LMFDB - Embedded newform 882.2.h.m.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.m.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-0.686141 + 1.18843i) q^{10} +4.37228 q^{11} +(1.18614 + 1.26217i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(2.31386 - 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.18614 - 3.78651i) q^{17} +(0.186141 - 2.99422i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} -7.37228 q^{23} +(1.68614 - 0.396143i) q^{24} -3.11684 q^{25} +(1.00000 + 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(0.686141 - 2.27567i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.37228 + 1.73205i) q^{33} +(-2.18614 - 3.78651i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 - 1.73205i) q^{37} -5.00000 q^{38} +(1.00000 - 3.31662i) q^{39} +1.37228 q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(-2.18614 - 3.78651i) q^{44} +(-3.68614 + 1.83324i) q^{45} +(-3.68614 + 6.38458i) q^{46} +(0.500000 - 1.65831i) q^{48} +(-1.55842 + 2.69927i) q^{50} +(-2.18614 + 7.25061i) q^{51} +2.00000 q^{52} +(-1.37228 + 2.37686i) q^{53} +(0.872281 + 5.12241i) q^{54} -6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} -2.74456 q^{58} +(-3.55842 - 6.16337i) q^{59} +(-1.62772 - 1.73205i) q^{60} +(7.05842 - 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.37228 - 2.37686i) q^{65} +(-2.18614 + 7.25061i) q^{66} +(-7.55842 - 13.0916i) q^{67} -4.37228 q^{68} +(12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(-2.68614 + 1.33591i) q^{72} +(2.55842 - 4.43132i) q^{73} -2.00000 q^{74} +(5.25544 - 1.23472i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(-2.37228 - 2.52434i) q^{78} +(-6.05842 + 10.4935i) q^{79} +(0.686141 - 1.18843i) q^{80} +(5.43070 - 7.17687i) q^{81} +(5.18614 + 8.98266i) q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} -9.11684 q^{86} +(3.25544 + 3.46410i) q^{87} -4.37228 q^{88} +(-1.62772 - 2.81929i) q^{89} +(-0.255437 + 4.10891i) q^{90} +(3.68614 + 6.38458i) q^{92} +(2.37228 + 2.52434i) q^{93} +(3.43070 + 5.94215i) q^{95} +(-1.18614 - 1.26217i) q^{96} +(-4.55842 - 7.89542i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 + 5 * q^9	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 4 q^{13} + 15 q^{15} - 2 q^{16} + 3 q^{17} - 5 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} - 18 q^{23} + q^{24} + 22 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 3 q^{30} - 4 q^{31} + 2 q^{32} - 18 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} - 20 q^{38} + 4 q^{39} - 6 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} - 9 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} - 3 q^{51} + 8 q^{52} + 6 q^{53} - 8 q^{54} - 24 q^{55} - 5 q^{57} + 12 q^{58} + 3 q^{59} - 18 q^{60} + 11 q^{61} - 8 q^{62} + 4 q^{64} - 6 q^{65} - 3 q^{66} - 13 q^{67} - 6 q^{68} + 21 q^{69} + 6 q^{71} - 5 q^{72} - 7 q^{73} - 8 q^{74} + 44 q^{75} - 10 q^{76} + 2 q^{78} - 7 q^{79} - 3 q^{80} - 7 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} - 2 q^{86} + 36 q^{87} - 6 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 + 5 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 4 * q^13 + 15 * q^15 - 2 * q^16 + 3 * q^17 - 5 * q^18 - 10 * q^19 - 3 * q^20 + 3 * q^22 - 18 * q^23 + q^24 + 22 * q^25 + 4 * q^26 - 16 * q^27 + 6 * q^29 - 3 * q^30 - 4 * q^31 + 2 * q^32 - 18 * q^33 - 3 * q^34 - 10 * q^36 - 4 * q^37 - 20 * q^38 + 4 * q^39 - 6 * q^40 - 15 * q^41 - q^43 - 3 * q^44 - 9 * q^45 - 9 * q^46 + 2 * q^48 + 11 * q^50 - 3 * q^51 + 8 * q^52 + 6 * q^53 - 8 * q^54 - 24 * q^55 - 5 * q^57 + 12 * q^58 + 3 * q^59 - 18 * q^60 + 11 * q^61 - 8 * q^62 + 4 * q^64 - 6 * q^65 - 3 * q^66 - 13 * q^67 - 6 * q^68 + 21 * q^69 + 6 * q^71 - 5 * q^72 - 7 * q^73 - 8 * q^74 + 44 * q^75 - 10 * q^76 + 2 * q^78 - 7 * q^79 - 3 * q^80 - 7 * q^81 + 15 * q^82 - 12 * q^83 - 12 * q^85 - 2 * q^86 + 36 * q^87 - 6 * q^88 - 18 * q^89 - 24 * q^90 + 9 * q^92 - 2 * q^93 - 15 * q^95 + q^96 - q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.37228			−0.613703			−0.306851	−	0.951757i	$-0.599275\pi$
$5$	−1.37228			−0.613703			−0.306851	+	0.951757i	$0.599275\pi$
$6$	−0.500000	+	1.65831i	−0.204124	+	0.677003i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$	−0.686141	+	1.18843i	−0.216977	+	0.375815i
$11$	4.37228			1.31829			0.659146	−	0.752015i	$-0.270918\pi$
$11$	4.37228			1.31829			0.659146	+	0.752015i	$0.270918\pi$
$12$	1.18614	+	1.26217i	0.342409	+	0.364357i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	2.31386	−	0.543620i	0.597436	−	0.140362i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.18614	−	3.78651i	0.530217	−	0.918363i	−0.469162	−	0.883112i	$-0.655444\pi$
$17$	2.18614	−	3.78651i	0.530217	−	0.918363i	0.999379	−	0.0352504i	$-0.0112229\pi$
$18$	0.186141	−	2.99422i	0.0438738	−	0.705744i
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	0.686141	+	1.18843i	0.153426	+	0.265741i
$21$		0			0
$22$	2.18614	−	3.78651i	0.466087	−	0.807286i
$23$	−7.37228			−1.53723			−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−7.37228			−1.53723			−0.768613	+	0.639713i	$0.779053\pi$
$24$	1.68614	−	0.396143i	0.344182	−	0.0808625i
$25$	−3.11684			−0.623369
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$		0			0
$29$	−1.37228	−	2.37686i	−0.254826	−	0.441372i	0.710022	−	0.704179i	$-0.248685\pi$
$29$	−1.37228	−	2.37686i	−0.254826	−	0.441372i	−0.964848	+	0.262807i	$0.915352\pi$
$30$	0.686141	−	2.27567i	0.125272	−	0.415479i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−7.37228	+	1.73205i	−1.28335	+	0.301511i
$34$	−2.18614	−	3.78651i	−0.374920	−	0.649381i
$35$		0			0
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−5.00000			−0.811107
$39$	1.00000	−	3.31662i	0.160128	−	0.531085i
$40$	1.37228			0.216977
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	0.102966	+	0.994685i	$0.467167\pi$
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	−0.912906	+	0.408171i	$0.866167\pi$
$42$		0			0
$43$	−4.55842	−	7.89542i	−0.695153	−	1.20404i	−0.970129	−	0.242589i	$-0.922003\pi$
$43$	−4.55842	−	7.89542i	−0.695153	−	1.20404i	0.274976	−	0.961451i	$-0.411330\pi$
$44$	−2.18614	−	3.78651i	−0.329573	−	0.570837i
$45$	−3.68614	+	1.83324i	−0.549497	+	0.273283i
$46$	−3.68614	+	6.38458i	−0.543492	+	0.941355i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	0.500000	−	1.65831i	0.0721688	−	0.239357i
$49$		0			0
$50$	−1.55842	+	2.69927i	−0.220394	+	0.381734i
$51$	−2.18614	+	7.25061i	−0.306121	+	1.01529i
$52$	2.00000			0.277350
$53$	−1.37228	+	2.37686i	−0.188497	+	0.326487i	−0.944749	−	0.327793i	$-0.893695\pi$
$53$	−1.37228	+	2.37686i	−0.188497	+	0.326487i	0.756252	+	0.654280i	$0.227028\pi$
$54$	0.872281	+	5.12241i	0.118702	+	0.697072i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	5.93070	+	6.31084i	0.785541	+	0.835892i
$58$	−2.74456			−0.360379
$59$	−3.55842	−	6.16337i	−0.463267	−	0.802402i	0.535854	−	0.844310i	$-0.319990\pi$
$59$	−3.55842	−	6.16337i	−0.463267	−	0.802402i	−0.999121	+	0.0419083i	$0.986656\pi$
$60$	−1.62772	−	1.73205i	−0.210138	−	0.223607i
$61$	7.05842	−	12.2255i	0.903738	−	1.56532i	0.0811364	−	0.996703i	$-0.474145\pi$
$61$	7.05842	−	12.2255i	0.903738	−	1.56532i	0.822602	−	0.568618i	$-0.192522\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	1.37228	−	2.37686i	0.170211	−	0.294813i
$66$	−2.18614	+	7.25061i	−0.269095	+	0.892488i
$67$	−7.55842	−	13.0916i	−0.923408	−	1.59939i	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−7.55842	−	13.0916i	−0.923408	−	1.59939i	−0.129307	−	0.991605i	$-0.541275\pi$
$68$	−4.37228			−0.530217
$69$	12.4307	−	2.92048i	1.49648	−	0.351585i
$70$		0			0
$71$	10.1168			1.20065			0.600324	−	0.799757i	$-0.295038\pi$
$71$	10.1168			1.20065			0.600324	+	0.799757i	$0.295038\pi$
$72$	−2.68614	+	1.33591i	−0.316565	+	0.157438i
$73$	2.55842	−	4.43132i	0.299441	−	0.518646i	−0.676567	−	0.736381i	$-0.736533\pi$
$73$	2.55842	−	4.43132i	0.299441	−	0.518646i	0.976008	+	0.217734i	$0.0698666\pi$
$74$	−2.00000			−0.232495
$75$	5.25544	−	1.23472i	0.606846	−	0.142573i
