LMFDB - Embedded newform 585.2.i.a.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.67124851824$
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:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.a.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +2.00000 q^{19} +(1.00000 - 1.73205i) q^{20} -6.92820i q^{21} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +8.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} -4.00000 q^{35} +6.00000 q^{36} +8.00000 q^{37} +(-1.50000 - 0.866025i) q^{39} +(6.00000 + 10.3923i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{45} +6.92820i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} -3.00000 q^{53} +(3.00000 - 1.73205i) q^{57} +(-3.00000 - 5.19615i) q^{59} -3.46410i q^{60} +(-5.50000 + 9.52628i) q^{61} +(-6.00000 - 10.3923i) q^{63} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-4.50000 - 2.59808i) q^{69} +6.00000 q^{71} +8.00000 q^{73} +1.73205i q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 6.06218i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 + 5.19615i) q^{83} +(12.0000 - 6.92820i) q^{84} +(1.50000 + 2.59808i) q^{85} +10.3923i q^{87} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-1.00000 - 1.73205i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^4 - q^5 + 4 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9} + 6 q^{12} - q^{13} - 3 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 3 q^{23} - q^{25} + 16 q^{28} - 6 q^{29} + 4 q^{31} - 8 q^{35} + 12 q^{36} + 16 q^{37} - 3 q^{39} + 12 q^{41} + q^{43} - 6 q^{45} - 9 q^{49} - 9 q^{51} + 2 q^{52} - 6 q^{53} + 6 q^{57} - 6 q^{59} - 11 q^{61} - 12 q^{63} - 16 q^{64} - q^{65} + 4 q^{67} - 6 q^{68} - 9 q^{69} + 12 q^{71} + 16 q^{73} + 4 q^{76} + 7 q^{79} + 8 q^{80} - 9 q^{81} - 6 q^{83} + 24 q^{84} + 3 q^{85} - 36 q^{89} - 8 q^{91} + 6 q^{92} + 12 q^{93} - 2 q^{95} - 14 q^{97}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^4 - q^5 + 4 * q^7 + 3 * q^9 + 6 * q^12 - q^13 - 3 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 3 * q^23 - q^25 + 16 * q^28 - 6 * q^29 + 4 * q^31 - 8 * q^35 + 12 * q^36 + 16 * q^37 - 3 * q^39 + 12 * q^41 + q^43 - 6 * q^45 - 9 * q^49 - 9 * q^51 + 2 * q^52 - 6 * q^53 + 6 * q^57 - 6 * q^59 - 11 * q^61 - 12 * q^63 - 16 * q^64 - q^65 + 4 * q^67 - 6 * q^68 - 9 * q^69 + 12 * q^71 + 16 * q^73 + 4 * q^76 + 7 * q^79 + 8 * q^80 - 9 * q^81 - 6 * q^83 + 24 * q^84 + 3 * q^85 - 36 * q^89 - 8 * q^91 + 6 * q^92 + 12 * q^93 - 2 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	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
$14$		0			0
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	−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
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		−	6.92820i		−	1.51186i
$22$		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
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$	8.00000			1.51186
$29$	−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
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.00000			−0.676123
$36$	6.00000			1.00000
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$	−1.50000	−	0.866025i	−0.240192	−	0.138675i
$40$		0			0
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$		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	$0.142372\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$			6.92820i			1.00000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		−	3.46410i		−	0.447214i
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$		0			0
$63$	−6.00000	−	10.3923i	−0.755929	−	1.30931i
$64$	−8.00000			−1.00000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$		0			0
$75$			1.73205i			0.200000i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$		0			0
$78$		0			0
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$	4.00000			0.447214
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	−0.982372	−	0.186938i	$-0.940144\pi$
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	0.653079	+	0.757290i	$0.273477\pi$
$84$	12.0000	−	6.92820i	1.30931	−	0.755929i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$		0			0
$87$			10.3923i			1.11417i
$88$		0			0
$89$	−18.0000			−1.90800			−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000			−1.90800			−0.953998	+	0.299813i	$0.903076\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$		0			0
