LMFDB - Embedded newform 429.2.s.b.166.12

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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.12
Character	$\chi$	$=$	429.166
Dual form			429.2.s.b.199.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80882 - 1.04432i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.18121 - 2.04591i) q^{4} -2.92121i q^{5} +(-1.80882 - 1.04432i) q^{6} +(0.684943 + 0.395452i) q^{7} -0.756961i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.80882 - 1.04432i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.18121 - 2.04591i) q^{4} -2.92121i q^{5} +(-1.80882 - 1.04432i) q^{6} +(0.684943 + 0.395452i) q^{7} -0.756961i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.05068 - 5.28394i) q^{10} +(-0.866025 + 0.500000i) q^{11} -2.36242 q^{12} +(1.90810 - 3.05928i) q^{13} +1.65191 q^{14} +(-2.52985 + 1.46061i) q^{15} +(1.57191 + 2.72263i) q^{16} +(0.549933 - 0.952512i) q^{17} +2.08864i q^{18} +(-6.90721 - 3.98788i) q^{19} +(-5.97655 - 3.45057i) q^{20} -0.790904i q^{21} +(-1.04432 + 1.80882i) q^{22} +(2.75257 + 4.76759i) q^{23} +(-0.655547 + 0.378480i) q^{24} -3.53350 q^{25} +(0.256529 - 7.52633i) q^{26} +1.00000 q^{27} +(1.61812 - 0.934223i) q^{28} +(4.25914 + 7.37705i) q^{29} +(-3.05068 + 5.28394i) q^{30} +2.39900i q^{31} +(6.99768 + 4.04011i) q^{32} +(0.866025 + 0.500000i) q^{33} -2.29722i q^{34} +(1.15520 - 2.00087i) q^{35} +(1.18121 + 2.04591i) q^{36} +(-0.737862 + 0.426005i) q^{37} -16.6585 q^{38} +(-3.60346 - 0.122821i) q^{39} -2.21125 q^{40} +(5.62044 - 3.24496i) q^{41} +(-0.825957 - 1.43060i) q^{42} +(0.929332 - 1.60965i) q^{43} +2.36242i q^{44} +(2.52985 + 1.46061i) q^{45} +(9.95777 + 5.74912i) q^{46} -2.87688i q^{47} +(1.57191 - 2.72263i) q^{48} +(-3.18724 - 5.52045i) q^{49} +(-6.39144 + 3.69010i) q^{50} -1.09987 q^{51} +(-4.00516 - 7.51744i) q^{52} +12.8446 q^{53} +(1.80882 - 1.04432i) q^{54} +(1.46061 + 2.52985i) q^{55} +(0.299342 - 0.518475i) q^{56} +7.97576i q^{57} +(15.4080 + 8.89582i) q^{58} +(4.73394 + 2.73314i) q^{59} +6.90113i q^{60} +(0.570486 - 0.988111i) q^{61} +(2.50532 + 4.33935i) q^{62} +(-0.684943 + 0.395452i) q^{63} +10.5890 q^{64} +(-8.93680 - 5.57396i) q^{65} +2.08864 q^{66} +(-0.866490 + 0.500268i) q^{67} +(-1.29917 - 2.25023i) q^{68} +(2.75257 - 4.76759i) q^{69} -4.82560i q^{70} +(-6.39988 - 3.69497i) q^{71} +(0.655547 + 0.378480i) q^{72} +12.6053i q^{73} +(-0.889770 + 1.54113i) q^{74} +(1.76675 + 3.06010i) q^{75} +(-16.3177 + 9.42104i) q^{76} -0.790904 q^{77} +(-6.64626 + 3.54100i) q^{78} -1.98358 q^{79} +(7.95337 - 4.59188i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.77755 - 11.7391i) q^{82} +17.9932i q^{83} +(-1.61812 - 0.934223i) q^{84} +(-2.78249 - 1.60647i) q^{85} -3.88208i q^{86} +(4.25914 - 7.37705i) q^{87} +(0.378480 + 0.655547i) q^{88} +(-9.33421 + 5.38911i) q^{89} +6.10137 q^{90} +(2.51673 - 1.34087i) q^{91} +13.0054 q^{92} +(2.07759 - 1.19950i) q^{93} +(-3.00438 - 5.20374i) q^{94} +(-11.6495 + 20.1774i) q^{95} -8.08022i q^{96} +(-13.5275 - 7.81011i) q^{97} +(-11.5302 - 6.65699i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.80882	−	1.04432i	1.27903	−	0.738446i	0.302356	−	0.953195i	$-0.402227\pi$
$2$	1.80882	−	1.04432i	1.27903	−	0.738446i	0.976669	+	0.214749i	$0.0688934\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.18121	−	2.04591i	0.590604	−	1.02296i
$5$		−	2.92121i		−	1.30641i	−0.757182	−	0.653204i	$-0.773425\pi$
$5$		−	2.92121i		−	1.30641i	0.757182	−	0.653204i	$-0.226575\pi$
$6$	−1.80882	−	1.04432i	−0.738446	−	0.426342i
$7$	0.684943	+	0.395452i	0.258884	+	0.149467i	0.623825	−	0.781564i	$-0.285578\pi$
$7$	0.684943	+	0.395452i	0.258884	+	0.149467i	−0.364941	+	0.931031i	$0.618911\pi$
$8$		−	0.756961i		−	0.267626i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.05068	−	5.28394i	−0.964711	−	1.67093i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−2.36242			−0.681971
$13$	1.90810	−	3.05928i	0.529210	−	0.848491i
$13$	1.90810	−	3.05928i	0.529210	−	0.848491i
$14$	1.65191			0.441493
$15$	−2.52985	+	1.46061i	−0.653204	+	0.377127i
$16$	1.57191	+	2.72263i	0.392977	+	0.680656i
$17$	0.549933	−	0.952512i	0.133378	−	0.231018i	−0.791598	−	0.611042i	$-0.790751\pi$
$17$	0.549933	−	0.952512i	0.133378	−	0.231018i	0.924977	+	0.380024i	$0.124084\pi$
$18$			2.08864i			0.492297i
$19$	−6.90721	−	3.98788i	−1.58462	−	0.914882i	−0.994172	−	0.107809i	$-0.965617\pi$
$19$	−6.90721	−	3.98788i	−1.58462	−	0.914882i	−0.590451	−	0.807073i	$-0.701050\pi$
$20$	−5.97655	−	3.45057i	−1.33640	−	0.771570i
$21$		−	0.790904i		−	0.172589i
$22$	−1.04432	+	1.80882i	−0.222650	+	0.385641i
$23$	2.75257	+	4.76759i	0.573950	+	0.994110i	0.996155	+	0.0876099i	$0.0279229\pi$
$23$	2.75257	+	4.76759i	0.573950	+	0.994110i	−0.422205	+	0.906500i	$0.638744\pi$
$24$	−0.655547	+	0.378480i	−0.133813	+	0.0772570i
$25$	−3.53350			−0.706699
$26$	0.256529	−	7.52633i	0.0503094	−	1.47603i
$27$	1.00000			0.192450
$28$	1.61812	−	0.934223i	0.305796	−	0.176552i
$29$	4.25914	+	7.37705i	0.790903	+	1.36988i	0.925408	+	0.378972i	$0.123722\pi$
$29$	4.25914	+	7.37705i	0.790903	+	1.36988i	−0.134505	+	0.990913i	$0.542944\pi$
$30$	−3.05068	+	5.28394i	−0.556976	+	0.964711i
$31$			2.39900i			0.430873i	0.976518	+	0.215437i	$0.0691174\pi$
$31$			2.39900i			0.430873i	−0.976518	+	0.215437i	$0.930883\pi$
$32$	6.99768	+	4.04011i	1.23703	+	0.714198i
$33$	0.866025	+	0.500000i	0.150756	+	0.0870388i
$34$		−	2.29722i		−	0.393971i
$35$	1.15520	−	2.00087i	0.195264	−	0.338208i
$36$	1.18121	+	2.04591i	0.196868	+	0.340986i
$37$	−0.737862	+	0.426005i	−0.121304	+	0.0700347i	−0.559424	−	0.828882i	$-0.688978\pi$
$37$	−0.737862	+	0.426005i	−0.121304	+	0.0700347i	0.438120	+	0.898916i	$0.355644\pi$
$38$	−16.6585			−2.70236
$39$	−3.60346	−	0.122821i	−0.577015	−	0.0196671i
$40$	−2.21125			−0.349629
$41$	5.62044	−	3.24496i	0.877765	−	0.506778i	0.00784391	−	0.999969i	$-0.497503\pi$
$41$	5.62044	−	3.24496i	0.877765	−	0.506778i	0.869921	+	0.493192i	$0.164170\pi$
$42$	−0.825957	−	1.43060i	−0.127448	−	0.220746i
$43$	0.929332	−	1.60965i	0.141722	−	0.245469i	−0.786423	−	0.617688i	$-0.788069\pi$
$43$	0.929332	−	1.60965i	0.141722	−	0.245469i	0.928145	+	0.372219i	$0.121403\pi$
$44$			2.36242i			0.356148i
$45$	2.52985	+	1.46061i	0.377127	+	0.217735i
$46$	9.95777	+	5.74912i	1.46819	+	0.847662i
$47$		−	2.87688i		−	0.419635i	−0.977741	−	0.209818i	$-0.932713\pi$
$47$		−	2.87688i		−	0.419635i	0.977741	−	0.209818i	$-0.0672870\pi$
$48$	1.57191	−	2.72263i	0.226885	−	0.392977i
$49$	−3.18724	−	5.52045i	−0.455319	−	0.788636i
$50$	−6.39144	+	3.69010i	−0.903887	+	0.521859i
$51$	−1.09987			−0.154012
$52$	−4.00516	−	7.51744i	−0.555415	−	1.04248i
$53$	12.8446			1.76434			0.882168	−	0.470935i	$-0.156083\pi$
$53$	12.8446			1.76434			0.882168	+	0.470935i	$0.156083\pi$
$54$	1.80882	−	1.04432i	0.246149	−	0.142114i
$55$	1.46061	+	2.52985i	0.196948	+	0.341124i
$56$	0.299342	−	0.518475i	0.0400012	−	0.0692841i
$57$			7.97576i			1.05642i
$58$	15.4080	+	8.89582i	2.02317	+	1.16808i
$59$	4.73394	+	2.73314i	0.616307	+	0.355825i	0.775430	−	0.631434i	$-0.217533\pi$
$59$	4.73394	+	2.73314i	0.616307	+	0.355825i	−0.159123	+	0.987259i	$0.550867\pi$
$60$			6.90113i			0.890932i
$61$	0.570486	−	0.988111i	0.0730432	−	0.126515i	−0.827190	−	0.561922i	$-0.810062\pi$
$61$	0.570486	−	0.988111i	0.0730432	−	0.126515i	0.900234	+	0.435407i	$0.143396\pi$
$62$	2.50532	+	4.33935i	0.318176	+	0.551098i
$63$	−0.684943	+	0.395452i	−0.0862947	+	0.0498223i
$64$	10.5890			1.32363
$65$	−8.93680	−	5.57396i	−1.10847	−	0.691364i
$66$	2.08864			0.257094
$67$	−0.866490	+	0.500268i	−0.105859	+	0.0611175i	−0.551995	−	0.833848i	$-0.686133\pi$
$67$	−0.866490	+	0.500268i	−0.105859	+	0.0611175i	0.446136	+	0.894965i	$0.352800\pi$
$68$	−1.29917	−	2.25023i	−0.157548	−	0.272881i
$69$	2.75257	−	4.76759i	0.331370	−	0.573950i
$70$		−	4.82560i		−	0.576769i
$71$	−6.39988	−	3.69497i	−0.759526	−	0.438512i	0.0695996	−	0.997575i	$-0.477828\pi$
$71$	−6.39988	−	3.69497i	−0.759526	−	0.438512i	−0.829125	+	0.559063i	$0.811161\pi$
$72$	0.655547	+	0.378480i	0.0772570	+	0.0446043i
$73$			12.6053i			1.47534i	0.675160	+	0.737672i	$0.264075\pi$
$73$			12.6053i			1.47534i	−0.675160	+	0.737672i	$0.735925\pi$
$74$	−0.889770	+	1.54113i	−0.103434	+	0.179152i
$75$	1.76675	+	3.06010i	0.204007	+	0.353350i
$76$	−16.3177	+	9.42104i	−1.87177	+	1.08067i
$77$	−0.790904			−0.0901319
$78$	−6.64626	+	3.54100i	−0.752540	+	0.400940i
