LMFDB - Embedded newform 315.2.t.a.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.131
Dual form			315.2.t.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+1.73205i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 0.866025i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(1.50000 + 0.866025i) q^{12} +(6.00000 + 3.46410i) q^{13} +(3.00000 + 3.46410i) q^{14} -1.73205i q^{15} -5.00000 q^{16} +(3.00000 + 5.19615i) q^{17} +(-4.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{20} +(-4.50000 + 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{22} +(-4.50000 + 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.00000 + 10.3923i) q^{26} -5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{30} +3.46410i q^{31} -5.19615i q^{32} +(3.00000 + 5.19615i) q^{33} +(-9.00000 + 5.19615i) q^{34} +(2.50000 + 0.866025i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-6.00000 - 10.3923i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-1.50000 - 7.79423i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(3.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-4.50000 - 7.79423i) q^{46} +9.00000 q^{47} +(7.50000 + 4.33013i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-1.50000 - 0.866025i) q^{50} -10.3923i q^{51} +(-6.00000 - 3.46410i) q^{52} +(3.00000 - 1.73205i) q^{53} +9.00000 q^{54} -3.46410i q^{55} +(3.00000 + 3.46410i) q^{56} +1.73205i q^{60} -12.1244i q^{61} -6.00000 q^{62} +(7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +6.92820i q^{65} +(-9.00000 + 5.19615i) q^{66} +5.00000 q^{67} +(-3.00000 - 5.19615i) q^{68} +9.00000 q^{69} +(-1.50000 + 4.33013i) q^{70} +6.92820i q^{71} +(-4.50000 + 2.59808i) q^{72} +(-9.00000 + 5.19615i) q^{73} +(3.00000 + 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-9.00000 + 1.73205i) q^{77} +(18.0000 - 10.3923i) q^{78} -10.0000 q^{79} +(-2.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 + 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.50000 - 0.866025i) q^{84} +(-3.00000 + 5.19615i) q^{85} +(1.50000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(7.50000 - 12.9904i) q^{89} +(-4.50000 - 2.59808i) q^{90} +(18.0000 - 3.46410i) q^{91} +(4.50000 - 2.59808i) q^{92} +(3.00000 - 5.19615i) q^{93} +15.5885i q^{94} +(-4.50000 + 7.79423i) q^{96} +(6.00000 - 3.46410i) q^{97} +(12.0000 + 1.73205i) q^{98} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^6 + 4 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{9} - 3 q^{10} - 6 q^{11} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 10 q^{16} + 6 q^{17} - 9 q^{18} - q^{20} - 9 q^{21} + 6 q^{22} - 9 q^{23} + 3 q^{24} - q^{25} - 12 q^{26} - 4 q^{28} + 6 q^{30} + 6 q^{33} - 18 q^{34} + 5 q^{35} - 3 q^{36} + 2 q^{37} - 12 q^{39} - 3 q^{40} + 6 q^{41} - 3 q^{42} - q^{43} + 6 q^{44} - 3 q^{45} - 9 q^{46} + 18 q^{47} + 15 q^{48} + 2 q^{49} - 3 q^{50} - 12 q^{52} + 6 q^{53} + 18 q^{54} + 6 q^{56} - 12 q^{62} + 15 q^{63} - 2 q^{64} - 18 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 9 q^{72} - 18 q^{73} + 6 q^{74} + 3 q^{75} - 18 q^{77} + 36 q^{78} - 20 q^{79} - 5 q^{80} - 9 q^{81} + 18 q^{82} - 12 q^{83} + 9 q^{84} - 6 q^{85} + 3 q^{86} + 6 q^{88} + 15 q^{89} - 9 q^{90} + 36 q^{91} + 9 q^{92} + 6 q^{93} - 9 q^{96} + 12 q^{97} + 24 q^{98}+O(q^{100}) $ 2 * q - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^6 + 4 * q^7 + 3 * q^9 - 3 * q^10 - 6 * q^11 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 10 * q^16 + 6 * q^17 - 9 * q^18 - q^20 - 9 * q^21 + 6 * q^22 - 9 * q^23 + 3 * q^24 - q^25 - 12 * q^26 - 4 * q^28 + 6 * q^30 + 6 * q^33 - 18 * q^34 + 5 * q^35 - 3 * q^36 + 2 * q^37 - 12 * q^39 - 3 * q^40 + 6 * q^41 - 3 * q^42 - q^43 + 6 * q^44 - 3 * q^45 - 9 * q^46 + 18 * q^47 + 15 * q^48 + 2 * q^49 - 3 * q^50 - 12 * q^52 + 6 * q^53 + 18 * q^54 + 6 * q^56 - 12 * q^62 + 15 * q^63 - 2 * q^64 - 18 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 9 * q^72 - 18 * q^73 + 6 * q^74 + 3 * q^75 - 18 * q^77 + 36 * q^78 - 20 * q^79 - 5 * q^80 - 9 * q^81 + 18 * q^82 - 12 * q^83 + 9 * q^84 - 6 * q^85 + 3 * q^86 + 6 * q^88 + 15 * q^89 - 9 * q^90 + 36 * q^91 + 9 * q^92 + 6 * q^93 - 9 * q^96 + 12 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.73205i			1.22474i	0.790569	+	0.612372i	$0.209785\pi$
$2$			1.73205i			1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.50000	−	2.59808i	0.612372	−	1.06066i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$			1.73205i			0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.50000	+	0.866025i	−0.474342	+	0.273861i
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	6.00000	+	3.46410i	1.66410	+	0.960769i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	6.00000	+	3.46410i	1.66410	+	0.960769i	0.693375	+	0.720577i	$0.256123\pi$
$14$	3.00000	+	3.46410i	0.801784	+	0.925820i
$15$		−	1.73205i		−	0.447214i
$16$	−5.00000			−1.25000
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	−4.50000	+	2.59808i	−1.06066	+	0.612372i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−4.50000	+	0.866025i	−0.981981	+	0.188982i
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.889432	−	0.457068i	$-0.848900\pi$
$23$	−4.50000	+	2.59808i	−0.938315	+	0.541736i	−0.0488832	+	0.998805i	$0.515566\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.00000	+	10.3923i	−1.17670	+	2.03810i
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	3.00000			0.547723
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		−	5.19615i		−	0.918559i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	−9.00000	+	5.19615i	−1.54349	+	0.891133i
$35$	2.50000	+	0.866025i	0.422577	+	0.146385i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$		0			0
$39$	−6.00000	−	10.3923i	−0.960769	−	1.66410i
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$	−1.50000	−	7.79423i	−0.231455	−	1.20268i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	3.00000	+	1.73205i	0.452267	+	0.261116i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	−4.50000	−	7.79423i	−0.663489	−	1.14920i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	7.50000	+	4.33013i	1.08253	+	0.625000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−1.50000	−	0.866025i	−0.212132	−	0.122474i
$51$		−	10.3923i		−	1.45521i
$52$	−6.00000	−	3.46410i	−0.832050	−	0.480384i
$53$	3.00000	−	1.73205i	0.412082	−	0.237915i	−0.279602	−	0.960116i	$-0.590203\pi$
$53$	3.00000	−	1.73205i	0.412082	−	0.237915i	0.691684	+	0.722200i	$0.256869\pi$
$54$	9.00000			1.22474
$55$		−	3.46410i		−	0.467099i
$56$	3.00000	+	3.46410i	0.400892	+	0.462910i
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$			1.73205i			0.223607i
$61$		−	12.1244i		−	1.55236i	−0.630509	−	0.776182i	$-0.717154\pi$
$61$		−	12.1244i		−	1.55236i	0.630509	−	0.776182i	$-0.282846\pi$
$62$	−6.00000			−0.762001
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$	−1.00000			−0.125000
$65$			6.92820i			0.859338i
$66$	−9.00000	+	5.19615i	−1.10782	+	0.639602i
$67$	5.00000			0.610847			0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000			0.610847			0.305424	+	0.952217i	$0.401202\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	9.00000			1.08347
$70$	−1.50000	+	4.33013i	−0.179284	+	0.517549i
$71$			6.92820i			0.822226i	0.911584	+	0.411113i	$0.134860\pi$
$71$			6.92820i			0.822226i	−0.911584	+	0.411113i	$0.865140\pi$
$72$	−4.50000	+	2.59808i	−0.530330	+	0.306186i
$73$	−9.00000	+	5.19615i	−1.05337	+	0.608164i	−0.923591	−	0.383379i	$-0.874760\pi$
