LMFDB - Embedded newform 882.2.f.k.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, 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:	$7.04280545828$
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			295.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.k.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} -1.37228 q^{10} +(-2.18614 + 3.78651i) q^{11} +(1.68614 + 0.396143i) q^{12} +(1.00000 + 1.73205i) q^{13} +(2.31386 + 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.37228 q^{17} +(-2.68614 - 1.33591i) q^{18} -5.00000 q^{19} +(-0.686141 + 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(1.18614 - 1.26217i) q^{24} +(1.55842 - 2.69927i) q^{25} +2.00000 q^{26} +(4.00000 + 3.31662i) q^{27} +(-1.37228 + 2.37686i) q^{29} +(1.62772 - 1.73205i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.18614 - 7.25061i) q^{33} +(2.18614 - 3.78651i) q^{34} +(-2.50000 + 1.65831i) q^{36} +2.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(0.686141 + 1.18843i) q^{40} +(5.18614 + 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +4.37228 q^{44} +(-3.43070 + 2.27567i) q^{45} +7.37228 q^{46} +(-0.500000 - 1.65831i) q^{48} +(-1.55842 - 2.69927i) q^{50} +(-5.18614 + 5.51856i) q^{51} +(1.00000 - 1.73205i) q^{52} +2.74456 q^{53} +(4.87228 - 1.80579i) q^{54} +6.00000 q^{55} +(5.93070 - 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +(3.55842 + 6.16337i) q^{59} +(-0.686141 - 2.27567i) q^{60} +(-7.05842 + 12.2255i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(1.37228 - 2.37686i) q^{65} +(-7.37228 - 1.73205i) q^{66} +(-7.55842 - 13.0916i) q^{67} +(-2.18614 - 3.78651i) q^{68} +(-12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(0.186141 + 2.99422i) q^{72} +5.11684 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.55842 + 5.16870i) q^{75} +(2.50000 + 4.33013i) q^{76} +(-2.37228 + 2.52434i) q^{78} +(-6.05842 + 10.4935i) q^{79} +1.37228 q^{80} +(-8.93070 + 1.11469i) q^{81} +10.3723 q^{82} +(-2.74456 + 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-1.37228 - 4.55134i) q^{87} +(2.18614 - 3.78651i) q^{88} -3.25544 q^{89} +(0.255437 + 4.10891i) q^{90} +(3.68614 - 6.38458i) q^{92} +(-3.37228 - 0.792287i) q^{93} +(3.43070 + 5.94215i) q^{95} +(-1.68614 - 0.396143i) 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} + 3 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9} + 6 q^{10} - 3 q^{11} + q^{12} + 4 q^{13} + 15 q^{15} - 2 q^{16} + 6 q^{17} - 5 q^{18} - 20 q^{19} + 3 q^{20} + 3 q^{22} + 9 q^{23} - q^{24} - 11 q^{25} + 8 q^{26} + 16 q^{27} + 6 q^{29} + 18 q^{30} + 4 q^{31} + 2 q^{32} - 3 q^{33} + 3 q^{34} - 10 q^{36} + 8 q^{37} - 10 q^{38} - 2 q^{39} - 3 q^{40} + 15 q^{41} - q^{43} + 6 q^{44} + 15 q^{45} + 18 q^{46} - 2 q^{48} + 11 q^{50} - 15 q^{51} + 4 q^{52} - 12 q^{53} + 8 q^{54} + 24 q^{55} - 5 q^{57} - 6 q^{58} - 3 q^{59} + 3 q^{60} - 11 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 18 q^{66} - 13 q^{67} - 3 q^{68} - 21 q^{69} + 6 q^{71} - 5 q^{72} - 14 q^{73} + 4 q^{74} - 11 q^{75} + 10 q^{76} + 2 q^{78} - 7 q^{79} - 6 q^{80} - 7 q^{81} + 30 q^{82} + 12 q^{83} - 12 q^{85} + q^{86} + 6 q^{87} + 3 q^{88} - 36 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 + 3 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9 + 6 * q^10 - 3 * q^11 + q^12 + 4 * q^13 + 15 * q^15 - 2 * q^16 + 6 * q^17 - 5 * q^18 - 20 * q^19 + 3 * q^20 + 3 * q^22 + 9 * q^23 - q^24 - 11 * q^25 + 8 * q^26 + 16 * q^27 + 6 * q^29 + 18 * q^30 + 4 * q^31 + 2 * q^32 - 3 * q^33 + 3 * q^34 - 10 * q^36 + 8 * q^37 - 10 * q^38 - 2 * q^39 - 3 * q^40 + 15 * q^41 - q^43 + 6 * q^44 + 15 * q^45 + 18 * q^46 - 2 * q^48 + 11 * q^50 - 15 * q^51 + 4 * q^52 - 12 * q^53 + 8 * q^54 + 24 * q^55 - 5 * q^57 - 6 * q^58 - 3 * q^59 + 3 * q^60 - 11 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 18 * q^66 - 13 * q^67 - 3 * q^68 - 21 * q^69 + 6 * q^71 - 5 * q^72 - 14 * q^73 + 4 * q^74 - 11 * q^75 + 10 * q^76 + 2 * q^78 - 7 * q^79 - 6 * q^80 - 7 * q^81 + 30 * q^82 + 12 * q^83 - 12 * q^85 + q^86 + 6 * q^87 + 3 * q^88 - 36 * 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.686141	−	1.18843i	−0.306851	−	0.531482i	0.670820	−	0.741620i	$-0.265942\pi$
$5$	−0.686141	−	1.18843i	−0.306851	−	0.531482i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	0.500000	+	1.65831i	0.204124	+	0.677003i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$	−1.37228			−0.433953
$11$	−2.18614	+	3.78651i	−0.659146	+	1.14167i	0.321691	+	0.946845i	$0.395749\pi$
$11$	−2.18614	+	3.78651i	−0.659146	+	1.14167i	−0.980837	+	0.194830i	$0.937584\pi$
$12$	1.68614	+	0.396143i	0.486747	+	0.114357i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	2.31386	+	0.543620i	0.597436	+	0.140362i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.37228			1.06043			0.530217	−	0.847862i	$-0.322110\pi$
$17$	4.37228			1.06043			0.530217	+	0.847862i	$0.322110\pi$
$18$	−2.68614	−	1.33591i	−0.633129	−	0.314876i
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	−0.686141	+	1.18843i	−0.153426	+	0.265741i
$21$		0			0
$22$	2.18614	+	3.78651i	0.466087	+	0.807286i
$23$	3.68614	+	6.38458i	0.768613	+	1.33128i	0.938315	+	0.345782i	$0.112386\pi$
$23$	3.68614	+	6.38458i	0.768613	+	1.33128i	−0.169701	+	0.985496i	$0.554280\pi$
$24$	1.18614	−	1.26217i	0.242120	−	0.257639i
$25$	1.55842	−	2.69927i	0.311684	−	0.539853i
$26$	2.00000			0.392232
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$		0			0
$29$	−1.37228	+	2.37686i	−0.254826	+	0.441372i	−0.964848	−	0.262807i	$-0.915352\pi$
$29$	−1.37228	+	2.37686i	−0.254826	+	0.441372i	0.710022	+	0.704179i	$0.248685\pi$
$30$	1.62772	−	1.73205i	0.297179	−	0.316228i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.18614	−	7.25061i	−0.380558	−	1.26217i
$34$	2.18614	−	3.78651i	0.374920	−	0.649381i
$35$		0			0
$36$	−2.50000	+	1.65831i	−0.416667	+	0.276385i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$	−3.37228	−	0.792287i	−0.539997	−	0.126867i
$40$	0.686141	+	1.18843i	0.108488	+	0.187907i
$41$	5.18614	+	8.98266i	0.809939	+	1.40286i	0.912906	+	0.408171i	$0.133833\pi$
$41$	5.18614	+	8.98266i	0.809939	+	1.40286i	−0.102966	+	0.994685i	$0.532833\pi$
$42$		0			0
$43$	−4.55842	+	7.89542i	−0.695153	+	1.20404i	0.274976	+	0.961451i	$0.411330\pi$
$43$	−4.55842	+	7.89542i	−0.695153	+	1.20404i	−0.970129	+	0.242589i	$0.922003\pi$
$44$	4.37228			0.659146
$45$	−3.43070	+	2.27567i	−0.511419	+	0.339237i
$46$	7.37228			1.08698
$47$		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
$51$	−5.18614	+	5.51856i	−0.726205	+	0.772753i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	2.74456			0.376995			0.188497	−	0.982074i	$-0.439638\pi$
$53$	2.74456			0.376995			0.188497	+	0.982074i	$0.439638\pi$
$54$	4.87228	−	1.80579i	0.663034	−	0.245737i
$55$	6.00000			0.809040
$56$		0			0
$57$	5.93070	−	6.31084i	0.785541	−	0.835892i
$58$	1.37228	+	2.37686i	0.180189	+	0.312097i
$59$	3.55842	+	6.16337i	0.463267	+	0.802402i	0.999121	−	0.0419083i	$-0.0133437\pi$
$59$	3.55842	+	6.16337i	0.463267	+	0.802402i	−0.535854	+	0.844310i	$0.680010\pi$
$60$	−0.686141	−	2.27567i	−0.0885804	−	0.293788i
$61$	−7.05842	+	12.2255i	−0.903738	+	1.56532i	−0.0811364	+	0.996703i	$0.525855\pi$
$61$	−7.05842	+	12.2255i	−0.903738	+	1.56532i	−0.822602	+	0.568618i	$0.807478\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	1.37228	−	2.37686i	0.170211	−	0.294813i
