LMFDB - Embedded newform 585.2.i.c.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.c.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.50000 + 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +(-0.500000 + 0.866025i) q^{20} -1.73205i q^{21} +(1.00000 + 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(4.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} +(1.50000 - 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(2.50000 + 4.33013i) q^{32} +3.46410i q^{33} +(-2.00000 + 3.46410i) q^{34} +1.00000 q^{35} +3.00000 q^{36} +4.00000 q^{37} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-1.50000 - 0.866025i) q^{42} +(4.00000 - 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-6.50000 + 11.2583i) q^{47} -1.73205i q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.00000 + 3.46410i) q^{51} +(-0.500000 + 0.866025i) q^{52} -10.0000 q^{53} +(-4.50000 - 2.59808i) q^{54} -2.00000 q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(-3.00000 - 5.19615i) q^{59} +1.73205i q^{60} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{62} +(-1.50000 - 2.59808i) q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(3.00000 + 1.73205i) q^{66} +(0.500000 + 0.866025i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(4.50000 + 2.59808i) q^{69} +(0.500000 - 0.866025i) q^{70} -6.00000 q^{71} +(4.50000 - 7.79423i) q^{72} -12.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +1.73205i q^{75} +(1.00000 + 1.73205i) q^{77} +(1.50000 - 0.866025i) q^{78} +(3.00000 - 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(-5.50000 + 9.52628i) q^{83} +(1.50000 - 0.866025i) q^{84} +(-2.00000 - 3.46410i) q^{85} +(-4.00000 - 6.92820i) q^{86} -1.73205i q^{87} +(-3.00000 + 5.19615i) q^{88} +5.00000 q^{89} +(1.50000 - 2.59808i) q^{90} +1.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(-12.0000 - 6.92820i) q^{93} +(6.50000 + 11.2583i) q^{94} +(7.50000 + 4.33013i) q^{96} +(1.00000 - 1.73205i) q^{97} +6.00000 q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 + q^4 + q^5 + q^7 + 6 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} + 3 q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} - 8 q^{17} - 3 q^{18} - q^{20} + 2 q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 2 q^{26} + 2 q^{28} + q^{29} + 3 q^{30} - 8 q^{31} + 5 q^{32} - 4 q^{34} + 2 q^{35} + 6 q^{36} + 8 q^{37} + 3 q^{39} + 3 q^{40} - 9 q^{41} - 3 q^{42} + 8 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} - 13 q^{47} + 6 q^{49} + q^{50} - 12 q^{51} - q^{52} - 20 q^{53} - 9 q^{54} - 4 q^{55} + 3 q^{56} - q^{58} - 6 q^{59} + q^{61} - 16 q^{62} - 3 q^{63} + 14 q^{64} - q^{65} + 6 q^{66} + q^{67} - 4 q^{68} + 9 q^{69} + q^{70} - 12 q^{71} + 9 q^{72} - 24 q^{73} + 4 q^{74} + 2 q^{77} + 3 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} - 18 q^{82} - 11 q^{83} + 3 q^{84} - 4 q^{85} - 8 q^{86} - 6 q^{88} + 10 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} - 24 q^{93} + 13 q^{94} + 15 q^{96} + 2 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 + q^4 + q^5 + q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 - 2 * q^11 + 3 * q^12 + q^13 - q^14 + 3 * q^15 + q^16 - 8 * q^17 - 3 * q^18 - q^20 + 2 * q^22 + 3 * q^23 + 9 * q^24 - q^25 + 2 * q^26 + 2 * q^28 + q^29 + 3 * q^30 - 8 * q^31 + 5 * q^32 - 4 * q^34 + 2 * q^35 + 6 * q^36 + 8 * q^37 + 3 * q^39 + 3 * q^40 - 9 * q^41 - 3 * q^42 + 8 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 - 13 * q^47 + 6 * q^49 + q^50 - 12 * q^51 - q^52 - 20 * q^53 - 9 * q^54 - 4 * q^55 + 3 * q^56 - q^58 - 6 * q^59 + q^61 - 16 * q^62 - 3 * q^63 + 14 * q^64 - q^65 + 6 * q^66 + q^67 - 4 * q^68 + 9 * q^69 + q^70 - 12 * q^71 + 9 * q^72 - 24 * q^73 + 4 * q^74 + 2 * q^77 + 3 * q^78 + 6 * q^79 + 2 * q^80 - 9 * q^81 - 18 * q^82 - 11 * q^83 + 3 * q^84 - 4 * q^85 - 8 * q^86 - 6 * q^88 + 10 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 - 24 * q^93 + 13 * q^94 + 15 * q^96 + 2 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		−	1.73205i		−	0.707107i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	3.00000			1.06066
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.00000			0.316228
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.50000	+	0.866025i	0.387298	+	0.223607i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		−	1.73205i		−	0.377964i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	4.50000	−	2.59808i	0.918559	−	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$		−	5.19615i		−	1.00000i
$28$	1.00000			0.188982
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$			3.46410i			0.603023i
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	1.00000			0.169031
$36$	3.00000			0.500000
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−1.50000	−	0.866025i	−0.231455	−	0.133631i
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	−2.00000			−0.301511
$45$	3.00000			0.447214
$46$	3.00000			0.442326
$47$	−6.50000	+	11.2583i	−0.948122	+	1.64220i	−0.198747	+	0.980051i	$0.563687\pi$
$47$	−6.50000	+	11.2583i	−0.948122	+	1.64220i	−0.749375	+	0.662145i	$0.769646\pi$
$48$		−	1.73205i		−	0.250000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−6.00000	+	3.46410i	−0.840168	+	0.485071i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−2.00000			−0.269680
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$			1.73205i			0.223607i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−8.00000			−1.01600
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$	7.00000			0.875000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	3.00000	+	1.73205i	0.369274	+	0.213201i
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	0.894951	−	0.446165i	$-0.147211\pi$
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	−0.833866	+	0.551967i	$0.813877\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	4.50000	+	2.59808i	0.541736	+	0.312772i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	4.50000	−	7.79423i	0.530330	−	0.918559i
$73$	−12.0000			−1.40449			−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000			−1.40449			−0.702247	+	0.711934i	$0.747820\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$			1.73205i			0.200000i
$76$		0			0
$77$	1.00000	+	1.73205i	0.113961	+	0.197386i
$78$	1.50000	−	0.866025i	0.169842	−	0.0980581i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	1.00000			0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−9.00000			−0.993884
$83$	−5.50000	+	9.52628i	−0.603703	+	1.04565i	0.388552	+	0.921427i	$0.372976\pi$
$83$	−5.50000	+	9.52628i	−0.603703	+	1.04565i	−0.992255	+	0.124218i	$0.960358\pi$
$84$	1.50000	−	0.866025i	0.163663	−	0.0944911i
$85$	−2.00000	−	3.46410i	−0.216930	−	0.375735i