$73$	−9.00000	+	5.19615i	−1.05337	+	0.608164i	−0.129779	+	0.991543i	$0.541427\pi$
$74$	3.00000	+	1.73205i	0.348743	+	0.201347i
$75$	1.50000	−	0.866025i	0.173205	−	0.100000i
$76$		0			0
$77$	−9.00000	+	1.73205i	−1.02565	+	0.197386i
$78$	18.0000	−	10.3923i	2.03810	−	1.17670i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−2.50000	−	4.33013i	−0.279508	−	0.484123i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	9.00000	+	5.19615i	0.993884	+	0.573819i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$	4.50000	−	0.866025i	0.490990	−	0.0944911i
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	1.50000	−	0.866025i	0.161749	−	0.0933859i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$	−4.50000	−	2.59808i	−0.474342	−	0.273861i
$91$	18.0000	−	3.46410i	1.88691	−	0.363137i
$92$	4.50000	−	2.59808i	0.469157	−	0.270868i
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$			15.5885i			1.60783i
$95$		0			0
$96$	−4.50000	+	7.79423i	−0.459279	+	0.795495i
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	−0.163448	−	0.986552i	$-0.552261\pi$
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	0.772655	+	0.634826i	$0.218928\pi$
$98$	12.0000	+	1.73205i	1.21218	+	0.174964i
$99$		−	10.3923i		−	1.04447i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	18.0000			1.78227
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	−0.821705	−	0.569914i	$-0.806977\pi$
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	0.0827075	+	0.996574i	$0.473643\pi$
$104$	−6.00000	+	10.3923i	−0.588348	+	1.01905i
$105$	−3.00000	−	3.46410i	−0.292770	−	0.338062i
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	3.00000	+	1.73205i	0.290021	+	0.167444i	0.637951	−	0.770077i	$-0.279782\pi$
$107$	3.00000	+	1.73205i	0.290021	+	0.167444i	−0.347930	+	0.937520i	$0.613115\pi$
$108$			5.19615i			0.500000i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	6.00000			0.572078
$111$	−3.00000	+	1.73205i	−0.284747	+	0.164399i
$112$	−10.0000	+	8.66025i	−0.944911	+	0.818317i
$113$	−12.0000	−	6.92820i	−1.12887	−	0.651751i	−0.185216	−	0.982698i	$-0.559298\pi$
$113$	−12.0000	−	6.92820i	−1.12887	−	0.651751i	−0.943649	+	0.330947i	$0.892632\pi$
$114$		0			0
$115$	−4.50000	−	2.59808i	−0.419627	−	0.242272i
$116$		0			0
$117$			20.7846i			1.92154i
$118$		0			0
$119$	15.0000	+	5.19615i	1.37505	+	0.476331i
$120$	3.00000			0.273861
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	21.0000			1.90125
$123$	−9.00000	+	5.19615i	−0.811503	+	0.468521i
$124$		−	3.46410i		−	0.311086i
$125$	−1.00000			−0.0894427
$126$	−4.50000	+	12.9904i	−0.400892	+	1.15728i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$		−	12.1244i		−	1.07165i
$129$			1.73205i			0.152499i
$130$	−12.0000			−1.05247
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	−3.00000	−	5.19615i	−0.261116	−	0.452267i
$133$		0			0
$134$			8.66025i			0.748132i
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$	−9.00000	+	5.19615i	−0.771744	+	0.445566i
$137$	−15.0000	−	8.66025i	−1.28154	−	0.739895i	−0.304407	−	0.952542i	$-0.598458\pi$
$137$	−15.0000	−	8.66025i	−1.28154	−	0.739895i	−0.977129	+	0.212647i	$0.931792\pi$
$138$			15.5885i			1.32698i
$139$	3.00000	+	1.73205i	0.254457	+	0.146911i	0.621803	−	0.783174i	$-0.286400\pi$
$139$	3.00000	+	1.73205i	0.254457	+	0.146911i	−0.367347	+	0.930084i	$0.619734\pi$
$140$	−2.50000	−	0.866025i	−0.211289	−	0.0731925i
$141$	−13.5000	−	7.79423i	−1.13691	−	0.656392i
$142$	−12.0000			−1.00702
$143$	−12.0000	−	20.7846i	−1.00349	−	1.73810i
$144$	−7.50000	−	12.9904i	−0.625000	−	1.08253i
$145$		0			0
$146$	−9.00000	−	15.5885i	−0.744845	−	1.29011i
$147$	−7.50000	+	9.52628i	−0.618590	+	0.785714i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	1.50000	−	0.866025i	0.122885	−	0.0709476i	−0.437298	−	0.899317i	$-0.644064\pi$
$149$	1.50000	−	0.866025i	0.122885	−	0.0709476i	0.560182	+	0.828369i	$0.310731\pi$
$150$	1.50000	+	2.59808i	0.122474	+	0.212132i
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$		0			0
$153$	−9.00000	+	15.5885i	−0.727607	+	1.26025i
$154$	−3.00000	−	15.5885i	−0.241747	−	1.25615i
$155$	−3.00000	+	1.73205i	−0.240966	+	0.139122i
$156$	6.00000	+	10.3923i	0.480384	+	0.832050i
$157$			10.3923i			0.829396i	0.909959	+	0.414698i	$0.136113\pi$
$157$			10.3923i			0.829396i	−0.909959	+	0.414698i	$0.863887\pi$
$158$		−	17.3205i		−	1.37795i
$159$	−6.00000			−0.475831
$160$	4.50000	−	2.59808i	0.355756	−	0.205396i
$161$	−4.50000	+	12.9904i	−0.354650	+	1.02379i
$162$	−13.5000	−	7.79423i	−1.06066	−	0.612372i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	18.0000	−	10.3923i	1.39707	−	0.806599i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	−1.50000	−	7.79423i	−0.115728	−	0.601338i
$169$	17.5000	+	30.3109i	1.34615	+	2.33161i
$170$	−9.00000	−	5.19615i	−0.690268	−	0.398527i
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	15.0000	+	8.66025i	1.13067	+	0.652791i
$177$		0			0
$178$	22.5000	+	12.9904i	1.68645	+	0.973670i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$			20.7846i			1.54491i	0.635071	+	0.772454i	$0.280971\pi$
$181$			20.7846i			1.54491i	−0.635071	+	0.772454i	$0.719029\pi$
$182$	6.00000	+	31.1769i	0.444750	+	2.31099i
$183$	−10.5000	+	18.1865i	−0.776182	+	1.34439i
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$	2.00000			0.147043
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$		−	20.7846i		−	1.51992i
$188$	−9.00000			−0.656392
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$		0			0
$191$			6.92820i			0.501307i	0.968077	+	0.250654i	$0.0806455\pi$
$191$			6.92820i			0.501307i	−0.968077	+	0.250654i	$0.919354\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	16.0000			1.15171			0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000			1.15171			0.575853	+	0.817554i	$0.304670\pi$
$194$	6.00000	+	10.3923i	0.430775	+	0.746124i
$195$	6.00000	−	10.3923i	0.429669	−	0.744208i
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			3.46410i			0.246807i	0.992357	+	0.123404i	$0.0393809\pi$
$197$			3.46410i			0.246807i	−0.992357	+	0.123404i	$0.960619\pi$
$198$	18.0000			1.27920
$199$	15.0000	−	8.66025i	1.06332	−	0.613909i	0.136973	−	0.990575i	$-0.456263\pi$
$199$	15.0000	−	8.66025i	1.06332	−	0.613909i	0.926349	+	0.376666i	$0.122929\pi$
$200$	−1.50000	−	0.866025i	−0.106066	−	0.0612372i
$201$	−7.50000	−	4.33013i	−0.529009	−	0.305424i
$202$	−4.50000	−	2.59808i	−0.316619	−	0.182800i
$203$		0			0
$204$			10.3923i			0.727607i
$205$	6.00000			0.419058
$206$	−7.50000	−	12.9904i	−0.522550	−	0.905083i
$207$	−13.5000	−	7.79423i	−0.938315	−	0.541736i
$208$	−30.0000	−	17.3205i	−2.08013	−	1.20096i
$209$		0			0
$210$	6.00000	−	5.19615i	0.414039	−	0.358569i
$211$	7.00000	−	12.1244i	0.481900	−	0.834675i	−0.517884	−	0.855451i	$-0.673280\pi$
$211$	7.00000	−	12.1244i	0.481900	−	0.834675i	0.999784	+	0.0207756i	$0.00661356\pi$
$212$	−3.00000	+	1.73205i	−0.206041	+	0.118958i
$213$	6.00000	−	10.3923i	0.411113	−	0.712069i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$	9.00000			0.612372
$217$	6.00000	+	6.92820i	0.407307	+	0.470317i
$218$	15.0000	−	8.66025i	1.01593	−	0.586546i
$219$	18.0000			1.21633
$220$			3.46410i			0.233550i
$221$			41.5692i			2.79625i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	−22.5000	+	12.9904i	−1.50671	+	0.869900i	−0.506742	+	0.862098i	$0.669150\pi$
$223$	−22.5000	+	12.9904i	−1.50671	+	0.869900i	−0.999970	+	0.00780243i	$0.997516\pi$
