LMFDB - Embedded newform 858.2.i.g.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.g.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} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(-2.50000 + 4.33013i) 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} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} +(0.500000 - 0.866025i) q^{30} +3.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.00000 - 8.66025i) q^{37} -5.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(1.00000 + 1.73205i) 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} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.00000 + 1.73205i) q^{56} -5.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(0.500000 - 0.866025i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) 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} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(-4.00000 + 6.92820i) q^{69} -2.00000 q^{70} +(0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(5.00000 - 8.66025i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-2.50000 - 4.33013i) q^{76} +2.00000 q^{77} +(-2.50000 - 2.59808i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} +4.00000 q^{86} +(-1.00000 + 1.73205i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(5.00000 + 5.19615i) q^{91} -8.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(1.00000 + 1.73205i) q^{94} +(2.50000 - 4.33013i) q^{95} +1.00000 q^{96} +(-2.50000 + 4.33013i) 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	\( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} - 5 q^{19} + q^{20} + 4 q^{21} - q^{22} + 8 q^{23} - q^{24} - 8 q^{25} - 7 q^{26} - 2 q^{27} + 2 q^{28} + 2 q^{29} + q^{30} + 6 q^{31} + q^{32} - q^{33} - 10 q^{34} - 2 q^{35} - q^{36} - 10 q^{37} - 10 q^{38} - 7 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{42} + 4 q^{43} - 2 q^{44} + q^{45} - 8 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} - 5 q^{52} - 2 q^{53} - q^{54} - q^{55} - 2 q^{56} - 10 q^{57} - 2 q^{58} + q^{59} + 2 q^{60} + 11 q^{61} + 3 q^{62} + 2 q^{63} + 2 q^{64} + 2 q^{65} - 2 q^{66} - 2 q^{67} - 5 q^{68} - 8 q^{69} - 4 q^{70} + q^{72} + 16 q^{73} + 10 q^{74} - 4 q^{75} - 5 q^{76} + 4 q^{77} - 5 q^{78} - 8 q^{79} + q^{80} - q^{81} - 2 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} + 8 q^{86} - 2 q^{87} - q^{88} - 2 q^{89} + 2 q^{90} + 10 q^{91} - 16 q^{92} + 3 q^{93} + 2 q^{94} + 5 q^{95} + 2 q^{96} - 5 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 5 * q^17 - 2 * q^18 - 5 * q^19 + q^20 + 4 * q^21 - q^22 + 8 * q^23 - q^24 - 8 * q^25 - 7 * q^26 - 2 * q^27 + 2 * q^28 + 2 * q^29 + q^30 + 6 * q^31 + q^32 - q^33 - 10 * q^34 - 2 * q^35 - q^36 - 10 * q^37 - 10 * q^38 - 7 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^42 + 4 * q^43 - 2 * q^44 + q^45 - 8 * q^46 + 4 * q^47 + q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 - 5 * q^52 - 2 * q^53 - q^54 - q^55 - 2 * q^56 - 10 * q^57 - 2 * q^58 + q^59 + 2 * q^60 + 11 * q^61 + 3 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 - 2 * q^67 - 5 * q^68 - 8 * q^69 - 4 * q^70 + q^72 + 16 * q^73 + 10 * q^74 - 4 * q^75 - 5 * q^76 + 4 * q^77 - 5 * q^78 - 8 * q^79 + q^80 - q^81 - 2 * q^82 + 12 * q^83 - 2 * q^84 + 5 * q^85 + 8 * q^86 - 2 * q^87 - q^88 - 2 * q^89 + 2 * q^90 + 10 * q^91 - 16 * q^92 + 3 * q^93 + 2 * q^94 + 5 * q^95 + 2 * q^96 - 5 * 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	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	−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
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	−1.00000			−0.235702
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	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	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.00000			−0.800000
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$	−1.00000			−0.192450
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$	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
$34$	−5.00000			−0.857493
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	−5.00000			−0.811107
$39$	−3.50000	+	0.866025i	−0.560449	+	0.138675i
$40$	1.00000			0.158114
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$	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
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	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
$51$	−5.00000			−0.700140
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	−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
$57$	−5.00000			−0.662266
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	−0.831641	−	0.555313i	$-0.812598\pi$
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	0.896736	+	0.442566i	$0.145932\pi$
$60$	1.00000			0.129099
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	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
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	−4.00000	+	6.92820i	−0.481543	+	0.834058i
$70$	−2.00000			−0.239046
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	2.00000			0.227921
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	2.50000	−	4.33013i	0.271163	−	0.469668i
$86$	4.00000			0.431331
$87$	−1.00000	+	1.73205i	−0.107211	+	0.185695i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$	1.00000			0.105409
$91$	5.00000	+	5.19615i	0.524142	+	0.544705i
$92$	−8.00000			−0.834058
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$	1.00000			0.102062
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$	−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	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	−2.50000	−	4.33013i	−0.247537	−	0.428746i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	1.00000	−	3.46410i	0.0980581	−	0.339683i
$105$	−2.00000			−0.195180
$106$	−0.500000	−	0.866025i	−0.0485643	−	0.0841158i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	19.0000			1.81987			0.909935	−	0.414751i	$-0.136131\pi$
$109$	19.0000			1.81987			0.909935	+	0.414751i	$0.136131\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	5.00000	−	8.66025i	0.474579	−	0.821995i
$112$	−2.00000			−0.188982
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	−0.944632	−	0.328133i	$-0.893581\pi$
