LMFDB - Embedded newform 1690.2.l.b.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(361,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,2,0,0,0,0,-2,2,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1690.361
Dual form			1690.2.l.b.1161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{6} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} -2.00000 q^{12} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} -1.00000i q^{18} +(-0.866025 - 0.500000i) q^{20} +(1.73205 - 1.00000i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{30} +6.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +6.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.19615 - 3.00000i) q^{37} +1.00000 q^{40} +(5.00000 - 8.66025i) q^{43} +(0.866025 + 0.500000i) q^{45} -12.0000i q^{47} +(-1.00000 + 1.73205i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(0.866025 - 0.500000i) q^{50} -12.0000 q^{51} +(3.46410 - 2.00000i) q^{54} +(5.19615 + 3.00000i) q^{58} +(10.3923 + 6.00000i) q^{59} +2.00000i q^{60} +(-5.00000 + 8.66025i) q^{61} +(-3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-10.3923 + 6.00000i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(5.19615 + 3.00000i) q^{71} +(-0.866025 - 0.500000i) q^{72} -6.00000i q^{73} +(-3.00000 + 5.19615i) q^{74} +(1.00000 + 1.73205i) q^{75} -8.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.50000 + 9.52628i) q^{81} +12.0000i q^{83} +(-5.19615 - 3.00000i) q^{85} +10.0000i q^{86} +(-6.00000 + 10.3923i) q^{87} +(-10.3923 + 6.00000i) q^{89} -1.00000 q^{90} +(10.3923 - 6.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} -2.00000i q^{96} +(-15.5885 - 9.00000i) q^{97} +(6.06218 + 3.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} - 8 q^{12} - 2 q^{16} + 12 q^{17} - 4 q^{25} - 16 q^{27} - 12 q^{29} + 4 q^{30} + 2 q^{36} + 4 q^{40} + 20 q^{43} - 4 q^{48} - 14 q^{49} - 48 q^{51} - 20 q^{61}+ \cdots + 24 q^{94}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 - 8 * q^12 - 2 * q^16 + 12 * q^17 - 4 * q^25 - 16 * q^27 - 12 * q^29 + 4 * q^30 + 2 * q^36 + 4 * q^40 + 20 * q^43 - 4 * q^48 - 14 * q^49 - 48 * q^51 - 20 * q^61 - 12 * q^62 - 4 * q^64 - 12 * q^68 - 12 * q^74 + 4 * q^75 - 32 * q^79 + 22 * q^81 - 24 * q^87 - 4 * q^90 + 24 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.73205	+	1.00000i	0.707107	+	0.408248i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−2.00000			−0.577350
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−1.73205	+	1.00000i	−0.447214	+	0.258199i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	1.73205	−	1.00000i	0.353553	−	0.204124i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$			6.00000i			1.07763i	0.842424	+	0.538816i	$0.181128\pi$
$31$			6.00000i			1.07763i	−0.842424	+	0.538816i	$0.818872\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			6.00000i			1.02899i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	−0.00783774	−	0.999969i	$-0.502495\pi$
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	0.862080	+	0.506772i	$0.169162\pi$
$38$		0			0
$39$		0			0
$40$	1.00000			0.158114
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$		0			0
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$		0			0
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	−1.00000	+	1.73205i	−0.144338	+	0.250000i
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−12.0000			−1.68034
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	3.46410	−	2.00000i	0.471405	−	0.272166i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	10.3923	+	6.00000i	1.35296	+	0.781133i	0.988663	−	0.150148i	$-0.0479752\pi$
$59$	10.3923	+	6.00000i	1.35296	+	0.781133i	0.364299	+	0.931282i	$0.381308\pi$
$60$			2.00000i			0.258199i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	−3.00000	−	5.19615i	−0.381000	−	0.659912i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$	−5.19615	−	3.00000i	−0.563602	−	0.325396i
$86$			10.0000i			1.07833i
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$		0			0
$89$	−10.3923	+	6.00000i	−1.10158	+	0.635999i	−0.936636	−	0.350304i	$-0.886078\pi$
$89$	−10.3923	+	6.00000i	−1.10158	+	0.635999i	−0.164946	+	0.986303i	$0.552745\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$		0			0
$93$	10.3923	−	6.00000i	1.07763	−	0.622171i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$		0			0
$96$		−	2.00000i		−	0.204124i
$97$	−15.5885	−	9.00000i	−1.58277	−	0.913812i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−15.5885	−	9.00000i	−1.58277	−	0.913812i	−0.588315	−	0.808632i	$-0.700208\pi$
$98$	6.06218	+	3.50000i	0.612372	+	0.353553i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	10.3923	−	6.00000i	1.02899	−	0.594089i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$	−10.3923	−	6.00000i	−0.986394	−	0.569495i
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$		−	10.0000i		−	0.905357i
$123$		0			0
$124$	5.19615	+	3.00000i	0.466628	+	0.269408i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	−0.964899	−	0.262620i	$-0.915413\pi$
