LMFDB - Embedded newform 429.2.bb.b.103.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(25,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	429.103
Dual form			429.2.bb.b.25.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.812362 + 1.11812i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.0277724 + 0.0854748i) q^{4} +(2.36802 + 3.25930i) q^{5} +(-0.812362 - 1.11812i) q^{6} +(-1.14719 + 0.372746i) q^{7} +(-2.74699 - 0.892552i) q^{8} +(-0.809017 - 0.587785i) q^{9} -5.56798 q^{10} +(2.11473 + 2.55498i) q^{11} -0.0898735 q^{12} +(-3.38343 + 1.24594i) q^{13} +(0.515162 - 1.58551i) q^{14} +(-3.83154 + 1.24494i) q^{15} +(3.08412 - 2.24074i) q^{16} +(4.95416 - 3.59941i) q^{17} +(1.31443 - 0.427084i) q^{18} +(2.61241 + 0.848825i) q^{19} +(-0.212822 + 0.292925i) q^{20} -1.20623i q^{21} +(-4.57470 + 0.288950i) q^{22} +1.88864 q^{23} +(1.69773 - 2.33673i) q^{24} +(-3.47044 + 10.6809i) q^{25} +(1.35546 - 4.79524i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.0637207 - 0.0877041i) q^{28} +(-1.30287 - 4.00983i) q^{29} +(1.72060 - 5.29547i) q^{30} +(5.18802 - 7.14070i) q^{31} -0.508010i q^{32} +(-3.08342 + 1.22169i) q^{33} +8.46337i q^{34} +(-3.93147 - 2.85638i) q^{35} +(0.0277724 - 0.0854748i) q^{36} +(-10.6498 + 3.46032i) q^{37} +(-3.07131 + 2.23144i) q^{38} +(-0.139422 - 3.60285i) q^{39} +(-3.59584 - 11.0669i) q^{40} +(-4.62939 - 1.50418i) q^{41} +(1.34871 + 0.979897i) q^{42} -2.30799 q^{43} +(-0.159655 + 0.251714i) q^{44} -4.02872i q^{45} +(-1.53426 + 2.11172i) q^{46} +(6.94647 + 2.25705i) q^{47} +(1.17803 + 3.62559i) q^{48} +(-4.48600 + 3.25927i) q^{49} +(-9.12329 - 12.5571i) q^{50} +(1.89232 + 5.82396i) q^{51} +(-0.200463 - 0.254595i) q^{52} +(5.81450 + 4.22448i) q^{53} +1.38207i q^{54} +(-3.31974 + 12.9428i) q^{55} +3.48403 q^{56} +(-1.61456 + 2.22225i) q^{57} +(5.54188 + 1.80067i) q^{58} +(5.63000 - 1.82930i) q^{59} +(-0.212822 - 0.292925i) q^{60} +(2.59398 - 1.88463i) q^{61} +(3.76961 + 11.6017i) q^{62} +(1.14719 + 0.372746i) q^{63} +(6.73625 + 4.89417i) q^{64} +(-12.0729 - 8.07722i) q^{65} +(1.13885 - 4.44009i) q^{66} -11.7021i q^{67} +(0.445248 + 0.323491i) q^{68} +(-0.583621 + 1.79620i) q^{69} +(6.38756 - 2.07544i) q^{70} +(-2.12509 - 2.92494i) q^{71} +(1.69773 + 2.33673i) q^{72} +(-5.26823 + 1.71175i) q^{73} +(4.78242 - 14.7188i) q^{74} +(-9.08572 - 6.60116i) q^{75} +0.246869i q^{76} +(-3.37836 - 2.14280i) q^{77} +(4.14169 + 2.77093i) q^{78} +(9.61797 + 6.98787i) q^{79} +(14.6065 + 4.74594i) q^{80} +(0.309017 + 0.951057i) q^{81} +(5.44260 - 3.95428i) q^{82} +(0.487663 + 0.671210i) q^{83} +(0.103102 - 0.0335000i) q^{84} +(23.4631 + 7.62363i) q^{85} +(1.87492 - 2.58061i) q^{86} +4.21619 q^{87} +(-3.52869 - 8.90602i) q^{88} +6.26927i q^{89} +(4.50459 + 3.27278i) q^{90} +(3.41704 - 2.69050i) q^{91} +(0.0524520 + 0.161431i) q^{92} +(5.18802 + 7.14070i) q^{93} +(-8.16670 + 5.93346i) q^{94} +(3.41968 + 10.5247i) q^{95} +(0.483146 + 0.156984i) q^{96} +(-4.36816 + 6.01226i) q^{97} -7.66360i q^{98} +(-0.209070 - 3.31003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Character values

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

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

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 $

$2$	−0.812362	+	1.11812i	−0.574427	+	0.790631i	−0.993071	−	0.117520i	$-0.962506\pi$
$2$	−0.812362	+	1.11812i	−0.574427	+	0.790631i	0.418644	+	0.908151i	$0.362506\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.0277724	+	0.0854748i	0.0138862	+	0.0427374i
$5$	2.36802	+	3.25930i	1.05901	+	1.45760i	0.880727	+	0.473625i	$0.157055\pi$
$5$	2.36802	+	3.25930i	1.05901	+	1.45760i	0.178285	+	0.983979i	$0.442945\pi$
$6$	−0.812362	−	1.11812i	−0.331646	−	0.456471i
$7$	−1.14719	+	0.372746i	−0.433599	+	0.140885i	−0.517680	−	0.855574i	$-0.673204\pi$
$7$	−1.14719	+	0.372746i	−0.433599	+	0.140885i	0.0840817	+	0.996459i	$0.473204\pi$
$8$	−2.74699	−	0.892552i	−0.971208	−	0.315565i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−5.56798			−1.76075
$11$	2.11473	+	2.55498i	0.637614	+	0.770356i
$11$	2.11473	+	2.55498i	0.637614	+	0.770356i
$12$	−0.0898735			−0.0259442
$13$	−3.38343	+	1.24594i	−0.938396	+	0.345562i
$13$	−3.38343	+	1.24594i	−0.938396	+	0.345562i
$14$	0.515162	−	1.58551i	0.137683	−	0.423744i
$15$	−3.83154	+	1.24494i	−0.989299	+	0.321443i
$16$	3.08412	−	2.24074i	0.771029	−	0.560185i
$17$	4.95416	−	3.59941i	1.20156	−	0.872985i	0.207123	−	0.978315i	$-0.433590\pi$
$17$	4.95416	−	3.59941i	1.20156	−	0.872985i	0.994437	+	0.105330i	$0.0335900\pi$
$18$	1.31443	−	0.427084i	0.309814	−	0.100665i
$19$	2.61241	+	0.848825i	0.599329	+	0.194734i	0.592941	−	0.805246i	$-0.297967\pi$
$19$	2.61241	+	0.848825i	0.599329	+	0.194734i	0.00638775	+	0.999980i	$0.497967\pi$
$20$	−0.212822	+	0.292925i	−0.0475885	+	0.0655000i
$21$		−	1.20623i		−	0.263221i
$22$	−4.57470	+	0.288950i	−0.975330	+	0.0616043i
$23$	1.88864			0.393808			0.196904	−	0.980423i	$-0.436911\pi$
$23$	1.88864			0.393808			0.196904	+	0.980423i	$0.436911\pi$
$24$	1.69773	−	2.33673i	0.346549	−	0.476983i
$25$	−3.47044	+	10.6809i	−0.694087	+	2.13618i
$26$	1.35546	−	4.79524i	0.265828	−	0.940425i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.0637207	−	0.0877041i	−0.0120421	−	0.0165745i
$29$	−1.30287	−	4.00983i	−0.241938	−	0.744607i	−0.996125	−	0.0879480i	$-0.971969\pi$
$29$	−1.30287	−	4.00983i	−0.241938	−	0.744607i	0.754188	−	0.656659i	$-0.228031\pi$
$30$	1.72060	−	5.29547i	0.314137	−	0.966816i
$31$	5.18802	−	7.14070i	0.931797	−	1.28251i	−0.0273580	−	0.999626i	$-0.508709\pi$
$31$	5.18802	−	7.14070i	0.931797	−	1.28251i	0.959155	−	0.282882i	$-0.0912906\pi$
$32$		−	0.508010i		−	0.0898044i
$33$	−3.08342	+	1.22169i	−0.536754	+	0.212669i
$34$			8.46337i			1.45146i
$35$	−3.93147	−	2.85638i	−0.664540	−	0.482817i
$36$	0.0277724	−	0.0854748i	0.00462874	−	0.0142458i
$37$	−10.6498	+	3.46032i	−1.75081	+	0.568874i	−0.996184	−	0.0872777i	$-0.972183\pi$
$37$	−10.6498	+	3.46032i	−1.75081	+	0.568874i	−0.754629	+	0.656151i	$0.772183\pi$
$38$	−3.07131	+	2.23144i	−0.498233	+	0.361988i
$39$	−0.139422	−	3.60285i	−0.0223253	−	0.576918i
$40$	−3.59584	−	11.0669i	−0.568552	−	1.74982i
$41$	−4.62939	−	1.50418i	−0.722989	−	0.234914i	−0.0756706	−	0.997133i	$-0.524110\pi$
$41$	−4.62939	−	1.50418i	−0.722989	−	0.234914i	−0.647319	+	0.762219i	$0.724110\pi$
$42$	1.34871	+	0.979897i	0.208111	+	0.151201i
$43$	−2.30799			−0.351965			−0.175982	−	0.984393i	$-0.556310\pi$
$43$	−2.30799			−0.351965			−0.175982	+	0.984393i	$0.556310\pi$
$44$	−0.159655	+	0.251714i	−0.0240689	+	0.0379473i
$45$		−	4.02872i		−	0.600566i
$46$	−1.53426	+	2.11172i	−0.226214	+	0.311357i
$47$	6.94647	+	2.25705i	1.01325	+	0.329224i	0.768147	−	0.640274i	$-0.221179\pi$
$47$	6.94647	+	2.25705i	1.01325	+	0.329224i	0.245100	+	0.969498i	$0.421179\pi$
$48$	1.17803	+	3.62559i	0.170034	+	0.523310i
$49$	−4.48600	+	3.25927i	−0.640858	+	0.465610i
$50$	−9.12329	−	12.5571i	−1.29023	−	1.77585i
$51$	1.89232	+	5.82396i	0.264978	+	0.815518i
$52$	−0.200463	−	0.254595i	−0.0277992	−	0.0353060i
$53$	5.81450	+	4.22448i	0.798683	+	0.580277i	0.910527	−	0.413449i	$-0.135676\pi$
$53$	5.81450	+	4.22448i	0.798683	+	0.580277i	−0.111845	+	0.993726i	$0.535676\pi$
$54$			1.38207i			0.188076i
$55$	−3.31974	+	12.9428i	−0.447633	+	1.74520i
$56$	3.48403			0.465573
$57$	−1.61456	+	2.22225i	−0.213854	+	0.294344i
$58$	5.54188	+	1.80067i	0.727685	+	0.236439i
$59$	5.63000	−	1.82930i	0.732963	−	0.238154i	0.0813289	−	0.996687i	$-0.474084\pi$
$59$	5.63000	−	1.82930i	0.732963	−	0.238154i	0.651635	+	0.758533i	$0.274084\pi$
$60$	−0.212822	−	0.292925i	−0.0274752	−	0.0378164i
$61$	2.59398	−	1.88463i	0.332125	−	0.241303i	−0.409207	−	0.912442i	$-0.634195\pi$
$61$	2.59398	−	1.88463i	0.332125	−	0.241303i	0.741332	+	0.671139i	$0.234195\pi$
$62$	3.76961	+	11.6017i	0.478741	+	1.47341i
$63$	1.14719	+	0.372746i	0.144533	+	0.0469616i
$64$	6.73625	+	4.89417i	0.842031	+	0.611771i
$65$	−12.0729	−	8.07722i	−1.49746	−	1.00186i
$66$	1.13885	−	4.44009i	0.140183	−	0.546537i
$67$		−	11.7021i		−	1.42963i	−0.699312	−	0.714817i	$-0.746510\pi$
$67$		−	11.7021i		−	1.42963i	0.699312	−	0.714817i	$-0.253490\pi$
$68$	0.445248	+	0.323491i	0.0539942	+	0.0392291i
$69$	−0.583621	+	1.79620i	−0.0702597	+	0.216237i
$70$	6.38756	−	2.07544i	0.763459	−	0.248063i
$71$	−2.12509	−	2.92494i	−0.252202	−	0.347126i	0.664079	−	0.747662i	$-0.268824\pi$
$71$	−2.12509	−	2.92494i	−0.252202	−	0.347126i	−0.916281	+	0.400536i	$0.868824\pi$
$72$	1.69773	+	2.33673i	0.200080	+	0.275386i
$73$	−5.26823	+	1.71175i	−0.616599	+	0.200345i	−0.600630	−	0.799527i	$-0.705083\pi$
$73$	−5.26823	+	1.71175i	−0.616599	+	0.200345i	−0.0159695	+	0.999872i	$0.505083\pi$
$74$	4.78242	−	14.7188i	0.555945	−	1.71102i
$75$	−9.08572	−	6.60116i	−1.04913	−	0.762237i
$76$			0.246869i			0.0283179i
$77$	−3.37836	−	2.14280i	−0.385000	−	0.244195i
$78$	4.14169	+	2.77093i	0.468954	+	0.313746i
