LMFDB - Embedded newform 429.2.s.a.166.6

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			166.6
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.529161 + 0.305511i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.813326 + 1.40872i) q^{4} +2.30641i q^{5} +(-0.529161 - 0.305511i) q^{6} +(-2.90273 - 1.67589i) q^{7} -2.21596i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.529161 + 0.305511i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.813326 + 1.40872i) q^{4} +2.30641i q^{5} +(-0.529161 - 0.305511i) q^{6} +(-2.90273 - 1.67589i) q^{7} -2.21596i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.704633 - 1.22046i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.62665 q^{12} +(-3.28188 + 1.49308i) q^{13} +2.04801 q^{14} +(-1.99741 + 1.15320i) q^{15} +(-0.949651 - 1.64484i) q^{16} +(0.704235 - 1.21977i) q^{17} -0.611022i q^{18} +(4.99398 + 2.88328i) q^{19} +(-3.24909 - 1.87586i) q^{20} -3.35178i q^{21} +(0.305511 - 0.529161i) q^{22} +(-2.52358 - 4.37098i) q^{23} +(1.91908 - 1.10798i) q^{24} -0.319513 q^{25} +(1.28049 - 1.79273i) q^{26} -1.00000 q^{27} +(4.72173 - 2.72609i) q^{28} +(-4.88383 - 8.45904i) q^{29} +(0.704633 - 1.22046i) q^{30} +6.69862i q^{31} +(4.84320 + 2.79622i) q^{32} +(-0.866025 - 0.500000i) q^{33} +0.860606i q^{34} +(3.86529 - 6.69488i) q^{35} +(-0.813326 - 1.40872i) q^{36} +(-8.24109 + 4.75800i) q^{37} -3.52349 q^{38} +(-2.93398 - 2.09565i) q^{39} +5.11092 q^{40} +(0.157908 - 0.0911683i) q^{41} +(1.02401 + 1.77363i) q^{42} +(-4.15664 + 7.19950i) q^{43} -1.62665i q^{44} +(-1.99741 - 1.15320i) q^{45} +(2.67076 + 1.54197i) q^{46} +10.2807i q^{47} +(0.949651 - 1.64484i) q^{48} +(2.11723 + 3.66714i) q^{49} +(0.169074 - 0.0976148i) q^{50} +1.40847 q^{51} +(0.565900 - 5.83761i) q^{52} -8.54619 q^{53} +(0.529161 - 0.305511i) q^{54} +(-1.15320 - 1.99741i) q^{55} +(-3.71372 + 6.43235i) q^{56} +5.76656i q^{57} +(5.16866 + 2.98413i) q^{58} +(10.3218 + 5.95929i) q^{59} -3.75172i q^{60} +(-2.04349 + 3.53944i) q^{61} +(-2.04650 - 3.54465i) q^{62} +(2.90273 - 1.67589i) q^{63} +0.381496 q^{64} +(-3.44365 - 7.56934i) q^{65} +0.611022 q^{66} +(-10.1326 + 5.85005i) q^{67} +(1.14555 + 1.98414i) q^{68} +(2.52358 - 4.37098i) q^{69} +4.72355i q^{70} +(-4.64115 - 2.67957i) q^{71} +(1.91908 + 1.10798i) q^{72} -3.53894i q^{73} +(2.90724 - 5.03549i) q^{74} +(-0.159757 - 0.276707i) q^{75} +(-8.12347 + 4.69009i) q^{76} +3.35178 q^{77} +(2.19279 + 0.212570i) q^{78} +13.7017 q^{79} +(3.79368 - 2.19028i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0557058 + 0.0964853i) q^{82} -2.23561i q^{83} +(4.72173 + 2.72609i) q^{84} +(2.81329 + 1.62425i) q^{85} -5.07959i q^{86} +(4.88383 - 8.45904i) q^{87} +(1.10798 + 1.91908i) q^{88} +(7.43698 - 4.29374i) q^{89} +1.40927 q^{90} +(12.0286 + 1.16606i) q^{91} +8.20999 q^{92} +(-5.80117 + 3.34931i) q^{93} +(-3.14087 - 5.44014i) q^{94} +(-6.65001 + 11.5182i) q^{95} +5.59244i q^{96} +(3.60101 + 2.07904i) q^{97} +(-2.24071 - 1.29367i) 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 $

$2$	−0.529161	+	0.305511i	−0.374173	+	0.216029i	−0.675280	−	0.737561i	$-0.735977\pi$
$2$	−0.529161	+	0.305511i	−0.374173	+	0.216029i	0.301107	+	0.953590i	$0.402644\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.813326	+	1.40872i	−0.406663	+	0.704361i
$5$			2.30641i			1.03146i	0.856752	+	0.515728i	$0.172479\pi$
$5$			2.30641i			1.03146i	−0.856752	+	0.515728i	$0.827521\pi$
$6$	−0.529161	−	0.305511i	−0.216029	−	0.124724i
$7$	−2.90273	−	1.67589i	−1.09713	−	0.633428i	−0.161663	−	0.986846i	$-0.551686\pi$
$7$	−2.90273	−	1.67589i	−1.09713	−	0.633428i	−0.935465	+	0.353418i	$0.885019\pi$
$8$		−	2.21596i		−	0.783462i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.704633	−	1.22046i	−0.222824	−	0.385943i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.62665			−0.469574
$13$	−3.28188	+	1.49308i	−0.910229	+	0.414106i
$13$	−3.28188	+	1.49308i	−0.910229	+	0.414106i
$14$	2.04801			0.547355
$15$	−1.99741	+	1.15320i	−0.515728	+	0.297756i
$16$	−0.949651	−	1.64484i	−0.237413	−	0.411211i
$17$	0.704235	−	1.21977i	0.170802	−	0.295838i	−0.767898	−	0.640572i	$-0.778697\pi$
$17$	0.704235	−	1.21977i	0.170802	−	0.295838i	0.938701	+	0.344734i	$0.112031\pi$
$18$		−	0.611022i		−	0.144019i
$19$	4.99398	+	2.88328i	1.14570	+	0.661469i	0.947835	−	0.318760i	$-0.103266\pi$
$19$	4.99398	+	2.88328i	1.14570	+	0.661469i	0.197863	+	0.980230i	$0.436600\pi$
$20$	−3.24909	−	1.87586i	−0.726518	−	0.419455i
$21$		−	3.35178i		−	0.731419i
$22$	0.305511	−	0.529161i	0.0651352	−	0.112817i
$23$	−2.52358	−	4.37098i	−0.526204	−	0.911412i	−0.999534	−	0.0305265i	$-0.990282\pi$
$23$	−2.52358	−	4.37098i	−0.526204	−	0.911412i	0.473330	−	0.880885i	$-0.343052\pi$
$24$	1.91908	−	1.10798i	0.391731	−	0.226166i
$25$	−0.319513			−0.0639026
$26$	1.28049	−	1.79273i	0.251124	−	0.351583i
$27$	−1.00000			−0.192450
$28$	4.72173	−	2.72609i	0.892323	−	0.515183i
$29$	−4.88383	−	8.45904i	−0.906905	−	1.57081i	−0.818340	−	0.574735i	$-0.805105\pi$
$29$	−4.88383	−	8.45904i	−0.906905	−	1.57081i	−0.0885649	−	0.996070i	$-0.528228\pi$
$30$	0.704633	−	1.22046i	0.128648	−	0.222824i
$31$			6.69862i			1.20311i	0.798832	+	0.601554i	$0.205451\pi$
$31$			6.69862i			1.20311i	−0.798832	+	0.601554i	$0.794549\pi$
$32$	4.84320	+	2.79622i	0.856165	+	0.494307i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$			0.860606i			0.147593i
$35$	3.86529	−	6.69488i	0.653353	−	1.13164i
$36$	−0.813326	−	1.40872i	−0.135554	−	0.234787i
$37$	−8.24109	+	4.75800i	−1.35483	+	0.782210i	−0.988921	−	0.148442i	$-0.952574\pi$
$37$	−8.24109	+	4.75800i	−1.35483	+	0.782210i	−0.365906	+	0.930652i	$0.619241\pi$
$38$	−3.52349			−0.571586
$39$	−2.93398	−	2.09565i	−0.469813	−	0.335572i
$40$	5.11092			0.808107
$41$	0.157908	−	0.0911683i	0.0246611	−	0.0142381i	−0.487619	−	0.873057i	$-0.662134\pi$
$41$	0.157908	−	0.0911683i	0.0246611	−	0.0142381i	0.512280	+	0.858819i	$0.328801\pi$
$42$	1.02401	+	1.77363i	0.158008	+	0.273677i
$43$	−4.15664	+	7.19950i	−0.633881	+	1.09791i	0.352870	+	0.935672i	$0.385206\pi$
$43$	−4.15664	+	7.19950i	−0.633881	+	1.09791i	−0.986751	+	0.162242i	$0.948128\pi$
$44$		−	1.62665i		−	0.245227i
$45$	−1.99741	−	1.15320i	−0.297756	−	0.171909i
$46$	2.67076	+	1.54197i	0.393782	+	0.227350i
$47$			10.2807i			1.49959i	0.661667	+	0.749797i	$0.269849\pi$
$47$			10.2807i			1.49959i	−0.661667	+	0.749797i	$0.730151\pi$
$48$	0.949651	−	1.64484i	0.137070	−	0.237413i
$49$	2.11723	+	3.66714i	0.302461	+	0.523878i
$50$	0.169074	−	0.0976148i	0.0239106	−	0.0138048i
$51$	1.40847			0.197225
$52$	0.565900	−	5.83761i	0.0784762	−	0.809531i
$53$	−8.54619			−1.17391			−0.586954	−	0.809620i	$-0.699673\pi$
$53$	−8.54619			−1.17391			−0.586954	+	0.809620i	$0.699673\pi$
$54$	0.529161	−	0.305511i	0.0720096	−	0.0415748i
$55$	−1.15320	−	1.99741i	−0.155498	−	0.269330i
$56$	−3.71372	+	6.43235i	−0.496266	+	0.859558i
$57$			5.76656i			0.763799i
$58$	5.16866	+	2.98413i	0.678679	+	0.391835i
$59$	10.3218	+	5.95929i	1.34378	+	0.775833i	0.987360	−	0.158491i	$-0.0506630\pi$
$59$	10.3218	+	5.95929i	1.34378	+	0.775833i	0.356423	+	0.934325i	$0.383996\pi$
$60$		−	3.75172i		−	0.484345i
$61$	−2.04349	+	3.53944i	−0.261643	+	0.453178i	−0.966679	−	0.255993i	$-0.917598\pi$
$61$	−2.04349	+	3.53944i	−0.261643	+	0.453178i	0.705036	+	0.709172i	$0.250931\pi$
$62$	−2.04650	−	3.54465i	−0.259906	−	0.450170i
$63$	2.90273	−	1.67589i	0.365710	−	0.211143i
$64$	0.381496			0.0476870
$65$	−3.44365	−	7.56934i	−0.427132	−	0.938861i
$66$	0.611022			0.0752116
$67$	−10.1326	+	5.85005i	−1.23789	+	0.714697i	−0.968663	−	0.248379i	$-0.920102\pi$
$67$	−10.1326	+	5.85005i	−1.23789	+	0.714697i	−0.269228	+	0.963076i	$0.586769\pi$
$68$	1.14555	+	1.98414i	0.138918	+	0.240613i
$69$	2.52358	−	4.37098i	0.303804	−	0.526204i
$70$			4.72355i			0.564573i
$71$	−4.64115	−	2.67957i	−0.550803	−	0.318006i	0.198643	−	0.980072i	$-0.436347\pi$
$71$	−4.64115	−	2.67957i	−0.550803	−	0.318006i	−0.749446	+	0.662066i	$0.769680\pi$
$72$	1.91908	+	1.10798i	0.226166	+	0.130577i
$73$		−	3.53894i		−	0.414201i	−0.978320	−	0.207101i	$-0.933597\pi$
$73$		−	3.53894i		−	0.414201i	0.978320	−	0.207101i	$-0.0664027\pi$
$74$	2.90724	−	5.03549i	0.337960	−	0.585364i
$75$	−0.159757	−	0.276707i	−0.0184471	−	0.0319513i
$76$	−8.12347	+	4.69009i	−0.931826	+	0.537990i
$77$	3.35178			0.381971
$78$	2.19279	+	0.212570i	0.248285	+	0.0240688i
$79$	13.7017			1.54156			0.770779	−	0.637103i	$-0.219867\pi$