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000			−0.200000
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$		0			0
$105$	−6.00000	+	3.46410i	−0.585540	+	0.338062i
$106$		0			0
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	12.0000	−	6.92820i	1.13899	−	0.657596i
$112$	8.00000	+	13.8564i	0.755929	+	1.30931i
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	0.786806	−	0.617200i	$-0.211733\pi$
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	−0.927914	+	0.372794i	$0.878400\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	−12.0000			−1.11417
$117$	−3.00000			−0.277350
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$	18.0000	+	10.3923i	1.62301	+	0.937043i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−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
$129$		−	1.73205i		−	0.152499i
$130$		0			0
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		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	$0.901346\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$	6.00000			0.498273
$146$		0			0
$147$	−13.5000	−	7.79423i	−1.11346	−	0.642857i
$148$	8.00000	+	13.8564i	0.657596	+	1.13899i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$		0			0
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		−	3.46410i		−	0.277350i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		0			0
$159$	−4.50000	+	2.59808i	−0.356873	+	0.206041i
$160$		0			0
$161$	−12.0000			−0.945732
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−12.0000	+	20.7846i	−0.937043	+	1.62301i
$165$		0			0
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	2.00000			0.152499
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$		0			0
$177$	−9.00000	−	5.19615i	−0.676481	−	0.390567i
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	−25.0000			−1.85824			−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$		0			0
$183$			19.0526i			1.40841i
$184$		0			0
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−18.0000	−	10.3923i	−1.30931	−	0.755929i
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$	−12.0000	+	6.92820i	−0.866025	+	0.500000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$		0			0
$195$			1.73205i			0.124035i
$196$	9.00000	−	15.5885i	0.642857	−	1.11346i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$		0			0
$201$	6.00000	+	3.46410i	0.423207	+	0.244339i
$202$		0			0
$203$	12.0000	+	20.7846i	0.842235	+	1.45879i
$204$	−9.00000	−	5.19615i	−0.630126	−	0.363803i
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	−9.00000			−0.625543
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	9.00000	−	5.19615i	0.616670	−	0.356034i
$214$		0			0
$215$	−1.00000			−0.0681994
$216$		0			0
$217$	16.0000			1.08615
$218$		0			0
$219$	12.0000	−	6.92820i	0.810885	−	0.468165i
$220$		0			0
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$		0			0
$223$	11.0000	−	19.0526i	0.736614	−	1.27585i	−0.217397	−	0.976083i	$-0.569757\pi$
$223$	11.0000	−	19.0526i	0.736614	−	1.27585i	0.954011	−	0.299770i	$-0.0969101\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$		0			0
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	6.00000	+	3.46410i	0.397360	+	0.229416i
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	27.0000			1.76883			0.884414	−	0.466702i	$-0.154558\pi$
$233$	27.0000			1.76883			0.884414	+	0.466702i	$0.154558\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		−	12.1244i		−	0.787562i
$238$		0			0
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	0.995223	+	0.0976302i	$0.0311262\pi$
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	−0.413061	+	0.910703i	$0.635540\pi$
$240$	6.00000	−	3.46410i	0.387298	−	0.223607i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−22.0000			−1.40841
$245$	−4.50000	+	7.79423i	−0.287494	+	0.497955i
$246$		0			0
$247$	−1.00000	−	1.73205i	−0.0636285	−	0.110208i
$248$		0			0
$249$			10.3923i			0.658586i
$250$		0			0
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$	12.0000	−	20.7846i	0.755929	−	1.30931i
$253$		0			0
$254$		0			0
$255$	4.50000	+	2.59808i	0.281801	+	0.162698i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		0			0
$259$	16.0000	−	27.7128i	0.994192	−	1.72199i
$260$	−2.00000			−0.124035
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	−0.816066	−	0.577959i	$-0.803849\pi$
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$264$		0			0
$265$	1.50000	+	2.59808i	0.0921443	+	0.159599i