$79$	9.61797	+	6.98787i	1.08211	+	0.786196i	0.978049	−	0.208375i	$-0.0668175\pi$
$79$	9.61797	+	6.98787i	1.08211	+	0.786196i	0.104057	+	0.994571i	$0.466817\pi$
$80$	14.6065	+	4.74594i	1.63306	+	0.530612i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	5.44260	−	3.95428i	0.601034	−	0.436677i
$83$	0.487663	+	0.671210i	0.0535279	+	0.0736749i	0.834942	−	0.550338i	$-0.185501\pi$
$83$	0.487663	+	0.671210i	0.0535279	+	0.0736749i	−0.781414	+	0.624013i	$0.785501\pi$
$84$	0.103102	−	0.0335000i	0.0112494	−	0.00365515i
$85$	23.4631	+	7.62363i	2.54493	+	0.826898i
$86$	1.87492	−	2.58061i	0.202178	−	0.278274i
$87$	4.21619			0.452023
$88$	−3.52869	−	8.90602i	−0.376159	−	0.949385i
$89$			6.26927i			0.664542i	0.943184	+	0.332271i	$0.107815\pi$
$89$			6.26927i			0.664542i	−0.943184	+	0.332271i	$0.892185\pi$
$90$	4.50459	+	3.27278i	0.474826	+	0.344981i
$91$	3.41704	−	2.69050i	0.358203	−	0.282041i
$92$	0.0524520	+	0.161431i	0.00546850	+	0.0168303i
$93$	5.18802	+	7.14070i	0.537973	+	0.740456i
$94$	−8.16670	+	5.93346i	−0.842331	+	0.611989i
$95$	3.41968	+	10.5247i	0.350851	+	1.07981i
$96$	0.483146	+	0.156984i	0.0493109	+	0.0160221i
$97$	−4.36816	+	6.01226i	−0.443520	+	0.610453i	−0.970990	−	0.239121i	$-0.923141\pi$
$97$	−4.36816	+	6.01226i	−0.443520	+	0.610453i	0.527470	+	0.849574i	$0.323141\pi$
$98$		−	7.66360i		−	0.774141i
$99$	−0.209070	−	3.31003i	−0.0210123	−	0.332670i
$100$	−1.00933			−0.100933
$101$	12.8144	+	9.31024i	1.27508	+	0.926403i	0.999393	−	0.0348431i	$-0.0110931\pi$
$101$	12.8144	+	9.31024i	1.27508	+	0.926403i	0.275692	+	0.961246i	$0.411093\pi$
$102$	−8.04915	−	2.61533i	−0.796984	−	0.258956i
$103$	0.414930	+	1.27702i	0.0408843	+	0.125829i	0.969415	−	0.245426i	$-0.0789277\pi$
$103$	0.414930	+	1.27702i	0.0408843	+	0.125829i	−0.928531	+	0.371255i	$0.878928\pi$
$104$	10.4063	−	0.402700i	1.02043	−	0.0394879i
$105$	3.93147	−	2.85638i	0.383672	−	0.278754i
$106$	−9.44696	+	3.06950i	−0.917570	+	0.298136i
$107$	1.19641	−	3.68219i	0.115662	−	0.355970i	−0.876423	−	0.481543i	$-0.840077\pi$
$107$	1.19641	−	3.68219i	0.115662	−	0.355970i	0.992084	+	0.125572i	$0.0400767\pi$
$108$	0.0727092	+	0.0528263i	0.00699644	+	0.00508321i
$109$			0.205808i			0.0197128i	0.999951	+	0.00985640i	$0.00313744\pi$
$109$			0.205808i			0.0197128i	−0.999951	+	0.00985640i	$0.996863\pi$
$110$	−11.7748	−	14.2261i	−1.12268	−	1.35640i
$111$		−	11.1978i		−	1.06285i
$112$	−2.70285	+	3.72016i	−0.255395	+	0.351522i
$113$	−3.17940	+	9.78518i	−0.299093	+	0.920513i	0.682723	+	0.730677i	$0.260796\pi$
$113$	−3.17940	+	9.78518i	−0.299093	+	0.920513i	−0.981816	+	0.189836i	$0.939204\pi$
$114$	−1.17314	−	3.61055i	−0.109874	−	0.338159i
$115$	4.47233	+	6.15564i	0.417047	+	0.574016i
$116$	0.306555	−	0.222726i	0.0284630	−	0.0206796i
$117$	3.46960	+	0.980745i	0.320765	+	0.0906700i
$118$	−2.52822	+	7.78107i	−0.232742	+	0.716306i
$119$	−4.34172	+	5.97586i	−0.398005	+	0.547806i
$120$	11.6364			1.06225
$121$	−2.05586	+	10.8062i	−0.186896	+	0.982380i
$122$			4.43138i			0.401199i
$123$	2.86112	−	3.93800i	0.257979	−	0.355077i
$124$	0.754434	+	0.245130i	0.0677502	+	0.0220134i
$125$	−23.8727	+	7.75670i	−2.13524	+	0.693780i
$126$	−1.34871	+	0.979897i	−0.120153	+	0.0872961i
$127$	−4.60499	+	3.34572i	−0.408627	+	0.296885i	−0.773046	−	0.634350i	$-0.781268\pi$
$127$	−4.60499	+	3.34572i	−0.408627	+	0.296885i	0.364419	+	0.931235i	$0.381268\pi$
$128$	−9.97825	+	3.24213i	−0.881961	+	0.286567i
$129$	0.713207	−	2.19502i	0.0627944	−	0.193261i
$130$	18.8389	−	6.93738i	1.65228	−	0.608448i
$131$	0.569272			0.0497375			0.0248688	−	0.999691i	$-0.492083\pi$
$131$	0.569272			0.0497375			0.0248688	+	0.999691i	$0.492083\pi$
$132$	−0.190058	−	0.229625i	−0.0165424	−	0.0199863i
$133$	−3.31334			−0.287303
$134$	13.0843	+	9.50631i	1.13031	+	0.821220i
$135$	3.83154	+	1.24494i	0.329766	+	0.107148i
$136$	−16.8217	+	5.46570i	−1.44245	+	0.468680i
$137$	3.45220	+	4.75154i	0.294941	+	0.405951i	0.930611	−	0.366009i	$-0.119276\pi$
$137$	3.45220	+	4.75154i	0.294941	+	0.405951i	−0.635670	+	0.771961i	$0.719276\pi$
$138$	−1.53426	−	2.11172i	−0.130605	−	0.179762i
$139$	−4.90115	−	15.0842i	−0.415710	−	1.27942i	−0.911614	−	0.411047i	$-0.865163\pi$
$139$	−4.90115	−	15.0842i	−0.415710	−	1.27942i	0.495904	−	0.868377i	$-0.334837\pi$
$140$	0.134962	−	0.415370i	0.0114064	−	0.0351052i
$141$	−4.29316	+	5.90902i	−0.361549	+	0.497630i
$142$	4.99678			0.419320
$143$	−10.3384	−	6.00979i	−0.864540	−	0.502564i
$144$	−3.81218			−0.317681
$145$	9.98402	−	13.7418i	0.829128	−	1.14120i
$146$	2.36576	−	7.28108i	0.195792	−	0.602586i
$147$	−1.71350	−	5.27361i	−0.141327	−	0.434960i
$148$	−0.591541	−	0.814186i	−0.0486243	−	0.0669257i
$149$	8.74050	+	12.0303i	0.716049	+	0.985557i	0.999646	+	0.0266137i	$0.00847241\pi$
$149$	8.74050	+	12.0303i	0.716049	+	0.985557i	−0.283596	+	0.958944i	$0.591528\pi$
$150$	14.7618	−	4.79640i	1.20530	−	0.391624i
$151$	3.14445	+	1.02169i	0.255892	+	0.0831443i	0.434154	−	0.900839i	$-0.357047\pi$
$151$	3.14445	+	1.02169i	0.255892	+	0.0831443i	−0.178262	+	0.983983i	$0.557047\pi$
$152$	−6.41866	−	4.66343i	−0.520622	−	0.378254i
$153$	−6.12368			−0.495070
$154$	5.14037	−	2.03668i	0.414223	−	0.164121i
$155$	35.5591			2.85617
$156$	0.304081	−	0.111977i	0.0243460	−	0.00896534i
$157$	7.47568	−	23.0078i	0.596624	−	1.83622i	0.0501559	−	0.998741i	$-0.484028\pi$
$157$	7.47568	−	23.0078i	0.596624	−	1.83622i	0.546468	−	0.837480i	$-0.315972\pi$
$158$	−15.6266	+	5.07738i	−1.24318	+	0.403934i
$159$	−5.81450	+	4.22448i	−0.461120	+	0.335023i
$160$	1.65576	−	1.20298i	0.130899	−	0.0951038i
$161$	−2.16663	+	0.703982i	−0.170755	+	0.0554815i
$162$	−1.31443	−	0.427084i	−0.103271	−	0.0335549i
$163$	−6.31460	+	8.69131i	−0.494598	+	0.680756i	−0.981228	−	0.192853i	$-0.938226\pi$
$163$	−6.31460	+	8.69131i	−0.494598	+	0.680756i	0.486630	+	0.873608i	$0.338226\pi$
$164$		−	0.437471i		−	0.0341607i
$165$	−11.2835	−	7.15680i	−0.878416	−	0.557156i
$166$	−1.14665			−0.0889975
$167$	−4.41029	+	6.07025i	−0.341279	+	0.469730i	−0.944814	−	0.327606i	$-0.893758\pi$
$167$	−4.41029	+	6.07025i	−0.341279	+	0.469730i	0.603536	+	0.797336i	$0.293758\pi$
$168$	−1.07662	+	3.31351i	−0.0830633	+	0.255643i
$169$	9.89526	−	8.43112i	0.761174	−	0.648548i
$170$	−27.5847	+	20.0414i	−2.11565	+	1.53711i
$171$	−1.61456	−	2.22225i	−0.123469	−	0.169940i
$172$	−0.0640984	−	0.197275i	−0.00488746	−	0.0150420i
$173$	−7.20840	+	22.1852i	−0.548044	+	1.68671i	0.165596	+	0.986194i	$0.447045\pi$
$173$	−7.20840	+	22.1852i	−0.548044	+	1.68671i	−0.713640	+	0.700513i	$0.752955\pi$
$174$	−3.42507	+	4.71421i	−0.259654	+	0.357383i
$175$		−	13.5467i		−	1.02403i
$176$	12.2471	+	3.14130i	0.923161	+	0.236784i
$177$			5.91973i			0.444954i
$178$	−7.00981	−	5.09292i	−0.525407	−	0.381731i
$179$	6.27597	−	19.3154i	0.469088	−	1.44370i	−0.384680	−	0.923050i	$-0.625688\pi$
$179$	6.27597	−	19.3154i	0.469088	−	1.44370i	0.853768	−	0.520654i	$-0.174312\pi$
$180$	0.344354	−	0.111887i	0.0256666	−	0.00833959i
$181$	12.7913	−	9.29345i	0.950773	−	0.690777i	−0.000216680	−	1.00000i	$-0.500069\pi$
$181$	12.7913	−	9.29345i	0.950773	−	0.690777i	0.950990	+	0.309223i	$0.100069\pi$
$182$	0.232430	+	6.00632i	0.0172288	+	0.445218i
$183$	0.990811	+	3.04940i	0.0732428	+	0.225418i
$184$	−5.18807	−	1.68571i	−0.382470	−	0.124272i
$185$	−36.4971	−	26.5167i	−2.68332	−	1.94955i
$186$	−12.1987			−0.894454
$187$	19.6731	+	5.04602i	1.43864	+	0.369002i
$188$			0.656432i			0.0478752i
$189$	−0.709005	+	0.975862i	−0.0515725	+	0.0709835i
$190$	−14.5459	−	4.72624i	−1.05527	−	0.342878i
$191$	2.84460	+	8.75477i	0.205828	+	0.633473i	0.999678	+	0.0253599i	$0.00807316\pi$
$191$	2.84460	+	8.75477i	0.205828	+	0.633473i	−0.793851	+	0.608113i	$0.791927\pi$
$192$	−6.73625	+	4.89417i	−0.486147	+	0.353206i
$193$	−11.6438	−	16.0263i	−0.838137	−	1.15360i	−0.986353	−	0.164642i	$-0.947353\pi$
$193$	−11.6438	−	16.0263i	−0.838137	−	1.15360i	0.148216	−	0.988955i	$-0.452647\pi$
$194$	−3.17390	−	9.76827i	−0.227873	−	0.701321i
$195$	11.4126	−	8.98605i	0.817276	−	0.643505i
$196$	−0.403173	−	0.292922i	−0.0287981	−	0.0209230i
$197$		−	14.1589i		−	1.00878i	−0.863475	−	0.504391i	$-0.831717\pi$
$197$		−	14.1589i		−	1.00878i	0.863475	−	0.504391i	$-0.168283\pi$
$198$	3.87085	+	2.45518i	0.275089	+	0.174482i
$199$	−4.56427			−0.323552			−0.161776	−	0.986827i	$-0.551722\pi$
$199$	−4.56427			−0.323552			−0.161776	+	0.986827i	$0.551722\pi$
$200$	19.0665	−	26.2428i	1.34821	−	1.85565i
$201$	11.1293	+	3.61613i	0.785001	+	0.255062i
$202$	−20.8199	+	6.76481i	−1.46489	+	0.475970i
$203$	2.98930	+	4.11442i	0.209808	+	0.288775i
$204$	−0.445248	+	0.323491i	−0.0311736	+	0.0226489i
$205$	−6.05992	−	18.6505i	−0.423243	−	1.30261i
$206$	−1.76494	−	0.573464i	−0.122969	−	0.0399551i
$207$	−1.52794	−	1.11011i	−0.106199	−	0.0771582i
$208$	−7.64307	+	11.4240i	−0.529952	+	0.792114i
$209$	3.35581	+	8.46970i	0.232126	+	0.585861i
$210$			6.71628i			0.463467i
