LMFDB - Embedded newform 858.2.i.a.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [858,2,Mod(133,858)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(858, 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("858.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 858 = 2 \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	858.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:	$6.85116449343$
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			133.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	858.133
Dual form			858.2.i.a.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +1.00000 q^{18} +(3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{30} +3.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -7.00000 q^{38} +(-2.50000 + 2.59808i) q^{39} +1.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(2.00000 - 3.46410i) q^{43} +1.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.00000 + 6.92820i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +7.00000 q^{51} +(3.50000 + 0.866025i) q^{52} +1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.00000 + 1.73205i) q^{56} -7.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-0.500000 + 0.866025i) q^{59} +1.00000 q^{60} +(-0.500000 + 0.866025i) q^{61} +(-1.50000 - 2.59808i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} +1.00000 q^{66} +(7.00000 + 12.1244i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(-4.00000 + 6.92820i) q^{69} +2.00000 q^{70} +(-2.00000 + 3.46410i) q^{71} +(-0.500000 + 0.866025i) q^{72} -16.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +2.00000 q^{77} +(3.50000 + 0.866025i) q^{78} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +2.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(-3.50000 + 6.06218i) q^{85} -4.00000 q^{86} +(-3.00000 + 5.19615i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +(7.00000 + 1.73205i) q^{91} +8.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(3.50000 - 6.06218i) q^{95} +1.00000 q^{96} +(1.50000 - 2.59808i) q^{97} +(1.50000 - 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - q^{10} - q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - q^{16} - 7 q^{17} + 2 q^{18} + 7 q^{19} - q^{20} + 4 q^{21} - q^{22} - 8 q^{23} - q^{24} - 8 q^{25} - 5 q^{26} + 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} + 6 q^{31} - q^{32} - q^{33} + 14 q^{34} - 2 q^{35} - q^{36} - 2 q^{37} - 14 q^{38} - 5 q^{39} + 2 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} + 2 q^{44} - q^{45} - 8 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} + 4 q^{50} + 14 q^{51} + 7 q^{52} + 2 q^{53} - q^{54} - q^{55} - 2 q^{56} - 14 q^{57} - 6 q^{58} - q^{59} + 2 q^{60} - q^{61} - 3 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 14 q^{67} - 7 q^{68} - 8 q^{69} + 4 q^{70} - 4 q^{71} - q^{72} - 32 q^{73} - 2 q^{74} + 4 q^{75} + 7 q^{76} + 4 q^{77} + 7 q^{78} - 16 q^{79} - q^{80} - q^{81} - 10 q^{82} + 4 q^{83} - 2 q^{84} - 7 q^{85} - 8 q^{86} - 6 q^{87} - q^{88} - 6 q^{89} + 2 q^{90} + 14 q^{91} + 16 q^{92} - 3 q^{93} + 6 q^{94} + 7 q^{95} + 2 q^{96} + 3 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 - q^10 - q^11 + 2 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - q^16 - 7 * q^17 + 2 * q^18 + 7 * q^19 - q^20 + 4 * q^21 - q^22 - 8 * q^23 - q^24 - 8 * q^25 - 5 * q^26 + 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 + 6 * q^31 - q^32 - q^33 + 14 * q^34 - 2 * q^35 - q^36 - 2 * q^37 - 14 * q^38 - 5 * q^39 + 2 * q^40 - 10 * q^41 - 2 * q^42 + 4 * q^43 + 2 * q^44 - q^45 - 8 * q^46 - 12 * q^47 - q^48 + 3 * q^49 + 4 * q^50 + 14 * q^51 + 7 * q^52 + 2 * q^53 - q^54 - q^55 - 2 * q^56 - 14 * q^57 - 6 * q^58 - q^59 + 2 * q^60 - q^61 - 3 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 14 * q^67 - 7 * q^68 - 8 * q^69 + 4 * q^70 - 4 * q^71 - q^72 - 32 * q^73 - 2 * q^74 + 4 * q^75 + 7 * q^76 + 4 * q^77 + 7 * q^78 - 16 * q^79 - q^80 - q^81 - 10 * q^82 + 4 * q^83 - 2 * q^84 - 7 * q^85 - 8 * q^86 - 6 * q^87 - q^88 - 6 * q^89 + 2 * q^90 + 14 * q^91 + 16 * q^92 - 3 * q^93 + 6 * q^94 + 7 * q^95 + 2 * q^96 + 3 * q^97 + 3 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/858\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$2$	−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
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.00000			0.288675
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$	1.00000			0.235702
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	2.00000			0.436436
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.00000			−0.800000
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$	1.00000			0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	7.00000			1.20049
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−7.00000			−1.13555
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$	1.00000			0.158114
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	1.00000			0.150756
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	7.00000			0.980196
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	1.00000			0.137361			0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000			0.137361			0.0686803	+	0.997639i	$0.478121\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	−7.00000			−0.927173
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	−0.896736	−	0.442566i	$-0.854068\pi$
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	0.831641	+	0.555313i	$0.187402\pi$
$60$	1.00000			0.129099
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	−1.50000	−	2.59808i	−0.190500	−	0.329956i
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$	−1.00000	−	3.46410i	−0.124035	−	0.429669i
$66$	1.00000			0.123091
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	0.876472	+	0.481452i	$0.159891\pi$
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	−0.0212861	+	0.999773i	$0.506776\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$	−4.00000	+	6.92820i	−0.481543	+	0.834058i
$70$	2.00000			0.239046
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−16.0000			−1.87266			−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000			−1.87266			−0.936329	+	0.351123i	$0.885800\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	2.00000			0.227921
$78$	3.50000	+	0.866025i	0.396297	+	0.0980581i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	−3.50000	+	6.06218i	−0.379628	+	0.657536i
$86$	−4.00000			−0.431331
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	1.00000			0.105409
$91$	7.00000	+	1.73205i	0.733799	+	0.181568i
$92$	8.00000			0.834058
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$	1.00000			0.102062
