LMFDB - Embedded newform 117.2.r.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(43,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("117.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, 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:	$0.934249703649$
Analytic rank:	$1$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.49
Dual form			117.2.r.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{6} +1.73205i q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{6} +1.73205i q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-3.00000 - 1.73205i) q^{11} -1.73205i q^{12} +(-2.50000 + 2.59808i) q^{13} +(1.50000 - 2.59808i) q^{14} +(1.50000 + 2.59808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} -5.19615i q^{18} +(-1.50000 - 0.866025i) q^{19} -1.73205i q^{20} +(1.50000 - 2.59808i) q^{21} +(3.00000 + 5.19615i) q^{22} -3.00000 q^{23} +(1.50000 - 2.59808i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(6.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-1.50000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -5.19615i q^{30} +(-7.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 + 5.19615i) q^{33} +(4.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(-4.50000 + 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +(6.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +12.1244i q^{41} +(-4.50000 + 2.59808i) q^{42} -1.00000 q^{43} -3.46410i q^{44} -5.19615i q^{45} +(4.50000 + 2.59808i) q^{46} +(-4.50000 + 2.59808i) q^{47} +(-7.50000 + 4.33013i) q^{48} +4.00000 q^{49} +3.46410i q^{50} +(4.50000 - 2.59808i) q^{51} +(-3.50000 - 0.866025i) q^{52} +6.00000 q^{53} +(-4.50000 + 7.79423i) q^{54} +(3.00000 + 5.19615i) q^{55} -3.00000 q^{56} +(1.50000 + 2.59808i) q^{57} +(-9.00000 + 5.19615i) q^{58} +(3.00000 - 1.73205i) q^{59} +(-1.50000 + 2.59808i) q^{60} -5.00000 q^{61} +(7.50000 + 12.9904i) q^{62} +(-4.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(6.00000 - 1.73205i) q^{65} -10.3923i q^{66} -12.1244i q^{67} -3.00000 q^{68} +(4.50000 + 2.59808i) q^{69} +(-4.50000 + 2.59808i) q^{70} +(-7.50000 - 4.33013i) q^{71} +(-4.50000 + 2.59808i) q^{72} -6.92820i q^{73} +9.00000 q^{74} +3.46410i q^{75} -1.73205i q^{76} +(3.00000 - 5.19615i) q^{77} +(-10.5000 - 2.59808i) q^{78} +(5.50000 + 9.52628i) q^{79} +(-7.50000 + 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(10.5000 - 18.1865i) q^{82} +(-4.50000 + 2.59808i) q^{83} +3.00000 q^{84} +(4.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{86} +(-9.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(13.5000 - 7.79423i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(-4.50000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(7.50000 + 12.9904i) q^{93} +9.00000 q^{94} +(1.50000 + 2.59808i) q^{95} +9.00000 q^{96} +15.5885i q^{97} +(-6.00000 - 3.46410i) q^{98} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 + 3 * q^6 + 3 * q^9	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{9} + 3 q^{10} - 6 q^{11} - 5 q^{13} + 3 q^{14} + 3 q^{15} + 5 q^{16} - 3 q^{17} - 3 q^{19} + 3 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 12 q^{26} - 3 q^{28} + 6 q^{29} - 15 q^{31} - 9 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 9 q^{37} + 3 q^{38} + 12 q^{39} + 3 q^{40} - 9 q^{42} - 2 q^{43} + 9 q^{46} - 9 q^{47} - 15 q^{48} + 8 q^{49} + 9 q^{51} - 7 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{57} - 18 q^{58} + 6 q^{59} - 3 q^{60} - 10 q^{61} + 15 q^{62} - 9 q^{63} - 2 q^{64} + 12 q^{65} - 6 q^{68} + 9 q^{69} - 9 q^{70} - 15 q^{71} - 9 q^{72} + 18 q^{74} + 6 q^{77} - 21 q^{78} + 11 q^{79} - 15 q^{80} - 9 q^{81} + 21 q^{82} - 9 q^{83} + 6 q^{84} + 9 q^{85} + 3 q^{86} - 18 q^{87} + 6 q^{88} + 27 q^{89} - 9 q^{90} - 9 q^{91} - 3 q^{92} + 15 q^{93} + 18 q^{94} + 3 q^{95} + 18 q^{96} - 12 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 + 3 * q^6 + 3 * q^9 + 3 * q^10 - 6 * q^11 - 5 * q^13 + 3 * q^14 + 3 * q^15 + 5 * q^16 - 3 * q^17 - 3 * q^19 + 3 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 12 * q^26 - 3 * q^28 + 6 * q^29 - 15 * q^31 - 9 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 9 * q^37 + 3 * q^38 + 12 * q^39 + 3 * q^40 - 9 * q^42 - 2 * q^43 + 9 * q^46 - 9 * q^47 - 15 * q^48 + 8 * q^49 + 9 * q^51 - 7 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^57 - 18 * q^58 + 6 * q^59 - 3 * q^60 - 10 * q^61 + 15 * q^62 - 9 * q^63 - 2 * q^64 + 12 * q^65 - 6 * q^68 + 9 * q^69 - 9 * q^70 - 15 * q^71 - 9 * q^72 + 18 * q^74 + 6 * q^77 - 21 * q^78 + 11 * q^79 - 15 * q^80 - 9 * q^81 + 21 * q^82 - 9 * q^83 + 6 * q^84 + 9 * q^85 + 3 * q^86 - 18 * q^87 + 6 * q^88 + 27 * q^89 - 9 * q^90 - 9 * q^91 - 3 * q^92 + 15 * q^93 + 18 * q^94 + 3 * q^95 + 18 * q^96 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	1.50000	+	2.59808i	0.612372	+	1.06066i
$7$			1.73205i			0.654654i	0.944911	+	0.327327i	$0.106148\pi$
$7$			1.73205i			0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$			1.73205i			0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		−	5.19615i		−	1.22474i
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$		−	1.73205i		−	0.387298i
$21$	1.50000	−	2.59808i	0.327327	−	0.566947i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	6.00000	−	1.73205i	1.17670	−	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$	−1.50000	+	0.866025i	−0.283473	+	0.163663i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		−	5.19615i		−	0.948683i
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−4.50000	+	2.59808i	−0.795495	+	0.459279i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	4.50000	−	2.59808i	0.771744	−	0.445566i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	−4.50000	+	2.59808i	−0.739795	+	0.427121i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−4.50000	+	2.59808i	−0.739795	+	0.427121i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$	6.00000	−	1.73205i	0.960769	−	0.277350i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$			12.1244i			1.89351i	0.321960	+	0.946753i	$0.395658\pi$
$41$			12.1244i			1.89351i	−0.321960	+	0.946753i	$0.604342\pi$
$42$	−4.50000	+	2.59808i	−0.694365	+	0.400892i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		−	3.46410i		−	0.522233i
$45$		−	5.19615i		−	0.774597i
$46$	4.50000	+	2.59808i	0.663489	+	0.383065i
