LMFDB - Embedded newform 462.2.i.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(67,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.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:	$3.68908857338$
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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.2.i.a.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.00000 - 5.19615i) q^{19} +3.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(-2.50000 - 4.33013i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} -6.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +5.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} +5.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.50000 - 4.33013i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(2.50000 + 4.33013i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +6.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(2.50000 + 4.33013i) q^{61} -4.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(2.50000 + 4.33013i) q^{68} +5.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-6.00000 + 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +1.00000 q^{83} +(0.500000 + 2.59808i) q^{84} -15.0000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} -3.00000 q^{90} +(-15.0000 - 5.19615i) q^{91} +5.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-9.00000 + 15.5885i) q^{95} +(0.500000 + 0.866025i) q^{96} +9.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + q^{11} - q^{12} + 12 q^{13} - q^{14} + 6 q^{15} - q^{16} + 5 q^{17} + q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} - 4 q^{25} + 6 q^{26} + 2 q^{27} + 4 q^{28} - 12 q^{29} + 3 q^{30} - 4 q^{31} + q^{32} + q^{33} + 10 q^{34} + 3 q^{35} + 2 q^{36} + 2 q^{37} + 6 q^{38} - 6 q^{39} + 3 q^{40} + 10 q^{41} + 5 q^{42} - 20 q^{43} + q^{44} - 3 q^{45} + 5 q^{46} - 9 q^{47} + 2 q^{48} + 11 q^{49} - 8 q^{50} + 5 q^{51} - 6 q^{52} - 2 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 12 q^{57} - 6 q^{58} + 12 q^{59} - 3 q^{60} + 5 q^{61} - 8 q^{62} + q^{63} + 2 q^{64} - 18 q^{65} - q^{66} - 5 q^{67} + 5 q^{68} + 10 q^{69} - 12 q^{70} + 8 q^{71} + q^{72} - 12 q^{73} - 2 q^{74} - 4 q^{75} + 12 q^{76} - 4 q^{77} - 12 q^{78} + q^{79} - 3 q^{80} - q^{81} + 5 q^{82} + 2 q^{83} + q^{84} - 30 q^{85} - 10 q^{86} + 6 q^{87} - q^{88} - 6 q^{89} - 6 q^{90} - 30 q^{91} + 10 q^{92} - 4 q^{93} + 9 q^{94} - 18 q^{95} + q^{96} + 18 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 + 3 * q^10 + q^11 - q^12 + 12 * q^13 - q^14 + 6 * q^15 - q^16 + 5 * q^17 + q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 + 2 * q^22 - 5 * q^23 + q^24 - 4 * q^25 + 6 * q^26 + 2 * q^27 + 4 * q^28 - 12 * q^29 + 3 * q^30 - 4 * q^31 + q^32 + q^33 + 10 * q^34 + 3 * q^35 + 2 * q^36 + 2 * q^37 + 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 5 * q^42 - 20 * q^43 + q^44 - 3 * q^45 + 5 * q^46 - 9 * q^47 + 2 * q^48 + 11 * q^49 - 8 * q^50 + 5 * q^51 - 6 * q^52 - 2 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 12 * q^57 - 6 * q^58 + 12 * q^59 - 3 * q^60 + 5 * q^61 - 8 * q^62 + q^63 + 2 * q^64 - 18 * q^65 - q^66 - 5 * q^67 + 5 * q^68 + 10 * q^69 - 12 * q^70 + 8 * q^71 + q^72 - 12 * q^73 - 2 * q^74 - 4 * q^75 + 12 * q^76 - 4 * q^77 - 12 * q^78 + q^79 - 3 * q^80 - q^81 + 5 * q^82 + 2 * q^83 + q^84 - 30 * q^85 - 10 * q^86 + 6 * q^87 - q^88 - 6 * q^89 - 6 * q^90 - 30 * q^91 + 10 * q^92 - 4 * q^93 + 9 * q^94 - 18 * q^95 + q^96 + 18 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	−1.00000			−0.408248
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	3.00000			0.670820
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	1.00000			0.213201
$23$	−2.50000	−	4.33013i	−0.521286	−	0.902894i	−0.999694	−	0.0247559i	$-0.992119\pi$
$23$	−2.50000	−	4.33013i	−0.521286	−	0.902894i	0.478407	−	0.878138i	$-0.341214\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$	1.00000			0.192450
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	5.00000			0.857493
$35$	1.50000	+	7.79423i	0.253546	+	1.31747i
$36$	1.00000			0.166667
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	−3.00000	+	5.19615i	−0.480384	+	0.832050i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$	2.50000	+	0.866025i	0.385758	+	0.133631i
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	2.50000	−	4.33013i	0.368605	−	0.638442i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	1.00000			0.144338
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−4.00000			−0.565685
$51$	2.50000	+	4.33013i	0.350070	+	0.606339i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−3.00000			−0.404520
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$	6.00000			0.794719
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	−4.00000			−0.508001
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$	1.00000			0.125000
$65$	−9.00000	−	15.5885i	−1.11631	−	1.93351i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$	5.00000			0.601929
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−6.00000	+	10.3923i	−0.702247	+	1.21633i	0.265429	+	0.964130i	$0.414486\pi$
$73$	−6.00000	+	10.3923i	−0.702247	+	1.21633i	−0.967676	+	0.252197i	$0.918847\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	6.00000			0.688247
$77$	−2.00000	+	1.73205i	−0.227921	+	0.197386i
$78$	−6.00000			−0.679366
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$	1.00000			0.109764			0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000			0.109764			0.0548821	+	0.998493i	$0.482522\pi$
$84$	0.500000	+	2.59808i	0.0545545	+	0.283473i
$85$	−15.0000			−1.62698
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	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	$0.936344\pi$
$90$	−3.00000			−0.316228
$91$	−15.0000	−	5.19615i	−1.57243	−	0.544705i
$92$	5.00000			0.521286
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	−9.00000	+	15.5885i	−0.923381	+	1.59934i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	9.00000			0.913812			0.456906	−	0.889515i	$-0.348958\pi$
$97$	9.00000			0.913812			0.456906	+	0.889515i	$0.348958\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$	−1.00000			−0.100504
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$	−2.50000	+	4.33013i	−0.247537	+	0.428746i
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	0.911078	−	0.412235i	$-0.135252\pi$
$103$	1.00000	+	1.73205i	0.0985329	+	0.170664i	−0.812545	+	0.582899i	$0.801918\pi$
$104$	−6.00000			−0.588348
$105$	−7.50000	−	2.59808i	−0.731925	−	0.253546i
$106$	−2.00000			−0.194257
$107$	6.50000	+	11.2583i	0.628379	+	1.08838i	0.987877	+	0.155238i	$0.0496145\pi$