$66$	−7.37228	−	1.73205i	−0.907465	−	0.213201i
$67$	−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	$-0.541275\pi$
$68$	−2.18614	−	3.78651i	−0.265108	−	0.459181i
$69$	−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	$0.295038\pi$
$72$	0.186141	+	2.99422i	0.0219369	+	0.352872i
$73$	5.11684			0.598881			0.299441	−	0.954115i	$-0.403200\pi$
$73$	5.11684			0.598881			0.299441	+	0.954115i	$0.403200\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.55842	+	5.16870i	0.179951	+	0.596830i
$76$	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	$0.927940\pi$
$80$	1.37228			0.153426
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$	10.3723			1.14543
$83$	−2.74456	+	4.75372i	−0.301255	+	0.521789i	−0.976420	−	0.215877i	$-0.930739\pi$
$83$	−2.74456	+	4.75372i	−0.301255	+	0.521789i	0.675166	+	0.737666i	$0.264072\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	4.55842	+	7.89542i	0.491547	+	0.851385i
$87$	−1.37228	−	4.55134i	−0.147124	−	0.487955i
$88$	2.18614	−	3.78651i	0.233043	−	0.403643i
$89$	−3.25544			−0.345076			−0.172538	−	0.985003i	$-0.555197\pi$
$89$	−3.25544			−0.345076			−0.172538	+	0.985003i	$0.555197\pi$
$90$	0.255437	+	4.10891i	0.0269255	+	0.433117i
$91$		0			0
$92$	3.68614	−	6.38458i	0.384307	−	0.665639i
$93$	−3.37228	−	0.792287i	−0.349689	−	0.0821563i
$94$		0			0
$95$	3.43070	+	5.94215i	0.351983	+	0.609652i
$96$	−1.68614	−	0.396143i	−0.172091	−	0.0404312i
$97$	4.55842	−	7.89542i	0.462838	−	0.801658i	−0.536263	−	0.844051i	$-0.680165\pi$
$97$	4.55842	−	7.89542i	0.462838	−	0.801658i	0.999101	+	0.0423924i	$0.0134980\pi$
$98$		0			0
$99$	11.7446	+	5.84096i	1.18037	+	0.587039i
$100$	−3.11684			−0.311684
$101$	3.68614	−	6.38458i	0.366785	−	0.635290i	−0.622276	−	0.782798i	$-0.713792\pi$
$101$	3.68614	−	6.38458i	0.366785	−	0.635290i	0.989061	+	0.147508i	$0.0471252\pi$
$102$	2.18614	+	7.25061i	0.216460	+	0.717917i
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	1.37228	−	2.37686i	0.133288	−	0.230861i
$107$	−1.62772			−0.157358			−0.0786788	−	0.996900i	$-0.525070\pi$
$107$	−1.62772			−0.157358			−0.0786788	+	0.996900i	$0.525070\pi$
$108$	0.872281	−	5.12241i	0.0839353	−	0.492905i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	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	0.831946	−	0.554856i	$-0.187227\pi$
$113$	−0.686141	−	1.18843i	−0.0645467	−	0.111798i	−0.896493	+	0.443058i	$0.853893\pi$
$114$	−2.50000	−	8.29156i	−0.234146	−	0.776576i
$115$	5.05842	−	8.76144i	0.471700	−	0.817009i
$116$	2.74456			0.254826
$117$	5.00000	−	3.31662i	0.462250	−	0.306622i
$118$	7.11684			0.655159
$119$		0			0
$120$	−2.31386	−	0.543620i	−0.211225	−	0.0496255i
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$	7.05842	+	12.2255i	0.639040	+	1.10685i
$123$	−17.4891	−	4.10891i	−1.57694	−	0.370488i
$124$	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
$129$	−4.55842	−	15.1186i	−0.401347	−	1.33112i
$130$	−1.37228	−	2.37686i	−0.120357	−	0.208464i
$131$	−3.68614	−	6.38458i	−0.322060	−	0.557824i	0.658853	−	0.752271i	$-0.271042\pi$
$131$	−3.68614	−	6.38458i	−0.322060	−	0.557824i	−0.980913	+	0.194448i	$0.937708\pi$
$132$	−5.18614	+	5.51856i	−0.451396	+	0.480329i
$133$		0			0
$134$	−15.1168			−1.30590
$135$	1.19702	−	7.02939i	0.103023	−	0.604994i
$136$	−4.37228			−0.374920
$137$	−8.18614	+	14.1788i	−0.699389	+	1.21138i	0.269289	+	0.963059i	$0.413211\pi$
$137$	−8.18614	+	14.1788i	−0.699389	+	1.21138i	−0.968678	+	0.248318i	$0.920122\pi$
$138$	−8.74456	+	9.30506i	−0.744387	+	0.792100i
$139$	−10.6168	−	18.3889i	−0.900509	−	1.55973i	−0.826835	−	0.562445i	$-0.809861\pi$
$139$	−10.6168	−	18.3889i	−0.900509	−	1.55973i	−0.0736742	−	0.997282i	$-0.523472\pi$
$140$		0			0
$141$		0			0
$142$	5.05842	−	8.76144i	0.424493	−	0.735244i
$143$	−8.74456			−0.731257
$144$	2.68614	+	1.33591i	0.223845	+	0.111326i
$145$	3.76631			0.312775
$146$	2.55842	−	4.43132i	0.211737	−	0.366738i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−7.37228	−	12.7692i	−0.603961	−	1.04609i	−0.992215	−	0.124538i	$-0.960255\pi$
$149$	−7.37228	−	12.7692i	−0.603961	−	1.04609i	0.388254	−	0.921552i	$-0.373078\pi$
$150$	5.25544	+	1.23472i	0.429105	+	0.100814i
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	−0.652295	−	0.757965i	$-0.726194\pi$
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	0.982565	+	0.185921i	$0.0595270\pi$
$152$	5.00000			0.405554
$153$	−0.813859	−	13.0916i	−0.0657966	−	1.05839i
$154$		0			0
$155$	1.37228	−	2.37686i	0.110224	−	0.190914i
$156$	1.00000	+	3.31662i	0.0800641	+	0.265543i
$157$	−4.05842	−	7.02939i	−0.323897	−	0.561007i	0.657391	−	0.753549i	$-0.271660\pi$
$157$	−4.05842	−	7.02939i	−0.323897	−	0.561007i	−0.981289	+	0.192543i	$0.938327\pi$
$158$	6.05842	+	10.4935i	0.481982	+	0.834818i
$159$	−3.25544	+	3.46410i	−0.258173	+	0.274721i
$160$	0.686141	−	1.18843i	0.0542442	−	0.0939537i
$161$		0			0
$162$	−3.50000	+	8.29156i	−0.274986	+	0.651447i
$163$	16.2337			1.27152			0.635760	−	0.771887i	$-0.280687\pi$
$163$	16.2337			1.27152			0.635760	+	0.771887i	$0.280687\pi$
$164$	5.18614	−	8.98266i	0.404970	−	0.701428i
$165$	−7.11684	+	7.57301i	−0.554046	+	0.589558i
$166$	2.74456	+	4.75372i	0.213019	+	0.368960i
$167$	8.74456	+	15.1460i	0.676675	+	1.17203i	0.975976	+	0.217876i	$0.0699129\pi$
$167$	8.74456	+	15.1460i	0.676675	+	1.17203i	−0.299302	+	0.954158i	$0.596754\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−6.00000			−0.460179
$171$	0.930703	+	14.9711i	0.0711727	+	1.14487i
$172$	9.11684			0.695153
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−4.62772	−	1.08724i	−0.350826	−	0.0824235i
$175$		0			0
$176$	−2.18614	−	3.78651i	−0.164787	−	0.285419i
$177$	−12.0000	−	2.81929i	−0.901975	−	0.211911i
$178$	−1.62772	+	2.81929i	−0.122003	+	0.211315i
$179$	14.7446			1.10206			0.551030	−	0.834485i	$-0.314235\pi$
$179$	14.7446			1.10206			0.551030	+	0.834485i	$0.314235\pi$
$180$	3.68614	+	1.83324i	0.274749	+	0.136642i
$181$	−18.1168			−1.34661			−0.673307	−	0.739363i	$-0.735127\pi$
$181$	−18.1168			−1.34661			−0.673307	+	0.739363i	$0.735127\pi$
$182$		0			0
$183$	−7.05842	−	23.4101i	−0.521774	−	1.73053i
$184$	−3.68614	−	6.38458i	−0.271746	−	0.470678i
$185$	−1.37228	−	2.37686i	−0.100892	−	0.174750i
$186$	−2.37228	+	2.52434i	−0.173944	+	0.185093i
$187$	−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	$0.144963\pi$
$192$	−1.18614	+	1.26217i	−0.0856023	+	0.0910892i
$193$	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	$0.752266\pi$
$194$	−4.55842	−	7.89542i	−0.327276	−	0.566858i
$195$	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	$0.568565\pi$
$198$	10.9307	−	7.25061i	0.776811	−	0.515278i
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	−1.55842	+	2.69927i	−0.110197	+	0.190867i
$201$	25.4891	+	5.98844i	1.79786	+	0.422392i
$202$	−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
$206$	−10.0000			−0.696733
$207$	18.4307	−	12.2255i	1.28102	−	0.849734i
$208$	−2.00000			−0.138675
$209$	10.9307	−	18.9325i	0.756093	−	1.30959i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−1.37228	−	2.37686i	−0.0942487	−	0.163243i
$213$	−12.0000	+	12.7692i	−0.822226	+	0.874929i
$214$	−0.813859	+	1.40965i	−0.0556343	+	0.0963614i
$215$	12.5109			0.853235
$216$	−4.00000	−	3.31662i	−0.272166	−	0.225668i
$217$		0			0
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$	−6.06930	+	6.45832i	−0.410125	+	0.436413i