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		−	1.73205i		−	0.185695i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	5.00000			0.529999			0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000			0.529999			0.264999	+	0.964249i	$0.414628\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	1.00000			0.104828
$92$	−1.50000	+	2.59808i	−0.156386	+	0.270868i
$93$	−12.0000	−	6.92820i	−1.24434	−	0.718421i
$94$	6.50000	+	11.2583i	0.670424	+	1.16121i
$95$		0			0
$96$	7.50000	+	4.33013i	0.765466	+	0.441942i
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	6.00000			0.606092
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	−1.00000			−0.100000
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$			6.92820i			0.685994i
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	1.50000	+	2.59808i	0.147087	+	0.254762i
$105$	1.50000	−	0.866025i	0.146385	−	0.0845154i
$106$	−5.00000	+	8.66025i	−0.485643	+	0.841158i
$107$	13.0000			1.25676			0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000			1.25676			0.628379	+	0.777908i	$0.283719\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	1.00000			0.0957826			0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000			0.0957826			0.0478913	+	0.998853i	$0.484750\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	6.00000	−	3.46410i	0.569495	−	0.328798i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	0.756487	−	0.654008i	$-0.226914\pi$
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	−0.944632	+	0.328133i	$0.893581\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	1.00000			0.0928477
$117$	3.00000			0.277350
$118$	−6.00000			−0.552345
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−0.500000	−	0.866025i	−0.0452679	−	0.0784063i
$123$	−13.5000	−	7.79423i	−1.21725	−	0.702782i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	−1.00000			−0.0894427
$126$	−3.00000			−0.267261
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$		−	13.8564i		−	1.21999i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	−3.00000	+	1.73205i	−0.261116	+	0.150756i
$133$		0			0
$134$	1.00000			0.0863868
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$	−12.0000			−1.02899
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	0.290424	+	0.956898i	$0.406204\pi$
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	−0.973910	+	0.226935i	$0.927130\pi$
$138$	4.50000	−	2.59808i	0.383065	−	0.221163i
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	0.999947	+	0.0103230i	$0.00328598\pi$
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	−0.491033	+	0.871141i	$0.663381\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$			22.5167i			1.89624i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−2.00000			−0.167248
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	1.00000			0.0830455
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$	9.00000	+	5.19615i	0.742307	+	0.428571i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	1.50000	+	0.866025i	0.122474	+	0.0707107i
$151$	−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
$153$	−6.00000	+	10.3923i	−0.485071	+	0.840168i
$154$	2.00000			0.161165
$155$	4.00000	−	6.92820i	0.321288	−	0.556487i
$156$			1.73205i			0.138675i
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	−0.961681	−	0.274169i	$-0.911597\pi$
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	0.243403	−	0.969925i	$-0.421736\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	−15.0000	+	8.66025i	−1.18958	+	0.686803i
$160$	−2.50000	+	4.33013i	−0.197642	+	0.342327i
$161$	3.00000			0.236433
$162$	−9.00000			−0.707107
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$	−3.00000	+	1.73205i	−0.233550	+	0.134840i
$166$	5.50000	+	9.52628i	0.426883	+	0.739383i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$		−	5.19615i		−	0.400892i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	8.00000			0.609994
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	−0.542583	−	0.840002i	$-0.682554\pi$
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	0.998755	+	0.0498898i	$0.0158870\pi$
$174$	−1.50000	−	0.866025i	−0.113715	−	0.0656532i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	−9.00000	−	5.19615i	−0.676481	−	0.390567i
$178$	2.50000	−	4.33013i	0.187383	−	0.324557i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	0.500000	−	0.866025i	0.0370625	−	0.0641941i
$183$		−	1.73205i		−	0.128037i
$184$	4.50000	+	7.79423i	0.331744	+	0.574598i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−12.0000	+	6.92820i	−0.879883	+	0.508001i
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	−13.0000			−0.948122
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$		0			0
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	10.5000	−	6.06218i	0.757772	−	0.437500i
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$			1.73205i			0.124035i
$196$	−3.00000	+	5.19615i	−0.214286	+	0.371154i
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$	6.00000			0.426401
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$	1.50000	+	0.866025i	0.105802	+	0.0610847i
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$	−0.500000	−	0.866025i	−0.0350931	−	0.0607831i
$204$	−6.00000	−	3.46410i	−0.420084	−	0.242536i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	16.0000			1.11477
$207$	9.00000			0.625543
$208$	1.00000			0.0693375
$209$		0			0
$210$		−	1.73205i		−	0.119523i
$211$	−3.00000	−	5.19615i	−0.206529	−	0.357718i	0.744090	−	0.668079i	$-0.232883\pi$
$211$	−3.00000	−	5.19615i	−0.206529	−	0.357718i	−0.950619	+	0.310361i	$0.899550\pi$
$212$	−5.00000	−	8.66025i	−0.343401	−	0.594789i
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$	6.50000	−	11.2583i	0.444331	−	0.769604i
$215$	8.00000			0.545595
$216$		−	15.5885i		−	1.06066i
$217$	−8.00000			−0.543075
$218$	0.500000	−	0.866025i	0.0338643	−	0.0586546i
$219$	−18.0000	+	10.3923i	−1.21633	+	0.702247i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$		−	6.92820i		−	0.464991i
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	−0.427443	−	0.904042i	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$	5.00000			0.334077
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	−4.00000			−0.266076
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		0			0
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$	1.50000	+	2.59808i	0.0989071	+	0.171312i
$231$	3.00000	+	1.73205i	0.197386	+	0.113961i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$	1.50000	−	2.59808i	0.0980581	−	0.169842i
$235$	−13.0000			−0.848026
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$		−	10.3923i		−	0.675053i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	−0.211360	−	0.977408i	$-0.567789\pi$
$241$	11.5000	−	19.9186i	0.740780	−	1.28307i	0.952141	−	0.305661i	$-0.0988773\pi$
$242$	7.00000			0.449977
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	1.00000			0.0640184
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$	−13.5000	+	7.79423i	−0.860729	+	0.496942i
