LMFDB - Embedded newform 496.2.i.g.129.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [496,2,Mod(129,496)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(496, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 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("496.129"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 496 = 2^{4} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	496.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,3,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.96057994026$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 62)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			129.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	496.129
Dual form			496.2.i.g.273.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} -3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(3.50000 - 6.06218i) q^{19} +(4.50000 + 7.79423i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -9.00000 q^{27} +2.00000 q^{29} +(-2.00000 + 5.19615i) q^{31} -9.00000 q^{33} +3.00000 q^{35} +(-0.500000 + 0.866025i) q^{37} -15.0000 q^{39} +(4.50000 + 7.79423i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{45} +8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(4.50000 + 7.79423i) q^{51} +(1.50000 + 2.59808i) q^{53} +(-1.50000 + 2.59808i) q^{55} +(-10.5000 - 18.1865i) q^{57} +(1.50000 - 2.59808i) q^{59} +6.00000 q^{61} +18.0000 q^{63} +(-2.50000 + 4.33013i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(6.00000 - 10.3923i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(-3.50000 - 6.06218i) q^{73} +(-6.00000 - 10.3923i) q^{75} +9.00000 q^{77} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.50000 + 4.33013i) q^{83} +3.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +6.00000 q^{89} +15.0000 q^{91} +(10.5000 + 12.9904i) q^{93} -7.00000 q^{95} +14.0000 q^{97} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - q^{5} - 3 q^{7} - 6 q^{9} - 3 q^{11} - 5 q^{13} - 6 q^{15} - 3 q^{17} + 7 q^{19} + 9 q^{21} + 8 q^{23} + 4 q^{25} - 18 q^{27} + 4 q^{29} - 4 q^{31} - 18 q^{33} + 6 q^{35} - q^{37} - 30 q^{39}+ \cdots - 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - q^5 - 3 * q^7 - 6 * q^9 - 3 * q^11 - 5 * q^13 - 6 * q^15 - 3 * q^17 + 7 * q^19 + 9 * q^21 + 8 * q^23 + 4 * q^25 - 18 * q^27 + 4 * q^29 - 4 * q^31 - 18 * q^33 + 6 * q^35 - q^37 - 30 * q^39 + 9 * q^41 - q^43 - 6 * q^45 + 16 * q^47 - 2 * q^49 + 9 * q^51 + 3 * q^53 - 3 * q^55 - 21 * q^57 + 3 * q^59 + 12 * q^61 + 36 * q^63 - 5 * q^65 - 3 * q^67 + 12 * q^69 - q^71 - 7 * q^73 - 12 * q^75 + 18 * q^77 + q^79 - 9 * q^81 + 5 * q^83 + 6 * q^85 + 6 * q^87 + 12 * q^89 + 30 * q^91 + 21 * q^93 - 14 * q^95 + 28 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$.

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		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	$0.982718\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	4.50000	+	7.79423i	0.981981	+	1.70084i
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$32$		0			0
$33$	−9.00000			−1.56670
$34$		0			0
$35$	3.00000			0.507093
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	−15.0000			−2.40192
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$		0			0
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$	−10.5000	−	18.1865i	−1.39076	−	2.40887i
$58$		0			0
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		0			0
$63$	18.0000			2.26779
$64$		0			0
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$		0			0
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$		0			0
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	−6.00000	−	10.3923i	−0.692820	−	1.20000i
$76$		0			0
$77$	9.00000			1.02565
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	2.50000	+	4.33013i	0.274411	+	0.475293i	0.969986	−	0.243160i	$-0.0781839\pi$
$83$	2.50000	+	4.33013i	0.274411	+	0.475293i	−0.695576	+	0.718453i	$0.744851\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	15.0000			1.57243
$92$		0			0
$93$	10.5000	+	12.9904i	1.08880	+	1.34704i
$94$		0			0
$95$	−7.00000			−0.718185
$96$		0			0
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−9.00000	+	15.5885i	−0.904534	+	1.56670i
$100$		0			0
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$		0			0
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$104$		0			0
$105$	4.50000	−	7.79423i	0.439155	−	0.760639i
$106$		0			0
$107$	−6.50000	+	11.2583i	−0.628379	+	1.08838i	0.359498	+	0.933146i	$0.382948\pi$
$107$	−6.50000	+	11.2583i	−0.628379	+	1.08838i	−0.987877	+	0.155238i	$0.950386\pi$
$108$		0			0
$109$	−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
$111$	1.50000	+	2.59808i	0.142374	+	0.246598i
$112$		0			0
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−15.0000	+	25.9808i	−1.38675	+	2.40192i
$118$		0			0
$119$	−4.50000	−	7.79423i	−0.412514	−	0.714496i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	27.0000			2.43451