$220$	−3.00000	−	5.19615i	−0.202260	−	0.350325i
$221$	4.37228	+	7.57301i	0.294111	+	0.509416i
$222$	1.00000	+	3.31662i	0.0671156	+	0.222597i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$	−8.37228	−	4.16381i	−0.558152	−	0.277588i
$226$	−1.37228			−0.0912828
$227$	−11.8723	+	20.5634i	−0.787991	+	1.36484i	0.139205	+	0.990264i	$0.455545\pi$
$227$	−11.8723	+	20.5634i	−0.787991	+	1.36484i	−0.927196	+	0.374577i	$0.877788\pi$
$228$	−8.43070	−	1.98072i	−0.558337	−	0.131176i
$229$	−10.0584	−	17.4217i	−0.664679	−	1.15126i	−0.979372	−	0.202065i	$-0.935235\pi$
$229$	−10.0584	−	17.4217i	−0.664679	−	1.15126i	0.314693	−	0.949194i	$-0.398098\pi$
$230$	−5.05842	−	8.76144i	−0.333542	−	0.577713i
$231$		0			0
$232$	1.37228	−	2.37686i	0.0900947	−	0.156049i
$233$	−11.7446			−0.769412			−0.384706	−	0.923039i	$-0.625697\pi$
$233$	−11.7446			−0.769412			−0.384706	+	0.923039i	$0.625697\pi$
$234$	−0.372281	−	5.98844i	−0.0243368	−	0.391477i
$235$		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	0.991236	+	0.132102i	$0.0421725\pi$
$239$	9.43070	+	16.3345i	0.610021	+	1.05659i	−0.381215	+	0.924487i	$0.624494\pi$
$240$	−1.62772	+	1.73205i	−0.105069	+	0.111803i
$241$	0.441578	−	0.764836i	0.0284445	−	0.0492674i	−0.851453	−	0.524431i	$-0.824278\pi$
$241$	0.441578	−	0.764836i	0.0284445	−	0.0492674i	0.879897	+	0.475164i	$0.157611\pi$
$242$	−8.11684			−0.521770
$243$	9.18614	−	12.5942i	0.589291	−	0.807921i
$244$	14.1168			0.903738
$245$		0			0
$246$	−12.3030	+	13.0916i	−0.784410	+	0.834688i
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−2.74456	−	9.10268i	−0.173930	−	0.576859i
$250$	−5.56930	+	9.64630i	−0.352233	+	0.610086i
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	−32.2337			−2.02651
$254$	−7.05842	+	12.2255i	−0.442885	+	0.767099i
$255$	10.1168	+	2.37686i	0.633541	+	0.148845i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.9307	+	18.9325i	0.681839	+	1.18098i	0.974419	+	0.224738i	$0.0721527\pi$
$257$	10.9307	+	18.9325i	0.681839	+	1.18098i	−0.292581	+	0.956241i	$0.594514\pi$
$258$	−15.3723	−	3.61158i	−0.957036	−	0.224847i
$259$		0			0
$260$	−2.74456			−0.170211
$261$	7.37228	+	3.66648i	0.456333	+	0.226949i
$262$	−7.37228			−0.455461
$263$	−6.68614	+	11.5807i	−0.412285	+	0.714099i	−0.995139	−	0.0984781i	$-0.968603\pi$
$263$	−6.68614	+	11.5807i	−0.412285	+	0.714099i	0.582854	+	0.812577i	$0.301936\pi$
$264$	2.18614	+	7.25061i	0.134548	+	0.446244i
$265$	−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
$269$	7.37228			0.449496			0.224748	−	0.974417i	$-0.427844\pi$
$269$	7.37228			0.449496			0.224748	+	0.974417i	$0.427844\pi$
$270$	−5.48913	−	4.55134i	−0.334058	−	0.276986i
$271$	18.2337			1.10762			0.553809	−	0.832644i	$-0.313174\pi$
$271$	18.2337			1.10762			0.553809	+	0.832644i	$0.313174\pi$
$272$	−2.18614	+	3.78651i	−0.132554	+	0.229591i
$273$		0			0
$274$	8.18614	+	14.1788i	0.494543	+	0.856573i
$275$	6.81386	+	11.8020i	0.410891	+	0.711684i
$276$	3.68614	+	12.2255i	0.221880	+	0.735891i
$277$	−11.1168	+	19.2549i	−0.667946	+	1.15692i	0.310531	+	0.950563i	$0.399493\pi$
$277$	−11.1168	+	19.2549i	−0.667946	+	1.15692i	−0.978477	+	0.206354i	$0.933840\pi$
$278$	−21.2337			−1.27351
$279$	5.00000	−	3.31662i	0.299342	−	0.198561i
$280$		0			0
$281$	−5.31386	+	9.20387i	−0.316998	+	0.549057i	−0.979860	−	0.199685i	$-0.936008\pi$
$281$	−5.31386	+	9.20387i	−0.316998	+	0.549057i	0.662862	+	0.748742i	$0.269342\pi$
$282$		0			0
$283$	4.94158	+	8.55906i	0.293746	+	0.508784i	0.974692	−	0.223550i	$-0.0717646\pi$
$283$	4.94158	+	8.55906i	0.293746	+	0.508784i	−0.680946	+	0.732333i	$0.738431\pi$
$284$	−5.05842	−	8.76144i	−0.300162	−	0.519896i
$285$	−11.5693	−	2.71810i	−0.685306	−	0.161006i
$286$	−4.37228	+	7.57301i	−0.258538	+	0.447802i
$287$		0			0
$288$	2.50000	−	1.65831i	0.147314	−	0.0977170i
$289$	2.11684			0.124520
$290$	1.88316	−	3.26172i	0.110583	−	0.191535i
$291$	4.55842	+	15.1186i	0.267219	+	0.886267i
$292$	−2.55842	−	4.43132i	−0.149720	−	0.259323i
$293$	−2.31386	−	4.00772i	−0.135177	−	0.234134i	0.790488	−	0.612478i	$-0.209827\pi$
$293$	−2.31386	−	4.00772i	−0.135177	−	0.234134i	−0.925665	+	0.378344i	$0.876494\pi$
$294$		0			0
$295$	4.88316	−	8.45787i	0.284308	−	0.492436i
$296$	−2.00000			−0.116248
$297$	−21.3030	+	7.89542i	−1.23612	+	0.458139i
$298$	−14.7446			−0.854130
$299$	−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
$303$	3.68614	+	12.2255i	0.211763	+	0.702339i
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$	19.3723			1.10925
$306$	−11.7446	−	5.84096i	−0.671392	−	0.333906i
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	16.8614	+	3.96143i	0.959212	+	0.225358i
$310$	−1.37228	−	2.37686i	−0.0779403	−	0.134997i
$311$	−13.1168	−	22.7190i	−0.743788	−	1.28828i	−0.950759	−	0.309931i	$-0.899694\pi$
$311$	−13.1168	−	22.7190i	−0.743788	−	1.28828i	0.206971	−	0.978347i	$-0.433639\pi$
$312$	3.37228	+	0.792287i	0.190918	+	0.0448544i
$313$	−1.44158	+	2.49689i	−0.0814828	+	0.141132i	−0.903887	−	0.427771i	$-0.859299\pi$
$313$	−1.44158	+	2.49689i	−0.0814828	+	0.141132i	0.822404	+	0.568904i	$0.192632\pi$
$314$	−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	$0.112775\pi$
$318$	1.37228	+	4.55134i	0.0769537	+	0.255227i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	−0.686141	−	1.18843i	−0.0383564	−	0.0664353i
$321$	1.93070	−	2.05446i	0.107761	−	0.114669i
$322$		0			0
$323$	−21.8614			−1.21640
$324$	5.43070	+	7.17687i	0.301706	+	0.398715i
$325$	6.23369			0.345783
$326$	8.11684	−	14.0588i	0.449550	−	0.778644i
$327$	−16.6060	+	17.6704i	−0.918312	+	0.977173i
$328$	−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	$0.0575207\pi$
$332$	5.48913			0.301255
$333$	−0.372281	−	5.98844i	−0.0204009	−	0.328164i
$334$	17.4891			0.956962
$335$	−10.3723	+	17.9653i	−0.566698	+	0.981550i
$336$		0			0
$337$	−4.55842	−	7.89542i	−0.248313	−	0.430091i	0.714745	−	0.699385i	$-0.246543\pi$
$337$	−4.55842	−	7.89542i	−0.248313	−	0.430091i	−0.963058	+	0.269294i	$0.913210\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	2.31386	+	0.543620i	0.125672	+	0.0295254i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−8.74456			−0.473545
$342$	13.4307	+	6.67954i	0.726249	+	0.361188i
$343$		0			0
$344$	4.55842	−	7.89542i	0.245774	−	0.425692i
$345$	5.05842	+	16.7769i	0.272336	+	0.903237i
$346$	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	$0.894515\pi$
$348$	−3.25544	+	3.46410i	−0.174510	+	0.185695i
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	0.405571	+	0.914063i	$0.367073\pi$
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	−0.994388	+	0.105797i	$0.966261\pi$
$350$		0			0
$351$	−1.74456	+	10.2448i	−0.0931179	+	0.546828i
$352$	−4.37228			−0.233043
$353$	−3.81386	+	6.60580i	−0.202991	+	0.351591i	−0.949491	−	0.313795i	$-0.898400\pi$
$353$	−3.81386	+	6.60580i	−0.202991	+	0.351591i	0.746500	+	0.665386i	$0.231733\pi$
$354$	−8.44158	+	8.98266i	−0.448665	+	0.477423i
$355$	−6.94158	−	12.0232i	−0.368421	−	0.638123i
$356$	1.62772	+	2.81929i	0.0862689	+	0.149422i
$357$		0			0
$358$	7.37228	−	12.7692i	0.389637	−	0.674871i
$359$	−6.86141			−0.362131			−0.181066	−	0.983471i	$-0.557955\pi$
$359$	−6.86141			−0.362131			−0.181066	+	0.983471i	$0.557955\pi$
$360$	3.43070	−	2.27567i	0.180814	−	0.119938i
$361$	6.00000			0.315789
$362$	−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
$366$	−23.8030	−	5.59230i	−1.24420	−	0.292314i