$107$	6.50000	+	11.2583i	0.628379	+	1.08838i	−0.359498	+	0.933146i	$0.617052\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$	−1.50000	−	2.59808i	−0.143019	−	0.247717i
$111$	−2.00000			−0.189832
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−7.50000	+	12.9904i	−0.699379	+	1.21136i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	12.0000			1.10469
$119$	−10.0000	+	8.66025i	−0.916698	+	0.793884i
$120$	−3.00000			−0.273861
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.50000	+	4.33013i	−0.226339	+	0.392031i
$123$	−2.50000	+	4.33013i	−0.225417	+	0.390434i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−3.00000			−0.268328
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$	9.00000	−	15.5885i	0.789352	−	1.36720i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$	−1.00000			−0.0870388
$133$	3.00000	+	15.5885i	0.260133	+	1.35169i
$134$	−5.00000			−0.431934
$135$	−1.50000	−	2.59808i	−0.129099	−	0.223607i
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	2.50000	+	4.33013i	0.212814	+	0.368605i
$139$	22.0000			1.86602			0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000			1.86602			0.933008	+	0.359856i	$0.117174\pi$
$140$	−7.50000	−	2.59808i	−0.633866	−	0.219578i
$141$	9.00000			0.757937
$142$	2.00000	+	3.46410i	0.167836	+	0.290701i
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	−12.0000			−0.993127
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	−2.00000			−0.164399
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	−0.988969	−	0.148124i	$-0.952676\pi$
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	0.622764	+	0.782410i	$0.286010\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	−5.00000			−0.404226
$154$	−2.50000	−	0.866025i	−0.201456	−	0.0697863i
$155$	12.0000			0.963863
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	12.0000	−	20.7846i	0.957704	−	1.65879i	0.229650	−	0.973273i	$-0.426242\pi$
$157$	12.0000	−	20.7846i	0.957704	−	1.65879i	0.728055	−	0.685519i	$-0.240425\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	−1.00000	−	1.73205i	−0.0793052	−	0.137361i
$160$	−3.00000			−0.237171
$161$	2.50000	+	12.9904i	0.197028	+	1.02379i
$162$	−1.00000			−0.0785674
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	−2.50000	+	4.33013i	−0.195217	+	0.338126i
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$	0.500000	+	0.866025i	0.0388075	+	0.0672166i
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$	−2.00000	+	1.73205i	−0.154303	+	0.133631i
$169$	23.0000			1.76923
$170$	−7.50000	−	12.9904i	−0.575224	−	0.996317i
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$	6.00000			0.454859
$175$	8.00000	−	6.92820i	0.604743	−	0.523723i
$176$	−1.00000			−0.0753778
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	−0.676927	−	0.736050i	$-0.736689\pi$
$179$	4.00000	−	6.92820i	0.298974	−	0.517838i	0.975901	+	0.218212i	$0.0700223\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−3.00000	−	15.5885i	−0.222375	−	1.15549i
$183$	−5.00000			−0.369611
$184$	2.50000	+	4.33013i	0.184302	+	0.319221i
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	−2.50000	−	4.33013i	−0.182818	−	0.316650i
$188$	9.00000			0.656392
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$	−18.0000			−1.30586
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.00000	+	5.19615i	−0.215945	+	0.374027i	−0.953564	−	0.301189i	$-0.902616\pi$
$193$	−3.00000	+	5.19615i	−0.215945	+	0.374027i	0.737620	+	0.675216i	$0.235950\pi$
$194$	4.50000	+	7.79423i	0.323081	+	0.559593i
$195$	18.0000			1.28901
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−2.50000	−	4.33013i	−0.176336	−	0.305424i
$202$	8.00000			0.562878
$203$	15.0000	+	5.19615i	1.05279	+	0.364698i
$204$	−5.00000			−0.350070
$205$	−7.50000	−	12.9904i	−0.523823	−	0.907288i
$206$	−1.00000	+	1.73205i	−0.0696733	+	0.120678i
$207$	−2.50000	+	4.33013i	−0.173762	+	0.300965i
$208$	−3.00000	−	5.19615i	−0.208013	−	0.360288i
$209$	−6.00000			−0.415029
$210$	−1.50000	−	7.79423i	−0.103510	−	0.537853i
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$	−2.00000	+	3.46410i	−0.137038	+	0.237356i
$214$	−6.50000	+	11.2583i	−0.444331	+	0.769604i
$215$	15.0000	+	25.9808i	1.02299	+	1.77187i
$216$	−1.00000			−0.0680414
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$	11.0000			0.745014
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$	15.0000	−	25.9808i	1.00901	−	1.74766i
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$	4.00000			0.266667
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	−0.872823	−	0.488037i	$-0.837713\pi$
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	0.0137585	−	0.999905i	$-0.495620\pi$
$230$	−15.0000			−0.989071
$231$	−0.500000	−	2.59808i	−0.0328976	−	0.170941i
$232$	6.00000			0.393919
$233$	14.5000	+	25.1147i	0.949927	+	1.64532i	0.745573	+	0.666424i	$0.232176\pi$
$233$	14.5000	+	25.1147i	0.949927	+	1.64532i	0.204354	+	0.978897i	$0.434491\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	−13.5000	+	23.3827i	−0.880643	+	1.52532i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$	−1.00000			−0.0649570
$238$	−12.5000	−	4.33013i	−0.810255	−	0.280680i
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−5.00000			−0.320092
$245$	3.00000	−	20.7846i	0.191663	−	1.32788i
$246$	−5.00000			−0.318788
$247$	−18.0000	−	31.1769i	−1.14531	−	1.98374i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−0.500000	+	0.866025i	−0.0316862	+	0.0548821i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−2.50000	−	0.866025i	−0.157485	−	0.0545545i
$253$	−5.00000			−0.314347
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$	7.50000	−	12.9904i	0.469668	−	0.813489i
$256$	−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	$0.689499\pi$
$258$	10.0000			0.622573
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$	18.0000			1.11631
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	6.00000			0.368577
$266$	−12.0000	+	10.3923i	−0.735767	+	0.637193i
$267$	6.00000			0.367194
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	1.50000	−	2.59808i	0.0912871	−	0.158114i
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$	−5.00000			−0.303170
$273$	12.0000	−	10.3923i	0.726273	−	0.628971i
$274$	2.00000			0.120824
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$	−2.50000	+	4.33013i	−0.150482	+	0.260643i
$277$	−9.00000	+	15.5885i	−0.540758	+	0.936620i	0.458103	+	0.888899i	$0.348529\pi$
$277$	−9.00000	+	15.5885i	−0.540758	+	0.936620i	−0.998861	+	0.0477206i	$0.984804\pi$
$278$	11.0000	+	19.0526i	0.659736	+	1.14270i