$79$	13.7017			1.54156			0.770779	+	0.637103i	$0.219867\pi$
$80$	3.79368	−	2.19028i	0.424146	−	0.244881i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.0557058	+	0.0964853i	−0.00615168	+	0.0106550i
$83$		−	2.23561i		−	0.245390i	−0.992444	−	0.122695i	$-0.960846\pi$
$83$		−	2.23561i		−	0.245390i	0.992444	−	0.122695i	$-0.0391537\pi$
$84$	4.72173	+	2.72609i	0.515183	+	0.297441i
$85$	2.81329	+	1.62425i	0.305144	+	0.176175i
$86$		−	5.07959i		−	0.547747i
$87$	4.88383	−	8.45904i	0.523602	−	0.906905i
$88$	1.10798	+	1.91908i	0.118111	+	0.204575i
$89$	7.43698	−	4.29374i	0.788318	−	0.455136i	−0.0510520	−	0.998696i	$-0.516257\pi$
$89$	7.43698	−	4.29374i	0.788318	−	0.455136i	0.839370	+	0.543560i	$0.182924\pi$
$90$	1.40927			0.148550
$91$	12.0286	+	1.16606i	1.26094	+	0.122236i
$92$	8.20999			0.855950
$93$	−5.80117	+	3.34931i	−0.601554	+	0.347307i
$94$	−3.14087	−	5.44014i	−0.323956	−	0.561108i
$95$	−6.65001	+	11.5182i	−0.682277	+	1.18174i
$96$			5.59244i			0.570776i
$97$	3.60101	+	2.07904i	0.365627	+	0.211095i	0.671546	−	0.740963i	$-0.265630\pi$
$97$	3.60101	+	2.07904i	0.365627	+	0.211095i	−0.305919	+	0.952057i	$0.598964\pi$
$98$	−2.24071	−	1.29367i	−0.226345	−	0.130681i
$99$		−	1.00000i		−	0.100504i
$100$	0.259868	−	0.450105i	0.0259868	−	0.0450105i
$101$	−1.43661	−	2.48827i	−0.142948	−	0.247593i	0.785658	−	0.618661i	$-0.212325\pi$
$101$	−1.43661	−	2.48827i	−0.142948	−	0.247593i	−0.928605	+	0.371069i	$0.878991\pi$
$102$	−0.745307	+	0.430303i	−0.0737964	+	0.0426064i
$103$	−4.24712			−0.418481			−0.209241	−	0.977864i	$-0.567099\pi$
$103$	−4.24712			−0.418481			−0.209241	+	0.977864i	$0.567099\pi$
$104$	3.30861	+	7.27252i	0.324436	+	0.713129i
$105$	7.73058			0.754427
$106$	4.52230	−	2.61095i	0.439245	−	0.253598i
$107$	4.30096	+	7.44948i	0.415790	+	0.720169i	0.995511	−	0.0946462i	$-0.0301720\pi$
$107$	4.30096	+	7.44948i	0.415790	+	0.720169i	−0.579721	+	0.814815i	$0.696839\pi$
$108$	0.813326	−	1.40872i	0.0782623	−	0.135554i
$109$			6.58226i			0.630466i	0.949014	+	0.315233i	$0.102083\pi$
$109$			6.58226i			0.630466i	−0.949014	+	0.315233i	$0.897917\pi$
$110$	1.22046	+	0.704633i	0.116366	+	0.0671841i
$111$	−8.24109	−	4.75800i	−0.782210	−	0.451609i
$112$			6.36605i			0.601535i
$113$	1.43767	−	2.49011i	0.135244	−	0.234250i	−0.790446	−	0.612531i	$-0.790151\pi$
$113$	1.43767	−	2.49011i	0.135244	−	0.234250i	0.925691	+	0.378281i	$0.123485\pi$
$114$	−1.76175	−	3.05143i	−0.165003	−	0.285793i
$115$	10.0813	−	5.82041i	0.940081	−	0.542756i
$116$	15.8886			1.47522
$117$	0.347892	−	3.58873i	0.0321627	−	0.331778i
$118$	−7.28251			−0.670410
$119$	−4.08841	+	2.36044i	−0.374784	+	0.216381i
$120$	2.55546	+	4.42618i	0.233280	+	0.404053i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	2.49724i		−	0.226090i
$123$	0.157908	+	0.0911683i	0.0142381	+	0.00822037i
$124$	−9.43649	−	5.44816i	−0.847422	−	0.489259i
$125$			10.7951i			0.965544i
$126$	−1.02401	+	1.77363i	−0.0912258	+	0.158008i
$127$	5.10475	+	8.84168i	0.452973	+	0.784572i	0.998569	−	0.0534760i	$-0.0170301\pi$
$127$	5.10475	+	8.84168i	0.452973	+	0.784572i	−0.545596	+	0.838048i	$0.683697\pi$
$128$	−9.88827	+	5.70899i	−0.874008	+	0.504609i
$129$	−8.31327			−0.731943
$130$	4.13476	+	2.95332i	0.362643	+	0.259024i
$131$	−4.94449			−0.432002			−0.216001	−	0.976393i	$-0.569301\pi$
$131$	−4.94449			−0.432002			−0.216001	+	0.976393i	$0.569301\pi$
$132$	1.40872	−	0.813326i	0.122614	−	0.0707909i
$133$	−9.66412	−	16.7388i	−0.837986	−	1.45143i
$134$	3.57451	−	6.19123i	0.308790	−	0.534841i
$135$		−	2.30641i		−	0.198504i
$136$	−2.70297	−	1.56056i	−0.231778	−	0.133817i
$137$	9.31487	+	5.37794i	0.795823	+	0.459469i	0.842009	−	0.539464i	$-0.181373\pi$
$137$	9.31487	+	5.37794i	0.795823	+	0.459469i	−0.0461853	+	0.998933i	$0.514706\pi$
$138$			3.08393i			0.262522i
$139$	−11.5649	+	20.0309i	−0.980918	+	1.69900i	−0.322084	+	0.946711i	$0.604383\pi$
$139$	−11.5649	+	20.0309i	−0.980918	+	1.69900i	−0.658834	+	0.752288i	$0.728950\pi$
$140$	6.28748	+	10.8902i	0.531389	+	0.920393i
$141$	−8.90335	+	5.14035i	−0.749797	+	0.432896i
$142$	3.27455			0.274794
$143$	2.09565	−	2.93398i	0.175247	−	0.245352i
$144$	1.89930			0.158275
$145$	19.5100	−	11.2641i	1.62022	−	0.935433i
$146$	1.08118	+	1.87267i	0.0894794	+	0.154983i
$147$	−2.11723	+	3.66714i	−0.174626	+	0.302461i
$148$		−	15.4792i		−	1.27238i
$149$	−4.75891	−	2.74756i	−0.389865	−	0.225089i	0.292236	−	0.956346i	$-0.405601\pi$
$149$	−4.75891	−	2.74756i	−0.389865	−	0.225089i	−0.682102	+	0.731257i	$0.738934\pi$
$150$	0.169074	+	0.0976148i	0.0138048	+	0.00797022i
$151$			1.76951i			0.144001i	0.997405	+	0.0720005i	$0.0229383\pi$
$151$			1.76951i			0.144001i	−0.997405	+	0.0720005i	$0.977062\pi$
$152$	6.38924	−	11.0665i	0.518236	−	0.897611i
$153$	0.704235	+	1.21977i	0.0569340	+	0.0986126i
$154$	−1.77363	+	1.02401i	−0.142923	+	0.0825168i
$155$	−15.4497			−1.24095
$156$	5.33847	−	2.42872i	0.427420	−	0.194453i
$157$	16.1075			1.28552			0.642758	−	0.766069i	$-0.277790\pi$
$157$	16.1075			1.28552			0.642758	+	0.766069i	$0.277790\pi$
$158$	−7.25038	+	4.18601i	−0.576809	+	0.333021i
$159$	−4.27309	−	7.40121i	−0.338878	−	0.586954i
$160$	−6.44923	+	11.1704i	−0.509856	+	0.883097i
$161$			16.9170i			1.33325i
$162$	0.529161	+	0.305511i	0.0415748	+	0.0240032i
$163$	−12.8901	−	7.44210i	−1.00963	−	0.582911i	−0.0985472	−	0.995132i	$-0.531420\pi$
$163$	−12.8901	−	7.44210i	−1.00963	−	0.582911i	−0.911084	+	0.412222i	$0.864753\pi$
$164$			0.296598i			0.0231604i
$165$	1.15320	−	1.99741i	0.0897768	−	0.155498i
$166$	0.683004	+	1.18300i	0.0530114	+	0.0918184i
$167$	15.3348	−	8.85354i	1.18664	−	0.685108i	0.229100	−	0.973403i	$-0.426422\pi$
$167$	15.3348	−	8.85354i	1.18664	−	0.685108i	0.957542	+	0.288295i	$0.0930884\pi$
$168$	−7.42743			−0.573039
$169$	8.54142	−	9.80021i	0.657032	−	0.753862i
$170$	−1.98491			−0.152235
$171$	−4.99398	+	2.88328i	−0.381900	+	0.220490i
$172$	−6.76140	−	11.7111i	−0.515552	−	0.892962i
$173$	1.89403	−	3.28055i	0.144000	−	0.249416i	−0.784999	−	0.619497i	$-0.787337\pi$
$173$	1.89403	−	3.28055i	0.144000	−	0.249416i	0.928999	+	0.370081i	$0.120670\pi$
$174$			5.96826i			0.452452i
$175$	0.927460	+	0.535470i	0.0701094	+	0.0404777i
$176$	1.64484	+	0.949651i	0.123985	+	0.0715826i
$177$			11.9186i			0.895855i
$178$	−2.62357	+	4.54416i	−0.196645	+	0.340599i
$179$	3.21689	+	5.57181i	0.240441	+	0.416457i	0.960840	−	0.277104i	$-0.0893745\pi$
$179$	3.21689	+	5.57181i	0.240441	+	0.416457i	−0.720399	+	0.693560i	$0.756041\pi$
$180$	3.24909	−	1.87586i	0.242173	−	0.139818i
$181$	4.21643			0.313404			0.156702	−	0.987646i	$-0.449914\pi$
$181$	4.21643			0.313404			0.156702	+	0.987646i	$0.449914\pi$
$182$	−6.72133	+	3.05785i	−0.498218	+	0.226663i
$183$	−4.08699			−0.302119
$184$	−9.68593	+	5.59217i	−0.714056	+	0.412260i
$185$	−10.9739	−	19.0073i	−0.806816	−	1.39745i
$186$	2.04650	−	3.54465i	0.150057	−	0.259906i
$187$			1.40847i			0.102998i
$188$	−14.4827	−	8.36156i	−1.05626	−	0.609830i
$189$	2.90273	+	1.67589i	0.211143	+	0.121903i
$190$		−	8.12661i		−	0.589566i
$191$	13.6499	−	23.6423i	0.987670	−	1.71069i	0.358258	−	0.933623i	$-0.383371\pi$
$191$	13.6499	−	23.6423i	0.987670	−	1.71069i	0.629412	−	0.777072i	$-0.283296\pi$
$192$	0.190748	+	0.330386i	0.0137661	+	0.0238435i
$193$	22.4342	−	12.9524i	1.61485	−	0.932334i	0.626625	−	0.779321i	$-0.284436\pi$
$193$	22.4342	−	12.9524i	1.61485	−	0.932334i	0.988224	−	0.153013i	$-0.0488975\pi$
$194$	−2.54068			−0.182410
$195$	4.83342	−	6.76696i	0.346128	−	0.484592i
$196$	−6.88798			−0.491999
$197$	−14.3261	+	8.27120i	−1.02069	+	0.589298i	−0.914305	−	0.405026i	$-0.867262\pi$
$197$	−14.3261	+	8.27120i	−1.02069	+	0.589298i	−0.106390	+	0.994325i	$0.533929\pi$
$198$	0.305511	+	0.529161i	0.0217117	+	0.0376058i
$199$	−2.25047	+	3.89793i	−0.159532	+	0.276317i	−0.934700	−	0.355438i	$-0.884332\pi$
$199$	−2.25047	+	3.89793i	−0.159532	+	0.276317i	0.775168	+	0.631755i	$0.217665\pi$
$200$			0.708030i			0.0500653i
$201$	−10.1326	−	5.85005i	−0.714697	−	0.412630i
$202$	1.52039	+	0.877798i	0.106974	+	0.0617617i
$203$			32.7391i			2.29783i
$204$	−1.14555	+	1.98414i	−0.0802042	+	0.138918i
$205$	0.210271	+	0.364200i	0.0146860	+	0.0254369i
$206$	2.24741	−	1.29754i	0.156584	−	0.0904040i
$207$	5.04717			0.350802
$208$	5.57252	+	3.98027i	0.386385	+	0.275982i
$209$	−5.76656			−0.398881
$210$	−4.09072	+	2.36178i	−0.282286	+	0.162978i
$211$	−6.08281	−	10.5357i	−0.418758	−	0.725310i	0.577057	−	0.816704i	$-0.304201\pi$
$211$	−6.08281	−	10.5357i	−0.418758	−	0.725310i	−0.995815	+	0.0913941i	$0.970868\pi$