$47$	−4.50000	+	2.59808i	−0.656392	+	0.378968i	−0.790901	−	0.611944i	$-0.790388\pi$
$47$	−4.50000	+	2.59808i	−0.656392	+	0.378968i	0.134509	+	0.990912i	$0.457054\pi$
$48$	−7.50000	+	4.33013i	−1.08253	+	0.625000i
$49$	4.00000			0.571429
$50$			3.46410i			0.489898i
$51$	4.50000	−	2.59808i	0.630126	−	0.363803i
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	−3.00000			−0.400892
$57$	1.50000	+	2.59808i	0.198680	+	0.344124i
$58$	−9.00000	+	5.19615i	−1.18176	+	0.682288i
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	−0.291839	−	0.956467i	$-0.594267\pi$
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	0.682406	+	0.730974i	$0.260934\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	−5.00000			−0.640184			−0.320092	−	0.947386i	$-0.603714\pi$
$61$	−5.00000			−0.640184			−0.320092	+	0.947386i	$0.603714\pi$
$62$	7.50000	+	12.9904i	0.952501	+	1.64978i
$63$	−4.50000	+	2.59808i	−0.566947	+	0.327327i
$64$	−1.00000			−0.125000
$65$	6.00000	−	1.73205i	0.744208	−	0.214834i
$66$		−	10.3923i		−	1.27920i
$67$		−	12.1244i		−	1.48123i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$		−	12.1244i		−	1.48123i	0.671932	−	0.740613i	$-0.265465\pi$
$68$	−3.00000			−0.363803
$69$	4.50000	+	2.59808i	0.541736	+	0.312772i
$70$	−4.50000	+	2.59808i	−0.537853	+	0.310530i
$71$	−7.50000	−	4.33013i	−0.890086	−	0.513892i	−0.0161155	−	0.999870i	$-0.505130\pi$
$71$	−7.50000	−	4.33013i	−0.890086	−	0.513892i	−0.873971	+	0.485979i	$0.838463\pi$
$72$	−4.50000	+	2.59808i	−0.530330	+	0.306186i
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$	9.00000			1.04623
$75$			3.46410i			0.400000i
$76$		−	1.73205i		−	0.198680i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	−10.5000	−	2.59808i	−1.18889	−	0.294174i
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	−7.50000	+	4.33013i	−0.838525	+	0.484123i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	10.5000	−	18.1865i	1.15953	−	2.00837i
$83$	−4.50000	+	2.59808i	−0.493939	+	0.285176i	−0.726207	−	0.687476i	$-0.758719\pi$
$83$	−4.50000	+	2.59808i	−0.493939	+	0.285176i	0.232268	+	0.972652i	$0.425385\pi$
$84$	3.00000			0.327327
$85$	4.50000	−	2.59808i	0.488094	−	0.281801i
$86$	1.50000	+	0.866025i	0.161749	+	0.0933859i
$87$	−9.00000	+	5.19615i	−0.964901	+	0.557086i
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.433800	−	0.901009i	$-0.357172\pi$
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.997197	+	0.0748225i	$0.0238390\pi$
$90$	−4.50000	+	7.79423i	−0.474342	+	0.821584i
$91$	−4.50000	−	4.33013i	−0.471728	−	0.453921i
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$	7.50000	+	12.9904i	0.777714	+	1.34704i
$94$	9.00000			0.928279
$95$	1.50000	+	2.59808i	0.153897	+	0.266557i
$96$	9.00000			0.918559
$97$			15.5885i			1.58277i	0.611319	+	0.791384i	$0.290639\pi$
$97$			15.5885i			1.58277i	−0.611319	+	0.791384i	$0.709361\pi$
$98$	−6.00000	−	3.46410i	−0.606092	−	0.349927i
$99$		−	10.3923i		−	1.04447i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−9.00000			−0.891133
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−4.50000	−	4.33013i	−0.441261	−	0.424604i
$105$	−4.50000	+	2.59808i	−0.439155	+	0.253546i
$106$	−9.00000	−	5.19615i	−0.874157	−	0.504695i
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		−	10.3923i		−	0.990867i
$111$	9.00000			0.854242
$112$	7.50000	+	4.33013i	0.708683	+	0.409159i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		−	5.19615i		−	0.486664i
$115$	4.50000	+	2.59808i	0.419627	+	0.242272i
$116$	6.00000			0.557086
$117$	−10.5000	−	2.59808i	−0.970725	−	0.240192i
$118$	−6.00000			−0.552345
$119$	−4.50000	−	2.59808i	−0.412514	−	0.238165i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	7.50000	+	4.33013i	0.679018	+	0.392031i
$123$	10.5000	−	18.1865i	0.946753	−	1.63982i
$124$		−	8.66025i		−	0.777714i
$125$			12.1244i			1.08444i
$126$	9.00000			0.801784
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	0.955366	−	0.295423i	$-0.0954607\pi$
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	−0.733527	+	0.679660i	$0.762127\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$	−10.5000	−	2.59808i	−0.920911	−	0.227866i
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	−3.00000	+	5.19615i	−0.261116	+	0.452267i
$133$	1.50000	−	2.59808i	0.130066	−	0.225282i
$134$	−10.5000	+	18.1865i	−0.907062	+	1.57108i
$135$	−4.50000	+	7.79423i	−0.387298	+	0.670820i
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$		−	5.19615i		−	0.443937i	−0.975054	−	0.221969i	$-0.928752\pi$
$137$		−	5.19615i		−	0.443937i	0.975054	−	0.221969i	$-0.0712483\pi$
$138$	−4.50000	−	7.79423i	−0.383065	−	0.663489i
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$	3.00000			0.253546
$141$	9.00000			0.757937
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$	12.0000	−	3.46410i	1.00349	−	0.289683i
$144$	15.0000			1.25000
$145$	−9.00000	+	5.19615i	−0.747409	+	0.431517i
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$	−6.00000	−	3.46410i	−0.494872	−	0.285714i
$148$	−4.50000	−	2.59808i	−0.369898	−	0.213561i
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	3.00000	−	5.19615i	0.244949	−	0.424264i
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	−0.862159	−	0.506637i	$-0.830888\pi$
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	0.00768132	+	0.999970i	$0.497555\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$	−9.00000			−0.727607
$154$	−9.00000	+	5.19615i	−0.725241	+	0.418718i
$155$	7.50000	+	12.9904i	0.602414	+	1.04341i
$156$	4.50000	+	4.33013i	0.360288	+	0.346688i
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.115050	+	0.993360i	$0.536703\pi$
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.802749	+	0.596316i	$0.796630\pi$
$158$		−	19.0526i		−	1.51574i
$159$	−9.00000	−	5.19615i	−0.713746	−	0.412082i
$160$	9.00000			0.711512
$161$		−	5.19615i		−	0.409514i
$162$	13.5000	−	7.79423i	1.06066	−	0.612372i
$163$	10.5000	+	6.06218i	0.822423	+	0.474826i	0.851251	−	0.524758i	$-0.175844\pi$
$163$	10.5000	+	6.06218i	0.822423	+	0.474826i	−0.0288280	+	0.999584i	$0.509178\pi$
$164$	−10.5000	+	6.06218i	−0.819912	+	0.473377i
$165$		−	10.3923i		−	0.809040i
$166$	9.00000			0.698535
$167$		−	5.19615i		−	0.402090i	−0.979582	−	0.201045i	$-0.935566\pi$
$167$		−	5.19615i		−	0.402090i	0.979582	−	0.201045i	$-0.0644338\pi$