$79$	−1.98358			−0.223170			−0.111585	−	0.993755i	$-0.535593\pi$
$79$	−1.98358			−0.223170			−0.111585	+	0.993755i	$0.535593\pi$
$80$	7.95337	−	4.59188i	0.889214	−	0.513388i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.77755	−	11.7391i	0.748456	−	1.29636i
$83$			17.9932i			1.97501i	0.157588	+	0.987505i	$0.449628\pi$
$83$			17.9932i			1.97501i	−0.157588	+	0.987505i	$0.550372\pi$
$84$	−1.61812	−	0.934223i	−0.176552	−	0.101932i
$85$	−2.78249	−	1.60647i	−0.301804	−	0.174246i
$86$		−	3.88208i		−	0.418615i
$87$	4.25914	−	7.37705i	0.456628	−	0.790903i
$88$	0.378480	+	0.655547i	0.0403461	+	0.0698816i
$89$	−9.33421	+	5.38911i	−0.989424	+	0.571244i	−0.905102	−	0.425194i	$-0.860206\pi$
$89$	−9.33421	+	5.38911i	−0.989424	+	0.571244i	−0.0843221	+	0.996439i	$0.526872\pi$
$90$	6.10137			0.643141
$91$	2.51673	−	1.34087i	0.263825	−	0.140561i
$92$	13.0054			1.35591
$93$	2.07759	−	1.19950i	0.215437	−	0.124382i
$94$	−3.00438	−	5.20374i	−0.309878	−	0.536724i
$95$	−11.6495	+	20.1774i	−1.19521	+	2.07016i
$96$		−	8.08022i		−	0.824684i
$97$	−13.5275	−	7.81011i	−1.37351	−	0.792997i	−0.382142	−	0.924103i	$-0.624814\pi$
$97$	−13.5275	−	7.81011i	−1.37351	−	0.792997i	−0.991368	+	0.131107i	$0.958147\pi$
$98$	−11.5302	−	6.65699i	−1.16473	−	0.672457i
$99$		−	1.00000i		−	0.100504i
$100$	−4.17380	+	7.22923i	−0.417380	+	0.722923i
$101$	6.80328	+	11.7836i	0.676951	+	1.17251i	0.975894	+	0.218243i	$0.0700325\pi$
$101$	6.80328	+	11.7836i	0.676951	+	1.17251i	−0.298943	+	0.954271i	$0.596634\pi$
$102$	−1.98945	+	1.14861i	−0.196985	+	0.113730i
$103$	−9.43118			−0.929281			−0.464641	−	0.885499i	$-0.653816\pi$
$103$	−9.43118			−0.929281			−0.464641	+	0.885499i	$0.653816\pi$
$104$	−2.31575	−	1.44435i	−0.227078	−	0.141631i
$105$	−2.31040			−0.225472
$106$	23.2334	−	13.4138i	2.25663	−	1.30287i
$107$	1.66213	+	2.87890i	0.160684	+	0.278313i	0.935114	−	0.354346i	$-0.115297\pi$
$107$	1.66213	+	2.87890i	0.160684	+	0.278313i	−0.774430	+	0.632660i	$0.781963\pi$
$108$	1.18121	−	2.04591i	0.113662	−	0.196868i
$109$			2.53808i			0.243104i	0.992585	+	0.121552i	$0.0387872\pi$
$109$			2.53808i			0.243104i	−0.992585	+	0.121552i	$0.961213\pi$
$110$	5.28394	+	3.05068i	0.503804	+	0.290871i
$111$	0.737862	+	0.426005i	0.0700347	+	0.0404346i
$112$			2.48646i			0.234948i
$113$	1.57020	−	2.71966i	0.147712	−	0.255845i	−0.782670	−	0.622437i	$-0.786142\pi$
$113$	1.57020	−	2.71966i	0.147712	−	0.255845i	0.930381	+	0.366593i	$0.119476\pi$
$114$	8.32925	+	14.4267i	0.780105	+	1.35118i
$115$	13.9271	−	8.04084i	1.29871	−	0.749812i
$116$	20.1238			1.86844
$117$	1.69536	+	3.18210i	0.156736	+	0.294185i
$118$	11.4171			1.05103
$119$	0.753345	−	0.434944i	0.0690591	−	0.0398713i
$120$	1.10562	+	1.91499i	0.100929	+	0.174814i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	2.38308i		−	0.215754i
$123$	−5.62044	−	3.24496i	−0.506778	−	0.292588i
$124$	4.90815	+	2.83372i	0.440765	+	0.254476i
$125$		−	4.28397i		−	0.383170i
$126$	−0.825957	+	1.43060i	−0.0735821	+	0.127448i
$127$	−0.971149	−	1.68208i	−0.0861755	−	0.149260i	0.819716	−	0.572770i	$-0.194131\pi$
$127$	−0.971149	−	1.68208i	−0.0861755	−	0.149260i	−0.905892	+	0.423510i	$0.860798\pi$
$128$	5.15827	−	2.97813i	0.455931	−	0.263232i
$129$	−1.85866			−0.163646
$130$	−21.9860	−	0.749376i	−1.92830	−	0.0657246i
$131$	−14.5999			−1.27560			−0.637800	−	0.770202i	$-0.720155\pi$
$131$	−14.5999			−1.27560			−0.637800	+	0.770202i	$0.720155\pi$
$132$	2.04591	−	1.18121i	0.178074	−	0.102811i
$133$	−3.15403	−	5.46294i	−0.273489	−	0.473697i
$134$	−1.04488	+	1.80979i	−0.0902640	+	0.156342i
$135$		−	2.92121i		−	0.251418i
$136$	−0.721014	−	0.416278i	−0.0618264	−	0.0356955i
$137$	−14.2954	−	8.25346i	−1.22134	−	0.705141i	−0.256137	−	0.966641i	$-0.582450\pi$
$137$	−14.2954	−	8.25346i	−1.22134	−	0.705141i	−0.965204	+	0.261500i	$0.915783\pi$
$138$		−	11.4982i		−	0.978795i
$139$	10.7438	−	18.6089i	0.911281	−	1.57838i	0.0990236	−	0.995085i	$-0.468428\pi$
$139$	10.7438	−	18.6089i	0.911281	−	1.57838i	0.812257	−	0.583299i	$-0.198239\pi$
$140$	−2.72907	−	4.72688i	−0.230648	−	0.399494i
$141$	−2.49145	+	1.43844i	−0.209818	+	0.121138i
$142$	−15.4349			−1.29527
$143$	−0.122821	+	3.60346i	−0.0102708	+	0.301336i
$144$	−3.14382			−0.261985
$145$	21.5500	−	12.4419i	1.78963	−	1.03324i
$146$	13.1640	+	22.8007i	1.08946	+	1.88700i
$147$	−3.18724	+	5.52045i	−0.262879	+	0.455319i
$148$			2.01280i			0.165451i
$149$	−20.3845	−	11.7690i	−1.66996	−	0.964152i	−0.967655	−	0.252277i	$-0.918821\pi$
$149$	−20.3845	−	11.7690i	−1.66996	−	0.964152i	−0.702306	−	0.711875i	$-0.747846\pi$
$150$	6.39144	+	3.69010i	0.521859	+	0.301296i
$151$			8.97016i			0.729982i	0.931011	+	0.364991i	$0.118928\pi$
$151$			8.97016i			0.729982i	−0.931011	+	0.364991i	$0.881072\pi$
$152$	−3.01867	+	5.22849i	−0.244846	+	0.424086i
$153$	0.549933	+	0.952512i	0.0444594	+	0.0770060i
$154$	−1.43060	+	0.825957i	−0.115281	+	0.0665575i
$155$	7.00799			0.562896
$156$	−4.50772	+	7.22729i	−0.360906	+	0.578646i
$157$	0.208325			0.0166261			0.00831306	−	0.999965i	$-0.497354\pi$
$157$	0.208325			0.0166261			0.00831306	+	0.999965i	$0.497354\pi$
$158$	−3.58793	+	2.07149i	−0.285440	+	0.164799i
$159$	−6.42228	−	11.1237i	−0.509320	−	0.882168i
$160$	11.8020	−	20.4417i	0.933033	−	1.61606i
$161$			4.35403i			0.343146i
$162$	−1.80882	−	1.04432i	−0.142114	−	0.0820495i
$163$	0.840612	+	0.485327i	0.0658418	+	0.0380138i	0.532560	−	0.846393i	$-0.321230\pi$
$163$	0.840612	+	0.485327i	0.0658418	+	0.0380138i	−0.466718	+	0.884406i	$0.654564\pi$
$164$		−	15.3319i		−	1.19722i
$165$	1.46061	−	2.52985i	0.113708	−	0.196948i
$166$	18.7907	+	32.5464i	1.45844	+	2.52609i
$167$	−10.4069	+	6.00844i	−0.805313	+	0.464947i	−0.845325	−	0.534252i	$-0.820593\pi$
$167$	−10.4069	+	6.00844i	−0.805313	+	0.464947i	0.0400129	+	0.999199i	$0.487260\pi$
$168$	−0.598683			−0.0461894
$169$	−5.71834	−	11.6748i	−0.439873	−	0.898060i
$170$	−6.71069			−0.514686
$171$	6.90721	−	3.98788i	0.528208	−	0.304961i
$172$	−2.19547	−	3.80267i	−0.167403	−	0.289951i
$173$	3.46187	−	5.99614i	0.263201	−	0.455878i	−0.703890	−	0.710309i	$-0.748555\pi$
$173$	3.46187	−	5.99614i	0.263201	−	0.455878i	0.967091	+	0.254432i	$0.0818884\pi$
$174$		−	17.7916i		−	1.34878i
$175$	−2.42024	−	1.39733i	−0.182953	−	0.105628i
$176$	−2.72263	−	1.57191i	−0.205226	−	0.118487i
$177$		−	5.46628i		−	0.410871i
$178$	−11.2559	+	19.4958i	−0.843666	+	1.46127i
$179$	−1.93305	−	3.34813i	−0.144483	−	0.250251i	0.784697	−	0.619879i	$-0.212818\pi$
$179$	−1.93305	−	3.34813i	−0.144483	−	0.250251i	−0.929180	+	0.369628i	$0.879485\pi$
$180$	5.97655	−	3.45057i	0.445466	−	0.257190i
$181$	−0.455152			−0.0338312			−0.0169156	−	0.999857i	$-0.505385\pi$
$181$	−0.455152			−0.0338312			−0.0169156	+	0.999857i	$0.505385\pi$
$182$	3.15201	−	5.05366i	0.233642	−	0.374602i
$183$	−1.14097			−0.0843431
$184$	3.60888	−	2.08358i	0.266050	−	0.153604i
$185$	1.24445	+	2.15545i	0.0914939	+	0.158472i
$186$	2.50532	−	4.33935i	0.183699	−	0.318176i
$187$			1.09987i			0.0804302i
$188$	−5.88584	−	3.39819i	−0.429269	−	0.247839i
$189$	0.684943	+	0.395452i	0.0498223	+	0.0287649i
$190$			48.6630i			3.53039i
$191$	−12.5455	+	21.7295i	−0.907762	+	1.57229i	−0.0905965	+	0.995888i	$0.528877\pi$
$191$	−12.5455	+	21.7295i	−0.907762	+	1.57229i	−0.817166	+	0.576403i	$0.804456\pi$
$192$	−5.29452	−	9.17038i	−0.382099	−	0.661815i
$193$	1.44596	−	0.834825i	0.104082	−	0.0600920i	−0.447055	−	0.894506i	$-0.647527\pi$
$193$	1.44596	−	0.834825i	0.104082	−	0.0600920i	0.551138	+	0.834414i	$0.314194\pi$
$194$	−32.6250			−2.34234
$195$	−0.358786	+	10.5265i	−0.0256932	+	0.753817i
$196$	−15.0592			−1.07565
$197$	8.21336	−	4.74199i	0.585178	−	0.337853i	−0.178011	−	0.984029i	$-0.556966\pi$
$197$	8.21336	−	4.74199i	0.585178	−	0.337853i	0.763188	+	0.646176i	$0.223633\pi$
$198$	−1.04432	−	1.80882i	−0.0742166	−	0.128547i
$199$	−5.74447	+	9.94971i	−0.407214	+	0.705316i	−0.994576	−	0.104008i	$-0.966833\pi$
$199$	−5.74447	+	9.94971i	−0.407214	+	0.705316i	0.587362	+	0.809324i	$0.300167\pi$
$200$			2.67472i			0.189131i
$201$	0.866490	+	0.500268i	0.0611175	+	0.0352862i
$202$	24.6117	+	14.2096i	1.73168	+	0.999784i
$203$			6.73715i			0.472855i
$204$	−1.29917	+	2.25023i	−0.0909602	+	0.157548i
$205$	−9.47923	−	16.4185i	−0.662058	−	1.14672i
$206$	−17.0593	+	9.84917i	−1.18857	+	0.686224i
$207$	−5.50513			−0.382633
$208$	11.3286	+	0.386127i	0.785498	+	0.0267731i
$209$	7.97576			0.551695
$210$	−4.17909	+	2.41280i	−0.288384	+	0.166499i
