LMFDB - Embedded newform 570.2.i.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
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			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.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)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +1.00000 q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.00000 q^{37} +(3.50000 - 2.59808i) q^{38} -2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(1.50000 - 2.59808i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-0.500000 + 0.866025i) q^{44} -1.00000 q^{45} +1.00000 q^{46} +(0.500000 - 0.866025i) q^{48} +2.00000 q^{49} +1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{55} +3.00000 q^{56} +(-3.50000 + 2.59808i) q^{57} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(0.500000 - 0.866025i) q^{66} +(1.00000 - 1.73205i) q^{67} +2.00000 q^{68} -1.00000 q^{69} +(1.50000 - 2.59808i) q^{70} +(-4.00000 - 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-4.50000 - 7.79423i) q^{74} -1.00000 q^{75} +(-4.00000 - 1.73205i) q^{76} +3.00000 q^{77} +(1.00000 + 1.73205i) q^{78} +(-7.00000 - 12.1244i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +6.00000 q^{83} -3.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} +1.00000 q^{88} +(2.50000 - 4.33013i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-3.00000 + 5.19615i) q^{91} +(-0.500000 - 0.866025i) q^{92} +(2.00000 + 3.46410i) q^{93} +(-3.50000 + 2.59808i) q^{95} -1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-1.00000 - 1.73205i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + q^5 + q^6 + 6 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6 q^{7} + 2 q^{8} - q^{9} + q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} - q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} + 3 q^{21} - q^{22} - q^{23} + q^{24} - q^{25} + 4 q^{26} - 2 q^{27} - 3 q^{28} + 2 q^{30} + 8 q^{31} - q^{32} + q^{33} - 2 q^{34} + 3 q^{35} - q^{36} + 18 q^{37} + 7 q^{38} - 4 q^{39} + q^{40} - q^{41} + 3 q^{42} + 10 q^{43} - q^{44} - 2 q^{45} + 2 q^{46} + q^{48} + 4 q^{49} + 2 q^{50} + 2 q^{51} - 2 q^{52} - 3 q^{53} + q^{54} + q^{55} + 6 q^{56} - 7 q^{57} - 12 q^{59} - q^{60} + 2 q^{61} - 4 q^{62} - 3 q^{63} + 2 q^{64} - 4 q^{65} + q^{66} + 2 q^{67} + 4 q^{68} - 2 q^{69} + 3 q^{70} - 8 q^{71} - q^{72} + 12 q^{73} - 9 q^{74} - 2 q^{75} - 8 q^{76} + 6 q^{77} + 2 q^{78} - 14 q^{79} + q^{80} - q^{81} - q^{82} + 12 q^{83} - 6 q^{84} + 2 q^{85} + 10 q^{86} + 2 q^{88} + 5 q^{89} + q^{90} - 6 q^{91} - q^{92} + 4 q^{93} - 7 q^{95} - 2 q^{96} - 8 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^5 + q^6 + 6 * q^7 + 2 * q^8 - q^9 + q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 - q^15 - q^16 - 2 * q^17 + 2 * q^18 + q^19 - 2 * q^20 + 3 * q^21 - q^22 - q^23 + q^24 - q^25 + 4 * q^26 - 2 * q^27 - 3 * q^28 + 2 * q^30 + 8 * q^31 - q^32 + q^33 - 2 * q^34 + 3 * q^35 - q^36 + 18 * q^37 + 7 * q^38 - 4 * q^39 + q^40 - q^41 + 3 * q^42 + 10 * q^43 - q^44 - 2 * q^45 + 2 * q^46 + q^48 + 4 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 - 3 * q^53 + q^54 + q^55 + 6 * q^56 - 7 * q^57 - 12 * q^59 - q^60 + 2 * q^61 - 4 * q^62 - 3 * q^63 + 2 * q^64 - 4 * q^65 + q^66 + 2 * q^67 + 4 * q^68 - 2 * q^69 + 3 * q^70 - 8 * q^71 - q^72 + 12 * q^73 - 9 * q^74 - 2 * q^75 - 8 * q^76 + 6 * q^77 + 2 * q^78 - 14 * q^79 + q^80 - q^81 - q^82 + 12 * q^83 - 6 * q^84 + 2 * q^85 + 10 * q^86 + 2 * q^88 + 5 * q^89 + q^90 - 6 * q^91 - q^92 + 4 * q^93 - 7 * q^95 - 2 * q^96 - 8 * q^97 - 2 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	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
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.00000			−0.288675
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.50000	−	2.59808i	−0.400892	−	0.694365i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	1.00000			0.235702
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$20$	−1.00000			−0.223607
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000			0.392232
$27$	−1.00000			−0.192450
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	1.00000			0.182574
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.00000			1.47959			0.739795	−	0.672832i	$-0.234922\pi$
$37$	9.00000			1.47959			0.739795	+	0.672832i	$0.234922\pi$
$38$	3.50000	−	2.59808i	0.567775	−	0.421464i
$39$	−2.00000			−0.320256
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$	1.50000	−	2.59808i	0.231455	−	0.400892i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−1.00000			−0.149071
$46$	1.00000			0.147442
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	2.00000			0.285714
$50$	1.00000			0.141421
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.500000	+	0.866025i	0.0674200	+	0.116775i
$56$	3.00000			0.400892
$57$	−3.50000	+	2.59808i	−0.463586	+	0.344124i
$58$		0			0
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.50000	+	2.59808i	−0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$	0.500000	−	0.866025i	0.0615457	−	0.106600i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.00000			0.242536
$69$	−1.00000			−0.120386
$70$	1.50000	−	2.59808i	0.179284	−	0.310530i
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	0.524868	−	0.851184i	$-0.324115\pi$
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	−0.999581	+	0.0289572i	$0.990781\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	0.967676	+	0.252197i	$0.0811531\pi$
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	−0.265429	+	0.964130i	$0.585514\pi$
$74$	−4.50000	−	7.79423i	−0.523114	−	0.906061i
$75$	−1.00000			−0.115470
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	3.00000			0.341882
$78$	1.00000	+	1.73205i	0.113228	+	0.196116i
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.500000	+	0.866025i	−0.0552158	+	0.0956365i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−3.00000			−0.327327
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$		0			0
$88$	1.00000			0.106600
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	−0.702564	−	0.711621i	$-0.747962\pi$
$89$	2.50000	−	4.33013i	0.264999	−	0.458993i	0.967563	+	0.252628i	$0.0812949\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−3.00000	+	5.19615i	−0.314485	+	0.544705i