$224$	−9.00000	−	10.3923i	−0.601338	−	0.694365i
$225$	−3.00000			−0.200000
$226$	12.0000	−	20.7846i	0.798228	−	1.38257i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	7.50000	−	4.33013i	0.495614	−	0.286143i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	7.50000	−	4.33013i	0.495614	−	0.286143i	0.726900	+	0.686743i	$0.240960\pi$
$230$	4.50000	−	7.79423i	0.296721	−	0.513936i
$231$	15.0000	+	5.19615i	0.986928	+	0.341882i
$232$		0			0
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$	−36.0000			−2.35339
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$		0			0
$237$	15.0000	+	8.66025i	0.974355	+	0.562544i
$238$	−9.00000	+	25.9808i	−0.583383	+	1.68408i
$239$	6.00000	+	3.46410i	0.388108	+	0.224074i	0.681340	−	0.731967i	$-0.261398\pi$
$239$	6.00000	+	3.46410i	0.388108	+	0.224074i	−0.293232	+	0.956041i	$0.594731\pi$
$240$			8.66025i			0.559017i
$241$	−16.5000	−	9.52628i	−1.06286	−	0.613642i	−0.136637	−	0.990621i	$-0.543629\pi$
$241$	−16.5000	−	9.52628i	−1.06286	−	0.613642i	−0.926222	+	0.376980i	$0.876963\pi$
$242$	−1.50000	+	0.866025i	−0.0964237	+	0.0556702i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			12.1244i			0.776182i
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$	−9.00000	−	15.5885i	−0.573819	−	0.993884i
$247$		0			0
$248$	−6.00000			−0.381000
$249$			20.7846i			1.31717i
$250$		−	1.73205i		−	0.109545i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−7.50000	−	2.59808i	−0.472456	−	0.163663i
$253$	18.0000			1.13165
$254$			19.0526i			1.19546i
$255$	9.00000	−	5.19615i	0.563602	−	0.325396i
$256$	19.0000			1.18750
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−3.00000			−0.186772
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$		−	6.92820i		−	0.429669i
$261$		0			0
$262$	27.0000	−	15.5885i	1.66807	−	0.963058i
$263$	1.50000	+	0.866025i	0.0924940	+	0.0534014i	0.545534	−	0.838089i	$-0.316327\pi$
$263$	1.50000	+	0.866025i	0.0924940	+	0.0534014i	−0.453040	+	0.891490i	$0.649660\pi$
$264$	−9.00000	+	5.19615i	−0.553912	+	0.319801i
$265$	3.00000	+	1.73205i	0.184289	+	0.106399i
$266$		0			0
$267$	−22.5000	+	12.9904i	−1.37698	+	0.794998i
$268$	−5.00000			−0.305424
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	4.50000	+	7.79423i	0.273861	+	0.474342i
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	0.818037	−	0.575165i	$-0.195062\pi$
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	−0.0890891	+	0.996024i	$0.528396\pi$
$272$	−15.0000	−	25.9808i	−0.909509	−	1.57532i
$273$	−30.0000	−	10.3923i	−1.81568	−	0.628971i
$274$	15.0000	−	25.9808i	0.906183	−	1.56956i
$275$	3.00000	−	1.73205i	0.180907	−	0.104447i
$276$	−9.00000			−0.541736
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−3.00000	+	5.19615i	−0.179928	+	0.311645i
$279$	−9.00000	+	5.19615i	−0.538816	+	0.311086i
$280$	−1.50000	+	4.33013i	−0.0896421	+	0.258775i
$281$	−7.50000	+	4.33013i	−0.447412	+	0.258314i	−0.706737	−	0.707477i	$-0.749833\pi$
$281$	−7.50000	+	4.33013i	−0.447412	+	0.258314i	0.259324	+	0.965790i	$0.416500\pi$
$282$	13.5000	−	23.3827i	0.803913	−	1.39242i
$283$			12.1244i			0.720718i	0.932814	+	0.360359i	$0.117346\pi$
$283$			12.1244i			0.720718i	−0.932814	+	0.360359i	$0.882654\pi$
$284$		−	6.92820i		−	0.411113i
$285$		0			0
$286$	36.0000	−	20.7846i	2.12872	−	1.22902i
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$	13.5000	−	7.79423i	0.795495	−	0.459279i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−12.0000			−0.703452
$292$	9.00000	−	5.19615i	0.526685	−	0.304082i
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	−0.473763	−	0.880652i	$-0.657105\pi$
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	0.999549	−	0.0300351i	$-0.00956192\pi$
$294$	−16.5000	−	12.9904i	−0.962300	−	0.757614i
$295$		0			0
$296$	3.00000	+	1.73205i	0.174371	+	0.100673i
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$	1.50000	+	2.59808i	0.0868927	+	0.150503i
$299$	−36.0000			−2.08193
$300$	−1.50000	+	0.866025i	−0.0866025	+	0.0500000i
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$	−15.0000	−	8.66025i	−0.863153	−	0.498342i
$303$	4.50000	−	2.59808i	0.258518	−	0.149256i
$304$		0			0
$305$	10.5000	−	6.06218i	0.601228	−	0.347119i
$306$	−27.0000	−	15.5885i	−1.54349	−	0.891133i
$307$			3.46410i			0.197707i	0.995102	+	0.0988534i	$0.0315175\pi$
$307$			3.46410i			0.197707i	−0.995102	+	0.0988534i	$0.968483\pi$
$308$	9.00000	−	1.73205i	0.512823	−	0.0986928i
$309$	15.0000			0.853320
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	18.0000	−	10.3923i	1.01905	−	0.588348i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−18.0000			−1.01580
$315$	1.50000	+	7.79423i	0.0845154	+	0.439155i
$316$	10.0000			0.562544
$317$		−	20.7846i		−	1.16738i	−0.811977	−	0.583690i	$-0.801608\pi$
$317$		−	20.7846i		−	1.16738i	0.811977	−	0.583690i	$-0.198392\pi$
$318$		−	10.3923i		−	0.582772i
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	−22.5000	−	7.79423i	−1.25388	−	0.434355i
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−6.00000	+	3.46410i	−0.332820	+	0.192154i
$326$	24.0000	+	13.8564i	1.32924	+	0.767435i
$327$			17.3205i			0.957826i
$328$	9.00000	+	5.19615i	0.496942	+	0.286910i
$329$	18.0000	−	15.5885i	0.992372	−	0.859419i
$330$	−9.00000	−	5.19615i	−0.495434	−	0.286039i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	6.00000			0.328798
$334$	−13.5000	−	7.79423i	−0.738687	−	0.426481i
$335$	2.50000	+	4.33013i	0.136590	+	0.236580i
$336$	22.5000	−	4.33013i	1.22748	−	0.236228i
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	0.178863	+	0.983874i	$0.442758\pi$
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	−0.941491	+	0.337037i	$0.890575\pi$
$338$	−52.5000	+	30.3109i	−2.85562	+	1.64870i
$339$	12.0000	+	20.7846i	0.651751	+	1.12887i
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	1.50000	−	0.866025i	0.0808746	−	0.0466930i
$345$	4.50000	+	7.79423i	0.242272	+	0.419627i
$346$		−	10.3923i		−	0.558694i
$347$			22.5167i			1.20876i	0.796697	+	0.604379i	$0.206579\pi$
$347$			22.5167i			1.20876i	−0.796697	+	0.604379i	$0.793421\pi$
$348$		0			0
$349$	7.50000	−	4.33013i	0.401466	−	0.231786i	−0.285650	−	0.958334i	$-0.592210\pi$
$349$	7.50000	−	4.33013i	0.401466	−	0.231786i	0.687116	+	0.726547i	$0.258876\pi$
$350$	−4.50000	+	0.866025i	−0.240535	+	0.0462910i
$351$	18.0000	−	31.1769i	0.960769	−	1.66410i
$352$	−9.00000	+	15.5885i	−0.479702	+	0.830868i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	−6.00000	+	3.46410i	−0.318447	+	0.183855i
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$	−18.0000	−	20.7846i	−0.952661	−	1.10004i
$358$		0			0
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$	−4.50000	−	2.59808i	−0.237171	−	0.136931i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	−36.0000			−1.89212
$363$		−	1.73205i		−	0.0909091i
$364$	−18.0000	+	3.46410i	−0.943456	+	0.181568i
$365$	−9.00000	−	5.19615i	−0.471082	−	0.271979i
$366$	−31.5000	−	18.1865i	−1.64653	−	0.950625i
$367$	22.5000	+	12.9904i	1.17449	+	0.678092i	0.954734	−	0.297462i	$-0.0961403\pi$
$367$	22.5000	+	12.9904i	1.17449	+	0.678092i	0.219757	+	0.975555i	$0.429474\pi$
$368$	22.5000	−	12.9904i	1.17289	−	0.677170i
$369$	18.0000			0.937043
$370$			3.46410i			0.180090i
$371$	3.00000	−	8.66025i	0.155752	−	0.449618i
$372$	−3.00000	+	5.19615i	−0.155543	+	0.269408i
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	36.0000			1.86152