$367$	11.1168	−	19.2549i	0.580295	−	1.00510i	−0.415150	−	0.909753i	$-0.636271\pi$
$367$	11.1168	−	19.2549i	0.580295	−	1.00510i	0.995444	−	0.0953465i	$-0.0303959\pi$
$368$	−7.37228			−0.384307
$369$	25.9307	−	17.2005i	1.34990	−	0.895421i
$370$	−2.74456			−0.142683
$371$		0			0
$372$	1.00000	+	3.31662i	0.0518476	+	0.171959i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	9.55842	+	16.5557i	0.494254	+	0.856073i
$375$	13.2119	−	14.0588i	0.682262	−	0.725993i
$376$		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
$381$	16.7446	−	17.8178i	0.857850	−	0.912836i
$382$	−0.941578	−	1.63086i	−0.0481753	−	0.0834421i
$383$	−10.6277	−	18.4077i	−0.543051	−	0.940592i	−0.998727	−	0.0504462i	$-0.983936\pi$
$383$	−10.6277	−	18.4077i	−0.543051	−	0.940592i	0.455676	−	0.890146i	$-0.349398\pi$
$384$	0.500000	+	1.65831i	0.0255155	+	0.0846254i
$385$		0			0
$386$	7.00000			0.356291
$387$	24.4891	+	12.1793i	1.24485	+	0.619107i
$388$	−9.11684			−0.462838
$389$	17.4891	−	30.2921i	0.886734	−	1.53587i	0.0430204	−	0.999074i	$-0.486302\pi$
$389$	17.4891	−	30.2921i	0.886734	−	1.53587i	0.843713	−	0.536794i	$-0.180365\pi$
$390$	4.62772	+	1.08724i	0.234334	+	0.0550546i
$391$	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
$395$	16.6277			0.836631
$396$	−0.813859	−	13.0916i	−0.0408980	−	0.657876i
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	5.00000	−	8.66025i	0.250627	−	0.434099i
$399$		0			0
$400$	1.55842	+	2.69927i	0.0779211	+	0.134963i
$401$	0.127719	+	0.221215i	0.00637797	+	0.0110470i	0.869197	−	0.494466i	$-0.164636\pi$
$401$	0.127719	+	0.221215i	0.00637797	+	0.0110470i	−0.862819	+	0.505513i	$0.831303\pi$
$402$	17.9307	−	19.0800i	0.894302	−	0.951624i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−7.37228			−0.366785
$405$	7.45245	+	9.84868i	0.370315	+	0.489385i
$406$		0			0
$407$	−4.37228	+	7.57301i	−0.216726	+	0.375380i
$408$	5.18614	−	5.51856i	0.256752	−	0.273209i
$409$	14.6753	+	25.4183i	0.725645	+	1.25685i	0.958708	+	0.284393i	$0.0917919\pi$
$409$	14.6753	+	25.4183i	0.725645	+	1.25685i	−0.233063	+	0.972462i	$0.574875\pi$
$410$	−7.11684	−	12.3267i	−0.351476	−	0.608774i
$411$	−8.18614	−	27.1504i	−0.403793	−	1.33923i
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$		0			0
$414$	−1.37228	−	22.0742i	−0.0674439	−	1.08489i
$415$	7.53262			0.369762
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	35.8030	+	8.41159i	1.75328	+	0.411917i
$418$	−10.9307	−	18.9325i	−0.534638	−	0.926020i
$419$	13.8030	+	23.9075i	0.674320	+	1.16796i	0.976667	+	0.214759i	$0.0688964\pi$
$419$	13.8030	+	23.9075i	0.674320	+	1.16796i	−0.302347	+	0.953198i	$0.597770\pi$
$420$		0			0
$421$	0.116844	−	0.202380i	0.00569463	−	0.00986338i	−0.863164	−	0.504924i	$-0.831521\pi$
$421$	0.116844	−	0.202380i	0.00569463	−	0.00986338i	0.868859	+	0.495060i	$0.164854\pi$
$422$	16.0000			0.778868
$423$		0			0
$424$	−2.74456			−0.133288
$425$	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
$429$	10.3723	−	11.0371i	0.500778	−	0.532877i
$430$	6.25544	−	10.8347i	0.301664	−	0.522497i
$431$	−29.4891			−1.42044			−0.710221	−	0.703979i	$-0.751405\pi$
$431$	−29.4891			−1.42044			−0.710221	+	0.703979i	$0.751405\pi$
$432$	−4.87228	+	1.80579i	−0.234418	+	0.0868811i
$433$	2.88316			0.138556			0.0692778	−	0.997597i	$-0.477931\pi$
$433$	2.88316			0.138556			0.0692778	+	0.997597i	$0.477931\pi$
$434$		0			0
$435$	−4.46738	+	4.75372i	−0.214194	+	0.227924i
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−18.4307	−	31.9229i	−0.881660	−	1.52708i
$438$	2.55842	+	8.48533i	0.122246	+	0.405445i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−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	$-0.0162747\pi$
$444$	3.37228	+	0.792287i	0.160041	+	0.0376003i
$445$	2.23369	+	3.86886i	0.105887	+	0.183402i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$	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	$0.215888\pi$
$450$	−7.79211	+	5.16870i	−0.367324	+	0.243655i
$451$	−45.3505			−2.13547
$452$	−0.686141	+	1.18843i	−0.0322733	+	0.0558991i
$453$	4.05842	+	13.4603i	0.190681	+	0.632418i
$454$	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	$0.880473\pi$
$458$	−20.1168			−0.939998
$459$	17.4891	+	14.5012i	0.816322	+	0.676859i
$460$	−10.1168			−0.471700
$461$	15.4307	−	26.7268i	0.718680	−	1.24479i	−0.242844	−	0.970065i	$-0.578080\pi$
$461$	15.4307	−	26.7268i	0.718680	−	1.24479i	0.961523	−	0.274724i	$-0.0885865\pi$
$462$		0			0
$463$	2.94158	+	5.09496i	0.136707	+	0.236783i	0.926248	−	0.376914i	$-0.123015\pi$
$463$	2.94158	+	5.09496i	0.136707	+	0.236783i	−0.789541	+	0.613697i	$0.789682\pi$
$464$	−1.37228	−	2.37686i	−0.0637066	−	0.110343i
$465$	1.37228	+	4.55134i	0.0636380	+	0.211063i
$466$	−5.87228	+	10.1711i	−0.272028	+	0.471167i
$467$	30.0951			1.39263			0.696317	−	0.717734i	$-0.254821\pi$
$467$	30.0951			1.39263			0.696317	+	0.717734i	$0.254821\pi$
$468$	−5.37228	−	2.67181i	−0.248334	−	0.123505i
$469$		0			0
$470$		0			0
$471$	13.6861	+	3.21543i	0.630624	+	0.148159i
$472$	−3.55842	−	6.16337i	−0.163790	−	0.283692i
$473$	−19.9307	−	34.5210i	−0.916415	−	1.58728i
$474$	−20.4307	−	4.80001i	−0.938413	−	0.220472i
$475$	−7.79211	+	13.4963i	−0.357527	+	0.619254i
$476$		0			0
$477$	−0.510875	−	8.21782i	−0.0233913	−	0.376268i
$478$	18.8614			0.862701
$479$	10.6277	−	18.4077i	0.485593	−	0.841072i	−0.514270	−	0.857628i	$-0.671937\pi$
$479$	10.6277	−	18.4077i	0.485593	−	0.841072i	0.999863	+	0.0165568i	$0.00527043\pi$
$480$	0.686141	+	2.27567i	0.0313179	+	0.103870i
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	−0.441578	−	0.764836i	−0.0201133	−	0.0348373i
$483$		0			0
$484$	−4.05842	+	7.02939i	−0.184474	+	0.319518i
$485$	−12.5109			−0.568090
$486$	−6.31386	−	14.2525i	−0.286402	−	0.646509i
$487$	−16.3505			−0.740913			−0.370457	−	0.928850i	$-0.620799\pi$
$487$	−16.3505			−0.740913			−0.370457	+	0.928850i	$0.620799\pi$
$488$	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	0.997903	−	0.0647303i	$-0.0206187\pi$
$491$	9.81386	+	16.9981i	0.442893	+	0.767114i	−0.555010	+	0.831844i	$0.687285\pi$
$492$	5.18614	+	17.2005i	0.233809	+	0.775458i
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	−10.0000			−0.449921
$495$	−1.11684	−	17.9653i	−0.0501984	−	0.807481i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$	−9.25544	−	2.17448i	−0.414746	−	0.0974408i
$499$	−0.441578	−	0.764836i	−0.0197677	−	0.0342387i	0.855972	−	0.517022i	$-0.172959\pi$
$499$	−0.441578	−	0.764836i	−0.0197677	−	0.0342387i	−0.875740	+	0.482783i	$0.839626\pi$
$500$	5.56930	+	9.64630i	0.249067	+	0.431396i
$501$	−29.4891	−	6.92820i	−1.31748	−	0.309529i
$502$	4.50000	−	7.79423i	0.200845	−	0.347873i
$503$	−2.23369			−0.0995952			−0.0497976	−	0.998759i	$-0.515858\pi$
$503$	−2.23369			−0.0995952			−0.0497976	+	0.998759i	$0.515858\pi$
$504$		0			0
$505$	−10.1168			−0.450194
$506$	−16.1168	+	27.9152i	−0.716481	+	1.24098i
$507$	4.50000	+	14.9248i	0.199852	+	0.662834i
$508$	7.05842	+	12.2255i	0.313167	+	0.542421i
$509$	8.48913	+	14.7036i	0.376274	+	0.651725i	0.990517	−	0.137392i	$-0.0438718\pi$
$509$	8.48913	+	14.7036i	0.376274	+	0.651725i	−0.614243	+	0.789117i	$0.710539\pi$
$510$	7.11684	−	7.57301i	0.315139	−	0.335339i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−20.0000	−	16.5831i	−0.883022	−	0.732163i
$514$	21.8614			0.964265
$515$	−6.86141	+	11.8843i	−0.302350	+	0.523685i
$516$	−10.8139	+	11.5070i	−0.476054	+	0.506567i
