LMFDB - Embedded newform 882.2.e.l.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	882.373
Dual form			882.2.e.l.655.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +(-0.686141 - 1.18843i) q^{10} +(-2.18614 + 3.78651i) q^{11} +(0.500000 - 1.65831i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(2.31386 - 0.543620i) q^{15} +1.00000 q^{16} +(2.18614 + 3.78651i) q^{17} +(2.50000 + 1.65831i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(-0.500000 + 1.65831i) q^{24} +(1.55842 - 2.69927i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(-2.31386 + 0.543620i) q^{30} +2.00000 q^{31} -1.00000 q^{32} +(5.18614 + 5.51856i) q^{33} +(-2.18614 - 3.78651i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(-0.686141 - 1.18843i) q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(-2.18614 + 3.78651i) q^{44} +(0.255437 - 4.10891i) q^{45} +(-3.68614 - 6.38458i) q^{46} +(0.500000 - 1.65831i) q^{48} +(-1.55842 + 2.69927i) q^{50} +(7.37228 - 1.73205i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.37228 - 2.37686i) q^{53} +(4.00000 - 3.31662i) q^{54} -6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +7.11684 q^{59} +(2.31386 - 0.543620i) q^{60} -14.1168 q^{61} -2.00000 q^{62} +1.00000 q^{64} -2.74456 q^{65} +(-5.18614 - 5.51856i) q^{66} +15.1168 q^{67} +(2.18614 + 3.78651i) q^{68} +(12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(2.50000 + 1.65831i) q^{72} +(2.55842 + 4.43132i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-3.69702 - 3.93398i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(-2.37228 - 2.52434i) q^{78} +12.1168 q^{79} +(0.686141 + 1.18843i) q^{80} +(3.50000 + 8.29156i) q^{81} +(5.18614 - 8.98266i) q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-4.62772 + 1.08724i) q^{87} +(2.18614 - 3.78651i) q^{88} +(-1.62772 + 2.81929i) q^{89} +(-0.255437 + 4.10891i) q^{90} +(3.68614 + 6.38458i) q^{92} +(1.00000 - 3.31662i) q^{93} -6.86141 q^{95} +(-0.500000 + 1.65831i) q^{96} +(-4.55842 - 7.89542i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 3 * q^5 - 2 * q^6 - 4 * q^8 - 10 * q^9	$ 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9} + 3 q^{10} - 3 q^{11} + 2 q^{12} - 4 q^{13} + 15 q^{15} + 4 q^{16} + 3 q^{17} + 10 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{23} - 2 q^{24} - 11 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 15 q^{30} + 8 q^{31} - 4 q^{32} + 15 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} + 24 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} + 16 q^{54} - 24 q^{55} - 5 q^{57} - 6 q^{58} - 6 q^{59} + 15 q^{60} - 22 q^{61} - 8 q^{62} + 4 q^{64} + 12 q^{65} - 15 q^{66} + 26 q^{67} + 3 q^{68} + 21 q^{69} + 6 q^{71} + 10 q^{72} - 7 q^{73} + 4 q^{74} - 55 q^{75} - 10 q^{76} + 2 q^{78} + 14 q^{79} - 3 q^{80} + 14 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} + q^{86} - 30 q^{87} + 3 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} + 4 q^{93} + 30 q^{95} - 2 q^{96} - q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 3 * q^5 - 2 * q^6 - 4 * q^8 - 10 * q^9 + 3 * q^10 - 3 * q^11 + 2 * q^12 - 4 * q^13 + 15 * q^15 + 4 * q^16 + 3 * q^17 + 10 * q^18 - 10 * q^19 - 3 * q^20 + 3 * q^22 + 9 * q^23 - 2 * q^24 - 11 * q^25 + 4 * q^26 - 16 * q^27 + 6 * q^29 - 15 * q^30 + 8 * q^31 - 4 * q^32 + 15 * q^33 - 3 * q^34 - 10 * q^36 - 4 * q^37 + 10 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 - q^43 - 3 * q^44 + 24 * q^45 - 9 * q^46 + 2 * q^48 + 11 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 + 16 * q^54 - 24 * q^55 - 5 * q^57 - 6 * q^58 - 6 * q^59 + 15 * q^60 - 22 * q^61 - 8 * q^62 + 4 * q^64 + 12 * q^65 - 15 * q^66 + 26 * q^67 + 3 * q^68 + 21 * q^69 + 6 * q^71 + 10 * q^72 - 7 * q^73 + 4 * q^74 - 55 * q^75 - 10 * q^76 + 2 * q^78 + 14 * q^79 - 3 * q^80 + 14 * q^81 + 15 * q^82 - 12 * q^83 - 12 * q^85 + q^86 - 30 * q^87 + 3 * q^88 - 18 * q^89 - 24 * q^90 + 9 * q^92 + 4 * q^93 + 30 * q^95 - 2 * q^96 - q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$3$	0.500000	−	1.65831i	0.288675	−	0.957427i
$4$	1.00000			0.500000
$5$	0.686141	+	1.18843i	0.306851	+	0.531482i	0.977672	−	0.210138i	$-0.0673912\pi$
$5$	0.686141	+	1.18843i	0.306851	+	0.531482i	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−0.500000	+	1.65831i	−0.204124	+	0.677003i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$	−0.686141	−	1.18843i	−0.216977	−	0.375815i
$11$	−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	$0.937584\pi$
$12$	0.500000	−	1.65831i	0.144338	−	0.478714i
$13$	−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
$16$	1.00000			0.250000
$17$	2.18614	+	3.78651i	0.530217	+	0.918363i	0.999379	+	0.0352504i	$0.0112229\pi$
$17$	2.18614	+	3.78651i	0.530217	+	0.918363i	−0.469162	+	0.883112i	$0.655444\pi$
$18$	2.50000	+	1.65831i	0.589256	+	0.390868i
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	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	$0.554280\pi$
$24$	−0.500000	+	1.65831i	−0.102062	+	0.338502i
$25$	1.55842	−	2.69927i	0.311684	−	0.539853i
$26$	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	$0.915352\pi$
$30$	−2.31386	+	0.543620i	−0.422451	+	0.0992510i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000			−0.176777
$33$	5.18614	+	5.51856i	0.902791	+	0.960658i
$34$	−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	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$	2.37228	+	2.52434i	0.379869	+	0.404218i
$40$	−0.686141	−	1.18843i	−0.108488	−	0.187907i
$41$	−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
$45$	0.255437	−	4.10891i	0.0380784	−	0.612520i
$46$	−3.68614	−	6.38458i	−0.543492	−	0.941355i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	0.500000	−	1.65831i	0.0721688	−	0.239357i
$49$		0			0
$50$	−1.55842	+	2.69927i	−0.220394	+	0.381734i
$51$	7.37228	−	1.73205i	1.03233	−	0.242536i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−1.37228	−	2.37686i	−0.188497	−	0.326487i	0.756252	−	0.654280i	$-0.227028\pi$
$53$	−1.37228	−	2.37686i	−0.188497	−	0.326487i	−0.944749	+	0.327793i	$0.893695\pi$
$54$	4.00000	−	3.31662i	0.544331	−	0.451335i
$55$	−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
$59$	7.11684			0.926534			0.463267	−	0.886219i	$-0.346677\pi$
$59$	7.11684			0.926534			0.463267	+	0.886219i	$0.346677\pi$
$60$	2.31386	−	0.543620i	0.298718	−	0.0701811i
$61$	−14.1168			−1.80748			−0.903738	−	0.428085i	$-0.859188\pi$
