LMFDB - Embedded newform 117.2.t.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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, 3]))

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

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.25
Dual form			117.2.t.b.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(3.00000 - 1.73205i) q^{5} +(3.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(3.00000 - 1.73205i) q^{5} +(3.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +3.46410i q^{19} +(-6.00000 - 3.46410i) q^{20} -6.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{27} -6.92820i q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.00000 + 1.73205i) q^{31} +6.00000 q^{33} +12.0000 q^{35} -6.00000 q^{36} +6.92820i q^{37} +(-4.50000 + 4.33013i) q^{39} +(6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{43} +6.92820i q^{44} -10.3923i q^{45} +(6.00000 + 3.46410i) q^{47} -6.92820i q^{48} +(2.50000 + 4.33013i) q^{49} +(4.50000 - 2.59808i) q^{51} +(-5.00000 - 5.19615i) q^{52} -9.00000 q^{53} -12.0000 q^{55} +(-3.00000 - 5.19615i) q^{57} +(-3.00000 + 1.73205i) q^{59} +12.0000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(9.00000 - 5.19615i) q^{63} +8.00000 q^{64} +(9.00000 - 8.66025i) q^{65} +(3.00000 + 5.19615i) q^{68} +(4.50000 + 2.59808i) q^{69} -10.3923i q^{73} +12.1244i q^{75} +(6.00000 - 3.46410i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(-0.500000 + 0.866025i) q^{79} +13.8564i q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 3.46410i) q^{83} +(6.00000 + 10.3923i) q^{84} +(-9.00000 + 5.19615i) q^{85} -10.3923i q^{87} +3.46410i q^{89} +(12.0000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(3.00000 - 5.19615i) q^{93} +(6.00000 + 10.3923i) q^{95} +(-6.00000 - 3.46410i) q^{97} +(-9.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 2 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 2 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} - 2 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{9} - 6 q^{11} + 6 q^{12} + 7 q^{13} - 6 q^{15} - 4 q^{16} - 6 q^{17} - 12 q^{20} - 12 q^{21} - 3 q^{23} + 7 q^{25} - 6 q^{29} - 6 q^{31} + 12 q^{33} + 24 q^{35} - 12 q^{36} - 9 q^{39} + 12 q^{41} + q^{43} + 12 q^{47} + 5 q^{49} + 9 q^{51} - 10 q^{52} - 18 q^{53} - 24 q^{55} - 6 q^{57} - 6 q^{59} + 24 q^{60} - 7 q^{61} + 18 q^{63} + 16 q^{64} + 18 q^{65} + 6 q^{68} + 9 q^{69} + 12 q^{76} - 12 q^{77} - q^{79} - 9 q^{81} - 12 q^{83} + 12 q^{84} - 18 q^{85} + 24 q^{91} - 6 q^{92} + 6 q^{93} + 12 q^{95} - 12 q^{97} - 18 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 2 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^9 - 6 * q^11 + 6 * q^12 + 7 * q^13 - 6 * q^15 - 4 * q^16 - 6 * q^17 - 12 * q^20 - 12 * q^21 - 3 * q^23 + 7 * q^25 - 6 * q^29 - 6 * q^31 + 12 * q^33 + 24 * q^35 - 12 * q^36 - 9 * q^39 + 12 * q^41 + q^43 + 12 * q^47 + 5 * q^49 + 9 * q^51 - 10 * q^52 - 18 * q^53 - 24 * q^55 - 6 * q^57 - 6 * q^59 + 24 * q^60 - 7 * q^61 + 18 * q^63 + 16 * q^64 + 18 * q^65 + 6 * q^68 + 9 * q^69 + 12 * q^76 - 12 * q^77 - q^79 - 9 * q^81 - 12 * q^83 + 12 * q^84 - 18 * q^85 + 24 * q^91 - 6 * q^92 + 6 * q^93 + 12 * q^95 - 12 * q^97 - 18 * 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 $

$2$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	−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
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.354593	−	0.935021i	$-0.384620\pi$
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.987048	+	0.160424i	$0.0512862\pi$
$6$		0			0
$7$	3.00000	+	1.73205i	1.13389	+	0.654654i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	3.00000	+	1.73205i	1.13389	+	0.654654i	0.188982	+	0.981981i	$0.439481\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−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	$0.841568\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$		0			0
$15$	−3.00000	+	5.19615i	−0.774597	+	1.34164i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−6.00000	−	3.46410i	−1.34164	−	0.774597i
$21$	−6.00000			−1.30931
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		−	6.92820i		−	1.30931i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$		0			0
$33$	6.00000			1.04447
$34$		0			0
$35$	12.0000			2.02837
$36$	−6.00000			−1.00000
$37$			6.92820i			1.13899i	0.821995	+	0.569495i	$0.192861\pi$
$37$			6.92820i			1.13899i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−4.50000	+	4.33013i	−0.720577	+	0.693375i
$40$		0			0
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.0480106	−	0.998847i	$-0.484712\pi$
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.889032	+	0.457845i	$0.151379\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$			6.92820i			1.04447i
$45$		−	10.3923i		−	1.54919i
$46$		0			0
$47$	6.00000	+	3.46410i	0.875190	+	0.505291i	0.869069	−	0.494690i	$-0.164718\pi$
$47$	6.00000	+	3.46410i	0.875190	+	0.505291i	0.00612051	+	0.999981i	$0.498052\pi$
$48$		−	6.92820i		−	1.00000i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$		0			0
$51$	4.50000	−	2.59808i	0.630126	−	0.363803i
$52$	−5.00000	−	5.19615i	−0.693375	−	0.720577i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$		0			0
$57$	−3.00000	−	5.19615i	−0.397360	−	0.688247i
$58$		0			0
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	−0.682406	−	0.730974i	$-0.739066\pi$
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	0.291839	+	0.956467i	$0.405733\pi$
$60$	12.0000			1.54919
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	9.00000	−	5.19615i	1.13389	−	0.654654i
$64$	8.00000			1.00000
$65$	9.00000	−	8.66025i	1.11631	−	1.07417i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	4.50000	+	2.59808i	0.541736	+	0.312772i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		−	10.3923i		−	1.21633i	−0.793812	−	0.608164i	$-0.791906\pi$
$73$		−	10.3923i		−	1.21633i	0.793812	−	0.608164i	$-0.208094\pi$
$74$		0			0
$75$			12.1244i			1.40000i
$76$	6.00000	−	3.46410i	0.688247	−	0.397360i
$77$	−6.00000	−	10.3923i	−0.683763	−	1.18431i