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$		0			0
$129$	1.50000	+	2.59808i	0.132068	+	0.228748i
$130$		0			0
$131$	−10.5000	+	18.1865i	−0.917389	+	1.58896i	−0.114024	+	0.993478i	$0.536374\pi$
$131$	−10.5000	+	18.1865i	−0.917389	+	1.58896i	−0.803365	+	0.595487i	$0.796959\pi$
$132$		0			0
$133$	10.5000	+	18.1865i	0.910465	+	1.57697i
$134$		0			0
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$		0			0
$137$	−5.50000	−	9.52628i	−0.469897	−	0.813885i	0.529511	−	0.848303i	$-0.322376\pi$
$137$	−5.50000	−	9.52628i	−0.469897	−	0.813885i	−0.999408	+	0.0344182i	$0.989042\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$		0			0
$143$	−7.50000	+	12.9904i	−0.627182	+	1.08631i
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$		0			0
$147$	−6.00000			−0.494872
$148$		0			0
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	5.50000	−	0.866025i	0.441771	−	0.0695608i
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$		0			0
$159$	9.00000			0.713746
$160$		0			0
$161$	−6.00000	+	10.3923i	−0.472866	+	0.819028i
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$		0			0
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	0.219533	+	0.975605i	$0.429547\pi$
$167$	−9.50000	+	16.4545i	−0.735132	+	1.27329i	−0.954665	+	0.297681i	$0.903787\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	−42.0000			−3.21182
$172$		0			0
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	0.846392	−	0.532560i	$-0.178770\pi$
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	−0.884407	+	0.466717i	$0.845437\pi$
$174$		0			0
$175$	6.00000	+	10.3923i	0.453557	+	0.785584i
$176$		0			0
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$		0			0
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	−0.254770	−	0.967002i	$-0.582000\pi$
$179$	9.50000	−	16.4545i	0.710063	−	1.22987i	0.964833	−	0.262864i	$-0.0846670\pi$
$180$		0			0
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	0.758030	−	0.652219i	$-0.226162\pi$
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	−0.943854	+	0.330364i	$0.892829\pi$
$182$		0			0
$183$	9.00000	−	15.5885i	0.665299	−	1.15233i
$184$		0			0
$185$	1.00000			0.0735215
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$	13.5000	−	23.3827i	0.981981	−	1.70084i
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	0.289980	+	0.957033i	$0.406351\pi$
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	−0.973805	+	0.227387i	$0.926982\pi$
$194$		0			0
$195$	7.50000	+	12.9904i	0.537086	+	0.930261i
$196$		0			0
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	0.999194	+	0.0401324i	$0.0127780\pi$
$197$	7.50000	+	12.9904i	0.534353	+	0.925526i	−0.464841	+	0.885394i	$0.653889\pi$
$198$		0			0
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	0.206184	−	0.978513i	$-0.433895\pi$
$200$		0			0
$201$	−9.00000			−0.634811
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$	−12.0000	−	20.7846i	−0.834058	−	1.44463i
$208$		0			0
$209$	−21.0000			−1.45260
$210$		0			0
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	−0.882723	−	0.469894i	$-0.844292\pi$
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	0.848301	+	0.529514i	$0.177626\pi$
$212$		0			0
$213$	−3.00000			−0.205557
$214$		0			0
$215$	1.00000			0.0681994
$216$		0			0
$217$	−10.5000	−	12.9904i	−0.712786	−	0.881845i
$218$		0			0
$219$	−21.0000			−1.41905
$220$		0			0
$221$	15.0000			1.00901
$222$		0			0
$223$	−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			0
$225$	−24.0000			−1.60000
$226$		0			0
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	0.969533	+	0.244962i	$0.0787754\pi$
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	−0.272623	+	0.962121i	$0.587891\pi$
$228$		0			0
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	13.5000	−	23.3827i	0.888235	−	1.53847i
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$		0			0
$237$	−1.50000	−	2.59808i	−0.0974355	−	0.168763i
$238$		0			0
$239$	−0.500000	−	0.866025i	−0.0323423	−	0.0560185i	0.849401	−	0.527748i	$-0.176963\pi$
$239$	−0.500000	−	0.866025i	−0.0323423	−	0.0560185i	−0.881743	+	0.471729i	$0.843630\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	−35.0000			−2.22700
$248$		0			0
$249$	15.0000			0.950586
$250$		0			0
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	−0.232740	−	0.972539i	$-0.574769\pi$
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	0.958613	−	0.284711i	$-0.0918976\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$		0			0
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$		0			0
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	0.994375	−	0.105919i	$-0.0337784\pi$
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	−0.588916	+	0.808194i	$0.700445\pi$
$258$		0			0
$259$	−1.50000	−	2.59808i	−0.0932055	−	0.161437i
$260$		0			0
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$		0			0
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	1.50000	−	2.59808i	0.0921443	−	0.159599i
$266$		0			0
