LMFDB - Embedded newform 429.2.s.a.166.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.3
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70879 + 0.986569i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.946639 - 1.63963i) q^{4} -1.03130i q^{5} +(-1.70879 - 0.986569i) q^{6} +(-0.142489 - 0.0822660i) q^{7} -0.210579i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.70879 + 0.986569i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.946639 - 1.63963i) q^{4} -1.03130i q^{5} +(-1.70879 - 0.986569i) q^{6} +(-0.142489 - 0.0822660i) q^{7} -0.210579i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.01745 + 1.76227i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.89328 q^{12} +(1.52780 + 3.26586i) q^{13} +0.324644 q^{14} +(0.893131 - 0.515650i) q^{15} +(2.10103 + 3.63909i) q^{16} +(-2.92505 + 5.06634i) q^{17} -1.97314i q^{18} +(4.05982 + 2.34394i) q^{19} +(-1.69095 - 0.976268i) q^{20} -0.164532i q^{21} +(-0.986569 + 1.70879i) q^{22} +(-1.41995 - 2.45943i) q^{23} +(0.182367 - 0.105289i) q^{24} +3.93642 q^{25} +(-5.83268 - 4.07338i) q^{26} -1.00000 q^{27} +(-0.269771 + 0.155752i) q^{28} +(2.72945 + 4.72754i) q^{29} +(-1.01745 + 1.76227i) q^{30} +4.77039i q^{31} +(-6.81569 - 3.93504i) q^{32} +(0.866025 + 0.500000i) q^{33} -11.5431i q^{34} +(-0.0848408 + 0.146949i) q^{35} +(0.946639 + 1.63963i) q^{36} +(3.32852 - 1.92172i) q^{37} -9.24984 q^{38} +(-2.06442 + 2.95604i) q^{39} -0.217170 q^{40} +(-1.98013 + 1.14323i) q^{41} +(0.162322 + 0.281150i) q^{42} +(-4.13182 + 7.15652i) q^{43} -1.89328i q^{44} +(0.893131 + 0.515650i) q^{45} +(4.85280 + 2.80176i) q^{46} -0.407945i q^{47} +(-2.10103 + 3.63909i) q^{48} +(-3.48646 - 6.03873i) q^{49} +(-6.72651 + 3.88355i) q^{50} -5.85010 q^{51} +(6.80106 + 0.586565i) q^{52} -3.70653 q^{53} +(1.70879 - 0.986569i) q^{54} +(-0.515650 - 0.893131i) q^{55} +(-0.0173235 + 0.0300051i) q^{56} +4.68788i q^{57} +(-9.32809 - 5.38558i) q^{58} +(1.08526 + 0.626577i) q^{59} -1.95254i q^{60} +(-7.30830 + 12.6583i) q^{61} +(-4.70632 - 8.15159i) q^{62} +(0.142489 - 0.0822660i) q^{63} +7.12465 q^{64} +(3.36808 - 1.57562i) q^{65} -1.97314 q^{66} +(2.97187 - 1.71581i) q^{67} +(5.53793 + 9.59198i) q^{68} +(1.41995 - 2.45943i) q^{69} -0.334805i q^{70} +(13.5798 + 7.84027i) q^{71} +(0.182367 + 0.105289i) q^{72} -13.0375i q^{73} +(-3.79182 + 6.56762i) q^{74} +(1.96821 + 3.40904i) q^{75} +(7.68637 - 4.43773i) q^{76} -0.164532 q^{77} +(0.611307 - 7.08794i) q^{78} +7.46629 q^{79} +(3.75299 - 2.16679i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.25575 - 3.90707i) q^{82} +1.16493i q^{83} +(-0.269771 - 0.155752i) q^{84} +(5.22491 + 3.01660i) q^{85} -16.3053i q^{86} +(-2.72945 + 4.72754i) q^{87} +(-0.105289 - 0.182367i) q^{88} +(11.3636 - 6.56077i) q^{89} -2.03490 q^{90} +(0.0509744 - 0.591034i) q^{91} -5.37673 q^{92} +(-4.13128 + 2.38519i) q^{93} +(0.402466 + 0.697092i) q^{94} +(2.41730 - 4.18689i) q^{95} -7.87008i q^{96} +(-15.4868 - 8.94134i) q^{97} +(11.9153 + 6.87928i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.70879	+	0.986569i	−1.20830	+	0.697610i	−0.962387	−	0.271683i	$-0.912420\pi$
$2$	−1.70879	+	0.986569i	−1.20830	+	0.697610i	−0.245909	+	0.969293i	$0.579086\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.946639	−	1.63963i	0.473319	−	0.819813i
$5$		−	1.03130i		−	0.461211i	−0.973047	−	0.230606i	$-0.925929\pi$
$5$		−	1.03130i		−	0.461211i	0.973047	−	0.230606i	$-0.0740707\pi$
$6$	−1.70879	−	0.986569i	−0.697610	−	0.402765i
$7$	−0.142489	−	0.0822660i	−0.0538557	−	0.0310936i	0.472830	−	0.881153i	$-0.343232\pi$
$7$	−0.142489	−	0.0822660i	−0.0538557	−	0.0310936i	−0.526686	+	0.850060i	$0.676566\pi$
$8$		−	0.210579i		−	0.0744508i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.01745	+	1.76227i	0.321745	+	0.557279i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	1.89328			0.546542
$13$	1.52780	+	3.26586i	0.423736	+	0.905786i
$13$	1.52780	+	3.26586i	0.423736	+	0.905786i
$14$	0.324644			0.0867649
$15$	0.893131	−	0.515650i	0.230606	−	0.133140i
$16$	2.10103	+	3.63909i	0.525257	+	0.909772i
$17$	−2.92505	+	5.06634i	−0.709429	+	1.22877i	0.255640	+	0.966772i	$0.417714\pi$
$17$	−2.92505	+	5.06634i	−0.709429	+	1.22877i	−0.965069	+	0.261995i	$0.915620\pi$
$18$		−	1.97314i		−	0.465073i
$19$	4.05982	+	2.34394i	0.931387	+	0.537737i	0.887250	−	0.461289i	$-0.152613\pi$
$19$	4.05982	+	2.34394i	0.931387	+	0.537737i	0.0441371	+	0.999025i	$0.485946\pi$
$20$	−1.69095	−	0.976268i	−0.378107	−	0.218300i
$21$		−	0.164532i		−	0.0359038i
$22$	−0.986569	+	1.70879i	−0.210337	+	0.364315i
$23$	−1.41995	−	2.45943i	−0.296081	−	0.512827i	0.679155	−	0.733995i	$-0.262346\pi$
$23$	−1.41995	−	2.45943i	−0.296081	−	0.512827i	−0.975236	+	0.221168i	$0.929013\pi$
$24$	0.182367	−	0.105289i	0.0372254	−	0.0214921i
$25$	3.93642			0.787284
$26$	−5.83268	−	4.07338i	−1.14388	−	0.798855i
$27$	−1.00000			−0.192450
$28$	−0.269771	+	0.155752i	−0.0509819	+	0.0294344i
$29$	2.72945	+	4.72754i	0.506845	+	0.877882i	0.999969	+	0.00792250i	$0.00252184\pi$
$29$	2.72945	+	4.72754i	0.506845	+	0.877882i	−0.493123	+	0.869959i	$0.664145\pi$
$30$	−1.01745	+	1.76227i	−0.185760	+	0.321745i
$31$			4.77039i			0.856787i	0.903592	+	0.428394i	$0.140920\pi$
$31$			4.77039i			0.856787i	−0.903592	+	0.428394i	$0.859080\pi$
$32$	−6.81569	−	3.93504i	−1.20486	−	0.695624i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$		−	11.5431i		−	1.97962i
$35$	−0.0848408	+	0.146949i	−0.0143407	+	0.0248389i
$36$	0.946639	+	1.63963i	0.157773	+	0.273271i
$37$	3.32852	−	1.92172i	0.547205	−	0.315929i	−0.200789	−	0.979634i	$-0.564351\pi$
$37$	3.32852	−	1.92172i	0.547205	−	0.315929i	0.747994	+	0.663706i	$0.231017\pi$
$38$	−9.24984			−1.50052
$39$	−2.06442	+	2.95604i	−0.330571	+	0.473346i
$40$	−0.217170			−0.0343375
$41$	−1.98013	+	1.14323i	−0.309244	+	0.178542i	−0.646588	−	0.762839i	$-0.723805\pi$
$41$	−1.98013	+	1.14323i	−0.309244	+	0.178542i	0.337344	+	0.941381i	$0.390471\pi$
$42$	0.162322	+	0.281150i	0.0250469	+	0.0433824i
$43$	−4.13182	+	7.15652i	−0.630097	+	1.09136i	0.357435	+	0.933938i	$0.383651\pi$
$43$	−4.13182	+	7.15652i	−0.630097	+	1.09136i	−0.987532	+	0.157421i	$0.949682\pi$
$44$		−	1.89328i		−	0.285422i
$45$	0.893131	+	0.515650i	0.133140	+	0.0768685i
$46$	4.85280	+	2.80176i	0.715506	+	0.413098i
$47$		−	0.407945i		−	0.0595049i	−0.999557	−	0.0297525i	$-0.990528\pi$
$47$		−	0.407945i		−	0.0595049i	0.999557	−	0.0297525i	$-0.00947190\pi$
$48$	−2.10103	+	3.63909i	−0.303257	+	0.525257i
$49$	−3.48646	−	6.03873i	−0.498066	−	0.862676i
$50$	−6.72651	+	3.88355i	−0.951273	+	0.549217i
$51$	−5.85010			−0.819178
$52$	6.80106	+	0.586565i	0.943137	+	0.0813419i
$53$	−3.70653			−0.509132			−0.254566	−	0.967055i	$-0.581933\pi$
$53$	−3.70653			−0.509132			−0.254566	+	0.967055i	$0.581933\pi$
$54$	1.70879	−	0.986569i	0.232537	−	0.134255i
$55$	−0.515650	−	0.893131i	−0.0695302	−	0.120430i
$56$	−0.0173235	+	0.0300051i	−0.00231494	+	0.00400960i
$57$			4.68788i			0.620925i
$58$	−9.32809	−	5.38558i	−1.22484	−	0.707161i
$59$	1.08526	+	0.626577i	0.141289	+	0.0815734i	0.568978	−	0.822353i	$-0.307339\pi$
$59$	1.08526	+	0.626577i	0.141289	+	0.0815734i	−0.427689	+	0.903926i	$0.640672\pi$
$60$		−	1.95254i		−	0.252071i
$61$	−7.30830	+	12.6583i	−0.935732	+	1.62074i	−0.162409	+	0.986724i	$0.551926\pi$
$61$	−7.30830	+	12.6583i	−0.935732	+	1.62074i	−0.773323	+	0.634012i	$0.781407\pi$
$62$	−4.70632	−	8.15159i	−0.597703	−	1.03525i
$63$	0.142489	−	0.0822660i	0.0179519	−	0.0103645i
$64$	7.12465			0.890582
$65$	3.36808	−	1.57562i	0.417758	−	0.195432i
$66$	−1.97314			−0.242877
$67$	2.97187	−	1.71581i	0.363072	−	0.209620i	−0.307356	−	0.951595i	$-0.599444\pi$
$67$	2.97187	−	1.71581i	0.363072	−	0.209620i	0.670427	+	0.741975i	$0.266111\pi$
$68$	5.53793	+	9.59198i	0.671573	+	1.16320i
$69$	1.41995	−	2.45943i	0.170942	−	0.296081i
$70$		−	0.334805i		−	0.0400169i
$71$	13.5798	+	7.84027i	1.61162	+	0.930469i	0.988995	+	0.147949i	$0.0472673\pi$
$71$	13.5798	+	7.84027i	1.61162	+	0.930469i	0.622625	+	0.782520i	$0.286066\pi$
$72$	0.182367	+	0.105289i	0.0214921	+	0.0124085i
$73$		−	13.0375i		−	1.52593i	−0.646441	−	0.762964i	$-0.723743\pi$
$73$		−	13.0375i		−	1.52593i	0.646441	−	0.762964i	$-0.276257\pi$
$74$	−3.79182	+	6.56762i	−0.440790	+	0.763471i
$75$	1.96821	+	3.40904i	0.227269	+	0.393642i
$76$	7.68637	−	4.43773i	0.881687	−	0.509042i
$77$	−0.164532			−0.0187502
$78$	0.611307	−	7.08794i	0.0692169	−	0.802551i
$79$	7.46629			0.840024			0.420012	−	0.907519i	$-0.362026\pi$