$212$	6.95084	−	12.0392i	0.477385	−	0.826856i
$213$		−	5.35913i		−	0.367202i
$214$	−4.55180	−	2.62798i	−0.311154	−	0.179645i
$215$	−16.6050	−	9.58689i	−1.13245	−	0.653821i
$216$			2.21596i			0.150777i
$217$	11.2262	−	19.4443i	0.762081	−	1.31996i
$218$	−2.01095	−	3.48307i	−0.136199	−	0.235903i
$219$	3.06481	−	1.76947i	0.207101	−	0.119570i
$220$	3.75172			0.252941
$221$	−0.489996	+	5.05462i	−0.0329607	+	0.340010i
$222$	5.81448			0.390243
$223$	−12.5417	+	7.24094i	−0.839853	+	0.484889i	−0.857214	−	0.514960i	$-0.827807\pi$
$223$	−12.5417	+	7.24094i	−0.839853	+	0.484889i	0.0173612	+	0.999849i	$0.494473\pi$
$224$	−9.37233	−	16.2334i	−0.626215	−	1.08464i
$225$	0.159757	−	0.276707i	0.0106504	−	0.0184471i
$226$			1.75689i			0.116867i
$227$	−8.54218	−	4.93183i	−0.566964	−	0.327337i	0.188972	−	0.981983i	$-0.439485\pi$
$227$	−8.54218	−	4.93183i	−0.566964	−	0.327337i	−0.755936	+	0.654646i	$0.772818\pi$
$228$	−8.12347	−	4.69009i	−0.537990	−	0.310609i
$229$			6.80287i			0.449547i	0.974411	+	0.224773i	$0.0721642\pi$
$229$			6.80287i			0.449547i	−0.974411	+	0.224773i	$0.927836\pi$
$230$	−3.55640	+	6.15987i	−0.234502	+	0.406170i
$231$	1.67589	+	2.90273i	0.110266	+	0.190986i
$232$	−18.7449	+	10.8224i	−1.23067	+	0.710525i
$233$	−13.6395			−0.893556			−0.446778	−	0.894645i	$-0.647429\pi$
$233$	−13.6395			−0.893556			−0.446778	+	0.894645i	$0.647429\pi$
$234$	0.912305	+	2.00530i	0.0596393	+	0.131090i
$235$	−23.7115			−1.54677
$236$	−16.7900	+	9.69369i	−1.09293	+	0.631006i
$237$	6.85083	+	11.8660i	0.445009	+	0.770779i
$238$	1.44228	−	2.49811i	0.0934893	−	0.161928i
$239$			16.4479i			1.06392i	0.846768	+	0.531962i	$0.178545\pi$
$239$			16.4479i			1.06392i	−0.846768	+	0.531962i	$0.821455\pi$
$240$	3.79368	+	2.19028i	0.244881	+	0.141382i
$241$	−25.2499	−	14.5780i	−1.62649	−	0.939053i	−0.985130	−	0.171810i	$-0.945038\pi$
$241$	−25.2499	−	14.5780i	−1.62649	−	0.939053i	−0.641357	−	0.767243i	$-0.721628\pi$
$242$			0.611022i			0.0392780i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.32405	−	5.75743i	−0.212801	−	0.368582i
$245$	−8.45793	+	4.88319i	−0.540357	+	0.311975i
$246$	−0.111412			−0.00710335
$247$	−20.6946	−	2.00614i	−1.31677	−	0.127648i
$248$	14.8439			0.942589
$249$	1.93610	−	1.11781i	0.122695	−	0.0708380i
$250$	−3.29802	−	5.71235i	−0.208585	−	0.361280i
$251$	−8.10888	+	14.0450i	−0.511828	+	0.886512i	0.488078	+	0.872800i	$0.337698\pi$
$251$	−8.10888	+	14.0450i	−0.511828	+	0.886512i	−0.999906	+	0.0137118i	$0.995635\pi$
$252$			5.45219i			0.343455i
$253$	4.37098	+	2.52358i	0.274801	+	0.158656i
$254$	−5.40246	−	3.11911i	−0.338981	−	0.195711i
$255$			3.24850i			0.203429i
$256$	3.10683	−	5.38118i	0.194177	−	0.336324i
$257$	5.03662	+	8.72368i	0.314176	+	0.544168i	0.979262	−	0.202598i	$-0.0649386\pi$
$257$	5.03662	+	8.72368i	0.314176	+	0.544168i	−0.665086	+	0.746767i	$0.731605\pi$
$258$	4.39906	−	2.53980i	0.273873	−	0.158121i
$259$	31.8956			1.98189
$260$	13.4639	+	1.30519i	0.834996	+	0.0809448i
$261$	9.76766			0.604603
$262$	2.61643	−	1.51060i	0.161644	−	0.0933250i
$263$	−6.08509	−	10.5397i	−0.375223	−	0.649905i	0.615138	−	0.788420i	$-0.289100\pi$
$263$	−6.08509	−	10.5397i	−0.375223	−	0.649905i	−0.990360	+	0.138515i	$0.955767\pi$
$264$	−1.10798	+	1.91908i	−0.0681916	+	0.118111i
$265$		−	19.7110i		−	1.21084i
$266$	10.2277	+	5.90499i	0.627103	+	0.362058i
$267$	7.43698	+	4.29374i	0.455136	+	0.262773i
$268$		−	19.0320i		−	1.16256i
$269$	1.61005	−	2.78869i	0.0981667	−	0.170030i	−0.812759	−	0.582600i	$-0.802035\pi$
$269$	1.61005	−	2.78869i	0.0981667	−	0.170030i	0.910926	+	0.412570i	$0.135369\pi$
$270$	0.704633	+	1.22046i	0.0428826	+	0.0742748i
$271$	16.9220	−	9.76990i	1.02794	−	0.593479i	0.111543	−	0.993760i	$-0.464421\pi$
$271$	16.9220	−	9.76990i	1.02794	−	0.593479i	0.916393	+	0.400280i	$0.131087\pi$
$272$	−2.67511			−0.162202
$273$	5.00448	+	11.0001i	0.302885	+	0.665759i
$274$	−6.57209			−0.397034
$275$	0.276707	−	0.159757i	0.0166860	−	0.00963369i
$276$	4.10499	+	7.11006i	0.247092	+	0.427975i
$277$	−0.168236	+	0.291394i	−0.0101083	+	0.0175082i	−0.871035	−	0.491220i	$-0.836551\pi$
$277$	−0.168236	+	0.291394i	−0.0101083	+	0.0175082i	0.860927	+	0.508729i	$0.169884\pi$
$278$		−	14.1328i		−	0.847626i
$279$	−5.80117	−	3.34931i	−0.347307	−	0.200518i
$280$	−14.8356	−	8.56534i	−0.886597	−	0.511877i
$281$			11.2484i			0.671024i	0.942036	+	0.335512i	$0.108909\pi$
$281$			11.2484i			0.671024i	−0.942036	+	0.335512i	$0.891091\pi$
$282$	3.14087	−	5.44014i	0.187036	−	0.323956i
$283$	−14.2113	−	24.6148i	−0.844777	−	1.46320i	−0.885815	−	0.464039i	$-0.846400\pi$
$283$	−14.2113	−	24.6148i	−0.844777	−	1.46320i	0.0410383	−	0.999158i	$-0.486933\pi$
$284$	7.54953	−	4.35872i	0.447982	−	0.258643i
$285$	−13.3000			−0.787826
$286$	−0.212570	+	2.19279i	−0.0125695	+	0.129663i
$287$	−0.611153			−0.0360752
$288$	−4.84320	+	2.79622i	−0.285388	+	0.164769i
$289$	7.50811	+	13.0044i	0.441653	+	0.764966i
$290$	−6.88261	+	11.9210i	−0.404161	+	0.700027i
$291$			4.15808i			0.243751i
$292$	4.98538	+	2.87831i	0.291747	+	0.168440i
$293$	7.27879	+	4.20241i	0.425231	+	0.245507i	0.697313	−	0.716767i	$-0.254379\pi$
$293$	7.27879	+	4.20241i	0.425231	+	0.245507i	−0.272082	+	0.962274i	$0.587712\pi$
$294$		−	2.58734i		−	0.150897i
$295$	−13.7445	+	23.8063i	−0.800238	+	1.38605i
$296$	10.5436	+	18.2620i	0.612832	+	1.06146i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$	3.35764			0.194503
$299$	14.8083	+	10.5771i	0.856387	+	0.611689i
$300$	0.519737			0.0300070
$301$	24.1312	−	13.9321i	1.39090	−	0.803035i
$302$	−0.540606	−	0.936357i	−0.0311084	−	0.0538813i
$303$	1.43661	−	2.48827i	0.0825309	−	0.142948i
$304$		−	10.9524i		−	0.628165i
$305$	−8.16338	−	4.71313i	−0.467434	−	0.269873i
$306$	−0.745307	−	0.430303i	−0.0426064	−	0.0245988i
$307$			14.9401i			0.852679i	0.904563	+	0.426339i	$0.140197\pi$
$307$			14.9401i			0.852679i	−0.904563	+	0.426339i	$0.859803\pi$
$308$	−2.72609	+	4.72173i	−0.155334	+	0.269046i
$309$	−2.12356	−	3.67811i	−0.120805	−	0.209241i
$310$	8.17539	−	4.72007i	0.464331	−	0.268082i
$311$	29.3984			1.66703			0.833516	−	0.552495i	$-0.186324\pi$
$311$	29.3984			1.66703			0.833516	+	0.552495i	$0.186324\pi$
$312$	−4.64388	+	6.50160i	−0.262908	+	0.368081i
$313$	5.04716			0.285282			0.142641	−	0.989774i	$-0.454441\pi$
$313$	5.04716			0.285282			0.142641	+	0.989774i	$0.454441\pi$
$314$	−8.52344	+	4.92101i	−0.481005	+	0.277709i
$315$	3.86529	+	6.69488i	0.217784	+	0.377214i
$316$	−11.1439	+	19.3018i	−0.626895	+	1.08581i
$317$		−	19.4140i		−	1.09040i	−0.838306	−	0.545200i	$-0.816454\pi$
$317$		−	19.4140i		−	1.09040i	0.838306	−	0.545200i	$-0.183546\pi$
$318$	4.52230	+	2.61095i	0.253598	+	0.146415i
$319$	8.45904	+	4.88383i	0.473616	+	0.273442i
$320$			0.879886i			0.0491871i
$321$	−4.30096	+	7.44948i	−0.240056	+	0.415790i
$322$	−5.16833	−	8.95182i	−0.288020	−	0.498865i
$323$	7.03388	−	4.06101i	0.391375	−	0.225961i
$324$	1.62665			0.0903696
$325$	1.04860	−	0.477059i	0.0581660	−	0.0264625i
$326$	9.09458			0.503702
$327$	−5.70040	+	3.29113i	−0.315233	+	0.182000i
$328$	−0.202026	−	0.349919i	−0.0111550	−	0.0193210i
$329$	17.2293	−	29.8421i	0.949885	−	1.64525i
$330$			1.40927i			0.0775775i
$331$	22.6569	+	13.0810i	1.24534	+	0.718996i	0.970176	−	0.242403i	$-0.0779355\pi$
$331$	22.6569	+	13.0810i	1.24534	+	0.718996i	0.275161	+	0.961398i	$0.411269\pi$
$332$	3.14935	+	1.81828i	0.172843	+	0.0997911i
$333$		−	9.51599i		−	0.521473i
$334$	−5.40971	+	9.36989i	−0.296006	+	0.512698i
$335$	−13.4926	−	23.3698i	−0.737179	−	1.27683i
$336$	−5.51316	+	3.18302i	−0.300767	+	0.173648i
$337$	−10.2445			−0.558054			−0.279027	−	0.960283i	$-0.590012\pi$
$337$	−10.2445			−0.558054			−0.279027	+	0.960283i	$0.590012\pi$
$338$	−1.52571	+	7.79538i	−0.0829877	+	0.424013i
$339$	2.87533			0.156167
$340$	−4.57624	+	2.64209i	−0.248181	+	0.143288i
$341$	−3.34931	−	5.80117i	−0.181375	−	0.314151i
$342$	1.76175	−	3.05143i	0.0952643	−	0.165003i
$343$			9.26951i			0.500507i
$344$	15.9538	+	9.21096i	0.860174	+	0.496622i
$345$	10.0813	+	5.82041i	0.542756	+	0.313360i
$346$			2.31458i			0.124433i
$347$	8.01962	−	13.8904i	0.430516	−	0.745675i	−0.566402	−	0.824129i	$-0.691665\pi$
$347$	8.01962	−	13.8904i	0.430516	−	0.745675i	0.996918	+	0.0784537i	$0.0249983\pi$
$348$	7.94429	+	13.7599i	0.425859	+	0.737609i
$349$	2.18253	−	1.26008i	0.116828	−	0.0674506i	−0.440447	−	0.897778i	$-0.645180\pi$
$349$	2.18253	−	1.26008i	0.116828	−	0.0674506i	0.557275	+	0.830328i	$0.311847\pi$