$211$	1.00575	+	1.74201i	0.0692386	+	0.119925i	0.898566	−	0.438838i	$-0.144610\pi$
$211$	1.00575	+	1.74201i	0.0692386	+	0.119925i	−0.829328	+	0.558762i	$0.811276\pi$
$212$	15.1721	−	26.2789i	1.04202	−	1.80484i
$213$			7.38994i			0.506351i
$214$	6.01298	+	3.47159i	0.411039	+	0.237313i
$215$	−4.70213	−	2.71478i	−0.320683	−	0.185146i
$216$		−	0.756961i		−	0.0515047i
$217$	−0.948689	+	1.64318i	−0.0644012	+	0.111546i
$218$	2.65057	+	4.59092i	0.179519	+	0.310937i
$219$	10.9165	−	6.30267i	0.737672	−	0.425895i
$220$	6.90113			0.465274
$221$	−1.86467	−	3.49988i	−0.125431	−	0.235427i
$222$	1.77954			0.119435
$223$	−13.9329	+	8.04414i	−0.933014	+	0.538676i	−0.887763	−	0.460300i	$-0.847742\pi$
$223$	−13.9329	+	8.04414i	−0.933014	+	0.538676i	−0.0452501	+	0.998976i	$0.514408\pi$
$224$	3.19534	+	5.53449i	0.213498	+	0.369789i
$225$	1.76675	−	3.06010i	0.117783	−	0.204007i
$226$		−	6.55916i		−	0.436309i
$227$	14.8378	+	8.56662i	0.984821	+	0.568587i	0.903722	−	0.428119i	$-0.140824\pi$
$227$	14.8378	+	8.56662i	0.984821	+	0.568587i	0.0810989	+	0.996706i	$0.474157\pi$
$228$	16.3177	+	9.42104i	1.08067	+	0.623924i
$229$			7.34582i			0.485425i	0.970098	+	0.242713i	$0.0780372\pi$
$229$			7.34582i			0.485425i	−0.970098	+	0.242713i	$0.921963\pi$
$230$	16.7944	−	29.0888i	1.10739	−	1.91806i
$231$	0.395452	+	0.684943i	0.0260188	+	0.0450659i
$232$	5.58414	−	3.22401i	0.366617	−	0.211666i
$233$	23.9636			1.56991			0.784954	−	0.619554i	$-0.212686\pi$
$233$	23.9636			1.56991			0.784954	+	0.619554i	$0.212686\pi$
$234$	6.38973	+	3.98532i	0.417710	+	0.260529i
$235$	−8.40397			−0.548215
$236$	11.1835	−	6.45682i	0.727987	−	0.420303i
$237$	0.991789	+	1.71783i	0.0644236	+	0.111585i
$238$	0.908442	−	1.57347i	0.0588855	−	0.101993i
$239$		−	1.31728i		−	0.0852079i	−0.999092	−	0.0426039i	$-0.986435\pi$
$239$		−	1.31728i		−	0.0852079i	0.999092	−	0.0426039i	$-0.0135654\pi$
$240$	−7.95337	−	4.59188i	−0.513388	−	0.296405i
$241$	−4.29990	−	2.48255i	−0.276981	−	0.159915i	0.355075	−	0.934838i	$-0.384455\pi$
$241$	−4.29990	−	2.48255i	−0.276981	−	0.159915i	−0.632056	+	0.774923i	$0.717789\pi$
$242$		−	2.08864i		−	0.134263i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.34773	−	2.33433i	−0.0862793	−	0.149440i
$245$	−16.1264	+	9.31060i	−1.03028	+	0.594832i
$246$	−13.5551			−0.864242
$247$	−25.3796	+	13.5218i	−1.61487	+	0.860372i
$248$	1.81595			0.115313
$249$	15.5826	−	8.99660i	0.987505	−	0.570136i
$250$	−4.47384	−	7.74891i	−0.282950	−	0.490084i
$251$	2.23941	−	3.87877i	0.141350	−	0.244826i	−0.786655	−	0.617393i	$-0.788189\pi$
$251$	2.23941	−	3.87877i	0.141350	−	0.244826i	0.928005	+	0.372567i	$0.121522\pi$
$252$			1.86845i			0.117701i
$253$	−4.76759	−	2.75257i	−0.299736	−	0.173052i
$254$	−3.51326	−	2.02838i	−0.220441	−	0.127272i
$255$			3.21294i			0.201202i
$256$	−4.36880	+	7.56699i	−0.273050	+	0.472937i
$257$	−3.90111	−	6.75692i	−0.243345	−	0.421485i	0.718320	−	0.695713i	$-0.244911\pi$
$257$	−3.90111	−	6.75692i	−0.243345	−	0.421485i	−0.961665	+	0.274227i	$0.911578\pi$
$258$	−3.36198	+	1.94104i	−0.209308	+	0.120844i
$259$	−0.673858			−0.0418715
$260$	−21.9601	+	11.6999i	−1.36191	+	0.725598i
$261$	−8.51829			−0.527269
$262$	−26.4085	+	15.2470i	−1.63153	+	0.941962i
$263$	5.30631	+	9.19079i	0.327201	+	0.566729i	0.981955	−	0.189113i	$-0.0605613\pi$
$263$	5.30631	+	9.19079i	0.327201	+	0.566729i	−0.654754	+	0.755842i	$0.727228\pi$
$264$	0.378480	−	0.655547i	0.0232939	−	0.0403461i
$265$		−	37.5217i		−	2.30494i
$266$	−11.4101	−	6.58763i	−0.699599	−	0.403914i
$267$	9.33421	+	5.38911i	0.571244	+	0.329808i
$268$			2.36369i			0.144385i
$269$	7.75657	−	13.4348i	0.472926	−	0.819132i	−0.526594	−	0.850117i	$-0.676531\pi$
$269$	7.75657	−	13.4348i	0.472926	−	0.819132i	0.999520	+	0.0309850i	$0.00986441\pi$
$270$	−3.05068	−	5.28394i	−0.185659	−	0.321570i
$271$	8.06775	−	4.65792i	0.490081	−	0.282948i	−0.234527	−	0.972110i	$-0.575354\pi$
$271$	8.06775	−	4.65792i	0.490081	−	0.282948i	0.724608	+	0.689161i	$0.242021\pi$
$272$	3.45778			0.209659
$273$	−2.41959	−	1.50912i	−0.146440	−	0.0913361i
$274$	−34.4770			−2.08283
$275$	3.06010	−	1.76675i	0.184531	−	0.106539i
$276$	−6.50271	−	11.2630i	−0.391417	−	0.677955i
$277$	9.62930	−	16.6784i	0.578569	−	1.00211i	−0.417075	−	0.908872i	$-0.636945\pi$
$277$	9.62930	−	16.6784i	0.578569	−	1.00211i	0.995644	−	0.0932382i	$-0.0297218\pi$
$278$		−	44.8800i		−	2.69173i
$279$	−2.07759	−	1.19950i	−0.124382	−	0.0718122i
$280$	−1.51458	−	0.874441i	−0.0905133	−	0.0522579i
$281$			7.40534i			0.441766i	0.975300	+	0.220883i	$0.0708938\pi$
$281$			7.40534i			0.441766i	−0.975300	+	0.220883i	$0.929106\pi$
$282$	−3.00438	+	5.20374i	−0.178908	+	0.309878i
$283$	−7.75070	−	13.4246i	−0.460731	−	0.798010i	0.538266	−	0.842775i	$-0.319080\pi$
$283$	−7.75070	−	13.4246i	−0.460731	−	0.798010i	−0.998998	+	0.0447647i	$0.985746\pi$
$284$	−15.1192	+	8.72907i	−0.897159	+	0.517975i
$285$	23.2989			1.38011
$286$	3.54100	+	6.64626i	0.209384	+	0.393001i
$287$	5.13290			0.302986
$288$	−6.99768	+	4.04011i	−0.412342	+	0.238066i
$289$	7.89515	+	13.6748i	0.464420	+	0.804400i
$290$	25.9866	−	45.0101i	1.52599	−	2.64309i
$291$			15.6202i			0.915674i
$292$	25.7894	+	14.8895i	1.50921	+	0.871344i
$293$	−1.57296	−	0.908147i	−0.0918931	−	0.0530545i	0.453349	−	0.891333i	$-0.350229\pi$
$293$	−1.57296	−	0.908147i	−0.0918931	−	0.0530545i	−0.545242	+	0.838278i	$0.683562\pi$
$294$			13.3140i			0.776487i
$295$	7.98409	−	13.8289i	0.464852	−	0.805147i
$296$	0.322469	+	0.558532i	0.0187431	+	0.0324640i
$297$	−0.866025	+	0.500000i	−0.0502519	+	0.0290129i
$298$	−49.1623			−2.84790
$299$	19.8375	+	0.676146i	1.14723	+	0.0391025i
$300$	8.34760			0.481949
$301$	1.27308	−	0.735012i	0.0733790	−	0.0423654i
$302$	9.36772	+	16.2254i	0.539052	+	0.933665i
$303$	6.80328	−	11.7836i	0.390838	−	0.676951i
$304$		−	25.0743i		−	1.43811i
$305$	−2.88648	−	1.66651i	−0.165280	−	0.0954242i
$306$	1.98945	+	1.14861i	0.113730	+	0.0656618i
$307$			29.0363i			1.65719i	0.559849	+	0.828595i	$0.310859\pi$
$307$			29.0363i			1.65719i	−0.559849	+	0.828595i	$0.689141\pi$
$308$	−0.934223	+	1.61812i	−0.0532323	+	0.0922010i
$309$	4.71559	+	8.16764i	0.268260	+	0.464641i
$310$	12.6762	−	7.31859i	0.719958	−	0.415668i
$311$	15.7918			0.895471			0.447735	−	0.894166i	$-0.352231\pi$
$311$	15.7918			0.895471			0.447735	+	0.894166i	$0.352231\pi$
$312$	−0.0929706	+	2.72768i	−0.00526342	+	0.154424i
$313$	−21.1348			−1.19461			−0.597306	−	0.802013i	$-0.703762\pi$
$313$	−21.1348			−1.19461			−0.597306	+	0.802013i	$0.703762\pi$
$314$	0.376821	−	0.217558i	0.0212652	−	0.0122775i
$315$	1.15520	+	2.00087i	0.0650882	+	0.112736i
$316$	−2.34302	+	4.05823i	−0.131805	+	0.228293i
$317$		−	20.5708i		−	1.15537i	−0.816259	−	0.577686i	$-0.803956\pi$
$317$		−	20.5708i		−	1.15537i	0.816259	−	0.577686i	$-0.196044\pi$
$318$	−23.2334	−	13.4138i	−1.30287	−	0.752211i
$319$	−7.37705	−	4.25914i	−0.413036	−	0.238466i
$320$		−	30.9329i		−	1.72920i
$321$	1.66213	−	2.87890i	0.0927711	−	0.160684i
$322$	4.54700	+	7.87564i	0.253395	+	0.438892i
$323$	−7.59700	+	4.38613i	−0.422709	+	0.244051i
$324$	−2.36242			−0.131245
$325$	−6.74225	+	10.8099i	−0.373993	+	0.599628i
$326$	2.02735			0.112284
$327$	2.19804	−	1.26904i	0.121552	−	0.0701782i
$328$	−2.45631	−	4.25445i	−0.135627	−	0.234913i
$329$	1.13767	−	1.97050i	0.0627216	−	0.108637i
$330$		−	6.10137i		−	0.335869i
$331$	13.9345	+	8.04511i	0.765912	+	0.442199i	0.831414	−	0.555653i	$-0.187532\pi$
$331$	13.9345	+	8.04511i	0.765912	+	0.442199i	−0.0655026	+	0.997852i	$0.520865\pi$
$332$	36.8125	+	21.2537i	2.02035	+	1.16645i
$333$		−	0.852009i		−	0.0466898i
$334$	−12.5495	+	21.7363i	−0.686677	+	1.18936i
$335$	1.46139	+	2.53120i	0.0798444	+	0.138294i
$336$	2.15334	−	1.24323i	0.117474	−	0.0678237i
$337$	−10.9426			−0.596081			−0.298041	−	0.954553i	$-0.596333\pi$
$337$	−10.9426			−0.596081			−0.298041	+	0.954553i	$0.596333\pi$
$338$	−22.5356	−	15.1457i	−1.22578	−	0.823820i
$339$	−3.14040			−0.170563
$340$	−6.57341	+	3.79516i	−0.356493	+	0.205821i
$341$	−1.19950	−	2.07759i	−0.0649566	−	0.112508i
$342$	8.32925	−	14.4267i	0.450394	−	0.780105i
$343$		−	10.5779i		−	0.571154i
$344$	−1.21844	−	0.703468i	−0.0656940	−	0.0379284i
$345$	−13.9271	−	8.04084i	−0.749812	−	0.432904i
$346$		−	14.4612i		−	0.777439i
$347$	2.98571	−	5.17139i	0.160281	−	0.277615i	−0.774688	−	0.632343i	$-0.782093\pi$
$347$	2.98571	−	5.17139i	0.160281	−	0.277615i	0.934969	+	0.354728i	$0.115427\pi$
$348$	−10.0619	−	17.4277i	−0.539373	−	0.934222i