$266$		0			0
$267$	−27.0000	+	15.5885i	−1.65237	+	0.953998i
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	6.00000	−	10.3923i	0.363803	−	0.630126i
$273$	−6.00000	+	3.46410i	−0.363137	+	0.209657i
$274$		0			0
$275$		0			0
$276$		−	10.3923i		−	0.625543i
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$		0			0
$279$	12.0000			0.718421
$280$		0			0
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	0.987615	+	0.156898i	$0.0501493\pi$
$282$		0			0
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−3.00000	−	1.73205i	−0.177705	−	0.102598i
$286$		0			0
$287$	48.0000			2.83335
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$			24.2487i			1.42148i
$292$	8.00000	+	13.8564i	0.468165	+	0.810885i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$	−3.00000	+	1.73205i	−0.173205	+	0.100000i
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$		0			0
$303$		−	25.9808i		−	1.49256i
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	11.0000			0.629858
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	6.00000	+	3.46410i	0.341328	+	0.197066i
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$		0			0
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$	14.0000			0.787562
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$		0			0
$319$		0			0
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$	−6.00000			−0.333849
$324$	9.00000	−	15.5885i	0.500000	−	0.866025i
$325$	1.00000			0.0554700
$326$		0			0
$327$	−15.0000	+	8.66025i	−0.829502	+	0.478913i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	−12.0000			−0.658586
$333$	12.0000	−	20.7846i	0.657596	−	1.13899i
$334$		0			0
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$	24.0000	+	13.8564i	1.30931	+	0.755929i
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$		0			0
$339$	−4.50000	−	2.59808i	−0.244406	−	0.141108i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$		0			0
$342$		0			0
$343$	−8.00000			−0.431959
$344$		0			0
$345$			5.19615i			0.279751i
$346$		0			0
$347$	−7.50000	−	12.9904i	−0.402621	−	0.697360i	0.591420	−	0.806363i	$-0.298567\pi$
$347$	−7.50000	−	12.9904i	−0.402621	−	0.697360i	−0.994041	+	0.109003i	$0.965234\pi$
$348$	−18.0000	+	10.3923i	−0.964901	+	0.557086i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$		0			0
$351$	−4.50000	+	2.59808i	−0.240192	+	0.138675i
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−18.0000	−	31.1769i	−0.953998	−	1.65237i
$357$			20.7846i			1.10004i
$358$		0			0
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	16.5000	+	9.52628i	0.866025	+	0.500000i
$364$	−4.00000	−	6.92820i	−0.209657	−	0.363137i
$365$	−4.00000	−	6.92820i	−0.209370	−	0.362639i
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	12.0000			0.625543
$369$	36.0000			1.87409
$370$		0			0
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$			13.8564i			0.718421i
$373$	−17.5000	−	30.3109i	−0.906116	−	1.56944i	−0.819413	−	0.573204i	$-0.805700\pi$
$373$	−17.5000	−	30.3109i	−0.906116	−	1.56944i	−0.0867031	−	0.996234i	$-0.527633\pi$
$374$		0			0
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	6.00000			0.309016
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	−24.0000	+	13.8564i	−1.22956	+	0.709885i
$382$		0			0
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.50000	−	2.59808i	−0.0762493	−	0.132068i
$388$	−28.0000			−1.42148
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$		0			0
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$		0			0
$393$	31.5000	+	18.1865i	1.58896	+	0.917389i
$394$		0			0
$395$	−7.00000			−0.352208
$396$		0			0
$397$	−4.00000			−0.200754			−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000			−0.200754			−0.100377	+	0.994949i	$0.532005\pi$
$398$		0			0
$399$		−	13.8564i		−	0.693688i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	30.0000			1.49256
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		0			0
$411$			10.3923i			0.512615i
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	−24.0000			−1.18096
$414$		0			0
$415$	6.00000			0.294528
$416$		0			0
$417$	−7.50000	−	4.33013i	−0.367277	−	0.212047i
$418$		0			0
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$	−12.0000	−	6.92820i	−0.585540	−	0.338062i
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$		0			0
$427$	22.0000	+	38.1051i	1.06465	+	1.84404i
$428$	−3.00000	−	5.19615i	−0.145010	−	0.251166i
$429$		0			0