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$			15.5885i			0.803913i
$377$		0			0
$378$	18.0000	−	15.5885i	0.925820	−	0.801784i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	−16.5000	−	9.52628i	−0.845321	−	0.488046i
$382$	−12.0000			−0.613973
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	0.957790	−	0.287469i	$-0.0928139\pi$
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	−0.727851	+	0.685736i	$0.759481\pi$
$384$	−10.5000	+	18.1865i	−0.535826	+	0.928078i
$385$	−6.00000	−	6.92820i	−0.305788	−	0.353094i
$386$			27.7128i			1.41055i
$387$	1.50000	−	2.59808i	0.0762493	−	0.132068i
$388$	−6.00000	+	3.46410i	−0.304604	+	0.175863i
$389$	−31.5000	−	18.1865i	−1.59711	−	0.922094i	−0.992040	−	0.125924i	$-0.959810\pi$
$389$	−31.5000	−	18.1865i	−1.59711	−	0.922094i	−0.605074	−	0.796170i	$-0.706856\pi$
$390$	18.0000	+	10.3923i	0.911465	+	0.526235i
$391$	−27.0000	−	15.5885i	−1.36545	−	0.788342i
$392$	12.0000	+	1.73205i	0.606092	+	0.0874818i
$393$			31.1769i			1.57267i
$394$	−6.00000			−0.302276
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$			10.3923i			0.522233i
$397$	21.0000	+	12.1244i	1.05396	+	0.608504i	0.923755	−	0.382983i	$-0.125103\pi$
$397$	21.0000	+	12.1244i	1.05396	+	0.608504i	0.130204	+	0.991487i	$0.458437\pi$
$398$	15.0000	+	25.9808i	0.751882	+	1.30230i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	25.5000	−	14.7224i	1.27341	−	0.735203i	0.297781	−	0.954634i	$-0.403753\pi$
$401$	25.5000	−	14.7224i	1.27341	−	0.735203i	0.975628	+	0.219431i	$0.0704201\pi$
$402$	7.50000	−	12.9904i	0.374066	−	0.647901i
$403$	−12.0000	+	20.7846i	−0.597763	+	1.03536i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$	−9.00000			−0.447214
$406$		0			0
$407$	−6.00000	+	3.46410i	−0.297409	+	0.171709i
$408$	18.0000			0.891133
$409$			1.73205i			0.0856444i	0.999083	+	0.0428222i	$0.0136349\pi$
$409$			1.73205i			0.0856444i	−0.999083	+	0.0428222i	$0.986365\pi$
$410$			10.3923i			0.513239i
$411$	15.0000	+	25.9808i	0.739895	+	1.28154i
$412$	7.50000	−	4.33013i	0.369498	−	0.213330i
$413$		0			0
$414$	13.5000	−	23.3827i	0.663489	−	1.14920i
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	18.0000	−	31.1769i	0.882523	−	1.52857i
$417$	−3.00000	−	5.19615i	−0.146911	−	0.254457i
$418$		0			0
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$420$	3.00000	+	3.46410i	0.146385	+	0.169031i
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	0.700306	−	0.713843i	$-0.253047\pi$
$421$	−5.50000	−	9.52628i	−0.268054	−	0.464282i	−0.968359	+	0.249561i	$0.919714\pi$
$422$	21.0000	+	12.1244i	1.02226	+	0.590204i
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−6.00000			−0.291043
$426$	18.0000	+	10.3923i	0.872103	+	0.503509i
$427$	−21.0000	−	24.2487i	−1.01626	−	1.17348i
$428$	−3.00000	−	1.73205i	−0.145010	−	0.0837218i
$429$			41.5692i			2.00698i
$430$	1.50000	+	0.866025i	0.0723364	+	0.0417635i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$			25.9808i			1.25000i
$433$			27.7128i			1.33179i	0.746044	+	0.665896i	$0.231951\pi$
$433$			27.7128i			1.33179i	−0.746044	+	0.665896i	$0.768049\pi$
$434$	−12.0000	+	10.3923i	−0.576018	+	0.498847i
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$		0			0
$438$			31.1769i			1.48969i
$439$		−	10.3923i		−	0.495998i	−0.968760	−	0.247999i	$-0.920227\pi$
$439$		−	10.3923i		−	0.495998i	0.968760	−	0.247999i	$-0.0797729\pi$
$440$	6.00000			0.286039
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$	−72.0000			−3.42469
$443$			31.1769i			1.48126i	0.671913	+	0.740630i	$0.265473\pi$
$443$			31.1769i			1.48126i	−0.671913	+	0.740630i	$0.734527\pi$
$444$	3.00000	−	1.73205i	0.142374	−	0.0821995i
$445$	15.0000			0.711068
$446$	−22.5000	−	38.9711i	−1.06541	−	1.84534i
$447$	−3.00000			−0.141895
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$		−	19.0526i		−	0.899146i	−0.893244	−	0.449573i	$-0.851576\pi$
$449$		−	19.0526i		−	0.899146i	0.893244	−	0.449573i	$-0.148424\pi$
$450$		−	5.19615i		−	0.244949i
$451$	−18.0000	+	10.3923i	−0.847587	+	0.489355i
$452$	12.0000	+	6.92820i	0.564433	+	0.325875i
$453$	15.0000	−	8.66025i	0.704761	−	0.406894i
$454$	18.0000	+	10.3923i	0.844782	+	0.487735i
$455$	12.0000	+	13.8564i	0.562569	+	0.649598i
$456$		0			0
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$	7.50000	+	12.9904i	0.350452	+	0.607001i
$459$	27.0000	−	15.5885i	1.26025	−	0.727607i
$460$	4.50000	+	2.59808i	0.209814	+	0.121136i
$461$	1.50000	+	2.59808i	0.0698620	+	0.121004i	0.898840	−	0.438276i	$-0.144411\pi$
$461$	1.50000	+	2.59808i	0.0698620	+	0.121004i	−0.828978	+	0.559281i	$0.811077\pi$
$462$	−9.00000	+	25.9808i	−0.418718	+	1.20873i
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$		0			0
$465$	6.00000			0.278243
$466$		0			0
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	0.829231	+	0.558906i	$0.188779\pi$
$468$		−	20.7846i		−	0.960769i
$469$	10.0000	−	8.66025i	0.461757	−	0.399893i
$470$	−13.5000	+	7.79423i	−0.622709	+	0.359521i
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$		0			0
$473$			3.46410i			0.159280i
$474$	−15.0000	+	25.9808i	−0.688973	+	1.19334i
$475$		0			0
$476$	−15.0000	−	5.19615i	−0.687524	−	0.238165i
$477$	9.00000	+	5.19615i	0.412082	+	0.237915i
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$	−9.00000			−0.410792
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	16.5000	−	28.5788i	0.751554	−	1.30173i
$483$	18.0000	−	15.5885i	0.819028	−	0.709299i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	6.00000	+	3.46410i	0.272446	+	0.157297i
$486$	13.5000	+	23.3827i	0.612372	+	1.06066i
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	0.817147	−	0.576429i	$-0.195554\pi$
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	−0.907776	+	0.419456i	$0.862221\pi$
$488$	21.0000			0.950625
$489$	−24.0000	+	13.8564i	−1.08532	+	0.626608i
$490$	4.50000	+	11.2583i	0.203289	+	0.508600i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$	9.00000	−	5.19615i	0.405751	−	0.234261i
$493$		0			0
$494$		0			0
$495$	9.00000	−	5.19615i	0.404520	−	0.233550i
$496$		−	17.3205i		−	0.777714i
$497$	12.0000	+	13.8564i	0.538274	+	0.621545i
$498$	−36.0000			−1.61320
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	1.00000			0.0447214
$501$	13.5000	−	7.79423i	0.603136	−	0.348220i
$502$			41.5692i			1.85533i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	−4.50000	+	12.9904i	−0.200446	+	0.578638i
$505$	−3.00000			−0.133498
$506$			31.1769i			1.38598i
$507$		−	60.6218i		−	2.69231i
$508$	−11.0000			−0.488046
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$	−9.00000	+	25.9808i	−0.398137	+	1.14932i
$512$			8.66025i			0.382733i
$513$		0			0
$514$	−9.00000	+	5.19615i	−0.396973	+	0.229192i
$515$	−7.50000	−	4.33013i	−0.330489	−	0.190808i
$516$		−	1.73205i		−	0.0762493i
$517$	−27.0000	−	15.5885i	−1.18746	−	0.685580i
$518$	9.00000	−	1.73205i	0.395437	−	0.0761019i
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$	−12.0000			−0.526235
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	0.750454	−	0.660922i	$-0.229835\pi$
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	−0.947603	+	0.319451i	$0.896501\pi$
$522$		0			0
$523$	−25.5000	−	14.7224i	−1.11504	−	0.643767i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−25.5000	−	14.7224i	−1.11504	−	0.643767i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	9.00000	+	15.5885i	0.393167	+	0.680985i
$525$	1.50000	−	4.33013i	0.0654654	−	0.188982i
