LMFDB - Embedded newform 117.2.e.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(40,117)]

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([2, 0]))

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

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

chi := DirichletCharacter("117.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (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:	$0.934249703649$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.79
Dual form			117.2.e.a.40.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.46410i q^{6} +(-1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.46410i q^{6} +(-1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +8.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(6.00000 + 3.46410i) q^{15} +(2.00000 - 3.46410i) q^{16} -5.00000 q^{17} +(3.00000 + 5.19615i) q^{18} -6.00000 q^{19} +(-4.00000 + 6.92820i) q^{20} -3.46410i q^{21} +(-2.00000 - 3.46410i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-5.50000 + 9.52628i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +4.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(-12.0000 + 6.92820i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(4.00000 + 6.92820i) q^{32} -3.46410i q^{33} +(5.00000 - 8.66025i) q^{34} +8.00000 q^{35} -6.00000 q^{36} -2.00000 q^{37} +(6.00000 - 10.3923i) q^{38} +(1.50000 + 0.866025i) q^{39} +(3.00000 + 5.19615i) q^{41} +(6.00000 + 3.46410i) q^{42} +(1.50000 - 2.59808i) q^{43} +4.00000 q^{44} -12.0000 q^{45} -6.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +6.92820i q^{48} +(1.50000 + 2.59808i) q^{49} +(-11.0000 - 19.0526i) q^{50} +(7.50000 - 4.33013i) q^{51} +(-1.00000 + 1.73205i) q^{52} +3.00000 q^{53} +(-9.00000 - 5.19615i) q^{54} +8.00000 q^{55} +(9.00000 - 5.19615i) q^{57} +(2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} -13.8564i q^{60} +(2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +(3.00000 + 5.19615i) q^{63} -8.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(6.00000 + 3.46410i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(5.00000 + 8.66025i) q^{68} +(-4.50000 - 2.59808i) q^{69} +(-8.00000 + 13.8564i) q^{70} +12.0000 q^{71} -4.00000 q^{73} +(2.00000 - 3.46410i) q^{74} -19.0526i q^{75} +(6.00000 + 10.3923i) q^{76} +(-2.00000 - 3.46410i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(-2.50000 + 4.33013i) q^{79} -16.0000 q^{80} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{82} +(-1.00000 + 1.73205i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(10.0000 + 17.3205i) q^{85} +(3.00000 + 5.19615i) q^{86} +3.46410i q^{87} -10.0000 q^{89} +(12.0000 - 20.7846i) q^{90} +2.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(12.0000 + 20.7846i) q^{95} +(-12.0000 - 6.92820i) q^{96} +(4.00000 - 6.92820i) q^{97} -6.00000 q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^7 + 3 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{7} + 3 q^{9} + 16 q^{10} - 2 q^{11} + 6 q^{12} - q^{13} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 10 q^{17} + 6 q^{18} - 12 q^{19} - 8 q^{20} - 4 q^{22} + 3 q^{23} - 11 q^{25} + 4 q^{26} + 8 q^{28} + 2 q^{29} - 24 q^{30} - 4 q^{31} + 8 q^{32} + 10 q^{34} + 16 q^{35} - 12 q^{36} - 4 q^{37} + 12 q^{38} + 3 q^{39} + 6 q^{41} + 12 q^{42} + 3 q^{43} + 8 q^{44} - 24 q^{45} - 12 q^{46} - 6 q^{47} + 3 q^{49} - 22 q^{50} + 15 q^{51} - 2 q^{52} + 6 q^{53} - 18 q^{54} + 16 q^{55} + 18 q^{57} + 4 q^{58} - 12 q^{59} + 5 q^{61} + 16 q^{62} + 6 q^{63} - 16 q^{64} - 4 q^{65} + 12 q^{66} - 4 q^{67} + 10 q^{68} - 9 q^{69} - 16 q^{70} + 24 q^{71} - 8 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 6 q^{78} - 5 q^{79} - 32 q^{80} - 9 q^{81} - 24 q^{82} - 2 q^{83} - 12 q^{84} + 20 q^{85} + 6 q^{86} - 20 q^{89} + 24 q^{90} + 4 q^{91} + 6 q^{92} + 12 q^{93} - 12 q^{94} + 24 q^{95} - 24 q^{96} + 8 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^7 + 3 * q^9 + 16 * q^10 - 2 * q^11 + 6 * q^12 - q^13 - 4 * q^14 + 12 * q^15 + 4 * q^16 - 10 * q^17 + 6 * q^18 - 12 * q^19 - 8 * q^20 - 4 * q^22 + 3 * q^23 - 11 * q^25 + 4 * q^26 + 8 * q^28 + 2 * q^29 - 24 * q^30 - 4 * q^31 + 8 * q^32 + 10 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^37 + 12 * q^38 + 3 * q^39 + 6 * q^41 + 12 * q^42 + 3 * q^43 + 8 * q^44 - 24 * q^45 - 12 * q^46 - 6 * q^47 + 3 * q^49 - 22 * q^50 + 15 * q^51 - 2 * q^52 + 6 * q^53 - 18 * q^54 + 16 * q^55 + 18 * q^57 + 4 * q^58 - 12 * q^59 + 5 * q^61 + 16 * q^62 + 6 * q^63 - 16 * q^64 - 4 * q^65 + 12 * q^66 - 4 * q^67 + 10 * q^68 - 9 * q^69 - 16 * q^70 + 24 * q^71 - 8 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 5 * q^79 - 32 * q^80 - 9 * q^81 - 24 * q^82 - 2 * q^83 - 12 * q^84 + 20 * q^85 + 6 * q^86 - 20 * q^89 + 24 * q^90 + 4 * q^91 + 6 * q^92 + 12 * q^93 - 12 * q^94 + 24 * q^95 - 24 * q^96 + 8 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$		−	3.46410i		−	1.41421i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	8.00000			2.52982
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$	6.00000	+	3.46410i	1.54919	+	0.894427i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−5.00000			−1.21268			−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000			−1.21268			−0.606339	+	0.795206i	$0.707363\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−4.00000	+	6.92820i	−0.894427	+	1.54919i
$21$		−	3.46410i		−	0.755929i
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	2.00000			0.392232
$27$			5.19615i			1.00000i
$28$	4.00000			0.755929
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$	−12.0000	+	6.92820i	−2.19089	+	1.26491i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	4.00000	+	6.92820i	0.707107	+	1.22474i
$33$		−	3.46410i		−	0.603023i
$34$	5.00000	−	8.66025i	0.857493	−	1.48522i
$35$	8.00000			1.35225
$36$	−6.00000			−1.00000
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	6.00000	−	10.3923i	0.973329	−	1.68585i
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$	6.00000	+	3.46410i	0.925820	+	0.534522i
$43$	1.50000	−	2.59808i	0.228748	−	0.396203i	−0.728689	−	0.684844i	$-0.759870\pi$
$43$	1.50000	−	2.59808i	0.228748	−	0.396203i	0.957437	+	0.288641i	$0.0932035\pi$
$44$	4.00000			0.603023
$45$	−12.0000			−1.78885
$46$	−6.00000			−0.884652
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$			6.92820i			1.00000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−11.0000	−	19.0526i	−1.55563	−	2.69444i
$51$	7.50000	−	4.33013i	1.05021	−	0.606339i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	−9.00000	−	5.19615i	−1.22474	−	0.707107i
$55$	8.00000			1.07872
$56$		0			0
$57$	9.00000	−	5.19615i	1.19208	−	0.688247i
$58$	2.00000	+	3.46410i	0.262613	+	0.454859i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		−	13.8564i		−	1.78885i
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	8.00000			1.01600
$63$	3.00000	+	5.19615i	0.377964	+	0.654654i