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	−3.50000	+	2.59808i	−0.359092	+	0.266557i
$96$	−1.00000			−0.102062
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$	−2.00000			−0.198030
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	−1.50000	+	2.59808i	−0.146385	+	0.253546i
$106$	3.00000			0.291386
$107$	−10.0000			−0.966736			−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	3.00000	+	5.19615i	0.287348	+	0.497701i	−0.685828	+	0.727764i	$0.740560\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$	−1.50000	−	2.59808i	−0.141737	−	0.245495i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	4.00000	+	1.73205i	0.374634	+	0.162221i
$115$	−1.00000			−0.0932505
$116$		0			0
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−10.0000			−0.909091
$122$	−2.00000			−0.181071
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$	3.00000			0.267261
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.803365	−	0.595487i	$-0.796959\pi$
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.114024	−	0.993478i	$-0.536374\pi$
$132$	−1.00000			−0.0870388
$133$	1.50000	+	12.9904i	0.130066	+	1.12641i
$134$	−2.00000			−0.172774
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	−3.00000			−0.253546
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$	1.00000			0.0833333
$145$		0			0
$146$	6.00000	−	10.3923i	0.496564	−	0.860073i
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$	−4.50000	+	7.79423i	−0.369898	+	0.640682i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$	0.500000	+	4.33013i	0.0405554	+	0.351220i
$153$	2.00000			0.161690
$154$	−1.50000	−	2.59808i	−0.120873	−	0.209359i
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	−7.00000	+	12.1244i	−0.556890	+	0.964562i
$159$	−3.00000			−0.237915
$160$	−1.00000			−0.0790569
$161$	−1.50000	+	2.59808i	−0.118217	+	0.204757i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	1.00000			0.0780869
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	1.50000	+	2.59808i	0.115728	+	0.200446i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−2.00000			−0.153393
$171$	−4.00000	−	1.73205i	−0.305888	−	0.132453i
$172$	−10.0000			−0.762493
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	0.577597	−	0.816322i	$-0.303991\pi$
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	−0.995754	+	0.0920525i	$0.970657\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	6.00000	−	10.3923i	0.450988	−	0.781133i
$178$	−5.00000			−0.374766
$179$	−13.0000			−0.971666			−0.485833	−	0.874052i	$-0.661484\pi$
$179$	−13.0000			−0.971666			−0.485833	+	0.874052i	$0.661484\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$181$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$182$	6.00000			0.444750
$183$	2.00000			0.147844
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	4.50000	+	7.79423i	0.330847	+	0.573043i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$		0			0
$189$	−3.00000			−0.218218
$190$	4.00000	+	1.73205i	0.290191	+	0.125656i
$191$	−10.0000			−0.723575			−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000			−0.723575			−0.361787	+	0.932261i	$0.617833\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−4.00000	+	6.92820i	−0.287183	+	0.497416i
$195$	−1.00000	−	1.73205i	−0.0716115	−	0.124035i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	5.00000			0.356235			0.178118	−	0.984009i	$-0.442999\pi$
$197$	5.00000			0.356235			0.178118	+	0.984009i	$0.442999\pi$
$198$	1.00000			0.0710669
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	−0.347879	−	0.937539i	$-0.613098\pi$
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	0.985873	−	0.167497i	$-0.0535685\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	2.00000			0.141069
$202$	−2.00000			−0.140720
$203$		0			0
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$	0.500000	−	0.866025i	0.0349215	−	0.0604858i
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	2.00000			0.138675
$209$	0.500000	+	4.33013i	0.0345857	+	0.299521i
$210$	3.00000			0.207020
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	4.00000	−	6.92820i	0.274075	−	0.474713i
$214$	5.00000	+	8.66025i	0.341793	+	0.592003i
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$	−1.00000			−0.0680414
$217$	12.0000			0.814613
$218$	3.00000	−	5.19615i	0.203186	−	0.351928i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−1.00000			−0.0674200
$221$	4.00000			0.269069
$222$	4.50000	−	7.79423i	0.302020	−	0.523114i
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	0.811422	−	0.584461i	$-0.198694\pi$
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	−0.911869	+	0.410481i	$0.865361\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	28.0000			1.85843			0.929213	−	0.369546i	$-0.120487\pi$
$227$	28.0000			1.85843			0.929213	+	0.369546i	$0.120487\pi$
$228$	−0.500000	−	4.33013i	−0.0331133	−	0.286770i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	0.500000	+	0.866025i	0.0329690	+	0.0571040i
$231$	1.50000	+	2.59808i	0.0986928	+	0.170941i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$		0			0
$236$	12.0000			0.781133
$237$	7.00000	−	12.1244i	0.454699	−	0.787562i
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	1.00000			0.0645497
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	−1.00000			−0.0637577
$247$	−8.00000	−	3.46410i	−0.509028	−	0.220416i
$248$	4.00000			0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.0364441	+	0.999336i	$0.511603\pi$
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.847228	+	0.531229i	$0.821730\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$	−0.500000	+	0.866025i	−0.0314347	+	0.0544466i
$254$	−1.00000			−0.0627456
$255$	2.00000			0.125245
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	10.0000			0.622573
$259$	27.0000			1.67770
$260$	1.00000	−	1.73205i	0.0620174	−	0.107417i
$261$		0			0
$262$	−10.5000	+	18.1865i	−0.648692	+	1.12357i
$263$	12.5000	+	21.6506i	0.770783	+	1.33504i	0.937134	+	0.348969i	$0.113468\pi$
$263$	12.5000	+	21.6506i	0.770783	+	1.33504i	−0.166351	+	0.986067i	$0.553199\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	−3.00000			−0.184289