$97$	1.50000	−	2.59808i	0.152302	−	0.263795i	−0.779771	−	0.626064i	$-0.784665\pi$
$97$	1.50000	−	2.59808i	0.152302	−	0.263795i	0.932073	+	0.362270i	$0.117998\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	1.00000			0.100504
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	−3.50000	−	6.06218i	−0.346552	−	0.600245i
$103$	12.0000			1.18240			0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000			1.18240			0.591198	+	0.806527i	$0.298655\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$	2.00000			0.195180
$106$	−0.500000	−	0.866025i	−0.0485643	−	0.0841158i
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$	2.00000			0.188982
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$	3.50000	+	6.06218i	0.327805	+	0.567775i
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	6.00000			0.557086
$117$	3.50000	+	0.866025i	0.323575	+	0.0800641i
$118$	1.00000			0.0920575
$119$	−7.00000	−	12.1244i	−0.641689	−	1.11144i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.00000			0.0905357
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$	−9.00000			−0.804984
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000			−0.352180
$130$	−2.50000	+	2.59808i	−0.219265	+	0.227866i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$	−0.500000	−	0.866025i	−0.0435194	−	0.0753778i
$133$	7.00000	+	12.1244i	0.606977	+	1.05131i
$134$	7.00000	−	12.1244i	0.604708	−	1.04738i
$135$	1.00000			0.0860663
$136$	−3.50000	+	6.06218i	−0.300123	+	0.519827i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	8.00000			0.681005
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	−0.109984	−	0.993933i	$-0.535080\pi$
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	0.915764	−	0.401718i	$-0.131587\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$	4.00000			0.335673
$143$	−2.50000	+	2.59808i	−0.209061	+	0.217262i
$144$	1.00000			0.0833333
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$	8.00000	+	13.8564i	0.662085	+	1.14676i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	2.00000			0.164399
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$	−3.50000	−	6.06218i	−0.282958	−	0.490098i
$154$	−1.00000	−	1.73205i	−0.0805823	−	0.139573i
$155$	3.00000			0.240966
$156$	−1.00000	−	3.46410i	−0.0800641	−	0.277350i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	16.0000			1.26098
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	10.0000			0.780869
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	−3.50000	−	6.06218i	−0.270838	−	0.469105i	0.698239	−	0.715865i	$-0.253967\pi$
$167$	−3.50000	−	6.06218i	−0.270838	−	0.469105i	−0.969077	+	0.246760i	$0.920634\pi$
$168$	2.00000			0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	7.00000			0.536875
$171$	3.50000	+	6.06218i	0.267652	+	0.463586i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.101598	+	0.994826i	$0.532395\pi$
$173$	−12.0000	+	20.7846i	−0.912343	+	1.58022i	−0.810745	+	0.585399i	$0.800938\pi$
$174$	6.00000			0.454859
$175$	4.00000	−	6.92820i	0.302372	−	0.523723i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	1.00000			0.0751646
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$	−2.00000	−	6.92820i	−0.148250	−	0.513553i
$183$	1.00000			0.0739221
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−1.50000	+	2.59808i	−0.109985	+	0.190500i
$187$	7.00000			0.511891
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	−7.00000			−0.507833
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.773272	+	0.634074i	$0.218619\pi$
$193$	13.0000	+	22.5167i	0.935760	+	1.62078i	0.162488	+	0.986710i	$0.448048\pi$
$194$	−3.00000			−0.215387
$195$	−2.50000	+	2.59808i	−0.179029	+	0.186052i
$196$	−3.00000			−0.214286
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	−0.929762	−	0.368161i	$-0.879988\pi$
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	0.146045	−	0.989278i	$-0.453346\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	−4.00000			−0.282843
$201$	7.00000	−	12.1244i	0.493742	−	0.855186i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	12.0000			0.842235
$204$	−3.50000	+	6.06218i	−0.245049	+	0.424437i
$205$	−5.00000	−	8.66025i	−0.349215	−	0.604858i
$206$	−6.00000	−	10.3923i	−0.418040	−	0.724066i
$207$	8.00000			0.556038
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	−7.00000			−0.484200
$210$	−1.00000	−	1.73205i	−0.0690066	−	0.119523i
$211$	−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	$-0.457467\pi$
$212$	−0.500000	+	0.866025i	−0.0343401	+	0.0594789i
$213$	4.00000			0.274075
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$	1.00000			0.0680414
$217$	−3.00000	+	5.19615i	−0.203653	+	0.352738i
$218$	0.500000	+	0.866025i	0.0338643	+	0.0586546i
$219$	8.00000	+	13.8564i	0.540590	+	0.936329i
$220$	1.00000			0.0674200
$221$	24.5000	+	6.06218i	1.64805	+	0.407786i
$222$	2.00000			0.134231
$223$	5.50000	+	9.52628i	0.368307	+	0.637927i	0.989301	−	0.145889i	$-0.0466041\pi$
$223$	5.50000	+	9.52628i	0.368307	+	0.637927i	−0.620994	+	0.783815i	$0.713271\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−12.0000			−0.798228
$227$	8.00000	−	13.8564i	0.530979	−	0.919682i	−0.468368	−	0.883534i	$-0.655158\pi$
$227$	8.00000	−	13.8564i	0.530979	−	0.919682i	0.999346	−	0.0361484i	$-0.0115089\pi$
$228$	3.50000	−	6.06218i	0.231793	−	0.401478i
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$	−4.00000	+	6.92820i	−0.263752	+	0.456832i
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	−9.00000			−0.589610			−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000			−0.589610			−0.294805	+	0.955557i	$0.595255\pi$
$234$	−1.00000	−	3.46410i	−0.0653720	−	0.226455i
$235$	−6.00000			−0.391397
$236$	−0.500000	−	0.866025i	−0.0325472	−	0.0563735i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	−7.00000	+	12.1244i	−0.453743	+	0.785905i
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	1.00000			0.0642824
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.500000	−	0.866025i	−0.0320092	−	0.0554416i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$	10.0000			0.637577
$247$	−24.5000	−	6.06218i	−1.55890	−	0.385727i
$248$	3.00000			0.190500
$249$	−1.00000	−	1.73205i	−0.0633724	−	0.109764i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	−0.964207	−	0.265149i	$-0.914579\pi$
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	0.711730	+	0.702454i	$0.247912\pi$
$252$	2.00000			0.125988
$253$	−4.00000	+	6.92820i	−0.251478	+	0.435572i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$	7.00000			0.438357
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$	4.00000			0.248548
$260$	3.50000	+	0.866025i	0.217061	+	0.0537086i