$517$		0			0
$518$		0			0
$519$	−3.00000	−	9.94987i	−0.131685	−	0.436751i
$520$	−1.37228	+	2.37686i	−0.0601785	+	0.104232i
$521$	−3.86141			−0.169171			−0.0845856	−	0.996416i	$-0.526957\pi$
$521$	−3.86141			−0.169171			−0.0845856	+	0.996416i	$0.526957\pi$
$522$	6.86141	−	4.55134i	0.300316	−	0.199207i
$523$	17.8832			0.781976			0.390988	−	0.920396i	$-0.372133\pi$
$523$	17.8832			0.781976			0.390988	+	0.920396i	$0.372133\pi$
$524$	−3.68614	+	6.38458i	−0.161030	+	0.278912i
$525$		0			0
$526$	6.68614	+	11.5807i	0.291530	+	0.504944i
$527$	4.37228	+	7.57301i	0.190460	+	0.329886i
$528$	7.37228	+	1.73205i	0.320837	+	0.0753778i
$529$	−15.6753	+	27.1504i	−0.681533	+	1.18045i
$530$	−3.76631			−0.163598
$531$	17.7921	−	11.8020i	0.772112	−	0.512161i
$532$		0			0
$533$	−10.3723	+	17.9653i	−0.449273	+	0.778164i
$534$	−1.62772	−	5.39853i	−0.0704383	−	0.233617i
$535$	1.11684	+	1.93443i	0.0482854	+	0.0836327i
$536$	7.55842	+	13.0916i	0.326474	+	0.565470i
$537$	−17.4891	+	18.6101i	−0.754711	+	0.803086i
$538$	3.68614	−	6.38458i	0.158921	−	0.275259i
$539$		0			0
$540$	−6.68614	+	2.47805i	−0.287726	+	0.106638i
$541$	28.2337			1.21386			0.606931	−	0.794755i	$-0.292401\pi$
$541$	28.2337			1.21386			0.606931	+	0.794755i	$0.292401\pi$
$542$	9.11684	−	15.7908i	0.391602	−	0.678275i
$543$	21.4891	−	22.8665i	0.922187	−	0.981296i
$544$	2.18614	+	3.78651i	0.0937300	+	0.162345i
$545$	−9.60597	−	16.6380i	−0.411475	−	0.712695i
$546$		0			0
$547$	−0.441578	+	0.764836i	−0.0188805	+	0.0327020i	−0.875311	−	0.483560i	$-0.839344\pi$
$547$	−0.441578	+	0.764836i	−0.0188805	+	0.0327020i	0.856431	+	0.516262i	$0.172677\pi$
$548$	16.3723			0.699389
$549$	37.9198	+	18.8588i	1.61838	+	0.804874i
$550$	13.6277			0.581088
$551$	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
$555$	4.62772	+	1.08724i	0.196436	+	0.0461508i
$556$	−10.6168	+	18.3889i	−0.450254	+	0.779864i
$557$	6.51087			0.275875			0.137937	−	0.990441i	$-0.455953\pi$
$557$	6.51087			0.275875			0.137937	+	0.990441i	$0.455953\pi$
$558$	−0.372281	−	5.98844i	−0.0157599	−	0.253511i
$559$	−18.2337			−0.771203
$560$		0			0
$561$	−9.55842	−	31.7017i	−0.403557	−	1.33845i
$562$	5.31386	+	9.20387i	0.224152	+	0.388242i
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$		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	$0.159214\pi$
$570$	−8.13859	+	8.66025i	−0.340888	+	0.362738i
$571$	−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	$-0.377164\pi$
$572$	4.37228	+	7.57301i	0.182814	+	0.316644i
$573$	0.941578	+	3.12286i	0.0393350	+	0.130459i
$574$		0			0
$575$	22.9783			0.958259
$576$	−0.186141	−	2.99422i	−0.00775586	−	0.124759i
$577$	−27.1168			−1.12889			−0.564444	−	0.825471i	$-0.690910\pi$
$577$	−27.1168			−1.12889			−0.564444	+	0.825471i	$0.690910\pi$
$578$	1.05842	−	1.83324i	0.0440246	−	0.0762528i
$579$	−11.8030	−	2.77300i	−0.490515	−	0.115242i
$580$	−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
$584$	−5.11684			−0.211737
$585$	−7.37228	−	3.66648i	−0.304806	−	0.151590i
$586$	−4.62772			−0.191169
$587$	−4.24456	+	7.35180i	−0.175192	+	0.303441i	−0.940228	−	0.340547i	$-0.889388\pi$
$587$	−4.24456	+	7.35180i	−0.175192	+	0.303441i	0.765036	+	0.643988i	$0.222721\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−4.88316	−	8.45787i	−0.201036	−	0.348205i
$591$	7.11684	−	7.57301i	0.292748	−	0.311512i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−3.25544			−0.133685			−0.0668424	−	0.997764i	$-0.521292\pi$
$593$	−3.25544			−0.133685			−0.0668424	+	0.997764i	$0.521292\pi$
$594$	−3.81386	+	22.3966i	−0.156485	+	0.918945i
$595$		0			0
$596$	−7.37228	+	12.7692i	−0.301980	+	0.523045i
$597$	−11.8614	+	12.6217i	−0.485455	+	0.516571i
$598$	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	$0.996449\pi$
$600$	−1.55842	−	5.16870i	−0.0636223	−	0.211011i
$601$	3.44158	−	5.96099i	0.140385	−	0.243154i	−0.787257	−	0.616625i	$-0.788499\pi$
$601$	3.44158	−	5.96099i	0.140385	−	0.243154i	0.927642	+	0.373472i	$0.121833\pi$
$602$		0			0
$603$	−37.7921	+	25.0684i	−1.53901	+	1.02087i
$604$	−8.11684			−0.330270
$605$	−5.56930	+	9.64630i	−0.226424	+	0.392178i
$606$	12.4307	+	2.92048i	0.504963	+	0.118636i
$607$	−6.11684	−	10.5947i	−0.248275	−	0.430025i	0.714772	−	0.699357i	$-0.246530\pi$
$607$	−6.11684	−	10.5947i	−0.248275	−	0.430025i	−0.963047	+	0.269332i	$0.913197\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	9.68614	−	16.7769i	0.392180	−	0.679276i
$611$		0			0
$612$	−10.9307	+	7.25061i	−0.441847	+	0.293088i
$613$	−1.76631			−0.0713407			−0.0356703	−	0.999364i	$-0.511357\pi$
$613$	−1.76631			−0.0713407			−0.0356703	+	0.999364i	$0.511357\pi$
$614$	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	0.948043	−	0.318142i	$-0.103059\pi$
$617$	4.93070	+	8.54023i	0.198503	+	0.343817i	−0.749540	+	0.661959i	$0.769725\pi$
$618$	11.8614	−	12.6217i	0.477136	−	0.507719i
$619$	−11.7337	+	20.3233i	−0.471617	+	0.816864i	−0.999473	−	0.0324697i	$-0.989663\pi$
$619$	−11.7337	+	20.3233i	−0.471617	+	0.816864i	0.527856	+	0.849334i	$0.322996\pi$
$620$	−2.74456			−0.110224
$621$	−6.43070	+	37.7639i	−0.258055	+	1.51541i
$622$	−26.2337			−1.05188
$623$		0			0
$624$	2.37228	−	2.52434i	0.0949673	−	0.101054i
$625$	−0.149468	−	0.258886i	−0.00597872	−	0.0103555i
$626$	1.44158	+	2.49689i	0.0576170	+	0.0997956i
$627$	10.9307	+	36.2530i	0.436530	+	1.44781i
$628$	−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
$633$	−26.9783	−	6.33830i	−1.07229	−	0.251925i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	9.68614	+	16.7769i	0.384383	+	0.665770i
$636$	4.62772	+	1.08724i	0.183501	+	0.0431119i
$637$		0			0
$638$	−12.0000			−0.475085
$639$	−1.88316	−	30.2921i	−0.0744965	−	1.19834i
$640$	−1.37228			−0.0542442
$641$	23.1060	−	40.0207i	0.912631	−	1.58072i	0.102298	−	0.994754i	$-0.467381\pi$
$641$	23.1060	−	40.0207i	0.912631	−	1.58072i	0.810333	−	0.585969i	$-0.199286\pi$
$642$	−0.813859	−	2.69927i	−0.0321205	−	0.106532i
$643$	−12.6753	−	21.9542i	−0.499864	−	0.865789i	0.500136	−	0.865947i	$-0.333283\pi$
$643$	−12.6753	−	21.9542i	−0.499864	−	0.865789i	−1.00000		0.000157386i	$0.999950\pi$
$644$		0			0
$645$	−14.8397	+	15.7908i	−0.584311	+	0.621764i
$646$	−10.9307	+	18.9325i	−0.430063	+	0.744891i
$647$	17.4891			0.687568			0.343784	−	0.939049i	$-0.388291\pi$
$647$	17.4891			0.687568			0.343784	+	0.939049i	$0.388291\pi$
$648$	8.93070	−	1.11469i	0.350831	−	0.0437892i
$649$	−31.1168			−1.22144
$650$	3.11684	−	5.39853i	0.122253	−	0.211748i
$651$		0			0
$652$	−8.11684	−	14.0588i	−0.317880	−	0.550585i
$653$	7.62772	+	13.2116i	0.298496	+	0.517010i	0.975792	−	0.218701i	$-0.0701818\pi$
$653$	7.62772	+	13.2116i	0.298496	+	0.517010i	−0.677296	+	0.735710i	$0.736848\pi$
$654$	7.00000	+	23.2164i	0.273722	+	0.907832i
$655$	−5.05842	+	8.76144i	−0.197649	+	0.342338i
$656$	−10.3723			−0.404970
$657$	−0.952453	−	15.3210i	−0.0371587	−	0.597727i
$658$		0			0
$659$	4.62772	−	8.01544i	0.180270	−	0.312237i	−0.761702	−	0.647927i	$-0.775636\pi$
$659$	4.62772	−	8.01544i	0.180270	−	0.312237i	0.941973	+	0.335690i	$0.108969\pi$
$660$	10.1168	+	2.37686i	0.393798	+	0.0925192i
$661$	4.94158	+	8.55906i	0.192205	+	0.332909i	0.945981	−	0.324223i	$-0.105103\pi$
$661$	4.94158	+	8.55906i	0.192205	+	0.332909i	−0.753776	+	0.657132i	$0.771769\pi$
$662$	−6.11684	−	10.5947i	−0.237738	−	0.411774i
$663$	−14.7446	−	3.46410i	−0.572631	−	0.134535i