$61$	−14.1168			−1.80748			−0.903738	+	0.428085i	$0.859188\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.74456			−0.340421
$66$	−5.18614	−	5.51856i	−0.638370	−	0.679287i
$67$	15.1168			1.84682			0.923408	−	0.383819i	$-0.125391\pi$
$67$	15.1168			1.84682			0.923408	+	0.383819i	$0.125391\pi$
$68$	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	$0.295038\pi$
$72$	2.50000	+	1.65831i	0.294628	+	0.195434i
$73$	2.55842	+	4.43132i	0.299441	+	0.518646i	0.976008	−	0.217734i	$-0.0698666\pi$
$73$	2.55842	+	4.43132i	0.299441	+	0.518646i	−0.676567	+	0.736381i	$0.736533\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−3.69702	−	3.93398i	−0.426895	−	0.454257i
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$		0			0
$78$	−2.37228	−	2.52434i	−0.268608	−	0.285825i
$79$	12.1168			1.36325			0.681626	−	0.731701i	$-0.261273\pi$
$79$	12.1168			1.36325			0.681626	+	0.731701i	$0.261273\pi$
$80$	0.686141	+	1.18843i	0.0767129	+	0.132871i
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$	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
$86$	4.55842	+	7.89542i	0.491547	+	0.851385i
$87$	−4.62772	+	1.08724i	−0.496144	+	0.116564i
$88$	2.18614	−	3.78651i	0.233043	−	0.403643i
$89$	−1.62772	+	2.81929i	−0.172538	+	0.298844i	−0.939306	−	0.343079i	$-0.888530\pi$
$89$	−1.62772	+	2.81929i	−0.172538	+	0.298844i	0.766769	+	0.641924i	$0.221863\pi$
$90$	−0.255437	+	4.10891i	−0.0269255	+	0.433117i
$91$		0			0
$92$	3.68614	+	6.38458i	0.384307	+	0.665639i
$93$	1.00000	−	3.31662i	0.103695	−	0.343918i
$94$		0			0
$95$	−6.86141			−0.703965
$96$	−0.500000	+	1.65831i	−0.0510310	+	0.169251i
$97$	−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
$101$	−3.68614	+	6.38458i	−0.366785	+	0.635290i	−0.989061	−	0.147508i	$-0.952875\pi$
$101$	−3.68614	+	6.38458i	−0.366785	+	0.635290i	0.622276	+	0.782798i	$0.286208\pi$
$102$	−7.37228	+	1.73205i	−0.729965	+	0.171499i
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	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	−0.824001	−	0.566588i	$-0.808263\pi$
$107$	0.813859	−	1.40965i	0.0786788	−	0.136276i	0.902680	+	0.430312i	$0.141597\pi$
$108$	−4.00000	+	3.31662i	−0.384900	+	0.319142i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	6.00000			0.572078
$111$	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	$0.187227\pi$
$114$	−5.93070	−	6.31084i	−0.555461	−	0.591065i
$115$	−5.05842	+	8.76144i	−0.471700	+	0.817009i
$116$	−1.37228	−	2.37686i	−0.127413	−	0.220686i
$117$	5.37228	−	2.67181i	0.496668	−	0.247009i
$118$	−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
$122$	14.1168			1.27808
$123$	12.3030	+	13.0916i	1.10932	+	1.18043i
$124$	2.00000			0.179605
$125$	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	$0.715445\pi$
$128$	−1.00000			−0.0883883
$129$	−15.3723	+	3.61158i	−1.35345	+	0.317982i
$130$	2.74456			0.240714
$131$	3.68614	+	6.38458i	0.322060	+	0.557824i	0.980913	−	0.194448i	$-0.0622915\pi$
$131$	3.68614	+	6.38458i	0.322060	+	0.557824i	−0.658853	+	0.752271i	$0.728958\pi$
$132$	5.18614	+	5.51856i	0.451396	+	0.480329i
$133$		0			0
$134$	−15.1168			−1.30590
$135$	−6.68614	−	2.47805i	−0.575451	−	0.213277i
$136$	−2.18614	−	3.78651i	−0.187460	−	0.324690i
$137$	−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	$0.920122\pi$
$138$	−12.4307	+	2.92048i	−1.05817	+	0.248608i
$139$	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
$142$	−10.1168			−0.848987
$143$	−4.37228	−	7.57301i	−0.365629	−	0.633287i
$144$	−2.50000	−	1.65831i	−0.208333	−	0.138193i
$145$	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
$149$	−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	$-0.373078\pi$
$150$	3.69702	+	3.93398i	0.301860	+	0.321208i
$151$	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	$0.0595270\pi$
$152$	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
$156$	2.37228	+	2.52434i	0.189935	+	0.202109i
$157$	−8.11684			−0.647795			−0.323897	−	0.946092i	$-0.604993\pi$
$157$	−8.11684			−0.647795			−0.323897	+	0.946092i	$0.604993\pi$
$158$	−12.1168			−0.963964
$159$	−4.62772	+	1.08724i	−0.367002	+	0.0862238i
$160$	−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	0.350593	+	0.936528i	$0.385980\pi$
$163$	−8.11684	+	14.0588i	−0.635760	+	1.10117i	−0.986354	+	0.164641i	$0.947353\pi$
$164$	−5.18614	+	8.98266i	−0.404970	+	0.701428i
$165$	−3.00000	+	9.94987i	−0.233550	+	0.774597i
$166$	−2.74456	−	4.75372i	−0.213019	−	0.368960i
$167$	−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
$171$	13.4307	−	6.67954i	1.02707	−	0.510797i
$172$	−4.55842	−	7.89542i	−0.347576	−	0.602020i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	4.62772	−	1.08724i	0.350826	−	0.0824235i
$175$		0			0
$176$	−2.18614	+	3.78651i	−0.164787	+	0.285419i
$177$	3.55842	−	11.8020i	0.267467	−	0.887089i
$178$	1.62772	−	2.81929i	0.122003	−	0.211315i
$179$	−7.37228	−	12.7692i	−0.551030	−	0.954412i	−0.998201	−	0.0599635i	$-0.980902\pi$
$179$	−7.37228	−	12.7692i	−0.551030	−	0.954412i	0.447170	−	0.894449i	$-0.352432\pi$
$180$	0.255437	−	4.10891i	0.0190392	−	0.306260i
$181$	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
$184$	−3.68614	−	6.38458i	−0.271746	−	0.470678i
$185$	−2.74456			−0.201784
$186$	−1.00000	+	3.31662i	−0.0733236	+	0.243187i
$187$	−19.1168			−1.39796
$188$		0			0
$189$		0			0
$190$	6.86141			0.497779
$191$	−1.88316			−0.136260			−0.0681302	−	0.997676i	$-0.521703\pi$
$191$	−1.88316			−0.136260			−0.0681302	+	0.997676i	$0.521703\pi$
$192$	0.500000	−	1.65831i	0.0360844	−	0.119678i
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	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	$0.568565\pi$
$198$	−11.7446	+	5.84096i	−0.834650	+	0.415099i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	−1.55842	+	2.69927i	−0.110197	+	0.190867i
$201$	7.55842	−	25.0684i	0.533130	−	1.76819i
$202$	3.68614	−	6.38458i	0.259356	−	0.449218i
$203$		0			0
$204$	7.37228	−	1.73205i	0.516163	−	0.121268i
$205$	−14.2337			−0.994124
$206$	−5.00000	−	8.66025i	−0.348367	−	0.603388i
$207$	1.37228	−	22.0742i	0.0953801	−	1.53427i
$208$	−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	$-0.0189888\pi$
$212$	−1.37228	−	2.37686i	−0.0942487	−	0.163243i
$213$	5.05842	−	16.7769i	0.346597	−	1.14953i
$214$	−0.813859	+	1.40965i	−0.0556343	+	0.0963614i
$215$	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
$219$	8.62772	−	2.02700i	0.583007	−	0.136972i
$220$	−6.00000			−0.404520
$221$	−8.74456			−0.588223
