LMFDB - Embedded newform 650.2.e.a.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-2,-1,0,-2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	650.451
Dual form			650.2.e.a.601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +2.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +1.00000 q^{18} +(-2.50000 - 4.33013i) q^{19} +2.00000 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.00000 + 1.73205i) q^{24} +(-1.00000 - 3.46410i) q^{26} -4.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.50000 - 9.52628i) q^{37} +5.00000 q^{38} +(-2.00000 - 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +3.00000 q^{47} +(-1.00000 - 1.73205i) q^{48} +(3.00000 - 5.19615i) q^{49} +12.0000 q^{51} +(3.50000 + 0.866025i) q^{52} +9.00000 q^{53} +(2.00000 - 3.46410i) q^{54} +(-0.500000 - 0.866025i) q^{56} +10.0000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(2.00000 - 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(5.50000 + 9.52628i) q^{74} +(-2.50000 + 4.33013i) q^{76} +3.00000 q^{77} +(7.00000 + 1.73205i) q^{78} -16.0000 q^{79} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} -2.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(3.50000 + 0.866025i) q^{91} +(4.00000 - 6.92820i) q^{93} +(-1.50000 + 2.59808i) q^{94} +2.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + 4 q^{12} - 5 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} + 2 q^{18} - 5 q^{19} + 4 q^{21} - 3 q^{22} - 2 q^{24} - 2 q^{26} - 8 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^11 + 4 * q^12 - 5 * q^13 + 2 * q^14 - q^16 - 6 * q^17 + 2 * q^18 - 5 * q^19 + 4 * q^21 - 3 * q^22 - 2 * q^24 - 2 * q^26 - 8 * q^27 - q^28 - 8 * q^31 - q^32 - 6 * q^33 + 12 * q^34 - q^36 + 11 * q^37 + 10 * q^38 - 4 * q^39 - 6 * q^41 - 2 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^47 - 2 * q^48 + 6 * q^49 + 24 * q^51 + 7 * q^52 + 18 * q^53 + 4 * q^54 - q^56 + 20 * q^57 - 8 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 12 * q^66 - 16 * q^67 - 6 * q^68 - 6 * q^71 - q^72 - 28 * q^73 + 11 * q^74 - 5 * q^76 + 6 * q^77 + 14 * q^78 - 32 * q^79 + 11 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 - 4 * q^86 - 3 * q^88 - 9 * q^89 + 7 * q^91 + 8 * q^93 - 3 * q^94 + 4 * q^96 - 10 * q^97 + 6 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.73205i	−0.408248	−	0.707107i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	2.00000			0.577350
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	1.00000			0.235702
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$		0			0
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	−4.00000			−0.769800
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	6.00000			1.02899
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	5.00000			0.811107
$39$	−2.00000	−	6.92820i	−0.320256	−	1.10940i
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$		0			0
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.00000	−	1.73205i	−0.144338	−	0.250000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	12.0000			1.68034
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$		0			0
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	10.0000			1.32453
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.00000			0.738549
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.305424	+	0.952217i	$0.598798\pi$
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	3.00000			0.341882
$78$	7.00000	+	1.73205i	0.792594	+	0.196116i
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$		0			0
$86$	−2.00000			−0.215666
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$		0			0
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	2.00000			0.204124
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	3.00000			0.301511
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$	−5.00000			−0.492665			−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000			−0.492665			−0.246332	+	0.969185i	$0.579225\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	11.0000	+	19.0526i	1.04407	+	1.80839i
$112$	1.00000			0.0944911
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$	−5.00000	+	8.66025i	−0.468293	+	0.811107i
$115$		0			0
$116$		0			0
$117$	3.50000	+	0.866025i	0.323575	+	0.0800641i
$118$		0			0
$119$	−3.00000	+	5.19615i	−0.275010	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	8.00000			0.724286
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−0.500000	+	0.866025i	−0.0443678	+	0.0768473i	0.842989	+	0.537931i	$0.180794\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$	−3.00000	+	5.19615i	−0.261116	+	0.452267i
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	−8.00000	−	13.8564i	−0.691095	−	1.19701i
