−38.0973	−	16.0630i	−1.34443	−	0.566851i
$804$	−0.785600			−0.0277060
$805$	−2.81046	+	8.64969i	−0.0990555	+	0.304862i
$806$	9.12900	−	6.63261i	0.321555	−	0.233624i
$807$	18.5603	+	13.4849i	0.653354	+	0.474689i
$808$	−9.99691	−	30.7673i	−0.351690	−	1.08239i
$809$	6.86474	+	21.1275i	0.241351	+	0.742803i	0.996215	+	0.0869215i	$0.0277029\pi$
$809$	6.86474	+	21.1275i	0.241351	+	0.742803i	−0.754864	+	0.655882i	$0.772297\pi$
$810$	4.82211	+	3.50347i	0.169432	+	0.123099i
$811$	−19.0339	+	13.8289i	−0.668369	+	0.485598i	−0.869479	−	0.493970i	$-0.835545\pi$
$811$	−19.0339	+	13.8289i	−0.668369	+	0.485598i	0.201110	+	0.979569i	$0.435545\pi$
$812$	0.0172146	−	0.0529810i	0.000604112	−	0.00185927i
$813$	11.1506			0.391067
$814$	−0.994639	+	1.14979i	−0.0348621	+	0.0403002i
$815$	91.3729			3.20065
$816$	6.48051	−	19.9450i	0.226863	−	0.698213i
$817$	16.5138	−	11.9980i	0.577745	−	0.419756i
$818$	32.6807	+	23.7439i	1.14265	+	0.830187i
$819$	0.317344	+	0.976685i	0.0110889	+	0.0341281i
$820$	0.173228	+	0.533140i	0.00604937	+	0.0186181i
$821$	5.54519	+	4.02882i	0.193529	+	0.140607i	0.680330	−	0.732906i	$-0.261836\pi$
$821$	5.54519	+	4.02882i	0.193529	+	0.140607i	−0.486801	+	0.873513i	$0.661836\pi$
$822$	−12.4398	+	9.03805i	−0.433888	+	0.315238i
$823$	−0.841045	+	2.58847i	−0.0293170	+	0.0902284i	−0.964644	−	0.263555i	$-0.915105\pi$
$823$	−0.841045	+	2.58847i	−0.0293170	+	0.0902284i	0.935327	+	0.353783i	$0.115105\pi$
$824$	−19.8802			−0.692561
$825$	−3.91449	+	46.0214i	−0.136285	+	1.60226i
$826$	15.4054			0.536024
$827$	−1.50490	+	4.63161i	−0.0523305	+	0.161057i	−0.973806	−	0.227379i	$-0.926984\pi$
$827$	−1.50490	+	4.63161i	−0.0523305	+	0.161057i	0.921476	+	0.388436i	$0.126984\pi$
$828$	−0.202334	+	0.147004i	−0.00703158	+	0.00510874i
$829$	−8.49011	−	6.16842i	−0.294874	−	0.214238i	0.430505	−	0.902588i	$-0.358335\pi$
$829$	−8.49011	−	6.16842i	−0.294874	−	0.214238i	−0.725379	+	0.688350i	$0.758335\pi$
$830$	−18.2757	−	56.2469i	−0.634360	−	1.95236i
$831$	−3.95531	−	12.1732i	−0.137208	−	0.422283i
$832$	6.81936	+	4.95456i	0.236419	+	0.171768i
$833$	−26.9765	+	19.5996i	−0.934680	+	0.679085i
$834$	5.55457	−	17.0952i	0.192339	−	0.591959i
$835$	−55.1391			−1.90817
$836$	−1.02488	+	0.239219i	−0.0354464	+	0.00827356i
$837$	8.23601			0.284678
$838$	4.67037	−	14.3739i	0.161335	−	0.496539i
$839$	35.4904	−	25.7853i	1.22526	−	0.890206i	0.228738	−	0.973488i	$-0.426540\pi$
$839$	35.4904	−	25.7853i	1.22526	−	0.890206i	0.996526	+	0.0832817i	$0.0265401\pi$
$840$	10.5125	+	7.63777i	0.362715	+	0.263528i
$841$	−8.90125	−	27.3952i	−0.306940	−	0.944663i
$842$	−15.1020	−	46.4791i	−0.520448	−	1.60177i