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$		0			0
$78$	−2.37228	−	2.52434i	−0.268608	−	0.285825i
$79$	−6.05842	+	10.4935i	−0.681626	+	1.18061i	0.292859	+	0.956156i	$0.405393\pi$
$79$	−6.05842	+	10.4935i	−0.681626	+	1.18061i	−0.974485	+	0.224455i	$0.927940\pi$
$80$	0.686141	−	1.18843i	0.0767129	−	0.132871i
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$	5.18614	+	8.98266i	0.572713	+	0.991969i
$83$	2.74456	+	4.75372i	0.301255	+	0.521789i	0.976420	−	0.215877i	$-0.0692612\pi$
$83$	2.74456	+	4.75372i	0.301255	+	0.521789i	−0.675166	+	0.737666i	$0.735928\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	−9.11684			−0.983095
$87$	3.25544	+	3.46410i	0.349020	+	0.371391i
$88$	−4.37228			−0.466087
$89$	−1.62772	−	2.81929i	−0.172538	−	0.298844i	0.766769	−	0.641924i	$-0.221863\pi$
$89$	−1.62772	−	2.81929i	−0.172538	−	0.298844i	−0.939306	+	0.343079i	$0.888530\pi$
$90$	−0.255437	+	4.10891i	−0.0269255	+	0.433117i
$91$		0			0
$92$	3.68614	+	6.38458i	0.384307	+	0.665639i
$93$	2.37228	+	2.52434i	0.245994	+	0.261762i
$94$		0			0
$95$	3.43070	+	5.94215i	0.351983	+	0.609652i
$96$	−1.18614	−	1.26217i	−0.121060	−	0.128820i
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	0.536263	−	0.844051i	$-0.319835\pi$
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	−0.999101	+	0.0423924i	$0.986502\pi$
$98$		0			0
$99$	11.7446	−	5.84096i	1.18037	−	0.587039i
$100$	1.55842	+	2.69927i	0.155842	+	0.269927i
$101$	7.37228			0.733569			0.366785	−	0.930306i	$-0.380459\pi$
$101$	7.37228			0.733569			0.366785	+	0.930306i	$0.380459\pi$
$102$	5.18614	+	5.51856i	0.513504	+	0.546419i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	1.37228	+	2.37686i	0.133288	+	0.230861i
$107$	0.813859	+	1.40965i	0.0786788	+	0.136276i	0.902680	−	0.430312i	$-0.141597\pi$
$107$	0.813859	+	1.40965i	0.0786788	+	0.136276i	−0.824001	+	0.566588i	$0.808263\pi$
$108$	4.87228	+	1.80579i	0.468835	+	0.173762i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	2.37228	+	2.52434i	0.225167	+	0.239600i
$112$		0			0
$113$	−0.686141	+	1.18843i	−0.0645467	+	0.111798i	−0.896493	−	0.443058i	$-0.853893\pi$
$113$	−0.686141	+	1.18843i	−0.0645467	+	0.111798i	0.831946	+	0.554856i	$0.187227\pi$
$114$	8.43070	−	1.98072i	0.789608	−	0.185511i
$115$	10.1168			0.943401
$116$	−1.37228	+	2.37686i	−0.127413	+	0.220686i
$117$	−0.372281	+	5.98844i	−0.0344174	+	0.553631i
$118$	−7.11684			−0.655159
$119$		0			0
$120$	−2.31386	+	0.543620i	−0.211225	+	0.0496255i
$121$	8.11684			0.737895
$122$	−7.05842	−	12.2255i	−0.639040	−	1.10685i
$123$	5.18614	−	17.2005i	0.467619	−	1.55092i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	11.1386			0.996266
$126$		0			0
$127$	−14.1168			−1.25267			−0.626334	−	0.779555i	$-0.715445\pi$
$127$	−14.1168			−1.25267			−0.626334	+	0.779555i	$0.715445\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	10.8139	+	11.5070i	0.952107	+	1.01313i
$130$	−1.37228	−	2.37686i	−0.120357	−	0.208464i
$131$	−7.37228			−0.644119			−0.322060	−	0.946719i	$-0.604375\pi$
$131$	−7.37228			−0.644119			−0.322060	+	0.946719i	$0.604375\pi$
$132$	5.18614	+	5.51856i	0.451396	+	0.480329i
$133$		0			0
$134$	−15.1168			−1.30590
$135$	5.48913	−	4.55134i	0.472429	−	0.391717i
$136$	−2.18614	+	3.78651i	−0.187460	+	0.324690i
$137$	16.3723			1.39878			0.699389	−	0.714741i	$-0.253455\pi$
$137$	16.3723			1.39878			0.699389	+	0.714741i	$0.253455\pi$
$138$	3.68614	−	12.2255i	0.313785	−	1.04071i
$139$	10.6168	−	18.3889i	0.900509	−	1.55973i	0.0736742	−	0.997282i	$-0.476528\pi$
$139$	10.6168	−	18.3889i	0.900509	−	1.55973i	0.826835	−	0.562445i	$-0.190139\pi$
$140$		0			0
$141$		0			0
$142$	5.05842	−	8.76144i	0.424493	−	0.735244i
$143$	−4.37228	+	7.57301i	−0.365629	+	0.633287i
$144$	−0.186141	+	2.99422i	−0.0155117	+	0.249518i
$145$	1.88316	+	3.26172i	0.156388	+	0.270871i
$146$	−2.55842	−	4.43132i	−0.211737	−	0.366738i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	14.7446			1.20792			0.603961	−	0.797014i	$-0.293588\pi$
$149$	14.7446			1.20792			0.603961	+	0.797014i	$0.293588\pi$
$150$	1.55842	−	5.16870i	0.127245	−	0.422023i
$151$	−8.11684			−0.660539			−0.330270	−	0.943887i	$-0.607140\pi$
$151$	−8.11684			−0.660539			−0.330270	+	0.943887i	$0.607140\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$	0.813859	−	13.0916i	0.0657966	−	1.05839i
$154$		0			0
$155$	1.37228	+	2.37686i	0.110224	+	0.190914i
$156$	−3.37228	+	0.792287i	−0.269999	+	0.0634337i
$157$	4.05842	+	7.02939i	0.323897	+	0.561007i	0.981289	−	0.192543i	$-0.0616734\pi$
$157$	4.05842	+	7.02939i	0.323897	+	0.561007i	−0.657391	+	0.753549i	$0.728340\pi$
$158$	6.05842	+	10.4935i	0.481982	+	0.834818i
$159$	1.37228	−	4.55134i	0.108829	−	0.360945i
$160$	−0.686141	−	1.18843i	−0.0542442	−	0.0939537i
$161$		0			0
$162$	−3.50000	−	8.29156i	−0.274986	−	0.651447i
$163$	−8.11684	−	14.0588i	−0.635760	−	1.10117i	−0.986354	−	0.164641i	$-0.947353\pi$
$163$	−8.11684	−	14.0588i	−0.635760	−	1.10117i	0.350593	−	0.936528i	$-0.385980\pi$
$164$	10.3723			0.809939
$165$	10.1168	−	2.37686i	0.787595	−	0.185038i
$166$	5.48913			0.426039
$167$	−8.74456	+	15.1460i	−0.676675	+	1.17203i	0.299302	+	0.954158i	$0.403246\pi$
$167$	−8.74456	+	15.1460i	−0.676675	+	1.17203i	−0.975976	+	0.217876i	$0.930087\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	−12.5000	−	8.29156i	−0.955899	−	0.634072i
$172$	−4.55842	+	7.89542i	−0.347576	+	0.602020i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	4.62772	−	1.08724i	0.350826	−	0.0824235i
$175$		0			0
$176$	−2.18614	+	3.78651i	−0.164787	+	0.285419i
$177$	8.44158	+	8.98266i	0.634508	+	0.675178i
$178$	−3.25544			−0.244005
$179$	−7.37228	+	12.7692i	−0.551030	+	0.954412i	0.447170	+	0.894449i	$0.352432\pi$
$179$	−7.37228	+	12.7692i	−0.551030	+	0.954412i	−0.998201	+	0.0599635i	$0.980902\pi$
$180$	3.43070	+	2.27567i	0.255710	+	0.169619i
$181$	18.1168			1.34661			0.673307	−	0.739363i	$-0.264873\pi$
$181$	18.1168			1.34661			0.673307	+	0.739363i	$0.264873\pi$
$182$		0			0
$183$	−7.05842	+	23.4101i	−0.521774	+	1.73053i
$184$	7.37228			0.543492
$185$	1.37228	+	2.37686i	0.100892	+	0.174750i
$186$	3.37228	−	0.792287i	0.247268	−	0.0580933i
$187$	9.55842	−	16.5557i	0.698981	−	1.21067i
$188$		0			0
$189$		0			0
$190$	6.86141			0.497779
$191$	0.941578	−	1.63086i	0.0681302	−	0.118005i	−0.829948	−	0.557841i	$-0.811630\pi$
$191$	0.941578	−	1.63086i	0.0681302	−	0.118005i	0.898078	+	0.439836i	$0.144963\pi$
$192$	−1.68614	+	0.396143i	−0.121687	+	0.0285892i
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	−9.11684			−0.654551
$195$	−1.37228	+	4.55134i	−0.0982711	+	0.325928i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	0.813859	−	13.0916i	0.0578385	−	0.930377i
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	3.11684			0.220394
$201$	17.9307	+	19.0800i	1.26473	+	1.34580i
$202$	3.68614	−	6.38458i	0.259356	−	0.449218i
$203$		0			0
$204$	7.37228	−	1.73205i	0.516163	−	0.121268i
$205$	7.11684	−	12.3267i	0.497062	−	0.860937i
$206$	−5.00000	+	8.66025i	−0.348367	+	0.603388i
$207$	−19.8030	+	9.84868i	−1.37640	+	0.684531i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−10.9307	−	18.9325i	−0.756093	−	1.30959i
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	2.74456			0.188497
$213$	−17.0584	+	4.00772i	−1.16882	+	0.274605i
$214$	1.62772			0.111269
$215$	6.25544	+	10.8347i	0.426617	+	0.738923i
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$		0			0
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$	−2.55842	+	8.48533i	−0.172882	+	0.573385i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	4.37228	+	7.57301i	0.294111	+	0.509416i
$222$	3.37228	−	0.792287i	0.226333	−	0.0531748i
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$		0			0
$225$	−8.37228	+	4.16381i	−0.558152	+	0.277588i
$226$	0.686141	+	1.18843i	0.0456414	+	0.0790532i
$227$	−23.7446			−1.57598			−0.787991	−	0.615687i	$-0.788879\pi$
$227$	−23.7446			−1.57598			−0.787991	+	0.615687i	$0.788879\pi$
$228$	2.50000	−	8.29156i	0.165567	−	0.549122i
$229$	−20.1168			−1.32936			−0.664679	−	0.747129i	$-0.731432\pi$