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$	6.00000			0.503509
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	6.00000	+	10.3923i	0.494872	+	0.857143i
$148$	−11.0000			−0.904194
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$		0			0
$156$	−5.00000	+	5.19615i	−0.400320	+	0.416025i
$157$	−17.0000			−1.35675			−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000			−1.35675			−0.678374	+	0.734717i	$0.737315\pi$
$158$	8.00000	−	13.8564i	0.636446	−	1.10236i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$		0			0
$161$		0			0
$162$	5.50000	+	9.52628i	0.432121	+	0.748455i
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$	2.00000			0.154303
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−2.50000	+	4.33013i	−0.191180	+	0.331133i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−4.50000	−	7.79423i	−0.337289	−	0.584202i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−2.50000	+	2.59808i	−0.185312	+	0.192582i
$183$	16.0000			1.18275
$184$		0			0
$185$		0			0
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	18.0000			1.31629
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−13.5000	+	23.3827i	−0.961835	+	1.66595i	−0.243947	+	0.969788i	$0.578442\pi$
$197$	−13.5000	+	23.3827i	−0.961835	+	1.66595i	−0.717888	+	0.696159i	$0.754891\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$		0			0
$201$	−16.0000	−	27.7128i	−1.12855	−	1.95471i
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$		0			0
$204$	−6.00000	−	10.3923i	−0.420084	−	0.727607i
$205$		0			0
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$		0			0
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	15.0000			1.03757
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	12.0000			0.822226
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$		0			0
$216$	−4.00000			−0.272166
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	14.0000	−	24.2487i	0.946032	−	1.63858i
$220$		0			0
$221$	21.0000	+	5.19615i	1.41261	+	0.349531i
$222$	−22.0000			−1.47654
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	12.0000			0.798228
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	−5.00000	−	8.66025i	−0.331133	−	0.573539i
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$		0			0
$236$		0			0
$237$	16.0000	−	27.7128i	1.03931	−	1.80014i
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	−2.00000			−0.128565
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$		0			0
$246$	12.0000			0.765092
$247$	17.5000	+	4.33013i	1.11350	+	0.275519i
$248$	−4.00000			−0.254000
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	0.999536	−	0.0304521i	$-0.00969471\pi$
$251$	7.50000	+	12.9904i	0.473396	+	0.819946i	−0.526140	+	0.850398i	$0.676361\pi$
$252$	1.00000			0.0629941
$253$		0			0
$254$	−0.500000	−	0.866025i	−0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$	2.00000	−	3.46410i	0.124515	−	0.215666i
$259$	−11.0000			−0.683507
$260$		0			0
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$	−2.50000	−	4.33013i	−0.153285	−	0.265497i
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$	16.0000			0.977356
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	6.00000			0.363803
$273$	−5.00000	+	5.19615i	−0.302614	+	0.314485i
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$	−19.0000			−1.13954
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	10.5000	+	2.59808i	0.620878	+	0.153627i
$287$	6.00000			0.354169
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	20.0000			1.17242
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$	−12.0000			−0.699854
$295$		0			0
$296$	5.50000	−	9.52628i	0.319681	−	0.553704i
$297$	6.00000	−	10.3923i	0.348155	−	0.603023i
$298$	−18.0000			−1.04271
$299$		0			0
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	8.00000	−	13.8564i	0.460348	−	0.797347i
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$	5.00000			0.286770
$305$		0			0
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	−1.50000	−	2.59808i	−0.0854704	−	0.148039i
$309$	5.00000	−	8.66025i	0.284440	−	0.492665i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$	−2.00000	−	6.92820i	−0.113228	−	0.392232i
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	8.50000	−	14.7224i	0.479683	−	0.830835i
$315$		0			0
$316$	8.00000	+	13.8564i	0.450035	+	0.779484i
$317$	−15.0000			−0.842484			−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000			−0.842484			−0.421242	+	0.906948i	$0.638406\pi$
$318$	−9.00000	−	15.5885i	−0.504695	−	0.874157i
$319$		0			0
$320$		0			0
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$		0			0
$323$	−15.0000	+	25.9808i	−0.834622	+	1.44561i
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−2.00000			−0.110770