$526$	−1.50000	+	2.59808i	−0.0654031	+	0.113282i
$527$	−18.0000	+	10.3923i	−0.784092	+	0.452696i
$528$	−15.0000	−	25.9808i	−0.652791	−	1.13067i
$529$	2.00000	−	3.46410i	0.0869565	−	0.150613i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$		0			0
$532$		0			0
$533$	36.0000	−	20.7846i	1.55933	−	0.900281i
$534$	−22.5000	−	38.9711i	−0.973670	−	1.68645i
$535$			3.46410i			0.149766i
$536$			8.66025i			0.374066i
$537$		0			0
$538$	22.5000	−	12.9904i	0.970044	−	0.560055i
$539$	−15.0000	+	19.0526i	−0.646096	+	0.820652i
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	−20.5000	+	35.5070i	−0.881364	+	1.52657i	−0.0315385	+	0.999503i	$0.510041\pi$
$541$	−20.5000	+	35.5070i	−0.881364	+	1.52657i	−0.849825	+	0.527064i	$0.823293\pi$
$542$	−12.0000	+	20.7846i	−0.515444	+	0.892775i
$543$	18.0000	−	31.1769i	0.772454	−	1.33793i
$544$	27.0000	−	15.5885i	1.15762	−	0.668350i
$545$	5.00000	−	8.66025i	0.214176	−	0.370965i
$546$	18.0000	−	51.9615i	0.770329	−	2.22375i
$547$	−22.0000	−	38.1051i	−0.940652	−	1.62926i	−0.764231	−	0.644942i	$-0.776881\pi$
$547$	−22.0000	−	38.1051i	−0.940652	−	1.62926i	−0.176421	−	0.984315i	$-0.556452\pi$
$548$	15.0000	+	8.66025i	0.640768	+	0.369948i
$549$	31.5000	−	18.1865i	1.34439	−	0.776182i
$550$	3.00000	+	5.19615i	0.127920	+	0.221565i
$551$		0			0
$552$			15.5885i			0.663489i
$553$	−20.0000	+	17.3205i	−0.850487	+	0.736543i
$554$	15.0000	+	8.66025i	0.637289	+	0.367939i
$555$	−3.00000	−	1.73205i	−0.127343	−	0.0735215i
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	−24.0000	+	13.8564i	−1.01691	+	0.587115i	−0.913208	−	0.407493i	$-0.866403\pi$
$557$	−24.0000	+	13.8564i	−1.01691	+	0.587115i	−0.103704	+	0.994608i	$0.533070\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$		−	6.92820i		−	0.293032i
$560$	−12.5000	−	4.33013i	−0.528221	−	0.182981i
$561$	−18.0000	+	31.1769i	−0.759961	+	1.31629i
$562$	−7.50000	−	12.9904i	−0.316368	−	0.547966i
$563$	9.00000			0.379305			0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000			0.379305			0.189652	+	0.981851i	$0.439264\pi$
$564$	13.5000	+	7.79423i	0.568453	+	0.328196i
$565$		−	13.8564i		−	0.582943i
$566$	−21.0000			−0.882696
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$	−12.0000			−0.503509
$569$		−	6.92820i		−	0.290445i	−0.989399	−	0.145223i	$-0.953610\pi$
$569$		−	6.92820i		−	0.290445i	0.989399	−	0.145223i	$-0.0463899\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	12.0000	+	20.7846i	0.501745	+	0.869048i
$573$	6.00000	−	10.3923i	0.250654	−	0.434145i
$574$	27.0000	−	5.19615i	1.12696	−	0.216883i
$575$		−	5.19615i		−	0.216695i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	24.0000	−	13.8564i	0.999133	−	0.576850i	0.0911414	−	0.995838i	$-0.470948\pi$
$577$	24.0000	−	13.8564i	0.999133	−	0.576850i	0.907992	+	0.418988i	$0.137615\pi$
$578$	−28.5000	−	16.4545i	−1.18544	−	0.684416i
$579$	−24.0000	−	13.8564i	−0.997406	−	0.575853i
$580$		0			0
$581$	−30.0000	−	10.3923i	−1.24461	−	0.431145i
$582$		−	20.7846i		−	0.861550i
$583$	−12.0000			−0.496989
$584$	−9.00000	−	15.5885i	−0.372423	−	0.645055i
$585$	−18.0000	+	10.3923i	−0.744208	+	0.429669i
$586$	27.0000	+	15.5885i	1.11536	+	0.643953i
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$	7.50000	−	9.52628i	0.309295	−	0.392857i
$589$		0			0
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	−24.0000	+	41.5692i	−0.985562	+	1.70704i	−0.346149	+	0.938179i	$0.612511\pi$
$593$	−24.0000	+	41.5692i	−0.985562	+	1.70704i	−0.639413	+	0.768864i	$0.720822\pi$
$594$	−27.0000	−	15.5885i	−1.10782	−	0.639602i
$595$	3.00000	+	15.5885i	0.122988	+	0.639064i
$596$	−1.50000	+	0.866025i	−0.0614424	+	0.0354738i
$597$	−30.0000			−1.22782
$598$		−	62.3538i		−	2.54984i
$599$		−	24.2487i		−	0.990775i	−0.868672	−	0.495388i	$-0.835026\pi$
$599$		−	24.2487i		−	0.990775i	0.868672	−	0.495388i	$-0.164974\pi$
$600$	1.50000	+	2.59808i	0.0612372	+	0.106066i
$601$	−6.00000	+	3.46410i	−0.244745	+	0.141304i	−0.617356	−	0.786684i	$-0.711796\pi$
$601$	−6.00000	+	3.46410i	−0.244745	+	0.141304i	0.372611	+	0.927988i	$0.378463\pi$
$602$	1.50000	−	4.33013i	0.0611354	−	0.176483i
$603$	7.50000	+	12.9904i	0.305424	+	0.529009i
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	4.50000	+	7.79423i	0.182800	+	0.316619i
$607$	9.00000	−	5.19615i	0.365299	−	0.210905i	−0.306104	−	0.951998i	$-0.599025\pi$
$607$	9.00000	−	5.19615i	0.365299	−	0.210905i	0.671403	+	0.741093i	$0.265692\pi$
$608$		0			0
$609$		0			0
$610$	10.5000	+	18.1865i	0.425133	+	0.736351i
$611$	54.0000	+	31.1769i	2.18461	+	1.26128i
$612$	9.00000	−	15.5885i	0.363803	−	0.630126i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−6.00000			−0.242140
$615$	−9.00000	−	5.19615i	−0.362915	−	0.209529i
$616$	−3.00000	−	15.5885i	−0.120873	−	0.628077i
$617$	−9.00000	−	5.19615i	−0.362326	−	0.209189i	0.307774	−	0.951459i	$-0.400416\pi$
$617$	−9.00000	−	5.19615i	−0.362326	−	0.209189i	−0.670101	+	0.742270i	$0.733749\pi$
$618$			25.9808i			1.04510i
$619$	−12.0000	−	6.92820i	−0.482321	−	0.278468i	0.239062	−	0.971004i	$-0.423160\pi$
$619$	−12.0000	−	6.92820i	−0.482321	−	0.278468i	−0.721383	+	0.692536i	$0.756493\pi$
$620$	3.00000	−	1.73205i	0.120483	−	0.0695608i
$621$	13.5000	+	23.3827i	0.541736	+	0.938315i
$622$			20.7846i			0.833387i
$623$	−7.50000	−	38.9711i	−0.300481	−	1.56135i
$624$	30.0000	+	51.9615i	1.20096	+	2.08013i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		−	10.3923i		−	0.414698i
$629$	12.0000			0.478471
$630$	−13.5000	+	2.59808i	−0.537853	+	0.103510i
$631$	−10.0000			−0.398094			−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000			−0.398094			−0.199047	+	0.979990i	$0.563785\pi$
$632$		−	17.3205i		−	0.688973i
$633$	−21.0000	+	12.1244i	−0.834675	+	0.481900i
$634$	36.0000			1.42974
$635$	5.50000	+	9.52628i	0.218261	+	0.378039i
$636$	6.00000			0.237915
$637$	30.0000	−	38.1051i	1.18864	−	1.50978i
$638$		0			0
$639$	−18.0000	+	10.3923i	−0.712069	+	0.411113i
$640$	10.5000	−	6.06218i	0.415049	−	0.239629i
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	0.278093	−	0.960554i	$-0.410298\pi$
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	−0.692818	+	0.721113i	$0.743631\pi$
$642$	9.00000	−	5.19615i	0.355202	−	0.205076i
$643$	−37.5000	−	21.6506i	−1.47886	−	0.853818i	−0.479142	−	0.877738i	$-0.659052\pi$
$643$	−37.5000	−	21.6506i	−1.47886	−	0.853818i	−0.999714	+	0.0239198i	$0.992385\pi$
$644$	4.50000	−	12.9904i	0.177325	−	0.511893i
$645$	−1.50000	+	0.866025i	−0.0590624	+	0.0340997i
$646$		0			0
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$	−13.5000	−	7.79423i	−0.530330	−	0.306186i
$649$		0			0
$650$	−6.00000	−	10.3923i	−0.235339	−	0.407620i
$651$	−3.00000	−	15.5885i	−0.117579	−	0.610960i
$652$	−8.00000	+	13.8564i	−0.313304	+	0.542659i
$653$	−30.0000	+	17.3205i	−1.17399	+	0.677804i	−0.954617	−	0.297837i	$-0.903735\pi$
$653$	−30.0000	+	17.3205i	−1.17399	+	0.677804i	−0.219374	+	0.975641i	$0.570401\pi$
$654$	−30.0000			−1.17309
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$	−15.0000	+	25.9808i	−0.585652	+	1.01438i
$657$	−27.0000	−	15.5885i	−1.05337	−	0.608164i
$658$	27.0000	+	31.1769i	1.05257	+	1.21540i
$659$	15.0000	−	8.66025i	0.584317	−	0.337356i	−0.178530	−	0.983934i	$-0.557134\pi$
$659$	15.0000	−	8.66025i	0.584317	−	0.337356i	0.762847	+	0.646579i	$0.223801\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$			25.9808i			1.01053i	0.862963	+	0.505267i	$0.168606\pi$
$661$			25.9808i			1.01053i	−0.862963	+	0.505267i	$0.831394\pi$