$64$	−8.00000			−1.00000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	6.00000	+	3.46410i	0.738549	+	0.426401i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	5.00000	+	8.66025i	0.606339	+	1.05021i
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$	−8.00000	+	13.8564i	−0.956183	+	1.65616i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		−	19.0526i		−	2.20000i
$76$	6.00000	+	10.3923i	0.688247	+	1.19208i
$77$	−2.00000	−	3.46410i	−0.227921	−	0.394771i
$78$	−3.00000	+	1.73205i	−0.339683	+	0.196116i
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−16.0000			−1.78885
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−12.0000			−1.32518
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$	−6.00000	+	3.46410i	−0.654654	+	0.377964i
$85$	10.0000	+	17.3205i	1.08465	+	1.87867i
$86$	3.00000	+	5.19615i	0.323498	+	0.560316i
$87$			3.46410i			0.371391i
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$	12.0000	−	20.7846i	1.26491	−	2.19089i
$91$	2.00000			0.209657
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	12.0000	+	20.7846i	1.23117	+	2.13246i
$96$	−12.0000	−	6.92820i	−1.22474	−	0.707107i
$97$	4.00000	−	6.92820i	0.406138	−	0.703452i	−0.588315	−	0.808632i	$-0.700208\pi$
$97$	4.00000	−	6.92820i	0.406138	−	0.703452i	0.994453	+	0.105180i	$0.0335417\pi$
$98$	−6.00000			−0.606092
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	22.0000			2.20000
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$			17.3205i			1.71499i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$		0			0
$105$	−12.0000	+	6.92820i	−1.17108	+	0.676123i
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$	−8.00000	+	13.8564i	−0.762770	+	1.32116i
$111$	3.00000	−	1.73205i	0.284747	−	0.164399i
$112$	4.00000	+	6.92820i	0.377964	+	0.654654i
$113$	−10.5000	−	18.1865i	−0.987757	−	1.71085i	−0.628979	−	0.777422i	$-0.716527\pi$
$113$	−10.5000	−	18.1865i	−0.987757	−	1.71085i	−0.358778	−	0.933423i	$-0.616806\pi$
$114$			20.7846i			1.94666i
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	−4.00000			−0.371391
$117$	−3.00000			−0.277350
$118$	24.0000			2.20938
$119$	5.00000	−	8.66025i	0.458349	−	0.793884i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	−9.00000	−	5.19615i	−0.811503	−	0.468521i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	24.0000			2.14663
$126$	−12.0000			−1.06904
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$			5.19615i			0.457496i
$130$	−4.00000	−	6.92820i	−0.350823	−	0.607644i
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$	−6.00000	+	3.46410i	−0.522233	+	0.301511i
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	8.00000			0.691095
$135$	18.0000	−	10.3923i	1.54919	−	0.894427i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	9.00000	−	5.19615i	0.766131	−	0.442326i
$139$	1.50000	+	2.59808i	0.127228	+	0.220366i	0.922602	−	0.385754i	$-0.126059\pi$
$139$	1.50000	+	2.59808i	0.127228	+	0.220366i	−0.795373	+	0.606120i	$0.792725\pi$
$140$	−8.00000	−	13.8564i	−0.676123	−	1.17108i
$141$		−	10.3923i		−	0.875190i
$142$	−12.0000	+	20.7846i	−1.00702	+	1.74421i
$143$	2.00000			0.167248
$144$	−6.00000	−	10.3923i	−0.500000	−	0.866025i
$145$	−8.00000			−0.664364
$146$	4.00000	−	6.92820i	0.331042	−	0.573382i
$147$	−4.50000	−	2.59808i	−0.371154	−	0.214286i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	33.0000	+	19.0526i	2.69444	+	1.55563i
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$		0			0
$153$	−7.50000	+	12.9904i	−0.606339	+	1.05021i
$154$	8.00000			0.644658
$155$	−8.00000	+	13.8564i	−0.642575	+	1.11297i
$156$		−	3.46410i		−	0.277350i
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	−0.891572	−	0.452880i	$-0.850397\pi$
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	0.0535803	−	0.998564i	$-0.482937\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$	−4.50000	+	2.59808i	−0.356873	+	0.206041i
$160$	16.0000	−	27.7128i	1.26491	−	2.19089i
$161$	−6.00000			−0.472866
$162$	18.0000			1.41421
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$	−12.0000	+	6.92820i	−0.934199	+	0.539360i
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−40.0000			−3.06786
$171$	−9.00000	+	15.5885i	−0.688247	+	1.19208i
$172$	−6.00000			−0.457496
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$	−6.00000	−	3.46410i	−0.454859	−	0.262613i
$175$	−11.0000	−	19.0526i	−0.831522	−	1.44024i
$176$	4.00000	+	6.92820i	0.301511	+	0.522233i
$177$	18.0000	+	10.3923i	1.35296	+	0.781133i
$178$	10.0000	−	17.3205i	0.749532	−	1.29823i
$179$	−19.0000			−1.42013			−0.710063	−	0.704138i	$-0.751334\pi$
$179$	−19.0000			−1.42013			−0.710063	+	0.704138i	$0.751334\pi$
$180$	12.0000	+	20.7846i	0.894427	+	1.54919i
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	−2.00000	+	3.46410i	−0.148250	+	0.256776i
$183$			8.66025i			0.640184i
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	−12.0000	+	6.92820i	−0.879883	+	0.508001i
$187$	5.00000	−	8.66025i	0.365636	−	0.633300i
$188$	12.0000			0.875190
$189$	−9.00000	−	5.19615i	−0.654654	−	0.377964i
$190$	−48.0000			−3.48229
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	0.285282	+	0.958444i	$0.407913\pi$
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	−0.972677	+	0.232161i	$0.925420\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	0.868255	+	0.496119i	$0.165242\pi$
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$		−	6.92820i		−	0.496139i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	24.0000			1.70993			0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000			1.70993			0.854965	+	0.518686i	$0.173579\pi$
$198$	−12.0000			−0.852803
$199$	17.0000			1.20510			0.602549	−	0.798082i	$-0.294152\pi$
$199$	17.0000			1.20510			0.602549	+	0.798082i	$0.294152\pi$
$200$		0			0
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	2.00000	+	3.46410i	0.140372	+	0.243132i
$204$	−15.0000	−	8.66025i	−1.05021	−	0.606339i
$205$	12.0000	−	20.7846i	0.838116	−	1.45166i
$206$		0			0
$207$	9.00000			0.625543
$208$	−4.00000			−0.277350
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		−	27.7128i		−	1.91237i
$211$	−0.500000	−	0.866025i	−0.0344214	−	0.0596196i	0.848301	−	0.529514i	$-0.177626\pi$
$211$	−0.500000	−	0.866025i	−0.0344214	−	0.0596196i	−0.882723	+	0.469894i	$0.844292\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	−12.0000			−0.818393
$216$		0			0
$217$	8.00000			0.543075
$218$	14.0000	−	24.2487i	0.948200	−	1.64233i
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$	−8.00000	−	13.8564i	−0.539360	−	0.934199i
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$			6.92820i			0.464991i
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	−16.0000			−1.06904
$225$	16.5000	+	28.5788i	1.10000	+	1.90526i
$226$	42.0000			2.79380
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$	−18.0000	−	10.3923i	−1.19208	−	0.688247i
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$	12.0000	+	20.7846i	0.791257	+	1.37050i
$231$	6.00000	+	3.46410i	0.394771	+	0.227921i
$232$		0			0