$247$		0			0
$248$	−12.0000	−	20.7846i	−0.762001	−	1.31982i
$249$			19.0526i			1.20741i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	−6.00000			−0.377217
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$	−6.00000	−	3.46410i	−0.375735	−	0.216930i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	0.973070	+	0.230508i	$0.0740389\pi$
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	−0.286909	+	0.957958i	$0.592628\pi$
$258$	−12.0000	−	6.92820i	−0.747087	−	0.431331i
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$	−1.00000			−0.0620174
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	−14.0000			−0.864923
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$			10.3923i			0.639602i
$265$	−5.00000	−	8.66025i	−0.307148	−	0.531995i
$266$		0			0
$267$	7.50000	−	4.33013i	0.458993	−	0.264999i
$268$	−0.500000	+	0.866025i	−0.0305424	+	0.0529009i
$269$	9.00000			0.548740			0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000			0.548740			0.274370	+	0.961624i	$0.411531\pi$
$270$		−	5.19615i		−	0.316228i
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	1.50000	−	0.866025i	0.0907841	−	0.0524142i
$274$	8.00000	+	13.8564i	0.483298	+	0.837096i
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$			5.19615i			0.312772i
$277$	10.0000	−	17.3205i	0.600842	−	1.04069i	−0.391852	−	0.920028i	$-0.628166\pi$
$277$	10.0000	−	17.3205i	0.600842	−	1.04069i	0.992694	−	0.120660i	$-0.0385012\pi$
$278$	12.0000			0.719712
$279$	−24.0000			−1.43684
$280$	3.00000			0.179284
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$	19.5000	+	11.2583i	1.16121	+	0.670424i
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	−1.00000	+	1.73205i	−0.0591312	+	0.102418i
$287$	−9.00000			−0.531253
$288$	15.0000			0.883883
$289$	−1.00000			−0.0588235
$290$	0.500000	−	0.866025i	0.0293610	−	0.0508548i
$291$		−	3.46410i		−	0.203069i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−2.00000	−	3.46410i	−0.116841	−	0.202375i	0.801673	−	0.597763i	$-0.203944\pi$
$293$	−2.00000	−	3.46410i	−0.116841	−	0.202375i	−0.918514	+	0.395388i	$0.870610\pi$
$294$	9.00000	−	5.19615i	0.524891	−	0.303046i
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	12.0000			0.697486
$297$	9.00000	+	5.19615i	0.522233	+	0.301511i
$298$	3.00000			0.173785
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$	−1.50000	+	0.866025i	−0.0866025	+	0.0500000i
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$			10.3923i			0.597022i
$304$		0			0
$305$	1.00000			0.0572598
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	−19.0000			−1.08439			−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000			−1.08439			−0.542194	+	0.840254i	$0.682406\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$	24.0000	+	13.8564i	1.36531	+	0.788263i
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	0.917143	−	0.398559i	$-0.130489\pi$
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	−0.803733	+	0.594990i	$0.797156\pi$
$312$	4.50000	+	2.59808i	0.254762	+	0.147087i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	−18.0000			−1.01580
$315$	1.50000	−	2.59808i	0.0845154	−	0.146385i
$316$	6.00000			0.337526
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$			17.3205i			0.971286i
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$	3.50000	+	6.06218i	0.195656	+	0.338886i
$321$	19.5000	−	11.2583i	1.08838	−	0.628379i
$322$	1.50000	−	2.59808i	0.0835917	−	0.144785i
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−1.00000			−0.0554700
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	1.50000	−	0.866025i	0.0829502	−	0.0478913i
$328$	−13.5000	−	23.3827i	−0.745413	−	1.29109i
$329$	6.50000	+	11.2583i	0.358357	+	0.620692i
$330$			3.46410i			0.190693i
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	−0.505296	−	0.862946i	$-0.668617\pi$
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	0.999981	+	0.00612670i	$0.00195020\pi$
$332$	−11.0000			−0.603703
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$	3.00000			0.164153
$335$	−0.500000	+	0.866025i	−0.0273179	+	0.0473160i
$336$	−1.50000	−	0.866025i	−0.0818317	−	0.0472456i
$337$	−10.0000	−	17.3205i	−0.544735	−	0.943508i	−0.998624	−	0.0524499i	$-0.983297\pi$
$337$	−10.0000	−	17.3205i	−0.544735	−	0.943508i	0.453889	−	0.891058i	$-0.350036\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	−6.00000	−	3.46410i	−0.325875	−	0.188144i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	16.0000			0.866449
$342$		0			0
$343$	13.0000			0.701934
$344$	12.0000	−	20.7846i	0.646997	−	1.12063i
$345$			5.19615i			0.279751i
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$	1.50000	−	0.866025i	0.0804084	−	0.0464238i
$349$	4.50000	−	7.79423i	0.240879	−	0.417215i	−0.720086	−	0.693885i	$-0.755897\pi$
$349$	4.50000	−	7.79423i	0.240879	−	0.417215i	0.960965	+	0.276670i	$0.0892308\pi$
$350$	1.00000			0.0534522
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$	−10.0000			−0.533002
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$	−9.00000	+	5.19615i	−0.478345	+	0.276172i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	2.50000	+	4.33013i	0.132500	+	0.229496i
$357$			6.92820i			0.366679i
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$	9.00000			0.474342
$361$	−19.0000			−1.00000
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	0.500000	+	0.866025i	0.0262071	+	0.0453921i
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$	−1.50000	−	0.866025i	−0.0784063	−	0.0452679i
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	3.00000			0.156386
$369$	−27.0000			−1.40556
$370$	4.00000			0.207950
$371$	−5.00000	+	8.66025i	−0.259587	+	0.449618i
$372$		−	13.8564i		−	0.718421i
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	−1.50000	+	0.866025i	−0.0774597	+	0.0447214i
$376$	−19.5000	+	33.7750i	−1.00564	+	1.74181i
$377$	1.00000			0.0515026
$378$	−4.50000	+	2.59808i	−0.231455	+	0.133631i
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$		0			0
$381$	19.5000	−	11.2583i	0.999015	−	0.576782i
$382$	−6.00000	−	10.3923i	−0.306987	−	0.531717i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$			5.19615i			0.265165i
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$	2.00000			0.101797
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$	2.00000			0.101535
$389$	15.5000	−	26.8468i	0.785881	−	1.36119i	−0.142590	−	0.989782i	$-0.545543\pi$
$389$	15.5000	−	26.8468i	0.785881	−	1.36119i	0.928471	−	0.371404i	$-0.121124\pi$
$390$	1.50000	+	0.866025i	0.0759555	+	0.0438529i
$391$	−6.00000	−	10.3923i	−0.303433	−	0.525561i
$392$	9.00000	+	15.5885i	0.454569	+	0.787336i
$393$	−21.0000	−	12.1244i	−1.05931	−	0.611593i
$394$	−12.0000	+	20.7846i	−0.604551	+	1.04711i
$395$	6.00000			0.301893