$349$	27.1872	−	15.6966i	1.45530	−	0.840217i	0.456525	−	0.889711i	$-0.349094\pi$
$349$	27.1872	−	15.6966i	1.45530	−	0.840217i	0.998774	+	0.0494932i	$0.0157606\pi$
$350$	−5.83703			−0.312002
$351$	1.90810	−	3.05928i	0.101847	−	0.163292i
$352$	−8.08022			−0.430677
$353$	−1.89593	+	1.09462i	−0.100910	+	0.0582606i	−0.549606	−	0.835424i	$-0.685222\pi$
$353$	−1.89593	+	1.09462i	−0.100910	+	0.0582606i	0.448696	+	0.893685i	$0.351889\pi$
$354$	−5.70855	−	9.88750i	−0.303406	−	0.525515i
$355$	−10.7938	+	18.6954i	−0.572876	+	0.992250i
$356$			25.4627i			1.34952i
$357$	−0.753345	−	0.434944i	−0.0398713	−	0.0230197i
$358$	−6.99305	−	4.03744i	−0.369594	−	0.213385i
$359$		−	32.9795i		−	1.74059i	−0.492528	−	0.870296i	$-0.663927\pi$
$359$		−	32.9795i		−	1.74059i	0.492528	−	0.870296i	$-0.336073\pi$
$360$	1.10562	−	1.91499i	0.0582714	−	0.100929i
$361$	22.3064	+	38.6358i	1.17402	+	2.03346i
$362$	−0.823286	+	0.475324i	−0.0432709	+	0.0249825i
$363$	−1.00000			−0.0524864
$364$	0.229484	−	6.73287i	0.0120282	−	0.352898i
$365$	36.8229			1.92740
$366$	−2.06381	+	1.19154i	−0.107877	+	0.0622828i
$367$	−3.31875	−	5.74825i	−0.173237	−	0.300056i	0.766312	−	0.642468i	$-0.222089\pi$
$367$	−3.31875	−	5.74825i	−0.173237	−	0.300056i	−0.939550	+	0.342412i	$0.888756\pi$
$368$	−8.65357	+	14.9884i	−0.451098	+	0.781325i
$369$			6.48992i			0.337852i
$370$	4.50197	+	2.59921i	0.234046	+	0.135127i
$371$	8.79779	+	5.07941i	0.456759	+	0.263710i
$372$		−	5.66744i		−	0.293843i
$373$	−14.3681	+	24.8863i	−0.743954	+	1.28857i	0.206728	+	0.978398i	$0.433718\pi$
$373$	−14.3681	+	24.8863i	−0.743954	+	1.28857i	−0.950682	+	0.310167i	$0.899615\pi$
$374$	1.14861	+	1.98945i	0.0593933	+	0.102872i
$375$	−3.71003	+	2.14199i	−0.191585	+	0.110612i
$376$	−2.17768			−0.112305
$377$	30.6953	+	1.04622i	1.58089	+	0.0538833i
$378$	1.65191			0.0849653
$379$	18.1497	−	10.4787i	0.932286	−	0.538256i	0.0447521	−	0.998998i	$-0.485750\pi$
$379$	18.1497	−	10.4787i	0.932286	−	0.538256i	0.887534	+	0.460743i	$0.152417\pi$
$380$	27.5209	+	47.6676i	1.41179	+	2.44529i
$381$	−0.971149	+	1.68208i	−0.0497535	+	0.0861755i
$382$			52.4062i			2.68133i
$383$	2.52005	+	1.45495i	0.128768	+	0.0743445i	0.563001	−	0.826457i	$-0.309647\pi$
$383$	2.52005	+	1.45495i	0.128768	+	0.0743445i	−0.434232	+	0.900801i	$0.642980\pi$
$384$	−5.15827	−	2.97813i	−0.263232	−	0.151977i
$385$			2.31040i			0.117749i
$386$	1.74365	−	3.02009i	0.0887494	−	0.153719i
$387$	0.929332	+	1.60965i	0.0472406	+	0.0818231i
$388$	−31.9576	+	18.4507i	−1.62240	+	0.936695i
$389$	−20.8262			−1.05593			−0.527965	−	0.849266i	$-0.677045\pi$
$389$	−20.8262			−1.05593			−0.527965	+	0.849266i	$0.677045\pi$
$390$	10.3440	+	19.4151i	0.523791	+	0.983124i
$391$	6.05491			0.306210
$392$	−4.17877	+	2.41261i	−0.211060	+	0.121855i
$393$	7.29996	+	12.6439i	0.368234	+	0.637800i
$394$	9.90430	−	17.1548i	0.498972	−	0.864244i
$395$			5.79446i			0.291551i
$396$	−2.04591	−	1.18121i	−0.102811	−	0.0593580i
$397$	−26.6533	−	15.3883i	−1.33769	−	0.772317i	−0.351228	−	0.936290i	$-0.614236\pi$
$397$	−26.6533	−	15.3883i	−1.33769	−	0.772317i	−0.986465	+	0.163973i	$0.947569\pi$
$398$			23.9963i			1.20282i
$399$	−3.15403	+	5.46294i	−0.157899	+	0.273489i
$400$	−5.55433	−	9.62039i	−0.277717	−	0.481019i
$401$	19.8554	−	11.4635i	0.991529	−	0.572460i	0.0857983	−	0.996313i	$-0.472656\pi$
$401$	19.8554	−	11.4635i	0.991529	−	0.572460i	0.905731	+	0.423853i	$0.139323\pi$
$402$	2.08976			0.104228
$403$	7.33920	+	4.57752i	0.365592	+	0.228023i
$404$	32.1444			1.59924
$405$	−2.52985	+	1.46061i	−0.125709	+	0.0725782i
$406$	7.03574	+	12.1863i	0.349178	+	0.604794i
$407$	0.426005	−	0.737862i	0.0211163	−	0.0365744i
$408$			0.832555i			0.0412176i
$409$	−9.18332	−	5.30199i	−0.454086	−	0.262167i	0.255468	−	0.966817i	$-0.417770\pi$
$409$	−9.18332	−	5.30199i	−0.454086	−	0.262167i	−0.709554	+	0.704651i	$0.751104\pi$
$410$	−34.2923	−	19.7987i	−1.69358	−	0.977788i
$411$			16.5069i			0.814227i
$412$	−11.1402	+	19.2954i	−0.548838	+	0.950615i
$413$	2.16165	+	3.74409i	0.106368	+	0.184235i
$414$	−9.95777	+	5.74912i	−0.489398	+	0.282554i
$415$	52.5620			2.58017
$416$	25.7121	−	13.6989i	1.26064	−	0.671645i
$417$	−21.4877			−1.05226
$418$	14.4267	−	8.32925i	0.705632	−	0.407397i
$419$	−4.61286	−	7.98971i	−0.225353	−	0.390323i	0.731072	−	0.682300i	$-0.239020\pi$
$419$	−4.61286	−	7.98971i	−0.225353	−	0.390323i	−0.956425	+	0.291977i	$0.905687\pi$
$420$	−2.72907	+	4.72688i	−0.133165	+	0.230648i
$421$			5.70936i			0.278257i	0.990274	+	0.139129i	$0.0444301\pi$
$421$			5.70936i			0.278257i	−0.990274	+	0.139129i	$0.955570\pi$
$422$	3.63843	+	2.10065i	0.177116	+	0.102258i
$423$	2.49145	+	1.43844i	0.121138	+	0.0699392i
$424$		−	9.72283i		−	0.472182i
$425$	−1.94319	+	3.36570i	−0.0942584	+	0.163260i
$426$	7.71747	+	13.3670i	0.373912	+	0.647635i
$427$	0.781501	−	0.451200i	0.0378195	−	0.0218351i
$428$	7.85330			0.379603
$429$	3.18210	−	1.69536i	0.153633	−	0.0818529i
$430$	−11.3404			−0.546882
$431$	−9.20618	+	5.31519i	−0.443446	+	0.256024i	−0.705058	−	0.709149i	$-0.749079\pi$
$431$	−9.20618	+	5.31519i	−0.443446	+	0.256024i	0.261612	+	0.965173i	$0.415746\pi$
$432$	1.57191	+	2.72263i	0.0756285	+	0.130992i
$433$	−8.56864	+	14.8413i	−0.411783	+	0.713229i	−0.995085	−	0.0990267i	$-0.968427\pi$
$433$	−8.56864	+	14.8413i	−0.411783	+	0.713229i	0.583302	+	0.812255i	$0.301760\pi$
$434$			3.96294i			0.190227i
$435$	−21.5500	−	12.4419i	−1.03324	−	0.596542i
$436$	5.19270	+	2.99801i	0.248685	+	0.143578i
$437$		−	43.9076i		−	2.10039i
$438$	13.1640	−	22.8007i	0.629001	−	1.08946i
$439$	14.7975	+	25.6300i	0.706245	+	1.22325i	0.966240	+	0.257642i	$0.0829456\pi$
$439$	14.7975	+	25.6300i	0.706245	+	1.22325i	−0.259996	+	0.965610i	$0.583721\pi$
$440$	1.91499	−	1.10562i	0.0912938	−	0.0527085i
$441$	6.37447			0.303546
$442$	−7.02784	−	4.38332i	−0.334280	−	0.208493i
$443$	−29.3218			−1.39312			−0.696560	−	0.717499i	$-0.745287\pi$
$443$	−29.3218			−1.39312			−0.696560	+	0.717499i	$0.745287\pi$
$444$	1.74314	−	1.00640i	0.0827257	−	0.0477617i
$445$	15.7427	+	27.2672i	0.746278	+	1.29259i
$446$	−16.8013	+	29.1007i	−0.795566	+	1.37796i
$447$			23.5380i			1.11331i
$448$	7.25289	+	4.18746i	0.342667	+	0.197839i
$449$	14.7815	+	8.53408i	0.697580	+	0.402748i	0.806446	−	0.591308i	$-0.201388\pi$
$449$	14.7815	+	8.53408i	0.697580	+	0.402748i	−0.108865	+	0.994057i	$0.534722\pi$
$450$		−	7.38020i		−	0.347906i
$451$	−3.24496	+	5.62044i	−0.152799	+	0.264656i
$452$	−3.70947	−	6.42499i	−0.174479	−	0.302206i
$453$	7.76839	−	4.48508i	0.364991	−	0.210728i
$454$	35.7852			1.67948
$455$	−3.91697	−	7.35192i	−0.183630	−	0.344663i
$456$	6.03734			0.282724
$457$	−20.0181	+	11.5575i	−0.936407	+	0.540635i	−0.888832	−	0.458233i	$-0.848483\pi$
$457$	−20.0181	+	11.5575i	−0.936407	+	0.540635i	−0.0475748	+	0.998868i	$0.515149\pi$
$458$	7.67139	+	13.2872i	0.358460	+	0.620872i
$459$	0.549933	−	0.952512i	0.0256687	−	0.0444594i
$460$		−	37.9916i		−	1.77137i
$461$	25.4398	+	14.6876i	1.18485	+	0.684072i	0.957131	−	0.289655i	$-0.0935407\pi$
$461$	25.4398	+	14.6876i	1.18485	+	0.684072i	0.227717	+	0.973727i	$0.426874\pi$
$462$	1.43060	+	0.825957i	0.0665575	+	0.0384270i
$463$		−	39.9044i		−	1.85451i	−0.374425	−	0.927257i	$-0.622160\pi$
$463$		−	39.9044i		−	1.85451i	0.374425	−	0.927257i	$-0.377840\pi$
$464$	−13.3900	+	23.1921i	−0.621614	+	1.07667i
$465$	−3.50400	−	6.06910i	−0.162494	−	0.281448i
$466$	43.3458	−	25.0257i	2.00795	−	1.15929i
$467$	26.0180			1.20397			0.601985	−	0.798507i	$-0.294377\pi$
$467$	26.0180			1.20397			0.601985	+	0.798507i	$0.294377\pi$
$468$	8.51288	+	0.290154i	0.393508	+	0.0134124i
$469$	−0.791329			−0.0365402
$470$	−15.2012	+	8.77644i	−0.701181	+	0.404827i
$471$	−0.104162	−	0.180414i	−0.00479955	−	0.00831306i
$472$	2.06888	−	3.58341i	0.0952280	−	0.164940i
$473$			1.85866i			0.0854615i
$474$	3.58793	+	2.07149i	0.164799	+	0.0951467i
$475$	24.4066	+	14.0912i	1.11985	+	0.646547i
$476$		−	2.05504i		−	0.0941926i
$477$	−6.42228	+	11.1237i	−0.294056	+	0.509320i
$478$	−1.37566	−	2.38272i	−0.0629214	−	0.108983i
$479$	−17.2859	+	9.98002i	−0.789813	+	0.455999i	−0.839897	−	0.542746i	$-0.817384\pi$
$479$	−17.2859	+	9.98002i	−0.789813	+	0.455999i	0.0500839	+	0.998745i	$0.484051\pi$
$480$	−23.6041			−1.07737
$481$	−0.104645	+	3.07018i	−0.00477138	+	0.139988i
$482$	−10.3703			−0.472355
$483$	3.77070	−	2.17702i	0.171573	−	0.0990577i
$484$	−1.18121	−	2.04591i	−0.0536913	−	0.0929961i
$485$	−22.8150	+	39.5168i	−1.03598	+	1.79436i
$486$			2.08864i			0.0947426i