$127$	−8.00000	−	13.8564i	−0.709885	−	1.22956i	0.255014	−	0.966937i	$-0.417920\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−20.0000			−1.76090
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$	6.00000	−	10.3923i	0.518321	−	0.897758i
$135$			4.00000i			0.344265i
$136$	5.19615	+	3.00000i	0.445566	+	0.257248i
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	−20.7846	+	12.0000i	−1.75038	+	1.01058i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$	−5.19615	+	3.00000i	−0.431517	+	0.249136i
$146$	3.00000	+	5.19615i	0.248282	+	0.430037i
$147$	−7.00000	+	12.1244i	−0.577350	+	1.00000i
$148$		−	6.00000i		−	0.493197i
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$	−1.73205	−	1.00000i	−0.141421	−	0.0816497i
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$		0			0
$153$	3.00000	+	5.19615i	0.242536	+	0.420084i
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	6.92820	−	4.00000i	0.551178	−	0.318223i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	−9.52628	−	5.50000i	−0.748455	−	0.432121i
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	0.848339	−	0.529454i	$-0.177603\pi$
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	−0.0343508	+	0.999410i	$0.510936\pi$
$164$		0			0
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	−0.0407502	−	0.999169i	$-0.512975\pi$
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	0.844931	+	0.534875i	$0.179641\pi$
$168$		0			0
$169$		0			0
$170$	6.00000			0.460179
$171$		0			0
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.101598	−	0.994826i	$-0.467605\pi$
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.810745	−	0.585399i	$-0.199062\pi$
$174$		−	12.0000i		−	0.909718i
$175$		0			0
$176$		0			0
$177$		−	24.0000i		−	1.80395i
$178$	6.00000	−	10.3923i	0.449719	−	0.778936i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	20.0000			1.47844
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$		0			0
$188$	−10.3923	−	6.00000i	−0.757937	−	0.437595i
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	1.00000	+	1.73205i	0.0721688	+	0.125000i
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.941932	−	0.335805i	$-0.890992\pi$
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.180150	+	0.983639i	$0.557658\pi$
$194$	18.0000			1.29232
$195$		0			0
$196$	−7.00000			−0.500000
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	20.7846	+	12.0000i	1.46603	+	0.846415i
$202$	5.19615	+	3.00000i	0.365600	+	0.211079i
$203$		0			0
$204$	−6.00000	+	10.3923i	−0.420084	+	0.727607i
$205$		0			0
$206$	3.46410	−	2.00000i	0.241355	−	0.139347i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$		0			0
$213$		−	12.0000i		−	0.822226i
$214$	−5.19615	−	3.00000i	−0.355202	−	0.205076i
$215$	−8.66025	−	5.00000i	−0.590624	−	0.340997i
$216$		−	4.00000i		−	0.272166i
$217$		0			0
$218$	3.00000	+	5.19615i	0.203186	+	0.351928i
$219$	−10.3923	+	6.00000i	−0.702247	+	0.405442i
$220$		0			0
$221$		0			0
$222$	12.0000			0.805387
$223$	−10.3923	+	6.00000i	−0.695920	+	0.401790i	−0.805826	−	0.592152i	$-0.798278\pi$
$223$	−10.3923	+	6.00000i	−0.695920	+	0.401790i	0.109906	+	0.993942i	$0.464945\pi$
$224$		0			0
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$		−	6.00000i		−	0.399114i
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$		0			0
$232$	5.19615	−	3.00000i	0.341144	−	0.196960i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	10.3923	−	6.00000i	0.676481	−	0.390567i
$237$	8.00000	+	13.8564i	0.519656	+	0.900070i
$238$		0			0
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$	1.73205	+	1.00000i	0.111803	+	0.0645497i
$241$	−20.7846	−	12.0000i	−1.33885	−	0.772988i	−0.352217	−	0.935918i	$-0.614572\pi$
$241$	−20.7846	−	12.0000i	−1.33885	−	0.772988i	−0.986638	+	0.162930i	$0.947905\pi$
$242$		−	11.0000i		−	0.707107i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	5.00000	+	8.66025i	0.320092	+	0.554416i
$245$	−6.06218	+	3.50000i	−0.387298	+	0.223607i
$246$		0			0
$247$		0			0
$248$	−6.00000			−0.381000
$249$	20.7846	−	12.0000i	1.31717	−	0.760469i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	−0.186722	−	0.982413i	$-0.559786\pi$
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	0.944156	−	0.329500i	$-0.106880\pi$
$252$		0			0
$253$		0			0
$254$	13.8564	+	8.00000i	0.869428	+	0.501965i
$255$			12.0000i			0.751469i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$	17.3205	−	10.0000i	1.07833	−	0.622573i
$259$		0			0
$260$		0			0
$261$	6.00000			0.371391
$262$		0			0
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	20.7846	+	12.0000i	1.27200	+	0.734388i
$268$			12.0000i			0.733017i
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.107031	−	0.994256i	$-0.465866\pi$
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.807535	−	0.589819i	$-0.200801\pi$
$270$	−2.00000	−	3.46410i	−0.121716	−	0.210819i
$271$	−5.19615	+	3.00000i	−0.315644	+	0.182237i	−0.649449	−	0.760405i	$-0.725000\pi$
$271$	−5.19615	+	3.00000i	−0.315644	+	0.182237i	0.333805	+	0.942642i	$0.391667\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	18.0000			1.08742
$275$		0			0
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$			4.00000i			0.239904i