$430$		0			0
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$	−37.0000			−1.77811			−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−37.0000			−1.77811			−0.889053	+	0.457804i	$0.848636\pi$
$434$		0			0
$435$	9.00000	−	5.19615i	0.431517	−	0.249136i
$436$	−10.0000	−	17.3205i	−0.478913	−	0.829502i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	6.50000	−	11.2583i	0.310228	−	0.537331i	0.978412	+	0.206666i	$0.0662612\pi$
$440$		0			0
$441$	−27.0000			−1.28571
$442$		0			0
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$	24.0000	+	13.8564i	1.13899	+	0.657596i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$	−27.0000	−	15.5885i	−1.27706	−	0.737309i
$448$	−16.0000	+	27.7128i	−0.755929	+	1.30931i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$		0			0
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		−	38.1051i		−	1.79033i
$454$		0			0
$455$	2.00000	+	3.46410i	0.0937614	+	0.162400i
$456$		0			0
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$		0			0
$459$			15.5885i			0.727607i
$460$	−6.00000			−0.279751
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$		0			0
$463$	−13.0000	−	22.5167i	−0.604161	−	1.04644i	−0.992183	−	0.124788i	$-0.960175\pi$
$463$	−13.0000	−	22.5167i	−0.604161	−	1.04644i	0.388022	−	0.921650i	$-0.373158\pi$
$464$	−12.0000	−	20.7846i	−0.557086	−	0.964901i
$465$		−	6.92820i		−	0.321288i
$466$		0			0
$467$	−3.00000			−0.138823			−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$	16.0000			0.738811
$470$		0			0
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−1.00000	+	1.73205i	−0.0458831	+	0.0794719i
$476$	−24.0000			−1.10004
$477$	−4.50000	+	7.79423i	−0.206041	+	0.356873i
$478$		0			0
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$	−18.0000	+	10.3923i	−0.819028	+	0.472866i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$	14.0000			0.635707
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$		0			0
$489$	−24.0000	+	13.8564i	−1.08532	+	0.626608i
$490$		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	$0.531533\pi$
$492$			41.5692i			1.87409i
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$		0			0
$495$		0			0
$496$	−16.0000			−0.718421
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$	−18.0000	−	10.3923i	−0.804181	−	0.464294i
$502$		0			0
$503$	−33.0000			−1.47140			−0.735699	−	0.677309i	$-0.763146\pi$
$503$	−33.0000			−1.47140			−0.735699	+	0.677309i	$0.763146\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$		0			0
$507$			1.73205i			0.0769231i
$508$	−16.0000	−	27.7128i	−0.709885	−	1.22956i
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$		0			0
$511$	16.0000	−	27.7128i	0.707798	−	1.22594i
$512$		0			0
$513$		−	10.3923i		−	0.458831i
$514$		0			0
$515$	2.00000	−	3.46410i	0.0881305	−	0.152647i
$516$	3.00000	−	1.73205i	0.132068	−	0.0762493i
$517$		0			0
$518$		0			0
$519$			25.9808i			1.14043i
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−28.0000			−1.22435			−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000			−1.22435			−0.612177	+	0.790721i	$0.709706\pi$
$524$	−21.0000	+	36.3731i	−0.917389	+	1.58896i
$525$	6.00000	+	3.46410i	0.261861	+	0.151186i
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−18.0000			−0.781133
$532$	16.0000			0.693688
$533$	6.00000	−	10.3923i	0.259889	−	0.450141i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$		0			0
$537$	13.5000	−	7.79423i	0.582568	−	0.336346i
$538$		0			0
$539$		0			0
$540$	−9.00000	−	5.19615i	−0.387298	−	0.223607i
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$		0			0
$543$	−37.5000	+	21.6506i	−1.60928	+	0.929118i
$544$		0			0
$545$	5.00000	+	8.66025i	0.214176	+	0.370965i
$546$		0			0
$547$	20.0000	−	34.6410i	0.855138	−	1.48114i	−0.0213785	−	0.999771i	$-0.506805\pi$
$547$	20.0000	−	34.6410i	0.855138	−	1.48114i	0.876517	−	0.481371i	$-0.159861\pi$
$548$	−12.0000			−0.512615
$549$	16.5000	+	28.5788i	0.704203	+	1.21972i
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	−14.0000	−	24.2487i	−0.595341	−	1.03116i
$554$		0			0
$555$	−12.0000	−	6.92820i	−0.509372	−	0.294086i
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$	8.00000	−	13.8564i	0.338062	−	0.585540i
$561$		0			0
$562$		0			0
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$		0			0
$565$	−1.50000	+	2.59808i	−0.0631055	+	0.109302i
$566$		0			0
$567$	−36.0000			−1.51186
$568$		0			0