$211$	17.3085	+	12.5754i	1.19157	+	0.865725i	0.993429	−	0.114449i	$-0.0365102\pi$
$211$	17.3085	+	12.5754i	1.19157	+	0.865725i	0.198139	+	0.980174i	$0.436510\pi$
$212$	−0.199604	+	0.614317i	−0.0137088	+	0.0421915i
$213$	3.43847	−	1.11723i	0.235600	−	0.0765511i
$214$	3.14521	+	4.32900i	0.215002	+	0.295925i
$215$	−5.46536	−	7.52242i	−0.372734	−	0.513025i
$216$	−2.74699	+	0.892552i	−0.186909	+	0.0607305i
$217$	−3.29000	+	10.1256i	−0.223340	+	0.687370i
$218$	−0.230118	−	0.167190i	−0.0155856	−	0.0113236i
$219$		−	5.53934i		−	0.374314i
$220$	−1.19848	+	0.0756989i	−0.0808014	+	0.00510362i
$221$	−12.2774	+	18.3510i	−0.825869	+	1.23442i
$222$	12.5205	+	9.09671i	0.840324	+	0.610531i
$223$	−5.30291	−	1.72302i	−0.355109	−	0.115382i	0.126030	−	0.992026i	$-0.459777\pi$
$223$	−5.30291	−	1.72302i	−0.355109	−	0.115382i	−0.481139	+	0.876645i	$0.659777\pi$
$224$	0.189359	+	0.582786i	0.0126521	+	0.0389391i
$225$	9.08572	−	6.60116i	0.605715	−	0.440078i
$226$	−8.35819	−	11.5041i	−0.555979	−	0.765239i
$227$	19.1796	−	6.23183i	1.27300	−	0.413621i	0.406887	−	0.913478i	$-0.366614\pi$
$227$	19.1796	−	6.23183i	1.27300	−	0.413621i	0.866108	+	0.499857i	$0.166614\pi$
$228$	−0.234787	−	0.0762868i	−0.0155491	−	0.00505222i
$229$	4.07364	−	5.60689i	0.269194	−	0.370513i	−0.652924	−	0.757424i	$-0.726458\pi$
$229$	4.07364	−	5.60689i	0.269194	−	0.370513i	0.922117	+	0.386910i	$0.126458\pi$
$230$	−10.5159			−0.693398
$231$	3.08190	−	2.55085i	0.202774	−	0.167834i
$232$			12.1779i			0.799516i
$233$	−16.4229	−	11.9319i	−1.07590	−	0.781686i	−0.0989354	−	0.995094i	$-0.531544\pi$
$233$	−16.4229	−	11.9319i	−1.07590	−	0.781686i	−0.976963	+	0.213408i	$0.931544\pi$
$234$	−3.91517	+	3.08271i	−0.255942	+	0.201523i
$235$	9.09300	+	27.9854i	0.593162	+	1.82557i
$236$	0.312718	+	0.430419i	0.0203562	+	0.0280179i
$237$	−9.61797	+	6.98787i	−0.624754	+	0.453911i
$238$	−3.15469	−	9.70913i	−0.204488	−	0.629349i
$239$	5.94028	+	1.93011i	0.384245	+	0.124849i	0.494769	−	0.869025i	$-0.335253\pi$
$239$	5.94028	+	1.93011i	0.384245	+	0.124849i	−0.110524	+	0.993873i	$0.535253\pi$
$240$	−9.02731	+	12.4250i	−0.582711	+	0.802032i
$241$		−	6.42528i		−	0.413889i	−0.978353	−	0.206944i	$-0.933648\pi$
$241$		−	6.42528i		−	0.413889i	0.978353	−	0.206944i	$-0.0663520\pi$
$242$	−10.4125	−	11.0772i	−0.669341	−	0.712071i
$243$	−1.00000			−0.0641500
$244$	0.233130	+	0.169379i	0.0149246	+	0.0108434i
$245$	−21.2459	−	6.90321i	−1.35735	−	0.441030i
$246$	2.07889	+	6.39816i	0.132545	+	0.407932i
$247$	−9.89652	+	0.382971i	−0.629700	+	0.0243679i
$248$	−20.6249	+	14.9849i	−1.30968	+	0.951540i
$249$	−0.789055	+	0.256379i	−0.0500043	+	0.0162474i
$250$	10.7203	−	32.9938i	0.678013	−	2.08671i
$251$	−6.24903	−	4.54019i	−0.394435	−	0.286574i	0.372835	−	0.927898i	$-0.378386\pi$
$251$	−6.24903	−	4.54019i	−0.394435	−	0.286574i	−0.767271	+	0.641324i	$0.778386\pi$
$252$			0.108408i			0.00682907i
$253$	3.99395	+	4.82543i	0.251098	+	0.303372i
$254$		−	7.86688i		−	0.493612i
$255$	−14.5010	+	19.9589i	−0.908088	+	1.24988i
$256$	−0.665172	+	2.04719i	−0.0415733	+	0.127949i
$257$	−5.38775	−	16.5818i	−0.336079	−	1.03434i	−0.966188	−	0.257838i	$-0.916990\pi$
$257$	−5.38775	−	16.5818i	−0.336079	−	1.03434i	0.630109	−	0.776506i	$-0.283010\pi$
$258$	1.87492	+	2.58061i	0.116727	+	0.160662i
$259$	10.9275	−	7.93933i	0.679005	−	0.493326i
$260$	0.355103	−	1.25626i	0.0220226	−	0.0779097i
$261$	−1.30287	+	4.00983i	−0.0806458	+	0.248202i
$262$	−0.462455	+	0.636515i	−0.0285706	+	0.0393240i
$263$	4.81811			0.297097			0.148549	−	0.988905i	$-0.452540\pi$
$263$	4.81811			0.297097			0.148549	+	0.988905i	$0.452540\pi$
$264$	9.56055	−	0.603869i	0.588411	−	0.0371655i
$265$			28.9549i			1.77868i
$266$	2.69163	−	3.70472i	0.165035	−	0.227151i
$267$	−5.96243	−	1.93731i	−0.364895	−	0.118562i
$268$	1.00023	−	0.324995i	0.0610988	−	0.0198522i
$269$	−5.72715	+	4.16102i	−0.349190	+	0.253702i	−0.748529	−	0.663102i	$-0.769240\pi$
$269$	−5.72715	+	4.16102i	−0.349190	+	0.253702i	0.399339	+	0.916803i	$0.369240\pi$
$270$	−4.50459	+	3.27278i	−0.274141	+	0.199175i
$271$	−26.3097	+	8.54854i	−1.59820	+	0.519287i	−0.966662	−	0.256057i	$-0.917576\pi$
$271$	−26.3097	+	8.54854i	−1.59820	+	0.519287i	−0.631539	+	0.775344i	$0.717576\pi$
$272$	7.21386	−	22.2020i	0.437404	−	1.34619i
$273$	1.50289	+	4.08120i	0.0909592	+	0.247006i
$274$	−8.11723			−0.490380
$275$	−34.6285	+	13.7203i	−2.08818	+	0.827365i
$276$	−0.169738			−0.0102171
$277$	3.17307	+	2.30537i	0.190652	+	0.138516i	0.679016	−	0.734123i	$-0.262406\pi$
$277$	3.17307	+	2.30537i	0.190652	+	0.138516i	−0.488365	+	0.872640i	$0.662406\pi$
$278$	20.8475	+	6.77375i	1.25035	+	0.406263i
$279$	−8.39440	+	2.72751i	−0.502560	+	0.163291i
$280$	8.25025	+	11.3555i	0.493047	+	0.678621i
$281$	1.32268	+	1.82051i	0.0789044	+	0.108603i	0.846645	−	0.532158i	$-0.178619\pi$
$281$	1.32268	+	1.82051i	0.0789044	+	0.108603i	−0.767740	+	0.640761i	$0.778619\pi$
$282$	−3.11940	−	9.60054i	−0.185758	−	0.571704i
$283$	0.748575	−	2.30388i	0.0444981	−	0.136951i	−0.926339	−	0.376691i	$-0.877062\pi$
$283$	0.748575	−	2.30388i	0.0444981	−	0.136951i	0.970837	+	0.239739i	$0.0770620\pi$
$284$	0.190989	−	0.262874i	0.0113331	−	0.0155987i
$285$	−11.0663			−0.655511
$286$	15.1182	−	6.67745i	0.893957	−	0.394846i
$287$	5.87149			0.346583
$288$	−0.298601	+	0.410989i	−0.0175952	+	0.0242178i
$289$	6.33467	−	19.4961i	0.372628	−	1.14683i
$290$	7.25438	+	22.3267i	0.425992	+	1.31107i
$291$	−4.36816	−	6.01226i	−0.256066	−	0.352445i
$292$	−0.292623	−	0.402761i	−0.0171245	−	0.0235698i
$293$	1.52179	−	0.494458i	0.0889037	−	0.0288866i	−0.264227	−	0.964460i	$-0.585117\pi$
$293$	1.52179	−	0.494458i	0.0889037	−	0.0288866i	0.353131	+	0.935574i	$0.385117\pi$
$294$	7.28852	+	2.36818i	0.425075	+	0.138115i
$295$	19.2942	+	14.0180i	1.12335	+	0.816162i
$296$	32.3434			1.87992
$297$	3.21263	+	0.824018i	0.186416	+	0.0478144i
$298$	−20.5517			−1.19053
$299$	−6.39008	+	2.35313i	−0.369548	+	0.136085i
$300$	0.311900	−	0.959930i	0.0180076	−	0.0554216i
$301$	2.64771	−	0.860292i	0.152611	−	0.0495864i
$302$	−3.69681	+	2.68589i	−0.212728	+	0.154556i
$303$	−12.8144	+	9.31024i	−0.736170	+	0.534859i
$304$	9.95898	−	3.23587i	0.571187	−	0.185590i
$305$	12.2852	+	3.99170i	0.703447	+	0.228564i
$306$	4.97465	−	6.84701i	0.284382	−	0.391418i
$307$		−	32.6932i		−	1.86590i	−0.360009	−	0.932949i	$-0.617226\pi$
$307$		−	32.6932i		−	1.86590i	0.360009	−	0.932949i	$-0.382774\pi$
$308$	0.0893303	−	0.348275i	0.00509007	−	0.0198448i
$309$	−1.34274			−0.0763860
$310$	−28.8868	+	39.7593i	−1.64066	+	2.25818i
$311$	−4.52315	+	13.9208i	−0.256484	+	0.789378i	0.737049	+	0.675839i	$0.236219\pi$
$311$	−4.52315	+	13.9208i	−0.256484	+	0.789378i	−0.993534	+	0.113539i	$0.963781\pi$
$312$	−2.83274	+	10.0215i	−0.160373	+	0.567353i
$313$	3.09857	−	2.25124i	0.175141	−	0.127248i	−0.496761	−	0.867887i	$-0.665477\pi$
$313$	3.09857	−	2.25124i	0.175141	−	0.127248i	0.671902	+	0.740640i	$0.265477\pi$
$314$	19.6525	+	27.0494i	1.10906	+	1.52648i
$315$	1.50169	+	4.62172i	0.0846106	+	0.260405i
$316$	−0.330172	+	1.01616i	−0.0185736	+	0.0571637i
$317$	18.6687	−	25.6952i	1.04854	−	1.44319i	0.158465	−	0.987365i	$-0.449346\pi$
$317$	18.6687	−	25.6952i	1.04854	−	1.44319i	0.890071	−	0.455821i	$-0.150654\pi$
$318$		−	9.93312i		−	0.557022i
$319$	7.48982	−	11.8085i	0.419350	−	0.661150i
$320$			33.5450i			1.87522i
$321$	3.13225	+	2.27572i	0.174825	+	0.127018i
$322$	0.972955	−	2.99445i	0.0542206	−	0.166874i
$323$	15.9976	−	5.19793i	0.890129	−	0.289221i
$324$	−0.0727092	+	0.0528263i	−0.00403940	+	0.00293479i
$325$	−1.56578	−	40.4621i	−0.0868541	−	2.24443i
$326$	−4.58818	−	14.1210i	−0.254116	−	0.782089i
$327$	−0.195735	−	0.0635981i	−0.0108242	−	0.00351698i
$328$	11.3743	+	8.26394i	0.628043	+	0.456300i
$329$	−8.81026			−0.485725
$330$	17.1684	−	6.80236i	0.945091	−	0.374458i
$331$		−	3.44051i		−	0.189108i	−0.995520	−	0.0945538i	$-0.969858\pi$
$331$		−	3.44051i		−	0.189108i	0.995520	−	0.0945538i	$-0.0301424\pi$
$332$	−0.0438279	+	0.0603240i	−0.00240537	+	0.00331071i
$333$	10.6498	+	3.46032i	0.583604	+	0.189625i
$334$	−3.20451	−	9.86248i	−0.175343	−	0.539651i
$335$	38.1405	−	27.7107i	2.08384	−	1.51400i
$336$	−2.70285	−	3.72016i	−0.147453	−	0.202951i
$337$	3.31585	+	10.2051i	0.180626	+	0.555909i	0.999846	−	0.0175707i	$-0.00559322\pi$
$337$	3.31585	+	10.2051i	0.180626	+	0.555909i	−0.819220	+	0.573479i	$0.805593\pi$
$338$	1.38847	+	17.9132i	0.0755231	+	0.974351i
$339$	−8.32378	−	6.04758i	−0.452085	−	0.328459i
$340$			2.21723i			0.120246i
$341$	29.2156	−	1.84533i	1.58211	−	0.0999304i
$342$	3.79635			0.205283
$343$	8.89447	−	12.2422i	0.480256	−	0.661016i
$344$	6.34002	+	2.06000i	0.341831	+	0.111068i
$345$	−7.23639	+	2.35124i	−0.389594	+	0.126587i
$346$	−18.9499	−	26.0822i	−1.01875	−	1.40219i
$347$	5.40394	−	3.92619i	0.290099	−	0.210769i	−0.433211	−	0.901292i	$-0.642620\pi$
$347$	5.40394	−	3.92619i	0.290099	−	0.210769i	0.723310	+	0.690523i	$0.242620\pi$
