LMFDB - Embedded newform 650.2.o.b.549.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(399,650)] 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([3, 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("650.399"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,-4,0,0,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
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			549.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.549
Dual form			650.2.o.b.399.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.0917517	−	0.995782i	$-0.470753\pi$
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.908248	+	0.418432i	$0.137420\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	2.00000i		−	0.577350i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.973123	−	0.230285i	$-0.0739659\pi$
$17$	5.19615	+	3.00000i	1.26025	+	0.727607i	0.287129	+	0.957892i	$0.407299\pi$
$18$			1.00000i			0.235702i
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	2.59808	+	1.50000i	0.553912	+	0.319801i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$		0			0
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$			4.00000i			0.769800i
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.52628	−	5.50000i	1.56611	−	0.904194i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	9.52628	−	5.50000i	1.56611	−	0.904194i	0.996616	−	0.0821995i	$-0.0261945\pi$
$38$			5.00000i			0.811107i
$39$	2.00000	−	6.92820i	0.320256	−	1.10940i
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	−1.73205	+	1.00000i	−0.267261	+	0.154303i
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$		0			0
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	−1.73205	−	1.00000i	−0.250000	−	0.144338i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$		0			0
$51$	12.0000			1.68034
$52$	−0.866025	−	3.50000i	−0.120096	−	0.485363i
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$		0			0
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		−	10.0000i		−	1.32453i
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	3.46410	−	2.00000i	0.439941	−	0.254000i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.00000			0.738549
$67$	−13.8564	+	8.00000i	−1.69283	+	0.977356i	−0.740613	+	0.671932i	$0.765465\pi$
$67$	−13.8564	+	8.00000i	−1.69283	+	0.977356i	−0.952217	+	0.305424i	$0.901202\pi$
$68$	5.19615	−	3.00000i	0.630126	−	0.363803i
$69$		0			0
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$		−	3.00000i		−	0.341882i
$78$	1.73205	+	7.00000i	0.196116	+	0.792594i
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	5.19615	+	3.00000i	0.573819	+	0.331295i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$		0			0
$86$	−2.00000			−0.215666
$87$		0			0
$88$	2.59808	−	1.50000i	0.276956	−	0.159901i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$		0			0
$93$	−6.92820	+	4.00000i	−0.718421	+	0.414781i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	2.00000			0.204124
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.870433	−	0.492287i	$-0.163839\pi$
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.00888289	+	0.999961i	$0.497172\pi$
$98$	5.19615	+	3.00000i	0.524891	+	0.303046i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−10.3923	+	6.00000i	−1.02899	+	0.594089i
$103$		−	5.00000i		−	0.492665i	−0.969185	−	0.246332i	$-0.920775\pi$
$103$		−	5.00000i		−	0.492665i	0.969185	−	0.246332i	$-0.0792255\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$	3.46410	+	2.00000i	0.333333	+	0.192450i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	11.0000	−	19.0526i	1.04407	−	1.80839i
$112$		−	1.00000i		−	0.0944911i
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.0760733	−	0.997102i	$-0.524238\pi$
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.901553	+	0.432670i	$0.857572\pi$
$114$	5.00000	+	8.66025i	0.468293	+	0.811107i
$115$		0			0
$116$		0			0
$117$	−0.866025	−	3.50000i	−0.0800641	−	0.323575i
$118$		0			0
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		−	8.00000i		−	0.724286i
$123$	−10.3923	−	6.00000i	−0.937043	−	0.541002i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	−0.866025	+	0.500000i	−0.0768473	+	0.0443678i	−0.537931	−	0.842989i	$-0.680794\pi$
$127$	−0.866025	+	0.500000i	−0.0768473	+	0.0443678i	0.461084	+	0.887357i	$0.347461\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	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	$0.628621\pi$
$132$	−5.19615	+	3.00000i	−0.452267	+	0.261116i
$133$	4.33013	−	2.50000i	0.375470	−	0.216777i
$134$	8.00000	−	13.8564i	0.691095	−	1.19701i
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	0.261329	−	0.965250i	$-0.415839\pi$
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	−0.705266	+	0.708942i	$0.749173\pi$
$138$		0			0
$139$	−9.50000	+	16.4545i	−0.805779	+	1.39565i	0.109984	+	0.993933i	$0.464920\pi$
$139$	−9.50000	+	16.4545i	−0.805779	+	1.39565i	−0.915764	+	0.401718i	$0.868413\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		−	6.00000i		−	0.503509i
$143$	−10.3923	−	3.00000i	−0.869048	−	0.250873i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	7.00000	+	12.1244i	0.579324	+	1.00342i
$147$	−10.3923	−	6.00000i	−0.857143	−	0.494872i
$148$		−	11.0000i		−	0.904194i
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	4.33013	+	2.50000i	0.351220	+	0.202777i