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.0294311	+	0.999567i	$0.509370\pi$
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.850935	+	0.525271i	$0.823964\pi$
$570$		0			0
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$		0			0
$573$			5.19615i			0.217072i
$574$		0			0
$575$	3.00000			0.125109
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−28.0000			−1.16566			−0.582828	−	0.812596i	$-0.698054\pi$
$577$	−28.0000			−1.16566			−0.582828	+	0.812596i	$0.698054\pi$
$578$		0			0
$579$	6.00000	+	3.46410i	0.249351	+	0.143963i
$580$	6.00000	+	10.3923i	0.249136	+	0.431517i
$581$	12.0000	+	20.7846i	0.497844	+	0.862291i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$		0			0
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	−0.989792	−	0.142520i	$-0.954479\pi$
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	0.618322	+	0.785925i	$0.287813\pi$
$588$		−	31.1769i		−	1.28571i
$589$	4.00000	+	6.92820i	0.164817	+	0.285472i
$590$		0			0
$591$	18.0000	−	10.3923i	0.740421	−	0.427482i
$592$	−16.0000	+	27.7128i	−0.657596	+	1.13899i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$	12.0000			0.491952
$596$	18.0000	−	31.1769i	0.737309	−	1.27706i
$597$	−10.5000	+	6.06218i	−0.429736	+	0.248108i
$598$		0			0
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	0.976710	+	0.214563i	$0.0688326\pi$
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	−0.302539	+	0.953137i	$0.597834\pi$
$600$		0			0
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	44.0000			1.79033
$605$	5.50000	−	9.52628i	0.223607	−	0.387298i
$606$		0			0
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$		0			0
$609$	36.0000	+	20.7846i	1.45879	+	0.842235i
$610$		0			0
$611$		0			0
$612$	−18.0000			−0.727607
$613$	26.0000			1.05013			0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000			1.05013			0.525065	+	0.851062i	$0.324041\pi$
$614$		0			0
$615$		−	20.7846i		−	0.838116i
$616$		0			0
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$	8.00000			0.321288
$621$	−13.5000	+	7.79423i	−0.541736	+	0.312772i
$622$		0			0
$623$	−36.0000	+	62.3538i	−1.44231	+	2.49815i
$624$	6.00000	−	3.46410i	0.240192	−	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$	−13.0000	+	22.5167i	−0.518756	+	0.898513i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−7.50000	−	4.33013i	−0.298098	−	0.172107i
$634$		0			0
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$	−9.00000	−	5.19615i	−0.356873	−	0.206041i
$637$	−4.50000	+	7.79423i	−0.178296	+	0.308819i
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	−0.0690201	−	0.997615i	$-0.521987\pi$
$641$	21.0000	−	36.3731i	0.829450	−	1.43665i	0.898470	−	0.439034i	$-0.144679\pi$
$642$		0			0
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	0.997197	−	0.0748254i	$-0.0238399\pi$
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	−0.563399	+	0.826185i	$0.690507\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$	−1.50000	+	0.866025i	−0.0590624	+	0.0340997i
$646$		0			0
$647$	9.00000			0.353827			0.176913	−	0.984226i	$-0.443389\pi$
$647$	9.00000			0.353827			0.176913	+	0.984226i	$0.443389\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	24.0000	−	13.8564i	0.940634	−	0.543075i
$652$	−16.0000	−	27.7128i	−0.626608	−	1.08532i
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$	10.5000	−	18.1865i	0.410269	−	0.710607i
$656$	−48.0000			−1.87409
$657$	12.0000	−	20.7846i	0.468165	−	0.810885i
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$		0			0
$663$	4.50000	+	2.59808i	0.174766	+	0.100901i
$664$		0			0
$665$	−8.00000			−0.310227
$666$		0			0
$667$	18.0000			0.696963
$668$	12.0000	−	20.7846i	0.464294	−	0.804181i
$669$		−	38.1051i		−	1.47323i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	3.50000	−	6.06218i	0.134915	−	0.233680i	−0.790650	−	0.612268i	$-0.790257\pi$
$673$	3.50000	−	6.06218i	0.134915	−	0.233680i	0.925565	+	0.378589i	$0.123591\pi$
$674$		0			0
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	−2.00000			−0.0769231
$677$	−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
$679$	28.0000	+	48.4974i	1.07454	+	1.86116i
$680$		0			0
$681$		−	20.7846i		−	0.796468i
$682$		0			0
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	12.0000			0.458831
$685$	6.00000			0.229248
$686$		0			0
$687$	−3.00000	−	1.73205i	−0.114457	−	0.0660819i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	1.50000	+	2.59808i	0.0571454	+	0.0989788i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	−30.0000			−1.14043