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	−11.0000			−0.602796
$334$	−7.50000	−	12.9904i	−0.410382	−	0.710802i
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	16.0000			0.871576			0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000			0.871576			0.435788	+	0.900049i	$0.356470\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	24.0000			1.30350
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−2.50000	−	4.33013i	−0.135185	−	0.234146i
$343$	−13.0000			−0.701934
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$		0			0
$346$	−15.0000			−0.806405
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	3.00000	+	5.19615i	0.161048	+	0.278944i	−0.774197	+	0.632945i	$0.781846\pi$
$348$		0			0
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$		0			0
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$	3.00000			0.159901
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$		0			0
$356$	9.00000			0.476999
$357$	−6.00000	−	10.3923i	−0.317554	−	0.550019i
$358$	12.0000	+	20.7846i	0.634220	+	1.09850i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−4.00000	+	6.92820i	−0.210235	+	0.364138i
$363$	−4.00000			−0.209946
$364$	−1.00000	−	3.46410i	−0.0524142	−	0.181568i
$365$		0			0
$366$	−8.00000	+	13.8564i	−0.418167	+	0.724286i
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	−4.50000	−	7.79423i	−0.233628	−	0.404656i
$372$	−8.00000			−0.414781
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486083\pi$
$373$	7.00000	+	12.1244i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$		0			0
$376$	3.00000			0.154713
$377$		0			0
$378$	−4.00000			−0.205738
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	−0.511922	−	0.859032i	$-0.671066\pi$
$379$	9.50000	−	16.4545i	0.487982	−	0.845210i	0.999904	+	0.0138218i	$0.00439975\pi$
$380$		0			0
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	−1.00000	−	1.73205i	−0.0510310	−	0.0883883i
$385$		0			0
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$		0			0
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	9.00000	−	15.5885i	0.453990	−	0.786334i
$394$	−13.5000	−	23.3827i	−0.680120	−	1.17800i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$	−10.0000			−0.501255
$399$	−5.00000	−	8.66025i	−0.250313	−	0.433555i
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	32.0000			1.59601
$403$	10.0000	−	10.3923i	0.498135	−	0.517678i
$404$	−6.00000			−0.298511
$405$		0			0
$406$		0			0
$407$	16.5000	+	28.5788i	0.817875	+	1.41660i
$408$	12.0000			0.594089
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$	−38.0000			−1.86087
$418$	−7.50000	+	12.9904i	−0.366837	+	0.635380i
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−11.5000	−	19.9186i	−0.559811	−	0.969622i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	9.00000			0.437079
$425$		0			0
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	12.0000			0.580042
$429$	21.0000	+	5.19615i	1.01389	+	0.250873i
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	0.607238	−	0.794520i	$-0.292277\pi$
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	−0.991693	+	0.128624i	$0.958944\pi$
$434$	−4.00000			−0.192006
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$		0			0
$438$	14.0000	+	24.2487i	0.668946	+	1.15865i
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−15.0000	+	15.5885i	−0.713477	+	0.741467i
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$	11.0000	−	19.0526i	0.522037	−	0.904194i
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	−36.0000			−1.70274
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	0.740087	−	0.672511i	$-0.234784\pi$
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	−0.952455	+	0.304679i	$0.901451\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	16.0000	−	27.7128i	0.751746	−	1.30206i
$454$	24.0000			1.12638
$455$		0			0
$456$	10.0000			0.468293
$457$	−2.00000	+	3.46410i	−0.0935561	+	0.162044i	−0.909005	−	0.416785i	$-0.863157\pi$
$457$	−2.00000	+	3.46410i	−0.0935561	+	0.162044i	0.815449	+	0.578829i	$0.196490\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$		0			0
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.669417	+	0.742887i	$0.266544\pi$
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.308651	+	0.951175i	$0.400123\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$	−1.00000	−	3.46410i	−0.0462250	−	0.160128i
$469$	16.0000			0.738811
$470$		0			0
$471$	17.0000	−	29.4449i	0.783319	−	1.35675i
$472$		0			0
$473$	−6.00000			−0.275880
$474$	16.0000	+	27.7128i	0.734904	+	1.27289i
$475$		0			0
$476$	6.00000			0.275010
$477$	−4.50000	−	7.79423i	−0.206041	−	0.356873i
$478$		0			0