$168$	4.50000	+	2.59808i	0.347183	+	0.200446i
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−9.00000			−0.690268
$171$		−	5.19615i		−	0.397360i
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−21.0000			−1.59660			−0.798300	−	0.602260i	$-0.794267\pi$
$173$	−21.0000			−1.59660			−0.798300	+	0.602260i	$0.794267\pi$
$174$	18.0000			1.36458
$175$	3.00000	−	1.73205i	0.226779	−	0.130931i
$176$	−15.0000	+	8.66025i	−1.13067	+	0.652791i
$177$	−6.00000			−0.450988
$178$	−27.0000			−2.02374
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$	4.50000	−	2.59808i	0.335410	−	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	+	10.3923i	0.222375	+	0.770329i
$183$	7.50000	+	4.33013i	0.554416	+	0.320092i
$184$		−	5.19615i		−	0.383065i
$185$	9.00000			0.661693
$186$		−	25.9808i		−	1.90500i
$187$	9.00000	−	5.19615i	0.658145	−	0.379980i
$188$	−4.50000	−	2.59808i	−0.328196	−	0.189484i
$189$	9.00000			0.654654
$190$		−	5.19615i		−	0.376969i
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$			5.19615i			0.374027i	0.982357	+	0.187014i	$0.0598809\pi$
$193$			5.19615i			0.374027i	−0.982357	+	0.187014i	$0.940119\pi$
$194$	13.5000	−	23.3827i	0.969244	−	1.67878i
$195$	−10.5000	−	2.59808i	−0.751921	−	0.186052i
$196$	2.00000	+	3.46410i	0.142857	+	0.247436i
$197$	7.50000	−	4.33013i	0.534353	−	0.308509i	−0.208434	−	0.978036i	$-0.566837\pi$
$197$	7.50000	−	4.33013i	0.534353	−	0.308509i	0.742787	+	0.669528i	$0.233503\pi$
$198$	−9.00000	+	15.5885i	−0.639602	+	1.10782i
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	−0.999000	−	0.0447181i	$-0.985761\pi$
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	0.538227	+	0.842800i	$0.319094\pi$
$200$	3.00000	−	1.73205i	0.212132	−	0.122474i
$201$	−10.5000	+	18.1865i	−0.740613	+	1.28278i
$202$	−9.00000	+	5.19615i	−0.633238	+	0.365600i
$203$	9.00000	+	5.19615i	0.631676	+	0.364698i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$	10.5000	−	18.1865i	0.733352	−	1.27020i
$206$	−19.5000	+	11.2583i	−1.35863	+	0.784405i
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$	5.00000	+	17.3205i	0.346688	+	1.20096i
$209$	3.00000	+	5.19615i	0.207514	+	0.359425i
$210$	9.00000			0.621059
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$	7.50000	+	12.9904i	0.513892	+	0.890086i
$214$			25.9808i			1.77601i
$215$	1.50000	+	0.866025i	0.102299	+	0.0590624i
$216$	9.00000			0.612372
$217$	7.50000	−	12.9904i	0.509133	−	0.881845i
$218$		0			0
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$	−13.5000	−	7.79423i	−0.906061	−	0.523114i
$223$	3.00000	+	1.73205i	0.200895	+	0.115987i	0.597073	−	0.802187i	$-0.296330\pi$
$223$	3.00000	+	1.73205i	0.200895	+	0.115987i	−0.396178	+	0.918174i	$0.629664\pi$
$224$	−4.50000	−	7.79423i	−0.300669	−	0.520774i
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$			10.3923i			0.691286i
$227$		−	12.1244i		−	0.804722i	−0.915481	−	0.402361i	$-0.868190\pi$
$227$		−	12.1244i		−	0.804722i	0.915481	−	0.402361i	$-0.131810\pi$
$228$	−1.50000	+	2.59808i	−0.0993399	+	0.172062i
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	−7.50000	−	4.33013i	−0.495614	−	0.286143i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$	−9.00000	+	5.19615i	−0.592157	+	0.341882i
$232$	9.00000	+	5.19615i	0.590879	+	0.341144i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	13.5000	+	12.9904i	0.882523	+	0.849208i
$235$	9.00000			0.587095
$236$	3.00000	+	1.73205i	0.195283	+	0.112747i
$237$		−	19.0526i		−	1.23760i
$238$	4.50000	+	7.79423i	0.291692	+	0.505225i
$239$	4.50000	+	2.59808i	0.291081	+	0.168056i	0.638429	−	0.769681i	$-0.279585\pi$
$239$	4.50000	+	2.59808i	0.291081	+	0.168056i	−0.347348	+	0.937736i	$0.612918\pi$
$240$	15.0000			0.968246
$241$		−	5.19615i		−	0.334714i	−0.985896	−	0.167357i	$-0.946477\pi$
$241$		−	5.19615i		−	0.334714i	0.985896	−	0.167357i	$-0.0535232\pi$
$242$		−	1.73205i		−	0.111340i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−2.50000	−	4.33013i	−0.160046	−	0.277208i
$245$	−6.00000	−	3.46410i	−0.383326	−	0.221313i
$246$	−31.5000	+	18.1865i	−2.00837	+	1.15953i
$247$	6.00000	−	1.73205i	0.381771	−	0.110208i
$248$	7.50000	−	12.9904i	0.476250	−	0.824890i
$249$	9.00000			0.570352
$250$	10.5000	−	18.1865i	0.664078	−	1.15022i
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	−0.972375	−	0.233423i	$-0.925007\pi$
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	0.688338	+	0.725390i	$0.258341\pi$
$252$	−4.50000	−	2.59808i	−0.283473	−	0.163663i
$253$	9.00000	+	5.19615i	0.565825	+	0.326679i
$254$		−	8.66025i		−	0.543393i
$255$	−9.00000			−0.563602
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$	−1.50000	−	2.59808i	−0.0933859	−	0.161749i
$259$	−4.50000	−	7.79423i	−0.279616	−	0.484310i
$260$	4.50000	+	4.33013i	0.279078	+	0.268543i
$261$	18.0000			1.11417
$262$	22.5000	−	12.9904i	1.39005	−	0.802548i
$263$	−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	$0.901515\pi$
$264$	−9.00000	+	5.19615i	−0.553912	+	0.319801i
$265$	−9.00000	−	5.19615i	−0.552866	−	0.319197i
$266$	−4.50000	+	2.59808i	−0.275913	+	0.159298i
$267$	−27.0000			−1.65237
$268$	10.5000	−	6.06218i	0.641390	−	0.370306i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$	13.5000	−	7.79423i	0.821584	−	0.474342i
$271$	13.5000	−	7.79423i	0.820067	−	0.473466i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	13.5000	−	7.79423i	0.820067	−	0.473466i	0.850439	+	0.526073i	$0.176336\pi$
$272$	7.50000	+	12.9904i	0.454754	+	0.787658i
$273$	3.00000	+	10.3923i	0.181568	+	0.628971i
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$			6.92820i			0.417786i
$276$			5.19615i			0.312772i
$277$	23.0000			1.38194			0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000			1.38194			0.690968	+	0.722885i	$0.257185\pi$
$278$		−	27.7128i		−	1.66210i
$279$		−	25.9808i		−	1.55543i
$280$	4.50000	+	2.59808i	0.268926	+	0.155265i
$281$	4.50000	−	2.59808i	0.268447	−	0.154988i	−0.359734	−	0.933055i	$-0.617133\pi$
$281$	4.50000	−	2.59808i	0.268447	−	0.154988i	0.628182	+	0.778067i	$0.283799\pi$
$282$	−13.5000	−	7.79423i	−0.803913	−	0.464140i
$283$	−23.0000			−1.36721			−0.683604	−	0.729853i	$-0.739588\pi$
$283$	−23.0000			−1.36721			−0.683604	+	0.729853i	$0.739588\pi$
$284$		−	8.66025i		−	0.513892i
$285$		−	5.19615i		−	0.307794i
$286$	−21.0000	−	5.19615i	−1.24176	−	0.307255i