$261$	6.00000			0.371391
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	11.5000	+	19.9186i	0.709120	+	1.22823i	0.965184	+	0.261573i	$0.0842411\pi$
$263$	11.5000	+	19.9186i	0.709120	+	1.22823i	−0.256063	+	0.966660i	$0.582426\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$	1.00000			0.0614295
$266$	7.00000	−	12.1244i	0.429198	−	0.743392i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	−14.0000			−0.855186
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	7.00000			0.424437
$273$	−2.00000	−	6.92820i	−0.121046	−	0.419314i
$274$	18.0000			1.08742
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	−0.652140	−	0.758099i	$-0.726128\pi$
$277$	5.50000	−	9.52628i	0.330463	−	0.572379i	0.982603	+	0.185720i	$0.0594618\pi$
$278$	−19.0000			−1.13954
$279$	−1.50000	+	2.59808i	−0.0898027	+	0.155543i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−25.0000			−1.49137			−0.745687	−	0.666296i	$-0.767879\pi$
$281$	−25.0000			−1.49137			−0.745687	+	0.666296i	$0.767879\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−13.5000	−	23.3827i	−0.802492	−	1.38996i	−0.917971	−	0.396647i	$-0.870174\pi$
$283$	−13.5000	−	23.3827i	−0.802492	−	1.38996i	0.115480	−	0.993310i	$-0.463159\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	−7.00000			−0.414644
$286$	3.50000	+	0.866025i	0.206959	+	0.0512092i
$287$	20.0000			1.18056
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$	−3.00000			−0.175863
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	−7.00000	+	12.1244i	−0.408944	+	0.708312i	−0.994772	−	0.102123i	$-0.967436\pi$
$293$	−7.00000	+	12.1244i	−0.408944	+	0.708312i	0.585827	+	0.810436i	$0.300770\pi$
$294$	−3.00000			−0.174964
$295$	−0.500000	+	0.866025i	−0.0291111	+	0.0504219i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$		0			0
$299$	−20.0000	+	20.7846i	−1.15663	+	1.20201i
$300$	−4.00000			−0.230940
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	−10.0000	−	17.3205i	−0.575435	−	0.996683i
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$	−7.00000			−0.401478
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$	−3.50000	+	6.06218i	−0.200082	+	0.346552i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$	−6.00000	−	10.3923i	−0.341328	−	0.591198i
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	10.0000			0.567048			0.283524	−	0.958965i	$-0.408496\pi$
$311$	10.0000			0.567048			0.283524	+	0.958965i	$0.408496\pi$
$312$	−2.50000	+	2.59808i	−0.141535	+	0.147087i
$313$	25.0000			1.41308			0.706542	−	0.707671i	$-0.250254\pi$
$313$	25.0000			1.41308			0.706542	+	0.707671i	$0.250254\pi$
$314$	−7.00000	−	12.1244i	−0.395033	−	0.684217i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	−2.00000			−0.112331			−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000			−0.112331			−0.0561656	+	0.998421i	$0.517887\pi$
$318$	−0.500000	+	0.866025i	−0.0280386	+	0.0485643i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	1.00000			0.0559017
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$	−8.00000	−	13.8564i	−0.445823	−	0.772187i
$323$	24.5000	+	42.4352i	1.36322	+	2.36116i
$324$	1.00000			0.0555556
$325$	4.00000	+	13.8564i	0.221880	+	0.768615i
$326$	−10.0000			−0.553849
$327$	0.500000	+	0.866025i	0.0276501	+	0.0478913i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	1.00000			0.0550482
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$	2.00000			0.109599
$334$	−3.50000	+	6.06218i	−0.191511	+	0.331708i
$335$	7.00000	+	12.1244i	0.382451	+	0.662424i
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	−12.0000			−0.651751
$340$	−3.50000	−	6.06218i	−0.189814	−	0.328768i
$341$	−1.50000	−	2.59808i	−0.0812296	−	0.140694i
$342$	3.50000	−	6.06218i	0.189258	−	0.327805i
$343$	−20.0000			−1.07990
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$	24.0000			1.29025
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	4.50000	+	7.79423i	0.240879	+	0.417215i	0.960965	−	0.276670i	$-0.0892308\pi$
$349$	4.50000	+	7.79423i	0.240879	+	0.417215i	−0.720086	+	0.693885i	$0.755897\pi$
$350$	−8.00000			−0.427618
$351$	−1.00000	−	3.46410i	−0.0533761	−	0.184900i
$352$	1.00000			0.0533002
$353$	8.00000	+	13.8564i	0.425797	+	0.737502i	0.996495	−	0.0836583i	$-0.0266604\pi$
$353$	8.00000	+	13.8564i	0.425797	+	0.737502i	−0.570697	+	0.821160i	$0.693327\pi$
$354$	−0.500000	−	0.866025i	−0.0265747	−	0.0460287i
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$	6.00000			0.317999
$357$	−7.00000	+	12.1244i	−0.370479	+	0.641689i
$358$	−4.50000	+	7.79423i	−0.237832	+	0.411938i
$359$	−21.0000			−1.10834			−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000			−1.10834			−0.554169	+	0.832404i	$0.686964\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−9.00000	−	15.5885i	−0.473029	−	0.819311i
$363$	1.00000			0.0524864
$364$	−5.00000	+	5.19615i	−0.262071	+	0.272352i
$365$	−16.0000			−0.837478
$366$	−0.500000	−	0.866025i	−0.0261354	−	0.0452679i
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$	10.0000			0.520579
$370$	−1.00000	+	1.73205i	−0.0519875	+	0.0900450i
$371$	−1.00000	+	1.73205i	−0.0519174	+	0.0899236i
$372$	3.00000			0.155543
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	−3.50000	−	6.06218i	−0.180981	−	0.313468i
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$	−6.00000			−0.309426
$377$	−15.0000	+	15.5885i	−0.772539	+	0.802846i
$378$	2.00000			0.102869
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	0.890565	−	0.454855i	$-0.150309\pi$
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	−0.839199	+	0.543825i	$0.816976\pi$
$380$	3.50000	+	6.06218i	0.179546	+	0.310983i
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$	−18.0000			−0.920960
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.00000			0.101929
$386$	13.0000	−	22.5167i	0.661683	−	1.14607i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	1.50000	+	2.59808i	0.0761510	+	0.131897i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$	3.50000	+	0.866025i	0.177229	+	0.0438529i
$391$	56.0000			2.83204
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$	3.00000	+	5.19615i	0.151330	+	0.262111i
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	−8.00000			−0.402524
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$	−7.00000			−0.350878
$399$	7.00000	−	12.1244i	0.350438	−	0.606977i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$	−14.0000			−0.698257
$403$	−3.00000	−	10.3923i	−0.149441	−	0.517678i
$404$	12.0000			0.597022
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−6.00000	−	10.3923i	−0.297775	−	0.515761i
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$	7.00000			0.346552