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$			13.8564i			1.54919i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−6.00000	−	3.46410i	−0.658586	−	0.380235i	0.133152	−	0.991096i	$-0.457490\pi$
$83$	−6.00000	−	3.46410i	−0.658586	−	0.380235i	−0.791738	+	0.610861i	$0.790823\pi$
$84$	6.00000	+	10.3923i	0.654654	+	1.13389i
$85$	−9.00000	+	5.19615i	−0.976187	+	0.563602i
$86$		0			0
$87$		−	10.3923i		−	1.11417i
$88$		0			0
$89$			3.46410i			0.367194i	0.983002	+	0.183597i	$0.0587741\pi$
$89$			3.46410i			0.367194i	−0.983002	+	0.183597i	$0.941226\pi$
$90$		0			0
$91$	12.0000	+	3.46410i	1.25794	+	0.363137i
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$		0			0
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	0.163448	−	0.986552i	$-0.447739\pi$
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	−0.772655	+	0.634826i	$0.781072\pi$
$98$		0			0
$99$	−9.00000	+	5.19615i	−0.904534	+	0.522233i
$100$	−14.0000			−1.40000
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$	−18.0000	+	10.3923i	−1.75662	+	1.01419i
$106$		0			0
$107$	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
$109$		−	3.46410i		−	0.331801i	−0.986143	−	0.165900i	$-0.946947\pi$
$109$		−	3.46410i		−	0.331801i	0.986143	−	0.165900i	$-0.0530530\pi$
$110$		0			0
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$	−12.0000	+	6.92820i	−1.13389	+	0.654654i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	−9.00000	−	5.19615i	−0.839254	−	0.484544i
$116$	12.0000			1.11417
$117$	3.00000	−	10.3923i	0.277350	−	0.960769i
$118$		0			0
$119$	−9.00000	−	5.19615i	−0.825029	−	0.476331i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$	6.00000	+	3.46410i	0.538816	+	0.311086i
$125$		−	6.92820i		−	0.619677i
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$			1.73205i			0.152499i
$130$		0			0
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$	−6.00000	−	10.3923i	−0.522233	−	0.904534i
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$		0			0
$135$	9.00000	+	15.5885i	0.774597	+	1.34164i
$136$		0			0
$137$	18.0000	+	10.3923i	1.53784	+	0.887875i	0.998965	+	0.0454914i	$0.0144854\pi$
$137$	18.0000	+	10.3923i	1.53784	+	0.887875i	0.538879	+	0.842383i	$0.318848\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	−12.0000	−	20.7846i	−1.01419	−	1.75662i
$141$	−12.0000			−1.01058
$142$		0			0
$143$	−12.0000	−	3.46410i	−1.00349	−	0.289683i
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$			20.7846i			1.72607i
$146$		0			0
$147$	−7.50000	−	4.33013i	−0.618590	−	0.357143i
$148$	12.0000	−	6.92820i	0.986394	−	0.569495i
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	−0.725213	−	0.688525i	$-0.758259\pi$
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	0.233674	+	0.972315i	$0.424925\pi$
$150$		0			0
$151$	18.0000	+	10.3923i	1.46482	+	0.845714i	0.999228	−	0.0392861i	$-0.0125084\pi$
$151$	18.0000	+	10.3923i	1.46482	+	0.845714i	0.465591	+	0.885000i	$0.345842\pi$
$152$		0			0
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$	12.0000	+	3.46410i	0.960769	+	0.277350i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$		0			0
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$		−	17.3205i		−	1.35665i	−0.734763	−	0.678323i	$-0.762707\pi$
$163$		−	17.3205i		−	1.35665i	0.734763	−	0.678323i	$-0.237293\pi$
$164$	−12.0000	−	6.92820i	−0.937043	−	0.541002i
$165$	18.0000	−	10.3923i	1.40130	−	0.809040i
$166$		0			0
$167$	6.00000	−	3.46410i	0.464294	−	0.268060i	−0.249554	−	0.968361i	$-0.580284\pi$
$167$	6.00000	−	3.46410i	0.464294	−	0.268060i	0.713848	+	0.700301i	$0.246951\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	9.00000	+	5.19615i	0.688247	+	0.397360i
$172$	−2.00000			−0.152499
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$		0			0
$175$	21.0000	−	12.1244i	1.58745	−	0.916515i
$176$	12.0000	−	6.92820i	0.904534	−	0.522233i
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$		0			0
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−18.0000	+	10.3923i	−1.34164	+	0.774597i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		−	12.1244i		−	0.896258i
$184$		0			0
$185$	12.0000	+	20.7846i	0.882258	+	1.52811i
$186$		0			0
$187$	9.00000	+	5.19615i	0.658145	+	0.379980i
$188$		−	13.8564i		−	1.01058i
$189$	−9.00000	+	15.5885i	−0.654654	+	1.13389i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$	−12.0000	+	6.92820i	−0.866025	+	0.500000i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$	−6.00000	+	20.7846i	−0.429669	+	1.48842i
$196$	5.00000	−	8.66025i	0.357143	−	0.618590i
$197$		−	24.2487i		−	1.72765i	−0.503793	−	0.863825i	$-0.668062\pi$
$197$		−	24.2487i		−	1.72765i	0.503793	−	0.863825i	$-0.331938\pi$
$198$		0			0
$199$	−17.0000			−1.20510			−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000			−1.20510			−0.602549	+	0.798082i	$0.705848\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.0000	+	10.3923i	−1.26335	+	0.729397i
$204$	−9.00000	−	5.19615i	−0.630126	−	0.363803i
$205$	12.0000	−	20.7846i	0.838116	−	1.45166i
$206$		0			0
$207$	−9.00000			−0.625543
$208$	−4.00000	+	13.8564i	−0.277350	+	0.960769i
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	9.00000	+	15.5885i	0.618123	+	1.07062i
$213$		0			0
$214$		0			0
$215$		−	3.46410i		−	0.236250i
$216$		0			0
$217$	−12.0000			−0.814613
$218$		0			0
$219$	9.00000	+	15.5885i	0.608164	+	1.05337i
$220$	12.0000	+	20.7846i	0.809040	+	1.40130i
$221$	−10.5000	+	2.59808i	−0.706306	+	0.174766i
$222$		0			0
$223$	−6.00000	−	3.46410i	−0.401790	−	0.231973i	0.285466	−	0.958389i	$-0.407852\pi$
$223$	−6.00000	−	3.46410i	−0.401790	−	0.231973i	−0.687256	+	0.726415i	$0.741185\pi$
$224$		0			0
$225$	−10.5000	−	18.1865i	−0.700000	−	1.21244i
$226$		0			0
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	0.767999	−	0.640451i	$-0.221253\pi$
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	−0.170648	+	0.985332i	$0.554586\pi$
$228$	−6.00000	+	10.3923i	−0.397360	+	0.688247i
$229$	3.00000	−	1.73205i	0.198246	−	0.114457i	−0.397591	−	0.917563i	$-0.630154\pi$
$229$	3.00000	−	1.73205i	0.198246	−	0.114457i	0.595837	+	0.803105i	$0.296820\pi$
$230$		0			0
$231$	18.0000	+	10.3923i	1.18431	+	0.683763i
$232$		0			0