$279$	4.00000			0.239474
$280$	−1.50000	−	7.79423i	−0.0896421	−	0.465794i
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$	4.50000	+	7.79423i	0.267971	+	0.464140i
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	−0.762978	−	0.646425i	$-0.776263\pi$
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	0.941309	+	0.337546i	$0.109597\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$	−9.00000	−	15.5885i	−0.533114	−	0.923381i
$286$	6.00000			0.354787
$287$	−12.5000	−	4.33013i	−0.737852	−	0.255599i
$288$	−1.00000			−0.0589256
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$	−4.50000	+	7.79423i	−0.263795	+	0.456906i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	8.00000			0.467365			0.233682	−	0.972313i	$-0.424922\pi$
$293$	8.00000			0.467365			0.233682	+	0.972313i	$0.424922\pi$
$294$	−5.50000	−	4.33013i	−0.320767	−	0.252538i
$295$	−36.0000			−2.09600
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	−15.0000	−	25.9808i	−0.867472	−	1.50251i
$300$	4.00000			0.230940
$301$	25.0000	+	8.66025i	1.44098	+	0.499169i
$302$	−9.00000			−0.517892
$303$	4.00000	+	6.92820i	0.229794	+	0.398015i
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$	−2.50000	−	4.33013i	−0.142915	−	0.247537i
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	−0.500000	−	2.59808i	−0.0284901	−	0.148039i
$309$	−2.00000			−0.113776
$310$	6.00000	+	10.3923i	0.340777	+	0.590243i
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	−0.398090	−	0.917346i	$-0.630327\pi$
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	0.993490	−	0.113917i	$-0.0363399\pi$
$312$	3.00000	−	5.19615i	0.169842	−	0.294174i
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	24.0000			1.35440
$315$	6.00000	−	5.19615i	0.338062	−	0.292770i
$316$	−1.00000			−0.0562544
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	0.711535	−	0.702650i	$-0.248000\pi$
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	−0.964281	+	0.264883i	$0.914667\pi$
$318$	1.00000	−	1.73205i	0.0560772	−	0.0971286i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$	−13.0000			−0.725589
$322$	−10.0000	+	8.66025i	−0.557278	+	0.482617i
$323$	−30.0000			−1.66924
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−12.0000	+	20.7846i	−0.665640	+	1.15292i
$326$	−0.500000	+	0.866025i	−0.0276924	+	0.0479647i
$327$	5.50000	+	9.52628i	0.304151	+	0.526804i
$328$	−5.00000			−0.276079
$329$	4.50000	+	23.3827i	0.248093	+	1.28913i
$330$	3.00000			0.165145
$331$	−17.5000	−	30.3109i	−0.961887	−	1.66604i	−0.717756	−	0.696295i	$-0.754831\pi$
$331$	−17.5000	−	30.3109i	−0.961887	−	1.66604i	−0.244131	−	0.969742i	$-0.578503\pi$
$332$	−0.500000	+	0.866025i	−0.0274411	+	0.0475293i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	−12.0000	−	20.7846i	−0.656611	−	1.13728i
$335$	15.0000			0.819538
$336$	−2.50000	−	0.866025i	−0.136386	−	0.0472456i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$	−5.00000	+	8.66025i	−0.271563	+	0.470360i
$340$	7.50000	−	12.9904i	0.406745	−	0.704502i
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$	−6.00000			−0.324443
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	10.0000			0.539164
$345$	−7.50000	−	12.9904i	−0.403786	−	0.699379i
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	−3.50000	+	6.06218i	−0.187890	+	0.325435i	−0.944547	−	0.328378i	$-0.893498\pi$
$347$	−3.50000	+	6.06218i	−0.187890	+	0.325435i	0.756657	+	0.653812i	$0.226831\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−19.0000			−1.01705			−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000			−1.01705			−0.508523	+	0.861048i	$0.669808\pi$
$350$	10.0000	+	3.46410i	0.534522	+	0.185164i
$351$	6.00000			0.320256
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	6.00000			0.317999
$357$	−2.50000	−	12.9904i	−0.132314	−	0.687524i
$358$	8.00000			0.422813
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−11.0000	−	19.0526i	−0.578147	−	1.00138i
$363$	1.00000			0.0524864
$364$	12.0000	−	10.3923i	0.628971	−	0.544705i
$365$	36.0000			1.88433
$366$	−2.50000	−	4.33013i	−0.130677	−	0.226339i
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	−0.623443	−	0.781869i	$-0.714267\pi$
$367$	7.00000	−	12.1244i	0.365397	−	0.632886i	0.988840	+	0.148983i	$0.0475999\pi$
$368$	−2.50000	+	4.33013i	−0.130322	+	0.225723i
$369$	−2.50000	−	4.33013i	−0.130145	−	0.225417i
$370$	6.00000			0.311925
$371$	4.00000	−	3.46410i	0.207670	−	0.179847i
$372$	4.00000			0.207390
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	0.942297	−	0.334777i	$-0.108661\pi$
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	−0.761074	+	0.648665i	$0.775328\pi$
$374$	2.50000	−	4.33013i	0.129272	−	0.223906i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	−36.0000			−1.85409
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	13.0000			0.667765			0.333883	−	0.942615i	$-0.391641\pi$
$379$	13.0000			0.667765			0.333883	+	0.942615i	$0.391641\pi$
$380$	−9.00000	−	15.5885i	−0.461690	−	0.799671i
$381$	−2.50000	+	4.33013i	−0.128079	+	0.221839i
$382$		0			0
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	0.745548	−	0.666452i	$-0.232188\pi$
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	−0.949938	+	0.312437i	$0.898855\pi$
$384$	−1.00000			−0.0510310
$385$	7.50000	+	2.59808i	0.382235	+	0.132410i
$386$	−6.00000			−0.305392
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$	−4.50000	+	7.79423i	−0.228453	+	0.395692i
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$	9.00000	+	15.5885i	0.455733	+	0.789352i
$391$	−25.0000			−1.26430
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	−4.00000			−0.201773
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$	1.50000	−	2.59808i	0.0754732	−	0.130723i
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$	−10.0000			−0.501255
$399$	−15.0000	−	5.19615i	−0.750939	−	0.260133i
$400$	4.00000			0.200000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	−12.0000	+	20.7846i	−0.597763	+	1.03536i
$404$	4.00000	+	6.92820i	0.199007	+	0.344691i
$405$	3.00000			0.149071
$406$	3.00000	+	15.5885i	0.148888	+	0.773642i
$407$	2.00000			0.0991363
$408$	−2.50000	−	4.33013i	−0.123768	−	0.214373i
$409$	−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	$0.246188\pi$
$410$	7.50000	−	12.9904i	0.370399	−	0.641549i
$411$	1.00000	+	1.73205i	0.0493264	+	0.0854358i
$412$	−2.00000			−0.0985329
$413$	−24.0000	+	20.7846i	−1.18096	+	1.02274i
$414$	−5.00000			−0.245737
$415$	−1.50000	−	2.59808i	−0.0736321	−	0.127535i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	−11.0000	+	19.0526i	−0.538672	+	0.933008i