$222$	−2.37228	−	2.52434i	−0.159217	−	0.169422i
$223$	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
$227$	11.8723	−	20.5634i	0.787991	−	1.36484i	−0.139205	−	0.990264i	$-0.544455\pi$
$227$	11.8723	−	20.5634i	0.787991	−	1.36484i	0.927196	−	0.374577i	$-0.122212\pi$
$228$	5.93070	+	6.31084i	0.392770	+	0.417946i
$229$	10.0584	+	17.4217i	0.664679	+	1.15126i	0.979372	+	0.202065i	$0.0647651\pi$
$229$	10.0584	+	17.4217i	0.664679	+	1.15126i	−0.314693	+	0.949194i	$0.601902\pi$
$230$	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	−0.607022	−	0.794685i	$-0.707636\pi$
$233$	5.87228	−	10.1711i	0.384706	−	0.666330i	0.991728	+	0.128354i	$0.0409695\pi$
$234$	−5.37228	+	2.67181i	−0.351197	+	0.174662i
$235$		0			0
$236$	7.11684			0.463267
$237$	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	$-0.0421725\pi$
$240$	2.31386	−	0.543620i	0.149359	−	0.0350905i
$241$	−0.441578	+	0.764836i	−0.0284445	+	0.0492674i	−0.879897	−	0.475164i	$-0.842389\pi$
$241$	−0.441578	+	0.764836i	−0.0284445	+	0.0492674i	0.851453	+	0.524431i	$0.175722\pi$
$242$	4.05842	+	7.02939i	0.260885	+	0.451867i
$243$	15.5000	−	1.65831i	0.994325	−	0.106381i
$244$	−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
$248$	−2.00000			−0.127000
$249$	9.25544	−	2.17448i	0.586540	−	0.137802i
$250$	−11.1386			−0.704467
$251$	−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
$254$	14.1168			0.885770
$255$	7.11684	+	7.57301i	0.445674	+	0.474240i
$256$	1.00000			0.0625000
$257$	−10.9307	−	18.9325i	−0.681839	−	1.18098i	−0.974419	−	0.224738i	$-0.927847\pi$
$257$	−10.9307	−	18.9325i	−0.681839	−	1.18098i	0.292581	−	0.956241i	$-0.405486\pi$
$258$	15.3723	−	3.61158i	0.957036	−	0.224847i
$259$		0			0
$260$	−2.74456			−0.170211
$261$	−0.510875	+	8.21782i	−0.0316224	+	0.508671i
$262$	−3.68614	−	6.38458i	−0.227731	−	0.394441i
$263$	−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	$0.301936\pi$
$264$	−5.18614	−	5.51856i	−0.319185	−	0.339644i
$265$	1.88316	−	3.26172i	0.115681	−	0.200366i
$266$		0			0
$267$	3.86141	+	4.10891i	0.236314	+	0.251461i
$268$	15.1168			0.923408
$269$	3.68614	+	6.38458i	0.224748	+	0.389275i	0.956244	−	0.292571i	$-0.0945108\pi$
$269$	3.68614	+	6.38458i	0.224748	+	0.389275i	−0.731496	+	0.681846i	$0.761177\pi$
$270$	6.68614	+	2.47805i	0.406906	+	0.150809i
$271$	9.11684	−	15.7908i	0.553809	−	0.959225i	−0.444186	−	0.895934i	$-0.646507\pi$
$271$	9.11684	−	15.7908i	0.553809	−	0.959225i	0.997995	−	0.0632906i	$-0.0201595\pi$
$272$	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
$276$	12.4307	−	2.92048i	0.748240	−	0.175792i
$277$	−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	$0.933840\pi$
$278$	−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
$283$	9.88316			0.587493			0.293746	−	0.955883i	$-0.405098\pi$
$283$	9.88316			0.587493			0.293746	+	0.955883i	$0.405098\pi$
$284$	10.1168			0.600324
$285$	−3.43070	+	11.3784i	−0.203217	+	0.673996i
$286$	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
$290$	−1.88316	+	3.26172i	−0.110583	+	0.191535i
$291$	−15.3723	+	3.61158i	−0.901139	+	0.211714i
$292$	2.55842	+	4.43132i	0.149720	+	0.259323i
$293$	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
$297$	−3.81386	−	22.3966i	−0.221303	−	1.29958i
$298$	7.37228	+	12.7692i	0.427065	+	0.739698i
$299$	−14.7446			−0.852700
$300$	−3.69702	−	3.93398i	−0.213447	−	0.227129i
$301$		0			0
$302$	−4.05842	+	7.02939i	−0.233536	+	0.404496i
$303$	8.74456	+	9.30506i	0.502362	+	0.534562i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	−9.68614	−	16.7769i	−0.554627	−	0.960642i
$306$	−0.813859	+	13.0916i	−0.0465252	+	0.748395i
$307$	−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
$310$	−1.37228	−	2.37686i	−0.0779403	−	0.134997i
$311$	−26.2337			−1.48758			−0.743788	−	0.668416i	$-0.766973\pi$
$311$	−26.2337			−1.48758			−0.743788	+	0.668416i	$0.766973\pi$
$312$	−2.37228	−	2.52434i	−0.134304	−	0.142912i
$313$	−2.88316			−0.162966			−0.0814828	−	0.996675i	$-0.525966\pi$
$313$	−2.88316			−0.162966			−0.0814828	+	0.996675i	$0.525966\pi$
$314$	8.11684			0.458060
$315$		0			0
$316$	12.1168			0.681626
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	4.62772	−	1.08724i	0.259510	−	0.0609694i
$319$	12.0000			0.671871
$320$	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
$324$	3.50000	+	8.29156i	0.194444	+	0.460642i
$325$	3.11684	+	5.39853i	0.172891	+	0.299457i
$326$	8.11684	−	14.0588i	0.449550	−	0.778644i
$327$	−23.6060	+	5.54601i	−1.30541	+	0.306695i
$328$	5.18614	−	8.98266i	0.286357	−	0.495984i
$329$		0			0
$330$	3.00000	−	9.94987i	0.165145	−	0.547723i
$331$	−12.2337			−0.672424			−0.336212	−	0.941786i	$-0.609146\pi$
$331$	−12.2337			−0.672424			−0.336212	+	0.941786i	$0.609146\pi$
$332$	2.74456	+	4.75372i	0.150627	+	0.260894i
$333$	5.37228	−	2.67181i	0.294399	−	0.146415i
$334$	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	$0.246543\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	1.62772	+	1.73205i	0.0884055	+	0.0940721i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−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
$345$	12.0000	+	12.7692i	0.646058	+	0.687469i
$346$	6.00000			0.322562
$347$	7.11684			0.382052			0.191026	−	0.981585i	$-0.438818\pi$
$347$	7.11684			0.382052			0.191026	+	0.981585i	$0.438818\pi$
$348$	−4.62772	+	1.08724i	−0.248072	+	0.0582822i
$349$	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
$353$	3.81386	−	6.60580i	0.202991	−	0.351591i	−0.746500	−	0.665386i	$-0.768267\pi$
$353$	3.81386	−	6.60580i	0.202991	−	0.351591i	0.949491	+	0.313795i	$0.101600\pi$
$354$	−3.55842	+	11.8020i	−0.189128	+	0.627267i
$355$	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
$359$	3.43070	−	5.94215i	0.181066	−	0.313615i	−0.761178	−	0.648543i	$-0.775379\pi$
$359$	3.43070	−	5.94215i	0.181066	−	0.313615i	0.942244	+	0.334928i	$0.108712\pi$
$360$	−0.255437	+	4.10891i	−0.0134627	+	0.216559i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−18.1168			−0.952200
$363$	−13.6861	+	3.21543i	−0.718336	+	0.168767i
$364$		0			0
$365$	−3.51087	+	6.08101i	−0.183768	+	0.318295i
$366$	7.05842	−	23.4101i	0.368950	−	1.22367i
$367$	−11.1168	+	19.2549i	−0.580295	+	1.00510i	0.415150	+	0.909753i	$0.363729\pi$
$367$	−11.1168	+	19.2549i	−0.580295	+	1.00510i	−0.995444	+	0.0953465i	$0.969604\pi$
$368$	3.68614	+	6.38458i	0.192153	+	0.332819i
$369$	27.8614	−	13.8564i	1.45041	−	0.721336i