$229$	−20.1168			−1.32936			−0.664679	+	0.747129i	$0.731432\pi$
$230$	5.05842	−	8.76144i	0.333542	−	0.577713i
$231$		0			0
$232$	1.37228	+	2.37686i	0.0900947	+	0.156049i
$233$	5.87228	+	10.1711i	0.384706	+	0.666330i	0.991728	−	0.128354i	$-0.0409695\pi$
$233$	5.87228	+	10.1711i	0.384706	+	0.666330i	−0.607022	+	0.794685i	$0.707636\pi$
$234$	5.00000	+	3.31662i	0.326860	+	0.216815i
$235$		0			0
$236$	−3.55842	+	6.16337i	−0.231634	+	0.401201i
$237$	6.05842	−	20.0935i	0.393537	−	1.30521i
$238$		0			0
$239$	9.43070	−	16.3345i	0.610021	−	1.05659i	−0.381215	−	0.924487i	$-0.624494\pi$
$239$	9.43070	−	16.3345i	0.610021	−	1.05659i	0.991236	−	0.132102i	$-0.0421725\pi$
$240$	−0.686141	+	2.27567i	−0.0442902	+	0.146894i
$241$	0.883156			0.0568891			0.0284445	−	0.999595i	$-0.490945\pi$
$241$	0.883156			0.0568891			0.0284445	+	0.999595i	$0.490945\pi$
$242$	4.05842	−	7.02939i	0.260885	−	0.451867i
$243$	−6.31386	+	14.2525i	−0.405034	+	0.914302i
$244$	−14.1168			−0.903738
$245$		0			0
$246$	−12.3030	−	13.0916i	−0.784410	−	0.834688i
$247$	10.0000			0.636285
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	−6.51087	−	6.92820i	−0.412610	−	0.439057i
$250$	5.56930	−	9.64630i	0.352233	−	0.610086i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	−32.2337			−2.02651
$254$	−7.05842	+	12.2255i	−0.442885	+	0.767099i
$255$	3.00000	−	9.94987i	0.187867	−	0.623085i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.8614			1.36368			0.681839	−	0.731503i	$-0.261181\pi$
$257$	21.8614			1.36368			0.681839	+	0.731503i	$0.261181\pi$
$258$	15.3723	−	3.61158i	0.957036	−	0.224847i
$259$		0			0
$260$	−2.74456			−0.170211
$261$	−6.86141	−	4.55134i	−0.424710	−	0.281721i
$262$	−3.68614	+	6.38458i	−0.227731	+	0.394441i
$263$	13.3723			0.824570			0.412285	−	0.911055i	$-0.364731\pi$
$263$	13.3723			0.824570			0.412285	+	0.911055i	$0.364731\pi$
$264$	7.37228	−	1.73205i	0.453733	−	0.106600i
$265$	1.88316	−	3.26172i	0.115681	−	0.200366i
$266$		0			0
$267$	3.86141	+	4.10891i	0.236314	+	0.251461i
$268$	−7.55842	+	13.0916i	−0.461704	+	0.799695i
$269$	3.68614	−	6.38458i	0.224748	−	0.389275i	−0.731496	−	0.681846i	$-0.761177\pi$
$269$	3.68614	−	6.38458i	0.224748	−	0.389275i	0.956244	+	0.292571i	$0.0945108\pi$
$270$	−1.19702	−	7.02939i	−0.0728480	−	0.427795i
$271$	9.11684	+	15.7908i	0.553809	+	0.959225i	0.997995	+	0.0632906i	$0.0201595\pi$
$271$	9.11684	+	15.7908i	0.553809	+	0.959225i	−0.444186	+	0.895934i	$0.646507\pi$
$272$	2.18614	+	3.78651i	0.132554	+	0.229591i
$273$		0			0
$274$	8.18614	−	14.1788i	0.494543	−	0.856573i
$275$	−13.6277			−0.821782
$276$	−8.74456	−	9.30506i	−0.526361	−	0.560099i
$277$	22.2337			1.33589			0.667946	−	0.744209i	$-0.267174\pi$
$277$	22.2337			1.33589			0.667946	+	0.744209i	$0.267174\pi$
$278$	−10.6168	−	18.3889i	−0.636756	−	1.10289i
$279$	−5.00000	−	3.31662i	−0.299342	−	0.198561i
$280$		0			0
$281$	−5.31386	−	9.20387i	−0.316998	−	0.549057i	0.662862	−	0.748742i	$-0.269342\pi$
$281$	−5.31386	−	9.20387i	−0.316998	−	0.549057i	−0.979860	+	0.199685i	$0.936008\pi$
$282$		0			0
$283$	−4.94158	−	8.55906i	−0.293746	−	0.508784i	0.680946	−	0.732333i	$-0.261569\pi$
$283$	−4.94158	−	8.55906i	−0.293746	−	0.508784i	−0.974692	+	0.223550i	$0.928235\pi$
$284$	−5.05842	−	8.76144i	−0.300162	−	0.519896i
$285$	−8.13859	−	8.66025i	−0.482089	−	0.512989i
$286$	4.37228	+	7.57301i	0.258538	+	0.447802i
$287$		0			0
$288$	2.50000	+	1.65831i	0.147314	+	0.0977170i
$289$	−1.05842	−	1.83324i	−0.0622601	−	0.107838i
$290$	3.76631			0.221165
$291$	10.8139	+	11.5070i	0.633920	+	0.674552i
$292$	−5.11684			−0.299441
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	−0.790488	−	0.612478i	$-0.790173\pi$
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	0.925665	+	0.378344i	$0.123506\pi$
$294$		0			0
$295$	4.88316	+	8.45787i	0.284308	+	0.492436i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	−17.4891	+	14.5012i	−1.01482	+	0.841446i
$298$	7.37228	−	12.7692i	0.427065	−	0.739698i
$299$	7.37228	−	12.7692i	0.426350	−	0.738460i
$300$	−3.69702	−	3.93398i	−0.213447	−	0.227129i
$301$		0			0
$302$	−4.05842	+	7.02939i	−0.233536	+	0.404496i
$303$	−12.4307	+	2.92048i	−0.714125	+	0.167777i
$304$	5.00000			0.286770
$305$	−9.68614	+	16.7769i	−0.554627	+	0.960642i
$306$	−10.9307	−	7.25061i	−0.624867	−	0.414490i
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$		0			0
$309$	16.8614	−	3.96143i	0.959212	−	0.225358i
$310$	2.74456			0.155881
$311$	13.1168	+	22.7190i	0.743788	+	1.28828i	0.950759	+	0.309931i	$0.100306\pi$
$311$	13.1168	+	22.7190i	0.743788	+	1.28828i	−0.206971	+	0.978347i	$0.566361\pi$
$312$	−1.00000	+	3.31662i	−0.0566139	+	0.187767i
$313$	1.44158	−	2.49689i	0.0814828	−	0.141132i	−0.822404	−	0.568904i	$-0.807368\pi$
$313$	1.44158	−	2.49689i	0.0814828	−	0.141132i	0.903887	+	0.427771i	$0.140701\pi$
$314$	8.11684			0.458060
$315$		0			0
$316$	12.1168			0.681626
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	−3.25544	−	3.46410i	−0.182556	−	0.194257i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	−1.37228			−0.0767129
$321$	−1.93070	−	2.05446i	−0.107761	−	0.114669i
$322$		0			0
$323$	−21.8614			−1.21640
$324$	−8.93070	−	1.11469i	−0.496150	−	0.0619273i
$325$	3.11684	−	5.39853i	0.172891	−	0.299457i
$326$	−16.2337			−0.899101
$327$	7.00000	−	23.2164i	0.387101	−	1.28387i
$328$	5.18614	−	8.98266i	0.286357	−	0.495984i
$329$		0			0
$330$	3.00000	−	9.94987i	0.165145	−	0.547723i
$331$	6.11684	−	10.5947i	0.336212	−	0.582337i	−0.647505	−	0.762061i	$-0.724187\pi$
$331$	6.11684	−	10.5947i	0.336212	−	0.582337i	0.983717	+	0.179725i	$0.0575207\pi$
$332$	2.74456	−	4.75372i	0.150627	−	0.260894i
$333$	−5.00000	−	3.31662i	−0.273998	−	0.181750i
$334$	8.74456	+	15.1460i	0.478481	+	0.828754i
$335$	10.3723	+	17.9653i	0.566698	+	0.981550i
$336$		0			0
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	−0.963058	−	0.269294i	$-0.913210\pi$
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	0.714745	+	0.699385i	$0.246543\pi$
$338$	9.00000			0.489535
$339$	0.686141	−	2.27567i	0.0372660	−	0.123597i
$340$	6.00000			0.325396
$341$	−4.37228	−	7.57301i	−0.236772	−	0.410102i
$342$	−13.4307	+	6.67954i	−0.726249	+	0.361188i
$343$		0			0
$344$	4.55842	+	7.89542i	0.245774	+	0.425692i
$345$	−17.0584	+	4.00772i	−0.918395	+	0.215768i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−3.55842	−	6.16337i	−0.191026	−	0.330867i	0.754564	−	0.656226i	$-0.227848\pi$
$347$	−3.55842	−	6.16337i	−0.191026	−	0.330867i	−0.945591	+	0.325359i	$0.894515\pi$
$348$	1.37228	−	4.55134i	0.0735620	−	0.243978i
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	0.994388	+	0.105797i	$0.0337393\pi$
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	−0.405571	+	0.914063i	$0.632927\pi$
$350$		0			0
$351$	−1.74456	−	10.2448i	−0.0931179	−	0.546828i
$352$	2.18614	+	3.78651i	0.116522	+	0.201821i
$353$	−7.62772			−0.405983			−0.202991	−	0.979181i	$-0.565066\pi$
$353$	−7.62772			−0.405983			−0.202991	+	0.979181i	$0.565066\pi$
$354$	12.0000	−	2.81929i	0.637793	−	0.149844i
$355$	−13.8832			−0.736841
$356$	−1.62772	+	2.81929i	−0.0862689	+	0.149422i
$357$		0			0
$358$	7.37228	+	12.7692i	0.389637	+	0.674871i
$359$	3.43070	+	5.94215i	0.181066	+	0.313615i	0.942244	−	0.334928i	$-0.108712\pi$
$359$	3.43070	+	5.94215i	0.181066	+	0.313615i	−0.761178	+	0.648543i	$0.775379\pi$
$360$	3.68614	−	1.83324i	0.194277	−	0.0966203i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	9.05842	−	15.6896i	0.476100	−	0.824630i
$363$	−13.6861	+	3.21543i	−0.718336	+	0.168767i
$364$		0			0
$365$	−3.51087	+	6.08101i	−0.183768	+	0.318295i
$366$	16.7446	+	17.8178i	0.875252	+	0.931353i
$367$	22.2337			1.16059			0.580295	−	0.814407i	$-0.302937\pi$
$367$	22.2337			1.16059			0.580295	+	0.814407i	$0.302937\pi$
$368$	3.68614	−	6.38458i	0.192153	−	0.332819i
$369$	−1.93070	+	31.0569i	−0.100508	+	1.61676i
$370$	2.74456			0.142683
$371$		0			0
$372$	1.00000	−	3.31662i	0.0518476	−	0.171959i
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	−9.55842	−	16.5557i	−0.494254	−	0.856073i