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	−0.287954	−	0.957644i	$-0.592975\pi$
$479$	15.0000	−	25.9808i	0.685367	−	1.18709i	0.973321	−	0.229447i	$-0.0736918\pi$
$480$		0			0
$481$	11.0000	+	38.1051i	0.501557	+	1.73744i
$482$	23.0000			1.04762
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	−10.0000			−0.453609
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	0.566429	−	0.824110i	$-0.308325\pi$
$487$	−9.50000	−	16.4545i	−0.430486	−	0.745624i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$		0			0
$494$	−12.5000	+	12.9904i	−0.562402	+	0.584465i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$	−6.00000	−	10.3923i	−0.268866	−	0.465690i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	−15.0000	−	25.9808i	−0.670151	−	1.16073i
$502$	−15.0000			−0.669483
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	0.948736	−	0.316068i	$-0.102363\pi$
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	−0.748091	+	0.663596i	$0.769030\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$		0			0
$506$		0			0
$507$	23.0000	+	12.1244i	1.02147	+	0.538462i
$508$	1.00000			0.0443678
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	7.00000	+	12.1244i	0.309662	+	0.536350i
$512$	1.00000			0.0441942
$513$	10.0000	+	17.3205i	0.441511	+	0.764719i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$		0			0
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	5.50000	−	9.52628i	0.241656	−	0.418561i
$519$	−30.0000			−1.31685
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	−0.671414	−	0.741082i	$-0.734313\pi$
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	0.977503	+	0.210921i	$0.0676463\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		0			0
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	6.00000			0.261116
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	5.00000			0.216777
$533$	−6.00000	−	20.7846i	−0.259889	−	0.900281i
$534$	18.0000			0.778936
$535$		0			0
$536$	−8.00000	+	13.8564i	−0.345547	+	0.598506i
$537$	24.0000	+	41.5692i	1.03568	+	1.79384i
$538$	6.00000			0.258678
$539$	9.00000	+	15.5885i	0.387657	+	0.671442i
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$		0			0
$546$	−2.00000	−	6.92820i	−0.0855921	−	0.296500i
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	8.00000	+	13.8564i	0.340195	+	0.589234i
$554$	1.00000			0.0424859
$555$		0			0
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	10.5000	−	18.1865i	0.444899	−	0.770588i	−0.553146	−	0.833084i	$-0.686573\pi$
$557$	10.5000	−	18.1865i	0.444899	−	0.770588i	0.998045	+	0.0624962i	$0.0199061\pi$
$558$	−4.00000			−0.169334
$559$	−7.00000	−	1.73205i	−0.296068	−	0.0732579i
$560$		0			0
$561$	−18.0000	+	31.1769i	−0.759961	+	1.31629i
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$	6.00000			0.252646
$565$		0			0
$566$	7.00000	+	12.1244i	0.294232	+	0.509625i
$567$	−11.0000			−0.461957
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	−0.944800	−	0.327647i	$-0.893744\pi$
$569$	−4.50000	+	7.79423i	−0.188650	+	0.326751i	0.756151	+	0.654398i	$0.227078\pi$
$570$		0			0
$571$	17.0000			0.711428			0.355714	−	0.934595i	$-0.384238\pi$
$571$	17.0000			0.711428			0.355714	+	0.934595i	$0.384238\pi$
$572$	−7.50000	+	7.79423i	−0.313591	+	0.325893i
$573$		0			0
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	−4.00000	−	6.92820i	−0.166234	−	0.287926i
$580$		0			0
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$	−10.0000	+	17.3205i	−0.414513	+	0.717958i
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	−14.0000			−0.579324
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	−0.921272	−	0.388918i	$-0.872849\pi$
$587$	−3.00000	+	5.19615i	−0.123823	+	0.214468i	0.797449	+	0.603386i	$0.206182\pi$
$588$	6.00000	−	10.3923i	0.247436	−	0.428571i
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	−27.0000	−	46.7654i	−1.11063	−	1.92367i
$592$	5.50000	+	9.52628i	0.226049	+	0.391528i
$593$	−24.0000			−0.985562			−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000			−0.985562			−0.492781	+	0.870153i	$0.664020\pi$
$594$	6.00000	+	10.3923i	0.246183	+	0.426401i
$595$		0			0
$596$	9.00000	−	15.5885i	0.368654	−	0.638528i
$597$	−20.0000			−0.818546
$598$		0			0
$599$	−18.0000			−0.735460			−0.367730	−	0.929933i	$-0.619865\pi$
$599$	−18.0000			−0.735460			−0.367730	+	0.929933i	$0.619865\pi$
$600$		0			0
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$	1.00000	+	1.73205i	0.0407570	+	0.0705931i
$603$	16.0000			0.651570
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$		0			0
$606$	−12.0000			−0.487467
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$		0			0
$611$	−7.50000	+	7.79423i	−0.303418	+	0.315321i
$612$	6.00000			0.242536