$350$	−0.654367			−0.0349774
$351$	3.28188	−	1.49308i	0.175174	−	0.0796947i
$352$	−5.59244			−0.298078
$353$	5.99518	−	3.46132i	0.319091	−	0.184227i	−0.331896	−	0.943316i	$-0.607688\pi$
$353$	5.99518	−	3.46132i	0.319091	−	0.184227i	0.650987	+	0.759088i	$0.274355\pi$
$354$	−3.64126	−	6.30684i	−0.193531	−	0.335205i
$355$	6.18017	−	10.7044i	0.328009	−	0.568129i
$356$			13.9688i			0.740347i
$357$	−4.08841	−	2.36044i	−0.216381	−	0.124928i
$358$	−3.40450	−	1.96559i	−0.179933	−	0.103885i
$359$		−	11.1808i		−	0.590099i	−0.955482	−	0.295049i	$-0.904664\pi$
$359$		−	11.1808i		−	0.590099i	0.955482	−	0.295049i	$-0.0953361\pi$
$360$	−2.55546	+	4.42618i	−0.134684	+	0.233280i
$361$	7.12659	+	12.3436i	0.375083	+	0.649664i
$362$	−2.23117	+	1.28816i	−0.117267	+	0.0677044i
$363$	1.00000			0.0524864
$364$	−11.4259	+	15.9966i	−0.598878	+	0.838451i
$365$	8.16223			0.427230
$366$	2.16267	−	1.24862i	0.113045	−	0.0652664i
$367$	−10.1548	−	17.5886i	−0.530076	−	0.918118i	−0.999384	−	0.0350841i	$-0.988830\pi$
$367$	−10.1548	−	17.5886i	−0.530076	−	0.918118i	0.469309	−	0.883034i	$-0.344503\pi$
$368$	−4.79305	+	8.30180i	−0.249855	+	0.432761i
$369$			0.182337i			0.00949206i
$370$	11.6139	+	6.70528i	0.603777	+	0.348591i
$371$	24.8073	+	14.3225i	1.28793	+	0.743586i
$372$		−	10.8963i		−	0.564948i
$373$	6.71221	−	11.6259i	0.347545	−	0.601966i	−0.638268	−	0.769815i	$-0.720349\pi$
$373$	6.71221	−	11.6259i	0.347545	−	0.601966i	0.985813	+	0.167849i	$0.0536820\pi$
$374$	−0.430303	−	0.745307i	−0.0222504	−	0.0385389i
$375$	−9.34884	+	5.39755i	−0.482772	+	0.278728i
$376$	22.7817			1.17488
$377$	28.6582	+	20.4696i	1.47597	+	1.05424i
$378$	−2.04801			−0.105338
$379$	−22.8567	+	13.1963i	−1.17407	+	0.677850i	−0.954636	−	0.297777i	$-0.903755\pi$
$379$	−22.8567	+	13.1963i	−1.17407	+	0.677850i	−0.219436	+	0.975627i	$0.570422\pi$
$380$	−10.8173	−	18.7360i	−0.554914	−	0.961139i
$381$	−5.10475	+	8.84168i	−0.261524	+	0.452973i
$382$			16.6807i			0.853461i
$383$	13.5873	+	7.84465i	0.694280	+	0.400843i	0.805213	−	0.592985i	$-0.202051\pi$
$383$	13.5873	+	7.84465i	0.694280	+	0.400843i	−0.110933	+	0.993828i	$0.535384\pi$
$384$	−9.88827	−	5.70899i	−0.504609	−	0.291336i
$385$			7.73058i			0.393987i
$386$	−7.91420	+	13.7078i	−0.402822	+	0.697708i
$387$	−4.15664	−	7.19950i	−0.211294	−	0.365971i
$388$	−5.85759	+	3.38188i	−0.297374	+	0.171689i
$389$	−17.4889			−0.886720			−0.443360	−	0.896344i	$-0.646214\pi$
$389$	−17.4889			−0.886720			−0.443360	+	0.896344i	$0.646214\pi$
$390$	−0.490273	+	5.05747i	−0.0248259	+	0.256095i
$391$	−7.10879			−0.359507
$392$	8.12626	−	4.69170i	0.410438	−	0.236967i
$393$	−2.47225	−	4.28206i	−0.124708	−	0.216001i
$394$	5.05388	−	8.75358i	0.254611	−	0.440999i
$395$			31.6016i			1.59005i
$396$	1.40872	+	0.813326i	0.0707909	+	0.0408712i
$397$	−5.98053	−	3.45286i	−0.300154	−	0.173294i	0.342358	−	0.939570i	$-0.388774\pi$
$397$	−5.98053	−	3.45286i	−0.300154	−	0.173294i	−0.642512	+	0.766276i	$0.722108\pi$
$398$		−	2.75018i		−	0.137854i
$399$	9.66412	−	16.7388i	0.483811	−	0.837986i
$400$	0.303426	+	0.525549i	0.0151713	+	0.0262775i
$401$	15.9589	−	9.21388i	0.796949	−	0.460119i	−0.0454539	−	0.998966i	$-0.514473\pi$
$401$	15.9589	−	9.21388i	0.796949	−	0.460119i	0.842403	+	0.538847i	$0.181140\pi$
$402$	7.14901			0.356560
$403$	−10.0016	−	21.9840i	−0.498214	−	1.09510i
$404$	4.67372			0.232526
$405$	1.99741	−	1.15320i	0.0992520	−	0.0573031i
$406$	−10.0022	−	17.3242i	−0.496399	−	0.859787i
$407$	4.75800	−	8.24109i	0.235845	−	0.408496i
$408$		−	3.12112i		−	0.154518i
$409$	0.806126	+	0.465417i	0.0398604	+	0.0230134i	0.519798	−	0.854289i	$-0.326007\pi$
$409$	0.806126	+	0.465417i	0.0398604	+	0.0230134i	−0.479937	+	0.877303i	$0.659341\pi$
$410$	−0.222534	−	0.128480i	−0.0109902	−	0.00634519i
$411$			10.7559i			0.530549i
$412$	3.45429	−	5.98301i	0.170181	−	0.294762i
$413$	−19.9742	−	34.5964i	−0.982869	−	1.70238i
$414$	−2.67076	+	1.54197i	−0.131261	+	0.0757835i
$415$	5.15623			0.253109
$416$	−20.0698	−	1.94557i	−0.984001	−	0.0953893i
$417$	−23.1297			−1.13267
$418$	3.05143	−	1.76175i	0.149251	−	0.0861698i
$419$	13.0072	+	22.5291i	0.635443	+	1.10062i	0.986421	+	0.164235i	$0.0525157\pi$
$419$	13.0072	+	22.5291i	0.635443	+	1.10062i	−0.350979	+	0.936384i	$0.614151\pi$
$420$	−6.28748	+	10.8902i	−0.306798	+	0.531389i
$421$		−	10.3012i		−	0.502048i	−0.967981	−	0.251024i	$-0.919233\pi$
$421$		−	10.3012i		−	0.502048i	0.967981	−	0.251024i	$-0.0807673\pi$
$422$	6.43756	+	3.71673i	0.313376	+	0.180928i
$423$	−8.90335	−	5.14035i	−0.432896	−	0.249932i
$424$			18.9380i			0.919713i
$425$	−0.225012	+	0.389733i	−0.0109147	+	0.0189048i
$426$	1.63727	+	2.83584i	0.0793262	+	0.137397i
$427$	11.8634	−	6.84935i	0.574111	−	0.331463i
$428$	−13.9923			−0.676345
$429$	3.58873	+	0.347892i	0.173265	+	0.0167964i
$430$	11.7156			0.564977
$431$	−5.16414	+	2.98152i	−0.248748	+	0.143615i	−0.619191	−	0.785241i	$-0.712539\pi$
$431$	−5.16414	+	2.98152i	−0.248748	+	0.143615i	0.370443	+	0.928855i	$0.379206\pi$
$432$	0.949651	+	1.64484i	0.0456901	+	0.0791376i
$433$	−1.48740	+	2.57626i	−0.0714800	+	0.123807i	−0.899550	−	0.436818i	$-0.856106\pi$
$433$	−1.48740	+	2.57626i	−0.0714800	+	0.123807i	0.828070	+	0.560625i	$0.189439\pi$
$434$			13.7189i			0.658526i
$435$	19.5100	+	11.2641i	0.935433	+	0.540072i
$436$	−9.27257	−	5.35352i	−0.444076	−	0.256387i
$437$		−	29.1048i		−	1.39227i
$438$	−1.08118	+	1.87267i	−0.0516610	+	0.0894794i
$439$	14.6249	+	25.3311i	0.698009	+	1.20899i	0.969156	+	0.246450i	$0.0792640\pi$
$439$	14.6249	+	25.3311i	0.698009	+	1.20899i	−0.271146	+	0.962538i	$0.587403\pi$
$440$	−4.42618	+	2.55546i	−0.211010	+	0.121827i
$441$	−4.23445			−0.201641
$442$	−1.28495	−	2.82440i	−0.0611190	−	0.134343i
$443$	16.9403			0.804856			0.402428	−	0.915452i	$-0.368166\pi$
$443$	16.9403			0.804856			0.402428	+	0.915452i	$0.368166\pi$
$444$	13.4054	−	7.73961i	0.636192	−	0.367305i
$445$	9.90311	+	17.1527i	0.469453	+	0.813116i
$446$	4.42438	−	7.66324i	0.209500	−	0.362865i
$447$		−	5.49512i		−	0.259910i
$448$	−1.10738	−	0.639347i	−0.0523188	−	0.0302063i
$449$	−29.3213	−	16.9286i	−1.38376	−	0.798912i	−0.391155	−	0.920325i	$-0.627924\pi$
$449$	−29.3213	−	16.9286i	−1.38376	−	0.798912i	−0.992602	+	0.121413i	$0.961258\pi$
$450$			0.195230i			0.00920321i
$451$	−0.0911683	+	0.157908i	−0.00429295	+	0.00743560i
$452$	2.33858	+	4.05055i	0.109998	+	0.190522i
$453$	−1.53244	+	0.884757i	−0.0720005	+	0.0415695i
$454$	6.02691			0.282857
$455$	−2.68941	+	27.7429i	−0.126081	+	1.30061i
$456$	12.7785			0.598407
$457$	−13.1529	+	7.59381i	−0.615265	+	0.355224i	−0.775023	−	0.631933i	$-0.782262\pi$
$457$	−13.1529	+	7.59381i	−0.615265	+	0.355224i	0.159758	+	0.987156i	$0.448929\pi$
$458$	−2.07835	−	3.59981i	−0.0971151	−	0.168208i
$459$	−0.704235	+	1.21977i	−0.0328709	+	0.0569340i
$460$			18.9356i			0.882876i
$461$	1.10145	+	0.635925i	0.0512999	+	0.0296180i	0.525431	−	0.850836i	$-0.323904\pi$
$461$	1.10145	+	0.635925i	0.0512999	+	0.0296180i	−0.474131	+	0.880454i	$0.657238\pi$
$462$	−1.77363	−	1.02401i	−0.0825168	−	0.0476411i
$463$			15.7563i			0.732258i	0.930564	+	0.366129i	$0.119317\pi$
$463$			15.7563i			0.732258i	−0.930564	+	0.366129i	$0.880683\pi$
$464$	−9.27587	+	16.0663i	−0.430621	+	0.745858i
$465$	−7.72487	−	13.3799i	−0.358232	−	0.620477i
$466$	7.21750	−	4.16703i	0.334344	−	0.193034i
$467$	−1.74294			−0.0806538			−0.0403269	−	0.999187i	$-0.512840\pi$
$467$	−1.74294			−0.0806538			−0.0403269	+	0.999187i	$0.512840\pi$
$468$	4.77257	+	3.40889i	0.220612	+	0.157576i
$469$	39.2162			1.81083
$470$	12.5472	−	7.24412i	0.578758	−	0.334146i
$471$	8.05373	+	13.9495i	0.371096	+	0.642758i
$472$	13.2056	−	22.8727i	0.607836	−	1.05280i
$473$		−	8.31327i		−	0.382245i
$474$	−7.25038	−	4.18601i	−0.333021	−	0.192270i
$475$	−1.59564	−	0.921245i	−0.0732132	−	0.0422696i
$476$		−	7.67924i		−	0.351977i
$477$	4.27309	−	7.40121i	0.195651	−	0.338878i
$478$	−5.02500	−	8.70356i	−0.229838	−	0.398092i
$479$	−13.8043	+	7.96990i	−0.630733	+	0.364154i	−0.781036	−	0.624486i	$-0.785308\pi$
$479$	−13.8043	+	7.96990i	−0.630733	+	0.364154i	0.150303	+	0.988640i	$0.451975\pi$
$480$	−12.8985			−0.588731
$481$	19.9422	−	27.9198i	0.909285	−	1.27303i
$482$	17.8150			0.811450
$483$	−14.6506	+	8.45851i	−0.666624	+	0.384875i
$484$	0.813326	+	1.40872i	0.0369694	+	0.0640328i
$485$	−4.79512	+	8.30539i	−0.217735	+	0.377128i
$486$			0.611022i			0.0277165i
$487$	14.7411	+	8.51080i	0.667985	+	0.385661i	0.795313	−	0.606199i	$-0.207307\pi$