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	10.0000	−	17.3205i	0.501255	−	0.868199i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−11.0000	−	19.0526i	−0.549314	−	0.951439i	−0.998322	−	0.0579116i	$-0.981556\pi$
$401$	−11.0000	−	19.0526i	−0.549314	−	0.951439i	0.449008	−	0.893528i	$-0.351777\pi$
$402$	1.50000	−	0.866025i	0.0748132	−	0.0431934i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−6.00000			−0.298511
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	−1.00000			−0.0496292
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$	−18.0000	+	10.3923i	−0.891133	+	0.514496i
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	−0.951720	−	0.306968i	$-0.900685\pi$
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	0.210017	−	0.977698i	$-0.432648\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$			27.7128i			1.36697i
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	−6.00000			−0.295241
$414$	4.50000	−	7.79423i	0.221163	−	0.383065i
$415$	−11.0000			−0.539969
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	18.0000	+	10.3923i	0.881464	+	0.508913i
$418$		0			0
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	0.961925	−	0.273314i	$-0.0881197\pi$
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	−0.717659	+	0.696395i	$0.754786\pi$
$420$	1.50000	+	0.866025i	0.0731925	+	0.0422577i
$421$	7.00000	−	12.1244i	0.341159	−	0.590905i	−0.643489	−	0.765455i	$-0.722514\pi$
$421$	7.00000	−	12.1244i	0.341159	−	0.590905i	0.984648	+	0.174550i	$0.0558472\pi$
$422$	−6.00000			−0.292075
$423$	19.5000	+	33.7750i	0.948122	+	1.64220i
$424$	−30.0000			−1.45693
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$			10.3923i			0.503509i
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	6.50000	+	11.2583i	0.314189	+	0.544192i
$429$	−3.00000	+	1.73205i	−0.144841	+	0.0836242i
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	26.0000			1.25238			0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000			1.25238			0.626188	+	0.779672i	$0.284614\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−32.0000			−1.53782			−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000			−1.53782			−0.768911	+	0.639356i	$0.779201\pi$
$434$	−4.00000	+	6.92820i	−0.192006	+	0.332564i
$435$	1.50000	−	0.866025i	0.0719195	−	0.0415227i
$436$	0.500000	+	0.866025i	0.0239457	+	0.0414751i
$437$		0			0
$438$			20.7846i			0.993127i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−6.00000			−0.286039
$441$	18.0000			0.857143
$442$	−4.00000			−0.190261
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	−0.994187	−	0.107671i	$-0.965661\pi$
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	0.590339	+	0.807155i	$0.298994\pi$
$444$	6.00000	+	3.46410i	0.284747	+	0.164399i
$445$	2.50000	+	4.33013i	0.118511	+	0.205268i
$446$	−8.50000	−	14.7224i	−0.402487	−	0.697127i
$447$	4.50000	+	2.59808i	0.212843	+	0.122885i
$448$	3.50000	−	6.06218i	0.165359	−	0.286411i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	3.00000			0.141421
$451$	18.0000			0.847587
$452$	2.00000	−	3.46410i	0.0940721	−	0.162938i
$453$			17.3205i			0.813788i
$454$	2.00000	+	3.46410i	0.0938647	+	0.162578i
$455$	0.500000	+	0.866025i	0.0234404	+	0.0405999i
$456$		0			0
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	−0.615986	−	0.787757i	$-0.711242\pi$
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	0.990211	+	0.139581i	$0.0445757\pi$
$458$	13.0000			0.607450
$459$			20.7846i			0.970143i
$460$	−3.00000			−0.139876
$461$	−6.50000	+	11.2583i	−0.302735	+	0.524353i	−0.976755	−	0.214361i	$-0.931233\pi$
$461$	−6.50000	+	11.2583i	−0.302735	+	0.524353i	0.674019	+	0.738714i	$0.264566\pi$
$462$	3.00000	−	1.73205i	0.139573	−	0.0805823i
$463$	18.0000	+	31.1769i	0.836531	+	1.44891i	0.892778	+	0.450497i	$0.148753\pi$
$463$	18.0000	+	31.1769i	0.836531	+	1.44891i	−0.0562469	+	0.998417i	$0.517913\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$		−	13.8564i		−	0.642575i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$	1.50000	+	2.59808i	0.0693375	+	0.120096i
$469$	1.00000			0.0461757
$470$	−6.50000	+	11.2583i	−0.299823	+	0.519308i
$471$	−27.0000	−	15.5885i	−1.24409	−	0.718278i
$472$	−9.00000	−	15.5885i	−0.414259	−	0.717517i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$	−9.00000	−	5.19615i	−0.413384	−	0.238667i
$475$		0			0
$476$	−4.00000			−0.183340
$477$	−15.0000	+	25.9808i	−0.686803	+	1.18958i
$478$	24.0000			1.09773
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$			8.66025i			0.395285i
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	−11.5000	−	19.9186i	−0.523811	−	0.907267i
$483$	4.50000	−	2.59808i	0.204757	−	0.118217i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	2.00000			0.0908153
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	1.50000	−	2.59808i	0.0679018	−	0.117609i
$489$	−18.0000	+	10.3923i	−0.813988	+	0.469956i
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		−	15.5885i		−	0.702782i
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	−8.00000			−0.359211
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$	16.5000	+	9.52628i	0.739383	+	0.426883i
$499$	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	$0.685590\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	4.50000	+	2.59808i	0.201045	+	0.116073i
$502$		0			0
$503$	39.0000			1.73892			0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000			1.73892			0.869462	+	0.494000i	$0.164466\pi$
$504$	−4.50000	−	7.79423i	−0.200446	−	0.347183i
$505$	−6.00000			−0.266996
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$			1.73205i			0.0769231i
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	−6.00000	+	3.46410i	−0.265684	+	0.153393i
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$	11.0000			0.486136
$513$		0			0
$514$	22.0000			0.970378
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$	12.0000	−	6.92820i	0.528271	−	0.304997i
$517$	−13.0000	−	22.5167i	−0.571739	−	0.990282i
$518$	−2.00000	−	3.46410i	−0.0878750	−	0.152204i
$519$		−	20.7846i		−	0.912343i
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$	−3.00000			−0.131306
$523$	21.0000			0.918266			0.459133	−	0.888368i	$-0.348160\pi$
$523$	21.0000			0.918266			0.459133	+	0.888368i	$0.348160\pi$
$524$	7.00000	−	12.1244i	0.305796	−	0.529655i
$525$	1.50000	+	0.866025i	0.0654654	+	0.0377964i
$526$	−8.00000	−	13.8564i	−0.348817	−	0.604168i
$527$	16.0000	+	27.7128i	0.696971	+	1.20719i
$528$	3.00000	+	1.73205i	0.130558	+	0.0753778i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−10.0000			−0.434372
$531$	−18.0000			−0.781133
$532$		0			0
$533$	4.50000	−	7.79423i	0.194917	−	0.337606i
$534$		−	8.66025i		−	0.374766i
$535$	6.50000	+	11.2583i	0.281020	+	0.486740i
$536$	1.50000	+	2.59808i	0.0647901	+	0.112220i
$537$	9.00000	−	5.19615i	0.388379	−	0.224231i
$538$	4.50000	−	7.79423i	0.194009	−	0.336033i
$539$	−12.0000			−0.516877