$266$	10.5000	−	7.79423i	0.643796	−	0.477895i
$267$	5.00000			0.305995
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$	−6.00000			−0.363137
$274$	4.00000			0.241649
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	22.0000			1.32185			0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000			1.32185			0.660926	+	0.750451i	$0.270164\pi$
$278$	−20.0000			−1.19952
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	−0.361895	−	0.932219i	$-0.617870\pi$
$281$	10.5000	−	18.1865i	0.626377	−	1.08492i	0.988273	−	0.152699i	$-0.0487965\pi$
$282$		0			0
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	8.00000			0.474713
$285$	−4.00000	−	1.73205i	−0.236940	−	0.102598i
$286$	2.00000			0.118262
$287$	−1.50000	−	2.59808i	−0.0885422	−	0.153360i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$	−12.0000			−0.702247
$293$	1.00000			0.0584206			0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000			0.0584206			0.0292103	+	0.999573i	$0.490701\pi$
$294$	1.00000	−	1.73205i	0.0583212	−	0.101015i
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	9.00000			0.523114
$297$	−1.00000			−0.0580259
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	9.00000	+	15.5885i	0.517892	+	0.897015i
$303$	2.00000			0.114897
$304$	3.50000	−	2.59808i	0.200739	−	0.149010i
$305$	2.00000			0.114520
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	−1.50000	+	2.59808i	−0.0854704	+	0.148039i
$309$	−6.50000	−	11.2583i	−0.369772	−	0.640464i
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$	−2.00000			−0.113228
$313$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$313$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$314$	−3.50000	+	6.06218i	−0.197516	+	0.342108i
$315$	−3.00000			−0.169031
$316$	14.0000			0.787562
$317$	−3.50000	+	6.06218i	−0.196580	+	0.340486i	−0.947417	−	0.320001i	$-0.896317\pi$
$317$	−3.50000	+	6.06218i	−0.196580	+	0.340486i	0.750838	+	0.660487i	$0.229650\pi$
$318$	1.50000	+	2.59808i	0.0841158	+	0.145693i
$319$		0			0
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−5.00000	−	8.66025i	−0.279073	−	0.483368i
$322$	3.00000			0.167183
$323$	7.00000	−	5.19615i	0.389490	−	0.289122i
$324$	1.00000			0.0555556
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$	−0.500000	−	0.866025i	−0.0276079	−	0.0478183i
$329$		0			0
$330$	1.00000			0.0550482
$331$	13.0000			0.714545			0.357272	−	0.934000i	$-0.383707\pi$
$331$	13.0000			0.714545			0.357272	+	0.934000i	$0.383707\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	−4.50000	+	7.79423i	−0.246598	+	0.427121i
$334$	3.00000			0.164153
$335$	2.00000			0.109272
$336$	1.50000	−	2.59808i	0.0818317	−	0.141737i
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	0.837503	−	0.546433i	$-0.184015\pi$
$337$	−1.00000	−	1.73205i	−0.0544735	−	0.0943508i	−0.891976	+	0.452082i	$0.850681\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	5.00000	+	8.66025i	0.271563	+	0.470360i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	4.00000			0.216612
$342$	0.500000	+	4.33013i	0.0270369	+	0.234146i
$343$	−15.0000			−0.809924
$344$	5.00000	+	8.66025i	0.269582	+	0.466930i
$345$	−0.500000	−	0.866025i	−0.0269191	−	0.0466252i
$346$	−5.50000	+	9.52628i	−0.295682	+	0.512136i
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	3.00000			0.160357
$351$	1.00000	−	1.73205i	0.0533761	−	0.0924500i
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	26.0000			1.38384			0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000			1.38384			0.691920	+	0.721974i	$0.256765\pi$
$354$	−12.0000			−0.637793
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	2.50000	+	4.33013i	0.132500	+	0.229496i
$357$	3.00000	−	5.19615i	0.158777	−	0.275010i
$358$	6.50000	+	11.2583i	0.343536	+	0.595021i
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	0.663123	−	0.748511i	$-0.269231\pi$
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	−0.979791	+	0.200026i	$0.935897\pi$
$360$	−1.00000			−0.0527046
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		0			0
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$	−3.00000	−	5.19615i	−0.157243	−	0.272352i
$365$	−6.00000	+	10.3923i	−0.314054	+	0.543958i
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	1.00000			0.0521286
$369$	1.00000			0.0520579
$370$	4.50000	−	7.79423i	0.233944	−	0.405203i
$371$	−4.50000	+	7.79423i	−0.233628	+	0.404656i
$372$	−4.00000			−0.207390
$373$	−37.0000			−1.91579			−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000			−1.91579			−0.957894	+	0.287123i	$0.907301\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$		0			0
$378$	1.50000	+	2.59808i	0.0771517	+	0.133631i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−0.500000	−	4.33013i	−0.0256495	−	0.222131i
$381$	1.00000			0.0512316
$382$	5.00000	+	8.66025i	0.255822	+	0.443097i
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$	−10.0000			−0.508329
$388$	8.00000			0.406138
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	−0.949432	−	0.313972i	$-0.898340\pi$
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	0.746624	+	0.665246i	$0.231673\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$	2.00000			0.101144
$392$	2.00000			0.101015
$393$	10.5000	−	18.1865i	0.529655	−	0.917389i
$394$	−2.50000	−	4.33013i	−0.125948	−	0.218149i
$395$	7.00000	−	12.1244i	0.352208	−	0.610043i
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	−18.0000			−0.902258
$399$	−10.5000	+	7.79423i	−0.525657	+	0.390199i
$400$	1.00000			0.0500000
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$	−1.00000	−	1.73205i	−0.0498755	−	0.0863868i
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	1.00000	+	1.73205i	0.0497519	+	0.0861727i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	9.00000			0.446113
$408$	1.00000	−	1.73205i	0.0495074	−	0.0857493i
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	0.480560	+	0.876962i	$0.340434\pi$
$409$	−10.5000	+	18.1865i	−0.519192	+	0.899266i	−0.999751	+	0.0223042i	$0.992900\pi$
$410$	−1.00000			−0.0493865
$411$	−4.00000			−0.197305
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	−18.0000	−	31.1769i	−0.885722	−	1.53412i
$414$	−0.500000	+	0.866025i	−0.0245737	+	0.0425628i
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	20.0000			0.979404