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$		0			0
$235$	24.0000			1.56559
$236$	6.00000	+	3.46410i	0.390567	+	0.225494i
$237$		−	1.73205i		−	0.112509i
$238$		0			0
$239$	−9.00000	+	5.19615i	−0.582162	+	0.336111i	−0.761992	−	0.647586i	$-0.775778\pi$
$239$	−9.00000	+	5.19615i	−0.582162	+	0.336111i	0.179830	+	0.983698i	$0.442445\pi$
$240$	−12.0000	−	20.7846i	−0.774597	−	1.34164i
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	0.0609515	−	0.998141i	$-0.480586\pi$
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	−0.833939	+	0.551856i	$0.813920\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	14.0000			0.896258
$245$	15.0000	+	8.66025i	0.958315	+	0.553283i
$246$		0			0
$247$	3.00000	+	12.1244i	0.190885	+	0.771454i
$248$		0			0
$249$	12.0000			0.760469
$250$		0			0
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$	−18.0000	−	10.3923i	−1.13389	−	0.654654i
$253$			10.3923i			0.653359i
$254$		0			0
$255$	9.00000	−	15.5885i	0.563602	−	0.976187i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		0			0
$259$	−12.0000	+	20.7846i	−0.745644	+	1.29149i
$260$	−24.0000	−	6.92820i	−1.48842	−	0.429669i
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	−27.0000	+	15.5885i	−1.65860	+	0.957591i
$266$		0			0
$267$	−3.00000	−	5.19615i	−0.183597	−	0.317999i
$268$		0			0
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$		−	20.7846i		−	1.26258i	−0.775549	−	0.631288i	$-0.782527\pi$
$271$		−	20.7846i		−	1.26258i	0.775549	−	0.631288i	$-0.217473\pi$
$272$	6.00000	−	10.3923i	0.363803	−	0.630126i
$273$	−21.0000	+	5.19615i	−1.27098	+	0.314485i
$274$		0			0
$275$	−21.0000	+	12.1244i	−1.26635	+	0.731126i
$276$		−	10.3923i		−	0.625543i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$		0			0
$279$			10.3923i			0.622171i
$280$		0			0
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	0.813227	−	0.581947i	$-0.197709\pi$
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	−0.0973670	+	0.995249i	$0.531042\pi$
$282$		0			0
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	0.743048	−	0.669238i	$-0.233379\pi$
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	−0.951101	+	0.308879i	$0.900046\pi$
$284$		0			0
$285$	−18.0000	−	10.3923i	−1.06623	−	0.615587i
$286$		0			0
$287$	24.0000			1.41668
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	12.0000			0.703452
$292$	−18.0000	+	10.3923i	−1.05337	+	0.608164i
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.869440	−	0.494039i	$-0.835520\pi$
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.00686959	+	0.999976i	$0.502187\pi$
$294$		0			0
$295$	−6.00000	+	10.3923i	−0.349334	+	0.605063i
$296$		0			0
$297$	9.00000	−	15.5885i	0.522233	−	0.904534i
$298$		0			0
$299$	−7.50000	−	7.79423i	−0.433736	−	0.450752i
$300$	21.0000	−	12.1244i	1.21244	−	0.700000i
$301$	3.00000	−	1.73205i	0.172917	−	0.0998337i
$302$		0			0
$303$		−	5.19615i		−	0.298511i
$304$	−12.0000	−	6.92820i	−0.688247	−	0.397360i
$305$			24.2487i			1.38848i
$306$		0			0
$307$			10.3923i			0.593120i	0.955014	+	0.296560i	$0.0958395\pi$
$307$			10.3923i			0.593120i	−0.955014	+	0.296560i	$0.904160\pi$
$308$	−12.0000	+	20.7846i	−0.683763	+	1.18431i
$309$	12.0000	+	6.92820i	0.682656	+	0.394132i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	−0.597522	−	0.801852i	$-0.703848\pi$
$313$	7.00000	−	12.1244i	0.395663	−	0.685309i	0.993186	+	0.116543i	$0.0371814\pi$
$314$		0			0
$315$	18.0000	−	31.1769i	1.01419	−	1.75662i
$316$	2.00000			0.112509
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.955894	−	0.293713i	$-0.0948910\pi$
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.223584	+	0.974685i	$0.428224\pi$
$318$		0			0
$319$	18.0000	−	10.3923i	1.00781	−	0.581857i
$320$	24.0000	−	13.8564i	1.34164	−	0.774597i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$		−	10.3923i		−	0.578243i
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$	7.00000	−	24.2487i	0.388290	−	1.34508i
$326$		0			0
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	−21.0000	−	12.1244i	−1.15426	−	0.666415i	−0.204342	−	0.978900i	$-0.565505\pi$
$331$	−21.0000	−	12.1244i	−1.15426	−	0.666415i	−0.949923	+	0.312485i	$0.898839\pi$
$332$			13.8564i			0.760469i
$333$	18.0000	+	10.3923i	0.986394	+	0.569495i
$334$		0			0
$335$		0			0
$336$	12.0000	−	20.7846i	0.654654	−	1.13389i
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$		0			0
$339$	−22.5000	−	12.9904i	−1.22203	−	0.705541i
$340$	18.0000	+	10.3923i	0.976187	+	0.563602i
$341$	12.0000			0.649836
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$		0			0
$345$	18.0000			0.969087
$346$		0			0
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$	−18.0000	+	10.3923i	−0.964901	+	0.557086i
$349$	15.0000	+	8.66025i	0.802932	+	0.463573i	0.844495	−	0.535563i	$-0.179901\pi$
$349$	15.0000	+	8.66025i	0.802932	+	0.463573i	−0.0415636	+	0.999136i	$0.513234\pi$
$350$		0			0
$351$	4.50000	+	18.1865i	0.240192	+	0.970725i
$352$		0			0
$353$	9.00000	+	5.19615i	0.479022	+	0.276563i	0.720009	−	0.693965i	$-0.244138\pi$
$353$	9.00000	+	5.19615i	0.479022	+	0.276563i	−0.240987	+	0.970528i	$0.577471\pi$
$354$		0			0
$355$		0			0
$356$	6.00000	−	3.46410i	0.317999	−	0.183597i
$357$	18.0000			0.952661
$358$		0			0
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		0			0
$363$	−1.50000	−	0.866025i	−0.0787296	−	0.0454545i
$364$	−6.00000	−	24.2487i	−0.314485	−	1.27098i
$365$	−18.0000	−	31.1769i	−0.942163	−	1.63187i
$366$		0			0
$367$	12.5000	−	21.6506i	0.652495	−	1.13015i	−0.330021	−	0.943974i	$-0.607056\pi$
$367$	12.5000	−	21.6506i	0.652495	−	1.13015i	0.982516	−	0.186180i	$-0.0596109\pi$
$368$	12.0000			0.625543
$369$		−	20.7846i		−	1.08200i
$370$		0			0
$371$	−27.0000	−	15.5885i	−1.40177	−	0.809312i
$372$	−12.0000			−0.622171
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	0.972556	−	0.232671i	$-0.0747464\pi$
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	−0.687776	+	0.725923i	$0.741413\pi$
$374$		0			0
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$		0			0
$377$	−6.00000	+	20.7846i	−0.309016	+	1.07046i
$378$		0			0
$379$		−	24.2487i		−	1.24557i	−0.782392	−	0.622786i	$-0.786001\pi$