$153$	5.19615	−	3.00000i	0.420084	−	0.242536i
$154$	1.50000	+	2.59808i	0.120873	+	0.209359i
$155$		0			0
$156$	−5.00000	−	5.19615i	−0.400320	−	0.416025i
$157$			17.0000i			1.35675i	0.734717	+	0.678374i	$0.237315\pi$
$157$			17.0000i			1.35675i	−0.734717	+	0.678374i	$0.762685\pi$
$158$	−13.8564	+	8.00000i	−1.10236	+	0.636446i
$159$	9.00000	+	15.5885i	0.713746	+	1.23625i
$160$		0			0
$161$		0			0
$162$	−9.52628	−	5.50000i	−0.748455	−	0.432121i
$163$	1.73205	+	1.00000i	0.135665	+	0.0783260i	0.566296	−	0.824202i	$-0.308376\pi$
$163$	1.73205	+	1.00000i	0.135665	+	0.0783260i	−0.430632	+	0.902528i	$0.641709\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−12.9904	+	7.50000i	−1.00523	+	0.580367i	−0.909790	−	0.415068i	$-0.863758\pi$
$167$	−12.9904	+	7.50000i	−1.00523	+	0.580367i	−0.0954356	+	0.995436i	$0.530424\pi$
$168$			2.00000i			0.154303i
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	12.9904	+	7.50000i	0.987640	+	0.570214i	0.904568	−	0.426329i	$-0.140193\pi$
$173$	12.9904	+	7.50000i	0.987640	+	0.570214i	0.0830722	+	0.996544i	$0.473527\pi$
$174$		0			0
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	−7.79423	−	4.50000i	−0.584202	−	0.337289i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−2.59808	+	2.50000i	−0.192582	+	0.185312i
$183$			16.0000i			1.18275i
$184$		0			0
$185$		0			0
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		−	18.0000i		−	1.31629i
$188$	−2.59808	−	1.50000i	−0.189484	−	0.109399i
$189$	−2.00000	+	3.46410i	−0.145479	+	0.251976i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−1.73205	+	1.00000i	−0.125000	+	0.0721688i
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−23.3827	+	13.5000i	−1.66595	+	0.961835i	−0.696159	+	0.717888i	$0.745109\pi$
$197$	−23.3827	+	13.5000i	−1.66595	+	0.961835i	−0.969788	+	0.243947i	$0.921558\pi$
$198$	2.59808	−	1.50000i	0.184637	−	0.106600i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	−16.0000	+	27.7128i	−1.12855	+	1.95471i
$202$	−5.19615	−	3.00000i	−0.365600	−	0.211079i
$203$		0			0
$204$	6.00000	−	10.3923i	0.420084	−	0.727607i
$205$		0			0
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$		0			0
$208$	−3.46410	−	1.00000i	−0.240192	−	0.0693375i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	7.79423	+	4.50000i	0.535310	+	0.309061i
$213$			12.0000i			0.822226i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	−4.00000			−0.272166
$217$	−3.46410	−	2.00000i	−0.235159	−	0.135769i
$218$	1.73205	−	1.00000i	0.117309	−	0.0677285i
$219$	−14.0000	−	24.2487i	−0.946032	−	1.63858i
$220$		0			0
$221$	21.0000	−	5.19615i	1.41261	−	0.349531i
$222$			22.0000i			1.47654i
$223$	16.4545	−	9.50000i	1.10187	−	0.636167i	0.165161	−	0.986267i	$-0.447186\pi$
$223$	16.4545	−	9.50000i	1.10187	−	0.636167i	0.936713	+	0.350100i	$0.113852\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	12.0000			0.798228
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.992102	−	0.125435i	$-0.0400326\pi$
$227$	20.7846	+	12.0000i	1.37952	+	0.796468i	0.387421	+	0.921903i	$0.373366\pi$
$228$	−8.66025	−	5.00000i	−0.573539	−	0.331133i
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$		0			0
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$		0			0
$233$			24.0000i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$233$			24.0000i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$		0			0
$236$		0			0
$237$	27.7128	−	16.0000i	1.80014	−	1.03931i
$238$	−5.19615	−	3.00000i	−0.336817	−	0.194461i
$239$		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	0.211360	+	0.977408i	$0.432211\pi$
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	−0.952141	+	0.305661i	$0.901123\pi$
$242$			2.00000i			0.128565i
$243$	8.66025	+	5.00000i	0.555556	+	0.320750i
$244$	4.00000	+	6.92820i	0.256074	+	0.443533i
$245$		0			0
$246$	12.0000			0.765092
$247$	−4.33013	−	17.5000i	−0.275519	−	1.11350i
$248$		−	4.00000i		−	0.254000i
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	7.50000	−	12.9904i	0.473396	−	0.819946i	−0.526140	−	0.850398i	$-0.676361\pi$
$251$	7.50000	−	12.9904i	0.473396	−	0.819946i	0.999536	+	0.0304521i	$0.00969471\pi$
$252$		−	1.00000i		−	0.0629941i
$253$		0			0
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	−0.139533	−	0.990217i	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$	−3.46410	+	2.00000i	−0.215666	+	0.124515i
$259$	11.0000			0.683507
$260$		0			0
$261$		0			0
$262$	7.79423	−	4.50000i	0.481529	−	0.278011i
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	−0.720672	−	0.693276i	$-0.756167\pi$
$263$	−7.79423	+	4.50000i	−0.480613	+	0.277482i	0.240059	+	0.970758i	$0.422833\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	−2.50000	+	4.33013i	−0.153285	+	0.265497i
$267$	15.5885	+	9.00000i	0.953998	+	0.550791i
$268$			16.0000i			0.977356i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$		−	6.00000i		−	0.363803i
$273$	5.19615	−	5.00000i	0.314485	−	0.302614i
$274$	6.00000			0.362473
$275$		0			0
$276$		0			0
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	0.525792	−	0.850613i	$-0.323769\pi$
$277$	0.866025	+	0.500000i	0.0520344	+	0.0300421i	−0.473757	+	0.880656i	$0.657103\pi$
$278$		−	19.0000i		−	1.13954i
$279$	−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	$0.557275\pi$
$282$	5.19615	+	3.00000i	0.309426	+	0.178647i