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	0.756487	+	0.654008i	$0.226914\pi$
$114$	−2.50000	−	4.33013i	−0.234146	−	0.405554i
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	−2.00000			−0.185695
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	1.00000			0.0920575
$119$	5.00000	+	8.66025i	0.458349	+	0.793884i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	11.0000			0.995893
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$	9.00000			0.804984
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	−0.964899	−	0.262620i	$-0.915413\pi$
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	0.255014	−	0.966937i	$-0.417920\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.00000			0.352180
$130$	3.50000	−	0.866025i	0.306970	−	0.0759555i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$	−0.500000	−	0.866025i	−0.0435194	−	0.0753778i
$133$	5.00000	+	8.66025i	0.433555	+	0.750939i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	1.00000			0.0860663
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$	−8.00000			−0.681005
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	−0.991303	−	0.131597i	$-0.957989\pi$
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	0.609618	+	0.792695i	$0.291323\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	1.00000	+	1.73205i	0.0842152	+	0.145865i
$142$		0			0
$143$	−3.50000	+	0.866025i	−0.292685	+	0.0724207i
$144$	1.00000			0.0833333
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	10.0000			0.821995
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$	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	$0.311315\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	−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
$163$	11.0000	−	19.0526i	0.861586	−	1.49231i	−0.00881059	−	0.999961i	$-0.502805\pi$
$163$	11.0000	−	19.0526i	0.861586	−	1.49231i	0.870397	−	0.492350i	$-0.163862\pi$
$164$	−2.00000			−0.156174
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	5.50000	+	9.52628i	0.425603	+	0.737166i	0.996477	−	0.0838722i	$-0.0267288\pi$
$167$	5.50000	+	9.52628i	0.425603	+	0.737166i	−0.570874	+	0.821038i	$0.693395\pi$
$168$	−2.00000			−0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	5.00000			0.383482
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	−0.672949	−	0.739689i	$-0.734973\pi$
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	0.977064	+	0.212947i	$0.0683062\pi$
$174$	−2.00000			−0.151620
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	1.00000			0.0751646
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−2.00000	+	6.92820i	−0.148250	+	0.513553i
$183$	11.0000			0.813143
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$	−1.50000	+	2.59808i	−0.109985	+	0.190500i
$187$	−5.00000			−0.365636
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	5.00000			0.362738
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	−0.983639	−	0.180150i	$-0.942342\pi$
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	0.335805	−	0.941932i	$-0.390992\pi$
$194$	−5.00000			−0.358979
$195$	3.50000	−	0.866025i	0.250640	−	0.0620174i
$196$	−3.00000			−0.214286
$197$	11.0000	+	19.0526i	0.783718	+	1.35744i	0.929762	+	0.368161i	$0.120012\pi$
$197$	11.0000	+	19.0526i	0.783718	+	1.35744i	−0.146045	+	0.989278i	$0.546654\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	0.389885	+	0.920864i	$0.372515\pi$
$199$	−8.50000	+	14.7224i	−0.602549	+	1.04365i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	4.00000			0.282843
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	4.00000			0.280745
$204$	2.50000	−	4.33013i	0.175035	−	0.303170i
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	−8.00000			−0.556038
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$	−5.00000			−0.345857
$210$	−1.00000	−	1.73205i	−0.0690066	−	0.119523i
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	0.809763	−	0.586756i	$-0.199595\pi$
$211$	−1.50000	−	2.59808i	−0.103264	−	0.178859i	−0.913028	+	0.407898i	$0.866262\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$		0			0
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$	3.00000	−	5.19615i	0.203653	−	0.352738i
$218$	9.50000	+	16.4545i	0.643421	+	1.11444i
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$	1.00000			0.0674200
$221$	−12.5000	−	12.9904i	−0.840841	−	0.873828i
$222$	10.0000			0.671156
$223$	−2.50000	−	4.33013i	−0.167412	−	0.289967i	0.770097	−	0.637927i	$-0.220208\pi$
$223$	−2.50000	−	4.33013i	−0.167412	−	0.289967i	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−4.00000			−0.266076
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	2.50000	−	4.33013i	0.165567	−	0.286770i
$229$	24.0000			1.58596			0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000			1.58596			0.792982	+	0.609245i	$0.208527\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$	−1.00000	−	1.73205i	−0.0656532	−	0.113715i
$233$	29.0000			1.89985			0.949927	−	0.312473i	$-0.101157\pi$
$233$	29.0000			1.89985			0.949927	+	0.312473i	$0.101157\pi$
$234$	1.00000	−	3.46410i	0.0653720	−	0.226455i
$235$	−2.00000			−0.130466
$236$	0.500000	+	0.866025i	0.0325472	+	0.0563735i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	−5.00000	+	8.66025i	−0.324102	+	0.561361i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	−1.00000			−0.0642824
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.50000	+	9.52628i	0.352101	+	0.609858i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−2.00000			−0.127515
$247$	−12.5000	−	12.9904i	−0.795356	−	0.826558i
$248$	−3.00000			−0.190500
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	−0.186722	−	0.982413i	$-0.559786\pi$
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	0.944156	−	0.329500i	$-0.106880\pi$
$252$	−2.00000			−0.125988
$253$	−4.00000	+	6.92820i	−0.251478	+	0.435572i
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	5.00000			0.313112
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	2.00000	+	3.46410i	0.124515	+	0.215666i
$259$	−20.0000			−1.24274
$260$	2.50000	+	2.59808i	0.155043	+	0.161126i
$261$	−2.00000			−0.123797
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$	1.00000			0.0614295