$487$	−16.7204	−	9.65355i	−0.757675	−	0.437444i	0.0707851	−	0.997492i	$-0.477450\pi$
$487$	−16.7204	−	9.65355i	−0.757675	−	0.437444i	−0.828460	+	0.560048i	$0.810783\pi$
$488$	−0.747961	−	0.431836i	−0.0338586	−	0.0195483i
$489$		−	0.970655i		−	0.0438945i
$490$	−19.4465	+	33.6823i	−0.878503	+	1.52161i
$491$	7.70258	+	13.3413i	0.347613	+	0.602083i	0.985825	−	0.167778i	$-0.0536591\pi$
$491$	7.70258	+	13.3413i	0.347613	+	0.602083i	−0.638212	+	0.769861i	$0.720326\pi$
$492$	−13.2778	+	7.66595i	−0.598610	+	0.345608i
$493$	9.36898			0.421957
$494$	−31.7860	+	50.9629i	−1.43012	+	2.29293i
$495$	−2.92121			−0.131299
$496$	−6.53158	+	3.77101i	−0.293276	+	0.169323i
$497$	−2.92237	−	5.06169i	−0.131086	−	0.227048i
$498$	18.7907	−	32.5464i	0.842029	−	1.45844i
$499$		−	18.2944i		−	0.818971i	−0.912317	−	0.409485i	$-0.865708\pi$
$499$		−	18.2944i		−	0.818971i	0.912317	−	0.409485i	$-0.134292\pi$
$500$	−8.76464	−	5.06027i	−0.391967	−	0.226302i
$501$	10.4069	+	6.00844i	0.464947	+	0.268438i
$502$		−	9.35465i		−	0.417518i
$503$	−5.27215	+	9.13164i	−0.235074	+	0.407160i	−0.959294	−	0.282409i	$-0.908866\pi$
$503$	−5.27215	+	9.13164i	−0.235074	+	0.407160i	0.724220	+	0.689569i	$0.242200\pi$
$504$	0.299342	+	0.518475i	0.0133337	+	0.0230947i
$505$	34.4225	−	19.8738i	1.53178	−	0.884374i
$506$	−11.4982			−0.511159
$507$	−7.25149	+	10.7896i	−0.322050	+	0.479184i
$508$	−4.58852			−0.203583
$509$	31.3386	−	18.0933i	1.38906	−	0.801974i	0.395850	−	0.918315i	$-0.370450\pi$
$509$	31.3386	−	18.0933i	1.38906	−	0.801974i	0.993209	+	0.116342i	$0.0371168\pi$
$510$	3.35534	+	5.81162i	0.148577	+	0.257343i
$511$	−4.98481	+	8.63394i	−0.220515	+	0.381943i
$512$			30.1622i			1.33300i
$513$	−6.90721	−	3.98788i	−0.304961	−	0.176069i
$514$	−14.1128	−	8.14802i	−0.622488	−	0.359394i
$515$			27.5505i			1.21402i
$516$	−2.19547	+	3.80267i	−0.0966502	+	0.167403i
$517$	1.43844	+	2.49145i	0.0632624	+	0.109574i
$518$	−1.21888	+	0.703723i	−0.0535547	+	0.0309198i
$519$	−6.92374			−0.303919
$520$	−4.21927	+	6.76481i	−0.185027	+	0.296657i
$521$	−4.68476			−0.205243			−0.102622	−	0.994720i	$-0.532723\pi$
$521$	−4.68476			−0.205243			−0.102622	+	0.994720i	$0.532723\pi$
$522$	−15.4080	+	8.89582i	−0.674390	+	0.389359i
$523$	11.7338	+	20.3235i	0.513082	+	0.888683i	0.999885	+	0.0151718i	$0.00482951\pi$
$523$	11.7338	+	20.3235i	0.513082	+	0.888683i	−0.486803	+	0.873512i	$0.661837\pi$
$524$	−17.2455	+	29.8702i	−0.753375	+	1.30488i
$525$			2.79466i			0.121969i
$526$	19.1963	+	11.0830i	0.836997	+	0.483240i
$527$	2.28508	+	1.31929i	0.0995394	+	0.0574691i
$528$			3.14382i			0.136817i
$529$	−3.65325	+	6.32761i	−0.158837	+	0.275113i
$530$	−39.1847	−	67.8699i	−1.70207	−	2.94808i
$531$	−4.73394	+	2.73314i	−0.205436	+	0.118608i
$532$	−14.9023			−0.646096
$533$	0.797098	−	23.3862i	0.0345261	−	1.01297i
$534$	22.5118			0.974182
$535$	8.40987	−	4.85544i	0.363590	−	0.209919i
$536$	0.378684	+	0.655899i	0.0163566	+	0.0283305i
$537$	−1.93305	+	3.34813i	−0.0834171	+	0.144483i
$538$		−	32.4013i		−	1.39692i
$539$	5.52045	+	3.18724i	0.237783	+	0.137284i
$540$	−5.97655	−	3.45057i	−0.257190	−	0.148489i
$541$		−	6.52430i		−	0.280502i	−0.990116	−	0.140251i	$-0.955209\pi$
$541$		−	6.52430i		−	0.280502i	0.990116	−	0.140251i	$-0.0447909\pi$
$542$	9.72871	−	16.8506i	0.417884	−	0.723796i
$543$	0.227576	+	0.394173i	0.00976622	+	0.0169156i
$544$	7.69651	−	4.44358i	0.329985	−	0.190517i
$545$	7.41429			0.317593
$546$	−5.95260	−	0.202890i	−0.254748	−	0.00868287i
$547$	−6.37525			−0.272586			−0.136293	−	0.990669i	$-0.543519\pi$
$547$	−6.37525			−0.272586			−0.136293	+	0.990669i	$0.543519\pi$
$548$	−33.7718	+	19.4981i	−1.44266	+	0.832919i
$549$	0.570486	+	0.988111i	0.0243477	+	0.0421715i
$550$	3.69010	−	6.39144i	0.157346	−	0.272532i
$551$		−	67.9398i		−	2.89433i
$552$	−3.60888	−	2.08358i	−0.153604	−	0.0886833i
$553$	−1.35864	−	0.784410i	−0.0577751	−	0.0333565i
$554$		−	40.2243i		−	1.70897i
$555$	1.24445	−	2.15545i	0.0528240	−	0.0914939i
$556$	−25.3814	−	43.9620i	−1.07641	−	1.86440i
$557$	−28.8979	+	16.6842i	−1.22444	+	0.706932i	−0.965862	−	0.259057i	$-0.916588\pi$
$557$	−28.8979	+	16.6842i	−1.22444	+	0.706932i	−0.258581	+	0.965990i	$0.583255\pi$
$558$	−5.01065			−0.212118
$559$	−3.15111	−	5.91445i	−0.133278	−	0.250155i
$560$	7.26348			0.306938
$561$	0.952512	−	0.549933i	0.0402151	−	0.0232182i
$562$	7.73355	+	13.3949i	0.326220	+	0.565030i
$563$	−5.23242	+	9.06282i	−0.220520	+	0.381952i	−0.954966	−	0.296715i	$-0.904109\pi$
$563$	−5.23242	+	9.06282i	−0.220520	+	0.381952i	0.734446	+	0.678667i	$0.237442\pi$
$564$			6.79638i			0.286179i
$565$	−7.94473	−	4.58689i	−0.334237	−	0.192972i
$566$	−28.0392	−	16.1884i	−1.17857	−	0.680450i
$567$		−	0.790904i		−	0.0332148i
$568$	−2.79695	+	4.84446i	−0.117357	+	0.203269i
$569$	8.05696	+	13.9551i	0.337765	+	0.585027i	0.984012	−	0.178102i	$-0.0569957\pi$
$569$	8.05696	+	13.9551i	0.337765	+	0.585027i	−0.646247	+	0.763129i	$0.723662\pi$
$570$	42.1434	−	24.3315i	1.76519	−	1.01914i
$571$	42.0710			1.76062			0.880309	−	0.474401i	$-0.157335\pi$
$571$	42.0710			1.76062			0.880309	+	0.474401i	$0.157335\pi$
$572$	7.22729	+	4.50772i	0.302188	+	0.188477i
$573$	25.0910			1.04819
$574$	9.28448	−	5.36039i	0.387527	−	0.223739i
$575$	−9.72618	−	16.8462i	−0.405610	−	0.702537i
$576$	−5.29452	+	9.17038i	−0.220605	+	0.382099i
$577$			27.6103i			1.14943i	0.818353	+	0.574716i	$0.194888\pi$
$577$			27.6103i			1.14943i	−0.818353	+	0.574716i	$0.805112\pi$
$578$	28.5617	+	16.4901i	1.18801	+	0.685899i
$579$	−1.44596	−	0.834825i	−0.0600920	−	0.0346942i
$580$		−	58.7858i		−	2.44095i
$581$	−7.11545	+	12.3243i	−0.295198	+	0.511299i
$582$	16.3125	+	28.2541i	0.676175	+	1.17117i
$583$	−11.1237	+	6.42228i	−0.460697	+	0.265984i
$584$	9.54175			0.394840
$585$	9.29559	−	4.95252i	0.384325	−	0.204762i
$586$	−3.79358			−0.156712
$587$	−31.0863	+	17.9477i	−1.28307	+	0.740779i	−0.977408	−	0.211362i	$-0.932210\pi$
$587$	−31.0863	+	17.9477i	−1.28307	+	0.740779i	−0.305659	+	0.952141i	$0.598877\pi$
$588$	7.52958	+	13.0416i	0.310515	+	0.537827i
$589$	9.56692	−	16.5704i	0.394198	−	0.682771i
$590$		−	33.3518i		−	1.37307i
$591$	−8.21336	−	4.74199i	−0.337853	−	0.195059i
$592$	−2.31970	−	1.33928i	−0.0953392	−	0.0550441i
$593$		−	29.4446i		−	1.20915i	−0.796550	−	0.604573i	$-0.793344\pi$
$593$		−	29.4446i		−	1.20915i	0.796550	−	0.604573i	$-0.206656\pi$
$594$	−1.04432	+	1.80882i	−0.0428490	+	0.0742166i
$595$	−1.27057	−	2.20068i	−0.0520881	−	0.0902192i
$596$	−48.1566	+	27.8032i	−1.97257	+	1.13887i
$597$	11.4889			0.470211
$598$	36.5885	−	19.4937i	1.49622	−	0.797157i
$599$	−17.4165			−0.711620			−0.355810	−	0.934558i	$-0.615795\pi$
$599$	−17.4165			−0.711620			−0.355810	+	0.934558i	$0.615795\pi$
$600$	2.31637	−	1.33736i	0.0945656	−	0.0545975i
$601$	−22.5992	−	39.1430i	−0.921841	−	1.59668i	−0.796564	−	0.604555i	$-0.793351\pi$
$601$	−22.5992	−	39.1430i	−0.921841	−	1.59668i	−0.125278	−	0.992122i	$-0.539982\pi$
$602$	1.53518	−	2.65900i	0.0625691	−	0.108373i
$603$		−	1.00054i		−	0.0407450i
$604$	18.3522	+	10.5956i	0.746740	+	0.431130i
$605$	−2.52985	−	1.46061i	−0.102853	−	0.0593821i
$606$		−	28.4192i		−	1.15445i
$607$	7.49138	−	12.9755i	0.304066	−	0.526658i	−0.672987	−	0.739654i	$-0.734989\pi$
$607$	7.49138	−	12.9755i	0.304066	−	0.526658i	0.977053	+	0.212997i	$0.0683224\pi$
$608$	−32.2230	−	55.8118i	−1.30681	−	2.26347i
$609$	5.83454	−	3.36857i	0.236428	−	0.136502i
$610$	−6.96149			−0.281862
$611$	−8.80116	−	5.48935i	−0.356057	−	0.222075i
$612$	2.59834			0.105032
$613$	34.5877	−	19.9692i	1.39698	−	0.806549i	0.402909	−	0.915240i	$-0.367999\pi$
$613$	34.5877	−	19.9692i	1.39698	−	0.806549i	0.994076	+	0.108691i	$0.0346658\pi$
$614$	30.3232	+	52.5213i	1.22374	+	2.11959i
$615$	−9.47923	+	16.4185i	−0.382239	+	0.662058i
$616$			0.598683i			0.0241216i
$617$	−0.867215	−	0.500687i	−0.0349128	−	0.0201569i	0.482442	−	0.875928i	$-0.339750\pi$
$617$	−0.867215	−	0.500687i	−0.0349128	−	0.0201569i	−0.517355	+	0.855771i	$0.673083\pi$
$618$	17.0593	+	9.84917i	0.686224	+	0.396192i
$619$		−	41.6163i		−	1.67270i	−0.548194	−	0.836351i	$-0.684685\pi$
$619$		−	41.6163i		−	1.67270i	0.548194	−	0.836351i	$-0.315315\pi$
$620$	8.27790	−	14.3378i	0.332449	−	0.575818i
$621$	2.75257	+	4.76759i	0.110457	+	0.191317i
$622$	28.5644	−	16.4917i	1.14533	−	0.661257i
$623$	−8.52453			−0.341528
$624$	−5.32991	−	10.0039i	−0.213367	−	0.400478i
$625$	−30.1819			−1.20728
$626$	−38.2290	+	22.0715i	−1.52794	+	0.882156i