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	−0.815017	−	0.579437i	$-0.803272\pi$
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	0.0942988	+	0.995544i	$0.469939\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$		−	6.00000i		−	0.354169i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	20.0000			1.17242
$292$	−12.1244	−	7.00000i	−0.709524	−	0.409644i
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	0.710084	−	0.704117i	$-0.248657\pi$
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	−0.254741	+	0.967009i	$0.581990\pi$
$294$	12.0000			0.699854
$295$		0			0
$296$	5.50000	+	9.52628i	0.319681	+	0.553704i
$297$	10.3923	−	6.00000i	0.603023	−	0.348155i
$298$		−	18.0000i		−	1.04271i
$299$		0			0
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	13.8564	−	8.00000i	0.797347	−	0.460348i
$303$	10.3923	+	6.00000i	0.597022	+	0.344691i
$304$	−5.00000			−0.286770
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	−2.59808	−	1.50000i	−0.148039	−	0.0854704i
$309$	−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	$0.176256\pi$
$312$	6.92820	+	2.00000i	0.392232	+	0.113228i
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	−8.50000	−	14.7224i	−0.479683	−	0.830835i
$315$		0			0
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$			15.0000i			0.842484i	0.906948	+	0.421242i	$0.138406\pi$
$317$			15.0000i			0.842484i	−0.906948	+	0.421242i	$0.861594\pi$
$318$	−15.5885	−	9.00000i	−0.874157	−	0.504695i
$319$		0			0
$320$		0			0
$321$	−12.0000	+	20.7846i	−0.669775	+	1.16008i
$322$		0			0
$323$	25.9808	−	15.0000i	1.44561	−	0.834622i
$324$	11.0000			0.611111
$325$		0			0
$326$	−2.00000			−0.110770
$327$	−3.46410	+	2.00000i	−0.191565	+	0.110600i
$328$	5.19615	−	3.00000i	0.286910	−	0.165647i
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	5.19615	+	3.00000i	0.285176	+	0.164646i
$333$		−	11.0000i		−	0.602796i
$334$	7.50000	−	12.9904i	0.410382	−	0.710802i
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$		−	16.0000i		−	0.871576i	−0.900049	−	0.435788i	$-0.856470\pi$
$337$		−	16.0000i		−	0.871576i	0.900049	−	0.435788i	$-0.143530\pi$
$338$	6.06218	+	11.5000i	0.329739	+	0.625518i
$339$	−24.0000			−1.30350
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	4.33013	+	2.50000i	0.234146	+	0.135185i
$343$		−	13.0000i		−	0.701934i
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	−15.0000			−0.806405
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	0.354001	−	0.935245i	$-0.384821\pi$
$347$	−5.19615	−	3.00000i	−0.278944	−	0.161048i	−0.632945	+	0.774197i	$0.718154\pi$
$348$		0			0
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	0.891548	−	0.452926i	$-0.149620\pi$
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	−0.838019	+	0.545640i	$0.816286\pi$
$350$		0			0
$351$	10.0000	+	10.3923i	0.533761	+	0.554700i
$352$		−	3.00000i		−	0.159901i
$353$	−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	$0.384378\pi$
$354$		0			0
$355$		0			0
$356$	9.00000			0.476999
$357$	10.3923	+	6.00000i	0.550019	+	0.317554i
$358$	20.7846	+	12.0000i	1.09850	+	0.634220i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−6.92820	+	4.00000i	−0.364138	+	0.210235i
$363$		−	4.00000i		−	0.209946i
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$		0			0
$366$	−8.00000	−	13.8564i	−0.418167	−	0.724286i
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.448320	−	0.893873i	$-0.352022\pi$
$367$	27.7128	−	16.0000i	1.44660	−	0.835193i	0.998277	+	0.0586798i	$0.0186891\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	−4.50000	+	7.79423i	−0.233628	+	0.404656i
$372$			8.00000i			0.414781i
$373$	12.1244	+	7.00000i	0.627775	+	0.362446i	0.779890	−	0.625917i	$-0.215275\pi$
$373$	12.1244	+	7.00000i	0.627775	+	0.362446i	−0.152115	+	0.988363i	$0.548608\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	3.00000			0.154713
$377$		0			0
$378$		−	4.00000i		−	0.205738i
$379$	−9.50000	−	16.4545i	−0.487982	−	0.845210i	0.511922	−	0.859032i	$-0.328934\pi$
$379$	−9.50000	−	16.4545i	−0.487982	−	0.845210i	−0.999904	+	0.0138218i	$0.995600\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	1.00000	−	1.73205i	0.0510310	−	0.0883883i
$385$		0			0
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	1.73205	−	1.00000i	0.0880451	−	0.0508329i
$388$	8.66025	−	5.00000i	0.439658	−	0.253837i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$		0			0
$392$	5.19615	−	3.00000i	0.262445	−	0.151523i
$393$	−15.5885	+	9.00000i	−0.786334	+	0.453990i
$394$	13.5000	−	23.3827i	0.680120	−	1.17800i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	11.2583	+	6.50000i	0.565039	+	0.326226i	0.755166	−	0.655534i	$-0.227556\pi$
$397$	11.2583	+	6.50000i	0.565039	+	0.326226i	−0.190126	+	0.981760i	$0.560890\pi$
$398$		−	10.0000i		−	0.501255i
$399$	5.00000	−	8.66025i	0.250313	−	0.433555i
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		−	32.0000i		−	1.59601i
$403$	−10.3923	+	10.0000i	−0.517678	+	0.498135i
$404$	6.00000			0.298511
$405$		0			0
$406$		0			0
$407$	−28.5788	−	16.5000i	−1.41660	−	0.817875i
$408$			12.0000i			0.594089i
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	−4.33013	−	2.50000i	−0.213330	−	0.123166i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$			38.0000i			1.86087i
$418$	12.9904	−	7.50000i	0.635380	−	0.366837i
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	19.9186	+	11.5000i	0.969622	+	0.559811i