$266$	−5.00000	+	8.66025i	−0.306570	+	0.530994i
$267$	1.00000	−	1.73205i	0.0611990	−	0.106000i
$268$	2.00000			0.122169
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$	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	$0.625523\pi$
$272$	5.00000			0.303170
$273$	−2.00000	+	6.92820i	−0.121046	+	0.419314i
$274$	−10.0000			−0.604122
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	−9.00000			−0.539784
$279$	−1.50000	+	2.59808i	−0.0898027	+	0.155543i
$280$	1.00000	−	1.73205i	0.0597614	−	0.103510i
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	4.50000	+	7.79423i	0.267497	+	0.463319i	0.968215	−	0.250120i	$-0.0804700\pi$
$283$	4.50000	+	7.79423i	0.267497	+	0.463319i	−0.700718	+	0.713439i	$0.747137\pi$
$284$		0			0
$285$	5.00000			0.296174
$286$	−2.50000	−	2.59808i	−0.147828	−	0.153627i
$287$	4.00000			0.236113
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	−5.00000			−0.293105
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	−0.342217	−	0.939621i	$-0.611178\pi$
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	0.984844	−	0.173442i	$-0.0554888\pi$
$294$	−3.00000			−0.174964
$295$	−0.500000	+	0.866025i	−0.0291111	+	0.0504219i
$296$	5.00000	+	8.66025i	0.290619	+	0.503367i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	4.00000			0.231714
$299$	−28.0000	+	6.92820i	−1.61928	+	0.400668i
$300$	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
$304$	5.00000			0.286770
$305$	−5.50000	+	9.52628i	−0.314929	+	0.545473i
$306$	2.50000	−	4.33013i	0.142915	−	0.247537i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	−22.0000			−1.24751			−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000			−1.24751			−0.623753	+	0.781622i	$0.714393\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	−15.0000			−0.847850			−0.423925	−	0.905697i	$-0.639348\pi$
$313$	−15.0000			−0.847850			−0.423925	+	0.905697i	$0.639348\pi$
$314$	7.00000	+	12.1244i	0.395033	+	0.684217i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$	0.500000	−	0.866025i	0.0280386	−	0.0485643i
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	−1.00000			−0.0559017
$321$	−2.00000	+	3.46410i	−0.111629	+	0.193347i
$322$	8.00000	+	13.8564i	0.445823	+	0.772187i
$323$	−12.5000	−	21.6506i	−0.695519	−	1.20467i
$324$	1.00000			0.0555556
$325$	4.00000	−	13.8564i	0.221880	−	0.768615i
$326$	22.0000			1.21847
$327$	9.50000	+	16.4545i	0.525351	+	0.909935i
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$	1.00000			0.0550482
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	−0.606980	−	0.794717i	$-0.707619\pi$
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	0.991735	+	0.128302i	$0.0409527\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	10.0000			0.547997
$334$	−5.50000	+	9.52628i	−0.300947	+	0.521255i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$	−4.00000			−0.217250
$340$	2.50000	+	4.33013i	0.135582	+	0.234834i
$341$	1.50000	+	2.59808i	0.0812296	+	0.140694i
$342$	2.50000	−	4.33013i	0.135185	−	0.234146i
$343$	20.0000			1.07990
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	8.00000			0.430083
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$	−1.00000	−	1.73205i	−0.0536056	−	0.0928477i
$349$	14.5000	+	25.1147i	0.776167	+	1.34436i	0.934136	+	0.356917i	$0.116172\pi$
$349$	14.5000	+	25.1147i	0.776167	+	1.34436i	−0.157969	+	0.987444i	$0.550495\pi$
$350$	−8.00000			−0.427618
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	1.00000			0.0533002
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	0.500000	+	0.866025i	0.0265747	+	0.0460287i
$355$		0			0
$356$	2.00000			0.106000
$357$	−5.00000	+	8.66025i	−0.264628	+	0.458349i
$358$	7.50000	−	12.9904i	0.396387	−	0.686563i
$359$	−23.0000			−1.21389			−0.606947	−	0.794742i	$-0.707606\pi$
$359$	−23.0000			−1.21389			−0.606947	+	0.794742i	$0.707606\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	−1.00000			−0.0524864
$364$	−7.00000	+	1.73205i	−0.366900	+	0.0907841i
$365$	−8.00000			−0.418739
$366$	5.50000	+	9.52628i	0.287490	+	0.497947i
$367$	4.50000	+	7.79423i	0.234898	+	0.406855i	0.959243	−	0.282582i	$-0.0911910\pi$
$367$	4.50000	+	7.79423i	0.234898	+	0.406855i	−0.724345	+	0.689438i	$0.757858\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$	−2.00000			−0.104116
$370$	−5.00000	+	8.66025i	−0.259938	+	0.450225i
$371$	−1.00000	+	1.73205i	−0.0519174	+	0.0899236i
$372$	−3.00000			−0.155543
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$	−2.50000	−	4.33013i	−0.129272	−	0.223906i
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$	−2.00000			−0.103142
$377$	−7.00000	+	1.73205i	−0.360518	+	0.0892052i
$378$	−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	$0.816976\pi$
$380$	2.50000	+	4.33013i	0.128247	+	0.222131i
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	−18.0000			−0.920960
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−2.00000			−0.101929
$386$	9.00000	−	15.5885i	0.458088	−	0.793432i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	2.50000	+	2.59808i	0.126592	+	0.131559i
$391$	−40.0000			−2.02289
$392$	−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
$395$	4.00000			0.201262
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	−17.0000			−0.852133
$399$	−5.00000	+	8.66025i	−0.250313	+	0.433555i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	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	$0.785466\pi$
$402$	2.00000			0.0997509
$403$	−3.00000	+	10.3923i	−0.149441	+	0.517678i
$404$	−12.0000			−0.597022
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	2.00000	+	3.46410i	0.0992583	+	0.171920i
$407$	5.00000	−	8.66025i	0.247841	−	0.429273i
$408$	5.00000			0.247537
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	0.210017	+	0.977698i	$0.432648\pi$
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	−0.951720	+	0.306968i	$0.900685\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$	−10.0000			−0.493264
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−1.00000	−	1.73205i	−0.0492068	−	0.0852286i
$414$	−4.00000	−	6.92820i	−0.196589	−	0.340503i
$415$	−6.00000			−0.294528
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$	−9.00000			−0.440732