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	5.00000			0.214967			0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000			0.214967			0.107483	+	0.994207i	$0.465721\pi$
$542$	−2.00000	+	3.46410i	−0.0859074	+	0.148796i
$543$	−10.5000	+	6.06218i	−0.450598	+	0.260153i
$544$	−10.0000	−	17.3205i	−0.428746	−	0.742611i
$545$	0.500000	+	0.866025i	0.0214176	+	0.0370965i
$546$		−	1.73205i		−	0.0741249i
$547$	−22.5000	+	38.9711i	−0.962031	+	1.66629i	−0.244641	+	0.969614i	$0.578670\pi$
$547$	−22.5000	+	38.9711i	−0.962031	+	1.66629i	−0.717390	+	0.696672i	$0.754663\pi$
$548$	−16.0000			−0.683486
$549$	−1.50000	−	2.59808i	−0.0640184	−	0.110883i
$550$	−2.00000			−0.0852803
$551$		0			0
$552$	13.5000	+	7.79423i	0.574598	+	0.331744i
$553$	−3.00000	−	5.19615i	−0.127573	−	0.220963i
$554$	−10.0000	−	17.3205i	−0.424859	−	0.735878i
$555$	6.00000	+	3.46410i	0.254686	+	0.147043i
$556$	−6.00000	+	10.3923i	−0.254457	+	0.440732i
$557$	22.0000			0.932170			0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000			0.932170			0.466085	+	0.884740i	$0.345664\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	8.00000			0.338364
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$		−	13.8564i		−	0.585018i
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	9.50000	+	16.4545i	0.400377	+	0.693474i	0.993771	−	0.111438i	$-0.0355457\pi$
$563$	9.50000	+	16.4545i	0.400377	+	0.693474i	−0.593394	+	0.804912i	$0.702212\pi$
$564$	−19.5000	+	11.2583i	−0.821098	+	0.474061i
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	13.0000			0.546431
$567$	−9.00000			−0.377964
$568$	−18.0000			−0.755263
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	0.921869	−	0.387503i	$-0.126662\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		−	20.7846i		−	0.868290i
$574$	−4.50000	+	7.79423i	−0.187826	+	0.325325i
$575$	−3.00000			−0.125109
$576$	10.5000	−	18.1865i	0.437500	−	0.757772i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	3.00000	+	1.73205i	0.124676	+	0.0719816i
$580$	0.500000	+	0.866025i	0.0207614	+	0.0359597i
$581$	5.50000	+	9.52628i	0.228178	+	0.395217i
$582$	−3.00000	−	1.73205i	−0.124354	−	0.0717958i
$583$	10.0000	−	17.3205i	0.414158	−	0.717342i
$584$	−36.0000			−1.48969
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$	−4.00000			−0.165238
$587$	−18.5000	+	32.0429i	−0.763577	+	1.32255i	0.177419	+	0.984135i	$0.443225\pi$
$587$	−18.5000	+	32.0429i	−0.763577	+	1.32255i	−0.940996	+	0.338418i	$0.890108\pi$
$588$			10.3923i			0.428571i
$589$		0			0
$590$	−3.00000	−	5.19615i	−0.123508	−	0.213922i
$591$	−36.0000	+	20.7846i	−1.48084	+	0.854965i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−4.00000			−0.164260			−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000			−0.164260			−0.0821302	+	0.996622i	$0.526172\pi$
$594$	9.00000	−	5.19615i	0.369274	−	0.213201i
$595$	−4.00000			−0.163984
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$	30.0000	−	17.3205i	1.22782	−	0.708881i
$598$	1.50000	+	2.59808i	0.0613396	+	0.106243i
$599$	−13.0000	−	22.5167i	−0.531166	−	0.920006i	−0.999338	−	0.0363689i	$-0.988421\pi$
$599$	−13.0000	−	22.5167i	−0.531166	−	0.920006i	0.468173	−	0.883637i	$-0.344912\pi$
$600$			5.19615i			0.212132i
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$	−8.00000			−0.326056
$603$	3.00000			0.122169
$604$	−10.0000			−0.406894
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	9.00000	+	5.19615i	0.365600	+	0.211079i
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$		0			0
$609$	−1.50000	−	0.866025i	−0.0607831	−	0.0350931i
$610$	0.500000	−	0.866025i	0.0202444	−	0.0350643i
$611$	−13.0000			−0.525924
$612$	−12.0000			−0.485071
$613$	24.0000			0.969351			0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000			0.969351			0.484675	+	0.874694i	$0.338938\pi$
$614$	−9.50000	+	16.4545i	−0.383389	+	0.664049i
$615$		−	15.5885i		−	0.628587i
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.706346	+	0.707867i	$0.250342\pi$
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.259858	+	0.965647i	$0.416324\pi$
$618$	24.0000	−	13.8564i	0.965422	−	0.557386i
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	0.113185	+	0.993574i	$0.463895\pi$
$619$	−20.0000	+	34.6410i	−0.803868	+	1.39234i	−0.917053	+	0.398766i	$0.869439\pi$
$620$	8.00000			0.321288
$621$	13.5000	−	7.79423i	0.541736	−	0.312772i
$622$	4.00000			0.160385
$623$	2.50000	−	4.33013i	0.100160	−	0.173483i
$624$	1.50000	−	0.866025i	0.0600481	−	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	9.00000	−	15.5885i	0.359139	−	0.622047i
$629$	−16.0000			−0.637962
$630$	−1.50000	−	2.59808i	−0.0597614	−	0.103510i
$631$	4.00000			0.159237			0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000			0.159237			0.0796187	+	0.996825i	$0.474630\pi$
$632$	9.00000	−	15.5885i	0.358001	−	0.620076i
$633$	−9.00000	−	5.19615i	−0.357718	−	0.206529i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	6.50000	+	11.2583i	0.257945	+	0.446773i
$636$	−15.0000	−	8.66025i	−0.594789	−	0.343401i
$637$	−3.00000	+	5.19615i	−0.118864	+	0.205879i
$638$	2.00000			0.0791808
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$	−3.00000			−0.118585
$641$	−20.5000	+	35.5070i	−0.809701	+	1.40244i	0.103370	+	0.994643i	$0.467038\pi$
$641$	−20.5000	+	35.5070i	−0.809701	+	1.40244i	−0.913071	+	0.407801i	$0.866296\pi$
$642$		−	22.5167i		−	0.888662i
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$	12.0000	−	6.92820i	0.472500	−	0.272798i
$646$		0			0
$647$	−7.00000			−0.275198			−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000			−0.275198			−0.137599	+	0.990488i	$0.543939\pi$
$648$	−13.5000	−	23.3827i	−0.530330	−	0.918559i
$649$	12.0000			0.471041
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$	−12.0000	+	6.92820i	−0.470317	+	0.271538i
$652$	−6.00000	−	10.3923i	−0.234978	−	0.406994i
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$		−	1.73205i		−	0.0677285i
$655$	7.00000	−	12.1244i	0.273513	−	0.473738i
$656$	−9.00000			−0.351391
$657$	−18.0000	+	31.1769i	−0.702247	+	1.21633i
$658$	13.0000			0.506793
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	−3.00000	−	1.73205i	−0.116775	−	0.0674200i
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	−0.999979	−	0.00652642i	$-0.997923\pi$
$661$	−13.0000	−	22.5167i	−0.505641	−	0.875797i	0.494337	−	0.869270i	$-0.335411\pi$
$662$	−9.00000	−	15.5885i	−0.349795	−	0.605863i
$663$	−6.00000	−	3.46410i	−0.233021	−	0.134535i
$664$	−16.5000	+	28.5788i	−0.640324	+	1.10907i
$665$		0			0
$666$	−6.00000	−	10.3923i	−0.232495	−	0.402694i
$667$	3.00000			0.116160
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$		−	29.4449i		−	1.13840i
$670$	0.500000	+	0.866025i	0.0193167	+	0.0334575i
$671$	1.00000	+	1.73205i	0.0386046	+	0.0668651i
$672$	7.50000	−	4.33013i	0.289319	−	0.167038i
$673$	−9.00000	+	15.5885i	−0.346925	+	0.600891i	−0.985701	−	0.168501i	$-0.946107\pi$