$348$	0.117094	+	0.360378i	0.00627688	+	0.0193183i
$349$	3.92453	+	1.27516i	0.210075	+	0.0682575i	0.412164	−	0.911110i	$-0.364773\pi$
$349$	3.92453	+	1.27516i	0.210075	+	0.0682575i	−0.202089	+	0.979367i	$0.564773\pi$
$350$	15.1468	+	11.0048i	0.809631	+	0.588231i
$351$	−2.00491	+	2.99672i	−0.107014	+	0.159953i
$352$	1.29796	−	1.07430i	0.0691813	−	0.0572605i
$353$			7.68323i			0.408937i	0.978873	+	0.204468i	$0.0655466\pi$
$353$			7.68323i			0.408937i	−0.978873	+	0.204468i	$0.934453\pi$
$354$	−6.61897	−	4.80897i	−0.351795	−	0.255594i
$355$	4.50099	−	13.8526i	0.238888	−	0.735221i
$356$	−0.535865	+	0.174113i	−0.0284008	+	0.00922797i
$357$	−4.34172	−	5.97586i	−0.229788	−	0.316276i
$358$	16.4986	+	22.7084i	0.871980	+	1.20018i
$359$	−20.1521	+	6.54782i	−1.06359	+	0.345581i	−0.787987	−	0.615692i	$-0.788877\pi$
$359$	−20.1521	+	6.54782i	−1.06359	+	0.345581i	−0.275600	+	0.961272i	$0.588877\pi$
$360$	−3.59584	+	11.0669i	−0.189517	+	0.583275i
$361$	−9.26712	−	6.73296i	−0.487743	−	0.354366i
$362$			21.8519i			1.14851i
$363$	−9.64199	−	5.29453i	−0.506073	−	0.277891i
$364$	0.324869	+	0.217349i	0.0170278	+	0.0113922i
$365$	−18.0544	−	13.1173i	−0.945010	−	0.686590i
$366$	−4.21450	−	1.36937i	−0.220295	−	0.0715783i
$367$	5.53331	+	17.0298i	0.288836	+	0.888947i	0.985222	+	0.171280i	$0.0547901\pi$
$367$	5.53331	+	17.0298i	0.288836	+	0.888947i	−0.696386	+	0.717667i	$0.745210\pi$
$368$	5.82477	−	4.23195i	0.303637	−	0.220605i
$369$	2.86112	+	3.93800i	0.148944	+	0.205004i
$370$	59.2978	−	19.2670i	3.08275	−	1.00164i
$371$	−8.24502	−	2.67897i	−0.428060	−	0.139085i
$372$	−0.466266	+	0.641760i	−0.0241748	+	0.0332737i
$373$	1.31388			0.0680303			0.0340152	−	0.999421i	$-0.489171\pi$
$373$	1.31388			0.0680303			0.0340152	+	0.999421i	$0.489171\pi$
$374$	−21.6238	+	17.8977i	−1.11814	+	0.925469i
$375$		−	25.1012i		−	1.29622i
$376$	−17.0674	−	12.4002i	−0.880183	−	0.639490i
$377$	9.40420	+	11.9437i	0.484341	+	0.615132i
$378$	−0.515162	−	1.58551i	−0.0264971	−	0.0815496i
$379$	−3.09714	−	4.26285i	−0.159089	−	0.218968i	0.722030	−	0.691862i	$-0.243209\pi$
$379$	−3.09714	−	4.26285i	−0.159089	−	0.218968i	−0.881119	+	0.472894i	$0.843209\pi$
$380$	−0.804622	+	0.584592i	−0.0412762	+	0.0299889i
$381$	−1.75895	−	5.41349i	−0.0901138	−	0.277342i
$382$	−12.0997	−	3.93144i	−0.619076	−	0.201150i
$383$	−9.70634	+	13.3596i	−0.495971	+	0.682646i	−0.981475	−	0.191589i	$-0.938636\pi$
$383$	−9.70634	+	13.3596i	−0.495971	+	0.682646i	0.485504	+	0.874234i	$0.338636\pi$
$384$		−	10.4918i		−	0.535405i
$385$	−1.01599	−	16.0853i	−0.0517796	−	0.819783i
$386$	27.3783			1.39352
$387$	1.86720	+	1.35660i	0.0949151	+	0.0689598i
$388$	−0.635211	−	0.206393i	−0.0322480	−	0.0104780i
$389$	1.59155	+	4.89830i	0.0806950	+	0.248354i	0.983262	−	0.182195i	$-0.0583202\pi$
$389$	1.59155	+	4.89830i	0.0806950	+	0.248354i	−0.902567	+	0.430548i	$0.858320\pi$
$390$	0.776297	+	20.0606i	0.0393093	+	1.01581i
$391$	9.35661	−	6.79798i	0.473184	−	0.343788i
$392$	15.2321	−	4.94921i	0.769337	−	0.249973i
$393$	−0.175915	+	0.541410i	−0.00887373	+	0.0273105i
$394$	15.8314	+	11.5022i	0.797575	+	0.579472i
$395$			47.8953i			2.40987i
$396$	0.277118	−	0.109798i	0.0139257	−	0.00551754i
$397$		−	25.2015i		−	1.26483i	−0.774632	−	0.632413i	$-0.782065\pi$
$397$		−	25.2015i		−	1.26483i	0.774632	−	0.632413i	$-0.217935\pi$
$398$	3.70784	−	5.10340i	0.185857	−	0.255811i
$399$	1.02388	−	3.15118i	0.0512581	−	0.157756i
$400$	13.2299	+	40.7175i	0.661496	+	2.03587i
$401$	−9.48639	−	13.0569i	−0.473728	−	0.652030i	0.503557	−	0.863962i	$-0.332024\pi$
$401$	−9.48639	−	13.0569i	−0.473728	−	0.652030i	−0.977284	+	0.211932i	$0.932024\pi$
$402$	−13.0843	+	9.50631i	−0.652586	+	0.474132i
$403$	−8.65645	+	30.6241i	−0.431208	+	1.52549i
$404$	−0.439902	+	1.35388i	−0.0218859	+	0.0673580i
$405$	−2.36802	+	3.25930i	−0.117668	+	0.161956i
$406$	−7.02881			−0.348834
$407$	−31.3624	−	19.8924i	−1.55458	−	0.986027i
$408$		−	17.6874i		−	0.875656i
$409$	−19.1128	+	26.3065i	−0.945066	+	1.30077i	0.00861890	+	0.999963i	$0.497256\pi$
$409$	−19.1128	+	26.3065i	−0.945066	+	1.30077i	−0.953685	+	0.300808i	$0.902744\pi$
$410$	25.7764	+	8.37525i	1.27300	+	0.413624i
$411$	−5.58577	+	1.81493i	−0.275526	+	0.0895237i
$412$	−0.0976297	+	0.0709322i	−0.00480987	+	0.00349458i
$413$	−5.77684	+	4.19712i	−0.284260	+	0.206527i
$414$	2.48248	−	0.806607i	0.122007	−	0.0396426i
$415$	−1.03288	+	3.17888i	−0.0507021	+	0.156045i
$416$	0.632951	+	1.71882i	0.0310330	+	0.0842721i
$417$	15.8605			0.776690
$418$	−12.1963	−	3.12826i	−0.596540	−	0.153008i
$419$	17.9498			0.876905			0.438453	−	0.898754i	$-0.355527\pi$
$419$	17.9498			0.876905			0.438453	+	0.898754i	$0.355527\pi$
$420$	0.353335	+	0.256713i	0.0172410	+	0.0125263i
$421$	−16.7632	−	5.44671i	−0.816990	−	0.265456i	−0.129435	−	0.991588i	$-0.541316\pi$
$421$	−16.7632	−	5.44671i	−0.816990	−	0.265456i	−0.687556	+	0.726132i	$0.741316\pi$
$422$	−28.1216	+	9.13726i	−1.36894	+	0.444795i
$423$	−4.29316	−	5.90902i	−0.208740	−	0.287307i
$424$	−12.2018	−	16.7944i	−0.592572	−	0.815606i
$425$	21.2518	+	65.4064i	1.03087	+	3.17268i
$426$	−1.54409	+	4.75222i	−0.0748114	+	0.230246i
$427$	−2.27330	+	3.12893i	−0.110013	+	0.151420i
$428$	0.347961			0.0168193
$429$	8.91039	−	7.97527i	0.430198	−	0.385050i
$430$	12.8508			0.619722
$431$	14.7231	−	20.2646i	0.709187	−	0.976112i	−0.290627	−	0.956836i	$-0.593864\pi$
$431$	14.7231	−	20.2646i	0.709187	−	0.976112i	0.999814	−	0.0192755i	$-0.00613596\pi$
$432$	1.17803	−	3.62559i	0.0566779	−	0.174437i
$433$	0.518992	+	1.59729i	0.0249411	+	0.0767610i	0.962752	−	0.270385i	$-0.0871509\pi$
$433$	0.518992	+	1.59729i	0.0249411	+	0.0767610i	−0.937811	+	0.347146i	$0.887151\pi$
$434$	−8.64896	−	11.9043i	−0.415163	−	0.571423i
$435$	9.98402	+	13.7418i	0.478697	+	0.658870i
$436$	−0.0175914	+	0.00571578i	−0.000842474	+	0.000273736i
$437$	4.93390	+	1.60312i	0.236021	+	0.0766877i
$438$	6.19365	+	4.49995i	0.295944	+	0.215016i
$439$	13.6356			0.650792			0.325396	−	0.945578i	$-0.394502\pi$
$439$	13.6356			0.650792			0.325396	+	0.945578i	$0.394502\pi$
$440$	20.6714	−	32.5907i	0.985470	−	1.55370i
$441$	5.54501			0.264048
$442$	−10.5449	−	28.6353i	−0.501568	−	1.36204i
$443$	3.94742	−	12.1489i	0.187548	−	0.577213i	−0.812435	−	0.583052i	$-0.801859\pi$
$443$	3.94742	−	12.1489i	0.187548	−	0.577213i	0.999983	+	0.00583884i	$0.00185857\pi$
$444$	0.957133	−	0.310991i	0.0454235	−	0.0147590i
$445$	−20.4335	+	14.8458i	−0.968639	+	0.703757i
$446$	6.23443	−	4.52958i	0.295209	−	0.214482i
$447$	−14.1424	+	4.59515i	−0.668914	+	0.217343i
$448$	−9.55206	−	3.10365i	−0.451293	−	0.146634i
$449$	21.0770	−	29.0100i	0.994684	−	1.36907i	0.0661541	−	0.997809i	$-0.478927\pi$
$449$	21.0770	−	29.0100i	0.994684	−	1.36907i	0.928530	−	0.371256i	$-0.121073\pi$
$450$			15.5215i			0.731689i
$451$	−5.94675	−	15.0089i	−0.280021	−	0.706743i
$452$	−0.924686			−0.0434936
$453$	−1.94338	+	2.67483i	−0.0913078	+	0.125674i
$454$	−8.61285	+	26.5076i	−0.404221	+	1.24406i
$455$	16.8608	+	4.76600i	0.790445	+	0.223433i
$456$	6.41866	−	4.66343i	0.300581	−	0.218385i
$457$	6.89131	+	9.48507i	0.322362	+	0.443693i	0.939186	−	0.343408i	$-0.111581\pi$
$457$	6.89131	+	9.48507i	0.322362	+	0.443693i	−0.616825	+	0.787101i	$0.711581\pi$
$458$	2.95990	+	9.10964i	0.138307	+	0.425666i
$459$	1.89232	−	5.82396i	0.0883260	−	0.271839i
$460$	−0.401944	+	0.553229i	−0.0187407	+	0.0257944i
$461$		−	15.8709i		−	0.739182i	−0.929195	−	0.369591i	$-0.879498\pi$
$461$		−	15.8709i		−	0.739182i	0.929195	−	0.369591i	$-0.120502\pi$
$462$	0.348540	+	5.51815i	0.0162156	+	0.256728i
$463$			17.5358i			0.814957i	0.913215	+	0.407478i	$0.133592\pi$
$463$			17.5358i			0.814957i	−0.913215	+	0.407478i	$0.866408\pi$
$464$	−13.0032	−	9.44738i	−0.603659	−	0.438584i
$465$	−10.9884	+	33.8187i	−0.509573	+	1.56830i
$466$	26.6827	−	8.66972i	1.23605	−	0.401617i
$467$	9.68859	−	7.03917i	0.448335	−	0.325734i	−0.340603	−	0.940207i	$-0.610631\pi$
$467$	9.68859	−	7.03917i	0.448335	−	0.325734i	0.788938	+	0.614473i	$0.210631\pi$
$468$	0.0125303	+	0.323801i	0.000579214	+	0.0149677i
$469$	4.36189	+	13.4245i	0.201414	+	0.619887i
$470$	−38.6778	−	12.5672i	−1.78408	−	0.579681i
$471$	19.5716	+	14.2196i	0.901811	+	0.655204i
$472$	−17.0983			−0.787013
$473$	−4.88076	−	5.89686i	−0.224418	−	0.271138i
$474$		−	16.4307i		−	0.754689i
$475$	−18.1324	+	24.9572i	−0.831973	+	1.14511i
$476$	−0.631365	−	0.205143i	−0.0289386	−	0.00940272i
$477$	−2.22094	−	6.83535i	−0.101690	−	0.312969i
$478$	−6.98376	+	5.07400i	−0.319430	+	0.232079i
$479$	−6.48731	−	8.92901i	−0.296413	−	0.407977i	0.634671	−	0.772782i	$-0.281136\pi$
$479$	−6.48731	−	8.92901i	−0.296413	−	0.407977i	−0.931084	+	0.364805i	$0.881136\pi$
$480$	0.632443	+	1.94646i	0.0288670	+	0.0888434i
$481$	31.7215	−	24.9768i	1.44638	−	1.13884i
$482$	7.18424	+	5.21966i	0.327233	+	0.237749i
$483$		−	2.27813i		−	0.103659i
$484$	−0.980751	+	0.124390i	−0.0445796	+	0.00565408i
$485$	−29.9397			−1.35949