$370$	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	$0.749977\pi$
$374$	19.1168			0.988508
$375$	5.56930	−	18.4713i	0.287597	−	0.953852i
$376$		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	$0.424769\pi$
$380$	−6.86141			−0.351983
$381$	−7.05842	+	23.4101i	−0.361614	+	1.19934i
$382$	1.88316			0.0963506
$383$	10.6277	+	18.4077i	0.543051	+	0.940592i	0.998727	+	0.0504462i	$0.0160643\pi$
$383$	10.6277	+	18.4077i	0.543051	+	0.940592i	−0.455676	+	0.890146i	$0.650602\pi$
$384$	−0.500000	+	1.65831i	−0.0255155	+	0.0846254i
$385$		0			0
$386$	7.00000			0.356291
$387$	−1.69702	+	27.2978i	−0.0862641	+	1.38763i
$388$	−4.55842	−	7.89542i	−0.231419	−	0.400829i
$389$	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	$-0.180365\pi$
$390$	1.37228	−	4.55134i	0.0694882	−	0.230466i
$391$	−16.1168	+	27.9152i	−0.815064	+	1.41173i
$392$		0			0
$393$	12.4307	−	2.92048i	0.627046	−	0.147319i
$394$	6.00000			0.302276
$395$	8.31386	+	14.4000i	0.418316	+	0.724544i
$396$	11.7446	−	5.84096i	0.590186	−	0.293519i
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	−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	$0.831303\pi$
$402$	−7.55842	+	25.0684i	−0.376980	+	1.25030i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−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
$408$	−7.37228	+	1.73205i	−0.364982	+	0.0857493i
$409$	29.3505			1.45129			0.725645	−	0.688069i	$-0.241541\pi$
$409$	29.3505			1.45129			0.725645	+	0.688069i	$0.241541\pi$
$410$	14.2337			0.702952
$411$	19.4198	+	20.6646i	0.957910	+	1.01931i
$412$	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
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−25.1861	−	26.8005i	−1.23337	−	1.31243i
$418$	10.9307	+	18.9325i	0.534638	+	0.926020i
$419$	−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
$425$	13.6277			0.661041
$426$	−5.05842	+	16.7769i	−0.245081	+	0.812843i
$427$		0			0
$428$	0.813859	−	1.40965i	0.0393394	−	0.0681378i
$429$	−14.7446	+	3.46410i	−0.711874	+	0.167248i
$430$	−6.25544	+	10.8347i	−0.301664	+	0.522497i
$431$	14.7446	+	25.5383i	0.710221	+	1.23014i	0.964774	+	0.263079i	$0.0847381\pi$
$431$	14.7446	+	25.5383i	0.710221	+	1.23014i	−0.254554	+	0.967059i	$0.581929\pi$
$432$	−4.00000	+	3.31662i	−0.192450	+	0.159571i
$433$	−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
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−36.8614			−1.76332
$438$	−8.62772	+	2.02700i	−0.412248	+	0.0968540i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	8.74456			0.415936
$443$	−22.8832			−1.08721			−0.543606	−	0.839341i	$-0.682941\pi$
$443$	−22.8832			−1.08721			−0.543606	+	0.839341i	$0.682941\pi$
$444$	2.37228	+	2.52434i	0.112583	+	0.119800i
$445$	−4.46738			−0.211774
$446$	−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	$0.215888\pi$
$450$	8.37228	−	4.16381i	0.394673	−	0.196284i
$451$	−22.6753	−	39.2747i	−1.06774	−	1.84937i
$452$	−0.686141	+	1.18843i	−0.0322733	+	0.0558991i
$453$	−9.62772	−	10.2448i	−0.452350	−	0.481344i
$454$	−11.8723	+	20.5634i	−0.557194	+	0.965088i
$455$		0			0
$456$	−5.93070	−	6.31084i	−0.277731	−	0.295532i
$457$	33.4674			1.56554			0.782769	−	0.622312i	$-0.213807\pi$
$457$	33.4674			1.56554			0.782769	+	0.622312i	$0.213807\pi$
$458$	−10.0584	−	17.4217i	−0.469999	−	0.814062i
$459$	−21.3030	−	7.89542i	−0.994338	−	0.368527i
$460$	−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	$0.123015\pi$
$464$	−1.37228	−	2.37686i	−0.0637066	−	0.110343i
$465$	4.62772	−	1.08724i	0.214605	−	0.0504196i
$466$	−5.87228	+	10.1711i	−0.272028	+	0.471167i
$467$	15.0475	−	26.0631i	0.696317	−	1.20606i	−0.273417	−	0.961896i	$-0.588154\pi$
$467$	15.0475	−	26.0631i	0.696317	−	1.20606i	0.969735	−	0.244162i	$-0.0785127\pi$
$468$	5.37228	−	2.67181i	0.248334	−	0.123505i
$469$		0			0
$470$		0			0
$471$	−4.05842	+	13.4603i	−0.187002	+	0.620216i
$472$	−7.11684			−0.327579
$473$	39.8614			1.83283
$474$	−6.05842	+	20.0935i	−0.278273	+	0.922926i
$475$	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
$479$	−10.6277	+	18.4077i	−0.485593	+	0.841072i	−0.999863	−	0.0165568i	$-0.994730\pi$
$479$	−10.6277	+	18.4077i	−0.485593	+	0.841072i	0.514270	+	0.857628i	$0.328063\pi$
$480$	−2.31386	+	0.543620i	−0.105613	+	0.0248128i
$481$	−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
$485$	6.25544	−	10.8347i	0.284045	−	0.491980i
$486$	−15.5000	+	1.65831i	−0.703094	+	0.0752226i
$487$	8.17527	+	14.1600i	0.370457	+	0.641650i	0.989636	−	0.143600i	$-0.0458679\pi$
$487$	8.17527	+	14.1600i	0.370457	+	0.641650i	−0.619179	+	0.785250i	$0.712535\pi$
$488$	14.1168			0.639040
$489$	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	$0.0206187\pi$
$492$	12.3030	+	13.0916i	0.554661	+	0.590214i
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	5.00000	+	8.66025i	0.224961	+	0.389643i
$495$	15.0000	+	9.94987i	0.674200	+	0.447214i
$496$	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	$0.839626\pi$
$500$	11.1386			0.498133
$501$	20.7446	+	22.0742i	0.926799	+	0.986204i
$502$	9.00000			0.401690
$503$	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
$506$	32.2337			1.43296
$507$	15.1753	−	3.56529i	0.673957	−	0.158340i
$508$	−14.1168			−0.626334
$509$	−8.48913	−	14.7036i	−0.376274	−	0.651725i	0.614243	−	0.789117i	$-0.289461\pi$
$509$	−8.48913	−	14.7036i	−0.376274	−	0.651725i	−0.990517	+	0.137392i	$0.956128\pi$
$510$	−7.11684	−	7.57301i	−0.315139	−	0.335339i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−4.36141	−	25.6121i	−0.192561	−	1.13080i
$514$	10.9307	+	18.9325i	0.482133	+	0.835078i
$515$	−6.86141	+	11.8843i	−0.302350	+	0.523685i
$516$	−15.3723	+	3.61158i	−0.676727	+	0.158991i
$517$		0			0
$518$		0			0
$519$	−3.00000	+	9.94987i	−0.131685	+	0.436751i
$520$	2.74456			0.120357
$521$	−1.93070	−	3.34408i	−0.0845856	−	0.146507i	0.820629	−	0.571461i	$-0.193623\pi$
$521$	−1.93070	−	3.34408i	−0.0845856	−	0.146507i	−0.905215	+	0.424955i	$0.860290\pi$
$522$	0.510875	−	8.21782i	0.0223604	−	0.359684i
$523$	8.94158	−	15.4873i	0.390988	−	0.677211i	−0.601592	−	0.798803i	$-0.705467\pi$
$523$	8.94158	−	15.4873i	0.390988	−	0.677211i	0.992580	+	0.121592i	$0.0388001\pi$
$524$	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
$528$	5.18614	+	5.51856i	0.225698	+	0.240164i
$529$	−15.6753	+	27.1504i	−0.681533	+	1.18045i
$530$	−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
$534$	−3.86141	−	4.10891i	−0.167099	−	0.177810i
$535$	2.23369			0.0965708