$233$	−7.00000			−0.458585			−0.229293	−	0.973358i	$-0.573641\pi$
$233$	−7.00000			−0.458585			−0.229293	+	0.973358i	$0.573641\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	24.0000			1.56559
$236$	−12.0000	+	20.7846i	−0.781133	+	1.35296i
$237$		−	8.66025i		−	0.562544i
$238$	10.0000	+	17.3205i	0.648204	+	1.12272i
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$	24.0000	−	13.8564i	1.54919	−	0.894427i
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	−0.923224	−	0.384262i	$-0.874456\pi$
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	0.794393	+	0.607404i	$0.207789\pi$
$242$	−14.0000			−0.899954
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−10.0000			−0.640184
$245$	6.00000	−	10.3923i	0.383326	−	0.663940i
$246$	18.0000	−	10.3923i	1.14764	−	0.662589i
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$		0			0
$249$		−	3.46410i		−	0.219529i
$250$	−24.0000	+	41.5692i	−1.51789	+	2.62907i
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	6.00000	−	10.3923i	0.377964	−	0.654654i
$253$	−6.00000			−0.377217
$254$	16.0000	−	27.7128i	1.00393	−	1.73886i
$255$	−30.0000	−	17.3205i	−1.87867	−	1.08465i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.50000	−	11.2583i	−0.405459	−	0.702275i	0.588916	−	0.808194i	$-0.299555\pi$
$257$	−6.50000	−	11.2583i	−0.405459	−	0.702275i	−0.994375	+	0.105919i	$0.966222\pi$
$258$	−9.00000	−	5.19615i	−0.560316	−	0.323498i
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$	8.00000			0.496139
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	−2.00000			−0.123560
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	−0.999083	−	0.0428069i	$-0.986370\pi$
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$264$		0			0
$265$	−6.00000	−	10.3923i	−0.368577	−	0.638394i
$266$	12.0000	+	20.7846i	0.735767	+	1.27439i
$267$	15.0000	−	8.66025i	0.917985	−	0.529999i
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$			41.5692i			2.52982i
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$	−10.0000	+	17.3205i	−0.606339	+	1.05021i
$273$	−3.00000	+	1.73205i	−0.181568	+	0.104828i
$274$	12.0000	+	20.7846i	0.724947	+	1.25564i
$275$	−11.0000	−	19.0526i	−0.663325	−	1.14891i
$276$			10.3923i			0.625543i
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	−6.00000			−0.359856
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−2.00000	+	3.46410i	−0.119310	+	0.206651i	−0.919494	−	0.393103i	$-0.871402\pi$
$281$	−2.00000	+	3.46410i	−0.119310	+	0.206651i	0.800184	+	0.599754i	$0.204735\pi$
$282$	18.0000	+	10.3923i	1.07188	+	0.618853i
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	0.998110	−	0.0614601i	$-0.0195757\pi$
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	−0.552281	+	0.833658i	$0.686242\pi$
$284$	−12.0000	−	20.7846i	−0.712069	−	1.23334i
$285$	−36.0000	−	20.7846i	−2.13246	−	1.23117i
$286$	−2.00000	+	3.46410i	−0.118262	+	0.204837i
$287$	−12.0000			−0.708338
$288$	24.0000			1.41421
$289$	8.00000			0.470588
$290$	8.00000	−	13.8564i	0.469776	−	0.813676i
$291$			13.8564i			0.812277i
$292$	4.00000	+	6.92820i	0.234082	+	0.405442i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$	9.00000	−	5.19615i	0.524891	−	0.303046i
$295$	−24.0000	+	41.5692i	−1.39733	+	2.42025i
$296$		0			0
$297$	−9.00000	−	5.19615i	−0.522233	−	0.301511i
$298$		0			0
$299$	1.50000	−	2.59808i	0.0867472	−	0.150251i
$300$	−33.0000	+	19.0526i	−1.90526	+	1.10000i
$301$	3.00000	+	5.19615i	0.172917	+	0.299501i
$302$	2.00000	+	3.46410i	0.115087	+	0.199337i
$303$		−	15.5885i		−	0.895533i
$304$	−12.0000	+	20.7846i	−0.688247	+	1.19208i
$305$	−20.0000			−1.14520
$306$	−15.0000	−	25.9808i	−0.857493	−	1.48522i
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	−4.00000	+	6.92820i	−0.227921	+	0.394771i
$309$		0			0
$310$	−16.0000	−	27.7128i	−0.908739	−	1.57398i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$314$	42.0000			2.37020
$315$	12.0000	−	20.7846i	0.676123	−	1.17108i
$316$	10.0000			0.562544
$317$	4.00000	−	6.92820i	0.224662	−	0.389127i	−0.731556	−	0.681782i	$-0.761205\pi$
$317$	4.00000	−	6.92820i	0.224662	−	0.389127i	0.956218	+	0.292655i	$0.0945387\pi$
$318$		−	10.3923i		−	0.582772i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	16.0000	+	27.7128i	0.894427	+	1.54919i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	30.0000			1.66924
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$	11.0000			0.610170
$326$	16.0000	−	27.7128i	0.886158	−	1.53487i
$327$	21.0000	−	12.1244i	1.16130	−	0.670478i
$328$		0			0
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		−	27.7128i		−	1.52554i
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	4.00000			0.219529
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	4.00000			0.218870
$335$	−8.00000	+	13.8564i	−0.437087	+	0.757056i
$336$	−12.0000	−	6.92820i	−0.654654	−	0.377964i
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	−0.954551	−	0.298047i	$-0.903665\pi$
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	0.219159	−	0.975689i	$-0.429669\pi$
$338$	−1.00000	−	1.73205i	−0.0543928	−	0.0942111i
$339$	31.5000	+	18.1865i	1.71085	+	0.987757i
$340$	20.0000	−	34.6410i	1.08465	−	1.87867i
$341$	8.00000			0.433224
$342$	−18.0000	−	31.1769i	−0.973329	−	1.68585i
$343$	−20.0000			−1.07990
$344$		0			0
$345$			20.7846i			1.11901i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$	6.00000	−	3.46410i	0.321634	−	0.185695i
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	−0.738883	−	0.673833i	$-0.764647\pi$
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	0.952998	+	0.302975i	$0.0979799\pi$
$350$	44.0000			2.35190
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$	−16.0000			−0.852803
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	−0.701734	−	0.712439i	$-0.747591\pi$
$353$	5.00000	−	8.66025i	0.266123	−	0.460939i	0.967857	+	0.251500i	$0.0809239\pi$
$354$	−36.0000	+	20.7846i	−1.91338	+	1.10469i
$355$	−24.0000	−	41.5692i	−1.27379	−	2.20627i
$356$	10.0000	+	17.3205i	0.529999	+	0.917985i
$357$			17.3205i			0.916698i
$358$	19.0000	−	32.9090i	1.00418	−	1.73929i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	−10.5000	−	6.06218i	−0.551107	−	0.318182i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$	8.00000	+	13.8564i	0.418739	+	0.725277i
$366$	−15.0000	−	8.66025i	−0.784063	−	0.452679i
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	−0.793370	−	0.608740i	$-0.791675\pi$
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	0.923869	+	0.382709i	$0.125009\pi$
$368$	12.0000			0.625543
$369$	18.0000			0.937043
$370$	−16.0000			−0.831800
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$		−	13.8564i		−	0.718421i
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	0.852791	−	0.522253i	$-0.174908\pi$
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	−0.878680	+	0.477412i	$0.841575\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$	−36.0000	+	20.7846i	−1.85903	+	1.07331i
$376$		0			0
$377$	−2.00000			−0.103005
$378$	18.0000	−	10.3923i	0.925820	−	0.534522i