$693$		0			0
$694$		0			0
$695$	−2.50000	+	4.33013i	−0.0948304	+	0.164251i
$696$		0			0
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$		0			0
$699$	40.5000	−	23.3827i	1.53185	−	0.884414i
$700$	−4.00000	+	6.92820i	−0.151186	+	0.261861i
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$	16.0000			0.603451
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.0000	−	51.9615i	−1.12827	−	1.95421i
$708$		−	20.7846i		−	0.781133i
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	−0.884192	−	0.467123i	$-0.845291\pi$
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	0.846637	+	0.532172i	$0.178624\pi$
$710$		0			0
$711$	−10.5000	−	18.1865i	−0.393781	−	0.682048i
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$		0			0
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$	27.0000	+	15.5885i	1.00833	+	0.582162i
$718$		0			0
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	6.00000	−	10.3923i	0.223607	−	0.387298i
$721$	16.0000			0.595871
$722$		0			0
$723$		−	17.3205i		−	0.644157i
$724$	−25.0000	−	43.3013i	−0.929118	−	1.60928i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		0			0
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	−0.421193	−	0.906971i	$-0.638389\pi$
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	0.996056	−	0.0887213i	$-0.0282781\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	−33.0000	+	19.0526i	−1.21972	+	0.704203i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$		0			0
$735$			15.5885i			0.574989i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$	8.00000	−	13.8564i	0.294086	−	0.509372i
$741$	−3.00000	−	1.73205i	−0.110208	−	0.0636285i
$742$		0			0
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	−0.937336	−	0.348428i	$-0.886716\pi$
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	0.166920	−	0.985970i	$-0.446618\pi$
$744$		0			0
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$		0			0
$747$	9.00000	+	15.5885i	0.329293	+	0.570352i
$748$		0			0
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$		0			0
$753$	−40.5000	+	23.3827i	−1.47590	+	0.852112i
$754$		0			0
$755$	−22.0000			−0.800662
$756$		−	41.5692i		−	1.51186i
$757$	−19.0000			−0.690567			−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000			−0.690567			−0.345283	+	0.938498i	$0.612217\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$	−20.0000	+	34.6410i	−0.724049	+	1.25409i
$764$	−6.00000			−0.217072
$765$	9.00000			0.325396
$766$		0			0
$767$	−3.00000	+	5.19615i	−0.108324	+	0.187622i
$768$	−24.0000	−	13.8564i	−0.866025	−	0.500000i
$769$	−16.0000	−	27.7128i	−0.576975	−	0.999350i	−0.995824	−	0.0912938i	$-0.970900\pi$
$769$	−16.0000	−	27.7128i	−0.576975	−	0.999350i	0.418849	−	0.908056i	$-0.362434\pi$
$770$		0			0
$771$	−4.50000	−	2.59808i	−0.162064	−	0.0935674i
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$		0			0
$777$		−	55.4256i		−	1.98838i
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$	−3.00000	+	1.73205i	−0.107417	+	0.0620174i
$781$		0			0
$782$		0			0
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	36.0000			1.28571
$785$	6.50000	−	11.2583i	0.231995	−	0.401827i
$786$		0			0
$787$	23.0000	+	39.8372i	0.819861	+	1.42004i	0.905784	+	0.423740i	$0.139283\pi$
$787$	23.0000	+	39.8372i	0.819861	+	1.42004i	−0.0859225	+	0.996302i	$0.527384\pi$
$788$	12.0000	+	20.7846i	0.427482	+	0.740421i
$789$		−	5.19615i		−	0.184988i
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	11.0000			0.390621
$794$		0			0
$795$	4.50000	+	2.59808i	0.159599	+	0.0921443i
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	−27.0000	−	46.7654i	−0.956389	−	1.65651i	−0.731157	−	0.682209i	$-0.761019\pi$
$797$	−27.0000	−	46.7654i	−0.956389	−	1.65651i	−0.225232	−	0.974305i	$-0.572314\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−27.0000	+	46.7654i	−0.953998	+	1.65237i
$802$		0			0
$803$		0			0
$804$			13.8564i			0.488678i
$805$	6.00000	+	10.3923i	0.211472	+	0.366281i
$806$		0			0
$807$	9.00000	−	5.19615i	0.316815	−	0.182913i
$808$		0			0
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−24.0000	+	41.5692i	−0.842235	+	1.45879i
$813$	30.0000	−	17.3205i	1.05215	−	0.607457i
$814$		0			0
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		−	20.7846i		−	0.727607i
$817$	1.00000	−	1.73205i	0.0349856	−	0.0605968i
$818$		0			0