$673$	−9.00000	+	15.5885i	−0.346925	+	0.600891i	0.638777	+	0.769392i	$0.279441\pi$
$674$	−20.0000			−0.770371
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	−1.00000			−0.0384615
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$	−6.00000	+	3.46410i	−0.230429	+	0.133038i
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	−6.00000	−	10.3923i	−0.230089	−	0.398527i
$681$			6.92820i			0.265489i
$682$	8.00000	−	13.8564i	0.306336	−	0.530589i
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	19.5000	+	11.2583i	0.743971	+	0.429532i
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−5.00000	−	8.66025i	−0.190485	−	0.329929i
$690$	4.50000	+	2.59808i	0.171312	+	0.0989071i
$691$	25.0000	−	43.3013i	0.951045	−	1.64726i	0.207875	−	0.978155i	$-0.433345\pi$
$691$	25.0000	−	43.3013i	0.951045	−	1.64726i	0.743170	−	0.669102i	$-0.233321\pi$
$692$	12.0000			0.456172
$693$	6.00000			0.227921
$694$	28.0000			1.06287
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$		−	5.19615i		−	0.196960i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−4.50000	−	7.79423i	−0.170328	−	0.295016i
$699$	6.00000	−	3.46410i	0.226941	−	0.131024i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	7.00000			0.264386			0.132193	−	0.991224i	$-0.457798\pi$
$701$	7.00000			0.264386			0.132193	+	0.991224i	$0.457798\pi$
$702$		−	5.19615i		−	0.196116i
$703$		0			0
$704$	−7.00000	+	12.1244i	−0.263822	+	0.456954i
$705$	−19.5000	+	11.2583i	−0.734412	+	0.424013i
$706$		0			0
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		−	10.3923i		−	0.390567i
$709$	−21.5000	+	37.2391i	−0.807449	+	1.39854i	0.107176	+	0.994240i	$0.465819\pi$
$709$	−21.5000	+	37.2391i	−0.807449	+	1.39854i	−0.914625	+	0.404303i	$0.867514\pi$
$710$	−6.00000			−0.225176
$711$	−9.00000	−	15.5885i	−0.337526	−	0.584613i
$712$	15.0000			0.562149
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$	6.00000	+	3.46410i	0.224544	+	0.129641i
$715$	−1.00000	−	1.73205i	−0.0373979	−	0.0647750i
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$	36.0000	+	20.7846i	1.34444	+	0.776215i
$718$	4.00000	−	6.92820i	0.149279	−	0.258558i
$719$	−26.0000			−0.969636			−0.484818	−	0.874615i	$-0.661114\pi$
$719$	−26.0000			−0.969636			−0.484818	+	0.874615i	$0.661114\pi$
$720$	1.50000	−	2.59808i	0.0559017	−	0.0968246i
$721$	16.0000			0.595871
$722$	−9.50000	+	16.4545i	−0.353553	+	0.612372i
$723$		−	39.8372i		−	1.48156i
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$	10.5000	−	6.06218i	0.389692	−	0.224989i
$727$	−16.5000	+	28.5788i	−0.611951	+	1.05993i	0.378960	+	0.925413i	$0.376282\pi$
$727$	−16.5000	+	28.5788i	−0.611951	+	1.05993i	−0.990911	+	0.134517i	$0.957052\pi$
$728$	3.00000			0.111187
$729$	−27.0000			−1.00000
$730$	−12.0000			−0.444140
$731$	−16.0000	+	27.7128i	−0.591781	+	1.02500i
$732$	1.50000	−	0.866025i	0.0554416	−	0.0320092i
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$	−16.0000	−	27.7128i	−0.590571	−	1.02290i
$735$			10.3923i			0.383326i
$736$	−7.50000	+	12.9904i	−0.276454	+	0.478832i
$737$	−2.00000			−0.0736709
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	6.00000			0.220714			0.110357	−	0.993892i	$-0.464801\pi$
$739$	6.00000			0.220714			0.110357	+	0.993892i	$0.464801\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$		0			0
$742$	5.00000	+	8.66025i	0.183556	+	0.317928i
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	−0.992000	−	0.126239i	$-0.959709\pi$
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	0.386674	−	0.922217i	$-0.373624\pi$
$744$	−36.0000	−	20.7846i	−1.31982	−	0.762001i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$	14.0000			0.512576
$747$	16.5000	+	28.5788i	0.603703	+	1.04565i
$748$	8.00000			0.292509
$749$	6.50000	−	11.2583i	0.237505	−	0.411370i
$750$			1.73205i			0.0632456i
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	0.993895	−	0.110333i	$-0.0351919\pi$
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	−0.592499	+	0.805571i	$0.701859\pi$
$752$	6.50000	+	11.2583i	0.237031	+	0.410549i
$753$		0			0
$754$	0.500000	−	0.866025i	0.0182089	−	0.0315388i
$755$	−10.0000			−0.363937
$756$		−	5.19615i		−	0.188982i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−13.0000	+	22.5167i	−0.472181	+	0.817842i
$759$	−9.00000	+	5.19615i	−0.326679	+	0.188608i
$760$		0			0
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$		−	22.5167i		−	0.815693i
$763$	0.500000	−	0.866025i	0.0181012	−	0.0313522i
$764$	12.0000			0.434145
$765$	−12.0000			−0.433861
$766$	12.0000			0.433578
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$	25.5000	+	14.7224i	0.920152	+	0.531250i
$769$	−8.50000	−	14.7224i	−0.306518	−	0.530904i	0.671080	−	0.741385i	$-0.265831\pi$
$769$	−8.50000	−	14.7224i	−0.306518	−	0.530904i	−0.977598	+	0.210480i	$0.932497\pi$
$770$	1.00000	+	1.73205i	0.0360375	+	0.0624188i
$771$	33.0000	+	19.0526i	1.18847	+	0.686161i
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−8.00000			−0.287740			−0.143870	−	0.989597i	$-0.545955\pi$
$773$	−8.00000			−0.287740			−0.143870	+	0.989597i	$0.545955\pi$
$774$	−24.0000			−0.862662
$775$	8.00000			0.287368
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		−	6.92820i		−	0.248548i
$778$	−15.5000	−	26.8468i	−0.555702	−	0.962504i
$779$		0			0
$780$	−1.50000	+	0.866025i	−0.0537086	+	0.0310087i
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−12.0000			−0.429119
$783$	−4.50000	−	2.59808i	−0.160817	−	0.0928477i
$784$	6.00000			0.214286
$785$	9.00000	−	15.5885i	0.321224	−	0.556376i
$786$	−21.0000	+	12.1244i	−0.749045	+	0.432461i
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	−12.0000	−	20.7846i	−0.427482	−	0.740421i
$789$		−	27.7128i		−	0.986602i
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	−4.00000			−0.142224
$792$	9.00000	+	15.5885i	0.319801	+	0.553912i
$793$	1.00000			0.0355110
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$	−15.0000	−	8.66025i	−0.531995	−	0.307148i
$796$	10.0000	+	17.3205i	0.354441	+	0.613909i
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	−0.999331	−	0.0365596i	$-0.988360\pi$
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	0.468004	−	0.883726i	$-0.344973\pi$
$798$		0			0
$799$	26.0000	−	45.0333i	0.919814	−	1.59316i
$800$	−5.00000			−0.176777
$801$	7.50000	−	12.9904i	0.264999	−	0.458993i
$802$	−22.0000			−0.776847
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$			1.73205i			0.0610847i
$805$	1.50000	+	2.59808i	0.0528681	+	0.0915702i
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	13.5000	−	7.79423i	0.475223	−	0.274370i
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	34.0000			1.19538			0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000			1.19538			0.597688	+	0.801729i	$0.296086\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	54.0000			1.89620			0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000			1.89620			0.948098	+	0.317978i	$0.103004\pi$