$379$	6.00000			0.308199			0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000			0.308199			0.154100	+	0.988055i	$0.450752\pi$
$380$	24.0000	−	41.5692i	1.23117	−	2.13246i
$381$	24.0000	−	13.8564i	1.22956	−	0.709885i
$382$	−19.0000	−	32.9090i	−0.972125	−	1.68377i
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	−8.00000	+	13.8564i	−0.407718	+	0.706188i
$386$	−48.0000			−2.44314
$387$	−4.50000	−	7.79423i	−0.228748	−	0.396203i
$388$	−16.0000			−0.812277
$389$	0.500000	−	0.866025i	0.0253510	−	0.0439092i	−0.853072	−	0.521794i	$-0.825263\pi$
$389$	0.500000	−	0.866025i	0.0253510	−	0.0439092i	0.878423	+	0.477885i	$0.158596\pi$
$390$	12.0000	+	6.92820i	0.607644	+	0.350823i
$391$	−7.50000	−	12.9904i	−0.379291	−	0.656952i
$392$		0			0
$393$	−1.50000	−	0.866025i	−0.0756650	−	0.0436852i
$394$	−24.0000	+	41.5692i	−1.20910	+	2.09423i
$395$	20.0000			1.00631
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	−17.0000	+	29.4449i	−0.852133	+	1.47594i
$399$			20.7846i			1.04053i
$400$	22.0000	+	38.1051i	1.10000	+	1.90526i
$401$	−13.0000	−	22.5167i	−0.649189	−	1.12443i	−0.983317	−	0.181901i	$-0.941775\pi$
$401$	−13.0000	−	22.5167i	−0.649189	−	1.12443i	0.334128	−	0.942528i	$-0.391558\pi$
$402$	−12.0000	+	6.92820i	−0.598506	+	0.345547i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	18.0000			0.895533
$405$	−18.0000	+	31.1769i	−0.894427	+	1.54919i
$406$	−8.00000			−0.397033
$407$	2.00000	−	3.46410i	0.0991363	−	0.171709i
$408$		0			0
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	0.925256	+	0.379344i	$0.123850\pi$
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	−0.134107	+	0.990967i	$0.542817\pi$
$410$	24.0000	+	41.5692i	1.18528	+	2.05296i
$411$			20.7846i			1.02523i
$412$		0			0
$413$	24.0000			1.18096
$414$	−9.00000	+	15.5885i	−0.442326	+	0.766131i
$415$	8.00000			0.392705
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$	−4.50000	−	2.59808i	−0.220366	−	0.127228i
$418$	12.0000	+	20.7846i	0.586939	+	1.01661i
$419$	0.500000	+	0.866025i	0.0244266	+	0.0423081i	0.877980	−	0.478697i	$-0.158891\pi$
$419$	0.500000	+	0.866025i	0.0244266	+	0.0423081i	−0.853554	+	0.521005i	$0.825557\pi$
$420$	24.0000	+	13.8564i	1.17108	+	0.676123i
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	0.353233	+	0.935536i	$0.385082\pi$
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	−0.986814	+	0.161859i	$0.948251\pi$
$422$	2.00000			0.0973585
$423$	9.00000	+	15.5885i	0.437595	+	0.757937i
$424$		0			0
$425$	27.5000	−	47.6314i	1.33395	−	2.31046i
$426$		−	41.5692i		−	2.01404i
$427$	5.00000	+	8.66025i	0.241967	+	0.419099i
$428$	−3.00000	−	5.19615i	−0.145010	−	0.251166i
$429$	−3.00000	+	1.73205i	−0.144841	+	0.0836242i
$430$	12.0000	−	20.7846i	0.578691	−	1.00232i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$	−35.0000			−1.68199			−0.840996	−	0.541041i	$-0.818030\pi$
$433$	−35.0000			−1.68199			−0.840996	+	0.541041i	$0.818030\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$	12.0000	−	6.92820i	0.575356	−	0.332182i
$436$	14.0000	+	24.2487i	0.670478	+	1.16130i
$437$	−9.00000	−	15.5885i	−0.430528	−	0.745697i
$438$			13.8564i			0.662085i
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	−10.0000			−0.475651
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	0.217667	+	0.976023i	$0.430155\pi$
$443$	−15.5000	+	26.8468i	−0.736427	+	1.27553i	−0.954094	+	0.299506i	$0.903178\pi$
$444$	−6.00000	−	3.46410i	−0.284747	−	0.164399i
$445$	20.0000	+	34.6410i	0.948091	+	1.64214i
$446$	−16.0000	−	27.7128i	−0.757622	−	1.31224i
$447$		0			0
$448$	8.00000	−	13.8564i	0.377964	−	0.654654i
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$	−66.0000			−3.11127
$451$	−12.0000			−0.565058
$452$	−21.0000	+	36.3731i	−0.987757	+	1.71085i
$453$			3.46410i			0.162758i
$454$	4.00000	+	6.92820i	0.187729	+	0.325157i
$455$	−4.00000	−	6.92820i	−0.187523	−	0.324799i
$456$		0			0
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	−0.615986	−	0.787757i	$-0.711242\pi$
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	0.990211	+	0.139581i	$0.0445757\pi$
$458$	−32.0000			−1.49526
$459$		−	25.9808i		−	1.21268i
$460$	−24.0000			−1.11901
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$	−12.0000	+	6.92820i	−0.558291	+	0.322329i
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	0.618050	−	0.786139i	$-0.287923\pi$
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		−	27.7128i		−	1.28515i
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$	8.00000			0.369406
$470$	−24.0000	+	41.5692i	−1.10704	+	1.91745i
$471$	31.5000	+	18.1865i	1.45144	+	0.837991i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	15.0000	+	8.66025i	0.688973	+	0.397779i
$475$	33.0000	−	57.1577i	1.51414	−	2.62257i
$476$	−20.0000			−0.916698
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	−12.0000			−0.548867
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$			55.4256i			2.52982i
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$	−4.00000	−	6.92820i	−0.182195	−	0.315571i
$483$	9.00000	−	5.19615i	0.409514	−	0.236433i
$484$	7.00000	−	12.1244i	0.318182	−	0.551107i
$485$	−32.0000			−1.45305
$486$	−27.0000	+	15.5885i	−1.22474	+	0.707107i
$487$	18.0000			0.815658			0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000			0.815658			0.407829	+	0.913058i	$0.366286\pi$
$488$		0			0
$489$	24.0000	−	13.8564i	1.08532	−	0.626608i
$490$	12.0000	+	20.7846i	0.542105	+	0.938953i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$			20.7846i			0.937043i
$493$	−5.00000	+	8.66025i	−0.225189	+	0.390038i
$494$	−12.0000			−0.539906
$495$	12.0000	−	20.7846i	0.539360	−	0.934199i
$496$	−16.0000			−0.718421
$497$	−12.0000	+	20.7846i	−0.538274	+	0.932317i
$498$	6.00000	+	3.46410i	0.268866	+	0.155230i
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	−24.0000	−	41.5692i	−1.07331	−	1.85903i
$501$	3.00000	+	1.73205i	0.134030	+	0.0773823i
$502$	15.0000	−	25.9808i	0.669483	−	1.15958i
$503$	29.0000			1.29305			0.646523	−	0.762894i	$-0.276222\pi$
$503$	29.0000			1.29305			0.646523	+	0.762894i	$0.276222\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$	6.00000	−	10.3923i	0.266733	−	0.461994i
$507$		−	1.73205i		−	0.0769231i
$508$	16.0000	+	27.7128i	0.709885	+	1.22956i
$509$	8.00000	+	13.8564i	0.354594	+	0.614174i	0.987048	−	0.160423i	$-0.0512858\pi$
$509$	8.00000	+	13.8564i	0.354594	+	0.614174i	−0.632455	+	0.774597i	$0.717953\pi$
$510$	60.0000	−	34.6410i	2.65684	−	1.53393i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$	32.0000			1.41421
$513$		−	31.1769i		−	1.37649i
$514$	26.0000			1.14681
$515$		0			0
$516$	9.00000	−	5.19615i	0.396203	−	0.228748i
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	4.00000	+	6.92820i	0.175750	+	0.304408i
$519$			5.19615i			0.228086i
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	12.0000			0.525226
$523$	−28.0000			−1.22435			−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000			−1.22435			−0.612177	+	0.790721i	$0.709706\pi$