$487$	14.7411	+	8.51080i	0.667985	+	0.385661i	−0.127328	+	0.991861i	$0.540640\pi$
$488$	7.84327	+	4.52831i	0.355048	+	0.204987i
$489$		−	14.8842i		−	0.673087i
$490$	2.98373	−	5.16798i	0.134791	−	0.233466i
$491$	−8.99679	−	15.5829i	−0.406020	−	0.703247i	0.588420	−	0.808555i	$-0.299750\pi$
$491$	−8.99679	−	15.5829i	−0.406020	−	0.703247i	−0.994440	+	0.105309i	$0.966417\pi$
$492$	−0.256862	+	0.148299i	−0.0115802	+	0.00668584i
$493$	−13.7575			−0.619605
$494$	11.5637	−	5.26086i	0.520274	−	0.236697i
$495$	2.30641			0.103665
$496$	11.0182	−	6.36135i	0.494731	−	0.285633i
$497$	8.98133	+	15.5561i	0.402868	+	0.697787i
$498$	−0.683004	+	1.18300i	−0.0306061	+	0.0530114i
$499$			12.8837i			0.576752i	0.957517	+	0.288376i	$0.0931153\pi$
$499$			12.8837i			0.576752i	−0.957517	+	0.288376i	$0.906885\pi$
$500$	−15.2073	−	8.77994i	−0.680091	−	0.392651i
$501$	15.3348	+	8.85354i	0.685108	+	0.395547i
$502$		−	9.90940i		−	0.442278i
$503$	−9.68324	+	16.7719i	−0.431755	+	0.747821i	−0.997025	−	0.0770852i	$-0.975439\pi$
$503$	−9.68324	+	16.7719i	−0.431755	+	0.747821i	0.565270	+	0.824906i	$0.308772\pi$
$504$	−3.71372	−	6.43235i	−0.165422	−	0.286519i
$505$	5.73897	−	3.31340i	0.255381	−	0.147444i
$506$	−3.08393			−0.137097
$507$	12.7579	+	2.49698i	0.566600	+	0.110895i
$508$	−16.6073			−0.736829
$509$	−33.8303	+	19.5319i	−1.49950	+	0.865737i	−1.00000		0.000576772i	$-0.999816\pi$
$509$	−33.8303	+	19.5319i	−1.49950	+	0.865737i	−0.499500	+	0.866314i	$0.666483\pi$
$510$	−0.992454	−	1.71898i	−0.0439466	−	0.0761177i
$511$	−5.93087	+	10.2726i	−0.262366	+	0.454432i
$512$		−	19.0393i		−	0.841426i
$513$	−4.99398	−	2.88328i	−0.220490	−	0.127300i
$514$	−5.33036	−	3.07749i	−0.235112	−	0.135742i
$515$		−	9.79558i		−	0.431645i
$516$	6.76140	−	11.7111i	0.297654	−	0.515552i
$517$	−5.14035	−	8.90335i	−0.226072	−	0.391569i
$518$	−16.8779	+	9.74444i	−0.741571	+	0.428146i
$519$	3.78805			0.166277
$520$	−16.7734	+	7.63101i	−0.735562	+	0.334642i
$521$	−9.26918			−0.406090			−0.203045	−	0.979169i	$-0.565084\pi$
$521$	−9.26918			−0.406090			−0.203045	+	0.979169i	$0.565084\pi$
$522$	−5.16866	+	2.98413i	−0.226226	+	0.130612i
$523$	10.0020	+	17.3239i	0.437355	+	0.757521i	0.997485	−	0.0708839i	$-0.0225820\pi$
$523$	10.0020	+	17.3239i	0.437355	+	0.757521i	−0.560130	+	0.828405i	$0.689249\pi$
$524$	4.02148	−	6.96541i	0.175679	−	0.304286i
$525$			1.07094i			0.0467396i
$526$	6.43998	+	3.71812i	0.280797	+	0.162118i
$527$	8.17078	+	4.71740i	0.355925	+	0.205493i
$528$			1.89930i			0.0826565i
$529$	−1.23696	+	2.14247i	−0.0537807	+	0.0931509i
$530$	6.02192	+	10.4303i	0.261576	+	0.453062i
$531$	−10.3218	+	5.95929i	−0.447928	+	0.258611i
$532$	31.4403			1.36311
$533$	−0.382113	+	0.534973i	−0.0165512	+	0.0231722i
$534$	−5.24714			−0.227066
$535$	−17.1815	+	9.91976i	−0.742823	+	0.428869i
$536$	12.9635	+	22.4534i	0.559938	+	0.969840i
$537$	−3.21689	+	5.57181i	−0.138819	+	0.240441i
$538$			1.96756i			0.0848274i
$539$	−3.66714	−	2.11723i	−0.157955	−	0.0911954i
$540$	3.24909	+	1.87586i	0.139818	+	0.0807242i
$541$		−	7.64518i		−	0.328692i	−0.986403	−	0.164346i	$-0.947449\pi$
$541$		−	7.64518i		−	0.328692i	0.986403	−	0.164346i	$-0.0525513\pi$
$542$	−5.96962	+	10.3397i	−0.256417	+	0.444128i
$543$	2.10821	+	3.65153i	0.0904721	+	0.156702i
$544$	6.82150	−	3.93839i	0.292469	−	0.168857i
$545$	−15.1814			−0.650298
$546$	−6.00884	−	4.29191i	−0.257155	−	0.183677i
$547$	2.36827			0.101260			0.0506299	−	0.998717i	$-0.483877\pi$
$547$	2.36827			0.101260			0.0506299	+	0.998717i	$0.483877\pi$
$548$	−15.1521	+	8.74804i	−0.647264	+	0.373698i
$549$	−2.04349	−	3.53944i	−0.0872142	−	0.151059i
$550$	−0.0976148	+	0.169074i	−0.00416231	+	0.00720933i
$551$		−	56.3258i		−	2.39956i
$552$	−9.68593	−	5.59217i	−0.412260	−	0.238019i
$553$	−39.7722	−	22.9625i	−1.69129	−	0.976465i
$554$		−	0.205592i		−	0.00873477i
$555$	10.9739	−	19.0073i	0.465815	−	0.806816i
$556$	−18.8120	−	32.5833i	−0.797806	−	1.38184i
$557$	0.932989	−	0.538661i	0.0395320	−	0.0228238i	−0.480104	−	0.877212i	$-0.659401\pi$
$557$	0.932989	−	0.538661i	0.0395320	−	0.0228238i	0.519636	+	0.854388i	$0.326068\pi$
$558$	4.09300			0.173271
$559$	2.89212	−	29.8341i	0.122324	−	1.26185i
$560$	−14.6827			−0.620457
$561$	−1.21977	+	0.704235i	−0.0514988	+	0.0297328i
$562$	−3.43651	−	5.95222i	−0.144961	−	0.251079i
$563$	12.3485	−	21.3883i	0.520429	−	0.901409i	−0.479289	−	0.877657i	$-0.659105\pi$
$563$	12.3485	−	21.3883i	0.520429	−	0.901409i	0.999718	−	0.0237522i	$-0.00756128\pi$
$564$		−	16.7231i		−	0.704171i
$565$	5.74321	+	3.31585i	0.241619	+	0.139499i
$566$	15.0402	+	8.68344i	0.632185	+	0.364992i
$567$			3.35178i			0.140762i
$568$	−5.93782	+	10.2846i	−0.249146	+	0.431533i
$569$	−6.01123	−	10.4118i	−0.252004	−	0.436484i	0.712073	−	0.702105i	$-0.247756\pi$
$569$	−6.01123	−	10.4118i	−0.252004	−	0.436484i	−0.964077	+	0.265621i	$0.914423\pi$
$570$	7.03785	−	4.06330i	0.294783	−	0.170193i
$571$	36.4913			1.52711			0.763557	−	0.645740i	$-0.223451\pi$
$571$	36.4913			1.52711			0.763557	+	0.645740i	$0.223451\pi$
$572$	2.42872	+	5.33847i	0.101550	+	0.223213i
$573$	27.2997			1.14046
$574$	0.323398	−	0.186714i	0.0134984	−	0.00779329i
$575$	0.806319	+	1.39658i	0.0336258	+	0.0582416i
$576$	−0.190748	+	0.330386i	−0.00794784	+	0.0137661i
$577$		−	15.9410i		−	0.663632i	−0.943344	−	0.331816i	$-0.892339\pi$
$577$		−	15.9410i		−	0.663632i	0.943344	−	0.331816i	$-0.107661\pi$
$578$	−7.94599	−	4.58762i	−0.330510	−	0.190820i
$579$	22.4342	+	12.9524i	0.932334	+	0.538283i
$580$			36.6456i			1.52162i
$581$	−3.74664	+	6.48937i	−0.155437	+	0.269225i
$582$	−1.27034	−	2.20029i	−0.0526573	−	0.0912051i
$583$	7.40121	−	4.27309i	0.306527	−	0.176973i
$584$	−7.84216			−0.324511
$585$	8.27707	+	0.802381i	0.342215	+	0.0331744i
$586$	−5.13553			−0.212147
$587$	−8.60168	+	4.96618i	−0.355029	+	0.204976i	−0.666898	−	0.745149i	$-0.732378\pi$
$587$	−8.60168	+	4.96618i	−0.355029	+	0.204976i	0.311869	+	0.950125i	$0.399045\pi$
$588$	−3.44399	−	5.96517i	−0.142028	−	0.245999i
$589$	−19.3140	+	33.4528i	−0.795819	+	1.37840i
$590$		−	16.7964i		−	0.691499i
$591$	−14.3261	−	8.27120i	−0.589298	−	0.340232i
$592$	15.6523	+	9.03687i	0.643306	+	0.371413i
$593$		−	10.6309i		−	0.436558i	−0.975886	−	0.218279i	$-0.929956\pi$
$593$		−	10.6309i		−	0.436558i	0.975886	−	0.218279i	$-0.0700443\pi$
$594$	−0.305511	+	0.529161i	−0.0125353	+	0.0217117i
$595$	−5.44414	−	9.42953i	−0.223188	−	0.386573i
$596$	7.74110	−	4.46933i	0.317088	−	0.183071i
$597$	−4.50094			−0.184211
$598$	−11.0674	−	1.07288i	−0.452579	−	0.0438732i
$599$	41.9670			1.71473			0.857363	−	0.514712i	$-0.172101\pi$
$599$	41.9670			1.71473			0.857363	+	0.514712i	$0.172101\pi$
$600$	−0.613172	+	0.354015i	−0.0250326	+	0.0144526i
$601$	8.55788	+	14.8227i	0.349083	+	0.604630i	0.986087	−	0.166231i	$-0.0531597\pi$
$601$	8.55788	+	14.8227i	0.349083	+	0.604630i	−0.637004	+	0.770861i	$0.719826\pi$
$602$	−8.51285	+	14.7447i	−0.346958	+	0.600948i
$603$		−	11.7001i		−	0.476465i
$604$	−2.49275	−	1.43919i	−0.101429	−	0.0585599i
$605$	1.99741	+	1.15320i	0.0812061	+	0.0468844i
$606$			1.75560i			0.0713162i
$607$	−9.90505	+	17.1561i	−0.402034	+	0.696343i	−0.993971	−	0.109641i	$-0.965030\pi$
$607$	−9.90505	+	17.1561i	−0.402034	+	0.696343i	0.591938	+	0.805984i	$0.298363\pi$
$608$	16.1246	+	27.9286i	0.653938	+	1.13265i
$609$	−28.3529	+	16.3695i	−1.14892	+	0.663327i
$610$	5.75965			0.233202
$611$	−15.3499	−	33.7400i	−0.620991	−	1.36497i
$612$	−2.29109			−0.0926118
$613$	−22.1206	+	12.7714i	−0.893444	+	0.515830i	−0.875067	−	0.484001i	$-0.839183\pi$
$613$	−22.1206	+	12.7714i	−0.893444	+	0.515830i	−0.0183766	+	0.999831i	$0.505850\pi$
$614$	−4.56438	−	7.90573i	−0.184203	−	0.319049i
$615$	−0.210271	+	0.364200i	−0.00847895	+	0.0146860i
$616$		−	7.42743i		−	0.299260i
$617$	27.9933	+	16.1620i	1.12697	+	0.650656i	0.943171	−	0.332308i	$-0.107827\pi$
$617$	27.9933	+	16.1620i	1.12697	+	0.650656i	0.183799	+	0.982964i	$0.441161\pi$
$618$	2.24741	+	1.29754i	0.0904040	+	0.0521948i
$619$			19.2216i			0.772580i	0.922377	+	0.386290i	$0.126244\pi$
$619$			19.2216i			0.772580i	−0.922377	+	0.386290i	$0.873756\pi$
$620$	12.5657	−	21.7644i	0.504650	−	0.874079i
$621$	2.52358	+	4.37098i	0.101268	+	0.175401i
$622$	−15.5565	+	8.98154i	−0.623758	+	0.360127i
$623$	−28.7834			−1.15318
$624$	−0.660752	+	6.81608i	−0.0264513	+	0.272861i
$625$	−26.4955			−1.05982
$626$	−2.67076	+	1.54196i	−0.106745	+	0.0616292i
$627$	−2.88328	−	4.99398i	−0.115147	−	0.199441i