$843$	−12.2493	−	8.89966i	−0.421889	−	0.306520i
$844$	−1.09502	+	0.795575i	−0.0376920	+	0.0273848i
$845$	−1.34435	+	4.13749i	−0.0462471	+	0.142334i
$846$	−1.77433			−0.0610028
$847$	11.1341	+	1.90790i	0.382574	+	0.0655562i
$848$	28.7657			0.987818
$849$	4.84478	−	14.9107i	0.166272	−	0.511734i
$850$	86.5733	−	62.8992i	2.96944	−	2.15743i
$851$	−0.551009	−	0.400332i	−0.0188884	−	0.0137232i
$852$	−0.279452	−	0.860065i	−0.00957387	−	0.0294654i
$853$	−10.1172	−	31.1375i	−0.346406	−	1.06613i	−0.960827	−	0.277150i	$-0.910610\pi$
$853$	−10.1172	−	31.1375i	−0.346406	−	1.06613i	0.614421	−	0.788979i	$-0.289390\pi$
$854$	8.12332	+	5.90194i	0.277974	+	0.201960i
$855$	−9.09057	+	6.60468i	−0.310891	+	0.225875i
$856$	5.19126	−	15.9771i	0.177434	−	0.546085i
$857$	3.58344			0.122408			0.0612039	−	0.998125i	$-0.480506\pi$
$857$	3.58344			0.122408			0.0612039	+	0.998125i	$0.480506\pi$
$858$	4.42513	−	1.03287i	0.151071	−	0.0352617i
$859$	20.9388			0.714422			0.357211	−	0.934024i	$-0.383728\pi$
$859$	20.9388			0.714422			0.357211	+	0.934024i	$0.383728\pi$
$860$	1.30525	−	4.01715i	0.0445087	−	0.136984i
$861$	0.871396	−	0.633107i	0.0296971	−	0.0215762i
$862$	−8.31446	−	6.04081i	−0.283192	−	0.205751i
$863$	7.69146	+	23.6719i	0.261820	+	0.805801i	0.992409	+	0.122982i	$0.0392459\pi$
$863$	7.69146	+	23.6719i	0.261820	+	0.805801i	−0.730588	+	0.682818i	$0.760754\pi$
$864$	0.214449	+	0.660006i	0.00729570	+	0.0224539i
$865$	72.5526	+	52.7125i	2.46686	+	1.79228i
$866$	−19.3239	+	14.0396i	−0.656652	+	0.477086i
$867$	4.46701	−	13.7480i	0.151707	−	0.466908i
$868$	1.03911			0.0352696
$869$	−2.35902	+	27.7342i	−0.0800243	+	0.940820i
$870$	−2.63178			−0.0892257
$871$	−1.97601	+	6.08153i	−0.0669546	+	0.206065i
$872$	−41.5843	+	30.2127i	−1.40822	+	1.02313i
$873$	−8.68995	−	6.31362i	−0.294110	−	0.213684i
$874$	2.22613	+	6.85131i	0.0752998	+	0.231749i
$875$	12.3232	+	37.9268i	0.416599	+	1.28216i
$876$	−1.23903	−	0.900207i	−0.0418629	−	0.0304152i
$877$	−10.8101	+	7.85403i	−0.365032	+	0.265212i	−0.755148	−	0.655554i	$-0.772435\pi$
$877$	−10.8101	+	7.85403i	−0.365032	+	0.265212i	0.390116	+	0.920766i	$0.372435\pi$
$878$	2.28295	−	7.02618i	0.0770457	−	0.237122i
$879$	−18.2813			−0.616614
$880$	35.2971	−	40.8031i	1.18987	−	1.37547i
$881$	23.6324			0.796196			0.398098	−	0.917343i	$-0.369670\pi$
$881$	23.6324			0.796196			0.398098	+	0.917343i	$0.369670\pi$
$882$	−2.51716	+	7.74702i	−0.0847572	+	0.260856i
$883$	−14.9214	+	10.8410i	−0.502144	+	0.364829i	−0.809835	−	0.586657i	$-0.800444\pi$
$883$	−14.9214	+	10.8410i	−0.502144	+	0.364829i	0.307691	+	0.951486i	$0.400444\pi$
$884$	0.557444	+	0.405006i	0.0187489	+	0.0136218i