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$	6.00000	−	5.19615i	0.292770	−	0.253546i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	7.00000	+	12.1244i	0.340755	+	0.590204i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	10.0000	+	17.3205i	0.485071	+	0.840168i
$426$	−4.00000			−0.193801
$427$	−2.50000	−	12.9904i	−0.120983	−	0.628649i
$428$	−13.0000			−0.628379
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$	−15.0000	+	25.9808i	−0.723364	+	1.25290i
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	0.469542	+	0.882910i	$0.344419\pi$
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	−0.999394	+	0.0348195i	$0.988914\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$	10.0000	+	3.46410i	0.480015	+	0.166282i
$435$	−18.0000			−0.863034
$436$	5.50000	+	9.52628i	0.263402	+	0.456226i
$437$	−15.0000	+	25.9808i	−0.717547	+	1.24283i
$438$	6.00000	−	10.3923i	0.286691	−	0.496564i
$439$	2.50000	+	4.33013i	0.119318	+	0.206666i	0.919498	−	0.393095i	$-0.128596\pi$
$439$	2.50000	+	4.33013i	0.119318	+	0.206666i	−0.800179	+	0.599761i	$0.795262\pi$
$440$	3.00000			0.143019
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	30.0000			1.42695
$443$	−1.00000	−	1.73205i	−0.0475114	−	0.0822922i	0.841292	−	0.540581i	$-0.181796\pi$
$443$	−1.00000	−	1.73205i	−0.0475114	−	0.0822922i	−0.888803	+	0.458289i	$0.848462\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	18.0000			0.851371
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$	−5.00000	+	8.66025i	−0.235180	+	0.407344i
$453$	−4.50000	−	7.79423i	−0.211428	−	0.366205i
$454$	−3.00000			−0.140797
$455$	9.00000	+	46.7654i	0.421927	+	2.19239i
$456$	−6.00000			−0.280976
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$	13.0000	−	22.5167i	0.607450	−	1.05213i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$	−7.50000	−	12.9904i	−0.349689	−	0.605680i
$461$	−10.0000			−0.465746			−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000			−0.465746			−0.232873	+	0.972507i	$0.574813\pi$
$462$	2.00000	−	1.73205i	0.0930484	−	0.0805823i
$463$	28.0000			1.30127			0.650635	−	0.759390i	$-0.274503\pi$
$463$	28.0000			1.30127			0.650635	+	0.759390i	$0.274503\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	−14.5000	+	25.1147i	−0.671700	+	1.16342i
$467$	−8.00000	−	13.8564i	−0.370196	−	0.641198i	0.619400	−	0.785076i	$-0.287376\pi$
$467$	−8.00000	−	13.8564i	−0.370196	−	0.641198i	−0.989595	+	0.143878i	$0.954043\pi$
$468$	6.00000			0.277350
$469$	10.0000	−	8.66025i	0.461757	−	0.399893i
$470$	−27.0000			−1.24542
$471$	12.0000	+	20.7846i	0.552931	+	0.957704i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$	−0.500000	−	0.866025i	−0.0229658	−	0.0397779i
$475$	24.0000			1.10120
$476$	−2.50000	−	12.9904i	−0.114587	−	0.595413i
$477$	2.00000			0.0915737
$478$	13.0000	+	22.5167i	0.594606	+	1.02989i
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	26.0000			1.18427
$483$	−12.5000	−	4.33013i	−0.568770	−	0.197028i
$484$	1.00000			0.0454545
$485$	−13.5000	−	23.3827i	−0.613003	−	1.06175i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	−0.817147	−	0.576429i	$-0.804446\pi$
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	0.907776	+	0.419456i	$0.137779\pi$
$488$	−2.50000	−	4.33013i	−0.113170	−	0.196016i
$489$	−1.00000			−0.0452216
$490$	19.5000	−	7.79423i	0.880920	−	0.352107i
$491$	−3.00000			−0.135388			−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000			−0.135388			−0.0676941	+	0.997706i	$0.521564\pi$
$492$	−2.50000	−	4.33013i	−0.112709	−	0.195217i
$493$	−15.0000	+	25.9808i	−0.675566	+	1.17011i
$494$	18.0000	−	31.1769i	0.809858	−	1.40272i
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$	4.00000			0.179605
$497$	−10.0000	−	3.46410i	−0.448561	−	0.155386i
$498$	−1.00000			−0.0448111
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$	−24.0000			−1.06799
$506$	−2.50000	−	4.33013i	−0.111139	−	0.192498i
$507$	−11.5000	+	19.9186i	−0.510733	+	0.884615i
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$	15.0000			0.664211
$511$	24.0000	−	20.7846i	1.06170	−	0.919457i
$512$	−1.00000			−0.0441942
$513$	−3.00000	−	5.19615i	−0.132453	−	0.229416i
$514$	−7.00000	+	12.1244i	−0.308757	+	0.534782i
$515$	3.00000	−	5.19615i	0.132196	−	0.228970i
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$	−9.00000			−0.395820
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$	−12.0000			−0.526742
$520$	9.00000	+	15.5885i	0.394676	+	0.683599i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	−3.00000	−	5.19615i	−0.131181	−	0.227212i	0.792951	−	0.609285i	$-0.208544\pi$
$523$	−3.00000	−	5.19615i	−0.131181	−	0.227212i	−0.924132	+	0.382073i	$0.875210\pi$
$524$	−4.00000			−0.174741
$525$	2.00000	+	10.3923i	0.0872872	+	0.453557i
$526$	−24.0000			−1.04645
$527$	10.0000	+	17.3205i	0.435607	+	0.754493i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−12.0000			−0.520756
$532$	−15.0000	−	5.19615i	−0.650332	−	0.225282i
$533$	30.0000			1.29944
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	19.5000	−	33.7750i	0.843059	−	1.46022i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$	9.00000			0.388018
$539$	6.50000	−	2.59808i	0.279975	−	0.111907i
$540$	3.00000			0.129099
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	0.891256	+	0.453500i	$0.149825\pi$
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	−0.0528859	+	0.998601i	$0.516842\pi$
$542$	−12.0000	+	20.7846i	−0.515444	+	0.892775i
$543$	11.0000	−	19.0526i	0.472055	−	0.817624i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	−33.0000			−1.41356
$546$	15.0000	+	5.19615i	0.641941	+	0.222375i
$547$	−42.0000			−1.79579			−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000			−1.79579			−0.897895	+	0.440209i	$0.854904\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	2.50000	−	4.33013i	0.106697	−	0.184805i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$	−5.00000			−0.212814
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$	−18.0000			−0.764747
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	−11.0000	+	19.0526i	−0.466504	+	0.808008i
$557$	16.0000	−	27.7128i	0.677942	−	1.17423i	−0.297658	−	0.954673i	$-0.596205\pi$
$557$	16.0000	−	27.7128i	0.677942	−	1.17423i	0.975600	−	0.219557i	$-0.0704612\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−60.0000			−2.53773
$560$	6.00000	−	5.19615i	0.253546	−	0.219578i
$561$	5.00000			0.211100
$562$	5.50000	+	9.52628i	0.232003	+	0.401842i
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	−0.646737	−	0.762713i	$-0.723867\pi$
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	0.983897	+	0.178735i	$0.0572004\pi$