$418$	3.50000	−	2.59808i	0.171191	−	0.127076i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$	−1.50000	−	2.59808i	−0.0731925	−	0.126773i
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	−11.5000	+	19.9186i	−0.559811	+	0.969622i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	2.00000			0.0970143
$426$	−8.00000			−0.387601
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	5.00000	−	8.66025i	0.241684	−	0.418609i
$429$	−2.00000			−0.0965609
$430$	10.0000			0.482243
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.108586	+	0.994087i	$0.534632\pi$
$431$	−19.0000	+	32.9090i	−0.915198	+	1.58517i	−0.806611	+	0.591082i	$0.798701\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	−0.991693	−	0.128624i	$-0.958944\pi$
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	0.607238	+	0.794520i	$0.292277\pi$
$434$	−6.00000	−	10.3923i	−0.288009	−	0.498847i
$435$		0			0
$436$	−6.00000			−0.287348
$437$	−4.00000	−	1.73205i	−0.191346	−	0.0828552i
$438$	12.0000			0.573382
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	−0.962607	−	0.270901i	$-0.912678\pi$
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	0.246696	−	0.969093i	$-0.420655\pi$
$440$	0.500000	+	0.866025i	0.0238366	+	0.0412861i
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$	−2.00000	−	3.46410i	−0.0951303	−	0.164771i
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	0.477028	+	0.878888i	$0.341714\pi$
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	−0.999653	+	0.0263261i	$0.991619\pi$
$444$	−9.00000			−0.427121
$445$	5.00000			0.237023
$446$	−1.50000	+	2.59808i	−0.0710271	+	0.123022i
$447$	−3.00000	+	5.19615i	−0.141895	+	0.245770i
$448$	3.00000			0.141737
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−0.500000	−	0.866025i	−0.0235441	−	0.0407795i
$452$	−5.00000	+	8.66025i	−0.235180	+	0.407344i
$453$	−9.00000	−	15.5885i	−0.422857	−	0.732410i
$454$	−14.0000	−	24.2487i	−0.657053	−	1.13805i
$455$	−6.00000			−0.281284
$456$	−3.50000	+	2.59808i	−0.163903	+	0.121666i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	0.500000	−	0.866025i	0.0233126	−	0.0403786i
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	−0.999898	−	0.0142861i	$-0.995452\pi$
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	0.487577	−	0.873080i	$-0.337881\pi$
$462$	1.50000	−	2.59808i	0.0697863	−	0.120873i
$463$	−25.0000			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$463$	−25.0000			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$464$		0			0
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	32.0000			1.48078			0.740392	−	0.672176i	$-0.234640\pi$
$467$	32.0000			1.48078			0.740392	+	0.672176i	$0.234640\pi$
$468$	2.00000			0.0924500
$469$	3.00000	−	5.19615i	0.138527	−	0.239936i
$470$		0			0
$471$	3.50000	−	6.06218i	0.161271	−	0.279330i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	−14.0000			−0.643041
$475$	−4.00000	−	1.73205i	−0.183533	−	0.0794719i
$476$	6.00000			0.275010
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−9.00000	+	15.5885i	−0.410365	+	0.710772i
$482$	−10.0000			−0.455488
$483$	−3.00000			−0.136505
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$	−1.00000			−0.0453609
$487$	−41.0000			−1.85789			−0.928944	−	0.370221i	$-0.879282\pi$
$487$	−41.0000			−1.85789			−0.928944	+	0.370221i	$0.879282\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	1.00000	+	1.73205i	0.0452216	+	0.0783260i
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$	0.500000	+	0.866025i	0.0225417	+	0.0390434i
$493$		0			0
$494$	1.00000	+	8.66025i	0.0449921	+	0.389643i
$495$	−1.00000			−0.0449467
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	0.647882	−	0.761741i	$-0.275655\pi$
$499$	−7.50000	−	12.9904i	−0.335746	−	0.581529i	−0.983628	+	0.180212i	$0.942322\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−3.00000			−0.134030
$502$	28.0000			1.24970
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	−0.748091	−	0.663596i	$-0.769030\pi$
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	0.948736	+	0.316068i	$0.102363\pi$
$504$	−1.50000	+	2.59808i	−0.0668153	+	0.115728i
$505$	2.00000			0.0889988
$506$	1.00000			0.0444554
$507$	−4.50000	+	7.79423i	−0.199852	+	0.346154i
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$	−1.00000	−	1.73205i	−0.0442807	−	0.0766965i
$511$	18.0000	+	31.1769i	0.796273	+	1.37919i
$512$	1.00000			0.0441942
$513$	−0.500000	−	4.33013i	−0.0220755	−	0.191180i
$514$	2.00000			0.0882162
$515$	−6.50000	−	11.2583i	−0.286424	−	0.496101i
$516$	−5.00000	−	8.66025i	−0.220113	−	0.381246i
$517$		0			0
$518$	−13.5000	−	23.3827i	−0.593156	−	1.02738i
$519$	5.50000	−	9.52628i	0.241423	−	0.418157i
$520$	−2.00000			−0.0877058
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	−0.268963	−	0.963150i	$-0.586681\pi$
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	0.968594	−	0.248646i	$-0.0799857\pi$
$524$	21.0000			0.917389
$525$	−3.00000			−0.130931
$526$	12.5000	−	21.6506i	0.545026	−	0.944013i
$527$	−4.00000	−	6.92820i	−0.174243	−	0.301797i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	1.50000	+	2.59808i	0.0651558	+	0.112853i
$531$	12.0000			0.520756
$532$	−12.0000	−	5.19615i	−0.520266	−	0.225282i
$533$	2.00000			0.0866296
$534$	−2.50000	−	4.33013i	−0.108186	−	0.187383i
$535$	−5.00000	−	8.66025i	−0.216169	−	0.374415i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	−6.50000	−	11.2583i	−0.280496	−	0.485833i
$538$	7.00000	−	12.1244i	0.301791	−	0.522718i
$539$	2.00000			0.0861461
$540$	1.00000			0.0430331
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$		0			0
$544$	2.00000			0.0857493
$545$	−3.00000	+	5.19615i	−0.128506	+	0.222579i
$546$	3.00000	+	5.19615i	0.128388	+	0.222375i
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	−0.886612	−	0.462514i	$-0.846947\pi$
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	0.843855	+	0.536571i	$0.180281\pi$
$548$	−2.00000	−	3.46410i	−0.0854358	−	0.147979i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	1.00000			0.0426401
$551$		0			0
$552$	−1.00000			−0.0425628
$553$	−21.0000	−	36.3731i	−0.893011	−	1.54674i
$554$	−11.0000	−	19.0526i	−0.467345	−	0.809466i
$555$	−4.50000	+	7.79423i	−0.191014	+	0.330847i