$423$	−2.59808	−	1.50000i	−0.126323	−	0.0729325i
$424$	−9.00000			−0.437079
$425$		0			0
$426$	−6.00000	−	10.3923i	−0.290701	−	0.503509i
$427$	−6.92820	+	4.00000i	−0.335279	+	0.193574i
$428$			12.0000i			0.580042i
$429$	−21.0000	+	5.19615i	−1.01389	+	0.250873i
$430$		0			0
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	3.46410	−	2.00000i	0.166667	−	0.0962250i
$433$	−13.8564	−	8.00000i	−0.665896	−	0.384455i	0.128624	−	0.991693i	$-0.458944\pi$
$433$	−13.8564	−	8.00000i	−0.665896	−	0.384455i	−0.794520	+	0.607238i	$0.792277\pi$
$434$	4.00000			0.192006
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$		0			0
$438$	24.2487	+	14.0000i	1.15865	+	0.668946i
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−15.5885	+	15.0000i	−0.741467	+	0.713477i
$443$			18.0000i			0.855206i	0.903967	+	0.427603i	$0.140642\pi$
$443$			18.0000i			0.855206i	−0.903967	+	0.427603i	$0.859358\pi$
$444$	−11.0000	−	19.0526i	−0.522037	−	0.904194i
$445$		0			0
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$			36.0000i			1.70274i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	0.952455	+	0.304679i	$0.0985491\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	−27.7128	+	16.0000i	−1.30206	+	0.751746i
$454$	−24.0000			−1.12638
$455$		0			0
$456$	10.0000			0.468293
$457$	−3.46410	+	2.00000i	−0.162044	+	0.0935561i	−0.578829	−	0.815449i	$-0.696490\pi$
$457$	−3.46410	+	2.00000i	−0.162044	+	0.0935561i	0.416785	+	0.909005i	$0.363157\pi$
$458$	−3.46410	+	2.00000i	−0.161867	+	0.0934539i
$459$	−12.0000	+	20.7846i	−0.560112	+	0.970143i
$460$		0			0
$461$	21.0000	−	36.3731i	0.978068	−	1.69406i	0.308651	−	0.951175i	$-0.400123\pi$
$461$	21.0000	−	36.3731i	0.978068	−	1.69406i	0.669417	−	0.742887i	$-0.266544\pi$
$462$	5.19615	+	3.00000i	0.241747	+	0.139573i
$463$		−	8.00000i		−	0.371792i	−0.982569	−	0.185896i	$-0.940481\pi$
$463$		−	8.00000i		−	0.371792i	0.982569	−	0.185896i	$-0.0595187\pi$
$464$		0			0
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$	−3.46410	−	1.00000i	−0.160128	−	0.0462250i
$469$	−16.0000			−0.738811
$470$		0			0
$471$	17.0000	+	29.4449i	0.783319	+	1.35675i
$472$		0			0
$473$		−	6.00000i		−	0.275880i
$474$	−16.0000	+	27.7128i	−0.734904	+	1.27289i
$475$		0			0
$476$	6.00000			0.275010
$477$	7.79423	+	4.50000i	0.356873	+	0.206041i
$478$		0			0
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$		0			0
$481$	11.0000	−	38.1051i	0.501557	−	1.73744i
$482$		−	23.0000i		−	1.04762i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$	−10.0000			−0.453609
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	0.824110	−	0.566429i	$-0.191675\pi$
$487$	16.4545	+	9.50000i	0.745624	+	0.430486i	−0.0784867	+	0.996915i	$0.525009\pi$
$488$	−6.92820	−	4.00000i	−0.313625	−	0.181071i
$489$	4.00000			0.180886
$490$		0			0
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$	−10.3923	+	6.00000i	−0.468521	+	0.270501i
$493$		0			0
$494$	12.5000	+	12.9904i	0.562402	+	0.584465i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−5.19615	+	3.00000i	−0.233079	+	0.134568i
$498$	−10.3923	−	6.00000i	−0.465690	−	0.268866i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	−15.0000	+	25.9808i	−0.670151	+	1.16073i
$502$			15.0000i			0.669483i
$503$	7.79423	+	4.50000i	0.347527	+	0.200645i	0.663596	−	0.748091i	$-0.269030\pi$
$503$	7.79423	+	4.50000i	0.347527	+	0.200645i	−0.316068	+	0.948736i	$0.602363\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$		0			0
$506$		0			0
$507$	−12.1244	−	23.0000i	−0.538462	−	1.02147i
$508$			1.00000i			0.0443678i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	7.00000	−	12.1244i	0.309662	−	0.536350i
$512$		−	1.00000i		−	0.0441942i
$513$	17.3205	+	10.0000i	0.764719	+	0.441511i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$		0			0
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−7.79423	+	4.50000i	−0.342790	+	0.197910i
$518$	−9.52628	+	5.50000i	−0.418561	+	0.241656i
$519$	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
$523$	−12.1244	+	7.00000i	−0.530161	+	0.306089i	−0.741082	−	0.671414i	$-0.765687\pi$
$523$	−12.1244	+	7.00000i	−0.530161	+	0.306089i	0.210921	+	0.977503i	$0.432354\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$		0			0
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	−20.7846	−	12.0000i	−0.905392	−	0.522728i
$528$			6.00000i			0.261116i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		−	5.00000i		−	0.216777i
$533$	−20.7846	−	6.00000i	−0.900281	−	0.259889i
$534$	−18.0000			−0.778936
$535$		0			0
$536$	−8.00000	−	13.8564i	−0.345547	−	0.598506i
$537$	−41.5692	−	24.0000i	−1.79384	−	1.03568i
$538$			6.00000i			0.258678i
$539$	−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	$0.358537\pi$
$542$	17.3205	+	10.0000i	0.743980	+	0.429537i
$543$	13.8564	−	8.00000i	0.594635	−	0.343313i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$		0			0
$546$	−2.00000	+	6.92820i	−0.0855921	+	0.296500i
$547$		−	34.0000i		−	1.45374i	−0.686778	−	0.726868i	$-0.740975\pi$
$547$		−	34.0000i		−	1.45374i	0.686778	−	0.726868i	$-0.259025\pi$
$548$	−5.19615	+	3.00000i	−0.221969	+	0.128154i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	13.8564	+	8.00000i	0.589234	+	0.340195i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	9.50000	+	16.4545i	0.402890	+	0.697826i