$279$	−5.19615	−	3.00000i	−0.311086	−	0.179605i
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	12.0000	−	20.7846i	0.714590	−	1.23771i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$			36.0000i			2.11036i
$292$	−5.19615	−	3.00000i	−0.304082	−	0.175562i
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.0300351	−	0.999549i	$-0.509562\pi$
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.880652	+	0.473763i	$0.842895\pi$
$294$		−	14.0000i		−	0.816497i
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	2.00000			0.115470
$301$		0			0
$302$	−9.00000	−	15.5885i	−0.517892	−	0.897015i
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$		0			0
$305$	8.66025	+	5.00000i	0.495885	+	0.286299i
$306$	−5.19615	−	3.00000i	−0.297044	−	0.171499i
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$	4.00000	+	6.92820i	0.227552	+	0.394132i
$310$	−5.19615	+	3.00000i	−0.295122	+	0.170389i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	3.46410	−	2.00000i	0.195491	−	0.112867i
$315$		0			0
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$		0			0
$320$			1.00000i			0.0559017i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$		0			0
$324$	11.0000			0.611111
$325$		0			0
$326$	−12.0000			−0.664619
$327$	−10.3923	+	6.00000i	−0.574696	+	0.331801i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$	10.3923	+	6.00000i	0.570352	+	0.329293i
$333$			6.00000i			0.328798i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	12.0000			0.651751
$340$	−5.19615	+	3.00000i	−0.281801	+	0.162698i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	8.66025	+	5.00000i	0.466930	+	0.269582i
$345$		0			0
$346$			24.0000i			1.29025i
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	−0.774197	−	0.632945i	$-0.781846\pi$
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	0.935245	+	0.354001i	$0.115179\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	25.9808	−	15.0000i	1.39072	−	0.802932i	0.397324	−	0.917679i	$-0.369939\pi$
$349$	25.9808	−	15.0000i	1.39072	−	0.802932i	0.993395	+	0.114747i	$0.0366057\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.19615	+	3.00000i	−0.276563	+	0.159674i	−0.631867	−	0.775077i	$-0.717711\pi$
$353$	−5.19615	+	3.00000i	−0.276563	+	0.159674i	0.355303	+	0.934751i	$0.384378\pi$
$354$	12.0000	+	20.7846i	0.637793	+	1.10469i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$			12.0000i			0.635999i
$357$		0			0
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	−1.73205	+	1.00000i	−0.0910346	+	0.0525588i
$363$	22.0000			1.15470
$364$		0			0
$365$	−6.00000			−0.314054
$366$	−17.3205	+	10.0000i	−0.905357	+	0.522708i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$		0			0
$369$		0			0
$370$	5.19615	+	3.00000i	0.270135	+	0.155963i
$371$		0			0
$372$		−	12.0000i		−	0.622171i
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$		0			0
$375$	1.73205	−	1.00000i	0.0894427	−	0.0516398i
$376$	12.0000			0.618853
$377$		0			0
$378$		0			0
$379$	−20.7846	+	12.0000i	−1.06763	+	0.616399i	−0.927534	−	0.373739i	$-0.878076\pi$
$379$	−20.7846	+	12.0000i	−1.06763	+	0.616399i	−0.140100	+	0.990137i	$0.544742\pi$
$380$		0			0
$381$	−16.0000	+	27.7128i	−0.819705	+	1.41977i
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	−1.73205	−	1.00000i	−0.0883883	−	0.0510310i
$385$		0			0
$386$	9.00000	−	15.5885i	0.458088	−	0.793432i
$387$	5.00000	+	8.66025i	0.254164	+	0.440225i
$388$	−15.5885	+	9.00000i	−0.791384	+	0.456906i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$		0			0
$392$	6.06218	−	3.50000i	0.306186	−	0.176777i
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$			8.00000i			0.402524i
$396$		0			0
$397$	25.9808	+	15.0000i	1.30394	+	0.752828i	0.981077	−	0.193618i	$-0.0620223\pi$
$397$	25.9808	+	15.0000i	1.30394	+	0.752828i	0.322860	+	0.946447i	$0.395356\pi$
$398$		−	16.0000i		−	0.802008i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	−0.736512	−	0.676425i	$-0.763528\pi$
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	0.217545	+	0.976050i	$0.430195\pi$
$402$	−24.0000			−1.19701
$403$		0			0
$404$	−6.00000			−0.298511
$405$	9.52628	−	5.50000i	0.473365	−	0.273297i
$406$		0			0
$407$		0			0
$408$		−	12.0000i		−	0.594089i
$409$	−10.3923	−	6.00000i	−0.513866	−	0.296681i	0.220555	−	0.975375i	$-0.429213\pi$
$409$	−10.3923	−	6.00000i	−0.513866	−	0.296681i	−0.734422	+	0.678694i	$0.762546\pi$
$410$		0			0
$411$			36.0000i			1.77575i
$412$	−2.00000	+	3.46410i	−0.0985329	+	0.170664i
$413$		0			0
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$	−8.00000			−0.391762
$418$		0			0
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$		−	30.0000i		−	1.46211i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$		−	30.0000i		−	1.46211i	0.682318	−	0.731055i	$-0.260972\pi$
$422$	3.46410	+	2.00000i	0.168630	+	0.0973585i
$423$	10.3923	+	6.00000i	0.505291	+	0.291730i
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$		0			0
$428$	6.00000			0.290021
$429$		0			0
$430$	10.0000			0.482243
$431$	−25.9808	+	15.0000i	−1.25145	+	0.722525i	−0.971397	−	0.237460i	$-0.923685\pi$