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$	4.00000			0.169334
$559$	−20.0000			−0.845910
$560$	1.50000	−	2.59808i	0.0633866	−	0.109789i
$561$	1.00000	−	1.73205i	0.0422200	−	0.0731272i
$562$	−21.0000			−0.885832
$563$	28.0000			1.18006			0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000			1.18006			0.590030	+	0.807382i	$0.299116\pi$
$564$		0			0
$565$	5.00000	+	8.66025i	0.210352	+	0.364340i
$566$	−1.00000	+	1.73205i	−0.0420331	+	0.0728035i
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$	−4.00000	−	6.92820i	−0.167836	−	0.290701i
$569$	31.0000			1.29959			0.649794	−	0.760111i	$-0.274855\pi$
$569$	31.0000			1.29959			0.649794	+	0.760111i	$0.274855\pi$
$570$	0.500000	+	4.33013i	0.0209427	+	0.181369i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$	−5.00000	−	8.66025i	−0.208878	−	0.361787i
$574$	−1.50000	+	2.59808i	−0.0626088	+	0.108442i
$575$	−0.500000	−	0.866025i	−0.0208514	−	0.0361158i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	42.0000			1.74848			0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000			1.74848			0.874241	+	0.485491i	$0.161359\pi$
$578$	−13.0000			−0.540729
$579$	7.00000	−	12.1244i	0.290910	−	0.503871i
$580$		0			0
$581$	18.0000			0.746766
$582$	−8.00000			−0.331611
$583$	−1.50000	+	2.59808i	−0.0621237	+	0.107601i
$584$	6.00000	+	10.3923i	0.248282	+	0.430037i
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−0.500000	−	0.866025i	−0.0206548	−	0.0357752i
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$	−2.00000			−0.0824786
$589$	2.00000	+	17.3205i	0.0824086	+	0.713679i
$590$	−12.0000			−0.494032
$591$	2.50000	+	4.33013i	0.102836	+	0.178118i
$592$	−4.50000	−	7.79423i	−0.184949	−	0.320341i
$593$	22.0000	−	38.1051i	0.903432	−	1.56479i	0.0804231	−	0.996761i	$-0.474373\pi$
$593$	22.0000	−	38.1051i	0.903432	−	1.56479i	0.823009	−	0.568029i	$-0.192294\pi$
$594$	0.500000	+	0.866025i	0.0205152	+	0.0355335i
$595$	3.00000	−	5.19615i	0.122988	−	0.213021i
$596$	−6.00000			−0.245770
$597$	18.0000			0.736691
$598$	−1.00000	+	1.73205i	−0.0408930	+	0.0708288i
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	0.275714	+	0.961240i	$0.411086\pi$
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	−0.970315	+	0.241845i	$0.922248\pi$
$600$	−1.00000			−0.0408248
$601$	25.0000			1.01977			0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000			1.01977			0.509886	+	0.860242i	$0.329688\pi$
$602$	15.0000	−	25.9808i	0.611354	−	1.05890i
$603$	1.00000	+	1.73205i	0.0407231	+	0.0705346i
$604$	9.00000	−	15.5885i	0.366205	−	0.634285i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$	−1.00000	−	1.73205i	−0.0406222	−	0.0703598i
$607$	−5.00000			−0.202944			−0.101472	−	0.994838i	$-0.532355\pi$
$607$	−5.00000			−0.202944			−0.101472	+	0.994838i	$0.532355\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$		0			0
$610$	−1.00000	−	1.73205i	−0.0404888	−	0.0701287i
$611$		0			0
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	0.955458	−	0.295126i	$-0.0953615\pi$
$613$	5.50000	+	9.52628i	0.222143	+	0.384763i	−0.733316	+	0.679888i	$0.762028\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$	1.00000			0.0403239
$616$	3.00000			0.120873
$617$	−8.00000	+	13.8564i	−0.322068	+	0.557838i	−0.980915	−	0.194439i	$-0.937711\pi$
$617$	−8.00000	+	13.8564i	−0.322068	+	0.557838i	0.658847	+	0.752277i	$0.271045\pi$
$618$	−6.50000	+	11.2583i	−0.261468	+	0.452876i
$619$	13.0000			0.522514			0.261257	−	0.965269i	$-0.415863\pi$
$619$	13.0000			0.522514			0.261257	+	0.965269i	$0.415863\pi$
$620$	−4.00000			−0.160644
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	8.00000	+	13.8564i	0.320771	+	0.555591i
$623$	7.50000	−	12.9904i	0.300481	−	0.520449i
$624$	1.00000	+	1.73205i	0.0400320	+	0.0693375i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.50000	+	2.59808i	−0.139777	+	0.103757i
$628$	7.00000			0.279330
$629$	−9.00000	−	15.5885i	−0.358854	−	0.621552i
$630$	1.50000	+	2.59808i	0.0597614	+	0.103510i
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$	−7.00000	−	12.1244i	−0.278445	−	0.482281i
$633$	11.5000	−	19.9186i	0.457084	−	0.791693i
$634$	7.00000			0.278006
$635$	1.00000			0.0396838
$636$	1.50000	−	2.59808i	0.0594789	−	0.103020i
$637$	−2.00000	+	3.46410i	−0.0792429	+	0.137253i
$638$		0			0
$639$	8.00000			0.316475
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$	−5.00000	+	8.66025i	−0.197334	+	0.341793i
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$	−10.0000			−0.393750
$646$	−8.00000	−	3.46410i	−0.314756	−	0.136293i
$647$	−39.0000			−1.53325			−0.766624	−	0.642096i	$-0.778065\pi$
$647$	−39.0000			−1.53325			−0.766624	+	0.642096i	$0.778065\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$	6.00000	+	10.3923i	0.235159	+	0.407307i
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	9.00000			0.352197			0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000			0.352197			0.176099	+	0.984373i	$0.443652\pi$
$654$	6.00000			0.234619
$655$	10.5000	−	18.1865i	0.410269	−	0.710607i
$656$	−0.500000	+	0.866025i	−0.0195217	+	0.0338126i
$657$	−12.0000			−0.468165
$658$		0			0
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$	−0.500000	−	0.866025i	−0.0194625	−	0.0337100i
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$	−6.50000	−	11.2583i	−0.252630	−	0.437567i
$663$	2.00000	+	3.46410i	0.0776736	+	0.134535i
$664$	6.00000			0.232845
$665$	−10.5000	+	7.79423i	−0.407173	+	0.302247i
$666$	9.00000			0.348743
$667$		0			0
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	1.50000	−	2.59808i	0.0579934	−	0.100447i
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	1.00000	−	1.73205i	0.0386046	−	0.0668651i
$672$	−3.00000			−0.115728
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−9.00000			−0.346154
$677$	−39.0000			−1.49889			−0.749446	−	0.662066i	$-0.769680\pi$
$677$	−39.0000			−1.49889			−0.749446	+	0.662066i	$0.769680\pi$
$678$	5.00000	−	8.66025i	0.192024	−	0.332595i
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$	1.00000	−	1.73205i	0.0383482	−	0.0664211i
$681$	14.0000	+	24.2487i	0.536481	+	0.929213i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$	3.50000	−	2.59808i	0.133826	−	0.0993399i
$685$	−4.00000			−0.152832