$662$		−	13.8564i		−	0.538545i
$663$	36.0000	−	62.3538i	1.39812	−	2.42162i
$664$	18.0000	−	10.3923i	0.698535	−	0.403300i
$665$		0			0
$666$			10.3923i			0.402694i
$667$		0			0
$668$	4.50000	−	7.79423i	0.174110	−	0.301568i
$669$	45.0000			1.73980
$670$	−7.50000	+	4.33013i	−0.289750	+	0.167287i
$671$	−21.0000	+	36.3731i	−0.810696	+	1.40417i
$672$	4.50000	+	23.3827i	0.173591	+	0.902007i
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	0.991835	−	0.127532i	$-0.0407054\pi$
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	−0.606363	+	0.795188i	$0.707372\pi$
$674$	−42.0000	−	24.2487i	−1.61778	−	0.934025i
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	−17.5000	−	30.3109i	−0.673077	−	1.16580i
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$	−36.0000	+	20.7846i	−1.38257	+	0.798228i
$679$	6.00000	−	17.3205i	0.230259	−	0.664700i
$680$	−9.00000	−	5.19615i	−0.345134	−	0.199263i
$681$	−18.0000	+	10.3923i	−0.689761	+	0.398234i
$682$	18.0000	+	10.3923i	0.689256	+	0.397942i
$683$	1.50000	−	0.866025i	0.0573959	−	0.0331375i	−0.471027	−	0.882119i	$-0.656117\pi$
$683$	1.50000	−	0.866025i	0.0573959	−	0.0331375i	0.528423	+	0.848981i	$0.322783\pi$
$684$		0			0
$685$		−	17.3205i		−	0.661783i
$686$	27.0000	−	17.3205i	1.03086	−	0.661300i
$687$	−15.0000			−0.572286
$688$	2.50000	+	4.33013i	0.0953116	+	0.165085i
$689$	24.0000			0.914327
$690$	−13.5000	+	7.79423i	−0.513936	+	0.296721i
$691$		−	13.8564i		−	0.527123i	−0.964643	−	0.263561i	$-0.915103\pi$
$691$		−	13.8564i		−	0.527123i	0.964643	−	0.263561i	$-0.0848971\pi$
$692$	6.00000			0.228086
$693$	−18.0000	−	20.7846i	−0.683763	−	0.789542i
$694$	−39.0000			−1.48042
$695$			3.46410i			0.131401i
$696$		0			0
$697$	36.0000			1.36360
$698$	7.50000	+	12.9904i	0.283879	+	0.491693i
$699$		0			0
$700$	−0.500000	−	2.59808i	−0.0188982	−	0.0981981i
$701$		−	13.8564i		−	0.523349i	−0.965156	−	0.261675i	$-0.915725\pi$
$701$		−	13.8564i		−	0.523349i	0.965156	−	0.261675i	$-0.0842747\pi$
$702$	54.0000	+	31.1769i	2.03810	+	1.17670i
$703$		0			0
$704$	3.00000	+	1.73205i	0.113067	+	0.0652791i
$705$		−	15.5885i		−	0.587095i
$706$	−9.00000	−	5.19615i	−0.338719	−	0.195560i
$707$	1.50000	+	7.79423i	0.0564133	+	0.293132i
$708$		0			0
$709$	−17.0000			−0.638448			−0.319224	−	0.947679i	$-0.603422\pi$
$709$	−17.0000			−0.638448			−0.319224	+	0.947679i	$0.603422\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	−15.0000	−	25.9808i	−0.562544	−	0.974355i
$712$	22.5000	+	12.9904i	0.843223	+	0.486835i
$713$	−9.00000	−	15.5885i	−0.337053	−	0.583792i
$714$	36.0000	−	31.1769i	1.34727	−	1.16677i
$715$	12.0000	−	20.7846i	0.448775	−	0.777300i
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$	7.50000	−	12.9904i	0.279508	−	0.484123i
$721$	−7.50000	+	21.6506i	−0.279315	+	0.806312i
$722$	28.5000	−	16.4545i	1.06066	−	0.612372i
$723$	16.5000	+	28.5788i	0.613642	+	1.06286i
$724$		−	20.7846i		−	0.772454i
$725$		0			0
$726$	3.00000			0.111340
$727$	19.5000	−	11.2583i	0.723215	−	0.417548i	−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	19.5000	−	11.2583i	0.723215	−	0.417548i	0.815935	+	0.578144i	$0.196223\pi$
$728$	6.00000	+	31.1769i	0.222375	+	1.15549i
$729$	−27.0000			−1.00000
$730$	9.00000	−	15.5885i	0.333105	−	0.576955i
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$	10.5000	−	18.1865i	0.388091	−	0.672194i
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	−0.385083	−	0.922882i	$-0.625827\pi$
$733$	6.00000	−	3.46410i	0.221615	−	0.127950i	0.606698	+	0.794933i	$0.292494\pi$
$734$	−22.5000	+	38.9711i	−0.830490	+	1.43845i
$735$	−12.0000	−	1.73205i	−0.442627	−	0.0638877i
$736$	13.5000	+	23.3827i	0.497617	+	0.861897i
$737$	−15.0000	−	8.66025i	−0.552532	−	0.319005i
$738$			31.1769i			1.14764i
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	0.988472	+	0.151403i	$0.0483792\pi$
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	−0.363117	+	0.931744i	$0.618287\pi$
$740$	−2.00000			−0.0735215
$741$		0			0
$742$	15.0000	+	5.19615i	0.550667	+	0.190757i
$743$	−15.0000	−	8.66025i	−0.550297	−	0.317714i	0.198945	−	0.980011i	$-0.436248\pi$
$743$	−15.0000	−	8.66025i	−0.550297	−	0.317714i	−0.749242	+	0.662297i	$0.769582\pi$
$744$	9.00000	+	5.19615i	0.329956	+	0.190500i
$745$	1.50000	+	0.866025i	0.0549557	+	0.0317287i
$746$	39.0000	−	22.5167i	1.42789	−	0.824394i
$747$	18.0000	−	31.1769i	0.658586	−	1.14070i
$748$			20.7846i			0.759961i
$749$	9.00000	−	1.73205i	0.328853	−	0.0632878i
$750$	−1.50000	+	2.59808i	−0.0547723	+	0.0948683i
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	−45.0000			−1.64098
$753$	−36.0000	−	20.7846i	−1.31191	−	0.757433i
$754$		0			0
$755$	−10.0000			−0.363937
$756$	9.00000	+	10.3923i	0.327327	+	0.377964i
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$		−	34.6410i		−	1.25822i
$759$	−27.0000	−	15.5885i	−0.980038	−	0.565825i
$760$		0			0
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$	16.5000	−	28.5788i	0.597732	−	1.03530i
$763$	−25.0000	−	8.66025i	−0.905061	−	0.313522i
$764$		−	6.92820i		−	0.250654i
$765$	−18.0000			−0.650791
$766$	−13.5000	+	7.79423i	−0.487775	+	0.281617i
$767$		0			0
$768$	−28.5000	−	16.4545i	−1.02841	−	0.593750i
$769$	22.5000	+	12.9904i	0.811371	+	0.468445i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	22.5000	+	12.9904i	0.811371	+	0.468445i	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	12.0000	−	10.3923i	0.432450	−	0.374513i
$771$		−	10.3923i		−	0.374270i
$772$	−16.0000			−0.575853
$773$	6.00000	+	10.3923i	0.215805	+	0.373785i	0.953521	−	0.301326i	$-0.0974291\pi$
$773$	6.00000	+	10.3923i	0.215805	+	0.373785i	−0.737716	+	0.675111i	$0.764096\pi$
$774$	4.50000	+	2.59808i	0.161749	+	0.0933859i
$775$	−3.00000	−	1.73205i	−0.107763	−	0.0622171i
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$	−3.00000	+	8.66025i	−0.107624	+	0.310685i
$778$	31.5000	−	54.5596i	1.12933	−	1.95606i
$779$		0			0
$780$	−6.00000	+	10.3923i	−0.214834	+	0.372104i
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$	27.0000	−	46.7654i	0.965518	−	1.67233i
$783$		0			0
$784$	−5.00000	+	34.6410i	−0.178571	+	1.23718i
$785$	−9.00000	+	5.19615i	−0.321224	+	0.185459i
$786$	−54.0000			−1.92612
$787$			1.73205i			0.0617409i	0.999523	+	0.0308705i	$0.00982794\pi$
$787$			1.73205i			0.0617409i	−0.999523	+	0.0308705i	$0.990172\pi$
$788$		−	3.46410i		−	0.123404i
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$	15.0000	−	8.66025i	0.533676	−	0.308118i
$791$	−36.0000	+	6.92820i	−1.28001	+	0.246339i
$792$	18.0000			0.639602
$793$	42.0000	−	72.7461i	1.49146	−	2.58329i
$794$	−21.0000	+	36.3731i	−0.745262	+	1.29083i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	−15.0000	+	8.66025i	−0.531661	+	0.306955i
$797$	18.0000	−	31.1769i	0.637593	−	1.10434i	−0.348367	−	0.937358i	$-0.613264\pi$
$797$	18.0000	−	31.1769i	0.637593	−	1.10434i	0.985959	−	0.166985i	$-0.0534030\pi$
$798$		0			0
$799$	27.0000	+	46.7654i	0.955191	+	1.65444i
$800$	4.50000	+	2.59808i	0.159099	+	0.0918559i
$801$	45.0000			1.59000
$802$	25.5000	+	44.1673i	0.900436	+	1.55960i
$803$	36.0000			1.27041
$804$	7.50000	+	4.33013i	0.264505	+	0.152712i
$805$	−13.5000	+	2.59808i	−0.475812	+	0.0915702i
$806$	−36.0000	−	20.7846i	−1.26805	−	0.732107i
$807$			25.9808i			0.914566i
$808$	−4.50000	−	2.59808i	−0.158309	−	0.0914000i
$809$	−16.5000	+	9.52628i	−0.580109	+	0.334926i	−0.761177	−	0.648544i	$-0.775378\pi$