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	−0.0624962	−	0.998045i	$-0.519906\pi$
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	0.833084	+	0.553146i	$0.186573\pi$
$558$		−	4.00000i		−	0.169334i
$559$	7.00000	−	1.73205i	0.296068	−	0.0732579i
$560$		0			0
$561$	−18.0000	−	31.1769i	−0.759961	−	1.31629i
$562$	5.19615	−	3.00000i	0.219186	−	0.126547i
$563$	−31.1769	−	18.0000i	−1.31395	−	0.758610i	−0.331202	−	0.943560i	$-0.607454\pi$
$563$	−31.1769	−	18.0000i	−1.31395	−	0.758610i	−0.982748	+	0.184950i	$0.940788\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	7.00000	−	12.1244i	0.294232	−	0.509625i
$567$			11.0000i			0.461957i
$568$	−5.19615	−	3.00000i	−0.218026	−	0.125877i
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	0.944800	−	0.327647i	$-0.106256\pi$
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	−0.756151	+	0.654398i	$0.772922\pi$
$570$		0			0
$571$	17.0000			0.711428			0.355714	−	0.934595i	$-0.384238\pi$
$571$	17.0000			0.711428			0.355714	+	0.934595i	$0.384238\pi$
$572$	−7.79423	+	7.50000i	−0.325893	+	0.313591i
$573$		0			0
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$	−16.4545	−	9.50000i	−0.684416	−	0.395148i
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$		0			0
$581$	−3.00000	+	5.19615i	−0.124461	+	0.215573i
$582$	−17.3205	+	10.0000i	−0.717958	+	0.414513i
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$	14.0000			0.579324
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−5.19615	+	3.00000i	−0.214468	+	0.123823i	−0.603386	−	0.797449i	$-0.706182\pi$
$587$	−5.19615	+	3.00000i	−0.214468	+	0.123823i	0.388918	+	0.921272i	$0.372849\pi$
$588$	−10.3923	+	6.00000i	−0.428571	+	0.247436i
$589$	−10.0000	+	17.3205i	−0.412043	+	0.713679i
$590$		0			0
$591$	−27.0000	+	46.7654i	−1.11063	+	1.92367i
$592$	−9.52628	−	5.50000i	−0.391528	−	0.226049i
$593$		−	24.0000i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$593$		−	24.0000i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$594$	−6.00000	+	10.3923i	−0.246183	+	0.426401i
$595$		0			0
$596$	9.00000	+	15.5885i	0.368654	+	0.638528i
$597$			20.0000i			0.818546i
$598$		0			0
$599$	18.0000			0.735460			0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000			0.735460			0.367730	+	0.929933i	$0.380135\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	−1.73205	−	1.00000i	−0.0705931	−	0.0407570i
$603$			16.0000i			0.651570i
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$	−12.0000			−0.487467
$607$	11.2583	+	6.50000i	0.456962	+	0.263827i	0.710766	−	0.703429i	$-0.248349\pi$
$607$	11.2583	+	6.50000i	0.456962	+	0.263827i	−0.253804	+	0.967256i	$0.581682\pi$
$608$	4.33013	−	2.50000i	0.175610	−	0.101388i
$609$		0			0
$610$		0			0
$611$	−7.50000	−	7.79423i	−0.303418	−	0.315321i
$612$		−	6.00000i		−	0.242536i
$613$	11.2583	−	6.50000i	0.454720	−	0.262533i	−0.255102	−	0.966914i	$-0.582109\pi$
$613$	11.2583	−	6.50000i	0.454720	−	0.262533i	0.709821	+	0.704382i	$0.248776\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$		0			0
$616$	3.00000			0.120873
$617$	−15.5885	−	9.00000i	−0.627568	−	0.362326i	0.152242	−	0.988343i	$-0.451351\pi$
$617$	−15.5885	−	9.00000i	−0.627568	−	0.362326i	−0.779809	+	0.626017i	$0.784684\pi$
$618$	8.66025	+	5.00000i	0.348367	+	0.201129i
$619$	1.00000			0.0401934			0.0200967	−	0.999798i	$-0.493603\pi$
$619$	1.00000			0.0401934			0.0200967	+	0.999798i	$0.493603\pi$
$620$		0			0
$621$		0			0
$622$	−25.9808	+	15.0000i	−1.04173	+	0.601445i
$623$			9.00000i			0.360577i
$624$	−7.00000	+	1.73205i	−0.280224	+	0.0693375i
$625$		0			0
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$	−25.9808	+	15.0000i	−1.03757	+	0.599042i
$628$	14.7224	+	8.50000i	0.587489	+	0.339187i
$629$	66.0000			2.63159
$630$		0			0
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	−0.440387	−	0.897808i	$-0.645159\pi$
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	0.997718	−	0.0675178i	$-0.0215080\pi$
$632$			16.0000i			0.636446i
$633$	−39.8372	−	23.0000i	−1.58339	−	0.914168i
$634$	−7.50000	−	12.9904i	−0.297863	−	0.515914i
$635$		0			0
$636$	18.0000			0.713746
$637$	−20.7846	−	6.00000i	−0.823516	−	0.237729i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		−	24.0000i		−	0.947204i
$643$	1.73205	+	1.00000i	0.0683054	+	0.0394362i	0.533764	−	0.845634i	$-0.320777\pi$
$643$	1.73205	+	1.00000i	0.0683054	+	0.0394362i	−0.465458	+	0.885070i	$0.654110\pi$
$644$		0			0
$645$		0			0
$646$	−15.0000	+	25.9808i	−0.590167	+	1.02220i
$647$	−7.79423	+	4.50000i	−0.306423	+	0.176913i	−0.645325	−	0.763908i	$-0.723278\pi$
$647$	−7.79423	+	4.50000i	−0.306423	+	0.176913i	0.338902	+	0.940822i	$0.389945\pi$
$648$	−9.52628	+	5.50000i	−0.374228	+	0.216060i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	1.73205	−	1.00000i	0.0678323	−	0.0391630i
$653$	23.3827	−	13.5000i	0.915035	−	0.528296i	0.0329874	−	0.999456i	$-0.489498\pi$
$653$	23.3827	−	13.5000i	0.915035	−	0.528296i	0.882048	+	0.471160i	$0.156165\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	−12.1244	−	7.00000i	−0.473016	−	0.273096i
$658$			3.00000i			0.116952i
$659$	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
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$		−	20.0000i		−	0.777322i
$663$	31.1769	−	30.0000i	1.21081	−	1.16510i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	5.50000	+	9.52628i	0.213121	+	0.369136i