$613$	−6.50000	+	11.2583i	−0.262533	+	0.454720i	−0.966914	−	0.255102i	$-0.917891\pi$
$613$	−6.50000	+	11.2583i	−0.262533	+	0.454720i	0.704382	+	0.709821i	$0.251224\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	3.00000			0.120873
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$	5.00000	+	8.66025i	0.201129	+	0.348367i
$619$	−1.00000			−0.0401934			−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000			−0.0401934			−0.0200967	+	0.999798i	$0.506397\pi$
$620$		0			0
$621$		0			0
$622$	−15.0000	+	25.9808i	−0.601445	+	1.04173i
$623$	9.00000			0.360577
$624$	7.00000	+	1.73205i	0.280224	+	0.0693375i
$625$		0			0
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$	−15.0000	+	25.9808i	−0.599042	+	1.03757i
$628$	8.50000	+	14.7224i	0.339187	+	0.587489i
$629$	−66.0000			−2.63159
$630$		0			0
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	0.997718	+	0.0675178i	$0.0215080\pi$
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	−0.440387	+	0.897808i	$0.645159\pi$
$632$	−16.0000			−0.636446
$633$	−23.0000	−	39.8372i	−0.914168	−	1.58339i
$634$	7.50000	−	12.9904i	0.297863	−	0.515914i
$635$		0			0
$636$	18.0000			0.713746
$637$	6.00000	+	20.7846i	0.237729	+	0.823516i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	24.0000			0.947204
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	0.885070	−	0.465458i	$-0.154110\pi$
$643$	1.00000	+	1.73205i	0.0394362	+	0.0683054i	−0.845634	+	0.533764i	$0.820777\pi$
$644$		0			0
$645$		0			0
$646$	−15.0000	−	25.9808i	−0.590167	−	1.02220i
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	1.00000	−	1.73205i	0.0391630	−	0.0678323i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−2.00000	−	3.46410i	−0.0782062	−	0.135457i
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	7.00000	+	12.1244i	0.273096	+	0.473016i
$658$	3.00000			0.116952
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	−0.824506	−	0.565854i	$-0.808547\pi$
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	0.902297	+	0.431116i	$0.141880\pi$
$662$	20.0000			0.777322
$663$	−30.0000	+	31.1769i	−1.16510	+	1.21081i
$664$	6.00000			0.232845
$665$		0			0
$666$	5.50000	−	9.52628i	0.213121	−	0.369136i
$667$		0			0
$668$	15.0000			0.580367
$669$	−19.0000	−	32.9090i	−0.734582	−	1.27233i
$670$		0			0
$671$	24.0000			0.926510
$672$	−1.00000	−	1.73205i	−0.0385758	−	0.0668153i
$673$	10.0000	−	17.3205i	0.385472	−	0.667657i	−0.606363	−	0.795188i	$-0.707372\pi$
$673$	10.0000	−	17.3205i	0.385472	−	0.667657i	0.991835	+	0.127532i	$0.0407054\pi$
$674$	−8.00000	+	13.8564i	−0.308148	+	0.533729i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−12.0000	+	20.7846i	−0.460857	+	0.798228i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$		0			0
$681$	48.0000			1.83936
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	0.802905	−	0.596107i	$-0.203287\pi$
$683$	−3.00000	−	5.19615i	−0.114792	−	0.198825i	−0.917697	+	0.397282i	$0.869953\pi$
$684$	5.00000			0.191180
$685$		0			0
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	4.00000	−	6.92820i	0.152610	−	0.264327i
$688$	−2.00000			−0.0762493
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$	6.50000	−	11.2583i	0.247272	−	0.428287i	−0.715496	−	0.698617i	$-0.753799\pi$
$691$	6.50000	−	11.2583i	0.247272	−	0.428287i	0.962768	+	0.270330i	$0.0871327\pi$
$692$	7.50000	−	12.9904i	0.285107	−	0.493820i
$693$	−1.50000	−	2.59808i	−0.0569803	−	0.0986928i
$694$	−6.00000			−0.227757
$695$		0			0
$696$		0			0
$697$	36.0000			1.36360
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$	−24.0000	+	41.5692i	−0.907763	+	1.57229i
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	4.00000	+	13.8564i	0.150970	+	0.522976i
$703$	−55.0000			−2.07436
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	−4.50000	+	7.79423i	−0.168645	+	0.292101i
$713$		0			0
$714$	12.0000			0.449089
$715$		0			0
$716$	−24.0000			−0.896922
$717$		0			0
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	2.50000	+	4.33013i	0.0931049	+	0.161262i
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$	46.0000			1.71076
$724$	−4.00000	−	6.92820i	−0.148659	−	0.257485i
$725$		0			0
$726$	2.00000	−	3.46410i	0.0742270	−	0.128565i
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$	3.50000	+	0.866025i	0.129719	+	0.0320970i
$729$	13.0000			0.481481
$730$		0			0
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$	−8.00000	−	13.8564i	−0.295689	−	0.512148i
$733$	25.0000			0.923396			0.461698	−	0.887037i	$-0.347240\pi$
$733$	25.0000			0.923396			0.461698	+	0.887037i	$0.347240\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$		0			0