$418$	−2.50000	−	4.33013i	−0.122279	−	0.211793i
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	0.910735	−	0.412991i	$-0.135516\pi$
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	−0.813029	+	0.582224i	$0.802183\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	1.50000	−	2.59808i	0.0730189	−	0.126472i
$423$	−1.00000	+	1.73205i	−0.0486217	+	0.0842152i
$424$	1.00000			0.0485643
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$		0			0
$427$	−11.0000	−	19.0526i	−0.532327	−	0.922018i
$428$	−4.00000			−0.193347
$429$	−2.50000	−	2.59808i	−0.120701	−	0.125436i
$430$	−4.00000			−0.192897
$431$	18.5000	+	32.0429i	0.891114	+	1.54345i	0.838542	+	0.544837i	$0.183408\pi$
$431$	18.5000	+	32.0429i	0.891114	+	1.54345i	0.0525716	+	0.998617i	$0.483258\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	−0.495388	−	0.868672i	$-0.664974\pi$
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	0.999986	−	0.00531724i	$-0.00169254\pi$
$434$	6.00000			0.288009
$435$	1.00000	−	1.73205i	0.0479463	−	0.0830455i
$436$	−9.50000	+	16.4545i	−0.454967	+	0.788027i
$437$	−40.0000			−1.91346
$438$	−4.00000	+	6.92820i	−0.191127	+	0.331042i
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$	0.500000	+	0.866025i	0.0238366	+	0.0412861i
$441$	−3.00000			−0.142857
$442$	5.00000	−	17.3205i	0.237826	−	0.823853i
$443$	−29.0000			−1.37783			−0.688916	−	0.724841i	$-0.741913\pi$
$443$	−29.0000			−1.37783			−0.688916	+	0.724841i	$0.741913\pi$
$444$	5.00000	+	8.66025i	0.237289	+	0.410997i
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$	2.50000	−	4.33013i	0.118378	−	0.205037i
$447$	4.00000			0.189194
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	−0.972161	−	0.234315i	$-0.924715\pi$
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	0.689003	+	0.724758i	$0.258049\pi$
$450$	4.00000			0.188562
$451$	−1.00000	+	1.73205i	−0.0470882	+	0.0815591i
$452$	−2.00000	−	3.46410i	−0.0940721	−	0.162938i
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$		0			0
$455$	−5.00000	−	5.19615i	−0.234404	−	0.243599i
$456$	5.00000			0.234146
$457$	2.00000	+	3.46410i	0.0935561	+	0.162044i	0.909005	−	0.416785i	$-0.136843\pi$
$457$	2.00000	+	3.46410i	0.0935561	+	0.162044i	−0.815449	+	0.578829i	$0.803510\pi$
$458$	12.0000	+	20.7846i	0.560723	+	0.971201i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$	8.00000			0.373002
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	−0.958652	−	0.284579i	$-0.908146\pi$
$461$	−5.00000	+	8.66025i	−0.232873	+	0.403348i	0.725779	+	0.687928i	$0.241479\pi$
$462$	−1.00000	+	1.73205i	−0.0465242	+	0.0805823i
$463$	−21.0000			−0.975953			−0.487976	−	0.872857i	$-0.662265\pi$
$463$	−21.0000			−0.975953			−0.487976	+	0.872857i	$0.662265\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	−1.50000	−	2.59808i	−0.0695608	−	0.120483i
$466$	14.5000	+	25.1147i	0.671700	+	1.16342i
$467$	−29.0000			−1.34196			−0.670980	−	0.741475i	$-0.734126\pi$
$467$	−29.0000			−1.34196			−0.670980	+	0.741475i	$0.734126\pi$
$468$	3.50000	−	0.866025i	0.161788	−	0.0400320i
$469$	−4.00000			−0.184703
$470$	−1.00000	−	1.73205i	−0.0461266	−	0.0798935i
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	−0.500000	+	0.866025i	−0.0230144	+	0.0398621i
$473$	4.00000			0.183920
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	10.0000	−	17.3205i	0.458831	−	0.794719i
$476$	−10.0000			−0.458349
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$	−1.00000			−0.0456435
$481$	35.0000	−	8.66025i	1.59586	−	0.394874i
$482$	28.0000			1.27537
$483$	8.00000	+	13.8564i	0.364013	+	0.630488i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	2.50000	−	4.33013i	0.113519	−	0.196621i
$486$	1.00000			0.0453609
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$	22.0000			0.994874
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$	−1.00000	−	1.73205i	−0.0450835	−	0.0780869i
$493$	−10.0000			−0.450377
$494$	5.00000	−	17.3205i	0.224961	−	0.779287i
$495$	1.00000			0.0449467
$496$	−1.50000	−	2.59808i	−0.0673520	−	0.116657i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	−5.50000	+	9.52628i	−0.245722	+	0.425603i
$502$	24.0000			1.07117
$503$	−10.5000	+	18.1865i	−0.468172	+	0.810897i	−0.999338	−	0.0363700i	$-0.988421\pi$
$503$	−10.5000	+	18.1865i	−0.468172	+	0.810897i	0.531167	+	0.847267i	$0.321754\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	−6.00000	−	10.3923i	−0.266996	−	0.462451i
$506$	−8.00000			−0.355643
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	16.0000			0.709885
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	2.50000	+	4.33013i	0.110702	+	0.191741i
$511$	8.00000	−	13.8564i	0.353899	−	0.612971i
$512$	−1.00000			−0.0441942
$513$	2.50000	−	4.33013i	0.110378	−	0.191180i
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	4.00000			0.176261
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	1.00000	+	1.73205i	0.0439799	+	0.0761755i
$518$	−10.0000	−	17.3205i	−0.439375	−	0.761019i
$519$	8.00000			0.351161
$520$	−1.00000	+	3.46410i	−0.0438529	+	0.151911i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	−1.00000	−	1.73205i	−0.0437688	−	0.0758098i
$523$	−12.5000	−	21.6506i	−0.546587	−	0.946716i	−0.998505	−	0.0546569i	$-0.982594\pi$
$523$	−12.5000	−	21.6506i	−0.546587	−	0.946716i	0.451918	−	0.892059i	$-0.350740\pi$
$524$	−3.00000	+	5.19615i	−0.131056	+	0.226995i
$525$	−8.00000			−0.349149
$526$	−10.5000	+	18.1865i	−0.457822	+	0.792971i
$527$	−7.50000	+	12.9904i	−0.326705	+	0.565870i
$528$	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
$532$	−10.0000			−0.433555
$533$	−7.00000	+	1.73205i	−0.303204	+	0.0750234i
$534$	2.00000			0.0865485
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	7.50000	−	12.9904i	0.323649	−	0.560576i
$538$	21.0000			0.905374
$539$	−1.50000	+	2.59808i	−0.0646096	+	0.111907i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	42.0000			1.80572			0.902861	−	0.429934i	$-0.141463\pi$
$541$	42.0000			1.80572			0.902861	+	0.429934i	$0.141463\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	−19.0000			−0.813871
$546$	−7.00000	+	1.73205i	−0.299572	+	0.0741249i
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$	5.50000	+	9.52628i	0.234734	+	0.406572i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$	−10.0000			−0.426014