$819$	−6.00000	+	10.3923i	−0.209657	+	0.363137i
$820$	24.0000			0.838116
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$		0			0
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	−0.963119	−	0.269075i	$-0.913282\pi$
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	0.248534	−	0.968623i	$-0.420051\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$		0			0
$831$		−	38.1051i		−	1.32185i
$832$	4.00000	+	6.92820i	0.138675	+	0.240192i
$833$	13.5000	+	23.3827i	0.467747	+	0.810162i
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$	18.0000	−	10.3923i	0.622171	−	0.359211i
$838$		0			0
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	−0.0705865	−	0.997506i	$-0.522487\pi$
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	0.899158	−	0.437623i	$-0.144180\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$		−	20.7846i		−	0.715860i
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$	1.00000			0.0344010
$846$		0			0
$847$	44.0000			1.51186
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$	19.5000	+	11.2583i	0.669238	+	0.386385i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	18.0000	+	10.3923i	0.616670	+	0.356034i
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$		0			0
$855$	−6.00000			−0.205196
$856$		0			0
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.126459	+	0.991972i	$0.540361\pi$
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.795843	+	0.605503i	$0.792972\pi$
$858$		0			0
$859$	18.5000	+	32.0429i	0.631212	+	1.09329i	0.987304	+	0.158840i	$0.0507755\pi$
$859$	18.5000	+	32.0429i	0.631212	+	1.09329i	−0.356092	+	0.934451i	$0.615891\pi$
$860$	−1.00000	−	1.73205i	−0.0340997	−	0.0590624i
$861$	72.0000	−	41.5692i	2.45375	−	1.41668i
$862$		0			0
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$		0			0
$865$	15.0000			0.510015
$866$		0			0
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	16.0000	+	27.7128i	0.543075	+	0.940634i
$869$		0			0
$870$		0			0
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$		0			0
$873$	21.0000	+	36.3731i	0.710742	+	1.23104i
$874$		0			0
$875$	2.00000	−	3.46410i	0.0676123	−	0.117108i
$876$	24.0000	+	13.8564i	0.810885	+	0.468165i
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$			10.3923i			0.349334i
$886$		0			0
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$		0			0
$889$	−32.0000	+	55.4256i	−1.07325	+	1.85892i
$890$		0			0
$891$		0			0
$892$	44.0000			1.47323
$893$		0			0
$894$		0			0
$895$	−4.50000	−	7.79423i	−0.150418	−	0.260532i
$896$		0			0
$897$			5.19615i			0.173494i
$898$		0			0
$899$	−24.0000			−0.800445
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	9.00000			0.299833
$902$		0			0
$903$	−6.00000	−	3.46410i	−0.199667	−	0.115278i
$904$		0			0
$905$	12.5000	+	21.6506i	0.415514	+	0.719691i
$906$		0			0
$907$	0.500000	−	0.866025i	0.0166022	−	0.0287559i	−0.857605	−	0.514309i	$-0.828048\pi$
$907$	0.500000	−	0.866025i	0.0166022	−	0.0287559i	0.874207	+	0.485553i	$0.161382\pi$
$908$	24.0000			0.796468
$909$	−22.5000	−	38.9711i	−0.746278	−	1.29259i
$910$		0			0
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	0.337991	+	0.941149i	$0.390253\pi$
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	−0.984055	+	0.177866i	$0.943081\pi$
$912$			13.8564i			0.458831i
$913$		0			0
$914$		0			0
$915$	16.5000	−	9.52628i	0.545473	−	0.314929i
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	84.0000			2.77392
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$		0			0
$921$	−6.00000	+	3.46410i	−0.197707	+	0.114146i
$922$		0			0
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$		0			0
$927$	12.0000			0.394132
$928$		0			0
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$		0			0
$931$	−9.00000	−	15.5885i	−0.294963	−	0.510891i
$932$	27.0000	+	46.7654i	0.884414	+	1.53185i
$933$	36.0000	+	20.7846i	1.17859	+	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−31.0000			−1.01273			−0.506363	−	0.862320i	$-0.669010\pi$
$937$	−31.0000			−1.01273			−0.506363	+	0.862320i	$0.669010\pi$
$938$		0			0
$939$		−	17.3205i		−	0.565233i
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	24.0000			0.781133
$945$			20.7846i			0.676123i
$946$		0			0
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$	21.0000	−	12.1244i	0.682048	−	0.393781i
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$		−	51.9615i		−	1.68497i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	3.00000			0.0970777