$627$	−3.98788	−	6.90721i	−0.159261	−	0.275847i
$628$	0.246075	−	0.426214i	0.00981946	−	0.0170078i
$629$			0.937096i			0.0373645i
$630$	4.17909	+	2.41280i	0.166499	+	0.0961282i
$631$	0.939365	+	0.542342i	0.0373955	+	0.0215903i	0.518581	−	0.855028i	$-0.326460\pi$
$631$	0.939365	+	0.542342i	0.0373955	+	0.0215903i	−0.481186	+	0.876619i	$0.659794\pi$
$632$			1.50149i			0.0597261i
$633$	1.00575	−	1.74201i	0.0399749	−	0.0692386i
$634$	−21.4825	−	37.2088i	−0.853179	−	1.47775i
$635$	−4.91371	+	2.83693i	−0.194995	+	0.112580i
$636$	−30.3442			−1.20323
$637$	−22.9701	−	0.782918i	−0.910110	−	0.0310204i
$638$	−17.7916			−0.704378
$639$	6.39988	−	3.69497i	0.253175	−	0.146171i
$640$	−8.69976	−	15.0684i	−0.343888	−	0.595632i
$641$	1.68704	−	2.92204i	0.0666340	−	0.115413i	−0.830784	−	0.556595i	$-0.812107\pi$
$641$	1.68704	−	2.92204i	0.0666340	−	0.115413i	0.897418	+	0.441182i	$0.145441\pi$
$642$		−	6.94319i		−	0.274026i
$643$	−2.83017	−	1.63400i	−0.111611	−	0.0644387i	0.443155	−	0.896445i	$-0.353859\pi$
$643$	−2.83017	−	1.63400i	−0.111611	−	0.0644387i	−0.554766	+	0.832006i	$0.687192\pi$
$644$	8.90797	+	5.14302i	0.351023	+	0.202663i
$645$			5.42956i			0.213789i
$646$	−9.16105	+	15.8674i	−0.360437	+	0.624295i
$647$	0.699592	+	1.21173i	0.0275038	+	0.0476379i	0.879450	−	0.475992i	$-0.157911\pi$
$647$	0.699592	+	1.21173i	0.0275038	+	0.0476379i	−0.851946	+	0.523630i	$0.824578\pi$
$648$	−0.655547	+	0.378480i	−0.0257523	+	0.0148681i
$649$	−5.46628			−0.214570
$650$	−0.906443	+	26.5943i	−0.0355536	+	1.04311i
$651$	1.89738			0.0743641
$652$	1.98588	−	1.14655i	0.0777729	−	0.0449022i
$653$	−7.23196	−	12.5261i	−0.283008	−	0.490185i	0.689116	−	0.724651i	$-0.257999\pi$
$653$	−7.23196	−	12.5261i	−0.283008	−	0.490185i	−0.972124	+	0.234466i	$0.924666\pi$
$654$	2.65057	−	4.59092i	0.103646	−	0.179519i
$655$			42.6495i			1.66645i
$656$	17.6696	+	10.2016i	0.689883	+	0.398304i
$657$	−10.9165	−	6.30267i	−0.425895	−	0.245891i
$658$		−	4.75235i		−	0.185266i
$659$	14.6770	−	25.4212i	0.571733	−	0.990271i	−0.424655	−	0.905355i	$-0.639605\pi$
$659$	14.6770	−	25.4212i	0.571733	−	0.990271i	0.996388	−	0.0849157i	$-0.0270621\pi$
$660$	−3.45057	−	5.97655i	−0.134313	−	0.232637i
$661$	23.0574	−	13.3122i	0.896829	−	0.517784i	0.0206586	−	0.999787i	$-0.493424\pi$
$661$	23.0574	−	13.3122i	0.896829	−	0.517784i	0.876170	+	0.482002i	$0.160090\pi$
$662$	33.6067			1.30616
$663$	−2.09865	+	3.36479i	−0.0815048	+	0.130678i
$664$	13.6201			0.528564
$665$	−15.9584	+	9.21360i	−0.618841	+	0.357288i
$666$	−0.889770	−	1.54113i	−0.0344779	−	0.0597175i
$667$	−23.4472	+	40.6117i	−0.907878	+	1.57249i
$668$			28.3889i			1.09840i
$669$	13.9329	+	8.04414i	0.538676	+	0.311005i
$670$	5.28678	+	3.05232i	0.204246	+	0.117921i
$671$			1.14097i			0.0440467i
$672$	3.19534	−	5.53449i	0.123263	−	0.213498i
$673$	−6.01580	−	10.4197i	−0.231892	−	0.401649i	0.726473	−	0.687195i	$-0.241158\pi$
$673$	−6.01580	−	10.4197i	−0.231892	−	0.401649i	−0.958365	+	0.285546i	$0.907825\pi$
$674$	−19.7931	+	11.4276i	−0.762403	+	0.440174i
$675$	−3.53350			−0.136004
$676$	−30.6402	−	2.09112i	−1.17847	−	0.0804276i
$677$	13.7989			0.530335			0.265168	−	0.964202i	$-0.414573\pi$
$677$	13.7989			0.530335			0.265168	+	0.964202i	$0.414573\pi$
$678$	−5.68040	+	3.27958i	−0.218155	+	0.125952i
$679$	−6.17705	−	10.6990i	−0.237053	−	0.410588i
$680$	−1.21604	+	2.10624i	−0.0466329	+	0.0807705i
$681$		−	17.1332i		−	0.656547i
$682$	−4.33935	−	2.50532i	−0.166162	−	0.0959338i
$683$	−13.2736	−	7.66350i	−0.507899	−	0.293236i	0.224071	−	0.974573i	$-0.428065\pi$
$683$	−13.2736	−	7.66350i	−0.507899	−	0.293236i	−0.731970	+	0.681337i	$0.761399\pi$
$684$		−	18.8421i		−	0.720445i
$685$	−24.1101	+	41.7600i	−0.921201	+	1.59557i
$686$	−11.0467	−	19.1335i	−0.421766	−	0.730521i
$687$	6.36167	−	3.67291i	0.242713	−	0.140130i
$688$	5.84330			0.222774
$689$	24.5087	−	39.2951i	0.933705	−	1.49702i
$690$	−33.5888			−1.27871
$691$	17.5433	−	10.1286i	0.667377	−	0.385310i	−0.127705	−	0.991812i	$-0.540761\pi$
$691$	17.5433	−	10.1286i	0.667377	−	0.385310i	0.795082	+	0.606502i	$0.207428\pi$
$692$	−8.17839	−	14.1654i	−0.310896	−	0.538487i
$693$	0.395452	−	0.684943i	0.0150220	−	0.0260188i
$694$		−	12.4721i		−	0.473436i
$695$	−54.3605	−	31.3851i	−2.06201	−	1.19050i
$696$	−5.58414	−	3.22401i	−0.211666	−	0.122206i
$697$		−	7.13804i		−	0.270373i
$698$	32.7845	−	56.7844i	1.24091	−	2.14932i
$699$	−11.9818	−	20.7531i	−0.453194	−	0.784954i
$700$	−5.71763	+	3.30107i	−0.216106	+	0.124769i
$701$	22.7355			0.858710			0.429355	−	0.903136i	$-0.358741\pi$
$701$	22.7355			0.858710			0.429355	+	0.903136i	$0.358741\pi$
$702$	0.256529	−	7.52633i	0.00968205	−	0.284063i
$703$	6.79542			0.256294
$704$	−9.17038	+	5.29452i	−0.345622	+	0.199545i
$705$	4.20199	+	7.27805i	0.158256	+	0.274107i
$706$	−2.28626	+	3.95992i	−0.0860446	+	0.149034i
$707$			10.7615i			0.404727i
$708$	−11.1835	−	6.45682i	−0.420303	−	0.242662i
$709$	19.1637	+	11.0642i	0.719709	+	0.415524i	0.814646	−	0.579959i	$-0.196931\pi$
$709$	19.1637	+	11.0642i	0.719709	+	0.415524i	−0.0949363	+	0.995483i	$0.530265\pi$
$710$			45.0888i			1.69215i
$711$	0.991789	−	1.71783i	0.0371950	−	0.0644236i
$712$	4.07934	+	7.06563i	0.152880	+	0.264796i
$713$	−11.4374	+	6.60341i	−0.428335	+	0.247300i
$714$	−1.81688			−0.0679952
$715$	10.5265	+	0.358786i	0.393668	+	0.0134178i
$716$	−9.13333			−0.341329
$717$	−1.14080	+	0.658641i	−0.0426039	+	0.0245974i
$718$	−34.4412	−	59.6539i	−1.28533	−	2.22626i
$719$	−13.8268	+	23.9488i	−0.515654	+	0.893139i	0.484181	+	0.874968i	$0.339118\pi$
$719$	−13.8268	+	23.9488i	−0.515654	+	0.893139i	−0.999835	+	0.0181714i	$0.994216\pi$
$720$			9.18377i			0.342259i
$721$	−6.45982	−	3.72958i	−0.240576	−	0.138897i
$722$	80.6962	+	46.5900i	3.00320	+	1.73390i
$723$			4.96510i			0.184654i
$724$	−0.537630	+	0.931202i	−0.0199808	+	0.0346078i
$725$	−15.0497	−	26.0668i	−0.558931	−	0.968097i
$726$	−1.80882	+	1.04432i	−0.0671314	+	0.0387584i
$727$	6.47028			0.239970			0.119985	−	0.992776i	$-0.461715\pi$
$727$	6.47028			0.239970			0.119985	+	0.992776i	$0.461715\pi$
$728$	−1.01499	−	1.90507i	−0.0376179	−	0.0706065i
$729$	1.00000			0.0370370
$730$	66.6058	−	38.4549i	2.46519	−	1.42328i
$731$	−1.02214	−	1.77040i	−0.0378052	−	0.0654806i
$732$	−1.34773	+	2.33433i	−0.0498134	+	0.0862793i
$733$		−	26.2710i		−	0.970341i	−0.874419	−	0.485171i	$-0.838757\pi$
$733$		−	26.2710i		−	0.970341i	0.874419	−	0.485171i	$-0.161243\pi$
$734$	−12.0060	−	6.93168i	−0.443150	−	0.255853i
$735$	16.1264	+	9.31060i	0.594832	+	0.343427i
$736$			44.4827i			1.63965i
$737$	0.500268	−	0.866490i	0.0184276	−	0.0319176i
$738$	6.77755	+	11.7391i	0.249485	+	0.432121i
$739$	−30.7435	+	17.7498i	−1.13092	+	0.652935i	−0.944165	−	0.329472i	$-0.893129\pi$
$739$	−30.7435	+	17.7498i	−1.13092	+	0.652935i	−0.186752	+	0.982407i	$0.559796\pi$
$740$	5.87983			0.216147
$741$	24.4001	+	15.2185i	0.896358	+	0.559066i
$742$	21.2181			0.778941
$743$	19.3153	−	11.1517i	0.708611	−	0.409117i	−0.101936	−	0.994791i	$-0.532504\pi$
$743$	19.3153	−	11.1517i	0.708611	−	0.409117i	0.810546	+	0.585674i	$0.199170\pi$
$744$	−0.907974	−	1.57266i	−0.0332880	−	0.0576564i
$745$	−34.3797	+	59.5474i	−1.25958	+	2.18165i
$746$			60.0197i			2.19748i
$747$	−15.5826	−	8.99660i	−0.570136	−	0.329168i
$748$	2.25023	+	1.29917i	0.0822766	+	0.0475024i
$749$			2.62917i			0.0960679i
$750$	−4.47384	+	7.74891i	−0.163361	+	0.282950i
$751$	−18.6244	−	32.2585i	−0.679615	−	1.17713i	−0.975097	−	0.221780i	$-0.928813\pi$
$751$	−18.6244	−	32.2585i	−0.679615	−	1.17713i	0.295481	−	0.955348i	$-0.404520\pi$
$752$	7.83265	−	4.52218i	0.285627	−	0.164907i
$753$	−4.47882			−0.163217
$754$	56.6147	−	30.1633i	2.06179	−	1.09848i
$755$	26.2038			0.953653
$756$	1.61812	−	0.934223i	0.0588505	−	0.0339774i
$757$	−18.3375	−	31.7614i	−0.666486	−	1.15439i	−0.978880	−	0.204435i	$-0.934464\pi$
$757$	−18.3375	−	31.7614i	−0.666486	−	1.15439i	0.312394	−	0.949953i	$-0.398869\pi$
$758$	21.8863	−	37.9081i	0.794945	−	1.37689i
$759$			5.50513i			0.199824i
$760$	15.2735	+	8.81818i	0.554029	+	0.319869i
$761$	34.9020	+	20.1507i	1.26519	+	0.730461i	0.974075	−	0.226226i	$-0.0726387\pi$
$761$	34.9020	+	20.1507i	1.26519	+	0.730461i	0.291120	+	0.956687i	$0.405972\pi$
$762$			4.05676i			0.146961i
$763$	−1.00369	+	1.73844i	−0.0363360	+	0.0629358i
$764$	29.6378	+	51.3341i	1.07226	+	1.85720i
$765$	2.78249	−	1.60647i	0.100601	−	0.0580821i
$766$	6.07774			0.219598
$767$	17.3942	−	9.26734i	0.628070	−	0.334624i
$768$	8.73761			0.315291