$375$	−18.7812	+	4.41248i	−0.969859	+	0.227860i
$376$		0			0
$377$	5.48913			0.282704
$378$		0			0
$379$	9.11684			0.468301			0.234150	−	0.972200i	$-0.424769\pi$
$379$	9.11684			0.468301			0.234150	+	0.972200i	$0.424769\pi$
$380$	3.43070	−	5.94215i	0.175991	−	0.304826i
$381$	23.8030	−	5.59230i	1.21946	−	0.286502i
$382$	−0.941578	−	1.63086i	−0.0481753	−	0.0834421i
$383$	−21.2554			−1.08610			−0.543051	−	0.839700i	$-0.682731\pi$
$383$	−21.2554			−1.08610			−0.543051	+	0.839700i	$0.682731\pi$
$384$	−0.500000	+	1.65831i	−0.0255155	+	0.0846254i
$385$		0			0
$386$	7.00000			0.356291
$387$	−22.7921	−	15.1186i	−1.15859	−	0.768520i
$388$	−4.55842	+	7.89542i	−0.231419	+	0.400829i
$389$	−34.9783			−1.77347			−0.886734	−	0.462280i	$-0.847031\pi$
$389$	−34.9783			−1.77347			−0.886734	+	0.462280i	$0.847031\pi$
$390$	3.25544	+	3.46410i	0.164845	+	0.175412i
$391$	−16.1168	+	27.9152i	−0.815064	+	1.41173i
$392$		0			0
$393$	12.4307	−	2.92048i	0.627046	−	0.147319i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	8.31386	−	14.4000i	0.418316	−	0.724544i
$396$	−10.9307	−	7.25061i	−0.549289	−	0.364357i
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	−5.00000	−	8.66025i	−0.250627	−	0.434099i
$399$		0			0
$400$	1.55842	−	2.69927i	0.0779211	−	0.134963i
$401$	−0.255437			−0.0127559			−0.00637797	−	0.999980i	$-0.502030\pi$
$401$	−0.255437			−0.0127559			−0.00637797	+	0.999980i	$0.502030\pi$
$402$	25.4891	−	5.98844i	1.27128	−	0.298676i
$403$	4.00000			0.199254
$404$	−3.68614	−	6.38458i	−0.183392	−	0.317645i
$405$	−7.45245	+	9.84868i	−0.370315	+	0.489385i
$406$		0			0
$407$	−4.37228	−	7.57301i	−0.216726	−	0.375380i
$408$	2.18614	−	7.25061i	0.108230	−	0.358959i
$409$	−14.6753	−	25.4183i	−0.725645	−	1.25685i	−0.958708	−	0.284393i	$-0.908208\pi$
$409$	−14.6753	−	25.4183i	−0.725645	−	1.25685i	0.233063	−	0.972462i	$-0.425125\pi$
$410$	−7.11684	−	12.3267i	−0.351476	−	0.608774i
$411$	−27.6060	+	6.48577i	−1.36170	+	0.319920i
$412$	5.00000	+	8.66025i	0.246332	+	0.426660i
$413$		0			0
$414$	−1.37228	+	22.0742i	−0.0674439	+	1.08489i
$415$	−3.76631	−	6.52344i	−0.184881	−	0.320223i
$416$	−2.00000			−0.0980581
$417$	−10.6168	+	35.2121i	−0.519909	+	1.72434i
$418$	−21.8614			−1.06928
$419$	−13.8030	+	23.9075i	−0.674320	+	1.16796i	0.302347	+	0.953198i	$0.402230\pi$
$419$	−13.8030	+	23.9075i	−0.674320	+	1.16796i	−0.976667	+	0.214759i	$0.931104\pi$
$420$		0			0
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	0.868859	−	0.495060i	$-0.164854\pi$
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	−0.863164	+	0.504924i	$0.831521\pi$
$422$	−8.00000	−	13.8564i	−0.389434	−	0.674519i
$423$		0			0
$424$	1.37228	−	2.37686i	0.0666439	−	0.115431i
$425$	−6.81386	+	11.8020i	−0.330521	+	0.572479i
$426$	−5.05842	+	16.7769i	−0.245081	+	0.812843i
$427$		0			0
$428$	0.813859	−	1.40965i	0.0393394	−	0.0681378i
$429$	4.37228	−	14.5012i	0.211096	−	0.700125i
$430$	12.5109			0.603328
$431$	14.7446	−	25.5383i	0.710221	−	1.23014i	−0.254554	−	0.967059i	$-0.581929\pi$
$431$	14.7446	−	25.5383i	0.710221	−	1.23014i	0.964774	−	0.263079i	$-0.0847381\pi$
$432$	−0.872281	−	5.12241i	−0.0419677	−	0.246452i
$433$	−2.88316			−0.138556			−0.0692778	−	0.997597i	$-0.522069\pi$
$433$	−2.88316			−0.138556			−0.0692778	+	0.997597i	$0.522069\pi$
$434$		0			0
$435$	−4.46738	−	4.75372i	−0.214194	−	0.227924i
$436$	14.0000			0.670478
$437$	18.4307	+	31.9229i	0.881660	+	1.52708i
$438$	6.06930	+	6.45832i	0.290002	+	0.308591i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	8.74456			0.415936
$443$	11.4416	−	19.8174i	0.543606	−	0.941553i	−0.455087	−	0.890447i	$-0.650392\pi$
$443$	11.4416	−	19.8174i	0.543606	−	0.941553i	0.998693	−	0.0511061i	$-0.0162747\pi$
$444$	1.00000	−	3.31662i	0.0474579	−	0.157400i
$445$	2.23369	+	3.86886i	0.105887	+	0.183402i
$446$	4.00000			0.189405
$447$	−24.8614	+	5.84096i	−1.17590	+	0.276268i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$	−0.580171	+	9.33252i	−0.0273495	+	0.439939i
$451$	−22.6753	+	39.2747i	−1.06774	+	1.84937i
$452$	1.37228			0.0645467
$453$	13.6861	−	3.21543i	0.643031	−	0.151074i
$454$	−11.8723	+	20.5634i	−0.557194	+	0.965088i
$455$		0			0
$456$	−5.93070	−	6.31084i	−0.277731	−	0.295532i
$457$	−16.7337	+	28.9836i	−0.782769	+	1.35580i	0.147554	+	0.989054i	$0.452860\pi$
$457$	−16.7337	+	28.9836i	−0.782769	+	1.35580i	−0.930323	+	0.366742i	$0.880473\pi$
$458$	−10.0584	+	17.4217i	−0.469999	+	0.814062i
$459$	3.81386	+	22.3966i	0.178016	+	1.04539i
$460$	−5.05842	−	8.76144i	−0.235850	−	0.408504i
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	−0.961523	−	0.274724i	$-0.911414\pi$
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	0.242844	−	0.970065i	$-0.421920\pi$
$462$		0			0
$463$	2.94158	−	5.09496i	0.136707	−	0.236783i	−0.789541	−	0.613697i	$-0.789682\pi$
$463$	2.94158	−	5.09496i	0.136707	−	0.236783i	0.926248	+	0.376914i	$0.123015\pi$
$464$	2.74456			0.127413
$465$	−3.25544	−	3.46410i	−0.150967	−	0.160644i
$466$	11.7446			0.544056
$467$	15.0475	+	26.0631i	0.696317	+	1.20606i	0.969735	+	0.244162i	$0.0785127\pi$
$467$	15.0475	+	26.0631i	0.696317	+	1.20606i	−0.273417	+	0.961896i	$0.588154\pi$
$468$	5.37228	−	2.67181i	0.248334	−	0.123505i
$469$		0			0
$470$		0			0
$471$	−9.62772	−	10.2448i	−0.443622	−	0.472057i
$472$	3.55842	+	6.16337i	0.163790	+	0.283692i
$473$	−19.9307	−	34.5210i	−0.916415	−	1.58728i
$474$	−14.3723	−	15.2935i	−0.660141	−	0.702454i
$475$	7.79211	+	13.4963i	0.357527	+	0.619254i
$476$		0			0
$477$	−0.510875	+	8.21782i	−0.0233913	+	0.376268i
$478$	−9.43070	−	16.3345i	−0.431350	−	0.747121i
$479$	21.2554			0.971186			0.485593	−	0.874185i	$-0.338604\pi$
$479$	21.2554			0.971186			0.485593	+	0.874185i	$0.338604\pi$
$480$	1.62772	+	1.73205i	0.0742949	+	0.0790569i
$481$	4.00000			0.182384
$482$	0.441578	−	0.764836i	0.0201133	−	0.0348373i
$483$		0			0
$484$	−4.05842	−	7.02939i	−0.184474	−	0.319518i
$485$	6.25544	+	10.8347i	0.284045	+	0.491980i
$486$	9.18614	+	12.5942i	0.416692	+	0.571286i
$487$	8.17527	−	14.1600i	0.370457	−	0.641650i	−0.619179	−	0.785250i	$-0.712535\pi$
$487$	8.17527	−	14.1600i	0.370457	−	0.641650i	0.989636	+	0.143600i	$0.0458679\pi$
$488$	−7.05842	+	12.2255i	−0.319520	+	0.553424i
$489$	19.2554	+	20.4897i	0.870761	+	0.926574i
$490$		0			0
$491$	9.81386	−	16.9981i	0.442893	−	0.767114i	−0.555010	−	0.831844i	$-0.687285\pi$
$491$	9.81386	−	16.9981i	0.442893	−	0.767114i	0.997903	+	0.0647303i	$0.0206187\pi$
$492$	−17.4891	+	4.10891i	−0.788471	+	0.185244i
$493$	−12.0000			−0.540453
$494$	5.00000	−	8.66025i	0.224961	−	0.389643i
$495$	−16.1168	+	8.01544i	−0.724398	+	0.360267i
$496$	2.00000			0.0898027
$497$		0			0
$498$	−9.25544	+	2.17448i	−0.414746	+	0.0974408i
$499$	0.883156			0.0395355			0.0197677	−	0.999805i	$-0.493707\pi$
$499$	0.883156			0.0395355			0.0197677	+	0.999805i	$0.493707\pi$
$500$	−5.56930	−	9.64630i	−0.249067	−	0.431396i
$501$	8.74456	−	29.0024i	0.390678	−	1.29573i
$502$	−4.50000	+	7.79423i	−0.200845	+	0.347873i
$503$	2.23369			0.0995952			0.0497976	−	0.998759i	$-0.484142\pi$
$503$	2.23369			0.0995952			0.0497976	+	0.998759i	$0.484142\pi$
$504$		0			0
$505$	−10.1168			−0.450194
$506$	−16.1168	+	27.9152i	−0.716481	+	1.24098i
$507$	−10.6753	−	11.3595i	−0.474105	−	0.504494i
$508$	7.05842	+	12.2255i	0.313167	+	0.542421i
$509$	16.9783			0.752548			0.376274	−	0.926508i	$-0.377205\pi$
$509$	16.9783			0.752548			0.376274	+	0.926508i	$0.377205\pi$
$510$	−7.11684	−	7.57301i	−0.315139	−	0.335339i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	24.3614	+	9.02895i	1.07558	+	0.398638i
$514$	10.9307	−	18.9325i	0.482133	−	0.835078i
$515$	13.7228			0.604699
$516$	4.55842	−	15.1186i	0.200673	−	0.665558i
$517$		0			0
$518$		0			0
$519$	−3.00000	+	9.94987i	−0.131685	+	0.436751i
$520$	−1.37228	+	2.37686i	−0.0601785	+	0.104232i
$521$	−1.93070	+	3.34408i	−0.0845856	+	0.146507i	−0.905215	−	0.424955i	$-0.860290\pi$
$521$	−1.93070	+	3.34408i	−0.0845856	+	0.146507i	0.820629	+	0.571461i	$0.193623\pi$
$522$	−7.37228	+	3.66648i	−0.322676	+	0.160478i