$812$	0.500000	−	0.866025i	0.0175466	−	0.0303915i
$813$	−6.00000	+	3.46410i	−0.210429	+	0.121491i
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$			6.92820i			0.242536i
$817$		0			0
$818$	−30.0000			−1.04893
$819$	1.50000	−	2.59808i	0.0524142	−	0.0907841i
$820$	9.00000			0.314294
$821$	18.5000	−	32.0429i	0.645654	−	1.11831i	−0.338495	−	0.940968i	$-0.609918\pi$
$821$	18.5000	−	32.0429i	0.645654	−	1.11831i	0.984150	−	0.177338i	$-0.0567487\pi$
$822$	24.0000	+	13.8564i	0.837096	+	0.483298i
$823$	18.5000	+	32.0429i	0.644869	+	1.11695i	0.984332	+	0.176327i	$0.0564216\pi$
$823$	18.5000	+	32.0429i	0.644869	+	1.11695i	−0.339462	+	0.940620i	$0.610245\pi$
$824$	24.0000	+	41.5692i	0.836080	+	1.44813i
$825$	−3.00000	−	1.73205i	−0.104447	−	0.0603023i
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−41.0000			−1.42571			−0.712855	−	0.701312i	$-0.752598\pi$
$827$	−41.0000			−1.42571			−0.712855	+	0.701312i	$0.752598\pi$
$828$	4.50000	+	7.79423i	0.156386	+	0.270868i
$829$	−11.0000			−0.382046			−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000			−0.382046			−0.191023	+	0.981586i	$0.561180\pi$
$830$	−5.50000	+	9.52628i	−0.190908	+	0.330662i
$831$		−	34.6410i		−	1.20168i
$832$	3.50000	+	6.06218i	0.121341	+	0.210168i
$833$	−12.0000	−	20.7846i	−0.415775	−	0.720144i
$834$	18.0000	−	10.3923i	0.623289	−	0.359856i
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$		0			0
$837$	−36.0000	+	20.7846i	−1.24434	+	0.718421i
$838$	10.0000			0.345444
$839$	14.0000	−	24.2487i	0.483334	−	0.837158i	−0.516483	−	0.856297i	$-0.672759\pi$
$839$	14.0000	−	24.2487i	0.483334	−	0.837158i	0.999817	+	0.0191389i	$0.00609246\pi$
$840$	4.50000	−	2.59808i	0.155265	−	0.0896421i
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$		−	46.7654i		−	1.61068i
$844$	3.00000	−	5.19615i	0.103264	−	0.178859i
$845$	−1.00000			−0.0344010
$846$	39.0000			1.34085
$847$	7.00000			0.240523
$848$	−5.00000	+	8.66025i	−0.171701	+	0.297394i
$849$	19.5000	+	11.2583i	0.669238	+	0.386385i
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−9.00000	−	5.19615i	−0.308335	−	0.178017i
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	0.242360	+	0.970186i	$0.422079\pi$
$853$	−21.0000	+	36.3731i	−0.719026	+	1.24539i	−0.961386	+	0.275204i	$0.911255\pi$
$854$	−1.00000			−0.0342193
$855$		0			0
$856$	39.0000			1.33299
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$			3.46410i			0.118262i
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$	−13.5000	+	7.79423i	−0.460079	+	0.265627i
$862$	13.0000	−	22.5167i	0.442782	−	0.766921i
$863$	27.0000			0.919091			0.459545	−	0.888154i	$-0.348012\pi$
$863$	27.0000			0.919091			0.459545	+	0.888154i	$0.348012\pi$
$864$	22.5000	−	12.9904i	0.765466	−	0.441942i
$865$	12.0000			0.408012
$866$	−16.0000	+	27.7128i	−0.543702	+	0.941720i
$867$	−1.50000	+	0.866025i	−0.0509427	+	0.0294118i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		−	1.73205i		−	0.0587220i
$871$	−0.500000	+	0.866025i	−0.0169419	+	0.0293442i
$872$	3.00000			0.101593
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$		0			0
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−18.0000	−	10.3923i	−0.608164	−	0.351123i
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$		0			0
$879$	−6.00000	−	3.46410i	−0.202375	−	0.116841i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−43.0000			−1.44871			−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$		−	10.3923i		−	0.349334i
$886$	8.50000	+	14.7224i	0.285563	+	0.494610i
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	0.983632	−	0.180190i	$-0.0576711\pi$
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	−0.647865	+	0.761755i	$0.724338\pi$
$888$	18.0000	−	10.3923i	0.604040	−	0.348743i
$889$	6.50000	−	11.2583i	0.218003	−	0.377592i
$890$	5.00000			0.167600
$891$	18.0000			0.603023
$892$	17.0000			0.569202
$893$		0			0
$894$	4.50000	−	2.59808i	0.150503	−	0.0868927i
$895$	3.00000	+	5.19615i	0.100279	+	0.173688i
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$			5.19615i			0.173494i
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	−8.00000			−0.266815
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$	40.0000			1.33259
$902$	9.00000	−	15.5885i	0.299667	−	0.519039i
$903$	−12.0000	−	6.92820i	−0.399335	−	0.230556i
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$	−3.50000	−	6.06218i	−0.116344	−	0.201514i
$906$	15.0000	+	8.66025i	0.498342	+	0.287718i
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	−0.737700	−	0.675129i	$-0.764088\pi$
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	0.953529	+	0.301302i	$0.0974213\pi$
$908$	−4.00000			−0.132745
$909$	9.00000	+	15.5885i	0.298511	+	0.517036i
$910$	1.00000			0.0331497
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	−0.999994	−	0.00349271i	$-0.998888\pi$
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	0.503022	+	0.864274i	$0.332222\pi$
$912$		0			0
$913$	−11.0000	−	19.0526i	−0.364047	−	0.630548i
$914$	−8.00000	−	13.8564i	−0.264616	−	0.458329i
$915$	1.50000	−	0.866025i	0.0495885	−	0.0286299i
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$	−14.0000			−0.462321
$918$	18.0000	+	10.3923i	0.594089	+	0.342997i
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$	−28.5000	+	16.4545i	−0.939107	+	0.542194i
$922$	6.50000	+	11.2583i	0.214066	+	0.370773i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$			3.46410i			0.113961i
$925$	−2.00000	+	3.46410i	−0.0657596	+	0.113899i
$926$	36.0000			1.18303
$927$	48.0000			1.57653
$928$	5.00000			0.164133
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	−0.570045	−	0.821614i	$-0.693074\pi$
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	0.996561	+	0.0828661i	$0.0264074\pi$
$930$	−12.0000	−	6.92820i	−0.393496	−	0.227185i
$931$		0			0
$932$	2.00000	+	3.46410i	0.0655122	+	0.113470i
$933$	6.00000	+	3.46410i	0.196431	+	0.113410i
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	8.00000			0.261628
$936$	9.00000			0.294174
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	0.500000	−	0.866025i	0.0163256	−	0.0282767i
$939$			24.2487i			0.791327i
$940$	−6.50000	−	11.2583i	−0.212007	−	0.367206i
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	0.889439	−	0.457054i	$-0.151096\pi$
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	−0.840540	+	0.541749i	$0.817762\pi$
$942$	−27.0000	+	15.5885i	−0.879708	+	0.507899i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$	−6.00000			−0.195283
$945$		−	5.19615i		−	0.169031i
$946$	16.0000			0.520205
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	−0.889368	−	0.457193i	$-0.848855\pi$
$947$	−1.50000	+	2.59808i	−0.0487435	+	0.0844261i	0.840624	+	0.541619i	$0.182188\pi$
$948$	9.00000	−	5.19615i	0.292306	−	0.168763i
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$		0			0