$628$	−13.1006	+	22.6909i	−0.522772	+	0.905467i
$629$			13.4030i			0.534412i
$630$	−4.09072	−	2.36178i	−0.162978	−	0.0940954i
$631$	31.5441	+	18.2120i	1.25575	+	0.725009i	0.972246	−	0.233961i	$-0.0751689\pi$
$631$	31.5441	+	18.2120i	1.25575	+	0.725009i	0.283506	+	0.958970i	$0.408502\pi$
$632$		−	30.3624i		−	1.20775i
$633$	6.08281	−	10.5357i	0.241770	−	0.418758i
$634$	5.93120	+	10.2731i	0.235558	+	0.407999i
$635$	−20.3925	+	11.7736i	−0.809252	+	0.467222i
$636$	13.9017			0.551237
$637$	−12.4238	−	8.87392i	−0.492250	−	0.351598i
$638$	−5.96826			−0.236286
$639$	4.64115	−	2.67957i	0.183601	−	0.106002i
$640$	−13.1673	−	22.8064i	−0.520482	−	0.901501i
$641$	−14.7880	+	25.6136i	−0.584091	+	1.01168i	0.410897	+	0.911682i	$0.365216\pi$
$641$	−14.7880	+	25.6136i	−0.584091	+	1.01168i	−0.994988	+	0.0999938i	$0.968118\pi$
$642$		−	5.25596i		−	0.207436i
$643$	−25.8761	−	14.9396i	−1.02045	−	0.589160i	−0.106219	−	0.994343i	$-0.533874\pi$
$643$	−25.8761	−	14.9396i	−1.02045	−	0.589160i	−0.914236	+	0.405183i	$0.867208\pi$
$644$	−23.8314	−	13.7591i	−0.939088	−	0.542183i
$645$		−	19.1738i		−	0.754967i
$646$	−2.48137	+	4.29785i	−0.0976281	+	0.169097i
$647$	7.97810	+	13.8185i	0.313652	+	0.543260i	0.979150	−	0.203139i	$-0.0651143\pi$
$647$	7.97810	+	13.8185i	0.313652	+	0.543260i	−0.665498	+	0.746399i	$0.731781\pi$
$648$	−1.91908	+	1.10798i	−0.0753886	+	0.0435256i
$649$	−11.9186			−0.467845
$650$	−0.409132	+	0.572800i	−0.0160475	+	0.0224671i
$651$	22.4523			0.879976
$652$	20.9677	−	12.1057i	0.821159	−	0.474096i
$653$	−7.09745	−	12.2931i	−0.277745	−	0.481068i	0.693079	−	0.720861i	$-0.256254\pi$
$653$	−7.09745	−	12.2931i	−0.277745	−	0.481068i	−0.970824	+	0.239794i	$0.922920\pi$
$654$	2.01095	−	3.48307i	0.0786344	−	0.136199i
$655$		−	11.4040i		−	0.445592i
$656$	−0.299915	−	0.173156i	−0.0117097	−	0.00676061i
$657$	3.06481	+	1.76947i	0.119570	+	0.0690335i
$658$			21.0550i			0.820810i
$659$	5.53394	−	9.58506i	0.215572	−	0.373381i	−0.737878	−	0.674934i	$-0.764172\pi$
$659$	5.53394	−	9.58506i	0.215572	−	0.373381i	0.953449	+	0.301554i	$0.0975052\pi$
$660$	1.87586	+	3.24909i	0.0730178	+	0.126471i
$661$	16.6505	−	9.61315i	0.647628	−	0.373908i	−0.139919	−	0.990163i	$-0.544684\pi$
$661$	16.6505	−	9.61315i	0.647628	−	0.373908i	0.787547	+	0.616255i	$0.211351\pi$
$662$	−15.9855			−0.621295
$663$	−4.62242	+	2.10296i	−0.179520	+	0.0816722i
$664$	−4.95403			−0.192254
$665$	38.6064	−	22.2894i	1.49709	−	0.864346i
$666$	2.90724	+	5.03549i	0.112653	+	0.195121i
$667$	−24.6495	+	42.6942i	−0.954433	+	1.65313i
$668$			28.8033i			1.11443i
$669$	−12.5417	−	7.24094i	−0.484889	−	0.279951i
$670$	14.2795	+	8.24427i	0.551665	+	0.318504i
$671$		−	4.08699i		−	0.157776i
$672$	9.37233	−	16.2334i	0.361545	−	0.626215i
$673$	0.900099	+	1.55902i	0.0346962	+	0.0600957i	0.882852	−	0.469651i	$-0.155620\pi$
$673$	0.900099	+	1.55902i	0.0346962	+	0.0600957i	−0.848156	+	0.529747i	$0.822287\pi$
$674$	5.42099	−	3.12981i	0.208809	−	0.120556i
$675$	0.319513			0.0122981
$676$	6.85881	+	20.0033i	0.263801	+	0.769356i
$677$	−43.6152			−1.67627			−0.838133	−	0.545466i	$-0.816353\pi$
$677$	−43.6152			−1.67627			−0.838133	+	0.545466i	$0.816353\pi$
$678$	−1.52151	+	0.878446i	−0.0584334	+	0.0337365i
$679$	−6.96850	−	12.0698i	−0.267426	−	0.463196i
$680$	3.59929	−	6.23415i	0.138026	−	0.239069i
$681$		−	9.86366i		−	0.377976i
$682$	3.54465	+	2.04650i	0.135731	+	0.0783646i
$683$	14.4961	+	8.36933i	0.554678	+	0.320244i	0.751007	−	0.660295i	$-0.229569\pi$
$683$	14.4961	+	8.36933i	0.554678	+	0.320244i	−0.196328	+	0.980538i	$0.562902\pi$
$684$		−	9.38018i		−	0.358660i
$685$	−12.4037	+	21.4839i	−0.473922	+	0.820857i
$686$	−2.83194	−	4.90506i	−0.108124	−	0.187276i
$687$	−5.89146	+	3.40144i	−0.224773	+	0.129773i
$688$	15.7894			0.601966
$689$	28.0475	−	12.7601i	1.06853	−	0.486123i
$690$	−7.11280			−0.270780
$691$	2.34472	−	1.35373i	0.0891975	−	0.0514982i	−0.454738	−	0.890625i	$-0.650267\pi$
$691$	2.34472	−	1.35373i	0.0891975	−	0.0514982i	0.543935	+	0.839127i	$0.316934\pi$
$692$	3.08092	+	5.33631i	0.117119	+	0.202856i
$693$	−1.67589	+	2.90273i	−0.0636619	+	0.110266i
$694$			9.80033i			0.372016i
$695$	−46.1994	−	26.6733i	−1.75244	−	1.01177i
$696$	−18.7449	−	10.8224i	−0.710525	−	0.410222i
$697$		−	0.256816i		−	0.00972758i
$698$	−0.769938	+	1.33357i	−0.0291426	+	0.0504764i
$699$	−6.81977	−	11.8122i	−0.257947	−	0.446778i
$700$	−1.50866	+	0.871023i	−0.0570218	+	0.0329216i
$701$	2.09380			0.0790818			0.0395409	−	0.999218i	$-0.487410\pi$
$701$	2.09380			0.0790818			0.0395409	+	0.999218i	$0.487410\pi$
$702$	−1.28049	+	1.79273i	−0.0483289	+	0.0676622i
$703$	−54.8745			−2.06963
$704$	−0.330386	+	0.190748i	−0.0124519	+	0.00718909i
$705$	−11.8557	−	20.5348i	−0.446513	−	0.773383i
$706$	−2.11494	+	3.66319i	−0.0795969	+	0.137866i
$707$			9.63039i			0.362188i
$708$	−16.7900	−	9.69369i	−0.631006	−	0.364311i
$709$	16.0045	+	9.24017i	0.601060	+	0.347022i	0.769458	−	0.638697i	$-0.220526\pi$
$709$	16.0045	+	9.24017i	0.601060	+	0.347022i	−0.168399	+	0.985719i	$0.553860\pi$
$710$			7.55244i			0.283438i
$711$	−6.85083	+	11.8660i	−0.256926	+	0.445009i
$712$	−9.51478	−	16.4801i	−0.356581	−	0.617617i
$713$	29.2795	−	16.9045i	1.09653	−	0.633080i
$714$	2.88457			0.107952
$715$	6.76696	+	4.83342i	0.253070	+	0.180760i
$716$	−10.4655			−0.391114
$717$	−14.2443	+	8.22393i	−0.531962	+	0.307128i
$718$	3.41585	+	5.91643i	0.127478	+	0.220799i
$719$	−23.3023	+	40.3608i	−0.869031	+	1.50521i	−0.00604266	+	0.999982i	$0.501923\pi$
$719$	−23.3023	+	40.3608i	−0.869031	+	1.50521i	−0.862988	+	0.505224i	$0.831410\pi$
$720$			4.38056i			0.163254i
$721$	12.3282	+	7.11771i	0.459128	+	0.265077i
$722$	−7.54222	−	4.35450i	−0.280692	−	0.162058i
$723$		−	29.1560i		−	1.08432i
$724$	−3.42933	+	5.93977i	−0.127450	+	0.220750i
$725$	1.56045	+	2.70278i	0.0579536	+	0.100379i
$726$	−0.529161	+	0.305511i	−0.0196390	+	0.0113386i
$727$	12.0926			0.448491			0.224245	−	0.974533i	$-0.428008\pi$
$727$	12.0926			0.448491			0.224245	+	0.974533i	$0.428008\pi$
$728$	2.58395	−	26.6550i	0.0957674	−	0.987901i
$729$	1.00000			0.0370370
$730$	−4.31913	+	2.49365i	−0.159858	+	0.0922941i
$731$	5.85450	+	10.1403i	0.216536	+	0.375052i
$732$	3.32405	−	5.75743i	0.122861	−	0.212801i
$733$			4.24689i			0.156863i	0.996920	+	0.0784313i	$0.0249911\pi$
$733$			4.24689i			0.156863i	−0.996920	+	0.0784313i	$0.975009\pi$
$734$	10.7470	+	6.20480i	0.396680	+	0.229023i
$735$	−8.45793	−	4.88319i	−0.311975	−	0.180119i
$736$		−	28.2260i		−	1.04042i
$737$	5.85005	−	10.1326i	0.215489	−	0.373238i
$738$	−0.0557058	−	0.0964853i	−0.00205056	−	0.00355167i
$739$	−10.2039	+	5.89120i	−0.375355	+	0.216711i	−0.675795	−	0.737089i	$-0.736200\pi$
$739$	−10.2039	+	5.89120i	−0.375355	+	0.216711i	0.300440	+	0.953801i	$0.402866\pi$
$740$	35.7014			1.31241
$741$	−8.60993	−	18.9251i	−0.316294	−	0.695232i
$742$	−17.5027			−0.642545
$743$	10.8129	−	6.24286i	0.396689	−	0.229028i	−0.288366	−	0.957520i	$-0.593112\pi$
$743$	10.8129	−	6.24286i	0.396689	−	0.229028i	0.685054	+	0.728492i	$0.259779\pi$
$744$	7.42195	+	12.8552i	0.272102	+	0.471294i
$745$	6.33699	−	10.9760i	0.232169	−	0.402129i
$746$			8.20262i			0.300319i
$747$	1.93610	+	1.11781i	0.0708380	+	0.0408984i
$748$	−1.98414	−	1.14555i	−0.0725474	−	0.0418853i
$749$		−	28.8318i		−	1.05349i
$750$	3.29802	−	5.71235i	0.120427	−	0.208585i
$751$	1.28919	+	2.23295i	0.0470434	+	0.0814815i	0.888588	−	0.458706i	$-0.151687\pi$
$751$	1.28919	+	2.23295i	0.0470434	+	0.0814815i	−0.841545	+	0.540187i	$0.818353\pi$
$752$	16.9101	−	9.76308i	0.616650	−	0.356023i
$753$	−16.2178			−0.591008
$754$	−21.4185	−	2.07631i	−0.780014	−	0.0756148i
$755$	−4.08122			−0.148531
$756$	−4.72173	+	2.72609i	−0.171728	+	0.0991470i
$757$	22.1261	+	38.3235i	0.804187	+	1.39289i	0.916838	+	0.399258i	$0.130732\pi$
$757$	22.1261	+	38.3235i	0.804187	+	1.39289i	−0.112651	+	0.993635i	$0.535934\pi$
$758$	8.06325	−	13.9660i	0.292870	−	0.507267i
$759$			5.04717i			0.183201i
$760$	25.5238	+	14.7362i	0.925847	+	0.534538i
$761$	−28.4841	−	16.4453i	−1.03255	−	0.596141i	−0.114834	−	0.993385i	$-0.536633\pi$
$761$	−28.4841	−	16.4453i	−1.03255	−	0.596141i	−0.917713	+	0.397244i	$0.869967\pi$
$762$		−	6.23823i		−	0.225987i
$763$	11.0312	−	19.1065i	0.399354	−	0.691702i
$764$	22.2036	+	38.4577i	0.803298	+	1.39135i
$765$	−2.81329	+	1.62425i	−0.101715	+	0.0587250i
$766$	−9.58650			−0.346374
$767$	−42.7725	−	4.14638i	−1.54443	−	0.149717i
$768$	6.21365			0.224216