$552$	4.00000	−	6.92820i	0.170251	−	0.294884i
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	−17.0000			−0.722261
$555$	−5.00000	+	8.66025i	−0.212238	+	0.367607i
$556$	−4.50000	−	7.79423i	−0.190843	−	0.330549i
$557$	−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
$559$	10.0000	+	10.3923i	0.422955	+	0.439548i
$560$	2.00000			0.0845154
$561$	−2.50000	−	4.33013i	−0.105550	−	0.182818i
$562$	−1.50000	−	2.59808i	−0.0632737	−	0.109593i
$563$	15.0000	−	25.9808i	0.632175	−	1.09496i	−0.354932	−	0.934892i	$-0.615496\pi$
$563$	15.0000	−	25.9808i	0.632175	−	1.09496i	0.987106	−	0.160066i	$-0.0511708\pi$
$564$	−2.00000			−0.0842152
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	−4.50000	+	7.79423i	−0.189149	+	0.327616i
$567$	−2.00000			−0.0839921
$568$		0			0
$569$	−6.50000	−	11.2583i	−0.272494	−	0.471974i	0.697006	−	0.717066i	$-0.254515\pi$
$569$	−6.50000	−	11.2583i	−0.272494	−	0.471974i	−0.969500	+	0.245092i	$0.921182\pi$
$570$	2.50000	+	4.33013i	0.104713	+	0.181369i
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$	1.00000	−	3.46410i	0.0418121	−	0.144841i
$573$	−18.0000			−0.751961
$574$	2.00000	+	3.46410i	0.0834784	+	0.144589i
$575$	−16.0000	−	27.7128i	−0.667246	−	1.15570i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	34.0000			1.41544			0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$	2.00000			0.0830455
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−2.50000	−	4.33013i	−0.103628	−	0.179490i
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$	−8.00000			−0.331042
$585$	2.50000	+	2.59808i	0.103362	+	0.107417i
$586$	22.0000			0.908812
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−7.50000	+	12.9904i	−0.309032	+	0.535259i
$590$	−1.00000			−0.0411693
$591$	−11.0000	+	19.0526i	−0.452480	+	0.783718i
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	2.00000	+	3.46410i	0.0819232	+	0.141895i
$597$	−17.0000			−0.695764
$598$	−20.0000	−	20.7846i	−0.817861	−	0.849946i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	2.00000			0.0814463
$604$	10.0000	−	17.3205i	0.406894	−	0.704761i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	−12.0000			−0.487467
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$	2.00000	+	3.46410i	0.0810441	+	0.140372i
$610$	−11.0000			−0.445377
$611$	−2.00000	+	6.92820i	−0.0809113	+	0.280285i
$612$	5.00000			0.202113
$613$	−6.50000	−	11.2583i	−0.262533	−	0.454720i	0.704382	−	0.709821i	$-0.251224\pi$
$613$	−6.50000	−	11.2583i	−0.262533	−	0.454720i	−0.966914	+	0.255102i	$0.917891\pi$
$614$		0			0
$615$	1.00000	−	1.73205i	0.0403239	−	0.0698430i
$616$	−2.00000			−0.0805823
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	2.00000	−	3.46410i	0.0804518	−	0.139347i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	1.50000	−	2.59808i	0.0602414	−	0.104341i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	−11.0000	−	19.0526i	−0.441060	−	0.763938i
$623$	−4.00000			−0.160257
$624$	2.50000	+	2.59808i	0.100080	+	0.104006i
$625$	11.0000			0.440000
$626$	−7.50000	−	12.9904i	−0.299760	−	0.519200i
$627$	−2.50000	−	4.33013i	−0.0998404	−	0.172929i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	50.0000			1.99363
$630$	1.00000	−	1.73205i	0.0398410	−	0.0690066i
$631$	4.50000	−	7.79423i	0.179142	−	0.310283i	−0.762445	−	0.647053i	$-0.776001\pi$
$631$	4.50000	−	7.79423i	0.179142	−	0.310283i	0.941587	+	0.336770i	$0.109334\pi$
$632$	4.00000			0.159111
$633$	1.50000	−	2.59808i	0.0596196	−	0.103264i
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$	1.00000			0.0396526
$637$	−10.5000	+	2.59808i	−0.416025	+	0.102940i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−4.00000			−0.157867
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	−0.934055	−	0.357129i	$-0.883756\pi$
$643$	−4.00000	+	6.92820i	−0.157745	+	0.273222i	0.776310	+	0.630351i	$0.217089\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$	−4.00000			−0.157500
$646$	12.5000	−	21.6506i	0.491806	−	0.851833i
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	1.00000			0.0392534
$650$	14.0000	−	3.46410i	0.549125	−	0.135873i
$651$	6.00000			0.235159
$652$	11.0000	+	19.0526i	0.430793	+	0.746156i
$653$	−20.5000	−	35.5070i	−0.802227	−	1.38950i	−0.918147	−	0.396239i	$-0.870315\pi$
$653$	−20.5000	−	35.5070i	−0.802227	−	1.38950i	0.115920	−	0.993259i	$-0.463018\pi$
$654$	−9.50000	+	16.4545i	−0.371479	+	0.643421i
$655$	−6.00000			−0.234439
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	−4.00000	+	6.92820i	−0.156055	+	0.270295i
$658$	4.00000			0.155936
$659$	−5.00000	+	8.66025i	−0.194772	+	0.337356i	−0.946826	−	0.321746i	$-0.895730\pi$
$659$	−5.00000	+	8.66025i	−0.194772	+	0.337356i	0.752054	+	0.659102i	$0.229063\pi$
$660$	0.500000	+	0.866025i	0.0194625	+	0.0337100i
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	14.0000			0.544125
$663$	5.00000	−	17.3205i	0.194184	−	0.672673i
$664$	−6.00000			−0.232845
$665$	−5.00000	−	8.66025i	−0.193892	−	0.335830i
$666$	5.00000	+	8.66025i	0.193746	+	0.335578i
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−11.0000			−0.425603
$669$	2.50000	−	4.33013i	0.0966556	−	0.167412i
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	11.0000			0.424650
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	0.991835	−	0.127532i	$-0.0407054\pi$
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	−0.606363	+	0.795188i	$0.707372\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$	4.00000			0.153960
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	−18.0000			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$678$	−2.00000	−	3.46410i	−0.0768095	−	0.133038i
$679$	5.00000	+	8.66025i	0.191882	+	0.332350i
$680$	−2.50000	+	4.33013i	−0.0958706	+	0.166053i
$681$		0			0
$682$	−1.50000	+	2.59808i	−0.0574380	+	0.0994855i
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	0.0465592	+	0.998916i	$0.485174\pi$
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	−0.888366	+	0.459136i	$0.848159\pi$
$684$	5.00000			0.191180
$685$	5.00000	−	8.66025i	0.191040	−	0.330891i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	12.0000	+	20.7846i	0.457829	+	0.792982i
$688$	−4.00000			−0.152499