$809$	−16.5000	+	9.52628i	−0.580109	+	0.334926i	0.181068	+	0.983471i	$0.442045\pi$
$810$		−	15.5885i		−	0.547723i
$811$		−	20.7846i		−	0.729846i	−0.931038	−	0.364923i	$-0.881095\pi$
$811$		−	20.7846i		−	0.729846i	0.931038	−	0.364923i	$-0.118905\pi$
$812$		0			0
$813$	−12.0000	−	20.7846i	−0.420858	−	0.728948i
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	16.0000			0.560456
$816$			51.9615i			1.81902i
$817$		0			0
$818$	−3.00000			−0.104893
$819$	36.0000	+	41.5692i	1.25794	+	1.45255i
$820$	−6.00000			−0.209529
$821$		−	12.1244i		−	0.423143i	−0.977363	−	0.211571i	$-0.932142\pi$
$821$		−	12.1244i		−	0.423143i	0.977363	−	0.211571i	$-0.0678581\pi$
$822$	−45.0000	+	25.9808i	−1.56956	+	0.906183i
$823$	56.0000			1.95204			0.976019	−	0.217687i	$-0.0698512\pi$
$823$	56.0000			1.95204			0.976019	+	0.217687i	$0.0698512\pi$
$824$	−7.50000	−	12.9904i	−0.261275	−	0.452541i
$825$	−6.00000			−0.208893
$826$		0			0
$827$		−	17.3205i		−	0.602293i	−0.953578	−	0.301147i	$-0.902631\pi$
$827$		−	17.3205i		−	0.602293i	0.953578	−	0.301147i	$-0.0973693\pi$
$828$	13.5000	+	7.79423i	0.469157	+	0.270868i
$829$	4.50000	−	2.59808i	0.156291	−	0.0902349i	−0.419815	−	0.907610i	$-0.637905\pi$
$829$	4.50000	−	2.59808i	0.156291	−	0.0902349i	0.576106	+	0.817375i	$0.304572\pi$
$830$	18.0000	+	10.3923i	0.624789	+	0.360722i
$831$	−15.0000	+	8.66025i	−0.520344	+	0.300421i
$832$	−6.00000	−	3.46410i	−0.208013	−	0.120096i
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$	9.00000	−	5.19615i	0.311645	−	0.179928i
$835$	−9.00000			−0.311458
$836$		0			0
$837$	18.0000			0.622171
$838$	9.00000	+	5.19615i	0.310900	+	0.179498i
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	0.950813	−	0.309764i	$-0.100250\pi$
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	−0.743670	+	0.668546i	$0.766917\pi$
$840$	6.00000	−	5.19615i	0.207020	−	0.179284i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	16.5000	−	9.52628i	0.568628	−	0.328297i
$843$	15.0000			0.516627
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	−17.5000	+	30.3109i	−0.602018	+	1.04273i
$846$	−40.5000	+	23.3827i	−1.39242	+	0.803913i
$847$	2.50000	+	0.866025i	0.0859010	+	0.0297570i
$848$	−15.0000	+	8.66025i	−0.515102	+	0.297394i
$849$	10.5000	−	18.1865i	0.360359	−	0.624160i
$850$		−	10.3923i		−	0.356453i
$851$			10.3923i			0.356244i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	45.0000	−	25.9808i	1.54077	−	0.889564i	0.541980	−	0.840391i	$-0.317675\pi$
$853$	45.0000	−	25.9808i	1.54077	−	0.889564i	0.998790	−	0.0491732i	$-0.0156586\pi$
$854$	42.0000	−	36.3731i	1.43721	−	1.24466i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$	−72.0000			−2.45804
$859$	−48.0000	+	27.7128i	−1.63774	+	0.945549i	−0.656130	+	0.754648i	$0.727808\pi$
$859$	−48.0000	+	27.7128i	−1.63774	+	0.945549i	−0.981609	+	0.190901i	$0.938859\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	−9.00000	+	25.9808i	−0.306719	+	0.885422i
$862$		0			0
$863$	−7.50000	−	4.33013i	−0.255303	−	0.147399i	0.366887	−	0.930265i	$-0.380424\pi$
$863$	−7.50000	−	4.33013i	−0.255303	−	0.147399i	−0.622190	+	0.782866i	$0.713757\pi$
$864$	−27.0000			−0.918559
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	−48.0000			−1.63111
$867$	28.5000	−	16.4545i	0.967911	−	0.558824i
$868$	−6.00000	−	6.92820i	−0.203653	−	0.235159i
$869$	30.0000	+	17.3205i	1.01768	+	0.587558i
$870$		0			0
$871$	30.0000	+	17.3205i	1.01651	+	0.586883i
$872$	15.0000	−	8.66025i	0.507964	−	0.293273i
$873$	18.0000	+	10.3923i	0.609208	+	0.351726i
$874$		0			0
$875$	−2.00000	+	1.73205i	−0.0676123	+	0.0585540i
$876$	−18.0000			−0.608164
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	0.976366	+	0.216124i	$0.0693416\pi$
$877$	20.0000	+	34.6410i	0.675352	+	1.16974i	−0.301014	+	0.953620i	$0.597325\pi$
$878$	18.0000			0.607471
$879$	−27.0000	+	15.5885i	−0.910687	+	0.525786i
$880$			17.3205i			0.583874i
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$	13.5000	+	33.7750i	0.454569	+	1.13726i
$883$	−23.0000			−0.774012			−0.387006	−	0.922077i	$-0.626491\pi$
$883$	−23.0000			−0.774012			−0.387006	+	0.922077i	$0.626491\pi$
$884$		−	41.5692i		−	1.39812i
$885$		0			0
$886$	−54.0000			−1.81417
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	−0.981957	−	0.189102i	$-0.939442\pi$
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	0.327212	−	0.944951i	$-0.393891\pi$
$888$	−3.00000	−	5.19615i	−0.100673	−	0.174371i
$889$	22.0000	−	19.0526i	0.737856	−	0.639002i
$890$			25.9808i			0.870877i
$891$	27.0000	−	15.5885i	0.904534	−	0.522233i
$892$	22.5000	−	12.9904i	0.753356	−	0.434950i
$893$		0			0
$894$		−	5.19615i		−	0.173785i
$895$		0			0
$896$	−21.0000	−	24.2487i	−0.701561	−	0.810093i
$897$	54.0000	+	31.1769i	1.80301	+	1.04097i
$898$	33.0000			1.10122
$899$		0			0
$900$	3.00000			0.100000
$901$	18.0000	+	10.3923i	0.599667	+	0.346218i
$902$	−18.0000	−	31.1769i	−0.599334	−	1.03808i
$903$	3.00000	+	3.46410i	0.0998337	+	0.115278i
$904$	12.0000	−	20.7846i	0.399114	−	0.691286i
$905$	−18.0000	+	10.3923i	−0.598340	+	0.345452i
$906$	15.0000	+	25.9808i	0.498342	+	0.863153i
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	−9.00000			−0.298511
$910$	−24.0000	+	20.7846i	−0.795592	+	0.689003i
$911$	27.0000	−	15.5885i	0.894550	−	0.516469i	0.0191219	−	0.999817i	$-0.493913\pi$
$911$	27.0000	−	15.5885i	0.894550	−	0.516469i	0.875428	+	0.483349i	$0.160580\pi$
$912$		0			0
$913$			41.5692i			1.37574i
$914$			17.3205i			0.572911i
$915$	−21.0000			−0.694239
$916$	−7.50000	+	4.33013i	−0.247807	+	0.143071i
$917$	−45.0000	−	15.5885i	−1.48603	−	0.514776i
$918$	27.0000	+	46.7654i	0.891133	+	1.54349i
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	−0.361447	−	0.932393i	$-0.617717\pi$
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	0.988199	−	0.153174i	$-0.0489495\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	3.00000	−	5.19615i	0.0988534	−	0.171219i
$922$	−4.50000	+	2.59808i	−0.148200	+	0.0855631i
$923$	−24.0000	+	41.5692i	−0.789970	+	1.36827i
$924$	−15.0000	−	5.19615i	−0.493464	−	0.170941i
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	−25.5000	−	14.7224i	−0.837982	−	0.483809i
$927$	−22.5000	−	12.9904i	−0.738997	−	0.426660i
$928$		0			0
$929$	15.0000			0.492134			0.246067	−	0.969253i	$-0.420862\pi$
$929$	15.0000			0.492134			0.246067	+	0.969253i	$0.420862\pi$
$930$			10.3923i			0.340777i
$931$		0			0
$932$		0			0
$933$	−18.0000	−	10.3923i	−0.589294	−	0.340229i
$934$	−4.50000	−	2.59808i	−0.147244	−	0.0850117i
$935$	18.0000	−	10.3923i	0.588663	−	0.339865i
$936$	−36.0000			−1.17670
$937$		−	45.0333i		−	1.47117i	−0.677430	−	0.735587i	$-0.736906\pi$
$937$		−	45.0333i		−	1.47117i	0.677430	−	0.735587i	$-0.263094\pi$
$938$	15.0000	+	17.3205i	0.489767	+	0.565535i
$939$		0			0
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	−27.0000			−0.880175			−0.440087	−	0.897955i	$-0.645053\pi$
$941$	−27.0000			−0.880175			−0.440087	+	0.897955i	$0.645053\pi$
$942$	27.0000	+	15.5885i	0.879708	+	0.507899i
$943$			31.1769i			1.01526i
$944$		0			0
$945$	4.50000	−	12.9904i	0.146385	−	0.422577i
$946$	−6.00000			−0.195077
$947$			36.3731i			1.18197i	0.806684	+	0.590983i	$0.201260\pi$
$947$			36.3731i			1.18197i	−0.806684	+	0.590983i	$0.798740\pi$
$948$	−15.0000	−	8.66025i	−0.487177	−	0.281272i
$949$	−72.0000			−2.33722
$950$		0			0
$951$	−18.0000	+	31.1769i	−0.583690	+	1.01098i
$952$	−9.00000	+	25.9808i	−0.291692	+	0.842041i
$953$			31.1769i			1.00992i	0.863143	+	0.504960i	$0.168493\pi$