$287$	−21.0000			−1.23959
$288$	−13.5000	−	7.79423i	−0.795495	−	0.459279i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	18.0000			1.05700
$291$	13.5000	−	23.3827i	0.791384	−	1.37072i
$292$	6.00000	−	3.46410i	0.351123	−	0.202721i
$293$	12.0000	−	6.92820i	0.701047	−	0.404750i	−0.106690	−	0.994292i	$-0.534025\pi$
$293$	12.0000	−	6.92820i	0.701047	−	0.404750i	0.807737	+	0.589542i	$0.200692\pi$
$294$	6.00000	+	10.3923i	0.349927	+	0.606092i
$295$	−6.00000			−0.349334
$296$	−4.50000	−	7.79423i	−0.261557	−	0.453030i
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$		0			0
$299$	7.50000	−	7.79423i	0.433736	−	0.450752i
$300$	−3.00000	+	1.73205i	−0.173205	+	0.100000i
$301$		−	1.73205i		−	0.0998337i
$302$	21.0000			1.20841
$303$	−9.00000	+	5.19615i	−0.517036	+	0.298511i
$304$	−7.50000	+	4.33013i	−0.430155	+	0.248350i
$305$	7.50000	+	4.33013i	0.429449	+	0.247942i
$306$	13.5000	+	7.79423i	0.771744	+	0.445566i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	6.00000			0.341882
$309$	−19.5000	+	11.2583i	−1.10932	+	0.640464i
$310$		−	25.9808i		−	1.47561i
$311$	−13.5000	+	23.3827i	−0.765515	+	1.32591i	0.174459	+	0.984664i	$0.444182\pi$
$311$	−13.5000	+	23.3827i	−0.765515	+	1.32591i	−0.939974	+	0.341246i	$0.889151\pi$
$312$	3.00000	+	10.3923i	0.169842	+	0.588348i
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	34.5000	−	19.9186i	1.94695	−	1.12407i
$315$	9.00000			0.507093
$316$	−5.50000	+	9.52628i	−0.309399	+	0.535895i
$317$	−7.50000	+	4.33013i	−0.421242	+	0.243204i	−0.695609	−	0.718421i	$-0.744865\pi$
$317$	−7.50000	+	4.33013i	−0.421242	+	0.243204i	0.274367	+	0.961625i	$0.411532\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	−18.0000	+	10.3923i	−1.00781	+	0.581857i
$320$	1.50000	+	0.866025i	0.0838525	+	0.0484123i
$321$			25.9808i			1.45010i
$322$	−4.50000	+	7.79423i	−0.250775	+	0.434355i
$323$	4.50000	−	2.59808i	0.250387	−	0.144561i
$324$	−9.00000			−0.500000
$325$	7.00000	+	1.73205i	0.388290	+	0.0960769i
$326$	−10.5000	−	18.1865i	−0.581541	−	1.00726i
$327$		0			0
$328$	−21.0000			−1.15953
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$	−9.00000	+	15.5885i	−0.495434	+	0.858116i
$331$			15.5885i			0.856819i	0.903585	+	0.428410i	$0.140926\pi$
$331$			15.5885i			0.856819i	−0.903585	+	0.428410i	$0.859074\pi$
$332$	−4.50000	−	2.59808i	−0.246970	−	0.142588i
$333$	−13.5000	−	7.79423i	−0.739795	−	0.427121i
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	−10.5000	+	18.1865i	−0.573676	+	0.993636i
$336$	−7.50000	−	12.9904i	−0.409159	−	0.708683i
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	14.5000	−	25.1147i	0.789865	−	1.36809i	0.926049	−	0.377403i	$-0.123183\pi$
$338$	−10.5000	+	19.9186i	−0.571125	+	1.08343i
$339$			10.3923i			0.564433i
$340$	4.50000	+	2.59808i	0.244047	+	0.140900i
$341$	15.0000	+	25.9808i	0.812296	+	1.40694i
$342$	−4.50000	+	7.79423i	−0.243332	+	0.421464i
$343$			19.0526i			1.02874i
$344$		−	1.73205i		−	0.0933859i
$345$	−4.50000	−	7.79423i	−0.242272	−	0.419627i
$346$	31.5000	+	18.1865i	1.69345	+	0.977714i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	−9.00000	−	5.19615i	−0.482451	−	0.278543i
$349$	−24.0000	−	13.8564i	−1.28469	−	0.741716i	−0.306988	−	0.951713i	$-0.599321\pi$
$349$	−24.0000	−	13.8564i	−1.28469	−	0.741716i	−0.977702	+	0.209997i	$0.932655\pi$
$350$	−6.00000			−0.320713
$351$	13.5000	+	12.9904i	0.720577	+	0.693375i
$352$	18.0000			0.959403
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	0.651102	−	0.758990i	$-0.274307\pi$
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	−0.331754	+	0.943366i	$0.607640\pi$
$354$	9.00000	+	5.19615i	0.478345	+	0.276172i
$355$	7.50000	+	12.9904i	0.398059	+	0.689458i
$356$	13.5000	+	7.79423i	0.715499	+	0.413093i
$357$	4.50000	+	7.79423i	0.238165	+	0.412514i
$358$			5.19615i			0.274625i
$359$			10.3923i			0.548485i	0.961661	+	0.274242i	$0.0884271\pi$
$359$			10.3923i			0.548485i	−0.961661	+	0.274242i	$0.911573\pi$
$360$	9.00000			0.474342
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	33.0000	+	19.0526i	1.73444	+	1.00138i
$363$		−	1.73205i		−	0.0909091i
$364$	1.50000	−	6.06218i	0.0786214	−	0.317744i
$365$	−6.00000	+	10.3923i	−0.314054	+	0.543958i
$366$	−7.50000	−	12.9904i	−0.392031	−	0.679018i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−7.50000	+	12.9904i	−0.390965	+	0.677170i
$369$	−31.5000	+	18.1865i	−1.63982	+	0.946753i
$370$	−13.5000	−	7.79423i	−0.701832	−	0.405203i
$371$			10.3923i			0.539542i
$372$	−7.50000	+	12.9904i	−0.388857	+	0.673520i
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	−18.0000			−0.930758
$375$	10.5000	−	18.1865i	0.542218	−	0.939149i
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	6.00000	+	20.7846i	0.309016	+	1.07046i
$378$	−13.5000	−	7.79423i	−0.694365	−	0.400892i
$379$	−10.5000	+	6.06218i	−0.539349	+	0.311393i	−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−10.5000	+	6.06218i	−0.539349	+	0.311393i	0.205466	+	0.978664i	$0.434129\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$		−	8.66025i		−	0.443678i
$382$	−4.50000	−	2.59808i	−0.230240	−	0.132929i
$383$	−3.00000	+	1.73205i	−0.153293	+	0.0885037i	−0.574684	−	0.818375i	$-0.694875\pi$
$383$	−3.00000	+	1.73205i	−0.153293	+	0.0885037i	0.421392	+	0.906879i	$0.361542\pi$
$384$	−10.5000	−	18.1865i	−0.535826	−	0.928078i
$385$	−9.00000	+	5.19615i	−0.458682	+	0.264820i
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	−13.5000	+	7.79423i	−0.685359	+	0.395692i
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	0.825491	−	0.564416i	$-0.190898\pi$
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	−0.901544	+	0.432688i	$0.857565\pi$
$390$	13.5000	+	12.9904i	0.683599	+	0.657794i
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$			6.92820i			0.349927i
$393$	22.5000	−	12.9904i	1.13497	−	0.655278i
$394$	−15.0000			−0.755689
$395$		−	19.0526i		−	0.958638i
$396$	9.00000	−	5.19615i	0.452267	−	0.261116i
$397$	−22.5000	−	12.9904i	−1.12924	−	0.651969i	−0.185498	−	0.982645i	$-0.559390\pi$
$397$	−22.5000	−	12.9904i	−1.12924	−	0.651969i	−0.943744	+	0.330676i	$0.892723\pi$
$398$	19.5000	−	11.2583i	0.977447	−	0.564329i
$399$	−4.50000	+	2.59808i	−0.225282	+	0.130066i
$400$	−10.0000			−0.500000
$401$		−	29.4449i		−	1.47041i	−0.677847	−	0.735203i	$-0.737087\pi$