$524$	1.00000	−	1.73205i	0.0436852	−	0.0756650i
$525$	33.0000	+	19.0526i	1.44024	+	0.831522i
$526$	−15.0000	−	25.9808i	−0.654031	−	1.13282i
$527$	10.0000	+	17.3205i	0.435607	+	0.754493i
$528$	−12.0000	−	6.92820i	−0.522233	−	0.301511i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	24.0000			1.04249
$531$	−36.0000			−1.56227
$532$	−24.0000			−1.04053
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$			34.6410i			1.49906i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$		0			0
$537$	28.5000	−	16.4545i	1.22987	−	0.710063i
$538$	10.0000	−	17.3205i	0.431131	−	0.746740i
$539$	−6.00000			−0.258438
$540$	−36.0000	−	20.7846i	−1.54919	−	0.894427i
$541$	36.0000			1.54776			0.773880	−	0.633332i	$-0.218313\pi$
$541$	36.0000			1.54776			0.773880	+	0.633332i	$0.218313\pi$
$542$	−24.0000	+	41.5692i	−1.03089	+	1.78555i
$543$	−16.5000	+	9.52628i	−0.708083	+	0.408812i
$544$	−20.0000	−	34.6410i	−0.857493	−	1.48522i
$545$	28.0000	+	48.4974i	1.19939	+	2.07740i
$546$		−	6.92820i		−	0.296500i
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	0.394432	+	0.918925i	$0.370941\pi$
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	−0.993028	+	0.117875i	$0.962392\pi$
$548$	−24.0000			−1.02523
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$	44.0000			1.87617
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	−5.00000	−	8.66025i	−0.212622	−	0.368271i
$554$	−14.0000	−	24.2487i	−0.594803	−	1.03023i
$555$	−12.0000	−	6.92820i	−0.509372	−	0.294086i
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$	12.0000	−	20.7846i	0.508001	−	0.879883i
$559$	−3.00000			−0.126886
$560$	16.0000	−	27.7128i	0.676123	−	1.17108i
$561$			17.3205i			0.731272i
$562$	−4.00000	−	6.92820i	−0.168730	−	0.292249i
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$	−18.0000	+	10.3923i	−0.757937	+	0.437595i
$565$	−42.0000	+	72.7461i	−1.76695	+	3.06045i
$566$	−30.0000			−1.26099
$567$	18.0000			0.755929
$568$		0			0
$569$	−19.0000	+	32.9090i	−0.796521	+	1.37962i	0.125347	+	0.992113i	$0.459996\pi$
$569$	−19.0000	+	32.9090i	−0.796521	+	1.37962i	−0.921869	+	0.387503i	$0.873338\pi$
$570$	72.0000	−	41.5692i	3.01575	−	1.74114i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		−	32.9090i		−	1.37479i
$574$	12.0000	−	20.7846i	0.500870	−	0.867533i
$575$	−33.0000			−1.37620
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$	−36.0000	−	20.7846i	−1.49611	−	0.863779i
$580$	8.00000	+	13.8564i	0.332182	+	0.575356i
$581$	−2.00000	−	3.46410i	−0.0829740	−	0.143715i
$582$	−24.0000	−	13.8564i	−0.994832	−	0.574367i
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$		0			0
$585$	6.00000	+	10.3923i	0.248069	+	0.429669i
$586$	−36.0000			−1.48715
$587$	11.0000	−	19.0526i	0.454019	−	0.786383i	−0.544613	−	0.838688i	$-0.683323\pi$
$587$	11.0000	−	19.0526i	0.454019	−	0.786383i	0.998631	+	0.0523045i	$0.0166566\pi$
$588$			10.3923i			0.428571i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$	−48.0000	−	83.1384i	−1.97613	−	3.42276i
$591$	−36.0000	+	20.7846i	−1.48084	+	0.854965i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$	18.0000	−	10.3923i	0.738549	−	0.426401i
$595$	−40.0000			−1.63984
$596$		0			0
$597$	−25.5000	+	14.7224i	−1.04365	+	0.602549i
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−15.5000	−	26.8468i	−0.633313	−	1.09693i	−0.986870	−	0.161517i	$-0.948361\pi$
$599$	−15.5000	−	26.8468i	−0.633313	−	1.09693i	0.353557	−	0.935413i	$-0.384972\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$	−12.0000			−0.489083
$603$	−12.0000			−0.488678
$604$	−4.00000			−0.162758
$605$	14.0000	−	24.2487i	0.569181	−	0.985850i
$606$	27.0000	+	15.5885i	1.09680	+	0.633238i
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	−24.0000	−	41.5692i	−0.973329	−	1.68585i
$609$	−6.00000	−	3.46410i	−0.243132	−	0.140372i
$610$	20.0000	−	34.6410i	0.809776	−	1.40257i
$611$	6.00000			0.242734
$612$	30.0000			1.21268
$613$	10.0000			0.403896			0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000			0.403896			0.201948	+	0.979396i	$0.435273\pi$
$614$	16.0000	−	27.7128i	0.645707	−	1.11840i
$615$			41.5692i			1.67623i
$616$		0			0
$617$	20.0000	+	34.6410i	0.805170	+	1.39459i	0.916176	+	0.400775i	$0.131259\pi$
$617$	20.0000	+	34.6410i	0.805170	+	1.39459i	−0.111007	+	0.993820i	$0.535408\pi$
$618$		0			0
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	−0.517473	−	0.855699i	$-0.673127\pi$
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	0.999794	+	0.0202954i	$0.00646066\pi$
$620$	32.0000			1.28515
$621$	−13.5000	+	7.79423i	−0.541736	+	0.312772i
$622$		0			0
$623$	10.0000	−	17.3205i	0.400642	−	0.693932i
$624$	6.00000	−	3.46410i	0.240192	−	0.138675i
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	−6.00000	−	10.3923i	−0.239808	−	0.415360i
$627$			20.7846i			0.830057i
$628$	−21.0000	+	36.3731i	−0.837991	+	1.45144i
$629$	10.0000			0.398726
$630$	24.0000	+	41.5692i	0.956183	+	1.65616i
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		0			0
$633$	1.50000	+	0.866025i	0.0596196	+	0.0344214i
$634$	8.00000	+	13.8564i	0.317721	+	0.550308i
$635$	32.0000	+	55.4256i	1.26988	+	2.19950i
$636$	9.00000	+	5.19615i	0.356873	+	0.206041i
$637$	1.50000	−	2.59808i	0.0594322	−	0.102940i
$638$	−8.00000			−0.316723
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$		0			0
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	−0.694025	−	0.719951i	$-0.744164\pi$
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	0.970508	+	0.241068i	$0.0774976\pi$
$642$		−	10.3923i		−	0.410152i
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	0.977787	+	0.209603i	$0.0672170\pi$
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	−0.307372	+	0.951589i	$0.599450\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$	18.0000	−	10.3923i	0.708749	−	0.409197i
$646$	−30.0000	+	51.9615i	−1.18033	+	2.04440i
$647$	−1.00000			−0.0393141			−0.0196570	−	0.999807i	$-0.506257\pi$
$647$	−1.00000			−0.0393141			−0.0196570	+	0.999807i	$0.506257\pi$
$648$		0			0
$649$	24.0000			0.942082
$650$	−11.0000	+	19.0526i	−0.431455	+	0.747303i
$651$	−12.0000	+	6.92820i	−0.470317	+	0.271538i
$652$	16.0000	+	27.7128i	0.626608	+	1.08532i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$			48.4974i			1.89640i
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	24.0000			0.937043
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$	24.0000			0.935617
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	−0.153378	−	0.988168i	$-0.549015\pi$
$659$	20.0000	−	34.6410i	0.779089	−	1.34942i	0.932467	−	0.361255i	$-0.117652\pi$
$660$	24.0000	+	13.8564i	0.934199	+	0.539360i
$661$	−24.0000	−	41.5692i	−0.933492	−	1.61686i	−0.777302	−	0.629128i	$-0.783412\pi$
$661$	−24.0000	−	41.5692i	−0.933492	−	1.61686i	−0.156190	−	0.987727i	$-0.549921\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	−7.50000	−	4.33013i	−0.291276	−	0.168168i
$664$		0			0
$665$	−48.0000			−1.86136
$666$	−6.00000	−	10.3923i	−0.232495	−	0.402694i