$536$	−15.1168			−0.652948
$537$	−24.8614	+	5.84096i	−1.07285	+	0.252056i
$538$	−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	0.384813	+	0.922995i	$0.374266\pi$
$541$	−14.1168	+	24.4511i	−0.606931	+	1.05123i	−0.991743	+	0.128240i	$0.959067\pi$
$542$	−9.11684	+	15.7908i	−0.391602	+	0.678275i
$543$	9.05842	−	30.0434i	0.388734	−	1.28929i
$544$	−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	0.856431	−	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
$549$	35.2921	+	23.4101i	1.50623	+	0.999120i
$550$	−6.81386	−	11.8020i	−0.290544	−	0.503237i
$551$	13.7228			0.584611
$552$	−12.4307	+	2.92048i	−0.529086	+	0.124304i
$553$		0			0
$554$	11.1168	−	19.2549i	0.472309	−	0.818064i
$555$	−1.37228	+	4.55134i	−0.0582501	+	0.193194i
$556$	10.6168	−	18.3889i	0.450254	−	0.779864i
$557$	−3.25544	−	5.63858i	−0.137937	−	0.238914i	0.788778	−	0.614678i	$-0.210714\pi$
$557$	−3.25544	−	5.63858i	−0.137937	−	0.238914i	−0.926716	+	0.375763i	$0.877381\pi$
$558$	5.00000	+	3.31662i	0.211667	+	0.140404i
$559$	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
$563$	3.00000			0.126435			0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000			0.126435			0.0632175	+	0.998000i	$0.479864\pi$
$564$		0			0
$565$	−1.88316			−0.0792250
$566$	−9.88316			−0.415420
$567$		0			0
$568$	−10.1168			−0.424493
$569$	−1.11684			−0.0468205			−0.0234103	−	0.999726i	$-0.507452\pi$
$569$	−1.11684			−0.0468205			−0.0234103	+	0.999726i	$0.507452\pi$
$570$	3.43070	−	11.3784i	0.143696	−	0.476587i
$571$	29.3505			1.22828			0.614141	−	0.789197i	$-0.289503\pi$
$571$	29.3505			1.22828			0.614141	+	0.789197i	$0.289503\pi$
$572$	−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
$576$	−2.50000	−	1.65831i	−0.104167	−	0.0690963i
$577$	−13.5584	−	23.4839i	−0.564444	−	0.977647i	−0.997101	−	0.0760878i	$-0.975757\pi$
$577$	−13.5584	−	23.4839i	−0.564444	−	0.977647i	0.432657	−	0.901559i	$-0.357576\pi$
$578$	1.05842	−	1.83324i	0.0440246	−	0.0762528i
$579$	−3.50000	+	11.6082i	−0.145455	+	0.482420i
$580$	1.88316	−	3.26172i	0.0781938	−	0.135436i
$581$		0			0
$582$	15.3723	−	3.61158i	0.637202	−	0.149705i
$583$	12.0000			0.496989
$584$	−2.55842	−	4.43132i	−0.105868	−	0.183369i
$585$	6.86141	+	4.55134i	0.283684	+	0.188175i
$586$	−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
$590$	−4.88316	−	8.45787i	−0.201036	−	0.348205i
$591$	−3.00000	+	9.94987i	−0.123404	+	0.409283i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−1.62772	+	2.81929i	−0.0668424	+	0.115774i	−0.897510	−	0.440995i	$-0.854626\pi$
$593$	−1.62772	+	2.81929i	−0.0668424	+	0.115774i	0.830667	+	0.556769i	$0.187959\pi$
$594$	3.81386	+	22.3966i	0.156485	+	0.918945i
$595$		0			0
$596$	−7.37228	−	12.7692i	−0.301980	−	0.523045i
$597$	16.8614	−	3.96143i	0.690091	−	0.162131i
$598$	14.7446			0.602950
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	3.69702	+	3.93398i	0.150930	+	0.160604i
$601$	−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
$605$	5.56930	−	9.64630i	0.226424	−	0.392178i
$606$	−8.74456	−	9.30506i	−0.355224	−	0.377992i
$607$	6.11684	+	10.5947i	0.248275	+	0.430025i	0.963047	−	0.269332i	$-0.0868030\pi$
$607$	6.11684	+	10.5947i	0.248275	+	0.430025i	−0.714772	+	0.699357i	$0.753470\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	9.68614	+	16.7769i	0.392180	+	0.679276i
$611$		0			0
$612$	0.813859	−	13.0916i	0.0328983	−	0.529195i
$613$	0.883156	+	1.52967i	0.0356703	+	0.0617828i	0.883309	−	0.468790i	$-0.155310\pi$
$613$	0.883156	+	1.52967i	0.0356703	+	0.0617828i	−0.847639	+	0.530573i	$0.821977\pi$
$614$	13.0000			0.524637
$615$	−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	$0.103059\pi$
$618$	−16.8614	+	3.96143i	−0.678265	+	0.159352i
$619$	11.7337	−	20.3233i	0.471617	−	0.816864i	−0.527856	−	0.849334i	$-0.677004\pi$
$619$	11.7337	−	20.3233i	0.471617	−	0.816864i	0.999473	+	0.0324697i	$0.0103373\pi$
$620$	1.37228	+	2.37686i	0.0551121	+	0.0954570i
$621$	−35.9198	−	13.3128i	−1.44141	−	0.534224i
$622$	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
$626$	2.88316			0.115234
$627$	−36.8614	+	8.66025i	−1.47210	+	0.345857i
$628$	−8.11684			−0.323897
$629$	−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	$0.407793\pi$
$632$	−12.1168			−0.481982
$633$	−18.9783	−	20.1947i	−0.754318	−	0.802667i
$634$	6.00000			0.238290
$635$	−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
$639$	−25.2921	−	16.7769i	−1.00054	−	0.663683i
$640$	−0.686141	−	1.18843i	−0.0271221	−	0.0469768i
$641$	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	$-0.199286\pi$
$642$	1.93070	+	2.05446i	0.0761988	+	0.0810829i
$643$	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
$646$	21.8614			0.860126
$647$	8.74456	+	15.1460i	0.343784	+	0.595452i	0.985132	−	0.171798i	$-0.0549578\pi$
$647$	8.74456	+	15.1460i	0.343784	+	0.595452i	−0.641348	+	0.767250i	$0.721624\pi$
$648$	−3.50000	−	8.29156i	−0.137493	−	0.325723i
$649$	−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
$653$	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	$0.736848\pi$
$654$	23.6060	−	5.54601i	0.923066	−	0.216866i
$655$	−5.05842	+	8.76144i	−0.197649	+	0.342338i
$656$	−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	$0.775636\pi$
$660$	−3.00000	+	9.94987i	−0.116775	+	0.387298i
$661$	9.88316			0.384410			0.192205	−	0.981355i	$-0.438436\pi$
$661$	9.88316			0.384410			0.192205	+	0.981355i	$0.438436\pi$
$662$	12.2337			0.475476
$663$	−4.37228	+	14.5012i	−0.169805	+	0.563181i
$664$	−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
$668$	−8.74456	+	15.1460i	−0.338337	+	0.586017i
$669$	6.74456	−	1.58457i	0.260760	−	0.0612632i
$670$	−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	0.992143	−	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
$675$	2.71876	+	15.9658i	0.104645	+	0.614523i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−34.4674			−1.32469			−0.662344	−	0.749199i	$-0.730438\pi$
$677$	−34.4674			−1.32469			−0.662344	+	0.749199i	$0.730438\pi$
$678$	−1.62772	−	1.73205i	−0.0625122	−	0.0665190i
$679$		0			0
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$	−28.1644	−	29.9696i	−1.07926	−	1.14844i
$682$	4.37228	−	7.57301i	0.167423	−	0.289986i
$683$	22.4198	+	38.8323i	0.857871	+	1.48588i	0.873956	+	0.486005i	$0.161546\pi$
$683$	22.4198	+	38.8323i	0.857871	+	1.48588i	−0.0160849	+	0.999871i	$0.505120\pi$
$684$	13.4307	−	6.67954i	0.513536	−	0.255398i