$951$		−	31.1769i		−	1.01098i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	15.0000	+	25.9808i	0.485643	+	0.841158i
$955$	12.0000			0.388311
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	3.00000	+	1.73205i	0.0969762	+	0.0559893i
$958$	3.00000	+	5.19615i	0.0969256	+	0.167880i
$959$	8.00000	+	13.8564i	0.258333	+	0.447447i
$960$	10.5000	+	6.06218i	0.338886	+	0.195656i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	4.00000			0.128965
$963$	19.5000	−	33.7750i	0.628379	−	1.08838i
$964$	23.0000			0.740780
$965$	−1.00000	+	1.73205i	−0.0321911	+	0.0557567i
$966$		−	5.19615i		−	0.167183i
$967$	−21.5000	−	37.2391i	−0.691393	−	1.19753i	−0.971381	−	0.237525i	$-0.923664\pi$
$967$	−21.5000	−	37.2391i	−0.691393	−	1.19753i	0.279988	−	0.960003i	$-0.409669\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$		0			0
$970$	1.00000	−	1.73205i	0.0321081	−	0.0556128i
$971$	8.00000			0.256732			0.128366	−	0.991727i	$-0.459027\pi$
$971$	8.00000			0.256732			0.128366	+	0.991727i	$0.459027\pi$
$972$		−	15.5885i		−	0.500000i
$973$	12.0000			0.384702
$974$	−8.00000	+	13.8564i	−0.256337	+	0.443988i
$975$	−1.50000	+	0.866025i	−0.0480384	+	0.0277350i
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$			20.7846i			0.664619i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	−6.00000			−0.191663
$981$	1.50000	−	2.59808i	0.0478913	−	0.0829502i
$982$		0			0
$983$	15.5000	−	26.8468i	0.494373	−	0.856280i	−0.505606	−	0.862765i	$-0.668731\pi$
$983$	15.5000	−	26.8468i	0.494373	−	0.856280i	0.999979	+	0.00648510i	$0.00206429\pi$
$984$	−40.5000	−	23.3827i	−1.29109	−	0.745413i
$985$	−12.0000	−	20.7846i	−0.382352	−	0.662253i
$986$	2.00000	+	3.46410i	0.0636930	+	0.110319i
$987$	19.5000	+	11.2583i	0.620692	+	0.358357i
$988$		0			0
$989$	24.0000			0.763156
$990$	3.00000	+	5.19615i	0.0953463	+	0.165145i
$991$	30.0000			0.952981			0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000			0.952981			0.476491	+	0.879180i	$0.341909\pi$
$992$	20.0000	−	34.6410i	0.635001	−	1.09985i
$993$		−	31.1769i		−	0.989369i
$994$	3.00000	+	5.19615i	0.0951542	+	0.164812i
$995$	10.0000	+	17.3205i	0.317021	+	0.549097i
$996$	−16.5000	+	9.52628i	−0.522823	+	0.301852i
$997$	−25.0000	+	43.3013i	−0.791758	+	1.37136i	0.133120	+	0.991100i	$0.457501\pi$
$997$	−25.0000	+	43.3013i	−0.791758	+	1.37136i	−0.924878	+	0.380265i	$0.875833\pi$
$998$	20.0000			0.633089
$999$		−	20.7846i		−	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.c.196.1	✓	2
3.2	odd	2		1755.2.i.c.586.1		2
9.2	odd	6		5265.2.a.l.1.1		1
9.4	even	3	inner	585.2.i.c.391.1	yes	2
9.5	odd	6		1755.2.i.c.1171.1		2
9.7	even	3		5265.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.c.196.1	✓	2	1.1	even	1	trivial
585.2.i.c.391.1	yes	2	9.4	even	3	inner
1755.2.i.c.586.1		2	3.2	odd	2
1755.2.i.c.1171.1		2	9.5	odd	6
5265.2.a.d.1.1		1	9.7	even	3
5265.2.a.l.1.1		1	9.2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.50000 + 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +(-0.500000 + 0.866025i) q^{20} -1.73205i q^{21} +(1.00000 + 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(4.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} +(1.50000 - 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(2.50000 + 4.33013i) q^{32} +3.46410i q^{33} +(-2.00000 + 3.46410i) q^{34} +1.00000 q^{35} +3.00000 q^{36} +4.00000 q^{37} +(1.50000 + 0.866025i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-1.50000 - 0.866025i) q^{42} +(4.00000 - 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-6.50000 + 11.2583i) q^{47} -1.73205i q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-6.00000 + 3.46410i) q^{51} +(-0.500000 + 0.866025i) q^{52} -10.0000 q^{53} +(-4.50000 - 2.59808i) q^{54} -2.00000 q^{55} +(1.50000 - 2.59808i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(-3.00000 - 5.19615i) q^{59} +1.73205i q^{60} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{62} +(-1.50000 - 2.59808i) q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(3.00000 + 1.73205i) q^{66} +(0.500000 + 0.866025i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(4.50000 + 2.59808i) q^{69} +(0.500000 - 0.866025i) q^{70} -6.00000 q^{71} +(4.50000 - 7.79423i) q^{72} -12.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +1.73205i q^{75} +(1.00000 + 1.73205i) q^{77} +(1.50000 - 0.866025i) q^{78} +(3.00000 - 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(-5.50000 + 9.52628i) q^{83} +(1.50000 - 0.866025i) q^{84} +(-2.00000 - 3.46410i) q^{85} +(-4.00000 - 6.92820i) q^{86} -1.73205i q^{87} +(-3.00000 + 5.19615i) q^{88} +5.00000 q^{89} +(1.50000 - 2.59808i) q^{90} +1.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(-12.0000 - 6.92820i) q^{93} +(6.50000 + 11.2583i) q^{94} +(7.50000 + 4.33013i) q^{96} +(1.00000 - 1.73205i) q^{97} +6.00000 q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 + q^4 + q^5 + q^7 + 6 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} + 3 q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} - 8 q^{17} - 3 q^{18} - q^{20} + 2 q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 2 q^{26} + 2 q^{28} + q^{29} + 3 q^{30} - 8 q^{31} + 5 q^{32} - 4 q^{34} + 2 q^{35} + 6 q^{36} + 8 q^{37} + 3 q^{39} + 3 q^{40} - 9 q^{41} - 3 q^{42} + 8 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} - 13 q^{47} + 6 q^{49} + q^{50} - 12 q^{51} - q^{52} - 20 q^{53} - 9 q^{54} - 4 q^{55} + 3 q^{56} - q^{58} - 6 q^{59} + q^{61} - 16 q^{62} - 3 q^{63} + 14 q^{64} - q^{65} + 6 q^{66} + q^{67} - 4 q^{68} + 9 q^{69} + q^{70} - 12 q^{71} + 9 q^{72} - 24 q^{73} + 4 q^{74} + 2 q^{77} + 3 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} - 18 q^{82} - 11 q^{83} + 3 q^{84} - 4 q^{85} - 8 q^{86} - 6 q^{88} + 10 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} - 24 q^{93} + 13 q^{94} + 15 q^{96} + 2 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 + q^4 + q^5 + q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 - 2 * q^11 + 3 * q^12 + q^13 - q^14 + 3 * q^15 + q^16 - 8 * q^17 - 3 * q^18 - q^20 + 2 * q^22 + 3 * q^23 + 9 * q^24 - q^25 + 2 * q^26 + 2 * q^28 + q^29 + 3 * q^30 - 8 * q^31 + 5 * q^32 - 4 * q^34 + 2 * q^35 + 6 * q^36 + 8 * q^37 + 3 * q^39 + 3 * q^40 - 9 * q^41 - 3 * q^42 + 8 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 - 13 * q^47 + 6 * q^49 + q^50 - 12 * q^51 - q^52 - 20 * q^53 - 9 * q^54 - 4 * q^55 + 3 * q^56 - q^58 - 6 * q^59 + q^61 - 16 * q^62 - 3 * q^63 + 14 * q^64 - q^65 + 6 * q^66 + q^67 - 4 * q^68 + 9 * q^69 + q^70 - 12 * q^71 + 9 * q^72 - 24 * q^73 + 4 * q^74 + 2 * q^77 + 3 * q^78 + 6 * q^79 + 2 * q^80 - 9 * q^81 - 18 * q^82 - 11 * q^83 + 3 * q^84 - 4 * q^85 - 8 * q^86 - 6 * q^88 + 10 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 - 24 * q^93 + 13 * q^94 + 15 * q^96 + 2 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

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