$667$	6.00000			0.232321
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$		−	27.7128i		−	1.07144i
$670$	−16.0000	−	27.7128i	−0.618134	−	1.07064i
$671$	5.00000	+	8.66025i	0.193023	+	0.334325i
$672$	24.0000	−	13.8564i	0.925820	−	0.534522i
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	−0.135615	−	0.990762i	$-0.543301\pi$
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	0.925832	−	0.377934i	$-0.123365\pi$
$674$	54.0000			2.08000
$675$	−49.5000	−	28.5788i	−1.90526	−	1.10000i
$676$	2.00000			0.0769231
$677$	−19.0000	+	32.9090i	−0.730229	+	1.26479i	0.226556	+	0.973998i	$0.427253\pi$
$677$	−19.0000	+	32.9090i	−0.730229	+	1.26479i	−0.956785	+	0.290796i	$0.906080\pi$
$678$	−63.0000	+	36.3731i	−2.41950	+	1.39690i
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$		0			0
$681$			6.92820i			0.265489i
$682$	−8.00000	+	13.8564i	−0.306336	+	0.530589i
$683$	42.0000			1.60709			0.803543	−	0.595247i	$-0.202946\pi$
$683$	42.0000			1.60709			0.803543	+	0.595247i	$0.202946\pi$
$684$	36.0000			1.37649
$685$	−48.0000			−1.83399
$686$	20.0000	−	34.6410i	0.763604	−	1.32260i
$687$	−24.0000	−	13.8564i	−0.915657	−	0.528655i
$688$	−6.00000	−	10.3923i	−0.228748	−	0.396203i
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$	−36.0000	−	20.7846i	−1.37050	−	0.791257i
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	−6.00000			−0.228086
$693$	−12.0000			−0.455842
$694$	66.0000			2.50533
$695$	6.00000	−	10.3923i	0.227593	−	0.394203i
$696$		0			0
$697$	−15.0000	−	25.9808i	−0.568166	−	0.984092i
$698$	8.00000	+	13.8564i	0.302804	+	0.524473i
$699$	10.5000	−	6.06218i	0.397146	−	0.229293i
$700$	−22.0000	+	38.1051i	−0.831522	+	1.44024i
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$			10.3923i			0.392232i
$703$	12.0000			0.452589
$704$	8.00000	−	13.8564i	0.301511	−	0.522233i
$705$	−36.0000	+	20.7846i	−1.35584	+	0.782794i
$706$	10.0000	+	17.3205i	0.376355	+	0.651866i
$707$	−9.00000	−	15.5885i	−0.338480	−	0.586264i
$708$		−	41.5692i		−	1.56227i
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$	96.0000			3.60282
$711$	7.50000	+	12.9904i	0.281272	+	0.487177i
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	−30.0000	−	17.3205i	−1.12272	−	0.648204i
$715$	−4.00000	−	6.92820i	−0.149592	−	0.259100i
$716$	19.0000	+	32.9090i	0.710063	+	1.22987i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	−24.0000	+	41.5692i	−0.894427	+	1.54919i
$721$		0			0
$722$	−17.0000	+	29.4449i	−0.632674	+	1.09582i
$723$		−	6.92820i		−	0.257663i
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	11.0000	+	19.0526i	0.408530	+	0.707594i
$726$	21.0000	−	12.1244i	0.779383	−	0.449977i
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−32.0000			−1.18437
$731$	−7.50000	+	12.9904i	−0.277398	+	0.480467i
$732$	15.0000	−	8.66025i	0.554416	−	0.320092i
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	0.805289	−	0.592883i	$-0.202010\pi$
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	−0.916096	+	0.400959i	$0.868677\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$			20.7846i			0.766652i
$736$	−12.0000	+	20.7846i	−0.442326	+	0.766131i
$737$	8.00000			0.294684
$738$	−18.0000	+	31.1769i	−0.662589	+	1.14764i
$739$	−22.0000			−0.809283			−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000			−0.809283			−0.404642	+	0.914475i	$0.632604\pi$
$740$	8.00000	−	13.8564i	0.294086	−	0.509372i
$741$	−9.00000	−	5.19615i	−0.330623	−	0.190885i
$742$	−6.00000	−	10.3923i	−0.220267	−	0.381514i
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$		0			0
$745$		0			0
$746$	2.00000			0.0732252
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$	−20.0000			−0.731272
$749$	−3.00000	+	5.19615i	−0.109618	+	0.189863i
$750$		−	83.1384i		−	3.03579i
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$	12.0000	+	20.7846i	0.437595	+	0.757937i
$753$	22.5000	−	12.9904i	0.819946	−	0.473396i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$	−8.00000			−0.291150
$756$			20.7846i			0.755929i
$757$	−17.0000			−0.617876			−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000			−0.617876			−0.308938	+	0.951082i	$0.599973\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$	9.00000	−	5.19615i	0.326679	−	0.188608i
$760$		0			0
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$			55.4256i			2.00786i
$763$	14.0000	−	24.2487i	0.506834	−	0.877862i
$764$	38.0000			1.37479
$765$	60.0000			2.16930
$766$	68.0000			2.45694
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$	24.0000	+	13.8564i	0.866025	+	0.500000i
$769$	−12.0000	−	20.7846i	−0.432731	−	0.749512i	0.564376	−	0.825518i	$-0.309117\pi$
$769$	−12.0000	−	20.7846i	−0.432731	−	0.749512i	−0.997107	+	0.0760054i	$0.975783\pi$
$770$	−16.0000	−	27.7128i	−0.576600	−	0.998700i
$771$	19.5000	+	11.2583i	0.702275	+	0.405459i
$772$	24.0000	−	41.5692i	0.863779	−	1.49611i
$773$	−4.00000			−0.143870			−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000			−0.143870			−0.0719350	+	0.997409i	$0.522917\pi$
$774$	18.0000			0.646997
$775$	44.0000			1.58053
$776$		0			0
$777$			6.92820i			0.248548i
$778$	1.00000	+	1.73205i	0.0358517	+	0.0620970i
$779$	−18.0000	−	31.1769i	−0.644917	−	1.11703i
$780$	−12.0000	+	6.92820i	−0.429669	+	0.248069i
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$	30.0000			1.07280
$783$	9.00000	+	5.19615i	0.321634	+	0.185695i
$784$	12.0000			0.428571
$785$	−42.0000	+	72.7461i	−1.49904	+	2.59642i
$786$	3.00000	−	1.73205i	0.107006	−	0.0617802i
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	−24.0000	−	41.5692i	−0.854965	−	1.48084i
$789$		−	25.9808i		−	0.924940i
$790$	−20.0000	+	34.6410i	−0.711568	+	1.23247i
$791$	42.0000			1.49335
$792$		0			0
$793$	−5.00000			−0.177555
$794$	−8.00000	+	13.8564i	−0.283909	+	0.491745i
$795$	18.0000	+	10.3923i	0.638394	+	0.368577i
$796$	−17.0000	−	29.4449i	−0.602549	−	1.04365i
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	0.847771	−	0.530362i	$-0.177944\pi$
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	−0.883193	+	0.469010i	$0.844611\pi$
$798$	−36.0000	−	20.7846i	−1.27439	−	0.735767i
$799$	15.0000	−	25.9808i	0.530662	−	0.919133i
$800$	−88.0000			−3.11127
$801$	−15.0000	+	25.9808i	−0.529999	+	0.917985i
$802$	52.0000			1.83618
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$		−	13.8564i		−	0.488678i
$805$	12.0000	+	20.7846i	0.422944	+	0.732561i
$806$	−4.00000	−	6.92820i	−0.140894	−	0.244036i
$807$	15.0000	−	8.66025i	0.528025	−	0.304855i
$808$		0			0
$809$	−3.00000			−0.105474			−0.0527372	−	0.998608i	$-0.516795\pi$
$809$	−3.00000			−0.105474			−0.0527372	+	0.998608i	$0.516795\pi$
$810$	−36.0000	−	62.3538i	−1.26491	−	2.19089i
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$	4.00000	−	6.92820i	0.140372	−	0.243132i
$813$	−36.0000	+	20.7846i	−1.26258	+	0.728948i
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$	32.0000	+	55.4256i	1.12091	+	1.94147i
$816$		−	34.6410i		−	1.21268i
$817$	−9.00000	+	15.5885i	−0.314870	+	0.545371i