$689$	1.00000	−	3.46410i	0.0380970	−	0.131972i
$690$	8.00000			0.304555
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	0.996502	+	0.0835727i	$0.0266331\pi$
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	−0.425875	+	0.904782i	$0.640034\pi$
$692$	4.00000	+	6.92820i	0.152057	+	0.263371i
$693$	−1.00000	+	1.73205i	−0.0379869	+	0.0657952i
$694$	−6.00000			−0.227757
$695$	4.50000	−	7.79423i	0.170695	−	0.295652i
$696$	1.00000	−	1.73205i	0.0379049	−	0.0656532i
$697$	−10.0000			−0.378777
$698$	−14.5000	+	25.1147i	−0.548833	+	0.950607i
$699$	14.5000	+	25.1147i	0.548440	+	0.949927i
$700$	−4.00000	−	6.92820i	−0.151186	−	0.261861i
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	50.0000			1.88579
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	24.0000			0.902613
$708$	−0.500000	+	0.866025i	−0.0187912	+	0.0325472i
$709$	25.0000	−	43.3013i	0.938895	−	1.62621i	0.171358	−	0.985209i	$-0.445185\pi$
$709$	25.0000	−	43.3013i	0.938895	−	1.62621i	0.767537	−	0.641004i	$-0.221482\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$	−10.0000			−0.374241
$715$	3.50000	−	0.866025i	0.130893	−	0.0323875i
$716$	15.0000			0.560576
$717$	7.50000	+	12.9904i	0.280093	+	0.485135i
$718$	−11.5000	−	19.9186i	−0.429176	−	0.743355i
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	−0.396605	−	0.917989i	$-0.629812\pi$
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	0.993305	−	0.115524i	$-0.0368548\pi$
$720$	−1.00000			−0.0372678
$721$	−4.00000	+	6.92820i	−0.148968	+	0.258020i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	28.0000			1.04133
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$	−5.00000	−	5.19615i	−0.185312	−	0.192582i
$729$	1.00000			0.0370370
$730$	−4.00000	−	6.92820i	−0.148047	−	0.256424i
$731$	10.0000	+	17.3205i	0.369863	+	0.640622i
$732$	−5.50000	+	9.52628i	−0.203286	+	0.352101i
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	−4.50000	+	7.79423i	−0.166098	+	0.287690i
$735$	1.50000	−	2.59808i	0.0553283	−	0.0958315i
$736$	8.00000			0.294884
$737$	1.00000	−	1.73205i	0.0368355	−	0.0638009i
$738$	−1.00000	−	1.73205i	−0.0368105	−	0.0637577i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	−10.0000			−0.367607
$741$	5.00000	−	17.3205i	0.183680	−	0.636285i
$742$	−2.00000			−0.0734223
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	0.771598	−	0.636111i	$-0.219458\pi$
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	−0.936687	+	0.350168i	$0.886124\pi$
$744$	−1.50000	−	2.59808i	−0.0549927	−	0.0952501i
$745$	−2.00000	+	3.46410i	−0.0732743	+	0.126915i
$746$	−23.0000			−0.842090
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	2.50000	−	4.33013i	0.0914091	−	0.158325i
$749$	8.00000			0.292314
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	4.50000	+	7.79423i	0.164207	+	0.284415i	0.936374	−	0.351005i	$-0.114160\pi$
$751$	4.50000	+	7.79423i	0.164207	+	0.284415i	−0.772166	+	0.635421i	$0.780827\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	24.0000			0.874609
$754$	−5.00000	−	5.19615i	−0.182089	−	0.189233i
$755$	20.0000			0.727875
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	−12.0000	−	20.7846i	−0.436147	−	0.755429i	0.561241	−	0.827652i	$-0.310324\pi$
$757$	−12.0000	−	20.7846i	−0.436147	−	0.755429i	−0.997389	+	0.0722229i	$0.976991\pi$
$758$	−1.00000	+	1.73205i	−0.0363216	+	0.0629109i
$759$	−8.00000			−0.290382
$760$	−2.50000	+	4.33013i	−0.0906845	+	0.157070i
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	−0.152928	−	0.988237i	$-0.548870\pi$
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	0.932303	−	0.361679i	$-0.117796\pi$
$762$	16.0000			0.579619
$763$	19.0000	−	32.9090i	0.687846	−	1.19138i
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$	2.50000	+	4.33013i	0.0903877	+	0.156556i
$766$	4.00000			0.144526
$767$	2.50000	+	2.59808i	0.0902698	+	0.0938111i
$768$	−1.00000			−0.0360844
$769$	3.00000	+	5.19615i	0.108183	+	0.187378i	0.915034	−	0.403376i	$-0.132163\pi$
$769$	3.00000	+	5.19615i	0.108183	+	0.187378i	−0.806851	+	0.590755i	$0.798830\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$	9.00000	−	15.5885i	0.324127	−	0.561405i
$772$	18.0000			0.647834
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	−12.0000			−0.431053
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$	−10.0000	−	17.3205i	−0.358748	−	0.621370i
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$	−10.0000			−0.358287
$780$	−1.00000	+	3.46410i	−0.0358057	+	0.124035i
$781$		0			0
$782$	−20.0000	−	34.6410i	−0.715199	−	1.23876i
$783$	−1.00000	−	1.73205i	−0.0357371	−	0.0618984i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	−14.0000			−0.499681
$786$	−3.00000	+	5.19615i	−0.107006	+	0.185341i
$787$	12.0000	−	20.7846i	0.427754	−	0.740891i	−0.568919	−	0.822393i	$-0.692638\pi$
$787$	12.0000	−	20.7846i	0.427754	−	0.740891i	0.996673	+	0.0815020i	$0.0259717\pi$
$788$	−22.0000			−0.783718
$789$	−10.5000	+	18.1865i	−0.373810	+	0.647458i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	4.00000	+	6.92820i	0.142224	+	0.246339i
$792$	1.00000			0.0355335
$793$	27.5000	+	28.5788i	0.976554	+	1.01486i
$794$	18.0000			0.638796
$795$	0.500000	+	0.866025i	0.0177332	+	0.0307148i
$796$	−8.50000	−	14.7224i	−0.301275	−	0.521823i
$797$	−23.5000	+	40.7032i	−0.832413	+	1.44178i	0.0637070	+	0.997969i	$0.479708\pi$
$797$	−23.5000	+	40.7032i	−0.832413	+	1.44178i	−0.896120	+	0.443812i	$0.853626\pi$
$798$	−10.0000			−0.353996
$799$	−5.00000	+	8.66025i	−0.176887	+	0.306378i
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	2.00000			0.0706665
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	1.00000	+	1.73205i	0.0352673	+	0.0610847i
$805$	−16.0000			−0.563926
$806$	−10.5000	+	2.59808i	−0.369847	+	0.0915133i
$807$	21.0000			0.739235
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.831897	+	0.554930i	$0.187255\pi$
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.0646355	+	0.997909i	$0.479412\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	27.0000			0.948098			0.474049	−	0.880498i	$-0.342792\pi$
$811$	27.0000			0.948098			0.474049	+	0.880498i	$0.342792\pi$
$812$	−2.00000	+	3.46410i	−0.0701862	+	0.121566i
$813$	−10.0000	+	17.3205i	−0.350715	+	0.607457i