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$	7.00000	+	12.1244i	0.267067	+	0.462573i
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$	−0.500000	+	0.866025i	−0.0190347	+	0.0329690i
$691$	23.0000			0.874961			0.437481	−	0.899228i	$-0.355871\pi$
$691$	23.0000			0.874961			0.437481	+	0.899228i	$0.355871\pi$
$692$	11.0000			0.418157
$693$	−1.50000	+	2.59808i	−0.0569803	+	0.0986928i
$694$	−9.00000	+	15.5885i	−0.341635	+	0.591730i
$695$	20.0000			0.758643
$696$		0			0
$697$	−1.00000	+	1.73205i	−0.0378777	+	0.0656061i
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	21.0000	+	36.3731i	0.793159	+	1.37379i	0.924002	+	0.382389i	$0.124898\pi$
$701$	21.0000	+	36.3731i	0.793159	+	1.37379i	−0.130843	+	0.991403i	$0.541768\pi$
$702$	−2.00000			−0.0754851
$703$	4.50000	+	38.9711i	0.169721	+	1.46982i
$704$	1.00000			0.0376889
$705$		0			0
$706$	−13.0000	−	22.5167i	−0.489261	−	0.847426i
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$	6.00000	+	10.3923i	0.225494	+	0.390567i
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	−8.00000			−0.300235
$711$	14.0000			0.525041
$712$	2.50000	−	4.33013i	0.0936915	−	0.162278i
$713$	−2.00000	+	3.46410i	−0.0749006	+	0.129732i
$714$	−6.00000			−0.224544
$715$	−2.00000			−0.0747958
$716$	6.50000	−	11.2583i	0.242916	−	0.420744i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	−0.999669	−	0.0257237i	$-0.991811\pi$
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	0.477557	−	0.878601i	$-0.341522\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−39.0000			−1.45244
$722$	13.0000	+	13.8564i	0.483810	+	0.515682i
$723$	10.0000			0.371904
$724$		0			0
$725$		0			0
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	0.993770	+	0.111454i	$0.0355509\pi$
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	−0.400362	+	0.916357i	$0.631116\pi$
$728$	−3.00000	+	5.19615i	−0.111187	+	0.192582i
$729$	1.00000			0.0370370
$730$	12.0000			0.444140
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−35.0000			−1.29275			−0.646377	−	0.763018i	$-0.723717\pi$
$733$	−35.0000			−1.29275			−0.646377	+	0.763018i	$0.723717\pi$
$734$		0			0
$735$	−1.00000	+	1.73205i	−0.0368856	+	0.0638877i
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	1.00000	−	1.73205i	0.0368355	−	0.0638009i
$738$	−0.500000	−	0.866025i	−0.0184053	−	0.0318788i
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	0.794443	−	0.607339i	$-0.207763\pi$
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	−0.923192	+	0.384338i	$0.874430\pi$
$740$	−9.00000			−0.330847
$741$	−1.00000	−	8.66025i	−0.0367359	−	0.318142i
$742$	9.00000			0.330400
$743$	11.5000	+	19.9186i	0.421894	+	0.730742i	0.996125	−	0.0879516i	$-0.0280321\pi$
$743$	11.5000	+	19.9186i	0.421894	+	0.730742i	−0.574231	+	0.818694i	$0.694699\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	18.5000	+	32.0429i	0.677333	+	1.17318i
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	2.00000			0.0731272
$749$	−30.0000			−1.09618
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$		0			0
$753$	−28.0000			−1.02038
$754$		0			0
$755$	−9.00000	−	15.5885i	−0.327544	−	0.567322i
$756$	1.50000	−	2.59808i	0.0545545	−	0.0944911i
$757$	9.50000	+	16.4545i	0.345283	+	0.598048i	0.985405	−	0.170225i	$-0.0544495\pi$
$757$	9.50000	+	16.4545i	0.345283	+	0.598048i	−0.640122	+	0.768273i	$0.721116\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	−1.00000			−0.0362977
$760$	−3.50000	+	2.59808i	−0.126958	+	0.0942421i
$761$	−45.0000			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$762$	−0.500000	−	0.866025i	−0.0181131	−	0.0313728i
$763$	9.00000	+	15.5885i	0.325822	+	0.564340i
$764$	5.00000	−	8.66025i	0.180894	−	0.313317i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	24.0000			0.866590
$768$	−1.00000			−0.0360844
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$	1.50000	−	2.59808i	0.0540562	−	0.0936282i
$771$	−2.00000			−0.0720282
$772$	14.0000			0.503871
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$	−4.00000	−	6.92820i	−0.143592	−	0.248708i
$777$	13.5000	+	23.3827i	0.484310	+	0.838849i
$778$	8.00000			0.286814
$779$	3.50000	−	2.59808i	0.125401	−	0.0930857i
$780$	2.00000			0.0716115
$781$	−4.00000	−	6.92820i	−0.143131	−	0.247911i
$782$	−1.00000	−	1.73205i	−0.0357599	−	0.0619380i
$783$		0			0
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	3.50000	−	6.06218i	0.124920	−	0.216368i
$786$	−21.0000			−0.749045
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	−2.50000	+	4.33013i	−0.0890588	+	0.154254i
$789$	−12.5000	+	21.6506i	−0.445012	+	0.770783i
$790$	−14.0000			−0.498098
$791$	30.0000			1.06668
$792$	−0.500000	+	0.866025i	−0.0177667	+	0.0307729i
$793$	2.00000	+	3.46410i	0.0710221	+	0.123014i
$794$	7.50000	−	12.9904i	0.266165	−	0.461011i
$795$	−1.50000	−	2.59808i	−0.0531995	−	0.0921443i
$796$	9.00000	+	15.5885i	0.318997	+	0.552518i
$797$	15.0000			0.531327			0.265664	−	0.964066i	$-0.414409\pi$
$797$	15.0000			0.531327			0.265664	+	0.964066i	$0.414409\pi$
$798$	12.0000	+	5.19615i	0.424795	+	0.183942i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.50000	+	4.33013i	0.0883332	+	0.152998i
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$	−3.00000			−0.105736
$806$	8.00000			0.281788
$807$	−7.00000	+	12.1244i	−0.246412	+	0.426798i
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	34.0000			1.19538			0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000			1.19538			0.597688	+	0.801729i	$0.296086\pi$
$810$	−1.00000			−0.0351364
$811$	5.50000	−	9.52628i	0.193131	−	0.334513i	−0.753155	−	0.657843i	$-0.771469\pi$
$811$	5.50000	−	9.52628i	0.193131	−	0.334513i	0.946286	+	0.323330i	$0.104802\pi$
$812$		0			0
$813$	1.00000	−	1.73205i	0.0350715	−	0.0607457i
$814$	−4.50000	−	7.79423i	−0.157725	−	0.273188i
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$	−2.00000			−0.0700140
$817$	−35.0000	+	25.9808i	−1.22449	+	0.908952i
$818$	21.0000			0.734248
$819$	−3.00000	−	5.19615i	−0.104828	−	0.181568i
$820$	0.500000	+	0.866025i	0.0174608	+	0.0302429i
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$	2.00000	+	3.46410i	0.0697580	+	0.120824i
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$	−13.0000			−0.452876