$564$	−4.50000	+	7.79423i	−0.189484	+	0.328196i
$565$	−15.0000	−	25.9808i	−0.631055	−	1.09302i
$566$	6.00000			0.252199
$567$	2.00000	−	1.73205i	0.0839921	−	0.0727393i
$568$	−4.00000			−0.167836
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	9.00000	−	15.5885i	0.376969	−	0.652929i
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$		0			0
$574$	−2.50000	−	12.9904i	−0.104348	−	0.542208i
$575$	20.0000			0.834058
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−3.00000	−	5.19615i	−0.124676	−	0.215945i
$580$	−18.0000			−0.747409
$581$	−2.50000	−	0.866025i	−0.103717	−	0.0359288i
$582$	−9.00000			−0.373062
$583$	1.00000	+	1.73205i	0.0414158	+	0.0717342i
$584$	6.00000	−	10.3923i	0.248282	−	0.430037i
$585$	−9.00000	+	15.5885i	−0.372104	+	0.644503i
$586$	4.00000	+	6.92820i	0.165238	+	0.286201i
$587$	−24.0000			−0.990586			−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000			−0.990586			−0.495293	+	0.868726i	$0.664939\pi$
$588$	1.00000	−	6.92820i	0.0412393	−	0.285714i
$589$	24.0000			0.988903
$590$	−18.0000	−	31.1769i	−0.741048	−	1.28353i
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−7.00000	−	12.1244i	−0.287456	−	0.497888i	0.685746	−	0.727841i	$-0.259476\pi$
$593$	−7.00000	−	12.1244i	−0.287456	−	0.497888i	−0.973202	+	0.229953i	$0.926143\pi$
$594$	1.00000			0.0410305
$595$	37.5000	+	12.9904i	1.53735	+	0.532554i
$596$	18.0000			0.737309
$597$	−5.00000	−	8.66025i	−0.204636	−	0.354441i
$598$	15.0000	−	25.9808i	0.613396	−	1.06243i
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	−0.833753	−	0.552137i	$-0.813812\pi$
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	0.895042	+	0.445983i	$0.147146\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−44.0000			−1.79480			−0.897399	−	0.441221i	$-0.854546\pi$
$601$	−44.0000			−1.79480			−0.897399	+	0.441221i	$0.854546\pi$
$602$	5.00000	+	25.9808i	0.203785	+	1.05890i
$603$	5.00000			0.203616
$604$	−4.50000	−	7.79423i	−0.183102	−	0.317143i
$605$	−1.50000	+	2.59808i	−0.0609837	+	0.105627i
$606$	−4.00000	+	6.92820i	−0.162489	+	0.281439i
$607$	−16.5000	−	28.5788i	−0.669714	−	1.15998i	−0.977984	−	0.208680i	$-0.933083\pi$
$607$	−16.5000	−	28.5788i	−0.669714	−	1.15998i	0.308270	−	0.951299i	$-0.400250\pi$
$608$	−6.00000			−0.243332
$609$	−12.0000	+	10.3923i	−0.486265	+	0.421117i
$610$	15.0000			0.607332
$611$	−27.0000	−	46.7654i	−1.09230	−	1.89192i
$612$	2.50000	−	4.33013i	0.101057	−	0.175035i
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	−0.0716275	−	0.997431i	$-0.522819\pi$
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	0.899615	−	0.436684i	$-0.143847\pi$
$614$	9.00000	+	15.5885i	0.363210	+	0.629099i
$615$	15.0000			0.604858
$616$	2.00000	−	1.73205i	0.0805823	−	0.0697863i
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	−1.00000	−	1.73205i	−0.0402259	−	0.0696733i
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$	−2.50000	−	4.33013i	−0.100322	−	0.173762i
$622$	21.0000			0.842023
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$	6.00000			0.240192
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	12.0000	+	20.7846i	0.478852	+	0.829396i
$629$	10.0000			0.398726
$630$	7.50000	+	2.59808i	0.298807	+	0.103510i
$631$	28.0000			1.11466			0.557331	−	0.830290i	$-0.311825\pi$
$631$	28.0000			1.11466			0.557331	+	0.830290i	$0.311825\pi$
$632$	−0.500000	−	0.866025i	−0.0198889	−	0.0344486i
$633$	−7.00000	+	12.1244i	−0.278225	+	0.481900i
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	−7.50000	−	12.9904i	−0.297628	−	0.515508i
$636$	2.00000			0.0793052
$637$	33.0000	+	25.9808i	1.30751	+	1.02940i
$638$	−6.00000			−0.237542
$639$	−2.00000	−	3.46410i	−0.0791188	−	0.137038i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	−0.136043	−	0.990703i	$-0.543438\pi$
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	0.925995	−	0.377535i	$-0.123228\pi$
$642$	−6.50000	−	11.2583i	−0.256535	−	0.444331i
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$	−12.5000	−	4.33013i	−0.492569	−	0.170631i
$645$	−30.0000			−1.18125
$646$	−15.0000	−	25.9808i	−0.590167	−	1.02220i
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	−0.983325	−	0.181857i	$-0.941789\pi$
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	0.649155	+	0.760656i	$0.275122\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	−24.0000			−0.941357
$651$	2.00000	+	10.3923i	0.0783862	+	0.407307i
$652$	−1.00000			−0.0391630
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	−5.50000	+	9.52628i	−0.215067	+	0.372507i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	12.0000			0.468165
$658$	−18.0000	+	15.5885i	−0.701713	+	0.607701i
$659$	31.0000			1.20759			0.603794	−	0.797140i	$-0.293655\pi$
$659$	31.0000			1.20759			0.603794	+	0.797140i	$0.293655\pi$
$660$	1.50000	+	2.59808i	0.0583874	+	0.101130i
$661$	−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	$0.191453\pi$
$662$	17.5000	−	30.3109i	0.680157	−	1.17807i
$663$	15.0000	+	25.9808i	0.582552	+	1.00901i
$664$	−1.00000			−0.0388075
$665$	36.0000	−	31.1769i	1.39602	−	1.20899i
$666$	2.00000			0.0774984
$667$	15.0000	+	25.9808i	0.580802	+	1.00598i
$668$	12.0000	−	20.7846i	0.464294	−	0.804181i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	7.50000	+	12.9904i	0.289750	+	0.501862i
$671$	5.00000			0.193023
$672$	−0.500000	−	2.59808i	−0.0192879	−	0.100223i
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	0.985517	−	0.169580i	$-0.0542410\pi$
$677$	9.00000	+	15.5885i	0.345898	+	0.599113i	−0.639618	+	0.768693i	$0.720908\pi$
$678$	−10.0000			−0.384048
$679$	−22.5000	−	7.79423i	−0.863471	−	0.299115i
$680$	15.0000			0.575224
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	−3.00000	−	5.19615i	−0.114708	−	0.198680i
$685$	−6.00000			−0.229248
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	26.0000			0.991962
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$	7.50000	−	12.9904i	0.285520	−	0.494535i
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	0.999876	+	0.0157341i	$0.00500851\pi$
$691$	13.5000	+	23.3827i	0.513564	+	0.889519i	−0.486312	+	0.873785i	$0.661658\pi$
$692$	−12.0000			−0.456172
$693$	2.50000	+	0.866025i	0.0949671	+	0.0328976i
$694$	−7.00000			−0.265716
$695$	−33.0000	−	57.1577i	−1.25176	−	2.16811i
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	12.5000	−	21.6506i	0.473471	−	0.820076i
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	−29.0000			−1.09688
$700$	2.00000	+	10.3923i	0.0755929	+	0.392792i
$701$	−10.0000			−0.377695			−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000			−0.377695			−0.188847	+	0.982006i	$0.560475\pi$