$737$	−24.0000	−	41.5692i	−0.884051	−	1.53122i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	−0.794443	−	0.607339i	$-0.792237\pi$
$739$	3.50000	−	6.06218i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$740$		0			0
$741$	−25.0000	+	25.9808i	−0.918398	+	0.954427i
$742$	9.00000			0.330400
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	−0.734725	−	0.678365i	$-0.762689\pi$
$743$	6.00000	−	10.3923i	0.220119	−	0.381257i	0.954844	+	0.297108i	$0.0960222\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$		0			0
$746$	−14.0000			−0.512576
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−9.00000	−	15.5885i	−0.329073	−	0.569970i
$749$	12.0000			0.438470
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	−30.0000			−1.09326
$754$		0			0
$755$		0			0
$756$	2.00000	−	3.46410i	0.0727393	−	0.125988i
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	−0.577761	−	0.816206i	$-0.696073\pi$
$757$	11.5000	−	19.9186i	0.417975	−	0.723953i	0.995736	+	0.0922527i	$0.0294068\pi$
$758$	9.50000	+	16.4545i	0.345056	+	0.597654i
$759$		0			0
$760$		0			0
$761$	1.50000	+	2.59808i	0.0543750	+	0.0941802i	0.891932	−	0.452170i	$-0.149350\pi$
$761$	1.50000	+	2.59808i	0.0543750	+	0.0941802i	−0.837557	+	0.546350i	$0.816017\pi$
$762$	2.00000			0.0724524
$763$	−1.00000	−	1.73205i	−0.0362024	−	0.0627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	2.00000			0.0721688
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$		0			0
$771$	12.0000	+	20.7846i	0.432169	+	0.748539i
$772$	4.00000			0.143963
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$		0			0
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$	11.0000	−	19.0526i	0.394623	−	0.683507i
$778$	15.0000	−	25.9808i	0.537776	−	0.931455i
$779$	30.0000			1.07486
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$		0			0
$786$	9.00000	+	15.5885i	0.321019	+	0.556022i
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	0.600620	−	0.799535i	$-0.294921\pi$
$787$	−11.0000	−	19.0526i	−0.392108	−	0.679150i	−0.992727	+	0.120384i	$0.961587\pi$
$788$	27.0000			0.961835
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$		0			0
$791$	−6.00000	+	10.3923i	−0.213335	+	0.369508i
$792$	3.00000			0.106600
$793$	28.0000	+	6.92820i	0.994309	+	0.246028i
$794$	13.0000			0.461353
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	0.950726	+	0.310031i	$0.100340\pi$
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	−0.206868	+	0.978369i	$0.566327\pi$
$798$	10.0000			0.353996
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$		0			0
$801$	9.00000			0.317999
$802$	7.50000	+	12.9904i	0.264834	+	0.458706i
$803$	21.0000	−	36.3731i	0.741074	−	1.28358i
$804$	−16.0000	+	27.7128i	−0.564276	+	0.977356i
$805$		0			0
$806$	4.00000	+	13.8564i	0.140894	+	0.488071i
$807$	12.0000			0.422420
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	−0.663316	−	0.748340i	$-0.730851\pi$
$809$	9.00000	−	15.5885i	0.316423	−	0.548061i	0.979739	+	0.200279i	$0.0641847\pi$
$810$		0			0
$811$	−49.0000			−1.72062			−0.860311	−	0.509769i	$-0.829731\pi$
$811$	−49.0000			−1.72062			−0.860311	+	0.509769i	$0.829731\pi$
$812$		0			0
$813$	−20.0000	−	34.6410i	−0.701431	−	1.21491i
$814$	−33.0000			−1.15665
$815$		0			0
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	5.00000			0.174821
$819$	−1.00000	−	3.46410i	−0.0349428	−	0.121046i
$820$		0			0
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	0.359708	+	0.933065i	$0.382876\pi$
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	−0.987912	+	0.155017i	$0.950457\pi$
$822$	6.00000	−	10.3923i	0.209274	−	0.362473i
$823$	−21.5000	−	37.2391i	−0.749443	−	1.29807i	−0.948090	−	0.318002i	$-0.896988\pi$
$823$	−21.5000	−	37.2391i	−0.749443	−	1.29807i	0.198647	−	0.980071i	$-0.436345\pi$
$824$	−5.00000			−0.174183
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	−0.275677	−	0.961250i	$-0.588902\pi$
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	0.970306	−	0.241882i	$-0.0777647\pi$
$830$		0			0
$831$	2.00000			0.0693792
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$	−36.0000			−1.24733
$834$	19.0000	−	32.9090i	0.657916	−	1.13954i
$835$		0			0
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$	16.0000			0.553041
$838$	18.0000	+	31.1769i	0.621800	+	1.07699i
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$	6.00000	−	10.3923i	0.206651	−	0.357930i
$844$	23.0000			0.791693
$845$		0			0
$846$	3.00000			0.103142
$847$	1.00000	−	1.73205i	0.0343604	−	0.0595140i
$848$	−4.50000	+	7.79423i	−0.154531	+	0.267655i
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$		0			0
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$	−4.00000	−	6.92820i	−0.136877	−	0.237078i