$885$	14.7194	+	45.3016i	0.494787	+	1.52280i
$886$	14.8747	+	45.7797i	0.499726	+	1.53800i
$887$	−20.5987	−	14.9658i	−0.691636	−	0.502503i	0.185562	−	0.982633i	$-0.440590\pi$
$887$	−20.5987	−	14.9658i	−0.691636	−	0.502503i	−0.877197	+	0.480130i	$0.840590\pi$
$888$	−0.787250	+	0.571970i	−0.0264184	+	0.0191941i
$889$	−0.690014	+	2.12364i	−0.0231423	+	0.0712247i
$890$	−76.8916			−2.57741
$891$	3.05609	+	1.28854i	0.102383	+	0.0431677i
$892$	−0.395683			−0.0132485
$893$	1.03364	−	3.18123i	0.0345896	−	0.106456i
$894$	18.0542	−	13.1172i	0.603824	−	0.438704i
$895$	21.4822	+	15.6077i	0.718070	+	0.521708i
$896$	−3.22447	−	9.92391i	−0.107722	−	0.331534i
$897$	0.629069	+	1.93607i	0.0210040	+	0.0646436i
$898$	−10.1488	−	7.37353i	−0.338670	−	0.246058i
$899$	−2.94202	+	2.13750i	−0.0981217	+	0.0712896i
$900$	−0.528696	+	1.62716i	−0.0176232	+	0.0542387i
$901$	43.1465			1.43742
$902$	−2.46453	−	4.07933i	−0.0820598	−	0.135827i
$903$	−8.11586			−0.270079
$904$	−1.48140	+	4.55928i	−0.0492706	+	0.151639i
$905$	42.1532	−	30.6261i	1.40122	−	1.01804i
$906$	6.80890	+	4.94696i	0.226211	+	0.164352i
$907$	16.5904	+	51.0600i	0.550875	+	1.69542i	0.706596	+	0.707617i	$0.250230\pi$
$907$	16.5904	+	51.0600i	0.550875	+	1.69542i	−0.155721	+	0.987801i	$0.549770\pi$
$908$	−0.367423	−	1.13081i	−0.0121934	−	0.0375273i
$909$	−8.99853	−	6.53782i	−0.298463	−	0.216846i
$910$	4.95205	−	3.59788i	0.164159	−	0.119268i
$911$	−1.97711	+	6.08491i	−0.0655045	+	0.201602i	−0.978452	−	0.206475i	$-0.933801\pi$
$911$	−1.97711	+	6.08491i	−0.0655045	+	0.201602i	0.912947	+	0.408077i	$0.133801\pi$
$912$	9.65786			0.319804
$913$	−17.0172	−	28.1672i	−0.563187	−	0.932198i
$914$	40.1314			1.32743
$915$	−9.59383	+	29.5268i	−0.317162	+	0.976124i
$916$	−0.312960	+	0.227379i	−0.0103405	+	0.00751280i
$917$	−3.02502	−	2.19781i	−0.0998950	−	0.0725780i
$918$	−2.37454	−	7.30809i	−0.0783715	−	0.241203i
$919$	5.72411	+	17.6170i	0.188821	+	0.581132i	0.999993	−	0.00367590i	$-0.00117008\pi$
$919$	5.72411	+	17.6170i	0.188821	+	0.581132i	−0.811172	+	0.584807i	$0.801170\pi$
$920$	20.8388	+	15.1403i	0.687035	+	0.499160i
$921$	10.4764	−	7.61154i	0.345209	−	0.250809i
$922$	−2.45305	+	7.54972i	−0.0807870	+	0.248637i
$923$	−7.36089			−0.242287
$924$	0.385575	+	0.162570i	0.0126845	+	0.00534816i
$925$	−4.65924			−0.153195
$926$	−6.40685	+	19.7182i	−0.210542	+	0.647982i
$927$	−5.52980	+	4.01764i	−0.181623	+	0.131957i
$928$	−0.247896	−	0.180107i	−0.00813759	−	0.00591231i
$929$	2.37966	+	7.32383i	0.0780740	+	0.240287i	0.982474	−	0.186398i	$-0.0596813\pi$
$929$	2.37966	+	7.32383i	0.0780740	+	0.240287i	−0.904400	+	0.426685i	$0.859681\pi$