$523$	8.94158	+	15.4873i	0.390988	+	0.677211i	0.992580	−	0.121592i	$-0.0388001\pi$
$523$	8.94158	+	15.4873i	0.390988	+	0.677211i	−0.601592	+	0.798803i	$0.705467\pi$
$524$	3.68614	+	6.38458i	0.161030	+	0.278912i
$525$		0			0
$526$	6.68614	−	11.5807i	0.291530	−	0.504944i
$527$	−8.74456			−0.380919
$528$	2.18614	−	7.25061i	0.0951396	−	0.315542i
$529$	31.3505			1.36307
$530$	−1.88316	−	3.26172i	−0.0817991	−	0.141680i
$531$	−17.7921	−	11.8020i	−0.772112	−	0.512161i
$532$		0			0
$533$	−10.3723	−	17.9653i	−0.449273	−	0.778164i
$534$	5.48913	−	1.28962i	0.237538	−	0.0558073i
$535$	−1.11684	−	1.93443i	−0.0482854	−	0.0836327i
$536$	7.55842	+	13.0916i	0.326474	+	0.565470i
$537$	7.37228	−	24.4511i	0.318137	−	1.05514i
$538$	−3.68614	−	6.38458i	−0.158921	−	0.275259i
$539$		0			0
$540$	−6.68614	−	2.47805i	−0.287726	−	0.106638i
$541$	−14.1168	−	24.4511i	−0.606931	−	1.05123i	−0.991743	−	0.128240i	$-0.959067\pi$
$541$	−14.1168	−	24.4511i	−0.606931	−	1.05123i	0.384813	−	0.922995i	$-0.374266\pi$
$542$	18.2337			0.783204
$543$	−30.5475	+	7.17687i	−1.31092	+	0.307989i
$544$	4.37228			0.187460
$545$	9.60597	−	16.6380i	0.411475	−	0.712695i
$546$		0			0
$547$	−0.441578	−	0.764836i	−0.0188805	−	0.0327020i	0.856431	−	0.516262i	$-0.172677\pi$
$547$	−0.441578	−	0.764836i	−0.0188805	−	0.0327020i	−0.875311	+	0.483560i	$0.839344\pi$
$548$	−8.18614	−	14.1788i	−0.349695	−	0.605689i
$549$	2.62772	−	42.2689i	0.112148	−	1.80399i
$550$	−6.81386	+	11.8020i	−0.290544	+	0.503237i
$551$	−6.86141	+	11.8843i	−0.292306	+	0.506288i
$552$	−12.4307	+	2.92048i	−0.529086	+	0.124304i
$553$		0			0
$554$	11.1168	−	19.2549i	0.472309	−	0.818064i
$555$	−3.25544	−	3.46410i	−0.138186	−	0.147043i
$556$	−21.2337			−0.900509
$557$	−3.25544	+	5.63858i	−0.137937	+	0.238914i	−0.926716	−	0.375763i	$-0.877381\pi$
$557$	−3.25544	+	5.63858i	−0.137937	+	0.238914i	0.788778	+	0.614678i	$0.210714\pi$
$558$	−5.37228	+	2.67181i	−0.227427	+	0.113107i
$559$	18.2337			0.771203
$560$		0			0
$561$	−9.55842	+	31.7017i	−0.403557	+	1.33845i
$562$	−10.6277			−0.448303
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$		0			0
$565$	0.941578	−	1.63086i	0.0396125	−	0.0686108i
$566$	−9.88316			−0.415420
$567$		0			0
$568$	−10.1168			−0.424493
$569$	0.558422	−	0.967215i	0.0234103	−	0.0405478i	−0.854083	−	0.520137i	$-0.825881\pi$
$569$	0.558422	−	0.967215i	0.0234103	−	0.0405478i	0.877493	+	0.479589i	$0.159214\pi$
$570$	−11.5693	+	2.71810i	−0.484585	+	0.113849i
$571$	−14.6753	−	25.4183i	−0.614141	−	1.06372i	−0.990535	−	0.137263i	$-0.956169\pi$
$571$	−14.6753	−	25.4183i	−0.614141	−	1.06372i	0.376394	−	0.926460i	$-0.377164\pi$
$572$	8.74456			0.365629
$573$	−0.941578	+	3.12286i	−0.0393350	+	0.130459i
$574$		0			0
$575$	22.9783			0.958259
$576$	2.68614	−	1.33591i	0.111923	−	0.0556628i
$577$	−13.5584	+	23.4839i	−0.564444	+	0.977647i	0.432657	+	0.901559i	$0.357576\pi$
$577$	−13.5584	+	23.4839i	−0.564444	+	0.977647i	−0.997101	+	0.0760878i	$0.975757\pi$
$578$	−2.11684			−0.0880491
$579$	−8.30298	−	8.83518i	−0.345060	−	0.367178i
$580$	1.88316	−	3.26172i	0.0781938	−	0.135436i
$581$		0			0
$582$	15.3723	−	3.61158i	0.637202	−	0.149705i
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−2.55842	+	4.43132i	−0.105868	+	0.183369i
$585$	0.510875	−	8.21782i	0.0211221	−	0.339765i
$586$	−2.31386	−	4.00772i	−0.0955846	−	0.165557i
$587$	4.24456	+	7.35180i	0.175192	+	0.303441i	0.940228	−	0.340547i	$-0.110612\pi$
$587$	4.24456	+	7.35180i	0.175192	+	0.303441i	−0.765036	+	0.643988i	$0.777279\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	9.76631			0.402073
$591$	10.1168	−	2.37686i	0.416151	−	0.0977710i
$592$	2.00000			0.0821995
$593$	−1.62772	−	2.81929i	−0.0668424	−	0.115774i	0.830667	−	0.556769i	$-0.187959\pi$
$593$	−1.62772	−	2.81929i	−0.0668424	−	0.115774i	−0.897510	+	0.440995i	$0.854626\pi$
$594$	3.81386	+	22.3966i	0.156485	+	0.918945i
$595$		0			0
$596$	−7.37228	−	12.7692i	−0.301980	−	0.523045i
$597$	−5.00000	+	16.5831i	−0.204636	+	0.678702i
$598$	−7.37228	−	12.7692i	−0.301475	−	0.522170i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	−5.25544	+	1.23472i	−0.214552	+	0.0504071i
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	0.787257	−	0.616625i	$-0.211501\pi$
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	−0.927642	+	0.373472i	$0.878167\pi$
$602$		0			0
$603$	−37.7921	−	25.0684i	−1.53901	−	1.02087i
$604$	4.05842	+	7.02939i	0.165135	+	0.286022i
$605$	−11.1386			−0.452848
$606$	−3.68614	+	12.2255i	−0.149739	+	0.496629i
$607$	−12.2337			−0.496550			−0.248275	−	0.968690i	$-0.579864\pi$
$607$	−12.2337			−0.496550			−0.248275	+	0.968690i	$0.579864\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	9.68614	+	16.7769i	0.392180	+	0.679276i
$611$		0			0
$612$	−11.7446	+	5.84096i	−0.474746	+	0.236107i
$613$	0.883156	−	1.52967i	0.0356703	−	0.0617828i	−0.847639	−	0.530573i	$-0.821977\pi$
$613$	0.883156	−	1.52967i	0.0356703	−	0.0617828i	0.883309	+	0.468790i	$0.155310\pi$
$614$	−6.50000	+	11.2583i	−0.262319	+	0.454349i
$615$	−7.11684	+	23.6039i	−0.286979	+	0.951801i
$616$		0			0
$617$	4.93070	−	8.54023i	0.198503	−	0.343817i	−0.749540	−	0.661959i	$-0.769725\pi$
$617$	4.93070	−	8.54023i	0.198503	−	0.343817i	0.948043	+	0.318142i	$0.103059\pi$
$618$	5.00000	−	16.5831i	0.201129	−	0.667071i
$619$	−23.4674			−0.943233			−0.471617	−	0.881804i	$-0.656329\pi$
$619$	−23.4674			−0.943233			−0.471617	+	0.881804i	$0.656329\pi$
$620$	1.37228	−	2.37686i	0.0551121	−	0.0954570i
$621$	29.4891	−	24.4511i	1.18336	−	0.981188i
$622$	26.2337			1.05188
$623$		0			0
$624$	2.37228	+	2.52434i	0.0949673	+	0.101054i
$625$	0.298936			0.0119574
$626$	−1.44158	−	2.49689i	−0.0576170	−	0.0997956i
$627$	25.9307	+	27.5928i	1.03557	+	1.10195i
$628$	4.05842	−	7.02939i	0.161949	−	0.280503i
$629$	−8.74456			−0.348669
$630$		0			0
$631$	14.3505			0.571286			0.285643	−	0.958336i	$-0.407793\pi$
$631$	14.3505			0.571286			0.285643	+	0.958336i	$0.407793\pi$
$632$	6.05842	−	10.4935i	0.240991	−	0.417409i
$633$	−8.00000	+	26.5330i	−0.317971	+	1.05459i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	19.3723			0.768766
$636$	−4.62772	+	1.08724i	−0.183501	+	0.0431119i
$637$		0			0
$638$	−12.0000			−0.475085
$639$	27.1753	−	13.5152i	1.07504	−	0.534652i
$640$	−0.686141	+	1.18843i	−0.0271221	+	0.0469768i
$641$	−46.2119			−1.82526			−0.912631	−	0.408785i	$-0.865953\pi$
$641$	−46.2119			−1.82526			−0.912631	+	0.408785i	$0.865953\pi$
$642$	−2.74456	+	0.644810i	−0.108319	+	0.0254486i
$643$	12.6753	−	21.9542i	0.499864	−	0.865789i	−0.500136	−	0.865947i	$-0.666717\pi$
$643$	12.6753	−	21.9542i	0.499864	−	0.865789i	1.00000		0.000157386i	$5.00974e-5\pi$
$644$		0			0
$645$	−14.8397	−	15.7908i	−0.584311	−	0.621764i
$646$	−10.9307	+	18.9325i	−0.430063	+	0.744891i
$647$	8.74456	−	15.1460i	0.343784	−	0.595452i	−0.641348	−	0.767250i	$-0.721624\pi$
$647$	8.74456	−	15.1460i	0.343784	−	0.595452i	0.985132	+	0.171798i	$0.0549578\pi$
$648$	−5.43070	+	7.17687i	−0.213338	+	0.281934i
$649$	−15.5584	−	26.9480i	−0.610721	−	1.05780i
$650$	−3.11684	−	5.39853i	−0.122253	−	0.211748i
$651$		0			0
$652$	−8.11684	+	14.0588i	−0.317880	+	0.550585i
$653$	−15.2554			−0.596991			−0.298496	−	0.954411i	$-0.596485\pi$
$653$	−15.2554			−0.596991			−0.298496	+	0.954411i	$0.596485\pi$
$654$	−16.6060	−	17.6704i	−0.649345	−	0.690966i
$655$	10.1168			0.395298
$656$	−5.18614	−	8.98266i	−0.202485	−	0.350714i
$657$	0.952453	−	15.3210i	0.0371587	−	0.597727i
$658$		0			0
$659$	4.62772	+	8.01544i	0.180270	+	0.312237i	0.941973	−	0.335690i	$-0.108969\pi$
$659$	4.62772	+	8.01544i	0.180270	+	0.312237i	−0.761702	+	0.647927i	$0.775636\pi$
$660$	−7.11684	−	7.57301i	−0.277023	−	0.294779i
$661$	−4.94158	−	8.55906i	−0.192205	−	0.332909i	0.753776	−	0.657132i	$-0.228231\pi$
$661$	−4.94158	−	8.55906i	−0.192205	−	0.332909i	−0.945981	+	0.324223i	$0.894897\pi$
$662$	−6.11684	−	10.5947i	−0.237738	−	0.411774i
$663$	−10.3723	−	11.0371i	−0.402826	−	0.428646i
$664$	−2.74456	−	4.75372i	−0.106510	−	0.184480i
$665$		0			0