$769$	34.1630	−	19.7240i	1.23195	−	0.711266i	0.264513	−	0.964382i	$-0.414789\pi$
$769$	34.1630	−	19.7240i	1.23195	−	0.711266i	0.967436	+	0.253116i	$0.0814554\pi$
$770$	−2.36178	−	4.09072i	−0.0851125	−	0.147419i
$771$	−5.03662	+	8.72368i	−0.181389	+	0.314176i
$772$			42.1381i			1.51658i
$773$	−38.6470	−	22.3128i	−1.39004	−	0.802537i	−0.396717	−	0.917941i	$-0.629851\pi$
$773$	−38.6470	−	22.3128i	−1.39004	−	0.802537i	−0.993319	+	0.115404i	$0.963184\pi$
$774$	4.39906	+	2.53980i	0.158121	+	0.0912911i
$775$		−	2.14030i		−	0.0768817i
$776$	4.60708	−	7.97970i	0.165385	−	0.286455i
$777$	15.9478	+	27.6224i	0.572123	+	0.990947i
$778$	9.25441	−	5.34304i	0.331787	−	0.191557i
$779$	1.05145			0.0376723
$780$	5.60162	+	12.3127i	0.200570	+	0.440865i
$781$	5.35913			0.191765
$782$	3.76169	−	2.17181i	0.134518	−	0.0776638i
$783$	4.88383	+	8.45904i	0.174534	+	0.302302i
$784$	4.02125	−	6.96501i	0.143616	−	0.248750i
$785$			37.1504i			1.32595i
$786$	2.61643	+	1.51060i	0.0933250	+	0.0538812i
$787$	33.3468	+	19.2528i	1.18868	+	0.686287i	0.958007	−	0.286744i	$-0.0925728\pi$
$787$	33.3468	+	19.2528i	1.18868	+	0.686287i	0.230676	+	0.973031i	$0.425906\pi$
$788$		−	26.9087i		−	0.958584i
$789$	6.08509	−	10.5397i	0.216635	−	0.375223i
$790$	−9.65464	−	16.7223i	−0.343497	−	0.594954i
$791$	−8.34632	+	4.81875i	−0.296761	+	0.171335i
$792$	−2.21596			−0.0787409
$793$	1.42183	−	14.6671i	0.0504907	−	0.520844i
$794$	4.21955			0.149746
$795$	17.0702	−	9.85549i	0.605418	−	0.349538i
$796$	−3.66074	−	6.34058i	−0.129751	−	0.224736i
$797$	9.47820	−	16.4167i	0.335735	−	0.581510i	−0.647891	−	0.761733i	$-0.724349\pi$
$797$	9.47820	−	16.4167i	0.335735	−	0.581510i	0.983626	+	0.180223i	$0.0576819\pi$
$798$			11.8100i			0.418069i
$799$	12.5401	+	7.24003i	0.443637	+	0.256134i
$800$	−1.54747	−	0.893430i	−0.0547112	−	0.0315875i
$801$			8.58748i			0.303424i
$802$	−5.62988	+	9.75124i	−0.198798	+	0.344328i
$803$	1.76947	+	3.06481i	0.0624432	+	0.108155i
$804$	16.4822	−	9.51599i	0.581282	−	0.335603i
$805$	−39.0175			−1.37519
$806$	12.0088	+	8.57749i	0.422992	+	0.302129i
$807$	3.22011			0.113353
$808$	−5.51393	+	3.18347i	−0.193979	+	0.111994i
$809$	8.19972	+	14.2023i	0.288287	+	0.499327i	0.973401	−	0.229109i	$-0.0735811\pi$
$809$	8.19972	+	14.2023i	0.288287	+	0.499327i	−0.685114	+	0.728436i	$0.740248\pi$
$810$	−0.704633	+	1.22046i	−0.0247583	+	0.0428826i
$811$		−	49.8949i		−	1.75205i	−0.482270	−	0.876023i	$-0.660187\pi$
$811$		−	49.8949i		−	1.75205i	0.482270	−	0.876023i	$-0.339813\pi$
$812$	−46.1203	−	26.6276i	−1.61850	−	0.934444i
$813$	16.9220	+	9.76990i	0.593479	+	0.342645i
$814$			5.81448i			0.203798i
$815$	17.1645	−	29.7298i	0.601247	−	1.04139i
$816$	−1.33755	−	2.31671i	−0.0468238	−	0.0811011i
$817$	−41.5164	+	23.9695i	−1.45247	+	0.838586i
$818$	−0.568760			−0.0198862
$819$	−7.02416	+	9.83408i	−0.245444	+	0.343631i
$820$	−0.684076			−0.0238890
$821$	7.89908	−	4.56053i	0.275680	−	0.159164i	−0.355786	−	0.934567i	$-0.615787\pi$
$821$	7.89908	−	4.56053i	0.275680	−	0.159164i	0.631466	+	0.775404i	$0.282454\pi$
$822$	−3.28604	−	5.69159i	−0.114614	−	0.198517i
$823$	18.1912	−	31.5081i	0.634107	−	1.09830i	−0.352597	−	0.935775i	$-0.614701\pi$
$823$	18.1912	−	31.5081i	0.634107	−	1.09830i	0.986704	−	0.162530i	$-0.0519653\pi$
$824$			9.41146i			0.327864i
$825$	0.276707	+	0.159757i	0.00963369	+	0.00556201i
$826$	21.1392	+	12.2047i	0.735526	+	0.424656i
$827$			13.0565i			0.454018i	0.973893	+	0.227009i	$0.0728947\pi$
$827$			13.0565i			0.454018i	−0.973893	+	0.227009i	$0.927105\pi$
$828$	−4.10499	+	7.11006i	−0.142658	+	0.247092i
$829$	−10.0482	−	17.4040i	−0.348989	−	0.604466i	0.637081	−	0.770797i	$-0.280142\pi$
$829$	−10.0482	−	17.4040i	−0.348989	−	0.604466i	−0.986070	+	0.166330i	$0.946808\pi$
$830$	−2.72847	+	1.57528i	−0.0947067	+	0.0546789i
$831$	−0.336472			−0.0116721
$832$	−1.25202	+	0.569605i	−0.0434061	+	0.0197475i
$833$	5.96410			0.206644
$834$	12.2393	−	7.06638i	0.423813	−	0.244689i
$835$	20.4199	+	35.3683i	0.706659	+	1.22397i
$836$	4.69009	−	8.12347i	0.162210	−	0.280956i
$837$		−	6.69862i		−	0.231538i
$838$	−13.7658	−	7.94768i	−0.475531	−	0.274548i
$839$	−0.859768	−	0.496388i	−0.0296825	−	0.0171372i	0.485085	−	0.874467i	$-0.338789\pi$
$839$	−0.859768	−	0.496388i	−0.0296825	−	0.0171372i	−0.514768	+	0.857330i	$0.672122\pi$
$840$		−	17.1307i		−	0.591065i
$841$	−33.2036	+	57.5104i	−1.14495	+	1.98312i
$842$	3.14712	+	5.45097i	0.108457	+	0.187853i
$843$	−9.74141	+	5.62421i	−0.335512	+	0.193708i
$844$	19.7892			0.681173
$845$	22.6033	+	19.7000i	0.777576	+	0.677700i
$846$	6.28174			0.215971
$847$	−2.90273	+	1.67589i	−0.0997390	+	0.0575843i
$848$	8.11589	+	14.0571i	0.278701	+	0.482724i
$849$	14.2113	−	24.6148i	0.487732	−	0.844777i
$850$		−	0.274975i		−	0.00943157i
$851$	41.5942	+	24.0144i	1.42583	+	0.823204i
$852$	7.54953	+	4.35872i	0.258643	+	0.149327i
$853$			11.6993i			0.400577i	0.979737	+	0.200289i	$0.0641880\pi$
$853$			11.6993i			0.400577i	−0.979737	+	0.200289i	$0.935812\pi$
$854$	−4.18510	+	7.24881i	−0.143211	+	0.248049i
$855$	−6.65001	−	11.5182i	−0.227426	−	0.393913i
$856$	16.5078	−	9.53077i	0.564224	−	0.325755i
$857$	−12.0788			−0.412604			−0.206302	−	0.978488i	$-0.566143\pi$
$857$	−12.0788			−0.412604			−0.206302	+	0.978488i	$0.566143\pi$
$858$	−2.00530	+	0.912305i	−0.0684598	+	0.0311456i
$859$	−19.8374			−0.676845			−0.338422	−	0.940994i	$-0.609893\pi$
$859$	−19.8374			−0.676845			−0.338422	+	0.940994i	$0.609893\pi$
$860$	27.0105	−	15.5945i	0.921052	−	0.531769i
$861$	−0.305576	−	0.529274i	−0.0104140	−	0.0180376i
$862$	1.82177	−	3.15540i	0.0620499	−	0.107474i
$863$			23.3431i			0.794608i	0.917687	+	0.397304i	$0.130054\pi$
$863$			23.3431i			0.794608i	−0.917687	+	0.397304i	$0.869946\pi$
$864$	−4.84320	−	2.79622i	−0.164769	−	0.0951294i
$865$	7.56628	+	4.36840i	0.257261	+	0.148530i
$866$		−	1.81767i		−	0.0617670i
$867$	−7.50811	+	13.0044i	−0.254989	+	0.441653i
$868$	18.2611	+	31.6291i	0.619821	+	1.07356i
$869$	−11.8660	+	6.85083i	−0.402526	+	0.232399i
$870$	−13.7652			−0.466685
$871$	24.5193	−	34.3279i	0.830804	−	1.16316i
$872$	14.5860			0.493946
$873$	−3.60101	+	2.07904i	−0.121876	+	0.0703649i
$874$	8.89183	+	15.4011i	0.300771	+	0.520950i
$875$	18.0914	−	31.3353i	0.611602	−	1.05933i
$876$			5.75662i			0.194498i
$877$	13.8154	+	7.97632i	0.466513	+	0.269341i	0.714779	−	0.699351i	$-0.246527\pi$
$877$	13.8154	+	7.97632i	0.466513	+	0.269341i	−0.248266	+	0.968692i	$0.579861\pi$
$878$	−15.4779	−	8.93615i	−0.522353	−	0.301580i
$879$			8.40482i			0.283488i
$880$	−2.19028	+	3.79368i	−0.0738344	+	0.127885i
$881$	26.7889	+	46.3998i	0.902542	+	1.56325i	0.824183	+	0.566323i	$0.191635\pi$
$881$	26.7889	+	46.3998i	0.902542	+	1.56325i	0.0783588	+	0.996925i	$0.475032\pi$
$882$	2.24071	−	1.29367i	0.0754485	−	0.0435602i
$883$	−19.8873			−0.669261			−0.334630	−	0.942349i	$-0.608611\pi$
$883$	−19.8873			−0.669261			−0.334630	+	0.942349i	$0.608611\pi$
$884$	−6.72202	−	4.80132i	−0.226086	−	0.161486i
$885$	−27.4891			−0.924036
$886$	−8.96412	+	5.17544i	−0.301156	+	0.173872i
$887$	−10.0467	−	17.4015i	−0.337337	−	0.584284i	0.646594	−	0.762834i	$-0.276193\pi$
$887$	−10.0467	−	17.4015i	−0.337337	−	0.584284i	−0.983931	+	0.178550i	$0.942859\pi$
$888$	−10.5436	+	18.2620i	−0.353818	+	0.612832i
$889$		−	34.2200i		−	1.14770i
$890$	−10.4807	−	6.05102i	−0.351313	−	0.202831i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$		−	23.5570i		−	0.788746i
$893$	−29.6421	+	51.3417i	−0.991936	+	1.71808i
$894$	1.67882	+	2.90780i	0.0561481	+	0.0972514i
$895$	−12.8509	+	7.41945i	−0.429557	+	0.248005i
$896$	38.2706			1.27853
$897$	−1.75587	+	18.1129i	−0.0586268	+	0.604773i
$898$	20.6876			0.690353
$899$	56.6639	−	32.7149i	1.88985	−	1.09110i
$900$	0.259868	+	0.450105i	0.00866228	+	0.0150035i
$901$	−6.01852	+	10.4244i	−0.200506	+	0.347287i
$902$		−	0.111412i		−	0.00370960i
$903$	24.1312	+	13.9321i	0.803035	+	0.463633i
$904$	−5.51800	−	3.18582i	−0.183526	−	0.105959i
$905$			9.72479i			0.323263i
$906$	0.540606	−	0.936357i	0.0179604	−	0.0311084i
$907$	−4.37087	−	7.57057i	−0.145132	−	0.251377i	0.784290	−	0.620394i	$-0.213027\pi$
$907$	−4.37087	−	7.57057i	−0.145132	−	0.251377i	−0.929422	+	0.369018i	$0.879694\pi$
$908$	13.8952	−	8.02237i	0.461127	−	0.266232i
$909$	2.87321			0.0952984
$910$	−7.05265	−	15.5021i	−0.233793	−	0.513890i
$911$	−19.7419			−0.654080			−0.327040	−	0.945011i	$-0.606051\pi$
$911$	−19.7419			−0.654080			−0.327040	+	0.945011i	$0.606051\pi$
$912$	9.48508	−	5.47621i	0.314082	−	0.181336i