$825$	−1.00000			−0.0348155
$826$	−18.0000	+	31.1769i	−0.626300	+	1.08478i
$827$	24.0000	−	41.5692i	0.834562	−	1.44550i	−0.0598250	−	0.998209i	$-0.519054\pi$
$827$	24.0000	−	41.5692i	0.834562	−	1.44550i	0.894387	−	0.447295i	$-0.147612\pi$
$828$	1.00000			0.0347524
$829$	−8.00000			−0.277851			−0.138926	−	0.990303i	$-0.544365\pi$
$829$	−8.00000			−0.277851			−0.138926	+	0.990303i	$0.544365\pi$
$830$	3.00000	−	5.19615i	0.104132	−	0.180361i
$831$	11.0000	+	19.0526i	0.381586	+	0.660926i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−2.00000	−	3.46410i	−0.0692959	−	0.120024i
$834$	−10.0000	−	17.3205i	−0.346272	−	0.599760i
$835$	−3.00000			−0.103819
$836$	−4.00000	−	1.73205i	−0.138343	−	0.0599042i
$837$	−4.00000			−0.138260
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$	−1.50000	+	2.59808i	−0.0517549	+	0.0896421i
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	11.0000	−	19.0526i	0.379085	−	0.656595i
$843$	21.0000			0.723278
$844$	23.0000			0.791693
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	−30.0000			−1.03081
$848$	3.00000			0.103020
$849$	1.00000	−	1.73205i	0.0343199	−	0.0594438i
$850$	−1.00000	−	1.73205i	−0.0342997	−	0.0594089i
$851$	−4.50000	+	7.79423i	−0.154258	+	0.267183i
$852$	4.00000	+	6.92820i	0.137038	+	0.237356i
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	−0.982990	−	0.183658i	$-0.941206\pi$
$853$	−19.0000	−	32.9090i	−0.650548	−	1.12678i	0.332443	−	0.943123i	$-0.392127\pi$
$854$	−6.00000			−0.205316
$855$	−0.500000	−	4.33013i	−0.0170996	−	0.148087i
$856$	−10.0000			−0.341793
$857$	20.0000	+	34.6410i	0.683187	+	1.18331i	0.974003	+	0.226536i	$0.0727399\pi$
$857$	20.0000	+	34.6410i	0.683187	+	1.18331i	−0.290816	+	0.956779i	$0.593927\pi$
$858$	1.00000	+	1.73205i	0.0341394	+	0.0591312i
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	−0.709242	−	0.704965i	$-0.750963\pi$
$859$	7.50000	−	12.9904i	0.255897	−	0.443226i	0.965139	+	0.261739i	$0.0842960\pi$
$860$	−5.00000	−	8.66025i	−0.170499	−	0.295312i
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	38.0000			1.29429
$863$	17.0000			0.578687			0.289343	−	0.957225i	$-0.406563\pi$
$863$	17.0000			0.578687			0.289343	+	0.957225i	$0.406563\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	5.50000	−	9.52628i	0.187006	−	0.323903i
$866$	16.0000			0.543702
$867$	13.0000			0.441503
$868$	−6.00000	+	10.3923i	−0.203653	+	0.352738i
$869$	−7.00000	−	12.1244i	−0.237459	−	0.411291i
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$	8.00000			0.270759
$874$	0.500000	+	4.33013i	0.0169128	+	0.146469i
$875$	−3.00000			−0.101419
$876$	−6.00000	−	10.3923i	−0.202721	−	0.351123i
$877$	0.500000	+	0.866025i	0.0168838	+	0.0292436i	0.874344	−	0.485307i	$-0.161292\pi$
$877$	0.500000	+	0.866025i	0.0168838	+	0.0292436i	−0.857460	+	0.514551i	$0.827959\pi$
$878$	−15.0000	+	25.9808i	−0.506225	+	0.876808i
$879$	0.500000	+	0.866025i	0.0168646	+	0.0292103i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$	2.00000			0.0673435
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	0.848709	+	0.528861i	$0.177381\pi$
$884$	−2.00000	+	3.46410i	−0.0672673	+	0.116510i
$885$	12.0000			0.403376
$886$	22.0000			0.739104
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$	4.50000	+	7.79423i	0.151010	+	0.261557i
$889$	1.50000	−	2.59808i	0.0503084	−	0.0871367i
$890$	−2.50000	−	4.33013i	−0.0838002	−	0.145146i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	3.00000			0.100447
$893$		0			0
$894$	6.00000			0.200670
$895$	−6.50000	−	11.2583i	−0.217271	−	0.376324i
$896$	−1.50000	−	2.59808i	−0.0501115	−	0.0867956i
$897$	1.00000	−	1.73205i	0.0333890	−	0.0578315i
$898$	4.50000	+	7.79423i	0.150167	+	0.260097i
$899$		0			0
$900$	1.00000			0.0333333
$901$	6.00000			0.199889
$902$	−0.500000	+	0.866025i	−0.0166482	+	0.0288355i
$903$	−15.0000	+	25.9808i	−0.499169	+	0.864586i
$904$	10.0000			0.332595
$905$		0			0
$906$	−9.00000	+	15.5885i	−0.299005	+	0.517892i
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	0.997016	−	0.0771920i	$-0.0245954\pi$
$907$	13.0000	+	22.5167i	0.431658	+	0.747653i	−0.565358	+	0.824845i	$0.691262\pi$
$908$	−14.0000	+	24.2487i	−0.464606	+	0.804722i
$909$	1.00000	+	1.73205i	0.0331679	+	0.0574485i
$910$	3.00000	+	5.19615i	0.0994490	+	0.172251i
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	4.00000	+	1.73205i	0.132453	+	0.0573539i
$913$	6.00000			0.198571
$914$	9.00000	+	15.5885i	0.297694	+	0.515620i
$915$	1.00000	+	1.73205i	0.0330590	+	0.0572598i
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−31.5000	−	54.5596i	−1.04022	−	1.80172i
$918$	1.00000	−	1.73205i	0.0330049	−	0.0571662i
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$	−1.00000			−0.0329690
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	−11.0000	+	19.0526i	−0.362266	+	0.627463i
$923$	16.0000			0.526646
$924$	−3.00000			−0.0986928
$925$	−4.50000	+	7.79423i	−0.147959	+	0.256273i
$926$	12.5000	+	21.6506i	0.410775	+	0.711484i
$927$	6.50000	−	11.2583i	0.213488	−	0.369772i
$928$		0			0
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$	4.00000			0.131165
$931$	1.00000	+	8.66025i	0.0327737	+	0.283828i
$932$	6.00000			0.196537
$933$	−8.00000	−	13.8564i	−0.261908	−	0.453638i
$934$	−16.0000	−	27.7128i	−0.523536	−	0.906791i
$935$	1.00000	−	1.73205i	0.0327035	−	0.0566441i
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$	−26.0000	+	45.0333i	−0.849383	+	1.47117i	0.0323768	+	0.999476i	$0.489692\pi$
$937$	−26.0000	+	45.0333i	−0.849383	+	1.47117i	−0.881760	+	0.471699i	$0.843641\pi$
$938$	−6.00000			−0.195907
$939$		0			0
$940$		0			0
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	−0.601418	−	0.798935i	$-0.705397\pi$
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	0.992607	+	0.121376i	$0.0387306\pi$
$942$	−7.00000			−0.228072
$943$	1.00000			0.0325645
$944$	−6.00000	+	10.3923i	−0.195283	+	0.338241i
$945$	−1.50000	−	2.59808i	−0.0487950	−	0.0845154i
$946$	5.00000	−	8.66025i	0.162564	−	0.281569i
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	0.773279	−	0.634066i	$-0.218615\pi$
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	−0.935757	+	0.352646i	$0.885282\pi$
$948$	7.00000	+	12.1244i	0.227349	+	0.393781i
$949$	−24.0000			−0.779073