$702$	3.00000	+	5.19615i	0.113228	+	0.196116i
$703$	6.00000	−	10.3923i	0.226294	−	0.391953i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−13.5000	−	23.3827i	−0.508439	−	0.880643i
$706$	−24.0000			−0.903252
$707$	−16.0000	+	13.8564i	−0.601742	+	0.521124i
$708$	−12.0000			−0.450988
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	0.614852	−	0.788642i	$-0.289216\pi$
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	−0.990410	+	0.138157i	$0.955882\pi$
$710$	6.00000	−	10.3923i	0.225176	−	0.390016i
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	20.0000			0.749006
$714$	10.0000	−	8.66025i	0.374241	−	0.324102i
$715$	−18.0000			−0.673162
$716$	4.00000	+	6.92820i	0.149487	+	0.258919i
$717$	−13.0000	+	22.5167i	−0.485494	+	0.840900i
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−18.5000	−	32.0429i	−0.689934	−	1.19500i	−0.971859	−	0.235564i	$-0.924306\pi$
$719$	−18.5000	−	32.0429i	−0.689934	−	1.19500i	0.281925	−	0.959436i	$-0.409027\pi$
$720$	3.00000			0.111803
$721$	−1.00000	−	5.19615i	−0.0372419	−	0.193515i
$722$	−17.0000			−0.632674
$723$	13.0000	+	22.5167i	0.483475	+	0.837404i
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	12.0000	−	20.7846i	0.445669	−	0.771921i
$726$	0.500000	+	0.866025i	0.0185567	+	0.0321412i
$727$	22.0000			0.815935			0.407967	−	0.912996i	$-0.366238\pi$
$727$	22.0000			0.815935			0.407967	+	0.912996i	$0.366238\pi$
$728$	15.0000	+	5.19615i	0.555937	+	0.192582i
$729$	1.00000			0.0370370
$730$	18.0000	+	31.1769i	0.666210	+	1.15391i
$731$	−25.0000	+	43.3013i	−0.924658	+	1.60156i
$732$	2.50000	−	4.33013i	0.0924027	−	0.160046i
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	0.970642	−	0.240527i	$-0.0773202\pi$
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	−0.693624	+	0.720338i	$0.743987\pi$
$734$	14.0000			0.516749
$735$	16.5000	+	12.9904i	0.608612	+	0.479157i
$736$	−5.00000			−0.184302
$737$	2.50000	+	4.33013i	0.0920887	+	0.159502i
$738$	2.50000	−	4.33013i	0.0920263	−	0.159394i
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	−0.759287	−	0.650756i	$-0.774452\pi$
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	0.943215	+	0.332184i	$0.107785\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$	36.0000			1.32249
$742$	5.00000	+	1.73205i	0.183556	+	0.0635856i
$743$	22.0000			0.807102			0.403551	−	0.914957i	$-0.367776\pi$
$743$	22.0000			0.807102			0.403551	+	0.914957i	$0.367776\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−27.0000	+	46.7654i	−0.989203	+	1.71335i
$746$	−3.50000	+	6.06218i	−0.128144	+	0.221952i
$747$	−0.500000	−	0.866025i	−0.0182940	−	0.0316862i
$748$	5.00000			0.182818
$749$	−6.50000	−	33.7750i	−0.237505	−	1.23411i
$750$	3.00000			0.109545
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	0.883694	−	0.468065i	$-0.155049\pi$
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	−0.847203	+	0.531269i	$0.821715\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	−18.0000	−	31.1769i	−0.655521	−	1.13540i
$755$	27.0000			0.982631
$756$	2.00000	−	1.73205i	0.0727393	−	0.0629941i
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	6.50000	+	11.2583i	0.236091	+	0.408921i
$759$	2.50000	−	4.33013i	0.0907443	−	0.157174i
$760$	9.00000	−	15.5885i	0.326464	−	0.565453i
$761$	−23.5000	−	40.7032i	−0.851874	−	1.47549i	−0.879515	−	0.475872i	$-0.842133\pi$
$761$	−23.5000	−	40.7032i	−0.851874	−	1.47549i	0.0276404	−	0.999618i	$-0.491201\pi$
$762$	−5.00000			−0.181131
$763$	−22.0000	+	19.0526i	−0.796453	+	0.689749i
$764$		0			0
$765$	7.50000	+	12.9904i	0.271163	+	0.469668i
$766$	4.00000	−	6.92820i	0.144526	−	0.250326i
$767$	36.0000	−	62.3538i	1.29988	−	2.25147i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	1.50000	+	7.79423i	0.0540562	+	0.280885i
$771$	−14.0000			−0.504198
$772$	−3.00000	−	5.19615i	−0.107972	−	0.187014i
$773$	−5.50000	+	9.52628i	−0.197821	+	0.342636i	−0.947822	−	0.318801i	$-0.896720\pi$
$773$	−5.50000	+	9.52628i	−0.197821	+	0.342636i	0.750000	+	0.661437i	$0.230053\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$	−9.00000			−0.323081
$777$	5.00000	+	1.73205i	0.179374	+	0.0621370i
$778$	21.0000			0.752886
$779$	−15.0000	−	25.9808i	−0.537431	−	0.930857i
$780$	−9.00000	+	15.5885i	−0.322252	+	0.558156i
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	−12.5000	−	21.6506i	−0.446999	−	0.774225i
$783$	−6.00000			−0.214423
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	−72.0000			−2.56979
$786$	−2.00000	−	3.46410i	−0.0713376	−	0.123560i
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.0526599	−	0.998613i	$-0.483230\pi$
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.838494	−	0.544911i	$-0.183437\pi$
$788$	12.0000	−	20.7846i	0.427482	−	0.740421i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$	3.00000			0.106735
$791$	−25.0000	−	8.66025i	−0.888898	−	0.307923i
$792$	1.00000			0.0355335
$793$	15.0000	+	25.9808i	0.532666	+	0.922604i
$794$	13.0000	−	22.5167i	0.461353	−	0.799086i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	−53.0000			−1.87736			−0.938678	−	0.344795i	$-0.887949\pi$
$797$	−53.0000			−1.87736			−0.938678	+	0.344795i	$0.887949\pi$
$798$	−3.00000	−	15.5885i	−0.106199	−	0.551825i
$799$	−45.0000			−1.59199
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	5.00000			0.176336
$805$	30.0000	−	25.9808i	1.05736	−	0.915702i
$806$	−24.0000			−0.845364
$807$	4.50000	+	7.79423i	0.158408	+	0.274370i
$808$	−4.00000	+	6.92820i	−0.140720	+	0.243733i
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	−0.967219	−	0.253946i	$-0.918272\pi$
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	0.703533	+	0.710663i	$0.251605\pi$
$810$	1.50000	+	2.59808i	0.0527046	+	0.0912871i
$811$	42.0000			1.47482			0.737410	−	0.675446i	$-0.236049\pi$
$811$	42.0000			1.47482			0.737410	+	0.675446i	$0.236049\pi$
$812$	−12.0000	+	10.3923i	−0.421117	+	0.364698i
$813$	−24.0000			−0.841717
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$	30.0000	+	51.9615i	1.04957	+	1.81790i
$818$	−10.0000			−0.349642
$819$	3.00000	+	15.5885i	0.104828	+	0.544705i
$820$	15.0000			0.523823
$821$	4.00000	+	6.92820i	0.139601	+	0.241796i	0.927346	−	0.374206i	$-0.122085\pi$
$821$	4.00000	+	6.92820i	0.139601	+	0.241796i	−0.787745	+	0.616002i	$0.788751\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	−5.00000	+	8.66025i	−0.174289	+	0.301877i	−0.939915	−	0.341409i	$-0.889096\pi$
$823$	−5.00000	+	8.66025i	−0.174289	+	0.301877i	0.765626	+	0.643286i	$0.222429\pi$
$824$	−1.00000	−	1.73205i	−0.0348367	−	0.0603388i
$825$	−4.00000			−0.139262