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$		0			0
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$	22.5000	−	38.9711i	1.36176	−	2.35864i
$274$		0			0
$275$	−12.0000			−0.723627
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	33.0000	−	5.19615i	1.97566	−	0.311086i
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$		0			0
$285$	−10.5000	+	18.1865i	−0.621966	+	1.07728i
$286$		0			0
$287$	−27.0000			−1.59376
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	21.0000	−	36.3731i	1.23104	−	2.13223i
$292$		0			0
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	−0.442908	−	0.896567i	$-0.646053\pi$
$293$	9.50000	−	16.4545i	0.554996	−	0.961281i	0.997904	−	0.0647140i	$-0.0206135\pi$
$294$		0			0
$295$	−3.00000			−0.174667
$296$		0			0
$297$	13.5000	+	23.3827i	0.783349	+	1.35680i
$298$		0			0
$299$	−10.0000	−	17.3205i	−0.578315	−	1.00167i
$300$		0			0
$301$	−1.50000	−	2.59808i	−0.0864586	−	0.149751i
$302$		0			0
$303$	−15.0000	+	25.9808i	−0.861727	+	1.49256i
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	−0.928506	−	0.371318i	$-0.878906\pi$
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	0.785823	+	0.618451i	$0.212239\pi$
$308$		0			0
$309$	−39.0000			−2.21863
$310$		0			0
$311$	−32.0000			−1.81455			−0.907277	−	0.420534i	$-0.861843\pi$
$311$	−32.0000			−1.81455			−0.907277	+	0.420534i	$0.861843\pi$
$312$		0			0
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	−0.947825	−	0.318791i	$-0.896723\pi$
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	0.749993	+	0.661445i	$0.230057\pi$
$314$		0			0
$315$	−9.00000	−	15.5885i	−0.507093	−	0.878310i
$316$		0			0
$317$	−14.5000	+	25.1147i	−0.814401	+	1.41058i	0.0953560	+	0.995443i	$0.469601\pi$
$317$	−14.5000	+	25.1147i	−0.814401	+	1.41058i	−0.909757	+	0.415141i	$0.863732\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	19.5000	+	33.7750i	1.08838	+	1.88514i
$322$		0			0
$323$	10.5000	+	18.1865i	0.584236	+	1.01193i
$324$		0			0
$325$	−20.0000			−1.10940
$326$		0			0
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$		0			0
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	0.999298	−	0.0374662i	$-0.0119287\pi$
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	−0.532096	+	0.846684i	$0.678595\pi$
$332$		0			0
$333$	6.00000			0.328798
$334$		0			0
$335$	−1.50000	+	2.59808i	−0.0819538	+	0.141948i
$336$		0			0
$337$	30.0000			1.63420			0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000			1.63420			0.817102	+	0.576493i	$0.195579\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$		0			0
$341$	16.5000	−	2.59808i	0.893525	−	0.140694i
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$	−12.0000			−0.646058
$346$		0			0
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	−0.961162	−	0.275983i	$-0.910997\pi$
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	0.719590	+	0.694399i	$0.244330\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	22.5000	+	38.9711i	1.20096	+	2.08013i
$352$		0			0
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	0.0769515	+	0.997035i	$0.475481\pi$
$353$	−15.5000	+	26.8468i	−0.824982	+	1.42891i	−0.901933	+	0.431875i	$0.857852\pi$
$354$		0			0
$355$	−0.500000	+	0.866025i	−0.0265372	+	0.0459639i
$356$		0			0
$357$	−27.0000			−1.42899
$358$		0			0
$359$	15.5000	+	26.8468i	0.818059	+	1.41692i	0.907111	+	0.420892i	$0.138283\pi$
$359$	15.5000	+	26.8468i	0.818059	+	1.41692i	−0.0890519	+	0.996027i	$0.528384\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	−3.00000	−	5.19615i	−0.157459	−	0.272727i
$364$		0			0
$365$	−3.50000	+	6.06218i	−0.183198	+	0.317309i
$366$		0			0
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$		0			0
$369$	27.0000	−	46.7654i	1.40556	−	2.43451i
$370$		0			0
$371$	−9.00000			−0.467257
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$		0			0
$375$	−13.5000	+	23.3827i	−0.697137	+	1.20748i
$376$		0			0
$377$	−5.00000	−	8.66025i	−0.257513	−	0.446026i
$378$		0			0
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	−0.878581	−	0.477593i	$-0.841509\pi$
$379$	−0.500000	+	0.866025i	−0.0256833	+	0.0444847i	0.852898	+	0.522077i	$0.174843\pi$
$380$		0			0
$381$	−19.5000	−	33.7750i	−0.999015	−	1.73035i
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	−4.50000	−	7.79423i	−0.229341	−	0.397231i
$386$		0			0
$387$	6.00000			0.304997
$388$		0			0
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	−0.412039	−	0.911166i	$-0.635183\pi$
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	0.995113	−	0.0987463i	$-0.0314832\pi$
$390$		0			0
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$		0			0
$393$	31.5000	+	54.5596i	1.58896	+	2.75217i
$394$		0			0
$395$	−1.00000			−0.0503155
$396$		0			0
$397$	−10.5000	+	18.1865i	−0.526980	+	0.912756i	0.472526	+	0.881317i	$0.343342\pi$
$397$	−10.5000	+	18.1865i	−0.526980	+	0.912756i	−0.999506	+	0.0314391i	$0.989991\pi$
$398$		0			0
$399$	63.0000			3.15394