$431$	−25.9808	+	15.0000i	−1.25145	+	0.722525i	−0.280052	+	0.959985i	$0.590352\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	1.00000	−	1.73205i	0.0480569	−	0.0832370i	−0.840996	−	0.541041i	$-0.818030\pi$
$433$	1.00000	−	1.73205i	0.0480569	−	0.0832370i	0.889053	+	0.457804i	$0.151364\pi$
$434$		0			0
$435$	10.3923	+	6.00000i	0.498273	+	0.287678i
$436$	−5.19615	−	3.00000i	−0.248851	−	0.143674i
$437$		0			0
$438$	6.00000	−	10.3923i	0.286691	−	0.496564i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$	−10.3923	+	6.00000i	−0.493197	+	0.284747i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	6.00000	−	10.3923i	0.284108	−	0.492090i
$447$			12.0000i			0.567581i
$448$		0			0
$449$	−10.3923	−	6.00000i	−0.490443	−	0.283158i	0.234315	−	0.972161i	$-0.424715\pi$
$449$	−10.3923	−	6.00000i	−0.490443	−	0.283158i	−0.724758	+	0.689003i	$0.758049\pi$
$450$			1.00000i			0.0471405i
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	31.1769	−	18.0000i	1.46482	−	0.845714i
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$	15.5885	−	9.00000i	0.729197	−	0.421002i	−0.0889312	−	0.996038i	$-0.528345\pi$
$457$	15.5885	−	9.00000i	0.729197	−	0.421002i	0.818128	+	0.575036i	$0.195012\pi$
$458$	3.00000	+	5.19615i	0.140181	+	0.242800i
$459$	−12.0000	+	20.7846i	−0.560112	+	0.970143i
$460$		0			0
$461$	25.9808	+	15.0000i	1.21004	+	0.698620i	0.962769	−	0.270326i	$-0.0871313\pi$
$461$	25.9808	+	15.0000i	1.21004	+	0.698620i	0.247276	+	0.968945i	$0.420465\pi$
$462$		0			0
$463$		−	12.0000i		−	0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$		−	12.0000i		−	0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−6.00000	−	10.3923i	−0.278243	−	0.481932i
$466$	−15.5885	+	9.00000i	−0.722121	+	0.416917i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$		0			0
$470$	10.3923	−	6.00000i	0.479361	−	0.276759i
$471$	4.00000	+	6.92820i	0.184310	+	0.319235i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$		0			0
$474$	−13.8564	−	8.00000i	−0.636446	−	0.367452i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	36.3731	−	21.0000i	1.66193	−	0.959514i	0.690134	−	0.723681i	$-0.257551\pi$
$479$	36.3731	−	21.0000i	1.66193	−	0.959514i	0.971794	−	0.235833i	$-0.0757819\pi$
$480$	−2.00000			−0.0912871
$481$		0			0
$482$	24.0000			1.09317
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−9.00000	+	15.5885i	−0.408669	+	0.707835i
$486$			10.0000i			0.453609i
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.0513038	−	0.998683i	$-0.516338\pi$
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.890537	+	0.454911i	$0.849671\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$		−	24.0000i		−	1.08532i
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$	−36.0000			−1.62136
$494$		0			0
$495$		0			0
$496$	5.19615	−	3.00000i	0.233314	−	0.134704i
$497$		0			0
$498$	−12.0000	+	20.7846i	−0.537733	+	0.931381i
$499$		−	12.0000i		−	0.537194i	−0.963253	−	0.268597i	$-0.913440\pi$
$499$		−	12.0000i		−	0.537194i	0.963253	−	0.268597i	$-0.0865599\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−20.7846	−	12.0000i	−0.928588	−	0.536120i
$502$			24.0000i			1.07117i
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	−0.700696	−	0.713460i	$-0.747127\pi$
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	0.968223	+	0.250090i	$0.0804603\pi$
$504$		0			0
$505$	−5.19615	+	3.00000i	−0.231226	+	0.133498i
$506$		0			0
$507$		0			0
$508$	−16.0000			−0.709885
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	−0.380402	−	0.924821i	$-0.624214\pi$
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	0.610718	+	0.791849i	$0.290881\pi$
$510$	−6.00000	−	10.3923i	−0.265684	−	0.460179i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−25.9808	−	15.0000i	−1.14596	−	0.661622i
$515$			4.00000i			0.176261i
$516$	−10.0000	+	17.3205i	−0.440225	+	0.762493i
$517$		0			0
$518$		0			0
$519$	−48.0000			−2.10697
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$		0			0
$525$		0			0
$526$	20.7846	+	12.0000i	0.906252	+	0.523225i
$527$	31.1769	+	18.0000i	1.35809	+	0.784092i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	−10.3923	+	6.00000i	−0.450988	+	0.260378i
$532$		0			0
$533$		0			0
$534$	−24.0000			−1.03858
$535$	5.19615	−	3.00000i	0.224649	−	0.129701i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$			30.0000i			1.29339i
$539$		0			0
$540$	3.46410	+	2.00000i	0.149071	+	0.0860663i
$541$			18.0000i			0.773880i	0.922105	+	0.386940i	$0.126468\pi$
$541$			18.0000i			0.773880i	−0.922105	+	0.386940i	$0.873532\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$	−2.00000	−	3.46410i	−0.0858282	−	0.148659i
$544$	5.19615	−	3.00000i	0.222783	−	0.128624i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−10.0000			−0.427569			−0.213785	−	0.976881i	$-0.568579\pi$
$547$	−10.0000			−0.427569			−0.213785	+	0.976881i	$0.568579\pi$
$548$	−15.5885	+	9.00000i	−0.665906	+	0.384461i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	8.00000i		−	0.339887i
$555$	−6.00000	+	10.3923i	−0.254686	+	0.441129i