$486$	0.812362	−	1.11812i	0.0368495	−	0.0507190i
$487$	3.31635	+	1.07755i	0.150278	+	0.0488283i	0.383190	−	0.923670i	$-0.374825\pi$
$487$	3.31635	+	1.07755i	0.150278	+	0.0488283i	−0.232912	+	0.972498i	$0.574825\pi$
$488$	−8.80776	+	2.86182i	−0.398709	+	0.129548i
$489$	−6.31460	−	8.69131i	−0.285556	−	0.393034i
$490$	24.9780	−	18.1476i	1.12839	−	0.819824i
$491$	−8.59803	−	26.4620i	−0.388023	−	1.19421i	−0.934263	−	0.356584i	$-0.883941\pi$
$491$	−8.59803	−	26.4620i	−0.388023	−	1.19421i	0.546240	−	0.837629i	$-0.316059\pi$
$492$	0.416059	+	0.135186i	0.0187574	+	0.00609465i
$493$	−20.8877	−	15.1758i	−0.940733	−	0.683483i
$494$	7.61135	−	11.3766i	0.342451	−	0.511858i
$495$	10.2933	−	8.51964i	0.462649	−	0.382929i
$496$		−	33.6478i		−	1.51083i
$497$	3.52815	+	2.56335i	0.158259	+	0.114982i
$498$	0.354335	−	1.09053i	0.0158781	−	0.0488679i
$499$	26.9933	−	8.77067i	1.20839	−	0.392629i	0.365548	−	0.930793i	$-0.380882\pi$
$499$	26.9933	−	8.77067i	1.20839	−	0.392629i	0.842840	+	0.538164i	$0.180882\pi$
$500$	−1.32600	−	1.82509i	−0.0593007	−	0.0816204i
$501$	−4.41029	−	6.07025i	−0.197037	−	0.271199i
$502$	10.1530	−	3.29889i	0.453148	−	0.147237i
$503$	−3.20690	+	9.86982i	−0.142989	+	0.440074i	−0.996747	−	0.0805959i	$-0.974318\pi$
$503$	−3.20690	+	9.86982i	−0.142989	+	0.440074i	0.853758	+	0.520670i	$0.174318\pi$
$504$	−2.81864	−	2.04786i	−0.125552	−	0.0912189i
$505$			63.8130i			2.83964i
$506$	−8.63995	+	0.545721i	−0.384093	+	0.0242603i
$507$	4.96067	+	12.0163i	0.220311	+	0.533663i
$508$	−0.413867	−	0.300692i	−0.0183624	−	0.0133410i
$509$	9.51701	+	3.09226i	0.421834	+	0.137062i	0.512239	−	0.858843i	$-0.328816\pi$
$509$	9.51701	+	3.09226i	0.421834	+	0.137062i	−0.0904051	+	0.995905i	$0.528816\pi$
$510$	−10.5364	−	32.4277i	−0.466560	−	1.43592i
$511$	5.40563	−	3.92742i	0.239131	−	0.173739i
$512$	−14.0824	−	19.3828i	−0.622362	−	0.856608i
$513$	2.61241	−	0.848825i	0.115341	−	0.0374765i
$514$	22.9173	+	7.44627i	1.01084	+	0.328441i
$515$	−3.17964	+	4.37640i	−0.140112	+	0.192847i
$516$	0.207427			0.00913145
$517$	8.92318	+	22.5211i	0.392441	+	0.990479i
$518$			18.6679i			0.820221i
$519$	−18.8718	−	13.7112i	−0.828381	−	0.601854i
$520$	25.9549	+	32.9638i	1.13820	+	1.44556i
$521$	−12.8025	−	39.4020i	−0.560887	−	1.72623i	−0.679866	−	0.733336i	$-0.737962\pi$
$521$	−12.8025	−	39.4020i	−0.560887	−	1.72623i	0.118979	−	0.992897i	$-0.462038\pi$
$522$	−3.42507	−	4.71421i	−0.149911	−	0.206335i
$523$	−31.9726	+	23.2295i	−1.39807	+	1.01575i	−0.403140	+	0.915138i	$0.632081\pi$
$523$	−31.9726	+	23.2295i	−1.39807	+	1.01575i	−0.994925	+	0.100616i	$0.967919\pi$
$524$	0.0158101	+	0.0486584i	0.000690666	+	0.00212565i
$525$	12.8836	+	4.18615i	0.562288	+	0.182699i
$526$	−3.91405	+	5.38723i	−0.170661	+	0.234894i
$527$		−	54.0500i		−	2.35445i
$528$	−6.77212	+	10.6770i	−0.294719	+	0.464656i
$529$	−19.4330			−0.844915
$530$	−32.3750	−	23.5218i	−1.40628	−	1.02172i
$531$	−5.63000	−	1.82930i	−0.244321	−	0.0793847i
$532$	−0.0920196	−	0.283207i	−0.00398955	−	0.0122786i
$533$	17.5374	−	0.678653i	0.759628	−	0.0293957i
$534$	7.00981	−	5.09292i	0.303344	−	0.220392i
$535$	14.8345	−	4.82002i	0.641351	−	0.208387i
$536$	−10.4447	+	32.1455i	−0.451142	+	1.38847i
$537$	16.4307	+	11.9376i	0.709037	+	0.515145i
$538$		−	9.78390i		−	0.421814i
$539$	−17.8141	−	4.56918i	−0.767306	−	0.196809i
$540$			0.362075i			0.0155812i
$541$	0.831289	−	1.14417i	0.0357399	−	0.0491918i	−0.790773	−	0.612109i	$-0.790321\pi$
$541$	0.831289	−	1.14417i	0.0357399	−	0.0491918i	0.826513	+	0.562918i	$0.190321\pi$
$542$	11.8147	−	36.3619i	0.507485	−	1.56188i
$543$	4.88586	+	15.0371i	0.209672	+	0.645305i
$544$	−1.82854	−	2.51676i	−0.0783978	−	0.107905i
$545$	−0.670789	+	0.487357i	−0.0287335	+	0.0208761i
$546$	−5.78417	−	1.63500i	−0.247540	−	0.0699716i
$547$	7.08478	−	21.8047i	0.302923	−	0.932303i	−0.677520	−	0.735504i	$-0.736945\pi$
$547$	7.08478	−	21.8047i	0.302923	−	0.932303i	0.980444	−	0.196799i	$-0.0630545\pi$
$548$	−0.310261	+	0.427037i	−0.0132537	+	0.0182421i
$549$	−3.20633			−0.136843
$550$	12.7900	−	49.8647i	0.545366	−	2.12624i
$551$		−	11.5813i		−	0.493378i
$552$	3.20640	−	4.41324i	0.136474	−	0.187840i
$553$	−13.6384	−	4.43138i	−0.579963	−	0.188441i
$554$	−5.15537	+	1.67508i	−0.219031	+	0.0711674i
$555$	36.4971	−	26.5167i	1.54922	−	1.12557i
$556$	1.15320	−	0.837849i	0.0489066	−	0.0355327i
$557$	−5.33826	+	1.73451i	−0.226189	+	0.0734934i	−0.419919	−	0.907562i	$-0.637942\pi$
$557$	−5.33826	+	1.73451i	−0.226189	+	0.0734934i	0.193730	+	0.981055i	$0.437942\pi$
$558$	3.76961	−	11.6017i	0.159580	−	0.491138i
$559$	7.80892	−	2.87561i	0.330282	−	0.121626i
$560$	−18.5255			−0.782846
$561$	−10.8784	+	17.1509i	−0.459285	+	0.724113i
$562$	−3.11005			−0.131189
$563$	0.452132	+	0.328493i	0.0190551	+	0.0138443i	0.597272	−	0.802039i	$-0.296251\pi$
$563$	0.452132	+	0.328493i	0.0190551	+	0.0138443i	−0.578217	+	0.815883i	$0.696251\pi$
$564$	−0.624304	−	0.202849i	−0.0262879	−	0.00854147i
$565$	−39.4218	+	12.8089i	−1.65849	+	0.538875i
$566$	1.96790	+	2.70858i	0.0827169	+	0.113850i
$567$	−0.709005	−	0.975862i	−0.0297754	−	0.0409823i
$568$	3.22695	+	9.93154i	0.135400	+	0.416718i
$569$	−6.93081	+	21.3308i	−0.290555	+	0.894235i	0.694124	+	0.719856i	$0.255792\pi$
$569$	−6.93081	+	21.3308i	−0.290555	+	0.894235i	−0.984678	+	0.174380i	$0.944208\pi$
$570$	8.98985	−	12.3735i	0.376543	−	0.518267i
$571$	−21.7285			−0.909310			−0.454655	−	0.890668i	$-0.650237\pi$
$571$	−21.7285			−0.909310			−0.454655	+	0.890668i	$0.650237\pi$
$572$	0.226563	−	1.05058i	0.00947306	−	0.0439269i
$573$	−9.20531			−0.384557
$574$	−4.76978	+	6.56503i	−0.199087	+	0.274019i
$575$	−6.55440	+	20.1724i	−0.273337	+	0.841245i
$576$	−2.57302	−	7.91893i	−0.107209	−	0.329956i
$577$	8.05319	+	11.0843i	0.335259	+	0.461444i	0.943049	−	0.332653i	$-0.107944\pi$
$577$	8.05319	+	11.0843i	0.335259	+	0.461444i	−0.607790	+	0.794097i	$0.707944\pi$
$578$	16.6530	+	22.9208i	0.692672	+	0.953382i
$579$	18.8400	−	6.12149i	0.782965	−	0.254401i
$580$	1.45186	+	0.471738i	0.0602852	+	0.0195878i
$581$	−0.809635	−	0.588234i	−0.0335893	−	0.0244041i
$582$	10.2710			0.425745
$583$	1.50261	+	23.7896i	0.0622317	+	0.985263i
$584$	15.9996			0.662068
$585$	5.01955	+	13.6309i	0.207533	+	0.563569i
$586$	−0.683378	+	2.10322i	−0.0282301	+	0.0868832i
$587$	30.1508	−	9.79660i	1.24446	−	0.404349i	0.388527	−	0.921438i	$-0.372984\pi$
$587$	30.1508	−	9.79660i	1.24446	−	0.404349i	0.855932	+	0.517088i	$0.172984\pi$
$588$	0.403173	−	0.292922i	0.0166266	−	0.0120799i
$589$	19.6145	−	14.2507i	0.808200	−	0.587192i
$590$	−31.3477	+	10.1855i	−1.29057	+	0.419330i
$591$	13.4660	+	4.37535i	0.553915	+	0.179978i
$592$	−25.0915	+	34.5354i	−1.03125	+	1.41940i
$593$		−	1.15348i		−	0.0473678i	−0.999719	−	0.0236839i	$-0.992460\pi$
$593$		−	1.15348i		−	0.0473678i	0.999719	−	0.0236839i	$-0.00753952\pi$
$594$	−3.53117	+	2.92271i	−0.144886	+	0.119920i
$595$	−29.7584			−1.21998
$596$	−0.785539	+	1.08120i	−0.0321769	+	0.0442877i
$597$	1.41044	−	4.34088i	0.0577253	−	0.177660i
$598$	2.55998	−	9.05648i	0.104685	−	0.370347i
$599$	19.4132	−	14.1046i	0.793204	−	0.576296i	−0.115709	−	0.993283i	$-0.536914\pi$
$599$	19.4132	−	14.1046i	0.793204	−	0.576296i	0.908913	+	0.416987i	$0.136914\pi$
$600$	19.0665	+	26.2428i	0.778388	+	1.07136i
$601$	−6.25442	−	19.2491i	−0.255123	−	0.785188i	−0.993805	−	0.111134i	$-0.964552\pi$
$601$	−6.25442	−	19.2491i	−0.255123	−	0.785188i	0.738682	−	0.674054i	$-0.235448\pi$
$602$	−1.18899	+	3.65933i	−0.0484595	+	0.149143i
$603$	−6.87830	+	9.46716i	−0.280106	+	0.385533i
$604$			0.297146i			0.0120907i
$605$	−40.0889	+	18.8886i	−1.62985	+	0.767930i
$606$		−	21.8914i		−	0.889276i
$607$	26.3862	+	19.1707i	1.07098	+	0.778115i	0.976089	−	0.217373i	$-0.0697487\pi$
$607$	26.3862	+	19.1707i	1.07098	+	0.778115i	0.0948942	+	0.995487i	$0.469749\pi$
$608$	0.431212	−	1.32713i	0.0174879	−	0.0538223i
$609$	−4.83678	+	1.57157i	−0.195996	+	0.0636831i
$610$	−14.4432	+	10.4936i	−0.584789	+	0.424874i
$611$	−26.3151	+	1.01833i	−1.06459	+	0.0411972i
$612$	−0.170069	−	0.523420i	−0.00687465	−	0.0211580i
$613$	−6.43832	−	2.09194i	−0.260041	−	0.0844925i	0.176095	−	0.984373i	$-0.443653\pi$
$613$	−6.43832	−	2.09194i	−0.260041	−	0.0844925i	−0.436136	+	0.899881i	$0.643653\pi$
$614$	36.5549	+	26.5587i	1.47524	+	1.07182i
$615$	19.6103			0.790764
$616$	7.36777	+	8.90163i	0.296856	+	0.358657i
$617$			9.32838i			0.375546i	0.982212	+	0.187773i	$0.0601270\pi$
$617$			9.32838i			0.375546i	−0.982212	+	0.187773i	$0.939873\pi$
$618$	1.09079	−	1.50135i	0.0438782	−	0.0603931i
$619$	−7.22172	−	2.34648i	−0.290266	−	0.0943130i	0.160265	−	0.987074i	$-0.448765\pi$
$619$	−7.22172	−	2.34648i	−0.290266	−	0.0943130i	−0.450531	+	0.892761i	$0.648765\pi$
$620$	0.987561	+	3.03940i	0.0396614	+	0.122065i
$621$	1.52794	−	1.11011i	0.0613141	−	0.0445473i
$622$	−11.8907	−	16.3662i	−0.476775	−	0.656224i
$623$	−2.33685	−	7.19207i	−0.0936238	−	0.288144i