$666$	−5.37228	+	2.67181i	−0.208172	+	0.103531i
$667$	10.1168	+	17.5229i	0.391726	+	0.678489i
$668$	17.4891			0.676675
$669$	−4.74456	−	5.04868i	−0.183435	−	0.195193i
$670$	20.7446			0.801432
$671$	30.8614	−	53.4535i	1.19139	−	2.06355i
$672$		0			0
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	0.992143	−	0.125109i	$-0.0399281\pi$
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	−0.604419	+	0.796666i	$0.706595\pi$
$674$	4.55842	+	7.89542i	0.175584	+	0.304120i
$675$	12.4674	−	10.3374i	0.479870	−	0.397887i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	17.2337	−	29.8496i	0.662344	−	1.14721i	−0.317654	−	0.948207i	$-0.602895\pi$
$677$	17.2337	−	29.8496i	0.662344	−	1.14721i	0.979998	−	0.199007i	$-0.0637718\pi$
$678$	−1.62772	−	1.73205i	−0.0625122	−	0.0665190i
$679$		0			0
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$	40.0367	−	9.40625i	1.53421	−	0.360448i
$682$	−8.74456			−0.334847
$683$	22.4198	−	38.8323i	0.857871	−	1.48588i	−0.0160849	−	0.999871i	$-0.505120\pi$
$683$	22.4198	−	38.8323i	0.857871	−	1.48588i	0.873956	−	0.486005i	$-0.161546\pi$
$684$	−0.930703	+	14.9711i	−0.0355863	+	0.572434i
$685$	−22.4674			−0.858434
$686$		0			0
$687$	33.9198	−	7.96916i	1.29412	−	0.304042i
$688$	9.11684			0.347576
$689$	−2.74456	−	4.75372i	−0.104560	−	0.181102i
$690$	−5.05842	+	16.7769i	−0.192571	+	0.638685i
$691$	2.94158	−	5.09496i	0.111903	−	0.193822i	−0.804635	−	0.593770i	$-0.797639\pi$
$691$	2.94158	−	5.09496i	0.111903	−	0.193822i	0.916537	+	0.399949i	$0.130972\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−7.11684			−0.270152
$695$	−14.5693	+	25.2348i	−0.552645	+	0.957209i
$696$	−3.25544	−	3.46410i	−0.123397	−	0.131306i
$697$	22.6753	+	39.2747i	0.858887	+	1.48764i
$698$	22.0000			0.832712
$699$	−13.9307	−	14.8236i	−0.526908	−	0.560681i
$700$		0			0
$701$	−3.76631			−0.142252			−0.0711258	−	0.997467i	$-0.522659\pi$
$701$	−3.76631			−0.142252			−0.0711258	+	0.997467i	$0.522659\pi$
$702$	−9.74456	−	3.61158i	−0.367785	−	0.136310i
$703$	−5.00000	+	8.66025i	−0.188579	+	0.326628i
$704$	4.37228			0.164787
$705$		0			0
$706$	−3.81386	+	6.60580i	−0.143536	+	0.248612i
$707$		0			0
$708$	3.55842	−	11.8020i	0.133734	−	0.443544i
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	0.0747503	+	0.997202i	$0.476184\pi$
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	−0.900978	+	0.433865i	$0.857149\pi$
$710$	−6.94158	+	12.0232i	−0.260513	+	0.451221i
$711$	−2.25544	+	36.2805i	−0.0845855	+	1.36062i
$712$	1.62772	+	2.81929i	0.0610013	+	0.105657i
$713$	7.37228	+	12.7692i	0.276094	+	0.478209i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$	14.7446			0.551030
$717$	−9.43070	+	31.2781i	−0.352196	+	1.16810i
$718$	6.86141			0.256065
$719$	4.37228	+	7.57301i	0.163059	+	0.282426i	0.935964	−	0.352095i	$-0.114531\pi$
$719$	4.37228	+	7.57301i	0.163059	+	0.282426i	−0.772906	+	0.634521i	$0.781197\pi$
$720$	0.255437	−	4.10891i	0.00951959	−	0.153130i
$721$		0			0
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	−1.48913	+	0.349857i	−0.0553812	+	0.0130113i
$724$	−9.05842	−	15.6896i	−0.336654	−	0.583101i
$725$	4.27719	+	7.40830i	0.158851	+	0.275138i
$726$	−4.05842	+	13.4603i	−0.150622	+	0.499557i
$727$	0.883156	+	1.52967i	0.0327544	+	0.0567324i	0.881938	−	0.471366i	$-0.156239\pi$
$727$	0.883156	+	1.52967i	0.0327544	+	0.0567324i	−0.849183	+	0.528098i	$0.822905\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	3.51087	+	6.08101i	0.129943	+	0.225068i
$731$	−39.8614			−1.47433
$732$	23.8030	−	5.59230i	0.879784	−	0.206697i
$733$	−23.8832			−0.882144			−0.441072	−	0.897472i	$-0.645402\pi$
$733$	−23.8832			−0.882144			−0.441072	+	0.897472i	$0.645402\pi$
$734$	11.1168	−	19.2549i	0.410330	−	0.710713i
$735$		0			0
$736$	−3.68614	−	6.38458i	−0.135873	−	0.235339i
$737$	−33.0475	−	57.2400i	−1.21732	−	2.10846i
$738$	25.9307	+	17.2005i	0.954522	+	0.633159i
$739$	−4.55842	+	7.89542i	−0.167684	+	0.290438i	−0.937605	−	0.347702i	$-0.886962\pi$
$739$	−4.55842	+	7.89542i	−0.167684	+	0.290438i	0.769921	+	0.638139i	$0.220296\pi$
$740$	1.37228	−	2.37686i	0.0504461	−	0.0873751i
$741$	−16.8614	+	3.96143i	−0.619419	+	0.145527i
$742$		0			0
$743$	−21.8614	+	37.8651i	−0.802017	+	1.38913i	0.116269	+	0.993218i	$0.462906\pi$
$743$	−21.8614	+	37.8651i	−0.802017	+	1.38913i	−0.918286	+	0.395917i	$0.870427\pi$
$744$	−2.37228	−	2.52434i	−0.0869721	−	0.0925467i
$745$	−20.2337			−0.741305
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$	13.7228	+	9.10268i	0.502091	+	0.333050i
$748$	−19.1168			−0.698981
$749$		0			0
$750$	−5.56930	+	18.4713i	−0.203362	+	0.674475i
$751$	0.116844			0.00426370			0.00213185	−	0.999998i	$-0.499321\pi$
$751$	0.116844			0.00426370			0.00213185	+	0.999998i	$0.499321\pi$
$752$		0			0
$753$	15.1753	−	3.56529i	0.553017	−	0.129926i
$754$	2.74456	−	4.75372i	0.0999511	−	0.173120i
$755$	11.1386			0.405375
$756$		0			0
$757$	11.7663			0.427654			0.213827	−	0.976872i	$-0.431407\pi$
$757$	11.7663			0.427654			0.213827	+	0.976872i	$0.431407\pi$
$758$	4.55842	−	7.89542i	0.165569	−	0.286775i
$759$	54.3505	−	12.7692i	1.97280	−	0.463491i
$760$	−3.43070	−	5.94215i	−0.124445	−	0.215545i
$761$	12.5109			0.453519			0.226759	−	0.973951i	$-0.427187\pi$
$761$	12.5109			0.453519			0.226759	+	0.973951i	$0.427187\pi$
$762$	7.05842	−	23.4101i	0.255700	−	0.848060i
$763$		0			0
$764$	−1.88316			−0.0681302
$765$	−1.11684	+	17.9653i	−0.0403796	+	0.649537i
$766$	−10.6277	+	18.4077i	−0.383995	+	0.665099i
$767$	14.2337			0.513949
$768$	1.18614	+	1.26217i	0.0428012	+	0.0455446i
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$		0			0
$771$	−36.8614	+	8.66025i	−1.32753	+	0.311891i
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	5.56930	−	9.64630i	0.200314	−	0.346953i	−0.748316	−	0.663343i	$-0.769137\pi$
$773$	5.56930	−	9.64630i	0.200314	−	0.346953i	0.948629	+	0.316389i	$0.102471\pi$
$774$	−24.4891	+	12.1793i	−0.880243	+	0.437774i
$775$	3.11684	+	5.39853i	0.111960	+	0.193921i
$776$	4.55842	+	7.89542i	0.163638	+	0.283429i
$777$		0			0
$778$	−17.4891	+	30.2921i	−0.627016	+	1.08602i
$779$	51.8614			1.85813
$780$	4.62772	−	1.08724i	0.165699	−	0.0389295i
$781$	44.2337			1.58281
$782$	16.1168	+	27.9152i	0.576337	+	0.998245i
$783$	13.3723	+	4.95610i	0.477886	+	0.177117i
$784$		0			0
$785$	−5.56930	−	9.64630i	−0.198777	−	0.344291i
$786$	3.68614	−	12.2255i	0.131480	−	0.436071i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$	−22.5475	+	5.29734i	−0.802714	+	0.188590i
$790$	−8.31386	−	14.4000i	−0.295794	−	0.512330i
$791$		0			0
$792$	−11.7446	+	5.84096i	−0.417325	+	0.207550i
$793$	14.1168	+	24.4511i	0.501304	+	0.868284i
$794$	22.0000			0.780751
$795$	−1.88316	+	6.24572i	−0.0667887	+	0.221513i
$796$	−10.0000			−0.354441
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	−0.329579	−	0.944128i	$-0.606907\pi$
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	0.982428	−	0.186640i	$-0.0597597\pi$
$798$		0			0
$799$		0			0
$800$	−1.55842	−	2.69927i	−0.0550985	−	0.0954335i
$801$	−8.13859	−	5.39853i	−0.287563	−	0.190748i
$802$	−0.127719	+	0.221215i	−0.00450990	+	0.00781138i
$803$	11.1861	−	19.3750i	0.394750	−	0.683728i
$804$	7.55842	−	25.0684i	0.266565	−	0.884096i
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$	−3.68614	+	12.2255i	−0.129758	+	0.430360i
$808$	−7.37228			−0.259356
$809$	−10.9307	+	18.9325i	−0.384303	+	0.665632i	−0.991672	−	0.128787i	$-0.958892\pi$
$809$	−10.9307	+	18.9325i	−0.384303	+	0.665632i	0.607369	+	0.794420i	$0.292225\pi$
$810$	4.80298	+	11.3784i	0.168760	+	0.399795i
$811$	24.8832			0.873766			0.436883	−	0.899518i	$-0.356082\pi$
$811$	24.8832			0.873766			0.436883	+	0.899518i	$0.356082\pi$
$812$		0			0
$813$	−21.6277	−	23.0140i	−0.758517	−	0.807136i
$814$	−8.74456			−0.306497
$815$	11.1386	+	19.2926i	0.390168	+	0.675791i
$816$	−5.18614	−	5.51856i	−0.181551	−	0.193188i
$817$	−22.7921	+	39.4771i	−0.797395	+	1.38113i
$818$	−29.3505			−1.02622
$819$		0			0
$820$	−14.2337			−0.497062
$821$	19.1168	−	33.1113i	0.667182	−	1.15559i	−0.311506	−	0.950244i	$-0.600833\pi$