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	27.5000	−	4.33013i	1.36987	−	0.215699i
$404$		0			0
$405$	9.00000			0.447214
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	−33.0000			−1.62777
$412$		0			0
$413$	4.50000	+	7.79423i	0.221431	+	0.383529i
$414$		0			0
$415$	2.50000	−	4.33013i	0.122720	−	0.212558i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	0.988861	−	0.148844i	$-0.0475552\pi$
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	−0.623333	+	0.781956i	$0.714222\pi$
$422$		0			0
$423$	−24.0000	−	41.5692i	−1.16692	−	2.02116i
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	−9.00000	+	15.5885i	−0.435541	+	0.754378i
$428$		0			0
$429$	22.5000	+	38.9711i	1.08631	+	1.88154i
$430$		0			0
$431$	2.50000	−	4.33013i	0.120421	−	0.208575i	−0.799513	−	0.600649i	$-0.794909\pi$
$431$	2.50000	−	4.33013i	0.120421	−	0.208575i	0.919934	+	0.392074i	$0.128242\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$		0			0
$437$	14.0000	−	24.2487i	0.669711	−	1.15997i
$438$		0			0
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	0.668184	−	0.743996i	$-0.267072\pi$
$439$	−6.50000	−	11.2583i	−0.310228	−	0.537331i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$		0			0
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	0.705278	−	0.708931i	$-0.250822\pi$
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	−0.966591	+	0.256323i	$0.917489\pi$
$444$		0			0
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$		0			0
$447$	1.50000	+	2.59808i	0.0709476	+	0.122885i
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	13.5000	−	23.3827i	0.635690	−	1.10105i
$452$		0			0
$453$	24.0000	−	41.5692i	1.12762	−	1.95309i
$454$		0			0
$455$	−7.50000	−	12.9904i	−0.351605	−	0.608998i
$456$		0			0
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$		0			0
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$		0			0
$461$	−42.0000			−1.95614			−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−42.0000			−1.95614			−0.978068	+	0.208288i	$0.933211\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	6.00000	−	15.5885i	0.278243	−	0.722897i
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	9.00000			0.415581
$470$		0			0
$471$	−15.0000	+	25.9808i	−0.691164	+	1.19713i
$472$		0			0
$473$	3.00000			0.137940
$474$		0			0
$475$	−14.0000	−	24.2487i	−0.642364	−	1.11261i
$476$		0			0
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$		0			0
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	−0.963884	−	0.266321i	$-0.914192\pi$
$479$	−5.50000	+	9.52628i	−0.251301	+	0.435267i	0.712583	+	0.701588i	$0.247525\pi$
$480$		0			0
$481$	5.00000			0.227980
$482$		0			0
$483$	18.0000	+	31.1769i	0.819028	+	1.41860i
$484$		0			0
$485$	−7.00000	−	12.1244i	−0.317854	−	0.550539i
$486$		0			0
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	0.963312	−	0.268384i	$-0.0864896\pi$
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	−0.714083	+	0.700061i	$0.753156\pi$
$488$		0			0
$489$	6.00000	−	10.3923i	0.271329	−	0.469956i
$490$		0			0
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$		0			0
$493$	−3.00000	+	5.19615i	−0.135113	+	0.234023i
$494$		0			0
$495$	18.0000			0.809040
$496$		0			0
$497$	3.00000			0.134568
$498$		0			0
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	−0.647882	−	0.761741i	$-0.724345\pi$
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	0.983628	+	0.180212i	$0.0576783\pi$
$500$		0			0
$501$	28.5000	+	49.3634i	1.27329	+	2.20540i
$502$		0			0
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	−0.748091	−	0.663596i	$-0.769030\pi$
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	0.948736	+	0.316068i	$0.102363\pi$
$504$		0			0
$505$	5.00000	+	8.66025i	0.222497	+	0.385376i
$506$		0			0
$507$	18.0000	+	31.1769i	0.799408	+	1.38462i
$508$		0			0
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	0.854732	−	0.519070i	$-0.173722\pi$
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	−0.876894	+	0.480684i	$0.840388\pi$
$510$		0			0
$511$	21.0000			0.928985
$512$		0			0
$513$	−31.5000	+	54.5596i	−1.39076	+	2.40887i
$514$		0			0
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$		0			0
$517$	−12.0000	−	20.7846i	−0.527759	−	0.914106i
$518$		0			0
$519$	−3.00000			−0.131685
$520$		0			0
$521$	−15.5000	+	26.8468i	−0.679067	+	1.17618i	0.296195	+	0.955128i	$0.404282\pi$
$521$	−15.5000	+	26.8468i	−0.679067	+	1.17618i	−0.975262	+	0.221052i	$0.929051\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$		0			0
$525$	36.0000			1.57117
$526$		0			0
$527$	−10.5000	−	12.9904i	−0.457387	−	0.565870i
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	22.5000	−	38.9711i	0.974583	−	1.68803i
$534$		0			0
$535$	13.0000			0.562039
$536$		0			0
$537$	−28.5000	−	49.3634i	−1.22987	−	2.13019i
$538$		0			0
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	0.365444	+	0.930834i	$0.380917\pi$
$541$	−14.5000	+	25.1147i	−0.623404	+	1.07977i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$	−15.0000			−0.643712