$401$		−	29.4449i		−	1.47041i	0.677847	−	0.735203i	$-0.262913\pi$
$402$	31.5000	−	18.1865i	1.57108	−	0.907062i
$403$	30.0000	−	8.66025i	1.49441	−	0.431398i
$404$	6.00000			0.298511
$405$	13.5000	−	7.79423i	0.670820	−	0.387298i
$406$	−9.00000	−	15.5885i	−0.446663	−	0.773642i
$407$	18.0000			0.892227
$408$	4.50000	+	7.79423i	0.222783	+	0.385872i
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	−0.344270	−	0.938871i	$-0.611874\pi$
$409$	6.00000	−	3.46410i	0.296681	−	0.171289i	0.640951	+	0.767582i	$0.278540\pi$
$410$	−31.5000	+	18.1865i	−1.55567	+	0.898169i
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$	13.0000			0.640464
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$			15.5885i			0.766131i
$415$	9.00000			0.441793
$416$	4.50000	−	18.1865i	0.220631	−	0.891668i
$417$		−	27.7128i		−	1.35710i
$418$		−	10.3923i		−	0.508304i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$	−4.50000	−	2.59808i	−0.219578	−	0.126773i
$421$	−7.50000	+	4.33013i	−0.365528	+	0.211037i	−0.671503	−	0.741002i	$-0.734351\pi$
$421$	−7.50000	+	4.33013i	−0.365528	+	0.211037i	0.305975	+	0.952039i	$0.401018\pi$
$422$	−19.5000	−	11.2583i	−0.949245	−	0.548047i
$423$	−13.5000	−	7.79423i	−0.656392	−	0.378968i
$424$			10.3923i			0.504695i
$425$	6.00000			0.291043
$426$		−	25.9808i		−	1.25877i
$427$		−	8.66025i		−	0.419099i
$428$	7.50000	−	12.9904i	0.362526	−	0.627914i
$429$	−21.0000	−	5.19615i	−1.01389	−	0.250873i
$430$	−1.50000	−	2.59808i	−0.0723364	−	0.125290i
$431$	19.5000	−	11.2583i	0.939282	−	0.542295i	0.0495468	−	0.998772i	$-0.484222\pi$
$431$	19.5000	−	11.2583i	0.939282	−	0.542295i	0.889735	+	0.456477i	$0.150889\pi$
$432$	−22.5000	−	12.9904i	−1.08253	−	0.625000i
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	−0.799681	−	0.600425i	$-0.794998\pi$
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	0.919824	+	0.392332i	$0.128332\pi$
$434$	−22.5000	+	12.9904i	−1.08003	+	0.623558i
$435$	18.0000			0.863034
$436$		0			0
$437$	4.50000	+	2.59808i	0.215264	+	0.124283i
$438$	18.0000	−	10.3923i	0.860073	−	0.496564i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	−9.00000	+	5.19615i	−0.429058	+	0.247717i
$441$	6.00000	+	10.3923i	0.285714	+	0.494872i
$442$	−4.50000	+	18.1865i	−0.214043	+	0.865045i
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	0.501129	−	0.865373i	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$	4.50000	+	7.79423i	0.213561	+	0.369898i
$445$	−27.0000			−1.27992
$446$	−3.00000	−	5.19615i	−0.142054	−	0.246045i
$447$		0			0
$448$		−	1.73205i		−	0.0818317i
$449$	13.5000	+	7.79423i	0.637104	+	0.367832i	0.783498	−	0.621394i	$-0.213433\pi$
$449$	13.5000	+	7.79423i	0.637104	+	0.367832i	−0.146394	+	0.989226i	$0.546767\pi$
$450$	−9.00000	+	5.19615i	−0.424264	+	0.244949i
$451$	21.0000	−	36.3731i	0.988851	−	1.71274i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	21.0000			0.986666
$454$	−10.5000	+	18.1865i	−0.492789	+	0.853536i
$455$	3.00000	+	10.3923i	0.140642	+	0.487199i
$456$	−4.50000	+	2.59808i	−0.210732	+	0.121666i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	7.50000	+	12.9904i	0.350452	+	0.607001i
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$			5.19615i			0.242272i
$461$			1.73205i			0.0806696i	0.999186	+	0.0403348i	$0.0128425\pi$
$461$			1.73205i			0.0806696i	−0.999186	+	0.0403348i	$0.987158\pi$
$462$	18.0000			0.837436
$463$	22.5000	+	12.9904i	1.04566	+	0.603714i	0.921432	−	0.388539i	$-0.127020\pi$
$463$	22.5000	+	12.9904i	1.04566	+	0.603714i	0.124231	+	0.992253i	$0.460353\pi$
$464$	−15.0000	−	25.9808i	−0.696358	−	1.20613i
$465$		−	25.9808i		−	1.20483i
$466$	27.0000	+	15.5885i	1.25075	+	0.722121i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−3.00000	−	10.3923i	−0.138675	−	0.480384i
$469$	21.0000			0.969690
$470$	−13.5000	−	7.79423i	−0.622709	−	0.359521i
$471$	34.5000	−	19.9186i	1.58968	−	0.917800i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	3.00000	+	1.73205i	0.137940	+	0.0796398i
$474$	−16.5000	+	28.5788i	−0.757870	+	1.31267i
$475$			3.46410i			0.158944i
$476$		−	5.19615i		−	0.238165i
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	−4.50000	−	7.79423i	−0.205825	−	0.356500i
$479$	−21.0000	−	12.1244i	−0.959514	−	0.553976i	−0.0634909	−	0.997982i	$-0.520223\pi$
$479$	−21.0000	−	12.1244i	−0.959514	−	0.553976i	−0.896024	+	0.444006i	$0.853557\pi$
$480$	−13.5000	−	7.79423i	−0.616188	−	0.355756i
$481$	4.50000	−	18.1865i	0.205182	−	0.829235i
$482$	−4.50000	+	7.79423i	−0.204969	+	0.355017i
$483$	−4.50000	+	7.79423i	−0.204757	+	0.354650i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	13.5000	−	23.3827i	0.613003	−	1.06175i
$486$	−27.0000			−1.22474
$487$	−7.50000	−	4.33013i	−0.339857	−	0.196217i	0.320352	−	0.947299i	$-0.396199\pi$
$487$	−7.50000	−	4.33013i	−0.339857	−	0.196217i	−0.660209	+	0.751082i	$0.729532\pi$
$488$		−	8.66025i		−	0.392031i
$489$	−10.5000	−	18.1865i	−0.474826	−	0.822423i
$490$	6.00000	+	10.3923i	0.271052	+	0.469476i
$491$	−3.00000			−0.135388			−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000			−0.135388			−0.0676941	+	0.997706i	$0.521564\pi$
$492$	21.0000			0.946753
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−10.5000	−	2.59808i	−0.472417	−	0.116893i
$495$	−9.00000	+	15.5885i	−0.404520	+	0.700649i
$496$	−37.5000	+	21.6506i	−1.68380	+	0.972142i
$497$	7.50000	−	12.9904i	0.336421	−	0.582698i
$498$	−13.5000	−	7.79423i	−0.604949	−	0.349268i
$499$	22.5000	+	12.9904i	1.00724	+	0.581529i	0.910382	−	0.413769i	$-0.135788\pi$
$499$	22.5000	+	12.9904i	1.00724	+	0.581529i	0.0968564	+	0.995298i	$0.469121\pi$
$500$	−10.5000	+	6.06218i	−0.469574	+	0.271109i
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$	13.5000	−	7.79423i	0.602534	−	0.347873i
$503$	−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	$0.321754\pi$
$504$	−4.50000	−	7.79423i	−0.200446	−	0.347183i
$505$	−9.00000	+	5.19615i	−0.400495	+	0.231226i
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	−10.5000	+	19.9186i	−0.466321	+	0.884615i
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$		−	1.73205i		−	0.0767718i	−0.999263	−	0.0383859i	$-0.987778\pi$
$509$		−	1.73205i		−	0.0767718i	0.999263	−	0.0383859i	$-0.0122216\pi$
$510$	13.5000	+	7.79423i	0.597790	+	0.345134i
$511$	12.0000			0.530849
$512$			8.66025i			0.382733i