$913$	1.11781	+	1.93610i	0.0369940	+	0.0640754i
$914$	4.63999	−	8.03669i	0.153477	−	0.265830i
$915$		−	9.42626i		−	0.311623i
$916$	−9.58336	−	5.53295i	−0.316643	−	0.182814i
$917$	14.3525	+	8.28643i	0.473962	+	0.273642i
$918$		−	0.860606i		−	0.0284042i
$919$	−14.5504	+	25.2020i	−0.479973	+	0.831337i	−0.999736	−	0.0229733i	$-0.992687\pi$
$919$	−14.5504	+	25.2020i	−0.479973	+	0.831337i	0.519764	+	0.854310i	$0.326020\pi$
$920$	−12.8978	−	22.3397i	−0.425229	−	0.736518i
$921$	−12.9385	+	7.47007i	−0.426339	+	0.246147i
$922$	−0.777129			−0.0255934
$923$	19.2325	+	1.86440i	0.633045	+	0.0613675i
$924$	−5.45219			−0.179364
$925$	2.63314	−	1.52024i	0.0865770	−	0.0499853i
$926$	−4.81373	−	8.33762i	−0.158189	−	0.273991i
$927$	2.12356	−	3.67811i	0.0697468	−	0.120805i
$928$		−	54.6251i		−	1.79316i
$929$	−16.2032	−	9.35490i	−0.531609	−	0.306924i	0.210063	−	0.977688i	$-0.432633\pi$
$929$	−16.2032	−	9.35490i	−0.531609	−	0.306924i	−0.741671	+	0.670764i	$0.765967\pi$
$930$	8.17539	+	4.72007i	0.268082	+	0.154777i
$931$			24.4182i			0.800275i
$932$	11.0934	−	19.2143i	0.363376	−	0.629386i
$933$	14.6992	+	25.4598i	0.481231	+	0.833516i
$934$	0.922297	−	0.532488i	0.0301785	−	0.0174236i
$935$	−3.24850			−0.106237
$936$	−7.95249	−	0.770917i	−0.259935	−	0.0251982i
$937$	−1.35447			−0.0442486			−0.0221243	−	0.999755i	$-0.507043\pi$
$937$	−1.35447			−0.0442486			−0.0221243	+	0.999755i	$0.507043\pi$
$938$	−20.7517	+	11.9810i	−0.677566	+	0.391193i
$939$	2.52358	+	4.37097i	0.0823539	+	0.142641i
$940$	19.2852	−	33.4029i	0.629013	−	1.08948i
$941$			15.6522i			0.510247i	0.966908	+	0.255124i	$0.0821162\pi$
$941$			15.6522i			0.510247i	−0.966908	+	0.255124i	$0.917884\pi$
$942$	−8.52344	−	4.92101i	−0.277709	−	0.160335i
$943$	−0.796989	−	0.460142i	−0.0259535	−	0.0149843i
$944$		−	22.6370i		−	0.736771i
$945$	−3.86529	+	6.69488i	−0.125738	+	0.217784i
$946$	2.53980	+	4.39906i	0.0825759	+	0.143026i
$947$	43.7643	−	25.2673i	1.42215	−	0.821078i	0.425666	−	0.904880i	$-0.360040\pi$
$947$	43.7643	−	25.2673i	1.42215	−	0.821078i	0.996482	+	0.0838022i	$0.0267064\pi$
$948$	−22.2878			−0.723875
$949$	5.28392	+	11.6143i	0.171523	+	0.377018i
$950$	1.12580			0.0365259
$951$	16.8130	−	9.70702i	0.545200	−	0.314772i
$952$	5.23066	+	9.05977i	0.169527	+	0.293629i
$953$	−22.8613	+	39.5970i	−0.740551	+	1.28267i	0.211693	+	0.977336i	$0.432102\pi$
$953$	−22.8613	+	39.5970i	−0.740551	+	1.28267i	−0.952245	+	0.305336i	$0.901231\pi$
$954$			5.22191i			0.169066i
$955$	54.5287	+	31.4822i	1.76451	+	1.01874i
$956$	−23.1705	−	13.3775i	−0.749386	−	0.432658i
$957$			9.76766i			0.315744i
$958$	4.86978	−	8.43471i	0.157336	−	0.272513i
$959$	−18.0257	−	31.2214i	−0.582080	−	1.00819i
$960$	−0.762004	+	0.439943i	−0.0245936	+	0.0141991i
$961$	−13.8715			−0.447468
$962$	−2.02281	+	20.8666i	−0.0652181	+	0.672766i
$963$	−8.60192			−0.277193
$964$	41.0728	−	23.7134i	1.32286	−	0.763756i
$965$	29.8735	+	51.7424i	0.961662	+	1.66565i
$966$	5.16833	−	8.95182i	0.166288	−	0.288020i
$967$			1.22663i			0.0394459i	0.999805	+	0.0197230i	$0.00627842\pi$
$967$			1.22663i			0.0394459i	−0.999805	+	0.0197230i	$0.993722\pi$
$968$	−1.91908	−	1.10798i	−0.0616816	−	0.0356119i
$969$	7.03388	+	4.06101i	0.225961	+	0.130458i
$970$		−	5.85985i		−	0.188148i
$971$	−1.43098	+	2.47854i	−0.0459224	+	0.0795400i	−0.888073	−	0.459703i	$-0.847956\pi$
$971$	−1.43098	+	2.47854i	−0.0459224	+	0.0795400i	0.842151	+	0.539243i	$0.181289\pi$
$972$	0.813326	+	1.40872i	0.0260874	+	0.0451848i
$973$	67.1393	−	38.7629i	2.15239	−	1.24268i
$974$	−10.4006			−0.333256
$975$	0.937447	+	0.669587i	0.0300223	+	0.0214439i
$976$	7.76242			0.248469
$977$	−39.6337	+	22.8825i	−1.26799	+	0.732077i	−0.974608	−	0.223917i	$-0.928115\pi$
$977$	−39.6337	+	22.8825i	−1.26799	+	0.732077i	−0.293386	+	0.955994i	$0.594782\pi$
$978$	4.54729	+	7.87614i	0.145406	+	0.251851i
$979$	−4.29374	+	7.43698i	−0.137229	+	0.237687i
$980$		−	15.8865i		−	0.507475i
$981$	−5.70040	−	3.29113i	−0.182000	−	0.105078i
$982$	9.52150	+	5.49724i	0.303843	+	0.175424i
$983$			16.4103i			0.523409i	0.965148	+	0.261704i	$0.0842845\pi$
$983$			16.4103i			0.523409i	−0.965148	+	0.261704i	$0.915715\pi$
$984$	0.202026	−	0.349919i	0.00644034	−	0.0111550i
$985$	−19.0767	−	33.0419i	−0.607836	−	1.05280i
$986$	7.27991	−	4.20306i	0.231839	−	0.133853i
$987$	34.4587			1.09683
$988$	19.6576	−	27.5213i	0.625390	−	0.875569i
$989$	41.9585			1.33420
$990$	−1.22046	+	0.704633i	−0.0387888	+	0.0223947i
$991$	−23.8560	−	41.3197i	−0.757809	−	1.31256i	−0.943965	−	0.330044i	$-0.892936\pi$
$991$	−23.8560	−	41.3197i	−0.757809	−	1.31256i	0.186156	−	0.982520i	$-0.440397\pi$
$992$	−18.7308	+	32.4427i	−0.594704	+	1.03006i
$993$			26.1620i			0.830225i
$994$	−9.50513	−	5.48779i	−0.301484	−	0.174062i
$995$	−8.99022	−	5.19051i	−0.285009	−	0.164550i
$996$			3.63656i			0.115229i
$997$	4.24500	−	7.35255i	0.134440	−	0.232858i	−0.790943	−	0.611890i	$-0.790410\pi$
$997$	4.24500	−	7.35255i	0.134440	−	0.232858i	0.925384	+	0.379032i	$0.123743\pi$
$998$	−3.93610	−	6.81753i	−0.124595	−	0.215805i
$999$	8.24109	−	4.75800i	0.260737	−	0.150536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.6	✓	24
13.2	odd	12		5577.2.a.z.1.6		12
13.4	even	6	inner	429.2.s.a.199.6	yes	24
13.11	odd	12		5577.2.a.be.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.6	✓	24	1.1	even	1	trivial
429.2.s.a.199.6	yes	24	13.4	even	6	inner
5577.2.a.z.1.6		12	13.2	odd	12
5577.2.a.be.1.7		12	13.11	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)

\(f(q)\)	\(=\)	\(q+(-0.529161 + 0.305511i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.813326 + 1.40872i) q^{4} +2.30641i q^{5} +(-0.529161 - 0.305511i) q^{6} +(-2.90273 - 1.67589i) q^{7} -2.21596i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.529161 + 0.305511i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.813326 + 1.40872i) q^{4} +2.30641i q^{5} +(-0.529161 - 0.305511i) q^{6} +(-2.90273 - 1.67589i) q^{7} -2.21596i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.704633 - 1.22046i) q^{10} +(-0.866025 + 0.500000i) q^{11} -1.62665 q^{12} +(-3.28188 + 1.49308i) q^{13} +2.04801 q^{14} +(-1.99741 + 1.15320i) q^{15} +(-0.949651 - 1.64484i) q^{16} +(0.704235 - 1.21977i) q^{17} -0.611022i q^{18} +(4.99398 + 2.88328i) q^{19} +(-3.24909 - 1.87586i) q^{20} -3.35178i q^{21} +(0.305511 - 0.529161i) q^{22} +(-2.52358 - 4.37098i) q^{23} +(1.91908 - 1.10798i) q^{24} -0.319513 q^{25} +(1.28049 - 1.79273i) q^{26} -1.00000 q^{27} +(4.72173 - 2.72609i) q^{28} +(-4.88383 - 8.45904i) q^{29} +(0.704633 - 1.22046i) q^{30} +6.69862i q^{31} +(4.84320 + 2.79622i) q^{32} +(-0.866025 - 0.500000i) q^{33} +0.860606i q^{34} +(3.86529 - 6.69488i) q^{35} +(-0.813326 - 1.40872i) q^{36} +(-8.24109 + 4.75800i) q^{37} -3.52349 q^{38} +(-2.93398 - 2.09565i) q^{39} +5.11092 q^{40} +(0.157908 - 0.0911683i) q^{41} +(1.02401 + 1.77363i) q^{42} +(-4.15664 + 7.19950i) q^{43} -1.62665i q^{44} +(-1.99741 - 1.15320i) q^{45} +(2.67076 + 1.54197i) q^{46} +10.2807i q^{47} +(0.949651 - 1.64484i) q^{48} +(2.11723 + 3.66714i) q^{49} +(0.169074 - 0.0976148i) q^{50} +1.40847 q^{51} +(0.565900 - 5.83761i) q^{52} -8.54619 q^{53} +(0.529161 - 0.305511i) q^{54} +(-1.15320 - 1.99741i) q^{55} +(-3.71372 + 6.43235i) q^{56} +5.76656i q^{57} +(5.16866 + 2.98413i) q^{58} +(10.3218 + 5.95929i) q^{59} -3.75172i q^{60} +(-2.04349 + 3.53944i) q^{61} +(-2.04650 - 3.54465i) q^{62} +(2.90273 - 1.67589i) q^{63} +0.381496 q^{64} +(-3.44365 - 7.56934i) q^{65} +0.611022 q^{66} +(-10.1326 + 5.85005i) q^{67} +(1.14555 + 1.98414i) q^{68} +(2.52358 - 4.37098i) q^{69} +4.72355i q^{70} +(-4.64115 - 2.67957i) q^{71} +(1.91908 + 1.10798i) q^{72} -3.53894i q^{73} +(2.90724 - 5.03549i) q^{74} +(-0.159757 - 0.276707i) q^{75} +(-8.12347 + 4.69009i) q^{76} +3.35178 q^{77} +(2.19279 + 0.212570i) q^{78} +13.7017 q^{79} +(3.79368 - 2.19028i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0557058 + 0.0964853i) q^{82} -2.23561i q^{83} +(4.72173 + 2.72609i) q^{84} +(2.81329 + 1.62425i) q^{85} -5.07959i q^{86} +(4.88383 - 8.45904i) q^{87} +(1.10798 + 1.91908i) q^{88} +(7.43698 - 4.29374i) q^{89} +1.40927 q^{90} +(12.0286 + 1.16606i) q^{91} +8.20999 q^{92} +(-5.80117 + 3.34931i) q^{93} +(-3.14087 - 5.44014i) q^{94} +(-6.65001 + 11.5182i) q^{95} +5.59244i q^{96} +(3.60101 + 2.07904i) q^{97} +(-2.24071 - 1.29367i) 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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