$956$	−18.0000	+	31.1769i	−0.582162	+	1.00833i
$957$		0			0
$958$		0			0
$959$	12.0000	+	20.7846i	0.387500	+	0.671170i
$960$	12.0000	+	6.92820i	0.387298	+	0.223607i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−4.50000	+	7.79423i	−0.145010	+	0.251166i
$964$	20.0000			0.644157
$965$	2.00000	−	3.46410i	0.0643823	−	0.111513i
$966$		0			0
$967$	14.0000	+	24.2487i	0.450210	+	0.779786i	0.998399	−	0.0565684i	$-0.0180159\pi$
$967$	14.0000	+	24.2487i	0.450210	+	0.779786i	−0.548189	+	0.836354i	$0.684683\pi$
$968$		0			0
$969$	−9.00000	+	5.19615i	−0.289122	+	0.166924i
$970$		0			0
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		−	31.1769i		−	1.00000i
$973$	−20.0000			−0.641171
$974$		0			0
$975$	1.50000	−	0.866025i	0.0480384	−	0.0277350i
$976$	−22.0000	−	38.1051i	−0.704203	−	1.21972i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$		0			0
$980$	−18.0000			−0.574989
$981$	−15.0000	+	25.9808i	−0.478913	+	0.829502i
$982$		0			0
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$	2.00000	−	3.46410i	0.0636285	−	0.110208i
$989$	−3.00000			−0.0953945
$990$		0			0
$991$	−55.0000			−1.74713			−0.873566	−	0.486705i	$-0.838199\pi$
$991$	−55.0000			−1.74713			−0.873566	+	0.486705i	$0.838199\pi$
$992$		0			0
$993$			34.6410i			1.09930i
$994$		0			0
$995$	3.50000	+	6.06218i	0.110957	+	0.192184i
$996$	−18.0000	+	10.3923i	−0.570352	+	0.329293i
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$		0			0
$999$		−	41.5692i		−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.a.196.1	✓	2
3.2	odd	2		1755.2.i.d.586.1		2
9.2	odd	6		5265.2.a.g.1.1		1
9.4	even	3	inner	585.2.i.a.391.1	yes	2
9.5	odd	6		1755.2.i.d.1171.1		2
9.7	even	3		5265.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.a.196.1	✓	2	1.1	even	1	trivial
585.2.i.a.391.1	yes	2	9.4	even	3	inner
1755.2.i.d.586.1		2	3.2	odd	2
1755.2.i.d.1171.1		2	9.5	odd	6
5265.2.a.g.1.1		1	9.2	odd	6
5265.2.a.i.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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +2.00000 q^{19} +(1.00000 - 1.73205i) q^{20} -6.92820i q^{21} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +8.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} -4.00000 q^{35} +6.00000 q^{36} +8.00000 q^{37} +(-1.50000 - 0.866025i) q^{39} +(6.00000 + 10.3923i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{45} +6.92820i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} -3.00000 q^{53} +(3.00000 - 1.73205i) q^{57} +(-3.00000 - 5.19615i) q^{59} -3.46410i q^{60} +(-5.50000 + 9.52628i) q^{61} +(-6.00000 - 10.3923i) q^{63} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-4.50000 - 2.59808i) q^{69} +6.00000 q^{71} +8.00000 q^{73} +1.73205i q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 6.06218i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 + 5.19615i) q^{83} +(12.0000 - 6.92820i) q^{84} +(1.50000 + 2.59808i) q^{85} +10.3923i q^{87} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-1.00000 - 1.73205i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^4 - q^5 + 4 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9} + 6 q^{12} - q^{13} - 3 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 3 q^{23} - q^{25} + 16 q^{28} - 6 q^{29} + 4 q^{31} - 8 q^{35} + 12 q^{36} + 16 q^{37} - 3 q^{39} + 12 q^{41} + q^{43} - 6 q^{45} - 9 q^{49} - 9 q^{51} + 2 q^{52} - 6 q^{53} + 6 q^{57} - 6 q^{59} - 11 q^{61} - 12 q^{63} - 16 q^{64} - q^{65} + 4 q^{67} - 6 q^{68} - 9 q^{69} + 12 q^{71} + 16 q^{73} + 4 q^{76} + 7 q^{79} + 8 q^{80} - 9 q^{81} - 6 q^{83} + 24 q^{84} + 3 q^{85} - 36 q^{89} - 8 q^{91} + 6 q^{92} + 12 q^{93} - 2 q^{95} - 14 q^{97}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^4 - q^5 + 4 * q^7 + 3 * q^9 + 6 * q^12 - q^13 - 3 * q^15 - 4 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 3 * q^23 - q^25 + 16 * q^28 - 6 * q^29 + 4 * q^31 - 8 * q^35 + 12 * q^36 + 16 * q^37 - 3 * q^39 + 12 * q^41 + q^43 - 6 * q^45 - 9 * q^49 - 9 * q^51 + 2 * q^52 - 6 * q^53 + 6 * q^57 - 6 * q^59 - 11 * q^61 - 12 * q^63 - 16 * q^64 - q^65 + 4 * q^67 - 6 * q^68 - 9 * q^69 + 12 * q^71 + 16 * q^73 + 4 * q^76 + 7 * q^79 + 8 * q^80 - 9 * q^81 - 6 * q^83 + 24 * q^84 + 3 * q^85 - 36 * q^89 - 8 * q^91 + 6 * q^92 + 12 * q^93 - 2 * q^95 - 14 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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