$79$	7.46629			0.840024			0.420012	+	0.907519i	$0.362026\pi$
$80$	3.75299	−	2.16679i	0.419597	−	0.242254i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.25575	−	3.90707i	0.249105	−	0.431463i
$83$			1.16493i			0.127868i	0.997954	+	0.0639338i	$0.0203647\pi$
$83$			1.16493i			0.127868i	−0.997954	+	0.0639338i	$0.979635\pi$
$84$	−0.269771	−	0.155752i	−0.0294344	−	0.0169940i
$85$	5.22491	+	3.01660i	0.566721	+	0.327196i
$86$		−	16.3053i		−	1.75825i
$87$	−2.72945	+	4.72754i	−0.292627	+	0.506845i
$88$	−0.105289	−	0.182367i	−0.0112239	−	0.0194403i
$89$	11.3636	−	6.56077i	1.20454	−	0.695440i	0.242976	−	0.970032i	$-0.421876\pi$
$89$	11.3636	−	6.56077i	1.20454	−	0.695440i	0.961561	+	0.274592i	$0.0885429\pi$
$90$	−2.03490			−0.214497
$91$	0.0509744	−	0.591034i	0.00534357	−	0.0619572i
$92$	−5.37673			−0.560563
$93$	−4.13128	+	2.38519i	−0.428394	+	0.247333i
$94$	0.402466	+	0.697092i	0.0415112	+	0.0718996i
$95$	2.41730	−	4.18689i	0.248010	−	0.429566i
$96$		−	7.87008i		−	0.803237i
$97$	−15.4868	−	8.94134i	−1.57245	−	0.907855i	−0.995868	−	0.0908171i	$-0.971052\pi$
$97$	−15.4868	−	8.94134i	−1.57245	−	0.907855i	−0.576584	−	0.817038i	$-0.695615\pi$
$98$	11.9153	+	6.87928i	1.20362	+	0.694912i
$99$			1.00000i			0.100504i
$100$	3.72637	−	6.45426i	0.372637	−	0.645426i
$101$	−4.40230	−	7.62501i	−0.438045	−	0.758716i	0.559494	−	0.828835i	$-0.310996\pi$
$101$	−4.40230	−	7.62501i	−0.438045	−	0.758716i	−0.997539	+	0.0701183i	$0.977662\pi$
$102$	9.99659	−	5.77153i	0.989810	−	0.571467i
$103$	16.1100			1.58737			0.793684	−	0.608330i	$-0.208160\pi$
$103$	16.1100			1.58737			0.793684	+	0.608330i	$0.208160\pi$
$104$	0.687720	−	0.321722i	0.0674365	−	0.0315475i
$105$	−0.169682			−0.0165592
$106$	6.33368	−	3.65675i	0.615182	−	0.355175i
$107$	4.44584	+	7.70042i	0.429796	+	0.744428i	0.996855	−	0.0792491i	$-0.0252523\pi$
$107$	4.44584	+	7.70042i	0.429796	+	0.744428i	−0.567059	+	0.823677i	$0.691919\pi$
$108$	−0.946639	+	1.63963i	−0.0910903	+	0.157773i
$109$		−	5.76503i		−	0.552190i	−0.961130	−	0.276095i	$-0.910960\pi$
$109$		−	5.76503i		−	0.552190i	0.961130	−	0.276095i	$-0.0890404\pi$
$110$	1.76227	+	1.01745i	0.168026	+	0.0970099i
$111$	3.32852	+	1.92172i	0.315929	+	0.182402i
$112$		−	0.691372i		−	0.0653285i
$113$	−1.61130	+	2.79086i	−0.151579	+	0.262542i	−0.931808	−	0.362952i	$-0.881769\pi$
$113$	−1.61130	+	2.79086i	−0.151579	+	0.262542i	0.780229	+	0.625494i	$0.215102\pi$
$114$	−4.62492	−	8.01059i	−0.433163	−	0.750261i
$115$	−2.53641	+	1.46440i	−0.236521	+	0.136556i
$116$	10.3352			0.959599
$117$	−3.59222	−	0.309814i	−0.332100	−	0.0286424i
$118$	−2.47265			−0.227626
$119$	0.833574	−	0.481264i	0.0764136	−	0.0441174i
$120$	−0.108585	−	0.188074i	−0.00991239	−	0.0171688i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	28.8406i		−	2.61110i
$123$	−1.98013	−	1.14323i	−0.178542	−	0.103081i
$124$	7.82166	+	4.51583i	0.702405	+	0.405534i
$125$		−	9.21612i		−	0.824315i
$126$	−0.162322	+	0.281150i	−0.0144608	+	0.0250469i
$127$	1.17613	+	2.03711i	0.104364	+	0.180765i	0.913478	−	0.406887i	$-0.133386\pi$
$127$	1.17613	+	2.03711i	0.104364	+	0.180765i	−0.809114	+	0.587652i	$0.800052\pi$
$128$	1.45685	−	0.841116i	0.128769	−	0.0743448i
$129$	−8.26364			−0.727573
$130$	−4.20087	+	6.01524i	−0.368441	+	0.527572i
$131$	−2.77752			−0.242673			−0.121336	−	0.992611i	$-0.538718\pi$
$131$	−2.77752			−0.242673			−0.121336	+	0.992611i	$0.538718\pi$
$132$	1.63963	−	0.946639i	0.142711	−	0.0823943i
$133$	−0.385653	−	0.667970i	−0.0334403	−	0.0579204i
$134$	−3.38553	+	5.86392i	−0.292466	+	0.506565i
$135$			1.03130i			0.0887601i
$136$	1.06686	+	0.615953i	0.0914827	+	0.0528176i
$137$	2.70067	+	1.55923i	0.230734	+	0.133214i	0.610910	−	0.791700i	$-0.290804\pi$
$137$	2.70067	+	1.55923i	0.230734	+	0.133214i	−0.380177	+	0.924914i	$0.624137\pi$
$138$			5.60353i			0.477004i
$139$	8.80207	−	15.2456i	0.746582	−	1.29312i	−0.202870	−	0.979206i	$-0.565027\pi$
$139$	8.80207	−	15.2456i	0.746582	−	1.29312i	0.949452	−	0.313912i	$-0.101640\pi$
$140$	0.160627	+	0.278215i	0.0135755	+	0.0235134i
$141$	0.353291	−	0.203973i	0.0297525	−	0.0171776i
$142$	−30.9399			−2.59642
$143$	2.95604	+	2.06442i	0.247197	+	0.172635i
$144$	−4.20206			−0.350171
$145$	4.87551	−	2.81488i	0.404889	−	0.233763i
$146$	12.8624	+	22.2784i	1.06450	+	1.84377i
$147$	3.48646	−	6.03873i	0.287559	−	0.498066i
$148$		−	7.27670i		−	0.598141i
$149$	16.3446	+	9.43655i	1.33900	+	0.773072i	0.986659	−	0.162799i	$-0.0520524\pi$
$149$	16.3446	+	9.43655i	1.33900	+	0.773072i	0.352341	+	0.935872i	$0.385386\pi$
$150$	−6.72651	−	3.88355i	−0.549217	−	0.317091i
$151$		−	2.44857i		−	0.199262i	−0.995024	−	0.0996308i	$-0.968234\pi$
$151$		−	2.44857i		−	0.199262i	0.995024	−	0.0996308i	$-0.0317662\pi$
$152$	0.493584	−	0.854912i	0.0400349	−	0.0693425i
$153$	−2.92505	−	5.06634i	−0.236476	−	0.409589i
$154$	0.281150	−	0.162322i	0.0226557	−	0.0130803i
$155$	4.91970			0.395160
$156$	2.89255	+	6.18317i	0.231589	+	0.495050i
$157$	−15.6586			−1.24970			−0.624848	−	0.780747i	$-0.714839\pi$
$157$	−15.6586			−1.24970			−0.624848	+	0.780747i	$0.714839\pi$
$158$	−12.7583	+	7.36602i	−1.01500	+	0.586009i
$159$	−1.85327	−	3.20995i	−0.146974	−	0.254566i
$160$	−4.05820	+	7.02902i	−0.320829	+	0.555693i
$161$			0.467255i			0.0368249i
$162$	1.70879	+	0.986569i	0.134255	+	0.0775122i
$163$	−0.478678	−	0.276365i	−0.0374930	−	0.0216466i	0.481136	−	0.876646i	$-0.340224\pi$
$163$	−0.478678	−	0.276365i	−0.0374930	−	0.0216466i	−0.518629	+	0.854999i	$0.673558\pi$
$164$			4.32889i			0.338030i
$165$	0.515650	−	0.893131i	0.0401433	−	0.0695302i
$166$	−1.14928	−	1.99062i	−0.0892018	−	0.154502i
$167$	−15.4944	+	8.94568i	−1.19899	+	0.692237i	−0.960330	−	0.278866i	$-0.910042\pi$
$167$	−15.4944	+	8.94568i	−1.19899	+	0.692237i	−0.238660	+	0.971103i	$0.576708\pi$
$168$	−0.0346469			−0.00267307
$169$	−8.33165	+	9.97916i	−0.640896	+	0.767628i
$170$	−11.9044			−0.913022
$171$	−4.05982	+	2.34394i	−0.310462	+	0.179246i
$172$	7.82268	+	13.5493i	0.596474	+	1.03312i
$173$	−3.52410	+	6.10392i	−0.267932	+	0.464072i	−0.968328	−	0.249683i	$-0.919674\pi$
$173$	−3.52410	+	6.10392i	−0.267932	+	0.464072i	0.700395	+	0.713755i	$0.253007\pi$
$174$		−	10.7712i		−	0.816559i
$175$	−0.560896	−	0.323834i	−0.0423998	−	0.0244795i
$176$	3.63909	+	2.10103i	0.274306	+	0.158371i
$177$			1.25315i			0.0941929i
$178$	−12.9453	+	22.4219i	−0.970291	+	1.68059i
$179$	−6.63321	−	11.4891i	−0.495789	−	0.858732i	0.504199	−	0.863588i	$-0.331788\pi$
$179$	−6.63321	−	11.4891i	−0.495789	−	0.858732i	−0.999988	+	0.00485528i	$0.998455\pi$
$180$	1.69095	−	0.976268i	0.126036	−	0.0727667i
$181$	4.28154			0.318244			0.159122	−	0.987259i	$-0.449134\pi$
$181$	4.28154			0.318244			0.159122	+	0.987259i	$0.449134\pi$
$182$	0.495992	+	1.06024i	0.0367654	+	0.0785904i
$183$	−14.6166			−1.08049
$184$	−0.517904	+	0.299012i	−0.0381804	+	0.0220434i
$185$	−1.98187	−	3.43270i	−0.145710	−	0.252377i
$186$	4.70632	−	8.15159i	0.345084	−	0.597703i
$187$			5.85010i			0.427802i
$188$	−0.668878	−	0.386177i	−0.0487829	−	0.0281648i
$189$	0.142489	+	0.0822660i	0.0103645	+	0.00598397i
$190$			9.53935i			0.692057i
$191$	−4.66514	+	8.08027i	−0.337558	+	0.584668i	−0.983973	−	0.178319i	$-0.942934\pi$
$191$	−4.66514	+	8.08027i	−0.337558	+	0.584668i	0.646415	+	0.762986i	$0.276268\pi$
$192$	3.56233	+	6.17013i	0.257089	+	0.445291i
$193$	−13.7931	+	7.96346i	−0.992850	+	0.573222i	−0.906125	−	0.423010i	$-0.860974\pi$
$193$	−13.7931	+	7.96346i	−0.992850	+	0.573222i	−0.0867253	+	0.996232i	$0.527640\pi$
$194$	35.2850			2.53332
$195$	3.04856	+	2.12903i	0.218312	+	0.152463i
$196$	−13.2017			−0.942978
$197$	11.0992	−	6.40813i	0.790786	−	0.456560i	−0.0494534	−	0.998776i	$-0.515748\pi$
$197$	11.0992	−	6.40813i	0.790786	−	0.456560i	0.840239	+	0.542216i	$0.182415\pi$
$198$	−0.986569	−	1.70879i	−0.0701124	−	0.121438i
$199$	10.4251	−	18.0568i	0.739016	−	1.28001i	−0.213923	−	0.976851i	$-0.568624\pi$
$199$	10.4251	−	18.0568i	0.739016	−	1.28001i	0.952939	−	0.303163i	$-0.0980426\pi$
$200$		−	0.828927i		−	0.0586140i
$201$	2.97187	+	1.71581i	0.209620	+	0.121024i
$202$	15.0452	+	8.68635i	1.05858	+	0.611169i
$203$		−	0.898162i		−	0.0630386i
$204$	−5.53793	+	9.59198i	−0.387733	+	0.671573i
$205$	1.17901	+	2.04210i	0.0823456	+	0.142627i
$206$	−27.5286	+	15.8937i	−1.91801	+	1.10736i
$207$	2.83991			0.197387
$208$	−8.67479	+	12.4215i	−0.601488	+	0.861273i
$209$	4.68788			0.324267
$210$	0.289950	−	0.167403i	0.0200085	−	0.0115519i
$211$	2.20774	+	3.82391i	0.151987	+	0.263249i	0.931958	−	0.362567i	$-0.118100\pi$