$826$	−30.0000	−	10.3923i	−1.04383	−	0.361595i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$	−2.50000	−	4.33013i	−0.0868810	−	0.150482i
$829$	27.0000	−	46.7654i	0.937749	−	1.62423i	0.168091	−	0.985771i	$-0.446240\pi$
$829$	27.0000	−	46.7654i	0.937749	−	1.62423i	0.769657	−	0.638457i	$-0.220427\pi$
$830$	1.50000	−	2.59808i	0.0520658	−	0.0901805i
$831$	−9.00000	−	15.5885i	−0.312207	−	0.540758i
$832$	6.00000			0.208013
$833$	32.5000	−	12.9904i	1.12606	−	0.450090i
$834$	−22.0000			−0.761798
$835$	36.0000	+	62.3538i	1.24583	+	2.15784i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	−2.00000	+	3.46410i	−0.0691301	+	0.119737i
$838$	−10.0000	−	17.3205i	−0.345444	−	0.598327i
$839$	−9.00000			−0.310715			−0.155357	−	0.987858i	$-0.549653\pi$
$839$	−9.00000			−0.310715			−0.155357	+	0.987858i	$0.549653\pi$
$840$	7.50000	+	2.59808i	0.258775	+	0.0896421i
$841$	7.00000			0.241379
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$	−5.50000	+	9.52628i	−0.189430	+	0.328102i
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	−34.5000	−	59.7558i	−1.18684	−	2.05566i
$846$	−9.00000			−0.309426
$847$	0.500000	+	2.59808i	0.0171802	+	0.0892710i
$848$	2.00000			0.0686803
$849$	3.00000	+	5.19615i	0.102960	+	0.178331i
$850$	−10.0000	+	17.3205i	−0.342997	+	0.594089i
$851$	5.00000	−	8.66025i	0.171398	−	0.296870i
$852$	−2.00000	−	3.46410i	−0.0685189	−	0.118678i
$853$	15.0000			0.513590			0.256795	−	0.966466i	$-0.417333\pi$
$853$	15.0000			0.513590			0.256795	+	0.966466i	$0.417333\pi$
$854$	10.0000	−	8.66025i	0.342193	−	0.296348i
$855$	18.0000			0.615587
$856$	−6.50000	−	11.2583i	−0.222165	−	0.384802i
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	−0.890507	−	0.454969i	$-0.849650\pi$
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	0.839268	+	0.543718i	$0.182984\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	22.5000	+	38.9711i	0.767690	+	1.32968i	0.938813	+	0.344428i	$0.111927\pi$
$859$	22.5000	+	38.9711i	0.767690	+	1.32968i	−0.171122	+	0.985250i	$0.554739\pi$
$860$	−30.0000			−1.02299
$861$	10.0000	−	8.66025i	0.340799	−	0.295141i
$862$	−22.0000			−0.749323
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	18.0000	−	31.1769i	0.612018	−	1.06005i
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$	8.00000			0.271694
$868$	2.00000	+	10.3923i	0.0678844	+	0.352738i
$869$	1.00000			0.0339227
$870$	−9.00000	−	15.5885i	−0.305129	−	0.528498i
$871$	−15.0000	+	25.9808i	−0.508256	+	0.880325i
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$	−4.50000	−	7.79423i	−0.152302	−	0.263795i
$874$	−30.0000			−1.01477
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$	12.0000			0.405442
$877$	1.50000	+	2.59808i	0.0506514	+	0.0877308i	0.890239	−	0.455493i	$-0.150537\pi$
$877$	1.50000	+	2.59808i	0.0506514	+	0.0877308i	−0.839588	+	0.543224i	$0.817204\pi$
$878$	−2.50000	+	4.33013i	−0.0843709	+	0.146135i
$879$	−4.00000	+	6.92820i	−0.134917	+	0.233682i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$	6.50000	−	2.59808i	0.218866	−	0.0874818i
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$	15.0000	+	25.9808i	0.504505	+	0.873828i
$885$	18.0000	−	31.1769i	0.605063	−	1.04800i
$886$	1.00000	−	1.73205i	0.0335957	−	0.0581894i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$	2.00000			0.0671156
$889$	−12.5000	−	4.33013i	−0.419237	−	0.145228i
$890$	−18.0000			−0.603361
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−8.00000	+	13.8564i	−0.267860	+	0.463947i
$893$	−27.0000	+	46.7654i	−0.903521	+	1.56494i
$894$	9.00000	+	15.5885i	0.301005	+	0.521356i
$895$	−24.0000			−0.802232
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	30.0000			1.00167
$898$	1.00000	+	1.73205i	0.0333704	+	0.0577993i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	5.00000	+	8.66025i	0.166574	+	0.288515i
$902$	5.00000			0.166482
$903$	−20.0000	+	17.3205i	−0.665558	+	0.576390i
$904$	−10.0000			−0.332595
$905$	33.0000	+	57.1577i	1.09696	+	1.89999i
$906$	4.50000	−	7.79423i	0.149502	−	0.258946i
$907$	−11.5000	+	19.9186i	−0.381851	+	0.661386i	−0.991327	−	0.131419i	$-0.958047\pi$
$907$	−11.5000	+	19.9186i	−0.381851	+	0.661386i	0.609476	+	0.792805i	$0.291380\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$	−8.00000			−0.265343
$910$	−36.0000	+	31.1769i	−1.19339	+	1.03350i
$911$	51.0000			1.68971			0.844853	−	0.534999i	$-0.179688\pi$
$911$	51.0000			1.68971			0.844853	+	0.534999i	$0.179688\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$	0.500000	−	0.866025i	0.0165476	−	0.0286613i
$914$	−13.0000	+	22.5167i	−0.430002	+	0.744785i
$915$	7.50000	+	12.9904i	0.247942	+	0.429449i
$916$	26.0000			0.859064
$917$	−2.00000	−	10.3923i	−0.0660458	−	0.343184i
$918$	5.00000			0.165025
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$	7.50000	−	12.9904i	0.247268	−	0.428280i
$921$	−9.00000	+	15.5885i	−0.296560	+	0.513657i
$922$	−5.00000	−	8.66025i	−0.164666	−	0.285210i
$923$	24.0000			0.789970
$924$	2.50000	+	0.866025i	0.0822440	+	0.0284901i
$925$	−8.00000			−0.263038
$926$	14.0000	+	24.2487i	0.460069	+	0.796862i
$927$	1.00000	−	1.73205i	0.0328443	−	0.0568880i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	13.0000	+	22.5167i	0.426516	+	0.738748i	0.996561	−	0.0828661i	$-0.0264074\pi$
$929$	13.0000	+	22.5167i	0.426516	+	0.738748i	−0.570045	+	0.821614i	$0.693074\pi$
$930$	−12.0000			−0.393496
$931$	6.00000	−	41.5692i	0.196642	−	1.36238i
$932$	−29.0000			−0.949927
$933$	10.5000	+	18.1865i	0.343755	+	0.595400i
$934$	8.00000	−	13.8564i	0.261768	−	0.453395i
$935$	−7.50000	+	12.9904i	−0.245276	+	0.424831i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$	12.5000	+	4.33013i	0.408139	+	0.141384i
$939$	−6.00000			−0.195803
$940$	−13.5000	−	23.3827i	−0.440321	−	0.762659i
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$	−12.0000	+	20.7846i	−0.390981	+	0.677199i
$943$	−12.5000	−	21.6506i	−0.407056	−	0.705042i
$944$	−12.0000			−0.390567
$945$	1.50000	+	7.79423i	0.0487950	+	0.253546i
$946$	−10.0000			−0.325128
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	0.999896	−	0.0144491i	$-0.00459946\pi$
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	−0.512461	+	0.858710i	$0.671266\pi$
$948$	0.500000	−	0.866025i	0.0162392	−	0.0281272i
$949$	−36.0000	+	62.3538i	−1.16861	+	2.02409i
$950$	12.0000	+	20.7846i	0.389331	+	0.674342i
$951$	9.00000			0.291845
$952$	10.0000	−	8.66025i	0.324102	−	0.280680i
$953$	−21.0000			−0.680257			−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000			−0.680257			−0.340128	+	0.940379i	$0.610471\pi$
$954$	1.00000	+	1.73205i	0.0323762	+	0.0560772i