$821$	19.1168	−	33.1113i	0.667182	−	1.15559i	0.978689	−	0.205350i	$-0.0658332\pi$
$822$	−8.18614	+	27.1504i	−0.285524	+	0.946977i
$823$	−11.1168	−	19.2549i	−0.387509	−	0.671185i	0.604605	−	0.796525i	$-0.293331\pi$
$823$	−11.1168	−	19.2549i	−0.387509	−	0.671185i	−0.992114	+	0.125341i	$0.959998\pi$
$824$	10.0000			0.348367
$825$	22.9783	−	5.39853i	0.800000	−	0.187953i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	18.4307	+	12.2255i	0.640511	+	0.424867i
$829$	24.1168	−	41.7716i	0.837613	−	1.45079i	−0.0542728	−	0.998526i	$-0.517284\pi$
$829$	24.1168	−	41.7716i	0.837613	−	1.45079i	0.891885	−	0.452261i	$-0.149383\pi$
$830$	−7.53262			−0.261461
$831$	−37.4891	+	8.80773i	−1.30048	+	0.305537i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$	25.1861	+	26.8005i	0.872125	+	0.928025i
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$	−10.9307	+	18.9325i	−0.378046	+	0.654795i
$837$	9.74456	+	3.61158i	0.336821	+	0.124834i
$838$	13.8030	+	23.9075i	0.476816	+	0.825870i
$839$	8.74456	+	15.1460i	0.301896	+	0.522899i	0.976565	−	0.215221i	$-0.0690472\pi$
$839$	8.74456	+	15.1460i	0.301896	+	0.522899i	−0.674670	+	0.738120i	$0.735714\pi$
$840$		0			0
$841$	10.7337	−	18.5913i	0.370127	−	0.641079i
$842$	0.233688			0.00805342
$843$	12.6060	+	13.4140i	0.434173	+	0.462002i
$844$	−16.0000			−0.550743
$845$	−6.17527	−	10.6959i	−0.212436	−	0.367949i
$846$		0			0
$847$		0			0
$848$	−1.37228	−	2.37686i	−0.0471243	−	0.0816217i
$849$	11.7228	+	12.4742i	0.402326	+	0.428114i
$850$	6.81386	+	11.8020i	0.233713	+	0.404804i
$851$	7.37228	+	12.7692i	0.252719	+	0.437721i
$852$	12.0000	+	12.7692i	0.411113	+	0.437464i
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	0.977518	−	0.210854i	$-0.0676245\pi$
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	−0.671364	+	0.741128i	$0.734291\pi$
$854$		0			0
$855$	17.1535	+	11.3784i	0.586638	+	0.389132i
$856$	−0.813859	−	1.40965i	−0.0278171	−	0.0481807i
$857$	51.9565			1.77480			0.887400	−	0.461000i	$-0.152509\pi$
$857$	51.9565			1.77480			0.887400	+	0.461000i	$0.152509\pi$
$858$	−10.3723	−	11.0371i	−0.354104	−	0.376801i
$859$	51.1168			1.74408			0.872042	−	0.489431i	$-0.162795\pi$
$859$	51.1168			1.74408			0.872042	+	0.489431i	$0.162795\pi$
$860$	6.25544	−	10.8347i	0.213309	−	0.369461i
$861$		0			0
$862$	−14.7446	−	25.5383i	−0.502202	−	0.869839i
$863$	9.43070	+	16.3345i	0.321025	+	0.556031i	0.980700	−	0.195520i	$-0.0626394\pi$
$863$	9.43070	+	16.3345i	0.321025	+	0.556031i	−0.659675	+	0.751551i	$0.729306\pi$
$864$	−4.87228	−	1.80579i	−0.165758	−	0.0614342i
$865$	−4.11684	+	7.13058i	−0.139977	+	0.242447i
$866$	−1.44158	+	2.49689i	−0.0489868	+	0.0848477i
$867$	2.51087	+	2.67181i	0.0852738	+	0.0907396i
$868$		0			0
$869$	−26.4891	+	45.8805i	−0.898582	+	1.55639i
$870$	−6.35053	+	1.49200i	−0.215303	+	0.0505835i
$871$	30.2337			1.02443
$872$	7.00000	−	12.1244i	0.237050	−	0.410582i
$873$	−22.7921	−	15.1186i	−0.771396	−	0.511686i
$874$	36.8614			1.24686
$875$		0			0
$876$	8.62772	−	2.02700i	0.291504	−	0.0684861i
$877$	44.7011			1.50945			0.754724	−	0.656043i	$-0.227771\pi$
$877$	44.7011			1.50945			0.754724	+	0.656043i	$0.227771\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$	−2.31386	+	7.67420i	−0.0780445	+	0.258844i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	14.2337			0.479545			0.239773	−	0.970829i	$-0.422927\pi$
$881$	14.2337			0.479545			0.239773	+	0.970829i	$0.422927\pi$
$882$		0			0
$883$	11.3505			0.381976			0.190988	−	0.981592i	$-0.438831\pi$
$883$	11.3505			0.381976			0.190988	+	0.981592i	$0.438831\pi$
$884$	4.37228	−	7.57301i	0.147056	−	0.254708i
$885$	−11.5842	−	12.3267i	−0.389399	−	0.414359i
$886$	−11.4416	−	19.8174i	−0.384387	−	0.665778i
$887$	−31.7228			−1.06515			−0.532574	−	0.846383i	$-0.678775\pi$
$887$	−31.7228			−1.06515			−0.532574	+	0.846383i	$0.678775\pi$
$888$	−2.37228	−	2.52434i	−0.0796085	−	0.0847112i
$889$		0			0
$890$	4.46738			0.149747
$891$	23.7446	−	31.3793i	0.795473	−	1.05125i
$892$	2.00000	−	3.46410i	0.0669650	−	0.115987i
$893$		0			0
$894$	−7.37228	+	24.4511i	−0.246566	+	0.817767i
$895$	10.1168	−	17.5229i	0.338169	−	0.585726i
$896$		0			0
$897$	−7.37228	+	24.4511i	−0.246153	+	0.816398i
$898$	16.5000	−	28.5788i	0.550612	−	0.953688i
$899$	−2.74456	+	4.75372i	−0.0915363	+	0.158546i
$900$	7.79211	+	5.16870i	0.259737	+	0.172290i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$	22.6753	+	39.2747i	0.755004	+	1.30770i
$903$		0			0
$904$	0.686141	−	1.18843i	0.0228207	−	0.0395266i
$905$	−24.8614			−0.826421
$906$	4.05842	−	13.4603i	0.134832	−	0.447187i
$907$	−8.88316			−0.294960			−0.147480	−	0.989065i	$-0.547116\pi$
$907$	−8.88316			−0.294960			−0.147480	+	0.989065i	$0.547116\pi$
$908$	11.8723	+	20.5634i	0.393995	+	0.682420i
$909$	19.8030	−	9.84868i	0.656824	−	0.326660i
$910$		0			0
$911$	21.6861	+	37.5615i	0.718494	+	1.24447i	0.961596	+	0.274467i	$0.0885015\pi$
$911$	21.6861	+	37.5615i	0.718494	+	1.24447i	−0.243103	+	0.970001i	$0.578165\pi$
$912$	−8.43070	+	1.98072i	−0.279168	+	0.0655881i
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$	16.7337	+	28.9836i	0.553501	+	0.958692i
$915$	9.68614	−	32.1253i	0.320214	−	1.06203i
$916$	10.0584	+	17.4217i	0.332340	+	0.575629i
$917$		0			0
$918$	21.3030	+	7.89542i	0.703103	+	0.260588i
$919$	14.9416	+	25.8796i	0.492877	+	0.853688i	0.999966	−	0.00820529i	$-0.00261185\pi$
$919$	14.9416	+	25.8796i	0.492877	+	0.853688i	−0.507089	+	0.861894i	$0.669279\pi$
$920$	−10.1168			−0.333542
$921$	21.9198	−	5.14987i	0.722283	−	0.169694i
$922$	−30.8614			−1.01637
$923$	−10.1168	+	17.5229i	−0.333000	+	0.576773i
$924$		0			0
$925$	3.11684	+	5.39853i	0.102481	+	0.177503i
$926$	−2.94158	−	5.09496i	−0.0966663	−	0.167431i
$927$	−26.8614	+	13.3591i	−0.882244	+	0.438770i
$928$	1.37228	−	2.37686i	0.0450473	−	0.0780243i
$929$	−4.88316	+	8.45787i	−0.160211	+	0.277494i	−0.934944	−	0.354794i	$-0.884551\pi$
$929$	−4.88316	+	8.45787i	−0.160211	+	0.277494i	0.774733	+	0.632288i	$0.217884\pi$
$930$	−4.62772	+	1.08724i	−0.151749	+	0.0356520i
$931$		0			0
$932$	5.87228	−	10.1711i	0.192353	−	0.333165i
$933$	−31.1168	−	33.1113i	−1.01872	−	1.08402i
$934$	30.0951			0.984742
$935$	−13.1168	+	22.7190i	−0.428967	+	0.742992i
$936$	0.372281	−	5.98844i	0.0121684	−	0.195738i
$937$	−38.4674			−1.25667			−0.628337	−	0.777941i	$-0.716264\pi$
$937$	−38.4674			−1.25667			−0.628337	+	0.777941i	$0.716264\pi$
$938$		0			0
$939$	−1.44158	+	4.78117i	−0.0470441	+	0.156028i
$940$		0			0
$941$	−0.941578	−	1.63086i	−0.0306946	−	0.0531645i	0.850270	−	0.526347i	$-0.176439\pi$
$941$	−0.941578	−	1.63086i	−0.0306946	−	0.0531645i	−0.880965	+	0.473182i	$0.843105\pi$
$942$	−13.6861	+	3.21543i	−0.445919	+	0.104765i
$943$	38.2337	−	66.2227i	1.24506	−	2.15651i
$944$	7.11684			0.231634
$945$		0			0
$946$	−39.8614			−1.29601
$947$	−8.44158	+	14.6212i	−0.274314	+	0.475127i	−0.969962	−	0.243257i	$-0.921784\pi$
$947$	−8.44158	+	14.6212i	−0.274314	+	0.475127i	0.695648	+	0.718383i	$0.255118\pi$
$948$	−20.4307	+	4.80001i	−0.663558	+	0.155897i
$949$	5.11684	+	8.86263i	0.166100	+	0.287693i
$950$	15.5842			0.505619
$951$	−3.00000	+	9.94987i	−0.0972817	+	0.322647i
$952$		0			0
$953$	10.8832			0.352540			0.176270	−	0.984342i	$-0.443597\pi$
$953$	10.8832			0.352540			0.176270	+	0.984342i	$0.443597\pi$
$954$	6.86141	+	4.55134i	0.222146	+	0.147355i
$955$	−1.29211	+	2.23800i	−0.0418117	+	0.0724200i
$956$	−18.8614			−0.610021
$957$	14.2337	+	15.1460i	0.460110	+	0.489602i
$958$	10.6277	−	18.4077i	0.343366	−	0.594727i
$959$		0			0
$960$	2.31386	−	0.543620i	0.0746795	−	0.0175453i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	4.06930	+	2.69927i	0.131131	+	0.0869826i
$964$	−0.441578	−	0.764836i	−0.0142223	−	0.0246337i
$965$	−4.80298	−	8.31901i	−0.154614	−	0.267799i
$966$		0			0
$967$	−24.0584	+	41.6704i	−0.773667	+	1.34003i	0.161874	+	0.986811i	$0.448246\pi$
$967$	−24.0584	+	41.6704i	−0.773667	+	1.34003i	−0.935541	+	0.353219i	$0.885087\pi$
$968$	−8.11684			−0.260885
$969$	36.8614	−	8.66025i	1.18416	−	0.278207i