$211$	2.20774	+	3.82391i	0.151987	+	0.263249i	−0.779971	+	0.625816i	$0.784766\pi$
$212$	−3.50875	+	6.07733i	−0.240982	+	0.417393i
$213$			15.6805i			1.07441i
$214$	−15.1940	−	8.77226i	−1.03864	−	0.599659i
$215$	7.38051	+	4.26114i	0.503347	+	0.290607i
$216$			0.210579i			0.0143281i
$217$	0.392441	−	0.679727i	0.0266406	−	0.0461429i
$218$	5.68761	+	9.85122i	0.385213	+	0.667209i
$219$	11.2908	−	6.51877i	0.762964	−	0.440497i
$220$	−1.95254			−0.131640
$221$	−21.0148	−	1.81245i	−1.41361	−	0.121918i
$222$	−7.58364			−0.508981
$223$	−16.4582	+	9.50217i	−1.10213	+	0.636312i	−0.936778	−	0.349923i	$-0.886208\pi$
$223$	−16.4582	+	9.50217i	−1.10213	+	0.636312i	−0.165347	+	0.986235i	$0.552874\pi$
$224$	0.647440	+	1.12140i	0.0432589	+	0.0749266i
$225$	−1.96821	+	3.40904i	−0.131214	+	0.227269i
$226$		−	6.35865i		−	0.422971i
$227$	−6.67095	−	3.85148i	−0.442767	−	0.255631i	0.262004	−	0.965067i	$-0.415617\pi$
$227$	−6.67095	−	3.85148i	−0.442767	−	0.255631i	−0.704770	+	0.709435i	$0.748950\pi$
$228$	7.68637	+	4.43773i	0.509042	+	0.293896i
$229$		−	15.4343i		−	1.01992i	−0.860197	−	0.509962i	$-0.829659\pi$
$229$		−	15.4343i		−	1.01992i	0.860197	−	0.509962i	$-0.170341\pi$
$230$	2.88946	−	5.00469i	0.190525	−	0.329999i
$231$	−0.0822660	−	0.142489i	−0.00541270	−	0.00937508i
$232$	0.995519	−	0.574763i	0.0653590	−	0.0377351i
$233$	6.99107			0.458000			0.229000	−	0.973426i	$-0.426454\pi$
$233$	6.99107			0.458000			0.229000	+	0.973426i	$0.426454\pi$
$234$	6.44399	−	3.01456i	0.421257	−	0.197068i
$235$	−0.420714			−0.0274443
$236$	2.05471	−	1.18628i	0.133750	−	0.0772206i
$237$	3.73315	+	6.46600i	0.242494	+	0.420012i
$238$	−0.949601	+	1.64476i	−0.0615535	+	0.106614i
$239$		−	18.1074i		−	1.17127i	−0.810574	−	0.585636i	$-0.800845\pi$
$239$		−	18.1074i		−	1.17127i	0.810574	−	0.585636i	$-0.199155\pi$
$240$	3.75299	+	2.16679i	0.242254	+	0.139866i
$241$	−16.2900	−	9.40505i	−1.04933	−	0.605833i	−0.126871	−	0.991919i	$-0.540493\pi$
$241$	−16.2900	−	9.40505i	−1.04933	−	0.605833i	−0.922463	+	0.386086i	$0.873827\pi$
$242$			1.97314i			0.126838i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	13.8366	+	23.9658i	0.885800	+	1.53425i
$245$	−6.22774	+	3.59559i	−0.397876	+	0.229714i
$246$	4.51149			0.287642
$247$	−1.45237	+	16.8399i	−0.0924122	+	1.07150i
$248$	1.00454			0.0637885
$249$	−1.00886	+	0.582465i	−0.0639338	+	0.0369122i
$250$	9.09235	+	15.7484i	0.575051	+	0.996017i
$251$	5.45229	−	9.44365i	0.344146	−	0.596078i	−0.641052	−	0.767497i	$-0.721502\pi$
$251$	5.45229	−	9.44365i	0.344146	−	0.596078i	0.985198	+	0.171419i	$0.0548352\pi$
$252$		−	0.311505i		−	0.0196229i
$253$	−2.45943	−	1.41995i	−0.154623	−	0.0892717i
$254$	−4.01951	−	2.32066i	−0.252206	−	0.145611i
$255$			6.03321i			0.377814i
$256$	−8.78429	+	15.2148i	−0.549018	+	0.950928i
$257$	4.41069	+	7.63953i	0.275131	+	0.476541i	0.970168	−	0.242433i	$-0.0779454\pi$
$257$	4.41069	+	7.63953i	0.275131	+	0.476541i	−0.695037	+	0.718974i	$0.744612\pi$
$258$	14.1208	−	8.15265i	0.879123	−	0.507562i
$259$	−0.632369			−0.0392935
$260$	0.604924	−	7.01393i	0.0375158	−	0.434985i
$261$	−5.45889			−0.337897
$262$	4.74619	−	2.74022i	0.293221	−	0.169291i
$263$	0.154305	+	0.267263i	0.00951483	+	0.0164802i	0.870744	−	0.491737i	$-0.163638\pi$
$263$	0.154305	+	0.267263i	0.00951483	+	0.0164802i	−0.861229	+	0.508217i	$0.830305\pi$
$264$	0.105289	−	0.182367i	0.00648011	−	0.0112239i
$265$			3.82255i			0.234817i
$266$	1.31800	+	0.760947i	0.0808117	+	0.0466566i
$267$	11.3636	+	6.56077i	0.695440	+	0.401512i
$268$		−	6.49701i		−	0.396868i
$269$	−5.42380	+	9.39429i	−0.330695	+	0.572780i	−0.982648	−	0.185479i	$-0.940616\pi$
$269$	−5.42380	+	9.39429i	−0.330695	+	0.572780i	0.651954	+	0.758259i	$0.273950\pi$
$270$	−1.01745	−	1.76227i	−0.0619199	−	0.107248i
$271$	11.4868	−	6.63190i	0.697772	−	0.402859i	−0.108745	−	0.994070i	$-0.534683\pi$
$271$	11.4868	−	6.63190i	0.697772	−	0.402859i	0.806517	+	0.591211i	$0.201350\pi$
$272$	−24.5825			−1.49053
$273$	0.537338	−	0.251372i	0.0325212	−	0.0152137i
$274$	−6.15316			−0.371726
$275$	3.40904	−	1.96821i	0.205573	−	0.118688i
$276$	−2.68836	−	4.65638i	−0.161821	−	0.280281i
$277$	10.8776	−	18.8406i	0.653574	−	1.13202i	−0.328675	−	0.944443i	$-0.606602\pi$
$277$	10.8776	−	18.8406i	0.653574	−	1.13202i	0.982249	−	0.187581i	$-0.0600647\pi$
$278$			34.7354i			2.08329i
$279$	−4.13128	−	2.38519i	−0.247333	−	0.142798i
$280$	0.0309443	+	0.0178657i	0.00184927	+	0.00106768i
$281$		−	14.3207i		−	0.854299i	−0.904181	−	0.427150i	$-0.859518\pi$
$281$		−	14.3207i		−	0.854299i	0.904181	−	0.427150i	$-0.140482\pi$
$282$	−0.402466	+	0.697092i	−0.0239665	+	0.0415112i
$283$	1.29859	+	2.24923i	0.0771934	+	0.133703i	0.902038	−	0.431657i	$-0.142071\pi$
$283$	1.29859	+	2.24923i	0.0771934	+	0.133703i	−0.824845	+	0.565360i	$0.808737\pi$
$284$	25.7102	−	14.8438i	1.52562	−	0.880818i
$285$	4.83461			0.286377
$286$	−7.08794	−	0.611307i	−0.419119	−	0.0361473i
$287$	0.376195			0.0222061
$288$	6.81569	−	3.93504i	0.401618	−	0.231875i
$289$	−8.61185	−	14.9162i	−0.506579	−	0.877421i
$290$	−5.55414	+	9.62005i	−0.326150	+	0.564909i
$291$		−	17.8827i		−	1.04830i
$292$	−21.3767	−	12.3418i	−1.25098	−	0.722251i
$293$	−23.6358	−	13.6461i	−1.38082	−	0.797216i	−0.388563	−	0.921422i	$-0.627028\pi$
$293$	−23.6358	−	13.6461i	−1.38082	−	0.797216i	−0.992256	+	0.124206i	$0.960362\pi$
$294$			13.7586i			0.802415i
$295$	0.646189	−	1.11923i	0.0376226	−	0.0651642i
$296$	−0.404673	−	0.700915i	−0.0235212	−	0.0407398i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	−37.2392			−2.15721
$299$	5.86275	−	8.39488i	0.339051	−	0.485489i
$300$	7.45274			0.430284
$301$	1.17748	−	0.679816i	0.0678686	−	0.0391840i
$302$	2.41568	+	4.18408i	0.139007	+	0.240767i
$303$	4.40230	−	7.62501i	0.252905	−	0.438045i
$304$			19.6987i			1.12980i
$305$	13.0545	+	7.53705i	0.747501	+	0.431570i
$306$	9.99659	+	5.77153i	0.571467	+	0.329937i
$307$		−	26.7870i		−	1.52882i	−0.644733	−	0.764408i	$-0.723031\pi$
$307$		−	26.7870i		−	1.52882i	0.644733	−	0.764408i	$-0.276969\pi$
$308$	−0.155752	+	0.269771i	−0.00887481	+	0.0153716i
$309$	8.05502	+	13.9517i	0.458234	+	0.793684i
$310$	−8.40672	+	4.85362i	−0.477470	+	0.275667i
$311$	6.31122			0.357877			0.178938	−	0.983860i	$-0.442734\pi$
$311$	6.31122			0.357877			0.178938	+	0.983860i	$0.442734\pi$
$312$	0.622480	+	0.434722i	0.0352410	+	0.0246113i
$313$	−10.4089			−0.588343			−0.294172	−	0.955753i	$-0.595044\pi$
$313$	−10.4089			−0.588343			−0.294172	+	0.955753i	$0.595044\pi$
$314$	26.7573	−	15.4483i	1.51000	−	0.871800i
$315$	−0.0848408	−	0.146949i	−0.00478024	−	0.00827962i
$316$	7.06788	−	12.2419i	0.397599	−	0.688662i
$317$		−	11.0949i		−	0.623152i	−0.950221	−	0.311576i	$-0.899143\pi$
$317$		−	11.0949i		−	0.623152i	0.950221	−	0.311576i	$-0.100857\pi$
$318$	6.33368	+	3.65675i	0.355175	+	0.205061i
$319$	4.72754	+	2.72945i	0.264691	+	0.152820i
$320$		−	7.34765i		−	0.410746i
$321$	−4.44584	+	7.70042i	−0.248143	+	0.429796i
$322$	−0.460980	−	0.798440i	−0.0256894	−	0.0444953i
$323$	−23.7504	+	13.7123i	−1.32151	+	0.762972i
$324$	−1.89328			−0.105182
$325$	6.01407	+	12.8558i	0.333601	+	0.713111i
$326$	1.09061			0.0604035
$327$	4.99266	−	2.88252i	0.276095	−	0.159404i
$328$	0.240739	+	0.416973i	0.0132926	+	0.0230235i
$329$	−0.0335600	+	0.0581277i	−0.00185022	+	0.00320468i
$330$			2.03490i			0.112017i
$331$	1.60684	+	0.927711i	0.0883201	+	0.0509916i	0.543510	−	0.839403i	$-0.317095\pi$
$331$	1.60684	+	0.927711i	0.0883201	+	0.0509916i	−0.455190	+	0.890395i	$0.650428\pi$
$332$	1.91005	+	1.10277i	0.104828	+	0.0605222i
$333$			3.84344i			0.210619i
$334$	17.6511	−	30.5725i	0.965823	−	1.67286i
$335$	−1.76951	−	3.06489i	−0.0966789	−	0.167453i
$336$	0.598746	−	0.345686i	0.0326643	−	0.0188587i
$337$	13.7660			0.749883			0.374941	−	0.927049i	$-0.377663\pi$
$337$	13.7660			0.749883			0.374941	+	0.927049i	$0.377663\pi$
$338$	4.39189	−	25.2720i	0.238887	−	1.37462i
$339$	−3.22261			−0.175028
$340$	9.89220	−	5.71127i	0.536480	−	0.309737i
$341$	2.38519	+	4.13128i	0.129166	+	0.223721i
$342$	4.62492	−	8.01059i	0.250087	−	0.433163i
$343$			2.29899i			0.124134i
$344$	1.50701	+	0.870073i	0.0812526	+	0.0469112i
$345$	−2.53641	−	1.46440i	−0.136556	−	0.0788405i
$346$		−	13.9071i		−	0.747649i
$347$	13.6055	−	23.5654i	0.730381	−	1.26506i	−0.226340	−	0.974048i	$-0.572676\pi$
$347$	13.6055	−	23.5654i	0.730381	−	1.26506i	0.956721	−	0.291008i	$-0.0939908\pi$
$348$	5.16760	+	8.95054i	0.277012	+	0.479799i
$349$	4.56308	−	2.63449i	0.244256	−	0.141021i	−0.372875	−	0.927881i	$-0.621628\pi$