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	−5.00000	+	8.66025i	−0.246932	+	0.427699i
$411$	18.0000			0.887875
$412$	−6.00000	+	10.3923i	−0.295599	+	0.511992i
$413$	−1.00000	−	1.73205i	−0.0492068	−	0.0852286i
$414$	−4.00000	−	6.92820i	−0.196589	−	0.340503i
$415$	2.00000			0.0981761
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$	−19.0000			−0.930434
$418$	3.50000	+	6.06218i	0.171191	+	0.296511i
$419$	10.0000	+	17.3205i	0.488532	+	0.846162i	0.999913	−	0.0131919i	$-0.00419923\pi$
$419$	10.0000	+	17.3205i	0.488532	+	0.846162i	−0.511381	+	0.859354i	$0.670866\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$	−18.0000			−0.877266			−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	−11.5000	+	19.9186i	−0.559811	+	0.969622i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	1.00000			0.0485643
$425$	14.0000	−	24.2487i	0.679100	−	1.17624i
$426$	−2.00000	−	3.46410i	−0.0969003	−	0.167836i
$427$	−1.00000	−	1.73205i	−0.0483934	−	0.0838198i
$428$	−12.0000			−0.580042
$429$	3.50000	+	0.866025i	0.168982	+	0.0418121i
$430$	−4.00000			−0.192897
$431$	−8.50000	−	14.7224i	−0.409431	−	0.709155i	0.585395	−	0.810748i	$-0.300939\pi$
$431$	−8.50000	−	14.7224i	−0.409431	−	0.709155i	−0.994826	+	0.101593i	$0.967606\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	−0.799681	−	0.600425i	$-0.794998\pi$
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	0.919824	+	0.392332i	$0.128332\pi$
$434$	6.00000			0.288009
$435$	−3.00000	+	5.19615i	−0.143839	+	0.249136i
$436$	0.500000	−	0.866025i	0.0239457	−	0.0414751i
$437$	−56.0000			−2.67884
$438$	8.00000	−	13.8564i	0.382255	−	0.662085i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$	−0.500000	−	0.866025i	−0.0238366	−	0.0412861i
$441$	−3.00000			−0.142857
$442$	−7.00000	−	24.2487i	−0.332956	−	1.15339i
$443$	−35.0000			−1.66290			−0.831450	−	0.555599i	$-0.812489\pi$
$443$	−35.0000			−1.66290			−0.831450	+	0.555599i	$0.812489\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	5.50000	−	9.52628i	0.260433	−	0.451082i
$447$		0			0
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$449$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$450$	−4.00000			−0.188562
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$	−16.0000			−0.750917
$455$	7.00000	+	1.73205i	0.328165	+	0.0811998i
$456$	−7.00000			−0.327805
$457$	−6.00000	−	10.3923i	−0.280668	−	0.486132i	0.690881	−	0.722968i	$-0.257223\pi$
$457$	−6.00000	−	10.3923i	−0.280668	−	0.486132i	−0.971549	+	0.236837i	$0.923889\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	−3.50000	+	6.06218i	−0.163366	+	0.282958i
$460$	8.00000			0.373002
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	−0.841798	−	0.539792i	$-0.818503\pi$
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	0.888373	+	0.459123i	$0.151836\pi$
$462$	−1.00000	+	1.73205i	−0.0465242	+	0.0805823i
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−1.50000	−	2.59808i	−0.0695608	−	0.120483i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	21.0000			0.971764			0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000			0.971764			0.485882	+	0.874024i	$0.338498\pi$
$468$	−2.50000	+	2.59808i	−0.115563	+	0.120096i
$469$	−28.0000			−1.29292
$470$	3.00000	+	5.19615i	0.138380	+	0.239681i
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	−0.500000	+	0.866025i	−0.0230144	+	0.0398621i
$473$	−4.00000			−0.183920
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$	14.0000			0.641689
$477$	−0.500000	+	0.866025i	−0.0228934	+	0.0396526i
$478$	−10.5000	−	18.1865i	−0.480259	−	0.831833i
$479$	8.50000	+	14.7224i	0.388375	+	0.672685i	0.992231	−	0.124408i	$-0.0397032\pi$
$479$	8.50000	+	14.7224i	0.388375	+	0.672685i	−0.603856	+	0.797093i	$0.706370\pi$
$480$	1.00000			0.0456435
$481$	−5.00000	+	5.19615i	−0.227980	+	0.236924i
$482$	−8.00000			−0.364390
$483$	−8.00000	−	13.8564i	−0.364013	−	0.630488i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$	1.00000			0.0453609
$487$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$487$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	−10.0000			−0.452216
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$	−5.00000	−	8.66025i	−0.225417	−	0.390434i
$493$	42.0000			1.89158
$494$	7.00000	+	24.2487i	0.314945	+	1.09100i
$495$	1.00000			0.0449467
$496$	−1.50000	−	2.59808i	−0.0673520	−	0.116657i
$497$	−4.00000	−	6.92820i	−0.179425	−	0.310772i
$498$	−1.00000	+	1.73205i	−0.0448111	+	0.0776151i
$499$	−26.0000			−1.16392			−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000			−1.16392			−0.581960	+	0.813217i	$0.697714\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	−3.50000	+	6.06218i	−0.156368	+	0.270838i
$502$	8.00000			0.357057
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.00691465	+	0.999976i	$0.502201\pi$
$503$	−19.5000	+	33.7750i	−0.869462	+	1.50595i	−0.862547	+	0.505976i	$0.831132\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	−6.00000	−	10.3923i	−0.266996	−	0.462451i
$506$	8.00000			0.355643
$507$	11.5000	+	6.06218i	0.510733	+	0.269231i
$508$	4.00000			0.177471
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$	−3.50000	−	6.06218i	−0.154983	−	0.268438i
$511$	16.0000	−	27.7128i	0.707798	−	1.22594i
$512$	1.00000			0.0441942
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$	12.0000			0.528783
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	−2.00000	−	3.46410i	−0.0878750	−	0.152204i
$519$	24.0000			1.05348
$520$	−1.00000	−	3.46410i	−0.0438529	−	0.151911i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	0.539782	−	0.841805i	$-0.318507\pi$
$523$	−10.5000	−	18.1865i	−0.459133	−	0.795242i	−0.998915	+	0.0465630i	$0.985173\pi$
$524$	3.00000	−	5.19615i	0.131056	−	0.226995i
$525$	−8.00000			−0.349149
$526$	11.5000	−	19.9186i	0.501424	−	0.868492i
$527$	−10.5000	+	18.1865i	−0.457387	+	0.792218i
$528$	1.00000			0.0435194
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−0.500000	−	0.866025i	−0.0217186	−	0.0376177i
$531$	−0.500000	−	0.866025i	−0.0216982	−	0.0375823i
$532$	−14.0000			−0.606977
$533$	−25.0000	+	25.9808i	−1.08287	+	1.12535i
$534$	6.00000			0.259645
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$	−4.50000	+	7.79423i	−0.194189	+	0.336346i
$538$	−3.00000			−0.129339
$539$	1.50000	−	2.59808i	0.0646096	−	0.111907i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	26.0000			1.11783			0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000			1.11783			0.558914	+	0.829226i	$0.311218\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$	−9.00000	−	15.5885i	−0.386227	−	0.668965i
$544$	−3.50000	−	6.06218i	−0.150061	−	0.259914i
$545$	−1.00000			−0.0428353