$953$			31.1769i			1.00992i	−0.863143	+	0.504960i	$0.831507\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$	−6.00000	+	3.46410i	−0.194155	+	0.112096i
$956$	−6.00000	−	3.46410i	−0.194054	−	0.112037i
$957$		0			0
$958$	−27.0000	−	15.5885i	−0.872330	−	0.503640i
$959$	−45.0000	+	8.66025i	−1.45313	+	0.279654i
$960$			1.73205i			0.0559017i
$961$	19.0000			0.612903
$962$	12.0000	+	20.7846i	0.386896	+	0.670123i
$963$			10.3923i			0.334887i
$964$	16.5000	+	9.52628i	0.531429	+	0.306821i
$965$	8.00000	+	13.8564i	0.257529	+	0.446054i
$966$	27.0000	+	31.1769i	0.868711	+	1.00310i
$967$	3.50000	−	6.06218i	0.112552	−	0.194946i	−0.804246	−	0.594296i	$-0.797431\pi$
$967$	3.50000	−	6.06218i	0.112552	−	0.194946i	0.916799	+	0.399350i	$0.130764\pi$
$968$	−1.50000	+	0.866025i	−0.0482118	+	0.0278351i
$969$		0			0
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	−0.167258	−	0.985913i	$-0.553491\pi$
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	0.937455	−	0.348107i	$-0.113175\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	9.00000	−	1.73205i	0.288527	−	0.0555270i
$974$	6.00000	−	3.46410i	0.192252	−	0.110997i
$975$	12.0000			0.384308
$976$			60.6218i			1.94046i
$977$			62.3538i			1.99488i	0.0715382	+	0.997438i	$0.477209\pi$
$977$			62.3538i			1.99488i	−0.0715382	+	0.997438i	$0.522791\pi$
$978$	−24.0000	−	41.5692i	−0.767435	−	1.32924i
$979$	−45.0000	+	25.9808i	−1.43821	+	0.830349i
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$	15.0000	−	25.9808i	0.478913	−	0.829502i
$982$		0			0
$983$	−24.0000	+	41.5692i	−0.765481	+	1.32585i	0.174511	+	0.984655i	$0.444166\pi$
$983$	−24.0000	+	41.5692i	−0.765481	+	1.32585i	−0.939992	+	0.341197i	$0.889168\pi$
$984$	−9.00000	−	15.5885i	−0.286910	−	0.496942i
$985$	−3.00000	+	1.73205i	−0.0955879	+	0.0551877i
$986$		0			0
$987$	−40.5000	+	7.79423i	−1.28913	+	0.248093i
$988$		0			0
$989$	4.50000	+	2.59808i	0.143092	+	0.0826140i
$990$	9.00000	+	15.5885i	0.286039	+	0.495434i
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	−0.901216	−	0.433370i	$-0.857324\pi$
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	0.0752991	−	0.997161i	$-0.476009\pi$
$992$	18.0000			0.571501
$993$	12.0000	+	6.92820i	0.380808	+	0.219860i
$994$	−24.0000	+	20.7846i	−0.761234	+	0.659248i
$995$	15.0000	+	8.66025i	0.475532	+	0.274549i
$996$		−	20.7846i		−	0.658586i
$997$	−6.00000	−	3.46410i	−0.190022	−	0.109709i	0.401971	−	0.915652i	$-0.368325\pi$
$997$	−6.00000	−	3.46410i	−0.190022	−	0.109709i	−0.591993	+	0.805943i	$0.701659\pi$
$998$	−30.0000	+	17.3205i	−0.949633	+	0.548271i
$999$	−9.00000	−	5.19615i	−0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.a.131.1	yes	2
3.2	odd	2		945.2.t.a.341.1		2
7.3	odd	6		315.2.be.a.311.1	yes	2
9.2	odd	6		315.2.be.a.236.1	yes	2
9.7	even	3		945.2.be.a.656.1		2
21.17	even	6		945.2.be.a.206.1		2
63.38	even	6	inner	315.2.t.a.101.1	✓	2
63.52	odd	6		945.2.t.a.521.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.a.101.1	✓	2	63.38	even	6	inner
315.2.t.a.131.1	yes	2	1.1	even	1	trivial
315.2.be.a.236.1	yes	2	9.2	odd	6
315.2.be.a.311.1	yes	2	7.3	odd	6
945.2.t.a.341.1		2	3.2	odd	2
945.2.t.a.521.1		2	63.52	odd	6
945.2.be.a.206.1		2	21.17	even	6
945.2.be.a.656.1		2	9.7	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+1.73205i q^{2} +(-1.50000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 0.866025i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(1.50000 + 0.866025i) q^{12} +(6.00000 + 3.46410i) q^{13} +(3.00000 + 3.46410i) q^{14} -1.73205i q^{15} -5.00000 q^{16} +(3.00000 + 5.19615i) q^{17} +(-4.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{20} +(-4.50000 + 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{22} +(-4.50000 + 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.00000 + 10.3923i) q^{26} -5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +3.00000 q^{30} +3.46410i q^{31} -5.19615i q^{32} +(3.00000 + 5.19615i) q^{33} +(-9.00000 + 5.19615i) q^{34} +(2.50000 + 0.866025i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-6.00000 - 10.3923i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-1.50000 - 7.79423i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(3.00000 + 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-4.50000 - 7.79423i) q^{46} +9.00000 q^{47} +(7.50000 + 4.33013i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-1.50000 - 0.866025i) q^{50} -10.3923i q^{51} +(-6.00000 - 3.46410i) q^{52} +(3.00000 - 1.73205i) q^{53} +9.00000 q^{54} -3.46410i q^{55} +(3.00000 + 3.46410i) q^{56} +1.73205i q^{60} -12.1244i q^{61} -6.00000 q^{62} +(7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +6.92820i q^{65} +(-9.00000 + 5.19615i) q^{66} +5.00000 q^{67} +(-3.00000 - 5.19615i) q^{68} +9.00000 q^{69} +(-1.50000 + 4.33013i) q^{70} +6.92820i q^{71} +(-4.50000 + 2.59808i) q^{72} +(-9.00000 + 5.19615i) q^{73} +(3.00000 + 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} +(-9.00000 + 1.73205i) q^{77} +(18.0000 - 10.3923i) q^{78} -10.0000 q^{79} +(-2.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 + 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.50000 - 0.866025i) q^{84} +(-3.00000 + 5.19615i) q^{85} +(1.50000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(7.50000 - 12.9904i) q^{89} +(-4.50000 - 2.59808i) q^{90} +(18.0000 - 3.46410i) q^{91} +(4.50000 - 2.59808i) q^{92} +(3.00000 - 5.19615i) q^{93} +15.5885i q^{94} +(-4.50000 + 7.79423i) q^{96} +(6.00000 - 3.46410i) q^{97} +(12.0000 + 1.73205i) q^{98} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^6 + 4 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{9} - 3 q^{10} - 6 q^{11} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 10 q^{16} + 6 q^{17} - 9 q^{18} - q^{20} - 9 q^{21} + 6 q^{22} - 9 q^{23} + 3 q^{24} - q^{25} - 12 q^{26} - 4 q^{28} + 6 q^{30} + 6 q^{33} - 18 q^{34} + 5 q^{35} - 3 q^{36} + 2 q^{37} - 12 q^{39} - 3 q^{40} + 6 q^{41} - 3 q^{42} - q^{43} + 6 q^{44} - 3 q^{45} - 9 q^{46} + 18 q^{47} + 15 q^{48} + 2 q^{49} - 3 q^{50} - 12 q^{52} + 6 q^{53} + 18 q^{54} + 6 q^{56} - 12 q^{62} + 15 q^{63} - 2 q^{64} - 18 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 9 q^{72} - 18 q^{73} + 6 q^{74} + 3 q^{75} - 18 q^{77} + 36 q^{78} - 20 q^{79} - 5 q^{80} - 9 q^{81} + 18 q^{82} - 12 q^{83} + 9 q^{84} - 6 q^{85} + 3 q^{86} + 6 q^{88} + 15 q^{89} - 9 q^{90} + 36 q^{91} + 9 q^{92} + 6 q^{93} - 9 q^{96} + 12 q^{97} + 24 q^{98}+O(q^{100}) \) 2 * q - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^6 + 4 * q^7 + 3 * q^9 - 3 * q^10 - 6 * q^11 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 10 * q^16 + 6 * q^17 - 9 * q^18 - q^20 - 9 * q^21 + 6 * q^22 - 9 * q^23 + 3 * q^24 - q^25 - 12 * q^26 - 4 * q^28 + 6 * q^30 + 6 * q^33 - 18 * q^34 + 5 * q^35 - 3 * q^36 + 2 * q^37 - 12 * q^39 - 3 * q^40 + 6 * q^41 - 3 * q^42 - q^43 + 6 * q^44 - 3 * q^45 - 9 * q^46 + 18 * q^47 + 15 * q^48 + 2 * q^49 - 3 * q^50 - 12 * q^52 + 6 * q^53 + 18 * q^54 + 6 * q^56 - 12 * q^62 + 15 * q^63 - 2 * q^64 - 18 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 9 * q^72 - 18 * q^73 + 6 * q^74 + 3 * q^75 - 18 * q^77 + 36 * q^78 - 20 * q^79 - 5 * q^80 - 9 * q^81 + 18 * q^82 - 12 * q^83 + 9 * q^84 - 6 * q^85 + 3 * q^86 + 6 * q^88 + 15 * q^89 - 9 * q^90 + 36 * q^91 + 9 * q^92 + 6 * q^93 - 9 * q^96 + 12 * q^97 + 24 * q^98

Introduction

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