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$557$	15.5885	−	9.00000i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$558$	6.00000			0.254000
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$			24.0000i			1.01058i
$565$	5.19615	+	3.00000i	0.218604	+	0.126211i
$566$	−12.1244	−	7.00000i	−0.509625	−	0.294232i
$567$		0			0
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	16.4545	+	9.50000i	0.684416	+	0.395148i
$579$	31.1769	+	18.0000i	1.29567	+	0.748054i
$580$			6.00000i			0.249136i
$581$		0			0
$582$	−18.0000	−	31.1769i	−0.746124	−	1.29232i
$583$		0			0
$584$	6.00000			0.248282
$585$		0			0
$586$	18.0000			0.743573
$587$	31.1769	−	18.0000i	1.28681	−	0.742940i	0.308725	−	0.951151i	$-0.400098\pi$
$587$	31.1769	−	18.0000i	1.28681	−	0.742940i	0.978084	+	0.208212i	$0.0667643\pi$
$588$	7.00000	+	12.1244i	0.288675	+	0.500000i
$589$		0			0
$590$			12.0000i			0.494032i
$591$	−10.3923	−	6.00000i	−0.427482	−	0.246807i
$592$	−5.19615	−	3.00000i	−0.213561	−	0.123299i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$		0			0
$595$		0			0
$596$	−5.19615	+	3.00000i	−0.212843	+	0.122885i
$597$	32.0000			1.30967
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−1.73205	+	1.00000i	−0.0707107	+	0.0408248i
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$	15.5885	+	9.00000i	0.634285	+	0.366205i
$605$	9.52628	+	5.50000i	0.387298	+	0.223607i
$606$		−	12.0000i		−	0.487467i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$		0			0
$609$		0			0
$610$	−10.0000			−0.404888
$611$		0			0
$612$	6.00000			0.242536
$613$	−5.19615	+	3.00000i	−0.209871	+	0.121169i	−0.601251	−	0.799060i	$-0.705331\pi$
$613$	−5.19615	+	3.00000i	−0.209871	+	0.121169i	0.391381	+	0.920229i	$0.371998\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$		0			0
$616$		0			0
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	0.600935	−	0.799298i	$-0.294795\pi$
$617$	5.19615	+	3.00000i	0.209189	+	0.120775i	−0.391745	+	0.920074i	$0.628129\pi$
$618$	−6.92820	−	4.00000i	−0.278693	−	0.160904i
$619$		−	36.0000i		−	1.44696i	−0.690344	−	0.723481i	$-0.742541\pi$
$619$		−	36.0000i		−	1.44696i	0.690344	−	0.723481i	$-0.257459\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$		0			0
$622$	−20.7846	+	12.0000i	−0.833387	+	0.481156i
$623$		0			0
$624$		0			0
$625$	1.00000			0.0400000
$626$	−8.66025	+	5.00000i	−0.346133	+	0.199840i
$627$		0			0
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$		−	36.0000i		−	1.43541i
$630$		0			0
$631$	5.19615	+	3.00000i	0.206856	+	0.119428i	0.599849	−	0.800113i	$-0.295227\pi$
$631$	5.19615	+	3.00000i	0.206856	+	0.119428i	−0.392994	+	0.919541i	$0.628561\pi$
$632$		−	8.00000i		−	0.318223i
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−13.8564	+	8.00000i	−0.549875	+	0.317470i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$			12.0000i			0.473602i
$643$	−31.1769	−	18.0000i	−1.22950	−	0.709851i	−0.262573	−	0.964912i	$-0.584571\pi$
$643$	−31.1769	−	18.0000i	−1.22950	−	0.709851i	−0.966925	+	0.255062i	$0.917904\pi$
$644$		0			0
$645$			20.0000i			0.787499i
$646$		0			0
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	−9.52628	+	5.50000i	−0.374228	+	0.216060i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	10.3923	−	6.00000i	0.406994	−	0.234978i
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	−0.966910	−	0.255119i	$-0.917885\pi$
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	0.262515	−	0.964928i	$-0.415448\pi$
$654$	6.00000	−	10.3923i	0.234619	−	0.406371i
$655$		0			0
$656$		0			0
$657$	5.19615	+	3.00000i	0.202721	+	0.117041i
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	36.3731	−	21.0000i	1.41475	−	0.816805i	0.418917	−	0.908024i	$-0.362410\pi$
$661$	36.3731	−	21.0000i	1.41475	−	0.816805i	0.995831	+	0.0912190i	$0.0290763\pi$
$662$	−12.0000			−0.466393
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−3.00000	−	5.19615i	−0.116248	−	0.201347i
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$	20.7846	+	12.0000i	0.803579	+	0.463947i
$670$	−10.3923	−	6.00000i	−0.401490	−	0.231800i
$671$		0			0
$672$		0			0
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	0.498886	−	0.866668i	$-0.333743\pi$
$674$	−19.0526	+	11.0000i	−0.733877	+	0.423704i
$675$	4.00000			0.153960
$676$		0			0
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$	−10.3923	+	6.00000i	−0.399114	+	0.230429i
$679$		0			0
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$			24.0000i			0.919682i
$682$		0			0
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$		0			0
$685$	−9.00000	+	15.5885i	−0.343872	+	0.595604i
$686$		0			0
$687$	−10.3923	+	6.00000i	−0.396491	+	0.228914i
$688$	−10.0000			−0.381246
$689$		0			0
$690$		0			0
$691$	31.1769	−	18.0000i	1.18603	−	0.684752i	0.228625	−	0.973515i	$-0.426577\pi$
$691$	31.1769	−	18.0000i	1.18603	−	0.684752i	0.957401	+	0.288762i	$0.0932437\pi$
$692$	−12.0000	−	20.7846i	−0.456172	−	0.790112i
$693$		0			0
$694$			6.00000i			0.227757i
$695$	−3.46410	−	2.00000i	−0.131401	−	0.0758643i
$696$	−10.3923	−	6.00000i	−0.393919	−	0.227429i
$697$		0			0
$698$	−15.0000	+	25.9808i	−0.567758	+	0.983386i