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	12.0000			0.409912			0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000			0.409912			0.204956	+	0.978771i	$0.434295\pi$
$858$	−15.0000	+	15.5885i	−0.512092	+	0.532181i
$859$	−31.0000			−1.05771			−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000			−1.05771			−0.528853	+	0.848713i	$0.677378\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$		0			0
$866$	16.0000			0.543702
$867$	−19.0000	−	32.9090i	−0.645274	−	1.11765i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	24.0000	−	41.5692i	0.814144	−	1.41014i
$870$		0			0
$871$	−16.0000	−	55.4256i	−0.542139	−	1.87803i
$872$	2.00000			0.0677285
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$		0			0
$876$	−28.0000			−0.946032
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$	−10.0000	−	17.3205i	−0.337484	−	0.584539i
$879$	−18.0000			−0.607125
$880$		0			0
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$	3.00000	−	5.19615i	0.101015	−	0.174964i
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$	−6.00000	−	20.7846i	−0.201802	−	0.699062i
$885$		0			0
$886$	−9.00000	+	15.5885i	−0.302361	+	0.523704i
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	−0.998588	−	0.0531258i	$-0.983082\pi$
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	0.545302	+	0.838240i	$0.316415\pi$
$888$	11.0000	+	19.0526i	0.369136	+	0.639362i
$889$	1.00000			0.0335389
$890$		0			0
$891$	16.5000	+	28.5788i	0.552771	+	0.957427i
$892$	19.0000			0.636167
$893$	−7.50000	−	12.9904i	−0.250978	−	0.434707i
$894$	18.0000	−	31.1769i	0.602010	−	1.04271i
$895$		0			0
$896$	1.00000			0.0334077
$897$		0			0
$898$	9.00000			0.300334
$899$		0			0
$900$		0			0
$901$	−27.0000	−	46.7654i	−0.899500	−	1.55798i
$902$	18.0000			0.599334
$903$	2.00000	+	3.46410i	0.0665558	+	0.115278i
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$		0			0
$906$	16.0000	+	27.7128i	0.531564	+	0.920697i
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	−6.00000			−0.199007
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−5.00000	+	8.66025i	−0.165567	+	0.286770i
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	−2.00000	−	3.46410i	−0.0661541	−	0.114582i
$915$		0			0
$916$	2.00000	+	3.46410i	0.0660819	+	0.114457i
$917$	4.50000	+	7.79423i	0.148603	+	0.257388i
$918$	−24.0000			−0.792118
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$	−42.0000			−1.38320
$923$	21.0000	+	5.19615i	0.691223	+	0.171033i
$924$	6.00000			0.197386
$925$		0			0
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	2.50000	+	4.33013i	0.0821108	+	0.142220i
$928$		0			0
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$929$	−21.0000	−	36.3731i	−0.688988	−	1.19336i	0.283178	−	0.959067i	$-0.408611\pi$
$930$		0			0
$931$	−30.0000			−0.983210
$932$	−12.0000	−	20.7846i	−0.393073	−	0.680823i
$933$	−30.0000	+	51.9615i	−0.982156	+	1.70114i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$	3.50000	+	0.866025i	0.114401	+	0.0283069i
$937$	−50.0000			−1.63343			−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000			−1.63343			−0.816714	+	0.577042i	$0.804207\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$	14.0000	−	24.2487i	0.456873	−	0.791327i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	17.0000	+	29.4449i	0.553890	+	0.959366i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	−0.152106	−	0.988364i	$-0.548606\pi$
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	0.932002	−	0.362454i	$-0.118061\pi$
$948$	−32.0000			−1.03931
$949$	35.0000	−	36.3731i	1.13615	−	1.18072i
$950$		0			0
$951$	15.0000	−	25.9808i	0.486408	−	0.842484i
$952$	−3.00000	+	5.19615i	−0.0972306	+	0.168408i
$953$	12.0000	+	20.7846i	0.388718	+	0.673280i	0.992277	−	0.124039i	$-0.0395847\pi$
$953$	12.0000	+	20.7846i	0.388718	+	0.673280i	−0.603559	+	0.797318i	$0.706251\pi$
$954$	9.00000			0.291386
$955$		0			0
$956$		0			0
$957$		0			0
$958$	15.0000	+	25.9808i	0.484628	+	0.839400i
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−38.5000	−	9.52628i	−1.24129	−	0.307140i
$963$	12.0000			0.386695
$964$	−11.5000	+	19.9186i	−0.370390	+	0.641534i
$965$		0			0
$966$		0			0
$967$	−5.00000			−0.160789			−0.0803946	−	0.996763i	$-0.525618\pi$
$967$	−5.00000			−0.160789			−0.0803946	+	0.996763i	$0.525618\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−30.0000	−	51.9615i	−0.963739	−	1.66924i
$970$		0			0
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$	9.50000	−	16.4545i	0.304556	−	0.527506i
$974$	19.0000			0.608799
$975$		0			0
$976$	8.00000			0.256074
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$		0			0
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	−39.0000			−1.24391			−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000			−1.24391			−0.621953	+	0.783054i	$0.713661\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$		0			0