$513$	−4.50000	+	7.79423i	−0.198680	+	0.344124i
$514$	−4.50000	−	2.59808i	−0.198486	−	0.114596i
$515$	−19.5000	+	11.2583i	−0.859273	+	0.496101i
$516$			1.73205i			0.0762493i
$517$	18.0000			0.791639
$518$			15.5885i			0.684917i
$519$	31.5000	+	18.1865i	1.38270	+	0.798300i
$520$	3.00000	+	10.3923i	0.131559	+	0.455733i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	−27.0000	−	15.5885i	−1.18176	−	0.682288i
$523$	12.5000	+	21.6506i	0.546587	+	0.946716i	0.998505	+	0.0546569i	$0.0174065\pi$
$523$	12.5000	+	21.6506i	0.546587	+	0.946716i	−0.451918	+	0.892059i	$0.649260\pi$
$524$	−15.0000			−0.655278
$525$	−6.00000			−0.261861
$526$	36.0000	−	20.7846i	1.56967	−	0.906252i
$527$	22.5000	−	12.9904i	0.980115	−	0.565870i
$528$	30.0000			1.30558
$529$	−14.0000			−0.608696
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$	9.00000	+	5.19615i	0.390567	+	0.225494i
$532$	3.00000			0.130066
$533$	−31.5000	−	30.3109i	−1.36442	−	1.31291i
$534$	40.5000	+	23.3827i	1.75261	+	1.01187i
$535$			25.9808i			1.12325i
$536$	21.0000			0.907062
$537$			5.19615i			0.224231i
$538$	4.50000	−	2.59808i	0.194009	−	0.112011i
$539$	−12.0000	−	6.92820i	−0.516877	−	0.298419i
$540$	−9.00000			−0.387298
$541$			13.8564i			0.595733i	0.954607	+	0.297867i	$0.0962751\pi$
$541$			13.8564i			0.595733i	−0.954607	+	0.297867i	$0.903725\pi$
$542$	−27.0000			−1.15975
$543$	33.0000	+	19.0526i	1.41617	+	0.817624i
$544$		−	15.5885i		−	0.668350i
$545$		0			0
$546$	4.50000	−	18.1865i	0.192582	−	0.778312i
$547$	−8.50000	−	14.7224i	−0.363434	−	0.629486i	0.625090	−	0.780553i	$-0.285062\pi$
$547$	−8.50000	−	14.7224i	−0.363434	−	0.629486i	−0.988524	+	0.151067i	$0.951729\pi$
$548$	4.50000	−	2.59808i	0.192230	−	0.110984i
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−9.00000	+	5.19615i	−0.383413	+	0.221364i
$552$	−4.50000	+	7.79423i	−0.191533	+	0.331744i
$553$	−16.5000	+	9.52628i	−0.701651	+	0.405099i
$554$	−34.5000	−	19.9186i	−1.46576	−	0.846260i
$555$	−13.5000	−	7.79423i	−0.573043	−	0.330847i
$556$	−8.00000	+	13.8564i	−0.339276	+	0.587643i
$557$	−16.5000	+	9.52628i	−0.699127	+	0.403641i	−0.807022	−	0.590521i	$-0.798922\pi$
$557$	−16.5000	+	9.52628i	−0.699127	+	0.403641i	0.107895	+	0.994162i	$0.465589\pi$
$558$	−22.5000	+	38.9711i	−0.952501	+	1.64978i
$559$	2.50000	−	2.59808i	0.105739	−	0.109887i
$560$	−7.50000	−	12.9904i	−0.316933	−	0.548944i
$561$	−18.0000			−0.759961
$562$	−9.00000			−0.379642
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	4.50000	+	7.79423i	0.189484	+	0.328196i
$565$			10.3923i			0.437208i
$566$	34.5000	+	19.9186i	1.45014	+	0.837241i
$567$	−13.5000	−	7.79423i	−0.566947	−	0.327327i
$568$	7.50000	−	12.9904i	0.314693	−	0.545064i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$	−4.50000	+	7.79423i	−0.188484	+	0.326464i
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	−0.808962	−	0.587861i	$-0.799970\pi$
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	0.913584	+	0.406651i	$0.133303\pi$
$572$	9.00000	+	8.66025i	0.376309	+	0.362103i
$573$	−4.50000	−	2.59808i	−0.187990	−	0.108536i
$574$	31.5000	+	18.1865i	1.31478	+	0.759091i
$575$	3.00000	+	5.19615i	0.125109	+	0.216695i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$		−	6.92820i		−	0.288425i	−0.989547	−	0.144212i	$-0.953935\pi$
$577$		−	6.92820i		−	0.288425i	0.989547	−	0.144212i	$-0.0460649\pi$
$578$		−	13.8564i		−	0.576351i
$579$	4.50000	−	7.79423i	0.187014	−	0.323917i
$580$	−9.00000	−	5.19615i	−0.373705	−	0.215758i
$581$	−4.50000	−	7.79423i	−0.186691	−	0.323359i
$582$	−40.5000	+	23.3827i	−1.67878	+	0.969244i
$583$	−18.0000	−	10.3923i	−0.745484	−	0.430405i
$584$	12.0000			0.496564
$585$	13.5000	+	12.9904i	0.558156	+	0.537086i
$586$	−24.0000			−0.991431
$587$	9.00000	+	5.19615i	0.371470	+	0.214468i	0.674100	−	0.738640i	$-0.264532\pi$
$587$	9.00000	+	5.19615i	0.371470	+	0.214468i	−0.302631	+	0.953108i	$0.597865\pi$
$588$		−	6.92820i		−	0.285714i
$589$	7.50000	+	12.9904i	0.309032	+	0.535259i
$590$	9.00000	+	5.19615i	0.370524	+	0.213922i
$591$	−15.0000			−0.617018
$592$			25.9808i			1.06780i
$593$		−	27.7128i		−	1.13803i	−0.822328	−	0.569014i	$-0.807325\pi$
$593$		−	27.7128i		−	1.13803i	0.822328	−	0.569014i	$-0.192675\pi$
$594$	27.0000	−	15.5885i	1.10782	−	0.639602i
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$		0			0
$597$	19.5000	−	11.2583i	0.798082	−	0.460773i
$598$	−18.0000	+	5.19615i	−0.736075	+	0.212486i
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$599$	−13.5000	+	23.3827i	−0.551595	+	0.955391i	−0.998160	+	0.0606393i	$0.980686\pi$
$600$	−6.00000			−0.244949
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	−0.998302	−	0.0582563i	$-0.981446\pi$
$601$	−11.0000	+	19.0526i	−0.448699	+	0.777170i	0.549602	+	0.835426i	$0.314779\pi$
$602$	−1.50000	+	2.59808i	−0.0611354	+	0.105890i
$603$	31.5000	−	18.1865i	1.28278	−	0.740613i
$604$	−10.5000	−	6.06218i	−0.427239	−	0.246667i
$605$		−	1.73205i		−	0.0704179i
$606$	18.0000			0.731200
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	9.00000			0.364998
$609$	−9.00000	−	15.5885i	−0.364698	−	0.631676i
$610$	−7.50000	−	12.9904i	−0.303666	−	0.525965i
$611$	4.50000	−	18.1865i	0.182051	−	0.735748i
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$	−10.5000	+	6.06218i	−0.424091	+	0.244849i	−0.696826	−	0.717240i	$-0.745405\pi$
$613$	−10.5000	+	6.06218i	−0.424091	+	0.244849i	0.272735	+	0.962089i	$0.412072\pi$
$614$	−21.0000	+	36.3731i	−0.847491	+	1.46790i
$615$	−31.5000	+	18.1865i	−1.27020	+	0.733352i
$616$	9.00000	+	5.19615i	0.362620	+	0.209359i
$617$	−24.0000	+	13.8564i	−0.966204	+	0.557838i	−0.898077	−	0.439839i	$-0.855036\pi$
$617$	−24.0000	+	13.8564i	−0.966204	+	0.557838i	−0.0681269	+	0.997677i	$0.521702\pi$
$618$	39.0000			1.56881
$619$	−22.5000	+	12.9904i	−0.904351	+	0.522127i	−0.878609	−	0.477541i	$-0.841528\pi$
$619$	−22.5000	+	12.9904i	−0.904351	+	0.522127i	−0.0257420	+	0.999669i	$0.508195\pi$
$620$	−7.50000	+	12.9904i	−0.301207	+	0.521706i
$621$			15.5885i			0.625543i
$622$	40.5000	−	23.3827i	1.62390	−	0.937560i
$623$	13.5000	+	23.3827i	0.540866	+	0.936808i
$624$	7.50000	−	30.3109i	0.300240	−	1.21341i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$			32.9090i			1.31531i
$627$		−	10.3923i		−	0.415029i
$628$	−23.0000			−0.917800
$629$		−	15.5885i		−	0.621552i