$664$	2.74456	−	4.75372i	0.106510	−	0.184480i
$665$		0			0
$666$	−5.37228	−	2.67181i	−0.208172	−	0.103531i
$667$	−20.2337			−0.783452
$668$	8.74456	−	15.1460i	0.338337	−	0.586017i
$669$	−2.00000	−	6.63325i	−0.0773245	−	0.256456i
$670$	10.3723	+	17.9653i	0.400716	+	0.694061i
$671$	−30.8614	−	53.4535i	−1.19139	−	2.06355i
$672$		0			0
$673$	10.0584	−	17.4217i	0.387724	−	0.671557i	−0.604419	−	0.796666i	$-0.706595\pi$
$673$	10.0584	−	17.4217i	0.387724	−	0.671557i	0.992143	+	0.125109i	$0.0399281\pi$
$674$	−9.11684			−0.351168
$675$	15.1861	−	5.62836i	0.584515	−	0.216636i
$676$	−9.00000			−0.346154
$677$	−17.2337	+	29.8496i	−0.662344	+	1.14721i	0.317654	+	0.948207i	$0.397105\pi$
$677$	−17.2337	+	29.8496i	−0.662344	+	1.14721i	−0.979998	+	0.199007i	$0.936228\pi$
$678$	1.62772	−	1.73205i	0.0625122	−	0.0665190i
$679$		0			0
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	−11.8723	−	39.3759i	−0.454947	−	1.50889i
$682$	−4.37228	+	7.57301i	−0.167423	+	0.289986i
$683$	−44.8397			−1.71574			−0.857871	−	0.513865i	$-0.828213\pi$
$683$	−44.8397			−1.71574			−0.857871	+	0.513865i	$0.828213\pi$
$684$	12.5000	−	8.29156i	0.477949	−	0.317036i
$685$	22.4674			0.858434
$686$		0			0
$687$	33.9198	+	7.96916i	1.29412	+	0.304042i
$688$	−4.55842	−	7.89542i	−0.173788	−	0.301010i
$689$	2.74456	+	4.75372i	0.104560	+	0.181102i
$690$	17.0584	+	4.00772i	0.649403	+	0.152571i
$691$	−2.94158	+	5.09496i	−0.111903	+	0.193822i	−0.916537	−	0.399949i	$-0.869028\pi$
$691$	−2.94158	+	5.09496i	−0.111903	+	0.193822i	0.804635	+	0.593770i	$0.202361\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−7.11684			−0.270152
$695$	−14.5693	+	25.2348i	−0.552645	+	0.957209i
$696$	1.37228	+	4.55134i	0.0520162	+	0.172518i
$697$	22.6753	+	39.2747i	0.858887	+	1.48764i
$698$	11.0000	+	19.0526i	0.416356	+	0.721150i
$699$	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	$0.522659\pi$
$702$	8.00000	+	6.63325i	0.301941	+	0.250356i
$703$	−10.0000			−0.377157
$704$	−2.18614	+	3.78651i	−0.0823933	+	0.142709i
$705$		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	$0.857149\pi$
$710$	−13.8832			−0.521026
$711$	32.5475	+	16.1870i	1.22063	+	0.607059i
$712$	3.25544			0.122003
$713$	−7.37228	+	12.7692i	−0.276094	+	0.478209i
$714$		0			0
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	−7.37228	−	12.7692i	−0.275515	−	0.477206i
$717$	−31.8030	−	7.47182i	−1.18770	−	0.279040i
$718$	−3.43070	+	5.94215i	−0.128033	+	0.221759i
$719$	8.74456			0.326117			0.163059	−	0.986616i	$-0.447864\pi$
$719$	8.74456			0.326117			0.163059	+	0.986616i	$0.447864\pi$
$720$	−0.255437	−	4.10891i	−0.00951959	−	0.153130i
$721$		0			0
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	0.441578	+	1.46455i	0.0164225	+	0.0544671i
$724$	9.05842	+	15.6896i	0.336654	+	0.583101i
$725$	4.27719	+	7.40830i	0.158851	+	0.275138i
$726$	9.62772	−	10.2448i	0.357318	−	0.380221i
$727$	−0.883156	+	1.52967i	−0.0327544	+	0.0567324i	−0.881938	−	0.471366i	$-0.843761\pi$
$727$	−0.883156	+	1.52967i	−0.0327544	+	0.0567324i	0.849183	+	0.528098i	$0.177095\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	−7.02175			−0.259887
$731$	−19.9307	+	34.5210i	−0.737164	+	1.27680i
$732$	−16.7446	+	17.8178i	−0.618897	+	0.658566i
$733$	−11.9416	−	20.6834i	−0.441072	−	0.763960i	0.556697	−	0.830716i	$-0.312068\pi$
$733$	−11.9416	−	20.6834i	−0.441072	−	0.763960i	−0.997769	+	0.0667560i	$0.978735\pi$
$734$	−11.1168	−	19.2549i	−0.410330	−	0.710713i
$735$		0			0
$736$	−3.68614	+	6.38458i	−0.135873	+	0.235339i
$737$	66.0951			2.43464
$738$	−1.93070	−	31.0569i	−0.0710702	−	1.14322i
$739$	9.11684			0.335369			0.167684	−	0.985841i	$-0.446371\pi$
$739$	9.11684			0.335369			0.167684	+	0.985841i	$0.446371\pi$
$740$	−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	−0.918286	−	0.395917i	$-0.870427\pi$
$743$	−21.8614	−	37.8651i	−0.802017	−	1.38913i	0.116269	−	0.993218i	$-0.462906\pi$
$744$	3.37228	+	0.792287i	0.123634	+	0.0290467i
$745$	−10.1168	+	17.5229i	−0.370652	+	0.641989i
$746$	10.0000			0.366126
$747$	14.7446	+	7.33296i	0.539475	+	0.268299i
$748$	19.1168			0.698981
$749$		0			0
$750$	−5.56930	−	18.4713i	−0.203362	−	0.674475i
$751$	−0.0584220	−	0.101190i	−0.00213185	−	0.00369247i	0.864958	−	0.501845i	$-0.167345\pi$
$751$	−0.0584220	−	0.101190i	−0.00213185	−	0.00369247i	−0.867089	+	0.498153i	$0.834012\pi$
$752$		0			0
$753$	−10.6753	+	11.3595i	−0.389028	+	0.413964i
$754$	−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
$759$	38.2337	−	40.6844i	1.38779	−	1.47675i
$760$	−3.43070	−	5.94215i	−0.124445	−	0.215545i
$761$	6.25544	+	10.8347i	0.226759	+	0.392759i	0.956846	−	0.290596i	$-0.0938536\pi$
$761$	6.25544	+	10.8347i	0.226759	+	0.392759i	−0.730086	+	0.683355i	$0.760520\pi$
$762$	−7.05842	−	23.4101i	−0.255700	−	0.848060i
$763$		0			0
$764$	−1.88316			−0.0681302
$765$	−15.0000	+	9.94987i	−0.542326	+	0.359738i
$766$	−21.2554			−0.767990
$767$	−7.11684	+	12.3267i	−0.256974	+	0.445093i
$768$	1.68614	+	0.396143i	0.0608434	+	0.0142946i
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$		0			0
$771$	−36.8614	−	8.66025i	−1.32753	−	0.311891i
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	11.1386			0.400627			0.200314	−	0.979732i	$-0.435804\pi$
$773$	11.1386			0.400627			0.200314	+	0.979732i	$0.435804\pi$
$774$	22.7921	−	15.1186i	0.819245	−	0.543426i
$775$	6.23369			0.223921
$776$	−4.55842	+	7.89542i	−0.163638	+	0.283429i
$777$		0			0
$778$	−17.4891	−	30.2921i	−0.627016	−	1.08602i
$779$	−25.9307	−	44.9133i	−0.929064	−	1.60919i
$780$	3.25544	−	3.46410i	0.116563	−	0.124035i
$781$	−22.1168	+	38.3075i	−0.791403	+	1.37075i
$782$	32.2337			1.15267
$783$	−13.3723	+	4.95610i	−0.477886	+	0.177117i
$784$		0			0
$785$	−5.56930	+	9.64630i	−0.198777	+	0.344291i
$786$	8.74456	−	9.30506i	0.311908	−	0.331901i
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$	−6.68614	−	22.1754i	−0.238033	−	0.789466i
$790$	8.31386	−	14.4000i	0.295794	−	0.512330i
$791$		0			0
$792$	−11.7446	−	5.84096i	−0.417325	−	0.207550i
$793$	−28.2337			−1.00261
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$	6.35053	+	1.49200i	0.225230	+	0.0529158i
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	−18.4307	−	31.9229i	−0.652849	−	1.13077i	−0.982428	−	0.186640i	$-0.940240\pi$
$797$	−18.4307	−	31.9229i	−0.652849	−	1.13077i	0.329579	−	0.944128i	$-0.393093\pi$
$798$		0			0
$799$		0			0
$800$	3.11684			0.110197
$801$	0.605969	+	9.74749i	0.0214109	+	0.344411i
$802$	0.255437			0.00901981
$803$	−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
$807$	−8.74456	+	9.30506i	−0.307823	+	0.327554i
$808$	−3.68614	+	6.38458i	−0.129678	+	0.224609i
$809$	21.8614			0.768606			0.384303	−	0.923207i	$-0.374442\pi$
$809$	21.8614			0.768606			0.384303	+	0.923207i	$0.374442\pi$
$810$	12.2554	−	1.52967i	0.430612	−	0.0537472i
$811$	−24.8832			−0.873766			−0.436883	−	0.899518i	$-0.643918\pi$
$811$	−24.8832			−0.873766			−0.436883	+	0.899518i	$0.643918\pi$
$812$		0			0
$813$	−21.6277	+	23.0140i	−0.758517	+	0.807136i
$814$	4.37228	+	7.57301i	0.153248	+	0.265434i
$815$	−11.1386	−	19.2926i	−0.390168	−	0.675791i
$816$	−2.18614	−	7.25061i	−0.0765302	−	0.253822i
$817$	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	$-0.0658332\pi$
$822$	−27.6060	−	6.48577i	−0.962869	−	0.226217i
$823$	−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	$0.959998\pi$
$824$	5.00000	+	8.66025i	0.174183	+	0.301694i