$769$	−31.7015	+	18.3029i	−1.14319	+	0.660019i	−0.947218	−	0.320591i	$-0.896119\pi$
$769$	−31.7015	+	18.3029i	−1.14319	+	0.660019i	−0.195969	+	0.980610i	$0.562785\pi$
$770$	2.41280	+	4.17909i	0.0869512	+	0.150604i
$771$	−3.90111	+	6.75692i	−0.140495	+	0.243345i
$772$		−	3.94441i		−	0.141963i
$773$	21.6502	+	12.4998i	0.778705	+	0.449585i	0.835971	−	0.548774i	$-0.184905\pi$
$773$	21.6502	+	12.4998i	0.778705	+	0.449585i	−0.0572663	+	0.998359i	$0.518238\pi$
$774$	3.36198	+	1.94104i	0.120844	+	0.0697692i
$775$		−	8.47686i		−	0.304498i
$776$	−5.91195	+	10.2398i	−0.212227	+	0.367587i
$777$	0.336929	+	0.583578i	0.0120873	+	0.0209357i
$778$	−37.6707	+	21.7492i	−1.35056	+	0.779746i
$779$	−51.7620			−1.85457
$780$	21.1125	+	13.1680i	0.755948	+	0.471491i
$781$	7.38994			0.264433
$782$	10.9522	−	6.32326i	0.391650	−	0.226119i
$783$	4.25914	+	7.37705i	0.152209	+	0.263634i
$784$	10.0201	−	17.3553i	0.357860	−	0.619832i
$785$		−	0.608561i		−	0.0217205i
$786$	26.4085	+	15.2470i	0.941962	+	0.543842i
$787$	−38.2699	−	22.0951i	−1.36417	−	0.787606i	−0.373998	−	0.927430i	$-0.622013\pi$
$787$	−38.2699	−	22.0951i	−1.36417	−	0.787606i	−0.990176	+	0.139823i	$0.955347\pi$
$788$		−	22.4051i		−	0.798149i
$789$	5.30631	−	9.19079i	0.188910	−	0.327201i
$790$	6.05127	+	10.4811i	0.215294	+	0.372901i
$791$	2.15099	−	1.24188i	0.0764805	−	0.0441561i
$792$	−0.756961			−0.0268974
$793$	−1.93436	−	3.63068i	−0.0686912	−	0.128929i
$794$	−64.2813			−2.28126
$795$	−32.4948	+	18.7609i	−1.15247	+	0.665379i
$796$	13.5708	+	23.5054i	0.481005	+	0.833126i
$797$	−20.6363	+	35.7431i	−0.730974	+	1.26608i	0.225493	+	0.974245i	$0.427601\pi$
$797$	−20.6363	+	35.7431i	−0.730974	+	1.26608i	−0.956467	+	0.291840i	$0.905733\pi$
$798$			13.1753i			0.466399i
$799$	−2.74026	−	1.58209i	−0.0969433	−	0.0559703i
$800$	−24.7263	−	14.2757i	−0.874206	−	0.504723i
$801$		−	10.7782i		−	0.380830i
$802$	23.9431	−	41.4707i	0.845461	−	1.46438i
$803$	−6.30267	−	10.9165i	−0.222416	−	0.385236i
$804$	2.04701	−	1.18184i	0.0721926	−	0.0416804i
$805$	12.7191			0.448288
$806$	18.0557	+	0.615412i	0.635983	+	0.0216770i
$807$	−15.5131			−0.546088
$808$	8.91974	−	5.14981i	0.313795	−	0.181170i
$809$	25.3570	+	43.9196i	0.891504	+	1.54413i	0.838073	+	0.545558i	$0.183682\pi$
$809$	25.3570	+	43.9196i	0.891504	+	1.54413i	0.0534304	+	0.998572i	$0.482984\pi$
$810$	−3.05068	+	5.28394i	−0.107190	+	0.185659i
$811$			2.28942i			0.0803923i	0.999192	+	0.0401961i	$0.0127983\pi$
$811$			2.28942i			0.0803923i	−0.999192	+	0.0401961i	$0.987202\pi$
$812$	13.7836	+	7.95798i	0.483710	+	0.279270i
$813$	−8.06775	−	4.65792i	−0.282948	−	0.163360i
$814$		−	1.77954i		−	0.0623729i
$815$	1.41775	−	2.45561i	0.0496615	−	0.0860162i
$816$	−1.72889	−	2.99452i	−0.0605232	−	0.104829i
$817$	−12.8382	+	7.41213i	−0.449151	+	0.259318i
$818$	−22.1479			−0.774384
$819$	−0.0971396	+	2.84999i	−0.00339433	+	0.0995867i
$820$	−44.7878			−1.56406
$821$	−15.2596	+	8.81014i	−0.532564	+	0.307476i	−0.742060	−	0.670334i	$-0.766151\pi$
$821$	−15.2596	+	8.81014i	−0.532564	+	0.307476i	0.209496	+	0.977809i	$0.432818\pi$
$822$	17.2385	+	29.8580i	0.601262	+	1.04142i
$823$	2.52644	−	4.37593i	0.0880663	−	0.152535i	−0.818627	−	0.574325i	$-0.805265\pi$
$823$	2.52644	−	4.37593i	0.0880663	−	0.152535i	0.906694	+	0.421790i	$0.138598\pi$
$824$			7.13903i			0.248700i
$825$	−3.06010	−	1.76675i	−0.106539	−	0.0615103i
$826$	7.82006	+	4.51491i	0.272095	+	0.157094i
$827$			2.05631i			0.0715049i	0.999361	+	0.0357525i	$0.0113828\pi$
$827$			2.05631i			0.0715049i	−0.999361	+	0.0357525i	$0.988617\pi$
$828$	−6.50271	+	11.2630i	−0.225985	+	0.391417i
$829$	12.7461	+	22.0768i	0.442689	+	0.766761i	0.997888	−	0.0649572i	$-0.0206911\pi$
$829$	12.7461	+	22.0768i	0.442689	+	0.766761i	−0.555199	+	0.831718i	$0.687358\pi$
$830$	95.0749	−	54.8915i	3.30010	−	1.90531i
$831$	−19.2586			−0.668073
$832$	20.2049	−	32.3948i	0.700479	−	1.12309i
$833$	−7.01106			−0.242919
$834$	−38.8673	+	22.4400i	−1.34586	+	0.777034i
$835$	17.5520	+	30.4009i	0.607411	+	1.05207i
$836$	9.42104	−	16.3177i	0.325833	−	0.564360i
$837$			2.39900i			0.0829216i
$838$	−16.6876	−	9.63461i	−0.576465	−	0.332822i
$839$	5.60530	+	3.23622i	0.193516	+	0.111727i	0.593628	−	0.804740i	$-0.297695\pi$
$839$	5.60530	+	3.23622i	0.193516	+	0.111727i	−0.400111	+	0.916467i	$0.631029\pi$
$840$			1.74888i			0.0603422i
$841$	−21.7806	+	37.7251i	−0.751056	+	1.30087i
$842$	5.96240	+	10.3272i	0.205478	+	0.355898i
$843$	6.41321	−	3.70267i	0.220883	−	0.127527i
$844$	4.75200			0.163571
$845$	−34.1045	+	16.7045i	−1.17323	+	0.574653i
$846$	6.00876			0.206585
$847$	0.684943	−	0.395452i	0.0235349	−	0.0135879i
$848$	20.1905	+	34.9709i	0.693344	+	1.20091i
$849$	−7.75070	+	13.4246i	−0.266003	+	0.460731i
$850$			8.11723i			0.278419i
$851$	−4.06203	−	2.34521i	−0.139244	−	0.0803928i
$852$	15.1192	+	8.72907i	0.517975	+	0.299053i
$853$			17.7273i			0.606970i	0.952836	+	0.303485i	$0.0981503\pi$
$853$			17.7273i			0.606970i	−0.952836	+	0.303485i	$0.901850\pi$
$854$	0.942394	−	1.63227i	0.0322480	−	0.0558553i
$855$	−11.6495	−	20.1774i	−0.398403	−	0.690054i
$856$	2.17921	−	1.25817i	0.0744839	−	0.0430033i
$857$	1.16474			0.0397868			0.0198934	−	0.999802i	$-0.493667\pi$
$857$	1.16474			0.0397868			0.0198934	+	0.999802i	$0.493667\pi$
$858$	3.98532	−	6.38973i	0.136057	−	0.218142i
$859$	23.3570			0.796931			0.398465	−	0.917183i	$-0.369543\pi$
$859$	23.3570			0.796931			0.398465	+	0.917183i	$0.369543\pi$
$860$	−11.1084	+	6.41344i	−0.378794	+	0.218697i
$861$	−2.56645	−	4.44523i	−0.0874644	−	0.151493i
$862$	−11.1015	+	19.2284i	−0.378119	+	0.654921i
$863$		−	47.0994i		−	1.60328i	−0.597806	−	0.801641i	$-0.703961\pi$
$863$		−	47.0994i		−	1.60328i	0.597806	−	0.801641i	$-0.296039\pi$
$864$	6.99768	+	4.04011i	0.238066	+	0.137447i
$865$	−17.5160	−	10.1129i	−0.595562	−	0.343848i
$866$			35.7936i			1.21632i
$867$	7.89515	−	13.6748i	0.268133	−	0.464420i
$868$	2.24120	+	3.88187i	0.0760713	+	0.131759i
$869$	1.71783	−	0.991789i	0.0582733	−	0.0336441i
$870$	−51.9732			−1.76206
$871$	−0.122887	+	3.60539i	−0.00416386	+	0.122164i
$872$	1.92123			0.0650610
$873$	13.5275	−	7.81011i	0.457837	−	0.264332i
$874$	−45.8536	−	79.4208i	−1.55102	−	2.68645i
$875$	1.69411	−	2.93428i	0.0572712	−	0.0991966i
$876$		−	29.7791i		−	1.00614i
$877$	0.291048	+	0.168037i	0.00982798	+	0.00567419i	0.504906	−	0.863174i	$-0.331527\pi$
$877$	0.291048	+	0.168037i	0.00982798	+	0.00567419i	−0.495078	+	0.868849i	$0.664861\pi$
$878$	53.5318	+	30.9066i	1.80661	+	1.04305i
$879$			1.81629i			0.0612621i
$880$	−4.59188	+	7.95337i	−0.154792	+	0.268108i
$881$	24.9561	+	43.2253i	0.840793	+	1.45630i	0.889225	+	0.457470i	$0.151244\pi$
$881$	24.9561	+	43.2253i	0.840793	+	1.45630i	−0.0484317	+	0.998826i	$0.515422\pi$
$882$	11.5302	−	6.65699i	0.388243	−	0.224152i
$883$	−40.7621			−1.37175			−0.685877	−	0.727718i	$-0.740581\pi$
$883$	−40.7621			−1.37175			−0.685877	+	0.727718i	$0.740581\pi$
$884$	−9.36302	−	0.319131i	−0.314912	−	0.0107335i
$885$	−15.9682			−0.536765
$886$	−53.0377	+	30.6213i	−1.78184	+	1.02874i
$887$	−7.58333	−	13.1347i	−0.254623	−	0.441021i	0.710170	−	0.704031i	$-0.248618\pi$
$887$	−7.58333	−	13.1347i	−0.254623	−	0.441021i	−0.964793	+	0.263010i	$0.915285\pi$
$888$	0.322469	−	0.558532i	0.0108213	−	0.0187431i
$889$		−	1.53617i		−	0.0515215i
$890$	56.9514	+	32.8809i	1.90902	+	1.10217i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$			38.0073i			1.27258i
$893$	−11.4726	+	19.8712i	−0.383917	+	0.664964i
$894$	24.5812	+	42.5758i	0.822117	+	1.42395i
$895$	−9.78062	+	5.64684i	−0.326930	+	0.188753i
$896$	4.71083			0.157378
$897$	−9.33320	−	17.5179i	−0.311627	−	0.584905i
$898$	35.6492			1.18963
$899$	−17.6976	+	10.2177i	−0.590246	+	0.340779i
$900$	−4.17380	−	7.22923i	−0.139127	−	0.240974i
$901$	7.06365	−	12.2346i	0.235324	−	0.407594i
$902$			13.5551i			0.451336i
$903$	−1.27308	−	0.735012i	−0.0423654	−	0.0244597i
$904$	−2.05868	−	1.18858i	−0.0684707	−	0.0395316i
$905$			1.32960i			0.0441973i
$906$	9.36772	−	16.2254i	0.311222	−	0.539052i
$907$	15.4545	+	26.7681i	0.513160	+	0.888819i	0.999884	+	0.0152629i	$0.00485851\pi$
$907$	15.4545	+	26.7681i	0.513160	+	0.888819i	−0.486724	+	0.873556i	$0.661808\pi$
$908$	35.0531	−	20.2379i	1.16328	−	0.671620i
$909$	−13.6066			−0.451301
$910$	−14.7628	−	9.20770i	−0.489383	−	0.305232i
$911$	−34.7951			−1.15281			−0.576407	−	0.817163i	$-0.695546\pi$
$911$	−34.7951			−1.15281			−0.576407	+	0.817163i	$0.695546\pi$