$624$	−8.50306	−	10.7992i	−0.340395	−	0.432314i
$625$	−36.3838	−	26.4344i	−1.45535	−	1.05738i
$626$			5.29340i			0.211567i
$627$	−9.09217	+	0.574284i	−0.363106	+	0.0229347i
$628$	2.17420			0.0867601
$629$	−40.3056	+	55.4759i	−1.60709	+	2.21197i
$630$	−6.38756	−	2.07544i	−0.254486	−	0.0826876i
$631$	20.3261	−	6.60435i	0.809169	−	0.262915i	0.124923	−	0.992166i	$-0.460132\pi$
$631$	20.3261	−	6.60435i	0.809169	−	0.262915i	0.684246	+	0.729251i	$0.260132\pi$
$632$	−20.1835	−	27.7801i	−0.802855	−	1.10503i
$633$	−17.3085	+	12.5754i	−0.687952	+	0.499827i
$634$	13.5646	+	41.7476i	0.538720	+	1.65801i
$635$	−21.8094	−	7.08632i	−0.865481	−	0.281212i
$636$	−0.522569	−	0.379669i	−0.0207212	−	0.0150548i
$637$	11.1172	−	16.6168i	0.440481	−	0.658383i
$638$	7.11890	+	17.9673i	0.281840	+	0.711333i
$639$			3.61542i			0.143024i
$640$	−34.1958	−	24.8447i	−1.35171	−	0.982073i
$641$	8.24967	−	25.3899i	0.325842	−	1.00284i	−0.645216	−	0.764000i	$-0.723233\pi$
$641$	8.24967	−	25.3899i	0.325842	−	1.00284i	0.971059	−	0.238840i	$-0.0767672\pi$
$642$	−5.08905	+	1.65353i	−0.200849	+	0.0652597i
$643$	11.1784	+	15.3858i	0.440834	+	0.606756i	0.970397	−	0.241514i	$-0.0776441\pi$
$643$	11.1784	+	15.3858i	0.440834	+	0.606756i	−0.529563	+	0.848271i	$0.677644\pi$
$644$	−0.120345	−	0.165641i	−0.00474227	−	0.00652718i
$645$	8.84314	−	2.87331i	0.348198	−	0.113136i
$646$	−7.18392	+	22.1098i	−0.282648	+	0.869900i
$647$	9.88111	+	7.17905i	0.388467	+	0.282238i	0.764827	−	0.644236i	$-0.222824\pi$
$647$	9.88111	+	7.17905i	0.388467	+	0.282238i	−0.376360	+	0.926473i	$0.622824\pi$
$648$		−	2.88836i		−	0.113465i
$649$	16.5797	+	10.5161i	0.650811	+	0.412792i
$650$	46.5135	+	31.1192i	1.82441	+	1.22059i
$651$	−8.61334	−	6.25796i	−0.337583	−	0.245269i
$652$	−0.918259	−	0.298360i	−0.0359618	−	0.0116847i
$653$	2.79215	+	8.59336i	0.109265	+	0.336284i	0.990708	−	0.136007i	$-0.0434270\pi$
$653$	2.79215	+	8.59336i	0.109265	+	0.336284i	−0.881443	+	0.472291i	$0.843427\pi$
$654$	0.230118	−	0.167190i	0.00899832	−	0.00653766i
$655$	1.34805	+	1.85543i	0.0526726	+	0.0724976i
$656$	−17.6481	+	5.73420i	−0.689041	+	0.223883i
$657$	5.26823	+	1.71175i	0.205533	+	0.0667818i
$658$	7.15712	−	9.85093i	0.279014	−	0.384029i
$659$	−37.2830			−1.45234			−0.726169	−	0.687516i	$-0.758701\pi$
$659$	−37.2830			−1.45234			−0.726169	+	0.687516i	$0.758701\pi$
$660$	0.298356	−	1.16321i	0.0116135	−	0.0452780i
$661$			18.4601i			0.718014i	0.933335	+	0.359007i	$0.116885\pi$
$661$			18.4601i			0.718014i	−0.933335	+	0.359007i	$0.883115\pi$
$662$	3.84691	+	2.79494i	0.149514	+	0.108628i
$663$	−13.6589	−	17.3473i	−0.530466	−	0.673713i
$664$	−0.740516	−	2.27907i	−0.0287376	−	0.0884452i
$665$	−7.84606	−	10.7992i	−0.304257	−	0.418774i
$666$	−12.5205	+	9.09671i	−0.485161	+	0.352490i
$667$	−2.46066	−	7.57312i	−0.0952770	−	0.293232i
$668$	−0.641338	−	0.208383i	−0.0248141	−	0.00806259i
$669$	3.27738	−	4.51092i	0.126711	−	0.174402i
$670$			65.1568i			2.51723i
$671$	10.3008	+	2.64207i	0.397656	+	0.101996i
$672$	−0.612778			−0.0236384
$673$	9.50624	+	6.90669i	0.366439	+	0.266233i	0.755733	−	0.654880i	$-0.227281\pi$
$673$	9.50624	+	6.90669i	0.366439	+	0.266233i	−0.389294	+	0.921114i	$0.627281\pi$
$674$	−14.1042	−	4.58274i	−0.543275	−	0.176521i
$675$	3.47044	+	10.6809i	0.133577	+	0.411108i
$676$	0.995463	+	0.611642i	0.0382871	+	0.0235247i
$677$	−19.6321	+	14.2635i	−0.754522	+	0.548192i	−0.897225	−	0.441573i	$-0.854421\pi$
$677$	−19.6321	+	14.2635i	−0.754522	+	0.548192i	0.142703	+	0.989766i	$0.454421\pi$
$678$	13.5238	−	4.39416i	0.519380	−	0.168757i
$679$	2.77009	−	8.52545i	0.106306	−	0.327177i
$680$	−57.6485	−	41.8841i	−2.21072	−	1.60618i
$681$			20.1666i			0.772787i
$682$	−21.6704	+	34.1657i	−0.829801	+	1.30827i
$683$		−	3.95235i		−	0.151232i	−0.997137	−	0.0756162i	$-0.975908\pi$
$683$		−	3.95235i		−	0.151232i	0.997137	−	0.0756162i	$-0.0240924\pi$
$684$	0.145106	−	0.199721i	0.00554827	−	0.00763654i
$685$	−7.31183	+	22.5035i	−0.279371	+	0.859814i
$686$	6.46271	+	19.8902i	0.246748	+	0.759411i
$687$	4.07364	+	5.60689i	0.155419	+	0.213916i
$688$	−7.11809	+	5.17160i	−0.271375	+	0.197165i
$689$	−24.9364	−	7.04873i	−0.950002	−	0.268535i
$690$	3.24959	−	10.0012i	0.123710	−	0.380740i
$691$	−6.37176	+	8.76997i	−0.242393	+	0.333625i	−0.912829	−	0.408342i	$-0.866107\pi$
$691$	−6.37176	+	8.76997i	−0.242393	+	0.333625i	0.670436	+	0.741967i	$0.266107\pi$
$692$	−2.09647			−0.0796957
$693$	1.47364	+	3.71932i	0.0559791	+	0.141285i
$694$			9.23175i			0.350433i
$695$	37.5579	−	51.6940i	1.42465	−	1.96087i
$696$	−11.5818	−	3.76317i	−0.439008	−	0.142642i
$697$	−28.3489	+	9.21112i	−1.07379	+	0.348896i
$698$	−4.61392	+	3.35221i	−0.174639	+	0.126883i
$699$	16.4229	−	11.9319i	0.621170	−	0.451307i
$700$	1.15790	−	0.376224i	0.0437644	−	0.0142199i
$701$	−1.25374	+	3.85860i	−0.0473530	+	0.145737i	−0.971937	−	0.235240i	$-0.924412\pi$
$701$	−1.25374	+	3.85860i	−0.0473530	+	0.145737i	0.924584	+	0.380977i	$0.124412\pi$
$702$	−1.72198	−	4.67615i	−0.0649920	−	0.176490i
$703$	−30.7588			−1.16009
$704$	1.74081	+	27.5608i	0.0656093	+	1.03874i
$705$	−29.4256			−1.10823
$706$	−8.59078	−	6.24156i	−0.323318	−	0.234904i
$707$	−18.1710	−	5.90412i	−0.683391	−	0.222047i
$708$	−0.505988	+	0.164405i	−0.0190162	+	0.00617873i
$709$	3.70434	+	5.09858i	0.139119	+	0.191481i	0.872892	−	0.487914i	$-0.162242\pi$
$709$	3.70434	+	5.09858i	0.139119	+	0.191481i	−0.733772	+	0.679395i	$0.762242\pi$
$710$	11.8325	+	16.2860i	0.444065	+	0.611203i
$711$	−3.67374	−	11.3066i	−0.137776	−	0.424031i
$712$	5.59565	−	17.2216i	0.209706	−	0.645408i
$713$	9.79830	−	13.4862i	0.366949	−	0.505062i
$714$	10.2088			0.382054
$715$	−4.89384	−	47.9273i	−0.183019	−	1.79238i
$716$	1.82528			0.0682140
$717$	−3.67130	+	5.05311i	−0.137107	+	0.188712i
$718$	9.04956	−	27.8517i	0.337727	−	1.03942i
$719$	−13.4155	−	41.2886i	−0.500313	−	1.53980i	−0.808511	−	0.588482i	$-0.799726\pi$
$719$	−13.4155	−	41.2886i	−0.500313	−	1.53980i	0.308198	−	0.951322i	$-0.400274\pi$
$720$	−9.02731	−	12.4250i	−0.336428	−	0.463054i
$721$	−0.952011	−	1.31033i	−0.0354548	−	0.0487993i
$722$	15.0565	−	4.89216i	0.560346	−	0.182067i
$723$	6.11081	+	1.98552i	0.227263	+	0.0738424i
$724$	1.14960	+	0.835235i	0.0427246	+	0.0310413i
$725$	47.3502			1.75854
$726$	13.7527	−	6.47983i	0.510411	−	0.240489i
$727$	−26.7657			−0.992684			−0.496342	−	0.868127i	$-0.665324\pi$
$727$	−26.7657			−0.992684			−0.496342	+	0.868127i	$0.665324\pi$
$728$	−11.7880	+	4.34089i	−0.436892	+	0.160884i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	29.3334	−	9.53100i	1.08568	−	0.352758i
$731$	−11.4341	+	8.30738i	−0.422907	+	0.307260i
$732$	−0.233130	+	0.169379i	−0.00861672	+	0.00626041i
$733$	43.0674	−	13.9934i	1.59073	−	0.516860i	0.625938	−	0.779873i	$-0.284716\pi$
$733$	43.0674	−	13.9934i	1.59073	−	0.516860i	0.964792	+	0.263013i	$0.0847163\pi$
$734$	−23.5364	−	7.64744i	−0.868744	−	0.282272i
$735$	13.1307	−	18.0728i	0.484333	−	0.666627i
$736$		−	0.959447i		−	0.0353657i
$737$	29.8985	−	24.7467i	1.10133	−	0.911555i
$738$	−6.72742			−0.247640
$739$	26.8554	−	36.9633i	0.987893	−	1.35972i	0.0554266	−	0.998463i	$-0.482348\pi$
$739$	26.8554	−	36.9633i	0.987893	−	1.35972i	0.932467	−	0.361256i	$-0.117652\pi$
$740$	1.25290	−	3.85602i	0.0460574	−	0.141750i
$741$	2.69396	−	9.53049i	0.0989653	−	0.350111i
$742$	9.69335	−	7.04263i	0.355854	−	0.258543i
$743$	29.6142	+	40.7605i	1.08644	+	1.49536i	0.852227	+	0.523173i	$0.175252\pi$
$743$	29.6142	+	40.7605i	1.08644	+	1.49536i	0.234215	+	0.972185i	$0.424748\pi$
$744$	−7.87801	−	24.2460i	−0.288822	−	0.888903i
$745$	−18.5126	+	56.9758i	−0.678248	+	2.08743i
$746$	−1.06735	+	1.46908i	−0.0390784	+	0.0537869i
$747$		−	0.829661i		−	0.0303557i
$748$	0.115063	+	1.82170i	0.00420712	+	0.0666078i
$749$			4.67014i			0.170643i
$750$	28.0662	+	20.3913i	1.02483	+	0.744584i
$751$	−13.5017	+	41.5541i	−0.492686	+	1.51633i	0.327847	+	0.944731i	$0.393677\pi$
$751$	−13.5017	+	41.5541i	−0.492686	+	1.51633i	−0.820533	+	0.571600i	$0.806323\pi$
$752$	26.4812	−	8.60426i	0.965669	−	0.313765i
$753$	6.24903	−	4.54019i	0.227727	−	0.165454i
$754$	−20.9941	+	0.812421i	−0.764561	+	0.0295866i
$755$	4.11612	+	12.6681i	0.149801	+	0.461040i
$756$	−0.103102	−	0.0335000i	−0.00374980	−	0.00121838i
$757$	22.9098	+	16.6449i	0.832669	+	0.604970i	0.920313	−	0.391182i	$-0.127934\pi$
$757$	22.9098	+	16.6449i	0.832669	+	0.604970i	−0.0876439	+	0.996152i	$0.527934\pi$
$758$	7.28238			0.264508
$759$	−5.82346	+	2.30733i	−0.211378	+	0.0837509i
$760$		−	31.9634i		−	1.15944i
$761$	0.870746	−	1.19848i	0.0315645	−	0.0434449i	−0.792943	−	0.609296i	$-0.791452\pi$
$761$	0.870746	−	1.19848i	0.0315645	−	0.0434449i	0.824508	+	0.565851i	$0.191452\pi$
$762$	7.48185	+	2.43100i	0.271039	+	0.0880658i
$763$	−0.0767140	−	0.236101i	−0.00277723	−	0.00854745i
$764$	−0.669310	+	0.486282i	−0.0242148	+	0.0175931i
$765$	−14.5010	−	19.9589i	−0.524285	−	0.721616i
$766$	−7.05262	−	21.7057i	−0.254821	−	0.784260i