$685$	−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
$689$	5.48913			0.209119
$690$	−12.0000	−	12.7692i	−0.456832	−	0.486114i
$691$	−5.88316			−0.223806			−0.111903	−	0.993719i	$-0.535695\pi$
$691$	−5.88316			−0.223806			−0.111903	+	0.993719i	$0.535695\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−7.11684			−0.270152
$695$	29.1386			1.10529
$696$	4.62772	−	1.08724i	0.175413	−	0.0412118i
$697$	−45.3505			−1.71777
$698$	−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	$0.522659\pi$
$702$	1.74456	+	10.2448i	0.0658443	+	0.386666i
$703$	−5.00000	−	8.66025i	−0.188579	−	0.326628i
$704$	−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
$709$	44.0000			1.65245			0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000			1.65245			0.826227	+	0.563337i	$0.190483\pi$
$710$	−6.94158	−	12.0232i	−0.260513	−	0.451221i
$711$	−30.2921	−	20.0935i	−1.13604	−	0.753566i
$712$	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
$716$	−7.37228	−	12.7692i	−0.275515	−	0.477206i
$717$	−22.3723	−	23.8063i	−0.835508	−	0.889062i
$718$	−3.43070	+	5.94215i	−0.128033	+	0.221759i
$719$	4.37228	−	7.57301i	0.163059	−	0.282426i	−0.772906	−	0.634521i	$-0.781197\pi$
$719$	4.37228	−	7.57301i	0.163059	−	0.282426i	0.935964	+	0.352095i	$0.114531\pi$
$720$	0.255437	−	4.10891i	0.00951959	−	0.153130i
$721$		0			0
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	1.04755	+	1.11469i	0.0389587	+	0.0414558i
$724$	18.1168			0.673307
$725$	−8.55437			−0.317701
$726$	13.6861	−	3.21543i	0.507940	−	0.119336i
$727$	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
$731$	19.9307	−	34.5210i	0.737164	−	1.27680i
$732$	−7.05842	+	23.4101i	−0.260887	+	0.865264i
$733$	11.9416	+	20.6834i	0.441072	+	0.763960i	0.997769	−	0.0667560i	$-0.0212649\pi$
$733$	11.9416	+	20.6834i	0.441072	+	0.763960i	−0.556697	+	0.830716i	$0.687932\pi$
$734$	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
$738$	−27.8614	+	13.8564i	−1.02559	+	0.510061i
$739$	−4.55842	−	7.89542i	−0.167684	−	0.290438i	0.769921	−	0.638139i	$-0.220296\pi$
$739$	−4.55842	−	7.89542i	−0.167684	−	0.290438i	−0.937605	+	0.347702i	$0.886962\pi$
$740$	−2.74456			−0.100892
$741$	−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	$0.870427\pi$
$744$	−1.00000	+	3.31662i	−0.0366618	+	0.121593i
$745$	10.1168	−	17.5229i	0.370652	−	0.641989i
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$	1.02175	−	16.4356i	0.0373839	−	0.601349i
$748$	−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
$753$	−4.50000	+	14.9248i	−0.163989	+	0.543890i
$754$	−5.48913			−0.199902
$755$	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	$0.431407\pi$
$758$	−9.11684			−0.331139
$759$	−16.1168	+	53.4535i	−0.585004	+	1.94024i
$760$	6.86141			0.248889
$761$	−6.25544	−	10.8347i	−0.226759	−	0.392759i	0.730086	−	0.683355i	$-0.239480\pi$
$761$	−6.25544	−	10.8347i	−0.226759	−	0.392759i	−0.956846	+	0.290596i	$0.906146\pi$
$762$	7.05842	−	23.4101i	0.255700	−	0.848060i
$763$		0			0
$764$	−1.88316			−0.0681302
$765$	16.1168	−	8.01544i	0.582706	−	0.289799i
$766$	−10.6277	−	18.4077i	−0.383995	−	0.665099i
$767$	−7.11684	+	12.3267i	−0.256974	+	0.445093i
$768$	0.500000	−	1.65831i	0.0180422	−	0.0598392i
$769$	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
$772$	−7.00000			−0.251936
$773$	5.56930	+	9.64630i	0.200314	+	0.346953i	0.948629	−	0.316389i	$-0.102471\pi$
$773$	5.56930	+	9.64630i	0.200314	+	0.346953i	−0.748316	+	0.663343i	$0.769137\pi$
$774$	1.69702	−	27.2978i	0.0609980	−	0.981200i
$775$	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
$779$	−25.9307	−	44.9133i	−0.929064	−	1.60919i
$780$	−1.37228	+	4.55134i	−0.0491356	+	0.162964i
$781$	−22.1168	+	38.3075i	−0.791403	+	1.37075i
$782$	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
$786$	−12.4307	+	2.92048i	−0.443389	+	0.104170i
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−6.00000			−0.213741
$789$	15.8614	+	16.8781i	0.564681	+	0.600875i
$790$	−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
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	−4.46738	−	4.75372i	−0.158441	−	0.168597i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	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
$801$	8.74456	−	4.34896i	0.308974	−	0.153663i
$802$	−0.127719	−	0.221215i	−0.00450990	−	0.00781138i
$803$	−22.3723			−0.789501
$804$	7.55842	−	25.0684i	0.266565	−	0.884096i
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$	12.4307	−	2.92048i	0.437581	−	0.102806i
$808$	3.68614	−	6.38458i	0.129678	−	0.224609i
$809$	−10.9307	−	18.9325i	−0.384303	−	0.665632i	0.607369	−	0.794420i	$-0.292225\pi$
$809$	−10.9307	−	18.9325i	−0.384303	−	0.665632i	−0.991672	+	0.128787i	$0.958892\pi$
$810$	7.45245	−	9.84868i	0.261852	−	0.346048i
$811$	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
$814$	4.37228	+	7.57301i	0.153248	+	0.265434i
$815$	−22.2772			−0.780336
$816$	7.37228	−	1.73205i	0.258081	−	0.0606339i
$817$	45.5842			1.59479
$818$	−29.3505			−1.02622
$819$		0			0
$820$	−14.2337			−0.497062
$821$	−38.2337			−1.33436			−0.667182	−	0.744894i	$-0.732500\pi$
$821$	−38.2337			−1.33436			−0.667182	+	0.744894i	$0.732500\pi$
$822$	−19.4198	−	20.6646i	−0.677344	−	0.720760i
$823$	22.2337			0.775018			0.387509	−	0.921866i	$-0.373336\pi$
$823$	22.2337			0.775018			0.387509	+	0.921866i	$0.373336\pi$
$824$	−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	$0.433096\pi$
$828$	1.37228	−	22.0742i	0.0476901	−	0.767133i
$829$	24.1168	+	41.7716i	0.837613	+	1.45079i	0.891885	+	0.452261i	$0.149383\pi$
$829$	24.1168	+	41.7716i	0.837613	+	1.45079i	−0.0542728	+	0.998526i	$0.517284\pi$
$830$	3.76631	−	6.52344i	0.130731	−	0.226432i
$831$	26.3723	+	28.0627i	0.914844	+	0.973483i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$	25.1861	+	26.8005i	0.872125	+	0.928025i
$835$	−24.0000			−0.830554
$836$	−10.9307	−	18.9325i	−0.378046	−	0.654795i
$837$	−8.00000	+	6.63325i	−0.276520	+	0.229279i
$838$	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
$842$	−0.116844	−	0.202380i	−0.00402671	−	0.00697446i
$843$	−17.9198	+	4.21010i	−0.617192	+	0.145004i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−6.17527	+	10.6959i	−0.212436	+	0.367949i
$846$		0			0
$847$		0			0
$848$	−1.37228	−	2.37686i	−0.0471243	−	0.0816217i
$849$	4.94158	−	16.3894i	0.169595	−	0.562481i
$850$	−13.6277			−0.467427
$851$	−14.7446			−0.505437
$852$	5.05842	−	16.7769i	0.173299	−	0.574767i