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$	−15.0000			−0.641354			−0.320677	−	0.947189i	$-0.603910\pi$
$547$	−15.0000			−0.641354			−0.320677	+	0.947189i	$0.603910\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$	−42.0000			−1.78926
$552$	−4.00000	+	6.92820i	−0.170251	+	0.294884i
$553$	8.00000	−	13.8564i	0.340195	−	0.589234i
$554$	−11.0000			−0.467345
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	9.50000	+	16.4545i	0.402890	+	0.697826i
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$	3.00000			0.127000
$559$	−14.0000	−	3.46410i	−0.592137	−	0.146516i
$560$	2.00000			0.0845154
$561$	−3.50000	−	6.06218i	−0.147770	−	0.255945i
$562$	12.5000	+	21.6506i	0.527281	+	0.913277i
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	−0.679974	−	0.733237i	$-0.738009\pi$
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	0.974988	+	0.222256i	$0.0713421\pi$
$564$	−6.00000			−0.252646
$565$	6.00000	−	10.3923i	0.252422	−	0.437208i
$566$	−13.5000	+	23.3827i	−0.567447	+	0.982848i
$567$	2.00000			0.0839921
$568$	−2.00000	+	3.46410i	−0.0839181	+	0.145350i
$569$	8.50000	+	14.7224i	0.356339	+	0.617196i	0.987346	−	0.158580i	$-0.0506917\pi$
$569$	8.50000	+	14.7224i	0.356339	+	0.617196i	−0.631008	+	0.775777i	$0.717358\pi$
$570$	3.50000	+	6.06218i	0.146599	+	0.253917i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	−1.00000	−	3.46410i	−0.0418121	−	0.144841i
$573$	−18.0000			−0.751961
$574$	−10.0000	−	17.3205i	−0.417392	−	0.722944i
$575$	16.0000	+	27.7128i	0.667246	+	1.15570i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	−16.0000	+	27.7128i	−0.665512	+	1.15270i
$579$	13.0000	−	22.5167i	0.540262	−	0.935760i
$580$	6.00000			0.249136
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$	1.50000	+	2.59808i	0.0621770	+	0.107694i
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$	−16.0000			−0.662085
$585$	3.50000	+	0.866025i	0.144707	+	0.0358057i
$586$	14.0000			0.578335
$587$	5.50000	+	9.52628i	0.227009	+	0.393192i	0.956920	−	0.290350i	$-0.0937719\pi$
$587$	5.50000	+	9.52628i	0.227009	+	0.393192i	−0.729911	+	0.683542i	$0.760439\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	10.5000	−	18.1865i	0.432645	−	0.749363i
$590$	1.00000			0.0411693
$591$	−11.0000	+	19.0526i	−0.452480	+	0.783718i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$	−0.500000	+	0.866025i	−0.0205152	+	0.0355335i
$595$	−7.00000	−	12.1244i	−0.286972	−	0.497050i
$596$		0			0
$597$	−7.00000			−0.286491
$598$	28.0000	+	6.92820i	1.14501	+	0.283315i
$599$	36.0000			1.47092			0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000			1.47092			0.735460	+	0.677568i	$0.236966\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	−14.0000			−0.570124
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	12.0000			0.487467
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$	−6.00000	−	10.3923i	−0.243132	−	0.421117i
$610$	1.00000			0.0404888
$611$	6.00000	+	20.7846i	0.242734	+	0.840855i
$612$	7.00000			0.282958
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	−0.999984	−	0.00563283i	$-0.998207\pi$
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	0.495114	−	0.868828i	$-0.335126\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$	−5.00000	+	8.66025i	−0.201619	+	0.349215i
$616$	2.00000			0.0805823
$617$	5.00000	−	8.66025i	0.201292	−	0.348649i	−0.747653	−	0.664090i	$-0.768819\pi$
$617$	5.00000	−	8.66025i	0.201292	−	0.348649i	0.948945	+	0.315441i	$0.102153\pi$
$618$	−6.00000	+	10.3923i	−0.241355	+	0.418040i
$619$	2.00000			0.0803868			0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000			0.0803868			0.0401934	+	0.999192i	$0.487203\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	−5.00000	−	8.66025i	−0.200482	−	0.347245i
$623$	12.0000			0.480770
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$	11.0000			0.440000
$626$	−12.5000	−	21.6506i	−0.499600	−	0.865333i
$627$	3.50000	+	6.06218i	0.139777	+	0.242100i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	14.0000			0.558217
$630$	−1.00000	+	1.73205i	−0.0398410	+	0.0690066i
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	−0.502379	−	0.864647i	$-0.667542\pi$
$631$	12.5000	−	21.6506i	0.497617	−	0.861898i	0.999996	+	0.00274930i	$0.000875132\pi$
$632$	−8.00000			−0.318223
$633$	−11.5000	+	19.9186i	−0.457084	+	0.791693i
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$	−2.00000	−	3.46410i	−0.0793676	−	0.137469i
$636$	1.00000			0.0396526
$637$	7.50000	−	7.79423i	0.297161	−	0.308819i
$638$	6.00000			0.237542
$639$	−2.00000	−	3.46410i	−0.0791188	−	0.137038i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	17.0000	−	29.4449i	0.671460	−	1.16300i	−0.306031	−	0.952022i	$-0.599001\pi$
$641$	17.0000	−	29.4449i	0.671460	−	1.16300i	0.977490	−	0.210981i	$-0.0676657\pi$
$642$	−12.0000			−0.473602
$643$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$643$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$	−4.00000			−0.157500
$646$	24.5000	−	42.4352i	0.963940	−	1.66959i
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	0.694987	−	0.719023i	$-0.255410\pi$
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	−0.970185	+	0.242365i	$0.922077\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	1.00000			0.0392534
$650$	10.0000	−	10.3923i	0.392232	−	0.407620i
$651$	6.00000			0.235159
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$	0.500000	−	0.866025i	0.0195515	−	0.0338643i
$655$	−6.00000			−0.234439
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	8.00000	−	13.8564i	0.312110	−	0.540590i
$658$	−12.0000			−0.467809
$659$	13.0000	−	22.5167i	0.506408	−	0.877125i	−0.493564	−	0.869709i	$-0.664306\pi$
$659$	13.0000	−	22.5167i	0.506408	−	0.877125i	0.999973	−	0.00741531i	$-0.00236039\pi$
$660$	−0.500000	−	0.866025i	−0.0194625	−	0.0337100i
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	0.995069	+	0.0991864i	$0.0316240\pi$
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	−0.411636	+	0.911348i	$0.635043\pi$
$662$	26.0000			1.01052
$663$	−7.00000	−	24.2487i	−0.271857	−	0.941742i
$664$	2.00000			0.0776151
$665$	7.00000	+	12.1244i	0.271448	+	0.470162i
$666$	−1.00000	−	1.73205i	−0.0387492	−	0.0671156i
$667$	−24.0000	+	41.5692i	−0.929284	+	1.60957i
$668$	7.00000			0.270838
$669$	5.50000	−	9.52628i	0.212642	−	0.368307i
$670$	7.00000	−	12.1244i	0.270434	−	0.468405i
$671$	1.00000			0.0386046
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	18.0000	+	31.1769i	0.693849	+	1.20178i	0.970567	+	0.240831i	$0.0774198\pi$
$673$	18.0000	+	31.1769i	0.693849	+	1.20178i	−0.276718	+	0.960951i	$0.589247\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$	−4.00000			−0.153960