$349$	4.56308	−	2.63449i	0.244256	−	0.141021i	0.617131	+	0.786860i	$0.288295\pi$
$350$	1.27794			0.0683086
$351$	−1.52780	−	3.26586i	−0.0815480	−	0.174319i
$352$	−7.87008			−0.419477
$353$	−24.8060	+	14.3218i	−1.32029	+	0.762271i	−0.983775	−	0.179406i	$-0.942582\pi$
$353$	−24.8060	+	14.3218i	−1.32029	+	0.762271i	−0.336517	+	0.941677i	$0.609249\pi$
$354$	−1.23632	−	2.14138i	−0.0657099	−	0.113813i
$355$	8.08567	−	14.0048i	0.429143	−	0.743297i
$356$		−	24.8427i		−	1.31666i
$357$	0.833574	+	0.481264i	0.0441174	+	0.0254712i
$358$	22.6695	+	13.0882i	1.19812	+	0.691735i
$359$		−	6.83251i		−	0.360606i	−0.983611	−	0.180303i	$-0.942292\pi$
$359$		−	6.83251i		−	0.360606i	0.983611	−	0.180303i	$-0.0577078\pi$
$360$	0.108585	−	0.188074i	0.00572292	−	0.00991239i
$361$	1.48810	+	2.57747i	0.0783213	+	0.135656i
$362$	−7.31625	+	4.22404i	−0.384533	+	0.222010i
$363$	1.00000			0.0524864
$364$	−0.920821	−	0.643075i	−0.0482641	−	0.0337063i
$365$	−13.4456			−0.703775
$366$	24.9767	−	14.4203i	1.30555	−	0.753761i
$367$	2.99462	+	5.18684i	0.156318	+	0.270751i	0.933538	−	0.358478i	$-0.116704\pi$
$367$	2.99462	+	5.18684i	0.156318	+	0.270751i	−0.777220	+	0.629229i	$0.783371\pi$
$368$	5.96672	−	10.3347i	0.311037	−	0.538732i
$369$		−	2.28645i		−	0.119028i
$370$	6.77319	+	3.91050i	0.352121	+	0.203297i
$371$	0.528140	+	0.304922i	0.0274197	+	0.0158307i
$372$			9.03167i			0.468270i
$373$	−1.28830	+	2.23139i	−0.0667054	+	0.115537i	−0.897449	−	0.441118i	$-0.854582\pi$
$373$	−1.28830	+	2.23139i	−0.0667054	+	0.115537i	0.830744	+	0.556655i	$0.187915\pi$
$374$	−5.77153	−	9.99659i	−0.298439	−	0.516911i
$375$	7.98140	−	4.60806i	0.412158	−	0.237959i
$376$	−0.0859046			−0.00443019
$377$	−11.2694	+	16.1367i	−0.580405	+	0.831083i
$378$	−0.324644			−0.0166979
$379$	26.3984	−	15.2411i	1.35600	−	0.782885i	0.366915	−	0.930255i	$-0.380414\pi$
$379$	26.3984	−	15.2411i	1.35600	−	0.782885i	0.989081	+	0.147370i	$0.0470807\pi$
$380$	−4.57662	−	7.92695i	−0.234776	−	0.406644i
$381$	−1.17613	+	2.03711i	−0.0602549	+	0.104364i
$382$		−	18.4100i		−	0.941935i
$383$	17.8056	+	10.2801i	0.909826	+	0.525288i	0.880375	−	0.474278i	$-0.157291\pi$
$383$	17.8056	+	10.2801i	0.909826	+	0.525288i	0.0294508	+	0.999566i	$0.490624\pi$
$384$	1.45685	+	0.841116i	0.0743448	+	0.0429230i
$385$			0.169682i			0.00864778i
$386$	15.7130	−	27.2157i	0.799771	−	1.38524i
$387$	−4.13182	−	7.15652i	−0.210032	−	0.363786i
$388$	−29.3209	+	16.9284i	−1.48854	+	0.859411i
$389$	2.74477			0.139166			0.0695828	−	0.997576i	$-0.477833\pi$
$389$	2.74477			0.139166			0.0695828	+	0.997576i	$0.477833\pi$
$390$	−7.30979	−	0.630440i	−0.370146	−	0.0319236i
$391$	16.6137			0.840193
$392$	−1.27163	+	0.734175i	−0.0642270	+	0.0370814i
$393$	−1.38876	−	2.40540i	−0.0700537	−	0.121336i
$394$	−12.6441	+	21.9003i	−0.637002	+	1.10332i
$395$		−	7.69998i		−	0.387428i
$396$	1.63963	+	0.946639i	0.0823943	+	0.0475704i
$397$	−7.12053	−	4.11104i	−0.357369	−	0.206327i	0.310557	−	0.950555i	$-0.399484\pi$
$397$	−7.12053	−	4.11104i	−0.357369	−	0.206327i	−0.667926	+	0.744228i	$0.732818\pi$
$398$			41.1404i			2.06218i
$399$	0.385653	−	0.667970i	0.0193068	−	0.0334403i
$400$	8.27053	+	14.3250i	0.413527	+	0.716249i
$401$	−11.6102	+	6.70315i	−0.579786	+	0.334740i	−0.761048	−	0.648695i	$-0.775315\pi$
$401$	−11.6102	+	6.70315i	−0.579786	+	0.334740i	0.181262	+	0.983435i	$0.441982\pi$
$402$	−6.77107			−0.337710
$403$	−15.5794	+	7.28820i	−0.776066	+	0.363051i
$404$	−16.6695			−0.829341
$405$	−0.893131	+	0.515650i	−0.0443801	+	0.0256228i
$406$	0.886099	+	1.53477i	0.0439764	+	0.0761693i
$407$	1.92172	−	3.32852i	0.0952561	−	0.164988i
$408$			1.23191i			0.0609885i
$409$	−24.6068	−	14.2067i	−1.21673	−	0.702477i	−0.252510	−	0.967594i	$-0.581256\pi$
$409$	−24.6068	−	14.2067i	−1.21673	−	0.702477i	−0.964216	+	0.265117i	$0.914589\pi$
$410$	−4.02935	−	2.32635i	−0.198996	−	0.114890i
$411$			3.11846i			0.153822i
$412$	15.2504	−	26.4144i	0.751332	−	1.30135i
$413$	−0.103092	−	0.178561i	−0.00507283	−	0.00878639i
$414$	−4.85280	+	2.80176i	−0.238502	+	0.137699i
$415$	1.20139			0.0589740
$416$	2.43826	−	28.2710i	0.119546	−	1.38610i
$417$	17.6041			0.862079
$418$	−8.01059	+	4.62492i	−0.391811	+	0.226212i
$419$	16.1250	+	27.9293i	0.787757	+	1.36444i	0.927338	+	0.374225i	$0.122091\pi$
$419$	16.1250	+	27.9293i	0.787757	+	1.36444i	−0.139580	+	0.990211i	$0.544575\pi$
$420$	−0.160627	+	0.278215i	−0.00783781	+	0.0135755i
$421$			24.0807i			1.17362i	0.809723	+	0.586812i	$0.199617\pi$
$421$			24.0807i			1.17362i	−0.809723	+	0.586812i	$0.800383\pi$
$422$	−7.54510	−	4.35617i	−0.367290	−	0.212055i
$423$	0.353291	+	0.203973i	0.0171776	+	0.00991749i
$424$			0.780517i			0.0379053i
$425$	−11.5142	+	19.9432i	−0.558522	+	0.967389i
$426$	−15.4700	−	26.7947i	−0.749522	−	1.29821i
$427$	2.08270	−	1.20245i	0.100789	−	0.0581906i
$428$	16.8344			0.813722
$429$	−0.309814	+	3.59222i	−0.0149580	+	0.173434i
$430$	−16.8156			−0.810923
$431$	1.25547	−	0.724848i	0.0604740	−	0.0349147i	−0.469458	−	0.882955i	$-0.655551\pi$
$431$	1.25547	−	0.724848i	0.0604740	−	0.0349147i	0.529932	+	0.848040i	$0.322217\pi$
$432$	−2.10103	−	3.63909i	−0.101086	−	0.175086i
$433$	14.7636	−	25.5714i	0.709495	−	1.22888i	−0.255550	−	0.966796i	$-0.582257\pi$
$433$	14.7636	−	25.5714i	0.709495	−	1.22888i	0.965045	−	0.262085i	$-0.0844101\pi$
$434$			1.54868i			0.0743390i
$435$	4.87551	+	2.81488i	0.233763	+	0.134963i
$436$	−9.45250	−	5.45740i	−0.452693	−	0.261362i
$437$		−	13.3131i		−	0.636854i
$438$	−12.8624	+	22.2784i	−0.614591	+	1.06450i
$439$	10.3111	+	17.8594i	0.492124	+	0.852384i	0.999959	−	0.00907053i	$-0.00288728\pi$
$439$	10.3111	+	17.8594i	0.492124	+	0.852384i	−0.507835	+	0.861455i	$0.669554\pi$
$440$	−0.188074	+	0.108585i	−0.00896610	+	0.00517658i
$441$	6.97293			0.332044
$442$	37.6980	−	17.6355i	1.79311	−	0.838835i
$443$	6.83637			0.324806			0.162403	−	0.986725i	$-0.448076\pi$
$443$	6.83637			0.324806			0.162403	+	0.986725i	$0.448076\pi$
$444$	6.30180	−	3.63835i	0.299070	−	0.172668i
$445$	−6.76611	−	11.7193i	−0.320744	−	0.555546i
$446$	18.7491	−	32.4744i	0.887796	−	1.53771i
$447$			18.8731i			0.892667i
$448$	−1.01518	−	0.586117i	−0.0479629	−	0.0276914i
$449$	−23.5694	−	13.6078i	−1.11231	−	0.642191i	−0.172881	−	0.984943i	$-0.555308\pi$
$449$	−23.5694	−	13.6078i	−1.11231	−	0.642191i	−0.939426	+	0.342752i	$0.888641\pi$
$450$		−	7.76711i		−	0.366145i
$451$	−1.14323	+	1.98013i	−0.0538325	+	0.0932406i
$452$	3.05064	+	5.28387i	0.143490	+	0.248532i
$453$	2.12052	−	1.22428i	0.0996308	−	0.0575219i
$454$	15.1990			0.713324
$455$	−0.609533	−	0.0525698i	−0.0285754	−	0.00246451i
$456$	0.987167			0.0462284
$457$	−1.86044	+	1.07412i	−0.0870276	+	0.0502454i	−0.542882	−	0.839809i	$-0.682667\pi$
$457$	−1.86044	+	1.07412i	−0.0870276	+	0.0502454i	0.455855	+	0.890054i	$0.349334\pi$
$458$	15.2270	+	26.3739i	0.711509	+	1.23237i
$459$	2.92505	−	5.06634i	0.136530	−	0.236476i
$460$			5.54502i			0.258538i
$461$	18.9635	+	10.9486i	0.883219	+	0.509926i	0.871718	−	0.490007i	$-0.163006\pi$
$461$	18.9635	+	10.9486i	0.883219	+	0.509926i	0.0115003	+	0.999934i	$0.496339\pi$
$462$	0.281150	+	0.162322i	0.0130803	+	0.00755191i
$463$			25.8415i			1.20096i	0.799640	+	0.600479i	$0.205023\pi$
$463$			25.8415i			1.20096i	−0.799640	+	0.600479i	$0.794977\pi$
$464$	−11.4693	+	19.8654i	−0.532448	+	0.922227i
$465$	2.45985	+	4.26058i	0.114073	+	0.197580i
$466$	−11.9463	+	6.89718i	−0.553400	+	0.319506i
$467$	−24.2118			−1.12039			−0.560193	−	0.828362i	$-0.689273\pi$
$467$	−24.2118			−1.12039			−0.560193	+	0.828362i	$0.689273\pi$
$468$	−3.90851	+	5.59661i	−0.180671	+	0.258703i
$469$	−0.564611			−0.0260713
$470$	0.718911	−	0.415063i	0.0331609	−	0.0191454i
$471$	−7.82932	−	13.5608i	−0.360756	−	0.624848i
$472$	0.131944	−	0.228533i	0.00607321	−	0.0105191i
$473$			8.26364i			0.379962i
$474$	−12.7583	−	7.36602i	−0.586009	−	0.338332i
$475$	15.9812	+	9.22673i	0.733267	+	0.423352i
$476$		−	1.82233i		−	0.0835265i
$477$	1.85327	−	3.20995i	0.0848553	−	0.146974i
$478$	17.8642	+	30.9418i	0.817091	+	1.41524i
$479$	−31.2625	+	18.0494i	−1.42842	+	0.824698i	−0.996996	−	0.0774525i	$-0.975321\pi$
$479$	−31.2625	+	18.0494i	−1.42842	+	0.824698i	−0.431422	+	0.902150i	$0.641988\pi$
$480$	−8.11641			−0.370462
$481$	11.3614	+	7.93445i	0.518034	+	0.361780i
$482$	37.1150			1.69054
$483$	−0.404655	+	0.233628i	−0.0184124	+	0.0106304i
$484$	−0.946639	−	1.63963i	−0.0430290	−	0.0745285i
$485$	−9.22119	+	15.9716i	−0.418713	+	0.725232i
$486$			1.97314i			0.0895034i