$379$		−	24.2487i		−	1.24557i	0.782392	−	0.622786i	$-0.213999\pi$
$380$	12.0000	−	20.7846i	0.615587	−	1.06623i
$381$	−24.0000	+	13.8564i	−1.22956	+	0.709885i
$382$		0			0
$383$	24.0000	−	13.8564i	1.22634	−	0.708029i	0.260080	−	0.965587i	$-0.416251\pi$
$383$	24.0000	−	13.8564i	1.22634	−	0.708029i	0.966263	+	0.257558i	$0.0829178\pi$
$384$		0			0
$385$	−36.0000	−	20.7846i	−1.83473	−	1.05928i
$386$		0			0
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$			13.8564i			0.703452i
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$		0			0
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$		0			0
$393$	22.5000	+	12.9904i	1.13497	+	0.655278i
$394$		0			0
$395$			3.46410i			0.174298i
$396$	18.0000	+	10.3923i	0.904534	+	0.522233i
$397$			27.7128i			1.39087i	0.718591	+	0.695433i	$0.244787\pi$
$397$			27.7128i			1.39087i	−0.718591	+	0.695433i	$0.755213\pi$
$398$		0			0
$399$		−	20.7846i		−	1.04053i
$400$	14.0000	+	24.2487i	0.700000	+	1.21244i
$401$	−27.0000	+	15.5885i	−1.34832	+	0.778450i	−0.988011	−	0.154384i	$-0.950661\pi$
$401$	−27.0000	+	15.5885i	−1.34832	+	0.778450i	−0.360305	+	0.932835i	$0.617327\pi$
$402$		0			0
$403$	−9.00000	+	8.66025i	−0.448322	+	0.431398i
$404$	6.00000			0.298511
$405$	−27.0000	−	15.5885i	−1.34164	−	0.774597i
$406$		0			0
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$		0			0
$409$	−3.00000	+	1.73205i	−0.148340	+	0.0856444i	−0.572333	−	0.820021i	$-0.693962\pi$
$409$	−3.00000	+	1.73205i	−0.148340	+	0.0856444i	0.423993	+	0.905666i	$0.360628\pi$
$410$		0			0
$411$	−36.0000			−1.77575
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	−12.0000			−0.590481
$414$		0			0
$415$	−24.0000			−1.17811
$416$		0			0
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$		0			0
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	0.954759	−	0.297382i	$-0.0961133\pi$
$419$	4.50000	+	7.79423i	0.219839	+	0.380773i	−0.734919	+	0.678155i	$0.762780\pi$
$420$	36.0000	+	20.7846i	1.75662	+	1.01419i
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	0.763056	−	0.646332i	$-0.223698\pi$
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	−0.178212	+	0.983992i	$0.557031\pi$
$422$		0			0
$423$	18.0000	−	10.3923i	0.875190	−	0.505291i
$424$		0			0
$425$	−10.5000	+	18.1865i	−0.509325	+	0.882176i
$426$		0			0
$427$	−21.0000	+	12.1244i	−1.01626	+	0.586739i
$428$	−3.00000	−	5.19615i	−0.145010	−	0.251166i
$429$	21.0000	−	5.19615i	1.01389	−	0.250873i
$430$		0			0
$431$			20.7846i			1.00116i	0.865690	+	0.500580i	$0.166880\pi$
$431$			20.7846i			1.00116i	−0.865690	+	0.500580i	$0.833120\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	7.00000			0.336399			0.168199	−	0.985753i	$-0.446205\pi$
$433$	7.00000			0.336399			0.168199	+	0.985753i	$0.446205\pi$
$434$		0			0
$435$	−18.0000	−	31.1769i	−0.863034	−	1.49482i
$436$	−6.00000	+	3.46410i	−0.287348	+	0.165900i
$437$	9.00000	−	5.19615i	0.430528	−	0.248566i
$438$		0			0
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	−0.770334	−	0.637641i	$-0.779911\pi$
$439$	3.50000	−	6.06218i	0.167046	−	0.289332i	0.937380	+	0.348309i	$0.113244\pi$
$440$		0			0
$441$	15.0000			0.714286
$442$		0			0
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	−0.987346	−	0.158583i	$-0.949307\pi$
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	0.631010	+	0.775775i	$0.282641\pi$
$444$	−12.0000	+	20.7846i	−0.569495	+	0.986394i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$		0			0
$447$	6.00000	−	10.3923i	0.283790	−	0.491539i
$448$	24.0000	+	13.8564i	1.13389	+	0.654654i
$449$		−	24.2487i		−	1.14437i	−0.820125	−	0.572184i	$-0.806096\pi$
$449$		−	24.2487i		−	1.14437i	0.820125	−	0.572184i	$-0.193904\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	15.0000	−	25.9808i	0.705541	−	1.22203i
$453$	−36.0000			−1.69143
$454$		0			0
$455$	42.0000	−	10.3923i	1.96899	−	0.487199i
$456$		0			0
$457$	−21.0000	−	12.1244i	−0.982339	−	0.567153i	−0.0793632	−	0.996846i	$-0.525289\pi$
$457$	−21.0000	−	12.1244i	−0.982339	−	0.567153i	−0.902975	+	0.429692i	$0.858622\pi$
$458$		0			0
$459$		−	15.5885i		−	0.727607i
$460$			20.7846i			0.969087i
$461$	−27.0000	−	15.5885i	−1.25752	−	0.726027i	−0.284925	−	0.958550i	$-0.591969\pi$
$461$	−27.0000	−	15.5885i	−1.25752	−	0.726027i	−0.972591	+	0.232523i	$0.925302\pi$
$462$		0			0
$463$	12.0000	−	6.92820i	0.557687	−	0.321981i	−0.194529	−	0.980897i	$-0.562318\pi$
$463$	12.0000	−	6.92820i	0.557687	−	0.321981i	0.752217	+	0.658916i	$0.228985\pi$
$464$	−12.0000	−	20.7846i	−0.557086	−	0.964901i
$465$		−	20.7846i		−	0.963863i
$466$		0			0
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$	−21.0000	+	5.19615i	−0.970725	+	0.240192i
$469$		0			0
$470$		0			0
$471$	−10.5000	−	6.06218i	−0.483814	−	0.279330i
$472$		0			0
$473$	−3.00000	+	1.73205i	−0.137940	+	0.0796398i
$474$		0			0
$475$	21.0000	+	12.1244i	0.963546	+	0.556304i
$476$			20.7846i			0.952661i
$477$	−13.5000	+	23.3827i	−0.618123	+	1.07062i
$478$		0			0
$479$	−33.0000	−	19.0526i	−1.50781	−	0.870534i	−0.999959	−	0.00908799i	$-0.997107\pi$
$479$	−33.0000	−	19.0526i	−1.50781	−	0.870534i	−0.507850	−	0.861446i	$-0.669560\pi$
$480$		0			0
$481$	6.00000	+	24.2487i	0.273576	+	1.10565i
$482$		0			0
$483$	9.00000	+	15.5885i	0.409514	+	0.709299i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−24.0000			−1.08978
$486$		0			0
$487$		−	3.46410i		−	0.156973i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$		−	3.46410i		−	0.156973i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$		0			0
$489$	15.0000	+	25.9808i	0.678323	+	1.17489i
$490$		0			0
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$	24.0000			1.08200
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$		0			0
$495$	−18.0000	+	31.1769i	−0.809040	+	1.40130i
$496$		−	13.8564i		−	0.622171i
$497$		0			0
$498$		0			0
$499$	36.0000	−	20.7846i	1.61158	−	0.930447i	0.622577	−	0.782558i	$-0.286086\pi$
$499$	36.0000	−	20.7846i	1.61158	−	0.930447i	0.989004	−	0.147889i	$-0.0472477\pi$
$500$	−12.0000	+	6.92820i	−0.536656	+	0.309839i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$			10.3923i			0.462451i