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$	6.00000	+	10.3923i	0.230429	+	0.399114i
$679$	3.00000	+	5.19615i	0.115129	+	0.199410i
$680$	−3.50000	+	6.06218i	−0.134219	+	0.232474i
$681$	−16.0000			−0.613121
$682$	−1.50000	+	2.59808i	−0.0574380	+	0.0994855i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−7.00000			−0.267652
$685$	−9.00000	+	15.5885i	−0.343872	+	0.595604i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	2.00000	+	3.46410i	0.0763048	+	0.132164i
$688$	−4.00000			−0.152499
$689$	−1.00000	−	3.46410i	−0.0380970	−	0.131972i
$690$	8.00000			0.304555
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	0.984873	−	0.173275i	$-0.0554350\pi$
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	−0.642497	+	0.766288i	$0.722102\pi$
$692$	−12.0000	−	20.7846i	−0.456172	−	0.790112i
$693$	−1.00000	+	1.73205i	−0.0379869	+	0.0657952i
$694$	2.00000			0.0759190
$695$	9.50000	−	16.4545i	0.360356	−	0.624154i
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	70.0000			2.65144
$698$	4.50000	−	7.79423i	0.170328	−	0.295016i
$699$	4.50000	+	7.79423i	0.170206	+	0.294805i
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	46.0000			1.73740			0.868698	−	0.495342i	$-0.164957\pi$
$701$	46.0000			1.73740			0.868698	+	0.495342i	$0.164957\pi$
$702$	−2.50000	+	2.59808i	−0.0943564	+	0.0980581i
$703$	−14.0000			−0.528020
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$	8.00000	−	13.8564i	0.301084	−	0.521493i
$707$	24.0000			0.902613
$708$	−0.500000	+	0.866025i	−0.0187912	+	0.0325472i
$709$	19.0000	−	32.9090i	0.713560	−	1.23592i	−0.249952	−	0.968258i	$-0.580415\pi$
$709$	19.0000	−	32.9090i	0.713560	−	1.23592i	0.963512	−	0.267664i	$-0.0862517\pi$
$710$	4.00000			0.150117
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$	14.0000			0.523937
$715$	−2.50000	+	2.59808i	−0.0934947	+	0.0971625i
$716$	9.00000			0.336346
$717$	−10.5000	−	18.1865i	−0.392130	−	0.679189i
$718$	10.5000	+	18.1865i	0.391857	+	0.678715i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$	1.00000			0.0372678
$721$	−12.0000	+	20.7846i	−0.446903	+	0.774059i
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$	−8.00000			−0.297523
$724$	−9.00000	+	15.5885i	−0.334482	+	0.579340i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	7.00000	+	1.73205i	0.259437	+	0.0641941i
$729$	1.00000			0.0370370
$730$	8.00000	+	13.8564i	0.296093	+	0.512849i
$731$	14.0000	+	24.2487i	0.517809	+	0.896871i
$732$	−0.500000	+	0.866025i	−0.0184805	+	0.0320092i
$733$	−37.0000			−1.36663			−0.683313	−	0.730125i	$-0.739462\pi$
$733$	−37.0000			−1.36663			−0.683313	+	0.730125i	$0.739462\pi$
$734$	8.50000	−	14.7224i	0.313741	−	0.543415i
$735$	1.50000	−	2.59808i	0.0553283	−	0.0958315i
$736$	8.00000			0.294884
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	0.997796	−	0.0663614i	$-0.0211390\pi$
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	−0.556369	+	0.830936i	$0.687806\pi$
$740$	2.00000			0.0735215
$741$	7.00000	+	24.2487i	0.257151	+	0.890799i
$742$	2.00000			0.0734223
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$	−1.50000	−	2.59808i	−0.0549927	−	0.0952501i
$745$		0			0
$746$	−13.0000			−0.475964
$747$	−1.00000	+	1.73205i	−0.0365881	+	0.0633724i
$748$	−3.50000	+	6.06218i	−0.127973	+	0.221655i
$749$	−24.0000			−0.876941
$750$	4.50000	−	7.79423i	0.164317	−	0.284605i
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	8.00000			0.291536
$754$	21.0000	+	5.19615i	0.764775	+	0.189233i
$755$	20.0000			0.727875
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	4.00000	+	6.92820i	0.145382	+	0.251810i	0.929516	−	0.368783i	$-0.120225\pi$
$757$	4.00000	+	6.92820i	0.145382	+	0.251810i	−0.784133	+	0.620593i	$0.786892\pi$
$758$	1.00000	−	1.73205i	0.0363216	−	0.0629109i
$759$	8.00000			0.290382
$760$	3.50000	−	6.06218i	0.126958	−	0.219898i
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$	4.00000			0.144905
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$	−3.50000	−	6.06218i	−0.126543	−	0.219179i
$766$	−32.0000			−1.15621
$767$	3.50000	+	0.866025i	0.126378	+	0.0312704i
$768$	1.00000			0.0360844
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$	7.00000	−	12.1244i	0.252099	−	0.436648i
$772$	−26.0000			−0.935760
$773$	−2.50000	+	4.33013i	−0.0899188	+	0.155744i	−0.907477	−	0.420103i	$-0.861994\pi$
$773$	−2.50000	+	4.33013i	−0.0899188	+	0.155744i	0.817558	+	0.575846i	$0.195327\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	−12.0000			−0.431053
$776$	1.50000	−	2.59808i	0.0538469	−	0.0932655i
$777$	−2.00000	−	3.46410i	−0.0717496	−	0.124274i
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$	−70.0000			−2.50801
$780$	−1.00000	−	3.46410i	−0.0358057	−	0.124035i
$781$	4.00000			0.143131
$782$	−28.0000	−	48.4974i	−1.00128	−	1.73426i
$783$	−3.00000	−	5.19615i	−0.107211	−	0.185695i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	14.0000			0.499681
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	22.0000			0.783718
$789$	11.5000	−	19.9186i	0.409411	−	0.709120i
$790$	4.00000	+	6.92820i	0.142314	+	0.246494i
$791$	12.0000	+	20.7846i	0.426671	+	0.739016i
$792$	1.00000			0.0355335
$793$	3.50000	+	0.866025i	0.124289	+	0.0307535i
$794$	26.0000			0.922705
$795$	−0.500000	−	0.866025i	−0.0177332	−	0.0307148i
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	7.50000	−	12.9904i	0.265664	−	0.460143i	−0.702074	−	0.712104i	$-0.747742\pi$
$797$	7.50000	−	12.9904i	0.265664	−	0.460143i	0.967737	+	0.251961i	$0.0810756\pi$
$798$	−14.0000			−0.495595
$799$	21.0000	−	36.3731i	0.742927	−	1.28679i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	6.00000			0.212000
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	8.00000	+	13.8564i	0.282314	+	0.488982i
$804$	7.00000	+	12.1244i	0.246871	+	0.427593i
$805$	16.0000			0.563926
$806$	−7.50000	+	7.79423i	−0.264176	+	0.274540i
$807$	−3.00000			−0.105605
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.704564	−	0.709640i	$-0.748858\pi$
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.262284	−	0.964991i	$-0.584476\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	7.00000			0.245803			0.122902	−	0.992419i	$-0.460780\pi$
$811$	7.00000			0.245803			0.122902	+	0.992419i	$0.460780\pi$
$812$	−6.00000	+	10.3923i	−0.210559	+	0.364698i
$813$	10.0000	−	17.3205i	0.350715	−	0.607457i
$814$	2.00000			0.0701000
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$	−3.50000	−	6.06218i	−0.122525	−	0.212219i
$817$	−14.0000	−	24.2487i	−0.489798	−	0.848355i
$818$	10.0000			0.349642
$819$	−5.00000	+	5.19615i	−0.174714	+	0.181568i
$820$	10.0000			0.349215
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	−0.458591	−	0.888648i	$-0.651646\pi$