$853$	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
$857$	−25.9783	+	44.9956i	−0.887400	+	1.53702i	−0.0444624	+	0.999011i	$0.514157\pi$
$857$	−25.9783	+	44.9956i	−0.887400	+	1.53702i	−0.842938	+	0.538011i	$0.819176\pi$
$858$	14.7446	−	3.46410i	0.503371	−	0.118262i
$859$	−25.5584	−	44.2685i	−0.872042	−	1.51042i	−0.859881	−	0.510495i	$-0.829462\pi$
$859$	−25.5584	−	44.2685i	−0.872042	−	1.51042i	−0.0121615	−	0.999926i	$-0.503871\pi$
$860$	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	−0.659675	−	0.751551i	$-0.729306\pi$
$863$	9.43070	−	16.3345i	0.321025	−	0.556031i	0.980700	+	0.195520i	$0.0626394\pi$
$864$	4.00000	−	3.31662i	0.136083	−	0.112834i
$865$	−4.11684	−	7.13058i	−0.139977	−	0.242447i
$866$	2.88316			0.0979736
$867$	2.51087	+	2.67181i	0.0852738	+	0.0907396i
$868$		0			0
$869$	−26.4891	+	45.8805i	−0.898582	+	1.55639i
$870$	4.46738	+	4.75372i	0.151458	+	0.161166i
$871$	−15.1168	+	26.1831i	−0.512215	+	0.887182i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−1.69702	+	27.2978i	−0.0574353	+	0.923892i
$874$	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	$-0.438896\pi$
$878$	−8.00000			−0.269987
$879$	−5.48913	−	5.84096i	−0.185144	−	0.197011i
$880$	−6.00000			−0.202260
$881$	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	$0.438831\pi$
$884$	−8.74456			−0.294111
$885$	16.4674	−	3.86886i	0.553545	−	0.130050i
$886$	22.8832			0.768775
$887$	15.8614	+	27.4728i	0.532574	+	0.922445i	0.999277	+	0.0380308i	$0.0121085\pi$
$887$	15.8614	+	27.4728i	0.532574	+	0.922445i	−0.466703	+	0.884414i	$0.654558\pi$
$888$	−2.37228	−	2.52434i	−0.0796085	−	0.0847112i
$889$		0			0
$890$	4.46738			0.149747
$891$	−39.0475	−	4.87375i	−1.30814	−	0.163277i
$892$	2.00000	+	3.46410i	0.0669650	+	0.115987i
$893$		0			0
$894$	24.8614	−	5.84096i	0.831490	−	0.195351i
$895$	10.1168	−	17.5229i	0.338169	−	0.585726i
$896$		0			0
$897$	−7.37228	+	24.4511i	−0.246153	+	0.816398i
$898$	−33.0000			−1.10122
$899$	−2.74456	−	4.75372i	−0.0915363	−	0.158546i
$900$	−8.37228	+	4.16381i	−0.279076	+	0.138794i
$901$	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
$905$	12.4307	+	21.5306i	0.413211	+	0.715702i
$906$	9.62772	+	10.2448i	0.319860	+	0.340362i
$907$	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	$0.119550\pi$
$908$	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	$0.578165\pi$
$912$	5.93070	+	6.31084i	0.196385	+	0.208973i
$913$	−24.0000			−0.794284
$914$	−33.4674			−1.10700
$915$	−32.6644	+	7.67420i	−1.07985	+	0.253701i
$916$	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	−0.507089	−	0.861894i	$-0.669279\pi$
$919$	14.9416	−	25.8796i	0.492877	−	0.853688i	0.999966	+	0.00820529i	$0.00261185\pi$
$920$	5.05842	−	8.76144i	0.166771	−	0.288856i
$921$	−6.50000	+	21.5581i	−0.214182	+	0.710362i
$922$	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
$926$	−2.94158	+	5.09496i	−0.0966663	+	0.167431i
$927$	1.86141	−	29.9422i	0.0611366	−	0.983431i
$928$	1.37228	+	2.37686i	0.0450473	+	0.0780243i
$929$	9.76631			0.320422			0.160211	−	0.987083i	$-0.448782\pi$
$929$	9.76631			0.320422			0.160211	+	0.987083i	$0.448782\pi$
$930$	−4.62772	+	1.08724i	−0.151749	+	0.0356520i
$931$		0			0
$932$	5.87228	−	10.1711i	0.192353	−	0.333165i
$933$	−13.1168	+	43.5036i	−0.429426	+	1.42425i
$934$	−15.0475	+	26.0631i	−0.492371	+	0.852811i
$935$	−13.1168	−	22.7190i	−0.428967	−	0.742992i
$936$	−5.37228	+	2.67181i	−0.175599	+	0.0873310i
$937$	−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
$941$	1.88316			0.0613891			0.0306946	−	0.999529i	$-0.490228\pi$
$941$	1.88316			0.0613891			0.0306946	+	0.999529i	$0.490228\pi$
$942$	4.05842	−	13.4603i	0.132231	−	0.438559i
$943$	−76.4674			−2.49012
$944$	7.11684			0.231634
$945$		0			0
$946$	−39.8614			−1.29601
$947$	16.8832			0.548629			0.274314	−	0.961640i	$-0.411549\pi$
$947$	16.8832			0.548629			0.274314	+	0.961640i	$0.411549\pi$
$948$	6.05842	−	20.0935i	0.196768	−	0.652607i
$949$	−10.2337			−0.332200
$950$	−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	$0.443597\pi$
$954$	0.510875	−	8.21782i	0.0165402	−	0.266062i
$955$	−1.29211	−	2.23800i	−0.0418117	−	0.0724200i
$956$	9.43070	−	16.3345i	0.305011	−	0.528294i
$957$	6.00000	−	19.8997i	0.193952	−	0.643268i
$958$	10.6277	−	18.4077i	0.343366	−	0.594727i
$959$		0			0
$960$	2.31386	−	0.543620i	0.0746795	−	0.0175453i
$961$	−27.0000			−0.870968
$962$	2.00000	+	3.46410i	0.0644826	+	0.111687i
$963$	−4.37228	+	2.17448i	−0.140895	+	0.0700717i
$964$	−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	$0.885087\pi$
$968$	4.05842	+	7.02939i	0.130443	+	0.225933i
$969$	−10.9307	+	36.2530i	−0.351145	+	1.16462i
$970$	−6.25544	+	10.8347i	−0.200850	+	0.347882i
$971$	−3.68614	+	6.38458i	−0.118294	+	0.204891i	−0.919092	−	0.394044i	$-0.871076\pi$
$971$	−3.68614	+	6.38458i	−0.118294	+	0.204891i	0.800798	+	0.598935i	$0.204409\pi$
$972$	15.5000	−	1.65831i	0.497163	−	0.0531904i
$973$		0			0
$974$	−8.17527	−	14.1600i	−0.261952	−	0.453715i
$975$	10.5109	−	2.46943i	0.336617	−	0.0790852i
$976$	−14.1168			−0.451869
$977$	22.8832			0.732097			0.366049	−	0.930596i	$-0.380710\pi$
$977$	22.8832			0.732097			0.366049	+	0.930596i	$0.380710\pi$
$978$	−19.2554	−	20.4897i	−0.615721	−	0.655187i
$979$	−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
$983$	25.3723	−	43.9461i	0.809250	−	1.40166i	−0.104134	−	0.994563i	$-0.533207\pi$
$983$	25.3723	−	43.9461i	0.809250	−	1.40166i	0.913384	−	0.407099i	$-0.133460\pi$
$984$	−12.3030	−	13.0916i	−0.392205	−	0.417344i
$985$	−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
$989$	33.6060	−	58.2072i	1.06861	−	1.85088i
$990$	−15.0000	−	9.94987i	−0.476731	−	0.316228i
$991$	10.2337	+	17.7253i	0.325084	+	0.563062i	0.981529	−	0.191312i	$-0.0612742\pi$
$991$	10.2337	+	17.7253i	0.325084	+	0.563062i	−0.656446	+	0.754373i	$0.727941\pi$
$992$	−2.00000			−0.0635001
$993$	−6.11684	+	20.2873i	−0.194112	+	0.643797i
$994$		0			0
$995$	−6.86141	+	11.8843i	−0.217521	+	0.376758i
$996$	9.25544	−	2.17448i	0.293270	−	0.0689011i
$997$	−6.05842	+	10.4935i	−0.191872	+	0.332332i	−0.945871	−	0.324544i	$-0.894789\pi$
$997$	−6.05842	+	10.4935i	−0.191872	+	0.332332i	0.753999	+	0.656876i	$0.228123\pi$
$998$	0.441578	+	0.764836i	0.0139779	+	0.0242104i
$999$	−1.74456	−	10.2448i	−0.0551955	−	0.324132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.l.373.1		4
3.2	odd	2		2646.2.e.n.1549.1		4
7.2	even	3		126.2.f.d.85.2	yes	4