$667$		0			0
$668$			15.0000i			0.580367i
$669$	19.0000	−	32.9090i	0.734582	−	1.27233i
$670$		0			0
$671$	24.0000			0.926510
$672$	1.73205	+	1.00000i	0.0668153	+	0.0385758i
$673$	−17.3205	+	10.0000i	−0.667657	+	0.385472i	−0.795188	−	0.606363i	$-0.792628\pi$
$673$	−17.3205	+	10.0000i	−0.667657	+	0.385472i	0.127532	+	0.991835i	$0.459295\pi$
$674$	8.00000	+	13.8564i	0.308148	+	0.533729i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	20.7846	−	12.0000i	0.798228	−	0.460857i
$679$	5.00000	+	8.66025i	0.191882	+	0.332350i
$680$		0			0
$681$	48.0000			1.83936
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	−5.19615	−	3.00000i	−0.198825	−	0.114792i	0.397282	−	0.917697i	$-0.369953\pi$
$683$	−5.19615	−	3.00000i	−0.198825	−	0.114792i	−0.596107	+	0.802905i	$0.703287\pi$
$684$	−5.00000			−0.191180
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	6.92820	−	4.00000i	0.264327	−	0.152610i
$688$		−	2.00000i		−	0.0762493i
$689$	22.5000	+	23.3827i	0.857182	+	0.890809i
$690$		0			0
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	0.962768	−	0.270330i	$-0.0871327\pi$
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	−0.715496	+	0.698617i	$0.753799\pi$
$692$	12.9904	−	7.50000i	0.493820	−	0.285107i
$693$	−2.59808	−	1.50000i	−0.0986928	−	0.0569803i
$694$	6.00000			0.227757
$695$		0			0
$696$		0			0
$697$		−	36.0000i		−	1.36360i
$698$	−1.73205	−	1.00000i	−0.0655591	−	0.0378506i
$699$	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	$0.463855\pi$
$702$	−13.8564	−	4.00000i	−0.522976	−	0.150970i
$703$		−	55.0000i		−	2.07436i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$			6.00000i			0.225653i
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$		0			0
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$	−7.79423	+	4.50000i	−0.292101	+	0.168645i
$713$		0			0
$714$	−12.0000			−0.449089
$715$		0			0
$716$	−24.0000			−0.896922
$717$		0			0
$718$	−5.19615	+	3.00000i	−0.193919	+	0.111959i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	2.50000	−	4.33013i	0.0931049	−	0.161262i
$722$	5.19615	+	3.00000i	0.193381	+	0.111648i
$723$			46.0000i			1.71076i
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$		0			0
$726$	2.00000	+	3.46410i	0.0742270	+	0.128565i
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$	0.866025	+	3.50000i	0.0320970	+	0.129719i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$	13.8564	+	8.00000i	0.512148	+	0.295689i
$733$			25.0000i			0.923396i	0.887037	+	0.461698i	$0.152760\pi$
$733$			25.0000i			0.923396i	−0.887037	+	0.461698i	$0.847240\pi$
$734$	−16.0000	+	27.7128i	−0.590571	+	1.02290i
$735$		0			0
$736$		0			0
$737$	41.5692	+	24.0000i	1.53122	+	0.884051i
$738$	5.19615	−	3.00000i	0.191273	−	0.110432i
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	0.794443	−	0.607339i	$-0.207763\pi$
$739$	−3.50000	−	6.06218i	−0.128750	−	0.223001i	−0.923192	+	0.384338i	$0.874430\pi$
$740$		0			0
$741$	−25.0000	−	25.9808i	−0.918398	−	0.954427i
$742$		−	9.00000i		−	0.330400i
$743$	−10.3923	+	6.00000i	−0.381257	+	0.220119i	−0.678365	−	0.734725i	$-0.737311\pi$
$743$	−10.3923	+	6.00000i	−0.381257	+	0.220119i	0.297108	+	0.954844i	$0.403978\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$		0			0
$746$	−14.0000			−0.512576
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$	−15.5885	−	9.00000i	−0.569970	−	0.329073i
$749$	−12.0000			−0.438470
$750$		0			0
$751$	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	$0.572942\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$		−	30.0000i		−	1.09326i
$754$		0			0
$755$		0			0
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	19.9186	−	11.5000i	0.723953	−	0.417975i	−0.0922527	−	0.995736i	$-0.529407\pi$
$757$	19.9186	−	11.5000i	0.723953	−	0.417975i	0.816206	+	0.577761i	$0.196073\pi$
$758$	16.4545	+	9.50000i	0.597654	+	0.345056i
$759$		0			0
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		−	2.00000i		−	0.0724524i
$763$	−1.73205	−	1.00000i	−0.0627044	−	0.0362024i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$			2.00000i			0.0721688i
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	−0.990726	−	0.135877i	$-0.956615\pi$
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	0.377690	−	0.925932i	$-0.376718\pi$
$770$		0			0
$771$	12.0000	−	20.7846i	0.432169	−	0.748539i
$772$		−	4.00000i		−	0.143963i
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.963802	−	0.266621i	$-0.0859071\pi$
$773$	33.7750	+	19.5000i	1.21480	+	0.701366i	0.251000	+	0.967987i	$0.419240\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$		0			0
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	19.0526	−	11.0000i	0.683507	−	0.394623i
$778$	−25.9808	+	15.0000i	−0.931455	+	0.537776i
$779$	−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
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	0.799535	−	0.600620i	$-0.205079\pi$
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	−0.120384	+	0.992727i	$0.538413\pi$
$788$			27.0000i			0.961835i
$789$	−9.00000	+	15.5885i	−0.320408	+	0.554964i
$790$		0			0
$791$	−6.00000	−	10.3923i	−0.213335	−	0.369508i
$792$		−	3.00000i		−	0.106600i
$793$	6.92820	+	28.0000i	0.246028	+	0.994309i
$794$	−13.0000			−0.461353
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.310031	−	0.950726i	$-0.600340\pi$