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	0.998887	−	0.0471726i	$-0.0150211\pi$
$824$	12.0000			0.418040
$825$	2.00000	−	3.46410i	0.0696311	−	0.120605i
$826$	−1.00000	+	1.73205i	−0.0347945	+	0.0602658i
$827$	34.0000			1.18230			0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000			1.18230			0.591148	+	0.806563i	$0.298675\pi$
$828$	−4.00000	+	6.92820i	−0.139010	+	0.240772i
$829$	−2.00000	−	3.46410i	−0.0694629	−	0.120313i	0.829202	−	0.558949i	$-0.188795\pi$
$829$	−2.00000	−	3.46410i	−0.0694629	−	0.120313i	−0.898665	+	0.438636i	$0.855462\pi$
$830$	−1.00000	−	1.73205i	−0.0347105	−	0.0601204i
$831$	−11.0000			−0.381586
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$	−21.0000			−0.727607
$834$	9.50000	+	16.4545i	0.328958	+	0.569772i
$835$	−3.50000	−	6.06218i	−0.121122	−	0.209790i
$836$	3.50000	−	6.06218i	0.121050	−	0.209665i
$837$	3.00000			0.103695
$838$	10.0000	−	17.3205i	0.345444	−	0.598327i
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	−0.788680	−	0.614804i	$-0.789235\pi$
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	0.926776	+	0.375615i	$0.122569\pi$
$840$	2.00000			0.0690066
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	9.00000	+	15.5885i	0.310160	+	0.537214i
$843$	12.5000	+	21.6506i	0.430523	+	0.745687i
$844$	23.0000			0.791693
$845$	−11.0000	+	6.92820i	−0.378412	+	0.238337i
$846$	−6.00000			−0.206284
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$	−0.500000	−	0.866025i	−0.0171701	−	0.0297394i
$849$	−13.5000	+	23.3827i	−0.463319	+	0.802492i
$850$	−28.0000			−0.960392
$851$	−8.00000	+	13.8564i	−0.274236	+	0.474991i
$852$	−2.00000	+	3.46410i	−0.0685189	+	0.118678i
$853$	37.0000			1.26686			0.633428	−	0.773802i	$-0.281647\pi$
$853$	37.0000			1.26686			0.633428	+	0.773802i	$0.281647\pi$
$854$	−1.00000	+	1.73205i	−0.0342193	+	0.0592696i
$855$	3.50000	+	6.06218i	0.119697	+	0.207322i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−49.0000			−1.67381			−0.836904	−	0.547350i	$-0.815637\pi$
$857$	−49.0000			−1.67381			−0.836904	+	0.547350i	$0.815637\pi$
$858$	−1.00000	−	3.46410i	−0.0341394	−	0.118262i
$859$	−26.0000			−0.887109			−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000			−0.887109			−0.443554	+	0.896248i	$0.646283\pi$
$860$	2.00000	+	3.46410i	0.0681994	+	0.118125i
$861$	−10.0000	−	17.3205i	−0.340799	−	0.590281i
$862$	−8.50000	+	14.7224i	−0.289511	+	0.501448i
$863$	−28.0000			−0.953131			−0.476566	−	0.879139i	$-0.658119\pi$
$863$	−28.0000			−0.953131			−0.476566	+	0.879139i	$0.658119\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	−5.00000			−0.169907
$867$	−16.0000	+	27.7128i	−0.543388	+	0.941176i
$868$	−3.00000	−	5.19615i	−0.101827	−	0.176369i
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$	6.00000			0.203419
$871$	35.0000	−	36.3731i	1.18593	−	1.23245i
$872$	−1.00000			−0.0338643
$873$	1.50000	+	2.59808i	0.0507673	+	0.0879316i
$874$	28.0000	+	48.4974i	0.947114	+	1.64045i
$875$	9.00000	−	15.5885i	0.304256	−	0.526986i
$876$	−16.0000			−0.540590
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$	−14.0000	+	24.2487i	−0.472477	+	0.818354i
$879$	14.0000			0.472208
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	23.0000	+	39.8372i	0.774890	+	1.34215i	0.934856	+	0.355026i	$0.115528\pi$
$881$	23.0000	+	39.8372i	0.774890	+	1.34215i	−0.159967	+	0.987122i	$0.551139\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	24.0000			0.807664			0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000			0.807664			0.403832	+	0.914833i	$0.367678\pi$
$884$	−17.5000	+	18.1865i	−0.588589	+	0.611679i
$885$	1.00000			0.0336146
$886$	17.5000	+	30.3109i	0.587924	+	1.01831i
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	0.699890	−	0.714250i	$-0.253232\pi$
$887$	−8.00000	−	13.8564i	−0.268614	−	0.465253i	−0.968504	+	0.248998i	$0.919899\pi$
$888$	−1.00000	+	1.73205i	−0.0335578	+	0.0581238i
$889$	8.00000			0.268311
$890$	−3.00000	+	5.19615i	−0.100560	+	0.174175i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−11.0000			−0.368307
$893$	−21.0000	+	36.3731i	−0.702738	+	1.21718i
$894$		0			0
$895$	−4.50000	−	7.79423i	−0.150418	−	0.260532i
$896$	2.00000			0.0668153
$897$	28.0000	+	6.92820i	0.934893	+	0.231326i
$898$		0			0
$899$	−9.00000	−	15.5885i	−0.300167	−	0.519904i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	−3.50000	+	6.06218i	−0.116602	+	0.201960i
$902$	10.0000			0.332964
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$	18.0000			0.598340
$906$	−10.0000	+	17.3205i	−0.332228	+	0.575435i
$907$	−13.0000	−	22.5167i	−0.431658	−	0.747653i	0.565358	−	0.824845i	$-0.308738\pi$
$907$	−13.0000	−	22.5167i	−0.431658	−	0.747653i	−0.997016	+	0.0771920i	$0.975405\pi$
$908$	8.00000	+	13.8564i	0.265489	+	0.459841i
$909$	12.0000			0.398015
$910$	−2.00000	−	6.92820i	−0.0662994	−	0.229668i
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$	3.50000	+	6.06218i	0.115897	+	0.200739i
$913$	−1.00000	−	1.73205i	−0.0330952	−	0.0573225i
$914$	−6.00000	+	10.3923i	−0.198462	+	0.343747i
$915$	1.00000			0.0330590
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	6.00000	−	10.3923i	0.198137	−	0.343184i
$918$	7.00000			0.231034
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$	−2.00000			−0.0658665
$923$	14.0000	+	3.46410i	0.460816	+	0.114022i
$924$	2.00000			0.0657952
$925$	4.00000	+	6.92820i	0.131519	+	0.227798i
$926$	2.50000	+	4.33013i	0.0821551	+	0.142297i
$927$	−6.00000	+	10.3923i	−0.197066	+	0.341328i
$928$	6.00000			0.196960
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	−1.50000	+	2.59808i	−0.0491869	+	0.0851943i
$931$	21.0000			0.688247
$932$	4.50000	−	7.79423i	0.147402	−	0.255308i
$933$	−5.00000	−	8.66025i	−0.163693	−	0.283524i
$934$	−10.5000	−	18.1865i	−0.343570	−	0.595082i
$935$	7.00000			0.228924
$936$	3.50000	+	0.866025i	0.114401	+	0.0283069i
$937$	−54.0000			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$938$	14.0000	+	24.2487i	0.457116	+	0.791748i
$939$	−12.5000	−	21.6506i	−0.407922	−	0.706542i
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	28.0000			0.912774			0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000			0.912774			0.456387	+	0.889781i	$0.349143\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$	−40.0000	+	69.2820i	−1.30258	+	2.25613i
$944$	1.00000			0.0325472
$945$	−1.00000	+	1.73205i	−0.0325300	+	0.0563436i
$946$	2.00000	+	3.46410i	0.0650256	+	0.112628i
$947$	0.500000	+	0.866025i	0.0162478	+	0.0281420i	0.874035	−	0.485863i	$-0.161495\pi$
$947$	0.500000	+	0.866025i	0.0162478	+	0.0281420i	−0.857787	+	0.514005i	$0.828161\pi$
$948$	−8.00000			−0.259828