$506$		0			0
$507$	−12.0000	+	19.0526i	−0.532939	+	0.846154i
$508$	−16.0000	−	27.7128i	−0.709885	−	1.22956i
$509$	24.0000	−	13.8564i	1.06378	−	0.614174i	0.137305	−	0.990529i	$-0.456156\pi$
$509$	24.0000	−	13.8564i	1.06378	−	0.614174i	0.926476	+	0.376354i	$0.122822\pi$
$510$		0			0
$511$	18.0000	−	31.1769i	0.796273	−	1.37919i
$512$		0			0
$513$	−18.0000			−0.794719
$514$		0			0
$515$	−24.0000	−	13.8564i	−1.05757	−	0.610586i
$516$	3.00000	−	1.73205i	0.132068	−	0.0762493i
$517$	−12.0000	−	20.7846i	−0.527759	−	0.914106i
$518$		0			0
$519$			36.3731i			1.59660i
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−15.0000	+	25.9808i	−0.655278	+	1.13497i
$525$	−21.0000	+	36.3731i	−0.916515	+	1.58745i
$526$		0			0
$527$	9.00000	−	5.19615i	0.392046	−	0.226348i
$528$	−12.0000	+	20.7846i	−0.522233	+	0.904534i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	24.0000			1.04053
$533$	18.0000	−	17.3205i	0.779667	−	0.750234i
$534$		0			0
$535$	9.00000	−	5.19615i	0.389104	−	0.224649i
$536$		0			0
$537$	13.5000	−	7.79423i	0.582568	−	0.336346i
$538$		0			0
$539$		−	17.3205i		−	0.746047i
$540$	18.0000	−	31.1769i	0.774597	−	1.34164i
$541$			6.92820i			0.297867i	0.988847	+	0.148933i	$0.0475840\pi$
$541$			6.92820i			0.297867i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$	10.5000	−	6.06218i	0.450598	−	0.260153i
$544$		0			0
$545$	−6.00000	−	10.3923i	−0.257012	−	0.445157i
$546$		0			0
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	−0.996657	−	0.0817056i	$-0.973963\pi$
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	0.569087	+	0.822277i	$0.307297\pi$
$548$		−	41.5692i		−	1.77575i
$549$	10.5000	+	18.1865i	0.448129	+	0.776182i
$550$		0			0
$551$	−18.0000	−	10.3923i	−0.766826	−	0.442727i
$552$		0			0
$553$	−3.00000	+	1.73205i	−0.127573	+	0.0736543i
$554$		0			0
$555$	−36.0000	−	20.7846i	−1.52811	−	0.882258i
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$		−	3.46410i		−	0.146779i	−0.997303	−	0.0733893i	$-0.976618\pi$
$557$		−	3.46410i		−	0.146779i	0.997303	−	0.0733893i	$-0.0233816\pi$
$558$		0			0
$559$	1.00000	−	3.46410i	0.0422955	−	0.146516i
$560$	−24.0000	+	41.5692i	−1.01419	+	1.75662i
$561$	−18.0000			−0.759961
$562$		0			0
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$	12.0000	+	20.7846i	0.505291	+	0.875190i
$565$	45.0000	+	25.9808i	1.89316	+	1.09302i
$566$		0			0
$567$		−	31.1769i		−	1.30931i
$568$		0			0
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	6.00000	+	24.2487i	0.250873	+	1.01389i
$573$		−	25.9808i		−	1.08536i
$574$		0			0
$575$	−21.0000			−0.875761
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$		−	10.3923i		−	0.432637i	−0.976323	−	0.216319i	$-0.930595\pi$
$577$		−	10.3923i		−	0.432637i	0.976323	−	0.216319i	$-0.0694050\pi$
$578$		0			0
$579$		0			0
$580$	36.0000	−	20.7846i	1.49482	−	0.863034i
$581$	−12.0000	−	20.7846i	−0.497844	−	0.862291i
$582$		0			0
$583$	27.0000	+	15.5885i	1.11823	+	0.645608i
$584$		0			0
$585$	−9.00000	−	36.3731i	−0.372104	−	1.50384i
$586$		0			0
$587$	36.0000	+	20.7846i	1.48588	+	0.857873i	0.999871	−	0.0160815i	$-0.00511913\pi$
$587$	36.0000	+	20.7846i	1.48588	+	0.857873i	0.486008	+	0.873954i	$0.338452\pi$
$588$			17.3205i			0.714286i
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$		0			0
$591$	21.0000	+	36.3731i	0.863825	+	1.49619i
$592$	−24.0000	−	13.8564i	−0.986394	−	0.569495i
$593$			3.46410i			0.142254i	0.997467	+	0.0711268i	$0.0226595\pi$
$593$			3.46410i			0.142254i	−0.997467	+	0.0711268i	$0.977341\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$	12.0000	+	6.92820i	0.491539	+	0.283790i
$597$	25.5000	−	14.7224i	1.04365	−	0.602549i
$598$		0			0
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	−0.921723	−	0.387849i	$-0.873218\pi$
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$600$		0			0
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$		0			0
$603$		0			0
$604$		−	41.5692i		−	1.69143i
$605$	3.00000	+	1.73205i	0.121967	+	0.0704179i
$606$		0			0
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$		0			0
$609$	18.0000	−	31.1769i	0.729397	−	1.26335i
$610$		0			0
$611$	24.0000	+	6.92820i	0.970936	+	0.280285i
$612$	18.0000			0.727607
$613$			20.7846i			0.839482i	0.907644	+	0.419741i	$0.137879\pi$
$613$			20.7846i			0.839482i	−0.907644	+	0.419741i	$0.862121\pi$
$614$		0			0
$615$			41.5692i			1.67623i
$616$		0			0
$617$	−9.00000	+	5.19615i	−0.362326	+	0.209189i	−0.670101	−	0.742270i	$-0.733749\pi$
$617$	−9.00000	+	5.19615i	−0.362326	+	0.209189i	0.307774	+	0.951459i	$0.400416\pi$
$618$		0			0
$619$	9.00000	+	5.19615i	0.361741	+	0.208851i	0.669844	−	0.742502i	$-0.266361\pi$
$619$	9.00000	+	5.19615i	0.361741	+	0.208851i	−0.308103	+	0.951353i	$0.599694\pi$
$620$	24.0000			0.963863
$621$	13.5000	−	7.79423i	0.541736	−	0.312772i
$622$		0			0
$623$	−6.00000	+	10.3923i	−0.240385	+	0.416359i
$624$	−6.00000	−	24.2487i	−0.240192	−	0.970725i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$			20.7846i			0.830057i
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$		−	20.7846i		−	0.828737i
$630$		0			0
$631$			48.4974i			1.93065i	0.261048	+	0.965326i	$0.415932\pi$
$631$			48.4974i			1.93065i	−0.261048	+	0.965326i	$0.584068\pi$
$632$		0			0
$633$	19.5000	+	11.2583i	0.775055	+	0.447478i
$634$		0			0
$635$	48.0000	−	27.7128i	1.90482	−	1.09975i
$636$	−27.0000	−	15.5885i	−1.07062	−	0.618123i
$637$	12.5000	+	12.9904i	0.495268	+	0.514698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	−36.0000	+	20.7846i	−1.41970	+	0.819665i	−0.996272	−	0.0862642i	$-0.972507\pi$
$643$	−36.0000	+	20.7846i	−1.41970	+	0.819665i	−0.423429	+	0.905929i	$0.639174\pi$
$644$	−18.0000	+	10.3923i	−0.709299	+	0.409514i
$645$	3.00000	+	5.19615i	0.118125	+	0.204598i
$646$		0			0
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$		0			0
$651$	18.0000	−	10.3923i	0.705476	−	0.407307i
$652$	−30.0000	+	17.3205i	−1.17489	+	0.678323i
$653$	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	$0.718768\pi$
$654$		0			0
$655$	−45.0000	−	25.9808i	−1.75830	−	1.01515i
$656$			27.7128i			1.08200i