$818$	−64.0000			−2.23771
$819$	3.00000	−	5.19615i	0.104828	−	0.181568i
$820$	−48.0000			−1.67623
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$821$	4.00000	−	6.92820i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$822$	−36.0000	−	20.7846i	−1.25564	−	0.724947i
$823$	−13.5000	−	23.3827i	−0.470580	−	0.815069i	0.528853	−	0.848713i	$-0.322622\pi$
$823$	−13.5000	−	23.3827i	−0.470580	−	0.815069i	−0.999434	+	0.0336440i	$0.989289\pi$
$824$		0			0
$825$	33.0000	+	19.0526i	1.14891	+	0.663325i
$826$	−24.0000	+	41.5692i	−0.835067	+	1.44638i
$827$	2.00000			0.0695468			0.0347734	−	0.999395i	$-0.488929\pi$
$827$	2.00000			0.0695468			0.0347734	+	0.999395i	$0.488929\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$	−8.00000	+	13.8564i	−0.277684	+	0.480963i
$831$		−	24.2487i		−	0.841178i
$832$	4.00000	+	6.92820i	0.138675	+	0.240192i
$833$	−7.50000	−	12.9904i	−0.259860	−	0.450090i
$834$	9.00000	−	5.19615i	0.311645	−	0.179928i
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	−24.0000			−0.830057
$837$	18.0000	−	10.3923i	0.622171	−	0.359211i
$838$	−2.00000			−0.0690889
$839$	18.0000	−	31.1769i	0.621429	−	1.07635i	−0.367791	−	0.929909i	$-0.619886\pi$
$839$	18.0000	−	31.1769i	0.621429	−	1.07635i	0.989220	−	0.146438i	$-0.0467809\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−26.0000	−	45.0333i	−0.896019	−	1.55195i
$843$		−	6.92820i		−	0.238620i
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	4.00000			0.137604
$846$	−36.0000			−1.23771
$847$	−14.0000			−0.481046
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$	−22.5000	−	12.9904i	−0.772198	−	0.445829i
$850$	55.0000	+	95.2628i	1.88648	+	3.26749i
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$	36.0000	+	20.7846i	1.23334	+	0.712069i
$853$	−18.0000	+	31.1769i	−0.616308	+	1.06748i	0.373845	+	0.927491i	$0.378039\pi$
$853$	−18.0000	+	31.1769i	−0.616308	+	1.06748i	−0.990153	+	0.139986i	$0.955294\pi$
$854$	−20.0000			−0.684386
$855$	72.0000			2.46235
$856$		0			0
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	−0.721345	−	0.692576i	$-0.756476\pi$
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	0.960461	+	0.278416i	$0.0898092\pi$
$858$		−	6.92820i		−	0.236525i
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	0.968657	+	0.248402i	$0.0799054\pi$
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	−0.269206	+	0.963083i	$0.586761\pi$
$860$	12.0000	+	20.7846i	0.409197	+	0.708749i
$861$	18.0000	−	10.3923i	0.613438	−	0.354169i
$862$		0			0
$863$	44.0000			1.49778			0.748889	−	0.662696i	$-0.230588\pi$
$863$	44.0000			1.49778			0.748889	+	0.662696i	$0.230588\pi$
$864$	−36.0000	+	20.7846i	−1.22474	+	0.707107i
$865$	−12.0000			−0.408012
$866$	35.0000	−	60.6218i	1.18935	−	2.06001i
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	−5.00000	−	8.66025i	−0.169613	−	0.293779i
$870$			27.7128i			0.939552i
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$		0			0
$873$	−12.0000	−	20.7846i	−0.406138	−	0.703452i
$874$	36.0000			1.21772
$875$	−24.0000	+	41.5692i	−0.811348	+	1.40530i
$876$	−12.0000	−	6.92820i	−0.405442	−	0.234082i
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	1.00000	+	1.73205i	0.0337484	+	0.0584539i
$879$	−27.0000	−	15.5885i	−0.910687	−	0.525786i
$880$	16.0000	−	27.7128i	0.539360	−	0.934199i
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	−9.00000	+	15.5885i	−0.303046	+	0.524891i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	5.00000	−	8.66025i	0.168168	−	0.291276i
$885$		−	83.1384i		−	2.79467i
$886$	−31.0000	−	53.6936i	−1.04147	−	1.80387i
$887$	7.50000	+	12.9904i	0.251825	+	0.436174i	0.964028	−	0.265799i	$-0.0856358\pi$
$887$	7.50000	+	12.9904i	0.251825	+	0.436174i	−0.712203	+	0.701974i	$0.752302\pi$
$888$		0			0
$889$	16.0000	−	27.7128i	0.536623	−	0.929458i
$890$	−80.0000			−2.68161
$891$	18.0000			0.603023
$892$	32.0000			1.07144
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$		0			0
$895$	38.0000	+	65.8179i	1.27020	+	2.20005i
$896$		0			0
$897$			5.19615i			0.173494i
$898$	4.00000	−	6.92820i	0.133482	−	0.231197i
$899$	−8.00000			−0.266815
$900$	33.0000	−	57.1577i	1.10000	−	1.90526i
$901$	−15.0000			−0.499722
$902$	12.0000	−	20.7846i	0.399556	−	0.692052i
$903$	−9.00000	−	5.19615i	−0.299501	−	0.172917i
$904$		0			0
$905$	−22.0000	−	38.1051i	−0.731305	−	1.26666i
$906$	−6.00000	−	3.46410i	−0.199337	−	0.115087i
$907$	−16.5000	+	28.5788i	−0.547874	+	0.948945i	0.450546	+	0.892753i	$0.351229\pi$
$907$	−16.5000	+	28.5788i	−0.547874	+	0.948945i	−0.998420	+	0.0561918i	$0.982104\pi$
$908$	−8.00000			−0.265489
$909$	13.5000	+	23.3827i	0.447767	+	0.775555i
$910$	16.0000			0.530395
$911$	8.50000	−	14.7224i	0.281618	−	0.487776i	−0.690166	−	0.723651i	$-0.742462\pi$
$911$	8.50000	−	14.7224i	0.281618	−	0.487776i	0.971783	+	0.235875i	$0.0757957\pi$
$912$		−	41.5692i		−	1.37649i
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$	30.0000	−	17.3205i	0.991769	−	0.572598i
$916$	16.0000	−	27.7128i	0.528655	−	0.915657i
$917$	−2.00000			−0.0660458
$918$	45.0000	+	25.9808i	1.48522	+	0.857493i
$919$	15.0000			0.494804			0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000			0.494804			0.247402	+	0.968913i	$0.420423\pi$
$920$		0			0
$921$	24.0000	−	13.8564i	0.790827	−	0.456584i
$922$	22.0000	+	38.1051i	0.724531	+	1.25493i
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		−	13.8564i		−	0.455842i
$925$	11.0000	−	19.0526i	0.361678	−	0.626444i
$926$	32.0000			1.05159
$927$		0			0
$928$	16.0000			0.525226
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$	48.0000	+	27.7128i	1.57398	+	0.908739i
$931$	−9.00000	−	15.5885i	−0.294963	−	0.510891i
$932$	7.00000	+	12.1244i	0.229293	+	0.397146i
$933$		0			0
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	−40.0000			−1.30814
$936$		0			0
$937$	23.0000			0.751377			0.375689	−	0.926746i	$-0.377406\pi$
$937$	23.0000			0.751377			0.375689	+	0.926746i	$0.377406\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$		−	10.3923i		−	0.339140i
$940$	−24.0000	−	41.5692i	−0.782794	−	1.35584i
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	0.935942	−	0.352155i	$-0.114551\pi$
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	−0.772946	+	0.634472i	$0.781218\pi$
$942$	−63.0000	+	36.3731i	−2.05265	+	1.18510i
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−48.0000			−1.56227
$945$			41.5692i			1.35225i
$946$	−12.0000			−0.390154
$947$	−9.00000	+	15.5885i	−0.292461	+	0.506557i	−0.974391	−	0.224860i	$-0.927807\pi$
$947$	−9.00000	+	15.5885i	−0.292461	+	0.506557i	0.681930	+	0.731417i	$0.261141\pi$
$948$	−15.0000	+	8.66025i	−0.487177	+	0.281272i
$949$	2.00000	+	3.46410i	0.0649227	+	0.112449i
$950$	66.0000	+	114.315i	2.14132	+	3.70888i
$951$			13.8564i			0.449325i
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	9.00000	+	15.5885i	0.291386	+	0.504695i
$955$	76.0000			2.45930
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−6.00000	−	3.46410i	−0.193952	−	0.111979i