$949$	16.0000	+	55.4256i	0.519382	+	1.79919i
$950$	28.0000			0.908440
$951$	1.00000	+	1.73205i	0.0324272	+	0.0561656i
$952$	−7.00000	−	12.1244i	−0.226871	−	0.392953i
$953$	13.0000	−	22.5167i	0.421111	−	0.729386i	−0.574937	−	0.818198i	$-0.694974\pi$
$953$	13.0000	−	22.5167i	0.421111	−	0.729386i	0.996048	+	0.0888114i	$0.0283068\pi$
$954$	1.00000			0.0323762
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	−10.5000	+	18.1865i	−0.339594	+	0.588195i
$957$	6.00000			0.193952
$958$	8.50000	−	14.7224i	0.274623	−	0.475660i
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−22.0000			−0.709677
$962$	7.00000	+	1.73205i	0.225689	+	0.0558436i
$963$	−12.0000			−0.386695
$964$	4.00000	+	6.92820i	0.128831	+	0.223142i
$965$	13.0000	+	22.5167i	0.418485	+	0.724837i
$966$	−8.00000	+	13.8564i	−0.257396	+	0.445823i
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	24.5000	−	42.4352i	0.787053	−	1.36322i
$970$	−3.00000			−0.0963242
$971$	−9.50000	+	16.4545i	−0.304870	+	0.528049i	−0.977232	−	0.212172i	$-0.931946\pi$
$971$	−9.50000	+	16.4545i	−0.304870	+	0.528049i	0.672363	+	0.740222i	$0.265280\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	19.0000	+	32.9090i	0.609112	+	1.05501i
$974$		0			0
$975$	10.0000	−	10.3923i	0.320256	−	0.332820i
$976$	1.00000			0.0320092
$977$	−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	$0.926302\pi$
$978$	5.00000	+	8.66025i	0.159882	+	0.276924i
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$	−3.00000			−0.0958315
$981$	0.500000	−	0.866025i	0.0159638	−	0.0276501i
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	−10.0000			−0.318950			−0.159475	−	0.987202i	$-0.550980\pi$
$983$	−10.0000			−0.318950			−0.159475	+	0.987202i	$0.550980\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	−11.0000	−	19.0526i	−0.350489	−	0.607065i
$986$	−21.0000	−	36.3731i	−0.668776	−	1.15835i
$987$	−12.0000			−0.381964
$988$	17.5000	−	18.1865i	0.556749	−	0.578591i
$989$	−32.0000			−1.01754
$990$	−0.500000	−	0.866025i	−0.0158910	−	0.0275241i
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$	−1.50000	+	2.59808i	−0.0476250	+	0.0824890i
$993$	26.0000			0.825085
$994$	−4.00000	+	6.92820i	−0.126872	+	0.219749i
$995$	3.50000	−	6.06218i	0.110957	−	0.192184i
$996$	2.00000			0.0633724
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	−0.939880	−	0.341506i	$-0.889063\pi$
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	0.765693	+	0.643206i	$0.222396\pi$
$998$	13.0000	+	22.5167i	0.411508	+	0.712752i
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	858.2.i.a.133.1	✓	2
13.9	even	3	inner	858.2.i.a.529.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
858.2.i.a.133.1	✓	2	1.1	even	1	trivial
858.2.i.a.529.1	yes	2	13.9	even	3	inner

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:	\( N \)	\(=\)	\( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	858.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +1.00000 q^{18} +(3.50000 - 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +2.00000 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{30} +3.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -7.00000 q^{38} +(-2.50000 + 2.59808i) q^{39} +1.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(2.00000 - 3.46410i) q^{43} +1.00000 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.00000 + 6.92820i) q^{46} -6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +7.00000 q^{51} +(3.50000 + 0.866025i) q^{52} +1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.00000 + 1.73205i) q^{56} -7.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-0.500000 + 0.866025i) q^{59} +1.00000 q^{60} +(-0.500000 + 0.866025i) q^{61} +(-1.50000 - 2.59808i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} +1.00000 q^{66} +(7.00000 + 12.1244i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(-4.00000 + 6.92820i) q^{69} +2.00000 q^{70} +(-2.00000 + 3.46410i) q^{71} +(-0.500000 + 0.866025i) q^{72} -16.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.00000 + 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +2.00000 q^{77} +(3.50000 + 0.866025i) q^{78} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +2.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(-3.50000 + 6.06218i) q^{85} -4.00000 q^{86} +(-3.00000 + 5.19615i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +(7.00000 + 1.73205i) q^{91} +8.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(3.50000 - 6.06218i) q^{95} +1.00000 q^{96} +(1.50000 - 2.59808i) q^{97} +(1.50000 - 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} - q^{10} - q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - q^{16} - 7 q^{17} + 2 q^{18} + 7 q^{19} - q^{20} + 4 q^{21} - q^{22} - 8 q^{23} - q^{24} - 8 q^{25} - 5 q^{26} + 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} + 6 q^{31} - q^{32} - q^{33} + 14 q^{34} - 2 q^{35} - q^{36} - 2 q^{37} - 14 q^{38} - 5 q^{39} + 2 q^{40} - 10 q^{41} - 2 q^{42} + 4 q^{43} + 2 q^{44} - q^{45} - 8 q^{46} - 12 q^{47} - q^{48} + 3 q^{49} + 4 q^{50} + 14 q^{51} + 7 q^{52} + 2 q^{53} - q^{54} - q^{55} - 2 q^{56} - 14 q^{57} - 6 q^{58} - q^{59} + 2 q^{60} - q^{61} - 3 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 14 q^{67} - 7 q^{68} - 8 q^{69} + 4 q^{70} - 4 q^{71} - q^{72} - 32 q^{73} - 2 q^{74} + 4 q^{75} + 7 q^{76} + 4 q^{77} + 7 q^{78} - 16 q^{79} - q^{80} - q^{81} - 10 q^{82} + 4 q^{83} - 2 q^{84} - 7 q^{85} - 8 q^{86} - 6 q^{87} - q^{88} - 6 q^{89} + 2 q^{90} + 14 q^{91} + 16 q^{92} - 3 q^{93} + 6 q^{94} + 7 q^{95} + 2 q^{96} + 3 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 - q^10 - q^11 + 2 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - q^16 - 7 * q^17 + 2 * q^18 + 7 * q^19 - q^20 + 4 * q^21 - q^22 - 8 * q^23 - q^24 - 8 * q^25 - 5 * q^26 + 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 + 6 * q^31 - q^32 - q^33 + 14 * q^34 - 2 * q^35 - q^36 - 2 * q^37 - 14 * q^38 - 5 * q^39 + 2 * q^40 - 10 * q^41 - 2 * q^42 + 4 * q^43 + 2 * q^44 - q^45 - 8 * q^46 - 12 * q^47 - q^48 + 3 * q^49 + 4 * q^50 + 14 * q^51 + 7 * q^52 + 2 * q^53 - q^54 - q^55 - 2 * q^56 - 14 * q^57 - 6 * q^58 - q^59 + 2 * q^60 - q^61 - 3 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 14 * q^67 - 7 * q^68 - 8 * q^69 + 4 * q^70 - 4 * q^71 - q^72 - 32 * q^73 - 2 * q^74 + 4 * q^75 + 7 * q^76 + 4 * q^77 + 7 * q^78 - 16 * q^79 - q^80 - q^81 - 10 * q^82 + 4 * q^83 - 2 * q^84 - 7 * q^85 - 8 * q^86 - 6 * q^87 - q^88 - 6 * q^89 + 2 * q^90 + 14 * q^91 + 16 * q^92 - 3 * q^93 + 6 * q^94 + 7 * q^95 + 2 * q^96 + 3 * q^97 + 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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