$657$	−27.0000	−	15.5885i	−1.05337	−	0.608164i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	−36.0000	−	20.7846i	−1.40130	−	0.809040i
$661$	18.0000	−	10.3923i	0.700119	−	0.404214i	−0.107273	−	0.994230i	$-0.534212\pi$
$661$	18.0000	−	10.3923i	0.700119	−	0.404214i	0.807392	+	0.590016i	$0.200879\pi$
$662$		0			0
$663$	13.5000	−	12.9904i	0.524297	−	0.504505i
$664$		0			0
$665$			41.5692i			1.61199i
$666$		0			0
$667$	18.0000			0.696963
$668$	−12.0000	−	6.92820i	−0.464294	−	0.268060i
$669$	12.0000			0.463947
$670$		0			0
$671$	21.0000	−	12.1244i	0.810696	−	0.468056i
$672$		0			0
$673$	−20.5000	+	35.5070i	−0.790217	+	1.36870i	0.135615	+	0.990762i	$0.456699\pi$
$673$	−20.5000	+	35.5070i	−0.790217	+	1.36870i	−0.925832	+	0.377934i	$0.876635\pi$
$674$		0			0
$675$	31.5000	+	18.1865i	1.21244	+	0.700000i
$676$	−22.0000	−	13.8564i	−0.846154	−	0.532939i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$	−18.0000			−0.689761
$682$		0			0
$683$			45.0333i			1.72315i	0.507628	+	0.861576i	$0.330522\pi$
$683$			45.0333i			1.72315i	−0.507628	+	0.861576i	$0.669478\pi$
$684$		−	20.7846i		−	0.794719i
$685$	72.0000			2.75098
$686$		0			0
$687$	−3.00000	+	5.19615i	−0.114457	+	0.198246i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−31.5000	+	7.79423i	−1.20005	+	0.296936i
$690$		0			0
$691$	6.00000	+	3.46410i	0.228251	+	0.131781i	0.609765	−	0.792582i	$-0.291264\pi$
$691$	6.00000	+	3.46410i	0.228251	+	0.131781i	−0.381514	+	0.924363i	$0.624597\pi$
$692$	−42.0000			−1.59660
$693$	−36.0000			−1.36753
$694$		0			0
$695$	−15.0000	−	8.66025i	−0.568982	−	0.328502i
$696$		0			0
$697$	−18.0000	+	10.3923i	−0.681799	+	0.393637i
$698$		0			0
$699$	−4.50000	+	2.59808i	−0.170206	+	0.0982683i
$700$	−42.0000	−	24.2487i	−1.58745	−	0.916515i
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	−24.0000			−0.905177
$704$	−24.0000	−	13.8564i	−0.904534	−	0.522233i
$705$	−36.0000	+	20.7846i	−1.35584	+	0.782794i
$706$		0			0
$707$	−9.00000	+	5.19615i	−0.338480	+	0.195421i
$708$	−12.0000			−0.450988
$709$	−21.0000	−	12.1244i	−0.788672	−	0.455340i	0.0508231	−	0.998708i	$-0.483816\pi$
$709$	−21.0000	−	12.1244i	−0.788672	−	0.455340i	−0.839495	+	0.543368i	$0.817149\pi$
$710$		0			0
$711$	1.50000	+	2.59808i	0.0562544	+	0.0974355i
$712$		0			0
$713$	9.00000	+	5.19615i	0.337053	+	0.194597i
$714$		0			0
$715$	−42.0000	+	10.3923i	−1.57071	+	0.388650i
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$	9.00000	−	15.5885i	0.336111	−	0.582162i
$718$		0			0
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$	36.0000	+	20.7846i	1.34164	+	0.774597i
$721$		−	27.7128i		−	1.03208i
$722$		0			0
$723$	24.0000			0.892570
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$	21.0000	+	36.3731i	0.779920	+	1.35086i
$726$		0			0
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.0111912	−	0.999937i	$-0.496438\pi$
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.860376	−	0.509661i	$-0.170229\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	−21.0000	+	12.1244i	−0.776182	+	0.448129i
$733$	3.00000	−	1.73205i	0.110808	−	0.0639748i	−0.443572	−	0.896239i	$-0.646289\pi$
$733$	3.00000	−	1.73205i	0.110808	−	0.0639748i	0.554380	+	0.832264i	$0.312956\pi$
$734$		0			0
$735$	−30.0000			−1.10657
$736$		0			0
$737$		0			0
$738$		0			0
$739$		−	27.7128i		−	1.01943i	−0.860343	−	0.509716i	$-0.829750\pi$
$739$		−	27.7128i		−	1.01943i	0.860343	−	0.509716i	$-0.170250\pi$
$740$	24.0000	−	41.5692i	0.882258	−	1.52811i
$741$	−15.0000	−	15.5885i	−0.551039	−	0.572656i
$742$		0			0
$743$	−9.00000	+	5.19615i	−0.330178	+	0.190628i	−0.655920	−	0.754830i	$-0.727719\pi$
$743$	−9.00000	+	5.19615i	−0.330178	+	0.190628i	0.325742	+	0.945459i	$0.394386\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$		0			0
$747$	−18.0000	+	10.3923i	−0.658586	+	0.380235i
$748$		−	20.7846i		−	0.759961i
$749$	9.00000	+	5.19615i	0.328853	+	0.189863i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−24.0000	+	13.8564i	−0.875190	+	0.505291i
$753$	31.5000	−	18.1865i	1.14792	−	0.662754i
$754$		0			0
$755$	72.0000			2.62035
$756$	36.0000			1.30931
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$		0			0
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$		0			0
$761$	45.0000	−	25.9808i	1.63125	−	0.941802i	0.647540	−	0.762031i	$-0.275798\pi$
$761$	45.0000	−	25.9808i	1.63125	−	0.941802i	0.983709	−	0.179771i	$-0.0575355\pi$
$762$		0			0
$763$	6.00000	−	10.3923i	0.217215	−	0.376227i
$764$	30.0000			1.08536
$765$			31.1769i			1.12720i
$766$		0			0
$767$	−9.00000	+	8.66025i	−0.324971	+	0.312704i
$768$	24.0000	+	13.8564i	0.866025	+	0.500000i
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	−0.387901	−	0.921701i	$-0.626800\pi$
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	0.604266	+	0.796782i	$0.293466\pi$
$770$		0			0
$771$	22.5000	+	12.9904i	0.810318	+	0.467837i
$772$		0			0
$773$		−	10.3923i		−	0.373785i	−0.982380	−	0.186893i	$-0.940158\pi$
$773$		−	10.3923i		−	0.373785i	0.982380	−	0.186893i	$-0.0598416\pi$
$774$		0			0
$775$			24.2487i			0.871039i
$776$		0			0
$777$		−	41.5692i		−	1.49129i
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$	42.0000	−	10.3923i	1.50384	−	0.372104i
$781$		0			0
$782$		0			0
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$	−20.0000			−0.714286
$785$	21.0000	+	12.1244i	0.749522	+	0.432737i
$786$		0			0
$787$	18.0000	−	10.3923i	0.641631	−	0.370446i	−0.143612	−	0.989634i	$-0.545872\pi$
$787$	18.0000	−	10.3923i	0.641631	−	0.370446i	0.785242	+	0.619188i	$0.212538\pi$
$788$	−42.0000	+	24.2487i	−1.49619	+	0.863825i
$789$			15.5885i			0.554964i
$790$		0			0
$791$			51.9615i			1.84754i
$792$		0			0
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$		0			0
$795$	27.0000	−	46.7654i	0.957591	−	1.65860i
$796$	17.0000	+	29.4449i	0.602549	+	1.04365i
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	0.999331	+	0.0365596i	$0.0116399\pi$
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	−0.468004	+	0.883726i	$0.655027\pi$
$798$		0			0
$799$	−18.0000	−	10.3923i	−0.636794	−	0.367653i
$800$		0			0
$801$	9.00000	+	5.19615i	0.317999	+	0.183597i
$802$		0			0
$803$	−18.0000	+	31.1769i	−0.635206	+	1.10021i