$699$	−18.0000	−	31.1769i	−0.680823	−	1.17922i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	12.0000	+	20.7846i	0.451946	+	0.782794i
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$		0			0
$708$	−20.7846	−	12.0000i	−0.781133	−	0.450988i
$709$	−15.5885	−	9.00000i	−0.585437	−	0.338002i	0.177854	−	0.984057i	$-0.443084\pi$
$709$	−15.5885	−	9.00000i	−0.585437	−	0.338002i	−0.763291	+	0.646055i	$0.776418\pi$
$710$			6.00000i			0.225176i
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	−6.00000	−	10.3923i	−0.224860	−	0.389468i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	31.1769	−	18.0000i	1.16432	−	0.672222i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$		−	1.00000i		−	0.0372678i
$721$		0			0
$722$	16.4545	+	9.50000i	0.612372	+	0.353553i
$723$			48.0000i			1.78514i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−19.0526	+	11.0000i	−0.707107	+	0.408248i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	5.19615	−	3.00000i	0.192318	−	0.111035i
$731$	−30.0000	−	51.9615i	−1.10959	−	1.92187i
$732$	10.0000	−	17.3205i	0.369611	−	0.640184i
$733$		−	18.0000i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$		−	18.0000i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$	−24.2487	−	14.0000i	−0.895036	−	0.516749i
$735$	12.1244	+	7.00000i	0.447214	+	0.258199i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	−6.00000			−0.220564
$741$		0			0
$742$		0			0
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	−0.830197	−	0.557470i	$-0.811772\pi$
$743$	−20.7846	+	12.0000i	−0.762513	+	0.440237i	0.0676840	+	0.997707i	$0.478439\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$		−	4.00000i		−	0.146450i
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$		0			0
$749$		0			0
$750$	−1.00000	+	1.73205i	−0.0365148	+	0.0632456i
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−10.3923	+	6.00000i	−0.378968	+	0.218797i
$753$	−48.0000			−1.74922
$754$		0			0
$755$	18.0000			0.655087
$756$		0			0
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	0.683226	−	0.730207i	$-0.260576\pi$
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	−0.973991	+	0.226587i	$0.927243\pi$
$758$	12.0000	−	20.7846i	0.435860	−	0.754931i
$759$		0			0
$760$		0			0
$761$	−10.3923	−	6.00000i	−0.376721	−	0.217500i	0.299670	−	0.954043i	$-0.403123\pi$
$761$	−10.3923	−	6.00000i	−0.376721	−	0.217500i	−0.676391	+	0.736543i	$0.736457\pi$
$762$		−	32.0000i		−	1.15924i
$763$		0			0
$764$		0			0
$765$	5.19615	−	3.00000i	0.187867	−	0.108465i
$766$		0			0
$767$		0			0
$768$	2.00000			0.0721688
$769$	−41.5692	+	24.0000i	−1.49902	+	0.865462i	−0.999999	−	0.00112544i	$-0.999642\pi$
$769$	−41.5692	+	24.0000i	−1.49902	+	0.865462i	−0.499025	+	0.866588i	$0.666308\pi$
$770$		0			0
$771$	30.0000	−	51.9615i	1.08042	−	1.87135i
$772$			18.0000i			0.647834i
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	0.403634	−	0.914920i	$-0.367747\pi$
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	−0.590527	+	0.807018i	$0.701080\pi$
$774$	−8.66025	−	5.00000i	−0.311286	−	0.179721i
$775$		−	6.00000i		−	0.215526i
$776$	9.00000	−	15.5885i	0.323081	−	0.559593i
$777$		0			0
$778$	−15.5885	+	9.00000i	−0.558873	+	0.322666i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	12.0000	+	20.7846i	0.428845	+	0.742781i
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$			4.00000i			0.142766i
$786$		0			0
$787$	31.1769	+	18.0000i	1.11134	+	0.641631i	0.939175	−	0.343438i	$-0.111592\pi$
$787$	31.1769	+	18.0000i	1.11134	+	0.641631i	0.172162	+	0.985069i	$0.444925\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−24.0000	+	41.5692i	−0.854423	+	1.47990i
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−30.0000			−1.06466
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	24.0000	−	41.5692i	0.850124	−	1.47246i	−0.0309726	−	0.999520i	$-0.509860\pi$
$797$	24.0000	−	41.5692i	0.850124	−	1.47246i	0.881096	−	0.472937i	$-0.156806\pi$
$798$		0			0
$799$	−62.3538	−	36.0000i	−2.20592	−	1.27359i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		−	12.0000i		−	0.423999i
$802$	6.00000	−	10.3923i	0.211867	−	0.366965i
$803$		0			0
$804$	20.7846	−	12.0000i	0.733017	−	0.423207i
$805$		0			0
$806$		0			0
$807$	−60.0000			−2.11210
$808$	5.19615	−	3.00000i	0.182800	−	0.105540i
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$	−5.50000	+	9.52628i	−0.193250	+	0.334719i
$811$		−	24.0000i		−	0.842754i	−0.906886	−	0.421377i	$-0.861547\pi$
$811$		−	24.0000i		−	0.842754i	0.906886	−	0.421377i	$-0.138453\pi$
$812$		0			0
$813$	10.3923	+	6.00000i	0.364474	+	0.210429i
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$	6.00000	+	10.3923i	0.210042	+	0.363803i
$817$		0			0
$818$	12.0000			0.419570
$819$		0			0
$820$		0			0
$821$	15.5885	−	9.00000i	0.544041	−	0.314102i	−0.202674	−	0.979246i	$-0.564963\pi$
$821$	15.5885	−	9.00000i	0.544041	−	0.314102i	0.746715	+	0.665144i	$0.231630\pi$
$822$	−18.0000	−	31.1769i	−0.627822	−	1.08742i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	−10.3923	+	6.00000i	−0.360722	+	0.208263i
$831$	16.0000			0.555034
$832$		0			0