$544$		0			0
$545$	1.00000	+	1.73205i	0.0428353	+	0.0741929i
$546$		0			0
$547$	6.50000	+	11.2583i	0.277920	+	0.481371i	0.970868	−	0.239616i	$-0.0770217\pi$
$547$	6.50000	+	11.2583i	0.277920	+	0.481371i	−0.692948	+	0.720988i	$0.743688\pi$
$548$		0			0
$549$	−18.0000	−	31.1769i	−0.768221	−	1.33060i
$550$		0			0
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$	1.50000	+	2.59808i	0.0637865	+	0.110481i
$554$		0			0
$555$	1.50000	−	2.59808i	0.0636715	−	0.110282i
$556$		0			0
$557$	−2.00000			−0.0847427			−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$		0			0
$559$	5.00000			0.211477
$560$		0			0
$561$	13.5000	−	23.3827i	0.569970	−	0.987218i
$562$		0			0
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$		0			0
$565$	0.500000	−	0.866025i	0.0210352	−	0.0364340i
$566$		0			0
$567$	−13.5000	−	23.3827i	−0.566947	−	0.981981i
$568$		0			0
$569$	12.5000	+	21.6506i	0.524027	+	0.907642i	0.999609	+	0.0279702i	$0.00890434\pi$
$569$	12.5000	+	21.6506i	0.524027	+	0.907642i	−0.475581	+	0.879672i	$0.657762\pi$
$570$		0			0
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	0.999638	+	0.0268925i	$0.00856117\pi$
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	−0.476530	+	0.879158i	$0.658105\pi$
$572$		0			0
$573$	9.00000			0.375980
$574$		0			0
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$		0			0
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	−0.895558	−	0.444945i	$-0.853223\pi$
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	0.833112	+	0.553104i	$0.186557\pi$
$578$		0			0
$579$	28.5000	+	49.3634i	1.18442	+	2.05147i
$580$		0			0
$581$	−15.0000			−0.622305
$582$		0			0
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$		0			0
$585$	30.0000			1.24035
$586$		0			0
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	24.5000	+	30.3109i	1.00950	+	1.24894i
$590$		0			0
$591$	45.0000			1.85105
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−4.50000	+	7.79423i	−0.184482	+	0.319532i
$596$		0			0
$597$	−63.0000			−2.57842
$598$		0			0
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	0.638468	−	0.769648i	$-0.279568\pi$
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	−0.985769	+	0.168106i	$0.946235\pi$
$600$		0			0
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	−0.303986	−	0.952676i	$-0.598318\pi$
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	0.977035	−	0.213079i	$-0.0683491\pi$
$602$		0			0
$603$	−9.00000	+	15.5885i	−0.366508	+	0.634811i
$604$		0			0
$605$	−2.00000			−0.0813116
$606$		0			0
$607$	−20.5000	−	35.5070i	−0.832069	−	1.44119i	−0.896394	−	0.443257i	$-0.853823\pi$
$607$	−20.5000	−	35.5070i	−0.832069	−	1.44119i	0.0643251	−	0.997929i	$-0.479511\pi$
$608$		0			0
$609$	9.00000	+	15.5885i	0.364698	+	0.631676i
$610$		0			0
$611$	−20.0000	−	34.6410i	−0.809113	−	1.40143i
$612$		0			0
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$		0			0
$615$	−13.5000	−	23.3827i	−0.544373	−	0.942881i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	−36.0000			−1.44463
$622$		0			0
$623$	−9.00000	+	15.5885i	−0.360577	+	0.624538i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	−31.5000	+	54.5596i	−1.25799	+	2.17890i
$628$		0			0
$629$	−1.50000	−	2.59808i	−0.0598089	−	0.103592i
$630$		0			0
$631$	13.5000	+	23.3827i	0.537427	+	0.930850i	0.999042	+	0.0437697i	$0.0139368\pi$
$631$	13.5000	+	23.3827i	0.537427	+	0.930850i	−0.461615	+	0.887080i	$0.652730\pi$
$632$		0			0
$633$	1.50000	+	2.59808i	0.0596196	+	0.103264i
$634$		0			0
$635$	−13.0000			−0.515889
$636$		0			0
$637$	−5.00000	+	8.66025i	−0.198107	+	0.343132i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	0.736725	−	0.676192i	$-0.236371\pi$
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	−0.953962	+	0.299927i	$0.903038\pi$
$642$		0			0
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	1.50000	−	2.59808i	0.0590624	−	0.102299i
$646$		0			0
$647$	−4.00000			−0.157256			−0.0786281	−	0.996904i	$-0.525054\pi$
$647$	−4.00000			−0.157256			−0.0786281	+	0.996904i	$0.525054\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$	−49.5000	+	7.79423i	−1.94006	+	0.305480i
$652$		0			0
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$		0			0
$655$	21.0000			0.820538
$656$		0			0
$657$	−21.0000	+	36.3731i	−0.819288	+	1.41905i
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.213925	−	0.976850i	$-0.568625\pi$
$662$		0			0
$663$	22.5000	−	38.9711i	0.873828	−	1.51351i
$664$		0			0
$665$	10.5000	−	18.1865i	0.407173	−	0.705244i
$666$		0			0
$667$	8.00000			0.309761
$668$		0			0
$669$	28.5000	+	49.3634i	1.10187	+	1.90850i
$670$		0			0
$671$	−9.00000	−	15.5885i	−0.347441	−	0.601786i
$672$		0			0
$673$	−13.5000	−	23.3827i	−0.520387	−	0.901336i	−0.999719	−	0.0237028i	$-0.992454\pi$
$673$	−13.5000	−	23.3827i	−0.520387	−	0.901336i	0.479332	−	0.877633i	$-0.340879\pi$
$674$		0			0
$675$	−18.0000	+	31.1769i	−0.692820	+	1.20000i
$676$		0			0
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$		0			0