$487$	−21.0745	−	12.1673i	−0.954975	−	0.551355i	−0.0603521	−	0.998177i	$-0.519222\pi$
$487$	−21.0745	−	12.1673i	−0.954975	−	0.551355i	−0.894623	+	0.446822i	$0.852556\pi$
$488$	2.66558	+	1.53897i	0.120665	+	0.0696660i
$489$		−	0.552730i		−	0.0249953i
$490$	7.09460	−	12.2882i	0.320501	−	0.555124i
$491$	4.43108	+	7.67486i	0.199972	+	0.346362i	0.948519	−	0.316720i	$-0.102582\pi$
$491$	4.43108	+	7.67486i	0.199972	+	0.346362i	−0.748547	+	0.663082i	$0.769248\pi$
$492$	−3.74893	+	2.16445i	−0.169015	+	0.0975808i
$493$	−31.9351			−1.43828
$494$	−14.1319	−	30.2086i	−0.635825	−	1.35915i
$495$	1.03130			0.0463535
$496$	−17.3599	+	10.0227i	−0.779481	+	0.450033i
$497$	−1.28998	−	2.23430i	−0.0578633	−	0.100222i
$498$	1.14928	−	1.99062i	0.0515007	−	0.0892018i
$499$			7.50728i			0.336072i	0.985781	+	0.168036i	$0.0537425\pi$
$499$			7.50728i			0.336072i	−0.985781	+	0.168036i	$0.946258\pi$
$500$	−15.1110	−	8.72434i	−0.675784	−	0.390164i
$501$	−15.4944	−	8.94568i	−0.692237	−	0.399663i
$502$			21.5163i			0.960318i
$503$	−10.8242	+	18.7480i	−0.482625	+	0.835931i	−0.999801	−	0.0199479i	$-0.993650\pi$
$503$	−10.8242	+	18.7480i	−0.482625	+	0.835931i	0.517176	+	0.855879i	$0.326983\pi$
$504$	−0.0173235	−	0.0300051i	−0.000771648	−	0.00133653i
$505$	−7.86366	+	4.54009i	−0.349928	+	0.202031i
$506$	5.60353			0.249107
$507$	−12.8080	−	2.22584i	−0.568825	−	0.0988530i
$508$	4.45347			0.197591
$509$	21.7399	−	12.5515i	0.963602	−	0.556336i	0.0663224	−	0.997798i	$-0.478873\pi$
$509$	21.7399	−	12.5515i	0.963602	−	0.556336i	0.897280	+	0.441462i	$0.145540\pi$
$510$	−5.95218	−	10.3095i	−0.263567	−	0.456511i
$511$	−1.07255	+	1.85770i	−0.0474466	+	0.0821799i
$512$		−	31.3008i		−	1.38331i
$513$	−4.05982	−	2.34394i	−0.179246	−	0.103487i
$514$	−15.0739	−	8.70290i	−0.664879	−	0.383868i
$515$		−	16.6143i		−	0.732112i
$516$	−7.82268	+	13.5493i	−0.344374	+	0.596474i
$517$	−0.203973	−	0.353291i	−0.00897071	−	0.0155377i
$518$	1.08058	−	0.623875i	0.0474781	−	0.0274115i
$519$	−7.04820			−0.309382
$520$	−0.331792	−	0.709245i	−0.0145500	−	0.0311025i
$521$	3.74297			0.163982			0.0819911	−	0.996633i	$-0.473872\pi$
$521$	3.74297			0.163982			0.0819911	+	0.996633i	$0.473872\pi$
$522$	9.32809	−	5.38558i	0.408279	−	0.235720i
$523$	−4.86923	−	8.43375i	−0.212916	−	0.368782i	0.739710	−	0.672926i	$-0.234963\pi$
$523$	−4.86923	−	8.43375i	−0.212916	−	0.368782i	−0.952626	+	0.304144i	$0.901630\pi$
$524$	−2.62931	+	4.55409i	−0.114862	+	0.198946i
$525$		−	0.647667i		−	0.0282665i
$526$	−0.527348	−	0.304465i	−0.0229935	−	0.0132753i
$527$	−24.1684	−	13.9536i	−1.05279	−	0.607830i
$528$			4.20206i			0.182871i
$529$	7.46747	−	12.9340i	0.324672	−	0.562349i
$530$	−3.77121	−	6.53192i	−0.163811	−	0.283729i
$531$	−1.08526	+	0.626577i	−0.0470964	+	0.0271911i
$532$	−1.46030			−0.0633119
$533$	−6.75886	−	4.72019i	−0.292759	−	0.204454i
$534$	−25.8906			−1.12040
$535$	7.94144	−	4.58499i	0.343338	−	0.198227i
$536$	−0.361313	−	0.625813i	−0.0156064	−	0.0270310i
$537$	6.63321	−	11.4891i	0.286244	−	0.495789i
$538$		−	21.4038i		−	0.922784i
$539$	−6.03873	−	3.48646i	−0.260107	−	0.150173i
$540$	1.69095	+	0.976268i	0.0727667	+	0.0420119i
$541$			31.0508i			1.33498i	0.744620	+	0.667489i	$0.232631\pi$
$541$			31.0508i			1.33498i	−0.744620	+	0.667489i	$0.767369\pi$
$542$	−13.0857	+	22.6650i	−0.562077	+	0.973546i
$543$	2.14077	+	3.70792i	0.0918692	+	0.159122i
$544$	39.8725	−	23.0204i	1.70952	−	0.986991i
$545$	−5.94547			−0.254676
$546$	−0.670201	+	0.959663i	−0.0286819	+	0.0410698i
$547$	42.2584			1.80684			0.903420	−	0.428757i	$-0.141048\pi$
$547$	42.2584			1.80684			0.903420	+	0.428757i	$0.141048\pi$
$548$	5.11311	−	2.95206i	0.218421	−	0.126106i
$549$	−7.30830	−	12.6583i	−0.311911	−	0.540245i
$550$	−3.88355	+	6.72651i	−0.165595	+	0.286819i
$551$			25.5906i			1.09020i
$552$	−0.517904	−	0.299012i	−0.0220434	−	0.0127268i
$553$	−1.06386	−	0.614222i	−0.0452401	−	0.0261194i
$554$			42.9262i			1.82376i
$555$	1.98187	−	3.43270i	0.0841256	−	0.145710i
$556$	−16.6648	−	28.8642i	−0.706743	−	1.22412i
$557$	−27.3410	+	15.7853i	−1.15847	+	0.668845i	−0.950938	−	0.309382i	$-0.899878\pi$
$557$	−27.3410	+	15.7853i	−1.15847	+	0.668845i	−0.207536	+	0.978227i	$0.566545\pi$
$558$	9.41264			0.398469
$559$	−29.6848	−	2.56019i	−1.25553	−	0.108285i
$560$	−0.713012			−0.0301302
$561$	−5.06634	+	2.92505i	−0.213901	+	0.123496i
$562$	14.1283	+	24.4710i	0.595968	+	1.03225i
$563$	20.8921	−	36.1862i	0.880499	−	1.52507i	0.0297113	−	0.999559i	$-0.490541\pi$
$563$	20.8921	−	36.1862i	0.880499	−	1.52507i	0.850787	−	0.525510i	$-0.176125\pi$
$564$		−	0.772354i		−	0.0325220i
$565$	2.87821	+	1.66174i	0.121087	+	0.0699098i
$566$	−4.43805	−	2.56231i	−0.186545	−	0.107702i
$567$			0.164532i			0.00690969i
$568$	1.65099	−	2.85961i	0.0692742	−	0.119986i
$569$	3.88860	+	6.73525i	0.163019	+	0.282357i	0.935950	−	0.352133i	$-0.114544\pi$
$569$	3.88860	+	6.73525i	0.163019	+	0.282357i	−0.772931	+	0.634490i	$0.781210\pi$
$570$	−8.26132	+	4.76967i	−0.346029	+	0.199780i
$571$	−31.8538			−1.33304			−0.666520	−	0.745488i	$-0.732217\pi$
$571$	−31.8538			−1.33304			−0.666520	+	0.745488i	$0.732217\pi$
$572$	6.18317	−	2.89255i	0.258531	−	0.120944i
$573$	−9.33029			−0.389778
$574$	−0.642837	+	0.371142i	−0.0268315	+	0.0154912i
$575$	−5.58953	−	9.68136i	−0.233100	−	0.403741i
$576$	−3.56233	+	6.17013i	−0.148430	+	0.257089i
$577$		−	9.26624i		−	0.385759i	−0.981222	−	0.192879i	$-0.938217\pi$
$577$		−	9.26624i		−	0.385759i	0.981222	−	0.192879i	$-0.0617826\pi$
$578$	29.4316	+	16.9924i	1.22419	+	0.706789i
$579$	−13.7931	−	7.96346i	−0.573222	−	0.330950i
$580$		−	10.6587i		−	0.442578i
$581$	0.0958341	−	0.165990i	0.00397587	−	0.00688641i
$582$	17.6425	+	30.5577i	0.731305	+	1.26666i
$583$	−3.20995	+	1.85327i	−0.132943	+	0.0767545i
$584$	−2.74543			−0.113607
$585$	−0.319511	+	3.70465i	−0.0132102	+	0.153168i
$586$	53.8515			2.22458
$587$	9.35659	−	5.40203i	0.386188	−	0.222966i	−0.294319	−	0.955707i	$-0.595093\pi$
$587$	9.35659	−	5.40203i	0.386188	−	0.222966i	0.680507	+	0.732742i	$0.261760\pi$
$588$	−6.60084	−	11.4330i	−0.272214	−	0.471489i
$589$	−11.1815	+	19.3669i	−0.460726	+	0.798001i
$590$			2.55004i			0.104984i
$591$	11.0992	+	6.40813i	0.456560	+	0.263595i
$592$	13.9866	+	8.07517i	0.574846	+	0.331888i
$593$		−	4.28911i		−	0.176133i	−0.996115	−	0.0880663i	$-0.971931\pi$
$593$		−	4.28911i		−	0.176133i	0.996115	−	0.0880663i	$-0.0280687\pi$
$594$	0.986569	−	1.70879i	0.0404794	−	0.0701124i
$595$	−0.496327	−	0.859664i	−0.0203474	−	0.0352428i
$596$	30.9448	−	17.8660i	1.26755	−	0.731820i
$597$	20.8502			0.853342
$598$	−1.73605	+	20.1291i	−0.0709925	+	0.823140i
$599$	24.4988			1.00099			0.500496	−	0.865739i	$-0.333151\pi$
$599$	24.4988			1.00099			0.500496	+	0.865739i	$0.333151\pi$
$600$	0.717872	−	0.414463i	0.0293070	−	0.0169204i
$601$	−6.68907	−	11.5858i	−0.272853	−	0.472595i	0.696738	−	0.717325i	$-0.254634\pi$
$601$	−6.68907	−	11.5858i	−0.272853	−	0.472595i	−0.969591	+	0.244730i	$0.921301\pi$
$602$	−1.34137	+	2.32332i	−0.0546702	+	0.0946916i
$603$			3.43162i			0.139746i
$604$	−4.01473	−	2.31791i	−0.163357	−	0.0943143i
$605$	−0.893131	−	0.515650i	−0.0363110	−	0.0209641i
$606$			17.3727i			0.705717i
$607$	−5.49370	+	9.51536i	−0.222982	+	0.386217i	−0.955712	−	0.294303i	$-0.904913\pi$
$607$	−5.49370	+	9.51536i	−0.222982	+	0.386217i	0.732730	+	0.680520i	$0.238246\pi$
$608$	−18.4470	−	31.9511i	−0.748124	−	1.29579i
$609$	0.777831	−	0.449081i	0.0315193	−	0.0181977i
$610$	−29.7433			−1.20427
$611$	1.33229	−	0.623259i	0.0538987	−	0.0252144i
$612$	−11.0759			−0.447715
$613$	−3.63385	+	2.09800i	−0.146770	+	0.0847375i	−0.571587	−	0.820542i	$-0.693672\pi$
$613$	−3.63385	+	2.09800i	−0.146770	+	0.0847375i	0.424817	+	0.905279i	$0.360339\pi$
$614$	26.4273	+	45.7733i	1.06652	+	1.84726i
$615$	−1.17901	+	2.04210i	−0.0475422	+	0.0823456i
$616$			0.0346469i			0.00139596i
$617$	36.2028	+	20.9017i	1.45747	+	0.841470i	0.998886	−	0.0471825i	$-0.0150242\pi$
$617$	36.2028	+	20.9017i	1.45747	+	0.841470i	0.458582	+	0.888652i	$0.348358\pi$
$618$	−27.5286	−	15.8937i	−1.10736	−	0.639337i
$619$		−	21.2204i		−	0.852920i	−0.904506	−	0.426460i	$-0.859761\pi$
$619$		−	21.2204i		−	0.852920i	0.904506	−	0.426460i	$-0.140239\pi$
$620$	4.65718	−	8.06647i	0.187037	−	0.323957i
$621$	1.41995	+	2.45943i	0.0569808	+	0.0986936i
$622$	−10.7845	+	6.22646i	−0.432421	+	0.249658i
$623$	−2.15891			−0.0864949
$624$	−15.0947	−	1.30186i	−0.604271	−	0.0521160i
$625$	10.1775			0.407101
$626$	17.7865	−	10.2691i	0.710893	−	0.410434i
$627$	2.34394	+	4.05982i	0.0936079	+	0.162134i