$833$	−42.0000			−1.45521
$834$	6.92820	−	4.00000i	0.239904	−	0.138509i
$835$	−6.00000	−	10.3923i	−0.207639	−	0.359641i
$836$		0			0
$837$		−	24.0000i		−	0.829561i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	−25.9808	−	15.0000i	−0.896956	−	0.517858i	−0.0207443	−	0.999785i	$-0.506604\pi$
$839$	−25.9808	−	15.0000i	−0.896956	−	0.517858i	−0.876211	+	0.481927i	$0.839937\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$	20.7846	−	12.0000i	0.715860	−	0.413302i
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−12.0000			−0.412568
$847$		0			0
$848$		0			0
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$		−	6.00000i		−	0.205798i
$851$		0			0
$852$	−10.3923	−	6.00000i	−0.356034	−	0.205557i
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$		0			0
$855$		0			0
$856$	−5.19615	+	3.00000i	−0.177601	+	0.102538i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	−8.66025	+	5.00000i	−0.295312	+	0.170499i
$861$		0			0
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$			12.0000i			0.408485i	0.978920	+	0.204242i	$0.0654731\pi$
$863$			12.0000i			0.408485i	−0.978920	+	0.204242i	$0.934527\pi$
$864$	−3.46410	−	2.00000i	−0.117851	−	0.0680414i
$865$	−20.7846	−	12.0000i	−0.706698	−	0.408012i
$866$			2.00000i			0.0679628i
$867$	−19.0000	+	32.9090i	−0.645274	+	1.11765i
$868$		0			0
$869$		0			0
$870$	−12.0000			−0.406838
$871$		0			0
$872$	6.00000			0.203186
$873$	15.5885	−	9.00000i	0.527589	−	0.304604i
$874$		0			0
$875$		0			0
$876$			12.0000i			0.405442i
$877$	15.5885	+	9.00000i	0.526385	+	0.303908i	0.739543	−	0.673109i	$-0.235042\pi$
$877$	15.5885	+	9.00000i	0.526385	+	0.303908i	−0.213158	+	0.977018i	$0.568375\pi$
$878$	6.92820	+	4.00000i	0.233816	+	0.134993i
$879$			36.0000i			1.21425i
$880$		0			0
$881$	15.0000	+	25.9808i	0.505363	+	0.875314i	0.999981	+	0.00620358i	$0.00197467\pi$
$881$	15.0000	+	25.9808i	0.505363	+	0.875314i	−0.494618	+	0.869111i	$0.664692\pi$
$882$	−6.06218	+	3.50000i	−0.204124	+	0.117851i
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$	−5.19615	+	3.00000i	−0.174568	+	0.100787i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	6.00000	−	10.3923i	0.201347	−	0.348743i
$889$		0			0
$890$	−10.3923	−	6.00000i	−0.348351	−	0.201120i
$891$		0			0
$892$			12.0000i			0.401790i
$893$		0			0
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	12.0000			0.400445
$899$	31.1769	−	18.0000i	1.03981	−	0.600334i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−5.19615	−	3.00000i	−0.172821	−	0.0997785i
$905$		−	2.00000i		−	0.0664822i
$906$	−18.0000	+	31.1769i	−0.598010	+	1.03578i
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	−10.3923	+	6.00000i	−0.344881	+	0.199117i
$909$	6.00000			0.199007
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$		0			0
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$		−	20.0000i		−	0.661180i
$916$	−5.19615	−	3.00000i	−0.171686	−	0.0991228i
$917$		0			0
$918$		−	24.0000i		−	0.792118i
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	−20.7846	+	12.0000i	−0.684876	+	0.395413i
$922$	−30.0000			−0.987997
$923$		0			0
$924$		0			0
$925$	−5.19615	+	3.00000i	−0.170848	+	0.0986394i
$926$	6.00000	+	10.3923i	0.197172	+	0.341512i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$		−	6.00000i		−	0.196960i
$929$	31.1769	+	18.0000i	1.02288	+	0.590561i	0.914937	−	0.403596i	$-0.132240\pi$
$929$	31.1769	+	18.0000i	1.02288	+	0.590561i	0.107944	+	0.994157i	$0.465573\pi$
$930$	10.3923	+	6.00000i	0.340777	+	0.196748i
$931$		0			0
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$	−24.0000	−	41.5692i	−0.785725	−	1.36092i
$934$	−15.5885	+	9.00000i	−0.510070	+	0.294489i
$935$		0			0
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$	−10.0000	−	17.3205i	−0.326338	−	0.565233i
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$		−	18.0000i		−	0.586783i	−0.955992	−	0.293392i	$-0.905216\pi$
$941$		−	18.0000i		−	0.586783i	0.955992	−	0.293392i	$-0.0947840\pi$
$942$	−6.92820	−	4.00000i	−0.225733	−	0.130327i
$943$		0			0
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$		0			0
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	−0.659256	−	0.751918i	$-0.729129\pi$
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	0.321552	+	0.946892i	$0.395796\pi$
$948$	16.0000			0.519656
$949$		0			0
$950$		0			0
$951$	−31.1769	+	18.0000i	−1.01098	+	0.583690i
$952$		0			0
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	−0.682635	−	0.730759i	$-0.739166\pi$
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	0.974174	+	0.225800i	$0.0724995\pi$
$954$		0			0
$955$		0			0
$956$	15.5885	+	9.00000i	0.504167	+	0.291081i
$957$		0			0
$958$	−21.0000	+	36.3731i	−0.678479	+	1.17516i
$959$		0			0
$960$	1.73205	−	1.00000i	0.0559017	−	0.0322749i
$961$	−5.00000			−0.161290
$962$		0			0
$963$	−6.00000			−0.193347
$964$	−20.7846	+	12.0000i	−0.669427	+	0.386494i
$965$	9.00000	+	15.5885i	0.289720	+	0.501810i
$966$		0			0
$967$		−	12.0000i		−	0.385894i	−0.981209	−	0.192947i	$-0.938195\pi$
$967$		−	12.0000i		−	0.385894i	0.981209	−	0.192947i	$-0.0618045\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$		0			0