$630$	−13.5000	−	7.79423i	−0.537853	−	0.310530i
$631$	−7.50000	−	4.33013i	−0.298570	−	0.172380i	0.343230	−	0.939251i	$-0.388479\pi$
$631$	−7.50000	−	4.33013i	−0.298570	−	0.172380i	−0.641800	+	0.766872i	$0.721812\pi$
$632$	−16.5000	+	9.52628i	−0.656335	+	0.378935i
$633$	−19.5000	−	11.2583i	−0.775055	−	0.447478i
$634$	15.0000			0.595726
$635$		−	8.66025i		−	0.343672i
$636$		−	10.3923i		−	0.412082i
$637$	−10.0000	+	10.3923i	−0.396214	+	0.411758i
$638$	36.0000			1.42525
$639$		−	25.9808i		−	1.02778i
$640$	−10.5000	−	18.1865i	−0.415049	−	0.718886i
$641$	39.0000			1.54041			0.770204	−	0.637798i	$-0.220155\pi$
$641$	39.0000			1.54041			0.770204	+	0.637798i	$0.220155\pi$
$642$	22.5000	−	38.9711i	0.888004	−	1.53807i
$643$	−3.00000	+	1.73205i	−0.118308	+	0.0683054i	−0.557986	−	0.829850i	$-0.688426\pi$
$643$	−3.00000	+	1.73205i	−0.118308	+	0.0683054i	0.439678	+	0.898155i	$0.355093\pi$
$644$	4.50000	−	2.59808i	0.177325	−	0.102379i
$645$	−1.50000	−	2.59808i	−0.0590624	−	0.102299i
$646$	−9.00000			−0.354100
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$647$	4.50000	+	7.79423i	0.176913	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$648$	−13.5000	−	7.79423i	−0.530330	−	0.306186i
$649$	−12.0000			−0.471041
$650$	−9.00000	−	8.66025i	−0.353009	−	0.339683i
$651$	−22.5000	+	12.9904i	−0.881845	+	0.509133i
$652$			12.1244i			0.474826i
$653$	−45.0000			−1.76099			−0.880493	−	0.474059i	$-0.842788\pi$
$653$	−45.0000			−1.76099			−0.880493	+	0.474059i	$0.842788\pi$
$654$		0			0
$655$	22.5000	−	12.9904i	0.879148	−	0.507576i
$656$	52.5000	+	30.3109i	2.04978	+	1.18344i
$657$	18.0000	−	10.3923i	0.702247	−	0.405442i
$658$			15.5885i			0.607701i
$659$	39.0000			1.51922			0.759612	−	0.650376i	$-0.225389\pi$
$659$	39.0000			1.51922			0.759612	+	0.650376i	$0.225389\pi$
$660$	9.00000	−	5.19615i	0.350325	−	0.202260i
$661$			46.7654i			1.81896i	0.415745	+	0.909481i	$0.363521\pi$
$661$			46.7654i			1.81896i	−0.415745	+	0.909481i	$0.636479\pi$
$662$	13.5000	−	23.3827i	0.524692	−	0.908794i
$663$	−4.50000	+	18.1865i	−0.174766	+	0.706306i
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	−4.50000	+	2.59808i	−0.174503	+	0.100749i
$666$	13.5000	+	23.3827i	0.523114	+	0.906061i
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	4.50000	−	2.59808i	0.174110	−	0.100523i
$669$	−3.00000	−	5.19615i	−0.115987	−	0.200895i
$670$	31.5000	−	18.1865i	1.21695	−	0.702607i
$671$	15.0000	+	8.66025i	0.579069	+	0.334325i
$672$			15.5885i			0.601338i
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	−0.326516	−	0.945192i	$-0.605875\pi$
$673$	17.0000	−	29.4449i	0.655302	−	1.13502i	0.981818	−	0.189824i	$-0.0607919\pi$
$674$	−43.5000	+	25.1147i	−1.67556	+	0.967384i
$675$	−9.00000	+	5.19615i	−0.346410	+	0.200000i
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	10.5000	+	18.1865i	0.403548	+	0.698965i	0.994151	−	0.107997i	$-0.0344436\pi$
$677$	10.5000	+	18.1865i	0.403548	+	0.698965i	−0.590603	+	0.806962i	$0.701110\pi$
$678$	9.00000	−	15.5885i	0.345643	−	0.598671i
$679$	−27.0000			−1.03616
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$	−10.5000	+	18.1865i	−0.402361	+	0.696909i
$682$		−	51.9615i		−	1.98971i
$683$	−19.5000	−	11.2583i	−0.746147	−	0.430788i	0.0781532	−	0.996941i	$-0.475098\pi$
$683$	−19.5000	−	11.2583i	−0.746147	−	0.430788i	−0.824300	+	0.566153i	$0.808431\pi$
$684$	4.50000	−	2.59808i	0.172062	−	0.0993399i
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	16.5000	−	28.5788i	0.629973	−	1.09115i
$687$	7.50000	+	12.9904i	0.286143	+	0.495614i
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$	−15.0000	+	15.5885i	−0.571454	+	0.593873i
$690$			15.5885i			0.593442i
$691$	−15.0000	−	8.66025i	−0.570627	−	0.329452i	0.186773	−	0.982403i	$-0.440197\pi$
$691$	−15.0000	−	8.66025i	−0.570627	−	0.329452i	−0.757400	+	0.652952i	$0.773531\pi$
$692$	−10.5000	−	18.1865i	−0.399150	−	0.691348i
$693$	18.0000			0.683763
$694$		−	20.7846i		−	0.788973i
$695$		−	27.7128i		−	1.05121i
$696$	−9.00000	−	15.5885i	−0.341144	−	0.590879i
$697$	−31.5000	−	18.1865i	−1.19315	−	0.688864i
$698$	24.0000	+	41.5692i	0.908413	+	1.57342i
$699$	27.0000	+	15.5885i	1.02123	+	0.589610i
$700$	3.00000	+	1.73205i	0.113389	+	0.0654654i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−9.00000	−	31.1769i	−0.339683	−	1.17670i
$703$	9.00000			0.339441
$704$	3.00000	+	1.73205i	0.113067	+	0.0652791i
$705$	−13.5000	−	7.79423i	−0.508439	−	0.293548i
$706$	−6.00000	−	10.3923i	−0.225813	−	0.391120i
$707$	9.00000	+	5.19615i	0.338480	+	0.195421i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$		−	12.1244i		−	0.455340i	−0.973738	−	0.227670i	$-0.926889\pi$
$709$		−	12.1244i		−	0.455340i	0.973738	−	0.227670i	$-0.0731107\pi$
$710$		−	25.9808i		−	0.975041i
$711$	−16.5000	+	28.5788i	−0.618798	+	1.07179i
$712$	13.5000	+	23.3827i	0.505934	+	0.876303i
$713$	22.5000	+	12.9904i	0.842632	+	0.486494i
$714$		−	15.5885i		−	0.583383i
$715$	−21.0000	−	5.19615i	−0.785355	−	0.194325i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	−4.50000	−	7.79423i	−0.168056	−	0.291081i
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	−0.230823	−	0.972996i	$-0.574142\pi$
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	0.958051	−	0.286599i	$-0.0925247\pi$
$720$	−22.5000	−	12.9904i	−0.838525	−	0.484123i
$721$	19.5000	+	11.2583i	0.726218	+	0.419282i
$722$			27.7128i			1.03136i
$723$	−4.50000	+	7.79423i	−0.167357	+	0.289870i
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	−12.0000			−0.445669
$726$	−1.50000	+	2.59808i	−0.0556702	+	0.0964237i
$727$	−0.500000	−	0.866025i	−0.0185440	−	0.0321191i	0.856605	−	0.515974i	$-0.172570\pi$
$727$	−0.500000	−	0.866025i	−0.0185440	−	0.0321191i	−0.875148	+	0.483854i	$0.839236\pi$
$728$	7.50000	−	7.79423i	0.277968	−	0.288873i
$729$	−27.0000			−1.00000
$730$	18.0000	−	10.3923i	0.666210	−	0.384636i
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$			8.66025i			0.320092i
$733$	16.5000	+	9.52628i	0.609441	+	0.351861i	0.772747	−	0.634714i	$-0.218882\pi$
$733$	16.5000	+	9.52628i	0.609441	+	0.351861i	−0.163305	+	0.986576i	$0.552216\pi$
$734$	12.0000	−	6.92820i	0.442928	−	0.255725i
$735$	6.00000	+	10.3923i	0.221313	+	0.383326i
$736$	13.5000	−	7.79423i	0.497617	−	0.287299i
$737$	−21.0000	+	36.3731i	−0.773545	+	1.33982i
$738$	63.0000			2.31906