$628$	−14.8231	+	25.6743i	−0.591505	+	1.02452i
$629$			22.4845i			0.896516i
$630$	0.289950	+	0.167403i	0.0115519	+	0.00666949i
$631$	1.11955	+	0.646373i	0.0445686	+	0.0257317i	0.522119	−	0.852873i	$-0.325142\pi$
$631$	1.11955	+	0.646373i	0.0445686	+	0.0257317i	−0.477550	+	0.878604i	$0.658475\pi$
$632$		−	1.57224i		−	0.0625404i
$633$	−2.20774	+	3.82391i	−0.0877496	+	0.151987i
$634$	10.9459	+	18.9589i	0.434717	+	0.752952i
$635$	2.10087	−	1.21294i	0.0833706	−	0.0481341i
$636$	−7.01750			−0.278262
$637$	14.3950	−	20.6123i	0.570351	−	0.816688i
$638$	−10.7712			−0.426434
$639$	−13.5798	+	7.84027i	−0.537207	+	0.310156i
$640$	−0.867442	−	1.50245i	−0.0342886	−	0.0593897i
$641$	−20.0501	+	34.7278i	−0.791931	+	1.37166i	0.132839	+	0.991138i	$0.457591\pi$
$641$	−20.0501	+	34.7278i	−0.791931	+	1.37166i	−0.924770	+	0.380527i	$0.875743\pi$
$642$		−	17.5445i		−	0.692427i
$643$	20.3819	+	11.7675i	0.803782	+	0.464064i	0.844792	−	0.535095i	$-0.179724\pi$
$643$	20.3819	+	11.7675i	0.803782	+	0.464064i	−0.0410100	+	0.999159i	$0.513058\pi$
$644$	0.766124	+	0.442322i	0.0301895	+	0.0174299i
$645$			8.52228i			0.335565i
$646$	27.0562	−	46.8628i	1.06451	−	1.84379i
$647$	19.9245	+	34.5102i	0.783312	+	1.35674i	0.930002	+	0.367553i	$0.119804\pi$
$647$	19.9245	+	34.5102i	0.783312	+	1.35674i	−0.146691	+	0.989182i	$0.546862\pi$
$648$	−0.182367	+	0.105289i	−0.00716403	+	0.00413616i
$649$	1.25315			0.0491906
$650$	−22.9599	−	16.0345i	−0.900562	−	0.628926i
$651$	0.784881			0.0307619
$652$	−0.906270	+	0.523235i	−0.0354923	+	0.0204915i
$653$	−7.72866	−	13.3864i	−0.302446	−	0.523852i	0.674244	−	0.738509i	$-0.264470\pi$
$653$	−7.72866	−	13.3864i	−0.302446	−	0.523852i	−0.976689	+	0.214658i	$0.931136\pi$
$654$	−5.68761	+	9.85122i	−0.222403	+	0.385213i
$655$			2.86445i			0.111923i
$656$	−8.32061	−	4.80390i	−0.324865	−	0.187561i
$657$	11.2908	+	6.51877i	0.440497	+	0.254321i
$658$		−	0.132437i		−	0.00516294i
$659$	17.3178	−	29.9953i	0.674606	−	1.16845i	−0.301977	−	0.953315i	$-0.597647\pi$
$659$	17.3178	−	29.9953i	0.674606	−	1.16845i	0.976584	−	0.215137i	$-0.0690200\pi$
$660$	−0.976268	−	1.69095i	−0.0380012	−	0.0658200i
$661$	40.5371	−	23.4041i	1.57671	−	0.910314i	0.581397	−	0.813620i	$-0.302506\pi$
$661$	40.5371	−	23.4041i	1.57671	−	0.910314i	0.995314	−	0.0966941i	$-0.0308268\pi$
$662$	−3.66101			−0.142289
$663$	−8.93779	−	19.1056i	−0.347115	−	0.742000i
$664$	0.245309			0.00951985
$665$	−0.688877	+	0.397724i	−0.0267135	+	0.0154231i
$666$	−3.79182	−	6.56762i	−0.146930	−	0.254490i
$667$	7.75137	−	13.4258i	0.300134	−	0.519848i
$668$			33.8733i			1.31060i
$669$	−16.4582	−	9.50217i	−0.636312	−	0.367375i
$670$	6.04745	+	3.49150i	0.233633	+	0.134888i
$671$			14.6166i			0.564268i
$672$	−0.647440	+	1.12140i	−0.0249755	+	0.0432589i
$673$	−24.4515	−	42.3513i	−0.942537	−	1.63252i	−0.760610	−	0.649209i	$-0.775100\pi$
$673$	−24.4515	−	42.3513i	−0.942537	−	1.63252i	−0.181927	−	0.983312i	$-0.558233\pi$
$674$	−23.5232	+	13.5811i	−0.906080	+	0.523126i
$675$	−3.93642			−0.151513
$676$	8.47503	+	23.1074i	0.325963	+	0.888748i
$677$	45.6941			1.75617			0.878084	−	0.478507i	$-0.158822\pi$
$677$	45.6941			1.75617			0.878084	+	0.478507i	$0.158822\pi$
$678$	5.50675	−	3.17933i	0.211486	−	0.122101i
$679$	1.47114	+	2.54808i	0.0564570	+	0.0977864i
$680$	0.635232	−	1.10025i	0.0243600	−	0.0421928i
$681$		−	7.70295i		−	0.295178i
$682$	−8.15159	−	4.70632i	−0.312140	−	0.180214i
$683$	27.5145	+	15.8855i	1.05281	+	0.607842i	0.923436	−	0.383753i	$-0.125369\pi$
$683$	27.5145	+	15.8855i	1.05281	+	0.607842i	0.129378	+	0.991595i	$0.458702\pi$
$684$			8.87545i			0.339361i
$685$	1.60803	−	2.78520i	0.0614398	−	0.106417i
$686$	−2.26812	−	3.92849i	−0.0865971	−	0.149991i
$687$	13.3665	−	7.71713i	0.509962	−	0.294427i
$688$	−34.7243			−1.32385
$689$	−5.66285	−	12.1050i	−0.215737	−	0.461164i
$690$	5.77892			0.220000
$691$	−9.12265	+	5.26696i	−0.347042	+	0.200365i	−0.663382	−	0.748281i	$-0.730879\pi$
$691$	−9.12265	+	5.26696i	−0.347042	+	0.200365i	0.316340	+	0.948646i	$0.397546\pi$
$692$	6.67210	+	11.5564i	0.253635	+	0.439309i
$693$	0.0822660	−	0.142489i	0.00312503	−	0.00541270i
$694$			53.6910i			2.03808i
$695$	−15.7228	−	9.07757i	−0.596400	−	0.344332i
$696$	0.995519	+	0.574763i	0.0377351	+	0.0217863i
$697$		−	13.3760i		−	0.506652i
$698$	−5.19822	+	9.00359i	−0.196756	+	0.340791i
$699$	3.49554	+	6.05444i	0.132213	+	0.229000i
$700$	−1.06193	+	0.613107i	−0.0401373	+	0.0231733i
$701$	17.2210			0.650427			0.325214	−	0.945641i	$-0.394564\pi$
$701$	17.2210			0.650427			0.325214	+	0.945641i	$0.394564\pi$
$702$	5.83268	+	4.07338i	0.220140	+	0.153740i
$703$	18.0176			0.679546
$704$	6.17013	−	3.56233i	0.232546	−	0.134260i
$705$	−0.210357	−	0.364349i	−0.00792250	−	0.0137222i
$706$	28.2589	−	48.9458i	1.06354	−	1.84210i
$707$			1.44864i			0.0544816i
$708$	2.05471	+	1.18628i	0.0772206	+	0.0445833i
$709$	5.63610	+	3.25400i	0.211668	+	0.122207i	0.602086	−	0.798431i	$-0.294336\pi$
$709$	5.63610	+	3.25400i	0.211668	+	0.122207i	−0.390418	+	0.920638i	$0.627670\pi$
$710$			31.9083i			1.19750i
$711$	−3.73315	+	6.46600i	−0.140004	+	0.242494i
$712$	−1.38156	−	2.39293i	−0.0517761	−	0.0896788i
$713$	11.7324	−	6.77373i	0.439383	−	0.253678i
$714$	−1.89920			−0.0710759
$715$	2.12903	−	3.04856i	0.0796212	−	0.114010i
$716$	−25.1170			−0.938667
$717$	15.6815	−	9.05372i	0.585636	−	0.338117i
$718$	6.74074	+	11.6753i	0.251562	+	0.435719i
$719$	−22.5358	+	39.0331i	−0.840443	+	1.45569i	0.0490768	+	0.998795i	$0.484372\pi$
$719$	−22.5358	+	39.0331i	−0.840443	+	1.45569i	−0.889520	+	0.456896i	$0.848961\pi$
$720$			4.33358i			0.161503i
$721$	−2.29550	−	1.32531i	−0.0854889	−	0.0493570i
$722$	−5.08571	−	2.93624i	−0.189271	−	0.109275i
$723$		−	18.8101i		−	0.699555i
$724$	4.05307	−	7.02013i	0.150631	−	0.260901i
$725$	10.7443	+	18.6096i	0.399031	+	0.691143i
$726$	−1.70879	+	0.986569i	−0.0634191	+	0.0366150i
$727$	38.1843			1.41618			0.708089	−	0.706123i	$-0.249558\pi$
$727$	38.1843			1.41618			0.708089	+	0.706123i	$0.249558\pi$
$728$	−0.124459	−	0.0107341i	−0.00461277	−	0.000397833i
$729$	1.00000			0.0370370
$730$	22.9757	−	13.2650i	0.850368	−	0.490960i
$731$	−24.1716	−	41.8664i	−0.894018	−	1.54848i
$732$	−13.8366	+	23.9658i	−0.511417	+	0.885800i
$733$			25.6025i			0.945651i	0.881156	+	0.472826i	$0.156766\pi$
$733$			25.6025i			0.945651i	−0.881156	+	0.472826i	$0.843234\pi$
$734$	−10.2344	−	5.90881i	−0.377757	−	0.218098i
$735$	−6.22774	−	3.59559i	−0.229714	−	0.132625i
$736$			22.3503i			0.823843i
$737$	1.71581	−	2.97187i	0.0632027	−	0.109470i
$738$	2.25575	+	3.90707i	0.0830352	+	0.143821i
$739$	−26.4450	+	15.2681i	−0.972797	+	0.561645i	−0.900088	−	0.435709i	$-0.856498\pi$
$739$	−26.4450	+	15.2681i	−0.972797	+	0.561645i	−0.0727091	+	0.997353i	$0.523164\pi$
$740$	−7.50445			−0.275869
$741$	−15.3099	+	7.16215i	−0.562425	+	0.263108i
$742$	−1.20331			−0.0441747
$743$	32.0859	−	18.5248i	1.17712	−	0.679610i	0.221772	−	0.975099i	$-0.428816\pi$
$743$	32.0859	−	18.5248i	1.17712	−	0.679610i	0.955346	+	0.295489i	$0.0954826\pi$
$744$	0.502271	+	0.869959i	0.0184142	+	0.0318943i
$745$	9.73190	−	16.8562i	0.356549	−	0.617562i
$746$		−	5.08397i		−	0.186137i
$747$	−1.00886	−	0.582465i	−0.0369122	−	0.0213113i
$748$	9.59198	+	5.53793i	0.350718	+	0.202487i
$749$		−	1.46297i		−	0.0534556i
$750$	−9.09235	+	15.7484i	−0.332006	+	0.575051i
$751$	−0.938997	−	1.62639i	−0.0342645	−	0.0593478i	0.848385	−	0.529380i	$-0.177576\pi$
$751$	−0.938997	−	1.62639i	−0.0342645	−	0.0593478i	−0.882649	+	0.470032i	$0.844242\pi$
$752$	1.48455	−	0.857105i	0.0541359	−	0.0312554i
$753$	10.9046			0.397385
$754$	3.33706	−	38.6923i	0.121528	−	1.40909i
$755$	−2.52521			−0.0919016
$756$	0.269771	−	0.155752i	0.00981147	−	0.00566466i
$757$	−10.8346	−	18.7661i	−0.393791	−	0.682066i	0.599155	−	0.800633i	$-0.295503\pi$
$757$	−10.8346	−	18.7661i	−0.393791	−	0.682066i	−0.992946	+	0.118567i	$0.962170\pi$
$758$	−30.0729	+	52.0878i	−1.09230	+	1.89191i
$759$		−	2.83991i		−	0.103082i
$760$	−0.881670	−	0.509032i	−0.0319815	−	0.0184645i
$761$	−10.7821	−	6.22506i	−0.390851	−	0.225658i	0.291678	−	0.956517i	$-0.405787\pi$
$761$	−10.7821	−	6.22506i	−0.390851	−	0.225658i	−0.682529	+	0.730859i	$0.739120\pi$
$762$		−	4.64133i		−	0.168138i
$763$	−0.474266	+	0.821453i	−0.0171696	+	0.0297386i
$764$	8.83241	+	15.2982i	0.319545	+	0.553469i
$765$	−5.22491	+	3.01660i	−0.188907	+	0.109065i
$766$	−40.5681			−1.46579
$767$	−0.388245	+	4.50160i	−0.0140187	+	0.162543i
$768$	−17.5686			−0.633952