$970$		−	18.0000i		−	0.577945i
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$		0			0
$974$	24.0000			0.769010
$975$		0			0
$976$	10.0000			0.320092
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.952183	−	0.305530i	$-0.901167\pi$
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.211495	+	0.977379i	$0.567833\pi$
$978$	12.0000	+	20.7846i	0.383718	+	0.664619i
$979$		0			0
$980$			7.00000i			0.223607i
$981$	5.19615	+	3.00000i	0.165900	+	0.0957826i
$982$	−10.3923	−	6.00000i	−0.331632	−	0.191468i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	31.1769	−	18.0000i	0.992875	−	0.573237i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.840528	−	0.541769i	$-0.817755\pi$
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.0489218	−	0.998803i	$-0.515578\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		−	24.0000i		−	0.761617i
$994$		0			0
$995$	13.8564	+	8.00000i	0.439278	+	0.253617i
$996$		−	24.0000i		−	0.760469i
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	−0.554554	−	0.832148i	$-0.687111\pi$
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	0.997938	+	0.0641836i	$0.0204443\pi$
$998$	6.00000	+	10.3923i	0.189927	+	0.328963i
$999$	−20.7846	+	12.0000i	−0.657596	+	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.b.361.1		4
13.2	odd	12		1690.2.a.d.1.1		1
13.3	even	3		130.2.d.a.51.1	✓	2
13.4	even	6	inner	1690.2.l.b.1161.1		4
13.5	odd	4		1690.2.e.f.991.1		2
13.6	odd	12		1690.2.e.f.191.1		2
13.7	odd	12		1690.2.e.b.191.1		2
13.8	odd	4		1690.2.e.b.991.1		2
13.9	even	3	inner	1690.2.l.b.1161.2		4
13.10	even	6		130.2.d.a.51.2	yes	2
13.11	odd	12		1690.2.a.i.1.1		1
13.12	even	2	inner	1690.2.l.b.361.2		4
39.23	odd	6		1170.2.b.a.181.1		2
39.29	odd	6		1170.2.b.a.181.2		2
52.3	odd	6		1040.2.k.a.961.1		2
52.23	odd	6		1040.2.k.a.961.2		2
65.3	odd	12		650.2.c.b.649.2		2
65.23	odd	12		650.2.c.c.649.2		2
65.24	odd	12		8450.2.a.b.1.1		1
65.29	even	6		650.2.d.a.51.2		2
65.42	odd	12		650.2.c.c.649.1		2
65.49	even	6		650.2.d.a.51.1		2
65.54	odd	12		8450.2.a.o.1.1		1
65.62	odd	12		650.2.c.b.649.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.d.a.51.1	✓	2	13.3	even	3
130.2.d.a.51.2	yes	2	13.10	even	6
650.2.c.b.649.1		2	65.62	odd	12
650.2.c.b.649.2		2	65.3	odd	12
650.2.c.c.649.1		2	65.42	odd	12
650.2.c.c.649.2		2	65.23	odd	12
650.2.d.a.51.1		2	65.49	even	6
650.2.d.a.51.2		2	65.29	even	6
1040.2.k.a.961.1		2	52.3	odd	6
1040.2.k.a.961.2		2	52.23	odd	6
1170.2.b.a.181.1		2	39.23	odd	6
1170.2.b.a.181.2		2	39.29	odd	6
1690.2.a.d.1.1		1	13.2	odd	12
1690.2.a.i.1.1		1	13.11	odd	12
1690.2.e.b.191.1		2	13.7	odd	12
1690.2.e.b.991.1		2	13.8	odd	4
1690.2.e.f.191.1		2	13.6	odd	12
1690.2.e.f.991.1		2	13.5	odd	4
1690.2.l.b.361.1		4	1.1	even	1	trivial
1690.2.l.b.361.2		4	13.12	even	2	inner
1690.2.l.b.1161.1		4	13.4	even	6	inner
1690.2.l.b.1161.2		4	13.9	even	3	inner
8450.2.a.b.1.1		1	65.24	odd	12
8450.2.a.o.1.1		1	65.54	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{6} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} -2.00000 q^{12} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} -1.00000i q^{18} +(-0.866025 - 0.500000i) q^{20} +(1.73205 - 1.00000i) q^{24} -1.00000 q^{25} -4.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{30} +6.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +6.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.19615 - 3.00000i) q^{37} +1.00000 q^{40} +(5.00000 - 8.66025i) q^{43} +(0.866025 + 0.500000i) q^{45} -12.0000i q^{47} +(-1.00000 + 1.73205i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(0.866025 - 0.500000i) q^{50} -12.0000 q^{51} +(3.46410 - 2.00000i) q^{54} +(5.19615 + 3.00000i) q^{58} +(10.3923 + 6.00000i) q^{59} +2.00000i q^{60} +(-5.00000 + 8.66025i) q^{61} +(-3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-10.3923 + 6.00000i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(5.19615 + 3.00000i) q^{71} +(-0.866025 - 0.500000i) q^{72} -6.00000i q^{73} +(-3.00000 + 5.19615i) q^{74} +(1.00000 + 1.73205i) q^{75} -8.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.50000 + 9.52628i) q^{81} +12.0000i q^{83} +(-5.19615 - 3.00000i) q^{85} +10.0000i q^{86} +(-6.00000 + 10.3923i) q^{87} +(-10.3923 + 6.00000i) q^{89} -1.00000 q^{90} +(10.3923 - 6.00000i) q^{93} +(6.00000 + 10.3923i) q^{94} -2.00000i q^{96} +(-15.5885 - 9.00000i) q^{97} +(6.06218 + 3.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} - 8 q^{12} - 2 q^{16} + 12 q^{17} - 4 q^{25} - 16 q^{27} - 12 q^{29} + 4 q^{30} + 2 q^{36} + 4 q^{40} + 20 q^{43} - 4 q^{48} - 14 q^{49} - 48 q^{51} - 20 q^{61}+ \cdots + 24 q^{94}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 - 8 * q^12 - 2 * q^16 + 12 * q^17 - 4 * q^25 - 16 * q^27 - 12 * q^29 + 4 * q^30 + 2 * q^36 + 4 * q^40 + 20 * q^43 - 4 * q^48 - 14 * q^49 - 48 * q^51 - 20 * q^61 - 12 * q^62 - 4 * q^64 - 12 * q^68 - 12 * q^74 + 4 * q^75 - 32 * q^79 + 22 * q^81 - 24 * q^87 - 4 * q^90 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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