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.978369	+	0.206868i	$0.933673\pi$
$798$			10.0000i			0.353996i
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	9.00000			0.317999
$802$	−12.9904	−	7.50000i	−0.458706	−	0.264834i
$803$	−36.3731	+	21.0000i	−1.28358	+	0.741074i
$804$	16.0000	+	27.7128i	0.564276	+	0.977356i
$805$		0			0
$806$	4.00000	−	13.8564i	0.140894	−	0.488071i
$807$		−	12.0000i		−	0.422420i
$808$	−5.19615	+	3.00000i	−0.182800	+	0.105540i
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	0.663316	−	0.748340i	$-0.269149\pi$
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	−0.979739	+	0.200279i	$0.935815\pi$
$810$		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
$813$	−34.6410	−	20.0000i	−1.21491	−	0.701431i
$814$	33.0000			1.15665
$815$		0			0
$816$	−6.00000	−	10.3923i	−0.210042	−	0.363803i
$817$	8.66025	−	5.00000i	0.302984	−	0.174928i
$818$			5.00000i			0.174821i
$819$	1.00000	−	3.46410i	0.0349428	−	0.121046i
$820$		0			0
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	−0.987912	−	0.155017i	$-0.950457\pi$
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	0.359708	−	0.933065i	$-0.382876\pi$
$822$	10.3923	−	6.00000i	0.362473	−	0.209274i
$823$	−37.2391	−	21.5000i	−1.29807	−	0.749443i	−0.318002	−	0.948090i	$-0.603012\pi$
$823$	−37.2391	−	21.5000i	−1.29807	−	0.749443i	−0.980071	+	0.198647i	$0.936345\pi$
$824$	5.00000			0.174183
$825$		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
$829$	−20.0000	−	34.6410i	−0.694629	−	1.20313i	−0.970306	−	0.241882i	$-0.922235\pi$
$829$	−20.0000	−	34.6410i	−0.694629	−	1.20313i	0.275677	−	0.961250i	$-0.411098\pi$
$830$		0			0
$831$	2.00000			0.0693792
$832$	−2.59808	+	2.50000i	−0.0900721	+	0.0866719i
$833$		−	36.0000i		−	1.24733i
$834$	−19.0000	−	32.9090i	−0.657916	−	1.13954i
$835$		0			0
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$		−	16.0000i		−	0.553041i
$838$	31.1769	+	18.0000i	1.07699	+	0.621800i
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	8.66025	−	5.00000i	0.298452	−	0.172311i
$843$	−10.3923	+	6.00000i	−0.357930	+	0.206651i
$844$	−23.0000			−0.791693
$845$		0			0
$846$	3.00000			0.103142
$847$	1.73205	−	1.00000i	0.0595140	−	0.0343604i
$848$	7.79423	−	4.50000i	0.267655	−	0.154531i
$849$	−14.0000	+	24.2487i	−0.480479	+	0.832214i
$850$		0			0
$851$		0			0
$852$	10.3923	+	6.00000i	0.356034	+	0.205557i
$853$			46.0000i			1.57501i	0.616308	+	0.787505i	$0.288628\pi$
$853$			46.0000i			1.57501i	−0.616308	+	0.787505i	$0.711372\pi$
$854$	4.00000	−	6.92820i	0.136877	−	0.237078i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$	15.5885	−	15.0000i	0.532181	−	0.512092i
$859$	31.0000			1.05771			0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000			1.05771			0.528853	+	0.848713i	$0.322622\pi$
$860$		0			0
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	25.9808	+	15.0000i	0.884908	+	0.510902i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$		0			0
$866$	16.0000			0.543702
$867$	32.9090	+	19.0000i	1.11765	+	0.645274i
$868$	−3.46410	+	2.00000i	−0.117579	+	0.0678844i
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$		0			0
$871$	−16.0000	+	55.4256i	−0.542139	+	1.87803i
$872$		−	2.00000i		−	0.0677285i
$873$	8.66025	−	5.00000i	0.293105	−	0.169224i
$874$		0			0
$875$		0			0
$876$	−28.0000			−0.946032
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	0.639040	−	0.769174i	$-0.279332\pi$
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	−0.346604	+	0.938012i	$0.612665\pi$
$878$	−17.3205	−	10.0000i	−0.584539	−	0.337484i
$879$	18.0000			0.607125
$880$		0			0
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	0.964263	−	0.264946i	$-0.0853542\pi$
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	−0.711582	+	0.702603i	$0.752021\pi$
$882$	5.19615	−	3.00000i	0.174964	−	0.101015i
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$	6.00000	−	20.7846i	0.201802	−	0.699062i
$885$		0			0
$886$	−9.00000	−	15.5885i	−0.302361	−	0.523704i
$887$	−23.3827	+	13.5000i	−0.785114	+	0.453286i	−0.838240	−	0.545302i	$-0.816415\pi$
$887$	−23.3827	+	13.5000i	−0.785114	+	0.453286i	0.0531258	+	0.998588i	$0.483082\pi$
$888$	19.0526	+	11.0000i	0.639362	+	0.369136i
$889$	−1.00000			−0.0335389
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$		−	19.0000i		−	0.636167i
$893$	−12.9904	−	7.50000i	−0.434707	−	0.250978i
$894$	−18.0000	−	31.1769i	−0.602010	−	1.04271i
$895$		0			0
$896$	1.00000			0.0334077
$897$		0			0
$898$			9.00000i			0.300334i
$899$		0			0
$900$		0			0
$901$	−27.0000	+	46.7654i	−0.899500	+	1.55798i
$902$		−	18.0000i		−	0.599334i
$903$	3.46410	+	2.00000i	0.115278	+	0.0665558i
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$		0			0
$906$	16.0000	−	27.7128i	0.531564	−	0.920697i
$907$	6.92820	−	4.00000i	0.230047	−	0.132818i	−0.380547	−	0.924762i	$-0.624264\pi$
$907$	6.92820	−	4.00000i	0.230047	−	0.132818i	0.610594	+	0.791944i	$0.290931\pi$
$908$	20.7846	−	12.0000i	0.689761	−	0.398234i
$909$	6.00000			0.199007
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−8.66025	+	5.00000i	−0.286770	+	0.165567i
$913$	15.5885	−	9.00000i	0.515903	−	0.297857i
$914$	2.00000	−	3.46410i	0.0661541	−	0.114582i
$915$		0			0
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	−7.79423	−	4.50000i	−0.257388	−	0.148603i
$918$		−	24.0000i		−	0.792118i