$769$	−27.3061	+	15.7652i	−0.984682	+	0.568507i	−0.903681	−	0.428207i	$-0.859145\pi$
$769$	−27.3061	+	15.7652i	−0.984682	+	0.568507i	−0.0810019	+	0.996714i	$0.525812\pi$
$770$	−0.167403	−	0.289950i	−0.00603278	−	0.0104491i
$771$	−4.41069	+	7.63953i	−0.158847	+	0.275131i
$772$			30.1541i			1.08527i
$773$	−13.1583	−	7.59696i	−0.473272	−	0.273244i	0.244336	−	0.969691i	$-0.421430\pi$
$773$	−13.1583	−	7.59696i	−0.473272	−	0.273244i	−0.717608	+	0.696447i	$0.754763\pi$
$774$	14.1208	+	8.15265i	0.507562	+	0.293041i
$775$			18.7783i			0.674535i
$776$	−1.88286	+	3.26120i	−0.0675906	+	0.117070i
$777$	−0.316184	−	0.547647i	−0.0113430	−	0.0196467i
$778$	−4.69024	+	2.70791i	−0.168153	+	0.0970833i
$779$	−10.7186			−0.384034
$780$	6.37670	−	2.98309i	0.228323	−	0.106812i
$781$	15.6805			0.561094
$782$	−28.3894	+	16.3906i	−1.01520	+	0.586127i
$783$	−2.72945	−	4.72754i	−0.0975424	−	0.168948i
$784$	14.6503	−	25.3751i	0.523226	−	0.906253i
$785$			16.1487i			0.576373i
$786$	4.74619	+	2.74022i	0.169291	+	0.0977403i
$787$	38.6953	+	22.3407i	1.37934	+	0.796361i	0.992080	−	0.125611i	$-0.0400892\pi$
$787$	38.6953	+	22.3407i	1.37934	+	0.796361i	0.387257	+	0.921972i	$0.373422\pi$
$788$		−	24.2647i		−	0.864395i
$789$	−0.154305	+	0.267263i	−0.00549339	+	0.00951483i
$790$	7.59657	+	13.1576i	0.270274	+	0.468128i
$791$	0.459186	−	0.265111i	0.0163268	−	0.00942626i
$792$	0.210579			0.00748259
$793$	−52.5060	−	4.52843i	−1.86454	−	0.160809i
$794$	16.2233			0.575743
$795$	−3.31042	+	1.91127i	−0.117409	+	0.0677859i
$796$	−19.7376	−	34.1866i	−0.699581	−	1.21171i
$797$	−21.5221	+	37.2773i	−0.762351	+	1.32043i	0.179285	+	0.983797i	$0.442622\pi$
$797$	−21.5221	+	37.2773i	−0.762351	+	1.32043i	−0.941636	+	0.336634i	$0.890712\pi$
$798$			1.52189i			0.0538744i
$799$	2.06679	+	1.19326i	0.0731177	+	0.0422145i
$800$	−26.8294	−	15.4900i	−0.948564	−	0.547654i
$801$			13.1215i			0.463627i
$802$	13.2263	−	22.9085i	0.467035	−	0.808929i
$803$	−6.51877	−	11.2908i	−0.230042	−	0.398445i
$804$	5.62658	−	3.24851i	0.198434	−	0.114566i
$805$	0.481880			0.0169840
$806$	19.4316	−	27.8242i	0.684449	−	0.980065i
$807$	−10.8476			−0.381853
$808$	−1.60566	+	0.927030i	−0.0564871	+	0.0326128i
$809$	−23.5119	−	40.7239i	−0.826636	−	1.43178i	−0.900663	−	0.434519i	$-0.856918\pi$
$809$	−23.5119	−	40.7239i	−0.826636	−	1.43178i	0.0740266	−	0.997256i	$-0.476415\pi$
$810$	1.01745	−	1.76227i	0.0357495	−	0.0619199i
$811$		−	0.903282i		−	0.0317185i	−0.999874	−	0.0158593i	$-0.994952\pi$
$811$		−	0.903282i		−	0.0317185i	0.999874	−	0.0158593i	$-0.00504837\pi$
$812$	−1.47265	−	0.850235i	−0.0516799	−	0.0298374i
$813$	11.4868	+	6.63190i	0.402859	+	0.232591i
$814$			7.58364i			0.265806i
$815$	−0.285015	+	0.493660i	−0.00998364	+	0.0172922i
$816$	−12.2912	−	21.2890i	−0.430279	−	0.745265i
$817$	−33.5489	+	19.3695i	−1.17373	+	0.677652i
$818$	56.0637			1.96022
$819$	0.486363	+	0.339662i	0.0169949	+	0.0118688i
$820$	4.46438			0.155903
$821$	−31.0712	+	17.9390i	−1.08439	+	0.626075i	−0.932078	−	0.362257i	$-0.882006\pi$
$821$	−31.0712	+	17.9390i	−1.08439	+	0.626075i	−0.152315	+	0.988332i	$0.548673\pi$
$822$	−3.07658	−	5.32879i	−0.107308	−	0.185863i
$823$	−18.3744	+	31.8254i	−0.640492	+	1.10936i	0.344831	+	0.938665i	$0.387936\pi$
$823$	−18.3744	+	31.8254i	−0.640492	+	1.10936i	−0.985323	+	0.170700i	$0.945397\pi$
$824$		−	3.39243i		−	0.118181i
$825$	3.40904	+	1.96821i	0.118688	+	0.0685243i
$826$	0.352325	+	0.203415i	0.0122590	+	0.00707771i
$827$		−	48.9358i		−	1.70166i	−0.525439	−	0.850831i	$-0.676099\pi$
$827$		−	48.9358i		−	1.70166i	0.525439	−	0.850831i	$-0.323901\pi$
$828$	2.68836	−	4.65638i	0.0934271	−	0.161821i
$829$	−8.30233	−	14.3801i	−0.288352	−	0.499440i	0.685065	−	0.728482i	$-0.259774\pi$
$829$	−8.30233	−	14.3801i	−0.288352	−	0.499440i	−0.973417	+	0.229042i	$0.926441\pi$
$830$	−2.05292	+	1.18526i	−0.0712580	+	0.0411408i
$831$	21.7553			0.754683
$832$	10.8851	+	23.2681i	0.377371	+	0.806676i
$833$	40.7923			1.41337
$834$	−30.0818	+	17.3677i	−1.04165	+	0.601395i
$835$	9.22567	+	15.9793i	0.319268	+	0.552988i
$836$	4.43773	−	7.68637i	0.153482	−	0.265839i
$837$		−	4.77039i		−	0.164889i
$838$	−55.1084	−	31.8169i	−1.90369	−	1.09909i
$839$	−10.3565	−	5.97935i	−0.357547	−	0.206430i	0.310457	−	0.950587i	$-0.399518\pi$
$839$	−10.3565	−	5.97935i	−0.357547	−	0.206430i	−0.668004	+	0.744157i	$0.732851\pi$
$840$			0.0357313i			0.00123285i
$841$	−0.399751	+	0.692389i	−0.0137845	+	0.0238755i
$842$	−23.7573	−	41.1489i	−0.818731	−	1.41808i
$843$	12.4021	−	7.16033i	0.427150	−	0.246615i
$844$	8.35971			0.287753
$845$	10.2915	+	8.59242i	0.354038	+	0.295588i
$846$	−0.804933			−0.0276742
$847$	−0.142489	+	0.0822660i	−0.00489597	+	0.00282669i
$848$	−7.78753	−	13.4884i	−0.267425	−	0.463194i
$849$	−1.29859	+	2.24923i	−0.0445676	+	0.0771934i
$850$		−	45.4384i		−	1.55852i
$851$	−9.45267	−	5.45750i	−0.324033	−	0.187081i
$852$	25.7102	+	14.8438i	0.880818	+	0.508541i
$853$			34.0868i			1.16711i	0.812073	+	0.583556i	$0.198339\pi$
$853$			34.0868i			1.16711i	−0.812073	+	0.583556i	$0.801661\pi$
$854$	−2.37260	+	4.10946i	−0.0811887	+	0.140623i
$855$	2.41730	+	4.18689i	0.0826700	+	0.143189i
$856$	1.62154	−	0.936199i	0.0554233	−	0.0319986i
$857$	−53.1305			−1.81490			−0.907452	−	0.420156i	$-0.861975\pi$
$857$	−53.1305			−1.81490			−0.907452	+	0.420156i	$0.861975\pi$
$858$	−3.01456	−	6.44399i	−0.102915	−	0.219994i
$859$	−3.60575			−0.123027			−0.0615133	−	0.998106i	$-0.519593\pi$
$859$	−3.60575			−0.123027			−0.0615133	+	0.998106i	$0.519593\pi$
$860$	13.9734	−	8.06752i	0.476488	−	0.275100i
$861$	0.188097	+	0.325794i	0.00641034	+	0.0111030i
$862$	−1.43023	+	2.47722i	−0.0487137	+	0.0843746i
$863$		−	12.6720i		−	0.431360i	−0.976464	−	0.215680i	$-0.930803\pi$
$863$		−	12.6720i		−	0.431360i	0.976464	−	0.215680i	$-0.0691968\pi$
$864$	6.81569	+	3.93504i	0.231875	+	0.133873i
$865$	6.29497	+	3.63440i	0.214035	+	0.123573i
$866$			58.2614i			1.97980i
$867$	8.61185	−	14.9162i	0.292474	−	0.506579i
$868$	−0.742999	−	1.28691i	−0.0252190	−	0.0436806i
$869$	6.46600	−	3.73315i	0.219344	−	0.126638i
$870$	−11.1083			−0.376606
$871$	10.1440	+	7.08429i	0.343717	+	0.240042i
$872$	−1.21399			−0.0411110
$873$	15.4868	−	8.94134i	0.524150	−	0.302618i
$874$	13.1343	+	22.7493i	0.444275	+	0.769508i
$875$	−0.758173	+	1.31319i	−0.0256309	+	0.0443941i
$876$		−	24.6837i		−	0.833984i
$877$	9.16500	+	5.29142i	0.309480	+	0.178678i	0.646694	−	0.762750i	$-0.276151\pi$
$877$	9.16500	+	5.29142i	0.309480	+	0.178678i	−0.337214	+	0.941428i	$0.609484\pi$
$878$	−35.2391	−	20.3453i	−1.18926	−	0.686621i
$879$		−	27.2923i		−	0.920546i
$880$	2.16679	−	3.75299i	0.0730424	−	0.126513i
$881$	13.5377	+	23.4479i	0.456095	+	0.789981i	0.998750	−	0.0499751i	$-0.0159142\pi$
$881$	13.5377	+	23.4479i	0.456095	+	0.789981i	−0.542655	+	0.839956i	$0.682581\pi$
$882$	−11.9153	+	6.87928i	−0.401208	+	0.231637i
$883$	37.9071			1.27567			0.637837	−	0.770171i	$-0.279829\pi$
$883$	37.9071			1.27567			0.637837	+	0.770171i	$0.279829\pi$
$884$	−22.8652	+	32.7407i	−0.769039	+	1.10119i
$885$	1.29238			0.0434428
$886$	−11.6819	+	6.74455i	−0.392461	+	0.226588i
$887$	−19.3811	−	33.5690i	−0.650752	−	1.12714i	−0.982941	−	0.183923i	$-0.941120\pi$
$887$	−19.3811	−	33.5690i	−0.650752	−	1.12714i	0.332188	−	0.943213i	$-0.392213\pi$
$888$	0.404673	−	0.700915i	0.0135799	−	0.0235212i
$889$		−	0.387021i		−	0.0129803i
$890$	23.1237	+	13.3505i	0.775109	+	0.447509i
$891$	−0.866025	−	0.500000i	−0.0290129	−	0.0167506i
$892$			35.9805i			1.20472i
$893$	0.956199	−	1.65619i	0.0319980	−	0.0554221i
$894$	−18.6196	−	32.2501i	−0.622733	−	1.07861i
$895$	−11.8487	+	6.84082i	−0.396057	+	0.228663i
$896$	−0.276781			−0.00924660
$897$	10.2016	+	0.879844i	0.340620	+	0.0293771i
$898$	53.7001			1.79199
$899$	−22.5522	+	13.0205i	−0.752158	+	0.434259i
$900$	3.72637	+	6.45426i	0.124212	+	0.215142i
$901$	10.8418	−	18.7786i	0.361193	−	0.625604i
$902$		−	4.51149i		−	0.150216i
$903$	1.17748	+	0.679816i	0.0391840	+	0.0226229i
$904$	0.587696	+	0.339306i	0.0195465	+	0.0112852i
$905$		−	4.41555i		−	0.146778i
$906$	−2.41568	+	4.18408i	−0.0802556	+	0.139007i
$907$	15.5016	+	26.8495i	0.514721	+	0.891522i	0.999854	+	0.0170821i	$0.00543767\pi$
$907$	15.5016	+	26.8495i	0.514721	+	0.891522i	−0.485133	+	0.874440i	$0.661229\pi$
$908$	−12.6300	+	7.29191i	−0.419140	+	0.241991i
$909$	8.80460			0.292030
$910$	1.09343	−	0.511516i	0.0362468	−	0.0169566i
$911$	−18.1328			−0.600767			−0.300383	−	0.953819i	$-0.597115\pi$
$911$	−18.1328			−0.600767			−0.300383	+	0.953819i	$0.597115\pi$