$955$		0			0
$956$	−13.0000	+	22.5167i	−0.420450	+	0.728241i
$957$	−3.00000	−	5.19615i	−0.0969762	−	0.167968i
$958$	−12.0000			−0.387702
$959$	−4.00000	+	3.46410i	−0.129167	+	0.111862i
$960$	3.00000			0.0968246
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−6.00000	+	10.3923i	−0.193448	+	0.335061i
$963$	6.50000	−	11.2583i	0.209460	−	0.362795i
$964$	13.0000	+	22.5167i	0.418702	+	0.725213i
$965$	18.0000			0.579441
$966$	−2.50000	−	12.9904i	−0.0804362	−	0.417959i
$967$	−21.0000			−0.675314			−0.337657	−	0.941269i	$-0.609634\pi$
$967$	−21.0000			−0.675314			−0.337657	+	0.941269i	$0.609634\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	15.0000	−	25.9808i	0.481869	−	0.834622i
$970$	13.5000	−	23.3827i	0.433459	−	0.750773i
$971$	17.0000	+	29.4449i	0.545556	+	0.944931i	0.998572	+	0.0534281i	$0.0170148\pi$
$971$	17.0000	+	29.4449i	0.545556	+	0.944931i	−0.453016	+	0.891503i	$0.649652\pi$
$972$	1.00000			0.0320750
$973$	−55.0000	−	19.0526i	−1.76322	−	0.610797i
$974$	4.00000			0.128168
$975$	−12.0000	−	20.7846i	−0.384308	−	0.665640i
$976$	2.50000	−	4.33013i	0.0800230	−	0.138604i
$977$	14.0000	−	24.2487i	0.447900	−	0.775785i	−0.550349	−	0.834934i	$-0.685506\pi$
$977$	14.0000	−	24.2487i	0.447900	−	0.775785i	0.998249	+	0.0591494i	$0.0188388\pi$
$978$	−0.500000	−	0.866025i	−0.0159882	−	0.0276924i
$979$	−6.00000			−0.191761
$980$	16.5000	+	12.9904i	0.527073	+	0.414963i
$981$	−11.0000			−0.351203
$982$	−1.50000	−	2.59808i	−0.0478669	−	0.0829079i
$983$	29.5000	−	51.0955i	0.940904	−	1.62969i	0.177152	−	0.984184i	$-0.443312\pi$
$983$	29.5000	−	51.0955i	0.940904	−	1.62969i	0.763752	−	0.645510i	$-0.223355\pi$
$984$	2.50000	−	4.33013i	0.0796971	−	0.138039i
$985$	36.0000	+	62.3538i	1.14706	+	1.98676i
$986$	−30.0000			−0.955395
$987$	−22.5000	−	7.79423i	−0.716183	−	0.248093i
$988$	36.0000			1.14531
$989$	25.0000	+	43.3013i	0.794954	+	1.37690i
$990$	−1.50000	+	2.59808i	−0.0476731	+	0.0825723i
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	−0.986148	−	0.165870i	$-0.946957\pi$
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	0.636721	+	0.771094i	$0.280290\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	35.0000			1.11069
$994$	−2.00000	−	10.3923i	−0.0634361	−	0.329624i
$995$	30.0000			0.951064
$996$	−0.500000	−	0.866025i	−0.0158431	−	0.0274411i
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	6.00000	−	10.3923i	0.189927	−	0.328963i
$999$	1.00000	+	1.73205i	0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.a.67.1	✓	2
3.2	odd	2		1386.2.k.j.991.1		2
7.2	even	3	inner	462.2.i.a.331.1	yes	2
7.3	odd	6		3234.2.a.a.1.1		1
7.4	even	3		3234.2.a.o.1.1		1
21.2	odd	6		1386.2.k.j.793.1		2
21.11	odd	6		9702.2.a.be.1.1		1
21.17	even	6		9702.2.a.ce.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.a.67.1	✓	2	1.1	even	1	trivial
462.2.i.a.331.1	yes	2	7.2	even	3	inner
1386.2.k.j.793.1		2	21.2	odd	6
1386.2.k.j.991.1		2	3.2	odd	2
3234.2.a.a.1.1		1	7.3	odd	6
3234.2.a.o.1.1		1	7.4	even	3
9702.2.a.be.1.1		1	21.11	odd	6
9702.2.a.ce.1.1		1	21.17	even	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.00000 - 5.19615i) q^{19} +3.00000 q^{20} +(2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(-2.50000 - 4.33013i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} -6.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +5.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} +5.00000 q^{41} +(2.50000 + 0.866025i) q^{42} -10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.50000 - 4.33013i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(2.50000 + 4.33013i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +6.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(2.50000 + 4.33013i) q^{61} -4.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(2.50000 + 4.33013i) q^{68} +5.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +4.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-6.00000 + 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +6.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} -6.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +1.00000 q^{83} +(0.500000 + 2.59808i) q^{84} -15.0000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} -3.00000 q^{90} +(-15.0000 - 5.19615i) q^{91} +5.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-9.00000 + 15.5885i) q^{95} +(0.500000 + 0.866025i) q^{96} +9.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 3 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} + 3 q^{10} + q^{11} - q^{12} + 12 q^{13} - q^{14} + 6 q^{15} - q^{16} + 5 q^{17} + q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} - 4 q^{25} + 6 q^{26} + 2 q^{27} + 4 q^{28} - 12 q^{29} + 3 q^{30} - 4 q^{31} + q^{32} + q^{33} + 10 q^{34} + 3 q^{35} + 2 q^{36} + 2 q^{37} + 6 q^{38} - 6 q^{39} + 3 q^{40} + 10 q^{41} + 5 q^{42} - 20 q^{43} + q^{44} - 3 q^{45} + 5 q^{46} - 9 q^{47} + 2 q^{48} + 11 q^{49} - 8 q^{50} + 5 q^{51} - 6 q^{52} - 2 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 12 q^{57} - 6 q^{58} + 12 q^{59} - 3 q^{60} + 5 q^{61} - 8 q^{62} + q^{63} + 2 q^{64} - 18 q^{65} - q^{66} - 5 q^{67} + 5 q^{68} + 10 q^{69} - 12 q^{70} + 8 q^{71} + q^{72} - 12 q^{73} - 2 q^{74} - 4 q^{75} + 12 q^{76} - 4 q^{77} - 12 q^{78} + q^{79} - 3 q^{80} - q^{81} + 5 q^{82} + 2 q^{83} + q^{84} - 30 q^{85} - 10 q^{86} + 6 q^{87} - q^{88} - 6 q^{89} - 6 q^{90} - 30 q^{91} + 10 q^{92} - 4 q^{93} + 9 q^{94} - 18 q^{95} + q^{96} + 18 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 3 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 + 3 * q^10 + q^11 - q^12 + 12 * q^13 - q^14 + 6 * q^15 - q^16 + 5 * q^17 + q^18 - 6 * q^19 + 6 * q^20 + 4 * q^21 + 2 * q^22 - 5 * q^23 + q^24 - 4 * q^25 + 6 * q^26 + 2 * q^27 + 4 * q^28 - 12 * q^29 + 3 * q^30 - 4 * q^31 + q^32 + q^33 + 10 * q^34 + 3 * q^35 + 2 * q^36 + 2 * q^37 + 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 5 * q^42 - 20 * q^43 + q^44 - 3 * q^45 + 5 * q^46 - 9 * q^47 + 2 * q^48 + 11 * q^49 - 8 * q^50 + 5 * q^51 - 6 * q^52 - 2 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 12 * q^57 - 6 * q^58 + 12 * q^59 - 3 * q^60 + 5 * q^61 - 8 * q^62 + q^63 + 2 * q^64 - 18 * q^65 - q^66 - 5 * q^67 + 5 * q^68 + 10 * q^69 - 12 * q^70 + 8 * q^71 + q^72 - 12 * q^73 - 2 * q^74 - 4 * q^75 + 12 * q^76 - 4 * q^77 - 12 * q^78 + q^79 - 3 * q^80 - q^81 + 5 * q^82 + 2 * q^83 + q^84 - 30 * q^85 - 10 * q^86 + 6 * q^87 - q^88 - 6 * q^89 - 6 * q^90 - 30 * q^91 + 10 * q^92 - 4 * q^93 + 9 * q^94 - 18 * q^95 + q^96 + 18 * q^97 - 2 * q^98 - 2 * q^99

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