$825$	−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	$0.433096\pi$
$828$	−19.8030	−	9.84868i	−0.688201	−	0.342265i
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$	3.76631	−	6.52344i	0.130731	−	0.226432i
$831$	−11.1168	−	36.8704i	−0.385639	−	1.27902i
$832$	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
$836$	−21.8614			−0.756093
$837$	−1.74456	+	10.2448i	−0.0603009	+	0.354113i
$838$	27.6060			0.953632
$839$	−8.74456	+	15.1460i	−0.301896	+	0.522899i	−0.976565	−	0.215221i	$-0.930953\pi$
$839$	−8.74456	+	15.1460i	−0.301896	+	0.522899i	0.674670	+	0.738120i	$0.264286\pi$
$840$		0			0
$841$	10.7337	+	18.5913i	0.370127	+	0.641079i
$842$	−0.116844	−	0.202380i	−0.00402671	−	0.00697446i
$843$	−5.31386	−	17.6241i	−0.183019	−	0.607005i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−12.3505			−0.424871
$846$		0			0
$847$		0			0
$848$	−1.37228	+	2.37686i	−0.0471243	+	0.0816217i
$849$	−16.6644	−	3.91515i	−0.571920	−	0.134368i
$850$	−6.81386	−	11.8020i	−0.233713	−	0.404804i
$851$	7.37228	+	12.7692i	0.252719	+	0.437721i
$852$	17.0584	+	4.00772i	0.584412	+	0.137302i
$853$	−8.94158	+	15.4873i	−0.306154	+	0.530274i	−0.977518	−	0.210854i	$-0.932376\pi$
$853$	−8.94158	+	15.4873i	−0.306154	+	0.530274i	0.671364	+	0.741128i	$0.265709\pi$
$854$		0			0
$855$	17.1535	−	11.3784i	0.586638	−	0.389132i
$856$	1.62772			0.0556343
$857$	25.9783	−	44.9956i	0.887400	−	1.53702i	0.0444624	−	0.999011i	$-0.485843\pi$
$857$	25.9783	−	44.9956i	0.887400	−	1.53702i	0.842938	−	0.538011i	$-0.180824\pi$
$858$	−4.37228	−	14.5012i	−0.149267	−	0.495063i
$859$	25.5584	+	44.2685i	0.872042	+	1.51042i	0.859881	+	0.510495i	$0.170538\pi$
$859$	25.5584	+	44.2685i	0.872042	+	1.51042i	0.0121615	+	0.999926i	$0.496129\pi$
$860$	−6.25544	−	10.8347i	−0.213309	−	0.369461i
$861$		0			0
$862$	−14.7446	+	25.5383i	−0.502202	+	0.869839i
$863$	−18.8614			−0.642050			−0.321025	−	0.947071i	$-0.604027\pi$
$863$	−18.8614			−0.642050			−0.321025	+	0.947071i	$0.604027\pi$
$864$	−0.872281	+	5.12241i	−0.0296756	+	0.174268i
$865$	8.23369			0.279954
$866$	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
$870$	1.88316	+	6.24572i	0.0638450	+	0.211750i
$871$	15.1168	−	26.1831i	0.512215	−	0.887182i
$872$	−14.0000			−0.474100
$873$	−24.4891	−	12.1793i	−0.828831	−	0.412205i
$874$	−36.8614			−1.24686
$875$		0			0
$876$	8.62772	+	2.02700i	0.291504	+	0.0684861i
$877$	−22.3505	−	38.7123i	−0.754724	−	1.30722i	−0.945512	−	0.325589i	$-0.894438\pi$
$877$	−22.3505	−	38.7123i	−0.754724	−	1.30722i	0.190788	−	0.981631i	$-0.438896\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$	7.80298	+	1.83324i	0.263188	+	0.0618337i
$880$	−3.00000	+	5.19615i	−0.101130	+	0.175162i
$881$	−14.2337			−0.479545			−0.239773	−	0.970829i	$-0.577073\pi$
$881$	−14.2337			−0.479545			−0.239773	+	0.970829i	$0.577073\pi$
$882$		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
$885$	4.88316	+	16.1956i	0.164145	+	0.544409i
$886$	−11.4416	−	19.8174i	−0.384387	−	0.665778i
$887$	−15.8614	−	27.4728i	−0.532574	−	0.922445i	−0.999277	−	0.0380308i	$-0.987892\pi$
$887$	−15.8614	−	27.4728i	−0.532574	−	0.922445i	0.466703	−	0.884414i	$-0.345442\pi$
$888$	2.37228	−	2.52434i	0.0796085	−	0.0847112i
$889$		0			0
$890$	4.46738			0.149747
$891$	15.3030	−	36.2530i	0.512669	−	1.21452i
$892$	4.00000			0.133930
$893$		0			0
$894$	17.4891	−	18.6101i	0.584924	−	0.622416i
$895$	−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
$899$	−5.48913			−0.183073
$900$	0.580171	+	9.33252i	0.0193390	+	0.311084i
$901$	12.0000			0.399778
$902$	−22.6753	+	39.2747i	−0.755004	+	1.30770i
$903$		0			0
$904$	0.686141	+	1.18843i	0.0228207	+	0.0395266i
$905$	12.4307	+	21.5306i	0.413211	+	0.715702i
$906$	13.6861	+	3.21543i	0.454692	+	0.106826i
$907$	4.44158	−	7.69304i	0.147480	−	0.255443i	−0.782815	−	0.622254i	$-0.786217\pi$
$907$	4.44158	−	7.69304i	0.147480	−	0.255443i	0.930296	+	0.366811i	$0.119550\pi$
$908$	23.7446			0.787991
$909$	−19.8030	−	9.84868i	−0.656824	−	0.326660i
$910$		0			0
$911$	21.6861	−	37.5615i	0.718494	−	1.24447i	−0.243103	−	0.970001i	$-0.578165\pi$
$911$	21.6861	−	37.5615i	0.718494	−	1.24447i	0.961596	−	0.274467i	$-0.0885015\pi$
$912$	2.50000	+	8.29156i	0.0827833	+	0.274561i
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$	16.7337	+	28.9836i	0.553501	+	0.958692i
$915$	−22.9783	+	24.4511i	−0.759638	+	0.808328i
$916$	−10.0584	+	17.4217i	−0.332340	+	0.575629i
$917$		0			0
$918$	21.3030	−	7.89542i	0.703103	−	0.260588i
$919$	−29.8832			−0.985754			−0.492877	−	0.870099i	$-0.664055\pi$
$919$	−29.8832			−0.985754			−0.492877	+	0.870099i	$0.664055\pi$
$920$	−5.05842	+	8.76144i	−0.166771	+	0.288856i
$921$	−15.4198	+	16.4082i	−0.508101	+	0.540668i
$922$	−15.4307	−	26.7268i	−0.508183	−	0.880199i
$923$	10.1168	+	17.5229i	0.333000	+	0.576773i
$924$		0			0
$925$	3.11684	−	5.39853i	0.102481	−	0.177503i
$926$	5.88316			0.193333
$927$	−25.0000	+	16.5831i	−0.821108	+	0.544661i
$928$	−2.74456			−0.0900947
$929$	4.88316	−	8.45787i	0.160211	−	0.277494i	−0.774733	−	0.632288i	$-0.782116\pi$
$929$	4.88316	−	8.45787i	0.160211	−	0.277494i	0.934944	+	0.354794i	$0.115449\pi$
$930$	4.62772	+	1.08724i	0.151749	+	0.0356520i
$931$		0			0
$932$	5.87228	+	10.1711i	0.192353	+	0.333165i
$933$	44.2337	+	10.3923i	1.44815	+	0.340229i
$934$	15.0475	−	26.0631i	0.492371	−	0.852811i
$935$	26.2337			0.857933
$936$	−5.00000	+	3.31662i	−0.163430	+	0.108407i
$937$	38.4674			1.25667			0.628337	−	0.777941i	$-0.283736\pi$
$937$	38.4674			1.25667			0.628337	+	0.777941i	$0.283736\pi$
$938$		0			0
$939$	−1.44158	−	4.78117i	−0.0470441	−	0.156028i
$940$		0			0
$941$	0.941578	+	1.63086i	0.0306946	+	0.0531645i	0.880965	−	0.473182i	$-0.156895\pi$
$941$	0.941578	+	1.63086i	0.0306946	+	0.0531645i	−0.850270	+	0.526347i	$0.823561\pi$
$942$	9.62772	−	10.2448i	0.313688	−	0.333795i
$943$	−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	$0.255118\pi$
$948$	−14.3723	+	15.2935i	−0.466790	+	0.496710i
$949$	5.11684	+	8.86263i	0.166100	+	0.287693i
$950$	7.79211	+	13.4963i	0.252809	+	0.437879i
$951$	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	$0.443597\pi$
$954$	−7.37228	−	3.66648i	−0.238686	−	0.118707i
$955$	−2.58422			−0.0836234
$956$	9.43070	−	16.3345i	0.305011	−	0.528294i
$957$	20.2337	+	4.75372i	0.654062	+	0.153666i
$958$	−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
$962$	4.00000			0.128965
$963$	0.302985	+	4.87375i	0.00976354	+	0.157054i
$964$	−0.883156			−0.0284445
$965$	4.80298	−	8.31901i	0.154614	−	0.267799i
$966$		0			0
$967$	−24.0584	−	41.6704i	−0.773667	−	1.34003i	−0.935541	−	0.353219i	$-0.885087\pi$
$967$	−24.0584	−	41.6704i	−0.773667	−	1.34003i	0.161874	−	0.986811i	$-0.448246\pi$
$968$	4.05842	+	7.02939i	0.130443	+	0.225933i
$969$	25.9307	−	27.5928i	0.833014	−	0.886408i
$970$	−6.25544	+	10.8347i	−0.200850	+	0.347882i
$971$	−7.37228			−0.236588			−0.118294	−	0.992979i	$-0.537742\pi$
$971$	−7.37228			−0.236588			−0.118294	+	0.992979i	$0.537742\pi$
$972$	−15.5000	−	1.65831i	−0.497163	−	0.0531904i
$973$		0			0
$974$	−8.17527	+	14.1600i	−0.261952	+	0.453715i
$975$	−7.39403	+	7.86797i	−0.236798	+	0.251977i
$976$	−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	$0.952623\pi$
$978$	8.11684	+	26.9205i	0.259548	+	0.860823i
$979$	7.11684	−	12.3267i	0.227455	−	0.393964i
$980$		0			0
$981$	−2.60597	−	41.9191i	−0.0832022	−	1.33837i
$982$	19.6277			0.626346