$804$		0			0
$805$	−18.0000	−	31.1769i	−0.634417	−	1.09884i
$806$		0			0
$807$	−27.0000	+	15.5885i	−0.950445	+	0.548740i
$808$		0			0
$809$	−51.0000			−1.79306			−0.896532	−	0.442978i	$-0.853922\pi$
$809$	−51.0000			−1.79306			−0.896532	+	0.442978i	$0.853922\pi$
$810$		0			0
$811$			34.6410i			1.21641i	0.793780	+	0.608205i	$0.208110\pi$
$811$			34.6410i			1.21641i	−0.793780	+	0.608205i	$0.791890\pi$
$812$	36.0000	+	20.7846i	1.26335	+	0.729397i
$813$	18.0000	+	31.1769i	0.631288	+	1.09342i
$814$		0			0
$815$	−30.0000	−	51.9615i	−1.05085	−	1.82013i
$816$			20.7846i			0.727607i
$817$	3.00000	+	1.73205i	0.104957	+	0.0605968i
$818$		0			0
$819$	27.0000	−	25.9808i	0.943456	−	0.907841i
$820$	−48.0000			−1.67623
$821$	−42.0000	−	24.2487i	−1.46581	−	0.846286i	−0.466541	−	0.884500i	$-0.654500\pi$
$821$	−42.0000	−	24.2487i	−1.46581	−	0.846286i	−0.999270	+	0.0382140i	$0.987833\pi$
$822$		0			0
$823$	15.5000	+	26.8468i	0.540296	+	0.935820i	0.998887	+	0.0471726i	$0.0150211\pi$
$823$	15.5000	+	26.8468i	0.540296	+	0.935820i	−0.458591	+	0.888648i	$0.651646\pi$
$824$		0			0
$825$	21.0000	−	36.3731i	0.731126	−	1.26635i
$826$		0			0
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$		0			0
$831$		−	45.0333i		−	1.56219i
$832$	28.0000	−	6.92820i	0.970725	−	0.240192i
$833$	−7.50000	−	12.9904i	−0.259860	−	0.450090i
$834$		0			0
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$	−24.0000			−0.830057
$837$	−9.00000	−	15.5885i	−0.311086	−	0.538816i
$838$		0			0
$839$	36.0000	+	20.7846i	1.24286	+	0.717564i	0.969675	−	0.244398i	$-0.0785902\pi$
$839$	36.0000	+	20.7846i	1.24286	+	0.717564i	0.273183	+	0.961962i	$0.411924\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	−24.0000			−0.826604
$844$	−13.0000	+	22.5167i	−0.447478	+	0.775055i
$845$	24.0000	−	38.1051i	0.825625	−	1.31086i
$846$		0			0
$847$			3.46410i			0.119028i
$848$	18.0000	−	31.1769i	0.618123	−	1.07062i
$849$	10.5000	+	6.06218i	0.360359	+	0.208053i
$850$		0			0
$851$	18.0000	−	10.3923i	0.617032	−	0.356244i
$852$		0			0
$853$	−27.0000	−	15.5885i	−0.924462	−	0.533739i	−0.0394064	−	0.999223i	$-0.512547\pi$
$853$	−27.0000	−	15.5885i	−0.924462	−	0.533739i	−0.885056	+	0.465485i	$0.845880\pi$
$854$		0			0
$855$	36.0000			1.23117
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	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	$0.586761\pi$
$860$	−6.00000	+	3.46410i	−0.204598	+	0.118125i
$861$	−36.0000	+	20.7846i	−1.22688	+	0.708338i
$862$		0			0
$863$			55.4256i			1.88671i	0.331785	+	0.943355i	$0.392349\pi$
$863$			55.4256i			1.88671i	−0.331785	+	0.943355i	$0.607651\pi$
$864$		0			0
$865$		−	72.7461i		−	2.47344i
$866$		0			0
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$	12.0000	+	20.7846i	0.407307	+	0.705476i
$869$	3.00000	−	1.73205i	0.101768	−	0.0587558i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−18.0000	+	10.3923i	−0.609208	+	0.351726i
$874$		0			0
$875$	12.0000	−	20.7846i	0.405674	−	0.702648i
$876$	18.0000	−	31.1769i	0.608164	−	1.05337i
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	−0.224886	−	0.974385i	$-0.572201\pi$
$877$	15.0000	−	8.66025i	0.506514	−	0.292436i	0.731400	+	0.681949i	$0.238867\pi$
$878$		0			0
$879$	15.0000	−	25.9808i	0.505937	−	0.876309i
$880$	24.0000	−	41.5692i	0.809040	−	1.40130i
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$	15.0000	+	15.5885i	0.504505	+	0.524297i
$885$		−	20.7846i		−	0.698667i
$886$		0			0
$887$	−28.5000	−	49.3634i	−0.956936	−	1.65746i	−0.729873	−	0.683582i	$-0.760421\pi$
$887$	−28.5000	−	49.3634i	−0.956936	−	1.65746i	−0.227063	−	0.973880i	$-0.572912\pi$
$888$		0			0
$889$	48.0000	+	27.7128i	1.60987	+	0.929458i
$890$		0			0
$891$			31.1769i			1.04447i
$892$			13.8564i			0.463947i
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$	−27.0000	+	15.5885i	−0.902510	+	0.521065i
$896$		0			0
$897$	18.0000	+	5.19615i	0.601003	+	0.173494i
$898$		0			0
$899$		−	20.7846i		−	0.693206i
$900$	−21.0000	+	36.3731i	−0.700000	+	1.21244i
$901$	27.0000			0.899500
$902$		0			0
$903$	−3.00000	+	5.19615i	−0.0998337	+	0.172917i
$904$		0			0
$905$	−21.0000	+	12.1244i	−0.698064	+	0.403027i
$906$		0			0
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	−0.979531	−	0.201291i	$-0.935486\pi$
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	0.664089	+	0.747653i	$0.268820\pi$
$908$		−	20.7846i		−	0.689761i
$909$	4.50000	+	7.79423i	0.149256	+	0.258518i
$910$		0			0
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	−0.998208	−	0.0598468i	$-0.980939\pi$
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	0.550933	+	0.834550i	$0.314272\pi$
$912$	24.0000			0.794719
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$		0			0
$915$	−21.0000	−	36.3731i	−0.694239	−	1.20246i
$916$	−6.00000	−	3.46410i	−0.198246	−	0.114457i
$917$		−	51.9615i		−	1.71592i
$918$		0			0
$919$	31.0000			1.02260			0.511298	−	0.859404i	$-0.329165\pi$
$919$	31.0000			1.02260			0.511298	+	0.859404i	$0.329165\pi$
$920$		0			0
$921$	−9.00000	−	15.5885i	−0.296560	−	0.513657i
$922$		0			0
$923$		0			0
$924$		−	41.5692i		−	1.36753i
$925$	42.0000	+	24.2487i	1.38095	+	0.797293i
$926$		0			0
$927$	−24.0000			−0.788263
$928$		0			0
$929$	27.0000	+	15.5885i	0.885841	+	0.511441i	0.872580	−	0.488471i	$-0.162445\pi$
$929$	27.0000	+	15.5885i	0.885841	+	0.511441i	0.0132613	+	0.999912i	$0.495779\pi$
$930$		0			0
$931$	−15.0000	+	8.66025i	−0.491605	+	0.283828i
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$		0			0
$934$		0			0
$935$	36.0000			1.17733
$936$		0			0
$937$	7.00000			0.228680			0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000			0.228680			0.114340	+	0.993442i	$0.463525\pi$
$938$		0			0
$939$			24.2487i			0.791327i
$940$	−24.0000	−	41.5692i	−0.782794	−	1.35584i
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	−0.177041	−	0.984203i	$-0.556653\pi$
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	0.763825	+	0.645424i	$0.223319\pi$
$942$		0			0
$943$	−18.0000	−	10.3923i	−0.586161	−	0.338420i
$944$		−	13.8564i		−	0.450988i
$945$			62.3538i			2.02837i
$946$		0			0