$814$	10.0000			0.350500
$815$	−11.0000	+	19.0526i	−0.385313	+	0.667382i
$816$	2.50000	+	4.33013i	0.0875175	+	0.151585i
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$	−30.0000			−1.04893
$819$	−7.00000	+	1.73205i	−0.244600	+	0.0605228i
$820$	2.00000			0.0698430
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	−5.00000	−	8.66025i	−0.174395	−	0.302061i
$823$	11.5000	−	19.9186i	0.400865	−	0.694318i	−0.592966	−	0.805228i	$-0.702043\pi$
$823$	11.5000	−	19.9186i	0.400865	−	0.694318i	0.993831	+	0.110910i	$0.0353764\pi$
$824$	4.00000			0.139347
$825$	2.00000	−	3.46410i	0.0696311	−	0.120605i
$826$	1.00000	−	1.73205i	0.0347945	−	0.0602658i
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	0.999875	−	0.0158163i	$-0.00503471\pi$
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	−0.513635	+	0.858009i	$0.671701\pi$
$830$	−3.00000	−	5.19615i	−0.104132	−	0.180361i
$831$	−17.0000			−0.589723
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$	−15.0000			−0.519719
$834$	−4.50000	−	7.79423i	−0.155822	−	0.269892i
$835$	−5.50000	−	9.52628i	−0.190335	−	0.329670i
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$	−3.00000			−0.103695
$838$	−2.00000	+	3.46410i	−0.0690889	+	0.119665i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$	2.00000			0.0690066
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	−1.50000	−	2.59808i	−0.0516627	−	0.0894825i
$844$	3.00000			0.103264
$845$	11.0000	+	6.92820i	0.378412	+	0.238337i
$846$	−2.00000			−0.0687614
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$	0.500000	+	0.866025i	0.0171701	+	0.0297394i
$849$	−4.50000	+	7.79423i	−0.154440	+	0.267497i
$850$	20.0000			0.685994
$851$	40.0000	−	69.2820i	1.37118	−	2.37496i
$852$		0			0
$853$	49.0000			1.67773			0.838864	−	0.544341i	$-0.183220\pi$
$853$	49.0000			1.67773			0.838864	+	0.544341i	$0.183220\pi$
$854$	11.0000	−	19.0526i	0.376412	−	0.651965i
$855$	2.50000	+	4.33013i	0.0854982	+	0.148087i
$856$	−2.00000	−	3.46410i	−0.0683586	−	0.118401i
$857$	−11.0000			−0.375753			−0.187876	−	0.982193i	$-0.560160\pi$
$857$	−11.0000			−0.375753			−0.187876	+	0.982193i	$0.560160\pi$
$858$	1.00000	−	3.46410i	0.0341394	−	0.118262i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	−2.00000	−	3.46410i	−0.0681994	−	0.118125i
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$	−18.5000	+	32.0429i	−0.630113	+	1.09139i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−4.00000	+	6.92820i	−0.136004	+	0.235566i
$866$	21.0000			0.713609
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	3.00000	+	5.19615i	0.101827	+	0.176369i
$869$	−2.00000	−	3.46410i	−0.0678454	−	0.117512i
$870$	2.00000			0.0678064
$871$	7.00000	−	1.73205i	0.237186	−	0.0586883i
$872$	−19.0000			−0.643421
$873$	−2.50000	−	4.33013i	−0.0846122	−	0.146553i
$874$	−20.0000	−	34.6410i	−0.676510	−	1.17175i
$875$	9.00000	−	15.5885i	0.304256	−	0.526986i
$876$	−8.00000			−0.270295
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	12.0000	−	20.7846i	0.404980	−	0.701447i
$879$	22.0000			0.742042
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	17.5000	−	4.33013i	0.588589	−	0.145638i
$885$	−1.00000			−0.0336146
$886$	−14.5000	−	25.1147i	−0.487137	−	0.843746i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$	−5.00000	+	8.66025i	−0.167789	+	0.290619i
$889$	−32.0000			−1.07325
$890$	−1.00000	+	1.73205i	−0.0335201	+	0.0580585i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	5.00000			0.167412
$893$	−5.00000	+	8.66025i	−0.167319	+	0.289804i
$894$	2.00000	+	3.46410i	0.0668900	+	0.115857i
$895$	7.50000	+	12.9904i	0.250697	+	0.434221i
$896$	2.00000			0.0668153
$897$	−20.0000	−	20.7846i	−0.667781	−	0.693978i
$898$	−12.0000			−0.400445
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	2.50000	−	4.33013i	0.0832871	−	0.144257i
$902$	−2.00000			−0.0665927
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$	2.00000			0.0664822
$906$	10.0000	−	17.3205i	0.332228	−	0.575435i
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	0.882150	−	0.470968i	$-0.156095\pi$
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	−0.848946	+	0.528480i	$0.822762\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$	2.00000	−	6.92820i	0.0662994	−	0.229668i
$911$	10.0000			0.331315			0.165657	−	0.986183i	$-0.447025\pi$
$911$	10.0000			0.331315			0.165657	+	0.986183i	$0.447025\pi$
$912$	2.50000	+	4.33013i	0.0827833	+	0.143385i
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$	−2.00000	+	3.46410i	−0.0661541	+	0.114582i
$915$	−11.0000			−0.363649
$916$	−12.0000	+	20.7846i	−0.396491	+	0.686743i
$917$	6.00000	−	10.3923i	0.198137	−	0.343184i
$918$	5.00000			0.165025
$919$	22.0000	−	38.1051i	0.725713	−	1.25697i	−0.232967	−	0.972485i	$-0.574843\pi$
$919$	22.0000	−	38.1051i	0.725713	−	1.25697i	0.958680	−	0.284487i	$-0.0918233\pi$
$920$	4.00000	+	6.92820i	0.131876	+	0.228416i
$921$		0			0
$922$	−10.0000			−0.329332
$923$		0			0
$924$	−2.00000			−0.0657952
$925$	20.0000	+	34.6410i	0.657596	+	1.13899i
$926$	−10.5000	−	18.1865i	−0.345051	−	0.597647i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	2.00000			0.0656532
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$	1.50000	−	2.59808i	0.0491869	−	0.0851943i
$931$	−15.0000			−0.491605
$932$	−14.5000	+	25.1147i	−0.474963	+	0.822661i
$933$	−11.0000	−	19.0526i	−0.360124	−	0.623753i
$934$	−14.5000	−	25.1147i	−0.474454	−	0.821779i
$935$	5.00000			0.163517
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	6.00000			0.196011			0.0980057	−	0.995186i	$-0.468754\pi$
$937$	6.00000			0.196011			0.0980057	+	0.995186i	$0.468754\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$	−7.50000	−	12.9904i	−0.244753	−	0.423925i
$940$	1.00000	−	1.73205i	0.0326164	−	0.0564933i
$941$	48.0000			1.56476			0.782378	−	0.622804i	$-0.214007\pi$
$941$	48.0000			1.56476			0.782378	+	0.622804i	$0.214007\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$	−8.00000	+	13.8564i	−0.260516	+	0.451227i
$944$	−1.00000			−0.0325472
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	2.00000	+	3.46410i	0.0650256	+	0.112628i
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.789741	−	0.613441i	$-0.789785\pi$