$912$	−17.0596	+	9.84936i	−0.564900	+	0.326145i
$913$	0.582465	+	1.00886i	0.0192768	+	0.0333884i
$914$	2.11940	−	3.67090i	0.0701034	−	0.121423i
$915$			15.0741i			0.498334i
$916$	−25.3064	−	14.6107i	−0.836147	−	0.482750i
$917$	0.395765	+	0.228495i	0.0130693	+	0.00754558i
$918$			11.5431i			0.380978i
$919$	4.15318	−	7.19353i	0.137001	−	0.237293i	−0.789359	−	0.613932i	$-0.789587\pi$
$919$	4.15318	−	7.19353i	0.137001	−	0.237293i	0.926360	+	0.376639i	$0.122920\pi$
$920$	0.308371	+	0.534114i	0.0101667	+	0.0176092i
$921$	23.1982	−	13.3935i	0.764408	−	0.441331i
$922$	−43.2062			−1.42292
$923$	−4.85806	+	56.3279i	−0.159905	+	1.85406i
$924$	−0.311505			−0.0102477
$925$	13.1024	−	7.56470i	0.430806	−	0.248726i
$926$	−25.4945	−	44.1577i	−0.837800	−	1.45111i
$927$	−8.05502	+	13.9517i	−0.264561	+	0.458234i
$928$		−	42.9619i		−	1.41029i
$929$	10.2712	+	5.93006i	0.336986	+	0.194559i	0.658939	−	0.752197i	$-0.271006\pi$
$929$	10.2712	+	5.93006i	0.336986	+	0.194559i	−0.321952	+	0.946756i	$0.604339\pi$
$930$	−8.40672	−	4.85362i	−0.275667	−	0.159157i
$931$		−	32.6882i		−	1.07131i
$932$	6.61802	−	11.4627i	0.216780	−	0.375475i
$933$	3.15561	+	5.46568i	0.103310	+	0.178938i
$934$	41.3728	−	23.8866i	1.35376	−	0.781593i
$935$	6.03321			0.197307
$936$	−0.0652403	+	0.756444i	−0.00213245	+	0.0247252i
$937$	42.7140			1.39540			0.697702	−	0.716388i	$-0.254206\pi$
$937$	42.7140			1.39540			0.697702	+	0.716388i	$0.254206\pi$
$938$	0.964801	−	0.557028i	0.0315019	−	0.0181876i
$939$	−5.20443	−	9.01433i	−0.169840	−	0.294172i
$940$	−0.398264	+	0.689813i	−0.0129899	+	0.0224992i
$941$		−	57.7585i		−	1.88287i	−0.337188	−	0.941437i	$-0.609476\pi$
$941$		−	57.7585i		−	1.88287i	0.337188	−	0.941437i	$-0.390524\pi$
$942$	26.7573	+	15.4483i	0.871800	+	0.503334i
$943$	5.62338	+	3.24666i	0.183122	+	0.105726i
$944$			5.26583i			0.171388i
$945$	0.0848408	−	0.146949i	0.00275987	−	0.00478024i
$946$	−8.15265	−	14.1208i	−0.265066	−	0.459107i
$947$	18.4042	−	10.6257i	0.598057	−	0.345288i	−0.170220	−	0.985406i	$-0.554448\pi$
$947$	18.4042	−	10.6257i	0.598057	−	0.345288i	0.768277	+	0.640118i	$0.221115\pi$
$948$	14.1358			0.459108
$949$	42.5787	−	19.9188i	1.38216	−	0.646590i
$950$	−36.4113			−1.18134
$951$	9.60847	−	5.54745i	0.311576	−	0.179889i
$952$	−0.101344	−	0.175533i	−0.00328458	−	0.00568906i
$953$	28.1557	−	48.7670i	0.912051	−	1.57972i	0.100889	−	0.994898i	$-0.467831\pi$
$953$	28.1557	−	48.7670i	0.912051	−	1.57972i	0.811162	−	0.584821i	$-0.198835\pi$
$954$			7.31351i			0.236784i
$955$	8.33317	+	4.81116i	0.269655	+	0.155685i
$956$	−29.6894	−	17.1412i	−0.960225	−	0.554386i
$957$			5.45889i			0.176461i
$958$	35.6140	−	61.6852i	1.15063	−	1.99296i
$959$	−0.256543	−	0.444346i	−0.00828422	−	0.0143487i
$960$	6.36325	−	3.67383i	0.205373	−	0.118572i
$961$	8.24339			0.265916
$962$	−27.2421	−	2.34952i	−0.878320	−	0.0757516i
$963$	−8.89168			−0.286530
$964$	−30.8415	+	17.8064i	−0.993339	+	0.573505i
$965$	8.21271	+	14.2248i	0.264377	+	0.457914i
$966$	0.460980	−	0.798440i	0.0148318	−	0.0256894i
$967$			57.0933i			1.83600i	0.396586	+	0.917998i	$0.370195\pi$
$967$			57.0933i			1.83600i	−0.396586	+	0.917998i	$0.629805\pi$
$968$	−0.182367	−	0.105289i	−0.00586148	−	0.00338413i
$969$	−23.7504	−	13.7123i	−0.762972	−	0.440502i
$970$		−	36.3894i		−	1.16839i
$971$	−8.42927	+	14.5999i	−0.270508	+	0.468534i	−0.968992	−	0.247092i	$-0.920525\pi$
$971$	−8.42927	+	14.5999i	−0.270508	+	0.468534i	0.698484	+	0.715626i	$0.253858\pi$
$972$	−0.946639	−	1.63963i	−0.0303634	−	0.0525910i
$973$	−2.50839	+	1.44822i	−0.0804154	+	0.0464279i
$974$	48.0157			1.53852
$975$	−8.12641	+	11.6362i	−0.260253	+	0.372658i
$976$	−61.4198			−1.96600
$977$	29.4083	−	16.9789i	0.940854	−	0.543202i	0.0506260	−	0.998718i	$-0.483878\pi$
$977$	29.4083	−	16.9789i	0.940854	−	0.543202i	0.890228	+	0.455515i	$0.150545\pi$
$978$	0.545306	+	0.944498i	0.0174370	+	0.0302017i
$979$	6.56077	−	11.3636i	0.209683	−	0.363182i
$980$			13.6149i			0.434912i
$981$	4.99266	+	2.88252i	0.159404	+	0.0920317i
$982$	−15.1436	−	8.74314i	−0.483251	−	0.279005i
$983$		−	27.5456i		−	0.878569i	−0.898348	−	0.439284i	$-0.855232\pi$
$983$		−	27.5456i		−	0.878569i	0.898348	−	0.439284i	$-0.144768\pi$
$984$	−0.240739	+	0.416973i	−0.00767449	+	0.0132926i
$985$	−6.60870	−	11.4466i	−0.210571	−	0.364719i
$986$	54.5703	−	31.5062i	1.73787	−	1.00336i
$987$	−0.0671200			−0.00213645
$988$	26.2362	+	18.3226i	0.834686	+	0.582920i
$989$	23.4680			0.746238
$990$	−1.76227	+	1.01745i	−0.0560087	+	0.0323366i
$991$	22.7883	+	39.4705i	0.723894	+	1.25382i	0.959428	+	0.281955i	$0.0909828\pi$
$991$	22.7883	+	39.4705i	0.723894	+	1.25382i	−0.235534	+	0.971866i	$0.575684\pi$
$992$	18.7717	−	32.5135i	0.596001	−	1.03230i
$993$			1.85542i			0.0588800i
$994$	4.40859	+	2.54530i	0.139832	+	0.0807321i
$995$	−18.6220	−	10.7514i	−0.590356	−	0.340842i
$996$			2.20554i			0.0698851i
$997$	−0.630847	+	1.09266i	−0.0199791	+	0.0346049i	−0.875842	−	0.482598i	$-0.839693\pi$
$997$	−0.630847	+	1.09266i	−0.0199791	+	0.0346049i	0.855863	+	0.517203i	$0.173027\pi$
$998$	−7.40645	−	12.8284i	−0.234447	−	0.406074i
$999$	−3.32852	+	1.92172i	−0.105310	+	0.0608005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.3	✓	24
13.2	odd	12		5577.2.a.be.1.2		12
13.4	even	6	inner	429.2.s.a.199.3	yes	24
13.11	odd	12		5577.2.a.z.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.3	✓	24	1.1	even	1	trivial
429.2.s.a.199.3	yes	24	13.4	even	6	inner
5577.2.a.z.1.11		12	13.11	odd	12
5577.2.a.be.1.2		12	13.2	odd	12

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70879 + 0.986569i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.946639 - 1.63963i) q^{4} -1.03130i q^{5} +(-1.70879 - 0.986569i) q^{6} +(-0.142489 - 0.0822660i) q^{7} -0.210579i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.70879 + 0.986569i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.946639 - 1.63963i) q^{4} -1.03130i q^{5} +(-1.70879 - 0.986569i) q^{6} +(-0.142489 - 0.0822660i) q^{7} -0.210579i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.01745 + 1.76227i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.89328 q^{12} +(1.52780 + 3.26586i) q^{13} +0.324644 q^{14} +(0.893131 - 0.515650i) q^{15} +(2.10103 + 3.63909i) q^{16} +(-2.92505 + 5.06634i) q^{17} -1.97314i q^{18} +(4.05982 + 2.34394i) q^{19} +(-1.69095 - 0.976268i) q^{20} -0.164532i q^{21} +(-0.986569 + 1.70879i) q^{22} +(-1.41995 - 2.45943i) q^{23} +(0.182367 - 0.105289i) q^{24} +3.93642 q^{25} +(-5.83268 - 4.07338i) q^{26} -1.00000 q^{27} +(-0.269771 + 0.155752i) q^{28} +(2.72945 + 4.72754i) q^{29} +(-1.01745 + 1.76227i) q^{30} +4.77039i q^{31} +(-6.81569 - 3.93504i) q^{32} +(0.866025 + 0.500000i) q^{33} -11.5431i q^{34} +(-0.0848408 + 0.146949i) q^{35} +(0.946639 + 1.63963i) q^{36} +(3.32852 - 1.92172i) q^{37} -9.24984 q^{38} +(-2.06442 + 2.95604i) q^{39} -0.217170 q^{40} +(-1.98013 + 1.14323i) q^{41} +(0.162322 + 0.281150i) q^{42} +(-4.13182 + 7.15652i) q^{43} -1.89328i q^{44} +(0.893131 + 0.515650i) q^{45} +(4.85280 + 2.80176i) q^{46} -0.407945i q^{47} +(-2.10103 + 3.63909i) q^{48} +(-3.48646 - 6.03873i) q^{49} +(-6.72651 + 3.88355i) q^{50} -5.85010 q^{51} +(6.80106 + 0.586565i) q^{52} -3.70653 q^{53} +(1.70879 - 0.986569i) q^{54} +(-0.515650 - 0.893131i) q^{55} +(-0.0173235 + 0.0300051i) q^{56} +4.68788i q^{57} +(-9.32809 - 5.38558i) q^{58} +(1.08526 + 0.626577i) q^{59} -1.95254i q^{60} +(-7.30830 + 12.6583i) q^{61} +(-4.70632 - 8.15159i) q^{62} +(0.142489 - 0.0822660i) q^{63} +7.12465 q^{64} +(3.36808 - 1.57562i) q^{65} -1.97314 q^{66} +(2.97187 - 1.71581i) q^{67} +(5.53793 + 9.59198i) q^{68} +(1.41995 - 2.45943i) q^{69} -0.334805i q^{70} +(13.5798 + 7.84027i) q^{71} +(0.182367 + 0.105289i) q^{72} -13.0375i q^{73} +(-3.79182 + 6.56762i) q^{74} +(1.96821 + 3.40904i) q^{75} +(7.68637 - 4.43773i) q^{76} -0.164532 q^{77} +(0.611307 - 7.08794i) q^{78} +7.46629 q^{79} +(3.75299 - 2.16679i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.25575 - 3.90707i) q^{82} +1.16493i q^{83} +(-0.269771 - 0.155752i) q^{84} +(5.22491 + 3.01660i) q^{85} -16.3053i q^{86} +(-2.72945 + 4.72754i) q^{87} +(-0.105289 - 0.182367i) q^{88} +(11.3636 - 6.56077i) q^{89} -2.03490 q^{90} +(0.0509744 - 0.591034i) q^{91} -5.37673 q^{92} +(-4.13128 + 2.38519i) q^{93} +(0.402466 + 0.697092i) q^{94} +(2.41730 - 4.18689i) q^{95} -7.87008i q^{96} +(-15.4868 - 8.94134i) q^{97} +(11.9153 + 6.87928i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

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