$983$	−25.3723	+	43.9461i	−0.809250	+	1.40166i	0.104134	+	0.994563i	$0.466793\pi$
$983$	−25.3723	+	43.9461i	−0.809250	+	1.40166i	−0.913384	+	0.407099i	$0.866540\pi$
$984$	17.4891	+	4.10891i	0.557533	+	0.130987i
$985$	4.11684	+	7.13058i	0.131174	+	0.227199i
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	−5.00000	+	8.66025i	−0.159071	+	0.275519i
$989$	−67.2119			−2.13722
$990$	−16.1168	−	8.01544i	−0.512227	−	0.254748i
$991$	−20.4674			−0.650168			−0.325084	−	0.945685i	$-0.605393\pi$
$991$	−20.4674			−0.650168			−0.325084	+	0.945685i	$0.605393\pi$
$992$	−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
$996$	−6.51087	+	6.92820i	−0.206305	+	0.219529i
$997$	6.05842	−	10.4935i	0.191872	−	0.332332i	−0.753999	−	0.656876i	$-0.771877\pi$
$997$	6.05842	−	10.4935i	0.191872	−	0.332332i	0.945871	+	0.324544i	$0.105211\pi$
$998$	−0.883156			−0.0279558
$999$	8.00000	+	6.63325i	0.253109	+	0.209867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.k.295.1		4
3.2	odd	2		2646.2.f.j.883.2		4
7.2	even	3		882.2.e.k.655.1		4
7.3	odd	6		882.2.h.m.79.1		4
7.4	even	3		882.2.h.n.79.2		4
7.5	odd	6		882.2.e.l.655.2		4
7.6	odd	2		126.2.f.d.43.2	✓	4
9.2	odd	6		7938.2.a.bs.1.1		2
9.4	even	3	inner	882.2.f.k.589.1		4
9.5	odd	6		2646.2.f.j.1765.2		4
9.7	even	3		7938.2.a.bh.1.2		2
21.2	odd	6		2646.2.e.m.2125.2		4
21.5	even	6		2646.2.e.n.2125.1		4
21.11	odd	6		2646.2.h.l.667.1		4
21.17	even	6		2646.2.h.k.667.2		4
21.20	even	2		378.2.f.c.127.1		4
28.27	even	2		1008.2.r.f.673.1		4
63.4	even	3		882.2.e.k.373.2		4
63.5	even	6		2646.2.h.k.361.2		4
63.13	odd	6		126.2.f.d.85.2	yes	4
63.20	even	6		1134.2.a.n.1.2		2
63.23	odd	6		2646.2.h.l.361.1		4
63.31	odd	6		882.2.e.l.373.1		4
63.32	odd	6		2646.2.e.m.1549.2		4
63.34	odd	6		1134.2.a.k.1.1		2
63.40	odd	6		882.2.h.m.67.1		4
63.41	even	6		378.2.f.c.253.1		4
63.58	even	3		882.2.h.n.67.2		4
63.59	even	6		2646.2.e.n.1549.1		4
84.83	odd	2		3024.2.r.f.2017.1		4
252.83	odd	6		9072.2.a.bb.1.2		2
252.139	even	6		1008.2.r.f.337.1		4
252.167	odd	6		3024.2.r.f.1009.1		4
252.223	even	6		9072.2.a.bm.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.2	✓	4	7.6	odd	2
126.2.f.d.85.2	yes	4	63.13	odd	6
378.2.f.c.127.1		4	21.20	even	2
378.2.f.c.253.1		4	63.41	even	6
882.2.e.k.373.2		4	63.4	even	3
882.2.e.k.655.1		4	7.2	even	3
882.2.e.l.373.1		4	63.31	odd	6
882.2.e.l.655.2		4	7.5	odd	6
882.2.f.k.295.1		4	1.1	even	1	trivial
882.2.f.k.589.1		4	9.4	even	3	inner
882.2.h.m.67.1		4	63.40	odd	6
882.2.h.m.79.1		4	7.3	odd	6
882.2.h.n.67.2		4	63.58	even	3
882.2.h.n.79.2		4	7.4	even	3
1008.2.r.f.337.1		4	252.139	even	6
1008.2.r.f.673.1		4	28.27	even	2
1134.2.a.k.1.1		2	63.34	odd	6
1134.2.a.n.1.2		2	63.20	even	6
2646.2.e.m.1549.2		4	63.32	odd	6
2646.2.e.m.2125.2		4	21.2	odd	6
2646.2.e.n.1549.1		4	63.59	even	6
2646.2.e.n.2125.1		4	21.5	even	6
2646.2.f.j.883.2		4	3.2	odd	2
2646.2.f.j.1765.2		4	9.5	odd	6
2646.2.h.k.361.2		4	63.5	even	6
2646.2.h.k.667.2		4	21.17	even	6
2646.2.h.l.361.1		4	63.23	odd	6
2646.2.h.l.667.1		4	21.11	odd	6
3024.2.r.f.1009.1		4	252.167	odd	6
3024.2.r.f.2017.1		4	84.83	odd	2
7938.2.a.bh.1.2		2	9.7	even	3
7938.2.a.bs.1.1		2	9.2	odd	6
9072.2.a.bb.1.2		2	252.83	odd	6
9072.2.a.bm.1.1		2	252.223	even	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.18614 + 1.26217i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.686141 - 1.18843i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 - 2.99422i) q^{9} -1.37228 q^{10} +(-2.18614 + 3.78651i) q^{11} +(1.68614 + 0.396143i) q^{12} +(1.00000 + 1.73205i) q^{13} +(2.31386 + 0.543620i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.37228 q^{17} +(-2.68614 - 1.33591i) q^{18} -5.00000 q^{19} +(-0.686141 + 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(1.18614 - 1.26217i) q^{24} +(1.55842 - 2.69927i) q^{25} +2.00000 q^{26} +(4.00000 + 3.31662i) q^{27} +(-1.37228 + 2.37686i) q^{29} +(1.62772 - 1.73205i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.18614 - 7.25061i) q^{33} +(2.18614 - 3.78651i) q^{34} +(-2.50000 + 1.65831i) q^{36} +2.00000 q^{37} +(-2.50000 + 4.33013i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(0.686141 + 1.18843i) q^{40} +(5.18614 + 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +4.37228 q^{44} +(-3.43070 + 2.27567i) q^{45} +7.37228 q^{46} +(-0.500000 - 1.65831i) q^{48} +(-1.55842 - 2.69927i) q^{50} +(-5.18614 + 5.51856i) q^{51} +(1.00000 - 1.73205i) q^{52} +2.74456 q^{53} +(4.87228 - 1.80579i) q^{54} +6.00000 q^{55} +(5.93070 - 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +(3.55842 + 6.16337i) q^{59} +(-0.686141 - 2.27567i) q^{60} +(-7.05842 + 12.2255i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(1.37228 - 2.37686i) q^{65} +(-7.37228 - 1.73205i) q^{66} +(-7.55842 - 13.0916i) q^{67} +(-2.18614 - 3.78651i) q^{68} +(-12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(0.186141 + 2.99422i) q^{72} +5.11684 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.55842 + 5.16870i) q^{75} +(2.50000 + 4.33013i) q^{76} +(-2.37228 + 2.52434i) q^{78} +(-6.05842 + 10.4935i) q^{79} +1.37228 q^{80} +(-8.93070 + 1.11469i) q^{81} +10.3723 q^{82} +(-2.74456 + 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-1.37228 - 4.55134i) q^{87} +(2.18614 - 3.78651i) q^{88} -3.25544 q^{89} +(0.255437 + 4.10891i) q^{90} +(3.68614 - 6.38458i) q^{92} +(-3.37228 - 0.792287i) q^{93} +(3.43070 + 5.94215i) q^{95} +(-1.68614 - 0.396143i) q^{96} +(4.55842 - 7.89542i) q^{97} +(11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9} + 6 q^{10} - 3 q^{11} + q^{12} + 4 q^{13} + 15 q^{15} - 2 q^{16} + 6 q^{17} - 5 q^{18} - 20 q^{19} + 3 q^{20} + 3 q^{22} + 9 q^{23} - q^{24} - 11 q^{25} + 8 q^{26} + 16 q^{27} + 6 q^{29} + 18 q^{30} + 4 q^{31} + 2 q^{32} - 3 q^{33} + 3 q^{34} - 10 q^{36} + 8 q^{37} - 10 q^{38} - 2 q^{39} - 3 q^{40} + 15 q^{41} - q^{43} + 6 q^{44} + 15 q^{45} + 18 q^{46} - 2 q^{48} + 11 q^{50} - 15 q^{51} + 4 q^{52} - 12 q^{53} + 8 q^{54} + 24 q^{55} - 5 q^{57} - 6 q^{58} - 3 q^{59} + 3 q^{60} - 11 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 18 q^{66} - 13 q^{67} - 3 q^{68} - 21 q^{69} + 6 q^{71} - 5 q^{72} - 14 q^{73} + 4 q^{74} - 11 q^{75} + 10 q^{76} + 2 q^{78} - 7 q^{79} - 6 q^{80} - 7 q^{81} + 30 q^{82} + 12 q^{83} - 12 q^{85} + q^{86} + 6 q^{87} + 3 q^{88} - 36 q^{89} + 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} - q^{96} + q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9 + 6 * q^10 - 3 * q^11 + q^12 + 4 * q^13 + 15 * q^15 - 2 * q^16 + 6 * q^17 - 5 * q^18 - 20 * q^19 + 3 * q^20 + 3 * q^22 + 9 * q^23 - q^24 - 11 * q^25 + 8 * q^26 + 16 * q^27 + 6 * q^29 + 18 * q^30 + 4 * q^31 + 2 * q^32 - 3 * q^33 + 3 * q^34 - 10 * q^36 + 8 * q^37 - 10 * q^38 - 2 * q^39 - 3 * q^40 + 15 * q^41 - q^43 + 6 * q^44 + 15 * q^45 + 18 * q^46 - 2 * q^48 + 11 * q^50 - 15 * q^51 + 4 * q^52 - 12 * q^53 + 8 * q^54 + 24 * q^55 - 5 * q^57 - 6 * q^58 - 3 * q^59 + 3 * q^60 - 11 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 18 * q^66 - 13 * q^67 - 3 * q^68 - 21 * q^69 + 6 * q^71 - 5 * q^72 - 14 * q^73 + 4 * q^74 - 11 * q^75 + 10 * q^76 + 2 * q^78 - 7 * q^79 - 6 * q^80 - 7 * q^81 + 30 * q^82 + 12 * q^83 - 12 * q^85 + q^86 + 6 * q^87 + 3 * q^88 - 36 * q^89 + 24 * q^90 + 9 * q^92 - 2 * q^93 - 15 * q^95 - q^96 + q^97 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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