$767$	−16.7695	+	13.2040i	−0.605513	+	0.476767i
$768$	−1.74144	−	1.26523i	−0.0628389	−	0.0456552i
$769$		−	27.8238i		−	1.00335i	−0.865056	−	0.501676i	$-0.832717\pi$
$769$		−	27.8238i		−	1.00335i	0.865056	−	0.501676i	$-0.167283\pi$
$770$	18.8107	+	11.9311i	0.677889	+	0.429967i
$771$	17.4351			0.627911
$772$	1.04647	−	1.44034i	0.0376632	−	0.0518389i
$773$	34.2269	+	11.1210i	1.23106	+	0.399995i	0.851097	−	0.525008i	$-0.175938\pi$
$773$	34.2269	+	11.1210i	1.23106	+	0.399995i	0.379960	+	0.925003i	$0.375938\pi$
$774$	−3.03369	+	0.985704i	−0.109044	+	0.0354304i
$775$	58.2645	+	80.1942i	2.09292	+	2.88066i
$776$	17.3656	−	12.6168i	0.623387	−	0.452917i
$777$	4.17395	+	12.8461i	0.149740	+	0.460851i
$778$	−6.76981	−	2.19964i	−0.242709	−	0.0788610i
$779$	−10.8171	−	7.85908i	−0.387563	−	0.281581i
$780$	1.08504	+	0.725928i	0.0388506	+	0.0259924i
$781$	2.97917	−	11.6150i	0.106603	−	0.415618i
$782$			15.9842i			0.571595i
$783$	−3.41097	−	2.47821i	−0.121898	−	0.0885641i
$784$	−6.53217	+	20.1039i	−0.233292	+	0.717998i
$785$	92.6919	−	30.1174i	3.30831	−	1.07494i
$786$	−0.462455	−	0.636515i	−0.0164952	−	0.0227037i
$787$	21.6064	+	29.7387i	0.770187	+	1.06007i	0.996298	+	0.0859695i	$0.0273987\pi$
$787$	21.6064	+	29.7387i	0.770187	+	1.06007i	−0.226111	+	0.974102i	$0.572601\pi$
$788$	1.21023	−	0.393228i	0.0431127	−	0.0140082i
$789$	−1.48888	+	4.58230i	−0.0530055	+	0.163134i
$790$	−53.5527	−	38.9083i	−1.90532	−	1.38430i
$791$		−	12.4106i		−	0.441271i
$792$	−2.38006	+	9.27923i	−0.0845717	+	0.329723i
$793$	−6.42841	+	9.60848i	−0.228279	+	0.341207i
$794$	28.1783	+	20.4727i	1.00001	+	0.726550i
$795$	−27.5377	−	8.94754i	−0.976662	−	0.317337i
$796$	−0.126761	−	0.390130i	−0.00449292	−	0.0138278i
$797$	−28.5786	+	20.7636i	−1.01231	+	0.735485i	−0.964692	−	0.263381i	$-0.915162\pi$
$797$	−28.5786	+	20.7636i	−1.01231	+	0.735485i	−0.0476158	+	0.998866i	$0.515162\pi$
$798$	2.69163	+	3.70472i	0.0952828	+	0.131146i
$799$	42.5380	−	13.8214i	1.50489	−	0.488967i
$800$	5.42601	+	1.76302i	0.191838	+	0.0623321i
$801$	3.68499	−	5.07195i	0.130203	−	0.179209i
$802$	22.3056			0.787637
$803$	−15.5144	−	9.84034i	−0.547490	−	0.347258i
$804$			1.05170i			0.0370908i
$805$	−7.42512	−	5.39467i	−0.261701	−	0.190137i
$806$	−27.2092	−	34.5568i	−0.958405	−	1.21721i
$807$	−2.18758	−	6.73267i	−0.0770063	−	0.237001i
$808$	−26.8913	−	37.0127i	−0.946032	−	1.30210i
$809$	30.7127	−	22.3141i	1.07980	−	0.784522i	0.102153	−	0.994769i	$-0.467427\pi$
$809$	30.7127	−	22.3141i	1.07980	−	0.784522i	0.977648	+	0.210247i	$0.0674268\pi$
$810$	−1.72060	−	5.29547i	−0.0604558	−	0.186064i
$811$	−29.7976	−	9.68181i	−1.04633	−	0.339974i	−0.265105	−	0.964219i	$-0.585407\pi$
$811$	−29.7976	−	9.68181i	−1.04633	−	0.339974i	−0.781229	+	0.624245i	$0.785407\pi$
$812$	−0.268659	+	0.369777i	−0.00942807	+	0.0129766i
$813$		−	27.6637i		−	0.970207i
$814$	47.7197	−	18.9072i	1.67258	−	0.662697i
$815$	−43.2807			−1.51606
$816$	18.8861	+	13.7216i	0.661147	+	0.480351i
$817$	−6.02941	−	1.95908i	−0.210942	−	0.0685394i
$818$	−13.8873	−	42.7408i	−0.485559	−	1.49440i
$819$	−4.34588	+	0.168175i	−0.151857	+	0.00587650i
$820$	1.42585	−	1.03594i	0.0497928	−	0.0361766i
$821$	−34.5595	+	11.2291i	−1.20614	+	0.391897i	−0.842015	−	0.539454i	$-0.818631\pi$
$821$	−34.5595	+	11.2291i	−1.20614	+	0.391897i	−0.364121	+	0.931352i	$0.618631\pi$
$822$	2.50836	−	7.71994i	0.0874891	−	0.269264i
$823$	−32.7714	−	23.8098i	−1.14234	−	0.829958i	−0.154895	−	0.987931i	$-0.549504\pi$
$823$	−32.7714	−	23.8098i	−1.14234	−	0.829958i	−0.987443	+	0.157973i	$0.949504\pi$
$824$		−	3.87832i		−	0.135108i
$825$	−2.34797	−	37.1735i	−0.0817459	−	1.29422i
$826$		−	9.86878i		−	0.343379i
$827$	13.0131	−	17.9110i	0.452509	−	0.622825i	−0.520425	−	0.853907i	$-0.674227\pi$
$827$	13.0131	−	17.9110i	0.452509	−	0.622825i	0.972934	+	0.231082i	$0.0742265\pi$
$828$	0.0524520	−	0.161431i	0.00182283	−	0.00561011i
$829$	10.6552	+	32.7935i	0.370072	+	1.13896i	0.946744	+	0.321988i	$0.104351\pi$
$829$	10.6552	+	32.7935i	0.370072	+	1.13896i	−0.576672	+	0.816976i	$0.695649\pi$
$830$	−2.71530	−	3.73729i	−0.0942494	−	0.129723i
$831$	−3.17307	+	2.30537i	−0.110073	+	0.0799725i
$832$	−28.8895	−	8.16614i	−1.00156	−	0.283110i
$833$	−10.4929	+	32.2939i	−0.363558	+	1.11892i
$834$	−12.8844	+	17.7339i	−0.446152	+	0.614075i
$835$	−30.2284			−1.04610
$836$	−0.630747	+	0.522061i	−0.0218148	+	0.0180559i
$837$		−	8.82639i		−	0.305085i
$838$	−14.5817	+	20.0700i	−0.503718	+	0.693308i
$839$	−32.3571	−	10.5135i	−1.11709	−	0.362965i	−0.308434	−	0.951246i	$-0.599805\pi$
$839$	−32.3571	−	10.5135i	−1.11709	−	0.362965i	−0.808656	+	0.588281i	$0.799805\pi$
$840$	−13.3492	+	4.33741i	−0.460591	+	0.149655i
$841$	9.08022	−	6.59716i	0.313111	−	0.227488i
$842$	19.7079	−	14.3186i	0.679179	−	0.493452i
$843$	−2.14014	+	0.695373i	−0.0737103	+	0.0239499i
$844$	−0.594178	+	1.82869i	−0.0204524	+	0.0629461i
$845$	50.9118	+	12.2866i	1.75142	+	0.422671i
$846$	10.0946			0.347059
$847$	−1.66949	−	13.1631i	−0.0573643	−	0.452289i
$848$	27.3985			0.940870
$849$	1.95979	+	1.42387i	0.0672600	+	0.0488672i
$850$	−90.3965	−	29.3716i	−3.10057	−	1.00744i
$851$	−20.1136	+	6.53530i	−0.689484	+	0.224027i
$852$	0.190989	+	0.262874i	0.00654319	+	0.00900593i
$853$	−7.20089	−	9.91117i	−0.246554	−	0.339352i	0.667747	−	0.744388i	$-0.267259\pi$
$853$	−7.20089	−	9.91117i	−0.246554	−	0.339352i	−0.914301	+	0.405036i	$0.867259\pi$
$854$	−1.65178	−	5.08366i	−0.0565228	−	0.173959i
$855$	3.41968	−	10.5247i	0.116950	−	0.359936i
$856$	−6.57308	+	9.04707i	−0.224663	+	0.309223i
$857$	−4.19758			−0.143386			−0.0716932	−	0.997427i	$-0.522840\pi$
$857$	−4.19758			−0.143386			−0.0716932	+	0.997427i	$0.522840\pi$
$858$	1.67886	+	16.4417i	0.0573152	+	0.561310i
$859$	−39.5473			−1.34934			−0.674668	−	0.738121i	$-0.735713\pi$
$859$	−39.5473			−1.34934			−0.674668	+	0.738121i	$0.735713\pi$
$860$	0.491191	−	0.676066i	0.0167495	−	0.0230537i
$861$	−1.81439	+	5.58412i	−0.0618342	+	0.190306i
$862$	10.6978	+	32.9244i	0.364368	+	1.12141i
$863$	−16.4389	−	22.6262i	−0.559586	−	0.770205i	0.431688	−	0.902023i	$-0.357918\pi$
$863$	−16.4389	−	22.6262i	−0.559586	−	0.770205i	−0.991274	+	0.131819i	$0.957918\pi$
$864$	−0.298601	−	0.410989i	−0.0101586	−	0.0139821i
$865$	−89.3778	+	29.0406i	−3.03893	+	0.987410i
$866$	−2.20757	−	0.717285i	−0.0750164	−	0.0243743i
$867$	16.5844	+	12.0493i	0.563236	+	0.409215i
$868$	−0.956853			−0.0324777
$869$	2.48552	+	39.3512i	0.0843155	+	1.33490i
$870$	−23.4757			−0.795899
$871$	14.5801	+	39.5931i	0.494027	+	1.34156i
$872$	0.183694	−	0.565352i	0.00622067	−	0.0191452i
$873$	7.06784	−	2.29648i	0.239210	−	0.0777241i
$874$	−5.80060	+	4.21438i	−0.196208	+	0.142554i
$875$	24.4953	−	17.7969i	0.828092	−	0.601644i
$876$	0.473474	−	0.153841i	0.0159972	−	0.00519781i
$877$	32.6293	+	10.6019i	1.10181	+	0.358001i	0.802801	−	0.596248i	$-0.203342\pi$
$877$	32.6293	+	10.6019i	1.10181	+	0.358001i	0.299014	+	0.954249i	$0.403342\pi$
$878$	−11.0770	+	15.2463i	−0.373832	+	0.514536i
$879$			1.60010i			0.0539701i
$880$	18.7630	+	47.3557i	0.632500	+	1.59636i
$881$	−28.0891			−0.946346			−0.473173	−	0.880970i	$-0.656891\pi$
$881$	−28.0891			−0.946346			−0.473173	+	0.880970i	$0.656891\pi$
$882$	−4.50455	+	6.19999i	−0.151676	+	0.208764i
$883$	13.9301	−	42.8725i	0.468786	−	1.44277i	−0.385372	−	0.922761i	$-0.625927\pi$
$883$	13.9301	−	42.8725i	0.468786	−	1.44277i	0.854158	−	0.520013i	$-0.174073\pi$
$884$	−1.90952	−	0.539759i	−0.0642240	−	0.0181541i
$885$	−19.2942	+	14.0180i	−0.648567	+	0.471212i
$886$	10.3772	+	14.2830i	0.348630	+	0.479848i
$887$	9.48649	+	29.1964i	0.318525	+	0.980320i	0.974279	+	0.225345i	$0.0723509\pi$
$887$	9.48649	+	29.1964i	0.318525	+	0.980320i	−0.655754	+	0.754975i	$0.727649\pi$
$888$	−9.99465	+	30.7604i	−0.335399	+	1.03225i
$889$	4.03572	−	5.55469i	0.135354	−	0.186298i
$890$		−	34.9072i		−	1.17009i
$891$	−1.77645	+	2.80076i	−0.0595131	+	0.0938289i
$892$		−	0.501117i		−	0.0167786i
$893$	16.2312	+	11.7927i	0.543157	+	0.394627i
$894$	6.35084	−	19.5459i	0.212404	−	0.653711i
$895$	77.8165	−	25.2841i	2.60112	−	0.845154i
$896$	10.2385	−	7.43871i	0.342044	−	0.248510i
$897$	−0.263317	−	6.80449i	−0.00879189	−	0.227195i
$898$	15.3145	+	47.1332i	0.511052	+	1.57286i
$899$	−35.3924	−	11.4997i	−1.18040	−	0.383536i
$900$	0.816565	+	0.593269i	0.0272188	+	0.0197756i
$901$	44.0116			1.46624
$902$	21.6127	+	5.54352i	0.719625	+	0.184579i
$903$			2.78396i			0.0926445i
$904$	17.4676	−	24.0420i	0.580963	−	0.799627i
$905$	60.5803	+	19.6837i	2.01376	+	0.654310i
$906$	−1.41206	−	4.34586i	−0.0469124	−	0.144382i
$907$	30.7588	−	22.3475i	1.02133	−	0.742038i	0.0547732	−	0.998499i	$-0.482556\pi$
$907$	30.7588	−	22.3475i	1.02133	−	0.742038i	0.966555	+	0.256461i	$0.0825564\pi$
$908$	1.06533	+	1.46630i	0.0353542	+	0.0486609i
$909$	−4.89468	−	15.0643i	−0.162346	−	0.499651i
$910$	−19.0260	+	14.9806i	−0.630706	+	0.496604i