$912$	−21.7150	+	12.5372i	−0.719056	+	0.415147i
$913$	−8.99660	−	15.5826i	−0.297744	−	0.515708i
$914$	−24.1394	+	41.8106i	−0.798459	+	1.38297i
$915$			3.33302i			0.110186i
$916$	15.0289	+	8.67695i	0.496569	+	0.286694i
$917$	−10.0001	−	5.77356i	−0.330233	−	0.190660i
$918$		−	2.29722i		−	0.0758197i
$919$	17.6755	−	30.6149i	0.583062	−	1.00989i	−0.412051	−	0.911161i	$-0.635188\pi$
$919$	17.6755	−	30.6149i	0.583062	−	1.00989i	0.995114	−	0.0987332i	$-0.0314791\pi$
$920$	−6.08660	−	10.5423i	−0.200669	−	0.347569i
$921$	25.1462	−	14.5182i	0.828595	−	0.478389i
$922$	61.3544			2.02060
$923$	−23.5155	+	12.5286i	−0.774023	+	0.412385i
$924$	1.86845			0.0614674
$925$	2.60723	−	1.50529i	0.0857253	−	0.0494935i
$926$	−41.6730	−	72.1797i	−1.36946	−	2.37197i
$927$	4.71559	−	8.16764i	0.154880	−	0.268260i
$928$			68.8297i			2.25945i
$929$	−29.3243	−	16.9304i	−0.962100	−	0.555469i	−0.0652812	−	0.997867i	$-0.520794\pi$
$929$	−29.3243	−	16.9304i	−0.962100	−	0.555469i	−0.896819	+	0.442398i	$0.854128\pi$
$930$	−12.6762	−	7.31859i	−0.415668	−	0.239986i
$931$			50.8412i			1.66625i
$932$	28.3060	−	49.0275i	0.927195	−	1.60595i
$933$	−7.89590	−	13.6761i	−0.258500	−	0.447735i
$934$	47.0618	−	27.1711i	1.53991	−	0.889067i
$935$	3.21294			0.105075
$936$	2.40872	−	1.28332i	0.0787316	−	0.0419467i
$937$	−0.726333			−0.0237283			−0.0118641	−	0.999930i	$-0.503777\pi$
$937$	−0.726333			−0.0237283			−0.0118641	+	0.999930i	$0.503777\pi$
$938$	−1.43137	+	0.826400i	−0.0467358	+	0.0269829i
$939$	10.5674	+	18.3033i	0.344855	+	0.597306i
$940$	−9.92685	+	17.1938i	−0.323778	+	0.560800i
$941$		−	22.1799i		−	0.723046i	−0.932363	−	0.361523i	$-0.882257\pi$
$941$		−	22.1799i		−	0.723046i	0.932363	−	0.361523i	$-0.117743\pi$
$942$	−0.376821	−	0.217558i	−0.0122775	−	0.00708841i
$943$	30.9412	+	17.8639i	1.00759	+	0.581730i
$944$			17.1850i			0.559324i
$945$	1.15520	−	2.00087i	0.0375787	−	0.0650882i
$946$	1.94104	+	3.36198i	0.0631087	+	0.109307i
$947$	33.4322	−	19.3021i	1.08640	−	0.627233i	0.153784	−	0.988105i	$-0.450854\pi$
$947$	33.4322	−	19.3021i	1.08640	−	0.627233i	0.932615	+	0.360872i	$0.117521\pi$
$948$	4.68604			0.152195
$949$	38.5632	+	24.0522i	1.25181	+	0.780767i
$950$	58.8627			1.90976
$951$	−17.8148	+	10.2854i	−0.577686	+	0.333527i
$952$	−0.329236	−	0.570253i	−0.0106706	−	0.0184820i
$953$	6.68112	−	11.5720i	0.216423	−	0.374855i	−0.737289	−	0.675577i	$-0.763894\pi$
$953$	6.68112	−	11.5720i	0.216423	−	0.374855i	0.953712	+	0.300722i	$0.0972277\pi$
$954$			26.8277i			0.868578i
$955$	63.4765	+	36.6482i	2.05405	+	1.18591i
$956$	−2.69505	−	1.55599i	−0.0871640	−	0.0503242i
$957$			8.51829i			0.275357i
$958$	−20.8447	+	36.1040i	−0.673460	+	1.16647i
$959$	−6.52770	−	11.3063i	−0.210790	−	0.365100i
$960$	−26.7887	+	15.4664i	−0.864600	+	0.499177i
$961$	25.2448			0.814348
$962$	3.01697	+	5.66267i	0.0972710	+	0.182572i
$963$	−3.32426			−0.107123
$964$	−10.1582	+	5.86482i	−0.327173	+	0.188893i
$965$	−2.43870	−	4.22396i	−0.0785047	−	0.135974i
$966$	4.54700	−	7.87564i	0.146297	−	0.253395i
$967$			18.2080i			0.585529i	0.956185	+	0.292765i	$0.0945752\pi$
$967$			18.2080i			0.585529i	−0.956185	+	0.292765i	$0.905425\pi$
$968$	−0.655547	−	0.378480i	−0.0210701	−	0.0121648i
$969$	7.59700	+	4.38613i	0.244051	+	0.140903i
$970$			95.3047i			3.06005i
$971$	13.2635	−	22.9731i	0.425647	−	0.737243i	−0.570833	−	0.821066i	$-0.693380\pi$
$971$	13.2635	−	22.9731i	0.425647	−	0.737243i	0.996481	+	0.0838231i	$0.0267131\pi$
$972$	1.18121	+	2.04591i	0.0378873	+	0.0656227i
$973$	14.7178	−	8.49735i	0.471832	−	0.272412i
$974$	−40.3256			−1.29212
$975$	12.7328	+	0.433987i	0.407776	+	0.0138987i
$976$	3.58701			0.114817
$977$	34.3824	−	19.8507i	1.09999	−	0.635079i	0.163771	−	0.986498i	$-0.447634\pi$
$977$	34.3824	−	19.8507i	1.09999	−	0.635079i	0.936218	+	0.351419i	$0.114301\pi$
$978$	−1.01367	−	1.75574i	−0.0324137	−	0.0561422i
$979$	5.38911	−	9.33421i	0.172237	−	0.298323i
$980$			43.9911i			1.40524i
$981$	−2.19804	−	1.26904i	−0.0701782	−	0.0405174i
$982$	27.8651	+	16.0879i	0.889211	+	0.513386i
$983$		−	12.6453i		−	0.403322i	−0.979455	−	0.201661i	$-0.935366\pi$
$983$		−	12.6453i		−	0.403322i	0.979455	−	0.201661i	$-0.0646340\pi$
$984$	−2.45631	+	4.25445i	−0.0783042	+	0.135627i
$985$	−13.8524	−	23.9930i	−0.441373	−	0.764480i
$986$	16.9467	−	9.78421i	0.539694	−	0.311593i
$987$	−2.27533			−0.0724246
$988$	−2.31420	+	67.8967i	−0.0736246	+	2.16008i
$989$	10.2322			0.325365
$990$	−5.28394	+	3.05068i	−0.167935	+	0.0969571i
$991$	−20.8107	−	36.0453i	−0.661075	−	1.14502i	−0.980334	−	0.197348i	$-0.936767\pi$
$991$	−20.8107	−	36.0453i	−0.661075	−	1.14502i	0.319258	−	0.947668i	$-0.396566\pi$
$992$	−9.69223	+	16.7874i	−0.307729	+	0.533001i
$993$		−	16.0902i		−	0.510608i
$994$	−10.5720	−	6.10378i	−0.335325	−	0.193600i
$995$	29.0652	+	16.7808i	0.921430	+	0.531988i
$996$		−	42.5075i		−	1.34690i
$997$	−4.70183	+	8.14380i	−0.148908	+	0.257917i	−0.930824	−	0.365467i	$-0.880909\pi$
$997$	−4.70183	+	8.14380i	−0.148908	+	0.257917i	0.781916	+	0.623384i	$0.214243\pi$
$998$	−19.1052	−	33.0912i	−0.604766	−	1.04748i
$999$	−0.737862	+	0.426005i	−0.0233449	+	0.0134782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.b.166.12	✓	28
13.2	odd	12		5577.2.a.bg.1.11		14
13.4	even	6	inner	429.2.s.b.199.12	yes	28
13.11	odd	12		5577.2.a.bf.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.12	✓	28	1.1	even	1	trivial
429.2.s.b.199.12	yes	28	13.4	even	6	inner
5577.2.a.bf.1.4		14	13.11	odd	12
5577.2.a.bg.1.11		14	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80882 - 1.04432i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.18121 - 2.04591i) q^{4} -2.92121i q^{5} +(-1.80882 - 1.04432i) q^{6} +(0.684943 + 0.395452i) q^{7} -0.756961i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.80882 - 1.04432i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.18121 - 2.04591i) q^{4} -2.92121i q^{5} +(-1.80882 - 1.04432i) q^{6} +(0.684943 + 0.395452i) q^{7} -0.756961i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.05068 - 5.28394i) q^{10} +(-0.866025 + 0.500000i) q^{11} -2.36242 q^{12} +(1.90810 - 3.05928i) q^{13} +1.65191 q^{14} +(-2.52985 + 1.46061i) q^{15} +(1.57191 + 2.72263i) q^{16} +(0.549933 - 0.952512i) q^{17} +2.08864i q^{18} +(-6.90721 - 3.98788i) q^{19} +(-5.97655 - 3.45057i) q^{20} -0.790904i q^{21} +(-1.04432 + 1.80882i) q^{22} +(2.75257 + 4.76759i) q^{23} +(-0.655547 + 0.378480i) q^{24} -3.53350 q^{25} +(0.256529 - 7.52633i) q^{26} +1.00000 q^{27} +(1.61812 - 0.934223i) q^{28} +(4.25914 + 7.37705i) q^{29} +(-3.05068 + 5.28394i) q^{30} +2.39900i q^{31} +(6.99768 + 4.04011i) q^{32} +(0.866025 + 0.500000i) q^{33} -2.29722i q^{34} +(1.15520 - 2.00087i) q^{35} +(1.18121 + 2.04591i) q^{36} +(-0.737862 + 0.426005i) q^{37} -16.6585 q^{38} +(-3.60346 - 0.122821i) q^{39} -2.21125 q^{40} +(5.62044 - 3.24496i) q^{41} +(-0.825957 - 1.43060i) q^{42} +(0.929332 - 1.60965i) q^{43} +2.36242i q^{44} +(2.52985 + 1.46061i) q^{45} +(9.95777 + 5.74912i) q^{46} -2.87688i q^{47} +(1.57191 - 2.72263i) q^{48} +(-3.18724 - 5.52045i) q^{49} +(-6.39144 + 3.69010i) q^{50} -1.09987 q^{51} +(-4.00516 - 7.51744i) q^{52} +12.8446 q^{53} +(1.80882 - 1.04432i) q^{54} +(1.46061 + 2.52985i) q^{55} +(0.299342 - 0.518475i) q^{56} +7.97576i q^{57} +(15.4080 + 8.89582i) q^{58} +(4.73394 + 2.73314i) q^{59} +6.90113i q^{60} +(0.570486 - 0.988111i) q^{61} +(2.50532 + 4.33935i) q^{62} +(-0.684943 + 0.395452i) q^{63} +10.5890 q^{64} +(-8.93680 - 5.57396i) q^{65} +2.08864 q^{66} +(-0.866490 + 0.500268i) q^{67} +(-1.29917 - 2.25023i) q^{68} +(2.75257 - 4.76759i) q^{69} -4.82560i q^{70} +(-6.39988 - 3.69497i) q^{71} +(0.655547 + 0.378480i) q^{72} +12.6053i q^{73} +(-0.889770 + 1.54113i) q^{74} +(1.76675 + 3.06010i) q^{75} +(-16.3177 + 9.42104i) q^{76} -0.790904 q^{77} +(-6.64626 + 3.54100i) q^{78} -1.98358 q^{79} +(7.95337 - 4.59188i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.77755 - 11.7391i) q^{82} +17.9932i q^{83} +(-1.61812 - 0.934223i) q^{84} +(-2.78249 - 1.60647i) q^{85} -3.88208i q^{86} +(4.25914 - 7.37705i) q^{87} +(0.378480 + 0.655547i) q^{88} +(-9.33421 + 5.38911i) q^{89} +6.10137 q^{90} +(2.51673 - 1.34087i) q^{91} +13.0054 q^{92} +(2.07759 - 1.19950i) q^{93} +(-3.00438 - 5.20374i) q^{94} +(-11.6495 + 20.1774i) q^{95} -8.08022i q^{96} +(-13.5275 - 7.81011i) q^{97} +(-11.5302 - 6.65699i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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