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	0.436650	+	0.899631i	$0.356165\pi$
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	−0.997429	+	0.0716652i	$0.977169\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$			42.0000i			1.38320i
$923$	5.19615	+	21.0000i	0.171033	+	0.691223i
$924$	−6.00000			−0.197386
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	−4.33013	−	2.50000i	−0.142220	−	0.0821108i
$928$		0			0
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$		0			0
$931$	−30.0000			−0.983210
$932$	20.7846	+	12.0000i	0.680823	+	0.393073i
$933$	51.9615	−	30.0000i	1.70114	−	0.982156i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$	3.50000	−	0.866025i	0.114401	−	0.0283069i
$937$			50.0000i			1.63343i	0.577042	+	0.816714i	$0.304207\pi$
$937$			50.0000i			1.63343i	−0.577042	+	0.816714i	$0.695793\pi$
$938$	13.8564	−	8.00000i	0.452428	−	0.261209i
$939$	−14.0000	−	24.2487i	−0.456873	−	0.791327i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−29.4449	−	17.0000i	−0.959366	−	0.553890i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	3.00000	+	5.19615i	0.0975384	+	0.168941i
$947$	41.5692	−	24.0000i	1.35082	−	0.779895i	0.362454	−	0.932002i	$-0.381939\pi$
$947$	41.5692	−	24.0000i	1.35082	−	0.779895i	0.988364	+	0.152106i	$0.0486057\pi$
$948$		−	32.0000i		−	1.03931i
$949$	−35.0000	−	36.3731i	−1.13615	−	1.18072i
$950$		0			0
$951$	15.0000	+	25.9808i	0.486408	+	0.842484i
$952$	−5.19615	+	3.00000i	−0.168408	+	0.0972306i
$953$	20.7846	+	12.0000i	0.673280	+	0.388718i	0.797318	−	0.603559i	$-0.206251\pi$
$953$	20.7846	+	12.0000i	0.673280	+	0.388718i	−0.124039	+	0.992277i	$0.539585\pi$
$954$	−9.00000			−0.291386
$955$		0			0
$956$		0			0
$957$		0			0
$958$	25.9808	+	15.0000i	0.839400	+	0.484628i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	9.52628	+	38.5000i	0.307140	+	1.24129i
$963$			12.0000i			0.386695i
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$		0			0
$966$		0			0
$967$			5.00000i			0.160789i	0.996763	+	0.0803946i	$0.0256180\pi$
$967$			5.00000i			0.160789i	−0.996763	+	0.0803946i	$0.974382\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$	30.0000	−	51.9615i	0.963739	−	1.66924i
$970$		0			0
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$	8.66025	−	5.00000i	0.277778	−	0.160375i
$973$	−16.4545	+	9.50000i	−0.527506	+	0.304556i
$974$	−19.0000			−0.608799
$975$		0			0
$976$	8.00000			0.256074
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$	−3.46410	+	2.00000i	−0.110770	+	0.0639529i
$979$	13.5000	−	23.3827i	0.431462	−	0.747314i
$980$		0			0
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	23.3827	+	13.5000i	0.746171	+	0.430802i
$983$		−	39.0000i		−	1.24391i	−0.783054	−	0.621953i	$-0.786339\pi$
$983$		−	39.0000i		−	1.24391i	0.783054	−	0.621953i	$-0.213661\pi$
$984$	6.00000	−	10.3923i	0.191273	−	0.331295i
$985$		0			0
$986$		0			0
$987$		−	6.00000i		−	0.190982i
$988$	−17.3205	−	5.00000i	−0.551039	−	0.159071i
$989$		0			0
$990$		0			0
$991$	11.0000	+	19.0526i	0.349427	+	0.605224i	0.986148	−	0.165870i	$-0.0530431\pi$
$991$	11.0000	+	19.0526i	0.349427	+	0.605224i	−0.636721	+	0.771094i	$0.719710\pi$
$992$	−3.46410	−	2.00000i	−0.109985	−	0.0635001i
$993$			40.0000i			1.26936i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	12.0000			0.380235
$997$	−35.5070	−	20.5000i	−1.12452	−	0.649242i	−0.181968	−	0.983304i	$-0.558247\pi$
$997$	−35.5070	−	20.5000i	−1.12452	−	0.649242i	−0.942551	+	0.334063i	$0.891580\pi$
$998$	−3.46410	+	2.00000i	−0.109654	+	0.0633089i
$999$	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.o.b.549.1		4
5.2	odd	4		650.2.e.a.601.1		2
5.3	odd	4		130.2.e.b.81.1	yes	2
5.4	even	2	inner	650.2.o.b.549.2		4
13.9	even	3	inner	650.2.o.b.399.2		4
15.8	even	4		1170.2.i.f.991.1		2
20.3	even	4		1040.2.q.c.81.1		2
65.3	odd	12		1690.2.a.a.1.1		1
65.8	even	4		1690.2.l.i.361.1		4
65.9	even	6	inner	650.2.o.b.399.1		4
65.18	even	4		1690.2.l.i.361.2		4
65.22	odd	12		650.2.e.a.451.1		2
65.23	odd	12		1690.2.a.g.1.1		1
65.28	even	12		1690.2.d.a.1351.2		2
65.33	even	12		1690.2.l.i.1161.2		4
65.38	odd	4		1690.2.e.e.991.1		2
65.42	odd	12		8450.2.a.w.1.1		1
65.43	odd	12		1690.2.e.e.191.1		2
65.48	odd	12		130.2.e.b.61.1	✓	2
65.58	even	12		1690.2.l.i.1161.1		4
65.62	odd	12		8450.2.a.k.1.1		1
65.63	even	12		1690.2.d.a.1351.1		2
195.113	even	12		1170.2.i.f.451.1		2
260.243	even	12		1040.2.q.c.321.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.b.61.1	✓	2	65.48	odd	12
130.2.e.b.81.1	yes	2	5.3	odd	4
650.2.e.a.451.1		2	65.22	odd	12
650.2.e.a.601.1		2	5.2	odd	4
650.2.o.b.399.1		4	65.9	even	6	inner
650.2.o.b.399.2		4	13.9	even	3	inner
650.2.o.b.549.1		4	1.1	even	1	trivial
650.2.o.b.549.2		4	5.4	even	2	inner
1040.2.q.c.81.1		2	20.3	even	4
1040.2.q.c.321.1		2	260.243	even	12
1170.2.i.f.451.1		2	195.113	even	12
1170.2.i.f.991.1		2	15.8	even	4
1690.2.a.a.1.1		1	65.3	odd	12
1690.2.a.g.1.1		1	65.23	odd	12
1690.2.d.a.1351.1		2	65.63	even	12
1690.2.d.a.1351.2		2	65.28	even	12
1690.2.e.e.191.1		2	65.43	odd	12
1690.2.e.e.991.1		2	65.38	odd	4
1690.2.l.i.361.1		4	65.8	even	4
1690.2.l.i.361.2		4	65.18	even	4
1690.2.l.i.1161.1		4	65.58	even	12
1690.2.l.i.1161.2		4	65.33	even	12
8450.2.a.k.1.1		1	65.62	odd	12
8450.2.a.w.1.1		1	65.42	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.o (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more