$911$	33.9346	+	24.6549i	1.12430	+	0.816854i	0.984856	−	0.173376i	$-0.0554676\pi$
$911$	33.9346	+	24.6549i	1.12430	+	0.816854i	0.139447	+	0.990230i	$0.455468\pi$
$912$			10.4715i			0.346746i
$913$	−0.683656	+	2.66540i	−0.0226257	+	0.0882117i
$914$	−16.2037			−0.535970
$915$	−7.59266	+	10.4504i	−0.251006	+	0.345479i
$916$	0.592382	+	0.192477i	0.0195729	+	0.00635961i
$917$	−0.653066	+	0.212194i	−0.0215661	+	0.00700726i
$918$	4.97465	+	6.84701i	0.164188	+	0.225985i
$919$	−42.3736	+	30.7862i	−1.39778	+	1.01554i	−0.402815	+	0.915281i	$0.631968\pi$
$919$	−42.3736	+	30.7862i	−1.39778	+	1.01554i	−0.994961	+	0.100262i	$0.968032\pi$
$920$	−6.79124	−	20.9013i	−0.223900	−	0.689095i
$921$	31.0930	+	10.1027i	1.02455	+	0.332897i
$922$	17.7456	+	12.8929i	0.584420	+	0.424606i
$923$	10.8344	+	7.24860i	0.356619	+	0.238590i
$924$	0.303625	+	0.192581i	0.00998853	+	0.00633546i
$925$		−	125.758i		−	4.13490i
$926$	−19.6071	−	14.2454i	−0.644330	−	0.468133i
$927$	0.414930	−	1.27702i	0.0136281	−	0.0419430i
$928$	−2.03704	+	0.661873i	−0.0668690	+	0.0217270i
$929$	−1.18827	−	1.63552i	−0.0389859	−	0.0536595i	0.789079	−	0.614292i	$-0.210558\pi$
$929$	−1.18827	−	1.63552i	−0.0389859	−	0.0536595i	−0.828065	+	0.560632i	$0.810558\pi$
$930$	−28.8868	−	39.7593i	−0.947237	−	1.30376i
$931$	−14.4859	+	4.70674i	−0.474755	+	0.154257i
$932$	0.563775	−	1.73512i	0.0184671	−	0.0568357i
$933$	−11.8418	−	8.60355i	−0.387682	−	0.281667i
$934$			16.5514i			0.541578i
$935$	30.1399	+	76.0697i	0.985679	+	2.48775i
$936$	−8.65560	−	5.79090i	−0.282917	−	0.189281i
$937$	18.1075	+	13.1558i	0.591545	+	0.429783i	0.842868	−	0.538121i	$-0.180866\pi$
$937$	18.1075	+	13.1558i	0.591545	+	0.429783i	−0.251323	+	0.967903i	$0.580866\pi$
$938$	−18.5537	−	6.02846i	−0.605799	−	0.196836i
$939$	1.18355	+	3.64259i	0.0386236	+	0.118871i
$940$	−2.13951	+	1.55444i	−0.0697831	+	0.0507004i
$941$	33.2697	+	45.7919i	1.08456	+	1.49277i	0.854397	+	0.519620i	$0.173927\pi$
$941$	33.2697	+	45.7919i	1.08456	+	1.49277i	0.230165	+	0.973152i	$0.426073\pi$
$942$	−31.7984	+	10.3319i	−1.03605	+	0.336633i
$943$	−8.74324	−	2.84085i	−0.284719	−	0.0925108i
$944$	13.2646	−	18.2571i	0.431725	−	0.594219i
$945$	−4.85957			−0.158082
$946$	10.5583	−	0.666892i	0.343281	−	0.0216825i
$947$		−	20.9516i		−	0.680835i	−0.940274	−	0.340417i	$-0.889432\pi$
$947$		−	20.9516i		−	0.680835i	0.940274	−	0.340417i	$-0.110568\pi$
$948$	−0.864401	−	0.628024i	−0.0280744	−	0.0203973i
$949$	15.6920	−	12.3555i	0.509383	−	0.401076i
$950$	−13.1750	−	40.5485i	−0.427454	−	1.31557i
$951$	18.6687	+	25.6952i	0.605373	+	0.833224i
$952$	17.2604	−	12.5404i	0.559414	−	0.406438i
$953$	8.45952	+	26.0357i	0.274031	+	0.843380i	0.989474	+	0.144710i	$0.0462248\pi$
$953$	8.45952	+	26.0357i	0.274031	+	0.843380i	−0.715443	+	0.698671i	$0.753775\pi$
$954$	9.44696	+	3.06950i	0.305857	+	0.0993788i
$955$	−21.7984	+	30.0029i	−0.705378	+	0.970870i
$956$			0.561348i			0.0181553i
$957$	8.91608	+	10.7723i	0.288216	+	0.348218i
$958$	15.2538			0.492826
$959$	−5.73145	−	4.16415i	−0.185078	−	0.134467i
$960$	−31.9031	−	10.3660i	−1.02967	−	0.334560i
$961$	−14.4945	−	44.6095i	−0.467565	−	1.43902i
$962$	2.15772	+	55.7586i	0.0695678	+	1.79773i
$963$	−3.13225	+	2.27572i	−0.100935	+	0.0733339i
$964$	0.549200	−	0.178446i	0.0176885	−	0.00574735i
$965$	24.6618	−	75.9011i	0.793891	−	2.44334i
$966$	2.54723	+	1.85067i	0.0819557	+	0.0595443i
$967$			16.1267i			0.518598i	0.965797	+	0.259299i	$0.0834915\pi$
$967$			16.1267i			0.518598i	−0.965797	+	0.259299i	$0.916508\pi$
$968$	15.2925	−	27.8495i	0.491520	−	0.895117i
$969$			16.8209i			0.540364i
$970$	24.3219	−	33.4762i	0.780928	−	1.07486i
$971$	−1.89836	+	5.84254i	−0.0609212	+	0.187496i	−0.976885	−	0.213764i	$-0.931428\pi$
$971$	−1.89836	+	5.84254i	−0.0609212	+	0.187496i	0.915964	+	0.401260i	$0.131428\pi$
$972$	−0.0277724	−	0.0854748i	−0.000890801	−	0.00274160i
$973$	11.2451	+	15.4776i	0.360503	+	0.496189i
$974$	−3.89890	+	2.83272i	−0.124929	+	0.0907661i
$975$	38.9656	+	11.0143i	1.24790	+	0.352741i
$976$	3.77714	−	11.6249i	0.120903	−	0.372103i
$977$	9.12407	−	12.5582i	0.291905	−	0.401773i	−0.637727	−	0.770263i	$-0.720125\pi$
$977$	9.12407	−	12.5582i	0.291905	−	0.401773i	0.929632	+	0.368490i	$0.120125\pi$
$978$	14.8477			0.474776
$979$	−16.0179	+	13.2578i	−0.511934	+	0.423721i
$980$		−	2.00771i		−	0.0641339i
$981$	0.120971	−	0.166502i	0.00386230	−	0.00531600i
$982$	36.5724	+	11.8831i	1.16707	+	0.379205i
$983$	9.59552	−	3.11777i	0.306050	−	0.0994415i	−0.151966	−	0.988386i	$-0.548560\pi$
$983$	9.59552	−	3.11777i	0.306050	−	0.0994415i	0.458016	+	0.888944i	$0.348560\pi$
$984$	−11.3743	+	8.26394i	−0.362601	+	0.263445i
$985$	46.1483	−	33.5287i	1.47041	−	1.06831i
$986$	33.9367	−	11.0267i	1.08076	−	0.351162i
$987$	2.72252	−	8.37905i	0.0866588	−	0.266708i
$988$	−0.307585	−	0.835266i	−0.00978557	−	0.0265734i
$989$	−4.35895			−0.138606
$990$	1.16410	+	18.4302i	0.0369974	+	0.585750i
$991$	53.9042			1.71232			0.856161	−	0.516709i	$-0.172843\pi$
$991$	53.9042			1.71232			0.856161	+	0.516709i	$0.172843\pi$
$992$	−3.62755	−	2.63557i	−0.115175	−	0.0836794i
$993$	3.27212	+	1.06318i	0.103838	+	0.0337389i
$994$	−5.73227	+	1.86253i	−0.181817	+	0.0590758i
$995$	−10.8083	−	14.8763i	−0.342646	−	0.471611i
$996$	−0.0438279	−	0.0603240i	−0.00138874	−	0.00191144i
$997$	−11.7976	−	36.3094i	−0.373635	−	1.14993i	−0.944395	−	0.328813i	$-0.893352\pi$
$997$	−11.7976	−	36.3094i	−0.373635	−	1.14993i	0.570760	−	0.821117i	$-0.306648\pi$
$998$	−12.1217	+	37.3068i	−0.383706	+	1.18093i
$999$	−6.58193	+	9.05925i	−0.208243	+	0.286622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.103.4	yes	56
11.3	even	5	inner	429.2.bb.b.25.11	yes	56
13.12	even	2	inner	429.2.bb.b.103.11	yes	56
143.25	even	10	inner	429.2.bb.b.25.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.4	✓	56	143.25	even	10	inner
429.2.bb.b.25.11	yes	56	11.3	even	5	inner
429.2.bb.b.103.4	yes	56	1.1	even	1	trivial
429.2.bb.b.103.11	yes	56	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.812362 + 1.11812i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.0277724 + 0.0854748i) q^{4} +(2.36802 + 3.25930i) q^{5} +(-0.812362 - 1.11812i) q^{6} +(-1.14719 + 0.372746i) q^{7} +(-2.74699 - 0.892552i) q^{8} +(-0.809017 - 0.587785i) q^{9} -5.56798 q^{10} +(2.11473 + 2.55498i) q^{11} -0.0898735 q^{12} +(-3.38343 + 1.24594i) q^{13} +(0.515162 - 1.58551i) q^{14} +(-3.83154 + 1.24494i) q^{15} +(3.08412 - 2.24074i) q^{16} +(4.95416 - 3.59941i) q^{17} +(1.31443 - 0.427084i) q^{18} +(2.61241 + 0.848825i) q^{19} +(-0.212822 + 0.292925i) q^{20} -1.20623i q^{21} +(-4.57470 + 0.288950i) q^{22} +1.88864 q^{23} +(1.69773 - 2.33673i) q^{24} +(-3.47044 + 10.6809i) q^{25} +(1.35546 - 4.79524i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.0637207 - 0.0877041i) q^{28} +(-1.30287 - 4.00983i) q^{29} +(1.72060 - 5.29547i) q^{30} +(5.18802 - 7.14070i) q^{31} -0.508010i q^{32} +(-3.08342 + 1.22169i) q^{33} +8.46337i q^{34} +(-3.93147 - 2.85638i) q^{35} +(0.0277724 - 0.0854748i) q^{36} +(-10.6498 + 3.46032i) q^{37} +(-3.07131 + 2.23144i) q^{38} +(-0.139422 - 3.60285i) q^{39} +(-3.59584 - 11.0669i) q^{40} +(-4.62939 - 1.50418i) q^{41} +(1.34871 + 0.979897i) q^{42} -2.30799 q^{43} +(-0.159655 + 0.251714i) q^{44} -4.02872i q^{45} +(-1.53426 + 2.11172i) q^{46} +(6.94647 + 2.25705i) q^{47} +(1.17803 + 3.62559i) q^{48} +(-4.48600 + 3.25927i) q^{49} +(-9.12329 - 12.5571i) q^{50} +(1.89232 + 5.82396i) q^{51} +(-0.200463 - 0.254595i) q^{52} +(5.81450 + 4.22448i) q^{53} +1.38207i q^{54} +(-3.31974 + 12.9428i) q^{55} +3.48403 q^{56} +(-1.61456 + 2.22225i) q^{57} +(5.54188 + 1.80067i) q^{58} +(5.63000 - 1.82930i) q^{59} +(-0.212822 - 0.292925i) q^{60} +(2.59398 - 1.88463i) q^{61} +(3.76961 + 11.6017i) q^{62} +(1.14719 + 0.372746i) q^{63} +(6.73625 + 4.89417i) q^{64} +(-12.0729 - 8.07722i) q^{65} +(1.13885 - 4.44009i) q^{66} -11.7021i q^{67} +(0.445248 + 0.323491i) q^{68} +(-0.583621 + 1.79620i) q^{69} +(6.38756 - 2.07544i) q^{70} +(-2.12509 - 2.92494i) q^{71} +(1.69773 + 2.33673i) q^{72} +(-5.26823 + 1.71175i) q^{73} +(4.78242 - 14.7188i) q^{74} +(-9.08572 - 6.60116i) q^{75} +0.246869i q^{76} +(-3.37836 - 2.14280i) q^{77} +(4.14169 + 2.77093i) q^{78} +(9.61797 + 6.98787i) q^{79} +(14.6065 + 4.74594i) q^{80} +(0.309017 + 0.951057i) q^{81} +(5.44260 - 3.95428i) q^{82} +(0.487663 + 0.671210i) q^{83} +(0.103102 - 0.0335000i) q^{84} +(23.4631 + 7.62363i) q^{85} +(1.87492 - 2.58061i) q^{86} +4.21619 q^{87} +(-3.52869 - 8.90602i) q^{88} +6.26927i q^{89} +(4.50459 + 3.27278i) q^{90} +(3.41704 - 2.69050i) q^{91} +(0.0524520 + 0.161431i) q^{92} +(5.18802 + 7.14070i) q^{93} +(-8.16670 + 5.93346i) q^{94} +(3.41968 + 10.5247i) q^{95} +(0.483146 + 0.156984i) q^{96} +(-4.36816 + 6.01226i) q^{97} -7.66360i q^{98} +(-0.209070 - 3.31003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Introduction

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