$679$	−21.0000	+	36.3731i	−0.805906	+	1.39587i
$680$		0			0
$681$	63.0000			2.41417
$682$		0			0
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		0			0
$685$	−5.50000	+	9.52628i	−0.210144	+	0.363980i
$686$		0			0
$687$	−10.5000	−	18.1865i	−0.400600	−	0.693860i
$688$		0			0
$689$	7.50000	−	12.9904i	0.285727	−	0.494894i
$690$		0			0
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	−0.999876	−	0.0157341i	$-0.994991\pi$
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	0.486312	−	0.873785i	$-0.338342\pi$
$692$		0			0
$693$	−27.0000	−	46.7654i	−1.02565	−	1.77647i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−27.0000			−1.02270
$698$		0			0
$699$	−27.0000	+	46.7654i	−1.02123	+	1.76883i
$700$		0			0
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	−0.688917	−	0.724840i	$-0.741914\pi$
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	0.972188	+	0.234200i	$0.0752470\pi$
$702$		0			0
$703$	3.50000	+	6.06218i	0.132005	+	0.228639i
$704$		0			0
$705$	−24.0000			−0.903892
$706$		0			0
$707$	15.0000	−	25.9808i	0.564133	−	0.977107i
$708$		0			0
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$		0			0
$711$	−6.00000			−0.225018
$712$		0			0
$713$	−8.00000	+	20.7846i	−0.299602	+	0.778390i
$714$		0			0
$715$	15.0000			0.560968
$716$		0			0
$717$	−3.00000			−0.112037
$718$		0			0
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	−0.923880	−	0.382682i	$-0.875001\pi$
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	0.793352	+	0.608763i	$0.208334\pi$
$720$		0			0
$721$	39.0000			1.45244
$722$		0			0
$723$	−37.5000	−	64.9519i	−1.39464	−	2.41559i
$724$		0			0
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		0			0
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	−0.286954	−	0.957944i	$-0.592643\pi$
$727$	18.5000	−	32.0429i	0.686127	−	1.18841i	0.973081	−	0.230463i	$-0.0740239\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	0.856644	−	0.515908i	$-0.172546\pi$
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	−0.875112	+	0.483921i	$0.839212\pi$
$734$		0			0
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$		0			0
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	0.998951	−	0.0457903i	$-0.0145806\pi$
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	−0.539131	+	0.842222i	$0.681247\pi$
$740$		0			0
$741$	−52.5000	+	90.9327i	−1.92864	+	3.34050i
$742$		0			0
$743$	40.0000			1.46746			0.733729	−	0.679442i	$-0.237778\pi$
$743$	40.0000			1.46746			0.733729	+	0.679442i	$0.237778\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$		0			0
$747$	15.0000	−	25.9808i	0.548821	−	0.950586i
$748$		0			0
$749$	−19.5000	−	33.7750i	−0.712514	−	1.23411i
$750$		0			0
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	−0.470311	−	0.882501i	$-0.655858\pi$
$751$	14.5000	−	25.1147i	0.529113	−	0.916450i	0.999424	−	0.0339490i	$-0.0108084\pi$
$752$		0			0
$753$	−34.5000	−	59.7558i	−1.25725	−	2.17762i
$754$		0			0
$755$	−8.00000	−	13.8564i	−0.291150	−	0.504286i
$756$		0			0
$757$	21.5000	+	37.2391i	0.781431	+	1.35348i	0.931108	+	0.364743i	$0.118843\pi$
$757$	21.5000	+	37.2391i	0.781431	+	1.35348i	−0.149677	+	0.988735i	$0.547824\pi$
$758$		0			0
$759$	−36.0000			−1.30672
$760$		0			0
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$762$		0			0
$763$	3.00000	−	5.19615i	0.108607	−	0.188113i
$764$		0			0
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$		0			0
$767$	−15.0000			−0.541619
$768$		0			0
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$		0			0
$771$	39.0000			1.40455
$772$		0			0
$773$	46.0000			1.65451			0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000			1.65451			0.827253	+	0.561830i	$0.189903\pi$
$774$		0			0
$775$	14.0000	+	17.3205i	0.502895	+	0.622171i
$776$		0			0
$777$	−9.00000			−0.322873
$778$		0			0
$779$	63.0000			2.25721
$780$		0			0
$781$	−1.50000	+	2.59808i	−0.0536742	+	0.0929665i
$782$		0			0
$783$	−18.0000			−0.643268
$784$		0			0
$785$	5.00000	+	8.66025i	0.178458	+	0.309098i
$786$		0			0
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.188119	+	0.982146i	$0.560239\pi$
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.756504	+	0.653989i	$0.773094\pi$
$788$		0			0
$789$	24.0000	−	41.5692i	0.854423	−	1.47990i
$790$		0			0
$791$	−3.00000			−0.106668
$792$		0			0
$793$	−15.0000	−	25.9808i	−0.532666	−	0.922604i
$794$		0			0
$795$	−4.50000	−	7.79423i	−0.159599	−	0.276433i
$796$		0			0
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$		0			0
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$		0			0
$803$	−10.5000	+	18.1865i	−0.370537	+	0.641789i
$804$		0			0
$805$	12.0000			0.422944
$806$		0			0
$807$	−63.0000			−2.21771
$808$		0			0
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		0			0
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	0.906575	−	0.422044i	$-0.138687\pi$
$811$	2.50000	+	4.33013i	0.0877869	+	0.152051i	−0.818788	+	0.574095i	$0.805354\pi$
$812$		0			0