$930$	−15.1698	−	46.6877i	−0.497436	−	1.53095i
$931$	−12.4234	−	9.02612i	−0.407160	−	0.295819i
$932$	−1.16504	+	0.846454i	−0.0381623	+	0.0277265i
$933$	−4.05402	+	12.4770i	−0.132723	+	0.408479i
$934$	57.8268			1.89215
$935$	52.9432	−	61.2017i	1.73143	−	2.00151i
$936$	2.90850			0.0950673
$937$	6.17036	−	18.9904i	0.201577	−	0.620390i	−0.798260	−	0.602314i	$-0.794246\pi$
$937$	6.17036	−	18.9904i	0.201577	−	0.620390i	0.999837	−	0.0180767i	$-0.00575430\pi$
$938$	7.27883	−	5.28838i	0.237662	−	0.172672i
$939$	−21.5526	−	15.6589i	−0.703342	−	0.511008i
$940$	−0.213892	−	0.658290i	−0.00697637	−	0.0214711i
$941$	8.75669	+	26.9503i	0.285460	+	0.878555i	0.986260	+	0.165198i	$0.0528263\pi$
$941$	8.75669	+	26.9503i	0.285460	+	0.878555i	−0.700801	+	0.713357i	$0.747174\pi$
$942$	−4.41701	−	3.20915i	−0.143914	−	0.104560i
$943$	1.72736	−	1.25500i	0.0562506	−	0.0408685i
$944$	12.6514	−	38.9369i	0.411767	−	1.26729i
$945$	4.46765			0.145333
$946$	−3.04356	+	35.7821i	−0.0989546	+	1.16338i
$947$	−20.0257			−0.650746			−0.325373	−	0.945586i	$-0.605490\pi$
$947$	−20.0257			−0.650746			−0.325373	+	0.945586i	$0.605490\pi$
$948$	−0.318612	+	0.980587i	−0.0103480	+	0.0318480i
$949$	−10.0853	+	7.32736i	−0.327381	+	0.237856i
$950$	39.8693	+	28.9667i	1.29353	+	0.939805i
$951$	−3.09275	−	9.51850i	−0.100289	−	0.308658i
$952$	−5.17665	−	15.9321i	−0.167776	−	0.516362i
$953$	14.4617	+	10.5070i	0.468459	+	0.340355i	0.796840	−	0.604190i	$-0.206503\pi$
$953$	14.4617	+	10.5070i	0.468459	+	0.340355i	−0.328382	+	0.944545i	$0.606503\pi$
$954$	8.52714	−	6.19533i	0.276076	−	0.200581i
$955$	27.0596	−	83.2810i	0.875629	−	2.69491i
$956$	0.669480			0.0216525
$957$	−1.42609	+	0.332865i	−0.0460990	+	0.0107600i
$958$	−34.7713			−1.12341
$959$	−3.56154	+	10.9613i	−0.115008	+	0.353959i
$960$	29.6670	−	21.5544i	0.957499	−	0.695664i
$961$	−29.7976	−	21.6492i	−0.961213	−	0.698362i
$962$	0.141650	+	0.435954i	0.00456698	+	0.0140557i
$963$	−1.78486	−	5.49323i	−0.0575162	−	0.177017i
$964$	0.874429	+	0.635310i	0.0281635	+	0.0204619i
$965$	−85.4596	+	62.0900i	−2.75104	+	1.99875i
$966$	0.885106	−	2.72408i	0.0284778	−	0.0876457i
$967$	22.4651			0.722428			0.361214	−	0.932483i	$-0.382362\pi$
$967$	22.4651			0.722428			0.361214	+	0.932483i	$0.382362\pi$
$968$	14.8836	−	28.3207i	0.478376	−	0.910263i
$969$	14.4861			0.465361
$970$	−19.7843	+	60.8899i	−0.635237	+	1.95506i
$971$	−34.3448	+	24.9529i	−1.10218	+	0.800778i	−0.981414	−	0.191904i	$-0.938534\pi$
$971$	−34.3448	+	24.9529i	−1.10218	+	0.800778i	−0.120762	+	0.992681i	$0.538534\pi$
$972$	0.0993922	+	0.0722127i	0.00318801	+	0.00231622i