$970$	12.5109			0.401700
$971$	−3.68614	−	6.38458i	−0.118294	−	0.204891i	0.800798	−	0.598935i	$-0.204409\pi$
$971$	−3.68614	−	6.38458i	−0.118294	−	0.204891i	−0.919092	+	0.394044i	$0.871076\pi$
$972$	15.5000	−	1.65831i	0.497163	−	0.0531904i
$973$		0			0
$974$	−8.17527	−	14.1600i	−0.261952	−	0.453715i
$975$	−3.11684	+	10.3374i	−0.0998189	+	0.331062i
$976$	7.05842	+	12.2255i	0.225935	+	0.391330i
$977$	−11.4416	−	19.8174i	−0.366049	−	0.634015i	0.622895	−	0.782305i	$-0.285956\pi$
$977$	−11.4416	−	19.8174i	−0.366049	−	0.634015i	−0.988944	+	0.148291i	$0.952623\pi$
$978$	27.3723	−	6.43087i	0.875269	−	0.205637i
$979$	−7.11684	−	12.3267i	−0.227455	−	0.393964i
$980$		0			0
$981$	−2.60597	+	41.9191i	−0.0832022	+	1.33837i
$982$	−9.81386	−	16.9981i	−0.313173	−	0.542431i
$983$	−50.7446			−1.61850			−0.809250	−	0.587464i	$-0.800126\pi$
$983$	−50.7446			−1.61850			−0.809250	+	0.587464i	$0.800126\pi$
$984$	−5.18614	+	17.2005i	−0.165328	+	0.548331i
$985$	8.23369			0.262347
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	−5.00000	−	8.66025i	−0.159071	−	0.275519i
$989$	33.6060	+	58.2072i	1.06861	+	1.85088i
$990$	−1.11684	+	17.9653i	−0.0354956	+	0.570975i
$991$	10.2337	−	17.7253i	0.325084	−	0.563062i	−0.656446	−	0.754373i	$-0.727941\pi$
$991$	10.2337	−	17.7253i	0.325084	−	0.563062i	0.981529	+	0.191312i	$0.0612742\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	−6.11684	+	20.2873i	−0.194112	+	0.643797i
$994$		0			0
$995$	−6.86141	+	11.8843i	−0.217521	+	0.376758i
$996$	−2.74456	+	9.10268i	−0.0869648	+	0.288430i
$997$	12.1168			0.383744			0.191872	−	0.981420i	$-0.438544\pi$
$997$	12.1168			0.383744			0.191872	+	0.981420i	$0.438544\pi$
$998$	0.441578	−	0.764836i	0.0139779	−	0.0242104i
$999$	9.74456	+	3.61158i	0.308304	+	0.114265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.m.67.1		4
3.2	odd	2		2646.2.h.k.361.2		4
7.2	even	3		882.2.e.l.373.1		4
7.3	odd	6		882.2.f.k.589.1		4
7.4	even	3		126.2.f.d.85.2	yes	4
7.5	odd	6		882.2.e.k.373.2		4
7.6	odd	2		882.2.h.n.67.2		4
9.2	odd	6		2646.2.e.n.2125.1		4
9.7	even	3		882.2.e.l.655.2		4
21.2	odd	6		2646.2.e.n.1549.1		4
21.5	even	6		2646.2.e.m.1549.2		4
21.11	odd	6		378.2.f.c.253.1		4
21.17	even	6		2646.2.f.j.1765.2		4
21.20	even	2		2646.2.h.l.361.1		4
28.11	odd	6		1008.2.r.f.337.1		4
63.2	odd	6		2646.2.h.k.667.2		4
63.4	even	3		1134.2.a.k.1.1		2
63.11	odd	6		378.2.f.c.127.1		4
63.16	even	3	inner	882.2.h.m.79.1		4
63.20	even	6		2646.2.e.m.2125.2		4
63.25	even	3		126.2.f.d.43.2	✓	4
63.31	odd	6		7938.2.a.bh.1.2		2
63.32	odd	6		1134.2.a.n.1.2		2
63.34	odd	6		882.2.e.k.655.1		4
63.38	even	6		2646.2.f.j.883.2		4
63.47	even	6		2646.2.h.l.667.1		4
63.52	odd	6		882.2.f.k.295.1		4
63.59	even	6		7938.2.a.bs.1.1		2
63.61	odd	6		882.2.h.n.79.2		4
84.11	even	6		3024.2.r.f.1009.1		4
252.11	even	6		3024.2.r.f.2017.1		4
252.67	odd	6		9072.2.a.bm.1.1		2
252.95	even	6		9072.2.a.bb.1.2		2
252.151	odd	6		1008.2.r.f.673.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.2	✓	4	63.25	even	3
126.2.f.d.85.2	yes	4	7.4	even	3
378.2.f.c.127.1		4	63.11	odd	6
378.2.f.c.253.1		4	21.11	odd	6
882.2.e.k.373.2		4	7.5	odd	6
882.2.e.k.655.1		4	63.34	odd	6
882.2.e.l.373.1		4	7.2	even	3
882.2.e.l.655.2		4	9.7	even	3
882.2.f.k.295.1		4	63.52	odd	6
882.2.f.k.589.1		4	7.3	odd	6
882.2.h.m.67.1		4	1.1	even	1	trivial
882.2.h.m.79.1		4	63.16	even	3	inner
882.2.h.n.67.2		4	7.6	odd	2
882.2.h.n.79.2		4	63.61	odd	6
1008.2.r.f.337.1		4	28.11	odd	6
1008.2.r.f.673.1		4	252.151	odd	6
1134.2.a.k.1.1		2	63.4	even	3
1134.2.a.n.1.2		2	63.32	odd	6
2646.2.e.m.1549.2		4	21.5	even	6
2646.2.e.m.2125.2		4	63.20	even	6
2646.2.e.n.1549.1		4	21.2	odd	6
2646.2.e.n.2125.1		4	9.2	odd	6
2646.2.f.j.883.2		4	63.38	even	6
2646.2.f.j.1765.2		4	21.17	even	6
2646.2.h.k.361.2		4	3.2	odd	2
2646.2.h.k.667.2		4	63.2	odd	6
2646.2.h.l.361.1		4	21.20	even	2
2646.2.h.l.667.1		4	63.47	even	6
3024.2.r.f.1009.1		4	84.11	even	6
3024.2.r.f.2017.1		4	252.11	even	6
7938.2.a.bh.1.2		2	63.31	odd	6
7938.2.a.bs.1.1		2	63.59	even	6
9072.2.a.bb.1.2		2	252.95	even	6
9072.2.a.bm.1.1		2	252.67	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +(-0.686141 + 1.18843i) q^{10} +4.37228 q^{11} +(1.18614 + 1.26217i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(2.31386 - 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.18614 - 3.78651i) q^{17} +(0.186141 - 2.99422i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} -7.37228 q^{23} +(1.68614 - 0.396143i) q^{24} -3.11684 q^{25} +(1.00000 + 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(0.686141 - 2.27567i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.37228 + 1.73205i) q^{33} +(-2.18614 - 3.78651i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 - 1.73205i) q^{37} -5.00000 q^{38} +(1.00000 - 3.31662i) q^{39} +1.37228 q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(-2.18614 - 3.78651i) q^{44} +(-3.68614 + 1.83324i) q^{45} +(-3.68614 + 6.38458i) q^{46} +(0.500000 - 1.65831i) q^{48} +(-1.55842 + 2.69927i) q^{50} +(-2.18614 + 7.25061i) q^{51} +2.00000 q^{52} +(-1.37228 + 2.37686i) q^{53} +(0.872281 + 5.12241i) q^{54} -6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} -2.74456 q^{58} +(-3.55842 - 6.16337i) q^{59} +(-1.62772 - 1.73205i) q^{60} +(7.05842 - 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.37228 - 2.37686i) q^{65} +(-2.18614 + 7.25061i) q^{66} +(-7.55842 - 13.0916i) q^{67} -4.37228 q^{68} +(12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(-2.68614 + 1.33591i) q^{72} +(2.55842 - 4.43132i) q^{73} -2.00000 q^{74} +(5.25544 - 1.23472i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(-2.37228 - 2.52434i) q^{78} +(-6.05842 + 10.4935i) q^{79} +(0.686141 - 1.18843i) q^{80} +(5.43070 - 7.17687i) q^{81} +(5.18614 + 8.98266i) q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} -9.11684 q^{86} +(3.25544 + 3.46410i) q^{87} -4.37228 q^{88} +(-1.62772 - 2.81929i) q^{89} +(-0.255437 + 4.10891i) q^{90} +(3.68614 + 6.38458i) q^{92} +(2.37228 + 2.52434i) q^{93} +(3.43070 + 5.94215i) q^{95} +(-1.18614 - 1.26217i) q^{96} +(-4.55842 - 7.89542i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 4 q^{13} + 15 q^{15} - 2 q^{16} + 3 q^{17} - 5 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} - 18 q^{23} + q^{24} + 22 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 3 q^{30} - 4 q^{31} + 2 q^{32} - 18 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} - 20 q^{38} + 4 q^{39} - 6 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} - 9 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} - 3 q^{51} + 8 q^{52} + 6 q^{53} - 8 q^{54} - 24 q^{55} - 5 q^{57} + 12 q^{58} + 3 q^{59} - 18 q^{60} + 11 q^{61} - 8 q^{62} + 4 q^{64} - 6 q^{65} - 3 q^{66} - 13 q^{67} - 6 q^{68} + 21 q^{69} + 6 q^{71} - 5 q^{72} - 7 q^{73} - 8 q^{74} + 44 q^{75} - 10 q^{76} + 2 q^{78} - 7 q^{79} - 3 q^{80} - 7 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} - 2 q^{86} + 36 q^{87} - 6 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^8 + 5 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 4 * q^13 + 15 * q^15 - 2 * q^16 + 3 * q^17 - 5 * q^18 - 10 * q^19 - 3 * q^20 + 3 * q^22 - 18 * q^23 + q^24 + 22 * q^25 + 4 * q^26 - 16 * q^27 + 6 * q^29 - 3 * q^30 - 4 * q^31 + 2 * q^32 - 18 * q^33 - 3 * q^34 - 10 * q^36 - 4 * q^37 - 20 * q^38 + 4 * q^39 - 6 * q^40 - 15 * q^41 - q^43 - 3 * q^44 - 9 * q^45 - 9 * q^46 + 2 * q^48 + 11 * q^50 - 3 * q^51 + 8 * q^52 + 6 * q^53 - 8 * q^54 - 24 * q^55 - 5 * q^57 + 12 * q^58 + 3 * q^59 - 18 * q^60 + 11 * q^61 - 8 * q^62 + 4 * q^64 - 6 * q^65 - 3 * q^66 - 13 * q^67 - 6 * q^68 + 21 * q^69 + 6 * q^71 - 5 * q^72 - 7 * q^73 - 8 * q^74 + 44 * q^75 - 10 * q^76 + 2 * q^78 - 7 * q^79 - 3 * q^80 - 7 * q^81 + 15 * q^82 - 12 * q^83 - 12 * q^85 - 2 * q^86 + 36 * q^87 - 6 * q^88 - 18 * q^89 - 24 * q^90 + 9 * q^92 - 2 * q^93 - 15 * q^95 + q^96 - q^97 + 24 * q^99

Introduction

L-functions

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Database

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