$813$	12.0000	−	20.7846i	0.420858	−	0.728948i
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	3.50000	+	6.06218i	0.122449	+	0.212089i
$818$		0			0
$819$	−45.0000	−	77.9423i	−1.57243	−	2.72352i
$820$		0			0
$821$	38.0000			1.32621			0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000			1.32621			0.663105	+	0.748527i	$0.269238\pi$
$822$		0			0
$823$	16.5000	−	28.5788i	0.575154	−	0.996196i	−0.420871	−	0.907120i	$-0.638276\pi$
$823$	16.5000	−	28.5788i	0.575154	−	0.996196i	0.996025	−	0.0890752i	$-0.0283911\pi$
$824$		0			0
$825$	−18.0000	+	31.1769i	−0.626680	+	1.08544i
$826$		0			0
$827$	−21.5000	−	37.2391i	−0.747628	−	1.29493i	−0.948957	−	0.315406i	$-0.897859\pi$
$827$	−21.5000	−	37.2391i	−0.747628	−	1.29493i	0.201328	−	0.979524i	$-0.435474\pi$
$828$		0			0
$829$	46.0000			1.59765			0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000			1.59765			0.798823	+	0.601566i	$0.205456\pi$
$830$		0			0
$831$	−3.00000	+	5.19615i	−0.104069	+	0.180253i
$832$		0			0
$833$	6.00000			0.207888
$834$		0			0
$835$	19.0000			0.657522
$836$		0			0
$837$	18.0000	−	46.7654i	0.622171	−	1.61645i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	45.0000	−	77.9423i	1.54988	−	2.68447i
$844$		0			0
$845$	12.0000			0.412813
$846$		0			0
$847$	3.00000	+	5.19615i	0.103081	+	0.178542i
$848$		0			0
$849$	−6.00000	+	10.3923i	−0.205919	+	0.356663i
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	21.0000	+	36.3731i	0.718185	+	1.24393i
$856$		0			0
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$		0			0
$861$	−40.5000	+	70.1481i	−1.38024	+	2.39064i
$862$		0			0
$863$	1.50000	+	2.59808i	0.0510606	+	0.0884395i	0.890426	−	0.455128i	$-0.150407\pi$
$863$	1.50000	+	2.59808i	0.0510606	+	0.0884395i	−0.839365	+	0.543568i	$0.817073\pi$
$864$		0			0
$865$	−0.500000	+	0.866025i	−0.0170005	+	0.0294457i
$866$		0			0
$867$	24.0000			0.815083
$868$		0			0
$869$	−3.00000			−0.101768
$870$		0			0
$871$	−7.50000	+	12.9904i	−0.254128	+	0.440162i
$872$		0			0
$873$	−42.0000	−	72.7461i	−1.42148	−	2.46208i
$874$		0			0
$875$	13.5000	−	23.3827i	0.456383	−	0.790479i
$876$		0			0
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	0.943820	−	0.330461i	$-0.107204\pi$
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	−0.758098	+	0.652141i	$0.773871\pi$
$878$		0			0
$879$	−28.5000	−	49.3634i	−0.961281	−	1.66499i
$880$		0			0
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	0.660438	−	0.750881i	$-0.270371\pi$
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	−0.980501	+	0.196515i	$0.937037\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$		0			0
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	−0.634141	−	0.773217i	$-0.718646\pi$
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	0.986696	+	0.162573i	$0.0519794\pi$
$888$		0			0
$889$	19.5000	+	33.7750i	0.654009	+	1.13278i
$890$		0			0
$891$	27.0000			0.904534
$892$		0			0
$893$	28.0000	−	48.4974i	0.936984	−	1.62290i
$894$		0			0
$895$	−19.0000			−0.635100
$896$		0			0
$897$	−60.0000			−2.00334
$898$		0			0
$899$	−4.00000	+	10.3923i	−0.133407	+	0.346603i
$900$		0			0
$901$	−9.00000			−0.299833
$902$		0			0
$903$	−9.00000			−0.299501
$904$		0			0
$905$	−2.50000	+	4.33013i	−0.0831028	+	0.143938i
$906$		0			0
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$		0			0
$909$	30.0000	+	51.9615i	0.995037	+	1.72345i
$910$		0			0
$911$	−7.50000	+	12.9904i	−0.248486	+	0.430391i	−0.963106	−	0.269122i	$-0.913266\pi$
$911$	−7.50000	+	12.9904i	−0.248486	+	0.430391i	0.714620	+	0.699513i	$0.246600\pi$
$912$		0			0
$913$	7.50000	−	12.9904i	0.248214	−	0.429919i
$914$		0			0
$915$	−18.0000			−0.595062
$916$		0			0
$917$	−31.5000	−	54.5596i	−1.04022	−	1.80172i
$918$		0			0
$919$	29.5000	+	51.0955i	0.973115	+	1.68548i	0.686020	+	0.727583i	$0.259356\pi$
$919$	29.5000	+	51.0955i	0.973115	+	1.68548i	0.287096	+	0.957902i	$0.407310\pi$
$920$		0			0
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$		0			0
$923$	−2.50000	+	4.33013i	−0.0822885	+	0.142528i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$	−39.0000	+	67.5500i	−1.28093	+	2.21863i
$928$		0			0
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$		0			0
$931$	−14.0000			−0.458831
$932$		0			0
$933$	−48.0000	+	83.1384i	−1.57145	+	2.72183i
$934$		0			0
$935$	−4.50000	−	7.79423i	−0.147166	−	0.254899i
$936$		0			0
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	−0.990430	−	0.138017i	$-0.955927\pi$
$937$	−11.5000	+	19.9186i	−0.375689	+	0.650712i	0.614741	+	0.788729i	$0.289260\pi$
$938$		0			0
$939$	10.5000	+	18.1865i	0.342655	+	0.593495i
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$		0			0
$945$	−27.0000			−0.878310
$946$		0			0
$947$	−6.50000	+	11.2583i	−0.211222	+	0.365847i	−0.952097	−	0.305796i	$-0.901078\pi$
$947$	−6.50000	+	11.2583i	−0.211222	+	0.365847i	0.740875	+	0.671642i	$0.234411\pi$
$948$		0			0
$949$	−17.5000	+	30.3109i	−0.568074	+	0.983933i
$950$		0			0