7.3	odd	6		882.2.h.n.67.2		4
7.4	even	3		882.2.h.m.67.1		4
7.5	odd	6		882.2.f.k.589.1		4
7.6	odd	2		882.2.e.k.373.2		4
9.2	odd	6		2646.2.h.k.667.2		4
9.7	even	3		882.2.h.m.79.1		4
21.2	odd	6		378.2.f.c.253.1		4
21.5	even	6		2646.2.f.j.1765.2		4
21.11	odd	6		2646.2.h.k.361.2		4
21.17	even	6		2646.2.h.l.361.1		4
21.20	even	2		2646.2.e.m.1549.2		4
28.23	odd	6		1008.2.r.f.337.1		4
63.2	odd	6		378.2.f.c.127.1		4
63.5	even	6		7938.2.a.bs.1.1		2
63.11	odd	6		2646.2.e.n.2125.1		4
63.16	even	3		126.2.f.d.43.2	✓	4
63.20	even	6		2646.2.h.l.667.1		4
63.23	odd	6		1134.2.a.n.1.2		2
63.25	even	3	inner	882.2.e.l.655.2		4
63.34	odd	6		882.2.h.n.79.2		4
63.38	even	6		2646.2.e.m.2125.2		4
63.40	odd	6		7938.2.a.bh.1.2		2
63.47	even	6		2646.2.f.j.883.2		4
63.52	odd	6		882.2.e.k.655.1		4
63.58	even	3		1134.2.a.k.1.1		2
63.61	odd	6		882.2.f.k.295.1		4
84.23	even	6		3024.2.r.f.1009.1		4
252.23	even	6		9072.2.a.bb.1.2		2
252.79	odd	6		1008.2.r.f.673.1		4
252.191	even	6		3024.2.r.f.2017.1		4
252.247	odd	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	63.16	even	3
126.2.f.d.85.2	yes	4	7.2	even	3
378.2.f.c.127.1		4	63.2	odd	6
378.2.f.c.253.1		4	21.2	odd	6
882.2.e.k.373.2		4	7.6	odd	2
882.2.e.k.655.1		4	63.52	odd	6
882.2.e.l.373.1		4	1.1	even	1	trivial
882.2.e.l.655.2		4	63.25	even	3	inner
882.2.f.k.295.1		4	63.61	odd	6
882.2.f.k.589.1		4	7.5	odd	6
882.2.h.m.67.1		4	7.4	even	3
882.2.h.m.79.1		4	9.7	even	3
882.2.h.n.67.2		4	7.3	odd	6
882.2.h.n.79.2		4	63.34	odd	6
1008.2.r.f.337.1		4	28.23	odd	6
1008.2.r.f.673.1		4	252.79	odd	6
1134.2.a.k.1.1		2	63.58	even	3
1134.2.a.n.1.2		2	63.23	odd	6
2646.2.e.m.1549.2		4	21.20	even	2
2646.2.e.m.2125.2		4	63.38	even	6
2646.2.e.n.1549.1		4	3.2	odd	2
2646.2.e.n.2125.1		4	63.11	odd	6
2646.2.f.j.883.2		4	63.47	even	6
2646.2.f.j.1765.2		4	21.5	even	6
2646.2.h.k.361.2		4	21.11	odd	6
2646.2.h.k.667.2		4	9.2	odd	6
2646.2.h.l.361.1		4	21.17	even	6
2646.2.h.l.667.1		4	63.20	even	6
3024.2.r.f.1009.1		4	84.23	even	6
3024.2.r.f.2017.1		4	252.191	even	6
7938.2.a.bh.1.2		2	63.40	odd	6
7938.2.a.bs.1.1		2	63.5	even	6
9072.2.a.bb.1.2		2	252.23	even	6
9072.2.a.bm.1.1		2	252.247	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(0.686141 + 1.18843i) q^{5} +(-0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 - 1.65831i) q^{9} +(-0.686141 - 1.18843i) q^{10} +(-2.18614 + 3.78651i) q^{11} +(0.500000 - 1.65831i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(2.31386 - 0.543620i) q^{15} +1.00000 q^{16} +(2.18614 + 3.78651i) q^{17} +(2.50000 + 1.65831i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(3.68614 + 6.38458i) q^{23} +(-0.500000 + 1.65831i) q^{24} +(1.55842 - 2.69927i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 + 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(-2.31386 + 0.543620i) q^{30} +2.00000 q^{31} -1.00000 q^{32} +(5.18614 + 5.51856i) q^{33} +(-2.18614 - 3.78651i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(-0.686141 - 1.18843i) q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(-2.18614 + 3.78651i) q^{44} +(0.255437 - 4.10891i) q^{45} +(-3.68614 - 6.38458i) q^{46} +(0.500000 - 1.65831i) q^{48} +(-1.55842 + 2.69927i) q^{50} +(7.37228 - 1.73205i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.37228 - 2.37686i) q^{53} +(4.00000 - 3.31662i) q^{54} -6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(1.37228 + 2.37686i) q^{58} +7.11684 q^{59} +(2.31386 - 0.543620i) q^{60} -14.1168 q^{61} -2.00000 q^{62} +1.00000 q^{64} -2.74456 q^{65} +(-5.18614 - 5.51856i) q^{66} +15.1168 q^{67} +(2.18614 + 3.78651i) q^{68} +(12.4307 - 2.92048i) q^{69} +10.1168 q^{71} +(2.50000 + 1.65831i) q^{72} +(2.55842 + 4.43132i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-3.69702 - 3.93398i) q^{75} +(-2.50000 + 4.33013i) q^{76} +(-2.37228 - 2.52434i) q^{78} +12.1168 q^{79} +(0.686141 + 1.18843i) q^{80} +(3.50000 + 8.29156i) q^{81} +(5.18614 - 8.98266i) q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.55842 + 7.89542i) q^{86} +(-4.62772 + 1.08724i) q^{87} +(2.18614 - 3.78651i) q^{88} +(-1.62772 + 2.81929i) q^{89} +(-0.255437 + 4.10891i) q^{90} +(3.68614 + 6.38458i) q^{92} +(1.00000 - 3.31662i) q^{93} -6.86141 q^{95} +(-0.500000 + 1.65831i) q^{96} +(-4.55842 - 7.89542i) q^{97} +(11.7446 - 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 3 * q^5 - 2 * q^6 - 4 * q^8 - 10 * q^9	\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 3 q^{5} - 2 q^{6} - 4 q^{8} - 10 q^{9} + 3 q^{10} - 3 q^{11} + 2 q^{12} - 4 q^{13} + 15 q^{15} + 4 q^{16} + 3 q^{17} + 10 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{23} - 2 q^{24} - 11 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 15 q^{30} + 8 q^{31} - 4 q^{32} + 15 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} + 24 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} + 16 q^{54} - 24 q^{55} - 5 q^{57} - 6 q^{58} - 6 q^{59} + 15 q^{60} - 22 q^{61} - 8 q^{62} + 4 q^{64} + 12 q^{65} - 15 q^{66} + 26 q^{67} + 3 q^{68} + 21 q^{69} + 6 q^{71} + 10 q^{72} - 7 q^{73} + 4 q^{74} - 55 q^{75} - 10 q^{76} + 2 q^{78} + 14 q^{79} - 3 q^{80} + 14 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} + q^{86} - 30 q^{87} + 3 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} + 4 q^{93} + 30 q^{95} - 2 q^{96} - q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 + 4 * q^4 - 3 * q^5 - 2 * q^6 - 4 * q^8 - 10 * q^9 + 3 * q^10 - 3 * q^11 + 2 * q^12 - 4 * q^13 + 15 * q^15 + 4 * q^16 + 3 * q^17 + 10 * q^18 - 10 * q^19 - 3 * q^20 + 3 * q^22 + 9 * q^23 - 2 * q^24 - 11 * q^25 + 4 * q^26 - 16 * q^27 + 6 * q^29 - 15 * q^30 + 8 * q^31 - 4 * q^32 + 15 * q^33 - 3 * q^34 - 10 * q^36 - 4 * q^37 + 10 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 - q^43 - 3 * q^44 + 24 * q^45 - 9 * q^46 + 2 * q^48 + 11 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 + 16 * q^54 - 24 * q^55 - 5 * q^57 - 6 * q^58 - 6 * q^59 + 15 * q^60 - 22 * q^61 - 8 * q^62 + 4 * q^64 + 12 * q^65 - 15 * q^66 + 26 * q^67 + 3 * q^68 + 21 * q^69 + 6 * q^71 + 10 * q^72 - 7 * q^73 + 4 * q^74 - 55 * q^75 - 10 * q^76 + 2 * q^78 + 14 * q^79 - 3 * q^80 + 14 * q^81 + 15 * q^82 - 12 * q^83 - 12 * q^85 + q^86 - 30 * q^87 + 3 * q^88 - 18 * q^89 - 24 * q^90 + 9 * q^92 + 4 * q^93 + 30 * q^95 - 2 * q^96 - q^97 + 24 * q^99

Introduction

L-functions

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Database

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