$947$	21.0000	+	12.1244i	0.682408	+	0.393989i	0.800762	−	0.598983i	$-0.204428\pi$
$947$	21.0000	+	12.1244i	0.682408	+	0.393989i	−0.118354	+	0.992972i	$0.537762\pi$
$948$	−3.00000	+	1.73205i	−0.0974355	+	0.0562544i
$949$	−9.00000	−	36.3731i	−0.292152	−	1.18072i
$950$		0			0
$951$	−42.0000			−1.36194
$952$		0			0
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$		0			0
$955$			51.9615i			1.68144i
$956$	18.0000	+	10.3923i	0.582162	+	0.336111i
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$		0			0
$959$	36.0000	+	62.3538i	1.16250	+	2.01351i
$960$	−24.0000	+	41.5692i	−0.774597	+	1.34164i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$		0			0
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$			27.7128i			0.892570i
$965$		0			0
$966$		0			0
$967$	−9.00000	+	5.19615i	−0.289420	+	0.167097i	−0.637680	−	0.770301i	$-0.720106\pi$
$967$	−9.00000	+	5.19615i	−0.289420	+	0.167097i	0.348260	+	0.937398i	$0.386773\pi$
$968$		0			0
$969$	9.00000	+	15.5885i	0.289122	+	0.500773i
$970$		0			0
$971$	−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
$973$		−	17.3205i		−	0.555270i
$974$		0			0
$975$	10.5000	+	42.4352i	0.336269	+	1.35902i
$976$	−14.0000	−	24.2487i	−0.448129	−	0.776182i
$977$	−21.0000	+	12.1244i	−0.671850	+	0.387893i	−0.796777	−	0.604273i	$-0.793463\pi$
$977$	−21.0000	+	12.1244i	−0.671850	+	0.387893i	0.124928	+	0.992166i	$0.460130\pi$
$978$		0			0
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		−	34.6410i		−	1.10657i
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$		0			0
$983$	9.00000	+	5.19615i	0.287055	+	0.165732i	0.636613	−	0.771183i	$-0.280335\pi$
$983$	9.00000	+	5.19615i	0.287055	+	0.165732i	−0.349558	+	0.936915i	$0.613668\pi$
$984$		0			0
$985$	−42.0000	−	72.7461i	−1.33823	−	2.31788i
$986$		0			0
$987$	−36.0000	−	20.7846i	−1.14589	−	0.661581i
$988$	18.0000	−	17.3205i	0.572656	−	0.551039i
$989$	−3.00000			−0.0953945
$990$		0			0
$991$	5.00000			0.158830			0.0794151	−	0.996842i	$-0.474695\pi$
$991$	5.00000			0.158830			0.0794151	+	0.996842i	$0.474695\pi$
$992$		0			0
$993$	42.0000			1.33283
$994$		0			0
$995$	−51.0000	+	29.4449i	−1.61681	+	0.933465i
$996$	−12.0000	−	20.7846i	−0.380235	−	0.658586i
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$		0			0
$999$	−36.0000			−1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.b.25.1	yes	2
3.2	odd	2		351.2.t.a.181.1		2
9.2	odd	6		1053.2.b.f.649.1		2
9.4	even	3		117.2.t.a.103.1	yes	2
9.5	odd	6		351.2.t.b.64.1		2
9.7	even	3		1053.2.b.e.649.2		2
13.12	even	2		117.2.t.a.25.1	✓	2
39.38	odd	2		351.2.t.b.181.1		2
117.25	even	6		1053.2.b.e.649.1		2
117.38	odd	6		1053.2.b.f.649.2		2
117.77	odd	6		351.2.t.a.64.1		2
117.103	even	6	inner	117.2.t.b.103.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.a.25.1	✓	2	13.12	even	2
117.2.t.a.103.1	yes	2	9.4	even	3
117.2.t.b.25.1	yes	2	1.1	even	1	trivial
117.2.t.b.103.1	yes	2	117.103	even	6	inner
351.2.t.a.64.1		2	117.77	odd	6
351.2.t.a.181.1		2	3.2	odd	2
351.2.t.b.64.1		2	9.5	odd	6
351.2.t.b.181.1		2	39.38	odd	2
1053.2.b.e.649.1		2	117.25	even	6
1053.2.b.e.649.2		2	9.7	even	3
1053.2.b.f.649.1		2	9.2	odd	6
1053.2.b.f.649.2		2	117.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(3.00000 - 1.73205i) q^{5} +(3.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(3.00000 - 1.73205i) q^{5} +(3.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +3.46410i q^{19} +(-6.00000 - 3.46410i) q^{20} -6.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{27} -6.92820i q^{28} +(-3.00000 + 5.19615i) q^{29} +(-3.00000 + 1.73205i) q^{31} +6.00000 q^{33} +12.0000 q^{35} -6.00000 q^{36} +6.92820i q^{37} +(-4.50000 + 4.33013i) q^{39} +(6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{43} +6.92820i q^{44} -10.3923i q^{45} +(6.00000 + 3.46410i) q^{47} -6.92820i q^{48} +(2.50000 + 4.33013i) q^{49} +(4.50000 - 2.59808i) q^{51} +(-5.00000 - 5.19615i) q^{52} -9.00000 q^{53} -12.0000 q^{55} +(-3.00000 - 5.19615i) q^{57} +(-3.00000 + 1.73205i) q^{59} +12.0000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(9.00000 - 5.19615i) q^{63} +8.00000 q^{64} +(9.00000 - 8.66025i) q^{65} +(3.00000 + 5.19615i) q^{68} +(4.50000 + 2.59808i) q^{69} -10.3923i q^{73} +12.1244i q^{75} +(6.00000 - 3.46410i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(-0.500000 + 0.866025i) q^{79} +13.8564i q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 3.46410i) q^{83} +(6.00000 + 10.3923i) q^{84} +(-9.00000 + 5.19615i) q^{85} -10.3923i q^{87} +3.46410i q^{89} +(12.0000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(3.00000 - 5.19615i) q^{93} +(6.00000 + 10.3923i) q^{95} +(-6.00000 - 3.46410i) q^{97} +(-9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 2 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 2 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} - 2 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{9} - 6 q^{11} + 6 q^{12} + 7 q^{13} - 6 q^{15} - 4 q^{16} - 6 q^{17} - 12 q^{20} - 12 q^{21} - 3 q^{23} + 7 q^{25} - 6 q^{29} - 6 q^{31} + 12 q^{33} + 24 q^{35} - 12 q^{36} - 9 q^{39} + 12 q^{41} + q^{43} + 12 q^{47} + 5 q^{49} + 9 q^{51} - 10 q^{52} - 18 q^{53} - 24 q^{55} - 6 q^{57} - 6 q^{59} + 24 q^{60} - 7 q^{61} + 18 q^{63} + 16 q^{64} + 18 q^{65} + 6 q^{68} + 9 q^{69} + 12 q^{76} - 12 q^{77} - q^{79} - 9 q^{81} - 12 q^{83} + 12 q^{84} - 18 q^{85} + 24 q^{91} - 6 q^{92} + 6 q^{93} + 12 q^{95} - 12 q^{97} - 18 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 2 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^9 - 6 * q^11 + 6 * q^12 + 7 * q^13 - 6 * q^15 - 4 * q^16 - 6 * q^17 - 12 * q^20 - 12 * q^21 - 3 * q^23 + 7 * q^25 - 6 * q^29 - 6 * q^31 + 12 * q^33 + 24 * q^35 - 12 * q^36 - 9 * q^39 + 12 * q^41 + q^43 + 12 * q^47 + 5 * q^49 + 9 * q^51 - 10 * q^52 - 18 * q^53 - 24 * q^55 - 6 * q^57 - 6 * q^59 + 24 * q^60 - 7 * q^61 + 18 * q^63 + 16 * q^64 + 18 * q^65 + 6 * q^68 + 9 * q^69 + 12 * q^76 - 12 * q^77 - q^79 - 9 * q^81 - 12 * q^83 + 12 * q^84 - 18 * q^85 + 24 * q^91 - 6 * q^92 + 6 * q^93 + 12 * q^95 - 12 * q^97 - 18 * q^99

Introduction

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