$951$	43.5000	+	75.3442i	1.41058	+	2.44320i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	1.50000	−	2.59808i	0.0485389	−	0.0840718i
$956$		0			0
$957$	−18.0000			−0.581857
$958$		0			0
$959$	33.0000			1.06563
$960$		0			0
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$		0			0
$963$	78.0000			2.51351
$964$		0			0
$965$	19.0000			0.611632
$966$		0			0
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	−0.742382	−	0.669977i	$-0.766304\pi$
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	0.951408	+	0.307933i	$0.0996374\pi$
$968$		0			0
$969$	63.0000			2.02385
$970$		0			0
$971$	0.500000	+	0.866025i	0.0160458	+	0.0277921i	0.873937	−	0.486040i	$-0.161559\pi$
$971$	0.500000	+	0.866025i	0.0160458	+	0.0277921i	−0.857891	+	0.513832i	$0.828226\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−30.0000	+	51.9615i	−0.960769	+	1.66410i
$976$		0			0
$977$	54.0000			1.72761			0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000			1.72761			0.863807	+	0.503824i	$0.168074\pi$
$978$		0			0
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$		0			0
$981$	6.00000	+	10.3923i	0.191565	+	0.331801i
$982$		0			0
$983$	−24.5000	−	42.4352i	−0.781429	−	1.35347i	−0.931110	−	0.364740i	$-0.881158\pi$
$983$	−24.5000	−	42.4352i	−0.781429	−	1.35347i	0.149681	−	0.988734i	$-0.452175\pi$
$984$		0			0
$985$	7.50000	−	12.9904i	0.238970	−	0.413908i
$986$		0			0
$987$	36.0000	+	62.3538i	1.14589	+	1.98474i
$988$		0			0
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	51.0000			1.61844
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		0			0
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	0.997963	+	0.0637961i	$0.0203207\pi$
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	−0.443732	+	0.896159i	$0.646346\pi$
$998$		0			0
$999$	4.50000	−	7.79423i	0.142374	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.i.g.129.1		2
4.3	odd	2		62.2.c.b.5.1	✓	2
12.11	even	2		558.2.e.b.253.1		2
20.3	even	4		1550.2.p.a.749.1		4
20.7	even	4		1550.2.p.a.749.2		4
20.19	odd	2		1550.2.e.d.501.1		2
31.25	even	3	inner	496.2.i.g.273.1		2
124.67	odd	6		1922.2.a.e.1.1		1
124.87	odd	6		62.2.c.b.25.1	yes	2
124.119	even	6		1922.2.a.c.1.1		1
372.335	even	6		558.2.e.b.397.1		2
620.87	even	12		1550.2.p.a.149.2		4
620.459	odd	6		1550.2.e.d.1451.1		2
620.583	even	12		1550.2.p.a.149.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.c.b.5.1	✓	2	4.3	odd	2
62.2.c.b.25.1	yes	2	124.87	odd	6
496.2.i.g.129.1		2	1.1	even	1	trivial
496.2.i.g.273.1		2	31.25	even	3	inner
558.2.e.b.253.1		2	12.11	even	2
558.2.e.b.397.1		2	372.335	even	6
1550.2.e.d.501.1		2	20.19	odd	2
1550.2.e.d.1451.1		2	620.459	odd	6
1550.2.p.a.149.1		4	620.583	even	12
1550.2.p.a.149.2		4	620.87	even	12
1550.2.p.a.749.1		4	20.3	even	4
1550.2.p.a.749.2		4	20.7	even	4
1922.2.a.c.1.1		1	124.119	even	6
1922.2.a.e.1.1		1	124.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	496.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} -3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(3.50000 - 6.06218i) q^{19} +(4.50000 + 7.79423i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -9.00000 q^{27} +2.00000 q^{29} +(-2.00000 + 5.19615i) q^{31} -9.00000 q^{33} +3.00000 q^{35} +(-0.500000 + 0.866025i) q^{37} -15.0000 q^{39} +(4.50000 + 7.79423i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{45} +8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(4.50000 + 7.79423i) q^{51} +(1.50000 + 2.59808i) q^{53} +(-1.50000 + 2.59808i) q^{55} +(-10.5000 - 18.1865i) q^{57} +(1.50000 - 2.59808i) q^{59} +6.00000 q^{61} +18.0000 q^{63} +(-2.50000 + 4.33013i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(6.00000 - 10.3923i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(-3.50000 - 6.06218i) q^{73} +(-6.00000 - 10.3923i) q^{75} +9.00000 q^{77} +(0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.50000 + 4.33013i) q^{83} +3.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +6.00000 q^{89} +15.0000 q^{91} +(10.5000 + 12.9904i) q^{93} -7.00000 q^{95} +14.0000 q^{97} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - q^{5} - 3 q^{7} - 6 q^{9} - 3 q^{11} - 5 q^{13} - 6 q^{15} - 3 q^{17} + 7 q^{19} + 9 q^{21} + 8 q^{23} + 4 q^{25} - 18 q^{27} + 4 q^{29} - 4 q^{31} - 18 q^{33} + 6 q^{35} - q^{37} - 30 q^{39}+ \cdots - 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - q^5 - 3 * q^7 - 6 * q^9 - 3 * q^11 - 5 * q^13 - 6 * q^15 - 3 * q^17 + 7 * q^19 + 9 * q^21 + 8 * q^23 + 4 * q^25 - 18 * q^27 + 4 * q^29 - 4 * q^31 - 18 * q^33 + 6 * q^35 - q^37 - 30 * q^39 + 9 * q^41 - q^43 - 6 * q^45 + 16 * q^47 - 2 * q^49 + 9 * q^51 + 3 * q^53 - 3 * q^55 - 21 * q^57 + 3 * q^59 + 12 * q^61 + 36 * q^63 - 5 * q^65 - 3 * q^67 + 12 * q^69 - q^71 - 7 * q^73 - 12 * q^75 + 18 * q^77 + q^79 - 9 * q^81 + 5 * q^83 + 6 * q^85 + 6 * q^87 + 12 * q^89 + 30 * q^91 + 21 * q^93 - 14 * q^95 + 28 * q^97 - 18 * q^99

Introduction

L-functions

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