$739$	−28.5000	+	16.4545i	−1.04839	+	0.605288i	−0.922198	−	0.386718i	$-0.873609\pi$
$739$	−28.5000	+	16.4545i	−1.04839	+	0.605288i	−0.126191	+	0.992006i	$0.540275\pi$
$740$	4.50000	+	7.79423i	0.165423	+	0.286522i
$741$	−10.5000	−	2.59808i	−0.385727	−	0.0954427i
$742$	9.00000	−	15.5885i	0.330400	−	0.572270i
$743$		−	12.1244i		−	0.444799i	−0.974956	−	0.222400i	$-0.928611\pi$
$743$		−	12.1244i		−	0.444799i	0.974956	−	0.222400i	$-0.0713890\pi$
$744$	−22.5000	+	12.9904i	−0.824890	+	0.476250i
$745$		0			0
$746$		−	24.2487i		−	0.887808i
$747$	−13.5000	−	7.79423i	−0.493939	−	0.285176i
$748$	9.00000	+	5.19615i	0.329073	+	0.189990i
$749$	22.5000	−	12.9904i	0.822132	−	0.474658i
$750$	−31.5000	+	18.1865i	−1.15022	+	0.664078i
$751$	−19.0000			−0.693320			−0.346660	−	0.937991i	$-0.612684\pi$
$751$	−19.0000			−0.693320			−0.346660	+	0.937991i	$0.612684\pi$
$752$			25.9808i			0.947421i
$753$	13.5000	−	7.79423i	0.491967	−	0.284037i
$754$	9.00000	−	36.3731i	0.327761	−	1.32463i
$755$	21.0000			0.764268
$756$	4.50000	+	7.79423i	0.163663	+	0.283473i
$757$	−3.50000	−	6.06218i	−0.127210	−	0.220334i	0.795385	−	0.606105i	$-0.207269\pi$
$757$	−3.50000	−	6.06218i	−0.127210	−	0.220334i	−0.922595	+	0.385771i	$0.873935\pi$
$758$	21.0000			0.762754
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$	−4.50000	+	2.59808i	−0.163232	+	0.0942421i
$761$	12.0000	−	6.92820i	0.435000	−	0.251147i	−0.266475	−	0.963842i	$-0.585859\pi$
$761$	12.0000	−	6.92820i	0.435000	−	0.251147i	0.701474	+	0.712695i	$0.252526\pi$
$762$	−7.50000	+	12.9904i	−0.271696	+	0.470592i
$763$		0			0
$764$	1.50000	+	2.59808i	0.0542681	+	0.0939951i
$765$	13.5000	+	7.79423i	0.488094	+	0.281801i
$766$	6.00000			0.216789
$767$	−3.00000	+	12.1244i	−0.108324	+	0.437785i
$768$			32.9090i

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{6} +1.73205i q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.50000 + 2.59808i) q^{6} +1.73205i q^{7} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-3.00000 - 1.73205i) q^{11} -1.73205i q^{12} +(-2.50000 + 2.59808i) q^{13} +(1.50000 - 2.59808i) q^{14} +(1.50000 + 2.59808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} -5.19615i q^{18} +(-1.50000 - 0.866025i) q^{19} -1.73205i q^{20} +(1.50000 - 2.59808i) q^{21} +(3.00000 + 5.19615i) q^{22} -3.00000 q^{23} +(1.50000 - 2.59808i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(6.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-1.50000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -5.19615i q^{30} +(-7.50000 - 4.33013i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 + 5.19615i) q^{33} +(4.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(-4.50000 + 2.59808i) q^{37} +(1.50000 + 2.59808i) q^{38} +(6.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} +12.1244i q^{41} +(-4.50000 + 2.59808i) q^{42} -1.00000 q^{43} -3.46410i q^{44} -5.19615i q^{45} +(4.50000 + 2.59808i) q^{46} +(-4.50000 + 2.59808i) q^{47} +(-7.50000 + 4.33013i) q^{48} +4.00000 q^{49} +3.46410i q^{50} +(4.50000 - 2.59808i) q^{51} +(-3.50000 - 0.866025i) q^{52} +6.00000 q^{53} +(-4.50000 + 7.79423i) q^{54} +(3.00000 + 5.19615i) q^{55} -3.00000 q^{56} +(1.50000 + 2.59808i) q^{57} +(-9.00000 + 5.19615i) q^{58} +(3.00000 - 1.73205i) q^{59} +(-1.50000 + 2.59808i) q^{60} -5.00000 q^{61} +(7.50000 + 12.9904i) q^{62} +(-4.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(6.00000 - 1.73205i) q^{65} -10.3923i q^{66} -12.1244i q^{67} -3.00000 q^{68} +(4.50000 + 2.59808i) q^{69} +(-4.50000 + 2.59808i) q^{70} +(-7.50000 - 4.33013i) q^{71} +(-4.50000 + 2.59808i) q^{72} -6.92820i q^{73} +9.00000 q^{74} +3.46410i q^{75} -1.73205i q^{76} +(3.00000 - 5.19615i) q^{77} +(-10.5000 - 2.59808i) q^{78} +(5.50000 + 9.52628i) q^{79} +(-7.50000 + 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(10.5000 - 18.1865i) q^{82} +(-4.50000 + 2.59808i) q^{83} +3.00000 q^{84} +(4.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{86} +(-9.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(13.5000 - 7.79423i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(-4.50000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +(7.50000 + 12.9904i) q^{93} +9.00000 q^{94} +(1.50000 + 2.59808i) q^{95} +9.00000 q^{96} +15.5885i q^{97} +(-6.00000 - 3.46410i) q^{98} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 + 3 * q^6 + 3 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{9} + 3 q^{10} - 6 q^{11} - 5 q^{13} + 3 q^{14} + 3 q^{15} + 5 q^{16} - 3 q^{17} - 3 q^{19} + 3 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 12 q^{26} - 3 q^{28} + 6 q^{29} - 15 q^{31} - 9 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 9 q^{37} + 3 q^{38} + 12 q^{39} + 3 q^{40} - 9 q^{42} - 2 q^{43} + 9 q^{46} - 9 q^{47} - 15 q^{48} + 8 q^{49} + 9 q^{51} - 7 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} - 6 q^{56} + 3 q^{57} - 18 q^{58} + 6 q^{59} - 3 q^{60} - 10 q^{61} + 15 q^{62} - 9 q^{63} - 2 q^{64} + 12 q^{65} - 6 q^{68} + 9 q^{69} - 9 q^{70} - 15 q^{71} - 9 q^{72} + 18 q^{74} + 6 q^{77} - 21 q^{78} + 11 q^{79} - 15 q^{80} - 9 q^{81} + 21 q^{82} - 9 q^{83} + 6 q^{84} + 9 q^{85} + 3 q^{86} - 18 q^{87} + 6 q^{88} + 27 q^{89} - 9 q^{90} - 9 q^{91} - 3 q^{92} + 15 q^{93} + 18 q^{94} + 3 q^{95} + 18 q^{96} - 12 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - 3 * q^5 + 3 * q^6 + 3 * q^9 + 3 * q^10 - 6 * q^11 - 5 * q^13 + 3 * q^14 + 3 * q^15 + 5 * q^16 - 3 * q^17 - 3 * q^19 + 3 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 12 * q^26 - 3 * q^28 + 6 * q^29 - 15 * q^31 - 9 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 9 * q^37 + 3 * q^38 + 12 * q^39 + 3 * q^40 - 9 * q^42 - 2 * q^43 + 9 * q^46 - 9 * q^47 - 15 * q^48 + 8 * q^49 + 9 * q^51 - 7 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 - 6 * q^56 + 3 * q^57 - 18 * q^58 + 6 * q^59 - 3 * q^60 - 10 * q^61 + 15 * q^62 - 9 * q^63 - 2 * q^64 + 12 * q^65 - 6 * q^68 + 9 * q^69 - 9 * q^70 - 15 * q^71 - 9 * q^72 + 18 * q^74 + 6 * q^77 - 21 * q^78 + 11 * q^79 - 15 * q^80 - 9 * q^81 + 21 * q^82 - 9 * q^83 + 6 * q^84 + 9 * q^85 + 3 * q^86 - 18 * q^87 + 6 * q^88 + 27 * q^89 - 9 * q^90 - 9 * q^91 - 3 * q^92 + 15 * q^93 + 18 * q^94 + 3 * q^95 + 18 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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