$950$	0.500000	+	4.33013i	0.0162221	+	0.140488i
$951$	−7.00000			−0.226991
$952$	−3.00000	−	5.19615i	−0.0972306	−	0.168408i
$953$	24.0000	+	41.5692i	0.777436	+	1.34656i	0.933415	+	0.358799i	$0.116814\pi$
$953$	24.0000	+	41.5692i	0.777436	+	1.34656i	−0.155979	+	0.987760i	$0.549853\pi$
$954$	−1.50000	+	2.59808i	−0.0485643	+	0.0841158i
$955$	−5.00000	−	8.66025i	−0.161796	−	0.280239i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	20.0000			0.646171
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−15.0000			−0.483871
$962$	18.0000			0.580343
$963$	5.00000	−	8.66025i	0.161123	−	0.279073i
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	7.00000	−	12.1244i	0.225338	−	0.390297i
$966$	1.50000	+	2.59808i	0.0482617	+	0.0835917i
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$	−10.0000			−0.321412
$969$	8.00000	+	3.46410i	0.256997	+	0.111283i
$970$	−8.00000			−0.256865
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	30.0000	−	51.9615i	0.961756	−	1.66581i
$974$	20.5000	+	35.5070i	0.656862	+	1.13772i
$975$	1.00000	−	1.73205i	0.0320256	−	0.0554700i
$976$	−2.00000			−0.0640184
$977$	8.00000			0.255943			0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000			0.255943			0.127971	+	0.991778i	$0.459153\pi$
$978$	1.00000	−	1.73205i	0.0319765	−	0.0553849i
$979$	2.50000	−	4.33013i	0.0799003	−	0.138391i
$980$	−2.00000			−0.0638877
$981$	−6.00000			−0.191565
$982$	16.5000	−	28.5788i	0.526536	−	0.911987i
$983$	−20.5000	−	35.5070i	−0.653848	−	1.13250i	−0.982181	−	0.187937i	$-0.939820\pi$
$983$	−20.5000	−	35.5070i	−0.653848	−	1.13250i	0.328333	−	0.944562i	$-0.393513\pi$
$984$	0.500000	−	0.866025i	0.0159394	−	0.0276079i
$985$	2.50000	+	4.33013i	0.0796566	+	0.137969i
$986$		0			0
$987$		0			0
$988$	7.00000	−	5.19615i	0.222700	−	0.165312i
$989$	−10.0000			−0.317982
$990$	0.500000	+	0.866025i	0.0158910	+	0.0275241i
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	6.50000	+	11.2583i	0.206271	+	0.357272i
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	18.0000			0.570638
$996$	−6.00000			−0.190117
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	−0.744548	−	0.667568i	$-0.767335\pi$
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	0.950405	+	0.311014i	$0.100668\pi$
$998$	−7.50000	+	12.9904i	−0.237408	+	0.411203i
$999$	−9.00000			−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.c.121.1	✓	2
3.2	odd	2		1710.2.l.i.1261.1		2
19.11	even	3	inner	570.2.i.c.391.1	yes	2
57.11	odd	6		1710.2.l.i.1531.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.c.121.1	✓	2	1.1	even	1	trivial
570.2.i.c.391.1	yes	2	19.11	even	3	inner
1710.2.l.i.1261.1		2	3.2	odd	2
1710.2.l.i.1531.1		2	57.11	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} +1.00000 q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.00000 q^{37} +(3.50000 - 2.59808i) q^{38} -2.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(1.50000 - 2.59808i) q^{42} +(5.00000 + 8.66025i) q^{43} +(-0.500000 + 0.866025i) q^{44} -1.00000 q^{45} +1.00000 q^{46} +(0.500000 - 0.866025i) q^{48} +2.00000 q^{49} +1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 + 0.866025i) q^{55} +3.00000 q^{56} +(-3.50000 + 2.59808i) q^{57} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.50000 + 2.59808i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(0.500000 - 0.866025i) q^{66} +(1.00000 - 1.73205i) q^{67} +2.00000 q^{68} -1.00000 q^{69} +(1.50000 - 2.59808i) q^{70} +(-4.00000 - 6.92820i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{73} +(-4.50000 - 7.79423i) q^{74} -1.00000 q^{75} +(-4.00000 - 1.73205i) q^{76} +3.00000 q^{77} +(1.00000 + 1.73205i) q^{78} +(-7.00000 - 12.1244i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +6.00000 q^{83} -3.00000 q^{84} +(1.00000 - 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} +1.00000 q^{88} +(2.50000 - 4.33013i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-3.00000 + 5.19615i) q^{91} +(-0.500000 - 0.866025i) q^{92} +(2.00000 + 3.46410i) q^{93} +(-3.50000 + 2.59808i) q^{95} -1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-1.00000 - 1.73205i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + q^5 + q^6 + 6 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + 6 q^{7} + 2 q^{8} - q^{9} + q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 3 q^{14} - q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} + 3 q^{21} - q^{22} - q^{23} + q^{24} - q^{25} + 4 q^{26} - 2 q^{27} - 3 q^{28} + 2 q^{30} + 8 q^{31} - q^{32} + q^{33} - 2 q^{34} + 3 q^{35} - q^{36} + 18 q^{37} + 7 q^{38} - 4 q^{39} + q^{40} - q^{41} + 3 q^{42} + 10 q^{43} - q^{44} - 2 q^{45} + 2 q^{46} + q^{48} + 4 q^{49} + 2 q^{50} + 2 q^{51} - 2 q^{52} - 3 q^{53} + q^{54} + q^{55} + 6 q^{56} - 7 q^{57} - 12 q^{59} - q^{60} + 2 q^{61} - 4 q^{62} - 3 q^{63} + 2 q^{64} - 4 q^{65} + q^{66} + 2 q^{67} + 4 q^{68} - 2 q^{69} + 3 q^{70} - 8 q^{71} - q^{72} + 12 q^{73} - 9 q^{74} - 2 q^{75} - 8 q^{76} + 6 q^{77} + 2 q^{78} - 14 q^{79} + q^{80} - q^{81} - q^{82} + 12 q^{83} - 6 q^{84} + 2 q^{85} + 10 q^{86} + 2 q^{88} + 5 q^{89} + q^{90} - 6 q^{91} - q^{92} + 4 q^{93} - 7 q^{95} - 2 q^{96} - 8 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^5 + q^6 + 6 * q^7 + 2 * q^8 - q^9 + q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 3 * q^14 - q^15 - q^16 - 2 * q^17 + 2 * q^18 + q^19 - 2 * q^20 + 3 * q^21 - q^22 - q^23 + q^24 - q^25 + 4 * q^26 - 2 * q^27 - 3 * q^28 + 2 * q^30 + 8 * q^31 - q^32 + q^33 - 2 * q^34 + 3 * q^35 - q^36 + 18 * q^37 + 7 * q^38 - 4 * q^39 + q^40 - q^41 + 3 * q^42 + 10 * q^43 - q^44 - 2 * q^45 + 2 * q^46 + q^48 + 4 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 - 3 * q^53 + q^54 + q^55 + 6 * q^56 - 7 * q^57 - 12 * q^59 - q^60 + 2 * q^61 - 4 * q^62 - 3 * q^63 + 2 * q^64 - 4 * q^65 + q^66 + 2 * q^67 + 4 * q^68 - 2 * q^69 + 3 * q^70 - 8 * q^71 - q^72 + 12 * q^73 - 9 * q^74 - 2 * q^75 - 8 * q^76 + 6 * q^77 + 2 * q^78 - 14 * q^79 + q^80 - q^81 - q^82 + 12 * q^83 - 6 * q^84 + 2 * q^85 + 10 * q^86 + 2 * q^88 + 5 * q^89 + q^90 - 6 * q^91 - q^92 + 4 * q^93 - 7 * q^95 - 2 * q^96 - 8 * q^97 - 2 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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