$986$		0			0
$987$	6.00000			0.190982
$988$	−5.00000	−	17.3205i	−0.159071	−	0.551039i
$989$		0			0
$990$		0			0
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	−0.636721	−	0.771094i	$-0.719710\pi$
$991$	11.0000	−	19.0526i	0.349427	−	0.605224i	0.986148	+	0.165870i	$0.0530431\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	40.0000			1.26936
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$	12.0000			0.380235
$997$	20.5000	+	35.5070i	0.649242	+	1.12452i	0.983304	+	0.181968i	$0.0582469\pi$
$997$	20.5000	+	35.5070i	0.649242	+	1.12452i	−0.334063	+	0.942551i	$0.608420\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$	−22.0000	+	38.1051i	−0.696049	+	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.a.451.1		2
5.2	odd	4		650.2.o.b.399.1		4
5.3	odd	4		650.2.o.b.399.2		4
5.4	even	2		130.2.e.b.61.1	✓	2
13.3	even	3	inner	650.2.e.a.601.1		2
13.4	even	6		8450.2.a.k.1.1		1
13.9	even	3		8450.2.a.w.1.1		1
15.14	odd	2		1170.2.i.f.451.1		2
20.19	odd	2		1040.2.q.c.321.1		2
65.3	odd	12		650.2.o.b.549.1		4
65.4	even	6		1690.2.a.g.1.1		1
65.9	even	6		1690.2.a.a.1.1		1
65.19	odd	12		1690.2.d.a.1351.2		2
65.24	odd	12		1690.2.l.i.361.1		4
65.29	even	6		130.2.e.b.81.1	yes	2
65.34	odd	4		1690.2.l.i.1161.2		4
65.42	odd	12		650.2.o.b.549.2		4
65.44	odd	4		1690.2.l.i.1161.1		4
65.49	even	6		1690.2.e.e.991.1		2
65.54	odd	12		1690.2.l.i.361.2		4
65.59	odd	12		1690.2.d.a.1351.1		2
65.64	even	2		1690.2.e.e.191.1		2
195.29	odd	6		1170.2.i.f.991.1		2
260.159	odd	6		1040.2.q.c.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.b.61.1	✓	2	5.4	even	2
130.2.e.b.81.1	yes	2	65.29	even	6
650.2.e.a.451.1		2	1.1	even	1	trivial
650.2.e.a.601.1		2	13.3	even	3	inner
650.2.o.b.399.1		4	5.2	odd	4
650.2.o.b.399.2		4	5.3	odd	4
650.2.o.b.549.1		4	65.3	odd	12
650.2.o.b.549.2		4	65.42	odd	12
1040.2.q.c.81.1		2	260.159	odd	6
1040.2.q.c.321.1		2	20.19	odd	2
1170.2.i.f.451.1		2	15.14	odd	2
1170.2.i.f.991.1		2	195.29	odd	6
1690.2.a.a.1.1		1	65.9	even	6
1690.2.a.g.1.1		1	65.4	even	6
1690.2.d.a.1351.1		2	65.59	odd	12
1690.2.d.a.1351.2		2	65.19	odd	12
1690.2.e.e.191.1		2	65.64	even	2
1690.2.e.e.991.1		2	65.49	even	6
1690.2.l.i.361.1		4	65.24	odd	12
1690.2.l.i.361.2		4	65.54	odd	12
1690.2.l.i.1161.1		4	65.44	odd	4
1690.2.l.i.1161.2		4	65.34	odd	4
8450.2.a.k.1.1		1	13.4	even	6
8450.2.a.w.1.1		1	13.9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +2.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +1.00000 q^{18} +(-2.50000 - 4.33013i) q^{19} +2.00000 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-1.00000 + 1.73205i) q^{24} +(-1.00000 - 3.46410i) q^{26} -4.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.50000 - 9.52628i) q^{37} +5.00000 q^{38} +(-2.00000 - 6.92820i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +3.00000 q^{47} +(-1.00000 - 1.73205i) q^{48} +(3.00000 - 5.19615i) q^{49} +12.0000 q^{51} +(3.50000 + 0.866025i) q^{52} +9.00000 q^{53} +(2.00000 - 3.46410i) q^{54} +(-0.500000 - 0.866025i) q^{56} +10.0000 q^{57} +(-4.00000 - 6.92820i) q^{61} +(2.00000 - 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(5.50000 + 9.52628i) q^{74} +(-2.50000 + 4.33013i) q^{76} +3.00000 q^{77} +(7.00000 + 1.73205i) q^{78} -16.0000 q^{79} +(5.50000 - 9.52628i) q^{81} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} -2.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(3.50000 + 0.866025i) q^{91} +(4.00000 - 6.92820i) q^{93} +(-1.50000 + 2.59808i) q^{94} +2.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + 4 q^{12} - 5 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} + 2 q^{18} - 5 q^{19} + 4 q^{21} - 3 q^{22} - 2 q^{24} - 2 q^{26} - 8 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 2 * q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^11 + 4 * q^12 - 5 * q^13 + 2 * q^14 - q^16 - 6 * q^17 + 2 * q^18 - 5 * q^19 + 4 * q^21 - 3 * q^22 - 2 * q^24 - 2 * q^26 - 8 * q^27 - q^28 - 8 * q^31 - q^32 - 6 * q^33 + 12 * q^34 - q^36 + 11 * q^37 + 10 * q^38 - 4 * q^39 - 6 * q^41 - 2 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^47 - 2 * q^48 + 6 * q^49 + 24 * q^51 + 7 * q^52 + 18 * q^53 + 4 * q^54 - q^56 + 20 * q^57 - 8 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 12 * q^66 - 16 * q^67 - 6 * q^68 - 6 * q^71 - q^72 - 28 * q^73 + 11 * q^74 - 5 * q^76 + 6 * q^77 + 14 * q^78 - 32 * q^79 + 11 * q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 - 4 * q^86 - 3 * q^88 - 9 * q^89 + 7 * q^91 + 8 * q^93 - 3 * q^94 + 4 * q^96 - 10 * q^97 + 6 * q^98 + 6 * q^99

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