$958$	−36.0000	−	62.3538i	−1.16311	−	2.01456i
$959$	12.0000	+	20.7846i	0.387500	+	0.671170i
$960$	−48.0000	−	27.7128i	−1.54919	−	0.894427i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−4.00000			−0.128965
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	8.00000			0.257663
$965$	48.0000	−	83.1384i	1.54517	−	2.67632i
$966$			20.7846i			0.668734i
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	−0.999858	−	0.0168544i	$-0.994635\pi$
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	0.485333	−	0.874330i	$-0.338699\pi$
$968$		0			0
$969$	−45.0000	+	25.9808i	−1.44561	+	0.834622i
$970$	32.0000	−	55.4256i	1.02746	−	1.77961i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		−	31.1769i		−	1.00000i
$973$	−6.00000			−0.192351
$974$	−18.0000	+	31.1769i	−0.576757	+	0.998973i
$975$	−16.5000	+	9.52628i	−0.528423	+	0.305085i
$976$	−10.0000	−	17.3205i	−0.320092	−	0.554416i
$977$	18.0000	+	31.1769i	0.575871	+	0.997438i	0.995946	+	0.0899487i	$0.0286703\pi$
$977$	18.0000	+	31.1769i	0.575871	+	0.997438i	−0.420075	+	0.907489i	$0.637996\pi$
$978$			55.4256i			1.77232i
$979$	10.0000	−	17.3205i	0.319601	−	0.553566i
$980$	−24.0000			−0.766652
$981$	−21.0000	+	36.3731i	−0.670478	+	1.16130i
$982$	24.0000			0.765871
$983$	26.0000	−	45.0333i	0.829271	−	1.43634i	−0.0693395	−	0.997593i	$-0.522089\pi$
$983$	26.0000	−	45.0333i	0.829271	−	1.43634i	0.898611	−	0.438747i	$-0.144577\pi$
$984$		0			0
$985$	−48.0000	−	83.1384i	−1.52941	−	2.64901i
$986$	−10.0000	−	17.3205i	−0.318465	−	0.551597i
$987$	18.0000	+	10.3923i	0.572946	+	0.330791i
$988$	6.00000	−	10.3923i	0.190885	−	0.330623i
$989$	9.00000			0.286183
$990$	24.0000	+	41.5692i	0.762770	+	1.32116i
$991$	37.0000			1.17534			0.587672	−	0.809099i	$-0.300045\pi$
$991$	37.0000			1.17534			0.587672	+	0.809099i	$0.300045\pi$
$992$	16.0000	−	27.7128i	0.508001	−	0.879883i
$993$			6.92820i			0.219860i
$994$	−24.0000	−	41.5692i	−0.761234	−	1.31850i
$995$	−34.0000	−	58.8897i	−1.07787	−	1.86693i
$996$	−6.00000	+	3.46410i	−0.190117	+	0.109764i
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$		0			0
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.a.79.1	yes	2
3.2	odd	2		351.2.e.a.235.1		2
9.2	odd	6		1053.2.a.a.1.1		1
9.4	even	3	inner	117.2.e.a.40.1	✓	2
9.5	odd	6		351.2.e.a.118.1		2
9.7	even	3		1053.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.a.40.1	✓	2	9.4	even	3	inner
117.2.e.a.79.1	yes	2	1.1	even	1	trivial
351.2.e.a.118.1		2	9.5	odd	6
351.2.e.a.235.1		2	3.2	odd	2
1053.2.a.a.1.1		1	9.2	odd	6
1053.2.a.d.1.1		1	9.7	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.46410i q^{6} +(-1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.46410i q^{6} +(-1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +8.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(6.00000 + 3.46410i) q^{15} +(2.00000 - 3.46410i) q^{16} -5.00000 q^{17} +(3.00000 + 5.19615i) q^{18} -6.00000 q^{19} +(-4.00000 + 6.92820i) q^{20} -3.46410i q^{21} +(-2.00000 - 3.46410i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-5.50000 + 9.52628i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +4.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(-12.0000 + 6.92820i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(4.00000 + 6.92820i) q^{32} -3.46410i q^{33} +(5.00000 - 8.66025i) q^{34} +8.00000 q^{35} -6.00000 q^{36} -2.00000 q^{37} +(6.00000 - 10.3923i) q^{38} +(1.50000 + 0.866025i) q^{39} +(3.00000 + 5.19615i) q^{41} +(6.00000 + 3.46410i) q^{42} +(1.50000 - 2.59808i) q^{43} +4.00000 q^{44} -12.0000 q^{45} -6.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +6.92820i q^{48} +(1.50000 + 2.59808i) q^{49} +(-11.0000 - 19.0526i) q^{50} +(7.50000 - 4.33013i) q^{51} +(-1.00000 + 1.73205i) q^{52} +3.00000 q^{53} +(-9.00000 - 5.19615i) q^{54} +8.00000 q^{55} +(9.00000 - 5.19615i) q^{57} +(2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} -13.8564i q^{60} +(2.50000 - 4.33013i) q^{61} +8.00000 q^{62} +(3.00000 + 5.19615i) q^{63} -8.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(6.00000 + 3.46410i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(5.00000 + 8.66025i) q^{68} +(-4.50000 - 2.59808i) q^{69} +(-8.00000 + 13.8564i) q^{70} +12.0000 q^{71} -4.00000 q^{73} +(2.00000 - 3.46410i) q^{74} -19.0526i q^{75} +(6.00000 + 10.3923i) q^{76} +(-2.00000 - 3.46410i) q^{77} +(-3.00000 + 1.73205i) q^{78} +(-2.50000 + 4.33013i) q^{79} -16.0000 q^{80} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{82} +(-1.00000 + 1.73205i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(10.0000 + 17.3205i) q^{85} +(3.00000 + 5.19615i) q^{86} +3.46410i q^{87} -10.0000 q^{89} +(12.0000 - 20.7846i) q^{90} +2.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(12.0000 + 20.7846i) q^{95} +(-12.0000 - 6.92820i) q^{96} +(4.00000 - 6.92820i) q^{97} -6.00000 q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^7 + 3 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{7} + 3 q^{9} + 16 q^{10} - 2 q^{11} + 6 q^{12} - q^{13} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 10 q^{17} + 6 q^{18} - 12 q^{19} - 8 q^{20} - 4 q^{22} + 3 q^{23} - 11 q^{25} + 4 q^{26} + 8 q^{28} + 2 q^{29} - 24 q^{30} - 4 q^{31} + 8 q^{32} + 10 q^{34} + 16 q^{35} - 12 q^{36} - 4 q^{37} + 12 q^{38} + 3 q^{39} + 6 q^{41} + 12 q^{42} + 3 q^{43} + 8 q^{44} - 24 q^{45} - 12 q^{46} - 6 q^{47} + 3 q^{49} - 22 q^{50} + 15 q^{51} - 2 q^{52} + 6 q^{53} - 18 q^{54} + 16 q^{55} + 18 q^{57} + 4 q^{58} - 12 q^{59} + 5 q^{61} + 16 q^{62} + 6 q^{63} - 16 q^{64} - 4 q^{65} + 12 q^{66} - 4 q^{67} + 10 q^{68} - 9 q^{69} - 16 q^{70} + 24 q^{71} - 8 q^{73} + 4 q^{74} + 12 q^{76} - 4 q^{77} - 6 q^{78} - 5 q^{79} - 32 q^{80} - 9 q^{81} - 24 q^{82} - 2 q^{83} - 12 q^{84} + 20 q^{85} + 6 q^{86} - 20 q^{89} + 24 q^{90} + 4 q^{91} + 6 q^{92} + 12 q^{93} - 12 q^{94} + 24 q^{95} - 24 q^{96} + 8 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^7 + 3 * q^9 + 16 * q^10 - 2 * q^11 + 6 * q^12 - q^13 - 4 * q^14 + 12 * q^15 + 4 * q^16 - 10 * q^17 + 6 * q^18 - 12 * q^19 - 8 * q^20 - 4 * q^22 + 3 * q^23 - 11 * q^25 + 4 * q^26 + 8 * q^28 + 2 * q^29 - 24 * q^30 - 4 * q^31 + 8 * q^32 + 10 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^37 + 12 * q^38 + 3 * q^39 + 6 * q^41 + 12 * q^42 + 3 * q^43 + 8 * q^44 - 24 * q^45 - 12 * q^46 - 6 * q^47 + 3 * q^49 - 22 * q^50 + 15 * q^51 - 2 * q^52 + 6 * q^53 - 18 * q^54 + 16 * q^55 + 18 * q^57 + 4 * q^58 - 12 * q^59 + 5 * q^61 + 16 * q^62 + 6 * q^63 - 16 * q^64 - 4 * q^65 + 12 * q^66 - 4 * q^67 + 10 * q^68 - 9 * q^69 - 16 * q^70 + 24 * q^71 - 8 * q^73 + 4 * q^74 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 5 * q^79 - 32 * q^80 - 9 * q^81 - 24 * q^82 - 2 * q^83 - 12 * q^84 + 20 * q^85 + 6 * q^86 - 20 * q^89 + 24 * q^90 + 4 * q^91 + 6 * q^92 + 12 * q^93 - 12 * q^94 + 24 * q^95 - 24 * q^96 + 8 * q^97 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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