$947$	−28.5000	−	49.3634i	−0.926126	−	1.60410i	−0.136385	−	0.990656i	$-0.543548\pi$
$948$	4.00000			0.129914
$949$	−8.00000	+	27.7128i	−0.259691	+	0.899596i
$950$	20.0000			0.648886
$951$	1.00000	+	1.73205i	0.0324272	+	0.0561656i
$952$	−5.00000	−	8.66025i	−0.162051	−	0.280680i
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	−0.513971	−	0.857808i	$-0.671826\pi$
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	0.999869	+	0.0162081i	$0.00515944\pi$
$954$	1.00000			0.0323762
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$	−2.00000			−0.0646508
$958$	−1.50000	+	2.59808i	−0.0484628	+	0.0839400i
$959$	10.0000	+	17.3205i	0.322917	+	0.559308i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−22.0000			−0.709677
$962$	25.0000	+	25.9808i	0.806032	+	0.837653i
$963$	−4.00000			−0.128898
$964$	14.0000	+	24.2487i	0.450910	+	0.780998i
$965$	9.00000	+	15.5885i	0.289720	+	0.501810i
$966$	−8.00000	+	13.8564i	−0.257396	+	0.445823i
$967$	−50.0000			−1.60789			−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000			−1.60789			−0.803946	+	0.594703i	$0.797270\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	12.5000	−	21.6506i	0.401558	−	0.695519i
$970$	5.00000			0.160540
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	−0.281880	−	0.959450i	$-0.590958\pi$
$971$	21.5000	−	37.2391i	0.689968	−	1.19506i	0.971848	−	0.235610i	$-0.0757087\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	9.00000	+	15.5885i	0.288527	+	0.499743i
$974$	−16.0000			−0.512673
$975$	14.0000	−	3.46410i	0.448359	−	0.110940i
$976$	−11.0000			−0.352101
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	11.0000	+	19.0526i	0.351741	+	0.609234i
$979$	1.00000	−	1.73205i	0.0319601	−	0.0553566i
$980$	3.00000			0.0958315
$981$	−9.50000	+	16.4545i	−0.303312	+	0.525351i
$982$	−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	$0.550980\pi$
$984$	1.00000	−	1.73205i	0.0318788	−	0.0552158i
$985$	−11.0000	−	19.0526i	−0.350489	−	0.607065i
$986$	−5.00000	−	8.66025i	−0.159232	−	0.275799i
$987$	4.00000			0.127321
$988$	17.5000	−	4.33013i	0.556749	−	0.137760i
$989$	32.0000			1.01754
$990$	0.500000	+	0.866025i	0.0158910	+	0.0275241i
$991$	26.0000	+	45.0333i	0.825917	+	1.43053i	0.901216	+	0.433370i	$0.142676\pi$
$991$	26.0000	+	45.0333i	0.825917	+	1.43053i	−0.0752991	+	0.997161i	$0.523991\pi$
$992$	1.50000	−	2.59808i	0.0476250	−	0.0824890i
$993$	14.0000			0.444277
$994$		0			0
$995$	8.50000	−	14.7224i	0.269468	−	0.466732i
$996$	−6.00000			−0.190117
$997$	4.50000	−	7.79423i	0.142516	−	0.246846i	−0.785927	−	0.618319i	$-0.787814\pi$
$997$	4.50000	−	7.79423i	0.142516	−	0.246846i	0.928444	+	0.371473i	$0.121147\pi$
$998$	−7.00000	−	12.1244i	−0.221581	−	0.383790i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
858.2.i.g.133.1	✓	2	1.1	even	1	trivial
858.2.i.g.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} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(-2.50000 + 4.33013i) 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} +(-3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} +(0.500000 - 0.866025i) q^{30} +3.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.00000 - 8.66025i) q^{37} -5.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(1.00000 + 1.73205i) 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} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{55} +(-1.00000 + 1.73205i) q^{56} -5.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(0.500000 - 0.866025i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) 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} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(-4.00000 + 6.92820i) q^{69} -2.00000 q^{70} +(0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(5.00000 - 8.66025i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-2.50000 - 4.33013i) q^{76} +2.00000 q^{77} +(-2.50000 - 2.59808i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} +4.00000 q^{86} +(-1.00000 + 1.73205i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(5.00000 + 5.19615i) q^{91} -8.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(1.00000 + 1.73205i) q^{94} +(2.50000 - 4.33013i) q^{95} +1.00000 q^{96} +(-2.50000 + 4.33013i) 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	\( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} - 5 q^{19} + q^{20} + 4 q^{21} - q^{22} + 8 q^{23} - q^{24} - 8 q^{25} - 7 q^{26} - 2 q^{27} + 2 q^{28} + 2 q^{29} + q^{30} + 6 q^{31} + q^{32} - q^{33} - 10 q^{34} - 2 q^{35} - q^{36} - 10 q^{37} - 10 q^{38} - 7 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{42} + 4 q^{43} - 2 q^{44} + q^{45} - 8 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} - 5 q^{52} - 2 q^{53} - q^{54} - q^{55} - 2 q^{56} - 10 q^{57} - 2 q^{58} + q^{59} + 2 q^{60} + 11 q^{61} + 3 q^{62} + 2 q^{63} + 2 q^{64} + 2 q^{65} - 2 q^{66} - 2 q^{67} - 5 q^{68} - 8 q^{69} - 4 q^{70} + q^{72} + 16 q^{73} + 10 q^{74} - 4 q^{75} - 5 q^{76} + 4 q^{77} - 5 q^{78} - 8 q^{79} + q^{80} - q^{81} - 2 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} + 8 q^{86} - 2 q^{87} - q^{88} - 2 q^{89} + 2 q^{90} + 10 q^{91} - 16 q^{92} + 3 q^{93} + 2 q^{94} + 5 q^{95} + 2 q^{96} - 5 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 5 * q^17 - 2 * q^18 - 5 * q^19 + q^20 + 4 * q^21 - q^22 + 8 * q^23 - q^24 - 8 * q^25 - 7 * q^26 - 2 * q^27 + 2 * q^28 + 2 * q^29 + q^30 + 6 * q^31 + q^32 - q^33 - 10 * q^34 - 2 * q^35 - q^36 - 10 * q^37 - 10 * q^38 - 7 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^42 + 4 * q^43 - 2 * q^44 + q^45 - 8 * q^46 + 4 * q^47 + q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 - 5 * q^52 - 2 * q^53 - q^54 - q^55 - 2 * q^56 - 10 * q^57 - 2 * q^58 + q^59 + 2 * q^60 + 11 * q^61 + 3 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 - 2 * q^67 - 5 * q^68 - 8 * q^69 - 4 * q^70 + q^72 + 16 * q^73 + 10 * q^74 - 4 * q^75 - 5 * q^76 + 4 * q^77 - 5 * q^78 - 8 * q^79 + q^80 - q^81 - 2 * q^82 + 12 * q^83 - 2 * q^84 + 5 * q^85 + 8 * q^86 - 2 * q^87 - q^88 - 2 * q^89 + 2 * q^90 + 10 * q^91 - 16 * q^92 + 3 * q^93 + 2 * q^94 + 5 * q^95 + 2 * q^96 - 5 * q^97 - 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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