$973$	−4.16342	−	12.8137i	−0.133473	−	0.410788i
$974$	3.59322	+	11.0588i	0.115134	+	0.354347i
$975$	11.2664	+	8.18555i	0.360815	+	0.262147i
$976$	21.5881	−	15.6847i	0.691019	−	0.502055i
$977$	−2.68919	+	8.27647i	−0.0860348	+	0.264788i	−0.984814	−	0.173614i	$-0.944455\pi$
$977$	−2.68919	+	8.27647i	−0.0860348	+	0.264788i	0.898779	+	0.438402i	$0.144455\pi$
$978$	−28.7764			−0.920167
$979$	−41.6655	+	9.72518i	−1.33164	+	0.310818i
$980$	−3.17764			−0.101506
$981$	−5.46116	+	16.8077i	−0.174361	+	0.536629i
$982$	23.2483	−	16.8909i	0.741883	−	0.539010i
$983$	22.4208	+	16.2896i	0.715111	+	0.519559i	0.884819	−	0.465936i	$-0.154282\pi$
$983$	22.4208	+	16.2896i	0.715111	+	0.519559i	−0.169707	+	0.985495i	$0.554282\pi$
$984$	−0.942674	−	2.90125i	−0.0300513	−	0.0924885i
$985$	12.5268	+	38.5535i	0.399137	+	1.22842i
$986$	2.74489	+	1.99428i	0.0874152	+	0.0635109i
$987$	−1.07595	+	0.781723i	−0.0342479	+	0.0248825i
$988$	−0.0980573	+	0.301789i	−0.00311962	+	0.00960120i
$989$	−16.0880			−0.511568
$990$	1.67543	−	19.6975i	0.0532486	−	0.626026i
$991$	30.9181			0.982144			0.491072	−	0.871119i	$-0.336605\pi$
$991$	30.9181			0.982144			0.491072	+	0.871119i	$0.336605\pi$
$992$	1.76620	−	5.43582i	0.0560770	−	0.172587i
$993$	−28.3489	+	20.5967i	−0.899626	+	0.653617i
$994$	8.37887	+	6.08760i	0.265761	+	0.193087i
$995$	−36.4555	−	112.199i	−1.15572	−	3.55693i
$996$	−0.376695	−	1.15935i	−0.0119360	−	0.0367354i
$997$	−1.94398	−	1.41239i	−0.0615665	−	0.0447307i	0.556576	−	0.830796i	$-0.312115\pi$
$997$	−1.94398	−	1.41239i	−0.0615665	−	0.0447307i	−0.618143	+	0.786066i	$0.712115\pi$
$998$	−37.9101	+	27.5433i	−1.20002	+	0.871869i
$999$	−0.103387	+	0.318194i	−0.00327104	+	0.0100672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.196.7	✓	36
11.4	even	5		4719.2.a.bq.1.13		18
11.5	even	5	inner	429.2.n.d.313.7	yes	36
11.7	odd	10		4719.2.a.br.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.196.7	✓	36	1.1	even	1	trivial
429.2.n.d.313.7	yes	36	11.5	even	5	inner
4719.2.a.bq.1.13		18	11.4	even	5
4719.2.a.br.1.6		18	11.7	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.423381 - 1.30303i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.0993922 + 0.0722127i) q^{4} +(-1.34435 - 4.13749i) q^{5} +(0.423381 + 1.30303i) q^{6} +(0.830818 + 0.603625i) q^{7} +(2.35303 - 1.70957i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.423381 - 1.30303i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.0993922 + 0.0722127i) q^{4} +(-1.34435 - 4.13749i) q^{5} +(0.423381 + 1.30303i) q^{6} +(0.830818 + 0.603625i) q^{7} +(2.35303 - 1.70957i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.96045 q^{10} +(-3.22981 + 0.753873i) q^{11} -0.122856 q^{12} +(-0.309017 + 0.951057i) q^{13} +(1.13829 - 0.827020i) q^{14} +(3.51956 + 2.55711i) q^{15} +(-1.15547 - 3.55619i) q^{16} +(-1.73313 - 5.33402i) q^{17} +(-1.10843 - 0.805318i) q^{18} +(2.08959 - 1.51817i) q^{19} +(0.165161 - 0.508313i) q^{20} -1.02695 q^{21} +(-0.385119 + 4.52772i) q^{22} -2.03571 q^{23} +(-0.898776 + 2.76615i) q^{24} +(-11.2664 + 8.18555i) q^{25} +(1.10843 + 0.805318i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.0389875 + 0.119991i) q^{28} +(-0.357214 - 0.259531i) q^{29} +(4.82211 - 3.50347i) q^{30} +(2.54507 - 7.83291i) q^{31} +0.693972 q^{32} +(2.16986 - 2.50833i) q^{33} -7.68418 q^{34} +(1.38058 - 4.24898i) q^{35} +(0.0993922 - 0.0722127i) q^{36} +(0.270672 + 0.196655i) q^{37} +(-1.09354 - 3.36557i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-10.2366 - 7.43735i) q^{40} +(-0.848531 + 0.616494i) q^{41} +(-0.434790 + 1.33815i) q^{42} +7.90290 q^{43} +(-0.375457 - 0.158304i) q^{44} -4.35041 q^{45} +(-0.861880 + 2.65259i) q^{46} +(1.04772 - 0.761210i) q^{47} +(3.02507 + 2.19784i) q^{48} +(-1.83722 - 5.65439i) q^{49} +(5.89604 + 18.1461i) q^{50} +(4.53739 + 3.29661i) q^{51} +(-0.0993922 + 0.0722127i) q^{52} +(-2.37727 + 7.31650i) q^{53} +1.37009 q^{54} +(7.46114 + 12.3498i) q^{55} +2.98688 q^{56} +(-0.798151 + 2.45646i) q^{57} +(-0.489415 + 0.355581i) q^{58} +(8.85798 + 6.43570i) q^{59} +(0.165161 + 0.508313i) q^{60} +(2.20527 + 6.78712i) q^{61} +(-9.12900 - 6.63261i) q^{62} +(0.830818 - 0.603625i) q^{63} +(2.60476 - 8.01664i) q^{64} +4.35041 q^{65} +(-2.34976 - 3.88937i) q^{66} +6.39450 q^{67} +(0.212924 - 0.655314i) q^{68} +(1.64692 - 1.19656i) q^{69} +(-4.95205 - 3.59788i) q^{70} +(2.27464 + 7.00062i) q^{71} +(-0.898776 - 2.76615i) q^{72} +(10.0853 + 7.32736i) q^{73} +(0.370845 - 0.269434i) q^{74} +(4.30340 - 13.2445i) q^{75} +0.317320 q^{76} +(-3.13844 - 1.32326i) q^{77} -1.37009 q^{78} +(2.59339 - 7.98163i) q^{79} +(-13.1603 + 9.56153i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.444059 + 1.36667i) q^{82} +(3.06616 + 9.43668i) q^{83} +(-0.102071 - 0.0741586i) q^{84} +(-19.7395 + 14.3416i) q^{85} +(3.34594 - 10.2977i) q^{86} +0.441540 q^{87} +(-6.31103 + 7.29548i) q^{88} +12.9003 q^{89} +(-1.84188 + 5.66873i) q^{90} +(-0.830818 + 0.603625i) q^{91} +(-0.202334 - 0.147004i) q^{92} +(2.54507 + 7.83291i) q^{93} +(-0.548299 - 1.68749i) q^{94} +(-9.09057 - 6.60468i) q^{95} +(-0.561435 + 0.407906i) q^{96} +(3.31927 - 10.2157i) q^{97} -8.14570 q^{98} +(-0.281091 + 3.30469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

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